From smart grids to smart cities : new challenges in optimizing energy grids 9781119116080, 1119116082, 9781119372257, 1119372259, 9781119372332, 111937233X, 978-1-84821-749-2, 177-177-180-1

Table of contents :
Content: Preface xi Introduction xviiMassimo LA SCALA and Sergio BRUNO Chapter 1. Unbalanced Three-Phase Optimal Power Flow for the Optimization of MV and LV Distribution Grids 1Sergio BRUNO and Massimo LA SCALA 1.1. Advanced distribution management system for smart distribution grids 1 1.2. Secondary distribution monitoring and control 5 1.2.1. Monitoring and representation of LV distribution grids 6 1.2.2. LV control resources and control architecture 7 1.3. Three-phase distribution optimal power flow for smart distribution grids 8 1.4. Problem formulation and solving algorithm 11 1.4.1. Main problem formulation 11 1.4.2. Application of the penalty method 12 1.4.3. Definition of an unconstrained problem 14 1.4.4. Application of a quasi-Newton method 15 1.4.5. Solving algorithm 18 1.5. Application of the proposed methodology to the optimization of a MV network 20 1.5.1. Case A: optimal load curtailment 23 1.5.2. Case B: conservative voltage regulation 26 1.5.3. Case C: voltage rise effects 28 1.5.4. Algorithm performance 30 1.6. Application of the proposed methodology to the optimization of a MV/LV network 31 1.6.1. Case D: LV network congestions 33 1.6.2. Case E: minimization of losses and reactive control 36 1.6.3. Algorithm performance 37 1.7. Conclusions 38 1.8. Acknowledgments 38 1.9. Bibliography 39 Chapter 2. Mixed Integer Linear Programming Models for Network Reconfiguration and Resource Optimization in Power Distribution Networks 43Alberto BORGHETTI 2.1. Introduction 43 2.2. Model for determining the optimal configuration of a radial distribution network 44 2.2.1. Objective function and constraints of the branch currents 46 2.2.2. Bus voltage constraints 48 2.2.3. Bus equations 50 2.2.4. Line equations 52 2.2.5. Radiality constraints 53 2.3. Test results of minimum loss configuration obtained by the MILP model 54 2.3.1. Illustrative example 54 2.3.2. Tests results for networks with several nodes and branches 57 2.3.3. Comparison between the MILP solutions for the test networks with the corresponding PF calculation results relevant to the obtained optimal network configurations 62 2.4. MILP model of the VVO problem 65 2.4.1. Objective function 66 2.4.2. Branch equations 67 2.4.3. Bus equations 69 2.4.4. Branch and node constraints 72 2.5. Test results obtained by the VVO MILP model 74 2.5.1. TS1 74 2.5.2. TS2 77 2.5.3. TS3 78 2.6. Conclusions 85 2.7. Acknowledgments 85 2.8. Bibliography 86 Chapter 3. The Role of Nature-inspired Metaheuristic Algorithms for Optimal Voltage Regulation in Urban Smart Grids 89Giovanni ACAMPORA, Davide CARUSO, Alfredo VACCARO, Autilia VITIELLO and Ahmed F. ZOBAA 3.1. Introduction 89 3.2. Emerging needs in urban power systems 92 3.3. Toward smarter grids 93 3.4. Smart grids optimization 97 3.5. Metaheuristic algorithms for smart grids optimization 99 3.5.1. Genetic algorithm 99 3.5.2. Random Hill Climbing algorithm 101 3.5.3. Particle Swarm Optimization algorithm 101 3.5.4. Evolution strategy 103 3.5.5. Differential evolution 106 3.5.6. Biogeography-based optimization 108 3.5.7. Evolutionary programming 109 3.5.8. Ant Colony Optimization algorithm 110 3.5.9. Group Search Optimization algorithm 113 3.6. Numerical results 115 3.6.1. Power system test 116 3.6.2. Real urban smart grid 124 3.7. Conclusions 127 3.8. Bibliography 127 Chapter 4. Urban Energy Hubs and Microgrids: Smart Energy Planning for Cities 129Eleonora RIVA SANSEVERINO, Vincenzo Domenico GENCO, Gianluca SCACCIANOCE, Valentina VACCARO, Raffaella RIVA SANSEVERINO, Gaetano ZIZZO, Maria Luisa DI SILVESTRE, Diego ARNONE and Giuseppe PATERNO 4.1. Introduction 129 4.1.1. Microgrids versus urban energy hubs 131 4.2. Approaches and tools for urban energy hubs 134 4.2.1. Policy 134 4.2.2. Analysis 135 4.2.3. Optimal design and operation tools 139 4.3. Methodology 143 4.3.1. Building type and urban energy parameter specification 143 4.3.2. Mobility simulator 147 4.3.3. Energy simulation and electrical load estimation for buildings 151 4.3.4. Optimization and simulation software for district 151 4.4. Application 152 4.4.1. Analysis 152 4.4.2. Simulations and optimization 160 4.4.3. Mobility and effects of policies and smart charging on peaking power 168 4.5. Conclusions 170 4.6 Bibliography 171 Chapter 5. Optimization of Multi-energy Carrier Systems in Urban Areas 177Sergio BRUNO, Silvia LAMONACA and Massimo LA SCALA 5.1. Introduction 177 5.2. Optimal control strategy for a small-scale multi-carrier energy system 180 5.2.1. The proposed architecture 180 5.2.2. Mathematical formulation 183 5.2.3. Test results 190 5.3. Optimal design of an urban energy district 198 5.3.1. Energy district for urban regeneration: the San Paolo Power Park 199 5.3.2. Optimal design of the energy district 201 5.3.3. Integer variables and design choices 205 5.3.4. Mathematical formulation of the optimal control problem 206 5.3.5. Test results 214 5.4. Conclusions 227 5.5. Acknowledgments 228 5.6. Bibliography 228 Chapter 6. Optimal Gas Flow Algorithm for Natural Gas Distribution Systems in Urban Environment 231Ugo STECCHI, Gaetano ABBATANTUONO and Massimo LA SCALA 6.1. Introduction 231 6.2. Natural gas network evolution 236 6.3. Implementing the monitoring and control system in the "Gas Smart Grids" pilot project 239 6.3.1. SCADA system 240 6.3.2. Controlling FRUs' setpoints 244 6.4. Basic equations under steady-state conditions 246 6.5. Gas load flow formulation 253 6.6. Gas optimal flow method 256 6.7. Optimizing turbo-expander operations 258 6.8. Optimizing pressure profiles on the low pressure distribution grids 262 6.9. Conclusions 270 6.10. Acknowledgements 270 6.11. Bibliography 270 Chapter 7. Multicarrier Energy System Optimal Power Flow 273Soheil DERAFSHI BEIGVAND, Hamdi ABDI and Massimo LA SCALA 7.1. Introduction 273 7.2. Basic concepts and assumptions 276 7.2.1. MEC and energy hub 276 7.2.2. CHP units 279 7.2.3. General assumptions 282 7.3. Problem formulation 283 7.3.1. Electrical power balance equations 283 7.3.2. Gas energy flow equation 283 7.3.3. Modeling of energy hubs 285 7.3.4. MECOPF problem 286 7.4. Time varying acceleration coefficient gravitational search algorithm 287 7.4.1. A brief comparison between the main structures of TVAC-GSA and PSO 291 7.5. TVAC-GSA-based MECOPF problem 292 7.6. Case study simulations and results 294 7.7. Conclusions 300 7.8. Appendix 1 301 7.9. Appendix 2 303 7.10. Bibliography 305 List of Authors 309 Index 311

Citation preview

From Smart Grids to Smart Cities

To my parents Maria and Armando

Advanced SmartGrids Set coordinated by Jean-Claude Sabonnadière and Nouredine Hadjsaïd

From Smart Grids to Smart Cities New Challenges in Optimizing Energy Grids Edited by

Massimo La Scala

First published 2017 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address: ISTE Ltd 27-37 St George’s Road London SW19 4EU UK

John Wiley & Sons, Inc. 111 River Street Hoboken, NJ 07030 USA

www.iste.co.uk

www.wiley.com

© ISTE Ltd 2017 The rights of Massimo La Scala to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988. Library of Congress Control Number: 2016956032 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN 978-1-84821-749-2

Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xi

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Massimo LA SCALA and Sergio BRUNO

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Chapter 1. Unbalanced Three-Phase Optimal Power Flow for the Optimization of MV and LV Distribution Grids . . . . . . . . . . . . . . . . . . Sergio BRUNO and Massimo LA SCALA 1.1. Advanced distribution management system for smart distribution grids . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2. Secondary distribution monitoring and control . . . . . . . . . 1.2.1. Monitoring and representation of LV distribution grids . . 1.2.2. LV control resources and control architecture . . . . . . . 1.3. Three-phase distribution optimal power flow for smart distribution grids . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4. Problem formulation and solving algorithm . . . . . . . . . . . 1.4.1. Main problem formulation . . . . . . . . . . . . . . . . . . 1.4.2. Application of the penalty method . . . . . . . . . . . . . 1.4.3. Definition of an unconstrained problem . . . . . . . . . . 1.4.4. Application of a quasi-Newton method . . . . . . . . . . . 1.4.5. Solving algorithm . . . . . . . . . . . . . . . . . . . . . . . 1.5. Application of the proposed methodology to the optimization of a MV network . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.1. Case A: optimal load curtailment . . . . . . . . . . . . . . 1.5.2. Case B: conservative voltage regulation . . . . . . . . . . 1.5.3. Case C: voltage rise effects . . . . . . . . . . . . . . . . . 1.5.4. Algorithm performance. . . . . . . . . . . . . . . . . . . .

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1.6. Application of the proposed methodology to the optimization of a MV/LV network . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6.1. Case D: LV network congestions . . . . . . . . . . . . . . 1.6.2. Case E: minimization of losses and reactive control . . . . 1.6.3. Algorithm performance. . . . . . . . . . . . . . . . . . . . 1.7. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.8. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . 1.9. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 2. Mixed Integer Linear Programming Models for Network Reconfiguration and Resource Optimization in Power Distribution Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Alberto BORGHETTI 2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Model for determining the optimal configuration of a radial distribution network . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1. Objective function and constraints of the branch currents . . 2.2.2. Bus voltage constraints . . . . . . . . . . . . . . . . . . . . . 2.2.3. Bus equations . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.4. Line equations . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.5. Radiality constraints . . . . . . . . . . . . . . . . . . . . . . 2.3. Test results of minimum loss configuration obtained by the MILP model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1. Illustrative example . . . . . . . . . . . . . . . . . . . . . . . 2.3.2. Tests results for networks with several nodes and branches. 2.3.3. Comparison between the MILP solutions for the test networks with the corresponding PF calculation results relevant to the obtained optimal network configurations . . . . . . . . . . . 2.4. MILP model of the VVO problem . . . . . . . . . . . . . . . . . 2.4.1. Objective function . . . . . . . . . . . . . . . . . . . . . . . 2.4.2. Branch equations . . . . . . . . . . . . . . . . . . . . . . . . 2.4.3. Bus equations . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.4. Branch and node constraints . . . . . . . . . . . . . . . . . . 2.5. Test results obtained by the VVO MILP model . . . . . . . . . . 2.5.1. TS1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2. TS2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.3. TS3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 3. The Role of Nature-inspired Metaheuristic Algorithms for Optimal Voltage Regulation in Urban Smart Grids . . . . . . . . . . . . . . Giovanni ACAMPORA, Davide CARUSO, Alfredo VACCARO, Autilia VITIELLO and Ahmed F. ZOBAA 3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Emerging needs in urban power systems . . . . . . . . 3.3. Toward smarter grids . . . . . . . . . . . . . . . . . . . 3.4. Smart grids optimization . . . . . . . . . . . . . . . . . 3.5. Metaheuristic algorithms for smart grids optimization . 3.5.1. Genetic algorithm . . . . . . . . . . . . . . . . . . . 3.5.2. Random Hill Climbing algorithm . . . . . . . . . . 3.5.3. Particle Swarm Optimization algorithm . . . . . . 3.5.4. Evolution strategy . . . . . . . . . . . . . . . . . . . 3.5.5. Differential evolution . . . . . . . . . . . . . . . . . 3.5.6. Biogeography-based optimization . . . . . . . . . . 3.5.7. Evolutionary programming . . . . . . . . . . . . . 3.5.8. Ant Colony Optimization algorithm . . . . . . . . . 3.5.9. Group Search Optimization algorithm . . . . . . . 3.6. Numerical results . . . . . . . . . . . . . . . . . . . . . 3.6.1. Power system test . . . . . . . . . . . . . . . . . . . 3.6.2. Real urban smart grid . . . . . . . . . . . . . . . . . 3.7. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 3.8. Bibliography . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 4. Urban Energy Hubs and Microgrids: Smart Energy Planning for Cities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Eleonora RIVA SANSEVERINO, Vincenzo Domenico GENCO, Gianluca SCACCIANOCE, Valentina VACCARO, Raffaella RIVA SANSEVERINO, Gaetano ZIZZO, Maria Luisa DI SILVESTRE, Diego ARNONE and Giuseppe PATERNÒ 4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1. Microgrids versus urban energy hubs . . . . . . . . . . . . . . . 4.2. Approaches and tools for urban energy hubs . . . . . . . . . . . . . 4.2.1. Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2. Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3. Optimal design and operation tools . . . . . . . . . . . . . . . . 4.3. Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1. Building type and urban energy parameter specification . . . . 4.3.2. Mobility simulator . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.3. Energy simulation and electrical load estimation for buildings . 4.3.4. Optimization and simulation software for district . . . . . . . .

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4.4. Application . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1. Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2. Simulations and optimization . . . . . . . . . . . . . . 4.4.3. Mobility and effects of policies and smart charging on peaking power . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 5. Optimization of Multi-energy Carrier Systems in Urban Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sergio BRUNO, Silvia LAMONACA and Massimo LA SCALA 5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Optimal control strategy for a small-scale multi-carrier energy system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1. The proposed architecture . . . . . . . . . . . . . . . . . . 5.2.2. Mathematical formulation . . . . . . . . . . . . . . . . . . 5.2.3. Test results. . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. Optimal design of an urban energy district . . . . . . . . . . . 5.3.1. Energy district for urban regeneration: the San Paolo Power Park . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2. Optimal design of the energy district . . . . . . . . . . . . 5.3.3. Integer variables and design choices . . . . . . . . . . . . 5.3.4. Mathematical formulation of the optimal control problem 5.3.5. Test results. . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . 5.6. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 6. Optimal Gas Flow Algorithm for Natural Gas Distribution Systems in Urban Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ugo STECCHI, Gaetano ABBATANTUONO and Massimo LA SCALA 6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 6.2. Natural gas network evolution . . . . . . . . . . . . . . . 6.3. Implementing the monitoring and control system in the “Gas Smart Grids” pilot project . . . . . . . . . . . . . . . . . 6.3.1. SCADA system . . . . . . . . . . . . . . . . . . . . . 6.3.2. Controlling FRUs’ setpoints . . . . . . . . . . . . . . 6.4. Basic equations under steady-state conditions . . . . . . 6.5. Gas load flow formulation . . . . . . . . . . . . . . . . .

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6.6. Gas optimal flow method . . . . . . . . . . . . . . . . . . . . . . . . 6.7. Optimizing turbo-expander operations . . . . . . . . . . . . . . . . . 6.8. Optimizing pressure profiles on the low pressure distribution grids 6.9. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.10. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . 6.11. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 7. Multicarrier Energy System Optimal Power Flow. . . . . . . . . . Soheil DERAFSHI BEIGVAND, Hamdi ABDI and Massimo LA SCALA 7.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 7.2. Basic concepts and assumptions . . . . . . . . . . . . . 7.2.1. MEC and energy hub . . . . . . . . . . . . . . . . . 7.2.2. CHP units . . . . . . . . . . . . . . . . . . . . . . . 7.2.3. General assumptions . . . . . . . . . . . . . . . . . 7.3. Problem formulation. . . . . . . . . . . . . . . . . . . . 7.3.1. Electrical power balance equations . . . . . . . . . 7.3.2. Gas energy flow equation . . . . . . . . . . . . . . 7.3.3. Modeling of energy hubs . . . . . . . . . . . . . . . 7.3.4. MECOPF problem . . . . . . . . . . . . . . . . . . 7.4. Time varying acceleration coefficient gravitational search algorithm . . . . . . . . . . . . . . . . . . . . . . . . 7.4.1. A brief comparison between the main structures of TVAC-GSA and PSO . . . . . . . . . . . . . . . . . . . . 7.5. TVAC-GSA-based MECOPF problem . . . . . . . . . 7.6. Case study simulations and results . . . . . . . . . . . . 7.7. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 7.8. Appendix 1 . . . . . . . . . . . . . . . . . . . . . . . . . 7.9. Appendix 2 . . . . . . . . . . . . . . . . . . . . . . . . . 7.10. Bibliography . . . . . . . . . . . . . . . . . . . . . . .

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List of Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Preface

New emerging technologies and regulations are among the forces which are driving the changes in energy systems. This favorable circumstance paves the way to the design of more advanced and effective energy architectures, the solution of old problems with new means, and the solution of issues unresolved because of the lack of tools and methodologies. Renewable Energy Sources (RES), such as wind and solar power, are rapidly becoming the backbone of the future electric power system since they are environmental-friendly although they create great distress in power grids which should accommodate larger and larger amounts of intermittent power generation. With the increase in efficiency of energy conversion and power electronics, storage systems have become more reliable, less expensive and cleaner, making viable the option of storing significant amount of power, under any form of chemical, thermal, mechanical or electric energy. The potential impact of electric vehicles in energy systems is also huge. The diffusion of such vehicles might move, with regard to the overall energy consumption balance, a significant amount of power from conventional transport fuels to electricity, requiring a complete redesign of most distribution power grids. They will introduce new randomness in the electric system operations due to “moving around” loads. At residential and urban levels, the increasing penetration of electric vehicles and distributed generation will rapidly transform consumers into “prosumers” that will be able to operate their own devices in order to generate, store and use energy. Managing these micro energy systems will require the achievement of a higher efficiency, which can be reached only through a radical integration of all energy services at urban/residential level (electric supply, natural gas supply, heating, cooling, water, transportation, etc.).

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A major example of a key enabling technology (KET) which can drive the transformation of energy infrastructures is the smart grid concept. Smart grids combine a number of technologies with end-user solutions and address new paradigms in the dispersed generation, storage and utilization of the electrical energy, which can find an effective application by a new regulation environment. In this multifaceted scenario, the energy hub constitutes another key paradigm. It can be conceived as a unit where multiple energy carriers can be converted and conditioned by using a wide spectrum of technologies, such as combined heat and power technology, power-electronic devices and heat exchangers. Consequently, energy hubs could be considered as the trait d’union between different energy infrastructures (i.e. electrical networks, natural gas distribution systems, heat distribution systems) and/or energy users (i.e. producers, consumers) allowing more market and energy efficiency, increasing reliability and facilitating the penetration of intermittent generation. This model can be applied on different scales including industrial plants, larger buildings, urban districts and isolated energy systems. Starting from the experience in the power sector, in this book, it is shown how some concepts and methodologies developed in this field can be effectively utilized in other realms. Different energy infrastructures share the same needs for more automation, optimization in operations, tools for planning and integration between multiple energy carriers to achieve better performances and efficiency. These issues require new methods and application software whose main core, generally, resides in optimization tools. The focus of this book is on distribution energy systems and urban energy infrastructures since they show the potential to improve their efficiency and flexibility through the implementation of smart monitoring, new control functions and the integration with other energy carriers. This assumption has been made with the firm belief that, in these areas, smart grids will provide more profound changes in response to challenging problems such as: a wide dispersed generation mostly due to intermittent RES, integrated production, utilization and storage of both thermal and electrical energy for enhancing energy efficiency, more advanced home distribution systems, demand response, etc. The dramatic changes modern towns are facing during these years require smarter operation of grids according to overall framework of the “smart city” paradigm. A new urbanization is giving rise to the so-called “mega-towns” which require more advanced and secure energy infrastructures. The entrance of new technologies such as photo voltaics widely utilized for residential and tertiary buildings, electrical vehicles, combined heat cooling and power (CHCP), heat pumps for demand response and energy districts changes the usual way energy grids have been operated in cities so far. Other issues are related to a different attitude of

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customers, which are willing to participate more actively to the energy market and choose among new energy services, this aim being nurtured by a forward-thinking regulation of the sector. The scope of the book is to provide an integrated vision of problems to researcher, engineers, practitioners, defining the contour of new subjects in energy system optimization. The authors involved in this book were encouraged by a common motivation: to bring together issues that, although in continuity with their previous experience, sketch a new scenario in the energy systems. The book begins with applications of smart grids in the power sector and concludes with applications to urban distribution systems involving other energy carriers such natural gas, heat/cool district heating, hydrogen. This cultural contamination and novelty is found in the theory as well as in real-world applications. It stems from power systems, which is doubtless the most complex and technologically advanced energy infrastructure, the first one to make a pervasive use of automation and Information and Communication Technologies (ICT) and to experience a drastic market re-regulation and dramatic technological advancements worldwide. Particular attention is devoted to the actual implementation of the methods proposed here. As a matter of fact, most of the chapters refer to applications developed in research activities which have now finalized to give way to the actual implementation of pilot projects. These projects are briefly described and funding resources are acknowledged in throughout the book. Some of the pilot projects addressed here pushed the equipment and material needs of the research activity and nurtured the support of some companies giving rise to a new laboratory called LabZERO located at the Politecnico di Bari and at the ENEA Research Center in Brindisi, Italy. It was set up carrying out the activities of the “Project ZERO”, concerning the development of research and experimentation activities in the field of green smart technologies and the use of simulation tools and equipment for fast prototyping to reduce the risks of applied research and support product innovation in the path “from concept to market”. Lab ZERO was conceived as a living lab, a usercentered, open-innovation ecosystem combining research, development and innovation processes within a public-private-people partnership. This experience is worth mentioning to underline the link of the book with real applications and to show how pilot projects area good instrument to draw the attention of public institutions and companies to engineering research issues. The above-mentioned ideas inspired the book whose topics are summarized here. In the Introduction, terminology, definitions, economical and technical drivers for smart grids are introduced. Smart grids are defined in a broad sense including all

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energy grids and the integration of advanced distribution grids. Potentials for operation and environmental issues enhancement, safe and secure operations and energy efficiency are addressed with a special insight to the urban environment and its evolution toward smart cities. In Chapter 1, the features of Advanced Distribution Management Systems are summarized and the optimal power flow (OPF) is presented as basic function, which can be applied effectively for controlling power distribution grids at both medium voltage (MV) and low voltage (LV) level. Specialized formulations, based on nonlinear programming algorithms and a three-phase unbalanced representation of the power grid, are developed for controlling active and reactive resources in distribution systems. Particular attention is devoted to the LV distribution system due to the lack of automation and tools accompanied by the profound changes these grids are experiencing nowadays. In Chapter 2, mixed integer linear programming (MILP)algorithms are presented for the solution of two optimization problems, which characterize distribution power network operations, namely: the minimum-loss configuration of the network the socalled voltage/var optimization (VVO) problem. The quality of the results and the effects of the proposed linearization are assessed on MV test systems by performing a comparison with nonlinear calculations for optimal configurations. In Chapter 3, metaheuristic-based optimization algorithms have been addressed for solving complex problems in the smart grid domain. A review of the most advanced metaheuristic algorithms in the task of solving a complex smart grid optimization problems and a comprehensive analysis of the expected performances of the optimization algorithms in terms of convergence, robustness and accuracy are presented in this chapter. The benefits and the limitations of the different solution techniques are highlighted through simulation results obtained on realistic power networks and an actual urban power grid. In Chapter 4, a review of approaches to urban energy systems study is presented. Urban energy systems are proposed as networks of multi-source hybrid energy hubs, where different energy flows are collected at the same bus and can be stored, delivered or transformed as needed. Since resources and infrastructures interact with each other, definition and boundaries of such energy systems at urban level and the possibility to generate new operational models based on existing critical urban infrastructures is a challenging problem. Thermal, electrical and mobility infrastructures operation are considered as qualifying features of the hub. An optimized design of the energy system serving two different districts is considered as a function of these urban features. The analysis, reported in the chapter, shows how there is a link between energy planning and urban features at district level paving the way to an energy-based territorial planning for urban contexts.

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Planning integrated energy systems in towns implies a complex design, which should take into account also a different operation of underlying grids. Interdependencies among different systems should be carefully represented and special solvers are required for optimization. In Chapter 5, an optimization approach was formulated and tested to be applied in operations in presence of multiple energy sources and storage systems according to two strategies aimed to fully take advantage of storage facilities: a greedy algorithm and optimal control. In addition, a design methodology was proposed to maximize the return of the investment in planning new multi-source hybrid energy systems considering optimized operations during the lifespan of the infrastructure. The approach is tested on a real case of an urban regeneration project, aimed to the development of energy facilities to provide discounted energy services in degraded suburban areas to attract new investments. The project includes the installation of a trigeneration plant, district heating and cooling and an on-site steam methane reformer to supply hydrogen to a fleet of public transport vehicles. In Chapter 6, it is shown how urban gas distribution grids are experiencing changes similar to electric distribution grids due to the deployment of gas smart meters and the more and more pervasive use of ICT tools and automation which allows more effective, safe and secure operations. In this chapter, selected results of a pilot project for the implementation of a gas smart grid in the middle-sized town of Bari in Italy are presented. A SCADA (supervisory control and data acquisition) prototype and a gas flow optimization algorithm (gas optimal flow algorithm) for pressure control across the natural gas grid are described in their actual implementation. This kind of real-time control shows the potential of increasing the power generated by turbo expanders at gas city gates, reducing metering and billing errors due to excessive pressure deviations, ensuring a safe distribution of odorants and providing load relief and peak shaving during emergency conditions. What reported in this chapter is an interesting example of a ‘transposition’ and shifting of experiences coming from two different realms: the power smart grid area and the urban natural gas distribution. Once presented issues relevant to the integration of different energy substrates in future cities and essential changes in the planning and optimization process, in Chapter 7, the focus is on the concurrent optimization of the distribution grids of two main energy carriers: power and natural gas. The complexity of both networks in terms of their structure, a possible future energy-hub-like architecture, energy flow equations, and different related equality and inequality constraints make the optimization problem highly nonlinear, non-convex and high dimensional. An optimization heuristic method, namely the time varying acceleration coefficient gravitational search algorithm (TVAC-GSA), is proposed to solve OPF problems in multi-carrier energy systems focusing on the interactions between power grid and gas network. The proposed algorithm is based on the Newtonian laws of gravitation

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and motion. The effectiveness of the approach is tested on a multi-carrier energy architecture characterized by the assumed presence of multiple energy hubs. The concurrent solution of the two grids provide better results than the ones associated to the solution of the two separated systems. Consequently, the concurrent optimization of multiple grids seems to be a good candidate for smart distribution systems, gaining efficiency in the overall system. After this effort, the authors share the feeling that many results are still on the shelf and many others are still coming out from pilot projects and, in general, what reported here is not exhaustive of the topic. Somehow, this book can appear linked to the Italian experience and regulation. This is due mainly to the territorial basis of the pilot projects and the affiliation of most the authors. It is believed that this not by itself detrimental since the Italian experience in the development of smart grids and smart cities presents some peculiarities such as the early large deployment of smart metering technologies and the setting up of an advanced regulatory framework. The book covers a wide ground of topics and applications and could not be written without benefitting from the published efforts of other researchers and Institutions reported in the references at the end of each chapter. The authors gratefully acknowledge the financial support from the Italian Ministry of Economic Development and Regione Puglia Government as well as the technical support from the Municipality of Bari for providing technical assistance and support in the implementation of some pilot projects. The authors also acknowledge the contribution of the many people who, in various ways, contributed to the realization of the projects mentioned in the book. This work would not have been possible without the patience of our families and the encouraging assistance of the publishing editors, to which I express, even on behalf of all contributors, our gratitude. Finally, I wish to express my sincere thanks to all the authors who contributed to the publication of this book. After all, the book reports the story of the cooperative efforts of a group of enthusiastic researchers working on the same challenging issue of transposing theoretical results on actual demonstrators useful for the everyday life. Massimo La Scala Bari, Italy October 2016

Introduction From Smart Grids to the Smart Cities: New Paradigms for Future Networks

In this chapter, terminology, definitions, and economic and technical drivers for smart grids and smart cities are introduced. Smart grids, defined according to a wider significance, which include all energy grids and the integration of advanced distribution grids, show significant potential for operation enhancement, safe and secure operations, and energy efficiency. Furthermore, towns are conceived as a natural place for relationships and social productive interactions. A natural convergence of social and technological networks is expected since towns represent a natural arena where these technologies can cooperate to enhance the quality of life of the citizens. The integration of energy grids can play a fundamental role for enhancing efficiency, environmental issues, operation and introducing new business models for innovative services. The implementation of suitable platforms gathering data from advanced distribution grids can provide fruitful information to policy makers and stakeholders, and create consensus in the citizenship.

I.1. The birth of smart grids The restructuring years, between the late 1980s and the early 2000s, were carriers of profound modifications in the electric power industry with the creation of energy markets, the unbundling of energy services and the affirmation of the “third party access” (TPA) principle. Despite the radical changes that had to be accommodated, in those years, investments in electrical infrastructures followed the business-as-usual scenario, whereas the general concern had been mostly focused on the generation side and on energy markets and services. Soon enough, power systems proved to be inadequate to bear the weight of restructuring.

Introduction written by Massimo LA SCALA and Sergio BRUNO.

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National bulk power systems were built with the aim to transport the energy generated in large power stations, located where fuel or hydro resources were more abundant and cost-efficient, towards end-users. High-voltage transmission grids were designed to transport electrical power over considerable distances from generation to load centers (cities or large industrial plants), where energy is supplied after a series of voltage transformation. Being traditionally planned and operated by vertical integrated utilities, the electrical power system was not flexible and resilient enough to withstand the operative conditions set by unpredictable market laws rather than centralized scheduling routines. The Californian energy crisis in 2000–2001 was the first example of how the lack of centralized long-term generation resource planning and the presence of power system physical bottlenecks could trigger strategic speculative behavior of independent producers at the expense of customers and security of supply. In the following years (2003–2004), an uncommon long series of large blackouts were experienced across the world, leading the power system community to interrogate itself if the restructuring process and the energy markets had been the causes of such events. Power system restructuring had not been directly responsible for such events, but it was soon clear that power systems were in need of new strategic investments and that new operative schemes with regard to power system reliability had to be enforced. Since those years, it has been recognized, first by the scientific community and then by energy market players and governmental actors who agreed that power system flexibility, resilience and efficiency had to be improved. These results would have to be accomplished through the deployment of more sensors and more control resources, the adoption of new technologies (for example, flexible AC transmission systems (FACTS)) and the development of advanced wide-area monitoring and control architectures based on fast computation and communication systems. The idea that power grids must enhance their abilities and evolve towards “supergrids” or “smart grids” became generally accepted. These same requirements (more automation, more sensors and control capabilities, more flexibility and efficiency) were soon to be applied to distribution grids as well, leading to a broader definition of the “smart grid” paradigm. Smart or, better, smarter distribution grids are in fact necessary to withstand other significant transformations of electrical power grids. Since the 1990s, a steady increase in distributed generation (DG) has been observed worldwide.

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Although there is no clear consensus about the definition, DG, basically, includes power generation facilities sufficiently smaller than central plants, usually 10 MW or less [INS 03, LAB 07], not centrally planned nor centrally dispatched [CON 03], usually located near the point of use and connected to the distribution networks [LAB 07, INT 02]. The newest definitions of DG tend to consider only those plants that are directly connected to MV and LV distribution systems as in the Italian regulation [AUT 15]. Development of DG was due to different drivers. When a consensus about the dangers of climate change and greenhouse emissions was reached, it became clear that electrical energy had to be produced in an environmentally friendly way mitigating, or even better eliminating, CO2 emissions. According to this vision, the future energy industry will rely mostly on production from renewable energy sources (RES), combined with fossil-fueled plants equipped with carbon capture and storage technologies and, perhaps, newgeneration nuclear power plants. The growing environmental concern led to the diffusion of incentive policies in the 2000s for the exploitation of renewable sources and to an ever-growing penetration of RES generating units in power systems. Thanks to the enforcement of TPA, independent producers adopting RES technologies (mostly wind or photovoltaics, but also biomasses and biogas) were soon injecting massive amounts of energy into power systems, giving rise to power system reliability concerns mostly due to the intermittent nature of certain energy sources and the fast filling up of transfer capacity in power corridors. Power congestions and RES overproduction are responsible for market inefficiencies (zero or negative energy prices are experienced with growing frequency, for example, Italy experienced for the first time a 2-hours zero price on 16 June 2013, whereas negative prices had already been often cleared in the German market) and for new concerns about power system security (dangerous power system static and dynamic conditions have been often experienced in northern Europe due to intermittent production from off-shore wind farms). The increasing penetration of RES generation affects not only transmission systems, but also distribution. Owing to renewable portfolio standards and government RES incentive programs worldwide, the number of small generation units connected directly to medium-voltage (MW) and low-voltage (LV) circuits has increased conspicuously in the late 2000s, following the general trend of proliferation of DG. Another driver for the diffusion of DG was due to the reduction in installation costs for fuel-fired generation technologies, which spread the use of small/medium-sized

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power stations based on both internal and external combustion cycles. In addition, due to the birth of energy markets for energy efficiency and incentive schemes, combined heat and power (CHP) generation units have been spreading out on power systems (usually using fuel or biomass for combustion or a mix of both). Incentives and reduced capital costs have made DG a reality, placing a great portion of the gross power generation near to the end-users. In this scenario, generation has been partly removed from the bulk power system and is now directly injected in MV and LV distribution systems. For example, according to the Italian Regulation Authority for Electricity Gas and Water (AEEGSI), approximately 16% of the overall gross Italian electricity generation is produced by DG (this number is conservative since it does not include those plants whose capacity is lower than 10 MVA and are not connected to distribution systems) [AUT 15]. This figure is shared by other countries such as the USA, where a capacity exceeding 200 GW was assessed in 2007 over a total nameplate capacity exceeding 1,100 GW [USD 07]. The diffusion of DG in distribution systems created a new category of energy customers that are not only consuming energy but can also produce it. End-users that can alternatively act as users and providers are often called “prosumers” (from the merge of the words producers and consumers). They can be found today in any sector: industrial, tertiary and commerce, and residential. The diffusion of prosumers consistently modifies the scope of distribution systems that have been designed and built with unidirectional schemes in order to convoy energy from the highest voltage level (HV) towards end-users at MV and LV levels. Distribution systems are therefore very large and passive networks with few automation (usually found at primary substations and in primary MV distribution feeders only), very little communication and limited local controls such as voltage regulation. The increase in DG production may create major security and operative problems at distribution level, worsened also by the fact that the greatest portion of DG is produced by intermittent RES. Typical consequences of DGs are congestions, violations of scheduled power exchanges, overvoltages due to reverse power flows on transformers, possible failures of relays and deterioration of power quality. Such concerns made distribution companies (DisCOs) aware that their systems had to evolve and gain “smartness”, enhancing monitoring and control functions available at control centers. The evolution of distribution grids towards “smart grids” or (probably better) “smart distribution grids” can be considered to have begun thanks to the diffusion of advanced digital meters, distribution automation, building automation, low-cost cabled and wireless communication systems and the setting up of specific plans for the modernization of distribution systems [BRO 08]. In Europe, for example, the European Commission has promulgated several directives for the development of

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smart grids and smart metering systems [EUR 09, EUR 06a], that have been already put in action by many EU Member States. The road towards the “smartification” of distribution grids is clearly a hard path because of the huge extension of such grids, the presence of a large variety of legacy systems, the heterogeneity of DisCos and their related networks. Moreover, as remarked previously, distribution systems were built to be passive networks, with a minimal ability of monitoring and controlling power flows. At the MV distribution level, the topology, the status of circuit breakers and major state variables and flows are generally known through SCADA systems; however, this is not true for LV distribution systems where, also, the population of active end-users and prosumers is in continuous growth. In this case, deploying advanced smart meters with a sufficiently fast time resolution is a fundamental action, as it can provide capillary information about loads and DG. The power system state is known only if most of its parts are monitored and smart control functions can be enabled only once the system state becomes observable [EKA 12]. The issue of monitoring and control MV and LV smart distribution grids is addressed in Chapter 1. I.2. Definition of a smart grid In the last 10 years, many attributes and definitions have been given to the notion of “smart grid”. The “smart grid” concept combines a number of technologies with end-user solutions and addresses a number of policy and regulatory drivers. Many possible definitions have been proposed, but a univocal clear one does not exist. Definitions are often overlapping but some discrepancies can be found. What is clear today is that the “smart grid” just represents the vision that we have of the power grids of the future. It is not an incidental circumstance that the European Technology Platform for Smart Grids, founded in 2005 in order to “formulate and promote a vision for the development of European electricity networks”, was initially called European Technology Platform for Electricity Networks of the Future. A good synthesis of what is a “smart grid” can be found in a recent document of the U.S. Department of Energy (DOE) that summarizes “the smart grid involves the application of advanced communications and control technologies and practices to improve reliability, efficiency, and security which are key ingredients in the ongoing modernization of the electricity delivery infrastructure” [USD 14]. This general definition nearly embraces any response that can be given to the question “what is a smart grid?”. However, the answers to the question “what can a smart grid do?” do not always coincide.

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This terminology arose right after the first reckless years of deregulation and the blackout season in 2003. The first needs, which smart grids were asked to respond to, were mostly based on the problem of preserving power system security and integrity in uncertain scenarios of ever-expanding electricity markets and international political crisis [AMI 04]. The first issue is related to the necessity to upgrade the power grids to allocate variable market transactions, increase capacity and operate the system in a completely different way. In addition, it should be remembered that the early 2000s were also years very close to the terrorist attacks of September 11 2001, and it should not surprise that one of the first prerogatives of smart grids was to develop self-healing mechanism and resilient emergency schemes in order to ensure survival when faced with to cyber or physical terrorist attacks [AMI 04]. In the USA, a very comprehensive early design of smart grids was developed by EPRI in 2004 with the IntelliGrid Architecture. This architecture includes most of the relevant power system functions contained in the modern definitions of smart grids. In a later vision given by the DOE in 2009, the smart grid: 1) enables informed participation by customers so that consumers can become an integral part of the electric power system, modifying the way they use and purchase electricity, participating in load balancing and helping to ensure reliability; 2) accommodates all generation and storage options, including all distributed energy resources (DER), even being diverse and widespread and in the form of renewables, DG and energy storage; 3) enables new products, services and markets, managing independent grid variables such as energy, capacity, location, time, rate of change, and quality; 4) provides the power quality for the range of needs of different end-users, proving varying grades of power quality with variable prices; 5) optimizes asset utilization and operating efficiency, increasing the efficiency of maintenance procedures, decreasing losses and controlling congestions; 6) operates resiliently to disturbances, attacks and natural disasters, reacting to such events isolating the faulted elements and keeping normal operation in the rest of the system [USD 09]. Concurrently to the USA and all other countries, the European Union (EU) developed its own power network strategic awareness. This vision is mostly founded on its own strategies and policies for 2020, concerning the meeting of the Kyoto protocol objectives, the low-carbonization of energy industry, the increase in energy efficiency and conservation, and the development of a green and sustainable economy [EUR 06b]. Smart grids are considered part of the interventions necessary to meet the EU challenges and opportunities of the 21st Century and fulfill the

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expectations of society. The main goals to be achieved are more or less similar to the DOE strategy: develop a user-centric approach, innovate and renew an ageing infrastructure, increase the security of supply and expand liberalized markets with new products and services. However, a much greater emphasis is put on the environmental issues, on the necessity to integrate RES generation units, increase the social responsibility and sustainability, optimize visual impacts and land-use, increase interoperability among the physical interconnected European infrastructures, and simplify and reduce permission times for new infrastructures. As remarked in [USD 09], due to the variety and high number of stakeholders, the definition of a smart grid might change according to the specific needs expressed by each participant (back again to the question “what should a smart grid do?”). The technology options at hand and the number of functionalities to be enabled are so many that a variety of broad definitions can be given at transmission, distribution and utilization level [GEL 09]. Most definitions put emphasis on the role of Information and Communication Technologies (ICTs), which improve system operation, billing and maintenance, and will be able to create a suitable communication platform for the development of the new energy services. However, in our opinion, the same emphasis should be devoted to the new actuators and devices (mostly derived from power electronics technologies) and control technologies, which will be able to “close the loop” at the operation level. Similar attention should be devoted to the regulatory framework, which is very important in eliminating barriers that can set technology free to fulfill the market needs and change the structure of the energy business. The creation of a real competitive market and consumer awareness can contribute to create new business models and opportunities by the use of emerging technologies, such as micro-grids, RES, electric vehicles and electrical storage. I.3. Drivers for smart grids The interest in smart grids has been increasing since this terminology was first generally accepted. Today, many national governments are encouraging smart grid initiatives, as they provide a cost-effective way to modernize the power system infrastructure, enabling, at the same time, the integration of low-carbon energy resources in power system operation and the fulfillment of security and power quality requirements [EKA 12]. Therefore, the accomplishment of smart grids is envisioned as an important economic and commercial opportunity to develop new products and services and promote the green economy. The social and economic impacts of smart grid technologies are potentially huge. In 2012, according to Bloomberg New Energy Finance analysts, smart grid

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technologies registered an increase of 7% in investments worldwide, with a global turnover estimated to be approximately $14 billion and an expected future yearly increase of 10% [BLO 13]. As reported in [USD 14], the electricity industry spent an estimated total $18 billion for smart grid technology deployed in the United States during the 4-year period of 2010–2013. Investments in Europe in 2012 were significantly smaller [BLO 13] than those in the rest of the world, mostly because of the inhomogeneous implementation stage of smart meters deployment campaigns. In Italy, approximately 35 million smart meters were installed starting from the year 2000, with a €2 billion investment by the major distribution utilities. Nowadays, a new generation of more advanced so-called “2.0 smart meters” is going to be deployed replacing the previous ones, placing Italy among vanguard experiences in this field with great development opportunities for the entire production chain. Expected figures for the European markets can be considered close to the expectations from the US power industry, where EPRI calculated that the investment needed to realize the envisioned power delivery system of the future is between $338 and $476 billion (with a total net benefit expected in the range between $1,294 and $2,028 billion) [EPR 11]. The expected benefits result from the growth of renewable power generation and storage, from the increased use of electric vehicles, and from the avoided expenses due to system inefficiencies, bottlenecks and ageing of power systems. In most fully industrialized countries, power systems started to take their modern form in the 1950s under the economic and industrial growth that followed the Second World War. Since the late 1990s, most transmission and distribution system components that were installed in the years of power system expansion had been arriving at the end of their life span. The capital costs of extensive large replacement campaigns are very high, but it is still an opportunity to install new devices that can provide a wider variety of functions with small incremental costs. The need to refurbish transmission and distribution grids is an obvious chance to innovate them with new designs and operating practices. A classic example is given by protection relays installed on transmission lines. The newest digital relays are intelligent electronic devices (IEDs) that have at their own disposal local computation capabilities and are able to establish a two-way communication channel with theoretically any other objects in the power system (substation controllers, SCADA server, other IEDs, etc.). The substitution of old protection relays with the newest digital ones is a process that has been going on in the last 20 years for replacing old components and achieving substation automation. However, these same components, with marginal extra costs, can be equipped with signal processing

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units capable of performing advanced measurement in order to be used also as digital fault recorder and phasor measurement units (PMUs). PMUs are fundamental components for developing wide-area monitoring and control architectures and, therefore, constitute a key-enabling technology for the achievement of smart transmission systems and for the increase in the overall transfer capacity of the existing power grids. Transmission system operators (TSOs) that, initially, perceived an unsurmountable economic obstacle for the penetration of this technology, thanks to the installation of digital protection relays, own today an ever-growing number of PMUs distributed on their systems. The need of reinforcing transmission power systems through the development of advanced monitoring and control architectures, through the installation of new sensors, control devices and actuators, and the setting up of advanced communication protocols and fast communication channels, derives also from the recognition that being up to old planning practices, like building new transmission lines, is almost impossible. New binding environmental legislation and requirements, together with the diffusion of “Not In My Backyard” (NIMBY) or “Not In Anyone’s Backyard” (NIABY) syndromes, make the authorization process and the construction of new overhead lines a very troublesome path. In many countries, the construction of new overhead lines, needed to increase the transfer capacity or to meet load and RES generation growth, has been delayed for years (if not stopped for good) due to difficulties in obtaining authorizations from local authorities and communities. After the unbundling of the power industry segments and the introduction of the TPA principle, market competition made many of the old fuel-fired plants obsolete. Old production plants were refurbished or repowered often increasing their power capacity, for example, for all those plants that were converted to the use of natural gas and to combined cycle. New fuel-fired power plants were also built together with large RES generation parks, changing significantly the distribution of power flows in the networks. As an example of such a revolution, it should be considered that, until the early 2000s, the Italian power system had been characterized by power flows following the North–South direction, due to excess of generation in the North (where all hydro resources are also located) and to considerable imports from the neighboring countries. Following the adequacy problems experienced by Italy in 2003, several new plants and repowering projects were authorized due to a special legislation implemented after the Italian general blackout. Moreover, with the increased penetration of RES technologies in the South (especially wind and photovoltaics), the shape of power exchanges in Italy has changed drastically, with the South exporting energy for most of the time. The Italian power flows in 2015 looked very different from that of a decade earlier (see Figure I.1). According to data by the

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Italian TSO (Terna), in 2015, renewables generated around 109.56 TWh, i.e. a relevant 38.85% of domestic production (in 2014, renewables shared even an incredible 43%). Hydroelectric power was characterized by a gross production of 43.89 TWh. Although wind and geothermal energy production remained pretty the same in recent years, solar power increased by about 3 TWh with regard to the previous year, reaching 25.2 TWh about 8.9% share of the total power production. Owing also to the intermittent nature of RES production, power system operation cannot rely on usual operating procedures, since they have to deal with everchanging operating states and power congestions often set by unpredictable market movements and by weather conditions.

Figure I.1. Electricity flows expressed in TWh among market zones and with neighboring countries in 2005 (left) and 2015 (right). Orange encircled numbers represent local demand. Source: Terna

Having to satisfy increasing needs with limited resources, power grids have to increase their efficiency, flexibility and adaptivity, with new monitoring and control functionalities, self-healing capabilities and higher levels of system automation. In other words, they have to evolve into smart grids. This is true also for distribution systems, whose monitoring and control capabilities have always been limited. With the increasing penetration of DG units connected at MV or LV levels, it has been observed how anomalous voltage profiles can be experienced on distribution feeders in the case of reversed power flows. This means that local generation must be coordinated with on-load tap changers and other

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control resources through more advanced monitoring and control systems or by means of further system automation. Smart grids are needed not only for solving problems but also for providing new opportunities. For example, demand response (DR) implemented at the distribution level opens the door to wider applications in power system operation with regard to load and generation balancing. DR can provide innovative ancillary services and be adopted as a “spinning reserve” during power system operation. Actually, from industrial to residential customers, any DER, being a load, generator or storage system, can theoretically offer reserve services, provided that a smart architecture exists and enables two-way communication between different hierarchical levels of control (for example, a Building Energy Management System (BEMS) communicating with the distribution management system). Other opportunities are to be found in the increase of energy efficiency and conservation. In Europe, a key document for the implementation of efficient and smart energy networks is the Energy Efficiency Directive (2012/27/EU), which establishes a set of binding measures to help the EU reach its 20% energy efficiency target by 2020. Under this Directive, all EU countries are required to use energy more efficiently at all stages of the energy chain from its production to its final consumption, and transpose the Directive’s provisions into their national laws by 5 June 2014. The main inputs provided by the directive are: – energy distributors or retail energy sales companies must reach 1.5% of energy savings every year through the implementation of energy efficiency measures; – each country has to achieve the same goal through different means, such as the improvement of heating systems overall efficiency and the installation of double glazed windows; – public sectors should buy energy-efficient buildings, services and products; – every year, EU governments must realize energy-efficient renovations on at least 3% of their buildings; – energy consumers must have easy and free access to data regarding their own energy consumes by means of advanced metering devices; – efficiency levels must be monitored in new energy generation capacities; – even large companies would make audits of their energy consumptions in order to find the better ways to reduce it. This regulation pushes EU governments to promote efficiency through measures and incentives in different fields, such as high-efficiency cogeneration, district heating and smart grid pilot projects. At the same time, it introduces new rules

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which set more freedom in the energy sector allowing for new forms of production and distribution of energy (such as microgrids, storage and small isolated systems for efficient energy utilization). The EU also promotes the development of the fourth industrial revolution, the so-called Industry 4.0 paradym, an innovative trend toward automation and digitalization in manufacturing. This concept applied to energy relies on the use of ICT technologies, energy automation, efficiency in manufacturing technologies. It is worth mentioning the Horizon 2020 programme, which supports studies and pilot projects in integrated industrial districts where both energy and matter flows are optimized concurrently to gain efficiency. In the EU, according to this strong and wide regulatory background, regulatory national agencies are receiving and accomplishing them inside national laws and standards. In this framework, it is interesting to mention the effort of the AEEGSI in yielding many official documents and resolutions, like the updated “539/2015/R/eel”, to support the implementation of what it is called “Sistema di Distribuzione Chiuso” (“Closed Distribution System”). These systems consist of electric networks which can operate as isolated networks under certain conditions, must own a certain number of RES and be able to grant some efficiency levels. This concept appears interesting since it opens up a window to a re-organization of distribution systems, where prosumers can decide to renounce to the interconnection with the local utility and produce, distribute and utilize energy on their own grid if efficiency and technical-economic conditions are satisfied. A by-product of smart grid technology is composed of microgrids and nanogrids. According to a commonly accepted definition, microgrids are electricity distribution systems containing loads and DER (such as distributed generators, storage devices or controllable loads) that can be operated in a controlled, coordinated way in both grid-connected or island mode. Nanogrids are small microgrids, typically serving a single building or a single load. Capacity ranges, according to various definitions, from 100 kW for grid-tied systems to 5 kW for remote systems not interconnected with a utility grid. Drivers for the microgrid/nanogrid market are surely based on the economic value this technology can bring in terms of new business models and services, the possibility to use RES and the not completely “confessed” desire of the “prosumer” to be autonomous and skip costs due the dispatching, distribution investments and related taxes. Finally, it should be observed that smart grid applications play a role in developing countries. In many developing countries or countries characterized by not densely populated areas, power grids have not been fully built and a large part of the population do not have access to electricity. Smart grids may represent an

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opportunity for the quantum leap in the electrification of remote areas, which starts from “scratch”, skipping the phase of building long-distance interconnectors and meshed grids and giving rise to more manageable, reliable and scalable designs. This can be the same transition, experienced in some developing countries, where the passage from landline to cellular phone networks was skipped jumping immediately to the most advanced technology. The microgrid and nanogrid approach can be utilized not only for developing isolated systems in remote areas and villages but also to develop standardized systems, container-sized to be easily carried and deployed to re-store energy for civil protection purposes in areas affected by major catastrophes such as earthquakes, storms and war, or to supply energy to environmentally protected areas [BRU 14]. I.4. From smart grids to smart cities Smart grid applications can be developed in different realms of the power system: transmission (and subtransmission), and primary and secondary distribution. Transmission and subtransmission systems provide their functions at regional, national and continental levels, whereas the typical influence areas of distribution systems are cities and districts (primary distribution), and blocks and buildings (secondary distribution). The EU developed within the European Electricity Grid Initiative its own roadmap 2010–2018 to the smart grid, organized with the following steps [HTT b]: Level 0: New generation technologies Level 1: Smart Pan-European Transmission network – Innovative transmission grid architectures – State-of-the-art transmission/power technologies – Novel monitoring, control and storage methodologies – Shared electricity market simulators Level 2: Smart network and processes – More automated MV distribution networks with self-healing capabilities – Monitored and controlled LV networks – IT-supported monitoring process

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Level 3: Smart integration – Renewable energy, DG, electric vehicles, electricity storage and aggregation Level 4: Smart Energy Management – Management of end-use energy efficiency, aggregation, retail Level 5: Smart customers – Customers aware and actively participating The sequence of these objectives shows how the building of new interconnectors for market integration in the EU is a particularly urgent measure, since the social welfare cost associated with delays in building critical infrastructures can be very high. It also appears straightforward that the first levels (Level 0 and 1) are related to the reinforcement of transmission systems, which can be privileged thanks to the fact that SCADA/EMS and substation automation have been under development and incremental improvement since the late 1970s. However, the most urgent measures must be reached in the “smartification” of distribution systems, whose degrees of automation and intelligence are often particularly limited, especially in the case of low-voltage distribution network. The evolution of the “smart (distribution) grid” can follow three subsequent implementation stages that have been defined: Smart Grid 1.0, 2.0 and 3.0 [CAR 11]. The 1.0 phase represents the first development stage that requires the creation of a “meter-centric smart grid”, where a smart measurement system was deployed. This step can be considered to be concluded in many countries and can be in the future incrementally improved or standardized. However, this step can be considered to be substantially technologically stable. The 2.0 phase is based on the development of what has been defined “operationcentric smart grid”. The main focus is the development of a distribution network control system and the interactions between smart meters and SCADA. This activity is centered on network and on utilities. At the current stage of development, there are several actual implementations at the MV level and mostly on-going research and tests at the LV level. The last stage, phase 3.0, will lead to the accomplishment of “customer-centricsmart grids”. At this stage of development, full functionalities for active customers will be developed. In order to reach this objective and improve the number of services offered to active energy end-users (active consumers or “prosumers”), the exploitation of new key enabling technologies will be requested, starting from a new

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conception of LV networks in terms of topology, control strategies and measurement systems. It should be remarked that the Smart Grid 3.0 specifically involves active customers, who have reached a general awareness level, empowering them at the center of new, and previously unexplored, business models. Smart Grid 3.0 will enable DR schemes and it is the necessary step for the evolution of urban power grids in smart cities. In the residential sector, an important role in the Smart Grid 3.0 will be played not only by the RES and DG technologies that will interact with all other energy systems (heating and cooling systems, water supply, etc.) but also by electrical vehicles (EVs). The presence of a massive number of EVs in power grids will require the development of innovative architectures with fully decentralized demand automation, and will allow for the setting up of innovative energy services and centralized control functions based on the exploitation of EVs storage capabilities and load aggregation schemes. It is possible to imagine a fourth level of development of smart grids, where the smart grid concept first developed in the power industry is integrated in the planning and operation functions of other realms, such as the natural gas distribution systems, water supply systems, district heating, cooling and transportation systems. This new stage is at the basis of the definition of the functionalities of a smart city. In a smart city, all urban infrastructures that ensure the social life will become progressively more interlaced and interdependent, individually smarter, and part of a collective super-system well coordinated and cooperative. In the following, the smart grid approach is envisioned as a process for the enhancement of electrical infrastructures that will become sentient active living systems and their integration with other living urban infrastructures as the first necessary step for the empowerment of inclusive, clean and efficient smart cities. I.5. The smart city: home of advanced energy solutions Smart cities are sustainable and liveable places where economic, social and environmental pillars are simultaneously supported through the adoption of advanced technology and the implementation of cross-cutting actions. Smart cities are a fertile ground for the growth of enterprises, welfare and human capital, providing affordable services and efficient infrastructures. The need for integrated approaches in the development of future efficient cities and societies arises from several sustainability concerns. Cities and, in general, highly populated areas, consume about 75% of the overall worldwide energy production, and are also the principal source of polluting emissions. In particular, CO2 emissions in

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cities cover 80% of the global ones. Cities are also growing and expanding at a feverish pace. As reported in [INT 14], every day, urban areas grow by almost 150,000 new inhabitants. At this pace, in 2050, the world’s urban population is expected to amount to approximately 6.3 billion citizens (with a 72% increase from the 3.6 billion in 2011). From these considerations, it appears clear that, in order to achieve goals in terms of social, economic and environmental sustainability, existing and new infrastructures and services must be improved to the highest levels of efficiency, requiring a leap in the integration of all infrastructures [INT 14]. A smart city is a complex system of systems, a cluster of interconnected networks: transport power grids, water supply and waste management, buildings, lighting systems, people, social relations, public services and governance. Some of these networks are actual physical infrastructures that, through material or energy flows, provide vital services to society and improve the quality of life. The improvement of efficacy and efficiency of all physical urban infrastructures is obtained by optimizing flows within each network and optimizing exchanges between interconnected networks, through the implementation of advanced monitoring and control functions and the deployment of innovative technologies. The infrastructures must be modernized and improved in order to allow for a better allocation of resources and an overall reduction in losses. Power grids, gas distribution systems, water distribution systems, waste management systems, district heating and cooling, and public and private transportation systems must be efficiently integrated with homes and with commercial and tertiary buildings, so that they can be suitably adapted to the needs of citizens, or more in general, of city’s stakeholders. It is important that energy resources, under any form, are optimized and exploited with a holistic approach, so that overall efficiency can improve while social and economic growth is enabled. Economic, energetic and social factors are, in fact, strictly intertwined. International practices have long proved, for example, how recessed areas can be quickly reindustrialized and revitalized by facilitating the access of new industries and businesses through the reduction in electricity tariffs. This was made, for example, in the 1980s with the project Appleseed aimed at the regeneration of the depressed urban area of Bronx in the city of New York [MAN 88]. In that case, special rates (with a discount on the electricity bill ranging between 15 and 30%) were introduced to attract new companies in that area with the successful goal to create more than 50,000 new jobs in 10 years. From that first successful experience, we can derive that cost-efficient systems and innovative technologies offer the opportunity to achieve a better allocation and use of energy resources, and to exploit the energetic variables as means for attracting investments useful for the re-development of depressed areas.

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More generally, technology can disclose city’s economic potentials and create new innovative services and business models. This is the case, for example, of smart grids (that are basically technologically advanced electric power grids) that can enable DR compensation schemes and ancillary services. The adoption of advanced technology solutions can increase efficiency, reduce costs, and improve prosperity and competitiveness of local enterprises. Technologies are also means for empowering active and aware behavior of all citizens, creating a suitable environment for the development of new sustainable people-oriented smart cities. I.6. The smart city: a people-oriented environment People play a significant role in the creation of a smart city. A people-oriented approach is needed because the role of human and relational capital is essential. In planning, urban renewal and regeneration must be integrated with technological innovation as means for achieving social inclusion of residents and higher living standards. The smart city must be planned and managed for satisfying all human needs and improving the quality of life in the urban environment. The network of urban relationships presents many levels of opportunities for the development of a technology on a human scale (human-oriented technology). The urban environment must be designed in order to create new interaction models between persons and the environment. The city becomes an interactive space in which human needs are interpreted and satisfied through technology. Streitz et al., in [STR 05], envisioned two ways of smart interaction between the environment and human beings. A “system-oriented, importunate smartness” can be based on smart choices that are embraced automatically according to past experience, observation of the human behavior or local control rules (for example, in smart homes, blinds and lights can be regulated automatically according to external light, to daily schedules or room’s occupation). A “people-oriented, empowering smartness”, instead, is characterized by the principle of “keeping the human-in-the-loop”: people who are in control of the urban space receive simple and intuitive information, provided by technology, and adopt responsible and informed actions based on recommendations and suggestions obtained from the system [STR 05]. The “human-in-the-loop” is active, aware and able to compare several options and make optimal decisions thanks to the inputs from the system. The idea behind these mottos is that at the basis of the new urban framework, the smart city, there should be the human being. The interaction between the smart city and humans is not necessarily automated, but is based on the human that compares several options, reacting to the signals arriving from the system.

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The human factor must be taken into account in relation to all the different stakeholders who operates in the city. In [INT 14], a city’s stakeholders have been classified into five classes: – governance and public administration: political leaders, managers and operators of the local government (city and metropolitan areas); – public and private DisCOs and service operators: water, electricity, natural gas, district heating and cooling, waste management, communication, transports, education, health, etc.; – end-users and prosumers: inhabitants, local enterprises, tertiary sector; – investors: private banks, venture capitalists, pension funds, international banks; – solution providers: technology providers, financiers and investors. The humans responsible for decision-making in any such bodies must be able to receive a suitable number of relevant pieces of information, being raw, pre-filtered or elaborated data, so that they can react to external inputs and adopt the most suitable actions (Figure I.2).

Monitoring (collection and presentation of information)

Human (smart decision making)

System

Control (enforcement of decisions)

Figure I.2. Smart decision-making with human-in-the-loop

To a certain extent, “human-in-the-loop” is a concept that can also be extended to the management of infrastructures. Embedding monitoring and control functions in decision-making is in fact one of the working principles of SCADA architectures,

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usually adopted for real-time operations of complex physical systems (power systems, gas transportation networks, district heating, large industrial plants, etc.). The classical SCADA approach is based on bi-directional communication between human operators, computing resources and field components as outlined in Figure I.3. Operators at the control center of the specific service operator (electricity, natural gas, water, etc.) can receive updated synthetic information about the state of the system through SCADA and are enabled to monitor main physical variables and to control the system state through the adoption of suitable actions. Relevant pieces of information are extracted from the field by sensors, transducers and relays, and transformed in transmittable packets of data that are then sent to the master station. Data are filtered, elaborated and presented to the operators by means of a human-machine interface, together with other possible relevant information, such as a set of possible decisions and analysis of the consequences of each decision. The control center operator makes a choice that is interpreted, transformed in a transferrable data and sent to the local controllers that are responsible for managing the field devices.

human operator

measurements

control actions

system state

human-machine interface (HMI)

local server, modem, A/D converters, controllers control signals

communication system master station / server

field devices, actuators, sensors

Figure I.3. Basic architecture of a SCADA system

This is usually done in electrical distribution grids and smart grids through the SCADA/DMS system, and in many other systems. However, in a smart city, the field of application of SCADA should be broadened. Similar monitoring and control architectures and functionalities should be extended to all other relevant infrastructures, enabling automated control, human-supervised automation or manual control. Moreover, the monitoring and control capabilities of the existing SCADA system must be improved, allowing to reach a wider number of components. For example, in smart distribution grids, all LV components that are presently not monitored nor controlled should be included in the action range of SCADA/DMS, as discussed in Chapter 1.

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In the control of physical infrastructures, technology must support this process, not only for ensuring the communication flows between humans and all devices in the field, but also for providing advanced measurement systems, innovative controls and actuators, and smartness through fast optimization algorithms and simulations. Smart technological solutions should also be able to lighten the job of humans, employing automatic control when the human input is not necessary or when a decision cannot be made fast enough. Technicians and other field operators can also be helped through advanced technologies, with GIS-based information, automatic fault detection and computeraided maintenance systems, in order to reduce the number of interventions and the time necessary to repair, minimize service interruptions and penalties, and reach higher standards in terms of security of supply and system reliability. With the due differences, the SCADA architecture and the “human-in-the-loop” concept share the same working principle: persons, made aware of their needs, of what is going on and the consequences of their actions, are enabled to embrace smart and conscious choices. An interesting application of these concepts can be found in a project, named “Res-Novae” [PRO 16], within the authors’ experience, about smart grids as an essential technology for the implementation of smart city concepts. In this project, among other objectives, utility operators and the public administration jointly developed a multi-level platform, obtained through the transition to smart grids, for acquiring, storing and processing data related to utility operations of energy infrastructures (power and gas). Data based on data sensing and mining of the physical infrastructures are elaborated to form synthetic indicators that policy makers and other municipality stakeholders can use to monitor energy production and consumption in order to single out the right policies for efficiency enhancement. This pilot project is going on in Bari, a medium-sized town in southern Italy. The municipality is currently engaged in a series of smart city initiatives promoted by the EU and mainly devoted to the reduction in CO2 emissions, energy efficiency and enhancement of the quality of life. The underlying idea is that performance measurement and monitoring for citywide and metropolitan management and strategy development are becoming essential tools that enable cities to clarify their mission and translate it into policies. Indicators can result helpful by enabling leaders, managers and policy makers to make intelligent decisions to allocate time and resources. In addition, another important result is to improve the communication of city performances to citizens, visitors and potential investors in order the obtain consensus and participation in the adopted policies. In both cases, the human is in the loop!

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I.7. Active energy users and prosumers End-users and, in particular, energy consumers should also be included “in-theloop”. This is a very innovative principle in the vision of smart grids and smart cities. Traditionally, in fact, energy consumers have always been characterized by very low elasticity with regard to their energy demand and scarce concern about energy costs (at least in the short term). This is true in particular for the residential and public administration sectors, whereas industrial and commercial sectors have been adopting demand side management measures since the first energy crises in the 1970s. The inelasticity of energy consumers is due to different reasons. Often energy costs can be perceived as irrelevant with respect to other recurring costs (for example, electricity bill vs. mortgage payment). Moreover, energy is considered as an indispensable commodity to be purchased no matter what. Another important reason is due to the delays in the decision-making control loops and the scarcity of available information. For example, in the residential sector, energy billing is monthly or bi-monthly. Bills are often calculated on the basis of average demand profiles and not on actual measurements, whereas the final balance that takes into account actual consumptions is made more or less yearly. Few other pieces of information, rather than monthly or yearly gross consumption, are usually available. This means that the human (house inhabitant) who is in charge of controlling the urban space (home) will receive feedback about his/her own energy behavior with an unacceptable delay. Delays and scarcity of information make putting causes and effect in relation very difficult (again, at least in the short term). However, in a smart city, this kind of uninformed and rigid energy behavior is destined to disappear. Citizens have a new role and they are no longer mere energy users but active energy actors. A new figure is born after the restructuring of the energy industry, after the capillary diffusion of DG and the advent of innovative urban districts, after a massive deployment of smart meters and other means of advanced monitoring. This modern citizen is often well aware of sustainability issues, is more responsive and informed, and is prone to take advantage of the new opportunities that come, for example, with the exploitation of RES, the installation of DG, the use of electric vehicles and the installation of batteries. This new active energy actor is often a “prosumer”. This term, first coined by the famous writer and futurist Alvin Toffler in his book Third Wave of 1980 [TOF 80] from the crasis of the words “producer” and “consumer”, indicates the role of the

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user of a good or a service that is at the same time a producer of the same good or service. Following an increased awareness on sustainability issues and several technological advancements, small-scale production systems, such as wind generators, photovoltaic panels, solar panels and micro-turbines, have been spreading in all sectors, from industrial to commercial, tertiary and residential. This means that a conspicuous number of energy users can today either consume or produce energy according to their needs or capabilities. More specifically, an energy prosumer is a user that can produce energy not only for its own needs but can also give it to other users. This transition, from passive consumers to active prosumers, can be obtained with regard to any energy vector, but clearly the most straightforward way to produce (and sell or exchange) energy is to produce electrical energy that can be injected in the distribution network and then sold. In general, the prosumer owns and manages DERs that, in the most comprehensive definitions, include any possible device for the production, transformation, consumption and storage of energy. Technologically, a prosumer has under its control a combination of components, starting from innovative smart grid devices, storage units, renewable and high efficiency production plants, ICT, smart meters and controllable loads. Thanks to the availability of such components, this new emerging figure is also an economic actor with the following characteristics: – it can produce, consume or store energy; – through its energy use and production, it optimizes technical, economic and environmental functions. The prosumer is one of the main possible actors in the optimization methodologies and techniques that will be proposed in the next chapters. Single prosumers or, most likely, aggregations of prosumers, can in fact provide significant local control capabilities to be exploited, in exchange for payment or other benefits, by energy service operators for reaching important targets in terms of energy provisioning, adequacy, security of supply, quality of the service, efficiency and energy conservation. Prosumers, first large commercial or industrial but later also small tertiary and residential end-users, will be enabled to participate in DR remuneration schemes, and will be able to modify their energy exchanges according to real-time pricing or top-down control signals. A prosumer, being an informed and conscious manager of its own energy resources and demands, will be in charge of the integration of all energy systems under its control and within the urban space that it occupies. Usually, the integrated

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management of multiple energy resources can be achieved through the optimal control of energy flow in an energy hub. There are many ways to integrate different energy systems at different geographical or hierarchical levels. At the residential end-users level, it can be assumed that energy hubs will assume the form of what is usually defined as home energy management systems or BEMS, respectively, in “smart houses” and “smart buildings”. I.8. Horizontal integration through energy hubs and energy districts Most of the investments for the modernization of infrastructures are aimed at the vertical integration of existing portions of physical networks with pervasive deployment of sensors and meters, actuators and field devices, low-cost or advanced communication systems, real-time local or centralized control systems, advanced analytics and computational resources. In a certain way, smart grids are advanced electrical power grids where the vertical integration of all these components has been completed. However, performances and efficiency of a smart city can be pushed up to their limits only if horizontal integration among all infrastructures is achieved. Horizontal integration is the core of today’s smart cities projects, as it defines the structure of the system of systems, but very few projects have started to address horizontal integration [BLO 13]. The main difficulties in horizontal integration have to be found in the inhomogeneity of the sectors to be integrated, the lack of standards and the scarce levels of interoperability, the wide number and variety of stakeholders, the presence of possible competing stakeholders, conflicts of interest and political resistances. Moreover, due to the high risks associated with the loss of vital infrastructures, and to the high level of complexity that characterizes already each vertically integrated system, it is not hard to imagine that each system is characterized by rigid security protocols. With regard to energy infrastructures, which constitute the domain of the applications proposed in this book, a possible way to achieve horizontal integration can be found in the setting up of physical or virtual hubs where energy, under any possible form, can be exchanged and transformed into other energy forms or stored, following supply/demand balancing needs, market requests or optimal control rules. An “energy-hub”, or alternatively a “hybrid energy system” [BRU 14] or “multicarrier energy system”, can be defined “as a unit that provides the basic features inand output, conversion, and storage of different energy carriers” [GEI 07]. The energy hub is a node of the complex textures of energy infrastructures where

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different energy systems are coupled through components that can produce, consume, convert or store energy. The domain of an energy hub is usually confined within the facilities of a single end-user or within the bounds of a closed area (a building, a university campus, a business park, etc.). The input ports of an energy hub can receive primary or secondary energy from external sources (electricity, natural gas, hot water from district heating, solid or liquid biomass, biogas, fossil fuels, etc.) or directly from RES generators (mainly solar photovoltaics, wind turbines, solar thermal, geothermal). The output ports of an energy hub are linked directly to the local loads, which normally consume electric and thermal energy, but can also utilize energy under other forms (for example, compressed air in an industrial plant). Within the energy hub, energy sources under any form can be stored, transformed, conditioned or supplied to the output ports. Efficiency and economic targets are reached controlling the exchanges between all energy subsystems by means of holistic approaches and optimization methods. Theoretically, the output energy can be exchanged with other hubs or sold through the energy distribution grid. However, regulations do often bind the use of energy to self-consumption. In certain cases, for example, in Closed Distribution Networks as defined by the European Directive 2009/72/EC, energy can be distributed liberally to other users as long as this happens within a geographically confined, industrial, commercial or shared services site [DIR 09]. The evolution of normative and regulations with regard to this issue will be relevant in shaping the actual functionalities and the energy service that can be developed within an energy hub. The dimension of an energy hub is not defined, nor its attributes; however, its working domain is supposed to be localized within a single facility or confined area. Energy hubs operating on larger domains (for example, urban districts or portions of metropolitan areas) can assume different forms, for example, what is defined in Chapter 5 as “energy district” or “multi-carrier” energy systems. I.9. Final remarks A major application of smart grids and advanced distribution energy systems is in the urban sector. A smarter operation of grids is needed to face the new challenges that are experienced by modern towns during these years. A new urbanization is giving rise to the so-called “mega-towns”. The entrance of new technologies, such as photovoltaics widely utilized for residential and tertiary buildings, EVs, CHP and district heating, heat pumps, changes the usual way grids have been operated so far. Another issue is a different attitude of customers, who are

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willing to participate more actively in the energy market and choose among new energy services. Usually, smart grids and smart city concepts are invoked to circumvent the problems arising from the new challenging era. In this book, emphasis is on the technological networks and energy distribution grids. Although ICT grids play an important role in the modernization of such services, the focus here is on the “more tangible” grids, which due to their material nature and impact are more resistant to epochal changes and need effective technologies and incisive policies to foster the transformation of the usual business models. Utopia would be to skip fluids and energy grids in a fully decentralized and dispersed generation of energy and vital fluids in a sort of selfish and autarchic vision, but this is a long way away from being a reality. Although we are developing in the right direction, with the introduction of power microgrids or cellular grids, dispersed generation of biogas or the reduction of hydric needs by collecting meteoric water, the general belief is that technological networks will still continue to exist to ensure reliability, security, adequacy, cooperation, efficient use of resources and reduction in storage needs. These same motivations pushed people in ancient times to move from rural areas to towns to obtain common and more advanced services and a secure, safe and more comfortable way of life. What is new is that distribution networks would provide new and more effective, efficient, market-oriented services and, at the same time, more flexible services that allow the customers to integrate their own local resources and switch among different services, providers and sources depending on their needs, taste and willingness to pay. I.10. Bibliography [AMI 04] AMIN M., “Balancing market priorities with security issues”, IEEE Power and Energy Magazine, vol. 2, no. 2, pp. 30–38, July–August 2004. [AUT 15] AUTORITÀ PER L’ENERGIA ELETTRICA IL GAS E IL SISTEMA IDRICO, Report on the status of Distributed Generation in Italy for the year 2013, available at: http://www.autorita.energia.it/it/docs/15/225-15.htm, 2015. [BLO 13] BLOOMBERG NEW ENERGY FINANCE, Smart grid infrastructure remains global growth marked, available at: http://about.bnef.com/press-releases/smart-gridinfrastructure-remains-global-growth-market/, 2013. [BRO 08] BROWN R.E., “Impact of smart grid on distribution system design”, Proceedings of IEEE PES General Meeting, Pittsburgh, 20–24 July 2008.

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[BRU 14] BRUNO S., DASSISTI M., LA SCALA M. et al., “Predictive dispatch across time of hybrid isolated power systems”, IEEE Transactions on Sustainable Energy, vol. 5, no. 3, pp. 738–746, July 2014. [CAR 11] CARVALLO A., COOPER J., The Advanced Smart Grid: Edge Power Driving Sustainability, Artech House, Norwood, 2011. [CON 03] CONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ELECTRIQUE, Impact of increasing contribution of dispersed generation on the power system, Final report WG 37-23, 2003. [EKA 12] EKANAYAKE J., JENKINS N., LIYANAGE K. et al., Smart Grid: Technology and Applications, Wiley, Oxford, 2012. [EPR 11] EPRI, Estimating the Costs and Benefits of the Smart Grid, Technical Report, available at: http://www.epri.com/abstracts/Pages/ProductAbstract.aspx?ProductId= 000000000001022519, 2011. [EUR 06a] EUROPEAN PARLIAMENT, Directive 2006/32/EC of the European Parliament and of the Council of 5 April 2006 on energy end-use efficiency and energy services and repealing Council Directive 93/76/EEC, 2006. [EUR 06b] EUROPEAN TECHNOLOGY PLATFORM SMART GRIDS, Vision and Strategy for Europe’s Electricity Networks of the Future, available at: http://ec.europa.eu/research/ energy/pdf/smartgrids_en.pdf, 2006. [EUR 09] EUROPEAN PARLIAMENT, Directive 2009/72/EC of the European Parliament and of the Council of 13 July 2009 concerning common rules for the internal market in electricity and repealing Directive 2003/54/EC, 2009. [GEI 07] GEIDL M., ANDERSSON G., “Optimal power flow of multiple energy carriers”, IEEE Transactions on Power Systems, vol. 22, no. 1, pp. 145–155, February 2007. [GEL 09] GELLINGS C.W., The Smart Grid: Enabling Energy Efficiency and Demand Response, Fairmont Press, Lilburn, 2009. [INS 03] INSTITUTE OF ELECTRICAL AND ELECTRONICS ENGINEERS (IEEE), P1547 standard series for interconnecting distributed resources with electric power systems, IEEE Standard, 2003. [INT 02] INTERNATIONAL ENERGY AGENCY (IEA), Distributed Generation in Liberalised Electricity Markets, available at: http://www.iea.org/textbase/nppdf/free/2000/ distributed2002.pdf, 2002. [INT 14] INTERNATIONAL ELECTROTECHNICAL COMMISSION (IEC), Orchestrating infrastructure for sustainable Smart Cities, White Paper, Geneva, Switzerland, available at: http://www.iec.ch/whitepaper/smartcities/, 2014. [LAB 07] LABBATE A., FULLI G., STARR F., PETEVES S.D., Distributed Power Generation in Europe: Technical issues for further integration, Joint Research Center European Commission, Technical and Scientific Reports, EUR 23234-EN, 2007. [MAN 88] MANAK J.R., “Project Appleseed: electric rate incentives”, IEEE Transaction on Power Systems, vol. 3, no. 4, pp. 1833–1839, November 1988.

Introduction

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[RES 16] RES NOVAE, Smart Cities Communities and Social Innovation, University and Research Italian Ministry, available at: http://resnovae-unical.eu/, 2016. [SMA 10] SMART GRIDS EU, European electricity grid initiative, available http://www.smartgrids.eu/documents/EEGI/EEGI_Implementation_plan_May%202010. pdf, 2010.

at:

[STR 05] STREITZ N.A., RÖCKER C., PRANTE Th. et al., “Designing smart artifacts for smart environments”, IEEE Computer, vol. 38, no. 3, pp. 41–49, March 2005. [TOF 80] TOFFLER A., The Third Wave, Bantam Books, New York, 1980. [USD 07] U.S. DEPARTMENT OF ENERGY, “The potential benefits of distributed generation and rate-related issues that may impede their expansion”, A Study Pursuant to Section 1817 of the Energy Policy Act of 2005, 2007. [USD 09] U.S. DEPARTMENT OF ENERGY, Smart Grid System Report, available at: http://energy.gov/oe/downloads/2009-smart-grid-system-report-july-2009, 2009. [USD 14] U.S. DEPARTMENT OF ENERGY, 2014 Smart Grid System Report, available at: http://energy.gov/sites/prod/files/2014/08/f18/SmartGrid-SystemReport2014.pdf, 2014.

1 Unbalanced Three-Phase Optimal Power Flow for the Optimization of MV and LV Distribution Grids

Smart distribution grids are developed around the concept of advanced distribution management systems (ADSM), whose features are summarized in this Chapter. Optimal power flow (OPF) techniques are a basic function of ADSM and can be applied effectively for controlling distribution grids at both MV and LV voltage levels. Specialized formulations of OPF need to be developed for defining control actions, such as move tap-ratio in on-load tap changers, switch capacitors or disconnectors, change reference signals or price signals to be sent to prosumers or active end-users. A methodology for controlling active and reactive resources in distribution systems, based on the solution of a three-phase unbalanced OPF, has been proposed and tested in this chapter. Particular attention is devoted to low voltage grids due to their importance. These grids are experiencing dramatic changes in power operations and show the potential to take full advantage of throughout metering and control. Test results showed the feasibility of the approach.

1.1. Advanced distribution management system for smart distribution grids Smart cities take form around advanced physical infrastructures which, thanks to the pervasive presence of sensors, monitoring, communication systems, and the implementation of optimization and control functions, acquire smartness and improve their overall flexibility, security, reliability and efficiency. The transformation required for achieving smartness in infrastructures of smart cities appears straightforward when electric power systems are considered. Several Chapter written by Sergio BRUNO and Massimo LA SCALA. From Smart Grids to Smart Cities: New Challenges in Optimizing Energy Grids, First Edition. Edited by Massimo La Scala. © ISTE Ltd 2017. Published by ISTE Ltd and John Wiley & Sons, Inc.

2

From Smart Grids to Smart Cities

“smart” functions oriented to the monitoring and control of transmission systems, such as state estimation, topology processor, contingency analysis or dynamic security assessment (DSA), have been customarily in use since the diffusion of control centers and SCADA/EMS in the 1980s. Therefore, a substantial improvement in the smartness of electrical power systems at urban level (basically primary and secondary distribution operating, respectively, at medium voltage MV and low voltage LV level) can be achieved if these same procedures and practices in use for transmission systems were scaled down to distribution. This basic idea was the principal objective of the earliest formulations of smart distribution networks, usually built around an extensive set of monitoring and control functions embedded centrally in the distribution management system (DMS), or in what it has also been defined as advanced DMS (ADMS). A smart grid, in fact, can be represented with a four-layer structure: the field constituted by physical components (buses, lines, transformers, loads, capacitors, etc.), the set of all measuring and actuating equipment, the ICT layer comprising all communication systems, and the control center (management system) [SAN 10]. The ICT layer is responsible for collecting information about the state of the grid and of its components from sensors, and sending such data to the control center where all evaluations and possible control actions are assessed. Being the place where all data and information are sent to be processed, and where necessary system response are elaborated, the ADMS can be considered the brain of a smart distribution grid, being, in other terms, what provides actual intelligence and “smartness” to the grid. A possible structure of an ADMS was outlined in Fan and Borlase [FAN 09], together with a list of suggested innovative and smart functions to be enabled in distribution systems. ADMS elaborates all available real-time, quasi-real-time and historical data in order to perform management applications that can be performed in a quasi-real-time power system operation framework or in the medium-long term for planning. Based on [FAN 09] and other early literature [HAD 10, MEL 11, MOH 10, MOM 09, ZHA 10], in [BRU 11a], an ADMS architecture for smart distribution systems was outlined (Figure 1.1). The proposed architecture is based on two main control loops starting from the SCADA/ADMS control center. The upper one controls all distribution system-connected devices, including all distributed energy resources (DERs), tap changers and storage facilities, whereas the second loop is interfaced with loads through an advanced metering infrastructure (AMI). SCADA is the core of the proposed architecture: it receives signals from remote terminal units (RTUs) or intelligent electronic devices (IED), such as bayarea controllers, loss-of-mains protection relays, circuit breakers, switching relays and transformers, so that a real-time snapshot of the distribution system can be acquired.

Unbalanced Three-Phase Optimal Power Flow for the Optimization of MV

3

Figure 1.1. Possible scheme of an ADMS

It should be noted that control centers and SCADA/DMS platforms had already been often adopted by Distribution System Operators (DSOs) for managing their own networks and performing substation automation and feeder control. However, even when supported by DMS monitoring and remote control functions, power system operation is still characterized by manual procedures that rely on the experience of operators. A full automation of distribution grids is the innovation required for the development of smart networks, and it is based on the presence of bidirectional communication paths between SCADA, control center and power system devices, DERs and, more generally, active customers and prosumers. Bidirectional communication enables substation automation and supports the enhancement of power system security and reliability through the implementation of smart control functions and through remote control of DERs, at both MV and LV levels. This idea is generally shared by regulators, standardization bodies and network operators, as shown by the most recent normative documents. For example, the draft IEEE Std P1547.8 asserts that DERs must be enabled to respond automatically to variations in grid voltage or following the broadcast of update reference signals or price signals [BAS 15]. This same idea is shared in Europe by other technical standards, for instance [CEI 14, VDE 11], that already define the way LV-distributed generation must contribute to static voltage stability and frequency regulation by means of either local measurements or remote signals. In

4

From Smart Grids to Smart Cities

the Italian standard [CEI 14] extend this principle to PV generators connected to LV that should be able to receive remote signals with protocol IEC 61850. If bilateral communication with DERs will be based on modern switchgear equipment and loss-of-mains protection relays, the integration of active customers into SCADA/ADMS passes from the setting up of bilateral communication with Automatic Meter Reading (AMR) devices and Automated Metering Infrastructure (AMI). Unilateral communication, meaning adopting AMR units for mere energy billing purposes, is clearly an incomplete investment that will not lead to the setting up of smart grids. The case of Italy, which has been the first country in the world to accomplish a massive deployment of smart meters (a penetration of approximately 90% was reached in 2009 [BRU 09]) but still is ranked among the last European countries in terms of actuated demand response schemes [SMA 16], is exemplary. In this specific case, the delay is not only due to the absence of a clear regulatory framework for the development of demand-side auxiliary services, but also due to the rigidity of the proprietary communication systems that have been built primarily for remote metering and billing functions. Non-synchronous electric measures are collected at data concentrators after the polling of AMR devices and then sent offline to the control center. Bottlenecks are also present on the control center-AMR route, due to a rule system at the server level that automatically assigns priorities to jobs. Control signals to smart meters can be sent only with delays that clearly exceed power system operation time requirements. After about 15 years, a second massive deployment of smart meters (the so-called Smart Meters 2.0) is going to occur in Italy in order to obtain faster communication and response, and provide new functions and services to the final customer. In all cases where missing links between metering infrastructure and SCADA are present, some technical solutions can be found [ZHA 10]. An interesting solution, presented in [ZHA 10], consists of a middleware named Meter Data Integration (MDI) installed between AMI and SCADA/ADMS (see Figure 1.1). MDI can adapt different AMI communication protocols to the international standards of SCADA and it is potentially able to manage an extremely large quantity of data from meters. This integration could bring many benefits assisting the monitoring and control system in ADMS applications, such as state estimation or supply and demand forecast, and improving management of DERs. The implementation of the MDI block guarantees the integration of SCADA and AMI, also ensuring satisfactory performances in the case of large distribution networks (according to [ZHA 10], such a system might be able to treat a million smart meters in approximately 15 min). Similar solutions can be adopted whenever interoperability issues are experienced due to legacy AMR/AMI.

Unbalanced Three-Phase Optimal Power Flow for the Optimization of MV

5

1.2. Secondary distribution monitoring and control Setting up all missing downstream and upstream communication links with power system components is not the only significant effort to be made in the way to smart distribution grids. It should be kept in mind that, at the present stage, the entire segment of secondary distribution is very often not monitored nor controlled. The first approaches to ADMS have considered the sole primary distribution, consumers and producers connected directly at the MV level, but the development of distribution grids for smart cities must necessarily include LV-connected customers and devices in the SCADA/ADMS control schemes. The growing diffusion of small-capacity DERs and the growing demand of demand response (DR) schemes suggest that a much wider number of active users will be willing to participate in the management of the grid shortly. The growth of active users (or prosumers) requires definition and implementation. The European Distribution System Operators’ Association for Smart Grids (EDSO) has recently embraced this idea. This association has recognized the fact that DSOs must become “real” system operators, able to monitor and control power flows and preserve quality of supply at any node of the distribution grid (at both MV and LV levels) as the main objective for the fulfillment of 2020 sustainability targets [MAL 14]. The diffusion of small active users that will be able to respond dynamically to price volatility or to substantial variation in power outputs due to intermittent energy sources can constitute, at the same time, the cause for further system stress and vulnerability, or an opportunity to better control system security and improve system flexibility and efficiency. The key in solving this dilemma is in the ability to monitor and control active users and distributed generation. It is a matter of fact that keeping distribution systems uncontrolled and managing distribution with the traditional “fit and forget” approach will either affect the power quality and security of the supply or, ultimately, create an insurmountable obstacle for the diffusion of smart green technologies. For example, distributors will not be able to accommodate more distributed generation because of the growing severity of security issues (congestions, voltage rises, unacceptable power quality, etc.). If the “green revolution” and the “smartification” of cities are to occur, electrical grids will have to be able to exploit faster communication channels and an increased number of sensors and control capabilities, enabling the DSOs to monitor and control the distribution grid at any voltage level.

6

From Smart Grids to Smart Cities

1.2.1. Monitoring and representation of LV distribution grids From a technical point of view, enabling monitoring and control functions in distribution systems appears an achievable target, even though the effort required for the modernization of such systems is huge. This is especially true, for example, in the case of secondary distribution that, presently, is in most cases managed by DSOs more or less like a black box. Very often, primary electrical characteristics, such as voltage and currents profiles, are unknown, except for aggregated data at MV/LV interface. Few measurements are used to represent the state of hundreds of nodes, circuits and end-users that, through secondary distribution, are connected to the primary substation. Load and generation imbalance is generally undetermined at the LV level, and even its modeling is not easy, as the exact location of single-phase objects (loads and generators) is not necessarily known at the central level. In certain cases, such information might not be available at all. This is the case, for example, of single-phase customers in condominiums that were connected to one of the three phases available at the delivery point following just a rotating order. Moreover, LV circuits in secondary distribution require the most frequent maintenance interventions because faults happen more often or because new customers must be accommodated. Circuit modifications are, usually, carried out manually by technicians who keep written notes of changes in the substations and no information of such modifications is transferred back to the control centers. Consequently, very often, an exhaustive and updated database of LV circuit designs and electrical characteristics might not be available at the centralized level. This means that a specific effort must be made to ensure that LV networks are properly managed and inventoried. Recent studies have focused on the opportunity of employing smart meters and AMI for developing LV grid monitoring and control. The setting up of such functions must deal with several issues due to the complexity of multi-phase unbalanced models, the efficiency and robustness of distribution state estimation (DSE) algorithms, and the relevant number of non-synchronized measurements obtained by the meters. Traditionally, the problem of DSE has been solved considering statistical models of loads, obtained exploiting available information on load nominal power, types of customers, historical consumption data and load patterns [ROY 93]. More recently, several studies have been aimed at solving specific problems related to distribution systems such as the presence of radial topologies and three-phase unbalanced systems [BAR 95, LU 95], the high resistance to reactance ratio and the very limited number of real-time measurements [BAR 09, SIN 09, WAN 04]. In [SIN 09, WAN 04], it was shown how accurate states of distribution systems can be obtained thanks to the exploitation of smart meters and AMI (pseudo-) measurements. In a few cases, DSE approaches have also been tested on actual LV networks. In [ABD 12], the technical feasibility of adopting smart meters and their instantaneous

Unbalanced Three-Phase Optimal Power Flow for the Optimization of MV

7

measurements (voltage, active and reactive power) for LV network observability and controllability was shown. Similar results were also obtained in [STI 11, STI 13], where data from smart meters have been used for monitoring and controlling voltages in critical nodes [STI 13] and for carrying out semi-automated load flow calculation in 4-wire LV networks [STI 11]. DSOs have already been making an effort to solve the problem of LV network observation. Methods and devices for the auto-detected inventory of LV grids have already been tested [VAR 15]. For example, successful tests were carried out installing a device in secondary substations that identifies the phase and the circuit, where a specific smart meter is physically connected through power line communication (PLC) [VAR 15]. Such results show how, with affordable investments, a complete vision of the LV distribution system is achievable, and that the issue of a correct representation of multi-phase connections can be overcome. 1.2.2. LV control resources and control architecture Another issue to be solved considers the actual availability of devices to be controlled at the LV level. Most pieces of equipment that are currently installed in secondary substations are legacy devices that cannot be adapted for the implementation of smart grids and, in the scenario of smartification of LV subsystems, should be necessarily replaced or modified. The clearest example of this is given by the fact that MV/LV transformers are very seldom, if ever, equipped with on-load tap changers (OLTC). Usually MV/LV transformer turns ratios can be adjusted manually through an off-circuit tap changer. This means that any change in turns ratio follows a manual procedure where the transformer has to be put temporarily out of service and customers are not served unless backup auxiliary circuits are available. For obvious reasons, the turns ratio is fixed once at the time of installation, and then changed only when noticeable security issues are experienced by customers (for example, frequent overvoltages due to the proximity of PV generators). The fixed setting of MV/LV tap changer must accommodate voltage profiles for all hours of the day and most seasons. At present times, end-users themselves constitute legacy, but the growing penetration of household small generation units, batteries, electric vehicles, home automation, heat pumps and smart appliances contributes to forming a vision where all such units will be coordinated, following control signals at local level, or centralized. DR programs will ensure that distributed control resources are available at the LV level. Theoretically, any electrical appliance might become a control resource. It has been estimated, for example, that about one-third of the overall LV active power

8

From Smart Grids to Smart Cities

demands are constituted by controllable electrical components [MOK 13]. The list of controllable loads might include not only BESS and EVs, but also private and public lightning systems, and any household electrical machine like washing machines or air conditioning systems, heat pumps and refrigerators. Supposedly, pushing this concept to its limit, any equipment with an inverter-controlled drive might be able to modulate both active and reactive power exchanges. Utility load management has been discussed and experimented since the 1970s [MOR 79]. In the short term, it is difficult to foresee the development of centralized control of residential appliances, although some hints come from the appliance market. Emblematic is the case of some heat pump manufacturers, which equipped their units with control boards under IEC 61850 protocol for substation automation. It is rather conceivable that DSOs will be able to send control signals in the form of price signals or energy balance requests that will be accommodated by customers participating in real-time balancing auxiliary services or other demand response schemes. Possible control schemes are usually developed within the transactive energy (TE) framework, with TE being “a system of economic and control mechanisms that allows the dynamic balance of supply and demand across the entire electrical infrastructure using value as a key operational parameters” [FOR 16]. Several adoptable control schemes have been presented in [FAR 14] showing how both centralized and decentralized control solutions are viable. The provision of market services from DERs can be organized aggregating resources in virtual power plants (VPPs) [RAH 16], following, for example, the third-party aggregator experience done at industrial/large tertiary level in the UK Demand Side STOR (Short-Term Operating Reserve) scheme [BAL 15]. Other forms of aggregation could be developed creating a local distribution area (LDA) used by the DSO for the provision of services [KRI 16]. The LDA comprehends the distribution infrastructure and all DERs, aggregators, VPPs and end-users connected at a single primary station or locational marginal price node. This layered optimization framework seems to be appropriate from a technical point of view, as DSO would be able to control and dispatch local resources for load/generation balancing at the transmission-distribution interconnection point, taking into account security and power quality requirements of the whole MV/LV infrastructure below. 1.3. Three-phase distribution optimal power flow for smart distribution grids In this chapter, a basic methodology for the control of smart distribution grids is shown together with some realistic applications aimed to solve operative problems that might be encountered in distribution systems, at both MV and LV levels. The

Unbalanced Three-Phase Optimal Power Flow for the Optimization of MV

9

methodology hereby presented is based on the formulation of a three-phase distribution optimal power flow (TDOPF) customized for use in distribution grids. The TDOPF methodology aims to optimize control resources in the presence of unbalanced conditions and in the quasi-real-time framework of ADMS. As shown below, the formulation is flexible enough to be applied to different optimization problems and control variables sets. Optimal power flow (OPF) is the most commonly adopted tool for power system operation and planning. OPF can solve a great number of optimization problems through simple manipulations of objective functions, inequality constraints and control variables, and it is definitely the most flexible tool available for controlling distribution systems in a DMS framework. Clearly, OPF must be suitably adapted to the evolution of distribution systems and to the new operative requirements. The birth of markets for energy and energy services, the diffusion of public incentive schemes for renewable resources and the growing demand for energy autonomy have all profoundly changed the structure of distribution systems. DSOs must face the new challenges introduced by the pervasive diffusion of distributed generation (DG) that is modifying the way in which distribution grids must be operated. DSOs must enhance distribution capacity, accommodate new generation capacity and satisfy growing load demand and high seasonal peaks, while avoiding expensive reinforcement investments. DSOs must also deal with degraded steady-state conditions, such as strong imbalance, low/highvoltage profiles, reverse power flows and conspicuous deviations of daily chronological demand curves from average profiles. Hence, the definition of TDOPF-based functions, specifically formulated to control the distribution system during its operation, is necessary. In order to be effective for distributed system operation, TDOPF must respond to several requirements. For example, the formulation and solution of load flow equations must take into account that networks are radial and characterized by high R/X ratios: the adoption of typical decoupled power flow routines is clearly not possible. Moreover, networks must be represented with a full multi-phase representation, allowing the use of 3-wire and 4-wire models and taking into account the possible presence of unbalanced conditions and single-phase components. Classically, distribution systems have always been unbalanced because of unequal three-phase loads, untransposed lines and conductor bundlings. However, the recent spreading of single-phase DG plants (mostly household photovoltaic panels, but also micro wind generators or micro turbines) has increased the average system imbalance. Given the randomness associated with renewable sources, the level of imbalance is also hardly estimable, raising even more the concern for network security and power quality at both MV and LV levels.

10

From Smart Grids to Smart Cities

Another necessary requirement for TDOPF is that it must deal with an increased number and variety of available control resources. Control resources can include any kind of DER, such as small generation, storage systems and EVs, DR, power electric devices and inverter-driven machines, disconnector switches, tap changers and switched capacitors. The formulation must therefore be flexible enough to treat sets of heterogeneous control variables. An example of a TDOPF platform for distribution grids to be employed in an ADMS framework was proposed in [BRO 11, BRU 11b, BRU 12]. A nonexhaustive list of power system operation tools that can be implemented through the SCADA/ADMS architecture is given in Figure 1.1. TDOPF can be suitably formulated to include several (quasi) real-time applications, such as congestion management, voltage-VAr optimization (VVO) or conservative voltage regulation (CVR). All such functions are in fact based on processing data collected at SCADA level and sending back control signals to field devices and actuators (interruptible loads, on-load tap changers, switching capacities, battery management systems, remote controllable switches, etc.). In most cases, the evaluation of optimal control signals can be based on the solution of a TDOPF problem. The TDOPF methodology proposed in [BRO 11, BRU 11b, BRU 12] was studied for controlling the MV primary distribution grid of a medium-sized town. Given the state of development of AMR/AMI technology on the specific system under study (the secondary distribution of the city of Trani, in Southern Italy), the methodology proposed was developed in order to implement active power load controlling techniques. The main idea was that, through the introduction of special discounted tariffs, the active load of customers could be redispatched in order to fulfill particular operational constraints. In the proposed architecture, load control signals were sent directly from the control center to households by setting the maximum available loading capacity at AMR level [BRU 11b]. AMR devices are usually able to receive a signal that can change the maximum power which can be consumed. This is usually done remotely in the case of changes in the contracted power (for example, a customer requiring a higher or smaller capacity) or for limiting the maximum power of non-paying customers. The main idea was to adjust this setting dynamically in order to limit the active power demand in specific corridors, using AMR devices as real-time actuators of centralized control. TDOPF routines can also be employed for VVO, which integrates the problems of voltage regulation and reactive power compensation [BRO 11]. This kind of control is usually performed by means of on-load tap changers and switching capacitors that are manually operated or controlled through local feedback [PAU 11]. In the proposed ADMS framework, set-points of such devices can be

Unbalanced Three-Phase Optimal Power Flow for the Optimization of MV

11

remotely controlled on the basis of TDOPF calculations, according to specific operational targets and aiming to improve voltage profiles across feeders, sustain voltage, reduce losses, improve energy efficiency and conservation. Clearly, any remote controllable reactive power resource can be integrated in VVO. The idea of employing distributed generation resources (for example, photovoltaic-PV) for local or centralized voltage regulation of smart grids is commonly accepted, even though some issues about control structure (control schemes for local or generalized control) and ancillary services remuneration (PV inverters participating at voltage regulation must be oversized and therefore are more expensive than the ones operating at a fixed power factor) should be still overcome. The control of voltage profiles can also be aimed at reducing the overall electricity demand, for example, during peaking hours. This practice is usually called conservative voltage reduction (CVR) and can be implemented through the coordinated control of OLTC and reactive resources [BRO 11]. The principle of CVR is to exploit the voltage dependency of loads for curtailing the overall power demand. Loads are not directly shed or curtailed, but they are supplied with voltages lower than the rated ones, but clearly still above the functional bottom limits. This methodology applies very well for peak shaving in residential and tertiary areas, whereas it can be less effective in industrial areas where motors are the bulk component of demand. 1.4. Problem formulation and solving algorithm 1.4.1. Main problem formulation TDOPF mathematical formulations and solutions are similar to the ones adopted for classical single-phase OPF routines [ALS 74, TIN 68]. Both three-phase and single-phase approaches must employ nonlinear optimization techniques. However, the main differentiation concerns the representation of power flow equations. Single-phase OPF is commonly based on the use of the sole positive sequence component model, whereas TDOPF usually adopts sequence or multi-phase models. Moreover, given the need to represent radial networks characterized by high R/X ratios, typical approaches based on decoupled Newton-Raphson load flow codes cannot be employed. The following formulation, derived by the developments reported in [BRU 11b], has been improved so that faster convergence properties can be achieved, allowing, for example, inclusion of a larger variety of LV control resources and a detailed representation of secondary distribution circuits. The optimization of LV system resources requires special care because a large number of available control resources are expected.

12

From Smart Grids to Smart Cities

The most compact formulation for TDOPF is given by min Cobj ( x , u) u

[1.1]

subject to f ( x , u) = 0

[1.2]

g ( x , u) ≤ 0

[1.3]

with x ∈ ℜn and u ∈ ℜm

where Cobj is an objective function, x is the vector of nodal voltages, u is the vector of the m independent control variables, f is the set of load flow equations and g is the set of inequality constraints that usually take into account thermal limits of transformers and lines, power quality or practical limitations on voltage profiles and other functional constraints. As stated before, any formulation of equations f is possible since the proposed method is sufficiently general to consider both full multi-phase and sequence models. The independent variables u are given by active and/or reactive power injected/absorbed by the controlled LV devices (dispatchable loads, DG and PV generators, storage, EV charging pedestals, etc.), or by the controlled set-point of any other devices (for example, the position of an on-load tap changer). 1.4.2. Application of the penalty method The most common approach to treat functional inequality constraints is to apply the penalty method [TIN 68]. This choice leads to the following formulation where inequality constraints [1.3] are transformed into penalty functions to be minimized together with the objective function: min C ( x , u) u

[1.4]

subject to f ( x , u) = 0

[1.5]

Unbalanced Three-Phase Optimal Power Flow for the Optimization of MV

13

with C ( x , u) = Cobj ( x , u) + ∑ C ip ( x , u)

[1.6]

i

where C is the overall objective function and C ip is the generic i-th penalty function. The only inequality constraints are given by the feasibility domain of control variables: umin ≤ u ≤ umax

[1.7]

In order to take into account the most common operative issues in distribution systems, different penalty functions can be introduced. The inequality constraints introduced here are the ones referred to the thermal limits of branches, the maximum capacity of power transformers and minimum/maximum voltage magnitude. A possible formulation of the penalty functions in [1.6] is given by nline nwires (i )

C1 = ∑

∑

i =1

⎛ I i , p − I max , i , p ⎜ I max , i , p ⎝

α1, i , p ⎜

p =1

⎞ ⎟⎟ ⎠

2

[1.8]

with

α1,i , p = 0 if

I i , p < I max , i , p

where I i , p is the current magnitude on the p-th conductor of the i-th branch, I max , i , p is the ampacity of each conductor of the i-th branch, nwires (i ) is the number of conductors for the i-th branch and α1,i , p is a weight factor.

C2 =

⎛ S j − S max , j ⎜ S max, j ⎝

ntrasf

∑ α 2, j ⎜ j =1

with α 2, j = 0 if

⎞ ⎟⎟ ⎠

2

[1.9]

S j < S max, j

where S j and S max , j are apparent power and maximum apparent power at the j-th transformer and α 2, j is a weight factor; nbus nwires (k )

C3 = ∑ k =1

∑

p =1

⎛ Vk , p − Vlim,k , p α 3, k , p ⎜ ⎜ Vlim,k , p ⎝

⎞ ⎟⎟ ⎠

2

[1.10]

14

From Smart Grids to Smart Cities

with ⎧Vlim,k , p = Vmax,k , p ⎪⎪ ⎨Vlim , k , p = Vmin , k , p ⎪ ⎪⎩Vlim , k , p = Vk , p

if

Vk , p > Vmax , k , p

if

Vk , p < Vmin , k , p

if

Vmin , k , p ≤ Vk , p ≤ Vmax , k , p

where Vk , p is the voltage magnitude referred to the ground at the p-th node of the

k-th bus, Vmin, k , p and Vmax,k , p are minimum and maximum phase voltage limits and nwires (k ) represent the number of nodes and the number of conductors connected to the k-th bus (i.e. two in single-phase circuits, three in three-phase circuits without neutral, four in three-phase circuits with neutral) α3 is a weight factor.

Please note that the index p, introduced in [1.8] and [1.10], allows inclusion of specific limitations on the fourth wire. This distinction must be made, for example, in all those cases where the neutral wire has a section smaller than the phases, or if neutral voltages must be kept within specific security limits. 1.4.3. Definition of an unconstrained problem The principal assumption for the development of the approach proposed in this chapter is to transform the constrained problems [1.4–1.6] into an unconstrained problem. This assumption is valid through the application of the implicit function theorem, whose conditions are satisfied in a large set of practical cases. Usually, the sole exception is given by operating points close to voltage instability. However, the idea of being close to voltage collapse in a MV or LV network is very far from reality. Under the Implicit Function Theorem [38] suppose that f : E n + m → E n is k times continuously differentiable (Ck-class) function whose mapping domain is T. Suppose that it exists a ( x , u )∈T ' f ( x , u ) = 0 and that the Jacobian with respect to

x, ∇ x f ( x , u ) , is not singular. Then there exists a neighbourhood of u , N (u ) ⊂ E

m

and a unique function γ ∈ C k [ N (u ) ], γ : N (u ) → E n with γ (u ) = x

and f (γ (u ), u ) = 0 for all u ∈N (u ) . Under the conditions given by this theorem, it is possible to assume the existence of a unique function γ (u ) = x that allows reformulation of the constrained

Unbalanced Three-Phase Optimal Power Flow for the Optimization of MV

15

problem [1.4–1.6] into an unconstrained problem, in the neighborhood of the solution of the load flow equations ( x , u ) . The optimization problem then becomes: [1.11]

min C (γ (u), u) u

with umin ≤ u ≤ umax

The solution of this problem [1.11] can then be found imposing the conditions ⎡ ∂C ∇C = ⎢ ⎣ ∂u1

∂C ∂u2

T

L

∂C ⎤ ⎥ =0. ∂um ⎦

[1.12]

1.4.4. Application of a quasi-Newton method In order to solve [1.12], having chosen an initial value of the control variable vector u0 , the Newton method can be applied iteratively through the rule uk +1 = uk − H k−1 ⋅∇C k

[1.13]

where the Hessian matrix H k and the gradient ∇C k are calculated at the generic k-th iteration. Typically, the iterative solution of equations [1.12] through [1.13] requires the calculation of the inverse matrix H k−1 at each iteration k. If the size of the problem is large, as in a realistic-sized network where a large number of control variables must be taken into account, the computational burden required for calculating the second derivatives and the inverse Hessian matrix might be too heavy, comparing with ADMS time requirements. For this reason, in the proposed approach a quasi-Newton method is applied, allowing approximation of the value of the Hessian matrix and of its inverse at each iteration k, through some simple calculations (mostly matrix multiplications and sums). This approach significantly reduces the time necessary for solving each iteration, as the only time consuming routine left is the evaluation of sensitivities ∇C k . The application of quasi-Newton methods to the solution of [1.12] requires the iterative update of control variables according to the rule: uk +1 = uk + α k ⋅ pk

[1.14]

16

From Smart Grids to Smart Cities

where αk is the step-length, and the direction pk is given by

pk = − Bk−1 ⋅∇C k

[1.15]

and Bk is the Hessian matrix approximation at the iteration k and Bk-1 is its inverse. -1 At the end of each iteration k, the inverse Bk+ 1 is evaluated, according to the chosen solving method, through a formula that can be represented generically as a function

Bk−+1 1 = h ( Bk−1 , yk , sk )

[1.16]

where sk = uk+1 − uk and yk = ∇C k+1 −∇C k . One the simplest formulations of [1.16] is given by the expression: Bk−+11 = λk +1 ⋅ I m

[1.17]

where λ k+1 is a scalar suitably chosen on the basis of computational and convergence properties and I m is the m-dimensional identity matrix. Several formulations have been proposed for the evaluation of λk +1 [BRE 03]. A suitable choice is given by the method proposed by Barzilai and Borwein [BAR 88, BRE 97], where λ k+1 =

y k T sk yk T yk

[1.18]

This methodology is appropriate whenever the computational cost of each iteration is negligible with respect to the overall algorithm or if the problem is characterized by good convergence properties (minor nonlinearities, convexity, etc.). If the problem requires more robustness or faster convergence, other methods based on a formulation of Bk-1+1 as a full matrix can be adopted. The most common formulas adopted for evaluating [1.16] are given by the BFGS (Broyden, Fletcher, Goldfarb and Shanno), the DFP (Davidon, Fletcher and Powell) and symmetric rank 1 (SR1) methods [NOC 06]: (BFGS)

⎛ ⎛ s yT ⎞ y sT ⎞ s sT Bk−+11 = ⎜ I − kT k ⎟ ⋅ Bk−1 ⋅ ⎜ I − kT k ⎟ + kT k y k sk ⎠ y k s k ⎠ y k sk ⎝ ⎝

[1.19]

Unbalanced Three-Phase Optimal Power Flow for the Optimization of MV

(DFP)

(SR1)

Bk−+11 = Bk−1 −

−1 k +1

B

−1 k

=B

Bk−1 yk ykT Bk−1 sk skT + T ykT Bk−1 yk y k sk

(s +

k

)(

− Bk−1 yk ⋅ sk − Bk−1 yk

(s

k

− Bk−1 yk

)

T

17

[1.20]

)

T

yk

[1.21]

Among the three methods, BFGS is considered the most efficient. BFGS has very effective self-correcting properties, whereas it is recognized that the DFP method is less successful in correcting bad Hessian approximations. Please note that the self-correcting properties of BFGS are ensured only if an adequate line search is performed. The formulation of the SR1 method in [1.21] does not guarantee that its denominator is non-singular. For such reason, BFGS is usually preferred unless specific algorithms are employed in order to avoid the SR1 method leading to numerical instability or breakdown. However, all three methods belong to the Broyden class of quasi-Newton updating formulas and, theoretically, they would yield the same Hessian approximation (and therefore the same iterates), provided that an exact linear search of αk is made [NOC 06]. Clearly, an exact linear search of αk is not always performed because it requires the solution of another optimization problem. In this specific case, it would require the computation of the same second derivatives that we wanted to avoid. Generally, good convergence properties, and better chances to reach the global minimum, are achieved if the two Wolfe conditions are respected. The solution

uˆ k +1 = uk + αˆ k ⋅ pk , obtained with a generic

αˆ k , fulfills,

respectively, the first Wolfe condition of sufficient decrease if C ( uˆ k +1 ) ≤ C ( uk ) + c1 ⋅ αˆ k ⋅∇C k T ⋅ pk

[1.22]

The second Wolfe condition, or curvature condition, is satisfied if ∇Cˆ k +1T ⋅ pk ≥ c 2 ⋅ ∇C k T ⋅ pk

[1.23]

with 0 < c1 < c 2 < 1 .

Even though both conditions should be satisfied for defining the most suitable step-length, in certain cases it might be convenient to consider the first condition

18

From Smart Grids to Smart Cities

only. Checking the second Wolfe condition requires the evaluation of the gradient ∇Cˆ k +1 . If the computational burden associated with the calculation of this gradient is high, it might be more efficient to accept a step-length that satisfies only the first condition, slowing the overall convergence behavior (the number of iterates) but decreasing the time necessary for each iterate. In the proposed approach, derivatives are calculated numerically. Therefore, it is rather convenient to consider only the first Wolfe condition instead of running the time-consuming sensitivity analysis procedure multiple times. This can be done if the line-search chooses the candidate step-length appropriately. The algorithm applied in this approach for the evaluation of the step-length is based on the iterative procedure, based on quadratic and cubic interpolation proposed in [NOC 06] and not reported here for the sake of brevity. This approach takes into account the sole sufficient decrease condition [1.22]. According to the common practice, the initial step-length can be set to 1 and c1 is chosen sufficiently small (for example, 10−4). 1.4.5. Solving algorithm

The structure of the solving algorithm is shown in Figure 1.2. The method starts with an initial guess of u0 that is used to evaluate the first set of sensitivities. As quasi-Newton methods calculate the inverse Hessian approximation based on the last two iterations, the algorithm requires an initialization and a first guess of the Hessian matrix. The common practice is to assume Q0 is equal to the identity matrix. The gradient ∇C k is calculated as proposed in [BRU 11b] through numerical partial derivatives of C , calculated applying, one at a time, a small deviation on control variables and observing the variation of C around the initial solution of the three-phase distribution load flow (DLF) for uk . At the generic k-th iteration, the control variable vector is updated moving the solution along the search direction pk with an optimal step-length αk . The algorithm stops whenever the sensitivities drop below a prefixed tolerance level ( ∇C k +1 ≤ ε ). The algorithm was implemented on a Matlab-OpenDSS platform based on a twoway data exchange between a Matlab code that evaluates sensitivities and assesses control variable variations, and the OpenDSS simulation engine that performs DLF and updates the network model following the control variable variations evaluated by the optimization routines. OpenDSS is an open-source software, developed by EPRI that has been designed specifically for solving distribution circuits and has recently established itself as a standard in smart grids analysis and planning.

Unbalanced Three-Phase Optimal Power Flow for the Optimization of MV

19

Figure 1.2. Flow-chart of the proposed algorithm

The two codes communicate by means of the COM interface that is available in the OpenDSS software package [HTT]. The COM interface makes it possible to use a code already written and optimized by someone else (in this case OpenDSS) in

20

From Smart Grids to Smart Cities

one’s own programming environment (Matlab). This is an important feature because it allows exploitation of the perks of a well-structured DLF engine, specifically optimized and compiled for solving, in fractions of a second, complex distribution networks characterized by radial configuration and high R/X ratios. The adoption of the OpenDSS DLF engine also allows treatment of any type of electric device easily and includes a large variety of control resources. The network model, in fact, is implemented with a structure that is different with respect to the classical nodal structure used in the IEEE Common Data Format. Each device is modeled as an object that is connected to a certain number of single-phase nodes; nodes are then connected by branches and wires. This means that any multi-phase device, being, for example, a single-phase or three-phase load or generator, can be easily connected to any system bus. Each object can have its own characteristics so, for example, differently for any classical nodal approach, an indefinite number of loads, each one characterized by its own model (number of phases, voltage dependence, ZIP model, etc.), can be connected to the same bus and then univocally monitored or controlled. The proposed hybrid platform makes it possible to respond to the specific TDOPF requirements that were introduced beforehand. The choice of using OpenDSS relies on the advantages already listed and, of course, on its “open sourceness”. However, any other DLF software, being a commercial or research product, is compatible with the proposed architecture, provided that an efficient data exchange interface is available. 1.5. Application of the proposed methodology to the optimization of a MV network

The test results presented in this section were obtained implementing the proposed algorithm on a realistic sized representation of the urban distribution network managed by a DSO (AMET-Trani) that supplies energy for a mediumsized city in the South of Italy (about 50,000 inhabitants, 35,000 customers, and a municipal area of approximately 100 km2). The system was modeled considering all HV and MV elements. The model is composed of two 150 kV/20 kV transformers equipped with controllable tap changers, eleven 20 kV feeders, 900 buses, 1,000 distribution lines (cabled and overhead), 100 controllable switches and 500 load buses. A simplified scheme of the distribution substation is given in Figure 1.3, whereas a planimetric map of the modeled urban network is given in Figure 1.4.

Unbalanced Three-Phase Optimal Power Flow for the Optimization of MV

21

Figure 1.3. Simplified scheme of the AMET primary substation

Figure 1.4. Planimetry of the AMET urban distribution network. For a color version of the figure, see www.iste.co.uk/lascala/smart.zip

Table 1.1 shows the rated power and current of a MV feeder supplied by the two HV/MV transformers. The maximum current is given by the threshold of overcurrent protection devices.

22

From Smart Grids to Smart Cities

Feeder #

Transformer

1 2 3 4 5 6 7 8 9 10 11

TRA TRA TRA TRA TRB TRB TRB TRB TRB TRB TRB

Rated voltage [kV] 20 20 20 20 20 20 20 20 20 20 20

Rated current [A] 187 187 187 187 85 104 85 187 85 128 128

Rated power [kVA] 6,470 6,470 6,470 6,470 2,940 3,600 2,940 6,470 2,940 4,430 4,430

Table 1.1. Main data of 20 kV feeders

The distribution system is radial and each node is supplied by a single feeder only. The configuration of the network can be modified, changing the state of some controllable switches, which, according to normal operational procedures, are fixed. The topology does not change unless significant disturbances are experienced (a permanent fault, for example) or unless maintenance works require energizing a branch through another route. In this section, secondary distribution circuits and MV/LV transformers have been neglected. LV elements are therefore not represented. Loads are modeled through equivalents at MV level. In this case, the system was represented under balanced conditions, assuming that aggregated loads are more or less balanced at MV level. The base case was obtained considering the actual operating conditions registered at noon on the third Wednesday of December 2009. In such conditions, the system supplied approximately 35 MW by means of the two 150/20 kV transformers located at the substation. The first 30 MVA transformer (TRA) carried approximately 21.5 MVA supplying energy for four urban feeders. The remaining seven feeders were supplied by a 25 MVA transformer (TRB) for a total amount of 11.3 MVA. Test cases were obtained considering the inputs of the largest distributed generation units directly connected at MV level (Table 1.2) and modifying the overall loading level.

Unbalanced Three-Phase Optimal Power Flow for the Optimization of MV

Generator # Rated power [kW] Feeder # Generator # Rated power [kW] Feeder #

1 1,000

2 2,000

3 1,000

4 1,000

5 4,000

6 1,000

7 1,000

1 8 1,000

2 9 1,000

4 10 1,000

10 11 3,000

5 12 1,000

5 13 3,000

5

6

8

8

8

9

9

23

Table 1.2. Distributed generation in the test system

1.5.1. Case A: optimal load curtailment

The first case was aimed at assessing load control in order to eliminate congestions on the HV/MV power transformers and distribution feeders. This base case was modified assuming the occurrence of a uniformly distributed load increase of 50%. The base case was also modified considering that the generators in Table 1.2 (mostly PV units) are producing approximately 20% of their nominal power. Having run a load flow with this model, the result is that the transformer TRA is overloaded and the feeders #1, #3, #4 and #6 are congested. Overloads and congestions can be cleared through the solution of the proposed TDOPF problem, adopting the penalty functions introduced in [1.8–1.10] and introducing an objective function aimed at minimizing the amount of load to be curtailed or shed: C0 =

nloads

∑ i =1

⎛ ui − u 0 α0 ⎜ 0 i ⎜ u i ⎝

⎞ ⎟ ⎟ ⎠

2

[1.24]

where nloads is the total number of curtailable loads, ui is the active load power of the i-th load, and α 0 is a weighting factor. As the primary concern is to study the performance of the proposed algorithm and assess the required computational effort, the optimization problem was solved considering that curtailable loads can be found at each load bus (more than five hundreds). This means that the number of control variables is equal to the number of loads (nloads is equal to 505). Consequently, the evaluation of the gradient through the numerical evaluation of the derivatives requires the solution of more than 500 distribution load flows.

24

From Smart Grids to Smart Cities

The algorithm converged in 11 iterations (see Table 1.3), reaching an optimal solution where all penalty functions are null. In Table 1.4, it is possible to follow how main constrained variables vary along the iterative process. As shown in Table 1.4, before control at iteration 0, feeders #1, #3, #4, and #6 were congested. Moreover, the transformer TRA, supplying power to the first four feeders, was overloaded. iter # 0 1 2 3 4 5 … 10 11

C0[p.u.] 0.0000 0.0000 0.0018 0.0018 0.0022 0.0023 … 0.0019 0.0019

C1 [p.u.] 0.6705 0.6643 0.1174 0.0575 0.0001 0.0000 … 0.0000 0.0000

C2 [p.u.] 0.0641 0.0632 0.0000 0.0000 0.0000 0.0000 … 0.0000 0.0000

C3 [p.u.] 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 … 0.0000 0.0000

C (tot) [p.u.] 0.7346 0.7275 0.1354 0.0593 0.0023 0.0023 … 0.0020 0.0019

Table 1.3. Case A: convergence behavior of the TDOPF

Figure 1.5. Case A: overall power demand at each feeder (before and after control)

The optimal load curtailment evaluated through the TDOPF is characterized by a load reduction of approximately 7,800 kW (8.4% of the overall requested active power). The distribution of load curtailment among feeders is shown in Figure 1.5. It can be seen how loads supplied by feeders #5, #7, #8, #9, #10 and #11 were unaffected by the control. Currents flowing in such feeders (see Table 1.3) are also unchanged (just some minor changes due to the voltage adjustments). As expected, the greatest curtailment was experienced by loads supplied by the congested feeders #1 and #3, which also contribute to the overload of transformer TRA.

S1 [kVA]

32,402

32,384

29,496

28,546

26,040

26,046

…

26,083

26,083

Iter #

0

1

2

3

4

5

…

10

11

17,895

17,896

…

17,821

17,927

17,844

17,811

19,877

19,891

S2 [kVA]

143.32

143.31

…

143.23

143.21

143.34

143.02

146.25

146.27

I2 [A]

187.26

187.28

…

186.22

186.01

223.10

238.89

273.43

273.65

I3 [A]

187.11

187.11

…

187.20

187.49

187.32

186.58

200.48

200.57

I4 [A]

37.03

37.03

…

37.05

37.02

36.97

36.96

36.28

36.27

I5 [A]

104.21

104.23

…

102.05

105.10

103.49

102.86

163.21

163.62

I6 [A]

79.98

79.98

…

80.00

79.98

79.93

79.92

79.30

79.29

I7 [A]

Table 1.4. Case A: main variables along the iterative process

187.21

187.20

…

187.22

187.03

213.57

224.59

252.11

252.28

I1 [A]

26.48

26.48

…

26.50

26.48

26.44

26.43

25.87

25.87

I8 [A]

53.88

53.88

…

53.91

53.87

53.81

53.78

52.87

52.87

I9 [A]

105.04

105.04

…

105.07

105.03

104.97

104.95

104.05

104.05

I10 [A]

78.36

78.36

…

78.39

78.36

78.32

78.30

77.69

77.69

I11 [A]

25 Unbalanced Three-Phase Optimal Power Flow for the Optimization of MV

26

From Smart Grids to Smart Cities

1.5.2. Case B: conservative voltage regulation

In this second test, the proposed TDOPF was applied to the CVR problem. The aim of this optimization is to minimize the consumption of active power by reducing voltage levels as much as possible. Voltages should never go below a certain level because they might cause malfunctioning of electric appliances or undesired triggering of protection relays. It is reasonable to accept that voltage magnitude at MV level should be kept above the value 0.95 p.u. Theoretically, even lower voltage levels can be accepted for short time periods, but, in the simulations, the bottom limit was set prudentially to 0.95, so that a few percent voltage drop in LV circuits is still possible. CVR bases its efficacy on the voltage dependency of loads. Clearly, if loads are modeled with a constant active power model, no real benefit can be gained from CVR. In order to make credible assumptions with regard to the average nature of aggregated loads connected to MV in residential areas, the following general load distribution has been assumed: approximately 50% fixed impedance model, 25% constant active power and quadratic reactive (somewhat like a motor) and 25% linear active power and quadratic reactive (mixed resistive/motor). The loads at each node were decomposed into three equivalent loads following this statistic. Having used an object-oriented system representation, this step is very easy, as any number of loads, and of any species (for example three-phase or single-phase loads characterized by any ZIP model), can be added at any system bus without much effort. A possible formulation of this problem is obtained by introducing an objective function aimed at minimizing the quantity of active power supplied to the network: ⎛ Pj C0 = min ∑ α ⎜ 0 ⎜P u j =1 ⎝ j ntrasf

⎞ ⎟⎟ ⎠

2

[1.25]

0

where P j is the active power carried by the j-th HV/MV transformer, and Pj is the initial active power. Please note that this formulation is possible as long as the transformers are transferring energy from the HV grid to the MV. If reverse power flows are experienced, this formulation is no longer valid. However, it would be rather peculiar that CVR was performed when the distribution system has already been exporting energy.

Unbalanced Three-Phase Optimal Power Flow for the Optimization of MV

27

The objective function [1.25] is minimized together with the penalty functions already introduced in [1.8–1.10]. Vmin and Vmax in [1.10] are set, respectively, to 0.95 and 1.05 p.u. The set of control variables u is given by the voltage reference signals of OLTC and the reactive power output of the DG units. Please note that tap changers can assume only a few discrete positions; usually 33 steps from −16 to +16 that correspond to equivalent ratios in the interval 0.9–1.1 p.u. For this reason, the problem should be treated as a mixed integer nonlinear problem (MINLP). However, given the small number of discrete variables, this problem can be more easily solved through decomposition techniques or by relaxing the integer variables. The latter scheme, utilized in the proposed code, is based on the assumption of the tap ratio as a continuous variable; the continuous value evaluated during the iterative process is then approximated to the nearest discrete step. The solution, obtained after seven iterations as shown in Table 1.5, is characterized by an acceptable voltage profile (no lower limit violations) with an overall active power decreased from 31.7 MW to 27.0 MW with an active power reduction of almost 15%. In Figure 1.6, it can be observed how the voltage level at all nodes has been decreased but no minimum voltage violations are present. The control of reactive resources was minimum, given the much lower sensitivity shown by these resources with respect to the other control variables (transformer equivalent turns ratio). Tap

Tap

position

position

TRA

TRB

2

4

2

4

10.293

1

3

9.796

0

0

20.013

8.665

−3

−7

42.2532

16.816

7.281

−16

−16

4.5076

16.800

8.844

−16

−6

3.8514

4.5333

16.798

9.004

−16

−5

0.0000

3.8520

4.5339

16.798

9.004

−16

−5

0.0000

0.0000

0.7277

18.005

8.997

−11

−5

C0

C1

C2

C3

C (tot)

P1

P2

[p.u.]

[p.u.]

[p.u.]

[p.u.]

[p.u.]

[kW]

[kW]

0

1.0000

0.0000

0.0000

0.0000

1.0000

21.286

10.459

1

1.0000

0.0000

0.0000

0.0000

1.0000

21.286

10.459

2

0.9721

0.0000

0.0000

0.0000

0.9721

21.027

3

0.9148

0.0000

0.0000

0.0000

0.9148

20.773

4

0.7851

0.0000

0.0000

0.0000

0.7851

5

0.5543

0.0000

0.0000

41.6989

6

0.6689

0.0000

0.0000

3.8387

7

0.6819

0.0000

0.0000

8

0.6819

0.0000

9

0.7277

0.0000

iter #

Table 1.5. Case B: convergence behavior of the TDOPF and main variables

28

From Smart Grids to Smart Cities

Figure 1.6. Case B: voltage profiles before and after control

1.5.3. Case C: voltage rise effects

An approach similar to that proposed in the previous case can be adopted for eliminating steady-state voltage rise effects caused by the inversion of flow on distribution lines due to excessive DG production. The case studied in this section was created by considering that each of the DG units in Table 1.2 is producing approximately 80% of its nominal power. In addition, load profiles were altered considering a 30% load decrease with respect to the base case. As a result, the energy flow in the second transformer TRB is reversed (from MV to HV). This condition can be dangerous because it causes a voltage rise in several nodes of the network. In the specific network under study, for example, this condition is typical for the rural feeders, where energy consumption can be very low in certain hours of the day and in certain seasons, and where the largest PV farms have also been installed. Reverse power flows are experienced in these feeders because most of the loads are linked to agriculture activities that, in central hours of summer days when PV farms reach their seasonal production peak, are characterized by very low consumption; fields, in fact, cannot be irrigated in sunny hours or when the temperature is too high. This is just an example of operating conditions that can cause reverse power flows but, clearly, with the growing penetration of DG, reverse power flows are expected to be experienced more and more frequently on MV distribution feeders.

Unbalanced Three-Phase Optimal Power Flow for the Optimization of MV

29

In order to control voltages and force them back to acceptable levels (i.e. below the 1.05 p.u. limit), a TDOPF was formulated considering the penalty functions [1.8–1.10] and a generic objective function aimed at reducing the control effort: ⎛ ui − u 0 C0 = ∑ α 0 ⎜ max i min ⎜u −u i =1 i ⎝ i m

⎞ ⎟ ⎟ ⎠

2

[1.26]

where m is the number of control variables. For this simulation, the set of control variables u is given by the voltage reference signals of OLTC and the reactive power output of the DG units. Vmin and Vmax in [1.10] are set, respectively, to 0.95 and 1.05 p.u. In Figure 1.7, it is shown how voltage magnitude was exceeding the upper limit for certain buses in proposed operating conditions and how such violations are not experienced anymore after control is applied. Clearly, the voltage profiles of all nodes supplied by the transformer TRA are unchanged since no control on the tap position was necessary (Table 1.6). Furthermore, it can be observed that, in the tested case, the reactive control was negligible with respect to the contribution of tap-changer adjustments, as the latter were more sensitive.

Figure 1.7. Case C: voltage profiles before and after control

30

From Smart Grids to Smart Cities

iter #

C0 [p.u.]

C1 [p.u.]

C2 [p.u.]

C3 [p.u.]

C (tot) [p.u.]

0 1 2 3 4 5

0.0000 0.1129 0.0879 0.0063 0.0035 0.0035

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.3973 0.0000 0.0000 0.0000 0.0000 0.0000

0.3973 0.1129 0.0879 0.0063 0.0035 0.0035

tap position TRA 0 0 0 0 0 0

tap position TRB 1 −16 −14 −3 −2 −2

Table 1.6. Case C: convergence behavior of the TDOPF and main variables

1.5.4. Algorithm performance

Table 1.7 shows the computational performance of the algorithm in cases A, B and C. The algorithm was run on a common desktop PC (Intel Core i7-4770, 3.40 GHz, 8 GB RAM, 64 bit). The time required for solving each DLF in the derivative numerical evaluation routine is quite small (from 1 to 10 ms). This means that the problem can be solved with a less performant method, accepting the risk of having more iterates before convergence. For this reason, all test cases showed better performances using the simplified Barzilai and Borwein formula, neglecting the line search routine. This is possible as long as the problem is not too complex and the system is supposed to be operating under balanced conditions.

A B

num. control resources 505 15

C

15

case

11 9

total elapsed time [s] 11.03 2.06

sensitivity evaluation time[s] 9.82 2.03

5

1.03

0.96

num. iteration

Table 1.7. Case C. Convergence behavior of the TDOPF and main variables

In the following section, the algorithm will be tested with a full representation of MV and LV circuits, where the hypothesis of balanced load is unfit. The DLF timings necessary for solving LV circuits will require the adoption of more performant solving methods.

Unbalanced Three-Phase Optimal Power Flow for the Optimization of MV

31

1.6. Application of the proposed methodology to the optimization of a MV/LV network

The network model used for tests is based on actual data concerning the MV and LV circuits adopted for primary and secondary distribution in a real urban distribution network in the city of Bari (Italy). Bari is a medium-sized Italian town with approximately 350.000 inhabitants and the area under investigation is only a part of a district counting approximately 60.000 people. The network model developed for tests comprises three whole MV feeders, supplying 22 secondary substations (Figure 1.8). LV circuits start from each MV/LV substation. For instance, a schematic representation of the LV circuits under the substation F1M1 is given in Figure 1.9. Each LV secondary distribution grid has been represented with a 4-wire model. A total number of 590 buses, 2,289 nodes, 576 lines and 24 transformers have been employed for representing the whole system. LV circuits extend for a total length of approximately 23 km. The presence of 21 PV generators with both single-phase and three-phase connections have also been assumed based on real data.

Figure 1.8. Schematic representation of the 20 kV distribution grid

Based on aggregated data (number of customers connected to each node), the presence of 2,587 single-phase and 549 three-phase loads have been hypothesized. Single-phase loads have been associated with each phase conductor averaging the load among phases, so that the final load configuration is unbalanced. For each load, a specific ZIP model was assumed [BOK 14]. Having classified all loads into four classes according to their contracted power (residential, small commercial, large commercial and industrial), different ZIP models were associated with each load using a random criteria. The ZIP models and coefficients that have been used are the ones experimentally determined in [BOK 14]. In order to simulate operating conditions, where TDOPF optimization can be applied, some hypothetical operative conditions have been tested.

F1M1

20kV/400V

00

59

55

01

60

61

65

63

42

43

48

64

45

44

49

50

38

47

40

36

35

06

51

39

37

07

52

08

09

53

33

10

54

34

11

13

12

31

14

32

15

16

18

17

19

20

23

24

25

PV generators

Generic load

Single-phase line with neutral

Three-phase line with neutral

21

22

Figure 1.9. Schematic representation of the 230 V/400 V circuits supplied by the F1M1 substation

62

58

41

02

56

46

03

57

04

05

29

26

30

27

28

32 From Smart Grids to Smart Cities

Unbalanced Three-Phase Optimal Power Flow for the Optimization of MV

33

1.6.1. Case D: LV network congestions

For this test, the loading level of each LV circuit was set so that the overall demand is 4,050 kW active and 1,990 kVAr reactive power. The 22 MV/LV transformers are rated in the classes 250, 315 and 400 kVA and can supply an overall rated power of 6,910 kVA theoretically. However, feeders and terminal circuits have been loaded, so that three different security problems have arisen altogether. Specifically, the LV distribution circuit in #F1M1 is characterized by currents violating the maximum ampacity, the LV circuit in #F1M4 has voltages violating minimum voltage magnitude constraints, and the MV/LV transformer in #F2M5 is overloaded. In order to find a new operative state, where all inequality constraints are respected, the availability of a set of active and reactive control resources was assumed. It was assumed that 48 interruptible loads, with a total power capability of approximately 350 kW, are distributed in the system and that the 21 photovoltaic generators can provide regulating reactive power up to half of the produced active power (i.e. a power factor of approximately 0.9) for a total capability of ±166 kVAr. The control effort required by the available control resources is minimized through the introduction of a cost function that can be formulated as ⎛ u − ui0 ⎞ C0 = ∑ α 0,i ⎜ maxi min ⎟ i =1 ⎝ ui − ui ⎠ nctrl

2

[1.27]

where ui and ui0 represent, respectively, the current and the initial value of the i-th control variable. For instance, ui0 is the amount of load available for curtailment or the initial reactive power supplied by a PV generator (most likely zero). The coefficient α 0,i takes into account the different costs of each control action. For example, reactive control resources can be characterized by a lower (if not null) cost, as they can be considered as cost-free control action. However, in the ideal context of active distribution grids where prosumers (or more generally active users) will be able to sell active and reactive regulating power, α 0,i can represent actual bidding of active users. In this formulation, each resource ui is constrained by hard constraints as in [1.7]. In the case of curtailable load, uimin is a positive or null number. A negative

34

From Smart Grids to Smart Cities

minimum constraint on active control resources might be adopted in the presence of resources that can inject active power (for example, BESS or electric vehicles operating in V2G mode). Hard constraints on reactive control resources are set, so that the power factor for each generator is never lower than 0.9. In Table 1.8, it is shown how the optimal solution, reached after eight iterations, is characterized by no constraint violations (i.e. all penalty functions are null). This optimal solution is reached by singling-out the control resources characterized by higher sensitivities with respect to the overall function [1.6]. Given the 4-wire model used in the overall formulation, the approach allows treatment of violations on a specific conductor and use of the control resources that are directly connected to that conductor. This is an important feature provided by this method, since any solution based on the sole direct sequence representation of the system is not capable of controlling security violations on single-phase circuits, nor capable of controlling flows and voltages on neutral conductors. iter # 0 1 2 3 4 5 6 7 8

C0 [p.u.] 0.000 0.065 0.071 0.074 0.077 0.077 0.077 0.077 0.076

C1 [p.u.] 172.100 0.910 0.181 0.046 0.022 0.014 0.003 0.000 0.000

C2 [p.u.] 28.282 14.065 6.904 0.320 0.001 0.000 0.000 0.000 0.000

C3 [p.u.] 1.789 0.023 0.003 0.002 0.002 0.001 0.001 0.000 0.000

C (tot) [p.u.] 202.171 15.063 7.159 0.442 0.102 0.092 0.081 0.077 0.076

Table 1.8. Case D1. Algorithm converge behavior

For instance, the curtailment requested on active control resources under the secondary substation #F1M1 is shown in Figure 1.10. This feeder is characterized by an overload on the three branches from bus F1M1_00 to F1M1_04 (see Figure 1.9). The highest curtailment is requested to loads #1, #2, #3 and #5, which are singlephase loads connected to phase A. Loads #4 and #7 are connected to phase B, and #6 to phase C. Load #8 is connected to phase A but belongs to a different LV feeder that is running parallel to the congested one; no control is requested to this load.

Unbalanced Three-Phase Optimal Power Flow for the Optimization of MV

35

Figure 1.10. Case D1: Active power supplied to curtailable loads under the secondary substation #F1M1, before and after control

case D1 D2 D3

num. active resources 48 48 48

num. reactive resources 21 0 63

active control [ΔkW] 82.12 83.33 82.10

reactive Control [ΔkVAr] 7.02 0.00 27.51

Table 1.9. Cases D1, D2, D3: active and reactive control

The solution found is characterized by an overall control of resources of 82.1 kW and 7.0 kVAr. It is possible to run the algorithm neglecting reactive control resources (case D2). The new solution requires the curtailment of approximately 83.3 kW, showing that the contribution of reactive resources is minimum for this specific operative case: the use of non cost-free control actions (load curtailment) cannot be avoided through reactive power rescheduling. This result is also confirmed by case D3, where it was assumed that 42 other distributed reactive resources were available in the network with a total capability of approximately ±50 kVAr. In Table 1.9, where all results are summarized, the overall active and reactive control is expressed as 1-norm of power changes.

36

From Smart Grids to Smart Cities

Other tests were carried out enabling only reactive control resources. These tests are not represented in Table 1.9 as no feasible solutions were found, even after increasing the number of available control resources. These results are expected given the high R/X ratio that characterizes LV circuits and the scarce control effectiveness that reactive power has in such circuits. 1.6.2. Case E: minimization of losses and reactive control

A second test was carried out considering the classical problem of loss reduction. A different operating condition was obtained by decreasing the average power factor of all loads to 0.8 and loading feeders, so that no congestions or voltage violations occur. This case is characterized by losses of 6.60%, calculated with respect to the total load. In order to reduce system losses, an objective function was introduced: Closs

⎛ = α loss ⎜ total losses ⎝

nloads

∑ i =1

⎞ PLi ⎟ ⎠

2

[1.28]

where PLi is the active power requested by the i-th load and α loss is a weight factor. Reactive control was boosted with respect to case D3, considering that the additional 42 distributed reactive resources have a total capability of approximately ±500 kVAr. The solution of the problem obtained by adding [1.20] in eqn. [1.6], and considering the availability of reactive resources only was reached after few iterations as shown in Table 1.10. With the rescheduling of 144 kVAr, the overall losses were reduced to 6.39%. Two other tests were carried out also considering the availability of active control resources (the same set of curtailable loads available for case A1). Table 1.11 gathers the results of all simulations. In all cases, the algorithm uses reactive power for power factor correction and active power for phase balancing. iter # 0 1 2 3 4 5 6

C0 [p.u.] 0.000 0.000 0.002 0.003 0.003 0.003 0.003

C1+C2+C3 [p.u.] 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Closs [p.u.] 4.071 4.070 3.839 3.835 3.836 3.835 3.835

C (tot) [p.u.] 4.071 4.070 3.841 3.838 3.839 3.838 3.838

Table 1.10. Case E1: algorithm convergence behavior

Unbalanced Three-Phase Optimal Power Flow for the Optimization of MV

case E1 E2 E3

num. active resources 0 48 48

num. reactive resources 63 0 63

active control [ΔkW] 0.00 132.89 99.21

reactive control [ΔkVAr] 144.41 0.00 150.29

37

losses [%] 6.39 6.24 6.15

Table 1.11. Cases E1, E2 and E3: active and reactive control

1.6.3. Algorithm performance

The computational effort required for running the algorithm on a common desktop PC (Intel Core i7-4770, 3.40 GHz, 8 GB RAM, 64 bit) is shown in Table 1.12 for all cases. It can be observed that the algorithm speed is drastically affected by the number of control resources. This is due to the fact that the greatest computational effort is required by the sub-algorithm that evaluates derivatives to compute ∇C k +1 and that the time required for such calculations grows linearly with the number of control variables. Moreover, the time necessary for solving each DLF is approximately 10–100 times higher than that in the previous case (average computation time is more than 100 ms per each DLF routine). Case D1 D2 D3 E1 E2 E3

num. control resources 69 48 111 63 48 111

num. iteration 8 8 8 6 7 9

total elapsed time [s] 124.8 85.8 195.1 92.9 96.1 236.2

sensitivity evaluation time[s] 120.4 81.7 190.4 85.4 79.0 225.4

Table 1.12. Computation time for cases D and E

In all tests, it was assessed that gradient evaluation requires more than 95% of the overall computing time. For this reason, the most efficient algorithm (BFGS) was adopted. A simplified formulation, similar to that used in the previous cases, is not suitable for solving this problem. For example, the solution of case D1 with the Barzilai– Borwein method would have required 24 iterations and a 278s running time.

38

From Smart Grids to Smart Cities

1.7. Conclusions

In this chapter, it has been demonstrated how OPF techniques can be successfully applied in a DMS framework for controlling smart distribution grids at both MV and LV voltage levels. Both centralized and decentralized approaches are viable, as control actions can be based on a direct command to controlled network devices (OLTCs, switched capacitors, disconnectors, etc.) or on the calculation of optimal reference signals or price signals to be sent to prosumers or active end-users. The development of tools for monitoring and controlling active and reactive power flows and voltages at any voltage level is a required step for the development of smart distribution grids. However, monitoring and control of MV and, especially, LV distribution networks require a substantial leap with regard to the problem of system modeling and inventorying. The classical “fit and forget” approach traditionally used for managing distribution is unfit to accommodate the growing number of distributed active resources. In this chapter, a methodology for controlling active and reactive resources in LV systems has been proposed. This methodology, based on the solution of a threephase unbalanced OPF, was tested on a detailed multi-phase representation of actual primary and secondary distribution systems. The formulation is general enough to consider the availability of a wide range of control resources and operational targets. Test results showed the feasibility of the approach in a DMS framework and showed potential capability of treating large numbers of single-phase and multiphase power devices. 1.8. Acknowledgments

Concerning developments reported in section 1.5, the authors gratefully acknowledge the Apulia region for financing the project “Smart-Grids: Advanced Technologies for utilities and energy” with 1,133,700 € as a Strategic Project in the Framework Program Agreement on the scientific research sector. Furthermore, the authors would like to thank Mr Walter Leggieri, Technical Director of AMET SpA Power Distribution Company, and all the personnel at the same utility for the help provided during the modeling of the system representation. Developments reported in section 1.6 are some of the results obtained during the research project PON RES NOVAE (Reti, Edifici, Strade, NuoviObiettivi Virtuosi per l’Ambiente e l’Energia) “Renewable energy and smart grids in smart cities”, which was financed with 23,391,010 €. The authors gratefully acknowledge the

Unbalanced Three-Phase Optimal Power Flow for the Optimization of MV

39

Italian Ministry for Education, University and Research and co-financing partners for the research funds under the research and competitiveness program to promote “Smart Cities, Communities and Social Innovation”. 1.9. Bibliography [ABD 12] ABDEL-MAJEED A., BRAUN M., “Low voltage system state estimation using smart meters”, Presented at the 47th International Universities Power Engineering Conference (UPEC), London, September 2012. [ALS 74] ALSAC O., STOTT B., “Optimal load flow with steady-state security”, IEEE Transactions Power Apparatus and Systems, vol. PAS-93, no. 3, pp. 745–751, 1974. [BAL 15] BALLANTI A., OCHOA L.F., “Initial assessment of voltage-led demand response from UK residential loads”, Innovative Smart Grid Technologies Conference (ISGT) 2015, Washington DC, USA, February 2015. [BAR 88] BARZILAI J., BORWEIN J.M., “Two-point step size gradient methods”, IMA Journal of Numerical Analysis, vol. 8, pp. 141–148, 1988. [BAR 95] BARAN M.E., KELLEY A.W., “A branch-current-based state estimation method for distribution systems,” IEEE Transactions Power Systems, vol. 10, pp. 483–491, 1995. [BAR 09] BARAN M., MCDERMOTT T.E., “ Distribution system state estimation using AMI data”, Presented at the IEEE/PES Power Systems Conference and Exposition 2009 (PSCE’09), Seattle, USA, March 2009. [BAS 15] BASSO T., CHAKRABORTY S., HOKE A. et al., “IEEE 1547 Standards advancing grid modernization”, 42nd IEEE Photovoltaic Specialist Conference (PVSC), New Orleans, June 2015. [BOK 14] BOKHARI A., ALKAN A., DOGAN R. et al., “Experimental determination of the ZIP coefficients for Modern Residential, Commercial, and Industrial Loads”, IEEE Transaction Power Delivery, vol. 29, no. 3, pp. 1372–1381, 2014. [BRE 97] BREZINSKI C., Projection Methods for System of Equations, North-Holland, Amsterdam, 1997. [BRE 03] BREZINSKI C., “A classification of quasi-Newton methods”, Numerical Algorithms, vol. 33, pp. 123–135, 2003. [BRO 11] BRONZINI M., BRUNO S., LA SCALA M. et al., “Coordination of Active and Reactive Distributed Resources in a Smart Grid”, Presented at PowerTech 2011, Trondheim, June 2011. [BRU 09] BRUNO S., LA SCALA M., LAMONACA S. et al., “Load control through smartmetering on distribution networks”, PowerTech 2009 Conference, Bucarest, Romania, June–July 2009.

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[BRU 11a] BRUNO S., LA SCALA M., STECCHI U., “Monitoring and Control of a Smart Distribution Network in Extended Real-Time DMS Framework”, Presented at Cigré International Symposium 2011, Bologna, September 2011. [BRU 11b] BRUNO S., LAMONACA S., ROTONDO G. et al., “Unbalanced three-phase optimal power flow for smart grids”, IEEE Transactions on Electron Devices, vol. 58, no. 10, pp. 4504–4513, 2011. [BRU 12] BRUNO S., LAMONACA S., LA SCALA M. et al., “Integration of optimal reconfiguration tools in Advanced Distribution Management System”, IEEE PES Innovative Smart Grid Technologies Europe 2012, Berlin, October 2012. [FAN 09] FAN J., BORLASE S., “The evolution of distribution”, IEEE Power & Energy, vol. 7, pp. 63–68, no. 2, 2009. [FAR 14] FARHANGI H., “A road map to integration: perspectives on smart grid development”, IEEE Power Energy Magazine, vol. 12, no. 3, 2014. [FIA 83] FIACCO A.V., Introduction to Sensitivity and Stability Analysis in Nonlinear Programming, Academic Press, New York, NY, 1983. [FOR 16] FORFIA D., KNIGHT M., MELTON R., “The view from the top of the mountain: building a community of practice with the GridWise Transactive Energy Framework”, IEEE Power and Energy Magazine, vol. 14, no. 3, pp. 25–33, 2016. [HAD 10] HADJSAID N., LE-THANH L., CAIRE R. et al., “Integrated ICT framework for distribution network with decentralized energy resources: Prototype, design and development”, IEEE PES General Meeting 2010, Minneapolis, 25–29 July 2010. [HTT] https://sourceforge.net/projects/electricdss/ [KRI 16] KRISTOV L., DE MARTINI P., TAFT J.D., “A tale of two visions: designing a decentralized transactive electric system”, IEEE Power and Energy Magazine, vol. 14, no. 3, pp. 63–69, 2016. [LU 95] LU C.N., TENG J.H., LIU W.H.E., “Distribution system state estimation,” IEEE Transaction Power System, vol. 10, pp. 229–240, 1995. [MAL 14] MALLET P., GRANSTROM P.-O., HALLBERG P. et al., “Power to the People!: European perspectives on the future of electric distribution”, IEEE Power Energy Magazine, vol. 12, no. 2, pp. 51–64, 2014. [MEL 11] MELIOPOULOS A.P.S., COKKINIDES G., HUANG R. et al., “Smart grid technologies for autonomous operation and control”, IEEE Transaction on Smart Grid, vol. 2, no. 1, 2011. [MOH 10] MOHAGHEGHI S., STOUPIS J. et al., “Demand response architecture: integration into the distribution management system”, 1st IEEE International Conference on Smart Grid Communication (SmartGridComm), 2010, Gaithersburg, MD, October 2010. [MOK 13] MOKHTARIA G., NOURBAKHSHA G., ZAREB F., et al., “Overvoltage prevention in LV smart grid using customer resources coordination”, Energy and Buildings, vol. 61, pp. 387–395, 2013.

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[MOM 09] MOMOH J.A., “Smart grid design for efficient and flexible power networks operation and control”, IEEE – Power Systems Conference and Exposition 2009, Seattle, March 2009. [MOR 79] MORGAN M.G., TALUKDAR S.N., “Electric power load management: Some technical, economic, regulatory and social issues”, Proceedings of the IEEE, vol. 67, no. 2, pp. 241–312, 1979. [NOC 06] NOCEDAL J., S.J., Numerical Optimization, Springer, New York, 2006. [PAU 11] PAUDYAL S., CANIZARES C., BHATTACHARYA K., “Optimal operation of distribution feeders in smart grids”, IEEE Transaction on Industrial Electronics, vol. 58, no. 10, pp. 4495–4503, 2011. [RAH 16] RAHIMI F., IPAKCHI A., FRED FLETCHER F., “The changing electrical landscape: end-to-end power system operation under the transactive energy paradigm”, IEEE Power and Energy Magazine, vol. 14, no. 3, pp. 52–62, 2016. [ROY 93] ROYTELMAN I., SHAHIDEHPOUR S.M., “State estimation for electric power distribution systems in quasi real-time conditions”, IEEE Transaction Power Delivery, vol. 8, no. 4, pp. 2009–2015, 1993. [SAN 10] SANTACANA E., RACKLIFFE G., TANG L., et al., “Getting smart”, IEEE Power & Energy, vol. 8, pp. 41–48, no. 2, 2010. [SIN 09] SINGH R., PAL B.C., JABR R.A., “Choice of estimator for distribution system state estimation”, IET Generation, Transmission & Distribution, vol. 3, no. 7, pp. 666–678, 2009. [SMA 16] SMART ENERGY DEMAND COALITION (SEDC), Report on “Mapping Demand Response in Europe Today – 2015”, available at: http://www.smartenergydemand.eu/, 2016. [STI 11] STIFTER M., BLETTERIE B., BURNIER D. et al., “Analysis environment for low voltage networks”, 2011 IEEE 1st Int. Workshop on Smart Grid Modeling and Simulation (SGMS), Brussels, October 2011. [STI 13] STIFTER M., PALENSKY P., “Smart meter data as a basis for smart control in low voltage distribution networks”, 2013 IEEE Int. Symposium on Industrial Electronics (ISIE), Taipei, May 2013. [TIN 68] TINNEY W.F., HART C.E., “Optimal power flow solutions”, IEEE Transaction Power Apparatus and Systems, vol. PAS-87, pp. 1886–1876, 1968. [VAR 15] VARELA J., PUGLISI L.J., WIEDEMANN T. et al., “Show Me!: large-scale smart grid demonstrations for European distribution networks”, IEEE Power Energy Magazine, vol. 3, no. 1, pp. 85–91, 2015. [WAN 04] WANG H., SCHULZ N.N., “A revised branch current based distribution system state estimation algorithm and meter placement impact”, IEEE Transaction Power System, vol. 19, no. 1, pp. 207–213, 2004.

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[ZHA 10] ZHAO L., ZHENYUAN W. et al., “A unified solution for advanced metering infrastructure integration with a distribution management system”, 1st IEEE International Conference on Smart Grid Communication (SmartGridComm), 2010, Gaithersburg, MD, October 2010.

2 Mixed Integer Linear Programming Models for Network Reconfiguration and Resource Optimization in Power Distribution Networks

This chapter describes mixed integer linear programming models allowing for the adequate representation of two optimization problems that characterize the operation of a power distribution network: the first is aimed at finding the minimum power loss configuration of the network, the second is the so-called Voltage/Var Optimization problem, i.e. the definition of the most efficient operating condition of voltage control apparatus and reactive power resources. The quality of the results and the effects of the proposed linearization are assessed by comparison with the results available in the literature and with the results obtained by power flow calculations performed for the optimal configurations.

2.1. Introduction The performance of the software tools that solve mixed integer linear programming (MILP) models has been much improved in recent years. These solvers are based on the integration of branch-and-bound and cutting-plane algorithms and implement local search techniques and heuristics that are particularly effective for determining a first feasible solution [LOD 10]. Therefore, MILP models able to adequately represent the characteristics of power system operation are expected to be of practical use. This chapter deals with two typical optimization problems relevant to the operation of power distribution systems: the first aims at finding the minimum-loss Chapter written by Alberto BORGHETTI. From Smart Grids to Smart Cities: New Challenges in Optimizing Energy Grids, First Edition. Edited by Massimo La Scala. © ISTE Ltd 2017. Published by ISTE Ltd and John Wiley & Sons, Inc.

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From Smart Grids to Smart Cities

configuration of the network and the second is the so-called Voltage/Var Optimization (VVO) problem that aims at minimizing bus voltage deviations and reactive power flows (PF) by also exploiting the reactive power capabilities of available embedded generators (EG). A MILP model has the form:

Aeq x = beq and Aineq x ≤ bineq ⎧ ⎪ T min ⎨c x : xL ≤ x ≤ xU ⎪ x j integer ∀j ∈ J ⎩

⎫ ⎪ ⎬ ⎪ ⎭

[2.1]

where c is the column vector of coefficients that define the objective function to be minimized, Aeq and beq are respectively the matrix and the column vector of known parameters that define the set of equality constraints, Aineq and bineq are respectively the matrix and the column vector of known parameters that define the set of inequality constraints and x is the column vector of the unknown variables constrained between lower and upper bounds xL and xU, some of them also restricted to be integers. The biggest challenge to obtain a MILP model that reasonably represents the problem of interest – i.e. to define the most appropriate values for c, Aeq, beq, Aineq, bineq, xL and xU of [2.1] – is the formulation of a linear approximation of the nonlinear relationships that represents the behavior and operating constraints of the network. This approach has been recently investigated for not only distribution networks – e.g. [BOR 12, FRA 13a, FRA 13b, FER 14] – but also the solution of the classical OPF problem in transmission systems – e.g. [ONE 12, COF 14]. This chapter is based on the approach presented in some recent contributions, namely [BOR 12], [BOR 13] and [BOR 15]. It describes the models and the assessment of both computational performances and accuracy by the comparison of the obtained results with those available in the literature relevant to various test networks and with the results obtained by PF calculations for the optimal configurations. 2.2. Model for determining the optimal configuration of a radial distribution network The typical minimum power loss configuration problem could be solved by the search of the radial network configuration that corresponds to the minimization of the network power losses taking into account the constraints defined by the need to feed all the loads, to permit the production of all the EG, to maintain the current

Mixed Integer Linear Programming Models

45

flows below the ampacity limits of cables and overhead lines and to maintain the bus voltage deviations lower than a predefined level of few percent with respect to the rated value. For the solution of the problem, the electric power distribution network of N buses and Nb lines is usually associated to a connected graph, each bus k being represented by one distinct element of the set K of the vertices of the graph and each line b being represented by one distinct element of the set B of edges of the graph. The point of connection of each load or EG is considered as a bus and each couple of connected busses defines a different line. Only simple graphs, characterized by the absence of parallel edges (i.e. edges having the same pair of vertex) as well as of self-loops (i.e. edges with indistinct end vertices), are considered here. Each configuration of the network is represented by a binary column vector u with Nb elements: ub = 1 indicates that line b is connected, ub = 0 indicates that the line is disconnected at both ends. For simplicity, this chapter does not consider the case of a line connected only at one end. The optimization model for the computation of the minimum loss configuration u can be written as follows: *

u * = arg min ∑ Ploss, b

[2.2]

b∈ B

subject to f ∈F

[2.3]

u* ∈ U

[2.4]

where Ploss, b are the losses of active power in branch b, f is the column vector that contains the voltage phasors of all nodes Vk and branch currents Ib, F is the region of possible operation of the network and U denotes the set of configurations corresponding to a tree of the graph, which corresponds to a configuration that does not contain closed paths and connects all the nodes. Objective function [2.2] minimizes the total value of line losses. Constraints [2.3] represent all the operating constraints that bound the bus voltage deviations below to a small percentage of the rated value Vr and limit each current below the relevant line capability. Moreover, constraints [2.3] also include the network equations, which incorporate the characteristics of loads and EG. Constraint [2.4] ensures a radial configuration.

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From Smart Grids to Smart Cities

We assume here that the status (connected or non-connected) of each line in the network can be changed and the characteristics of all loads and EG are known. Moreover, for sake of simplicity, in the model description, all the substations are considered as a single slack bus s and the magnitude of voltage phasor of the slack bus Vs = Vs e j 0 is assumed equal to the rated value of the network. The following sections describe the various parts of the proposed MILP model of problems [2.2]–[2.4]: the objective function, the line current bounds and the constraints on the bus voltage deviations with respect to the rated value, the representation of the network equations and the implementation of the radiality constraint. 2.2.1. Objective function and constraints of the branch currents Both the objective function and the maximum line current constraints require the evaluation of the square value of the real and imaginary parts of each line current phasor, i.e. I bre 2 and I bim 2 . Piecewise linear functions (PLFs) are adopted for the MILP representation of these square values. A review and a comparison between different PLF approaches proposed for the representation of generic nonlinear functions are reported in [KEH 04]. For the PLF models of I bre 2 and I bim 2 , the following simplifying conditions apply: 1) the optimization problem searches for the minimum values of the line currents; 2) line current constraints are upper bounds, i.e. I b ≤ I b , max ; 3) the PLF models need to approximate square functions. These simplifying conditions permit to avoid additional binary variables. According to simplifying condition 3), the slope and the ordinate intercept of each interval of the two PLFs (one relevant to I bre 2 and the other relevant to I bim 2 ) could be written as:

λbre, i = I bre, i +1 + I bre, i , Λ bre, i = I bre, i 2 − λbre, i ⋅ I bre, i ∀i =1. .. zbre − 1

[2.5]

im 2 im im im λbim, i = I bim, i +1 + I bim, i , Λ im b , i = I b , i − λb , i ⋅ I b , i , ∀i = 1. .. zb − 1

[2.6]

Mixed Integer Linear Programming Models

47

where zbre is the number of breakpoints of the PLF that approximate I bre 2 , being the coordinates of each breakpoint i given by ( I bre, i , I bre, i 2 ). Analogously, zbim is the number of breakpoints of the PLF relevant to I bim 2 , each defined by coordinates ( I bim, i , I bim, i 2 ). As shown by [2.5] and [2.6], the x-coordinates of the breakpoints are the absolute values of I bre and I bim . The following linear constraints permit the evaluation of I bre and I bim , at the same time ensuring that current I b is null if line b is not connected (i.e. if ub* = 0):

I bre − I bre ≤ 0 and − I bre − I bre ≤ 0 and I bre − I b , max ⋅ ub* ≤ 0

[2.7]

I bim − I bim ≤ 0 and − I bim − I bim ≤ 0 and I bim − I b , max ⋅ ub* ≤ 0

[2.8]

The PLFs of I bre 2 and I bim 2 are written as − I bre 2 + λbre, i ⋅ I bre ≤ −Λ bre, i ∀i = 1. .. zbre − 1

[2.9]

− I bim 2 + λbim, i ⋅ I bim ≤ −Λ im ∀i = 1. .. zbim − 1 b, i

[2.10]

Since I b2 = I bre 2 + I bim 2 , the objective function [2.2] becomes Nb

∑R I b =1

re 2 b b

Nb

+ ∑ Rb I bim 2

[2.11]

b =1

and line ampacity constraints are written as I bre 2 + I bim 2 ≤ I b2, max ∀b ∈ B

[2.12]

Constraints [2.7]–[2.10] can be replaced by − I bre 2 + λbre, i ⋅ I bre ≤ −Λ bre, i − I bre 2 − λbre, i ⋅ I bre ≤ −Λ bre, i

∀i =1. .. zbre − 1

[2.13]

48

From Smart Grids to Smart Cities

− I bim 2 + λbim, i ⋅ I bim ≤ −Λ im b, i − I bim 2 − λbim, i ⋅ I bim ≤ −Λ im b, i

∀i =1. .. zbim − 1

[2.14]

with − I b, max ⋅ ub* ≤ I bre ≤ I b , max ⋅ ub*

[2.15]

− I b , max ⋅ ub* ≤ I bim ≤ I b , max ⋅ ub*

[2.16]

Formulation [2.13]–[2.16] avoids variables I bre and I bim .

2.2.2. Bus voltage constraints

Also the bus voltage constraints require a PLF representation of the square value of the real and imaginary parts of each bus voltage phasor, i.e. Vkre 2 and Vkim 2 . For the bus voltages, simplifying conditions 1) and 2) do not apply. Therefore, the PLF representation of Vkre 2 and Vkim 2 includes additional binary variables. The coordinates of the zkre PLF breakpoints relevant to Vkre 2 are ( Vkre, i , Vkre, i 2 ) and those of the zkim PLF breakpoints relevant to Vkim 2 are ( Vkim, i , Vkim, i 2 ), while the slope of each interval is

λkre, i = Vkre, i +1 + Vkre, i

∀i = 1. .. zkre − 1

[2.17]

λkim, i = Vkim, i +1 + Vkim, i

∀i = 1. .. zkim − 1

[2.18]

Each absolute value Vkre is defined by adding a new binary variable, zkre , and two non-negative continuous variables, Vkre +

Vkre − Vkre + Vkre

−

+

−

and Vkre : +

= 0 and Vkre − Vkre − Vkre

+

−

−

=0

Vkre − zkre ⋅ Vk , max ≤ 0 and Vkre − (1 − zkre ) ⋅ Vk , max ≤ 0

Analogous constraints define Vkim .

[2.19]

Mixed Integer Linear Programming Models

49

By applying the so-called incremental method, the PLF model of Vkre 2 can be written as

zkre −1

∑v

re k ,i

zkre −1

zkre −1

i =1

i =1

∑ λkre, i ⋅ vkre, i +

−Vkre 2 +

+

zkre −1

∑V

i =1

zkre −1

re k,i

∑V

re 2 k,i

⋅ wkre, i = 0

⋅ wkre, i − Vkre = 0

[2.20]

i =1

∑w

re k ,i

= 1 and vkre,i − Vk , max ⋅ wkre, i ≤ 0 ∀i = 1. .. zkre − 1.

i =1

where non-negative continuous variable vkre, i is added in order to represent the difference between Vkre and abscissa Vkre, i

of the immediately preceding PLF

breakpoint. The last two constraints of [2.20] guarantee that Vkre 2 is defined by only one interval of the corresponding PLF representation by means of additional binary variable wkre, i . An analogous incremental model define Vkim 2 . Being Vk2 = Vkre 2 + Vkim 2 , the upper and lower bounds Vk, max and Vk, min to each bus voltage amplitude are enforced by Vkre 2 + Vkim 2 ≤ Vk2, max and − Vkre 2 − Vkim 2 ≤ −Vk2, min

[2.21]

A PLF representation of Vkre 2 equivalent to [2.19]–[2.20] is provided by the following constraints: re 2 k

−V

+

zkre −1

∑λ

re k,i

⋅v −

2

(

zkre

∑

(

)

zkre −1

2 zkre −1

i =1

i = zkre

∑ Vkre, i 2 ⋅ wkre, i + )

−1

∑

re k,i

v +

i =1

zkre −1

)

i = zkre

i =1

+

(

2 zkre −1 re k ,i

∑V

re k,i

∑

⋅w −

i =1

(

)

re k

+1

⋅ vkre, i +

Vkre, i − z re +12 ⋅ wkre, i = 0 k

2 re k,i

λkre, i − z

(

zkre

)

∑

i = zkre

(

re k , i − zkre +1

V

re k,i

re k

⋅ w −V = 0

∑ i =1

0 ≤ vkre, i ≤ Vkre, i + 1 − Vkre, i ⋅ wkre, i ∀i = 1... zkre − 1

(

)

− Vkre, i − z re + 2 − Vkre, i − z re +1 ⋅ wkre, i ≤ vkre, i ≤ 0 ∀i = zkre ... 2 ( zkre − 1) k

k

)

2 zkre −1

−1

wkre, i = 1

[2.22]

50

From Smart Grids to Smart Cities

A set of constraints analogous to [2.22] defines Vkim 2 . In general, the number of binary variables in [2.22], i.e. 2 ( zkre − 1) ( N − 1) , is larger than those required by the model defined by [2.19] and [2.20], i.e. N + ( N − 1) ( zkre − 1) . However, [2.22] appears simpler than [2.19]–[2.20], as it avoids several variables (i.e., zkre , Vkre , Vkre

+

−

and Vkre ) and it involves a smaller

number of equality constraints. 2.2.3. Bus equations

Network equations define the equilibrium of the currents at each bus k and the voltage variation in each connected line b, taking into account the current–voltage relationships defined by loads and EG. The phasor of the current injected into bus k is represented by the sum of current phasor Ink defined by the injected active and reactive powers (Pk, Qk) assuming Vk = Vs and a correction denoted as ΔInk , which is a function of the amplitude and phase deviations of bus voltage Vk with respect to Vs, deviations usually very small.

Adopting the symmetric approximation, each line b is represented by the usual one-phase Π equivalent circuit with a resistance Rb, a reactance Xb and two equal shunt capacitances Cb. The line current at terminal k is composed of current I b flowing in Rb and Xb and current I bsh, k flowing in Cb. The inclusion of I bsh, k is adopted for the accurate evaluation of voltage amplitudes in the presence of cable lines, while its contribution is neglected in the ampacity constraints. For each bus k, k ≠ s , the current equilibrium is defined by two linear equality constraints:

∑I

re b

∑I

im b

b ∈ Bk+

b ∈ Bk+

−

∑I

b ∈ Bk−

−

re b

∑I

b ∈ Bk−

+

∑I

sh , re b, k

− ωCk ⋅ Vkim = Inkre + ΔInkre

[2.23]

+ ωCk ⋅ Vkre = Inkim + ΔInkim

[2.24]

b∈ Bk im b

+

∑I

sh , im b, k

b ∈ Bk

where Ck represents a capacitor bank connected to bus k, ω is the rated value of the angular frequency and Bk is the set of lines b connected to bus k ( Bk+ is the set of lines leaving k and Bk− is the set of lines entering k).

Mixed Integer Linear Programming Models

51

The following three current–voltage relationships have been implemented for the definition of ΔInkre and ΔInkim : a) Constant current at bus k: Vkim Pk2 + Qk2 Vs Qk

ΔInkre = − Ink

ΔInkim = Ink

Vkim Pk2 + Qk2 Vs Pk

[2.25]

[2.26]

being the phase deviation of Vk so small that it is approximated by the ratio Vkim / Vs .

b) Constant Pk and Qk (PQ node): ΔInkre = − Inkre ⋅

ΔInkim = Inkre ⋅

Vkre − Vs V im − Inkim ⋅ k Vs Vs

Vkim V re − Vs − Inkim ⋅ k Vs Vs

[2.27]

[2.28]

c) Constant Pk and constant Vk (PV node): constraints [2.23], [2.24], [2.27] and [2.28] are applied with Inkim as a continuous variable and the two following constraints are added: −

Qmax,k

3Vk

≤ Inkim ≤ −

Vkre 2 + Vkim 2 = Vk2

Qmin,k

3Vk

[2.29] [2.30]

Variable Inkim permits to adapt the reactive power production of an EG between the upper and lower limits [2.29]. Even when the relationship between ΔInkre and ΔInkim is linear, as for the cases a) and b), a solution procedure with two iterations is implemented, which is more convenient from the computational point of view, as will be shown in section V. In the first iteration, ΔInkre and ΔInkim are null, while in the second both are calculated

52

From Smart Grids to Smart Cities

by using the values Vkre and Vkim obtained in the first iteration. When PV nodes are present, i.e. case c), only the two-iteration procedure is applied in order to avoid the nonlinearity associated with the multiplication between Inkim and Vkre in [2.28]. 2.2.4. Line equations

The equations of the differences between voltage phasors at the terminals h and k of each line b are represented by the following linear constraints: Vhre − Vkre − Rb ⋅ I bre + X b ⋅ I bim + Δvbre = 0 Δvbre + BN ⋅ ub* ≤ BN and − Δvbre + BN ⋅ ub* ≤ BN Vhim − Vkim − X b ⋅ I bre − Rb ⋅ I bim + Δvbim = 0 Δvbim + BN ⋅ ub* ≤ BN and − Δvbim + BN ⋅ ub* ≤ BN

[2.31]

[2.32]

where the value of BN is adequately large. Constraints [2.31] and [2.32] ensure that auxiliary variables Δvbre and Δvbim are null when line b is connected and equal to the voltage difference between unconnected busses when disconnected. Similarly, the real and imaginary parts of current I bsh of each line connected to bus k are represented by the following constraints: I bsh, k, re ωCb + Vkim + Δvbre, k = 0 Δvbre, k + BN ⋅ ub* ≤ BN and − Δvbre, k + BN ⋅ ub* ≤ BN

I bsh, k,im ωCb − Vkre + Δvbim, k = 0 Δvbim, k + BN ⋅ ub* ≤ BN and − Δvbim, k + BN ⋅ ub* ≤ BN

[2.33]

[2.34]

Auxiliary variables Δvbre, k and Δvbim, k are null when line b is connected and equal to − Vkim and Vkre , respectively, when disconnected (being I bsh, k, re and I bsh, k,im null).

Mixed Integer Linear Programming Models

53

2.2.5. Radiality constraints

Radial operation of the distribution network is often represented by one of the following two requirements: (1) among all the lines connected to each bus, there should be at most one with the flow entering the bus, e.g. [KHO 09]; (2) the number of connected lines should be equal to the number of buses excluding the substations, i.e. the slack bus, e.g. [FAN 96]: Nb

∑u

* b

= N −1

[2.35]

b =1

Requirement (1) could not be applied in the presence of EG, since there is the possibility that a load is fed at the same time by more than a source. As analyzed in [ROM 10, LAV 12], requirement (2) should be completed by additional constraints that guarantee the link of all the busses, including those with zero injection. For such a purpose, the following model is adapted from [LAV 12]:

∑χ

b ∈ Bk+

b

−

∑χ

b ∈ Bk−

b

≤ −1

∀k ∈ K , k ≠ s

− ( N − 1) u ≤ χ b ≤ ( N − 1) u * b

[2.36]

* b

where χb are auxiliary continuous variables. In [2.36], the equality constraints of the formulation presented in [LAV 12] are replaced by inequality constraints. Another way is to introduce constraints that directly ensure the opening of at least one of the lines of each simple cycle (i.e. each connected cycle without repeated vertices). The number Nc of all possible distinct simple cycles could be very large. However, efficient algorithms are available in order to find all the cycles in a graph by using search strategies, e.g. [TAR 73], or by the union of two or more cycles of a cycle basis, e.g. [DIE 10]. The latter approach has been implemented and is described here. First, a spanning tree is obtained by applying a depth-first search methodology. The Nb − (N − 1) fundamental cycles associated with the spanning tree are then defined by adding just one edge and removing all the leaf nodes (i.e. the nodes linked with one line only). As the set of the fundamental cycles forms a basis for the cycle space, all the simple cycles are found by the union of two or more fundamental cycles. For each cycle y, a vector of binary parameters l y is defined so that each 1-0 element l b , y indicates whether line b is included in cycle y or not. The union of two cycles is achieved by applying the exclusive OR logic operation to each couple of corresponding elements of l y vectors. Therefore, the resulting cycle is composed of

54

From Smart Grids to Smart Cities

only the lines included in one or the other of the two original cycles. Then, the implemented procedure inspects the obtained cycle in order to check whether or not it is a new simple cycle and, in that case, adds the relevant l y vector to matrix L, whose columns finally represent all the Ny distinct simple cycles in the graph. With the matrix L known, constraint [2.4] is represented by the following set of integer linear constraints: Nb

∑l b =1

Nb

b, y

⋅ ub* ≤ ∑ l b , y − 1

∀y = 1...N y

[2.37]

b =1

In the proposed MILP model, both constraints [2.35] and [2.36] are implemented. They are sufficient to ensure that a radial configuration is obtained. However, the addition of cycle-opening constraints [2.37], even if limited to the cycles obtained by a small number of combinations of the fundamental cycles, has been found often useful in order to facilitate the convergence of the numerical solution, as illustrated in the following section. 2.3. Test results of minimum loss configuration obtained by the MILP model

The MILP model has been tested by using the Cplex V12.3 MIP solver on two 3.07 GHz Intel 6 core processors with 48 GB RAM, running on 64-bit Windows operating system. As a compromise between computational time and accuracy, the MILP solution has been obtained with zbre = zbim = 31 for the PLFs of I b 2 , implemented by using constraints [2.13]–[2.16], and with zkre = zkim =4 for the PLFs of Vk 2 , implemented by using constraints [2.22], in all the tests. Moreover, a maximum voltage phase deviation of 5° with respect to the slack bus is assumed, i.e. the break points relevant to V are allocated between Vk , min cos(π / 36) and Vk , max , while those relevant to re 2

k

Vkim 2 are allocated between 0 and Vk , max sin(π / 36) .

2.3.1. Illustrative example

In this section, the illustrative case study proposed in [ROM 10] is adopted in order to illustrate the MILP model capability to take into account the presence of EG, as well as the effects of bus-voltage bounds and line ampacity constraints. As

Mixed Integer Linear Programming Models

55

shown in Figure 2.1, the network is composed of a substation, five buses, seven lines and a generator.

Figure 2.1. Illustrative example

The substation is represented by the slack bus with Vs = 20 kV (both the active and reactive powers injected in the slack bus, PS and Qs, are provided by the solution). Generator G is represented as a PV node with PG = 5 MW and VG = 0.97 p.u. (QG is provided by the solution). All the other four buses are represented by PQ nodes with the total power request PL = 17.5 MW and QL = 0.63 Mvar (the values relevant to each load are reported in [ROM 10]). The network contains two fundamental cycles and three distinct simple cycles. The model contains 215 variables (67 binary) and 1105 constraints (67 equality). Because of the nonlinear representation of the PV bus, the two-iteration procedure is applied. The same three different tests presented in [ROM 10] are here repeated by using the MILP model, namely: – the base test in which the voltage and current operating constraints are not binding (i.e. Vk, max=1.1 p.u., Vk, min = 0.9 p.u. and Ib, max = 600 A); – the voltage test, in which a minimum voltage bound Vk, min = 0.97 p.u. has been imposed at every load bus; – the current test, in which a maximum line-current constraint Ib, max = 368.9A has been enforced at line 5. In agreement with [ROM 10], the minimum-losses radial configuration is obtained with: lines 4 and 6 open in the base test; lines 3 and 6 open in the voltage test and lines 4 and 7 open in the current test. While in the base test line 3 is open instead of line 4 after the first iteration, in the other two tests, the same minimum-losses configuration is also obtained at the end of the first of the two iterations.

56

From Smart Grids to Smart Cities

In order to verify the accuracy of the proposed model, each MILP solution is compared with the results provided by the PF calculation applied to the corresponding optimal network configuration1. The results are reported in Table 2.1, which also shows the time spent to obtain the Cplex solution for each of the two iterations. Base test

Losses (kW)

Voltage test

Current test

PF

MILP

PF

MILP

PF

MILP

637.658

632.204

647.114

644.529

855.206

859.356

0.9681

0.9683

0.97

0.97

0.9455

0.9461

bus Vmin (p.u.) at the end of line 1 496.55

495.11

at G 497.4

at the end of line 5

496.64

551.64

554.6

Imax (A) in line 7

in line 1

in line 6

PL (MW)

17.5

17.484

17.5

17.492

17.5

17.449

QL (Mvar)

0.63

0.6

0.63

0.589

0.63

0.579

PG (MW)

5

4.95

5

4.968

5

4.965

QG (Mvar)

−10.26

−10.179

−10.27

−10.248

−12.66

−12.86

VG (p.u.)

0.97

0.97

=Vmin

=Vmin

0.97

0.97

Ps (MW)

13.138

13.165

13.147

13.168

13.355

13.343

Qs (Mvar)

11.103

10.99

11.137

11.071

13.668

13.818

CPU time (s)

0.28 + 0.59

0.28 + 0.61

0.13 + 0.41

Table 2.1. Comparison between the MILP solution and PF results

1 The EMTP-rv load flow code [MAH 07] has been used for the PF calculations.

Mixed Integer Linear Programming Models

57

2.3.2. Tests results for networks with several nodes and branches

The MILP model described in the previous sections has been applied to the following five test networks, chosen among the most frequently adopted models in the literature on the subject: a) the 15-bus 16-line 3-feeder system originally studied in [CIN 88]; b) the 32-bus 37-line system originally studied in [BAR 89b]; c) the 69-bus 74-line system first adopted in [CHI 90] as an enlargement of the radial network described in [BAR 89a]; d) the 83-bus 96-line system originally analyzed by Su and Lee in [SU 03]; e) the 135-bus 158-line system originally analyzed in [MAN 00]. This section compares the minimum-losses configurations obtained by applying the proposed MILP model with those reported in the literature, while section 2.3.3 compares the MILP solutions with the corresponding PF results. Moreover, the results obtained by the two-iteration procedure are compared with those obtained by the direct (single-iteration) solution, which can be applied due to the absence of PV nodes. The differences between MILP and PF results are generally negligible. Compared with the two-iteration procedure, the direct solution usually allows a more accurate representation of the PQ nodes (as shown by the total load active and reactive powers values of Tables 2.3 and 2.4). However, as already mentioned, the accuracy of the evaluation of the losses, as well as that of bus voltages and line currents, mostly depends on the adopted PLF representation, while it is not significantly affected by the adoption of the two-iteration procedure. The twoiteration procedure requires, in general, less computational effort, as demonstrated by the total CPU time. Tables 2.3 and 2.4 also illustrate the advantages achieved by adding radiality constraints to the model for the test networks with the largest number of busses and lines. Network (a): 15-bus 16-line system

The substation has constant voltage Vs = 23 kV. All the other 15 buses are represented by PQ nodes as indicated in [CIN 88]. The system also includes seven capacitor banks, one at the end of lines 12, 13, 15, 18, 20, 24 and 25. The network contains three fundamental cycles and seven distinct simple cycles.

58

From Smart Grids to Smart Cities

In order to illustrate the capability of the MILP model to represent the capacitor banks accurately, the calculation is carried out twice: the first by including the reactive power production of the capacitors in the PQ node constant values, while the second time by explicitly representing the capacitance of the capacitor banks. For both the calculations, the same minimum-losses radial configuration is obtained. This is shown in Figure 2.2, in which the three open lines are 17, 19 and 26. The same configuration is also obtained at the end of the first iteration of the twoiteration procedure.

Figure 2.2. Optimal configuration of the 15-bus system

The obtained configuration is in agreement with those presented in the literature (see [ROM 10] for a thorough review) and corresponds to power losses equal to 466.127 kW if the capacitor banks are represented with a constant reactive power injection or 468.33 kW if they are represented as capacitances. Network (b): 32-bus 37-line system

The substation has constant voltage Vs=12.66 kV and all the other 32 buses are represented by PQ nodes as indicated in [BAR 89b]. The network contains five fundamental cycles and 26 distinct simple cycles. The obtained minimum-losses radial configuration is shown in Figure 2.3, in which the five open lines are 7, 9, 14, 32 and 37. The same configuration is also obtained at the end of the first iteration of the two-iteration procedure. The obtained configuration is in agreement with those presented in the literature (see [ROM 10] for a thorough review) and corresponds to power losses equal to 139.552 kW.

Mixed Integer Linear Programming Models

59

Figure 2.3. Optimal configuration of the 32-bus system

Network (c): 69-bus 74-line system

The substation has constant voltage Vs= 12.66 / 3 kV and all the other 69 buses are represented by PQ nodes as indicated in [CHI 90]. The network contains five fundamental cycles and 26 distinct simple cycles. As in [CHI 90] and also in [ROM 10, CAR 08, CHA 94 and AUG 95], three load conditions are examined, indicated as normal-loaded, heavy-loaded (obtained by multiplying each load demand by 1.2) and light-loaded (obtained by multiplying each load demand by 0.5). The minimum-losses radial configuration for all the three load conditions is shown in Figure 2.4, in which the five open lines are 15, 59, 62, 70 and 71. The same configuration is also obtained at the end of the first iteration of the twoiteration procedure.

Figure 2.4. Optimal configuration of the 69-bus system

The obtained configuration is equivalent to the solution usually reported in the literature for the normal-loaded condition [RAJ 08, ROM 10, RAM 05, CHI 90, CHA 94] and corresponds to power losses equal to 30.093 kW. It is important to note that opening one of the lines 56, 57, 58 instead of line 59 is indifferent as the loads at the end of the three lines 56, 57 and 58 are null.

60

From Smart Grids to Smart Cities

The conclusion that the minimum-losses configuration of Figure 2.4 applies for all the three considered load conditions has been already presented in [GUI 10, AUG 95]. The configuration of Figure 2.4 differs from the one obtained in [ROM 10] and [CHI 90], both for the heavy case – in [ROM 10], lines 13 and 64 are open instead of 15 and 62; in [CHI 90], line 13 is open instead of 71 – and for the light case – in [ROM 10], lines 10 and 64 are open instead of 70 and 62; in [CHI 90], lines 10, 20 and 54 are open instead of 70, 71 and 59. Network losses calculated by using the PF code for the heavy-case configurations of [ROM 10] and [CHI 90] are equal to 44.770 and 44.424 kW, respectively, while the losses for the light-case configurations of [ROM 10] and [CHI 90] are equal to 7.674 and 8.087 kW, respectively. These values are larger than the losses corresponding to the configuration of Figure 2.4 for both load conditions: 44.210 and 7.177 kW, respectively. Network (d): 83-bus 96-line system

The 83-bus 96-line system represents a real distribution network that consists of 11 feeders with 13 tie switches [SU 03]. The substations have constant voltage Vs=11.4 kV. All the other 83 buses are represented by PQ nodes as indicated in [SU 03]. The network contains 13 fundamental cycles and 136 distinct simple cycles. The obtained minimum-losses radial configuration is shown in Figure 2.5, in which the 13 open lines are 7, 13, 34, 39, 42, 55, 62, 72, 83, 86, 89, 90 and 92. After the first iteration of the two-iteration procedure, lines 63 and 84 are open instead of lines 55 and 62.

Figure 2.5. Optimal configuration of the 83-bus system

Mixed Integer Linear Programming Models

61

The same minimum-losses configuration has been obtained also in [RAJ 08]. In the configuration reported in [SU 03] and also in [CHI 05, SU 05, WU 10], line 41 is open instead of line 42, resulting in a network losses value (calculated by using the PF code) equal to 471.078 MW. The system analyzed in [AHU 10] has the same structure of the system here analyzed but significantly differs in the values of several loads. The configuration obtained in [AHU 10], if applied to the system here analyzed, corresponds to losses equal to 472.321 kW. Both these loss values are larger than the one corresponding to the configuration of Figure 2.5 equal to 469.878 kW. Network (e): 135-bus 156-line system

The 135-bus 158-line system represents a real distribution network with eight feeders and 21 tie switches [MAN 00]. The substations have constant voltage Vs=13.8 kV. All the other 135 buses are represented by PQ nodes as indicated in [MAN 00]. The network contains 21 fundamental cycles and 65,955 distinct simple cycles. The minimum-losses radial configuration is shown in Figure 2.6, in which 21 lines are open: 7, 35, 51, 90, 96, 106, 118, 126, 135, 137, 138, 141, 142, 144, 145, 146, 147, 148, 150, 151 and 155. The same configuration is also obtained at the end of the first iteration of the two-iteration procedure.

Figure 2.6. Optimal configuration of the 135-bus system

62

From Smart Grids to Smart Cities

The obtained configuration corresponds to the solution presented in [CAR 08]. In the best solution obtained in [MAN 00], lines 136, 139, 143, 149, 152, 154 and 156 are open instead of lines 7, 35, 90, 96, 118, 126 and 135, resulting in a power losses value equal to 285.737 kW. Also, [CEB 10] and [GUI 10] present different configurations. In [CEB 10], lines 139, 53, 84, 128 and 156 are open instead of lines 35, 142, 146, 155 and 135, resulting in a losses value equal to 280.195 kW. In [GUI 10], lines 38, 156, 53 and 128 are open instead of lines 35, 135, 142 and 155, corresponding to a losses value equal to 280.441 kW for the same load condition of our calculation. These values are larger than the one corresponding to the configuration of Figure 2.6 equal to 280.166 kW. 2.3.3. Comparison between the MILP solutions for the test networks with the corresponding PF calculation results relevant to the obtained optimal network configurations

This section compares the MILP solutions for the test networks described in section V with the corresponding PF calculation results relevant to the obtained optimal network configurations. The PF results are shown in Table 2.2. The percentage differences (with sign) between the MILP solutions and the corresponding PF results are shown in Tables 2.3 and 2.4. For the adopted number of zbre = zbim = 31, there is an appreciable difference only for the very small losses value corresponding to the light-loaded operating conditions of the 69-bus system. Tables 2.3 and 2.4 report the total number of variables, the number of binary variables, the number of constraints, the final relative objective gap (i.e. the difference between the best upper bound of the solution and the best solution value divided by the best solution value) and the total computer time spent. They also compare the results obtained by the adoption of the direct solution of the MILP model (single iteration) and those obtained by applying the two-iteration procedure. When the number of variables and constraints, which increases the computational effort required by the adoption of the single-iteration procedure, is very high and for the case of the 135-bus system, the model is not solved to optimality within the 2 h time limit. Tables 2.3 and 2.4 also compare the computational effort required for the solution of the MILP model with and without cycle-opening constraints. The number of cycles has been limited to those obtained with a maximum of five combinations of the fundamental cycles.

Mixed Integer Linear Programming Models

69-bus system

15-bus system Q constant Losses (kW)

63

32-bus

83-bus 135-bus

C

system Normal Heavy

constant

load

Light

system system

load

load

44.21

7.177 469.878 280.166

466.127

468.33 139.552 30.093

Vmin (p.u.)

0.9716

0.9707 0.9378 0.9452 0.9335 0.9734 0.9532 0.9589

(at the end of

(20)

Min. bus voltage (20)

(31)

(61)

(61)

(61)

(71)

(105)

116.14

140.3

57.16

(1 and

(1 and

(1 and (15 and (39 and

2)

2)

2)

16)

40)

line no.) Max. line current Imax (A) (in line no.) Total load active power PL (MW) Load reactive power QL (Mvar) Slack bus active power Ps (MW)

355.76

357.43 207.13

258.31 145.57

(16)

(16)

(1)

28.7

28.7

3.715

1.108

1.329

0.554

28.35

18.313

5.9

17.3

2.3

0.898

1.078

0.449

20.7

7.933

29.166

29.168

3.855

1.138

1.374

0.561

28.82

18.593

6.445

6.873

2.402

0.931

1.126

0.457

21.948

8.544

Slack bus reactive power Qs (Mvar) Table 2.2. PF results corresponding to the obtained minimum-losses configuration

15-bus system Q constant Iterations Losses

One

Two

C constant One

0.142% −0.033% 0.228%

Bus Vmin 0.031%

0.031%

0.031%

83-bus system

135-bus system

Two

One

Two

Two

0.007%

0.065%

−0.260%

0.263%

0.031%

0.021%

0.042%

0.021%

Line Imax −0.031% −0.143% 0.025% −0.115% −0.054%

−0.190%

−0.124%

Total load −0.003% −0.070% 0.024% −0.059% 0.035% PL

−0.102%

−0.076%

Total load −0.339% −0.390% −0.121% −0.133% −0.251% QL

−0.382%

−0.403%

Slack bus −0.003% −0.072% 0.027% −0.058% 0.031% Ps

−0.111%

−0.081%

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From Smart Grids to Smart Cities

Slack bus −0.310% −0.372% −0.306% −0.364% −0.251% Qs No. of variables

536 (172 binary)

−0.392%

−0.386% 3,296 (696 binary)

3,356 (1092 binary)

Without opening-cycles radiality constraints No. of constraints

15,591 (1,036 equality)

2,571 (166 equality)

Relative objective gap

0

0 and 0

0

CPU time (s)

1.11

0.78 + 0.84

1.13

0 and 0

0

23,179 (1684 equality) 9.89E-5 and 9.97E-5

0 and 0

0.64 + 0.86 419.31 22.56 + 21.58 852.05 + 916.95

With opening-cycles radiality constraints No. of constraints

15,699 (1,036 equality)

2,578 (166 equality)

Relative objective gap

0

4.41E-5 and 0

0

CPU time (s)

1.17

0.91 + 0.52

1.02

0 and 0

6.09E-5

1.05 + 0.41 178.48

30,557 (1684 equality)

9.28E-5 and 0

6.89E-5 and 5.59E-5

5.94 + 4.86 107.89 + 99.81

Table 2.3. Percent difference between the MILP solutions and the corresponding PF result, number of variables, number of constraints, final relative objective gap and CPU time

69-bus system 32-bus system Iterations One Losses 1.276% Bus Vmin 0.096% Line Imax −0.140% Total −0.162% load PL Total −0.174% load QL Slack bus −0.182% Ps

Normal load Heavy load Two One Two One Two 0.894% 1.941% 1.532% 1.240% 0.683% 0.107% 0.085% 0.095% 0.107% 0.139% −0.295% −0.095% −0.224% −0.157% −0.335%

Light load One Two 10.376% 10.286% 0.031% 0.031% 0.308% 0.278%

−0.296% −0.090% −0.181% −0.075% −0.301%

0.025%

−0.004%

−0.348% −0.223% −0.334% −0.278% −0.464% −0.042% −0.071% −0.337% −0.088% −0.264% −0.146% −0.364%

0.024%

−0.007%

Mixed Integer Linear Programming Models

65

Slack bus −0.208% −0.375% −0.215% −0.322% −0.266% −0.444% −0.043% −0.073% Qs No. of 1,295 (421 binary) 2,738 (902 binary) variables Without opening-cycles radiality constraints No. of constrain 6,010 (400 equality) 12,189 (844 equality) ts Final 0 and 1.10 0 and relative 1.24E-4 0 and 0 4.88E-5 0 0 and 0 3.33E-8 E-7 4.65E-7 objective gap 27.73 + 24.50 + 22.92 + 16.62 + CPU 264.74 111.83 151.03 28.08 25.61 23.83 21.47 15.81 time (s) With opening-cycles radiality constraints No. of 6,036 (400 equality) 12,215 (844 equality) constraints Final relative 0 0 and 0 4.78E-5 0 and 0 0 0 and 0 6.47E-5 0 and 0 objective gap 24.84 + 24.05 + 4.59 + 10.73 + CPU time 169.63 226.67 110.30 27.78 4.5 7.87 6.78 8.73 (s) Table 2.4. Percent difference between the MILP solutions and the corresponding PF results, number of variables, number of constraints, final relative objective gap and CPU time

The limited differences between MILP solutions and PF results are due to the approximations introduced by the PLF representation, while the adoption of the proposed two-iteration procedure does not appear to affect the accuracy. The use of the two-iteration procedure permits to deal with the presence of PV nodes and to limit the required computational times that appear reasonable for all the tests. Moreover, in eight out of 10 tests, the configuration obtained at the end of the first of the two iterations corresponds to the final one. 2.4. MILP model of the VVO problem

As already mentioned, the VVO aim can be summarized as the detection of the most efficient operating condition of voltage control apparatus and reactive power resources in a given instant with the knowledge of both load consumptions and generators active power productions. The control variables to be optimized are the

66

From Smart Grids to Smart Cities

position of on-load tap changers (LTCs), switching status of the capacitor banks and EG reactive power compensation levels. The optimization model is presented in four parts: (i) objective function to be minimized, (ii) branch equations that represent the voltage differences between the two terminals of each line or transformer, (iii) bus equations that describe the power balance at each node and (iv) constraints relevant to bus voltages and branch currents. 2.4.1. Objective function

The two main objectives considered here are the minimization of the active power from the substation and the operation with bus voltages near to the rated value. The active power value at the substation is assumed positive if it is imported from the transmission grid. It could also be negative and, in this condition, the objective is the maximization of the power exported by the distribution network. In order to combine the two objectives, a specified percentage of bus voltage difference from the rated value is admitted without penalization. If a bus voltage deviation is larger than this percentage, a penalization factor is added to the objective function. The penalization increases with the square of the voltage deviation. The square increase of the penalization is represented by a PLF. With respect to the minimization of the network losses, the adoption of the active power minimization from the substation avoids the PLFs related to the square of branch currents. The active power minimization from the substation is equivalent to loss minimization if active and reactive powers injected or absorbed at each bus are independent of voltage, while some different results are obtained if the voltage dependence is taken into consideration. In order to always guarantee the existence of a feasible solution, i.e. an operating condition of the network that complies with all the constraints, an additional binary variable is associated with each load and generator that allows disconnection. In the objective function, these load or generator shedding decisions are hampered by large penalties. The shedding decision variables indicate the extent to which the input data should be changed in order to avoid model infeasibility. The use of these shedding decisions as preventive correction means to improve the robustness of the system against contingencies is beyond the goals of the proposed model. The considered objective to be minimized is

∑V

s

b∈Bs

N

N

k =1

k =1

I bre + wmin ∑ χ kmin + wmax ∑ χ kmax + ∑ wkL ukL + k ∈K L

∑

k ∈K EG

wkEG ukEG

[2.38]

Mixed Integer Linear Programming Models

67

where Bs is the set of branches connected to the slack bus, i.e. is the set of the initial branches of the feeders connected to the substation; Ib indicates the current in branch b; χ kmin and χ kmax are the square of the violations of the minimum and maximum voltage bounds at node k, respectively, while wmin and wmax are the weights that penalize the corresponding violations; KL and KEG are the set of nodes where a load or EG is connected, respectively; ukL and ukEG are the binary variables that allow to disconnect a load or generator at node k, respectively, and wkL and wkEG are the chosen coefficients that severely penalize each disconnection. For each node k, χ kmin and χ kmax are provided by a PLF of the square of the voltage violation. The constraints that define the PLF are the following: − χ kmin + λiΔV ΔVkmin ≤ −Λ iΔV

and − χ kmax + λiΔV ΔVkmax ≤ −Λ iΔV

∀i = 1. .. zΔV − 1 [2.39]

where ΔVkmin and ΔVkmax are the non-negative continuous variables that correspond to the absolute value of the voltage violations of the minimum or maximum limits at node k (i.e. Vkmin and Vkmax ), respectively; λiΔV is the slope Λ iΔV is the ordinate intercept of PLF interval i and zΔV is the number of PLF breakpoints. Slope λiΔV and ordinate intercept Λ iΔV are calculated as:

λiΔV = ΔVi +1 + ΔVi , Λ iΔV = ΔVi 2 − λiΔV ΔVi ∀i = 1. .. zΔV − 1.

[2.40]

2.4.2. Branch equations

If branch b is a line connected to nodes h and k, three current phasors are introduced: I b represents the current flowing through the longitudinal impedance of the one-phase Π equivalent circuit, while I bsh,h and I bsh,k represent the currents flowing in the shunt admittance connected to nodes h and k, respectively. If branch b is a transformer, I b represents the current flowing in the short-circuit impedance and I bsh,h is the current of the magnetizing branch, both referred to primary side h. The current at the secondary side k is obtained by dividing I b by the turn ratio that takes into account the tap position. If branch b is a line, it is represented by the usual one-phase Π equivalent circuit with resistance Rb, reactance Xb and two equal susceptances Bb that take into account line shunt capacitance Cb. If it is a transformer, Rb and Xb represent the summation of

68

From Smart Grids to Smart Cities

the resistance and leakage reactance of the windings referred to the primary side, respectively, and Bb represents the magnetizing branch. The real and imaginary parts of current I bsh of each branch b connected to bus h are defined by: I bsh,, h re + Bb Vhim = 0 and

I bsh,, him − Bb Vhre = 0

[2.41]

If branch b is a line or a fixed-ratio transformer, the equations of the differences between voltage phasors at the terminals h and k are: Vhre − Vkre − Rb I bre + X b I bim = 0

and

Vhim − Vkim − X b I bre − Rb I bim = 0 [2.42]

If branch b is a transformer equipped with an LTC, for each tap position t, the following constraints are applied Vhre − rb , t Vkre − Rb I bre, t + X b I bim, t + Δvbre, t = 0 Vhim − rb, t Vkim − X b I bre, t − Rb I bim, t + Δvbim. t = 0

[2.43]

re

where I b , t and I bim, t define the phasor the current at the primary side h when the transformer b works at tap position t corresponding to the turn ratio rb, t. Each tap position t is associated with a binary variable ub, t that is equal to 1 if t is the selected tap position and 0 for other positions. If t is the selected tap position, i.e. if ub, t = 1, auxiliary variables Δvbre, t and Δvbim.t should be null, while their value should adapt to the voltage differences between the transformer terminals if ub, t = 0. If I bre, t and I bim, t are forced to be null if ub, t = 0,

Ib

could be defined as the summation of all I b , t . The relevant set of constraints is: Δvbre, t + BN ub , t ≤ BN Δvbim, t + BN ub , t ≤ BN − I bmax ub, t ≤ I bre, t ≤ I bmax ub , t nb ,t

∑u

b, t

t =1

and − Δvbre, t + BN ub , t ≤ BN ⎫ ⎪ and − Δvbim, t + BN ub , t ≤ BN ⎬ ∀t = 1...nb ,t and − I bmax ub, t ≤ I bim, t ≤ I bmax ub , t ⎪⎭ [2.44]

nb , t

nb , t

t =1

t =1

= 1 , I bre − ∑ I bre, t = 0 and I bim − ∑ I bim, t = 0

where nb, t is the number of tap positions, I bmax is the maximum feasible value of

I b and the value of BN is adequately large.

Mixed Integer Linear Programming Models

69

2.4.3. Bus equations

For each bus, Kirchhoff’s current law for the Cartesian coordinates of the phasors is used in the model. The substation is represented as slack bus s and the magnitude of the voltage phasor of the slack bus is assumed equal to the rated value. At slack bus s, the voltage is Vs = Vs e j 0 . At each node k, three current variables are defined, namely I L,k , I C,k and I EG,k , which indicate the current requested by the load, drawn by the capacitor bank and injected by the generator connected to node k, respectively. The current equilibrium is defined by

∑I

re b

∑I

im b

b ∈ Bk+

b ∈ Bk+

∑I

−

b ∈ Bk−

−

re b

∑I

b∈ Bk−

+

∑I

sh, re b, k

re + I L,rek + I C,re k − I EG, k = 0

b ∈ Bk im b

+

∑I

sh, im b, k

[2.45]

im + I L,imk + I C,imk − I EG, k = 0

b ∈ Bk

where Bk is the set of lines b connected to node k (where Bk+ is the set of lines leaving k and Bk− is the set of lines entering k). If k is connected to the secondary side of an LTC transformer, the corresponding variables I bre and I bim in the second summation are replaced by

nt

∑r

b, t

I bre, t and

t =1

nt

∑r

b, t

I bim, t , respectively.

t =1

2.4.3.1. Load model

Cartesian coordinates I L,rek and I L,imk of the load current are defined by the following set of constraints: I L,rek − I L,Z, kre − I L,I, rek − I L,P, kre + ΔI L,rek = 0 − BN ukL ≤ ΔI L,rek ≤ BN ukL I

min, re L, k

(1 − uL, k ) ≤ I

re L, k

≤I

im and I L,imk − I L,Z, kim − I L,I, imk − I L,P, im k + ΔI L, k = 0

[2.46]

and − BN ukL ≤ ΔI L,imk ≤ BN ukL max, re L, k

(1 − uL , k ) and I

min, im L, k

(1 − uL, k ) ≤ I

im L, k

≤I

max, im L, k

(1 − uL, k )

where I L,mink and I L,maxk are the lower and upper bounds of load current I L, k , respectively. Binary variable ukL , already introduced in [2.38], causes the disconnection of the load at bus k when equal to 1. Indeed, auxiliary variables ΔI L,rek and ΔI L.imk become null if ukL = 0, while they allow IL, k to be zero if ukL = 1.

70

From Smart Grids to Smart Cities

The ZIP load model could be represented as the weighted summation of three parts, namely constant power, constant current and constant impedance: ⎡ ⎛ V ⎞2 ⎤ ⎛V ⎞ PL = P ⎢ aP ⎜ ⎟ + bP ⎜ ⎟ + cP ⎥ ⎢⎣ ⎝ V0 ⎠ ⎥⎦ ⎝ V0 ⎠ ⎡ ⎛ V ⎞2 ⎤ ⎛V ⎞ QL = QL0 ⎢ aQ ⎜ ⎟ + bQ ⎜ ⎟ + cQ ⎥ ⎢⎣ ⎝ V0 ⎠ ⎥⎦ ⎝ V0 ⎠ 0 L

[2.47]

where aP + bP + cP = aQ + bQ + cQ = 1 , and PL0 and QL0 are the real and reactive power consumed at a rated voltage V0, respectively. Therefore, current I L, k is the summation of three parts, each one related to an element of the ZIP load model: I L,Z k constant impedance, I L,I k constant current and I L,P k constant power. Following the same approach of section 2.2.3, the currents of the three components of the ZIP load model are expressed by the following linear constraints: – Constant impedance: I L,Z, kre − GL, k Vkre + BL, k Vkim = 0 and I L,Z, kim − GL, k Vkim − BL, k Vkre = 0

[2.48]

where GL, k = aP, k PL,0 k and BL, k = −aQ, k QL,0 k . – Constant current: I L,I, rek + InkI sin(∠InkI )

Vkim V im = InkI,re and I L,I,imk − InkI cos(∠InkI ) k = InkI, im [2.49] Vs Vs

where InkI, re = bP, k PL,0 k and InkI, im = −bQ , k QL,0 k . This linear approximation is based on the assumption that the phase of Vk is small so that it can be approximated by the ratio Vkim / Vs . – Constant power: I L,P, kre + InkP, re

Vkre V im V im V re + InkP, im k = 2 InkP, re and I L,P, kim − InkP, re k + InkP, im k = 2 InkP, im Vs Vs Vs Vs

[2.50]

where InkP, re = cP, k PL,0 k and InkP, im = −cQ , k QL,0 k . This linear approximation is based on the assumption that the difference between Vk and Vs is small.

Mixed Integer Linear Programming Models

71

2.4.3.2. Capacitor banks

The variable capacitor bank at node k is represented by the following constraints: im I kC,, swre ωCk , sw + Vkim + ΔvkC,, swre = 0 and I kC,, swim ωCk , sw − Vkre + ΔvkC,, sw =0 ⎫ ⎪ C, re C C, re C Δvk , sw + BN uk , sw ≤ BN and − Δvk , sw + BN uk , sw ≤ BN ⎪ ⎬ ∀sw = 1...nC,k C, im C C, im C Δvk , sw + BN uk , sw ≤ BN and − Δvk , sw + BN uk , sw ≤ BN ⎪ re C min, im C C, im max, im C ⎪ ≤ ≤ u and I u I I u I C,min,k re ukC, sw ≤ I kC,, swre ≤ I C,max, k k , sw C, k k , sw k , sw C, k k , sw ⎭ nC, k

∑u

sw = 1

C k , sw

nC, k

nC, k

sw = 1

sw = 1

≤ 1 , I C,re k − ∑ I kC,, swre = 0 and I C,imk − ∑ I kC,, swim = 0

[2.51] where nC,k is the number of switching positions (other than the complete disconnection), ωCk , sw is the susceptance of the bank corresponding to switching position sw, I C,mink and I C,maxk are the lower and upper bounds of capacitor current I C, k , respectively, ukC, sw is the binary variable whose value when equal to 1 indicates that im are auxiliary switching position sw is selected otherwise is null, ΔvkC,,swre and ΔvkC,,sw

variables that are null if ukC, sw = 1 and slackly bounded by BN if ukC, sw = 0 . At most only one switching position may be selected and if all ukC, sw are null, then the capacitor is completely disconnected from the node. 2.4.3.3. Embedded generators

Reactive power output QkEG of the generator at node k is discretized in nEG,

k

different compensation levels, while active output PkEG is assumed fixed. QkEG , g is the reactive output corresponding to the compensation level g. The linear model of the generator at node k is: ⎫ ⎪ ⎪ im re ⎪ EG, im EG, re Vk EG, im Vk EG, im EG, im + Ink , g + ΔI k , g = 2 Ink , g I k , g − Ink ⎪⎪ Vs Vs ⎬ ∀g = 1...nEG, k EG, re EG EG, re EG ⎪ ΔI k , g + BN uk , g ≤ BN and − ΔI k , sw + BN uk , g ≤ BN [2.52] ⎪ EG, im EG EG, im EG ⎪ ΔI k , g + BN uk , g ≤ BN and − ΔI k , g + BN uk , g ≤ BN min, re EG EG, re max, re EG min, im EG EG, im max, im EG ⎪ ≤ I EG, ≤ I EG, I EG, k uk , g ≤ I k , g k uk , g and I EG, k uk , g ≤ I k , g k uk , g ⎪ ⎭ re + InkEG, re I kEG, ,g

im Vkre im Vk re + InkEG, + ΔI kEG, = 2 InkEG, re ,g ,g Vs Vs

nEG, k

nEG , k

nEG , k

g =1

g =1

g =1

re ∑ ukEG, g + ukEG = 1 , I EG, k −

im ∑ I kEG,, g re = 0 and I EG, k −

∑I

EG, im k, g

=0

72

From Smart Grids to Smart Cities

min max where InkEG, re = PkEG and InkEG, im = −QkEG , g , and I EG, k and I EG, k are the lower and

upper bounds of I EG, k , respectively, ukEG,g is the binary variable whose value when equal to 1 indicates that compensation level g is selected otherwise it is null, re im ΔI kEG, and ΔI kEG, are auxiliary variables that are null if ukEG,g = 1 and slackly ,g ,g bounded by BN if ukEG,g = 0 . If its value is equal to 1, binary variable ukEG allows the complete EG disconnection at node k (i.e. all ukEG,g can be null). EG down = 0 and Assuming that nEG, k reactive output levels are available below Qk down up EG up nEG, above (i.e. nEG, k = nEG, have been k + nEG, k + 1 ), two definitions of Qk , g k

implemented: EG down EG – QkEG is the variation of reactive power for , g = ( g − nEG, k − 1) ΔQk , where ΔQk

each step; down down EG ⎡ ⎤ EG , where Δpf kEG – QkEG , g = sgn( g − nEG, k − 1) tan ⎣arccos(1 − g − nEG, k − 1 Δpf k ) ⎦ Pk

is the variation of the power factor for each step. 2.4.4. Branch and node constraints

A regular polygon with z I sides is adopted for the linear representation of the maximum current limit in branch b. Each of the vertices of the polygon has coordinates

(I

re b

cos ⎡⎣( i − 1 2 ) α ⎤⎦ , I bim sin ⎡⎣( i − 1 2 ) α ⎤⎦

)

with i = 1…

zI

and

α = 2π / z I . As the polygon should be inscribed in the circle with equation I bre 2 + I bim 2 = I bmax 2 , then the circle inscribed in the polygon has radius equal to I bmax cos(α 2) . The set of linear constraints that represent the polygon is given by the equations of lines tangent to the inscribed circle. The model enforces the phasor coordinates to be inside all the linear constraints, i.e. cos(i α ) I bre + sin(i α ) I bim ≤ I bmax cos(a / 2) ∀i = 1...z I

[2.53]

A similar model is adopted for violations ΔVkmin and ΔVkmax of the voltage RMS value at bus k with respect to Vkmin or Vkmax , respectively. Assuming that the maximum voltage phase difference between a bus and the slack bus is lower

Mixed Integer Linear Programming Models

73

π

than π / 18 (i.e. 10°), angle α is now defined as α =

, where zV is the 9( zV − 1) odd number of sides of the polygon considered in the model. The set of constraints that define ΔVkmax is ⎡ ⎤ z −1 cos ⎢(i − V − 1) α ⎥ Vkre 2 ⎣ ⎦ ⎡ ⎤ z −1 + sin ⎢(i − V − 1) α ⎥ Vkim − ΔVkmax 2 ⎣ ⎦ max ≤ Vk cos(α 2) ∀i = 1...zV

[2.54]

For the case of ΔVkmin , the radius of the inscribed circle is Vkmin . The model forces the voltage phasor to be larger than at least one of the linear constraints defined by the polygon sides by means of additional binary variable wk ,i : ⎡ ⎤ ⎡ ⎤ z −1 z −1 cos ⎢(i − V − 1) α ⎥ Vkre + sin ⎢ (i − V − 1) α ⎥ Vkim + BN wk ,i 2 2 ⎣ ⎦ ⎣ ⎦ min k

+ ΔV

min k

≥V

∀i = 1...zV

and

zV

∑w

k ,i

[2.55]

≤ zV − 1

i =1

The results presented in the next section have been obtained with z I = 23 and

zV = 5. In order to enforce that the power factor at branch b connected to slack bus s is higher than pfbmin , the following model is adopted: Pb − Vs I bre = 0 Pb − ΔPb+ − Pb = 0 ΔPb+ + BN wbP ≤ BN − Pb + ΔPb− − Pb = 0 ΔPb− − BN wbP ≤ 0

and and and and and

Qb − tan ⎡⎣ arccos( pfbmin ) ⎤⎦ Pb ≤ 0

⎫ Qb + Vs I bim = 0 ⎪ + Qb − ΔQb − Qb = 0 ⎪ ΔQb+ + BN wbQ ≤ BN ⎪⎪ − Qb + ΔQb− − Qb = 0 ⎬ ⎪ ΔQb− − BN wbQ ≤ 0 ⎪ ⎪ ⎪⎭

∀b ∈ Bs

[2.56]

74

From Smart Grids to Smart Cities

where ΔPb− , ΔPb+ , ΔQb− and ΔQb+ are non-negative continuous variables, while wbP and wbQ are binary variables, which are introduced for the definition of Pb and Qb , i.e. the absolute value of active and reactive powers Pb and Qb .

2.5. Test results obtained by the VVO MILP model

The MILP model has been tested by using the Cplex V12.4 MIP solver on two 3.07 GHz Intel 6 core processors with 48 GB RAM, running on 64-bit Windows operating system. For the test, reference should be made to three different test systems: – TS1 the 69 node test system with line and load data presented in [BAR 89a] to which five capacitor banks and two LTC transformers are added as described in [BAL 90]; – TS2 a 138-node 10-capacitor 4-LTC system obtained by making two copies of system 1 as in [BAL 90], both connected to the common substation; – TS3 a balanced version of the IEEE 34 node test feeder [KER 91]. For all the test systems, the behavior of the MILP model has been tested with and without assuming the presence of EG. 2.5.1. TS1

The 69-node 5-capacitor 2-LTC system has the radial configuration shown in Figure 2.7 and it is fed from a substation with voltage Vs = 12.66 ej0 kV. All the loads are represented by a constant power model. Five capacitors are connected to node 11 (600 kvar), node 18 (600 kvar), node 47 (600 kvar), node 52 (900 kvar) and node 69 (600 kvar) with step increments of 300 kvar. The two LTC transformers are located before node 8 (LTC at the secondary side with ±5 tap increments of 0.5%) and before node 47 (LTC at the secondary side with ±10 tap increments of 0.5%). The circuit impedances of the two transformers are taken into account by the parameters of branch 7-8 and 46-47, respectively. The lower and upper bus voltage constraints are 0.95 and 1.05 p.u. and the minimum power factor limit at the substation is 0.9, while the current branch limits are set large enough so they are never binding the solution.

Mixed Integer Linear Programming Models

47

75

52

Figure 2.7. Test system TS1

Two load levels are considered, one corresponding to the data in [BAR 89a] (medium load) and the other obtained by multiplying each load demand by 1.5 (high load). Both calculations have been repeated by adding two generators, one at node 22 of 2 MW and the other at node 32 of 3 MW. The first has the possibility to control the reactive output in ±4 discrete levels with a minimum power factor limit of 0.9 and the other has the possibility to control the reactive output in ±8 discrete levels with a minimum power factor limit of 0.8. When the two generators work, capacitors at nodes 11 and 18 are disconnected. Table 2.5 shows the optimal values of the control variables calculated by the MILP model, the number of variables (total and the one of the binary variables), the number of constraints, the final relative objective gap (i.e. the difference between the best upper bound of the solution and the best solution value divided by the best solution value) and the computer time spent to obtain the solution. In parenthesis, Table 2.5 also indicates the percentage difference between the MILP results and those obtained by the corresponding PF calculation. These differences provide an indication of the influence of the adopted linear approximation on the accuracy of the results provided by the MILP model. Without EG and without regulation (i.e. with all capacitors disconnected and LTC taps in the 0 position), the system at medium-load level has losses equal to 225 kW and minimum voltage equal to 0.91 p.u. (node 54). Therefore, a feasible solution is achieved with a 38.36% loss reduction. For the high-load condition, the achieved loss reduction is 38.21% (as without regulation losses would be 561 kW), with a solution that also satisfies the voltage requirements, while without regulation, the minimum bus voltage would be equal to 0.86 p.u. (node 54). When EG is present, the system without regulation has losses equal to 354 kW and minimum voltage equal to 0.92 p.u. (node 54) at medium-load level and the corresponding values of 610 kW and 0.87 p.u. (node 54) at high–load level. The achieved loss reduction, thanks to the regulation and the reactive compensation

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capability of the generators, is 19.9 and 25.5% at medium and high load, respectively. Moreover, the obtained operating conditions meet the voltage limits. For this test system, the number of PF calculations that would be required by an exhaustive search procedure is 74.84×103 without EG and 1.27×106 with the considered two generators. Being a combinatorial problem, the number of PF rapidly increases with the number of control variables. However, as shown by Table 2.5, there is a limited difference between CPU times required by the solution of the proposed MILP models with and without EG. Without EG

With EG

Medium load

High load

Medium load

High load

Steps of capacitors at nodes 11,18,69,47,52

1, 1, 0, 1, 3

2, 1, 0, 2, 3

–, –, 2, 2, 3

–, –, 2, 2, 3

LTC tap at nodes 8 and 47

−5 and −10

−5 and −10

+2 and −4

−4, −10

+1, 0

0, +5

Q levels of EG at nodes 22 and 32 Losses

Min. voltage

Max. voltage

Max. current

138.696 kW (0.03%)

346.34 kW (0.02%)

283.195 kW (−0.18%)

454.492 kW (−0.096%)

0.9815 p.u. (0.0006%)

0.9523 p.u. (0.005%)

0.9531 (0.007%)

0.9566 (0.001%)

at node 46

at node 46

at node 54

at node 46

1.0243 p.u. (−0.001%)

1 p.u. (0%)

1.0483 (−0.013%)

1.0496 (−0.02%)

at node 47

at node 0

at node 22

at node 22

184.64 A (0.02%)

289.26 A (−0.005%)

130.90 A (−0.073%) 201.36 A (0.068%)

Mixed Integer Linear Programming Models

in lines 0–1 and in lines 0–1 and 1–2 1–2

in line 28–32

in line 2–2e

Tot. active load

3802.5 kW (0.006%)

5704.8 kW (0.026%)

3801.7 kW (−0.013%)

5703.5 kW (0.004%)

Tot. reactive load

2696.2 kvar (0.06%)

4035.9 kvar (−0.15%)

2688.7 kvar (−0.22%)

4036.9 kvar (−0.123%)

Tot. active gen.

4993.9 kW (−0.122%)

4993.3 kW (−0.134%)

Tot. reactive gen.

449.95 kvar (−1.28%)

1651.2 kvar (−0.524%)

77

P at slack bus

3941.2 kW (0.009%)

6051.2 kW (0.027)

−909.1 kW (−0.55%)

1164.7 kW (0.56%)

Q at slack bus

926.99 kvar (0.18%)

1901.3 kvar (−0.31%)

363.21 kvar (−0.10%)

535.84 kvar (0.65%)

No. of variables

1220 (200 binary)

1336 (224 binary)

No. of constraints

3684 (656 equality)

3908 (706 equality)

Obj. function

3.94×103

6.05×103

−9.09×102

1.16×103

Relative obj. gap

8.02×10−5

0

9.42×10−5

0

CPU time (s)

4.81

0.83

8.49

2.39

Table 2.5. MILP solutions for TS1 (within parenthesis the percentage deviation with respect to the PF results)

2.5.2. TS2

The same calculations carried out for system TS1 have been repeated for the case of the 138-node double system TS2, fed from a substation with Vs=12.66 ej0 kV as

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From Smart Grids to Smart Cities

TS1. For all the four cases corresponding to those already carried out for system TS1, the expected results are obtained, i.e. the optimization procedure provides the same capacitor switching positions, LTC taps and EG reactive compensation levels corresponding to those reported in Table 2.5 for both the feeders that compose TS2. Table 2.6 reports the value of the losses for the entire system (that should be twice than the corresponding value reported in Table 2.5), the characteristics of the MILP model and solution performance for the four examined cases. For system TS2, the number of PF calculations required for a complete search procedure would be quite high, namely 5.6×109 and 1.62×1012 for the case without EG and with four generators, respectively. However, as shown in Table 2.6, approximately 10 s is enough for the solution of the MILP model. Without EG

Losses

With EG

Medium load

High load

Medium load

High load

277.413 kW (0.036%)

692.732 kW (0.029%)

566.395 kW (−0.18%)

909.012 kW (0.093%)

No. of variables

2431 (399 binary)

2663 (447 binary)

No. of constraints

7354 (1306 equality)

7802 (1406 equality)

Obj. function

7.88×103

1.21×104

−1.82×103

2.33×103

Relative obj. gap

9.69×10−5

0

7.14×10−5

4.2×10−5

CPU time (s)

9.25

6.03

10.19

8.72

Table 2.6. MILP solutions for TS2 (in parenthesis the percentage deviation with respect to the PF results)

2.5.3. TS3

TS3 including the substation has 35 nodes and 34 branches. The radial configuration is shown in Figure 2.8. The data of the balanced system, i.e. the data

Mixed Integer Linear Programming Models

79

of lines and loads, are provided in Tables 2.7 and 2.8. Rb, Xb and Cb, presented in Table 2.7, are the branch parameters. The magnetizing branches of the transformers and regulators are neglected. Parameters PL0 and QL0 in Table 2.8 define the active and reactive power of the loads at rated voltage conditions and the last column defines the parameters aP, bP, cP and aQ, bQ, cQ of [2.47]: Z defines aP = 1, aQ = 1 and the other parameters equal to 0 (constant impedance), I defines bP = 1, bQ = 1 and the other parameters equal to 0 (constant current) and P defines cP = 1, cQ = 1 and the other parameters equal to 0 (constant power). As shown in Figure 2.8, three LTC transformers are connected: a 69/24.9 kV transformer before bus 800 at the substation (LTC at the secondary side with ±12 tap increments of 1.5%), two regulators connected before nodes 850 and 832 (both LTC are at the secondary side with ±16 tap increments of 0.625%). Moreover, there is a 24.9/4.16 kV transformer with fixed ratio feeding bus 888. The slack bus is at the primary side of the substation transformer with voltage Vs = 69 ej0 kV. Two capacitors are connected to nodes 844 and 848 of 300 and 450 kvar, respectively, with the possibility to disconnect them. 848

822

846

820

844 864

818

substation 800

802

806

808

812

814

842 824

850

858

816 0

810

834

890 852

830

856

854

Rb (Ω)

Xb (Ω)

Cb (F)

38.088

0

862

838

Figure 2.8. Test system TS3

Node from Node to

860

888

832

828

840

836

826

1

800

4.761

800

802

0.547322

0.407164 7.98E-09

802

806

0.36700

0.273021 5.35E-09

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From Smart Grids to Smart Cities

806

808

6.837277

5.086399 9.97E-08

808

810

1.231261

0.915962 1.79E-08

808

812

7.955256

5.918087 1.16E-07

812

814

6.306927

4.691859 9.19E-08

814

850

0.002121

3.10005

816

818

0.36276

0.269865 5.29E-09

816

824

2.165951

1.611298 3.16E-08

818

820

10.21455

7.598824 1.49E-07

820

822

2.914806

2.168387 4.25E-08

824

826

0.642785

0.478181 9.37E-09

824

828

0.178198

0.132565 2.6E-09

828

830

4.336145

3.225752 6.32E-08

830

854

0.110313

0.082064 1.61E-09

832

858

1.039487

0.773297 1.52E-08

832

888

11.78019

25.29641

834

860

0.428523

0.318788 6.25E-09

834

842

0.059399

0.044188 8.66E-10

836

840

0.182441

0.135721 2.66E-09

836

862

0.059399

0.044188 8.66E-10

842

844

0.286389

0.213051 4.18E-09

844

846

0.77219

0.574449 1.13E-08

846

848

0.112434

0.083642 1.64E-09

0

0

Mixed Integer Linear Programming Models

850

816

0.065763

0.048923 9.59E-10

852

832

0.002121

3.10005

854

856

4.94923

3.681839 7.22E-08

854

852

7.813122

5.812351 1.14E-07

858

864

0.343667

0.255661 5.01E-09

858

834

1.236777

0.920065 1.8E-08

860

836

0.568536

0.422946 8.29E-09

862

838

1.031001

0.766984 1.5E-08

888

890

2.2402

1.666533 3.27E-08

0

Table 2.7. Data of the branches of system TS3

Node

P0 (kW)

Q0 (kvar) Type of model

802

55

29

P

808

16

8

I

816

5

2

I

818

34

17

Z

820

135

70

P

824

44

22

P

828

7

3

P

830

45

20

Z

832

15

7

Z

834

146

73

Z

81

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From Smart Grids to Smart Cities

836

40

20

I

840

27

21

I

842

9

5

P

844

450

338

Z

846

23

11

P

848

60

48

P

854

4

2

P

858

34

18

P

860

142

91

P

862

28

14

P

890

450

225

I

Table 2.8. Data of the loads of system TS3 (type of load: Z = constant impedance, I = constant current, P = constant power)

As in the previous tests, the lower and upper bus voltage constraints are 0.95 and 1.05 p.u., respectively, the minimum power factor limit at the substation is 0.9 and the current branch limits are not binding. Table 2.9 shows the results obtained for the following three operating conditions without the presence of EG: – one LTC: only the LTC of the substation transformer is operating while those of the two regulators are fixed in the 0 position; – two LTCs: the LTCs of both the substation transformer and of the regulator connected to bus 850 are operating while the LTC of the remaining regulator is fixed in the 0 position; – three LTCs: all the three available LTCs are operating. Without EG, the system without regulation (i.e. with all capacitors disconnected and LTC taps in the 0 position) has losses equal to 233 kW and minimum bus

Mixed Integer Linear Programming Models

83

voltage equal to 0.75 p.u. at node 890. With the action of three LTCs, the calculated operating condition satisfies all the constraints, although losses are increasing due to the increased consumption of voltage-dependent loads. With one or two LTCs, the obtained solution violates the minimum voltage limit at node 890 and the relevant penalties are added to the objective function value. The last column of Table 2.9 shows the results obtained by adding three generators to the configuration with two LTCs: two identical generators of 1 MW are connected to nodes 822 and 856, respectively, and a third generator of 500 kW is connected at node 888. All the generators have the possibility to control the reactive output in ±4 discrete levels with a minimum power factor limit of 0.9. Without EG

With 3 generators and 2 LTCs

1 LTC

2 LTCs

3 LTCs

1, 1

1, 1

0, 1

1, 1

−6, –, –

−3, −12, –

−3, −10, −12

+1, −4, –

Steps of capacitors at nodes 844, 848 LTC tap at nodes 800, 850, 832 Q levels of generators at

−2, +1,+4

nodes 822, 856, 888 Losses

Min. voltage

Max. voltage

199.165 kW

217.816 kW

253.153 kW

93.209 kW

(1.06%)

(1.04%)

(0.67%)

(−0.15%)

0.8932 p.u.

0.9148 p.u.

0.9507 p.u.

0.9501 p.u.

(−0.07%)

(−0.11%)

(−0.1%)

(−0.04%)

at node 890

at node 890

at node 890

at node 890

1.0946 p.u.

1.0503 p.u.

1.0491 p.u.

1.0494 p.u.

(0.0006%)

(−0.04%)

(−0.057%)

(−0.04%)

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From Smart Grids to Smart Cities

at node 800 70.203 A Max. current

(0.56%) in line 888−890

at node 850

at node 832

70.262 A (0.64%) 70.196 A (0.55%) in line 888−890

in line 888−890

at node 822 69.813 A (0.001%) in line 888−890

Tot. active

1718.3 kW

1758.6 kW

1811.9 kW

1786.9 kW

load

(0.41%)

(0.37%)

(0.18%)

(−0.03%)

Tot. reactive

100.9 kvar

1037.5 kvar

load

(−0.32%)

(−0.03%)

1076.7 kvar (0.2%)

1057.8 kvar (−0.14%)

Tot. active

2497.3 kW

gen.

(−0.11%)

Tot. reactive

133.2 kvar

gen.

(−5.75%) 1917.5 kW

1976.4 kW

2065.1 kW

−617.1 kW

(0.48%)

(0.44%)

(0.25%)

(−0.32%)

Q at slack

254.1 kvar

271.06 kvar

629.23 kvar

−11.5 kvar

bus

(−0.13%)

(1.19%)

(0.74%)

(−38.8%)

No. of

664 (119

variables

binary)

P at slack bus

849 (162 binary) 1034 (205 binary) 1002 (197 binary)

No. of

1967 (341

2362 (410

2757 (479

2672 (473

constraints

equality)

equality)

equality)

equality)

Obj. function

8.39×107

5.2×106

2.07×103

−6.17×102

−4.66×10−6

0

9.8×10−5

0

0.06

0.7

8.84

8.18

Relative obj. gap CPU time (s)

Table 2.9. MILP solutions for TS3 (in parenthesis the percentage deviation with respect to the PF results)

Mixed Integer Linear Programming Models

85

As in Tables 2.5 and 2.6, the values in parenthesis indicate the percentage difference between the MILP results and those obtained by the corresponding PF calculations. The discrepancies appear satisfactorily limited. A significant percentage difference is only observed for the very small value of the reactive power absorbed from the slack bus when EG is present. Table 2.9 also shows that the CPU time required by the MILP model solution has a limited increase with the number of control variables. On the contrary, the number of PF calculations required by an exhaustive search procedure rapidly increases: 52 with one LTC, 1.72×103 with two LTCs, 56.63×103 with three LTCs and 1.25×106 with two LTCs and three generators. 2.6. Conclusions

In this chapter, we described an approach able to represent both the minimum power loss problem and the VVO of MV distribution feeders with MILP models. It has been shown that the quality of the obtained results and the relevant computation effort is promising. Indeed, the optimization results show reduced deviations from those obtained by PF calculations for the corresponding optimal set of control variable values. The computation time is limited, and increases moderately with the number of control variables. Moreover, the proposed approach does not require the knowledge of an initial feasible operating condition. The models incorporate the main operating constraints and characteristics of the distribution system taking into account also the load voltage dependence. The formulation of the MILP models presented in this chapter assumes that the network is balanced. The same approach can be applied for the development of three-phase models in order to represent unbalanced distribution networks as shown in [BOR 15], but in this case, the required computational effort increases significantly. It is worth noting, however, that for MV networks composed of three-phase lines and transformers with only three-phase generators and loads connected (typical, e.g. in several European countries), also the balanced model may be considered adequate for online applications, taking into account the uncertainty that always affects the knowledge of both network parameters and system operating conditions. 2.7. Acknowledgments

The research described in this chapter is based on the results obtained in the framework of the research activities supported in part of the Italian Ministry of Economic Development in the framework of CERSE research project SMARTGEN by ENIACJU/CALL 2011-1/296131 E2SG “Energy to Smart Grid”. IBM ILOG

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CPLEX Optimization Studio has been used thanks to the IBM Academic Initiative. EMTP-RV simulation environment has been used in the framework of the Powersys Company Education partnership. Helpful discussions with Prof. Carlo Alberto Nucci are gratefully acknowledged. 2.8. Bibliography [AHU 10] AHUJA A., DAS S., PAHWA A., “An AIS-ACO hybrid approach for multi-objective distribution system reconfiguration”, Studies in Computational Intelligence, vol. 302, no. 3, pp. 19–73, 2010. [AUG 95] AUGUGLIARO A., DUSONCHET L., MANGIONE S., “An efficient greedy approach for minimum loss reconfiguration of distribution networks”, Electric Power Systems Research, vol. 35, no. 3, pp. 167–176, 1995. [BAL 90] BALDICK R., WU F., “Efficient integer optimization algorithms for optimal coordination of capacitors and regulators”, IEEE Transactions on Power Systems, vol. 5, no. 3, pp. 805–812, 1990. [BAR 89a] BARAN M., WU F., “Optimal capacitor placement on radial distribution systems”, IEEE Transactions on Power Delivery, vol. 4, no. 1, pp. 725–734, 1989. [BAR 89b] BARAN M., WU F., “Network reconfiguration in distribution systems for loss reduction and load balancing”, IEEE Transactions on Power Delivery, vol. 4, no. 2, pp. 1401–1407, 1989. [BOR 12] BORGHETTI A., “A mixed-integer linear programming approach for the computation of the minimum-losses radial configuration of electrical distribution networks”, IEEE Transactions on Power Systems, vol. 27, no. 3, pp. 1264–1273, 2012. [BOR 13] BORGHETTI A., “Using mixed integer programming for the volt/var optimization in distribution feeders”, Electric Power Systems Research, vol. 98, pp. 39–50, 2013. [BOR 15] BORGHETTI A., NAPOLITANO F., NUCCI C.A., “Volt/var optimization of unbalanced distribution feeders via mixed integer linear programming”, International Journal of Electrical Power & Energy Systems, 72, pp. 40–47, 2015. [CAR 08] CARRENO E.M., ROMERO R., PADILHA-FELTRIN A., “An efficient codification to solve distribution network reconfiguration for loss reduction problem”, IEEE Transactions on Power Systems, vol. 23, no. 4, pp. 1542–1551, 2008. [CEB 10] CEBRIAN J.C., KAGAN N., “Reconfiguration of distribution networks to minimize loss and disruption costs using genetic algorithms”, Electric Power Systems Research, vol. 80, no. 1, pp. 53–62, 2010. [CHA 94] CHANG H.-C., KUO C.-C., “Network reconfiguration in distribution systems using simulated annealing”, Electric Power Systems Research, vol. 29, no. 3, pp. 227–238, 1994.

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[CHI 90] CHIANG H.-D., JEAN-JUMEAU R., “Optimal network reconfigurations in distribution systems. II. Solution algorithms and numerical results”, IEEE Transactions on Power Delivery, vol. 5, no. 3, pp. 1568–1574, 1990. [CHI 05] CHIOU J., CHANG C., SU C., “Variable scaling hybrid disfferential evolution for solving network reconfiguration of distribution systems”, IEEE Tansactions on Power Systems, vol. 20, no. 2, pp. 668–674, 2005. [CIN 88] CINVALAR S., GRAINGER J.J., YIN H. et al., “Distribution feeder reconfiguration for loss reduction”, IEEE Transactions on Power Delivery, vol. 3, no. 3, pp. 1217–1223, 1988. [COF 14] COFFRIN C., VAN HENTENRYCK P., “A linear-programming approximation of AC power flows”, INFORMS Journal on Computing, vol. 26, no. 4, pp. 718–734, 2014. [DIE 10] DIESTEL R., Graph Theory, 4th ed., Springer-Verlag, Heidelberg, 2010. [FAN 96] FAN J.-Y., ZHANG, L., MCDONALD J.D., “Distribution network reconfiguration: single loop optimization”, IEEE Transactions on Power Systems, vol. 11, no. 3, pp. 1643– 1647, 1996. [FER 14] FERREIRA R.S., BORGES C.L.T., PEREIRA M.V.F., “A flexible mixed-integer linear programming approach to the AC optimal power flow in distribution systems”, IEEE Transactions on Power Systems, vol. 29, no. 5, pp. 2447–2459, 2014. [FRA 13a] FRANCO J.F., RIDER M.J., LAVORATO M., et al., “A mixed-integer LP model for the optimal allocation of voltage regulators and capacitors in radial distribution systems”, International Journal of Electrical Power & Energy Systems, vol. 48, pp. 123–130, 2013. [FRA 13b] FRANCO J.F., RIDER M.J., LAVORATO M., et al., “A mixed-integer LP model for the reconfiguration of radial electric distribution systems considering distributed generation”, Electric Power Systems Research, vol. 97, pp. 51–60, 2013. [GUI 10] GUIMARÃES M.A.N., CASTRO C.A., ROMERO R., “Distribution systems operation optimisation through reconfiguration and capacitor allocation by a dedicated genetic algorithm”, IET Generation, Transmission & Distribution, vol. 4, no. 11, p. 1213, 2010. [KEH 04] KEHA A.B., DE FARIAS I.R., NEMHAUSER G.L., “Models for representing piecewise linear cost functions”, Operations Research Letters, vol. 32, pp. 44–48, 2004. [KER 91] KERSTING W.H., “Radial distribution test feeders”, IEEE Transactions on Power Systems, vol. 6, no. 3, pp. 975–985, 1991. [KHO 09] KHODR H.M., MARTINEZ-CRESPO J., MATOS M.A., et al., “Distribution systems reconfiguration based on OPF using benders decomposition”, IEEE Transactions on Power Delivery, vol. 24, no. 4, pp. 2166–2176, 2009. [LAV 12] LAVORATO M., FRANCO J.F., RIDER M.J., et al., “Imposing radiality constraints in distribution system optimization problems”, IEEE Transactions on Power Systems, vol. 27, no. 1, pp. 172–180, 2012.

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[LOD 10] LODI A., “Mixed integer programming computation”, in JÜNGER M. et al. (eds), 50 Years of Integer Programming 1958-2008, Springer, Berlin, Heidelberg, 2010. [MAH 07] MAHSEREDJIAN J., DENNETIÈRE S., DUBÉ L., et al., “On a new approach for the simulation of transients in power systems”, Electric Power Systems Research, vol. 77, no. 11, pp. 1514–1520, 2007. [MAN 00] MANTOVANI J.R.S., CASARI F., ROMERO R.A., “Reconfiguração de sistemas de distribuição radiais utilizando o critério de queda de tensão”, Revista Brasileira de Controle & Automação – SBA, vol. 11, no. 3, pp. 150–159, 2000. [ONE 12] O’NEILL R.P., CASTILLO A., CAIN M.B., The IV formulation and linear approximations of the AC optimal power flow problem, available at: http://www.ferc.gov/, 2012. [RAJ 08] RAJU G.K.V., BIJWE P.R., “An efficient algorithm for minimum loss reconfiguration of distribution system based on sensitivity and heuristics”, IEEE Transactions on Power Systems, vol. 23, no. 3, pp. 1280–1287, 2008. [RAM 05] RAMOS E., EXPÓSITO A., “Path-based distribution network modeling: application to reconfiguration for loss reduction”, IEEE Transactions on Power Systems, vol. 20, no. 2, pp. 556–564, 2005. [ROM 10] ROMERO-RAMOS E., RIQUELME-SANTOS J., REYES J., “A simpler and exact mathematical model for the computation of the minimal power losses tree”, Electric Power Systems Research, vol. 80, pp. 562–571, 2010. [SU 03] SU C., MEMBER S., LEE C., “Network reconfiguration of distribution systems using improved mixed-integer hybrid differential evolution”, IEEE Transactions on Power Delivery, vol. 18, no. 3, pp. 1022–1027, 2003. [SU 05] SU C.T., CHANG C.F., CHIOU J.P., “Distribution network reconfiguration for loss reduction by ant colony search algorithm”, Electric Power Systems Research, vol. 75, no. 2–3, pp. 190–199, 2005. [TAR 73] TARJAN R., “Enumeration of the elementary circuits of a directed graph”, SIAM Journal on Computing, vol. 3, no. 2, pp. 211–216, 1973. [WU 10] WU Y.K., LEE C.Y., LIU L.C., et al., “Study of reconfiguration for the distribution system with distributed generators”, IEEE Transactions on Power Delivery, vol. 25, no. 3, pp. 1678–1685, 2010.

3 The Role of Nature-inspired Metaheuristic Algorithms for Optimal Voltage Regulation in Urban Smart Grids

Over the years, metaheuristic algorithms have emerged as one of the most suitable methodologies for solving complex optimization problems in the smart grids domain. Indeed, several algorithms, ranging from the traditional genetic algorithms to the emerging biogeography-based optimization algorithm, have been successfully applied to solve problems such as the Optimal Voltage Regulation in the Urban Smart Grids. In this swarm of different solution techniques, a comprehensive analysis of the performance in terms of accuracy is necessary in order to identify the best optimization algorithm in the smart grids domain. To bridge this gap, this chapter presents a comparison study among the metaheuristic algorithms most used in the task of solving complex smart grid optimization problems. Detailed simulation results obtained on realistic power networks are discussed in order to outline the benefits and the limitations of the different metaheuristics compared.

3.1. Introduction Population growth over the last century represents one of the most demanding issues to address in modern urban societies. From 1950 to today, the global population has increased 2.9 times, and now exceeds 7 billion, half of whom reside in urban areas, and every day 5,000 people move into cities. As a result, it has been estimated that by 2050, three-quarters of the global population will reside in urban areas [UGO 14a].

Chapter written by Giovanni ACAMPORA, Davide CARUSO, Alfredo VACCARO, Autilia VITIELLO and Ahmed F. ZOBAA. From Smart Grids to Smart Cities: New Challenges in Optimizing Energy Grids, First Edition. Edited by Massimo La Scala. © ISTE Ltd 2017. Published by ISTE Ltd and John Wiley & Sons, Inc.

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Addressing the problems induced by overpopulation is a significant challenge, but it also presents a big opportunity to revise the concept of city, as it is currently perceived, conceptualizing new urban paradigms. In this context, the deployment of the Smart City concept has been considered as one of the most promising research directions. Traditionally, the definition of “Smart City” just took into consideration the aspects relating to the technology, and in particular, those relating to Information and Communication Technology (ICT). Recently, this definition has assumed wider meanings, and according to the “Smart Cities Council”, the Smart City has been defined as a novel urban paradigm using ICT to improve the quality of life, by improving the sustainability, security, safety and workability [SMA 13]. In this context, the aim is to exploit new technologies to induce a deep transformation of the traditional models of environmental sustainability, integration between services, mobility, communication and interaction between citizens, companies and public administration. According to this vision, the urban structure of a Smart City model is organized into three layers. The first is composed of devices used to acquire, receive and transmit data (sensors, smart phone, cameras and mobile devices). The second one is composed of the communication system, which disseminates data and information to the users, and the urban elements. Finally, the third layer is responsible for data storage and processing [UGO 14b]. Smart cities can be classified according to six main dimensions: Smart Economy, Smart Mobility, Smart Environment, Smart People, Smart Living and Smart Governance. ICT is the factor that links all these sectors and can profoundly change the way of life in modern cities [UGO 14a]. A distinctive feature of the Smart City is its ability to learn and adapt to rapid changes, which requires the development of advanced information services, and smart semantic middleware aimed at assuring the cooperation and the interoperability between the different urban elements [MAT 15]. In order to address this issue, there is a need for a systematic and holistic approach, aimed at allowing the heterogeneous elements to interact and cooperate through standard and welldefined interfaces. The urban smart grid is among the most fundamental elements of a smart city, which can benefit from this holistic approach. In fact, it could supply electrical power to the smart city in a reliable way, overcoming the drawbacks of conventional electrical grids. In particular, the electrical grid is one century old and it has been continuously modified in order to meet the changing user needs. The traditional electrical grid is a centralized system in which electricity flows from central power plants to electrical loads in a one-way direction. This way of dispatching is no longer

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capable of responding to the ever-changing and rising energy demand of Smart Cities. To support the evolution of traditional electrical grids toward active, reconfigurable and self-healing networks, the Smart Grid introduces the concept of user-centric grids, where information and energy can be flexibly exchanged between producers and consumers according to Web energy-based paradigms [PAU 14]. This is obtained by integrating the communication and the electrical networks, in order to increase the efficiency, quality reliability and flexibility of the power distribution network [STR 13]. Furthermore, Smart Grids aim at increasing the exploitation of renewable energy, overcoming the problems induced by a large pervasion of distributed generators, and allowing the users to play a more active role in grid management. In addressing these complex issues, the smart grid deploys advanced tools for on-line solutions of constrained optimization problems, which aim at identifying the state of the grid controllers assuring a secure, reliable and economic power system operation. In this context, the stream of data acquired by the grid sensors should be analyzed promptly in order to identify proper control actions aimed at mitigating the effect of system perturbations, or adapting the power system state to new load and/or generation patterns. These optimization analyses, which are complex and NP-hard problems, should be performed according to strict time constraints to provide the Smart Grid operators with updated information quickly in order to better manage and mitigate the impact of data uncertainties. This has stimulated the research for advanced computing frameworks aimed at reducing the complexities of smart grid optimization by proposing alternative formalizations of the problem equations, and more effective solution techniques. In this context, metaheuristic optimization has been identified as one of the most promising enabling methodologies. In particular, a metaheuristic-based solution paradigm can be defined as an iterative process coordinating the operations of subordinate heuristics, to efficiently generate high-quality solutions, manipulating at each iteration a set of candidate solutions. The subordinate heuristics may include high-level searching techniques, local optimizers or hybrid combination of different methods [VOS 99]. Metaheuristic algorithms can be divided into two main groups: single-solution algorithms and population-based algorithms. The former aim at improving a single individual, such as simulated annealing and hill-climbing, whereas the latter aim at improving a population of individuals, by performing different operations during the optimum search. Some population-based algorithms are based on the concept of evolution, which means that the best individuals of every generation of solutions survive whereas poor individuals die. In this way, there will be an improvement in the quality of solutions from one generation to the next, until the end of the

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optimization process. Moreover, there are some population-based algorithms that belong to the category of swarm intelligence, such as particle swarm optimization. These types of algorithms try to reproduce the behavior of individuals of a swarm to find the optimum solution. In the following sections, a comparison study of the most used metaheuristic algorithms in the task of solving a complex smart grid optimization problem, namely the voltage regulation problem, will be presented, and detailed simulation results obtained on realistic power networks will be discussed in order to outline the benefits and the limitations of the different solution techniques. 3.2. Emerging needs in urban power systems The electrical grid was built one century ago and it has been renewed for decades to respond to changes of user needs. In traditional electrical grids, electricity is produced by central power plants and delivered to the user in a one-way direction. This way of dispatching is no longer capable of effectively addressing most of the challenging issues of modern power distribution systems, including the massive pervasion of renewable power generators, the strictest power quality limits, the complex interactions with the energy markets, the rising levels of security and reliability constraints and the need for maximizing the exploitation of existing electrical infrastructures. In this complex domain, the distribution system operators should face the following technical issues: 1) Increase in short-circuit current: the presence of distributed generation in a medium-voltage grid increases the short-circuit current compared with the case of a traditional passive grid. For this reason, the connection of a distributed generation system to the grid must be preceded by the evaluation of the total short-circuit current, in order to prove the respect of the short-circuit interruption rate of the protection systems. It can be calculated as the summation of the current coming from the high-voltage grid and the current originating from the distributed generation plant. 2) Selectivity of the protective systems: a protective system is selective when it is able to disconnect a portion of grid closer to the power failure. In a passive grid, the most used protective systems are based on non-directional relays, because there is no need to know the direction of the current, given that it can just flow toward loads. This means that they open the circuit when the current exceeds a fixed value. If there is a renewable energy generator connected to the grid, it contributes to feed the power failure, by involving the protection system of the line that is not affected by the failure. Therefore, distributed generation requires the use of a directional protective system, in order only to open the faulty line.

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3) Exploitation of lines and transformers: when a distributed generation system is connected to the grid, there is a need to verify that the current of the line does not exceed the capacity of the line, in order to avoid damaging components. 4) Perturbation of the voltage levels: the voltage profile of a grid can vary in two ways: slow voltage variations and rapid voltage variations. The former is related to the transient due to the connection and disconnection of generators to the grid. The latter is related to the voltage increase where the active power is injected. In a passive grid, the voltage is maximum at the start and minimum at the end. The presence of a distributed generator perturbs the levels of voltage of the grid. If some power is injected in the middle of the line, then the voltage level changes. 5) Inversion of power flows: this occurs when the power flow moves from the medium-voltage distribution grid toward the high-voltage transmission grid. There is a need to take into account this phenomenon in the management of the grid. 6) Islanding: in this type of operating, a grid portion works as an independent island fed by the distributed generator. This could cause some security problems, because it could keep feeding the high-voltage system even when the transformer room is off, and could be a risk for the operators who work on a disconnected line. Moreover, the distribution system operator may not be able to guarantee the energy supply to the user with the parameters (voltage and frequency) agreed in the supply contract. For this reason, the generation system is equipped with an interface that turns off the transformer room when it is off. Another relevant issue to address in modern power distribution systems is the socalled peak load management. The entire grid must be designed to fulfill this peak, even though it only lasts for a few hours a day. In order to fulfill the peak, some additional auxiliary generators are used. The power generated by these generators has high marginal cost; therefore, a reduction of the peak load results in an economic benefit. Obviously, the reduction of the peak also means reducing the contingencies caused by the peak. The problem of the peak load can be solved or attenuated by involving users in the management of the grid. The user could reduce its power absorption during the periods of peak load. In this way, the user becomes a “prosumer”, that is, a producer and a consumer. This is only possible if the users can communicate with the distribution system operator. 3.3. Toward smarter grids The Smart Grid introduces a bi-directional exchange of information and energy between producers and consumers. It is defined as the union of a telecommunication network and an electricity distribution system, which allows management of the electrical distribution grid in a smart way, trying to minimize the perturbations, and the deviation of the voltage from its nominal value. Furthermore, the Smart grid

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aims to increase the integration of renewable power generators, trying to overcome the problems of distributed generation and allowing the users to play a more active role in grid management. The implementation of a Smart Grid can be realized in different steps. The first step is the local control of the distributed generators. They are equipped with a local interface, which guarantees minimal services, such as the disconnection of the generators in case of high or low voltage. The second step concerns the problems relating to the voltage regulation. The traditional voltage regulation systems are based on the measurement of the output current of transformers. Assuming loads are passive, the voltage is maximum at the start of a line and minimum at the end. The greater the load, the more the current load, and therefore if the load current is high, the voltage is low. At this point, the traditional regulation system increases the voltage. This procedure is no longer valid, because the distributed generators sensibly perturb the voltage profile, and a more sophisticated solution based on a Distribution Management System (DMS) should be deployed. The DMS is typically based on a Supervisory Control and Data Acquisition System, which identifies the optimal setpoints of the voltage regulation devices in order to keep the bus voltage close to the nominal value. The DMS is used in large extra-urban grids with a high penetration of wind energy. The third step consists of reinforcing the grid, installing new lines in order to make the grid a meshed system. In a network, it is not possible to fully control power flows in the lines, because they depend on physical equations. However, by using advanced control systems (flexible AC transmission systems, FACTS), it is possible to regulate power flows and reduce power losses. FACTS are used in transmission networks, but the trend is to use them in distribution systems (DFACTS). The third step also consists of reconfiguring the grid in case of outage, in order to contain the effects of the power failure in a restricted area (self-healing network). This can be reached by modifying the switches setting in order to change the topology of the network. The fourth step consists of dividing the distribution grid into islands, portions of a network that works autonomously, in case of outage. However, to feed loads in an appropriate way, there is a need for some traditional power production systems or some storage systems for power balancing and voltage regulation. The actual distribution grids have a radial structure, whereas the Smart grid should have a strongly interconnected structure. Furthermore, it should be divided into local areas responsible for their own management which participate in the energy market by

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selling and buying energy with either neighboring local areas or the energy transmission system [BIC 06]. Implementation of Smart Grids needs the deployment of many components, which can relate to home appliances or grid components: – Smart appliances: with this type of appliance, users can pre-set when the appliances work. In this way, appliances could work during low demand periods and reduce the peak load. According to initial tests, users can save 25% energy, just presetting these appliances. – Smart power meters: devices that link costumer and power providers, to detect power failures, automate billing data collection, and send repair crews to the area of power failure. – Smart substations: which control data such as breaker, transformer, power factor performance, battery status and security. – Smart distribution: that is, analysis tools and automated monitoring able to detect and even prevent failure on the basis of real-time data about failure history, weather, etc., and self healing, self-optimizing and self-balancing. – Smart generation: able to automatically keep power factor, voltage and frequency within their operating ranges on the basis of feedback from many points in the network and able to predict the behaviour of power generators to optimize power generation. These components can be developed by employing the Smart grid technologies, which can be grouped in eight categories [IEA 11]: – Wide-area monitoring and control: its main function is the real-time monitoring; it also makes it possible to show the performance of power system elements over wide geographic areas, in order to help the network operators to optimize the use of power system components. These technologies, together with advanced tools, such as wide-area adaptive protection, wide-area monitoring systems and wide-area situational awareness, control and automation, improve reliability and transmission capacity, provide information to system operators and attenuate wide-area disturbances. – ICT integration: a communications infrastructure that consists of public networks, such as the Internet, cable, cellular or telephone and private utility communication networks, such as meter mesh networks, radio networks, etc. This communication system enables a bi-directional exchange of data between users and grid operators.

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– Renewable and distributed generation integration: smart grids can help to overcome or attenuate the problems relating to distributed generation, through automation of the control of generation and demand. – Transmission enhancement applications: many components can improve the behaviour of the transmission system. Some of these components are the FACTS, which are able to optimize the power transfer capability and the control of the transmission system. There are also the high-voltage direct current lines (HVDC), which are able to connect areas separated by many kilometers, or to connect large off-shore wind farms and solar plants with the transmission grid. Another important component is the DLR (dynamic line rating), which is a system that identifies the real-time current transport capability of sections of grid, increasing the exploitation of transmission assets. Finally, there are high-temperature superconductors, which can reduce power losses and limit current faults. – Distribution grid management: the processing of real-time data coming from meters and sensors enables localization of faults, reconfigure feeders, optimize voltage and reactive power or control distributed generation. This system allows optimization of the use of network’s assets. – Advanced metering infrastructure (AMI): it is an infrastructure that enables two-way flow of data, providing, together with smart meters, customers and utilities with information on time, electricity consumption and price. AMI provides many other functionalities: - Capacity for a provider to manage its revenues more efficiently through debt management and cash collection; - Remote connection and disconnection; - Losses and theft detection; - Capacity to localize intensity and position of failures remotely through a function that transmits a signal when the meter is down; - Improved fault detection from more accurate load profiles; - Capacity to collect, store and describe user energy consumption data near real time; - Remote consumer price signals, which can provide price information. – Electrical vehicle charging infrastructure: this manages the charging of electrical vehicles connected to the grid during low energy demand. In the long term, new functionalities will be implemented, such as the participation of batteries in the network regulation, provision of capacity reserve and peak-load shaving. – Customer-side systems: energy management systems, smart appliances, distributed generation and energy storage devices, with which it is possible to

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manage the electrical consumption at the residential, service and industrial levels. The energy efficiency and the reduction of peak load can be sped up with local storage, smart appliances and energy dashboards. Making the grid “Smart” through the large-scale deployment of these technologies allows management of the distribution grids with criteria similar to those adopted in transmission grids. 3.4. Smart grids optimization The backbone of future Smart Grids is the capability of distributed entities, such as software modules, remote processing units and pervasive sensor networks, to acquire, process and share data according to fixed time constraints determined by the specific application domain. In this context, the enhancement of the energy management systems, which are traditionally based on low scalable architectures, mixed communication technologies and legacy proprietary platforms, with advanced modules for on-line smart grid optimization is one of the main technological challenges we face. In addressing this issue, pervasive storage and processing of massive data sets represents one of the most complex issues to address, since the number of grid sensors is expected to increase over several orders of magnitude, and the corresponding data streaming should be processed promptly by the smart grid optimization function in order to extract actionable information in useful times. In solving these complex issues, metaheuristic algorithms could play an important role, since it could allow smart grid operators to represent and discover the intrinsic semantic of the measured data, obtaining a full understanding of the information context and assessing the degree of confidence of the corresponding content. In particular, the smart grid optimization function considered in this chapter as a benchmark for assessing the performance of metaheuristic algorithms is the voltage regulation problem. The objective function typically considered in this study is the voltage deviation of the load buses, which can be described as follows [DUM 12]: Fobj =

∑ V −V i

i∈N L

refi

[3.1]

where NL is the number of load buses and Vi and Vref-i are the voltage magnitude and the nominal voltage of the i-th bus, respectively.

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The control variables of the optimization problems are:

uT = [VG1 ...VGn , T1...TNT , QC1 ...QCNC ]

[3.2]

where VGi are the set points of the generator voltage magnitudes, T is the tap ratio of the tap changing transformers, Qc is the output reactive power of shunt VAR compensators and NC and NT represent the number of shunt VAR compensators and the number of controlled transformers, respectively. The dependent variables are: xT = ⎡⎣ PGs , VL1 ...VLNPQ , δ1 ,..., δ NB , QG1 ...QGNG ⎤⎦

[3.3]

where PGs is the slack bus power, VLi is the voltage magnitude of the i-th load bus, δi is the voltage angle of the i-th bus and QGi is the reactive power of the i-th generator. The equality constraints of this optimization problem are described by the power flow equations: NB

PGi − PDi − Vi ∑ V j [Gij cos(δ i − δ j ) + Bij sin(δ i − δ j )] = 0

[3.4]

j =1

NB

QGi − QDi − Vi ∑ V j [Gij sin(δ i − δ j ) + Bij cos(δ i − δ j )] = 0

[3.5]

j =1

where Gij is the conductance of the branch i–j, Bij is the susceptance of the branch i–j, PGi and QGi are the active and reactive power generated, PDi and QDi are the active and reactive power demanded at the i-th bus and NB is the number of buses. The control variables must be limited within their operating range: ⎧QGimin ≤ QGi ≤ QGimax ⎪ min max ⎪VGi ≤ VGi ≤ VGi ⎨ min max ⎪Ti ≤ Ti ≤ Ti ⎪Q min ≤ Q ≤ Q max ci ci ⎩ ci

i = 1,..., NG i = 1,..., N G i = 1,..., N T i = 1,..., NC

[3.6]

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To assure that the network works correctly, the bus voltage magnitudes and the active power flow on each line must be restricted within proper operating ranges:

VLimin ≤ VLi ≤ VLimax S

min li

≤S

i = 1,..., NPQ i = 1,..., NL

max li

[3.7]

To describe these inequality constraints, the penalty method is typically adopted, while the inequality constraints on the voltage magnitudes and the reactive power generated could be represented by adding them to the objective function as follows: J = Fobj + λV

NPQ

∑ (V

Li

i =1

NG

− VLilim ) 2 + λQ ∑ (QGi − QGilim ) 2

[3.8]

i =1

where λv and λQ are two penalty factors chosen arbitrarily and Vlim and Qlim are the limit values calculated as follows [SIN 15]: ⎧⎪VLimax VLilim ⎨ min ⎪⎩VLi

VLi > VLimax VLi < VLimin

[3.9]

max ⎪⎧QGi QGilim ⎨ min ⎪⎩QGi

QGi > QGimax QGi < QGimin

[3.10]

3.5. Metaheuristic algorithms for smart grids optimization

In this section, the most advanced metaheuristic algorithms for on-line smart grids optimization will be analyzed. 3.5.1. Genetic algorithm

Genetic algorithm is one of the first evolutionary algorithms proposed for smart grid optimization. Figure 3.1 shows the pseudo-code of a genetic algorithm:

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Parents ← {randomly generated population} While not (termination criterion) Calculate the fitness of each parent in the population Children ← ∅ While Children < Parents Use fitnesses to probabilistically select a pair of parents for mating Mate the parents to create children c1 and c2 Children ← ChildrenÈ {c1 ,c2 } Loop Randomly mutate some of the children Parents ← Children Next generation Figure 3.1. Pseudo-code of the Genetic Algorithm [SIM 13]

First, the algorithm creates a random population. After that, the fitness value [AND 07] of every individual is evaluated and a set of “children” is initialized to zero. A loop repeats until the number of children is higher than the number of parents. At each iteration, the algorithm performs the crossover operation, where every parent passes some features to their two children, in order to generate two individuals with a better fitness value. It can be performed in three different ways: – asexual; – sexual; – multi-recombination. For the asexual crossover, there is only one parent that produces one or more children. For the sexual crossover, there are two parents that generate one or more individuals and for the multi-recombination crossover, there are more than two parents that produce one or more offspring. In the sexual crossover, the two parents are probabilistically selected based on their fitness value. After the crossover process, every feature of some individuals is randomly mutated, according to a mutation probability, which is the probability that a feature of a solution is mutated. At the end of every generation, the set of parents is updated to the set of children. This entire process repeats until the termination criteria are met [SIM 13].

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3.5.2. Random Hill Climbing algorithm

The hill climbing algorithm is a simple local-based algorithm. One of the variants of the hill-climbing algorithm is the Random Hill Climbing algorithm. The following pseudo-code outlines the random hill-climbing algorithm: x0 ← randomly generated individual While not ( termination criterion )

Compute the fitness f ( x0 ) of x0

q ← randomly chosen solution feature index ∈ [1, n ] x1 ← x0 Replace the q-th solution feature of x1 with a random mutation

Compute the fitness f ( x1 ) of x1 If f ( x1 ) > f ( x0 ) then x0 ← x1 End if Next generation Figure 3.2. Pseudo-code of the Random Hill Climbing Algorithm [SIM 13]

The initial individual of the population is randomly chosen. Then, the optimization loop starts and the fitness value of the current individual is evaluated. Further, the index of the solution feature being mutated is randomly chosen and this feature is replaced with a random mutation. The fitness value of the mutated solution is evaluated. Subsequently, the algorithm compares the fitness value of the mutated solution with the fitness value of the previous individual. If the value of the current fitness value is higher than the previous one, the algorithm updates the current solution, otherwise it keeps the previous individual. The algorithm stops when a termination condition is met [SIM 13]. 3.5.3. Particle Swarm Optimization algorithm

The Particle Swarm Optimization algorithm emulates the behavior of groups of individuals. The difference between PSO and other evolutionary algorithms is essentially the motion of the particles through the search space at each iteration, with a velocity vi. The velocity depends on two factors: the inertia and the influence of neighbors. The position of every individual changes at every iteration, but the algorithm remembers the best performance and the related best position assumed by individuals in the previous iterations. The second factor is that all the individuals

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know the best position and the best fitness value of their neighbors at each generation. The pseudo-code shown in Figure 3.3 explains the Particle Swarm Optimization algorithm: Initialize a random population of individuals { xi } , i ∈ [1, N ]

Initialize each individual's n-element velocity vector vi , i ∈ [1, N ]

Initialize the best-so-far position of each individual: bi ← xi , i ∈ [1, N ] Define the neighborhood size σ vmax then vi ← vi vmax / vi End if xi ← xi + vi

bi ← arg min { f ( xi ) , f ( bi )} Next individual Next generation Figure 3.3. Pseudo-code of the Particle Swarm Optimization Algorithm [SIM 13]

After the initialization of population, velocity and best position of every individual, further parameters such as the neighborhood size, the maximum influence values and the maximum velocity must be chosen. The maximum influence values, Φ1, max and Φ2, max, are the upper bounds of the cognition learning rate Φ1 and the social learning rate Φ2, respectively. The latter are random numbers ranging between zero and Φ1, max, and zero and Φ2, max, respectively. In order to avoid the possibility of the single particle leaving the search space at each generation, the max velocity of every particle must be restricted by the corresponding range of the search space.

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After the initialization and the evaluation of the set of nearest neighbors and their minimum fitness value, the algorithm generates the random vectors Φ1 and Φ2 in order to evaluate the velocity of the particle as follows:

vi ← vi + φ1 (bi − xi ) + φ2 (h i − xi )

[3.11]

The update equation: xi ← xi + vi

[3.12]

enables searching for the best solution within the search domain at each iteration. It could conduct the particle outside the search space; for this reason, the xi value must be restricted within its upper and lower bounds. At the end of the loop, the current individual is compared with the best individual’s position, and the best fit individual is kept. The optimization loop ends when one of the termination conditions is reached [SIM 13]. 3.5.4. Evolution strategy

Evolution strategies are made of different variants. In this section, three variants will be analysed [SIM 13]: – the (1 + 1) evolution strategy; – the (µ + 1) evolution strategy; – the (µ + λ) evolution strategy. 3.5.4.1. (1+1) Evolution Strategy

The (1+1) evolution strategy algorithm was the first ES used and the most simple. After the initialization of the variance, the candidate solution is chosen randomly and its fitness value is evaluated. Then, the current solution is mutated and an evaluation of its fitness value is performed. Then, the individual to be passed to the next generation is chosen between the two individuals. This procedure repeats until one of the termination criteria is met.

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The pseudo-code represented in Figure 3.4 outlines the (1+1) evolution strategy algorithm: Initialize the non-negative mutation variance σ 2 x0 ← randomly generated individual While not ( termination criterion )

(

)

Generate a random vector r with ri Δ N 0, σ 2 for i ∈ [1, n ] x1 ← x0 + r If x1 is better than x0 then x0 ← x1 End if Next generation Figure 3.4. Pseudo-code of the (1+1) Evolution Strategy Algorithm [SIM 13]

The mutation is performed by generating a random vector r, where each element is randomly chosen between 0 and σ2, and by adding this vector to the solution of the preceding generation. The tuning parameter σ2 is the non-negative mutation variance. This parameter should be set so that it is large enough in order to explore the whole search space and small enough in order to find the optimum with the desired accuracy. It would be appropriate to have a large variance at the beginning, in order to approach to the optimum solution, and then a smaller variance, in order to detect the optimum with accuracy. If the values of the variance are all equal, the variance is named isotropic. Otherwise, if the variance has different value for every gene, the variance is called non-isotropic. The parameter σi assumes a different value according to the domain of the i-th element xi and the form of the objective function in the dimension i-th [SIM 13]. 3.5.4.2. (µ+1) Evolution Strategy

The (μ+1) evolution strategy represents a generalization of the (1+1) evolution strategy. In this algorithm, the population is made of more than one parent. The child is created by combining the features of the parents and then it is mutated. There is a variance associated with each individual that manages the extent of mutations. The individuals to be passed to the next generations are chosen from the best individuals between child and parents. In fact, the worst individual between parents and child is removed, at each generation. For this reason, this approach could be named extinction of the worst. Figure 3.5 shows the pseudo-code of the (μ+1) evolution strategy.

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{( xk , σ k )} ← randomly generated individuals, k ∈ [1, μ ]. Each x k is a candidate solution, and each σ k is a standard deviation vector. Note that xk ∈ R m , and σ k is a standard deviation vector. While not (termination criteria) Randomly select two parents from the population {(xk , σ k )} Use a recombination method to combine the two parents and obtain a child, which is denoted as (x μ +1 , σ μ +1 ) ∑ μ +1 ← diag(σ μ2 +1 ,1 , ..., σ μ2 +1, n ) ∈ R n× m Generate a random vector r from N(0, ∑ μ +1 ) x μ +1 ← x μ +1 + r Remove the worst individual from the population: that is, {(xk , σ k )} ← the best μ individuals from {(x1 , σ 1 ), ..., (x μ +1 , σ μ +1 )} Next generation

Figure 3.5. Pseudo-code of the (µ+1) Evolution Strategy Algorithm [SIM 13]

There is one more recombination option that is called the intermediate sexual crossover, where the features of the child are chosen as the midpoint of the features of their parents. Another recombination option is intermediate sexual crossover, where the child’s features are chosen as the midpoint of their parent’s features. Another recombination method is the global crossover, where the features of the child can be randomly selected from between every individual of the population. A combination of global crossover and intermediate crossover can be realized in order to obtain a new recombination method called intermediate global crossover. 3.5.4.3. (µ + λ) and (µ, λ) Evolution Strategies

In the (μ + λ) evolution strategy, there is a population of μ individuals and a production of λ children each generation. Following every generation, there are (μ + λ) individuals, between children and parents, and the algorithm selects the parents of the following generation as the μ individuals with the best fitness function value of the current generation. Another type of evolution strategy is the (µ, λ) ES. In this algorithm, none of the parents pass to the next generation. That is, the parents of the next generation are chosen as the best µ individuals among the children.

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Figurre 3.6 outliness the (µ+λ)-ES S and the (µ, λ)-ES. λ {( xk , σ k )} ← randomlyy generated inddividuals, k ∈[1, μ ]. Each xk is a candidatte solution, andd each σ k is a standard deviation vector. Note th hat xk ∈ Rm , andd σ k ∈ Rm with each e element positive. While not n (termination criteria) F k = 1, ... , λ For p {(xk , σ k )} Randomlyy select two parrents from the population Use a recombination meethod to combin ne the two pareents and obtain a child, which is denoted d as (x',σ ' ) ∑ ' ← diag(( σ 'k1)2 ,...,( σ 'knn )2 ) ∈ Rm × n Generate a random vecttor r from N(0, ∑ 'k ) x ← x' + r x' N k Next If this is a ( μ + λ )-ES then {(xk , σ k )} ← the best μ inndividuals from m {(x1 , σ1 )} ∪ {(x'k ,σ 'k )} e if this is a ( μ , λ )-ES thenn else {(xk , σ k )} ← the best μ inndividuals from m {(x'k , σ 'k )} E if End Next geeneration Figure 3.6. Pseudo-code of the (µ + λ)--ES and (µ, λ))-ES [SIM 13]

3.5.5. Differential D e evolution The individuals trreated by thiss algorithm arre n-dimensioonal vectors. They are b adding thee scaled diffeerence of two o random vecttors to anotheer vector. created by This metthod is represeented in Figurre 3.7.

Figure 3.7. 3 Applicatio on of Differentiial Evolution Algorithm A on a two-dimension t nal optimizatio on problem [SIM 13]

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Figure 3.8 outlines the differential evolution algorithm: F = stepsize parameter ∈ [0.4,0.9]

c = crossover rate ∈ [ 0.1,1]

Initialize a population of candidate solutions { xi } for i ∈ [1, N ]

While not (termination criterion) For each individual xi , i ∈ [1, N ]

r1 ← random integer ∈ [1, N ] : r1 ≠ i

r2 ← random integer ∈ [1, N ] : r2 ∉ {i, r1}

r3 ← random integer ∈ [1, N ] : r3 ∉ {i, r1 , r2 }

vi ← xr1+ F ( xr 2 − xr 3 ) ( mutant vector ) ℑr ← random integer ∈ [1, n ] For each dimension j ∈ [1, n ]

rcj ← random number ∈ [0,1]

(

)

If rcj < c or ( j = ℑr ) then uij ← vij else uij ← xij End if Next dimension Next individual For each population index i ∈ [1, N ] If f ( ui ) < f ( xi ) then xi ← ui

Next population index Next generation Figure 3.8. Pseudo-code of the Differential Evolution Algorithm [SIM 13]

First, it is necessary to choose two tuning parameters: the step-size parameter F and the crossover rate c. After the initialization of the population, the optimization loop starts and for every individual xi, three random integers are chosen: r1, r2 and r3. A new vector vi is created by adding a random vector xr1 to the scaled difference between two other random vectors xr2 and xr3. Then, a crossover operation is

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implemented by combining the mutant vector vi with the current individual xi. The crossover rules are the following: if the random number rcf is less than the crossover rate c, or the j (position of the variable) is equal to a random integer Jr, the element of the trial vector uij is the correspondent of the mutant vector vi. Otherwise, the trial vector uij is equal to the current individual xij. The individual with the best-fitness function value is kept for the next generation, whereas the one with the worst-fitness value is discarded [SIM 13].

3.5.6. Biogeography-based optimization

Biogeography studies the distribution of biological organisms in geographic areas [SIM 08]. The habitat suitability index (HSI) indicates the level of “livability” of an island. It depends on factors such as topographic diversity, temperature, land area, rainfall and vegetative diversity. Such characteristics are named suitability index variables (SIVs). Considering an optimization problem, an individual with a good fitness function value can be seen as an island with a large HIS whereas an individual with a poor fitness function value as an island with a small HSI. Good individuals have a tendency to exchange their features with low-level individuals, the same way species of islands with large HSI have a tendency to emigrate to the island’s with small HSI. This occurr because islands with high habitability host a lot of species, and island with low habitability host only a small number of species. Similarly, poor individuals receive features from good individuals, the same way islands with low HSI accept immigrants from islands with high HSI because of a lack of species. The exchange of features between good individuals and poor individuals can increase the quality of the fitness function value of those individuals. After a random initialization of a population of candidate solutions the optimization loop starts. For every individual, an immigration probability and an emigration probability proportional to its fitness value are set. The immigration probability represents the probability that a solution feature is replaced by the solution feature chosen through the emigration probability. Then, a temporary population of individuals, zk, is created in order to perform the exchange of features between the individuals selected. The immigration probability λk is used to select the features that must be replaced by the features of individuals selected through the emigration rate µk. After the exchange of features between the selected elements, a probabilistic mutation of the individuals is performed and the set of individuals is updated to the new generation. The optimization loop ends when one of the termination criteria is met [SIM 13].

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Figure 3.9 outlines the biogeography-based optimization algorithm: Initialize a population of candidate solutions { xk } for k ∈ [1, N ]

While not ( termination criterion )

For each xk , set emigration probability μk ∝ fitness of xk , with μk ∈ [ 0,1] For each individual xk , set immigration probability λk = 1 − μk

{ zk } ← { xk } For each individual zk For each solution feature s Use λk to probabilistically decide whether to immigrate to z If immigration then N

Use {μi }i =1 to probabilistically select emigrating individual x j zk ( s ) ← x j ( s )

End if Next solution feature Probabilistically mutate { zk } Next individual

{ x k } ←{ z k } Next generation Figure 3.9. Pseudo-code of the Biogeography-Based Optimization Algorithm [SIM 13]

3.5.7. Evolutionary programming

This algorithm does not involve the operation of recombination like some other evolutionary algorithms, but only includes the operation of mutation. The algorithm starts creating an initial population randomly. The generation of a new individual is performed through the following relation:

x 'i ← xi + ri β f (x i ) + γ

[3.13]

where ri is a random vector, whose elements are taken from a Gaussian distribution with a mean of 0 and a variance of 1, and β and γ are tuning parameters. The term

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“βf(xi)+γ” represents the variance of the mutation of xi. Often, the default values of β and γ are 1 and 0, respectively. Then, a number of individuals equal to the population number are generated. In this way, there are 2N individuals: xi and xi’. The N individuals representing the next generation can be selected in different ways. One of them consists of selecting the best individuals. Other methods can be the roulette-wheel selection or tournament selection. The basic EP algorithm is outlined in Figure 3.10: Select non-negative EP parameters β and γ . Nominally β = 1 and γ = 0.

{ xi } ← {randomly generated population} , i ∈ [1, N ] While not (termination criterion) Calculate the cost f ( xi ) of each individual in the population For each individual xi , i ∈ [1, N ]

Generate a random vector ri with each element Δ N ( 0, 1) xi, ← xi + ri β f ( xi ) + γ

Next individual

{ xi } ← best N individuals from { xi , x 'i } Next generation Figure 3.10. Pseudo-code of the basic Evolutionary Programming Algorithm [SIM 13]

3.5.8. Ant Colony Optimization

This algorithm is based on the behavior of ant colonies during the transportation of food from the source food to the nest. Ants are able to detect the shortest path between these two points by making use of a pheromone. When they succeed in finding food, they lay down the pheromone along the path travelled. The pheromone attracts more ants. By considering a short path and a long path from the nest to the source food, the first ants choose the path randomly and release the pheromone on their path. Ants that follow the shorter path take less time to transport food, and this means that they can make more travels. For this reason, there is more pheromone on the shorter path than the longer path. This drives the following ants to take the

The Role of Nature-inspired Metaheuristic Algorithms for Optimal Voltage Regulation

111

shorter path, because there is more pheromone. Obviously, there will always be some ants that take the longer street, because the choice of the street to follow is also random. The ACO optimization algorithm can be explained by solving the traveling salesman problem. Every ant deposits pheromone during the trip between two cities. Obviously, pheromone can also evaporate with the passing of time. The quantity of pheromone deposited on the path between two cities, determines the likelihood that an ant will follow that path. This likelihood decreases as the length of the path increases. During its travel, an ant deposits pheromone according to the quality of its solution. If the solution is poor the ant lays down less pheromone and vice versa. The algorithm aims at guiding the ants to find the shortest distance between the cities. Figure 3.11 shows the pseudo-code of the Ant Colony optimization algorithm applied to the travelling salesman problem. This algorithm can be applied to a problem with a continuous domain, by dividing every variable xi of the problem into discretized intervals. We consider that n is the dimension of the problem f(x), where x = [x1, x2 … xn] and: xi ∈ ⎡⎣ xi , min , xi , max ⎤⎦ xi , min = bi , 1 < bi , 2 < ........ < bi , Bi = xi , max

[3.14]

where the i-th domain has been divided in Bi−1 discrete intervals. If the domain of the solution xi lies between bij and bi,j+1, the pheromone of an interval is updated at each generation, according to the following relation: if

xi ∈ ⎡⎣bi j , bi , j+1 ⎤⎦ then τ ij ←τ ij + Q / f ( x )

[3.15]

where f(x) is always positive for any x, τij and Q represent the pheromone between cities i and j, and the standard ant system deposition constant, respectively. The new solution is probabilistically built by considering the quantity of pheromone at each generation. If there is much pheromone in the interval [bij, bij+1], then it is likely that the i-th feature of the solution to be created, lies in that interval. Through the discretization of the problem dimensions, it is possible to use the ACO to solve continuous problems [SIM 13].

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From Smart Grids to Smart Cities

n = number of cities

α , β = relative importance of pheromone vs. heuristic information Q = deposition constant

ρ = evaporation rate ∈ (0, 1) τ ij = τ 0 (initial pheromone between cities i and j) for i ∈ [1, n] and j ∈ [1, n] dij = distance between cities i and j for i ∈ [1, n] and j ∈ [1, n] While not (termination criteria) For q = 1 to n -1 For each ant k ∈ [1, N] Initialize the starting city ck1 of each ant k ∈ [1, N] Initialize the set of cities visited by ant k: Ck ← {ck1}for k ∈ [1, N] For each city j ∈ [1,n], j ∉ Ck α β / dim ) probability pij(k) ← (rijα , dijβ ) / (∑ m =1, m ∉ C rim n

k

Next j Let ant k go to city j with probability pij(k) Use ck , q +1 to denote the city selected in the previous line Ck ← Ck ∪ {ck , q +1} Next ant Next q Lk ← total path length constructed by ant k, for k ∈ [1, N] For each city i ∈ [1, n] and each city j ∈ [1, n] For each ant k ∈ [1, N] If ant k went from city i to city j Δτ ij(k) ← Q/Lk else Δτ ij(k) ← 0 End if Next ant

τ ij ← (1 – ρ )τ ij + ∑ k =1 Δτ ij( k ) N

Next city pair Next generation

Figure 3.11. Pseudo-code of Ant Colony Optimization Algorithm to solve the travelling salesman problem [SIM 13]

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Figure 3.12 shows the ACO algorithm for continuous optimization: n = number of dimensions d i Divide the i-th dimension into Bi − 1 intervals as shown in Equation 3.4, i ∈ [1, n]

α = importance of pheromone amounts Q = deposition constant ρ = evaporation rate ∈ (0, 1) τ ij = τ 0 (initial pheromone) for i ∈ [1, n] and j ∈ [1, Bi – 1] dij = distance between cities i and j for i ∈ [1, n] and j ∈ [1, n] Randomly initialize a population of ants (candidate solutions), α k , k ∈ [1, N] While not (termination criteria) For each ant ak , k ∈ [1, N] For each dimension i ∈ [1, n] For each discretized interval [bij , bi , j +1 ], j ∈ [1, Bi − 1] α Probability pij(k) ← τ ijα / ∑ mi=1 τ im B −1

Next discretized interval ak (x i ) ← U[bij , bi , j +1 ] with probability pij( k ) Next dimension Next ant Lk ← cost of solution constructed by ant ak , k ∈ [1, N] For each dimension i ∈ [1, n] For each discretized interval [bij , bi , j +1 ], j ∈ [1, Bi -1] For each ant ak , k ∈ [1, N] If ak (x i ) ∈ [bij , bi , j +1 ] Δτ ij(k) ← Q / Lk else Δτ ij(k) ← 0 End if Next ant

τ ij ← (1 – ρ )τ ij +∑ k =1 Δτ ij(k) N

Next discretized interval Next dimension Next generation

Figure 3.12. Pseudo-code of the Ant Colony Optimization Algorithm to solve a continuous-domain optimization problem [SIM 13]

3.5.9. Group Search Optimization algorithm

This algorithm is similar to the particle swarm optimization algorithm, but it is based on the behaviors of land-based animals. It reproduces the way in which animals search for food. This algorithm includes three types of animals: producers,

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From Smart Grids to Smart Cities

scroungers and rangers. The heading angle and the position in the search space of each individual are indicated as xi and Φi,1=[ Φi,1 … Φi,n-1], respectively. There is just a producer in the population and, at each generation, it is selected as the best individual. In each generation, the producer performs a local search by scanning three positions in his vicinity in order to find a location with a betterfitness function value. By indicating the location of the producer with xp, the three positions mentioned before are: x1 = x p + r1lmax D (φ p ) x 2 = x p + r1lmax D(φ p + r2 θ max / 2)

[3.16]

x 3 = x p + r1lmax D(φ p − r2 θ max / 2)

where r1 and r2 represent a normally distributed and a uniformly distributed random variable, respectively; D is a polar to Cartesian coordinate transformation; Φp is the heading angle of xp; lmax and ϑmax are tuning parameters. The former establishes how deep the producer is able to see, and the latter defines how much the producer can change the direction of his gaze. The producer moves to one of the three positions mentioned before, when its fitness function value decreases in that position. Otherwise, it stays in its position and varies its heading angle Φp to a new value, at random. The scroungers follow the producer in a zigzag pattern. This enables them to explore new positions with better fitness function values. A scrounger moves following this relation:

x4 ← x4 + r3 o ( x p − x4 )

[3.17]

where r3 is a vector of random variables and ͦ is an element-by-element multiplication. The rangers randomly move from one place to another of the search space in order to find zones with low fitness function values. The following relations model the Rangers’ movement:

φi ← φi + ρα max xi ← xi + α max lmax r1 D(φi )

[3.18]

where αmax and lmax are tuning parameters that indicate the search direction the producer is able to see and the maximum distance covered by a ranger in a generation, respectively; ρ and r1 are random variables, the former is uniformly distributed and the latter is normally distributed [SIM 13].

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Figure 3.13 outlines the GSO algorithm: N = population size Initialize a random population of candidate solutions {xi } for i ∈ [1, N] Randomly initialize the heading angle φi of each candidate solution xi While not (termination criteria) Find the producer: x p ← arg min xi {f(x i ) : i ∈ [1, N]} {x1 , x2 , x3 } ← scanning result of Equation (3.6) If min{f(x1 ), f(x2 ), f(x3 )} < f(x p ) then x p ← arg min {f(x1 ), f(x2 ), f(x3 )} else

ρ ← U[ – 1,1] φ (x p ) ← φ (x p ) + ρα max End if For each xi ≠ x p r2 ← U [0, 1] If r2 < 0.8 Let xi scrounge using Equation (3.7) else Let xi range using Equation (3.8) End if Next individual Next generation

Figure 3.13. Pseudo-code of the Group Search Optimization Algorithm [SIM 13]

3.6. Numerical results

In this section, the effectiveness of the described metaheuristic algorithms in the task of solving the optimal voltage regulation problem on realistic power networks will be analyzed. The considered case studies include both IEEE test power systems, which have been considered in order to compare the performance of the optimization algorithms in standard operation scenario, and a real urban smart grid located in the south of Italy. In this context, it should be noted that although the IEEE test power systems refer to transmission power networks, their topology resembles the expected configuration of future urban grids, which are expected to evolve from a weakly meshed to a highly meshed system topology.

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The tests were performed by assuming the following conditions: – 35 executions for every algorithm and 40,000 function evaluations were performed for each execution, for the three test power systems, and the best fitness value was considered; – Each algorithm was terminated when the maximum number of fitness function evaluations was met. 3.6.1. Power system test 3.6.1.1. IEEE 30-Bus

The IEEE 30-Bus test power system represents a section of the American electrical Power System located in the Midwestern United States [THE]. The data related to this Power System are given in [DUM 12]. This system has 24 load buses, 41 branches and six generators. The control variables are 19, namely six generators’ voltage set-points, at the buses 1, 2, 5, 8, 11 and 13, four transformers with offnominal tap ratio at the branches 6–9, 6–10, 4–12 and 28-27, and nine shunt VAR compensation devices at buses 10, 12, 15, 17, 20, 21, 23, 24 and 29. The total system demand is 2.834 p.u. at 100 MVA base [DUM 12, SIN 15]. In order to find the best parameters for each algorithm, an empirical analysis has been performed. The best parameters for each algorithm are shown in Tables 3.1–3.4. Population size ACO 30

Number of bins per domain

Local pheromone decay rate

Exploration constant

Max. pheromone

Min. pheromone

50

0

0

inf

0

Table 3.1. Ant colony optimization (ACO) parameters

Population size

Migration blend parameter

Number of difference vectors

Number of Initial offspring population size lambda

Adaptation constant

BBO 30

0

–

–

–

–

DE

30

–

1

–

–

–

EP

100

–

–

100

–

–

ES

5

–

–

–

1

0.817

Table 3.2. Biogeography-based optimization (BBO), differential evolution (DE), evolutionary programming (EP), evolutionary strategy (ES) parameters

The Role of Nature-inspired Metaheuristic Algorithms for Optimal Voltage Regulation

Population size GA 30 GSO 30 RHC 1

Mutation rate 0.01 – –

Number of elites 2 – –

117

Mutation probability – – 0.1

Table 3.3. Genetic algorithm (GA), group search optimizer (GSO), random hill climbing (RHC) parameters

Population size PSO 50

Cognitive constant 2.1

Social constant for neighborhood interaction 2.1

Social constant for global interaction

Constriction coefficient

2.1

0.9

Table 3.4. Particle swarm optimization (PSO) parameters

The obtained results are summarized in Figure 3.14, which depicts the best value of the control variables, and Table 3.5, which shows the mean values of the fitness function for each algorithm after 35 executions. A penalty method has been adopted to consider the inequality constraints. This means that if the value of the fitness function is very large, the algorithm failed to compute a feasible solution. On analyzing the results shown in Table 3.5, we can observe that the algorithms DE, EP and GA cannot find a feasible solution at almost each execution, since their mean value is large. In particular, DE obtains a mean value above 5,000 and this means that it finds an infeasible solution at almost each execution. However, the mean value reached by EP and GA is much smaller, and this indicates that they cannot reach a feasible solution in just a few executions. On the other hand, the other algorithms perform well and always find a feasible solution, in fact their mean value is very small. The results show that BBO is the best algorithm since it obtains the minimum mean value, 0.1657. The second best algorithm is GSO, and the third is ACO. For the IEEE 30-BUS test power system, most of the metaheuristic algorithms are able to find the settings of the control variables able to minimize the voltage deviation and the results reached are very similar to each other, except for three algorithms.

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119

Figure 3.14. Best values of the control variables of all the algorithms for an IEEE 30-BUS test power system: a) generation voltages; b) transformer tap-ratios; c) reactive power generated by the shunt capacitors. For a color version of the figure, see www.iste.co.uk/lascala/smart.zip

30-BUS DE Mean

EP

GA

GSO

RHC

PSO

BBO

ACO

ES

5.15E+03 1.7447 27.659 0.1777 0.1893 0.223 0.1657 0.1808 0.1859 Table 3.5. Mean value of the best-fitness function values for the IEEE 30-BUS test power system

3.6.1.2. IEEE 57-Bus

The IEEE 57-bus test power system represents a section of the American electrical Power System, located in the Midwestern US [THE]. The data related to this Power System are given in [SIM 09]. This system has 80 branches and seven generator buses at 1, 2, 3, 6, 8, 9 and 12 buses. The 25 control variables include seven generator voltage magnitudes,

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15 transformers with off-nominal tap ratio and three shunt VAR compensation devices. The total system demand is: Pload = 12.508 p.u. and Qload = 3.364 p.u. at 100 MVA base [DUM 12]. In order to find the best parameters for each algorithm, a sensitivity analysis has been performed. The best parameters of the used algorithms are shown in Tables 3.6–3.9. Population size ACO 60

Number of bins per domain

Local pheromone decay rate

Exploration constant

Max. pheromone

Min. pheromone

70

0

0

Inf

0

Table 3.6. Ant colony optimization (ACO) parameters

Number of Migration blend difference parameter vectors

Initial population size

Number of offspring lambda

Adaptation constant

BBO 60

0

–

–

–

–

DE

25

–

1

–

–

–

EP

150

–

–

150

–

–

ES

5

–

–

–

1

0.817

Population size

Table 3.7. Biogeography-based optimization (BBO), differential evolution (DE), evolutionary programming (EP), evolutionary strategy (ES) parameters

Population size Mutation rate

Number of elites Mutation probability

60

0.01

2

–

GSO 60

–

–

–

RHC 1

–

–

0.1

GA

Table 3.8. Genetic algorithm (GA), group search optimizer (GSO), random hill climbing (RHC) parameters

The Role of Nature-inspired Metaheuristic Algorithms for Optimal Voltage Regulation

Population size PSO 100

Cognitive constant

Social constant for Social constant neighborhood for global interaction interaction

Constriction coefficient

2.1

2.1

0.9

2.1

121

Table 3.9. Particle swarm optimization (PSO) parameters

The obtained results are summarized in Figure 3.15, which reports the best values of the control variables, and in Table 3.10, which shows the mean values of the best fitness function values obtained by each algorithm after 35 executions. On analyzing these data, we can note that evolutionary programming and differential evolution never find a feasible solution, whereas genetic algorithm, evolution strategies and particle swarm optimization fail in some executions. By analysing the data in table 3.10, the large mean value obtained by DE, EP, GA and ES suggests that they fail to reach a feasible solution at almost each execution. Particularly, EP always finds a solution that violates the constraints, as can be seen from its huge mean value. In contrast, the remaining algorithms are always able to find a feasible solution since their mean value is small. In particular, BBO is the algorithm that reaches the minimum mean value, with 0.8823, followed by GSO and ACO. For an IEEE 57-BUS test power system, only four out of nine metaheuristic algorithms applied are able to find the settings of the control variables to efficiently minimize the voltage deviation.

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Figure 3.15. Best values of the control variables of all the algorithms for an IEEE 57-BUS test power system: a) generation voltages; b) transformer tap-ratios; c) reactive power generated by the shunt capacitors. For a color version of the figure, see www.iste.co.uk/lascala/smart.zip

57-BUS DE Mean

EP

GA

GSO

RHC

PSO

BBO

ACO

ES

9715.480 1E+07 107768 0.9196 1.3099 4.6052 0.8823 1.0425 572.21 Table 3.10. Mean value of the best-fitness function values for the IEEE 57-BUS test power system

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3.6.1.3. IEEE 118-Bus

The IEEE 118-bus test power system represents a section of the American electrical Power System, located in the Midwestern United States [THE]. The data related to this Power System are given in [MAH 10]. This system has 64 load buses, 186 branches and 54 generator buses. The 77 control variables include 54 generators’ voltage magnitudes, nine transformers with off-nominal tap ratio and 14 shunt VAR compensation devices [DUM 12, MAH 10]. The total system demand is: Pload = 42.4200 p.u. and Qload = 14.3800 p.u. at 100 MVA base. In order to find the best parameters for each algorithm, a sensitive analysis has been performed. The best parameters of the used algorithms are shown in Tables 3.11–3.14. Population size ACO 100

Number of bins per domain

Local pheromone decay rate

Exploration constant

Max. pheromone

Min. pheromone

100

0

0

Inf

0

Table 3.11. Ant colony optimization (ACO) parameters

Population size BBO 100

Number of Migration blend difference parameter vectors

Initial population size

Number of Adaptation offspring constant

0

–

–

–

–

DE

200

–

1

–

–

–

EP

300

–

–

300

–

–

ES

5

–

–

–

1

0.817

Table 3.12. Biogeography-based optimization (BBO), differential evolution (DE), evolutionary programming (EP), evolutionary strategy (ES) parameters

Population size

Mutation rate

Number of elites

Mutation probability

GA

200

0.01

2

–

GSO

200

–

–

–

RHC

1

–

–

0.1

Table 3.13. Genetic algorithm (GA), group search optimizer (GSO), random hill climbing (RHC) parameters

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From Smart Grids to Smart Cities

Population size PSO 200

Cognitive constant

Social constant for neighborhood interaction

Social constant for Constriction coefficient global interaction

2.1

2.1

2.1

0.9

Table 3.14. Particle swarm optimization (PSO) parameters

The results obtained for this case study, which are reported in Table 3.15, demonstrate that many metaheuristic algorithms fail to find a feasible solution at every execution, such as differential evolution, evolutionary programming, genetic algorithm, group search optimizer and particle swarm optimization, whereas the remaining algorithms are able to find inadmissible solution only in a few executions. Biogeography-based optimization reaches the minimum mean value because it is the only algorithm that finds feasible solutions most of the executions. 118-BUS DE Mean

EP

GA

GSO

RHC

PSO

BBO

ACO

ES

4.39E+09 7E+09 5E+08 2E+08 36022 3E+07 11.815 10,144 2001.4 Table 3.15. Mean value of the best-fitness function values for an IEEE 118-BUS test power system

3.6.2. Real urban smart grid

In order to prove the effectiveness of metaheuristic algorithms in solving complex optimization problems in realistic operation scenarios, a real case study based on a large-scale urban smart grid has been considered. Thus, the network under investigation is a portion of a real power distribution system located in the south of Italy composed of 1,310 buses, 22 substations, 1,318 lines and 10 wind power plants. In this context, one of the more relevant issues that need to be addressed is how to determine the set point of the primary voltage controllers installed at each substation, which is important information for the Transmission System Operator to optimize ancillary service scheduling on the electricity market. To solve this problem, the following algorithms have been considered: BBO, ACO, ES and GSO. The parameters of such algorithms are summarized in Tables 3.16 and 3.17.

The Role of Nature-inspired Metaheuristic Algorithms for Optimal Voltage Regulation

Population size BBO 50

Migration blend parameter

Number of offspring lambda

Adaptation constant

0

–

–

GSO 50

–

–

–

ES

–

1

0.817

5

125

Table 3.16. Biogeography-based optimization (BBO), group search algorithm (GSO), evolutionary strategy (ES) parameters

Population size ACO 50

Number of bins per domain

Local pheromone decay rate phi

Exploration constant q0

Max. pheromone tauMax

Min. pheromone tauMin

50

0

0

inf

0

Table 3.17. Ant colony optimization (ACO) parameters

The obtained results are summarized in Figures 3.16 and 3.17, which report the best-fitness function values at each execution and the control variables related to the best-fitness function value obtained by the algorithms considered, respectively. Table 3.18 shows the mean values of the fitness function obtained after 35 executions by the considered algorithms. The obtained results show that each algorithm succeeds in finding a feasible solution at each execution and the differences between the algorithms are quite small. This means that all four algorithms considered perform well on this network. The mean values outlined in Table 3.18 provide an overall understanding of the performance of the four algorithms. On analyzing these data, we can observe that BBO outperforms the other algorithms, but the differences between them are quite small. In fact, the values range from 13.47 to 14.30, where the former figure represents the best-fitness function value of BBO and the latter the one of GSO. The difference with the second-best mean value is very small, in fact ES reaches a value of 13.70. Finally, it is worth noting that during the analysis of the four algorithms, BBO turned out to be the best algorithm, even if the results of all the algorithms are very

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close to each other. The last observation, together with the fact that constraints, for each algorithm, are never violated, makes it possible to state that despite the large number of loads, each algorithm performs well on this network and that this grid is very reliable.

Figure 3.16. Best-fitness values of biogeography-based optimization (BBO), evolutionary strategy (ES), group search optimizer (GSO), ant colony optimization (ACO) for a real urban grid

Figure 3.17. Best values of the control variables of biogeography-based optimization (BBO), evolutionary strategy (ES), group search optimizer (GSO), ant colony optimization (ACO) for a real urban grid

The Role of Nature-inspired Metaheuristic Algorithms for Optimal Voltage Regulation

ES

ACO

BBO

127

GSO

Mean 13.7087 14.0186 13.4725 14.3049 Table 3.18. Mean value of the best-fitness function values of biogeography-based optimization (BBO), evolutionary strategy (ES), group search optimizer (GSO), ant colony optimization (ACO) for a real urban grid

3.7. Conclusions

In this chapter, the performance of the most advanced metaheuristic algorithms for on-line smart grid optimization was assessed. To this aim, the optimal voltage regulation problem has been considered as a benchmark to test the accuracy, the convergence proprieties and the robustness of nine metaheuristic algorithms. The results obtained on several IEEE test power systems and a real urban smart grid, under various operation scenarios, demonstrated the BBO algorithm that represents the most promising solution technique, allowing us to obtain the lowest minimum value of the objective function in each analyzed conditions. Finally, differential evolution obtains poor results in every network, and evolutionary programming obtains poor results in every test system, except the smallest one. Moreover, every algorithm strives to find acceptable solution in the IEEE 118-BUS test power system, because of its large dimension. 3.8. Bibliography [AND 07] ANDRIES P. ENGELBRECHT Computational Intelligence An introduction, John Wiley and Sons, p. 597, 2007. [BIC 06] BICHLIEN HOANG, “Emerging tech Smart Grids”, IEEE Emerging Technology portal, 2006. [DUM 12] DUMAN S., SONMEZ Y., GUVENC U. et al., “Optimal reactive power dispatch using a gravitational search algorithm”, IET Generation, Transmission & Distribution, vol. 6, pp. 563–576, 2012. [IEA 11] INTERNATIONAL ENERGY AGENCY, “Technology Roadmap Smart Grids”, 2011. [MAH 10] MAHADEVAN K., KANNAN P.S., “Comprehensive learning particle swarm optimization for reactive power dispatch”, Applied Soft Computing, vol. 10, pp. 641–652, 2010.

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[MAT 15] MATTONI B., GUGLIERMETTI F., BISEGNA F., “A multilevel method to assess and design the renovation and integration of Smart Cities (MATRICS)”, Sustainable Cities and Society, vol. 15, pp. 105–119, available at: http://dx.doi.org/10.1016/j.scs.2014. 12.002, 2015. [PAU 14] PAUL S., RABBANI M.S., KUNDU R.K. et al., “A review of smart technology (Smart Grid) and its features”, 1st International Conference on Non Conventional Energy (ICONCE), pp. 200–203, January 2014. [SIM 08] SIMON D., “Biogeography-based optimization”, IEEE Transactions on Evolutionary Computation, vol. 12, no. 6, pp. 702–713, 2008. [SIM 09] SIMON D., CHAOHUA DAI S., CHEN W., et al., “Seeker optimization algorithm for optimal reactive power dispatch”, IEEE Transactions on Power Systems, vol. 24, no. 3, available at: http://www2.ee.washington. edu/research/pstca/. pp. 1218–1231, 2009. [SIM 13] SIMON D., Evolutionary Optimization Algorithms, John Wiley and Sons, 2013. [SIN 15] SINGH R.P., MUKHERJEE V., GHOSHAL S.P., “Particle swarm optimization with an aging leader and challengers”, Applied Soft Computing, vol. 29, pp. 298–309, 2015. [SMA 13] SMART CITIES COUNCIL, Smart Cities Readiness Guide, p. 5, available at: http://smartcitiescouncil.com/smart-cities-information-center/the-scc-readiness-guide, 2013. [STR 13] STRASSER T., ANDRÉN F., MERDAN M. et al., “Review of trends and challenges in smart grids: an automation point of view”, Industrial Applications of Holonic and MultiAgent Systems, Lecture Notes in Computer Science, vol. 8062, pp. 1–12, 2013. [UGO 14a] UGOLINI M., BUSCHMANN J., NERI A., “Smart City: verso la società del futuro”, AEIT, ICT, Smart City e società, July/August 2014. [UGO 14b] UGOLINI M., MAYER M., AICT, ICT, Smart City e società, Editorial ICT, Smart City e società, July/August 2014. [VOS 99] VOSS S., MARTELLO S., OSMAN I.H. et al. (eds), Meta-heuristics – Advances and Trends in Local Search Paradigms for Optimization, Kluwer, Dordrecht, 1999.

4 Urban Energy Hubs and Microgrids: Smart Energy Planning for Cities

In this chapter, the authors try to link urban design features with energy consumption and consequent pollution parameters. After a review of a selected set of approaches to Urban Energy Systems study with a special focus on electrical power systems, urban energy systems are proposed as networks of multi-source hybrid energy hubs, where different energy flows are collected at the same bus and can be stored, delivered or transformed as needed. Resources at the hub and infrastructures interact with each other; therefore, both definition and boundaries of such energy systems at urban level are difficult to be clearly outlined. Similarly, the possibility to generate new operational models based on existing critical urban infrastructures is also challenging. This contribution proposes a preliminary study of urban energy hubs. Operations of thermal, electrical and mobility infrastructures are considered as qualifying features of the hub, but still the interconnected operation is not taken into account. The application part shows, indeed, the analysis and optimized design of the energy system serving two different urban districts. The related optimized parametric design of power generation infrastructures is considered as a function of urban features. The results about emissions and costs provide some interesting conclusions about the linkage between energy planning and urban features at district level, thus allowing, as possible application of this work, an energy-based territorial planning for urban contexts.

4.1. Introduction Many European countries are striving for a strong reduction of CO2 emissions by 2050, as well as a reduction in energy demand per capita. The European Commission is searching for cost-efficient ways to address European economy policy toward more climate-friendly and less energy-consuming paths. Its low-carbon economy roadmap Chapter written by Eleonora RIVA SANSEVERINO, Vincenzo Domenico GENCO, Gianluca SCACCIANOCE, Valentina VACCARO, Raffaella RIVA SANSEVERINO, Gaetano ZIZZO, Maria Luisa DI SILVESTRE, Diego ARNONE and Giuseppe PATERNÒ. From Smart Grids to Smart Cities: New Challenges in Optimizing Energy Grids, First Edition. Edited by Massimo La Scala. © ISTE Ltd 2017. Published by ISTE Ltd and John Wiley & Sons, Inc.

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suggests that by 2050, the EU should reduce emissions to 80% below 1990 levels. To achieve this target, there should be a 40% emissions cut by 2030 and 60% by 2040. All sectors need to contribute and the transition should be feasible and affordable; in particular, power generation and distribution, as well as transport and buildings, are among the main sectors to implement the CO2 curtailment. They are also the three main pillars on which urban energy systems structure is based [GRU 14, EVI 15a]. The power sector has the largest potential for cutting emissions. It can almost totally eliminate CO2 emissions by 2050. Electricity could indeed partially replace fossil fuels in transport and heating. Moreover, electricity can be produced with zero emissions using wind, solar, water and biomass or other low-emission sources such as nuclear power plants or fossil fuel power stations equipped with carbon capture & storage technology. This will of course require high investments in the smart grids and microgrids [GUE 11, GUE 13] technology. Emissions from transport in cities could be reduced to more than 60% below 1990 levels by 2050. In a short time, most progress can be found in petrol and diesel engines that could still be made more fuel-efficient. In the longer term, plug-in hybrid and electric cars will bring steeper emissions reductions. As far as the EU roadmap is planning, emissions from residential and tertiary buildings can be almost completely cut by around 90% in 2050. Energy performance will improve drastically through: – passive housing technology in new buildings; – refurbishing old buildings to improve energy efficiency; – substituting electricity and Renewable Energy Sources (RES), for fossil fuels in heating, cooling and cooking. Lighter energy bills can largely cover these investments in the longer term. As can be evidenced from the picture outlined above, electrical energy is going to play a key role in the smart urban energy system too. In all existing virtuous examples of the smart city concept [RIV 15], the district scale is able to propose perfect examples of circular economy and resource sharing. Urban energy systems can thus be seen as sets of energy hubs [GEI 07] defined as “entities consuming power at their input ports connected to, e.g. electrical distribution grids and natural gas infrastructures, and provide certain required energy services such as electricity, heating, cooling, compressed air, etc. at the output ports. Within the hub, energy is converted and conditioned using e.g. combined heat and power technology, transformers, power electronic devices, compressors, heat exchangers, and other equipment. Real facilities that can be considered as energy hubs are for example industrial plants (steel works, paper mills), larger buildings (airports, hospitals, and shopping malls), rural and urban districts, and island energy systems (trains, ships, and aircrafts)”. Because in most cases, in urban settlements, other forms of energy are turned into electrical energy and vice versa, other forms of energy are created thanks to electrical energy. In

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this view, the power system will soon host most of the energy resources and can be considered of central interest for further considerations and deeper studies. To this extent, one of the most important infrastructures of a urban energy hub is a microgrid which, taking the definition from the Department of Energy (USA), is defined as “a group of interconnected loads and distributed energy resources within clearly defined electrical boundaries that acts as a single controllable entity with respect to the grid. A microgrid, can connect and disconnect from the grid to enable it to operate in both grid-connected or island-mode”. In the CIGRÉ definition of microgrid, energy resources are generation, loads and storage devices (heat, flywheel, chemical, etc.). 4.1.1. Microgrids versus urban energy hubs Microgrids are one of the physical infrastructures over which the Urban Energy Hub operates. When serving an Urban Energy Hub [GUE 11, GUE 13], the following issues must be accounted for in the operation of a microgrid: – the interdependency of urban infrastructures (electric mobility infrastructure, gas infrastructure, water system, waste recycling, wastewater treatment); – limited penetration of RES, that in cities cannot be considered as relevant as it is in standard microgrids (as they are known and defined). As far as the first issue is concerned, it can be said that, although infrastructures and urban systems are often seen individually [WIL 12], i.e. transportation or wastewater/drainage and water supply, they are usually highly interactive and interdependent (see Figure 4.1).

Figure 4.1. Example of urban energy hub

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Figure 4.1 shows an example of the urban energy hub concept on which energy planning at district level in cities should be carried out. Wastewater treatment using a Membrane Bio-Reactor (MBR) [PAT 11] provides low-salinity gradient water that suitably combined with brine or salted water through Salinity Gradient Power technologies (Reverse Electrodialysis (RED) or Pressure-Retarded Osmosis (PRO) [PRA 14, TED 16, TED 15]) can produce electrical energy. An ongoing European project, REAPOWER [REA 16], is proving that this way of producing and eventually storing energy is very energy intensive and occupies limited volumes. Natural gas feeds cogeneration systems delivering electrical energy and heat. Heat could also be delivered through district heating or by burning biomass. Electricity, salted water and heat can be stored and delivered when needed so as to cope with different demand curves and renewable energy production. Such dependencies can be studied both during planning and normal operation as well as during strong cascading failure events. During planning and normal operation, the demand curve of other forms of resources (the energy multi-carrier concept in urban context) affects the operating condition of the power system and thus the microgrid. Electric mobility, electric heating as well as mini-hydro installations on water pipes are examples of how the demand of other urban services can affect electrical urban infrastructures. This systemic approach, whose optimal spatial scale has been identified by the scientific community in the district or neighborhood scale [CAR 09, ALL 15], seems to be the key for the optimized planning of the city. Recent studies, in fact, focus on the definition of integrated approaches applied to the energy field of the urban settlements [ALL 15, EVI 15b]. The main focus is on the interaction between buildings and energy infrastructures, such as thermal networks, systems for the production of heat from waste and energy production from renewable energy systems. In [ALL 15], it is indeed specified that it is no longer enough to simulate and study the use of energy by configuring the individual building as a system isolated from the micro-climatic and urban context in which it is located, as well as modeling urban energy systems without considering the “served buildings”. The work [ALL 15], with regard to this aspect, identifies three different fields of interaction at district level or urban systems: – the district energy systems, which include the ICT network, the electrical power grid, the heating/cooling distribution network (District Heating (DH) or District Cooling (DC)) and the transport network [MAN 14]; – the energy production from renewable sources (including solar, bio energy, wind and seasonal storage systems); – the urban microclimate and its relation to energy consumption.

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In this context, the buildings play an important role both as regards the electrical energy demand as well as the electrical energy supply. Many studies have been carried out in the field of risk analysis to study interdependencies of urban infrastructures and increased vulnerabilities under outages [BEC 15] or climate change effects [WIL 12]. The ICT infrastructure and the electrical infrastructure are studied in [BEC 15]. The study in [STE 16] proposes a dynamic dependency analysis for critical infrastructures taking into account large-scale, cross-sectoral, cascading and common-cause failures. Such an analysis is carried out by means of a critical infrastructure dependency analysis (CIDA) tool, which implements an extended risk-based methodology. The paper shows the cascading effect of a substation failure over other critical infrastructures. As far as the penetration of RES in urban contexts is concerned, the study carried out in [EVI 15a], based on past experience, proves that the potential of local supply-side technologies is limited in the urban environment, especially for renewable energies. Locally harvested commercially available renewable energy can, at most, cover a few percent points of the energy needs of a large high-density (HD) city and some percentage points in smaller, low-density (LD) cities due to the mismatch between urban energy demand density, which is high, and renewable energy supply densities at the local level, which is low in cities. The study in [LUN 15] shows that the installation of electric storage systems could significantly increase the share of renewable energy consumed annually. In addition, to store the excess electric power from renewable sources, a conversion system for the conversion of electric energy into thermal energy can be employed. Heat is indeed easier and cheaper to store with respect to electricity, for example, by means of hot or cold water accumulations in DH/DC systems. In this way, a parallel optimized management of the two systems – electrical and thermal – can be carried out. Increased production of electricity from RES may go beyond the traditional limits of self-consumption as well as offering higher flexibility to the electricity system. Looking at more recent implementations, and also to the future, two cases demonstrate that Microgrids in cities can increase the resilience of the Urban Energy System. One is the PowerMatching City which is a field project implemented in the small city of Hoogkerk, a neighborhood in Groningen city (NL) [POW 15]. Since 2009, the European field trial has been connecting the supply and demand of electricity and heat in a smart way. The objective of this project is to take full advantage of features of both centralized and decentralized renewable energy systems. By the end of 2011, 42 households were part of the Power Matching City, more clustered than before. A centralized system activates appliances and electric vehicles (EVs) recharging when energy from renewable sources is plenty and therefore much cheaper than average.

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The second case study from Siemens shows the advantages of microgrids during a weather storm in the United States [SIE 13]. In 2012, Superstorm Sandy seriously affected the electrical grid of New York City. The tri-generation plant at Co-Op City, a housing development in the Bronx, incorporates a 40 MW steam turbine, generates power, heat and cooling, whose microgrid serves 14,000 apartments in 35 towers. During the weather storm, the microgrid continued to provide electricity, heat, hot water and air-conditioning (A/C) for 60,000 residents, while neighboring areas remained without any form of energy supply. The upfront investment for this microgrid paid back after just 5 years, aided by the sale of surplus power back to the grid. Highly dense population settlements in the form of districts can indeed benefit from high-efficiency centralized plants, such as tri-generation or cogeneration units for providing electrical energy, heat, hot water and A/C. 4.2. Approaches and tools for urban energy hubs Three types of issues can arise while studying Urban Energy hubs: – policy: exploring systemic and individual impacts of different choices; – analysis: co-simulation approaches to consider the contribution deriving from the different critical infrastructures; – design and operation: choosing size, typologies for new infrastructures and optimal operation of resources and systems. 4.2.1. Policy With regard to the first issue, one of the most interesting topics to analyze is the exploration of new assets of the demand of urban services. The latter to be deployed needs an efficient urban energy system. What has been observed in existing cities is that systemic features of urban energy use are generally more relevant determinants affecting the energy efficiency use rather than those of single consumers or of technological artifacts [GRU]. As an example, “the share of high occupancy public and/or non-motorized transport modes in urban mobility is a more important determinant of urban transport energy use than the efficiency of the urban vehicle fleet (be it buses or hybrid automobiles). Denser, multifamily dwellings in compact settlement forms with a corresponding higher share of non-automobile mobility (even without thermal retrofit) can use less total energy than low-density, single-family ‘Passivhaus-standard’ (or even ‘active’ net energy generating) homes in dispersed suburbs deploying two hybrid automobiles for work commutes and daily family chores”. This calls for the aggregation and management of electrical energy consumption through demand response policies or other measures, especially in cities.

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4.2.2. Analysis The analysis of Urban Energy hubs refers to the possibility to simulate the behavior of the different parts of the system and to deploy output features, namely thermal and electrical demand curves. In urban contexts, it seems convenient that such analyses be carried out by means of co-simulation tools, as suggested in [MOL 14, ALL 15]. Such co-simulation in most cases refers to different time scales and different scales of the buildings (individual building/district) and typically accounting for thermal issues, considering the electrical infrastructure and relevant components under largely simplified hypotheses. Some authors have tried to co-simulate electrical and thermal systems. In [MOL 14], a multi-domain customized simulation platform allows for a holistic analysis of urban energy systems. The platform allows for long-term simulations of a large number of buildings, including internal energy supply or energy conversion systems, together with exogenous energy sources such as the main electrical grid. The simulation of all these physical systems allows for the evaluation of sophisticated energy management algorithms. However, the question about the usefulness of getting to such level of details in planning or energy management still remains. Other simulation environments are also widely used in the literature for urban energy systems modeling. Some multi-disciplinary tools have capabilities that clearly span many or all of the areas of interest such as building systems, user behavior, district energy network and RES production. CitySim [THO 14, MIL 15] is an example of multi-disciplinary tool; it simulates multiple buildings up to the city scale using simplified models. The thermal performance of each building’s systems, as an example, is simulated by an electrical analogy using a resistor-capacitor network with two nodes. The tool CitySim was developed to support decision-making for sustainable urban planning by modeling resource flows of urban configurations. It consists of a simple resistor-capacitor thermal model for simulating the energy performance of the building stock and a radiation model for shortwave radiation to identify solar gains on facades and roofs. In addition to incident shortwave radiation, CitySim accounts for longwave radiation exchange between external surfaces and the environment. It also integrates a number of energy system models for heat pumps, boilers, cogeneration plants and buildingintegrated PV systems. A stochastic occupant behavior model is included to represent uncertainties regarding the behavior of people within the buildings [ALL 15]. In some works, a co-simulation involving Energyplus (mostly used as building-level simulation tool) and CitySim was implemented. This allowed for

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detecting the behavior of several buildings starting from the Building Information Model (BIM). Energyplus employs a detailed model at building scale, while Citysim considers simplified models in order to account for the behavior of the district. CitySim has indeed more advanced capabilities for radiation exchange calculations from a set of urban buildings and EnergyPlus has a more advanced calculation engine for building heating and cooling load at single building scale. CitySim and EnergyPlus, however, do not account for the presence of the electrical infrastructure and its behavior. It is also worth mentioning here EnergyPlan [ØST 15]. EnergyPlan performs hourly multi-domain simulations of the operation of large energy systems, including electricity, heating, cooling, industry and transport. It was developed at Aalborg University, Denmark. The model is disseminated as a freeware and can manage the simulation of different scenarios including very up-to-date energy generation technologies. It can be used for different types of energy system analysis: technical, market exchange and feasibility analysis studies. Inputs are electrical and thermal load curves with 1 h resolution, weather data and energy sources availability data, efficiencies and capital cost of energy conversion technologies, O&M costs, emission constraints and optimization strategies. Outputs are energy production, costs and emissions for the selected strategy. These tools can be used not only for feasibility evaluation of large-scale Distributed Generation (DG) system projects, but also for the analysis of DG in urban districts [MAN 11, KEI 12]. Most software tools also provide in-cloud computational features, such as EnergyPlus, achieving 5–10 times faster computation than desktop runtimes. Among the simulation tools that account mostly for the electrical system behavior, both Hybrid2 and GRID-Lab are quite reliable computation engines, with different features. The Hybrid2 [HYB 15] software package is a free user-friendly tool to perform detailed long-term performance and economic analysis on a wide variety of hybrid electrical power systems, using time series data to predict the performance of the hybrid power system. It was designed to study a wide variety of hybrid power systems, which may include three types of electrical loads, multiple wind turbines of different types, photovoltaic, multiple diesel generators, battery storage and four types of power conversion devices. Systems can be modeled on the AC, DC or both buses. A variety of different control strategies/options may be implemented, which incorporate detailed diesel dispatch as well as interactions between diesel gensets and batteries. An economic analysis tool is also included, which calculates the economic worth of the project using many economic and performance parameters. The Hybrid2 code employs a user-friendly Graphical User Interface (GUI) and a glossary of terms commonly associated with hybrid power systems. Hybrid2 is also packaged with a library of equipment to assist the user in designing hybrid power systems.

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GridLAB-D [GRI 15] is a recent free open source program, which is run as a console application, so it does not provide a GUI. Because of this, the software may not be user-friendly. A new power distribution system simulation and analysis tool provides valuable information to users who design and operate distribution grids and to utilities that wish to take advantage of the latest energy technologies. GridLAB-D incorporates the most advanced modeling techniques, with highperformance algorithms to deliver the best in end-use modeling. GridLAB-D was developed by the US Department of Energy (DOE) at Pacific Northwest National Laboratory (PNNL) under funding for Office of Electricity in collaboration with industry and academia. The core of GridLAB-D has an advanced algorithm that simultaneously coordinates the state of millions of independent devices, each of which is described by multiple differential equations. With the ability to study distribution utility system behavior over periods of time that range from seconds to decades, GridLAB-D simulates the interactions between physical phenomena, business systems, markets and regional economics and customer interactions, and how they each affect the power system. RETScreen [RET 15] can be defined as simulation software aiming at decision support between alternatives. It is a free energy management simulation program for energy efficiency, renewable energy and cogeneration, aimed at evaluating renewable energy projects feasibility as well as ongoing energy performance. The software can be used to evaluate the energy production and savings, costs, emission reductions, financial viability and risks for various types of Renewable-energy and Energy-efficient Technologies (RETs). The software also includes product, project, benchmark, hydrology and climate databases. RETScreen software consists of two separate programs, one helping decision makers to determine the technical and financial viability of potential clean energy projects, and the other providing energy management software that allows project owners to verify the ongoing energy performance of their facilities. Fundamental to the RETScreen software is the comparison between a base case, typically the conventional technology, and a renewable energy-based solution. RETScreen ultimately does not address the issue of absolute costs but rather of the incremental costs as compared to the base case. RAPSim [RAP 15] is a freeware developed at the Institute of Networked and Embedded Systems of the Alpen Adria University Klagenfurt. It provides basic models for the simulation of various RES and load demands within a microgrid. RAPSim is able to simulate the performance of the applied RES considering some uncertainty of the meteorological conditions. The simulator is further able to conduct power flow analysis for the microgrid, which helps in analyzing the impact of the RES on the power system. Finally, the user can easily implement own models or algorithms and modify existing ones. This software is helpful in simulating smart microgrids, in modeling its components as a part of a self-organizing system and in placing optimally RES in the power system to achieve the best power quality and

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flow connditions. Thee proposed sooftware tool for f microgridd simulation ccombines models for f RES and power p grid sim mulation meth hods. Further, it is intendedd to keep the softw ware modularr and open too use in com mbination withh other tools, e.g. for importinng meteorological data. Whatt is missing inn the existingg literature abo out urban eneergy hubs sim mulation is the conssideration off the differennt urban serv vices networkks and their possible interactioons at design and a operation levels. Co-siimulation shoould therefore be addressed d to the possibble interactionns among the diffeerent services networks. Inddeed, efficienccy can be attained at both uutilization and suppply-side levelss (renewable generation, g effficient use off electrical andd thermal energy) as well as at the t infrastructtural level, wh here quality isssues are also involved (see Figuure 4.2).

Figure 4.2. Fea atures of the urban u energy hub h

Urbaan infrastructuures may indeeed also be afffected by conccurrent optimiization in managinng resources at a supply andd utilization leevels. Such innteractions arre neither modeledd through co-simulation noor studied in the literaturee. Take mini--hydro in drinkable water systeems as an exxample [KOU U 14, CAS 15]. Both worrks show t wire pow wer systems for f the integration of the efficciency of in--pipe water to renewable resources at a urban and building b scales. With capaccity to operatee across a m or microo-hydro generrators can large rannge of heat annd flow condiitions, these minibe deplooyed in municcipalities, enerrgy-intensive industries i andd agricultural irrigation districts providing a consistent c amount of clean and continuoous energy wiithout the me helping inn pipeline intermitttency of windd and solar ennergies and att the same tim managem ment and mainntenance.

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Also, the electrical power infrastructure and the natural gas infrastructure have several couplings at the compressor and pumping stations that cause inter-linkages between the two infrastructures. Gas networks, which are in buried infrastructures, in contrast to road and electric power grids, can provide more stable service during severe weather events. Gas could also contribute broadly to economic resiliency of cities, as an alternative to microgrids technology, by providing diversification, redundancy and backup systems in urban microgrids [EVA 13]. Infrastructure

DER presence

Simulation of control

Simulation time step

MESCOS

Electrical-Thermal

Yes

Yes (complex)

Second

CITYSIM

Thermal

Yes

No

Hourly

ENERGYPLUS

Thermal

Yes

No

Minute

ENERGYPLAN

Electrical-ThermalTransport

Yes

Yes (simple)

Hourly

HYBRID2

Electrical

Yes

Yes (complex)

5 min

GRID-LAB

Electrical (detailed)

Yes

Yes (complex)

Sub-seconds

RETSCREEN

Electrical-Thermal

Yes

Yes (simple)

Hourly

RAPSIM

Electrical (detailed)

Yes

No

Minutes

Table 4.1. Simulation tools for Urban Energy systems

4.2.3. Optimal design and operation tools As far as the optimal operation and design issues are concerned, the problem is about providing optimized units size and operational dispatch given as inputs the demand curves of those flows that can be considered as energy carriers, i.e. heat, electricity, mobility and water. Both [MAN 11] and [KEI 12] provide reviews about approaches specifically designed for urban energy systems. Both papers refer to energy hubs not accounting much for the infrastructural issues. In many works, however, it is common to find operation and design issues solved for urban microgrids and energy hubs by means of highly efficient software tools often available as freeware. In this work, a wide overview of optimization software tools for microgrid analysis and planning is given. The most common optimization software tools are HOMER [SIN 15, LAM 06] and DER-CAM [HOM 15], which can be used to run simulations of urban energy systems. HOMER supports the design and optimization of microgrid systems by

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evaluating different configurations based on different parameters, but primarily on lifecycle cost. Moreover, HOMER allows for the evaluation of the technical feasibility of the system, through simulations carried out over an entire year of operation. HOMER allows the modeler to create a complete microgrid framework. It is possible to handle different energy carriers (electricity, heat, hydrogen) and simulate several devices that can generate, absorb or transform these energy carriers: electrical generators, grid, boilers (dispatchable energy sources); PV modules, wind turbines, hydro turbines (unpredictable renewable sources); electrical converter (AC/DC and DC/AC), electrolyzers (conversion device) and batteries and hydrogen tanks (storage device). Loads are of two types: electrical (primary or deferrable) and thermal. All the economic and technical parameters of these elements should be configured by the user on an hourly scale in order to perform the simulations. For this purpose, the software provides databases with complete information, especially for loads or resources. In fact, HOMER sets the data of natural renewable sources over a year. Once the microgrid structure is defined, the modeler can set any simulation options regarding the economic evaluation (interests, project lifetime, etc.) and system control condition (objective of minimization, dispatch strategy, etc.). In the optimization process, HOMER simulates many different system configurations in search of the one that meets the technical constraints at the lowest lifecycle cost. In the sensitivity analysis process, HOMER performs multiple optimizations under a range of input assumptions to gauge the effects of uncertainty or changes in the model inputs. HOMER can also perform sensitivity analyses to assess how and to what extent quantities are inter-related. The second optimal operation and planning tool, DER-CAM, conceived at the Berkeley Labs in the United States, is a techno-economic optimization decision support tool. It outputs, as an example, the lowest-cost layout of distributed generation technologies for a specific building. It focuses on the analytics, planning and operations of these systems, which involve several Distributed Energy Resources (DER) and two energy carriers, electricity and thermal energy. However, it is also possible to optimize the layout of microgrids. In DER-CAM, the resolution of the input data can arrive to 5 min [DER 15]. The free DER-CAM Web optimization tool is called WebOpt. In this free version, it is not possible to define the microgrid framework, but it is possible to set the proprieties of all the devices and technologies expected to be installed in the studied system. The first step concerns the optimization settings: here the investment in DER and some features of these technologies and many optimization options are chosen. In particular, user can decide the optimization objective, a cost minimization or a CO2 minimization (this is led by cost constraints). It is also possible to calculate a multi-objective optimization: WebOpt provides from a minimum of five to a maximum of 10 points of the optimal frontier. After that, the user must set the load profiles. There are several loads modeled by the software: electricity, cooling,

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refrigeration, space-heating, water-heating, natural gas only. For each of these loads, three load values can be set: week, weekend and peak. WebOpt also provides a very large database of final user load profiles, for new construction, before and after 1980. Additionally, the user can insert load data manually. Furthermore, this tool allows defining fixed plus time-of-use (TOU) pricing for both energy and power (demand) charges in the Utility tariffs tab. Eventually, after having performed an optimization, a table can be outputted, in which summaries, annual reports, data on detail analyses and graphics of electrical load, heat and building cooling are reported. Each energy carrier provider is also indicated. iHOGA [IHO 15] is a free (educational version) simulation and optimization program for hybrid renewable systems for the generation of electrical energy (DC and AC) and/or hydrogen. The optimization is achieved by minimizing total system costs throughout the whole of its useful lifespan, when those costs are referred to or updated for the initial investment by means of the net present cost (NPC) index. The optimization is therefore mono-objective and financially driven. However, the application allows for multi-objective optimization, where additional objective functions may also be minimized using genetic algorithms: CO2 emissions or unmet load (energy not served). The hybrid system may comprise a very large range of electrical devices and technologies. It simulates both stand-alone or grid-connected systems. iHOGA uses very accurate models for resources, components, economical calculations and control strategies that can be optimized. Finally, it considers the evaluation of lifecycle emissions and the possibility of purchasing and/or selling the energy with the electrical grid. Infrastructure

DER presence

Simulation of control included

Simulation time step

Optimization

HOMER

ElectricalThermal

Yes

Yes (set by the user)

Up to 1 min resolution

Lifecycle cost or net present cost

DERCAM (WebOpt)

Electrical(*)

Yes

No

5 min

Minimum cost & emissions

iHOGA

Electrical

Yes

Yes

1h

Net present cost, emissions, unmet load

(*) Not under the freeware version.

Table 4.2. Optimization tools for urban energy systems

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However, all cited software tools, for both analysis and optimal design and operation, perform simulations referring to an energy planning point of view and none addresses the problem of linking energy features with contextual features. As already outlined, such linkage may be relevant in urban contexts, where the urban form significantly affects consumptions of all resources. An interesting recent attempt to fill this gap is proposed by the Pro Forma project [ENT 16] of the Massachusetts Institute of Technology laboratories. On their website, the software can be downloaded for free. The online analysis and design tool estimates the energy use of a city’s residents based on their neighborhood’s design characteristics. In the Urban Taxonomy, it explores the many forms that clean energy neighborhoods can take and produces results. The software evaluates the operational energy consumption by differently integrating high- and low-rise buildings with different patterns of form. Orientations, proximity of buildings as well as the energy consumption inherently are considered in each form adoption. As an example, in HD perimeters blocks districts, city streets surrounding the blocks maximize opportunities for shops, restaurants, services, schools and parking structures to be integrated in the fabric, all conveniently accessible because of the streets layout. In this way, individual transportation impact is limited. Animated public streets encourage walking and use of the public realm, tending to reduce the use of cars and the time spent by people in their apartments, reducing energy consumption. The density that may be achieved by this prototype makes mass transit more feasible. Considerations about embodied1 energy in this case suggest that taller structures require heavier construction, more steel and therefore have more embodied energy. As with passive measures, this prototype has less potential of incorporating renewable energy systems than a more organized form, notwithstanding individual opportunities on a building by building basis. All these considerations lead to the definition of energy consumption and carbon emissions per year based on average building height, building coverage, south facing walls, building function mix, commercial areas in percent of whole area and roof PV coverage. However, the approach does not consider inter-related infrastructural issues (how the operation or the demand on one infrastructure affects the others) and a clear methodology of how the energy assessments about mobility and consumptions are performed is not outlined. In the next section, the authors propose a new approach for finding a nexus between urban planning parameters and electrical and thermal planning features so as to provide the urban planning expert, tools to address energy planning in cities. 1 The energy used in manufacturing materials, transporting materials to the construction site, and then assembling the materials into the neighborhood’s physical spaces and infrastructures. This includes not only buildings and streets, but also the full scope of lifecycle analysis (LCA), from excavation to demolition.

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Electricaal mobility deemand is conssidered throug gh a statisticall model and results are integrateed in the co-simulation tool. The approacch can easily integrate i infraastructural operationn issues couplling it with theermal or electrrical grids sim mulators. This approach wass applied to tw wo different disstricts of a sm mall city in Siciily. 4.3. Metthodology The proposed p methhodology triess to integrate different simuulation tools too set up a co-simullation environnment so as too devise an op ptimized layoout of the resoources for retrofittinng of urban ennergy hubs. The T ultimate go oal is to identiify a meaninggful nexus between urban param meters and energy e featurees in order to offer toolls for an qualification of o districts. Figure 4.3 immediaate preliminarry analysis foor energy req shows thhe methodologgical approachh to the probleem. Electricall, thermal andd mobility simulatoors are integraated to devisee the optimizeed layout of renewable r souurces and other eneergy generatioon sources in the t district. So olutions produuce different eeffects on the envirronment basedd on the so-caalled “urban morphology”. m This methodologyy is used heree for differentt districts of the t same city showing a index-baseed representatiion of the differentt housing denssities, in orderr to produce an differentt urban morphhologies. The starting pointt of the methoodology is to ddefine the main urbban features of the analyzzed districts. Through the analysis of m municipal cartograpphies and thee urban reguulatory framew work, the maain indices oof “urban morphollogies” are ideentified speciffying the mean ning and the possible p energy needs.

Figure 4.3. Methodologic cal approach

4.3.1. Building B type e and urban n energy parrameter spe ecification The first point of the methoddology is the characterization of the bbuildings, because these facilitiees define the major m consump ption in the diistrict togetherr with the d for thee transports. energy demand

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Units and formula

Parameter

Meaning and use

Basic urban energy parameter District’s inhabitant (Di)

n.

–

Total number of the district’s buildings (Bn)

n.

–

District’s area (Da)

m2

–

2

m

–

District’s green area (Dg)

m2

Provides information about the district’s surface that may be available for installation of integrated vertical axis RES small wind that have less environmental impact and more possibilities of installation in urban environment, integrated PV systems on roofs, etc. Green spaces, if with high-growing trees, also have a mitigating effect of the Urban heat island2 (Uhi).

District’s streets area (Ds)

m2

Gives indications of non-permeable surfaces of the district affecting Uhi.

District’s built area (Db)

m

Gives indications on the installation potential of PV systems on buildings in the district. It indicates the total area of the roofs of the district.

Available district’s roof area (Dra)

m2

Indicates the useful area for installation of PV systems. It is calculated by applying a percentage reduction to the total area of the roofs of the district (Dr). This percentage depends on the exposure of roofs (not considering the slopes exposed to the north) and the shadows created by obstacles (i.e. volumes skylight and/or technical room of the building’s lift). This can be simulated by means of specific software or displacement maps of the district.

District’s thermal transfer surface (Dts)

m2

Equals the sum of the dispersant surfaces of the buildings of the district (roof area, external surfaces and building’s ground area).

District’s roof area (Dr)

2

2 Urban systems are now considered with higher temperatures than rural areas contiguous to them. They are defined as “urban heat island effect”. The phenomenon is characterized by a differential temperature between the center and periphery up to 10–15°C higher in urban areas. The factors influencing this phenomenon are both geographical and are based on urban planning studies (e.g. altitude, vegetation, size and urban morphology, human activities such as traffic flow).

Urban Energy Hubs and Microgrids: Smart Energy Planning for Cities

Average district’s building height (H)

m2

145

–

Equals the sum of the heated volume of the district’s buildings. Gives an indication of the average compactness of the district’s buildings that is also linked to the prevailing architectural style of the district Sdf = Dts/Bgv (e.g. if they are buildings blocks, more compact, Shape district factor (Sdf) (1/m) or in-line buildings, less compact). Moreover, in general, low Sdf values are indicative of highly efficient building shapes from an energy point of view. Gives an indication of the “building density” of the district, in the planning level it represents Territorial density index Tdix=Bgv/Da the maximum volume that can be built per unit 3 2 (Tdix) (m /m ) area; high values of this parameter identify high-density urban contexts. Parameters that characterize the urban microclimate (these parameters will not be detailed in this paper) Is parameter that affects the microclimate of the site, thus impacting greatly on the demand for energy in buildings. It is in fact linked to the possibility of natural ventilation. In general, the microclimate conditions in rural or low-density areas differ much from those in urban or highAverage distance between M density areas. The temperature of the latter is the buildings (Bd) indeed much higher because of the value of Uhi; the wind speed is less because of the height, the proximity and density of the buildings in the district and the solar radiation is influenced by the effect of shading and reflection given by the neighboring buildings [SAN 01, RAT 05]. Expresses the ratio between the depth of urban canyons and their density. The value is expressed by a real number between 0 and 1. In terms of Uhi, a meaningful value of Svf (tall buildings, divided by a narrow street) translates Sky View Factor (Svf) the possibility of a stronger heat accumulation of the interested buildings. This happens because the solar radiation is “caught” in the canyon, bounces on a building heating them more that in an open situation. District’s heating buildings volume (Bgv)

m3

Table 4.3. Basic urban-energy parameters for residential districts

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The factors affecting the consumption of buildings in urban areas, and therefore the energy demand to be met [SAL 09], can be identified as follows: 1) efficiency of urban form, and in particular its density (MIT studies show that efficient urban morphology can reduce energy consumption and CO2 emissions by a factor of two). This factor can be characterized by the parameters of Table 4.3 characterizing the urban microclimate; 2) the building’s performance, which is determined by geometric characteristics, thermo-physical characteristics of the envelope and efficiency of equipment and systems [SAN 01, RAT 05]; 3) the inhabitants’ behavior, which has a significant impact on the different modes of use of equipment and systems in buildings and on the consequent energy consumption linked to them; 4) the type of energy used (the difference of the contribution to the greenhouse effect varies up to a factor of 10 between energy from fossil fuels and renewable energy). An engineering bottom-up approach is used for building characterization [SWA 09, PAR 05]. From the analysis of the buildings in the contexts to be analyzed, through a survey that refers to the main engineering characteristics of the buildings and refers to point 2 in the previous list, it is possible to identify the “building typologies” (archetypes) that cluster the different buildings of the districts [FER 16]. It is assumed that point 2 could be summed up by the geometric and shape parameters of the buildings and by the energy parameters related to the construction period of the buildings. By the use of simulation software, it is possible to calculate the thermal consumption, Heating (H) and Domestic Hot Water (DHW) demand of the identified building typologies. The total thermal loads of the building stock of the district are then calculated by multiplying the consumption of each building typology for the respective number of buildings of the district attributable to each of them. Table 4.4 shows the main features for the modeling of each building typology in order to evaluate the thermal loads. For what concerns the inhabitants behavior (point 3 of the list above), this can be standardized referring to the typical use of the heating systems related to the specific climate zone where the district is located. Standard consumption can also be taken as regards the demand for electricity, referring regulatory or experimental scientific papers (in the case of Sicily, Italy, see, for example, [FIL 14]).

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Identified building typology

147

Geometrical characteristics of the identified building typology Total floors Dwellings External building Heated surface area Floors (n.) volume, V surface, S (m2) (n.) (m2) (m3)

S/V(*) (1/m)

Architectural and energy characteristics of the identified building typology A

Value of transmittance (W/m2K)

Construction period Ground floor

External walls

Heating and DHW system type

Roof Windows

Heating(**), H

Domestic hot water(**) DHW

Type(***)

(*) “Shape ratio” is the ratio between the external building surface (S) and the heated volume (V) that this surface envelopes. (**) System type and type of energy (electricity, gas, etc.). (***) Autonomous for dwelling or centralized; Combined (H+DHW) or not.

Table 4.4. Parameter for the building typologies characterization to evaluate the thermal loads

4.3.2. Mobility simulator The electric mobility has been simulated considering a Monte Carlo approach [DI 13]. The simulator has as inputs the number of vehicles in the parking lot, the types of EVs (battery electric vehicles, plug-in hybrid electric vehicles, extended range electric vehicles) and the number of vehicles in each district. The two districts host 22 and 125 families, respectively, in the LD and HD assets. The software, implemented by the authors, allows for evaluating the load consumption profile for groups of EVs showing different features. The approach combines different social and economical features. In this way, the daily consumption of EVs is deduced; the software then calculates the initial state of charge of each EV and computes the daily need of recharge. The simulation software allows considering different types of EVs or hybrid vehicles. In order to model the stochastic nature of the phenomenon, it is required to numerically express the following issues: – the vehicles recharge starts at a time related to the final use of the vehicle or to the strategy implemented by the control system;

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– The initial State of Charge (SOC) of the battery depends on the distance travelled by the vehicle and thus also on the final use of the vehicle (student/professional/housewife). Once the final use of the vehicle is devised, it is possible to represent the hour at which the recharge starts as a random variable, with a probability density function f(t), which is determined by the adopted strategy. Similarly, the initial SOC of the battery serving the EV (residual capacity since the last recharge), E is a random variable with values ranging from 0 to the maximum capacity of the battery, whose probability distribution h(E) depends on the distance travelled since the last recharge. On the basis of the model proposed in [LIN 01], the probability distribution related to the distance travelled is of lognormal type, with a probability of occurrence of negative distances, which is null and with a “tail” that reaches infinite values of travelled distances:

g (d ; μ , σ ) =

1 d 2πσ

2

e

−

( ln ( d − μ ) )2 2σ 2

d >0

[4.1]

where d is the daily distance travelled by the vehicle, μ is the average and σ is the standard deviation of the probability function. The basic input of the probability distribution is the average distance of each trip. The average distance, also called VMT (Vehicle Miles Travelled) [CER 12], can be deduced according to many factors such as those describing the structure and demographics of the household, including the number of household members of driving age and household income, the vehicle ownership of the household and the characteristics of the transportation system in the region in which the household is located (such as freeway lanes-miles). The study [CER 12] recalls that there is still the question of increases in local traffic congestion simply due to the concentration of activity, namely due to the form of the urban settlement. Existing studies suggest, however, that compact mixed-use areas (HD districts) are better able to manage their traffic effectively. In general, grids provide more regularity, which allows for better signal coordination while also inducing a larger number of citizens to walk in highly connected areas (assuming it is a fine-grained, and not a superblock, grid). Besides providing more effective capacity between any couple of places in the district, these grids lead to efficiency due to a larger number of feasible paths. An obstacle along one path need not lead to gridlock, but simply to the creation of a new system of paths to work around the obstacle. The grids also help to channelize traffic, such that different travelers with different headings and different travel styles can plot their own ideal path and free up space for others on the facilities they do not use.

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Given these data about the distance travelled, the initial SOC can be deduced using the following expression: ⎛ αd ⎞ Ei = ⎜ 1 − ⎟ *100% dR ⎠ ⎝

[4.2]

where Ei is the initial SOC of the battery serving the vehicle, d is the daily distance traveled (random variable with a distribution described in [4.1]), α is the number of days the EV has travelled and dR is the maximum autonomy of the EV in terms of distance, which is taken 128 km for Full Electric Vehicles (FEV). For equations [4.1] and [4.2], the probability density function returning the initial SOC can be deduced:

h( E ; μ , σ ) =

1 dR

α

(1 − E ) 2πσ 2

e

⎡ ⎛ ⎛ d R ⎞ ⎞⎤ ⎢ln(1− E ) −⎜ μ − ln ⎜ ⎟ ⎟⎥ ⎝ α ⎠ ⎠⎦ ⎝ ⎣ − 2σ 2

2

,0 < E 0) and negative value (revenue) when

i the system is exporting ( uˆEXT > 0). Limitations can be applied to the maximum imported or exported power, due, for example, to contractual obligations: i i ˆi − PEXP max ≤ u EXT ≤ PIMP max

[5.11]

5.2.2.2. Renewable generating units

Since production from renewable energy sources (RES) is characterized by a negligible marginal price, and the optimization procedure proposed here is related to an operation problem and not a planning problem, the power produced by PV is considered costless. This means that the optimizer will exploit renewable generation i as much as possible. The discretized power input from PV, namely uˆ PV , is constrained only by maximum available power output, as expected. It is assumed that whenever RES production exceeds load plus storage charging power, generation can be curtailed or dump loads can be activated. Equation [5.9] is given by: i i ≤ PPV 0 ≤ uˆPV max

[5.12]

Usually, all producible power is employed unless peculiar circumstances occurr. A possible case would be when the storage units are full and the electrical link with the external grid is congested or disconnected. 5.2.2.3. Gas turbine and gas boiler

In the proposed system (Figure 5.1), the presence of a gas turbine is assumed. Clearly, the formulation is general enough to be extended to any other generator. i is limited in [5.9] considering the existence The power output of the gas turbine uˆGT of technical–economical feasibility limits: i i if PGT min ≤ uˆGT ≤ PGT max ⎪⎧uˆ i uˆGT = ⎨ GT ⎪⎩otherwise 0

∀i

[5.13]

Operating costs have been associated to natural gas consumption, and are modeled considering the nonlinear dependence of efficiency with respect to electrical power output. Such dependence can be formulated by interpolating efficiency/power output data found in technical sheets. Having fixed the cost of natural gas cgas and said η GT the efficiency as a function of power output, cost in [5.7] is calculated as: i i cGT (uˆGT ) = cgas ⋅ηGT (uˆGT ) ⋅ Δt

[5.14]

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Further variable costs, such as operation and maintenance (O&M) costs, can also be added. The amount of thermal energy produced through cogeneration is calculated considering a linear dependence with the electrical power output. The boiler thermal output is limited by its rating: i ≤ PBTi max 0 ≤ uˆBT

[5.15]

whereas gas consumption costs are easily derived considering the efficiency η BT of the boiler. 5.2.2.4. Battery energy storage system

The quantity of power exchanged with the BESS at each time step is described i i and uˆ DB , that represent BESS charging and discharging by two variables, uˆCB power, respectively. Each variable is limited by maximum charge and discharge power: i ≤ PCB max 0 ≤ uˆCB

[5.16]

i ≤ PDB max 0 ≤ uˆDB

[5.17]

Charge-related inequality constraints are aimed at limiting the state of charge (SOC) of the battery. Roundtrip efficiency is adopted, according to the assumption of a single bus model [BAR 96]. Under these assumptions, equations [5.6] and [5.10] are: i

i i qˆ Bi = QB0 + ∑ (η B rte ⋅ uˆCB − uˆDB ) ⋅ Δt

[5.18]

qmin B ≤ qˆBi ≤ qmax B

[5.19]

k =1

where η B rte is the BESS round trip efficiency and QB0 is the initial charge of BESS. Knowing the maximum rated BESS capacity QB max , the two charging limits in [5.19] can be derived having fixed a minimum and maximum SOC: qmin B = SOCmin ⋅ QB max qmax B = SOCmax ⋅ QB max

[5.20]

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The maximum and minimum SOC can be set so that the life span of the battery is maximized and a good level of reserve is always kept during real-time operation. Usually, minimum SOC sets an expected number of lifecycles nlife cycles . From these quantities, it is possible to calculate what is defined as battery throughput and represents the expected value of energy that will be cycling through the battery, completing a charge/discharge cycle, before the battery has to be substituted [LAM 06]. BESS life throughput can be evaluated, conservatively, as:

QtpB = QB max ⋅ (1 − SOCmin ) ⋅ nlife cycles

[5.21]

The BESS throughput is used in order to asses wear costs of the battery. Wear cost is simply formulated as the ratio of the substitution cost of batteries to the total throughput. In the proposed model, wear cost is associated to the discharge phase only, so that battery charge has no cost and is always maximized. The cost function appearing in [5.7] is formulated as: cB =

substitution cost i ⋅ uˆ DB ⋅ Δt QtpB

[5.22]

5.2.2.5. Water pumping storage system

A pumping storage system can be formulated similarly to the BESS. Pumped and generated powers are limited by pump and hydroelectric turbine requirements: i ≤ PCW max 0 ≤ uˆCW

[5.23]

i ≤ PDW max 0 ≤ uˆDW

[5.24]

In the pumping system, the role of the maximum SOC is played by the maximum level of water storable in the reservoir. Roundtrip efficiency is also introduced, taking into account losses in pump, pipes and turbine. Constraints in [5.6] and [5.10] can be written as: i

i i qˆWi = QW0 + ∑ (ηW rte ⋅ uˆCW − uˆDW ) ⋅ Δt

[5.25]

qmin W ≤ qˆWi ≤ qmaxW

[5.26]

k =1

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where ηW rte is the pumping storage round trip efficiency and QW0 is the initial charge. Minimum and maximum storable energy is expressed as a function of minimum and maximum volume of storable water and geodetic fall. As in the previous storage case, a cost cW associated to the sole discharging phase is defined. This cost can be assessed considering the average number of working hours before a major maintenance intervention is necessary. 5.2.2.6. Power balance, loads and interruptible loads

In the proposed methodology, chronological load curves are assumed as inputs of the optimization problem. The two power balance equations are given for each time step by: i i i i i i i i uˆ EXT + uˆGT + uˆPV − uˆCB + uˆDB − uˆCW + uˆDW + uˆ LS = PELi

[5.27]

i i i k2, GT ⋅ uˆGT + uˆBT − uˆTdiss = PTLi

[5.28]

where PELi and PTLi are respectively the average forecasted electric and thermal i represents the quantity of electric load that is loads at the i-th time step; uˆ LS interrupted, and therefore is multiplied by a positive coefficient in [5.27], similarly i represents the quantity of thermal power generation to generation sources; uˆTdiss

surplus that must be dissipated and k2, GT is a coefficient that takes into account the relationship between the quantity of electric power produced by the gas turbine and the thermal heating power available to thermal loads, according to the electrical and thermal efficiency of the gas turbine and the efficiency of the heat exchanger. i is a control variable It is also assumed that the amount of interrupted load uˆLS limited by the actual total demand at a specific time:

i ≤ PELi 0 ≤ uˆ LS

[5.29]

Interruption costs can vary according to the quantity, interruption duration and typology of curtailed load. A simple, but not limiting, hypothesis consists in assuming that interruptible and firm loads have two different constant interruption

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costs ( cL int and cL firm ). If PLi int is the cumulative amount of interruptible loads, the overall interruption cost is: i cL int ⋅ uˆLS ⎪⎧ i cLS (uˆLS )=⎨ i i i ⎪⎩cL firm (uˆLS − PL int ) + cL int ⋅ PL int

i ≤ PLi int if 0 ≤ uˆ LS i ≤ PELi if PLi int ≤ uˆLS

[5.30]

5.2.3. Test results

Tests are aimed at showing the feasibility of the proposed methodology for the solution of an operating problem for a small-scale multi-carrier energy system that could represent, for example, a small–medium enterprise or a set of buildings. It is supposed, according to the scheme in Figure 5.1, that generation resources are employed to satisfy the internal electric and thermal demand. The optimal dispatch is calculated considering the load and generation forecast in a 72 h time window (Figures 5.3–5.5). The forecasted scenario is characterized by a day (the second one) where PV generation is drastically reduced due to unfavorable weather conditions and the electric load is simultaneously increased.

Figure 5.3. Electric demand forecast

It was assumed that a 100 kWh BESS system with a charge/discharge time of 4 h, a 120 kWh pumping storage unit with a charge/discharge time of 12 h and a 200 kWt gas boiler are installed.

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Figure 5.4. Heating energy demand forecast

Figure 5.5. Photovoltaics generation forecast

The gas turbine is rated 100 kW. The minimum power output of the cogeneration unit is 30% of rated power, whereas efficiency is 0.6 of maximum efficiency at 25%, 0.9 at 50%, 1.0 at 75% and 1.0 at 100%. It was also assumed that for each kWh of electricity produced by the gas turbine, 1.5 kWht is cogenerated. Other efficiencies are η B rte = 0.8 and ηW rte = 0.5.

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For the BESS, a 30% SOCmin, a total number of 2,400 cycles before substitution and a wear cost of about 0.12 €/kWh were hypothesized. Other substitution costs are negligible with respect to BESS wear cost. Interruption costs were set at 0.5 €/kWh for interruptible and 2.5 €/kWh for firm loads. The gas cost was assumed to be 0.40 €/Nm3. 5.2.3.1. Case A, greedy optimization

In this first case, the problem is solved considering a greedy optimization strategy, where resources are optimized for each time interval. The size of time steps Δt is set to 1 h. The overall operating cost for the 3 days is about €970. The overall supplied demand is 6,520 kWh (electric) and 5,700 kWht (thermal) with a production of about 2,300 kWh from the PV generators. The average cost of energy is quite low, but it should be remembered that this cost considers only short-term variable costs and it does not include capital costs. A consistent amount of electric power demand is covered by RES generation, which is modeled with a null marginal cost. In Figures 5.6–5.8, the time-varying behavior of all discretized variables is shown. It can be noted how this approach does not allow storage resources to be treated properly. Whenever extra production is available, the greedy strategy prefers an instantaneous revenue (selling energy to the grid) rather than storing energy for future times (Figures 5.6–5.7). This result was clearly expected, since the greedy technique does not have a picture of future forecasts but optimizes resources for a single time interval.

Figure 5.6. Case A, generated electric power). For a color version of the figure, see www.iste.co.uk/lascala/smart.zip

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Figure 5.7. Case A, electric power demand). For a color version of the figure, see www.iste.co.uk/lascala/smart.zip

Figure 5.8. Case A, generated thermal power). For a color version of the figure, see www.iste.co.uk/lascala/smart.zip

5.2.3.2. Case B, optimal control (24 h observation window)

In the second case, the optimal control algorithm is employed considering that the optimization is carried out on a day-by-day schedule. The solution is

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subsequently obtained by solving three separate optimization problems, keeping in mind to update the initial state of storage units in the second and third day according to the results of the previous simulation. The size of the time steps Δt is still set to 1 h. The overall operating cost for the 3 days is estimated at €925, with a substantial reduction from the previous case. In this case, the method is able to optimize the storage resources, so that less electric energy is imported and exported (Figures 5.9–5.10). Figure 5.11 shows how the two storage units are charged. The adopted optimal strategy tends to use all storage resources within a single day. This is the reason why both storage units are emptied at the end of each day. It can also be noted how the pumping storage, which is characterized by a slower charge/discharge, never reaches the maximum capacity. Clearly, since the observation is restricted to 1 day, resources at the first day cannot be optimized in order to withstand the generation shortage and overload of the day after. Thermal power is always satisfied (Figure 5.12). An increase of surplus thermal energy generation occurs because the cogeneration unit is operated at higher rates in order to charge the storage units.

Figure 5.9. Case B, generated electric power). For a color version of the figure, see www.iste.co.uk/lascala/smart.zip

Optimization of Multi-energy Carrier Systems in Urban Areas

Figure 5.10. Case B, electric power demand). For a color version of the figure, see www.iste.co.uk/lascala/smart.zip

Figure 5.11. Case B, storage state of charge

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Figure 5.12. Case B, generated thermal power). For a color version of the figure, see www.iste.co.uk/lascala/smart.zip

5.2.3.3. Case C, optimal control (72 h observation window)

The optimal control algorithm is employed considering a 72 h observation window. The solution is obtained solving a single optimization problem. The size of the time steps Δt is still set to 1 h. The overall operating cost for the 3 days is estimated at €885, with a significant cost reduction from the first case (about 10%) and a notable decrease from the previous one. Also in this case, the method is able to optimize inner resources, reducing the overall imported and exported energy (Figures 5.13 and 5.14). Figure 5.15 shows how, in contrast to Case B, the method is able to consider the generation shortage and overload forecasted for the second day, since the first day. The pumping storage unit, whose charge is significantly lower than the BESS, is not discharged at the end of the first day, so that it can reach full charge at the load peak in the second day. The main drawback of treating larger time observation windows is that forecasted parameters may be affected by higher errors. However, as shown in [BRU 14a], an efficient strategy is to adopt a smaller observation window (e.g. 24 h) and moving its starting point along the hour of the day, refreshing the inputs of the algorithm with actual updated operating states or forecasts. In any case, the size of this observation window must be comparable with the charging/discharging speed of the employed storage units. In [BRU 14a], where only fast storage units were adopted, 8 h was sufficient to obtain suitable results. In this case, given the low speed of the pumping storage unit, the use of a 24 h time window appears more appropriate.

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In this case, thermal power is always satisfied (Figure 5.16), and the increase of surplus thermal energy generation is due to the use of the cogeneration unit for charging the storage units. This result suggests that thermal energy storage might be useful to use this extra thermal energy instead of burning natural gas in the auxiliary boiler when the cogenerator is off. The profitability of such an investment can be studied through an optimal design methodology, as shown in the next section of this chapter.

Figure 5.13. Case C, generated electric power). For a color version of the figure, see www.iste.co.uk/lascala/smart.zip

Figure 5.14. Case C, electric power demand). For a color version of the figure, see www.iste.co.uk/lascala/smart.zip

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Figure 5.15. Case C, storage state of charge

Figure 5.16. Case C, generated thermal power). For a color version of the figure, see www.iste.co.uk/lascala/smart.zip

5.3. Optimal design of an urban energy district

This section collects some results of the “San Paolo Power Park” research project [BRU 09, BRU 10] started in 2007 with a collaboration between the natural gas distributor for the City of Bari and the Department of Electrical and Information

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Engineering of the Politecnico di Bari. The main objective of this project was to combine innovative and efficient systems for the production of heat and electricity to achieve significant energy savings, provide discounted energy services to a degraded urban district and promote the birth of new business activities. The project was aimed substantially at the design of an energy district, in which combining low environmental impact methods (photovoltaic generation, combined heat and cooling power (CHCP) generation, district heating and cooling and hydrogen production for urban mobility) is possible to fulfill urban regeneration objectives, improving the quality of life of citizens. The project is part of the Strategic Plan for the development of the metropolitan area of the city of Bari. The experience accumulated during this project aggregated different research groups at the Politecnico di Bari, which promoted a new laboratory, named Lab ZERO, for the development of green technologies, smart grids and energy districts. 5.3.1. Energy district for urban regeneration: the San Paolo Power Park

Very often, urban degraded areas and neighborhoods in large cities, characterized by urbanization processes not yet completed or by primary and secondary infrastructures in need of major renovations, are very good candidates for the realization of experimental projects in the fields of energy and advanced urban services. Apart from direct improvements in the quality of life (e.g. increasing the security of supply or enlarging the areas covered by water, gas, electricity, heating and public services), the fulfillment of significant objectives in terms of energy efficiency and conservation can be directly translated into a social economical advantage if they can provide a substantial reduction of energy tariffs. Well-known examples and best practices have demonstrated how the reduction of energy costs can drive the economic growth of depressed areas, favoring the expansion of industrial and manufacturing activities, thus increasing the number of jobs and social welfare [AKI 00, SHI 02, MAN 88]. An emblematic example can be found in the Appleseed Project, implemented in the mid-1980s for the regeneration of a depressed urban area in New York (Bronx). The project showed how a general 25% reduction in energy tariffs was able to steer the local economy, producing 50,000 new jobs and contributing to a “renaissance” of the entire area [MAN 88]. Urban regeneration, led by the introduction of discounted energy services, can generate greater social and economical impacts if accompanied by the adoption of sustainable and clean technologies for energy and mobility that will change working and living places, making the area more attractive for new professional and business activities.

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In general, the regeneration of urban districts and the enhancement of the quality of life of citizens have been important concerns addressed by the European Union. Urban regeneration was, for example, one of the main themes of the CONCERTO program [HTT]. CONCERTO is a European Commission plan of actions included in the European Research Framework Programmes FP6 and FP7, which aims to “demonstrate that the optimization of the building sector of total communities is more efficient and cheaper than optimization of each building individually”. This initiative, started in 2005, has so far gathered results from 58 pilot cities in 23 countries, following demonstration projects for the use of renewable energy sources for cities, the development of sustainable buildings and districts, the readiness of technologies and the reduction of energy costs (“inexpensive energy”). The San Paolo Power Park was designed to be located in the San Paolo district of the city of Bari (Italy), a portion of the city characterized by the presence of widespread social housing. The San Paolo district, with about 60,000 inhabitants, is somewhat isolated from the rest of the city, being about 8 km far away from downtown. This district is a very good candidate for this type of intervention. This area has long been a degraded part of the city, and it is very close to large civilian complexes, such as a hospital, police and military barracks, and the city airport, which represent concentrated loads for the energy services supplied by the power park [BRU 10] (see Figure 5.17). Refurbishment of the social housing settlement constitutes an important opportunity to integrate district heating/cooling services.

Figure 5.17. Map of the main end users in the San Paolo district (Bari, Italy)

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The San Paolo Power Park project integrates conventional and renewable energy resources. The core of the designed plant is a natural gas-fueled CHP/CHCP power plant and a heat/cool distribution network (Figure 5.18). The power park can also employ cogenerated thermal energy to feed saturated high-temperature steam to steam methane reforming (SMR) for the production of hydrogen, with the idea of using this hydrogen for fueling part of the urban bus fleet [BRU 09]. The project also includes PV generators, whose size was defined based on the available surfaces and current incentive programs. Since the power produced is sold to the external grid and does not have to respect any power balance equation, the choice of the optimal size of PV generators is out of the scope of the proposed optimal design problem.

Figure 5.18. Simplified scheme of the San Paolo Power Park

5.3.2. Optimal design of the energy district

A large number of decision variables, including volatile and heuristic parameters such as energy prices and load profiles [LOZ 10, CAR 07], significantly affect the optimal design of a CHCP plant, which, consequently represents a complex planning problem. The proposed energy district architecture integrates CHCP with other energy facilities in a multi-carrier system, such as multi-generation plants [CHI 09] or multi-source multi-product systems [GEI 07a]. A common representation to manage multi-carrier systems is to consider them as energy hubs, where input, output and conversion of multiple energy carriers are optimized [CHI 09].

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In general, the design of a multi-carrier system cannot be optimized without considering a representation of its complex behavior during different operating conditions. It is necessary to represent and simulate the optimization process that will be adopted in the real plant in order to capture its behavior during operating conditions. The optimization of operating conditions has to take into account equality and inequality constraints that express the relationships between simultaneous production and consumption of energy in different forms (e.g. electric, thermal heating and cooling loads). Moreover the optimal design should be able to assess average system reliability and security of supply [SHA 15]. This means that the problems of long-term (planning) and short-term (operation) optimization have to be solved concurrently, usually through the definition and the solution of a mixed integer nonlinear programming (MINLP) problem. The problem under study is aimed at the optimal design of a CHCP trigeneration facility for district heating and cooling, which will supply energy services and products to residential and civilian end users. Being a new investment, the optimal solution can be considered the one that maximizes a specific financial performance index (e.g. the return of investment (ROI) or the internal rate of return (IRR)). The overall optimization problem can be formulated as: max ROI ( z , u )

[5.31]

z, u

subject to

h ( z, u ) = 0

[5.32]

g ( z, u ) ≤ 0

[5.33]

where:

z is the set of integer control variables defining the design choices that can be made for selecting system components, that is, z identifies commercial size and associated principal data available by technical sheets for each component;

u is the set of continuous control variables that describe the time-varying behavior of each component during system operation; h is the set of equality constraints that regulate all energy exchanges; g is the set of inequality constraints that take into account technical constraints of the equipment.

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The ROI in [5.31] is defined as:

( Rk (z, u) − Ck (z, u) ) n k =1 (1 + i ) N

∑ ROI =

k

CC (z )

[5.34]

where i is the adopted discount rate, k is the generic time period, N is the total number of time periods along the life of the plant and nk is the number of years that have passed from the initial investment during the time period k . It is important to note that CC is the capital cost of the initial investment and it is clearly dependent on the sole discrete variables. Rk and Ck represent revenues and costs respectively in the k-th time period and are, in general, a function of all control variables. Equations [5.31]–[5.33] represent a MINLP problem that can be solved, for example, through the decomposition of the overall optimization problem into two sub-problems. The first problem is an unconstrained integer problem that is aimed at choosing the optimal size and characteristics of the main components (e.g. rated power of the cogenerator and chiller), whereas the second problem is a constrained optimal control problem aimed at optimizing daily operating conditions and the use of system components. Consequently, the overall design process can be seen as a two-stage optimization problem, where optimal dispatch solutions are calculated and associated to each design choice. The first sub-problem can be simply formulated as: max ROI ( z , u )

[5.35]

z

where

( Rk (u ) − Ck (u ) ) n k =1 (1 + i ) N

∑ ROI =

k

CC (z )

[5.36]

and u contains all time-varying optimized system trajectories that are known after the solution of the second optimization problem. The second sub-problem assumes that a system configuration z is known and associates to this configuration an optimal u calculated by solving the problem: N

min ∑ ( Ck (z , u) – Rk (z , u) ) u

k =1

[5.37]

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subject to

h ( z , u) = 0

[5.38]

g ( z , u) ≤ 0

[5.39]

The search of an optimal design solution can follow the scheme proposed in Figure 5.19. The search starts with choosing a possible configuration z that identifies all system components and their technical characteristics (rated power, capacity, efficiency, etc.) from a database of commercially available components or on the base of simplified models. Having fixed a configuration and possible candidate solution z, and having identified all technical parameters that characterize the system, the time domain response of all components is evaluated according to an optimal control management strategy. This response is assessed basing on a set of forecasted or historical time series (chronological curves) describing the possible load and generation profiles or expected energy prices and tariffs. The optimal solution u that solves the problem [5.37]–[5.39] is found, allowing optimized costs and revenues to be associated to the configuration z . The overall candidate solution (z , u ) is then compared to other possible system configurations until the one solving [5.35] is found. Often, the search of an optimal solution can be obtained through a heuristic fullspace search, given the limited extension of the variable sample space (the size of the equipment can vary in a limited range) and given the discrete nature of the control variables that must be assessed (sizes of actual commercially available components). However, in certain cases, for example, if the number and composition of plant components is not yet defined and the variable space is very large, or if the solution of the optimization sub-problem requires a significant computational effort, full-space search might be not feasible. In the case under investigation, the presence of storage units introduces the time variable and dynamic constraints in the short-term optimization sub-problem, because of the limits on maximum and minimum storage capability. As shown in the previous section and in [BRU 14a], a good candidate solver for the short-term optimization sub-problem, when storage components are involved, can be based on the application of the nonlinear optimal control problem. Solving this type of problem for a medium-sized hybrid system and a reasonable time window (for example a single day) can require up to several minutes on ordinary PCs. The idea of repeating thousands of such simulations, one for each possible configuration, is clearly scarcely appealing for complex problems.

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Figure 5.19. Decomposition of the overall problem into a two-stage optimization

Even in the presence of large variable spaces and high computational requirements per each time domain simulation, the first sub-problem can be solved efficiently with any metaheuristics methodology. In this chapter, the simulated annealing method will be adopted thanks to its simplicity and efficacy in solving combinatorial configuration problems, even in the presence of large solution spaces. 5.3.3. Integer variables and design choices

The control variable vector z can be modeled as a vector containing integer indices that identify the possible design choices for each system component. In the case of the system under study, z is formulated as z = ⎡⎣ zGEN

with

zC

zCstore

zTboil

zGEN ∈ {1, 2,K, nGEN } ,

z NGref ⎤⎦

T

zC ∈ {1, 2,K, nC } ,

[5.40]

zCstore ∈{1, 2,K, nCstore } ,

zTboil ∈{1, 2,K, nTboil } and z NGref ∈ {1, 2, K, nNGref } , where nGEN is the number of possible choices for the cogenerating unit, nC is the number of possible choices for the absorption chiller, nCstore is the number of possible choices for the cool thermal

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storage, nTboil is the number of possible choices for the auxiliary boiler and nNGref is the number of possible choices for the steam methane reforming unit. The number of possible z configurations is given by the product of the dimension of the intervals listed above. Each possible value of a generic z x corresponds to a planning choice for the generic x-th component. The set of possible components can be constituted by machines with different sizes, different efficiencies, technical performances, costs, etc. For the sake of clarity, fixing zGEN means fixing all technical and economical parameters of the cogenerator. This means that all the parameters identified by the design choice could be expressed as function of zGEN . In the case of the cogenerator, the rated maximum electrical power

max PGENe (zGEN ) , the technical minimum

min PGENe (zGEN ) , the electric efficiency ηGENe (zGEN ) and the thermal efficiency

ηGENt (zGEN ) could all be expressed as a function of zGEN . For the purpose of lucidity, however, in the solution of the optimal control subproblem, the dependence on variables z is not shown, since the vector z is fixed all along the solution of this second optimization problem. For simplicity of notation, in the following, all parameters or functions that have been fixed after the choice of a design configuration z will be represented with a overbar symbol (in max min the previous example, PGENe , PGENe , etc.). 5.3.4. Mathematical formulation of the optimal control problem

The second sub-problem is an optimization problem formulated in order to minimize operating costs and maximize profits from the selling of energy services to the end users along a selected time window T. The cost function to be minimized is, in general, a nonlinear function of power inputs and outputs: min ∫ u

T

t =0

∑ [c (u (t )) − r (u (t ))] ⋅ dt x

x

x

x

[5.41]

x

where u x is the power injected or demanded by the x-th component and represents, in general, the control variables of the problem, u is the vector of control variables collecting all u x and cx and rx are nonlinear functions that associate a cost and revenue to the x-th power flow, respectively.

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Since they are referred to physical exchanges, variables must be constrained by equality and inequality constraints. The equality constraints are given by the energy balancing equations, which derive from the thermal energy balancing equation at the cooling and heating manifold, or the one that regulates the relationship between the cogenerated cooling and thermal power. In general, any of these relations can be expressed in the following form:

∑k

j, x

(t , u(t )) ⋅ u x (t ) = 0 ∀t ∀j

[5.42]

x

where coefficients k j , x are in general considered dependent on time and operating conditions and j represents the generic j-th energy balancing equation. Inequality constraints take into account technical limitations (e.g. technical minimum power output or maximum rated power): umin x ≤ u x (t ) ≤ umax x

∀t , ∀x

[5.43]

The presence of storage units requires the introduction of state variables referred to the quantity of energy stored. If s denotes the generic storage system and qs the energy stored in it, the following differential equations and constraints must be added to the formulation:

q&s = f s (u(t ), qs (t ))

[5.44]

qs (0) = qs0

[5.45]

with

and qsmin ≤ qs (t ) ≤ qsmax

∀t ∀s

[5.46]

where qs0 is the initial charge and f s is a generally nonlinear function that associates power inputs/outputs to the energy stored, also taking into account efficiency or standby losses. Inequality constraints [5.46] take into account the limitations on storing capability.

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5.3.4.1. Discretization of the optimal control problem

The optimization problem [5.41]–[5.46] can be solved through discretization, by assuming that along the generic time step i, state and control variables remain constant. If the time grid is uniform and the size of a single time step Δt is fixed, the selected time window T can be divided into nT = T / Δt time steps. All discretized variables will be represented from now on with the overline hat symbol. The problem becomes: nT

min ∑∑ ( cxi (uˆ xi ) − rxi (uˆ xi ) ) uˆ

i =1

[5.47]

x

subject to:

k j , i T ⋅ uˆi = const ∀i, ∀j

[5.48]

umin ≤ uˆi ≤ umax

[5.49]

∀i

ψ (uˆ )T ⋅ uˆ ≤ const

[5.50]

where cxi and rxi are costs and revenues associated to the power uˆ xi , assumed constant in the i-th time interval; uˆi is a vector collecting all uˆ xi at the i-th time step, uˆ collects all uˆi ; k j , i is a vector collecting all k j , x calculated at the i-th time step T (each transposed vector k j , i can be considered as the j-th row of the coupling

matrix in the general formulation of an energy hub [GEI 07a]). Since storage efficiency is assumed dependent on the storage charging power, equation [5.44] assumes the following form:

qˆsi = qs0 + ψi (uˆ1 , uˆ 2 ,L, uˆi )T ⋅ uˆi ⋅ Δt ∀i

[5.51]

where qˆsi is the energy stored at the end of the i-th time interval, ψi is the set of nonlinear functions that takes into account all charged and discharged energy flows in the previous intervals and the sign of uˆi . The condition

qsmin ≤ qs0 + ψi (uˆ1 , uˆ 2 ,L, uˆi )T ⋅ uˆi ⋅ Δt ≤ qˆsmax is synthesized by equation [5.50].

∀i ∀s

[5.52]

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A more detailed description of how equations [5.47]–[5.50] are formulated is given in the following subsections. 5.3.4.2. Equality and inequality constraints

Equality constraints represent the power balance nodal equation as usually done during the construction of the coupling matrix in the energy hub formulation [GEI 07a]. Figure 5.20 shows a schematic representation of the energy flows that must be balanced in the system under study.

Figure 5.20. Schematic representation of the San Paolo Power Park multi-carrier system

The cogenerator is modeled considering that the overall cogenerated thermal power can be used for both heating and cooling by the adoption of an absorption chiller. i , For each discretized period i, having defined the electrical power output uˆGENe max min the maximum electrical capacity PGENe and the technical minimum PGENe , with

min i max PGENe ≤ uˆGENe ≤ PGENe

[5.53]

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the condition that links the heating and cooling thermal flows available to the end users is: i uˆGENe −

i ηGENe i ηGENt

⎛ uˆ i ⋅ ⎜ C + uˆTi ⎜ COP i ⎝

⎞ ⎟⎟ = 0 ⎠

[5.54]

i i where ηGENe and ηGENt are respectively the electric and thermal efficiencies of the

cogenerator, COPi is the coefficient of performance of the chiller, and uˆCi and uˆTi are respectively the cooling and heating thermal flow outputs. The index i on such variables takes into account the fact that efficiencies might not be constant with time and that efficiencies may depend on the actual production. In this formulation, they are considered independent of the control variables and, therefore, equation [5.54] is formulated as a linear constraint as in [5.48]. A second linear constraint regulates the nodal cooling power balance: i i i uˆCi + uˆCnot − uˆCstore − PˆCload =0

[5.55]

i is a constant and represents the average cooling load during the i-th where PˆCload i period, uˆCnot is a control variable that represents the amount of cooling power not i supplied and uˆCstore is a control variable representing the amount of cooling power injected into the chilled water storage system (i.e. it is positive when charging and negative when discharging). Equation [5.55] is linear and can be expressed in the same compact form as [5.48].

The control variables are constrained by

0 ≤ uˆCi ≤ PCmax

[5.56]

i i ≤ PˆCload 0 ≤ uˆCnot

[5.57]

min i max − PCstore ≤ uˆCstore ≤ PCstore

[5.58]

max is the where PCmax is the maximum capacity of the absorption chiller, PCstore min maximum charging power of the storage system and PCstore is the maximum discharging power.

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A third equality constraint is given by the heating nodal power balance: i i i i uˆTi + uˆTboil + uˆTnot − uˆTref − PˆTload =0

[5.59]

i is a constant and represents the average heating load during the i-th where PˆTload i period, uˆTnot is a control variable that represents the amount of cooling power not i supplied, uˆTboil is a control variable that represents the thermal power supplied by the

i boiler and uˆTref is the net quantity of thermal power that is spent in the steam-

reforming cycle. Equation [5.59] is linear and can be expressed in the compact form [5.48]. The control variables are constrained by:

0 ≤ uˆTi ≤ PTmax

[5.60]

i i ≤ PˆTload 0 ≤ uˆTnot

[5.61]

i max 0 ≤ uˆTboil ≤ PTboil

[5.62]

max is where PTmax is the thermal maximum capacity of the cogeneration unit and PTboil the maximum capacity of the boiler.

Assuming that the amount of cogenerated thermal energy that can be used to i produce 1 kg of hydrogen is kTref , if the maximum daily hydrogen production is i K Hmax2 (expressed in kg/h), the control variable uˆTref is constrained in the interval:

i 0 ≤ uTref ≤

K Hmax2 i kTref

[5.63]

Two inequality constraints that take into account the storage limits must be i added. If qˆCstore is the quantity of cooling energy stored at the end of the i-th period, the following relations can be written: i i i −1 i if uˆCstore ≥ 0 qˆCstored = qˆCstored + uˆCstore ⋅ Δt i i i −1 if uˆCstore < 0 qˆCstored = qˆCstored +

i uˆCstore

η

i Cstore

⋅ Δt

[5.64]

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i where ηCstore is the efficiency that takes into account the energy losses in the storage system. In this formulation, this efficiency is applied to the sole discharge phase (i.e. the quantity of energy discharged from the storage is higher than the energy utilized).

max min If QCstored and QCstored represent respectively the maximum and minimum quantity of cooling energy that can be stored, the inequality constraints to be introduced are given by: min i max QCstored ≤ qˆCstore ≤ QCstored

[5.65]

which, given the formulation of [5.64], can be expressed in the form of two nonlinear inequality constraints: min 1 2 i i 0 max ⎤ ≤ QCstored QCstored ≤ ⎡⎣ψ i ( uˆCstore + qCstored , uˆCstore , K , uˆCstore ) ⋅ uˆCstore ⎦

[5.66]

Having considered that for each time interval, the control variables can be collected in a vector: i uˆ i = ⎡⎣uˆGENe

uˆTi

uˆCi

i uˆCstore

i uˆCnot

i uˆTboil

i uˆTnot

i ⎤⎦ uˆTref

T

[5.67]

and that: uˆ = ⎡⎣ uˆ1T

uˆ 2 T

T

L uˆ nT T ⎤⎦ ,

[5.68]

all equality constraints given by [5.54], [5.55] and [5.59] can be written in a compact form as in [5.48], all linear inequality constraints [5.53], [5.56]–[5.58], [5.60]–[5.63] can assume the form of [5.49] and all nonlinear constraints [5.66], one for each time step, can be easily rewritten in compact form as in [5.50]. 5.3.4.3. Costs and revenues

In this section, all costs and revenues in equation [5.47] are explicitly formulated as a function of control variables uˆi . The natural gas necessary to fire the cogenerator is supposed to be bought by the i . The cost for the generic i-th time natural gas distribution network at a price π NG interval is: i i cGEN = π NG ⋅

i 1 uˆGENe ⋅ i ⋅ Δt hNG ηGENe

[5.69]

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where hNG is the heat of combustion of natural gas (e.g. expressed in kWh/Nm3). In the power park architecture, the electricity produced by the cogenerator is directly sold to the grid. The revenues are: i i i rGENe = π EL ⋅η EL ⋅ uˆGENe ⋅ Δt

[5.70]

i is the time-dependent price of electricity and η EL is an efficiency that where π EL takes into account electrical power losses and electricity self-consumption (e.g. all the power requested by auxiliary circuits).

The thermal energy sold to end users produce a revenue for both heating and cooling energy. If π Ci and π Ti are the selling prices of cooling and heating energy, respectively, the revenues are formulated as:

rCi = π Ci ⋅ηC ⋅ uˆCi ⋅ Δt

[5.71]

rTi = π Ti ⋅ηT ⋅ uˆTi ⋅ Δt

[5.72]

with ηC and ηT being efficiencies taking into account losses in the distribution circuits of cooling and heating energy, respectively. In the proposed formulation, a cost is associated to the thermal load that is not supplied. This value of lost load (VOLL) can be either due to penalties to be paid to i i end users or a social welfare cost. If VOLL is π VOLLC and π VOLLT for cooling and heating load, respectively, the costs associated to the energy not supplied are: i i i cCnot = π VOLLC ⋅ uˆCnot ⋅ Δt

[5.73]

i i i cTnot = π VOLLT ⋅ uˆTnot ⋅ Δt

[5.74]

Analogously to the formulation [5.69], the natural gas consumption in the auxiliary boiler is taken into account considering the cost: i i cTboil = π NG ⋅

i 1 uˆTboil ⋅ i ⋅ Δt hNG ηTboil

i is the efficiency of the boiler. where ηTboil

[5.75]

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The use of the steam methane reformer also introduces costs and revenues. Costs are due to the consumption of natural gas necessary for the reforming transformation. Moreover, since the reforming reaction requires steam at a temperature of about 850°C, the portion of cogenerated steam that is sent to the reformer requires a further consumption of natural gas. The expected revenue is given by the selling of hydrogen at a price π Hi 2 . This price is net of taxes and compression, storage and dispensing costs (CSD) [MEL 13]. Such costs, which have a significant impact in the definition of the hydrogen retail prices, are associated to processes that are not modeled in this formulation, and therefore are supposed to be covered by the final retail price. The price π Hi 2 is supposed to take into account all variable energy costs and installation capital costs. In general, costs and revenues for steam reforming are formulated with the following equations: i i i = π NG ⋅ k NGref ⋅ cNGref

rHi 2 = π Hi 2 ⋅

i uˆTref i kTref

i uˆTref i kTref

⋅ Δt

⋅ Δt

[5.76]

[5.77]

i represents the amount of natural gas necessary for the reaction and where k NGref

steam superheating, net of methane produced by the final stage of methanation (if i i present). The two coefficients kTref and k NGref depend on the overall efficiency of the reforming process and the technology adopted. 5.3.5. Test results

In this section, test results for the specific San Paolo Power Park design project are shown. For each candidate configuration z, revenues and costs are calculated after solving the optimal control sub-problem for 12 representative daily load configurations (one for each month of the year). Each design candidate solution then requires the solution of 12 separate optimal control problems, one for each simulated month. ROI is calculated considering that daily chronological curves do not change within the same month. Of course, more daily configurations can be taken into account depending on the available computing resources. 5.3.5.1. Load chronological curves

As previously mentioned, the power park project is aimed at offering discounted energy services to a set of residential and civilian customers in a socially degraded

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215

area of the city. This project was developed considering that energy will be supplied to four major civilian facilities and to a set of residential customers. The four major facilities are police barracks, a police station, an airport and a hospital, whereas residential customers are associated to two social housing areas (areas A and B in Figure 5.17). The load duration curves for these four major end users have been modeled adopting daily thermal load profiles reported in the literature [LOZ 10, LOS 03, CAR 06, CHO 04a, CHO 04b]. These profiles have been suitably adapted in order to replicate actual aggregated load demand historical data (mostly data on monthly consumption). The fifth user represents an aggregation of residential customers (about 5,000 apartments). Monthly heating and cooling thermal demands for all users are reported in Tables 5.1 and 5.2, respectively. Figure 5.21a and 5.21b show the cumulative aggregated yearly load duration curves for both heating and cooling demand. Example of adopted chronological curves for summer (July) and winter (December) peaking conditions are illustrated in Figures 5.22 and 5.23, respectively. Month

User 1 [MWht]

User 2 [MWht]

User 3 [MWht]

User 4 [MWht]

User 5 [MWht]

Jan.

909

812

579

1,248

6,412

Feb.

808

581

414

874

4,583

Mar.

632

422

301

865

3,334

Apr.

455

176

126

492

1,390

May

354

51

37

366

404

Jun.

202

42

30

293

334

Jul.

177

26

18

158

203

Aug.

177

14

10

206

113

Sep.

303

36

26

269

283

Oct.

404

118

84

400

935

Nov.

606

488

348

722

3,855

Dec.

758

913

651

706

7,208

TOT

5,785

3,681

2,626

6,599

29,053

Table 5.1. Thermal heat monthly demand

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User 1

User 2

User 3

User 4

User 5

[MWht]

[MWht]

[MWht]

[MWht]

[MWht]

Jan.

202

0

0

0

0

Feb.

227

0

0

0

0

Mar.

303

0

0

0

0

Apr.

227

0

0

0

0

May

328

0

0

0

0

Jun.

606

241

172

432

1,401

Jul.

611

703

502

1,261

4,089

Aug.

596

523

373

938

3,041

Sep.

404

207

147

370

1,201

Oct.

263

0

0

0

0

Nov.

177

0

0

0

0

Dec.

152

0

0

0

0

TOT

4,097

1,674

1,194

3,001

9,732

Month

Table 5.2. Cooling monthly demand

a)

b)

Figure 5.21. Thermal load duration curves: a) heating loads, b) cooling loads

Optimization of Multi-energy Carrier Systems in Urban Areas

a)

217

b)

Figure 5.22. Daily chronological curves in summer: a) heating loads, b) cooling loads

a)

b)

Figure 5.23. Daily chronological curves in winter: a) heating loads, b) cooling loads

5.3.5.2. Technical and economical parameters

For simplicity, it was assumed in the simulations that all efficiencies and coupling coefficients are constant and do not depend on the operating conditions or external factors (e.g. seasonal efficiency variations). The main hypotheses are presented in Table 5.3. Efficiencies are referred to average data on state-of-the-art technologies. The overall efficiency of the steam reforming process is about 70%. max min The limits PCstore and PCstore are calculated for each candidate solution considering a maximum charge/discharge speed of 5 h.

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ηGENe

31.4 [%]

ηGENt

53.6 [%]

COP

1.6 [p.u.]

ηCstore

80.0 [%]

ηEL

97.0 [%]

ηTboil

90.0 [%]

hNG

9.59 [kWh/Nm3]

kTref

22 [kWht/kgH2]

kNGref

4.82 [Nm3/kgH2]

Table 5.3. System parameters

The electricity produced in the power park is meant to be sold directly to the energy market. For this reason, there was no need to model electricity load profiles. Each customer is supposed to be buying electricity directly from the network (market) and not be supplied by the power park. In the calculations, the entire electricity production, having deducted a 3% necessary for self-consumption, is considered injected in the power system and sold at the average price of 70 €/MWh. The cogenerated thermal energy is used for districting heating. In this case, thermal losses due to the distribution in the heating network, having a 10 km extension, can be estimated at around 7%. Cooling and heating services will be sold at discounted tariffs (6.5 c€/kWht for heating and 5.6 c€/kWht for cooling energy). These prices have been obtained by applying a 25% discount on current heat and cool tariffs, coherently with urban regeneration objectives, which should promote the moving of new business activities in the selected area in analogy with the above quoted Appleseed Project [MAN 88]. Production costs were evaluated considering a natural gas cost of 0.32 €/Nm3. Total investment costs were calculated considering two components. First is a fixed component, which takes into account all the costs that have a null or negligible dependence on the variables z such as, for example, the district heating and cooling network, whose cost mainly depends on the digging works and their extension. It was assumed that fixed costs are €7,000,000. The second investment cost entry is given by those costs that are strongly dependent on components’ size: gas turbine, heat recovery unit, absorption chiller, auxiliary boiler, cool thermal energy storage system (TESS) and steam reforming unit. In most cases, where technology can be considered consolidated, the capital

Optimization of Multi-energy Carrier Systems in Urban Areas

219

costs of such components are calculated considering a simple linear dependence on the installed power (or capacity). However, the methodology applied to solve the first (integer) sub-problem permits to adopt any model for the characterization of system components (e.g. costs and technical data can be derived by a database collecting information on actual commercial products). For the sake of simplicity, all parameters such as per-unit costs, prices, efficiencies, etc., are considered constant in the whole simulation (as in Table 5.3). The CHCP plant is assumed to cost 450,000 €/MW, and to have electric and thermal efficiencies of 31% and 54%, respectively. The heat recovery unit is assumed to cost 50,000 €/MW. Its size was assumed equal to the maximum rated thermal power output of the gas turbine, which is a control variable. Consequently, the recovery boiler size is not a control variable of the optimal design problem. The absorption chiller has a per-unit cost of 90,000 €/MW and a coefficient of performance (COP) of 1.6. The auxiliary boiler costs 33,000 €/MW and has an efficiency of 90%. The yearly O&M cost is assumed fixed at 3% of the total initial capital costs. It was also assumed that the plant has an average annual availability of about 97%. With regard to the thermal energy storage system, it was assumed that a chilled water (CHW) storage is adopted. Ice-based TESS is usually preferred to CHW, because exploiting the latent heat necessary for the phase change in the water–ice passage requires moderately compact storage volumes. However, absorption chillers do not work very well with latent heat storage technologies [IEA 02] and, therefore, apply better to the system configuration under study. In large-scale applications, CHW technology can guarantee significant cost savings and capital cost even lower than conventional (non-TESS) chiller plant [AND 07]. The principal drawback of this technology is that it requires a relatively large store tank volume. The cost of the CHW storage is estimated at 30,000 €/MWh. It is also supposed that the charging/discharge speed is about 5 h and, therefore, the maximum and minimum charge/discharge power is, numerically, one-fifth of the total capacity. The cost of the steam methane reforming unit was modeled according to [MEL 13], and is given by: ⎛K ⎞ CCNGref = 3, 000, 000 ⋅ ⎜ H 2 ⎟ ⎝ 450 ⎠

0.707

[€]

[5.78]

where K H 2 is the plant productivity expressed in kilograms of hydrogen per day. The selling price of hydrogen is considered varying in the range of 4–5 €/kg. Another important cost figure is given by the value associated to thermal load not supplied (value of lost load). For both cooling and heating loads, it was assumed a cost of €500 per unsupplied MWht.

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5.3.5.3. Case D. Optimal design of a CHCP plant without hydrogen production

This case aims at studying the optimal design of the CHCP plant when no steam reforming unit is installed. The mathematical formulation of this problem remains close to the one developed in section 5.3.4, with the sole exception that all control variables and revenue/cost functions related to the hydrogen production have to be neglected. The same formulation can be kept assuming that the maximum hydrogen production is zero. However, a simplification of the number of control variables permits to reduce the complexity of the problem and the time required for each iteration. For this reason, the algorithm was slightly modified in order to neglect the hydrogen production. The optimal design choice was found considering that the number of possible choices nGEN equals 11 (with an electric capacity ranging in the interval 5–15 MW), nC equals 11 (with a cooling capacity ranging in the interval 16–40 MWt), nTboil equals 9 (with a cooling capacity ranging in the interval 0–16 MWt) and nCstore equals 11 (with a cooling capacity ranging in the interval 0–100 MWht). The overall search space contains about 12,000 solutions. The simulated annealing algorithm was carried out considering a maximum number of 500 iterations. In Figure 5.24a and 5.24b, the convergence behavior can be observed. Figure 5.24a shows how the candidate solution changes along the iterative process. According to the classical Metropolis law, worse solutions are accepted as candidates with a lower probability as the simulated annealing algorithm progresses. The best solution characterized by an ROI of about 0.40 is found after about 350 iterations (Figure 5.24b), whereas acceptable sub-optimal solutions can be found already after about 200 iterations. The final best solution corresponds to a configuration where the maximum max generation capacity of the cogenerator PGENe is 7 MW, the maximum boiler capacity max PTboil is 12 MWt, the maximum chilling capacity PCmax is 18 MWt and the cooling max storage unit has a maximum capacity QCstored of 50 MWht.

Figures 5.25–5.28 show the optimal power flows calculated for the two peaking months (July for cooling and December for thermal demand). The thermal capacity of the CHCP is chosen so that it barely covers the winter peaks (Figure 5.23a), which are instead satisfied with the additional contribution of the auxiliary boiler that covers the thermal heating load (Figure 5.28a). This condition corresponds to standard design criteria for CHP/CHCP plants. The common praxis is to undersize them, so that they can work with the highest efficiencies for the longest amount of hours.

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The presence of the cool water storage system permits to satisfy the occasional summer peaks without increasing the capacity of the CHCP plant and the absorption chiller, even though for few hours in the month of July, the peak cannot be fully satisfied (Figure 5.25b). The expected amount of unsupplied load is very small and the expected costs are not high enough to justify the installation of larger capacities. However, solutions that are more conservative can be found considering higher i i VOLL or eliminating the control variables uˆCnot and uˆTnot from the problem formulation. The profitability of the investment appears to be not very high: ROI is about 40%, payback time 10 years with a capital cost of about €14.8M. However, it should be kept in mind that this maximization was made considering only technical and financial factors. Since, the project is characterized by other impacts in terms of social and economical sustainability, a more complex cost/benefit analysis would be appropriate in order to estimate the overall benefits for society (and not only the financial ones). It should also be considered that discounted tariffs were applied to the district and cooling services to reach the social aim of the regeneration of the district on an energy-based policy. It is not coincidental that the project was a candidate for funding in the strategic plan of the metropolitan area under investigation. Furthermore, the adopted discount rate (8%) is more appropriate for business investments than for strategic development actions (as in this case) or research pilot projects. It was kept high, conservatively.

a)

b)

Figure 5.24. Case D, convergence of the simulated annealing problem: a) candidate solutions; b) best solution across iterations

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a)

b)

Figure 5.25. Case D, summer day: a) thermal cooling generation; b) thermal cooling consumption

a)

b)

Figure 5.26. Case D, summer day: a) thermal heating generation; b) thermal heating consumption

a)

b)

Figure 5.27. Case D, winter day: a) thermal cooling generation; b) thermal cooling consumption

Optimization of Multi-energy Carrier Systems in Urban Areas

a)

223

b)

Figure 5.28. Case D, winter day: a) thermal heating generation; b) thermal heating consumption

5.3.5.4. Case E1. Optimal design of the CHCP plant with hydrogen production

This case is aimed at finding an optimal design of the power park considering also the presence of a steam-reforming unit. This first simulation is carried out considering a price of hydrogen of 4 €/kg. The optimal design choice was found considering the same nGEN , nC , nTboil and nCstore possible choices for the elements already considered in case D. In this case, it was also considered a set of nNGref possible design choices is constituted by 11 elements with a daily hydrogen production ranging in the interval 0–2,000 kg/day. The overall search space contains more than 130,000 solutions. Since the search space is much larger than that in the previous case, the maximum number of iterations of the simulated annealing algorithm was set to 1,000. Figures 5.29a and 5.29b show the convergence behavior of the algorithm. The best solution characterized by an ROI of about 0.39 is found after about 550 iterations, whereas acceptable sub-optimal solutions can be found after about 100 iterations. The best solution corresponds to a configuration where the maximum max generation capacity of the cogenerator PGENe is 7 MW, the maximum boiler capacity max PTboil is 14 MWt, the maximum chilling capacity PCmax is 18 MWt, the maximum

max of the cooling storage unit is 50 MWht and the steam reforming capacity QCstored unit producibility is 0 kg/day. This means that the selling price of hydrogen is not enough to justify the installation of any steam reformer unit.

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This solution is comparable to the same one found in the previous case. Small differences (even just the size of the boiler) are due to the fact that the meta-heuristics approach cannot explore the entire solution space. If the problem is very large, the algorithm might converge to sub-optimal solutions in the neighborhood of the global maximum. However, once a sub-optimal solution is found, exploring the closest neighborhood is usually feasible and easy with minimal extra computation cost.

a)

b)

Figure 5.29. Case E1, convergence of the simulated annealing problem: a) candidate solutions; b) best solution across iterations

5.3.5.5. Case E2. Optimal design of the CHCP plant with hydrogen production

In this second case, all hypotheses remain the same of the previous one, but the price of hydrogen is set to 5 €/kg. The best solution corresponds to a configuration max where the maximum generation capacity of the cogenerator PGENe is 8 MW, the max maximum boiler capacity PTboil is 12 MWt, the maximum chilling capacity PCmax is max 22 MWt, the maximum capacity of the cooling storage unit QCstored is 30 MWht, and the steam reforming unit producibility is 2,000 kg/day.

In this case, the expected revenues from hydrogen are high enough to justify the installation of the steam-reforming unit. With this configuration, a higher ROI (about 0.61) is reached and an increased size of the cogenerator is required. Since more cool thermal energy can be produced by the chiller, the CHW storage system is significantly smaller than that in the previous case. As shown in Figure 5.30, the solution was found after 750 iterations (even if suboptimal solutions were already found after about 300 iterations). As in the previous case, the auxiliary boiler permits to fulfill the winter peaks (Figure 5.34a) and cover the summer heating demand during the summer cooling demand peaks. The presence of stored cooling energy reduces the expected loss of load during the summer peaks (Figure 5.31b).

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The ROI is higher than that in the previous case (about 61%). However, it should be kept in mind that the capital cost is now estimated at €27.8M, approximately twice that of the optimal configuration in case D. Clearly, financial constraints may be added in the maximization problem, so that the initial cost does not exceed a certain amount, or other costs can be computed considering the difference between the cost investment and the initial equity. The feasibility of the project should also better address the effect of the hydrogen cost parameter, which seems very influential for this energy district design. In any case, it must be kept in mind that strategic development actions can also accept low ROI (if not negative), as long as significant additional social benefits are to be expected.

a)

b)

Figure 5.30. Case E2, convergence of the simulated annealing problem: a) candidate solutions; b) best solution across iterations

a)

b)

Figure 5.31. Case E2, summer day: a) thermal cooling generation; b) thermal cooling consumption

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a)

b)

Figure 5.32. Case E2, summer day: a) thermal heating generation; b) thermal heating consumption

a)

b)

Figure 5.33. Case E2, winter day: a) thermal cooling generation; b) thermal cooling consumption

a)

b)

Figure 5.34. Case E2, winter day: a) thermal heating generation; b) thermal heating consumption

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5.4. Conclusions

A desirable approach to achieve integration and coordination of energy infrastructures in a Smart City is to develop multi-energy carrier systems where different energy resources are optimized following a holistic approach. Most methodologies for the optimization of multi-carrier systems are based on the energy hub concept that permits to treat mathematically the coupling of different energy resources. Two optimization methodologies, the first aiming to solve an operating problem and the second to solve a planning problem, were presented. The proposed discrete optimal control methodology allows us to minimize energy costs, optimizing energy flows along selected time windows. The methodology makes use of updated forecasts for load and generation, allowing to treat properly energy inputs of any intermittent renewable generation unit (photovoltaics, thermal solar, wind generation, etc.) and multiple storage systems. Test results showed how the proposed methodology can be used to achieve a power balance of electric and thermal loads, with minimum cost, in a complex system where several energy sources coexist (a natural gas-fueled cogeneration plant, PV generators, boiler, battery and pumping storage systems). The method is general enough to include any number and typology of component for energy generation, storage, transformation and consumption. The second proposed optimization methodology is a planning tool that allows us to find the optimal design of multi-carrier system, solving a MINLP problem. The optimization problem is decomposed into two stages and two sub-problems that are solved, respectively, with a metaheuristic (simulated annealing) and an optimal control technique. The optimal control sub-problem is aimed at estimating expected costs and revenues along the useful life of the multi-carrier system, basing on longterm forecasts of loads, whereas the first sub-problem searches for the configuration characterized by the best economical performance. The methodology was tested on an urban regeneration project aimed at the development of energy facilities to provide discounted energy services for a degraded part of the city of Bari. The project includes the installation of a trigeneration plant and the distribution of heating and cooling energy to a vast residential area, including also four main civilian end users (airport, barracks, hospital). The system is also coupled with an on-site steam methane reformer, which utilized the thermal energy wasted by the trigeneration plant. The reformer produces hydrogen, which is supplied to a fleet of public transport vehicles.

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5.5. Acknowledgments

Regarding the first experimentation proposed in section 5.2, the authors gratefully acknowledge the Apulia Region for the grant of the project “Energy Router e Strumenti di Controllo Cloud per Smart Grid” financed within the call “Cluster Tecnologici Regionali” for €2,255,159. Regarding the feasibility study described in section 5.3, the authors gratefully acknowledge AMGAS Bari S.p.A., the urban gas distribution company in Bari (Italy) for funding the “San Paolo Power Park” research project and the Municipality of Bari for providing city planning data utilized in the design and feasibility study of the energy district. The authors also gratefully acknowledge the Apulia Region for the grant of the project “Laboratory for the development of renewables and energy efficiency in energy districts: Project ZERO (Zero Emission Research Option”, 2013–2016, financed for €2,319,400 under the Framework Programme Agreement on “Scientific Research” of the Apulia Region for the constitution of “Networks of Public Research Laboratories”. 5.6. Bibliography [AKI 00] AKI H., OYAMA T., TSUJI K., “Analysis on the energy pricing and its reduction effect on environmental impact in urban area including DHC”, Proceedings of IEEE – Power Engineering Society Winter Meeting, vol. 2, pp. 1097–1102, 2000. [AND 07] ANDREPONT J.S., “Reducing energy costs and minimizing capital requirements: case studies of thermal energy storage (TES)”, Proceedings of 29th Industrial Energy Technology Conference, New Orleans, 2007. [BAR 96] BARLEY C.D., WINN C.B., “Optimal dispatch strategy in remote hybrid power systems”, Solar Energy, vol. 58, no. 4–6, pp. 165–179, 1996. [BRU 09] BRUNO S., LAMONACA S., LA SCALA M. et al., “Improving efficiency in a power park by the integration of a hydrogen steam reformer”, Asia-Pacific Power and Energy Engineering Conference (APPEEC) 2009, Wuhan, China, 2009. [BRU 10] BRUNO S., LAMONACA S., LA SCALA M. et al., “Optimal design of trigeneration and district energy in the presence of energy storage”, International Conference on Renewable Energy and Power Quality (ICREPQ) 2010, Granada, 2010. [BRU 14a] BRUNO S., DASSISTI M., LA SCALA M. et al., “Predictive dispatch across time of hybrid isolated power systems”, IEEE Transaction on Sustainable Energy, vol. 5, no. 3, pp. 738–746, 2014.

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[BRU 14b] BRUNO S., DASSISTI M., LA SCALA M. et al., “Managing networked hybrid-energy systems: a predictive dispatch approach”, Proceedings of the 19th World Congress of the International Federation of Automatic Control (IFAC 2014), Cape Town, South Africa, 2014. [CAR 06] CARDONA E., PIACENTINO A., CARDONA F., “Energy saving in airports by trigeneration. Part I: aAssessing economic and technical potential”, Applied Thermal Engineering, vol. 26, pp. 1427–1436, 2006. [CAR 07] CARDONA E., PIACENTINO A., “Optimal design of CHCP plants in the civil sector by thermoeconomics”, Applied Energy, vol. 84, no. 7–8, pp. 729–748, 2007. [CHI 09] CHICCO G., MANCARELLA P., “Distributed multi-generation: a comprehensive view”, Renewable and Sustainable Energy Reviews, vol. 13, no. 3, pp. 535–551, 2009. [CHO 04a] CHOW T., FONG K.F. et al., “Energy modelling of district cooling system for new urban development”, Energy and Buildings, vol. 36, pp. 1153–1162, 2004. [CHO 04b] CHOW T., AU W.H. et al., “Applying district-cooling technology in Hong Kong”, Applied Energy, vol. 79, pp. 275–289, 2004. [GEI 07a] GEIDL M., ANDERSSON G., “Optimal power flow of multiple energy carriers”, IEEE Transactions on Power Systems, vol. 22, no. 1, pp. 145–155, 2007. [GEI 07b] GEIDL M., KOEPPEL G., FAVRE-PERROD P. et al., “Energy hubs for the future power”, IEEE Power & Energy Magazine, vol. 5, no. 1, pp. 24–30, 2007. [HTT] http://www.concertoplus.eu/ [IEA 02] IEA, “District heating and cooling: optimization of cool thermal storage and distribution”, report available at: http://www.svenskfjarrvarme.se, 2002. [LAM 06] LAMBERT T., GILMAN P., LILIENTHAL P., “Micropower system modeling with homer”, in FARRET F.A., SIMÕES M.G., (eds), Integration of Alternative Sources of Energy, Wiley, 2006. [LOS 03] LOSCHI R., “Valutazioni tecnico-economiche sulla gestione del servizio energie e della cogenerazione in un complesso ospedaliero”, Atti del Convegno AEIT - La cogenerazione diffusa è un’opzione valida per la produzione dei flussi energetici necessari?, Milan, 2003. [LOZ 10] LOZANO M.A., RAMOS J.C., SERRA L.M., “Cost optimization of the design of CHCP (combined heat, cooling and power) systems under legal constraints”, Energy, vol. 35, no. 2, pp. 794–805, 2010. [MAN 88] MANAK J.R., “Project appleseed: electric rate incentives”, IEEE Transaction on Power Systems, vol. 3, no. 4, pp. 1833–1839, 1988.

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[MEL 13] MELAINA M., PENEV M., “Hydrogen station cost estimates. Comparing hydrogen station cost calculator results with other recent estimates”, report, National Renewable Energy Laboratory, available online at: http://www.nrel.gov/docs/fy13osti/56412.pdf, 2013. [SHA 15] SHAHMOHAMMADI A., MORADI-DALVAND M., GHASEMI H. et al., “Optimal design of multicarrier energy systems considering reliability constraints”, IEEE Transactions on Power Delivery, vol. 30, no. 2, pp. 878–886, 2015. [SHI 02] SHINJI T., “Electricity supply project in Roppongi area and new technology incorporated in urban power plant”, Proceedings of Transmission and Distribution Conference and Exhibition 2002, Asia Pacific IEEE/PES, vol. 2, pp. 960–963, 2002.

6 Optimal Gas Flow Algorithm for Natural Gas Distribution Systems in Urban Environment

Natural gas distribution networks play a crucial role in supplying a primary energy carrier to industrial, tertiary and residential customers. Thanks to the driving evolution of electric smart grids, these networks are now experiencing similar changes due to the deployment of gas smart meters and a more and more pervasive use of ICT tools and automation which allows more effective, safe and secure operations. This chapter presents selected results of a Smart Gas Grid project that was developed and implemented as a pilot project on the natural gas urban distribution grid which supplies the city of Bari (Italy). A SCADA (Supervisory Control and Data Acquisition) prototype and a gas flow optimization algorithm (Gas Optimal Flow algorithm) for pressure regulation are described in their actual implementation. Results prove that these hardware and software tools can enhance network operations and show potential for further applications.

6.1. Introduction In recent years, the availability of low cost information and telecommunication technologies, together with new actuators and sensors, has had a large impact on distribution services for public utilities. A few years ago, smart grids issues were discussed in research or academic environments only and these new concepts were almost unknown in the industrial sector. Nowadays, technologies for smart grids

Chapter written by Ugo STECCHI, Gaetano ABBATANTUONO and Massimo LA SCALA. From Smart Grids to Smart Cities: New Challenges in Optimizing Energy Grids, First Edition. Edited by Massimo La Scala. © ISTE Ltd 2017. Published by ISTE Ltd and John Wiley & Sons, Inc.

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are widespread in utilities’ investment policies and the innovation connected to these applications represents a primary focus for infrastructural development and innovation. Over the last decade, electrical grids have paved the way for the smart grid evolution in the public utilities industry. They also play a crucial role in spreading this kind of transition to other public utilities. Gas distribution has recently experienced such phenomena and it is today under development to implement interventions aimed to enhance security, safety and energy efficiency. Gas networks are complex structures that consist of passive pipes and active controllable elements, such as valves and compressors. Natural gas infrastructures are essential for both industrial and residential users, and nowadays they are one of the most relevant energy carriers for electricity generation in large power stations equipped with CCGTs. Different pressure levels are adopted for ensuring the different functions associated with the natural gas transportation such as long distance transport, regional transport and primary or secondary distribution. In general, there are different nominal pressures standardized on the basis of technical norms or regional regulations such as, for example, European standards EN 1594 [EN 13] and EN 12007 [EN 12]. In Italy, pressure values are fixed on the basis of a Ministerial Decree issued in 1984 [DEC 84], and in the following sections we refer to this regulation to describe the natural gas system, but of course different pressure levels may be applied in different gas systems all over the world. Long distance transmission capacity pipelines run across nations and continents and transport natural gas from extraction wells to national hubs; these represent the backbone of gas supply at the national level and are operated at very high pressure: in general, higher than 60 bar. From large transportation hubs, a high pressure capillary network transports gas in regions and provinces (12 or 24 bar). To increase the transmission capacity of the network, compression stations are installed along pipelines. Natural gas urban distribution grids are operated at lower levels of pressure. They originate at the city-gate nodes, where gas transportation pipes at high pressure (12–24 bar) supply one or more gas primary decompression stations (the so-called Regulation and Measurement station or ReMe station for brevity). From these pipes, gas is supplied to major users such as thermal power plants and large industrial sites (primary distribution) or sent, by means of Reduction and Measurement substations, to local medium pressure distribution grids (secondary distribution).

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Figure 6.1. Picture showing a Regulation and Measurement station at a city-gate gas network

City-gate infrastructures reduce the gas pressure from a high to medium level (≤5 bar) and they represent the origin of the distribution network operated at medium pressure. Along those pipes, it is possible to find many other different reduction cabinets (Final Reduction Unit or FRU) from which low pressure secondary distribution networks originate. Medium pressure pipelines supply gas to small and medium enterprises, large commercial customers or to FRUs. These cabinets are secondary decompression stations that laminate gas flow from medium to low levels of pressure (≤0.025 bar). From FRUs, low pressure grids supply gas to final residential or tertiary customers in a range of a district or a part of it.

Figure 6.2. Final Reduction Unit in an urban distribution grid during a maintenance intervention

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Figure 6.3. Urban Medium Pressure Distribution Grid of the town of Bari (Italy) with a zoomed-in image of the detail of the low pressure grid (courtesy of Amgas Bari SpA). For a color version of the figure, see www.iste.co.uk/lascala/smart.zip

Similar to power grids, natural gas networks are designed and built following the same topological principles. Even for gas distribution services, in fact, there are radial, branched or meshed lines: the first and second configurations are typical of high pressure transportation pipelines, while medium and low pressure subsystems form looped paths whose complications are further increased by the great variety of diameters used for gas pipes. The design and construction of gas distribution systems must be subjected to careful evaluations concerning site selection, such that the site must be easily attainable and safe from possible floods and ground settlements. Outdoor and underground plants should be installed away from busy roads and parking lots in order to facilitate maintenance, and equipped with appropriate protective measures from incidents (iron grates and fences) and malicious events (anti-intrusion sensors). Depending on the pressure and incoming flow rates, security distances from buildings must be taken into account. Due to their peculiar constructive features, urban low pressure gas distribution grids are not only the most widespread, but also the frailest parts of the whole gas

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network. Distribution companies are obligated by technical and security standards to guarantee adequate pressure levels to users and the uniform distribution of mercaptan odorant across the grid to improve the detection of leaks. Consequently, it is necessary to monitor pressure values constantly. This is usually performed at the city-gate ReMe stations and selected FRUs, but it is highly desirable to carry out complete pressure monitoring at each FRU across the whole medium pressure grid. The main parameters to control are ingoing and outgoing pressures and the state of cathodic protections (to prevent corrosion of pipes). Regulation and Measurement substations also monitor outgoing flow with gas odorant quantities to add into distribution systems, so that leaks can be readily detected. This chapter deals with crucial issues on the evolution of natural gas distribution grids, starting from research and field tests activities conducted as part of a research project named “Smart Grid Project”, granted by the Apulia Regional Government in Italy and developed by the authors since 2009 [SMA 16]. This project was carried out by Politecnico di Bari together with local municipal utilities for natural gas distribution (AMGAS SpA in Bari, Italy) and power distribution (AMET in Trani, Italy). The project aimed to introduce tangible and effective innovation, both hardware and software, across gas and electric grids, in order to favor their evolution toward smart grids. The main focus, relevant for this chapter, is about the development of a “Gas Smart Grid” in the urban medium and low pressure gas distribution grids. The main objective achieved by the project was the design, implementation and testing of a SCADA prototype integrated with an optimization algorithm for controlling turboexpander outputs gas flows and pressures in the range of quality levels determined by technical standards and national authorities. In the “Gas Smart Grid” project, great attention has been devoted to Final Reduction Units (FRU), the grid component aimed at reducing pressure from main urban pipes at medium pressure to final distribution pipes at low pressure. FRUs, however, constitute just a small part of a larger system and they manage the whole urban gas distribution grid characterized by using a huge number of complex and heterogeneous quantities that must be constantly acquired from the field. This condition is pushing gas distributors to adopt modern and advanced solutions. One of the goals of the Smart Grid Project was the design, set up and installation of a prototype of a SCADA system equipped with the remote control of three of the 180 FRUs that supply the urban gas distribution grid of the Bari municipality, a medium-sized town in Italy. This system can monitor in real-time the main variables (upstream pressure, downstream pressure, flow rate, blockage filter and door closure for safety reasons) and send measurements via a web server to the control center of

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the gas distribution utility. SCADA software collects, processes and records these data. Moreover, an optimization algorithm for gas flow control over the distribution networks was developed to control FRUs and other equipment to obtain a desirable profile of pressures. A remotely controlled electric drive can be coupled with the expansion valve installed at each FRU to actuate the optimized control strategy. 6.2. Natural gas network evolution Nowadays, automation and information technologies are largely adopted in high pressure natural gas transportation systems, because of their strategic importance at the cross-border level. Scientific and academic research has already considered long-distance transportation systems proposing optimization and simulation tools. Studies have focused on possible optimization methodologies to be applied to gas transmission networks. In [CHA 01], it can be seen how, since 2001, software for the optimization of gas production and operating pressure levels on the Korean gas pipe network was already available. A similar study can be found in [MAR 06] and [ILK 05], where the authors developed a mixed integer solver for the solution of the stationary gas optimization problem on large systems. The method was applied to the German E.ON Ruhrgas AG, comprehending some hundreds of pipes with a total length of about 11,000 km, many hundreds of control valves and 26 compressor stations. Numerical applications to gas transmission networks can be found in [HER 09], where different relevant issues concerning these systems are treated, including pipelines design, malfunctioning prevention, efficiency analysis and anti-terrorist countermeasures at big industrial plants. Natural gas distribution grids have been considered in literature as well. The main ideas concern supplying improvement (quality, safety, maintenance and reliability) or the possibility of exploiting natural gas at the urban level as a supplementary energy carrier to be utilized together with other energy carriers. In these cases, the contribution from automation and ICT plays a crucial role in infrastructures’ renewal, where the possibility of monitoring and controling gas flows in real-time is the “next big thing” for DSOs (Distribution System Operators). Methods for modeling and simulation of a gas distribution network can be found in [DJE 11], where a MATLAB-Simulink library was built to solve the system dynamics concerning pipelines and to find optimal topologies and pressures sets. In general, however, studies on gas distribution networks [DJE 08, WU 07, OSI 95] are aimed at optimizing pipe diameters and lengths, and so they can be very useful for network planning and design but difficult to apply in operation.

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Natural gas distribution grids show a general lack of ICT and automation technology integration, compared to power distribution systems. Power systems are usually considered to be more challenging to operate and require more accurate regulations and therefore they are characterized by a very high level of automation when compared to gas grids. There is also a substantial difference in the degree of automation between the completely monitored and controlled long-distance gas transportation system and distribution systems which are historically characterized by very limited automation. Even though SCADA technologies are largely adopted at a higher pressure levels, it should be observed that there is an innate diffidence in adopting too complex and pervasive remote control in urban gas distribution grids. This is due to the perception of the potential danger which can derive from any leakage or improper maneuver. Consequently, in many distribution companies manual settings of basic control parameters are preferred to remote control because of the safety issue. Therefore, it is expected that the next step is the complete automation of gas distribution systems, installing fast sensors and actuators for real-time operation. The aim is not only to report anomalies to the system operators, but also to remotely control the setpoints of active components and actuators to provide the best operation. For this purpose, smart and powerful management and control tools are necessary even for these infrastructures that, in most cases, have not experienced significant improvements for decades. Integrated systems for remote control and optimization of an urban gas distribution grid need to be developed. New architectures are needed to acquire and send real-time measurements to local distribution company control centers and also to automatically calculate the optimal settings for pressures and gas flows across pipes and nodes. Optimal Gas Flow algorithms need to be proposed and implemented on actual gas distribution networks, as will be discussed in the subsequent paragraphs. Furthermore, the presence of some self-healing properties can be ensured by fast control of valve drives during emergency cases to make the system secure and automatically restore ordinary operating conditions, according to one of the principal “Smart Grid” paradigms. About a decade ago, the smart grid term referred to power systems only. Now, smart grid terminology has also been extended to ordinary natural gas networks when referring to a retrofit implementation of gas smart meters. It should be noted that Advanced Metering Infrastructures are also going to be implemented in the gas sector. In Italy, some regulations, such as Deliberation 631/2013/R/GAS [AUT 13] and 554/2015/R/GAS [AUT 15] from the Energy Regulator AEEGSI, encourage and incentivize smart metering. This is equivalent to what had happened in the

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electric sector. As an example, the natural gas distribution grid, which is the object of our investigation in the medium-sized town of Bari (350,000 inhabitants), is experiencing a major deployment of smart meters as well today. This large scale roll out is going to replace about 110000 meters in the next two years, while 13,000 final users have been already equipped with the new smart ones (as of June 2016). The first practical application of smart metering is automatic billing. But other functions were added to modern gas smart meters, such as the compensation of billing errors due to temperature changes, switching off the supply in case of delay in paying the bill or under emergency conditions, gas load profiling, forecasting, etc. Following electric market liberalization, even natural gas systems are trying to introduce new players as providers and producers. The new available technologies in the field of power to gas allows production of methane by coupling a water electrolyzer to produce hydrogen and a methanation unit to extract carbon dioxide from air and mix it with hydrogen. This technology can be considered as a form of storage of excess electricity that is produced by renewables. Moreover, the European Directive 2009/28/CE [EUR 09] represents a further motivation for a deep renovation of gas distribution systems, because it allows and regulates the injection of biogas, which is produced by anaerobic digestion of biomasses and is subjected to particular purifying processes, into gas networks. This process can be easily compared to what happened for electric networks, which were called to embrace the large presence of Renewable Energy Sources and dispersed generation. Similarly, biomass digesters can play the role of a “gas distributed generation” which can be integrated inside the traditional and vertically integrated gas distribution grid. This technical upgrade will force engineers and managers to face new technical challenges. Biogas cannot be injected in any distribution branch. For example, the use of pipes characterized by limited flows feeding a limited number of customers should be avoided. In such cases, injected biogas may exceed the gas demand, thereby not guaranteeing a good mix of the two gases and pressure could rise until dangerous levels are reached. Gas demand, moreover, is strictly related to weather conditions: distribution systems deliver larger gas volumes during cold seasons, because its primary use in residential areas is by far building heating. For this reason, biogas injections could represent a significant option for ordinary gas distribution, especially during winter. This implies the necessity of defining different tariffs for gas, seasonal or time-ofday both for supply and injection in gas grids, just as it happens in the power industry.

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Another key decision is with regard to the choice between the installation of a large, centralized digester or using smaller, distributed biomass plants connected through a biogas microgrid; this configuration can provide advantages for the operational reliability, because it would significantly reduce the possibility of a total operational stop in case of a decrease in biogas production in just one or two digesters. On the other hand, production costs and safety issues are better addressed when using a centralized plant that produces the same amount of biogas [HEN 14]. Despite the above-mentioned considerations and many other possible technological considerations, the integration between biomass plants and gas networks could grant many economic and environmental advantages. This is the reason behind carrying out many projects that are devoted to enhancing this synergy in several European countries. The British “Biomethane to Grid”, for example, was started in 2010 with the connection of the Didcot plant digesters and the national distribution grid and was able, by 2014, to connect four more similar plants to the same network [BAL 14]. Other demonstrator projects have been developed in Spain [GUT 14], Ireland [HUS 13] and mostly in Germany, where in 2010, 35 biomass plants were already operating in connection with gas distribution networks, with a total injection capacity of 25,000 Sm3/h and 35 other plants were under development and construction. This number grew further up to 151 in November 2013 but, according to the German Government, 1,000 injection plants have to be realized by 2020 and most of the injected biogas will be used in CHP plants to achieve perfect optimization of electricity and heat generation [WEI 10]. These numbers show the potential of the natural gas distribution sector to replicate what happened in the electricity realm with distributed generation and Smart Grids. 6.3. Implementing the monitoring and control system in the “Gas Smart Grids” pilot project Modern natural gas distributions networks should be operated under real-time monitoring and control with an aim of achieving the optimization of various parameters, such as pressure and flow to enhance commercial quality, safety, security and energy efficiency. As an example of good practice, it should be observed that, since 2008, the AEEGSI., the Italian regulation Authority for electric energy, gas and water systems (Autorità per l’Energia Elettrica, il Gas e i Sistemi Idrici), through notification 120/08 has highlighted the importance of supervisory control and monitoring systems for gas grids. As mentioned above, the same Authority established incentives to encourage DSOs to adopt such technologies.

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The pilot project “Gas Smart Grids” mentioned above and described in this chapter was oriented to provide advantages for DSO, such as follows: – real-time information on network conditions, in order to regulate pressure to optimal levels in a short – medium term (load leveling); – real-time pressure regulation on different network areas for peak shaving under emergency conditions; – improvement of security under every condition: emergency, maintenance, diagnostics or development planning; – complete data and statistics on network operation and load forecasting. 6.3.1. SCADA system The real-time monitoring and control prototype has been implemented in three different FRUs, corresponding to the extreme peripheral nodes of the urban network considered by the operator to be the most critical ones from the pressure profile and the reachability of the gas odorant viewpoints as well as being hard to quickly restore under contingency conditions. At the time of the experimentation, the controlled FRUs were three in number, but after the successful experience, the Gas Company started a campaign for deployment of the technology across the entire grid, monitoring and controlling about 180 FRUs. This system provides five different signals acquired by different wired sensors, by means of a remote transmission unit (RTU) working as data reader, logger and transmitter. The RTU consists of a small cabinet for outdoor applications (IP56) with a PLC and a GPRS modem. Each RTU transmits its data to the control center equipped with its own SCADA system. In this experimentation, measurements acquired from the field are as follows: – gas flow rate Q [Sm3/h], acquired by using a thermal mass sensor coupled with a pressure sensor; – upstream pressure Pin [bar] acquired by using a ceramic dry sensor; – downstream pressure Pout [bar] given by using the same type of pressure sensor; – filter blockage level ΔP [bar] recorded by a differential pressure sensor; – door closure signal acquired for security and safety purposes by means of an ATEX-standardized micro-switch.

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Acquuired values of o flow rate and a pressure are a transmitteed through a 44–20 mA signal, while w door opening o is thrrough an on– –off switch. The proposedd system architectture is represeented in Figuure 6.4 by meeans a block diagram incluuding the RTUs annd the other main m componeents. Sensors acquire a data from f the field and send these to the PLC devvice. Pressurees, flows and d filter blockaage sensor signals are s to th he PLC. Figurre 6.5 shows the exact communnicated througgh 4–20 mA standards placemennt of sensors inside i one FR RU.

Figure 6.4. Remotte monitoring system s archite ecture

Figure 6.5. Pllacement of se F ensors inside a F FRU (left) and d on an upstre eam pipe (rightt)

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From m Figure 6.5, it i is possible to t observe thee actual placeement of sensoors inside one FRU U as follows: – thee upstream preessure transm mitter (1) placced on the sm maller pipe cooming out from thee undergroundd medium presssure grid at 5 bars; – thee differential pressure p transm mitter placed on the filter (22) and the dow wnstream pressure transmitter (33) installed onn the large pip pe at 0.025 bar from whichh the low pressure subsystem deeparts; – thee flow transm mitter (4), locaated inside a crawl space few meters upstream before sensor s (1) andd coupled wiith another pressure p transm mitter (5) in order to compenssate the two measurements m and obtain thee desired diffeerential quantiity. Data acquired by each e sensor arre transferred to the RTUs, basically connsisting of a IP56 cabineet together witth other electrric equipment.. a PLC sllotted inside an Finallly, it should be b observed thhat two monitoring FRUs and a the controol system are suppplied by the urban u electric low voltage grid. The thirrd FRU is in a remote rural areea and consequuently it is poowered by a PV P module with a solar chaarger and an electtric storage battery. b In Figure F 6.6, tw wo of these prototypal R RTUs are represennted. They onlly differ in thhe power sourcce (PV or grid connected),, but they share thee rest of the haardware and control c equipm ment.

Figure 6.6. Picture P of diffe erent RTU prottotypes: a stan nd-alone RTU U pow wered by a PV V (right); switchboard details s of a grid-con nnected RTU ((left)

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The PLC is coupled with a GSM/GPRS modem to send its signals to the control center. There are two different kinds of signals: measurements and alarms. Measurement signals (pressure, flow and differential pressure at the filter) are sent via web (IP protocol) every 15 min, while alarms are sent in real time (overpressure alarm, GSM network fault and door open) and displayed on the control center monitor or even on mobiles via sms (as requested by deliberation AAEGSI 120/08 of Italian Regulatory Authority). In the control center, the SCADA system displays measurements and alarms to the operator through a specifically developed and customizable graphic interface. Figures 6.7 and 6.8 respectively show the main page of the graphic interface, where a general overview of the grid with the monitored peripherals and detailed information of a selected RTU with acquired trend graphs of last measurement signals can be observed. A bar on the top displays RTU connections and local time, while a bar at the bottom contains icons to historical records and alarms.

Figure 6.7. Screenshot of the real SCADA desktop interface: main overview of an urban MP grid. For a color version of the figure, see www.iste.co.uk/lascala/smart.zip

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Figure 6.8. Screenshot S off the real SCAD DA desktop in nterface and a real-time mon nitoring interfa ace of a selectted FRU. For a color version n of th he figure, see www.iste.co.u w uk/lascala/sma art.zip

6.3.2. Controlling C F FRUs’ setpo oints The ordinary o contrrol system of the FRUs is a mechanical device d that senses only local preessure and triees to keep it constant c indep pendent of thee flows suppliied to gas loads. A FRU basically consists of a cabineet equipped with w a pilot-ccontroller pressure regulator thhat is conneccted upstream m to medium m pressure ppipes and w pressure onees. The pressu ure regulator laminates l the gas flow downstreeam with low from meedium (≤5 bar)) to low levelss of pressure (generally ( set at 0.025 bar). A low w pressure urbban gas netwoork shows draastic changes seasonally s onlly twice a year: at the t beginningg and at the ennd of the wintter season. Thhe highest conntribution to gas deemand, in factt, is representeed by boilers and heating systems, that aare turned on durinng winter, cauusing a relevaant variation of pressure, flow f and speeed of gas over the grid. It couldd be very important therefo ore, for both security s and quuality-ofr that DSOs D perform m a preventivee and complette grid analysiis of their service reasons, readiness to face thesse modificatioons of their operative o rangges and avoidd possible i a static wayy since they coontrol the malfuncttions. Usuallyy, regulators inn FRU work in downstreeam gas flow with pressuree settings whiich are updateed manually, uusually at

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every change of the season. The downstream pressure, however, can change on the basis of gas demand. When critical or emergency conditions occur, the pressure can drop to lower levels causing quality problems for final users. In a worst-case scenario, a critical pressure drop will no longer be able to ensure the correct mix of odorant through the grid, especially in the furthest pipes, with dangerous effects on safety requirements. Figure 6.9 depicts the sketch of a two stage ordinary pressure control system, where the main valve membrane (first stage) reacts rapidly to variations in the pressure downstream, causing the immediate adjustment of the position of the main valve. At the same time, the pilot diaphragm (second stage) deflects a part of the input pressure on the other side of the main valve diaphragm, in order to control the final position of the shutter in the main valve. The handle on the pilot regulator fixes the setpoint and allows the pressure to be accurately adjusted. The two-stage pressure regulator provides a quick response and a sufficiently accurate control in a fixed range of pressures and flows.

Figure 6.9. Schematic representation of a two-stage pressure regulator. For a color version of the figure, see www.iste.co.uk/lascala/smart.zip

FRUs are generally also equipped with shut-off valves, for intercepting inlet and outlet pipes, pressure gauges, filters and odorization systems. Pressure drop variations on the FRU regulator affects gas flow through the device; this correlation corresponds to the flow coefficient Kv and it describes how a

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fluid is allowed to flow through the orifice. The flow rate of the valve is related to pressure drop and flow by the following equation: Q = K v ΔP

[6.1]

The parameter Kv depends on the friction inside the valve that causes pressure drop and it is proportional to the cross-sectional area of the outstream pipe. Kv values under real conditions are generally available in the technical data sheets of the pressure regulator that are provided with the FRU. Flow coefficient Kv can be changed by using the handle of the pilot regulator, allowing the control of the secondary pressure at the low pressure side. Traditionally, the setpoints of FRU’s regulators are set twice in a year following the seasonal behavior of the distribution system. These setpoints can be fixed on the basis of the operator experience and in some cases, by means of a grid analysis that is usually performed by using relaxation methods, such as the Hardy-Cross method [CRO 36]. In contrast, in the proposed prototype, the presence of FRUs, whose setpoints can be controlled directly by the control center through a valve drive, is considered. This feature, of course, simplifies the campaign of seasonal change of setpoints performed manually. But, what is most important is the possibility of changing the setpoints and, consequently, the pressure profile on the low pressure grid, in realtime and by remote control, according to different objectives. These objectives can be various and some of them are illustrated in the following test results. In order to reach the goal of the implementation of a piece of software for optimizing gas distribution operations, it was necessary to develop a more modern algorithm for Gas Load Flow calculation based on the Newton–Raphson method. Finally, based on this algorithm, an optimization procedure was implemented by following the strategy of the gradient descent method. The representation and modeling of the distribution grid, Gas Load Flow algorithm based on the Newton–Raphson method and the optimization solver, named here as Optimal Gas Flow are described in the following sections. 6.4. Basic equations under steady-state conditions General equations of a natural gas pipe can be obtained by applying the principle of mass conservation through control volume as in Figure 6.7, momentum and energy conservation.

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Flow continuity The rate of mass entering from the left hand face of the control volume must be equal to the mass rate leaving through the right hand face.

Control Volume

ρ+δρ

V+dv A+dA

ρ

V A

dx

Figure 6.10. Schematic showing gas control volume

dρ

ρ

+

dV dA + =0 V A

[6.2]

where – ρ is the gas density, – V is the velocity of the gas, – A is the area of the cross-section of the pipe. Momentum conservation If the flow is steady and gravitational forces are being neglected, the only forces on the control volume are the pressure and the frictional force exerted on the surface of the control volume, which is given by the following equation:

ρVAdV = − Ad ρ − dF μ where dFµ is the frictional force.

[6.3]

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If frictional force can be considered negligible, equation [6.2] for compressible gas is modified as follows: −

dP

ρ

= VdV

[6.4]

where P is the pressure. Energy conservation The steady-state flow energy equation through the considered control volume, when no work is applied, is as follows:

c pT

V2 (V + dV ) 2 + dq = c p (T + dT ) + 2 2

[6.5]

where – cp is the gas specific heat at constant pressure, – T is the temperature and its product by cp is equal to enthalpy per mass for a perfect gas, – q is the heat transferred into the control volume per unit mass of fluid flowing through it. Relationship between pressure drops and flows in gas pipes Equations representing the link between pressure drops and flows in each pipe of the network have been obtained by considering practical experience and heuristics accumulated in this field. The formulation changes between pipes operated at medium pressure (1.5–5 bar) and low pressure (17 mbar–25 mbar). Usually, a gas flow analysis is performed on medium pressure distribution grids. In this study, however, it was necessary to consider both kinds of pipes operated at medium and low pressure due to the need to analyze the flows upstream and downstream of the FRUs. For high and medium pressure flow calculations, it must be taken into account that pressure drop in pipes can sensibly affect the gas volume per mass unit; in this

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case, the reduced Renouard [6.6] and Weymouth [6.7] pressure drop equations have been classically adopted for both laminar and turbulent flows [COE 07]: 2 Pin2 − Pout = 48600 ⋅ dLQ1.82 D −4.82

[6.6]

2 Pin2 − Pout = 151500 ⋅ dLQ 2 D −5.33

[6.7]

where – Q is the gas flow [Sm3/h]; – Pin is the inlet pressure [kg/cm2]; – Pout is the outlet pressure [kg/cm2]; – d is the gas density; – D is the internal diameter of the pipe [mm]; – L is the length of the pipe [km]. In contrast, low pressure networks are not affected by wide pressure drops and they can be represented according to a specific reduced Renouard [6.8] or the Spitzglass [6.9] equation as follows:

pin − pout = 232 ⋅106 dLQ1.82 D −4.82 ;

[6.8]

⎛ 91, 44 ⎞ pin − pout = 87.1 ⋅106 ⎜1 + + 0.00118 D ⎟ dLQ 2 D −5 D ⎝ ⎠

[6.9]

where pin is the inlet gauge pressure [mm water]; pout is the outlet gauge pressure [mm water]. In the proposed algorithm, however, it was decided to use the Fergusson equation [6.10] for the pressure drop calculation under steady-conditions, since it is proven to be effective and accurate for both medium and low pressure regimes, which is given as follows: 2 A ( Pin2 − Pout ) = KLQ2 D−5

[6.10]

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where – A = e− S – S = 1.96 ⋅10−5

( H out − H in ) ρ0T0 g T zP0

⎛T – K = 1.68 ⋅10−5 ρ0 f ⎜ ⎝ T0

−S ⎞ ⎞ −5 ⎛ 1 − e ⎟ zP0 D ⎜ ⎟ S ⎝ ⎠ ⎠

– Hin is the altitude of the pipe at the inlet part [m] – Hout is the altitude of the pipe at the outlet part [m] – f = is the friction coefficient in the pipe – T is the temperature of gas in the pipe [K] – T0 is the standard ambient temperature : 298.15 [K] – P0 is the pressure under standard conditions: 1.033 [kg/cm2] – ρ0 is the gas density under standard condition – z is the gas compressibility factor – g is the gravitational constant Note that A is a coefficient which depends on the pipeline slope between the initial and final sections of the pipe and (Hf − Hi) is the altitude difference between the opposite extremes of a pipe. Basically, coefficient K deals with factors such as friction, density and temperature, while A takes into account the possible slope between the initial and final sections of the pipe, gas compressibility and gas density. If Hin = Hout, the pipe lays on a horizontal plane, and then S = 0 and the Fergusson equation can be simplified as follows:

(P

2 in

2 − Pout ) = KLQ2 D−5

[6.11]

Gas load behavior Solving gas networks, usually load nodes, are characterized by the fact that gas demands are sufficiently known and independent of pressure since this variable is considered within ordinary limits, close to the nominal value and stabilized.

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However, gas demand is a function of the pressure at the delivery node and this behavior becomes significant for large deviations in the pressure as under deteriorated operating conditions. During the experimentation of the Gas Smart Grid project, it was possible to verify through actual measurements that changes in the pressure significantly affect the demand in residential areas of a town. This was a side-effect of the project due to the implementation of the gas SCADA prototype. In fact, the DSO was able to acquire real-time measured values from the grid and in particular, from the most critical peripheral nodes. Until then, the distribution company could only acquire pressure levels by reading gauges in the FRU, while cumulative flow measurements were available at city-gates only. The new measurement system allows assessment of flows in each part of the low pressure network supplied by each FRU, which was previously unknown. Such data will be useful for many applications, such as profiling and forecasting the customers’ behavior (for homogenous and aggregated loads), identifying the load model through the estimation of its dependence from the pressure, applying gas peak-shaving policies under emergency conditions, etc. For this purpose, a campaign of measurements was conducted to identify gas load dependency from the pressure. After several months of prototype operation, a first archive record was available. It was possible to select a FRU characterized by a constant load in a given time period (typically from 10–12 am) in order to consider the demand constant during the acquisition of data and the period of time needed to damp out transients. In this experiment, outlet pressure set-point P0 at the FRU regulator was stepped up to a value P, in order to observe the steady-state changes in the gas demand Q when all the transients were damped out. The demand was typically in the range of 50–60 Sm3/h for the selected FRU at that period of the year (Spring 2013). Figure 6.11 shows pressure and flow profiles during one of the mentioned tests, carried out in the selected hours. The pressure P0 was monitored and revealed stable values at 25 mbar with a flow Q0L fluctuating in the typical range of 55–60 Sm3/h. This condition corresponds to the area marked with the letter A in the figure. It can be observed how pressure remains stable until a step up has been given after 40 min from P0 to P (30 mbar) corresponding to a flow spike from 55 up to 90 Sm3/h (zone B in the graph). The pressure rises quickly enough, while the flow transient lasts about 20 min. After this, the pressure remains stable at 30 mbar and Q0L rises up to a higher value QL in a range of 65–70 Sm3/h (zone C). It is possible to understand how flow is affected by pressure variations, under the assumption of a constant gas demand, by observing their behavior in Figure 6.11.

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Figure 6.11. Graph showing flow behavior due to a pressure variation at a selected FRU

Because of these observations, it is possible to introduce pressure-dependent loads in gas flow calculations. Based on physics, it is possible to assume that the demand can be considered dependent on the relative pressure by using an exponential model. In this case, a generic exponential law can be hypothesized based on formulae available for gas pipe or nozzle discharge flow rate, modified Darcy formulae, etc. In reality, the problem is more complex since flow regulators of various burners associated to each customer are involved in the aggregated demand. Consequently, the gas demand model needs to be assessed and real-time monitoring can be helpful in this regard. The dependency of the demand Q from pressure P can be described with the following equation:

⎛P⎞ QL = QL0 ⎜ ⎟ ⎝ P0 ⎠

kP

[6.12]

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where kP is the exponential factor which characterizes the pressure dependency of the demand. Through measurements, kP can be assessed as a sensistivity factor: ΔQ Q = kP ΔP P

[6.13]

It should be remarked that kP assessment is more relevant for studies which imply a significant pressure deviation from nominal values. For small perturbations that are approximately equal to the nominal value, a constant demand independent of the pressure is acceptable. Consequently, an accurate knowledge of the load model is unavoidable when calculating gas flows during outages or under degraded operating conditions.

6.5. Gas load flow formulation

An analysis tool for gas network steady-state simulation aims to achieve an assessment of the pressure at each node of the grid in order to check if the acceptable pressure drops (ΔP) across pipes, maximum flows and flow speed limits are satisfied [ABB 16]. There are different possible representations of an urban gas distribution grid. The representation adopted in the mentioned project is presented here. Natural gas flows due to the simplifications of basic equations under steady-state conditions have to satisfy the following equality constraints similar to the Kirchoff’s laws adopted in circuit analysis: – the quantity of gas flowing into a node must be equal to the quantity of gas flowing out of that node; – the algebraic sum of the pressure drop ΔP in any closed loop is equivalent to the total ΔP available in that loop. As previously mentioned, the urban gas distribution company is supplied by a long-distance transport operator through a high pressure network. Accordingly, the distribution company just has to reduce the pressure to an acceptable pressure level for the medium pressure primary distribution network by the ReMe stations. Usually, compressors are not needed since just gas expansion or lamination is

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required to reduce the pressure. For this purpose, this interface stations between high and medium pressure grids are, generally, equipped with lamination valves. Recently, turbo-expanders were installed in city-gate stations allowing the recovery of one part of the energy used for high pressure compression and an accurate and continuous regulation of the pressure of the medium pressure distribution grid. At each load node, the demand must be satisfied with particular pressure requirements guaranteeing the pressure within a range of values to the customer for ensuring the proper operation of utilization devices (boilers, gas stoves, dispersed cogeneration, etc.). As in circuits, the grid can be represented by using an oriented planar graph and Kirchoff’s laws can be adopted under steady-state conditions. The flow conservation equation ensuring the gas balance at a generic node i, whose pressure is Pi, can be schematized as shown in Figure 6.12.

Figure 6.12. Schematic showing the gas flow balance at node i

As in circuit analysis, it is possible to build the branch incidence matrix called A. This is a rectangular matrix, whose generic i,l-th element is equal to – +1, if the branch l enters the node i; – −1, if the branch l exits from node i; – 0, if j is not incident on i. As in PQ and PV nodes in power system analysis, here, the nodes in a gas network can be distinguished between load nodes and pressure nodes. Load nodes or flow constant nodes (denoted here as Q-nodes) are characterized by the fact that gas demands are known, so that pressure can be determined. They

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can be considered the dual of so-called “PQ” or “load” nodes in power system load flow. This is true whenever the pressure is stabilized and is within ordinary limits. However, as described in the previous section, load nodes can also be considered as a function of the pressure at the delivery node. This assumption, which is useful when considering severe contingencies or under severely deteriorated operating conditions, does not imply any difference in following developments, but a direct dependency of loads on the pressure of the pipe they are supplied by. In contrast, pressure nodes (here denominated as P-nodes) have fixed pressure values and are associated with nodes characterized by a constant pressure and an almost infinite flow capacity. They are associated with the interface nodes between high pressure and medium pressure grids (ReMe stations). Thus, for these nodes, the pressure is fixed and flow has to be evaluated. They play the same role of “slack” buses in power systems. In order to consider the real limited capacity of the high pressure network, the same tricks adopted for power systems when flow limits are exceeded, such as declassing the node or re-dispatch flows among other high pressure nodes, can be utilized. It is assumed that the grid is characterized by l branches and N nodes with np pressure nodes and nq Q-nodes. As in power systems, by the first Kirchoff law, the following equations can be expressed: [6.14] where – Ql is a (N-np)-dimensional load vector, expressing total gas demand at each node [Sm3/h]; – Ar is the (N-np) x l dimensional matrix denoted the reduced incidence matrix of A since it is obtained by eliminating the rows representing np P-nodes or ReMe stations, assumed as “slack” buses, from A; – Q is an l-dimensional flow vector, expressing total gas flow through pipes and can be written on the basis of branch flows obtained through equation [6.11] or similar equations such as equations [6.6] and [6.7] for medium pressure pipes or [6.8] and [6.9] for low pressure pipes.

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It is now possible to write equation [6.14] as follows: 0

[6.15]

where f(x) is the vector of nodal balances for the whole network and x is the vector of unknowns constituted by the independent nodal pressures P. Once the set of equations is determined [6.15], it is possible to implement an algorithm for gas flow calculations using the Newton–Raphson method, an iterative method characterized by a fast and quadratic convergence behavior. After evaluation of pressures at each node of the grid, the next step consists of calculating flows for each pipe and at the interface between ReMe nodes by applying equations, such as the one adopted here, i.e. the Ferguson equation. 6.6. Gas optimal flow method

In this paragraph, an algorithm that is able to optimize gas flows and pressures across medium and low pressure grids is presented. This approach is named “Optimal Gas Flow” for brevity and also for it to be analogous with the “Optimal Power Flow” method adopted for power systems, since they share the same Nonlinear Programming optimization methodology. The general Optimal Gas Flow (OGF) problem can be formulated as a general nonlinear optimization problem, where inequality constraints are treated with penalty functions since the inequality limits in the current problem can be considered as soft constraints. The following formulation holds good:

min C (x, u)

[6.16]

u

is subject to: f (x,u) = 0

[6.17]

with C (x, u) = Cobj (x, u) + ∑ C ip (x, u) i

[6.18]

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with x ∈ℜ N-Np and u ∈ℜ p , where C(x, u) is the global objective function and Cip is

the ith penalty function which takes into account technical limits, acceptable pressure values and other functional constraints such as maximum flow speed, mass losses and so on, x is the state variables vector which basically consists of pressures at each node, u is the control variables vector and f is the function associated with the set of gas flow equations given by equation [6.15]. Two different problems solved in the mentioned experimentation are proposed here. For the sake of brevity, it is assumed that the general formulation is based on equations [6.16]–[6.18] and just the objective, penalty function and control variables change different problems. The overall solution of problem [6.16]–[6.18] can be obtained by any nonlinear method. Without lack of generality, the standard gradient descent method is proposed here, which is the one adopted in the experimentation because of its simplicity and effectiveness for the proposed problem. By introducing Lagrangian multipliers the constrained problem [6.16]–[6.18] can be formulated as an unconstrained one: min

, ,



, ,

,

f

x, u

[6.19]

The necessary first order conditions are given as follows: ∂L ∂C ∂f T = +λ =0 ∂x ∂x ∂x

[6.20]

∂L ∂C ∂f T = +λ =0 ∂u ∂u ∂u

[6.21]

∂L = f(x,u) = 0 ∂x

[6.22]

The partial derivative is of L with respect to lambda. Substitute x with lambda in the derivative In order to solve first-order conditions, the gradient descent method has been applied as represented synthetically by the flow chart shown in Figure 6.13.

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Figure e 6.13. Flow chart c of “Optim mal Gas Flow” solvers

6.7. Opttimizing turrbo-expande er operations The problem liess in maximizzing the amo ount of enerrgy recoveredd by the gulation and Measurementt station), turbo-exxpander locateed at the city--gate (the Reg where thhe pressure is lowered from m high to med dium levels. Inn order to achhieve this objectivee, it is necessaary to minimizze the pressurre at the mediuum pressure siide of the turbo-exxpander, sincee the upstream m pressure on n the high preessure side is basically fixed annd not conttrollable andd, in generall, depends on o the longg-distance transporttation grid. Thhe problem is constrained since the downnstream pressuure has to be minim mized, therebyy ensuring thhe correct presssure profile all a across the grid and satisfyinng quality and safety connstraints at th he same timee. Consequenntly, it is assumedd that the conntrol variablees are the preessures at thee outlet of thhe turboexpanderrs. It is also assumed a that more m than onee ReMe Statioon is equippedd with its own turbbo-expander. Thus, T a vectorr of control vaariables is defiined as follow ws: u = [ pout1 , pout 2 , …, pout i , …, pout ] o m

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259

where pouti is the pressure at the outlet of each of the m turbo-expanders. The objective function is given as follows: Cobj ( u ) = ∑ pout i

[6.23]

i

Note that inequality constraints on the control variables pouti can be considered as hard limits since they can be restricted during the iterative process, if they do not satisfy operation limits of turbo-expanders, such as follows:

pMAXi < pouti < pMINi Other constraints on the maximum and minimum pressures and flows across the medium pressure grid can be taken into account through penalty functions. The following penalty functions have been assumed: C1p =

nodes

∑ α (P − P ) 1, i

i

2

[6.24]

lim, i

i =1

with:

Plim,i = Pmax,i, if Pi > Pmax,i ; Plim,i = Pmin,i, if Pi < Pmin,I; α1,i = 0, if Pmin,i ≤ Pi ≤ Pmax,i where Pmin,i and Pmax,i are respectively minimum and maximum pressures at the ith node, and α1,i is a weight coefficient; C p2 =

pipes

∑ α (Q − Q ) 2, l

l

2

lim, l

[6.25]

l =1

with:

Qlim,l = Qmax,l, if Ql > Qmax,l ; Qlim,l = Qmin,l, if Ql < Qmin,l, α2,l = 0, if Qmin,l ≤ Ql ≤ Qmax,l where Qmin,l and Qmax,l are respectively minimum and maximum gas flows across the lth pipe, and α2,l is a weight coefficient. Gas flows should fulfill mandatory

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requirements on speed limits, varying according to the different pipe classes, as indicated in national regulations. In the proposed algorithm, the limits have been selected according to Italian specifications [UNI 04]. The proposed algorithm has been tested on the medium pressure natural gas network of Bari, in order to find the optimal output pressure values for turbo-expanders to be set. The aim of the optimization is to lower the outstream pressure as much as possible, thereby guaranteeing secure and safe network operation conditions. This is equivalent to maximizing the ratio Pin/Pout at turboexpanders and to recover as much power as possible. This ratio is directly proportional to power generation with a given flow supply. Since Pin is generally fixed from the high pressure network (12 bar), for the ratio maximization, the sole possibility is to lower Pout. Figure 6.14 shows the performance of a typical city-gate turbo-expander. From the figure, it is possible to observe how variations in the pressure ratio affect power generation.

Figure 6.14. Graph showing the turbo-expander relationship between gas flow and power generation

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The test network (the medium pressure grid) consists of 410 pipelines and 429 nodes (180 of them are final nodes – FRUs); the twin ReMe stations are basically equivalent to slack buses in electric power systems and they can supply up to 45,000 Sm3/h each. Starting from the nominal gas demand supplied by each FRU to the lower pressure grids, the algorithm calculates the optimal pressure values outstream from turbo-expanders and the pressure in the final nodes of the grid (FRUs), taking into account pressure and speed constraints through pipes. The result of the optimization is an outstream pressure of 4.5 bar for both turbo-expanders and a gas flow of 29,000 Sm3/h for ReMe 1 and 37,000 Sm3/h for ReMe 2. Since the medium pressure grid is generally operated at 5 bar, corresponding to a Pin/Pout ratio of 2.4, the algorithm has found a new pressure level that increases the pressure ratio in turbo-expanders up to 2.67. This ratio variation raises the power generated by turbo-expanders to 50 kW for ReMe 1 and 80 kW for ReMe 2. Furthermore, in Figure 6.15, the pressure levels at the 180 FRUs (final nodes of the medium pressure grid) have been plotted. The dotted line represents the pressure in nodes under normal conditions, while the solid line represents the new pressure values after the calculations to maximize the ratio in ReMe stations. The first two nodes correspond to ReMe stations and they have an outstream pressure of 4.5 bar; closer FRUs have similar levels of pressure, while the furthest nodes of the grid are affected by pressure drops in pipes. It is important to ensure a minimum pressure value upstream at the furthest FRU, otherwise it will not be able to laminate the nominal gas flows and gas odorant cannot be distributed safely across the low pressure grid. In the Bari gas grid, the minimum pressure level required to ensure the nominal gas flow is 3 bar (inlet FRU).

Figure 6.15. Graph showing pressures values upstream each FRU.

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6.8. Optimizing pressure profiles on the low pressure distribution grids

The gas demand of medium/low pressure distribution systems is not only due to residential users (although they normally constitute the major part of custom demand), but also to commercial, tertiary or small industrial customers that could need significant volumes without forewarnings. Their requests, in fact, can change according to industrial processes to be executed, or to daily, weekly or monthly working duties. Even residential demand, however, changes very much according to climatic conditions; load profiles are considerably different even during the 24 h of a day, with the night/day request ratio being equal to 1/10 in many cases. Hourly gas flow is also strictly related to the contemporaneity factor, depending on gas utilization (single or centralized boilers, heat pumps, etc.), on personal habits, social and economic conditions and so on. Changes in the demand of the distribution grid can give rise to pressure fluctuations which need to be monitored and controlled to guarantee the fulfillment of commercial quality and safety standards. As mentioned above, pressure is usually remotely supervised and monitored on few FRUs on the medium pressure grid, but it is very hard to find gas systems where capillary pressure is monitored on the low pressure grids. Consequently, an operation experience is adopted to fix setpoints at the FRUs basically twice a year on a seasonal basis. In the project described in this chapter, it was assumed that FRUs’ setpoints could be modified remotely and simulation tools were able to evaluate the pressure profile downstream of the FRU in order to check if all constraints on the low pressure grid were satisfied. The OGF algorithm can be adopted to fix new setpoints in real time to guarantee an optimal pressure profile under normal operating conditions or the best feasible ones under emergency conditions. The control variable u is represented in this case by the setpoints of the remotely controlled FRU as discussed in section 6.7. In this case, the objective function is aimed at minimizing the mismatch between nodal pressure values Pi and a desirable value P0i, considering operational goals such as Quality-of-Service and continuity of supply. This value is extremely important for low pressure grids, because gas distribution companies must guarantee that gas pressures, while reaching the final customers, are in the nominal operating range of user devices, In Italy, a Decree has

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set the relative pressure values in a fairly tight range of 17–25 mbar [UNI 04]. Lower pressure values would denote poor gas supply on the furthest nodes of the grid or even on the whole system, in case of very high gas demand or under emergency conditions; on the other hand, very high pressure levels would lead the distribution company to possible economic losses due to billing errors caused by meters which do not compensate for pressure deviations from nominal values. It should be remarked that this kind of real-time pressure regulation will lead DSO operators to new operational possibilities under emergency conditions. In fact, when there is a lack of gas due to degraded operating conditions, load relief or peak-shaving, actions can be considered to reduce the demand. In this case, the desirable pressure can be intentionally reduced in order to reduce the overall gas demand, thereby exploiting the dependence of gas demand on the pressure at the delivery point. Finally, it can be observed that the OGF algorithm can also be used for operational and maintenance planning. In fact, a possible application lies in simulating possible outages regarding one or more FRUs supplying a low pressure gas network. By imposing appropriate pressure and gas flow levels for these gas sources, it could easily be foreseen if and how long the grid could bear the shutdown of a reduction unit without compromising its technical performances and the capacity to adequately supply every end user. If this capability cannot be ensured due to a lack of redundancy in pipes, FRUs and supply points, the distribution company can identify the weakest zones and, eventually, decide to invest to avoid inconveniences to the customers. Consequently, the objective function Cobj can be formulated as follows: ∑

[6.26]

,

The penalty functions take into account physical limits on pipes and nodes, so that every variable is kept within a suitable range. These functions are formulated as follows: ∑

,

with:

Plim,i = Pmax,i , if Pi > Pmax,i ;

,

[6.27]

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Plim,i = Pmin,i, if Pi < Pmin,i, α1,i = 0, if Pmin,i ≤ Pi ≤ Pmax,i where Pmin,i and Pmax,i are respectively the minimum and maximum pressures at the ith node and α1,i is a weight coefficient; ∑

,

,

[6.28]

with

Qlim,l = Qmax,l, if Ql > Qmax,l ; Qlim,l = Qmin,l, if Ql < Qmin,l, α2,l = 0, if Qmin,l ≤ Ql ≤ Qmax,l where Qmin,l and Qmax,l are respectively minimum and maximum gas flows across the lth pipe and α2,l is a weight coefficient. Gas flows must remain under mandatory speed limits, varying according to the different pipe classes, as indicated in national regulations. In the proposed algorithm, the limits have been selected according to Italian specifications [UNI 04, DEC 11]. The described algorithm has been implemented on a section of a real, urban and low pressure distribution system. The grid chosen for testing is placed in Loseto, a suburban district of Bari, with an old rural residential cluster that in recent years has been surrounded by modern residential buildings. Small commercial activities are also carried out in this area, which has a total population of almost 4,500 inhabitants with 1,015 points of delivery (end-users) for the gas network. Gas supply to these customers is guaranteed by 2 FRUs that reduce the pressure from 4.5 to 0.25 bar and have a maximum flow of 3,000 Sm3/h each, from which a low pressure (0.25 bar), 6.5 km-extended grid departs; the grid is obviously made of pipes with different diameters and materials (Figure 6.16). The network graph consists of 143 pipelines and 132 nodes, including 2 nodes representing FRUs. This particular grid has been chosen for optimization because 2 FRUs are equipped with the described technology. Furthermore, some gas demand profiles are collected and sent to DSO using a certain number of smart meters that allow a check of the results with real data available on the low pressure grid.

Optimal Gas Flow Algorithm for Natural Gas Distribution Systems in Urban Environment

Figure 6.16. Map of the test network: medium pressure pipelines in green eliminate and low pressure ones in red. For a color version of the figure, see www.iste.co.uk/lascala/smart.zip

265

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Figurre 6.16 repressents a snapshhot of the disttribution grid on a cartograaphic map of the Looseto district in Bari; red liines representt low pressuree pipes while the green line is thhe medium preessure pipe thaat links the FR RUs. Somee assumptionss have been made: m – thee Loseto area is i basically flat; therefore, to simplify thhe mathematiccal model and for the purpose of achieving faster calculations, the heeight gradientts among med to equal zero; z nodes haave been assum – thee following adimensional coonstants have been b associateed with naturaal gas: - coompressibilityy factor = 0.9998; - frriction = 0.05;; - reelative densityy= 0.7682 – som me other physical features have h been imp posed as follow ws: - attmospheric prressure = 1,013 [mbar]; - avverage gas floow temperaturre = 284 [K]. Bothh FRUs generaally do not suupply more th han 1,000 Sm3/h flow. Their normal operatingg conditions are displayedd in the subssequent figurres, which shhow daily average trends of pressure and flow w. These dataa are real on-field records, acquired W 2013. during Winter

Figure 6.17.. Pressure and d gas flows in normal ope erating conditio ons, FRU #1

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Figure 6.18. Graph showing pressure and gas flows under normal operating conditions, FRU #2

It can be easily observed that both load profiles follow very similar trajectories, because residential loads with similar gas consumptions form the majority of customers. FRU #1 shows a higher gas flow and consequently a lower pressure level, because it supplies the larger part of the grid; the minimum pressure rate for this unit, in fact, reaches 23.6 mbar, while for FRU #2 it never falls below the limit of 24 mbar. Furthermore, high peak pressure drops are recorded between 7:00 and 8:00 am and then between 5:00 and 6:00 pm According to acquired data, FRU #1 normally gives rise to considerably higher drops when compared to unit #2 because of the topology of the low pressure grid supplied by these two units and the nature of gas loads. The following diagrams show the results provided by the OGF algorithm in terms of operating pressure levels that outstream from FRUs during typical daily behavior. Both FRUs show new pressure trends (dashed–dotted lines) with a general downward shifting trend, witnessing an ordinary operation (solid line) that guarantees abundant fulfillment of quality standards at each node. However, from Figure 6.19, it can be observed that the optimization algorithm may consider, under some conditions, the possibility of increasing pressure levels. This is the case of FRU #1 between 7:00 and 8:00 am. This unit supplies to the only school located on this grid in Loseto. In that period of the day, the customer demands a greater quantity of gas from the grid to turn on its main heater, causing a decrease in the pressure that could also give rise to excessive pressure drops on many other nodes downstream. In this case, the optimization solver increases the pressure from 24.1 up to 24.7 mbar to improve the Quality-of-Service.

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Figure 6.19. A comparative diagram of pressures at FRU#1 before and after optimization

Figure 6.20. A comparative diagram of pressures at FRU#2 before and after optimization

A new setting of reference signals at the two FRUs provides two main benefits. The first effect of the optimized set of pressures is to avoid an excessive pressure drop downstream of FRU #1 and an unbalanced operation between the two supplying nodes of this low pressure distribution grid. As can be observed, the optimized behavior is characterized by a more balanced operation of the network and, consequently, less mechanical stress is undergone by FRU #1 filters and membranes. Another important advantage is that the obtained sets of pressure at the FRUs are on average 0.5 mbar lower than the normal ones. In this way, the DSO is able to

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assure to the customers a flat pressures regime over time. A constant pressure value at the delivery point also contributes to an accurate billing. In fact, the mass of gas delivered may vary depending on the value of pressure: the higher the pressure, the higher the mass and vice versa. Even temperature can affect these measures. Ordinary domestic gas meters read gas volumes without any compensation in terms of pressure and temperature variations. Recent domestic smart meters are not equipped with a pressure compensation device; they can only compensate temperature variations. Large-volume meters for industrial or large commercial customers are equipped differently with a retrofit kit including an additional probe for pressure and temperature adjustments and a wireless data transmitter. It is evident that an average pressure level, close to the nominal values of meters across the grid, guarantees less billing errors for the numerous meters that are not compensated in pressure. In Figure 6.21, pressure deviations due to optimization have been plotted for each node of the low pressure grid at three crucial hours of the day: 8 am, 5 pm (respectively plotted in blue and green) representing two peak hours and 3 am (red line) when the gas demand is at its minimum. FRU #1 and FRU #2 are labeled as node 1 and 2, respectively. A positive value means that the pressure is increased due to optimization. It should be remarked that a 0.5 mbar pressure drop at the FRUs can lead to considerably higher differences at the terminal nodes of the grid (from −2.5 to +0.5 mbar) labeled with a higher progressive number. Thus, small variations at the FRU nodes can cause large pressure deviations at the furthest nodes. Such behavior justifies the utilization of diffuse monitoring and real-time optimization tools such as the one proposed here in order to guarantee commercial quality and safe operations in gas distribution grids.

Figure 6.21. Graph showing estimated hourly pressure deviations at each node after optimization. For a color version of the figure, see www.iste.co.uk/lascala/smart.zip

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6.9. Conclusions

It has been shown how SCADA systems, smart metering and remote control of setpoints of regulators can provide benefits in monitoring and control of the gas distribution grids. Consequently, better commercial quality and economic effectiveness of the operation can be achieved. This was shown through an experiment conducted on an actual gas distribution system in a medium-sized town in Italy. These results show the potential of more advanced automation of these grids and their transition toward Gas Smart Grids. A complete automation of grid systems in towns (power, gas, water and heating/cooling) and their coordinated control is an essential feature for the implementation of the smart city concept. 6.10. Acknowledgements

The authors gratefully acknowledge Apulia Regional Government in Italy for funding the “Smart Grid Project” with €1,133,700 which allowed the described research activity and the implementation of the pilot project; AMGAS Bari S.p.A., the urban gas distribution company for its technical support in the experimentation and testing of the proposed methods and equipment; and Mr. Vito Donato Bisceglia, Technical Director of this utility, for providing necessary information and support in completing the project. 6.11. Bibliography [ABB 16] ABBATANTUONO G., LAMONACA S., LA SCALA M. et al., “Monitoring and emergency control of natural gas distribution urban networks”, 2016 IEEE Workshop on Environmental, Energy, and Structural Monitoring Systems (EESMS); IEEE Conference Publications, Bari, Italy, June, 2016. [AUT 13] AUTORITÀ PER L’ENERGIA ELETTRICA, il gas e il sistema idrico, “Delibera 27 dicembre 2013 n. 631/2013/R/gas Modifiche e integrazioni agli obblighi di messa in servizio degli smart meter gas”, available at: http://www.autorita.energia.it/it/docs/ 13/631-13.htm, 2013. [AUT 15] AUTORITÀ PER L’ENERGIA ELETTRICA, il gas e il sistema idrico, “Delibera 20 novembre 2015 n. 554/2015/R/gas Disposizioni in materia di obblighi di messa in servizio degli smart meter gas e modifiche e integrazioni della RTDG”, available at: http://www.autorita.energia.it/it/docs/15/554-15.htm, 2015.

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[BAL 14] BALDWIN J., “Biomethane to Grid – UK Project Review”, European Biomethane Workshop – Markets, value chains and applications. Final conference of Green Gas Grids, Biomaster and Urban Biogas projects, available at http://european-biogas.eu/wpcontent/uploads/2014/03/18_John-Baldwin_Injection-of-biomethane.pdf, Brussels, March 2014. [CHA 01] CHANG S., “A program development for unsteady gas flow analysis in complex pipe networks”, PSIG Annual Meeting, Salt Lake City, Utah, October 2001. [COE 07] COELHO P.M., PINHO C., “Considerations about equations for steady state flow in natural gas analysis”, Journal of the Brazilian Society of Mechanical Science & Engineering, vol. XXIX, no. 3, 2007. [CRO 36] CROSS H., “Analysis of flow in networks of conduits or conductors”, University of Illinois Bulletin, Engineering Experiment Station, vol. XXXIV, no. 22, Bulletin no. 286, 1936. [DEC 84] DECRETO MINISTERIALE DEL 24/11/1984, Ministero dell’Interno “Norme di sicurezza antincendio per il trasporto, la distribuzione, l’accumulo e l’utilizzazione del gas naturale con densità non superiore a 0.8”, 1984. [DEC 11] DECRETO DEL PRESIDENTE DELLA REPUBBLICA 1 AGOSTO 2011, n. 151 “Regolamento recante semplificazione della disciplina dei procedimenti relativi alla prevenzione degli incendi, a norma dell’articolo 49, comma 4-quater, del decreto-legge 31 maggio 2010, n. 78”, 2011. [DJE 08] DJEBEDJIAN B., EL-NAGGAR M., SHAHIN I., “Gas distribution network optimization by genetic algorithm”, 9th International Congress of Fluid Dynamics & Propulsion, Alexandria, Egypt, December 2008. [DJE 11] DJEBEDJIAN B., SHAHIN I., “Optimal design of gas distribution network: a case study”, Mansoura Engineering Journal, vol. 36, no. 3, pp. 35–51, 2011. [EN 12] EN 12007-1:2012 “Gas infrastructure. Pipelines for maximum operating pressure up to and including 16 bar. General functional requirements”, 2012. [EN 13] EN 1594:2013 “Gas infrastructure. Pipelines for maximum operating pressure over 16 bar. Functional requirements”, 2013. [EUR 09] EUROPEAN PARLIAMENT, Council of the European Union, “Directive 2009/28/EC of the European Parliament and of the Council of 23 April 2009 on the promotion of the use of energy from renewable sources and amending and subsequently repealing Directives 2001/77/EC and 2003/30/EC”, available at: http://eur-lex.europa.eu/legal-content/en/ALL/ ?uri=CELEX:32009L0028&qid=1472228244543, 2009. [GUT 14] GUTIERREZ TERRON A.M., “BIOGRID – Biogas injection into natural gas grid and USA as vehicle fuel by upgrading it with a novel CO2 capture and storage technology”, Technical report, 2014. [HEN 14] HENGEVELD E.J., VAN GEMERT W.J.T., BEKKERING J. et al., “When does decentralized production of biogas and centralized upgrading and injection into the natural gas grid make sense?”, Biomass and Bioenergy, vol. 67, pp. 363–371, 2014.

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[HER 09] HERRAN-GONZALEZ A., DE LA CRUZ J.M., DE ANDRES-TORO B. et al., “Modeling and simulation of a gas distribution pipeline network”, Applied Mathematical Modeling, vol. 33, no. 3, pp. 1584–1600, 2009 [HUS 13] HUSSEY B., “Biogas injection into the Natural Gas Grid”, Consultation paper, The Commission for Energy Regulation, Dublin, 2013. [ILK 05] IL’KAEV R., SELEZNEV V., ALESHIN V. et al., “Numerical Simulation of Gas Pipeline Networks: Theory, computational implementation, and industrial applications”, Ed. URSS.ru, 2005 . [MAR 06] MARTIN A., MOLLER M., MORITZ S., “Mixed integer models for the stationary case of gas network optimization”, Mathematical Programming, vol. 105, no. 2, pp. 563–582, 2006. [OSI 95] OSIADACZ A.J., GÓRECKI M., “Optimization of pipe sizes for distribution gas network design”, PSIG 27th Annual Meeting, Albuquerque, New Mexico, October 1995. [SMA 16] www.smartgridproject.it. [UNI 04] UNI – Ente Italiano di Normazione, Technical Standard, “UNI 9165:2004 Gas distribution networks - Pipeworks with maximum operating pressure up to 5 bar - Design, construction, testing, operation, maintenance and rehabilitation”, available at http://store.uni.com/magento-1.4.0.1/index.php/uni-9165-2004.html, April 2004 . [WEI 10] WEILAND P., “Experience with grid injection in Germany”, International Workshop “Digestate and biogas utilisation – practices and perspectives”, Copenaghen, May 2010. [WU 07] WU Y., LAI K.K., LIU Y., “Deterministic global optimization approach to steadystate distribution gas pipeline networks”, Optimization and Engineering, vol. 8, no. 3, pp. 259–275, 2007.

7 Multicarrier Energy System Optimal Power Flow

In the cities of the future, different energy substrates will be integrated and this matter has led to some essential changes in the planning and optimization process. This chapter presents a new modified optimization algorithm based on a powerful heuristic method, namely Time Varying Acceleration Coefficient Gravitational Search Algorithm (TVAC-GSA), to solve Optimal Power Flow (OPF) problems in multi-carrier energy systems focusing on the interactions between the power grid and the gas network. The proposed algorithm is based on the Newtonian laws of gravitation and motion. The complexity of both electrical and gas networks in terms of the special structure of distribution systems, the energy hub structure, energy flow equations, and different related equality and inequality constraints makes the optimization problem highly nonlinear, non-convex and high-dimensional. The effectiveness of the proposed algorithm to solve such a complex OPF problem is verified by using a new introduced multi-carrier energy grid. The obtained results by the suggested approach in comparison with separated OPFs demonstrate its accuracy and its ability in finding an operating point with lower cost value. Based on these advantages, the method seems to be a good candidate to optimize smart distribution systems coupled with gas networks, thereby gaining efficiency in the overall system.

7.1. Introduction Nowadays, operations in distribution power systems have been experiencing essential changes due the utilization of micro-turbines, Combined Heat and Cooling Power (CHCP), new energy convertors, Distributed Generation (DG), a widespread use of renewables, use of multiple energy carriers in industrial parks and large tertiary facilities, etc. This new scenario implies more strong interactions between electrical and gas grids which, in some cases, can give rise to more complex operations, but it can also be an opportunity for energy efficiency and optimization. Chapter written by Soheil DERAFSHI BEIGVAND, Hamdi ABDI and Massimo LA SCALA From Smart Grids to Smart Cities: New Challenges in Optimizing Energy Grids, First Edition. Edited by Massimo La Scala. © ISTE Ltd 2017. Published by ISTE Ltd and John Wiley & Sons, Inc.

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Optimization, efficiency enhancement and cost reduction is possible and attractive in towns where quite often a single multi-utility company operates different systems such as the power grid, the gas grid, district heating and cooling, etc. This is particularly desirable in the so-called smart city concept, where optimization of services, energy efficiency and emission control are basic objectives to create a comfortable and productive living environment. Usually, energy infrastructures are optimized and operated independently. Recently, the employment of several energy converters in a specific infrastructure, named the energy hub [GEI 07a], has allowed different energy grids to interact. This technological possibility has turned the separated operations of single energy grids into an integrated operation as shown in [DER 16a]. In this context, the energy hub provides the necessary means to integrate multiple energy carriers. In particular, energy carriers such as electricity and natural gas appear to be prone to simultaneous optimization. Gas-fired units [ŞEV 15], dispersed generation [LEV 13, LIN 13], CHP units [DER 16b, MOH 13] and tri-generation in the hubs provide a more effective energy conversion between various carriers [GEI 07a, MOE 14, SHA 15]. As a result, a hub can consume and convert different forms of energy to supply different demand types (electricity and heating/cooling activity). A novel operation concept in which different carriers are simultaneously optimized can be achieved through necessary and fundamental modifications to traditional operation and optimization methods which consider only one form of energy. Without claiming to be exhaustive, Refs [WON 68, BEN 95, CAR 79] show three examples of traditional approaches. In [CAR 79], the OPF problem was proposed for power systems and constitutes a basic piece of literature in this field. Optimization of a gas-based network by using dynamic programming can be found in [WON 68]. [BEN 95] introduces the optimization of a district heating network as a single carrier system. More recently, an integrated approach for the optimization of several energy carriers has been considered. For instance, a general framework was developed in [GRO 95] to describe municipal and regional energy systems in terms of data-flow networks. This work provided an approach for dynamic and stochastic optimization of primary energy demands, emissions of pollutants and monetary cost. In [AN 03], natural gas and electricity Optimal Power Flows (OPFs) were presented in which the energy conversion between electrical and gas infrastructures at generator units was considered. Optimization of a single hub in the form of a new optimization model, namely optimal power dispatch, was addressed in [GEI 05a]. In this work, a general optimization framework for power conversion considering several energy carriers (such as natural gas, electricity and district heating) was introduced. The OPF

Multicarrier Energy System Optimal Power Flow

275

problem of multicarrier networks focusing on energy hubs was proposed in [GEI 07a]. In [MOE 14], a decomposed solution was applied to this problem in which the main problem was decomposed into separate single energy carrier OPF problems. Also, energy flow optimization in multicarrier systems was implemented in [SHA 15] through a modified teaching–learning based optimization. Recently, a novel heuristic optimization algorithm, namely Gravitational Search Algorithm (GSA), was proposed in [RAS 09]. This algorithm is based on the Newtonian laws and has been successfully applied to different nonlinear problems. The results showed its capability to explore the whole optimization set. Due to its characteristics, a modified version of it (called Time Varying Acceleration Coefficient – GSA or TVAC-GSA) seems to be a good candidate to solve difficulties linked to real world Multiple Energy Carriers Optimal Power Flow (MECOPF) problems. In this chapter, a new algorithm based on the introduced TVAC-GSA to solve the MECOPF problem is proposed which focuses on electric–gas systems with electricity–heat demands. In fact, a heuristic approach is proposed to solve convergence difficulties due to the structure of the problem, which cannot be overcome with more classical optimization techniques (such as gradients-based, interior point, quasi-Newton methods, etc.). Furthermore, performances of the proposed method are compared mainly on the basis of economic benefits which can be obtained while searching the global optimum (or the less expensive solution) and the related operating point costs. The main feature of the proposed approach is related to its ability to solve and find a better quality solution of non-convex, non-differential, high-dimensional and highly nonlinear MECOPF problems. In this chapter, the main complexities associated with the multicarrier system structure and several dispatched hubs equipped with CHP units/furnaces/transformers are addressed. It should be noted that the contribution in this area is derived from the capability of the proposed algorithm in finding an optimum without convergence problems and mostly yielding a good quality solution which results in economic benefits which is the main performance indicator. Without lack of generality, a multi-carrier energy system including a power distribution grid combined with a gas network is presented to show how the joint optimization of multiple carriers can be carried out. However, it is possible to assess that other carriers can be treated similarly. The formulation of this kind of problem is based on the essential components of a hybrid network as presented in [GEI 07a, DER 16a]. As a final note, the use of the terms “multiple energy carriers” and “multicarrier” is preferred to the term “hybrid”, which is more often adopted for

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such systems in this study. Also, the term “energy flow” is employed to refer generically to terms such as “power flow” and “gas flow”. 7.2. Basic concepts and assumptions 7.2.1. MEC and energy hub Multicarrier networks are simultaneously optimized to meet demands more efficiently. In general, they include several energy systems, such as electrical and gas infrastructures. The related grids transmit energy from sources to demand centers, as shown in Figure 7.1. Due to the increasing utilization of DGs such as CHP units and tri-generations, multiple energy carriers allow more flexibility in the network operation in comparison with a single carrier. In fact, these devices allow for converting one type of carrier (gas) into several forms (electricity–heat–cool). Gas Production

Sources

Electrical Generation

Transmission

Several Energy Hubs

Conversion

Electricity

Demand

Heat

Figure 7.1. A schematic layout of a multicarrier energy system

In general, a hub establishes an interface between its input ports (where the energy is delivered by transmission grids and/or energy sources) and loads. In other words, each hub, like a unit, utilizes different carriers (such as electricity, natural gas, etc.) at its inputs and provides various energy services (such as electricity, heat, cool, etc.) at the output ports. Moreover, it enables the integration of an arbitrary number of energy carriers and products [GEI 07a]. This concept is shown in

Multicarrier Energy System Optimal Power Flow

277

Figure 7.2(a). A special energy hub including a CHP, a transformer and a gas furnace (as the convertor elements), which utilizes electricity and natural gas and distributes power and heat is illustrated in Figure 7.2(b). Carriers

Energy Hub

Pα

Conversion

Lα Electricity (Se)

Pβ

Conversion

Lβ Natural Gas (P ) g

Pω

Conversion

a)

Demands

Lω

Energy Hub Electricity (Le) ν Heat (Lh)

1-ν Transformer

CHP

Furnace

b)

Figure 7.2. Schematic showing the energy hub concept: a) a general representation; b) a special case of energy hub

Table 7.1 presents the basic energy hub elements. Accordingly, in general, three components including direct connections, power conversions and storages constitute the energy hubs. These components are as follows: – Direct connection: it delivers an input carrier into output without converting it into another form or significantly changing its quality, e.g. electric cables, overhead lines, pipelines, etc. – Converter: it can transform the input power into other forms or quantities, e.g. steam and gas turbines, combustion engines, electric machines, fuel cells, etc. – Storage: it stores different forms of energies, e.g. thermal and electrical storage devices. Note that thermal storage includes the possibility to store heat and cool energies in different means (water, ice, etc.) but also in the heated/cooled materials or in building envelopes. It should be noted that the power plants (e.g. co- and tri-generations), industrial plants (e.g. refineries), big buildings (e.g. airports, hospitals and shopping malls), and bounded geographical areas (e.g. cities) can be modeled as energy hubs. In this view point, an energy hub can be applied to any size of the modeled system [GEI 07a]. Four types of conversions can be classified according to the number of inputs and outputs as illustrated in Table 7.2. According to this table, different types of converters are as follows: – single input and single output convertor: it can convert one type of energy into another carrier, e.g. gas furnaces; – single input and multiple outputs convertor: it converts an input carrier into several types, e.g. tri-generations;

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– multiple inputs and single output convertor: it can convert two or more types of energy into one carrier, e.g. heat pumps; – multiple inputs and multiple outputs convertor: it converts multiple inputs into several forms of energies at its output, e.g. reversible fuel cell. In the context of multiple energy carriers, the whole energy supply infrastructure can be considered as a network of interconnected energy hubs. In this chapter, the focus is on energy distribution systems – basically urban distribution systems which can be operated on a local basis (town or district) by a single operator. A new model of towns, usually identified with the “smart city” attribute, should consider the possibility to integrate different energy distribution systems in order to yield more coordinate and optimized operations under normal as well as emergency conditions. In [GEI 07b], it has been hypothesized that there is a town in which energy distribution systems are organized in hubs associated to different functional areas of the town. Figure 7.3 shows a pictorial example of a town which is roughly divided into three areas including industrial, commercial and private/residential areas. Each area is interfaced with natural gas and electrical distribution systems through an energy hub. The internal layout of the hubs is adapted to the specific load requirements. An adjacent network, a photovoltaic plant connected to Hub #3, and wind and hydro plants connected to the electrical grid through bus #4, supply the system. The latter node may represent a more remote station outside the town where hydro reservoirs are available [GEI 07b]. Adjacent Electrical System Bus #1

Industrial Area Hub #1

Adjacent Pipeline System

Residential Area

Bus #3

Hub #3

Solar Energy

Wind Energy Bus #4

Hub #2 Commercial Area Electricity

Pumped Hydro Bus #2

Gas

Other Carriers e.g. Heat, Cool, ...

Figure 7.3. A town as a system of interconnected hubs

Multicarrier Energy System Optimal Power Flow

Energy hub element

Description

Example(s)

Direct connection

An input carrier is delivered to the output without converting it into another form or significantly changing its quality (e.g. voltage and pressure). The power is transformed into other forms or qualities.

– Electric cables – Overhead lines – Pipelines

Converter

Storage devices

Different energy carriers are stored.

279

– Steam and gas turbines – Combustion engines – Electric machines – Fuel cells – Thermal storage capacity – Electrical storage device

Table 7.1. Basic energy hub elements [GEI 07a] Convertor Type Single input and single output

Example

Single input and multiple outputs

Multiple inputs and single output

Multiple inputs and multiple outputs

Description It converts natural gas to heat. It converts natural gas in order to provide heating, cooling, and electricity. It converts heat and electricity into heat.

It converts hydrogen and water into electricity and heat.

Table 7.2. Converter types [GEI 07a]

7.2.2. CHP units In present developmental stages, one of the components which creates coupling between the power grid and the gas grid is called Combined Heat and Power (CHP) or analogously the process is called Combined Heat Cooling and Power (CHCP) production. These technologies were largely successful and are largely utilized and incentivized by different countries. In fact, a large amount of the input energy in the

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conventional electrical generation is lost to the atmosphere as waste heat. Combined heat and power is the simultaneous production of heat and electricity energies in a single process. A CHP unit uses the generated heat in the electrical power generation process rather than releasing it wastefully into the atmosphere. CHP is sometimes referred to as cogeneration, or cogen, and where there is cooling energy created in the same process, it is termed as a tri-generation unit which is also known as CHCP [DEN 12]. To make better use of the fuel, combined heat and power production is largely utilized [DER 16b]. This technology has been introduced to increase the thermal efficiency of the combined cycle plants, from 50–60% [BAS 10] to 80–90% [KAR 07, VAS 07] which is mainly due to better use of low enthalpy heat. In other words, the efficiency of a CHP unit can typically be about 20–30% higher than the combined efficiency of heat-only boilers and conventional power stations. Figure 7.4 compares the efficiency of a typical CHP unit with the separated generation of heat and electricity. This figure indicates that in the conventional process, about 41 and 12% of the input energy (i.e. 133% fuel) in the production of electricity and heat with 42 and 81% efficiencies, respectively, are lost. In contrast, in a cogeneration plant, 20% of the input fuel is lost and 30 and 50% of the input are converted into electricity and heat energies, respectively. In the right circumstances, where there is a large heating or cooling demand in addition to an electrical load, cogeneration can be an economic means for improving the efficiency of energy supply and achieving environmental targets in emissions reduction. Cogen usually involves the burning of fossil fuels but can also use biomass (including solid biomass, biogas and waste) [DEN 12]. Conventional Generation

Combined Heat and Power

Loss (41 %)

Power Station Input Fuel Electricity Production at 42% efficiency (71 %) Boiler Input Fuel (62 %)

Heat production at 81% efficiency

Electrical Out (30 %) Heat Out (50 %)

CHP Electrical Out (30 %) CHP Heat Out (50 %)

CHP Production at 80% efficiency

Loss (20 %)

Loss (12 %) Total separate heat & electricity generation input = 133 %

CHP production is 25 % more efficient than separate heat and power production.

Total separate heat & electricity losses = 53 %

CHP Input = 100 % CHP Losses = 20 %

Overall efficiency = 60 %

Overall efficiency = 80 %

Figure 7.4. A comparison of conventional electricity and heat production to CHP units

CHP Input (100 %)

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281

Some of the main advantages of employing CHP units are as follows: – cost reduction; – emission (CO2, etc.) reduction; – security enhancement of energy supply; – conservation of valuable fuel resources. It is important to note that the complete advantage of the natural gas-fired CHP technology is achieved when the generation of electricity and heat is combined. For this to be technically and economically feasible, it generally requires a simultaneous demand for both heat and power on the premises. Also, CHP installation has been widely recognized as a key measure to reduce CO2 levels, the main greenhouse gas, while delivering the same amount of useful energy. It is estimated that for every 1 MWe of CHP installed, carbon dioxide emissions are reduced by at least 1,000 tons per year. In fact, these units can reduce the environment emissions of the generation sector by 13–18% [KAR 07]. Employing CHP units in many countries is strongly supported by the regulation due to their efficiency and environmental benefits. The role of CHPs in energy hubs, microgrids and power parks is becoming more and more important due to the need to disseminate power production and shorten the distance between locations where energy is converted and used. These technologies show their potential in urban areas where the concern about the environment is higher and the new urbanization of large cities is challenging energy needs [DER 16b]. Based on the electrical output, CHP applications are divided into the following three categories: 1) Large scale CHPs ( ≥ 1 MWe ): the prime mover in this type of CHPs can be a gas turbine or spark ignition gas engine. They drive a generator to produce the electrical power and then the exhaust gases pass through a recovery unit which provides the heat in the required form such as steam or hot water. Additional heat in the form of steam or hot water can be produced by using a technique called afterfiring. This technique involves burning more gas in the oxygen-rich gases prior to the process in the waste heat boiler. These CHPs can be used in larger industrial and commercial processes such as chemical/pharmaceutical plants, breweries, airports, universities, food processing plants, etc.

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2) Small scale CHPs ( 50 kWe ≤ < 1 MWe ): the prime mover in the small scale CHPs is a reciprocating engine. Moreover, “microturbines” are introduced for this type of cogenerations. This technology can be used in hospitals, hotels, industrial processes, commercial buildings, etc. where a continuous demand for both electricity and heat exists. 3) Micro-CHPs ( ≤ 50 kWe ): they use different technologies such as internal combustion engines, external combustion engines, micro-turbines and fuel cells. Each CHP unit includes the following four basic elements: – a prime mover; – an electrical generator; – a heat recovery system; – a control system. As discussed, the prime mover may be a steam turbine, reciprocating engine or gas turbine. It is an important element and drives an electrical generator; and then, waste heat is recovered by using a heat recovery system. A control system controls these processes.

7.2.3. General assumptions In this study, for constructing each problem element, following assumptions are used: – power flow through each convertor is only characterized by its efficiency; – within each hub, losses only occur in convertor devices [DER 16a]; – storage devices will not be considered explicitly [GEI 07a, DER 16a, GEI 05b]; – the gross heating value is assumed to be equal to one [DER 16a]; – the pipelines only (without compressor unit) are considered lossless (there is no pipeline leakage) [DER 16a]; – as commonly practiced for electricity and natural gas, the cost of each type of energy (here, electricity and gas) is stated as a polynomial function of its generated power [GEI 07a, AN 03, GEI 05a, SAA 11];

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283

7.3. Problem formulation 7.3.1. Electrical power balance equations The power balance equations for an electrical network can be presented as [7.1] and [7.2].

Pegi − Pedi = Vi

Qegi − Qedi = Vi

Ne

∑ V (G

)

[7.1]

)

[7.2]

ij

cos (θij ) + Bij sin (θij )

∑ V (G

sin (θij ) − Bij cos (θij )

j

j =1

Ne

j

j =1

ij

with j = 1,…, N e , where Pegi and Qeg i denote the active and reactive power generations at the i th node, respectively; Pedi and Qed i are the real and imaginary parts of electrical demand at the i th node, respectively; V and θ represent the voltage magnitude and phase angle of the i th bus in the power system; Gij and Bij denote the conductance and susceptance of the transmission line between buses i and j , respectively and finally, N e denotes the total number of electrical buses. 7.3.2. Gas energy flow equation Similar to the electrical grid, power flows of a pipeline system can be analyzed by stating the nodal power balance and line equations. Equation [7.3] represents the flow balance for the ith node [GEI 07a, DER 16a] in the pipeline grids: Qi =

∑Q

[7.3]

ij

j ∈N i

where Qi denotes the volume flow injected at the i th node; N i is the set of nodes connected to the i th node; and Qij represents the pipeline flow which can be stated as follows [GEI 07a]:

Qij = kij sij

⎧ +1, if ρi ≥ ρ j ⎩−1, if otherwise

ρi2 − ρ 2j with sij = ⎨

[7.4]

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where ρ i and ρ j are the upstream and downstream pressures, respectively, as shown in Figure 7.5 and kij represents the properties of the pipeline and fluid (for more details, see [GEI 07a]).

k

Qkj

ρk

Qcom

i C

ρi

Qij

–Qij

j

ρj

Figure 7.5. Model of a pipeline equipped with compressor (C) [DER 16a]

Note that Figure 7.5 shows a pipeline equipped with a compressor unit. The power consumption of this unit (i.e. Qcom ) can be expressed as a function of the pressure difference between the output and input of the compressor (i.e. ( ρ i − ρ k ) ), multiplied by a constant characterizing the compressor unit (i.e. k com ) and the volume flow rate through it (i.e. Qij ) [GEI 07a, DER 16a], as follows: Qcom = kcom Qij ( ρi − ρ k )

[7.5]

Also, the compression ratio ρ cr of the mentioned compressor can be defined as follows:

ρcr =

ρi ρk

[7.6]

Consequently

Qkj = Qij + Qcom

[7.7]

For more information related to power flow computation in natural gas systems, see [VAS 13, SHA 13, DEB 09]. It is clear that, in a pipeline equipped with a compressor unit as shown in Figure 7.5, natural gas flows from node k to node j which is due to the compression ratio assumed as a positive number [GEI 07a, DER 16a, GEI 07b]. It should be noted that, in this study, energy flows in the gas systems are described by conservation laws such as [7.4] or [7.7] and physical losses in the pipelines are usually not considered [GEI 07a, DER 16a, GEI 07b].

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285

7.3.3. Modeling of energy hubs A general model representing a hub with multiple inputs and outputs (Figure 7.2(a)) can be stated as [7.8] in which the coupling matrix C denotes the mapping of input carriers to the output ones. ⎡ Lα ⎤ ⎡cαα cβα … cωα ⎤ ⎡ Pα ⎤ ⎢ ⎥ ⎢c cββ … cωβ ⎥⎥ ⎢ Pβ ⎥ ⎢ Lβ ⎥ = ⎢ αβ ⎢ ⎥ ⎢ M ⎥ ⎢ M M O M ⎥⎢ M ⎥ ⎥⎢ ⎥ ⎢ ⎥ ⎢ Lω ⎦ ⎢⎣cαω cβω … cωω ⎥⎦ ⎣ Pω ⎦ ⎣{ 144424443 { L

C

[7.8]

P

In [7.8], P represents the power inputs vector; L denotes the power outputs vector; moreover, subscript {α , β , …} describes energy carriers such as electricity, natural gas, etc. and the entries of matrix C (i.e. cαα , cαβ , and etc.) are coupling factors. Each coupling factor in [7.8] relates an input to a certain output (i.e. energy conversion). Note that, generally, for a multiple input and multiple output hub, coupling factors are not always equal to converter efficiencies. This is because the delivered power at the input port may be split into several converters. Therefore, another coupling factor, namely dispatch factor ν , should be considered. It defines how power flows from an input are distributed among the hub convertors. For example, a hub presented in Figure 7.2(b) shows that ν times the total input power flows into the CHP unit and (1 −ν ) times the input is converted by the gas furnace, so that 0 ≤ ν ≤ 1 [GEI 07a]. Therefore, generally, each coupling factor contains “dispatch factor × converter efficiency” [GEI 07a, DER 16a, DER 16b]. So, matrix C defines a linear transformation based on the assumed constant efficiencies. As an example, according to [7.8] and dispatch factors, the energy hub presented in Figure 7.2(b) (which is the one used for case study simulations) can be formulated as follows:

Lei = ηTi Sei +ν iηGTe Qgi i

Lhi = ⎡ν iηGTh + (1 −ν i )η Fi ⎤ Qgi i ⎣ ⎦

[7.9] [7.10]

with i = 1, 2, …, N hub , where S ei = Pei + jQei and Qgi are the electricity and natural gas inputs of the i th hub; Lei and Lhi denote electricity and heat as outputs; ηTi ,

η F , ηGTei and ηGThi represent the efficiencies of transformer (electricity–electricity), i

gas furnace (gas–heat), CHP unit (gas–electricity) and CHP unit (gas–heat) of the i th hub, respectively and ν i is the dispatch factor of the i th hub.

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For a network with N hub hubs, total electricity (i.e. Letotal ) and heat (i.e. Lhtotal ) demands can be written as follows: Letotal =

N hub

∑L i =1

ei

+

∑S

i∈OED

[7.11]

ed i

N hub

Lhtotal = ∑ Lhi

[7.12]

i =1

where OED denotes a set of other electrical demands directly connected to the electrical network (not through a hub). 7.3.4. MECOPF problem In this chapter, the optimal operation problem is to optimize an objective function subject to various constraints related to both electrical and gas-based pipeline systems as [7.13], where P g and Q g denote the active and reactive generated powers in the i th generator bus, respectively; V g

and V l are the

voltage magnitudes of the generator and load buses, respectively; QNi denotes the supplied gas by the i th adjacent network (gas source); subscripts min and max represent the minimum and maximum values of a quantity, respectively and finally, OF represents the objective function which should be minimized. Minimize OF ⎧ ⎧ Power balance equations Vi g, min ≤ Vi g ≤ Vi g, max , , ⎪ Power ⎪⎪ as[7.1]and [7.2] for i ∈{generator buses} ⎪ ⎪ network ⎨ g ⎪ Qi , min ≤ Qig ≤ Qig, max ⎪ ⎪ ⎪⎪constraints ⎪⎩ for i ∈{generator buses} s.t. ⎨ QNi , min ≤ QNi ≤ QNi , max ⎧ balance equation as ⎪ Pipeline ⎪Gas , for i ∈{gas production units} ⎪ [7.3] employing [7.7] ⎪ system ⎨ 0 ≤νi ≤ 1 Hub balance equation ⎪ , ⎪ ⎪ for i ∈{energy hubs} as [7.8] ⎪constraints ⎩ ⎪⎩

Vil, min ≤ Vil ≤ Vil, max

,

for i ∈{load buses}

Pi g, min ≤ Pi g ≤ Pi g, max for i ∈{generator buses}

[7.13] ,

ρi , min ≤ ρi ≤ ρi , max for i ∈{gas buses}

,

ρcri , min ≤ ρcri ≤ ρcri , max for i ∈{compressor units}

In this chapter, energy cost minimization is considered for OF. In this case, the objective function is the total energy cost including active power generation and gas power production costs, which is represented as follows: N eg

(

) ( N an

( )

OF = ∑ aei + bei Pi g + cei ( Pi g ) + ∑ ag i + bg i QNi + cg i QNi i =1

2

i =1

2

)

[7.14]

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287

where ae , be , ce , π , ω , ag , bg and cg represent the cost coefficients and N eg and N an denote the number of generators and adjacent networks (gas sources), respectively. 7.4. Time varying acceleration coefficient gravitational search algorithm In order to solve the optimization problem formulated in the previous section, a solver based on a population-based search algorithm is proposed. Members of a population-based search algorithm pass the following three steps in each iteration to implement the concepts of exploration and exploitation [RAS 09]: – self-adaptation: in this step, each agent (member) improves its performance; – co-operation: in this step, agents (members) collaborate with each other by information transferring; – competition: members compete to survive. These steps can be implemented in different ways since they have usually stochastic forms. The principles behind the implementation of the population-based heuristic algorithms are usually inspired by nature. These concepts guide an algorithm to find a global optimum. However, all population-based search algorithms provide satisfactory results, but there is enough evidence that no heuristic algorithm can provide a superior performance than others in solving all optimization problems. Thus, it is very important to select these kind of solvers on the basis of the specific application and thorough simulations and testing. In order to solve the problem proposed in the previous section, here a modification of the Gravitational Search Algorithm (GSA) is proposed. GSA was firstly proposed by Rashedi et al. [RAS 09] in 2009. This algorithm is based on the Newtonian laws. It is capable of handling large-scale nonlinear problems as shown in [DER 16a, DER 16b, RAS 09, BHA 12, ABD 16]. The solver proposed here is named as Time Varying Acceleration Coefficient Gravitational Search Algorithm (TVAC-GSA) and was presented in [DER 16a]. The main principles of TVAC-GSA are summarized in this section. Suppose that there are N masses (as N agents) and the position of each mass corresponds to a potential solution of the problem. Therefore, the position of the i th mass can be stated as follows: T

X i = ⎡⎣ xi1 , …, xid , …, xin ⎤⎦ i = 1, 2, …, N

[7.15]

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where xid represents the position of the i th mass in the d th dimension and ( ·)

T

denotes the transposition of ( ·) . Based on the gravity law, each mass attracts every other mass and the gravitational force between the i th mass because of the j th mass in d th dimension at specific time t is represented as [7.16]. This is because of the fact that the gravity acts between separated masses without any intermediary force and any intermediary and delay [RAS 09]. Moreover, the gravitational force between heavier masses with short distance is the highest (Figure 7.6).

Fijd = G ( t ) ×

M i (t ) M j (t ) Rij ( t ) + ε

× ( x dj ( t ) − xid ( t ) )

[7.16]

where

⎛ ⎞ −δ t G ( t ) = G0 exp ⎜ ⎟ , Rij ( t ) = X i ( t ) , X j ( t ) ⎝ Iteration max ⎠

2

and where G ( t ) is the gravitational constant which is reduced with time (iteration and age of universe) to control search accuracy [RAS 09]; G0 is the initial value of G ( t ) ; Iteration max represents the maximum number of iterations; δ is a constant

term and Rij ( t ) denotes the Euclidian distance between the i th and j th mass. Note

that according to [DER 16a, DER 16b, ABD 16], Rij ( t ) provides a better performance than Rij2 ( t ) (unlike the law of gravity).

The total gravitational force that acts on the i th mass in the d th dimension is a randomly weighted sum of d th components of the forces exerted from other agents as shown in [7.17]. At the beginning of the optimization process, the reduction of the number of masses with lapse of time, as shown in [7.17], allows the exploration of the solution space to avoid being trapped in a local optimum. Also, the exploitation power fades with lapse of time. Therefore, a set of agents with heavier masses ( K best agents corresponding to good solutions) only apply their gravitational force to the others [RAS 09]. K best with an initial value of K 0 is a function of time which is reduced with the iteration linearly. Consequently, the performance of GSA will be improved.

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289

Figure 7.6. The concept of gravitational forces between particles [DER 16a]

Fi d ( t ) =

N

∑ rand

j∈K best j ≠i

j

× Fijd ( t )

[7.17]

where rand j denotes a random number in the interval [ 0,1] . The acceleration aid ( t ) of the i th mass at time t in dimension d , according to the Newton’s law of motion is as follows:

aid ( t ) =

Fi d ( t )

M ii ( t )

[7.18]

where M ii represents the inertial mass of the i th agent. Inertial mass denotes the resistance of a mass to change its state of motion when a force is applied [RAS 09]. Accordingly, large inertial masses accelerate more slowly than lighter ones and vice versa. Heavy masses correspond to better solutions; this means that they should undergo very little change in their position and must attract all other solutions which depend on the other masses and distance between them. Thus, successively, they change their motions slowly.

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The ( t + 1) th velocity of i th mass in the dimension d can be calculated as shown below: vid ( t + 1) = rand i × vid ( t ) + aid ( t )

[7.19]

The original GSA ensures that each individual mass is influenced by the performance of all masses. Hence, in order to improve the performance of GSA, the greater reliance on the best previous experience is selected for the suggested TVAC-GSA. In fact, by introducing the best searched solution (i.e. M best ) which is obtained from solutions saved up to the current iteration, the updated position of the i th mass in the dimension d can be stated as follows [DER 16a]: xid ( t + 1) = xid ( t ) + vid ( t + 1) + SC ( t ) × rand i' × ( M best − xid ( t ) )

[7.20]

where SC ( t ) is the social component acceleration coefficient in time t and randi'

denotes a random number in the interval [ 0,1] .

According to the experimental results, the convergence and solution quality of the proposed TVAC-GSA are affected by the selection of the acceleration coefficient SC ( t ) . In fact, high values of SC ( t ) lead masses to be trapped into a local optimum prematurely, whereas low values result in masses wandering around the search space. A good strategy is to increase SC ( t ) during the optimization process as follows [DER 16a]: SC ( t ) = SCinitial +

SCfinal − SCinitial ×t Iteration max

[7.21]

where SCinitial and SC final represent the initial and final values of social component acceleration coefficient, respectively. The updated mass i at time t may be expressed as follows: mi ( t ) =

fit i ( t ) − worst ( t )

best ( t ) − worst ( t )

, M i (t ) =

∑

mi ( t ) m (t ) j =1 j

N

where best ( t ) = min fit j ( t ) , worst ( t ) = max fit j ( t ) j∈{1, …, N }

j∈{1, …, N }

[7.22]

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291

and where fit i ( t ) represents the fitness value of the i th mass at time t. Some remarks of the proposed algorithm can be summarized as follows to show the main features which contribute to its efficacy: – each mass can “observe and feel” the performance of the other masses; the gravitational force is an information-transferring tool [RAS 09]; – the force interacting with a mass is mainly due to its neighborhood masses; thus, each mass can see the space around itself [RAS 09]; – a heavy mass has a large effective attraction radius. Hence, it has a greater intensity of attraction than small masses. Therefore, masses (candidate solutions) with a higher performance have a greater gravitational mass. As a result, the other masses tend to move toward the best position [RAS 09]; – the inertia mass is against the motion and make the agent movement slow. Hence, masses with heavy inertia mass move slowly. Thus, the proposed algorithm can search the solution space more locally [DER 16a]; – gravitational constant adjusts the search accuracy. Therefore, it decreases with iteration [DER 16a]; – TVAC-GSA is a memory-less algorithm. However, it works efficiently like algorithms with memory. Experimental results indicated a good convergence rate of the TVAC-GSA [DER 16a]. 7.4.1. A brief comparison between the main structures of TVAC-GSA and PSO

In order to fully understand how TVAC-GSA works, it is interesting to compare the main differences between its main structure and another well-known heuristic algorithm such as Particle Swarm Optimization (PSO) [DER 16a]: – in both PSO and TVAC-GSA, the optimization is obtained by the agent’s movement in the search space; however, the movement strategy is different; – in PSO, the direction of an agent is calculated using only two best positions, i.e. pbest and gbest. But, in TVAC-GSA, the direction of an agent is calculated based on the overall force obtained by all other masses and the best position obtained so far; – in PSO, the updating procedure is performed without considering the quality of the solutions and the fitness values are not important in the updating procedure; differently, in TVAC-GSA the force is proportional to the fitness value, and thus, the masses see the search space around themselves in the area of influence of the force.

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7.5. TVAC-GSA-based MECOPF problem

The proposed TVAC-GSA-based MECOPF algorithm is illustrated in Figure 7.7 and its steps are presented below: – Step 1. Initialize the parameters of TVAC-GSA such as N , G0 , δ , Iteration max , SCinitial and SC final .

– Step 2. Set initial control variables as the initial positions of all masses to satisfy different equality and inequality constraints. In fact, each set can represent a MECOPF solution. – Step 3. Run the energy flow program to determine the dependent variables. These variables must be checked to see whether satisfy the inequality constraints. If any of them do not satisfy any of these constraints, remove the related mass and then re-initialize it. – Step 4. Calculate the value of fitness for all masses as follows: Fitness = OF + Penalty × ∑ Power Mismatch

[7.23]

where Power Mismatch denotes the power mismatches which can be calculated by using nodal power balance equations [7.1]–[7.3] and Penalty is a weighting factor (penalty parameter). Note that, in the above formula, in order to achieve a feasible solution, the weighting factors of the penalty function are increased during the iterative process. – Step 5. Update G ( t ) , best ( t ) , worst ( t ) and M i ( t ) for each set of masses.

Also, calculate the total gravitational force by using [7.17] for all agents. Then, determine their acceleration and velocity through [7.18] and [7.19], respectively. Finally, update the position of each mass by using [7.20] and [7.21]. – Step 6. Check that all variables are within their limits. If any of the variables are observed to violate, set it at its limit. – Step 7. If the age (iteration) of the algorithm is equal or less than the maximum iteration (i.e. t ≤ Iteration max ), then repeat Steps 4–6. Otherwise, go to Step 8. – Step 8. Print the best results.

Multicarrier Energy System Optimal Power Flow

Initialize the TVAC-GSA parameters (N, G0, δ , Iterationmax, SCinitial, and SCfinal)

Step 1

Set the initial independent variables withing their limits

Step 2

Run energy flow program and determine the dependent variables

Step 3

NO

Are dependent variables within their limits?

For the related mass(es)

YES Evaluate the fitness for each mass

Step 4

Update G(t), worst (t), best(t), d Mi(t), and ai (t)

Step 5

d

d

Update vi (t+1), and xi (t+1)

NO Are variables within their limits?

Set it/they at its/their limit

Step 6

YES NO

Meeting end of criterion?

Step 7

YES Print the best results

Step 8

Figure 7.7. TVAC-GSA-based MECOPF flowchart [DER 16a]

293

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From Smart Grids to Smart Cities

7.6. Case study simulations and results

The proposed algorithm to solve the MECOPF problem is programmed in a MATLAB software environment and the best results are presented here. It should be noted that, all quantities presented in this chapter ensure that all constraints are satisfied. Note that, in order to achieve the best quality solution and convergence speed, the optimum setting of various TVAC-GSA parameters should be selected. Hence, different trials for a specific system should be performed to find the best setting. Based on this, TVAC-GSA parameters are selected as follows: G0 = 0.00005 , δ = 0.0001 , N = K 0 = 30 , Iteration max = 200 , SCinitial = 0.5 and SC final = 2.5 . In order to test the performance of the proposed algorithm, a set of five benchmark functions were evaluated and the obtained results are presented in Appendix 1 (section 7.8). A hybrid power and gas test case, as shown in Figure 7.8, is proposed to evaluate the performance of the proposed algorithm. The electrical system is based on a modified version of a distribution network introduced in [DER 15] including generators G1 and G2 at buses 1 and 4, respectively, and 12 electrical distribution lines. Generators G1 and G2 are units representative of fossil fueled units characterized by a technology that is different from the CHP. In fact, generators associated to CHP are not represented explicitly in the figures but included in the box which represents the plant. The pipeline network (gas-based system) contains two gas sources at buses 1 ( N1 ) and 8 ( N 2 ) (adjacent networks); two compressors at connections 1–7 and 8–10 and eight pipelines. Also, there are six distributed energy hubs with different structures (see Figure 7.9) to supply 12 electricity and heat loads. Hubs 1–6 are installed at buses 7, 12, 5, 10, 2 and 4, respectively. In this study, loads of Hub#2 and #3 show demands of two district heating systems. Data of the hybrid power and gas grid are presented in Appendix 2 (section 7.9). The PV and PQ bus voltages are considered within intervals [0.9, 1.1] pu and [0.95, 1.05] pu, respectively. Moreover, node pressures and compression ratios should be within the intervals [0.8, 1.2], and [1.2, 1.8] pu, respectively

Multicarrier Energy System Optimal Power Flow

295

[GEI 07a, DER 16a]. It is important to note that kWe, kWth, and kWg denote kWelectrical, kW-thermal and kW-gas, respectively. Moreover, mu denotes monetary units. In order to show the effectiveness of the approach, Figures 7.8 and 7.9 illustrate two different cases obtained by solving two separate OPFs for the power and the gas grid and a single optimization procedure obtained with the MECOPF method, respectively. Figure 7.8 depicts the complete results of the two separated OPFs for both electrical and gas grids (i.e. electrical and gas networks are independently optimized) where the two networks are considered decoupled. Based on the system structure, this condition can occur without using CHP units. In this case, all electrical and heat demands should be separately supplied through the power system and gas network, respectively. It is important to note that Hub #4 at bus 10 includes a transformer and a CHP unit as shown in Figure 7.9. In Figure 7.8, a gas demand (2,857.14 kWg) equivalent to the one required by the CHP unit to generate the actual heat load (1,000 kWth) in Hub #4 has been considered to eliminate the contribution of the local production of electricity of the same CHP unit and achieve two optimal operating points for power and gas. The optimal value of the overall objective function is 333.88 mu. Total electrical and gas productions are 6,426.23 kWe and 23,025.26 kWg, respectively, to supply 6,384 kWe, 14,500 kWth and 2,857.14 kWg demands. An integrated operation and optimization for the presented grid can be achieved by using CHP units in which electrical and gas networks are simultaneously optimized. The optimal operation of the multi-carrier energy system is illustrated in Figure 7.9 and compared with the separated OPFs in Table 7.3, where the comprehensive results of MECOPF are depicted. This figure shows that CHP units in Hub #1 and #2 consume all input gases. Moreover, the gas flow in pipeline 11–5 and electrical power flow in lines 3–6, 6–7, 11–12 are reversed after integrated optimization. In this case, the total generation cost is 311.66 mu. This indicates that the system operation cost is reduced by 6.65% in comparison with the separated OPFs. Table 7.3 shows that the total electricity generation by all generators by all generators is reduced by about 61% in comparison with the separated OPFs.

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This means that the difference needed to supply electrical loads is provided by CHPs. Consequently, the gas production is increased by 22.63%. The total power losses are increased by about 24%. 3866.23 kWe 395.19 kvar

C1

1875.00 kWg V6=1.047