Integrating Wind Energy to Weak Power Grids using High Voltage Direct Current Technology [1st ed.] 978-3-030-03408-5, 978-3-030-03409-2

Table of contents :
Front Matter ....Pages i-xvii
Introduction (Nilanjan Ray Chaudhuri)....Pages 1-24
Modeling and Control of HVDC Systems (Nilanjan Ray Chaudhuri)....Pages 25-55
Modeling and Control of Inverter-Interfaced Wind Farms (Nilanjan Ray Chaudhuri)....Pages 57-76
Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC Transmission (Nilanjan Ray Chaudhuri)....Pages 77-141
Power System Restoration Using DFIG-Based Wind Farms and VSC-HVDC Transmission Systems (Nilanjan Ray Chaudhuri)....Pages 143-170
Integration of Wind Farms Using MTDC Grids: Frequency Support Perspective (Nilanjan Ray Chaudhuri)....Pages 171-230
Back Matter ....Pages 231-241

Citation preview

Nilanjan Ray Chaudhuri

Integrating Wind Energy to Weak Power Grids using High Voltage Direct Current Technology

Integrating Wind Energy to Weak Power Grids using High Voltage Direct Current Technology

Nilanjan Ray Chaudhuri

Integrating Wind Energy to Weak Power Grids using High Voltage Direct Current Technology

123

Nilanjan Ray Chaudhuri School of Electrical Engineering and Computer Science The Pennsylvania State University University Park PA, USA

ISBN 978-3-030-03408-5 ISBN 978-3-030-03409-2 (eBook) https://doi.org/10.1007/978-3-030-03409-2 Library of Congress Control Number: 2018961401 © Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Dedicated to my Parents

Preface

This book is about the integration of wind energy to weak power grids through high-voltage direct current (HVDC) technology. Wind generation is a renewable source of clean energy, which is witnessing strong growth around the world. Wind generation capacity grew by 10% in 2017, while wind generation output increased by 17%. The falling price of wind power is fueling this growth. For example, the cost of wind power for onshore installations is now comparable to or in many cases even cheaper than gas-based generation. Installation of onshore wind turbines is cheaper—although it faces challenges including wildlife death in the form of bird and bat mortality, noise, and aesthetics issues among others. Most of these issues can be solved with offshore wind turbine installations, which are more expensive. Modern wind turbine technology leverages power electronic converters for improved tracking of maximum power. This is also known as variable-speed wind generation technology. The power electronic converter-interfaced turbines can be categorized into two types—the so-called Type 3 and Type 4 turbines. The Type 3 turbines use doubly fed induction generators (DFIGs), whereas Type 4 turbines employ the full-converter technology. Both have their advantages and disadvantages. In many cases, one common aspect of onshore and offshore wind energy is that the wind energy potential is high in locations remote from the load centers. For example, the midwest region in the USA has the highest onshore wind energy potential, which is located far from most of the load centers. Similarly, offshore wind energy potential is high in deep seas, which are particularly attractive due to far less turbulence compared to the onshore scenario and avoidance of shipping lanes. Due to the remote location of the wind farms, the high-voltage direct current (HVDC) technology can be more economical than the AC technology. Parallel to the growth of wind energy market, the HVDC technology has also witnessed significant expansion around the globe including China, India, and European countries. HVDC transmissions using overhead lines are suitable only for onshore systems. For offshore case, subsea cable is the only option, resulting in a shorter break-even distance. HVDC transmission relies on two types of converter technologies—linecommutated converter (LCC) and voltage source converter (VSC). The LCC vii

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technology relies upon the AC system voltage for operation, while VSCs can operate without any support from the AC system. In addition, LCC technology demands a large footprint. These factors rule out LCC HVDC for offshore transmission. For onshore applications both LCC and VSC HVDC are extensively used, where the former has significantly higher capacity. Unlike LCC, the VSC technology has still not realized its full potential. The power rating of VSC HVDC installations are increasing. At the time of writing, the maximum power rating reached the 1GW mark in the INELFE project involving transmission between France and Spain, which is still significantly lower compared to the capacity of the latest LCC HVDC installations in China. Most of the HVDC interconnections are “point-to-point” in nature, which implies that there is one rectifier station that converts power from AC to DC and one inverter station converting it back to AC. Power generated by a wind farm can be transmitted to remote load centers by interfacing the wind farms to the rectifier station. One of the concerns of system planners is that following an (N − 1) contingency involving a single-point failure in the point-to-point link, the remote AC grid will experience loss of generation. With increasing size of wind farms, such a loss could amount to multiple of gigawatts, leading to stability issues in the AC grid. In addition to this, when multiple such wind farms are supposed to deliver power to load centers across countries and continents, the issues like wind curtailment, installed capacity to meet load demand, and exchange of energy among multiple entities through market mechanisms should also be taken into consideration. These have prompted the idea of using HVDC grids with multiple terminals—also known as multiterminal DC (MTDC) grids. A few MTDC grids based on LCC technology are operating for a while, whereas two installations based on VSC technology were commissioned in the recent past. Different visions of MTDC grids exist, e.g., the Pan-European Supergrid has been planned to integrate offshore wind resources in the North Sea and Baltic Sea along with solar energy from sub-Saharan Africa. In both pointto-point and multiterminal HVDC systems, different challenges arise due to the remote location of wind farms. For onshore wind farms in sparsely populated areas, the local AC grids are “weak” in nature due to low inertia and low short circuit capacity of the grids. On the other hand, offshore wind farms do not have any local grid support. The goal of this book is to present treatment of such scenarios, primarily in the context of frequency dynamics and frequency support. To that end, modeling of HVDC systems including LCC and VSC technologies and point-to-point and multiterminal configurations are presented. Modeling of Type 3 and Type 4 turbinebased wind farms is also included. There are classic books dedicated to LCC HVDC and VSC HVDC, and quite a few books were recently published on multiterminal HVDC. Also, there are books that are solely focused on wind farm modeling and control. The coverage of the modeling aspect in this book is by no means as detailed as in those books. Only particular modeling philosophies have been detailed, which serve the purpose of the studies undertaken in the context of weak grid scenarios. No attempt has been made to be encyclopedic in terms of different types of models reported in literature.

Preface

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For onshore wind farms integrated by LCC HVDC, the focus is on understanding and regulating frequency dynamics of weak AC grids interfacing wind farms and HVDC systems. Frequency-domain analysis is used for determining the interaction among phase-lock-loop and converter controls of the wind farm. For a progressively weak AC grid, analysis and control are performed by imposing frequency control at the LCC station. Due to the weak nature of the rectifier-end AC grid, the reactive power and AC voltage strongly affect frequency dynamics. Moreover, frequency dynamics of rectifier and inverter-side grids show coupling. Such phenomena are analyzed, and special measures for improving frequency dynamics are discussed. Other means of frequency support involving conversion of retired coal-fired plants to synchronous condensers are also evaluated through frequency-domain analysis. Power grids become extremely weak following blackouts due to the absence of voltage and frequency support and lack of inertia. Under such circumstances, system restoration needs to be performed very carefully. With the aid of synchrophasor technology, Type 3 turbine-based wind farms can be used as black-start units in such grids, while VSC HVDC links assist in restoring other parts of the grid. A treatment of system restoration in a hybrid simulation platform is demonstrated where a portion closer to the wind farm and HVDC is represented using EMT-type models, while the rest of the grid is modeled in phasor framework. The motivation and need for such a modeling approach are also established. For offshore wind farm interconnection, the focus of the book has been on frequency support features extracted from such farms and regulation of such functionalities through MTDC grids. Extraction of both inertial and primary frequency support from wind farms and other AC grids and exchange of the same among multiple AC areas can potentially lead to new ancillary service market regimes. Ideas of quantification of frequency support features and selective participation of AC areas are presented. Finally, a hybrid MTDC grid system model that integrates onshore and offshore wind farms through LCC and VSC HVDC converter stations and frequency support mechanisms therein are discussed. The intended audience of the book are graduate students with research interest in the integration of wind energy systems and HVDC technology. Researchers in academia, national labs, and industry would find this book equally useful. Power system planners, operators, and practicing engineers from utilities and ISOs/RTOs focused on system-level studies should find interest in this book. It is also expected that this book will trigger some thought-provoking discussions in the regulatory bodies focused on market and reliability coordination (e.g., FERC and NERC in the USA). Vendors of wind energy and HVDC systems should find this useful for projects relating system support functionalities. Boalsburg, PA, USA September 2018

Nilanjan Ray Chaudhuri

Acknowledgments

The material presented in this book is the culmination of research carried out in my group at Penn State. First and foremost, I would like to thank the National Science Foundation (NSF), USA, for sponsoring this research. Most of the research material was produced with support from grant award ECCS1656983. Chapters 4, 5, and 6 are developed based on research papers published from my group, which has been acknowledged in appropriate places throughout the book. Graduate students involved in producing results in Chap. 4 are Mr. Amirthagunaraj Yogarathinam, Ms. Jagdeep Kaur, and Mr. Sai Gopal Vennelaganti. Chapters 5 and 6 are developed based on Mr. Pooyan Moradi Farsani’s work and Mr. Sai Gopal Vennelaganti’s research, respectively. Last but not least, from the very inception, this book could not have been possible without my wife Emily’s continuous encouragement and support.

xi

Contents

1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Wind Energy Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 High Voltage Direct Current (HVDC) Technologies. . . . . . . . . . . . . . . . . 1.3.1 AC vs DC Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.2 Line-Commutated Converter (LCC) Technology . . . . . . . . . . 1.3.3 Latest Developments in LCC Technology . . . . . . . . . . . . . . . . . . 1.3.4 Voltage Source Converter (VSC) Technology . . . . . . . . . . . . . . 1.4 Multiterminal DC (MTDC) Electric Power Grids . . . . . . . . . . . . . . . . . . . 1.5 Existing MTDC Systems in the World . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6 Focus and Scope of the Monograph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 3 6 6 8 11 12 17 19 22 23

2

Modeling and Control of HVDC Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Configurations of DC Transmission. . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Line-Commutated Converter (LCC)-Based HVDC . . . . . . . . . . . . . . . . . . 2.2.1 Modeling Philosophies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 State-Space Averaged Phasor Model. . . . . . . . . . . . . . . . . . . . . . . . 2.3 Voltage Source Converter (VSC)-Based HVDC . . . . . . . . . . . . . . . . . . . . . 2.3.1 Overall Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Modeling of Two-Level VSC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 VSC Controls: Grid-Connected Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Control of Real and Reactive Power . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Control of DC-Side Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.3 Control of AC-Side Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 VSC Controls: Islanded Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 MTDC Grid Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.1 Model of Asymmetric Bipolar MTDC Grid . . . . . . . . . . . . . . . . 2.6.2 Unified Model of MTDC Grid Connected to AC Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25 25 26 27 27 28 33 33 33 36 37 42 44 45 46 46 48 xiii

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2.6.3 Simulation of Contingencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.4 Control Strategies of MTDC Converters. . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50 51 53

3

Modeling and Control of Inverter-Interfaced Wind Farms . . . . . . . . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 DFIG-Based Wind Energy System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Wind Turbine Model and Characteristics . . . . . . . . . . . . . . . . . . . 3.2.2 Doubly Fed Induction Generator Model . . . . . . . . . . . . . . . . . . . . 3.2.3 GSC and DC Bus Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.4 Turbine Pitch Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Control Strategy of DFIGs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Grid-Connected Mode of Control . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Isolated Mode of Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Full-Converter-Based Wind Energy System. . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 PMSG-Based Direct-Drive WTG Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.1 Generator-Side Converter Control . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.2 Grid-Side Converter Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57 57 57 59 61 64 64 65 65 70 72 73 73 74 76

4

Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Case Study I: Impact of Inertia and Effective Short Circuit Ratio on Frequency Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 State-Space Averaged Phasor Model of the System . . . . . . . . 4.2.2 Validation Using Detailed Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Dynamic Model Representing Weak AC System . . . . . . . . . . . . . . . . . . . . 4.4 LCC-HVDC Frequency Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Analysis of Frequency Dynamics in a Progressively Weak System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.1 Results and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.2 Improving Control of Frequency in Very Weak System . . . 4.6 Performance Across Operating Points: Inclusion of Pitch Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Case Study II: Coupled Frequency Dynamics of Rectifier and Inverter-Side AC Grids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8 Full-Order Model of the System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8.1 Four-State Nonlinear Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.9 Application I: Revealing Voltage-Frequency Coupling Phenomenon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.9.1 Experiment-I: Without Eacr and Eaci Variations in Four-State Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.9.2 Experiment-II: With Eacr and Eaci Variations in Four-State Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.9.3 Analysis of Voltage-Frequency Coupling . . . . . . . . . . . . . . . . . . .

77 77 79 80 83 83 84 86 89 91 95 97 99 99 103 105 105 106

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4.10

107 108

Application II: Firing Angle Correction Strategy . . . . . . . . . . . . . . . . . . . . 4.10.1 Results and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.11 Application III: Analytical Insight and Energy Bound on Frequency Deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.11.1 Analytical Insight I: Decoupling of Rectifier-Side Frequency Dynamics from Inverter-Side Disturbance . . . . . 4.11.2 Analytical Insight II: Per-Unit Energy Bound on Frequency Deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.11.3 Analytical Insight III: Droop Control of Wind Farm . . . . . . . 4.11.4 Analytical Insight IV: Synchronizing and Damping Torque. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.12 Results and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.13 Case Study III: Displaced Conventional Generation Converted to Synchronous Condensers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.14 Effect of Synchronous Condenser on System Performance . . . . . . . . . 4.14.1 Load Flow Analysis Considering Synchronous Condenser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.14.2 Results and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.15 Test System with Detailed Model of Weak AC Grid. . . . . . . . . . . . . . . . . 4.16 Challenges and Proposed Solutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.17 Results and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.17.1 Frequency-Domain Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.17.2 Time-Domain Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Power System Restoration Using DFIG-Based Wind Farms and VSC-HVDC Transmission Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Black-Start Process Using DFIG-Based Wind Farms. . . . . . . . . . . . . . . . 5.2.1 Step I: DC Bus Pre-charging Controls . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Step II: Self-Supporting DC Bus, Line Charging, and Load Pickup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.3 Step III: PMU-Enabled Autonomous Synchronization . . . . 5.2.4 Step IV: Hot-Swapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 VSC-HVDC Controls for Black-Start . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Hybrid Simulation Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Need for Hybrid Co-simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Hybrid Simulation Architecture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7 Case Study I. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7.1 Non-hybrid Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7.2 Hybrid Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.8 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.8.1 System Restoration: Non-hybrid vs Hybrid Simulation. . . . 5.8.2 Additional Load Pickup: Hybrid Simulation . . . . . . . . . . . . . . .

110 111 112 114 117 117 119 122 122 124 126 126 128 128 131 139 143 143 145 145 146 149 150 151 152 153 153 155 155 155 157 157 159

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5.9

Case Study II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 5.9.1 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 6

Integration of Wind Farms Using MTDC Grids: Frequency Support Perspective. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Methods of Frequency Support in AC-MTDC Systems . . . . . . . . . . . . . 6.2.1 Ratio-Based Selective Frequency Support . . . . . . . . . . . . . . . . . . 6.3 Chapter Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Topic I: Frequency Support in Asynchronous AC-MTDC System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Study System: Full-Order Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6 N th-Order Model of the System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7 AC-Side Disturbance: Primary Frequency Support . . . . . . . . . . . . . . . . . . 6.7.1 Selective Power Routing Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7.2 Characteristic Features of Selective Power Routing. . . . . . . . 6.7.3 Monopolar Representation of N th-Order Model . . . . . . . . . . . 6.7.4 Static Design of Frequency-Droop Coefficients . . . . . . . . . . . . 6.7.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.8 AC-Side Disturbance: Inertial and Primary Frequency Support. . . . . 6.8.1 MPC Without Frequency Droop . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.8.2 MPC with Frequency Droop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.9 Inertial-Droop Control: Modified N th-Order Model . . . . . . . . . . . . . . . . 6.10 Ratio-Based Inertial and Primary Frequency Support . . . . . . . . . . . . . . . 6.10.1 Monopolar Representation of Modified N th-Order Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.10.2 Design of Inertial and Frequency-Droop Coefficients . . . . . 6.10.3 Simulation Results of Modified N th-Order and Full-Order Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.11 DC-Side Disturbance: Converter Outage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.11.1 Converter Outage Problem and Its Constraints . . . . . . . . . . . . . 6.11.2 Proposed Solution to Converter Outage Problem . . . . . . . . . . 6.11.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.12 Topic II: Frequency Support in Asynchronous AC-MTDC System with Offshore Wind Farm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.13 Study System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.14 Inertial and Primary Frequency Support with OWFs . . . . . . . . . . . . . . . . 6.14.1 Wind Farm Controller for Emulating the N th-Order Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.14.2 Simulation Results of Full-Order Model with OWF . . . . . . . 6.15 Topic III: Frequency Support in Asynchronous AC-H-MTDC System with Offshore and Onshore Wind Farm . . . . . . . . . . . . . . . . . . . . . 6.16 Modeling Bipolar H-MTDC Grid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.17 Control Strategies in H-MTDC Grids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

171 171 172 174 175 176 177 178 181 182 183 184 184 186 190 190 194 195 197 198 198 202 205 207 207 209 211 211 212 213 215 215 217 219

Contents

xvii

6.18 Frequency Support in H-MTDC Grids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 6.19 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 A Space Phasor and dq Reference Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.2 Space Phasor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.2.1 dq-Frame Representation of a Space Phasor . . . . . . . . . . . . . . .

231 231 231 232

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235

Chapter 1

Introduction

Abstract This chapter gives a brief background of the context and scope of this monograph. To that end, the relevance of performing research on integration of wind energy in a weak grid scenario using high voltage direct current (HVDC) technology is presented. Different wind energy conversion technologies are introduced followed by line-commutated converter (LCC) and voltage source converter (VSC) technologies. Next, the concept of multiterminal direct current (MTDC) grids is presented. Finally, the focus and scope of the monograph is elaborated. The first focus is on the challenge of regulating frequency in a weak grid interfacing LCC-HVDC and wind farms. The second problem is restoration of weak grids using wind farms and VSCHVDC. The final problem deals with integration of wind farms through MTDC grids and provision of frequency support to weak asynchronous AC grids.

1.1 Background Modern power grids around the globe are witnessing an unprecedented proliferation of wind energy. Interestingly, most of the onshore wind energy potential is located in areas that are hardly inhabited, e.g., in the Mid-West region in the USA. Similarly, a huge offshore wind potential is available and is increasingly being harnessed by European countries. Due to the absence of a strong power grid in such areas, both onshore and offshore, wind farm integration faces challenges. Moreover, due to long distance from load centers, High Voltage Direct Current (HVDC) technology is more economical than AC transmission to deliver power from wind farms. As an example, the 2008 Department of Energy (DoE) report [22] studied a 20% wind power penetration in the Eastern Interconnection. In this study, a majority of wind farms were concentrated in Midwest due to high wind energy potential, see Fig. 1.1. Since these AC systems are far away from the load centers, they are “weak” in nature. To deliver such a large amount of wind power to the grid over such a long distance, HVDC technology is more economical than AC transmission systems [2]. In the Joint Coordinated System Plan (JCSP) report [17], line-commutated converter (LCC)-based HVDC systems were proposed to connect these wind farms in the weak AC grids in the Midwest region. The LCC technology was preferred over © Springer Nature Switzerland AG 2019 N. R. Chaudhuri, Integrating Wind Energy to Weak Power Grids using High Voltage Direct Current Technology, https://doi.org/10.1007/978-3-030-03409-2_1

1

2

1 Introduction

Fig. 1.1 The US onshore and offshore wind energy potential at 50-m hub height (credit: NREL)

the voltage source converter (VSC) technology since the latter suffers from lower efficiency and cannot meet the power capacity requirement (a few GWs) of such large onshore wind farms. On the contrary, VSC technology is the preferred choice for offshore wind farms (OWFs) due to advantages that are well documented in HVDC text books [3], e.g., much lower footprint, cheaper cables, bidirectional power flow without voltage polarity reversal, etc. The offshore wind potential of the USA is shown in Fig. 1.1. Presently, three offshore wind projects are planned in the Atlantic Wind Connection project, namely New Jersey Energy Link, Delmarva Energy Link, and Bay Link, respectively [4]; all of which are going to be based on VSC technology. In this book, we will focus on different challenges facing integration of both onshore and offshore wind generation to “weak” grids using HVDC technology. We will analyze application of LCC-HVDC in integrating onshore wind farms. System restoration (black start) using wind farms and VSC-HVDC will be analyzed. We will also focus on the application of multiterminal DC (MTDC) technology to integrate the onshore and the offshore wind farms. Wind energy integration in weak grids using HVDC technology is a relatively new area of research. Of late, a lot of attention is being focused on the integrating offshore wind using VSC-HVDC. Much less attention has been paid towards onshore wind farms connected through LCC-HVDC in weak grids. The idea of

1.2 Wind Energy Technologies

3

system restoration (Black-start) using wind generators assisted by HVDC technology and the treatment of both onshore and offshore wind integration in a unified framework using MTDC technology are relatively new at the time of writing.

1.2 Wind Energy Technologies Wind energy conversion system can be divided into the following major components: turbine and mechanical interface, generator, power electronic converter (if present), and control systems. Figure 1.2 shows different components of a wind turbine. A modern wind turbine typically has a three-blade rotor spinning about the rotor hub, which is coupled to the generator’s rotor shaft. The shaft can be mechanically connected through a gearbox or direct coupling. The rotor hub is connected to an enclosure called the “nacelle.” The nacelle houses the gearbox (if present), generator, power electronic converters (if present), and control systems. The turbine rotor and the nacelle are mounted on the turbine tower. Wind sensors are mounted on the nacelle, which help reorient the rotor hub and the nacelle in the direction of wind using the “yaw” control. The blades are also rotated around their long axes to regulate the angle of attack from wind by the “pitch angle” control. This ensures that the power output and the speed do not go above dangerously high levels. Typically, a turbine starts producing power above 12-mph wind speed, known as “cut-in” speed, and produces its rated output at around 28–30 mph. The pitch angle controller feathers the blade to stop power production when the wind speed is around 50 mph, also known as the “cut-out” speed. Different types of wind turbine–generator systems are in use, which can be broadly classified as either fixed-speed (Type 1 and 2) or variable-speed systems (Type 3 and 4). Figure 1.3a shows simplified schematic of a Type 1 wind power

Hub

Nacelle

Tower

Wind Sensor Generator Gearbox Yaw Control

Brake Pitch Control

Fig. 1.2 Components of a wind turbine

Blade

4

1 Introduction

Gear Asynchronous machine Ps box

PCC

VW

grid Ptur

Pt Qt

Wind turbine (a)

Gear Asynchronous Ps machine box

PCC

VW

grid Ptur Wind turbine

Pt Qt

Variable Resistance (b)

Gear Asynchronous machine Ps box

PCC

VW

grid Ptur

AC AC = DC DC

Wind turbine

Pr

RSC

Pt Qt

GSC

(c) Gear box

Ps

VW

PCC

AC AC = DC DC Ptur Wind turbine

Asynchronous/ Synchronous machine

grid Pt Qt

(d)

Fig. 1.3 (a) Schematic of constant-speed wind power system. Schematic of variable-speed wind power system based on: (b) asynchronous generator and converter, (c) doubly fed induction generator and converter, (d) gearless synchronous generator and converter

1.2 Wind Energy Technologies

5

system. It is composed of a wind turbine coupled with an asynchronous generator via a gearbox. In this case, the asynchronous generator is a squirrel cage induction machine that produces power when operated above the synchronous speed. The gearbox is used to interface the slowly rotating turbine shaft and the generator with higher rotor speed. In this type of wind power system, the machine is directly connected to grid without any power electronic interface. Since the asynchronous machine consumes reactive power, it is equipped with shunt capacitors, which can be seen in Fig. 1.3a. For a constant wind speed under steady state, the turbine speed is almost linearly related to the torque. With a sudden change of wind speed, the inertia of the rotating mass including the turbine, drive train, and generator rotor results in a slow change in rotor speed and power output. Figure 1.3b shows the schematic of a Type 2 wind turbine. It is very similar to the Type 1 system as it also uses an asynchronous machine directly connected to the grid and requires shunt capacitors for supplying reactive power. In this case however, the asynchronous machine is a wound-rotor induction generator with rotor current controlled by variable resistors. The variable resistors can be introduced by using power electronic switches. These switches and their controller module can be separately connected to the rotor winding using slip rings or they can be mounted on the rotor, eliminating the slip ring. These variable resistors can control the rotor currents very fast and help maintain a constant power output in the presence of wind gusts. They can also improve the dynamic response of the machine during system disturbances. Similar to Type 1 turbines, the asynchronous machines provide power output when operated above the synchronous speed. The two dominant types of variable-speed wind energy systems are shown in Fig. 1.3c, d. Figure 1.3c shows a Type 3 wind generator, which is based on the doubly fed induction generator (DFIG) topology. In this case, the asynchronous machine is a wound-rotor induction generator. A power electronic converter system consisting of two AC–DC and DC–AC VSCs in back-to-back configuration is used, which allows bidirectional power exchange between the generator rotor and the grid. The VSC connected to the rotor is called the rotor-side converter (RSC), and the VSC connected to the stator terminals is called the grid-side converter (GSC). Each of RSC and GSC typically has a rating of 25%–30% of the rating of the generator. As it can be seen from Fig. 1.3c, the stator of DFIG is directly connected to the grid and hence the stator frequency is determined by the grid frequency. When the wind speed changes, the RSC can regulate the speed of the rotor to extract maximum power from the turbine, see the turbine characteristics in Fig. 1.4, which leads to a variable rotor frequency. This operation is known as maximum power point tracking (MPPT). Both RSC and GSC can provide the reactive power demanded by the asynchronous machine. Type 3 wind turbines can generate power at subsynchronous and supersynchronous speeds of the generator. Since the rotor speed is controlled over a wide range to ensure MPPT, Type 3 wind turbines are called “variable-speed.” A Type 4 wind energy system is illustrated in Fig. 1.3d, which is based on a full converter (FC) topology. Here, the stator is connected to the grid via two backto-back AC–DC and DC–AC VSCs. Each of these have the same rating as the generator. The generator can be an asynchronous generator (squirrel-cage induction

6

1 Introduction

P

WF

MPPT power curve

V

W3

V

V

W1

W2

V

V

W1

W2

V

W3

r_dfg

Fig. 1.4 Torque-speed characteristics of a wind turbine across different wind speeds. The loci of maximum power output of the wind turbine are highlighted

machine) or a synchronous generator (with rotor exciter or with permanent magnet rotor). The turbine–generator mechanical interface may or may not include a gear box. The latter option is known as the “direct drive” option, which becomes realistic when a synchronous machine with high number of poles is used because such a generator can operate with a low speed. The converter system adjusts the frequency of stator circuit excitation to allow a variable rotor speed demanded by the MPPT operation. Most modern wind farms are based on Type 3 and Type 4 wind turbines [15]. These two types of wind power systems will be described in more detail later in Chap. 3.

1.3 High Voltage Direct Current (HVDC) Technologies 1.3.1 AC vs DC Transmission The main motivation for developing overhead HVDC transmission lines is their cost-effectiveness in transmitting bulk power over long distances. For cable-based (underground or offshore) power transmission however, it is the only option beyond a certain distance. Figure 1.5 shows in very crude terms the variation in cost vs transmission distance for AC transmission compared with HVDC transmission. The HVDC technology needs a rectifier station converting AC to DC at one end of the transmission line. At the other end, another station converts DC back to AC. In simple terms, the cost associated with the converter stations is shown for a zero transmission distance in Fig. 1.5. As it is shown in Fig. 1.5, for over a certain distance, called the “break-even distance,” HVDC transmission costs lesser than

1.3 High Voltage Direct Current (HVDC) Technologies

7

AC line

cost

DC line

Break-even distance

Transmission distance Fig. 1.5 AC and DC transmission cost by length

its AC counterpart. The break-even distance is about 700–900 km for overhead HVDC lines. There are multiple reasons behind lower cost of DC transmission. These include: • AC transmission system requires at least three conductors, each for one phase. For DC transmission, two conductors (e.g., positive and negative) can transmit the same power. • The tower structure is less costly for DC transmission, since it does not need to hold three conductors as in the AC system. Also, the right-of-way requirement of the DC transmission is less since the tower span is shorter. • For a given AC system with rated AC voltage Vac and a DC system with rated DC voltage Vdc , the ratio of insulation length per phase of the AC system to the insulation length per pole of the DC√system is given by (k.k1 /k2 )(Vac /Vdc ). Here, typical values of k, k1 , and k2 are 2, 2.5, and 1.7, respectively [3]. Clearly, the length of insulation is higher for the AC system when the rated voltages are the same. • The losses in DC transmission are lower compared to their AC counterpart [3]. • For very long lines, dynamic stability limit and the need for reactive power compensation becomes restrictive for AC transmission. Figure 1.6 shows two HVDC lines crossing over near Wing, North Dakota, USA. There is only one example of such a crossover in North America [1]. The left tower carries the Square Butte line, which is a ±250-kV bipole with a single conductor per pole. The right tower carries the HVDC line transmitting power from Coal Creek Station power plant south of Underwood, North Dakota—also known as the CU line. The CU line is a ±400-kV bipole with two conductors per pole. In comparison, two 345-kV AC line are shown in Fig. 1.7.

8

1 Introduction

Fig. 1.6 Two HVDC transmission lines crossing over near Wing, North Dakota, USA. Photo credit: Wtshymanski [1] under license (https://creativecommons.org/licenses/by-sa/3.0/)

For underground or subsea cable transmission, the break-even distance is not determined by the cost advantage. Typically beyond 50 Km [8], the charging current in AC cables become so high that the DC transmission is the only option in such cases.

1.3.2 Line-Commutated Converter (LCC) Technology Line-commutated converter (LCC) technology relies on the AC system voltage for both turn on and turn off of the switching devices. Historically, two types of devices have been used in LCC-HVDC transmission systems. Mercury arc valves were used in the first LCC-HVDC system connecting Gotland to mainland Sweden in 1954. They were in use until 1970, when thyristors started to be used in LCC-HVDC [18]. LCC is a mature technology widely used in HVDC systems around the world. The Graetz bridge is the basic building block in LCC-HVDC. It is a three-phase 6-pulse full-wave bridge consisting six thyristor valves arranged in the configuration shown in Fig. 1.8. In this application, each thyristor valve is comprised of a suitable number of series-connected thyristors to achieve desired DC voltage rating. The control of LCC stations is achieved by regulating the firing angle of the thyristors. Thyristors are turned on by gate pulses when they are forward biased. However, they can only be turned off when the commutating AC voltage becomes negative. LCCs

1.3 High Voltage Direct Current (HVDC) Technologies

9

Fig. 1.7 Two 345-kV AC transmission lines

require a relatively strong synchronous voltage source in order to commutate (i.e., to transfer the current from one phase to another) in a synchronized firing sequence of the thyristor valves. LCCs can only operate with the AC current lagging the voltage, which demands reactive power. The typical reactive power consumption under full load is 50–60% of the real power consumption. The consumption of reactive power changes with the loading condition. Large capacitor banks are installed to meet the reactive power need of the converters. Since the reactive power demand changes with loading condition, breakers are connected to these banks to switch them on and off as needed—please see Fig. 1.8. The flow of DC current in this type of converter is unidirectional and hence, power reversal from one station to the other is done by reversing the polarity of DC voltage in both stations. Tap-changing transformers are usually used to connect the converters’ AC side to the grid (Fig. 1.8). These transformers are used to bring the firing angles of the converter stations within the nominal operating range. Usually, three single-phase banks are used for the converter transformers to improve reliability. Large reactors are connected to the DC side of these converters to smoothen the DC voltage and current ripples. In addition, shunt filters are

10

1 Introduction

Ldc

Tap-changing transformer

vdc

Vgabc

C1 R1

C3

C4

L1

R2 L2 C2

C5 C6

Capacitor Banks

Filters

Fig. 1.8 Graetz bridge: a three-phase 6-pulse full-wave bridge converter. Tap-changing transformer, switched capacitor banks, and filters are connected in the AC side. Inductors are connected in the DC side

Ldc Y-Y

6-pulse bridge vdc

Vgabc

6-pulse bridge

Delta-Y

Filters & Capacitor Banks

Fig. 1.9 A three-phase 12-pulse bridge converter formed by connecting two Graetz bridges in series on the DC side and in parallel on the AC side. One tap-changing transformer has a Y –Y configuration, while the other has a Delta–Y configuration

needed to reduce the harmonics in the AC side. The footprint of LCC-HVDC converter stations is generally large due to the need for filters, capacitor banks, and transformers. Harmonic currents and voltages in the AC and the DC sides create overheating of capacitors and nearby generators in addition to interference with telecommunication lines. For a p-pulse bridge, the AC-side current harmonics are of the order (np ± 1) and the DC-side voltage harmonics are of the order np, where n = 1, 2, . . .. The magnitude of the kth-order harmonic is 1/k of the fundamental component. To remove the lower-order harmonics, it is a common practice to connect two Graetz bridges in series in the DC side and in parallel in the AC side as shown in Fig. 1.9.

1.3 High Voltage Direct Current (HVDC) Technologies

11

The AC side of one bridge is interfaced using a Y –Delta transformer and the other using a Y –Y transformer. This results in the cancellation of the 5th and the 7th harmonic currents and the configuration is called a 12-pulse bridge. Filter design is one of the most challenging aspects of an HVDC project. Typically, for a 12-pulse bridge, two filters are tuned to produce low-impedance path for the 11th and the 13th harmonic current. Another high-pass filter can be used for the rest of the higher-order harmonics. On the DC side, usually DC filters involving large inductors are used to reduce the DC voltage harmonics. This, however, can be quite challenging since grids connected to the HVDC can pose a wide range of Thevenin’s impedances based on different loading scenarios. The impedance angle can vary from inductive to capacitive region. The filters need to be designed to ensure an acceptable total harmonic distortion (THD) and meet the telephonic interference standards usually determined by the telephone influence factor (TIF) [5] across all operating conditions. There are instances where these requirements could not be met by standard filter design. For example, in the Tianshengqiao–Guangzhou project Siemens used an active DC filter to meet the TIF requirement [6]. When there is a fault in the overhead DC transmission line, the inverter keeps operating with ignition advance angle β limited to 80◦ , which results in a small inverter voltage. The rectifier is switched to an inversion mode by increasing the firing angle α to a value as high as 140◦ . This helps in taking away the fault energy and the DC fault current extinguishes typically within 10 ms. One of the design criteria for determining the size of the DC-side inductors is the allowable rate-ofrise of DC fault current.

1.3.3 Latest Developments in LCC Technology As the global trend of integration of renewable energy continues, the demand of very long distance power transmission becomes a necessity. For example, in China the need for such very long distance transmission is driven by the demand to serve loads in their mega cities in the east coast from hydro power plants in the west and coal-fired plants in the northwest. When thousands of megawatts of power is transmitted over substantially long distances, ultra high voltage DC (UHVDC) transmission has often become the preferred option. The UHVDC systems have DC voltage ratings of ±800 kV or above. World’s first UHVDC transmission system was the Yunnan–Guangdong ±800-kV HVDC link in China, which transmits 5 GW power over 1373 km since June 2010. The rectifier station is located in Puer in the Yunnan Province and the inverter station is situated in Jiangmen in the Guangdong Province. Due to such high voltage in the DC side, two 12-pulse groups are used per pole. Thyristor valves in the latest installations have the current-carrying capacity of 6.25 kA and blocking capacity of 7.2 kV (https://www.abb-conversations.com/2015/ 11/thyristors-the-heart-of-hvdc/). Under normal condition, a single component has the capability to switch more than 20-MW power. The latest device fabrication

12

1 Introduction

Table 1.1 UHVDC projects in China Sl. no. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

Project Yunnan–Guangdong Xiangjiaba–Shanghai Jinping–Southern Jiangsu Nuozhadu–Guangdong Hami–Zhengzhou Xiluodu–Zhejiang West Lingzhou–Shaoxing Shanxi North–Jiangsu Jiuquan–Hunan Xilingol League–Jiangsu Shanghaimiao–Shandong Zhundong–Wannan

Rating ±800 kV, 5 GW ±800 kV, 6.4 GW ±800 kV, 7.2 GW ±800 kV, 5 GW ±800 kV, 8 GW ±800 kV, 8 GW ±800 kV, 8 GW ±800 kV, 8 GW ±800 kV, 8 GW ±800 kV, 10 GW ±800 kV, 10 GW ±1100 kV, 12 GW

Distance (km) 1373 1907 2059 1413 2192 1653 1720 1119 2383 1620 1238 3400

technology has enabled power saving in the range of 1 kW per device under rated condition. Structured blocking junctions that are substantially deeper than the active part towards the edges and finer cathode patterns with elaborate distribution around amplifying gate electrode have increased the efficiency of modern UHVDC installations to as high as 99.6% (https://www.abb-conversations.com/2015/11/ thyristors-the-heart-of-hvdc/). Table 1.1 shows the UHVDC projects in China.

1.3.4 Voltage Source Converter (VSC) Technology Unlike LCC, voltage source converter (VSC) is still a developing technology. This type of converters typically uses self-commutating devices, which can be turned off independent of the AC system voltage. The most widely used self-commutating device in VSC-HVDC is the insulated-gate bipolar-junction transistor (IGBT), which is shown in Fig. 1.10a. IGBTs operate as transistors with high voltage and current ratings and moderate forward voltage drop. It enjoys fast turn-on and turnon capabilities with low switching loss, which makes it suitable for high-power converters that use pulse-width modulation (PWM) for switching. The IGBTs are connected to anti-parallel diodes to ensure bidirectional current conduction, see Fig. 1.10b. VSCs are built with three general topologies, which are called two-level, three-level, and multi-level depending upon how many levels of DC-side voltage they possess. Half-bridge two-level VSC consists of two semiconductor switches connected to each other as shown in Fig. 1.11. The semiconductor switches should be turned on and off in a controlled manner to generate an AC voltage in the presence of DC voltage on the other end of VSC. The capacitors act as filters to reduce the distortion in the DC-side voltage. This type of VSCs can also be built with

1.3 High Voltage Direct Current (HVDC) Technologies

13

Fig. 1.10 (a) Insulated gate bipolar junction transistor (IGBT). (b) IGBT with anti-parallel diode

p

Vdc 2 DC system

AC system

Vdc 2

n Fig. 1.11 Schematic of a half-bridge, single-phase, two-level VSC

four switches as full-bridge converters. The VSC shown in Fig. 1.11 is a singlephase VSC. Three-phase VSC can also be built, which consists of three half-bridge converters for the three phases (see Fig. 1.12). The AC side requires series inductors which can be contributed by AC chokes and transformers. The AC filters are used to attenuate high-frequency harmonics. Both the magnitude and phase angle of the AC voltage vgabc (Fig. 1.12) can be controlled by VSCs irrespective of the direction of AC current. This enables independent control of active and reactive power exchange with the AC system.

14

1 Introduction

Rdc

Ldc

idc

Vgabc

R

L

Vtabc

Cdc

vdc

C

Fig. 1.12 A three-phase 2-level 6-pulse bridge configuration of a VSC with IGBTs coupled with anti-parallel diodes

idc

vdc

Fig. 1.13 Schematic diagram of a full-bridge

We can have less harmonics in terminal voltage by using more than two levels. For example, a full-bridge, shown in Fig. 1.13, can be used to synthesize three-level VSCs. The full-bridges can be connected in parallel from their DC ports, while their AC outputs are combined by three corresponding single-phase transformers whose grid-side windings are connected as a wye configuration [8, 23]. Increasing the number of levels beyond three can reduce the harmonic distortions even further. One configuration of multi-level VSC, which has come to use in recent years is known as the modular multi-level converter (MMC) [8, 21]. In this configuration,

1.3 High Voltage Direct Current (HVDC) Technologies

SM 2

v s1 vs 2

SM N

vsN

SM1

vdc 2

0

i1 j

idiffj v j

vdc 2

SM N

SM N

1

2

SM 2 N

v1 j

P, Q

L Lt

R

L i2 j

15

Rt

ij

PCC

R

vs N vs N

vgi

1

2

v2 j

vs 2 N

Fig. 1.14 Schematic showing one leg of a three-phase MMC. SM indicates a submodule

multiple half-bridge converters, also called submodules (SMs), are connected in series from their AC-side terminals to generate a multi-level AC voltage waveform. The configuration of one phase of a three-phase MMC is shown in Fig. 1.14. This structure consists of two so-called arms in each phase. In each of the arms, there are N series-connected SMs, which are each connected to a capacitor in the DC dc side. If each of the DC bus is charged to the voltage v2N , then the AC voltage vdc dc output of each SM can be either “0” or 2N for the upper arm and “0” or − v2N for the lower arm. Thus, appropriate switching and bypassing sequence of these SMs in the upper arm can produce voltage variation between “0” and v2dc in the AC terminal. In fact, as consecutive submodules in the series connection are turned on, the voltage increases in a staircase manner, whereas consecutive bypassing of SMs leads to voltage reduction in the same fashion. This can effectively generate a smooth positive half-cycle of the AC voltage. Similarly, the negative half-cycle can be produced by the lower arm. The harmonic content can be significantly reduced by increasing the number of SMs. The details of operation of three-level and multilevel VSCs can be found in [21, 23].

16

1 Introduction

Following are some of the key features of VSC-HVDC systems: • Reactive power consumption: Since VSCs can independently regulate active and reactive powers, it is possible to maintain unity power factor at both rectifier and inverter terminals in the absence of external VAr compensation. In addition, AC voltage regulation can also be performed by the VSC terminals. • Harmonics: The harmonic content of the VSC depends on its topology and switching strategy. For example, a 2-level VSC controlled by sinusoidal PWM with frequency multiplier mf (ratio of switching frequency fs to fundamental frequency f ) will have harmonics of the order of h1 mf ± h2 , where h1 and h2 are integers [10]. For all practical purposes, h2 can go up to 2, beyond which the harmonics are significantly attenuated. For an MMC with N half-bridge modules per arm, the order of harmonics is given by hN ± 1 [10]. Moreover, due to phase symmetry, the even harmonics are absent. In case of a 3-phase system, Fig. 1.12, the triplen harmonics are also absent. • Efficiency: Losses in VSC systems include conduction and switching loss—the latter is significantly reduced in MMC topology. With advancement in technology, efficiency of VSC-HVDC is approaching ≈ 99.0%, which however is still lower than LCC-HVDC (efficiency ≈ 99.6%) (https://www.abb-conversations. com/2015/11/thyristors-the-heart-of-hvdc/). • Power flow reversal: Unlike LCC, the current in the DC side of the converter station can be reversed without any change in the circuit arrangement. Therefore, power flow reversal in VSC-HVDC can be achieved by DC current reversal, while maintaining the same polarity of DC voltages. • Cables: Since the voltage polarity of the DC cables always remains the same in VSC-HVDC, polymeric (e.g., cross-linked polyethylene, and XLPE) cables which are stronger and lighter and particularly suited for harsh subsea environment are used. • Faults: AC-side faults are cleared by opening AC circuit breakers similar to LCCHVDC. Fault in the DC side creates a major challenge for VSC-HVDC. Unlike LCC technology where DC current can be regulated during DC fault [12], VSC technology using half-bridge modules is defenseless under such faults where the AC grids feed the fault uncontrollably. Different protection strategies include: (a) opening AC circuit breakers from both sides to isolate the DC system, (b) use of fault-blocking converter topologies like MMC with full-bridge modules, and (c) use of DC circuit breakers. However, high-power DC circuit breaker technology is still not commercially available. VSC-HVDC systems require significantly less filtering and hence, the footprint of this type of stations is much less than LCC. The LCC technology relies on AC system voltage for turning off the thyristors. This means that they face serious challenges when connected to a weak grid. There is no such restriction for a VSCHVDC link, which can work even with weak or isolated AC systems and offer black-start capability. Some of the differences between VSC-HVDC and LCCHVDC links are shown in Table 1.2.

1.4 Multiterminal DC (MTDC) Electric Power Grids

17

Table 1.2 A comparison between VSC and LCC technologies LCC Depends on external AC grid for commutation Always consumes Q irrespective of P Needs significant filtering and VAr support Requires stronger AC systems for operation Requires additional equipment for black-start operation Reversal of power is done by reversing DC voltage polarity Can control DC fault current

VSC Relies on self-commutation Can independently regulate P and Q Limited filtering and VAr requirement Operates better than LCC in weak AC systems Has black-start capability Reversal of power is done by reversing DC current Most topologies are defenseless against DC fault

1.4 Multiterminal DC (MTDC) Electric Power Grids Traditionally, DC transmission systems are called “point-to-point” HVDC links since they have two converter terminals. Figure 1.15a shows an example system where an onshore and an offshore wind farm are connected to two asynchronous AC grids via point-to-point HVDC links. Unfortunately, such point-to-point schemes suffer from certain issues, which can be overcome by an HVDC grid with multiple terminals—also known as multiterminal DC (MTDC) grid. Figure 1.15b shows such an MTDC grid. This grid is “Hybrid” in nature since it uses both LCC and VSC technologies. The onshore wind farm is connected to a weak grid and transmits power to a remote AC grid through an LCC-HVDC link. The offshore wind farm is connected to a VSC-HVDC station, which carries power to a remote onshore AC grid. In a recently published paper by Prof. Jim McCalley [13], it was established that in the context of the USA, an optimized national transmission overlay consisting hybrid AC/DC networks, with ±800 kV LCC-HVDC being the preferred technology in most regions, lowers the overall cost of energy. An independent NOAA study [16] concluded “. . . the US could decrease its carbon emissions by up to 80% by the early 2030s, without an increase in electric costs. The key requirement would be a 48–state network of HVDC transmission, creating a national market for electricity not possible in the current AC grid.” Such an argument leads to support the idea that MTDC grids can help lower energy cost in a national and/or continental scale. Other advantages of MTDC scheme over the point-to-point scheme include: (a) improved reliability, (b) reduction in generation capacity and spinning reserve, (c) reduction in renewable energy curtailment, (d) reduced gross variability in renewable generation, (e) ease of annual and preventive maintenance of the generators and the converter systems, (f) emerging energy markets between multiple regions, and so on. More details can be found in [8].

S

G1

Point – to - point

(a)

Very low inertia (weak) AC grid

VSC

4

1

LCC

VSC

LCC

3

S OffshoreWind Farm

AC Grid #2

Remote onshore Wind Farm

AC Grid #1

S

G1

MTDC

(b)

Very low inertia (weak) AC grid

LCC

1

LCC

2

VSC

4

VSC

3

Fig. 1.15 Single-line diagram of (a) point-to-point HVDC, and (b) MTDC grid that transmits power from offshore and onshore wind farms

Remote onshore Wind Farm

AC Grid #1

2

S

OffshoreWind Farm

AC Grid #2

18 1 Introduction

1.5 Existing MTDC Systems in the World

19

Fig. 1.16 Sketch of possible renewable resources for a sustainable supply of power to Europe, the Middle East and North Africa [9]

The potential of MTDC grid is evident in its ability to establish interconnections across countries and continents to share their versatile energy resources including renewable energy resources. Such a diverse and humongous interconnection is named the “supergrid.” For example, there is a plan to capture the rich offshore wind resources of North Sea, solar resources in sub-Saharan Africa, and to interconnect the major generation and load centers of the UK, Scandinavia, and continental Europe [9], see Fig. 1.16. A subsea MTDC grid will serve as the backbone in interconnecting these incredibly diverse pan-European supergrids.

1.5 Existing MTDC Systems in the World As of 2018, there are four operational MTDC systems in the world. These are listed below: (1) The Zhoushan project: The Zhoushan project in China was built in 2014, which has five converter terminals, see Fig. 1.17. This project establishes a critical interconnection between Mainland China and five isolated islands

20

1 Introduction

Fig. 1.17 Zhoushan project: five-terminal HVDC network interconnecting five Islands and Mainland China built in 2014 [19]

enhancing the grid reliability and raising electric power supply capacity by 1000 MW [19]. The islands have relatively weak connection to the mainland power grid due to the geographical locations. Therefore, transmitting power through the DC system is the preferred option in such scenarios. Moreover, this MTDC grid enables the transfer of higher levels of wind power from these islands to Mainland China. (2) The Nanao project: A three-terminal MTDC system was constructed in Shantou, China in 2013. The objective of this project is to deliver large wind power from the Island of Nanao to the Mainland China. As shown in Fig. 1.18, Sucheng converter station with a capacity of 200 MW is located at the mainland to receive the wind energy from two wind intensive areas of the island. A number of commissioned wind farms with capacities of 84 and 45 MW are connected to AC buses at Jinniu and Qingao, respectively. Thus, two converter stations, Jinniu station (100 MW) and Qingao station (50 MW), were designed to export generation from both the existing and planned wind farms. (3) The Hydro-Quebec-New-England Interconnection: This project was developed in two phases between 1986 and 1992. The converter stations are located in Radisson, Nicolet, Des Cantons, Comerford, and Sandy Pond, see Fig. 1.19. Hydro generation from northern Quebec near Radisson is transported south through this radial MTDC network all the way to Boston area [11]. The load centers in Montreal, New Hampshire, and Boston area are fed using “taps” along this path, each tap representing a converter station. As of 2018, only three converter stations are operational in this interconnection. Two converter stations at Des Cantons and Comerford were decommissioned in 2007. (4) The SACOI Interconnection: The SACOI interconnection is a three-terminal radial MTDC system. As shown in Fig. 1.19, this system has portions of the DC lines that are overhead and segments that consist of subsea cables. The Lucciana converter station was equippedwith high-speed changeover

1.5 Existing MTDC Systems in the World

21

Fig. 1.18 The three-terminal HVDC network of the Nanao project to transfer wind power into mainland China built in 2013 [14]

Fig. 1.19 The five-terminal Hydro-Quebec-New-England and the three-terminal SACOI interconnections [7, 11, 20]

switches to facilitate bidirectional power flow between Corsica and Sardinia although the power flow is unidirectional from Sardinia to Italy. Following the decommissioning of the converter stations at Codrongianos and Dalmazio in 1992, two 300 MW stations were built in Suvereto and Codrongianos [7, 20].

22

1 Introduction

1.6 Focus and Scope of the Monograph The focus of the monograph is integration of wind energy to weak AC grids using HVDC technology. In the context of interfacing HVDC converters in an AC grid, there are two well-known measures of “weakness” of the grid [12]: (1) effective short circuit ratio (ESCR), and (2) effective inertia constant. ESCR is defined by: Short circuit MVA of AC system including HVDC AC switchyard MW rating of the DC link (1.1) The ability of an AC system to maintain a desired voltage and frequency depends upon the rotational inertia of the AC system. A measure of effective inertia constant is given by: ESCR =

Hdc =

total rotational inertia of AC system, MW.s MW rating of the DC link

(1.2)

As mentioned in [12], ESCR of at least 2.5 and Hdc of at least 2.0–3.0 s is necessary for satisfactory operation. Systems with very low short circuit MVA and inertia might need synchronous condensers to increase effective ESCR and Hdc . The monograph focuses on a few scenarios of weak AC grids interfacing wind energy resources using HVDC technology. These scenarios are mentioned next: 1. Large onshore wind farms in remote geographical locations are usually connected to weak local grids, which can have low ESCR and Hdc . LCC-HVDC converter stations interface these farms to transmit the power to load centers that are far from the wind generation sites. Different challenges arise in operation of such system. Among them, the focus will be on frequency dynamics of the weak grids. For example, unacceptably low-frequency nadir can lead to the tripping of under-frequency relays. Different studies are presented, which aim to analyze different aspects of frequency dynamics in such systems. 2. Following a blackout, during the early stages of restoration, an AC grid remains extremely weak in nature. This is due to the lack of generating resources in the grid providing voltage and reactive power support combined with dearth of inertia in the system providing adequate frequency stabilization. Presently, synchronous generators are used for the restoration of such systems. However, with increasing wind penetration, the wind farms are expected to assist in the black-start process. If VSC-HVDC transmission systems are present, they are known to possess black-start capability. Studies are presented to investigate the restoration problem of weak AC systems aided by wind farms in coordination with VSC-HVDC systems. 3. Integration of numerous onshore and offshore wind energy resources to the AC systems using MTDC grids has been planned in Europe and elsewhere. While the onshore wind farms can be connected to weak AC grids, the OWFs are not

References

23

even connected to an AC grid, giving rise to virtually zero ESCR and Hdc . In addition, multiple asynchronous AC grids are connected using the MTDC grids, e.g., AC grid #1 and #2 in Fig. 1.15. With the significant increase of wind penetration, some of these AC grids will be less dependent on conventional generation and shut down those plants. This will result in low Hdc for such systems leading to unacceptable post-disturbance frequency dynamics in terms of nadir and steady-state deviation. Thus, these areas will require frequency support from other areas including the wind farms in order to operate satisfactorily. Unlike traditional AC interconnections, in MTDC-based interconnections, if the AC areas are not connected through additional AC lines, then the DC grid acts as a “firewall” between surrounding AC areas. This firewall blocks the exchange of frequency support functionality among the asynchronous AC areas, which is naturally present in AC interconnections. Studies are present to delve deeper into this subject matter. The monograph is outlined as follows: Chap. 2 presents modeling and control of HVDC systems. LCC- and VSC-HVDC technologies are covered in brief. Models of both point-to-point and MTDC grid are considered. In Chap. 3, modeling and control of inverter-interfaced wind farms with special emphasis on DFIGs is covered. This is followed by Chaps. 4 to 5, which deal with the scenarios described earlier.

References 1. https://en.wikipedia.org/wiki/Square_Butte_(transmission_line) 2. Arrillaga, J., Smith, B.D.: AC-DC Power System Analysis. Institution of Electrical Engineers, Stevenage (1998) 3. Arrillaga, J., Liu, Y.H., Watson, N.R.: Flexible Power Transmission: The HVDC Options. Wiley, Chichester (2007) 4. Atlantic Wind Connection: http://atlanticwindconnection.com/awc-projects/awc-technology 5. Ball, W.C., Poarch, C.K.: Telephone influence factor (TIF) and its measurement. Trans. Am. Inst. Electr. Eng. Part I Commun. Electron. 79(6), 659–664 (1961) 6. Baoshu, P., Hong, R., Jianguo, Y., Albrecht, H., Huang, H., Lips, H., Sadek, K., Weingarten, U.: Tian–Guang HVDC power transmission project - design aspects and realization experience. In: 2002 Cigre’ session 14–110, Paris, pp. 1–8 (2002) 7. Billon, V.C., Taisne, J.P., Arcidiacono, V., Mazzoldi, F.: The corsican tapping: from design to commissioning tests of the third terminal of the Sardinia-Corsica-Italy HVDC. IEEE Trans. Power Delivery 4(1), 794–799 (1989) 8. Chaudhuri, N.R., Chaudhuri, B., Majumder, R., Yazdani, A.: Multi-Terminal Direct-Current Grids: Modeling, Analysis, and Control. Wiley, Hoboken (2014) 9. DESERTEC Foundation: www.desertec.org 10. Hingorani, N.G., Gyugyi, L.: Understanding FACTS: Concepts and Technology of Flexible AC Transmission Systems. IEEE Press, New York (2000) 11. Interconnection, H.Q.N.E.: http://new.abb.com/systems/hvdc/references/quebec-new-england 12. Kundur, P.: Power System Stability and Control. The EPRI Power System Engineering Series. McGraw-Hill, New York (1994)

24

1 Introduction

13. Li, Y., McCalley, J.: Design of a high capacity inter-regional transmission overlay for the U.S. IEEE Trans. Power Syst. 30(1), 513–521 (2015) 14. Li, X., Yuan, Z., Fu, J., Wang, Y., Liu, T., Zhu, Z.: Nanao multi-terminal VSC-HVDC project for integrating large-scale wind generation. In: 2014 IEEE PES General Meeting | Conference Exposition, pp. 1–5 (2014) 15. Liserre, M., Cardenas, R., Molinas, M., Rodriguez, J.: Overview of multi-MW wind turbines and wind parks. IEEE Trans. Ind. Electr. 58(4), 1081–1095 (2011) 16. McDonald, A., Clack, C.: Low cost and low carbon emission wind and solar energy systems are feasible for large geographic domains. In: Sustainable Energy and Atmospheric Sciences Seminar, NOAA, NREL, and CU-Boulder RASEI (2014) 17. Midwest ISO, PJM, SPP and TVA: Tech. Rep., 2008. Joint coordinated system plan 2008. Available: http://www.jcspstudy.org/ 18. Peake, O.: The history of high voltage direct current transmission. Aust. J. Multi-Disciplinary Eng. 8(1), 47–55 (2010) 19. Pipelzadeh, Y., Chaudhuri, B., Green, T., Wu, Y., Pang, H., Cao, J.: Modelling and dynamic operation of the Zhoushan DC grid: Worlds first five-terminal VSC-HVDC project. In: 2015 International High Voltage Direct Current Conference, October 18–22, 2015 Seoul, Korea, pp. 1–10 (2015) 20. SACOI: Wikipedia. Available: https://en.wikipedia.org/wiki 21. Sharifabadi, K., Harnefors, L., Nee, H., Norrga, S., Teodorescu, R.: Design, Control, and Application of Modular Multilevel Converters for HVDC Transmission Systems. Wiley, Newark (2016) 22. U.S. Department of Energy: Tech. Rep. May 2008. 20% wind energy by 2030: increasing wind energy’s contribution to U.S. electricity supply 23. Yazdani, A., Iravani, R.: Voltage-Sourced Converters in Power Systems: Modeling, Control, and Applications. Wiley, Oxford (2010)

Chapter 2

Modeling and Control of HVDC Systems

Abstract This chapter gives a brief overview of modeling and control of high voltage DC (HVDC) systems. First, different configurations of HVDC transmission systems are mentioned, which is followed by the state-space averaged modeling of line-commutated converter (LCC) HVDC systems and their control modes. Next, voltage source converter (VSC) HVDC modeling and control in a synchronously rotating dq reference frame is presented. Both grid-connected and islanded modes of control are discussed. Finally, modeling of multiterminal DC (MTDC) grids is briefly presented. The model of AC-MTDC grids in a unified framework is also given. At the end, different control philosophies of MTDC grid are elaborated. This includes discussion of four control options including DC voltage control, voltage droop control, and frequency droop control.

2.1 Introduction HVDC technology can be divided into two categories—line-commutated converter (LCC) and voltage source converter (VSC). These technologies were broadly described in the previous chapter. In this chapter, the modeling and control philosophies of LCC-HVDC and its VSC counterpart are presented. The objective, by no means, is to ensure a comprehensive coverage of this topic as there are many text books [4, 5, 23, 32, 36] solely on HVDC technology. On the contrary, the goal is to ensure a reasonable degree of completeness given the subject matter of the monograph. The content of this chapter is organized as described next. First, the configuration of HVDC transmission is presented. After this, a brief literature review of different modeling philosophies of LCC-HVDC is presented followed by state-space averaged phasor model and controls. Next, the modeling and control philosophies of VSC in general and VSC-HVDC in particular are covered. Finally, a broad overview of MTDC grid modeling and controls are presented.

© Springer Nature Switzerland AG 2019 N. R. Chaudhuri, Integrating Wind Energy to Weak Power Grids using High Voltage Direct Current Technology, https://doi.org/10.1007/978-3-030-03409-2_2

25

26

2 Modeling and Control of HVDC Systems +

+

=

=

S

S

S

S

=

=

-

= S

S

(a)

=

-

= S

S

-

+

(d)

(b)

=

=

S

S

S

S

=

-

=

S

S

=

=

= -

(c)

(e)

Fig. 2.1 Configurations of converter stations. (a) Symmetric monopole, (b) asymmetric monopole with ground return, (c) asymmetric monopole with metallic return, (d) symmetric bipole, and (e) asymmetric bipole with metallic return

2.1.1 Configurations of DC Transmission Different configurations of DC transmission systems are in use. Figure 2.1a–c shows the converter stations in monopole configuration. In this configuration, each converter station has only one independent converter bridge or group of bridges. In the symmetric monopole structure, there exist two DC transmission lines— one with positive and the other with negative polarity. The center point of the valve groups in each converter station is grounded as shown in Fig. 2.1a. The asymmetric monopole structures are shown in Fig. 2.1b, c, where both have a transmission line with negative polarity. One of the configurations has a ground return with both stations grounded. The other has metallic return with one of the stations grounded. Usually, monopolar configuration is used at the earlier phase of HVDC projects as most projects employ bipolar configurations shown in Fig. 2.1d, e due to reliability consideration. Unlike monopolar configuration, bipolar structure consists of two asymmetric monopolar structures, connected in mirror image, where one transmits power in positive polarity and the other in negative polarity. This simply leads to symmetric bipole structure with ground return as shown in Fig. 2.1d and asymmetric bipole structure with metallic return as shown in Fig. 2.1e. The feasibility of ground return depends on a lot of factors including soil resistivity, nearby pipelines, maritime regulations (if offshore), and so on.

2.2 Line-Commutated Converter (LCC)-Based HVDC

27

2.2 Line-Commutated Converter (LCC)-Based HVDC 2.2.1 Modeling Philosophies Extensive literature exists on LCC-HVDC modeling. The IEEE working group on dynamic performance and modeling of DC systems reported a functional model of two-terminal LCC-HVDC systems in [20]. The model is suitable for both steady-state and transient stability analysis. The advantage of this model lies in the modularity in its structure and controls, which makes extension to multiterminal systems relatively easy. Reference [21] presented steady-state models valid under balanced and unbalanced conditions. The models are based on equivalent positive, negative, and zero sequence circuits of LCC-HVDC. More recently in [25], a simple analytical model using Matlab/Simulink was proposed to investigate the steadystate operation of the 6-pulse single-bridge HVDC system. The model is based on dividing each cycle of operation into twelve intervals, out of which six intervals are commutation intervals with three valves conducting. In 1985, a benchmark system was established by Cigre’ for digital simulation [3]. Reference [11] develops a simplified model bringing the DC- and AC-side dynamics into consideration. Techniques of small-signal assessment and transient stability analysis have been used to analyze the dynamic behavior of LCC-HVDC systems. For example, [31] developed a linear time-invariant (LTI) state-space model of the small-signal dynamics for an HVDC system, and [40] has developed an LTI small-signal model for HVDC main circuit in a synchronously rotating d − q frame using sampled data modeling approach. Reference [27] develops a state-space model of the LCC-HVDC system, considering both DC voltage and current references as input variables. These small-signal models are valid only in the vicinity of the operating point. The two-part papers [38] and [39] present a frequency-domain model of an LCCHVDC link showing that voltage and current expressions can be derived using space-vector transfer functions between superimposed oscillations in the control signal and the AC and DC sides. The Part I paper [38] takes into account a fixed commutation overlap angle, whereas Part II [39] considers a variable overlap. Karawita and Annakkage [22] adopt the state-space modeling method and establish a model for LCC-HVDC system in a control block-diagram form, which can simplify understanding and modeling of HVDC systems. This model was derived to analyze interactions in the subsynchronous frequency range. Reference [42] presents a linearized model of LCC-HVDC based on mass-spring-damping concept. It establishes a linear mathematical model for LCC-HVDC system, which is based on two algebraic equations for rectifier and inverter, and differential equations for DC transmission line, rectifier controllers, and inverter controllers. This mathematical model is then converted to an analytical diagram model [42], and used it to build a mass-spring-damping model for HVDC. Dynamic average-value models (AVMs) have been developed to overcome the challenges of simulating switching phenomena in power electronic-based systems.

28

2 Modeling and Control of HVDC Systems

The switching effects are averaged in these models, which result in much faster simulation studies. A dynamic averaged modeling methodology is described in [6] using the CIGRE’ benchmark HVDC system [3]. For the purpose of modeling, the HVDC system is divided into seven subsystems. Two converters, which are modeled using parametric AVM method, two AC subsystems, two controller subsystems, and the DC transmission line subsystem. Reference [16] represents an AVM of LCCHVDC system using dynamic phasors. It represents low-frequency dynamics of the converters and AC and DC systems. Using dynamic phasors, voltages and currents can be represented with time-varying Fourier coefficients. The user can select the desired number of Fourier coefficients to approximate the original signal with the desired accuracy. There are some excellent text books available on HVDC modeling. Readers can refer to [4, 5, 23, 32] and references therein. In this monograph, we will represent the LCC-HVDC system by a state-space averaged phasor model, which is described next.

2.2.2 State-Space Averaged Phasor Model In this section, the nonlinear state-space averaged phasor model of LCC-HVDC is derived in the form of the following differential and algebraic equations (DAEs): x˙ = f (x, u, z) 0 = g (x, u, z)

(2.1)

where x, u, and z are the state variables, input variables, and algebraic variables, respectively. Figure 2.2 shows a schematic of the LCC-HVDC with its rectifier operating under current control (CC) and inverter operating under extinction angle control. During the normal operation, the rectifier and inverter control functions can be regulated using proportional-integral (PI) controllers acting upon the DC current and the inverter extinction angle, respectively. For notations, subscripts r and i are used for the rectifier and the inverter, respectively.

2.2.2.1

LCC-HVDC Station Model

The rectifier and the inverter stations can be represented by their respective algebraic equations [26]: √ 3 2BTr tapr Eacr cos αr − Rcr Idr vdr = π √ 3 2BTi tapi Eaci cos γi − Rci Idi vdi = π

(2.2)

(2.3)

tapr r r

K ir

1

xr1 s

K pr

Ldc 2

Cdc

Rdc 2

-

Ldc 2

I

* d

Vdm

Rdc 2

I dr

Rectifier current controller

-

Vdr

I dr Vdi

I di

i

i

Kii

xi1

1 s

i

i * i

K di I d* I di

-

caps & filters

Vgi

Inverter extinction angle controller

-

K pi

tapi

Ti :1 Eaci

Min over a cycle

Inverter

Fig. 2.2 Schematic of LCC-HVDC with its controllers. Under normal condition, rectifier operates in current control and inverter in extinction angle control

caps & filters

r

Eacr 1: T

Rectifier

2.2 Line-Commutated Converter (LCC)-Based HVDC 29

30

2 Modeling and Control of HVDC Systems

Here, vd represents the average DC voltage of the converter; Id is the converter DC current; Eac denotes AC-side commutating voltage phasor magnitude; B denotes the number of bridges; Rc is the equivalent commutating resistance representing commutation overlap; α denotes the firing angle and γ denotes the extinction angle; T is converter transformer turns ratio; and tap is the converter transformer tap ratio.

2.2.2.2

DC Line Model

The DC line is represented by a T-model, see Fig. 2.2, which has three dynamic states—Idr , Idi , and Vdm :  √      BTr tapr Rdc + 2Rcr 2 6 2 Idr − vdm − Ldc Ldc π Ldc  ∗   × Eacr cos Kpr Id − Idr + Kir xr1

I˙dr = −





Rdc I˙di = − Ldc



 Idi +

2 Ldc



 vdm −

2 Ldc

(2.4)

vdi 



  f Idi , xi1 , vdm , Id∗ , γi∗ , Eaci

(2.5) v˙dm

1 = (Idr − Idi ) Cdc

(2.6)

Here, Idr and Idi are the rectifier- and inverter-side DC current, respectively; vdm is the voltage at the midpoint of the DC line; Ldc , Rdc , and Cdc are the total series inductance, series resistance, and shunt capacitance, respectively, of the T-model of the DC transmission line. The rest of the notations will be described next in the models of the rectifier and inverter station controls.

2.2.2.3

Rectifier Control

As shown in Fig. 2.3, the rectifier control system operates in CC mode. The Cigre’ benchmark model [3] is being followed, where the current reference for the rectifier station is limited by voltage-dependent current order limit (VDCOL), which is obtained as a function of DC voltage Vdm at the midpoint of the transmission line. This voltage is estimated from the inverter-side DC voltage, DC line resistance, and line current. The error between the measured DC current at the rectifier side Idr ∗ is fed to a PI controller with gains K and the current order Idr pr and Kir , which produces the necessary firing angle order αr . The state variable of the rectifier-side controller xr1 shown in Fig. 2.3 can be expressed as: x˙r1 = (Id∗ − Idr )

(2.7)

2.2 Line-Commutated Converter (LCC)-Based HVDC

VDCOL

31

K pr

r max

Id

r

r

Idr

1 s xr1

Kir

r min

Fig. 2.3 Rectifier-side current control of LCC-HVDC following Cigre’ benchmark model [3]

2.2.2.4

Inverter Control

As shown in Fig. 2.4, the extinction angle control or γ control and current control have been implemented on the inverter side, which is typically followed in the literature—for example, in the Cigre’ benchmark model [3]. The current reference is chosen as (Id∗ − Imargin ) for the inverter CC control. A typical value of the margin current Imargin is 10% of the rated DC current. Under normal condition, the rectifier operates in CC mode, which drives the inverter CC controller into saturation (i.e., it hits the βicmin ) limit. Therefore, it is easy to see from Fig. 2.4 that the inverter operates in constant extinction angle control under normal condition. As shown in Fig. 2.4, the reference value of the extinction angle is changed with loading condition to maintain adequate commutation margin for the inverter. The state variable of the inverter-side controllers can be expressed as: x˙i1 = (γi∗ − γi + Δγi ),

or

x˙i1 = (Id∗ − Idi − Imargin )

(2.8)

The extinction angle of each valve is measured, and the minimum value of the extinction angles among the 12 valves, see Fig. 2.4, is used as the feedback signal, since the corresponding valve faces the highest risk of commutation failure. When rectifier looses control over current, for example due to low AC-side voltage leading to the hitting of the lower limit αmin , a mode-switching takes place in the inverter-side and it assumes current control.   Please note, vdi = f Idi , xi1 , vdm , Id∗ , γi∗ , Eaci in Eq. (2.5) is obtained by substituting the following expression in Eqs. (2.2), (2.3):   Idi γi − K1pi cos−1 − cos γi + √ 6Xci π  3 2Ti tap  i EaciKii  xi1 = − Kπpi + γi∗ + Kdi Id∗ − Idi + K pi

(2.9)

This relationship can be obtained in a straightforward manner from the converter and controller equations.

32

2 Modeling and Control of HVDC Systems Current order for rectifier

VDCOL

Id

Id

K pi

I margin

iC max

_

I di

iC

_

1 s xi1

iC min

Kii

K di

max

K pi

_ i

i max

i

_

i min of 12

i

1 s xi1

i

Kii

i min

Fig. 2.4 Inverter-side control of LCC-HVDC from Cigre’ benchmark model [3]

2.2.2.5

AC Network Interface, Cap Bank and Filters

For most stability studies, the dynamics of the AC transmission network is considered to be much faster compared to other components. Therefore, the AC network is modeled algebraically using a Y -bus matrix. The set of algebraic equations: 0 = [I ] − [Ybus ][Vbus ]

(2.10)

is solved at each solution time step. It takes the current injection vector [I ] from HVDC, AC generators among others, and the capacitors and filter banks as the input and generates node voltage vector [Vbus ] as output. The capacitor banks and filters at the rectifier and the inverter stations are modeled as constant impedance loads at the fundamental frequency. The active and the reactive components of the load connected to the ith bus are modeled by a shunt admittance YiL connected to the load bus. For a given load with active and reactive L power consumption of PiL and QL i , respectively, the corresponding value of Yi can be calculated as: YiL =

PiL − j QL i |Vi |2

(2.11)

where Vi is the voltage of the ith load bus. For other AC system loads, static load models of constant impedance–constant current–constant power (ZIP) are assumed in this monograph.

2.3 Voltage Source Converter (VSC)-Based HVDC

33

In the overall state-space model of the LCC-HVDC system shown in Eq. (2.1), the state variables x, input variables u, and the algebraic variables z can be T  x = Idr xr1 Idi xi1 vdm , summarized as: T T   u = Id∗ γi∗ , z = Eacr Eaci

2.3 Voltage Source Converter (VSC)-Based HVDC 2.3.1 Overall Structure Figure 2.5 shows the structure of a VSC-HVDC system with the control scheme of its converters in grid-connected mode. As described in Sect. 1.3.4 of Chap. 1, the VSCs are built using IGBTs and anti-parallel diodes. The DC/AC voltage conversion is achieved by controlled turn on and turn off of these IGBTs. The VSC can independently control the active and reactive power exchange with the AC system by regulating the magnitude and phase angle of its AC terminal voltage. The real power flow can be reversed by altering the DC current direction, while keeping the DC-link voltage polarity the same. In a VSC-HVDC system, one converter station controls the DC-link voltage, while the other usually sets the active power reference. Furthermore, each converter can independently control the AC side voltage or reactive power at either end. The VSC-HVDC system shown in Fig. 2.5 is a monopolar configuration. It is also possible to have a bipolar structure in which there are two VSC stations at each end, positive and negative pole station—please see Sect. 2.1.1. For an asymmetric bipole structure, the HVDC link consists of a positive and a negative pole cable and a metallic return. It was mentioned in Chap. 1 that DC and AC filters are connected to the DC and AC sides of a VSC—see Fig. 1.12. The modeling of two-level, three-phase VSCs and the details of their control scheme are the subject matter of the following sections.

2.3.2 Modeling of Two-Level VSC As shown in Fig. 2.6, the circuit consists of three half-bridge converters, one per AC-side terminal. The IGBT switches are controlled in a manner such that if the upper one is “on,” the lower one in the same phase leg is “off.” For example, if switch S1 in Fig. 2.6 is “on,” then S4 will be “off” and vice versa. This results in a switched AC output voltage varying between −vdc /2 and vdc /2. To produce a switched waveform with fundamental frequency equal to the desired value of ωs , a widely used strategy called sinusoidal pulse-width modulation (SPWM) [41] can be used.

/

/

igdi

* igqi

igqi

i

* gdi

vtqi

* gqr

vtqr

vtdr K i (s )

K i (s )

K i (s )

L

v

v

* gdr

L * gqi

* gdi

PWM

negative pole

Vdcr

rectifier

L

v

v

Vdci

positive pole

L

K i (s )

vtdi

inverter

inverter-side controls

PLL

vti

Fig. 2.5 Grid-connected mode: configuration VSC-HVDC system with its control structure

K v ( s)

Pext

G2

System #2

PLL

G1

* igqr

igqr

igdr

* igdr

/

/

System #1

rectifier-side controls

vtr

34 2 Modeling and Control of HVDC Systems

2.3 Voltage Source Converter (VSC)-Based HVDC

35

idc

iga

vga

igb

vdc

vgb

igc

vgc

Fig. 2.6 Simplified schematic of the two-level three-phase VSC

Ts 1 Carrier

0

-1 S4

me

m

1

Modulang signal 0

0

S1

me

Fig. 2.7 Pulse-width modulation (PWM) switching strategy

In this approach, a sinusoidal signal of frequency ωs called “modulating signal” is compared with a high-frequency triangular waveform called “carrier waveform.” Depending on the signum of the difference between the modulating signal and the carrier signal, the upper and the lower switch in a phase leg can be controlled. Figure 2.7 shows the PWM scheme for a generic modulating signal, which controls S1 and S4. A typical modulating signal, carrier signal, and switching pattern for SPWM technique is shown in Fig. 2.8. To produce AC voltage whose fundamental component is a set of balanced threephase sinusoidal signals with desired frequency ωs , the following set of modulating signals are applied:

36

2 Modeling and Control of HVDC Systems

m

1 0

m carrier

-1

vt /vdc

0.5 0 -0.5 time

Fig. 2.8 Waveforms of the modulating signal (m), carrier signal, and AC-side terminal voltage, based on the SPWM switching strategy

ma (t) = m(t) cos [ωs t + φo ]   mb (t) = m(t) cos ωs t + φo − 2π 3   mc (t) = m(t) cos ωs t + φo − 4π 3

(2.12)

The fundamental components of the AC-side voltages can be described as: vga (t) = 12 vdc (t)ma (t) = 12 vdc m(t) cos [ωs t + φo ]   vgb (t) = 12 vdc (t)mb (t) = 12 vdc m(t) cos ωs t + φo − 2π 3   vgc (t) = 12 vdc (t)mc (t) = 12 vdc m(t) cos ωs t + φo − 4π 3

(2.13)

Please note that going forward, we are only interested in these fundamental frequency components of the switched voltage waveforms at the converter terminals for modeling and controls of VSCs.

2.4 VSC Controls: Grid-Connected Mode In this control mode, the converter stations are connected to a power grid providing a source of AC voltage at the point of common coupling (PCC). As shown in Fig. 2.5, one of the stations controls real and reactive power (or AC voltage), while the other maintains the DC bus voltage. Control of real and reactive power is described next followed by DC and AC voltage regulation.

2.4 VSC Controls: Grid-Connected Mode

37

2.4.1 Control of Real and Reactive Power Figure 2.9 shows the two-level VSC connected to AC and DC sides. Since the impedance of capacitors C in the AC-side filter shown in Fig. 1.12 is high for the fundamental frequency, we have neglected them. Also, the resistance and inductance of the DC-side filter is neglected. The real and reactive power Pt and Qt in Fig. 2.9 are regulated using a hierarchical control structure. The outer control layer uses reference powers as input and generates reference currents in a synchronously rotating d − q reference frame. The inner loops track those current references. This is known as “current mode” control. In this control mode, the converters can be protected against overcurrent. The KVL equations of the AC side of the VSC shown in Fig. 2.9 can be written as: diga dt digb L dt di L dtgc

L

= −Riga + vga − vta = −Rigb + vgb − vtb

(2.14)

= −Rigc + vgc − vtc

The concept of space phasors is widely used to analyze and control VSCs. Basics of this concept is described in appendix A and is used here to synthesize VSC 2π controls. Multiplying the two sides of equations in (2.14) by 23 ej 0 , 23 ej 3 , and 2 j 4π 3 3e

, respectively, and adding the resulting equations, we can obtain L

dIg = −RIg + Vg − Vt dt

(2.15)

The over bars in this equation denote space phasors. It can be seen from (2.15) that the space phasor of AC-side currents can be controlled by the space phasor of the VSC terminal voltage. In this case, the AC system voltage phasor acts as a disturbance input. If each space phasor in (2.15) is expressed in d − q frame components (see, Appendix A), the AC side of the system in Fig. 2.9 can be expressed in d − q frame. Thus, we can obtain dIgd dt dIgq L dt

L

= −RIgd + LωIgq + Vgd − Vtd = −RIgq − LωIgd + Vgq − Vtq

(2.16)

From the rotating frame concept described in Appendix A, we have the following relations for real and reactive power: P (t) = Re Q(t) = Im

 

∗ 3 2 V (t)I (t)

 

∗ 3 2 V (t)I (t)

(2.17)

vdc / 2

0

vdc / 2

vdc

idc

idc

Fig. 2.9 Two-level VSC interfacing DC and AC systems through LC filters

Cdc

il

Pdc

itc vtc

ita vta

igc vgc

L

itb vtb

R

Qt

Pt

igb vgb

iga vga

Pg Qg

S S

S

38 2 Modeling and Control of HVDC Systems

2.4 VSC Controls: Grid-Connected Mode

39

v tq 1

igq

Ls

v gq

R

mq

L

L 1

igd

Ls

R

v gd

md

v td Fig. 2.10 Control plant dynamics in rotating dq frame

    Replacing V t and I g in (2.17) with Vtd + j Vtq ej γ and Igd + j Igq ej γ , respectively, we have   Vtd Igd + Vtq Igq   Qt (t) = 32 −Vtd Igq + Vtq Igd

Pt (t) =

3 2

(2.18)

If the AC system voltage components Vtd and Vtq are known, Pt and Qt can then be regulated by controlling the AC-side current components Igd and Igq of the VSC.

2.4.1.1

Plant Dynamics

The plant dynamics for the current-mode control is given by Eq. (2.16). It represents a multi-input-multi-output (MIMO) plant. It has two control inputs, Vgd and Vgq , and two outputs Igd and Igq . On the other hand, Vtd and Vtq are the disturbance signals. Assuming that SPWM technique is used for converter switching, the control inputs Vgd and Vgq are proportional to the dq frame components of the threephase modulating signals, md and mq . The overall plant is shown in Fig. 2.10. The controller should produce the modulation indices md and mq .

40

2 Modeling and Control of HVDC Systems

v tq /

mq

v

* gq

K i (s )

uq

* i gq

eq

i gq

L L

i gd /

md

v

* gd

K i (s )

ud

* i gd

ed

v td Fig. 2.11 Current controller structure

q t

(t )

vt

vtq t

vtd

(t )

(t )

d

Fig. 2.12 Space phasor of voltage vt in stationary (αβ) and rotating dq reference frames

2.4.1.2

Controller Structure

The controller structure used for regulating the current is shown in Fig. 2.11. It has the following notable features: 1. It uses a phase-locked loop (PLL) to align the voltage space-phasor vt to the daxis. Figure 2.12 shows the space phasor rotating at the angular speed ωt , which is equal to the grid frequency. A dq reference frame rotating at an angular speed ω is also shown. To ensure that vt is aligned to the d-axis, a PLL makes sure that ωt = ω and θt (t) = γ (t).

2.4 VSC Controls: Grid-Connected Mode Fig. 2.13 Block diagram of a PLL

vta

abc vtd

vtb

vtq

vtc

2.

3.

4.

5.

6.

41

dq

s

H (s)

( t) 1 s

There are many different ways to realize the PLL function. One popular approach from [15] is shown in Fig. 2.13. The idea is to drive vtq to zero by using a controller H (s)—zero reference signal is not explicitly shown in this figure. The output of the controller generates the deviation in angular speed of the rotating dq frame from the synchronous speed. Upon integration, it produces the angle γ (t), which in turn is used to convert the abc quantities of measured voltages to dq quantities. The transformation is described in Appendix A. In the simplest case, H (s) can be a proportional-integrator (PI) controller. However, often a more complicated controller is used. The advantage of setting vtq to zero is that, in Eq. (2.18), the expressions for Pt and Qt become Pt = 32 vtd igd and Qt = − 32 vtd igq . This simplifies the control of real and reactive power to a great extent as the control of real power solely depends on the d-component of current, while the reactive power can be regulated through the q-component. The outer layer of the hierarchical control in Fig. 2.5 shows the regulation of real and reactive powers. The PLL sets the dq frame and the components of currents in that frame are computed from the measured three-phase currents. The advantage of converting sinusoidal three-phase signals to dq frame is that they become DC quantities. Therefore, tracking of these currents becomes easier, and controllers Ki in Fig. 2.11can be simple PI compensators. As shown in Fig. 2.10, the d- and the q-channels in the MIMO plant has crosscoupling. This implies that a disturbance in the d-channel will affect the q-axis quantities and vice versa. The cross-coupling terms are LωIgd and LωIgq , which can result in poor performance of the controllers. To avoid this, these terms are treated as disturbances. Appropriate feedforward signals shown in Fig. 2.11 are used for disturbance rejection, which in turn decouple the two channels. The plant in Fig. 2.10 also shows three other disturbance inputs—vdc , vtd , and vtq . These measurable disturbances are also rejected in the control structure (Fig. 2.11) using feedforward terms. Since the plant structure is the same for the d- and q-channels, identical PI controllers can be used for both. The PI controller structure is of the form: Ki (s) =

kp s + ki s

(2.19)

where kp and ki are proportional and integral gains, respectively. One design objective of the controllers could be attaining a first-order closed-loop response.

42

2 Modeling and Control of HVDC Systems

This ensures a non-oscillatory reference tracking. Let the first-order transfer function be Igd (s) Igq (s) 1 ∗ (s) = I ∗ (s) = τ s + 1 Igd i gq

(2.20)

where τi is the desired time constant of the closed-loop step response. To that end, the controller parameters are designed by canceling the plant pole, − R L using the ki compensator zero, − kp . The set of controller gains to achieve this would be kp =

L τi

ki =

R τi

(2.21)

The controller generates the modulation indices md and mq at its output.

2.4.2 Control of DC-Side Voltage Any imbalance in real power within the area between DC system and VSC shown in Fig. 2.9 results in variations in DC voltage. Pdc should be controlled via the VSC to ensure the power balance. Power balance can be formulated as follows in this system: Pext

d − dt



1 2 Cdc Vdc 2

 = Pdc

(2.22)

where Pdc = Vdc idc and Pext = Vdc il . The third term in the left-hand side of Eq. (2.22) is equal to the rate of change of stored energy in the DC bus capacitor. Lumping the converter losses into a term Ploss , we can rewrite Eq. (2.22) as: 

Cdc 2



2 dVdc = Pext − Ploss − Pg dt

(2.23)

where Pg is the VSC AC-side terminal power. Equation (2.23) shows a dynamic 2 is the state variable, P is the control input, and P system in which Vdc g ext and Ploss are the disturbance input. Since the VSC system enables the control of Pt and Qt , we express the control input, Pg , in terms of Pt . It can be seen from Fig. 2.9 that the dynamics of shown system can be expressed by the below equation: L

dig = −Ri g + Vg − Vt dt

(2.24)

2.4 VSC Controls: Grid-Connected Mode

43

∗ Multiplying both sides of (2.24) by 32 ig∗ , assuming i g i g = iˆg2 , and applying real operator, we get

      di g ∗ 3 ∗ 3L 3 3 ˆ2 ∗ Re i = − R ig + Re Vg ig − Re Vt i 2 dt g 2 2 2 g

(2.25)

The second and third terms in the right side of (2.25) are Pg and Pt , respectively. Hence, we have   di g ∗ 3L 3 ig = − R iˆg2 + Pg − Pt (2.26) Re 2 dt 2 Solving (2.26) for Pg gives   di g ∗ 3 ˆ2 3L Re Pg = Pt + R ig + i 2 2 dt g

(2.27)

The second term in the right side of (2.27) is the real power loss in the resistor, and the third term is the instantaneous real power consumed by the inductor shown in Fig. 2.9. Hence, substituting Pg from (2.27) in (2.23), we obtain 

Cdc 2



2 dVdc  = Pext − Ploss − Pt dt

(2.28)

 where Ploss  Ploss

= Ploss

  di g ∗ 3 2 3L + Rig + i Re 2 2 dt g

(2.29)

2 is the output, P is the control input, and P  Based on (2.28), Vdc t ext and Ploss are disturbance inputs. Figure 2.14 shows the diagram of plant described by (2.28). Hence, we can form the control scheme shown in Fig. 2.15. In this control scheme, 2 is compared with a reference value and the error is fed to a compensator, K (s), Vdc v ∗ to the inner current control loop. Figure 2.5 also to deliver reference current idg shows this controller. Pext can be measured and used as a feed-forward signal to 2 . We note that P  the output of Kv (s) to mitigate its impact on Vdc loss is a small term compared to Pext . Also, Ploss cannot be estimated with certainty and hence we cannot mitigate its impact by a feed-forward term. Therefore, to eliminate the 2 due to changes in P steady-state error of Vdc loss , Kv (s) should have an integrator. On option is to have Kv (s) as a PI controller designed by combining pole placement technique with symmetrical optimum criterion described in [30].

44

2 Modeling and Control of HVDC Systems

Fig. 2.14 Block diagram of the control plant describing DC voltage dynamics

2 sCdc

Ploss Pt

igd

Pext (.) 2 * igd

(.) 2

/

Kv ( s ) Pext

Fig. 2.15 Block diagram illustrating the process of DC voltage control

I q max

Vmax

Q max

PI

_ Q min

_

Vmin

PI I q min

PLL Fig. 2.16 Cascaded PI-based AC voltage-reactive power control

2.4.3 Control of AC-Side Voltage The AC-side voltage vt at the PCC can be regulated by different approaches. One popular approach is to use a cascaded PI structure shown in Fig. 2.16. In this scheme, there are two outer loops. The outermost loop controls the reactive power Qt . For example, it might be desirable to operate the VSC at unity power factor by setting Q∗t to zero. The reactive power error is input to a PI controller, which generates the AC voltage reference vt∗ . The measured terminal voltage vt is fed back and the ∗ . error is again fed into a PI controller that produces the q-axis current reference iqg The PI regulator for reactive power control is slower than the PI compensator for voltage control. Under normal circumstances, the reference terminal voltage varies

2.5 VSC Controls: Islanded Mode

45

very slowly to maintain Q∗t . The slowly varying AC voltage reference is tracked efficiently by the faster inner control. However, the AC voltage reference can be allowed to vary only within a certain range. When either of the limits Vmax or Vmin are hit, the controllers stop tracking reactive power. On the contrary, it starts tracking a fixed voltage reference (either of the limits) and delivers/draws the reactive power required to maintain this voltage reference.

2.5 VSC Controls: Islanded Mode There are situations where VSCs are connected to small grids or islands, or under certain circumstances do not have any voltage support from the external AC system. In such cases, VSC should control the voltage magnitude and frequency of the AC system. This application of VSCs is very useful when they are connected to a blacked out system without any reasonable voltage and frequency support. This mode will be applied for power system restoration using VSC-HVDC systems, which will be discussed in Chap. 5. Another example is VSC station connected to OWFs or offshore drilling platforms. For OWFs, power generated by the wind farms is transmitted to the onshore grid, whereas power is delivered to drilling platforms from onshore grid. Interconnection of OWFs to VSC-HVDC will be discussed in Chap. 6. There are different ways of achieving voltage/frequency (v/f ) control in islanded mode—a typical approach is described here. The three modulating signals used for the switching of the two-level three-phase VSCs can be described as: ma (t) = m(t) cos [2πfm t + δ]

 mb (t) = m(t) cos 2πfm t − 2π + δ 3   4π mc (t) = m(t) cos 2πfm t − 3 + δ

(2.30)

where m(t) is the magnitude and fm is the frequency of the modulating signal. The frequency of the system, which is connected to the VSC can be determined by the frequency of the modulating signal, fm . Hence, fm should be set as the nominal frequency of the system, e.g., 60 Hz. One can use the magnitude of the modulating signal to control the magnitude of the AC terminal voltage. Figure 2.17a shows the mechanism of v/f control. The actual AC voltage magnitude is compared with the desired reference value, and the error is fed to a PI controller to generate the magnitude of the d-axis component of modulating signal, md . The q-axis component, mq , can be set equal to zero. A free-running integrator with the rated frequency can generate the angle of d − q-axis modulating signals. In the above approach, the d-axis is aligned with the modulation index space phasor, leading to δ = 0 in Eq. (2.30). Another approach can have an arbitrary angle δ or the angle may come from some other control input. This is shown in

46

2 Modeling and Control of HVDC Systems

-

0 2 fm

-

PI

dq to abc

mabc

1 s

2 fm

PI

Mag /Ang to dq

dq to abc

mabc

1 s

(a)

(b)

Fig. 2.17 Block diagram of voltage/frequency control of VSC in islanded mode

Fig. 2.17b. The voltage magnitude controllers in this case produce the magnitude of the modulation index m(t). It results in generation of modulating signals in dqframe as: md (t) = m(t) cos δ mq (t) = m(t) sin δ

(2.31)

These signals can then be converted to abc frame based on relationships described in Appendix A, and be used for converter switching.

2.6 MTDC Grid Systems A comprehensive model of the AC-MTDC system has been presented in [12, 13]. The aim of this section is to briefly describe the modeling of a generic MTDC grid interconnecting the AC networks and describe different control modes of the converter stations therein. The following topics are covered: First, an asymmetric bipole MTDC grid model with the provision of metallic return network is described. Following this, the modeling required for nonlinear time-domain simulation of combined AC-MTDC grid is presented. Next, the method of simulating contingencies in the MTDC grid is described. Finally, control philosophies of MTDC converter stations are described.

2.6.1 Model of Asymmetric Bipolar MTDC Grid The asymmetric bipolar configuration was discussed in Sect. 2.1.1. The schematic of an MTDC grid in this configuration is shown in Fig. 2.18—only the ith and the j th converter stations are illustrated for clarity. This system consists of the following: (a) DC transmission network, and (b) converter stations and controls.

ID_n

Cs_n

Is_n

Cc_p

Iline_p

Ic_p l

Rp Lp

Negative pole: Identical to positive pole, notations with subscript ‘n’

Metallic return: Identical to positive pole, notations with subscript ‘m’

If

Rf

r_p

n

Ip_qr q_p

Rc, Lc

Rc, Lc

j th converter station

Fig. 2.18 Bipolar MTDC grid with cable network modeled by cascaded pi sections connecting the ith and the j th converter stations [12]

i th converter station

Rc, Lc

Rg

Is_p

Cs_p

Ud_m

UD_n

Rc, Lc

UD_p

ID_p

2.6 MTDC Grid Systems 47

48

2 Modeling and Control of HVDC Systems

The DC transmission network has a positive, a negative, and a metallic return network. There are a number of ways to model these cables—please see [8] and references therein. One approach is to represent these networks by cascaded π sections shown in Fig. 2.18. The number of π sections can be determined based on the accuracy of the cable impedance as a function of frequency. A higher number of π section will lead to a more accurate representation, while it will increase the number of dynamic states of the model. The complexity-vs-accuracy tradeoff needs to be determined based on the time constant of the transient response of interest. The generic model of the DC cable network can be represented by a set of differential and algebraic equations which can be represented in a block diagram shown in Fig. 2.19. The algebraic equations are simple KCL equations at each node, while the differential equations represent the KVL equations involving the capacitances and inductances [12]. The block diagram [12] is quite self-explanatory. The following points are worthnoting: • CCIP is the incidence matrix of dimension [NnodeP × NbrP ]. The entries of CCIP are CCIP (i, j ) = 1(-1), if the ith cable enters (leaves) the j th node and CCIP (i, j ) = 0, otherwise. • The connectivity between the nodes is determined by the matrix CCUP of dimension [NbrP × NnodeP ]. Assuming that the current in a branch will flow from the ith to the j th node if i < j , the elements of CCUP are determined as CCUP (i, j ) = 1, if i < j , CCUP (i, j ) = -1, if i > j , all other entries are zeros where the ith and the j th node are not connected. Note that CCIP = −CCUPT . • If denotes the fault current and Rf is the fault resistance for a pole-to-ground fault. • Positive and negative poles can be modeled in an identical manner due to symmetry, whereas the metallic return network can have slight different equations based on the location of the grounding resistance Rg —see Fig. 2.18. Other types of grounding can also be taken into account. Modeling of VSCs and their controls was described before. However, in an ACMTDC grid system, the controls of VSC stations need certain modifications, which will be described briefly towards the end of this chapter. The unified model of the MTDC grid connected to AC systems is described next.

2.6.2 Unified Model of MTDC Grid Connected to AC Systems The MTDC grids are going to be interconnected to surrounding AC grid systems. Figure 2.20 shows the MTDC grid and the AC grid model in a unified framework [12]. The AC grid can be modeled in a traditional phasor platform. In this platform, differential and algebraic equations are used to model different components of the AC grid. The AC transmission system is modeled using a set of algebraic equations where the network connectivity is determined by the [Ybus ]

Negative Pole Network

CCIm

Metallic Return Network

-1

1 ncCc_m

1 Rg

Rm

1 Lm -

CCUm

Ud _m

Fig. 2.19 Dynamic model of DC cable network in block-diagram form [12]

ID_n

Is _ n

ID _ p

Positive Pole Network

Pdc _ P

Ud _ p I line_ p

CCIP

-

Is _ p

If

- Ic _ p

RP

1 Lp

Cs _ p

1

1 Rs _ p

1 R f

1 ncCc_ p

-

-

CCUP

Uqr_ p

-

2.6 MTDC Grid Systems 49

50

2 Modeling and Control of HVDC Systems AC grid model MTDC Grid

Static and dynamic models of different components in AC grid

DC cable network model

Input parameters like wind speed, reference generator terminal voltages, synchronous speed, mechanical torque input, real and reactive power consumed by loads

Solve

Positive/negative pole converters and controls

PLL

(in dq frame)

in network Real-Imaginary frame

(in real-imag frame) dq-frame to RealImaginary frame

Fig. 2.20 Unified model of MTDC grid connected to AC systems [12]

matrix. Readers can refer to standard textbooks on AC system modeling [26, 35] for more details. A set of nodal current injection equations interface the AC grid and the MTDC grid models. These equations are solved using the Ybus matrix and the injected current from the components of the AC grid (e.g., generators, loads, and so on) and the MTDC converter stations in a network real-imaginary reference frame to obtain the AC bus voltages. The AC bus voltages are fed back into the AC grid model. As described before, a PLL is used to lock the d-axis of a synchronously rotating reference frame to the voltage space phasor at the PCC. The converter and corresponding controller equations are described in this dq-frame as shown in Fig. 2.20. Eventually, the current injections from the MTDC converters are transformed back to the network real-imaginary frame and used for solving the nodal current injection equations described earlier.

2.6.3 Simulation of Contingencies Three types of contingencies pertaining the MTDC grid are considered [12]: • DC line fault: The DC line-to-ground fault can be simulated by inserting a shunt resistance Rf , which can be switched in as shown in Fig. 2.19. In effect, this modifies the differential and algebraic equations. • DC line outage: A DC line outage can happen following a fault. DC breakers in both ends of the line can isolate it. This can be simulated by inserting a variable series resistance shown in Fig. 2.19. The magnitude of this resistance can be increased to a very high value over a short period of time to simulate breaker opening. • Converter outage: Converter outage can be simulated by opening the AC- and the DC-side breakers. The AC breaker opening can be simulated by increasing

2.6 MTDC Grid Systems

51

the resistance interfacing the converter station with the AC grid. The DC-side opening can be simulated by making DC-side power Pdc_p/n zero. This ensures that the DC bus of the converter station remains connected to the DC switchyard.

2.6.4 Control Strategies of MTDC Converters As described in the overall structure of point-to-point VSC-HVDC, one converter controls DC-link voltage, while the other regulates real power. This aspect becomes different in an MTDC grid. On the other hand, the reactive power/AC voltage control philosophy remains the same. The reason behind this is that real power flow experiences interaction from each converter station, whereas reactive power does not exist in the DC side. There are different control options for the real power channel of the converters, which are described next. 1. Option I: One converter station can be in DC voltage control and other stations in real power control. The issue with this is that following the outage of a converter station or other disturbances, the entire burden of the power imbalance needs to be handled by the converter in DC voltage control mode. This can adversely affect the AC grid connected to this station and also lead to converter overloading and sizing issues. Also, outage of the station controlling DC voltage can lead to the collapse of the DC grid unless a healthy converter is switched to DC voltage control mode. 2. Option II: To solve some of the issues mentioned above, multiple converter stations can be in DC voltage control mode along with the remaining converter stations controlling real power. The issue with this idea is determining appropriate DC voltage reference for multiple converter stations. 3. Option III: To avoid issues in Options I and II, each converter station can be operated in some form of droop control philosophy. This is also known as autonomous power sharing control mode. In this mode, following a converter outage or other contingencies the imbalance in power is shared equitably among all converter stations. There exists a significant literature applying different kinds of droop control philosophies in MTDC grids [1, 2, 7, 13, 14, 17– 19, 24, 28, 29, 33, 34, 37, 43]. Figure 2.21a shows a DC current–DC voltage droop control with droop coefficient Kvgi , which generates the d-axis reference current for the inner current control loop using a PI controller. Since the unit of Kvgi is admittance, the current–voltage droop can be translated into a power–voltage squared droop that preserves the unit of the droop coefficient, see Fig. 2.21b. Since system operators have explicit access to power reference in this mode, it can have certain advantages from dispatch and power market standpoint. One can also have a power–voltage droop instead. Here, Pcgi denotes the converter real power at the PCC.

52

2 Modeling and Control of HVDC Systems

kvgi PI

-

* I dgi

(a)

kvgi kvgi ( VDCg ) 2max / 4

Prefgi

-

2 DCg min

kvgi ( V

)

PCgi

PI

* I dgi

/4

(b)

kvgi

2 2 (VDCgcom VDCgref )/4

2 DCg max

kvgi ( V

Prefgi

Pvgi

-

)

2 DCg min

kvgi ( V

)

/4

Pvgi

PI

* I dgi

/4

PCgi (c)

Pf max

f0

-

2 2 (VDCgcom VDCgref )/4

k fgi

kvgi

Pf min

fi

g

p (positive-pole) or n (negative-pole)

kvgi ( VDCg ) 2max / 4

Prefgi

-

Pvgi

PI 2 DCg min

kvgi ( V

)

* I dgi

/4

PCgi (d)

Fig. 2.21 Different droop control strategies in MTDC grid

Instead of using local voltage signals, there have been proposals to employ a common DC voltage signal VDCgcom for droop control [9, 10]. This signal can be communicated from a common node in the DC grid to all stations through the fiber-optic channels embedded in power cables. The philosophy imitates the governor droop principle in AC grids where frequency is a universal quantity, which is same throughout the AC system in steady state. Here, the common DC voltage is equivalent to frequency in governor droop. This scheme is shown in Fig. 2.21c.

References

53

There could be many different ways to achieve autonomous power sharing— these are only a few approaches to do so. However, the fundamental principle that the controller should ensure sharing of burden among healthy converter stations following a contingency/disturbance remains universal. 4. Option IV: Weak AC grids surrounding the MTDC system might require ancillary service provisions following contingencies. Our particular focus is on the frequency support issue. An example scenario is that following the loss of generation in an AC grid with low inertia, the frequency nadir could be significant, which in turn can lead to under-frequency relay tripping. In an interconnected AC grid, frequency support from one AC area to the other comes naturally through the inertia of other machines and governor droop action. However, MTDC grids act as a “firewall” that blocks this support from one asynchronous AC area to the other. This problem was mentioned briefly in Sect. 1.6 of Chap. 1. To provide frequency support, a frequency droop control can be added to the droop controllers mentioned earlier. An example can be seen from Fig. 2.21d. This aspect will be dealt with in detail in Chap. 6. It should be noted that some converters in the MTDC grid will operate in islanded mode, for example, the ones connected to OWFs.

References 1. Abdel-Khalik, A.S., Abu-Elanien, A.E.B., Elserougi, A.A., Ahmed, S., Massoud, A.M.: A droop control design for multiterminal HVDC of offshore wind farms with three-wire bipolar transmission lines. IEEE Trans. Power Syst. 31(2), 1546–1556 (2016) 2. Abdelwahed, M.A., El-Saadany, E.F.: Power sharing control strategy of multiterminal VSCHVDC transmission systems utilizing adaptive voltage droop. IEEE Trans. Sustainable Energy 8(2), 605–615 (2017) 3. Ainsworth, J.D.: Proposed benchmark model for study of HVDC controls by simulator or digital computer. In: Proceedings of the CIGRE SC-14 Colloquium HVDC With Weak AC Systems, Maidstone (1985) 4. Arrillaga, J., Smith, B.D.: AC-DC power system analysis. Institution of Electrical Engineers, Stevenage (1998) 5. Arrillaga, J., Liu, Y.H., Watson, N.R.: Flexible Power Transmission: The HVDC Options. Wiley, Chichester (2007) 6. Atighechi, H., Chiniforoosh, S., Jatskevich, J., Davoudi, A., Martinez, J.A., Faruque, M.O., Sood, V., Saeedifard, M., Cano, J.M., Mahseredjian, J., Aliprantis, D.C., Strunz, K.: Dynamic average-value modeling of CIGRE HVDC benchmark system. IEEE Trans. Power Delivery 29(5), 2046–2054 (2014). https://doi.org/10.1109/TPWRD.2014.2340870 7. Beerten, J., Belmans, R.: Analysis of power sharing and voltage deviations in droop-controlled DC grids. IEEE Trans. Power Syst. 28(4), 4588–4597 (2013) 8. Beerten, J., D’Arco, S., Suul, J.A.: Frequency-dependent cable modelling for small-signal stability analysis of VSC-HVDC systems. IET Gener. Transm. Distrib. 10(6), 1370–1381 (2016) 9. Berggren, B., Majumder, R., Sao, C., Lindén, K.: Method and control device for controlling power flow within a DC power transmission network, Assignee: ABB, Filed: 06/30/2010, US8553437 B2, issued Oct 08, 2013

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10. Berggren, B., Lindén, K., Majumder, R.: DC grid control through the pilot voltage droop concept - methodology for establishing droop constants. IEEE Trans. Power Syst. 30(5), 2312– 2320 (2015) 11. Brandt, R.M., Annakkage, U.D., Brandt, D.P., Kshatriya, N.: Validation of a two-time step HVDC transient stability simulation model including detailed HVDC controls and DC line L/R dynamics. In: 2006 IEEE Power Engineering Society General Meeting, pp. 6 (2006). https:// doi.org/10.1109/PES.2006.1708868 12. Chaudhuri, N.R., Majumder, R., Chaudhuri, B., Pan, J.: Stability analysis of VSC MTDC grids connected to multimachine AC systems. IEEE Trans. Power Delivery 26(4), 2774–2784 (2011) 13. Chaudhuri, N.R., Chaudhuri, B., Majumder, R., Yazdani, A.: Multi-Terminal Direct-Current Grids: Modeling, Analysis, and Control. Wiley (2014) 14. Chen, X., Wang, L., Sun, H., Chen, Y.: Fuzzy logic based adaptive droop control in multiterminal HVDC for wind power integration. IEEE Trans. Energy Convers. 32(3), 1200– 1208 (2017) 15. Chung, S.K.: A phase tracking system for three phase utility interface inverters. IEEE Trans. on Power Electron. 15(3), 431–438 (2000) 16. Daryabak, M., Filizadeh, S., Jatskevich, J., Davoudi, A., Saeedifard, M., Sood, V.K., Martinez, J.A., Aliprantis, D., Cano, J., Mehrizi-Sani, A.: Modeling of LCC-HVDC systems using dynamic phasors. IEEE Trans. Power Delivery 29(4), 1989–1998 (2014). https://doi.org/10. 1109/TPWRD.2014.2308431 17. Dong, H., Xu, Z., Song, P., Tang, G., Xu, Q., Sun, L.: Optimized power redistribution of offshore wind farms integrated VSC-MTDC transmissions after onshore converter outage. IEEE Trans. Ind. Electron. 64(11), 8948–8958 (2017) 18. Eriksson, R., Beerten, J., Ghandhari, M., Belmans, R.: Optimizing DC voltage droop settings for AC/DC system interactions. IEEE Trans. Power Delivery 29(1), 362–369 (2014) 19. Gavriluta, C., Candela, J.I., Rocabert, J., Luna, A., Rodriguez, P.: Adaptive droop for control of multiterminal DC bus integrating energy storage. IEEE Trans. Power Delivery 30(1), 16–24 (2015) 20. Grund, C.E.: Functional model of two-terminal HVDC systems for transient and steady-state stability IEEE working group on dynamic performance and modeling of DC systems. IEEE Power Eng. Rev. PER-4(6), 36–37 (1984). https://doi.org/10.1109/MPER.1984.5526094 21. Hu, L.: Sequence impedance and equivalent circuit of HVDC systems. IEEE Trans. Power Syst. 13(2), 354–360 (1998). https://doi.org/10.1109/59.667351 22. Karawita, C., Annakkage, U.D.: Control block diagram representation of an HVDC system for sub-synchronous frequency interaction studies. In: 9th IET International Conference on AC and DC Power Transmission (ACDC 2010), pp. 1–5 (2010). https://doi.org/10.1049/cp.2010. 0998 23. Kimbark, E.: Direct Current Transmission, vol. 1. Wiley-Interscience, New York (1971). http:// books.google.com/books?id=eMMiAAAAMAAJ. Accessed Feb 2014 24. Kirakosyan, A., El-Saadany, E.F., Moursi, M.S.E., Acharya, S.S., Hosani, K.A.: Control approach for the multi-terminal HVDC system for the accurate power sharing. IEEE Trans. Power Syst. PP(99), 1–1 (2017) 25. Kumar, R., Leibfried, T.: Analytical modelling of HVDC transmission system converter using Matlab/Simulink. In: IEEE Systems Technical Conference on Industrial and Commercial Power 2005, pp. 140–146 (2005). https://doi.org/10.1109/ICPS.2005.1436367 26. Kundur, P.: Power System Stability and Control. The EPRI Power System Engineering Series. McGraw-Hill, New York (1994) 27. Kwon, D.H., Kim, Y.J., Moon, S.I.: Modeling and analysis of an LCC HVDC system using DC voltage control to improve transient response and short-term power transfer capability. IEEE Trans. Power Delivery 33(4), 1922–1933 (2018). https://doi.org/10.1109/TPWRD.2018. 2805905 28. Li, G., Du, Z., Shen, C., Yuan, Z., Wu, G.: Coordinated design of droop control in MTDC grid based on model predictive control. IEEE Trans. Power Syst. 33(3), 2816–2828 (2017)

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29. Marten, A.K., Sass, F., Westermann, D.: Continuous p-v-characteristic parameterization for multi-terminal HVDC systems. IEEE Trans. Power Delivery 32(4), 1665–1673 (2017) 30. Nicolau, V.: On PID controller design by combining pole placement technique with symmetrical optimum criterion. In: 2008 IEEE Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century, pp. 1–5 (2013) 31. Osauskas, C., Wood, A.: Small-signal dynamic modeling of HVDC systems. IEEE Trans. Power Delivery 18(1), 220–225 (2003). https://doi.org/10.1109/TPWRD.2002.803843 32. Padiyar, K.R.: HVDC power Transmission Systems. New Age International, New Delhi (2012) 33. Prieto-Araujo, E., Bianchi, F.D., Junyent-Ferre, A., Gomis-Bellmunt, O.: Methodology for droop control dynamic analysis of multiterminal VSC-HVDC grids for offshore wind farms. IEEE Trans. Power Delivery 26(4), 2476–2485 (2011) 34. Rouzbehi, K., Miranian, A., Luna, A., Rodriguez, P.: DC voltage control and power sharing in multiterminal DC grids based on optimal DC power flow and voltage-droop strategy. IEEE J. Emerg. Sel. Top. Power Electron. 2(4), 1171–1180 (2014) 35. Sauer, P.W., Pai, M.A.: Power system dynamics and stability. Prentice Hall, Upper Saddle River (1998) 36. Sharifabadi, K., Harnefors, L., Nee, H., Norrga, S., Teodorescu, R.: Design, Control, and Application of Modular Multilevel Converters for HVDC Transmission Systems. Wiley, Newark (2016) 37. Thams, F., Eriksson, R., Molinas, M.: Interaction of droop control structures and its inherent effect on the power transfer limits in multiterminal VSC-HVDC. IEEE Trans. Power Delivery 32(1), 182–192 (2017) 38. Toledo, P.F.D., Angquist, L., H.-p. Nee: Frequency domain model of an HVDC link with a line-commutated current-source converter. Part I: fixed overlap. IET Gener. Transm. Distrib. 3(8), 757–770 (2009). https://doi.org/10.1049/iet-gtd.2008.0587 39. Toledo, P.F.D., Angquist, L., H.-p. Nee: Frequency domain model of an HVDC link with a linecommutated current-source converter. Part II: varying overlap. IET Gener. Transm. Distrib. 3(8), 771–782 (2009). https://doi.org/10.1049/iet-gtd.2008.0588 40. Yang, X., Chen, C.: HVDC dynamic modelling for small signal analysis. IEE Proc. Gener. Transm. Distrib. 151(6), 740–746 (2004). https://doi.org/10.1049/ip-gtd:20040798 41. Yazdani, A., Iravani, R.: Voltage-Sourced Converters in Power Systems: Modeling, Control, and Applications. Wiley, Oxford (2010) 42. Zhang, M., Yuan, X.: Modeling of LCC HVDC system based on mass-damping-spring concept. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). https:// doi.org/10.1109/PESGM.2016.7741661 43. Zhao, X., Li, K.: Adaptive backstepping droop controller design for multi-terminal highvoltage direct current systems. IET Gener. Transm. Distrib. 9(10), 975–983 (2015)

Chapter 3

Modeling and Control of Inverter-Interfaced Wind Farms

Abstract Modeling and control of Type 3 and Type 4 wind turbines are introduced in this chapter. Both of these wind energy conversion systems are known as variable-speed wind turbines. The Type 3 version, also known as the doubly fed induction generator (DFIG)-based technology, consists of a wind turbine, induction generator, and two partially rated back-to-back voltage source converters (VSCs). The modeling of turbine and induction generator are first presented. The tiereactances of the VSCs are also integrated in the model. This is followed by the description of converter controls. Both grid-connected mode and isolated mode of controls are elaborated. Finally, the modeling and control of a Type 4 wind turbine based on permanent magnet synchronous generator and full-converter system are discussed.

3.1 Introduction Chapter 1 introduced different types of wind generation technologies. Among these technologies, Type 3 turbines based on doubly fed induction generators (DFIGs) (shown in Fig. 1.3c) are used in about 50% of variable speed wind farms while the rest are driven by Type 4 or full-converter technology [9]. In this chapter, the modeling and controls of DFIG and full-converter-based wind energy systems are presented.

3.2 DFIG-Based Wind Energy System Figure 1.3c showed a schematic of a wind energy system based on DFIG. A more detailed diagram with the overall control architecture is shown in Fig. 3.1. It can be seen in Fig. 3.1, this structure consists of a wind turbine, a gearbox connecting turbine and generator shaft, an induction generator, and a converter system. The stator of the machine is directly connected to the power grid (or isolated loads) and the rotor is connected to a 2-level VSC by means of slip rings and brushes. This VSC © Springer Nature Switzerland AG 2019 N. R. Chaudhuri, Integrating Wind Energy to Weak Power Grids using High Voltage Direct Current Technology, https://doi.org/10.1007/978-3-030-03409-2_3

57

58

3 Modeling and Control of Inverter-Interfaced Wind Farms

VW Gearbox

vs

Ps

PWF , QWF

Qs

DFIG

PGSC QGSC

Pt Wind turbine

R fr Turbine Pitch Control

RSC

L fr

vt

ir

R fg

GSC

vg L fg vdc

C

ig

DC Link

PWM Inner current Control loops

Inner current Control loops

Real power and Stator voltage control

DC voltage and reactive power control

Fig. 3.1 Main components of a DFIG-based wind turbine with its overall control architecture

is called the rotor-side convertor (RSC). The RSC is connected to another 2-level VSC via a common DC link. This VSC connected to the grid (or isolated load) is called grid-side convertor (GSC). The converters need only be rated to handle the rotor power, which is about 25% of the turbine rating. As shown in Fig. 3.1, the wind turbine is regulated by the pitch controller. The RSC and the GSC have a hierarchical control structure. The slower outer loops control real power, DC voltage, reactive power, and AC voltage. The faster inner loops control the converter AC currents. Finally, the inner loops generate the modulating signals, which leads to the generation of switching pulses using SPWM technique mentioned in Sect. 2.3.2 of Chap. 2. The rotor current ir is regulated by the RSC to control the electromagnetic torque and the field current, which in turn regulates the total power PW F and the stator output voltage vs . The GSC keeps the DC-link voltage vdc constant and regulates the reactive power QGSC as shown in Fig. 3.1. The DFIG can work either in subsynchronous or in supersynchronous operation modes due to the capability of the converters to handle bidirectional power flow. A wind farm consists of many wind turbines. In most of the literature, an aggregated model of the wind farm is considered where all wind turbines and DFIG are lumped together. This type of model loses the turbine-level granularity, but is suitable for studies where the response from individual turbines is not very important. Examples include planning studies of bulk power system. Depending on the focus of the study such as power quality, steady-state stability, dynamical stability, and protection, different modeling details can be considered.

3.2 DFIG-Based Wind Energy System

59

In dynamical studies of wind energy systems with DFIGs, the modeling is mostly done in a modular fashion. This approach allows the testing of different models for a particular component to determine which degree of complexity should be used. Modeling of different components of DFIG and their controls are described next.

3.2.1 Wind Turbine Model and Characteristics Operation of a wind turbine can be characterized by its mechanical power output as a function of wind speed, which is given by the following equation: Pm = 0.5ρAVw3 Cp (λ, β)

(3.1)

where ρ is the air mass density, A = π r 2 is the turbine swept area, r is the turbine radius, and Vw is the wind speed. Cp is a nonlinear function of λ and β referred to as the performance coefficient or power efficiency and is smaller than 0.59 [7]. It can assume different forms—an example from [1] is: 

 rCf rCf Cp = 0.5 − 0.022β − 2 e−0.255 λ λ

(3.2)

where β is the turbine pitch angle [6], λ is the tip-speed ratio, and Cf is blade design constant. λ is defined by: λ=

rωtur Vw

(3.3)

where ωtur is the rotational angular speed of turbine blades in mech. rad/s. Equations (3.1) and (3.3) show that the mechanical power of wind turbine can be controlled via β and ωtur . The pitch angle, β, is usually set based on the power output needed from wind farm. If electrical power is below rated value and the purpose is to generate the maximum available power, β is set to zero. It is set to 90◦ to stop power generation in cases like extreme wind conditions and is actively controlled in case the power generation needs to be regulated below the maximum power level. Figure 3.2 shows the variation of Cp with respect to λ for two different values of β. As it can be seen, the value of Cp increases by increasing λ, reaches a peak for an optimum value of λ, and then decreases. It is usually desirable for wind turbine systems to harness the maximum power possible from wind. For this purpose, pitch angle β should be set to zero. Moreover, λ should be adjusted to the optimum value, λopt , which maximizes Cp . Under this condition, based on (3.1) we can write:   0.5ρAr 3 Cp max 3 Pm max = (3.4) ωtur λ3opt

60

3 Modeling and Control of Inverter-Interfaced Wind Farms 0.45 0.4 0.35 0.3

Cp

0.25

β = 15

0.2

o

loci of maximum power point

0.15 0.1

β = 30

o

0.05 0 -0.05 0

2

4

6

8

10

12

λ Fig. 3.2 Typical performance-coefficient versus tip-speed ratio characteristic curve of a wind turbine

where Cp max is the maximum value  of Cp corresponding to λopt and β=0.  Defining Kopt =

0.5ρAr 3 Cp max λ3opt

, Eq. (3.4) can be written as:

3 Pm max = Kopt ωtur

(3.5)

Equation (3.5) indicates that the maximum attainable turbine power is proportional to the cube of turbine speed [5, 15]. We can also have a similar equation for torque as: 2 Tm max = Kopt ωtur

(3.6)

In a per-unitized form, we can write: 2 Tm max = Kopt ωr_dfg

(3.7)

where ωr_dfg is the generator rotor speed in p.u. These relations are applied to achieve maximum power point tracking (MPPT). As shown in Fig. 3.1, the generator is connected to the wind turbine via shafts and gearbox. Another set of equations are needed to model the mechanical interface between the turbine and the generator. This interface can be represented by sixmass, three-mass, two-mass, and lumped one-mass models [11]. In the one-mass or lumped model, all types of wind turbine drive-train components are lumped together and work as a single rotating mass. These components include the blades, hub, and

3.2 DFIG-Based Wind Energy System

61

shaft of wind turbine, gearbox, and the generator shaft and rotating mass. In this case the dynamic behavior can be described by: ω˙ r_dfg =

Tm − Te 2(Ht + Hg )

(3.8)

In (3.8), Ht and Hg are the inertia constants of the turbine and generator rotor, respectively, Tm is the input mechanical torque applied to the wind turbine rotor, and Te is the electromagnetic torque of the induction generator. The turbine-generator rotational dynamics can also be represented by a twomass model to include the torsional mode. In this case, the state equations of the generator-turbine mechanical side are shown below:  1 1  ω˙ r_dfg = −Csh ωel ωr_dfg +Ksh θtw + Csh ωel ωt − 2Hg 2Hg



 i + e i eqs qs ds ds



ω

(3.9)    1 1  −Csh ωel ωr_dfg − Ksh θtw + Csh ωel ωt + ω˙ t = Tm r, ρ, Vw , ωr_dfg 2Ht 2Ht (3.10)   θ˙tw = ωel ωt − ωr_dfg (3.11) Here, ωel is the base angular electrical speed, ω is the synchronous speed in p.u., θtw is the shaft angle of twist, Csh is the drive-train damping coefficient, Ksh is the shaft  /e are the q/d-axes stator stiffness, iqs / ids are the q/d-axes stator currents, eqs ds transient e.m.f.s, and ωt is the turbine rotor speed in p.u.

3.2.2 Doubly Fed Induction Generator Model DFIG can be considered as a traditional induction generator with a nonzero rotor voltage. As it can be seen in Fig. 3.1, this machine consists of rotor and stator windings, which are connected to back-to-back VSCs. The stator windings are connected to the grid, which imposes the stator frequency, f . Stator currents create a rotating magnetic field in the air gap. The rotational speed of this field, ωωel , is proportional to the grid frequency and is defined by: ωωel = 2πf

(3.12)

The induction machine operates with the rotor rotating at a different speed from the rotational speed of the magnetic field. This results in flow of current with a different frequency in rotor windings. This frequency is related to the stator synchronous frequency by: fr = sl f

(3.13)

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3 Modeling and Control of Inverter-Interfaced Wind Farms

where sl , referred to as machine slip, is defined by: sl =

ω − ωr_dfg ω

(3.14)

The modeling of DFIG is done in a synchronously rotating dq-reference frame [8] with the d-axis leading the q-axis per IEEE convention. For power system studies, different types of DFIG models have been proposed—readers are referred to [10] for a comprehensive list. Traditionally, the tie-reactors interfacing GSC and RSC, shown in Fig. 3.1, are not considered. Such a model is described next.

Model Neglecting Tie-Reactors The state-space equations of the DFIG with the usual notations [10] are given by: 





ωr_dfg eqs e Ls diqs  = −R1 iqs + ωLs ids + − ds − vqs + Kmrr vqr ωel dt ω ωTr 





eqs ωr_dfg eds Ls dids  = −R1 ids − ωLs iqs + + − vds + Kmrr vdr ωel dt ω ωTr 

(3.16)



eqs 1 deqs  = −R2 ids − + sl eds − Kmrr vdr ωel ω dt ωTr 

(3.17)



e 1 deds  = −R2 iqs − ds − sl eqs + Kmrr vdr ωel ω dt ωTr 

(3.15)

(3.18)



The variables eqs and eds are proportional to the rotor flux λqr and λdr , respectively, can be written as: 

eqs = Kmrr ωλdr 

eds = −Kmrr ωλqr

(3.19) (3.20)

Model with Tie-Reactors In this model, the tie-reactors of GSC and RSC, shown in Fig. 3.1, are included [18]. In this model the q-axis is aligned with the stator flux. The proposed model leads to certain modifications in Eqs. (3.15)–(3.18). The model is described as follows:

3.2 DFIG-Based Wind Energy System

1 ωel



2 Lf r Kmrr Ls + a 



63

  diqs Kmrr Lm iqs = − Rs + dt aTr   2 sLf r Kmrr   + ω Ls + ids + (1 − sl ) eqs a

1  Kmrr vqt eds − vqs + ωaTr a     2 2 Lf r Kmrr sl Lf r Kmrr dids 1   = − ω Ls + Ls + iqs ωel a dt a   Kmrr Lm 1  ids + − Rs + e aTr ωaTr qs −

(3.21)

(3.22)

Kmrr vdt a     2 ω 2 R deqs Lf r Kmrr Lf r Kmrr r_dfg s =− +1 iqs + R2 − ids   dt aLs aLs   2 Lf r Kmrr 1   eqs + − + sl eds  aTr ω aLs 

+ (1 − sl ) eds − vds +

1 ωel ω



2 Lf r Kmrr  aLs

2 Lf r Kmrr Kmrr vdt vds −  a aLs (3.23)     2 R 2 ω deds Lf r Kmrr L K s f r mrr r_dfg = − R2 − +1 ids iqs −   dt aLs aLs   2 Lf r Kmrr 1   e − + sl eqs −  aTr ω ds aLs

−

1 ωel ω



2 Lf r Kmrr  aLs

2 Lf r Kmrr Kmrr vqt vqs +  a aLs    dims ωel  Rs iqs + vqs =− dt Lm

+

(3.24) (3.25)

    Lss iqr = eqs Xm − Kmrr iqs = ims − iqs Lm

(3.26)

    Lss idr = eds Xm − Kmrr ids = − ids Lm

(3.27)

64

3 Modeling and Control of Inverter-Interfaced Wind Farms

     λqs = − eds ω + Ls iqs

(3.28)

     λds = eqs ω + Ls ids

(3.29)



where Lss = Ls + Lm ,, Lrr = Lr + Lm , Ls = Lss − (L2m /Lrr ), Tr = Lrr /(Rr +  Rf r ), Kmrr = Lm /Lrr , , σ = Ls /Lss , a = 1 + (Lf r /Lrr ), R1 = Rs + R2 , and 2 R2 = Kmrr (Rr + Rf r )/a. Here, Lm is mutual inductance, ims is magnetizing current, Rfg /Lfg are GSC filter resistance/inductance, Rf r /Lf r are RSC filter resistance/inductance, Rr /Rs are rotor/stator resistance, Lr /Ls are rotor/stator leakage inductances, vqs /vds are q/d-axis stator terminal voltages, vqt /vdt are q/d-axis RSC terminal voltages, iqr / idr are q/d-axis rotor currents, and λqs /λds are q/d-axis stator flux linkages.

3.2.3 GSC and DC Bus Model The GSC tie-rector dynamics and the DC bus dynamics is modeled in the rotating reference frame where the q-axis is aligned with vs :  3  vdt idr + vqt iqr + vdg idg + vqg iqg C       Rfg + Kpg Kig Kpg ∗ iqg + xg1 + i =− Lfg Lfg Lfg qg 2 v˙dc =−

.

iqg .

idg



Rfg + Kpg =− Lfg



 idg +

Kig Lfg



 xg2 −

Kpg Lfg



2Q∗gsc 3vqs

(3.30)

(3.31)  (3.32)

where iqg , vqg / idg , vdg are q/d-axis GSC current, terminal voltages, C is the DC bus capacitor, Kpg and Kig are the PI controller gains, and xg1 and xg2 are the corresponding dynamic states of the GSC current control loop. The GSC controls will be described later in detail.

3.2.4 Turbine Pitch Control Usually, a mechanism is needed to control the amount of wind energy captured by the turbine. This is achieved via the pitch control mechanism. This mechanism is also useful in protecting the turbine during extreme wind conditions. High wind speeds or a reduction in the load demand in an isolated wind farm can result in the turbine speeding up. As shown in Fig. 3.3, in the pitch angle control mechanism, the rotational speed of the turbine is continuously measured and compared to a pre-set

3.3 Control Strategy of DFIGs Fig. 3.3 Block diagram of turbine pitch control (active only when ωr_df g crosses a threshold)

65

K pp

r _ dfg

Kip s

r _ dfg

threshold level. The error is fed to a PI controller which generates the pitch angle, β. With this process in use, an increase in the rotational speed beyond the threshold level causes β to increase, which results in less wind power input and hence, a decrease in rotational speed.

3.3 Control Strategy of DFIGs Common control methods for DFIGs can be broadly categorized into two modes of their operation depending on their connectivity to power grid and isolated loads. As mentioned earlier, two back-to-back VSCs are used for controlling DFIG, which are switched based on SPWM described in Sect. 2.3.2 of Chap. 2. These include the rotor-side converter (RSC), connected to induction machine rotor, and the grid-side converter (GSC), connected to induction machine stator. The generator is controlled via these converters, which is based on decoupled current control strategy. As mentioned in Chap. 2, in this commonly used strategy, rotor and stator currents of the induction machine are converted to a rotating d − q frame using transformations described in Appendix A. Each of these current components can be used to control variables including AC and DC-link voltages, and real and reactive powers. These control schemes are discussed in detail in the following sections.

3.3.1 Grid-Connected Mode of Control In grid-connected mode of control, the DFIG-based wind farm is assumed to be connected to a power grid that can provide a source of voltage and frequency. In this condition, it is usually desirable to harness the maximum available power from wind. Also, the AC voltage at the terminal of the DFIG needs to be regulated. RSC control structure is designed to achieve these objectives. On the other hand, GSC control aims to regulate DFIG’s DC-bus voltage and the reactive power [13]. 3.3.1.1

RSC Control

Figure 3.4 shows the control scheme of a grid-connected DFIG-based wind turbine. In this mode of operation, RSC is responsible for AC voltage control at PCC and MPPT. Standard vector control approach was considered for RSC controls [13] as shown in Fig. 3.5. The RSC control consists of two decoupled loops with cascaded

66

3 Modeling and Control of Inverter-Interfaced Wind Farms

PI controllers in each loop. The slower outer loops regulate electrical torque and ∗ and i ∗ for the faster inner current reactive power, and produces the set points idr qr control loops. As shown in Fig. 3.4, the q-axis rotor current iqr can be used for AC voltage control, and d-axis rotor current idr can be used for MPPT. Since the stator is connected to grid and the effect of stator resistance is not significant, stator magnetizing current, ims , can be considered to be constant. The q-axis of the reference frame is aligned with the stator flux vector position. This will give us the angle θo as shown in Fig. 3.4. For this purpose, the stator flux is estimated measuring the stator voltage vt and the stator current is , and the q-axis is locked with the estimated flux vector using a PLL. The PLL model was described in Sect. 2.4.1.2 in Chap. 2. The following relationship is used for flux estimation in a stationary α − β reference frame, which can later be converted to a rotating d-q frame (see Appendix A). λαs =



(vαs − Rs iαs )dt , λβs =



(vβs − Rs iβs )dt

(3.33)

An encoder measures the rotor angle of DFIG, θr . Subtracting θr from θo gives the slip angle θslip (see Fig. 3.4). For MPPT and the stator terminal voltage control of RSC, the stator flux is aligned with the q-axis. With the modified reference frame, the expressions for the RSC terminal voltages vdt and vqt can be written as: L2

vdt = −(Rr + Rf r )idr − (σ Lrr + Lf r ) didtdr − sl ω(σ Lrr + Lf r )iqr − sl ω Lssm ims

vqt = −(Rr + Rf r )iqr − (σ Lrr + Lf r )

diqr dt

+ sl ω(σ Lrr + Lf r )idr

(3.34) Equations (3.34) constitute the “Plant” of the current controller, which is highlighted in Fig. 3.5. Based upon the structure of this plant, appropriate feed-forward signals L2

sl ω(σ Lrr + Lf r )idr and sl ω(σ Lrr + Lf r )idr + Lssm ims are used to reject measurable disturbances and decouple the “d” and “q” channels of the current controller. The RSC terminal voltages commanded by the current controller are given by: ∗    ∗ =K x vdt ir rr2 + Kpr idr − idr − sl ω{ σ Lrr + Lf r iqr +   ∗ =K x ∗ vqt ir rr1 + Kpr iqr − iqr + sl ω σ Lrr + Lf r idr

L2m Lss ims }

(3.35)

Here, the dynamic states of the PI controllers are given by:    ∗   V  − |vs | − iqr dt + K i ms vc s    Lss Kopt 2 = ωr_dfg − idr dt L2 i

xrr1 = xrr2

(3.36)

m ms

∗ for RSC is determined from As shown in Fig. 3.4, the d-axis reference current idr the torque reference through the MPPT algorithm as follows:

Tm∗ =

L2m ∗ Lss ims idr

2 = Kopt ωr_dfg

(3.37)

r _ dfg

vs

-

ims

2

L2mims

Lss K opt

K vc

i

i

-

-

iqr idr

* dr

* qr

DFIG

Wind turbine

s

sl

Lrr

L fr

sl

Lrr

o

L fr iqr

ir

R fr

-

L2m ims Lss

L fr idr

vt RSC

PWM

1

* qg

* dg

v

v

ˆ

C

vdc DC Link

I dc

I ext

Qg

s li p

v

* dt

* qt

v

Qs

Ps

Fig. 3.4 Grid-connected DFIG-based wind farm control scheme

is

vs

d dt

vs*

r

encoder

VW

r _ dfg

vg

L fg idg

L fg iqg

GSC

is

vqs

-

Kip

ig

R fg L fg

iWF

AC grid

idg iqg

i

* dg

* iqg

-

K pp

0 Ploss

3 2

Pdc

K v (s )

* Qgsc

PWF , QWF

-

PGSC QGSC -

r _ d fg

vdc

* vdc

0

-

2

2

vds vqs

PLL2

vs PCC

3.3 Control Strategy of DFIGs 67

68

3 Modeling and Control of Inverter-Interfaced Wind Farms

sl

iqr

iqr*

Lrr

L fr idr

K pr

1 s

vqt*

-

xrr1

Rr R fr s

1 s

Lrr

xrr 2

Lrr L fr

Lrr L fr

vdc 2

2 vdc

iqr

1

Lrr L fr

K pr

-

sl

vqt

mdt

K ir

idr idr*

Plant

1 -

K ir

L fr iqr

* dt

v

mqt

vdt

Rr R fr s

Lrr L fr

idr

L2m ims Lss

Fig. 3.5 Inner current control loop of RSC with the “Plant.” The stator flux is aligned with q-axis ∗ ensures that the magnetizing current i The q-axis current reference iqr ms drawn by the induction machine is supplied through the RSC while injecting/absorbing appropriatereactive power depending on the difference between actual (|Vs |) and  reference (Vs∗ ) voltage magnitude, which is controlled by the voltage droop constant Kvc (Fig. 3.4).

3.3.1.2

GSC Control

The GSC is also regulated based on vector control strategy where the q-axis of the rotating frame is aligned with the voltage vs . Figure 3.4 shows GSC control scheme for a grid-connected DFIG. The position of the voltage vector is estimated using a PLL indicated as PLL2. The objective is to maintain a constant DC-link voltage between RSC and GSC. The q-channel of GSC current is used for this purpose while the d-channel is utilized for reactive power control. Assuming that the stator supplies all of demanded reactive power, Q∗gsc is usually set to zero as shown in Fig. 3.4. In the modified reference frame, where the q-axis is aligned with the stator terminal voltage, the expressions for the GSC terminal voltages vdg and vqg can be written as follows: vdg = Rfg idg + Lfg

didg − ωLfg iqg + vds dt

(3.38)

vqg = Rfg iqg + Lfg

diqg + ωLfg idg + vqs dt

(3.39)

As shown in Fig. 3.6, these equations determine the “Plant” of the inner current control loops. Based upon the structure of this plant, appropriate feed-forward

3.3 Control Strategy of DFIGs

iqg * qg

i

K pg 1 s

xg1

+

* vqg

+

1 s

xg 2

+ v

K ig

-

vdg

mdg

sL fg

L fg

+ * dg

iqg

1 R fg

L fg

vdc 2

L fg iqg

K pg

Plant

-

L fg idg 2 vdc

-

vqg

mqg

-

K ig

idg i

vsd

vsq

-

* dg

69

-

1 R fg

idg

sL fg

vsq

vsd

Fig. 3.6 Inner current control loop of GSC with the “Plant.” The stator terminal voltage is aligned with q-axis Fig. 3.7 GSC DC voltage controller and plant

vdc

2

2

_

2 Cs

K v ( s)

vdc

Plant

signals are used in the inner current control loops for measurable disturbance rejection and decoupling of the d and the q channels. The terminal voltage references computed by the inner current control loops are given by:   ∗ ∗ = Kig xg2 + Kpg iqg − iqg − ωLfg idg + vqs vqg   2Q∗gsc ∗ = Kig xg1 + Kpg − − idg + ωLfg iqg + vds vdg 3vqs

(3.40)

(3.41)

The dynamic states of the GSC current control loops as shown in Fig. 3.6 can be written as:    ∗ (3.42) iqg − iqg dt xg1 =

xg2

   2Q∗gsc − = − idg dt 3vqs

(3.43)

∗ is calculated from the reactive power reference as: i ∗ = For the outer loops, idg dg

2Q∗

∗ is determined by the DC-link voltage controller. . On the other hand, iqg − 3vGSC sd Figure 3.7 shows the plant and the controller after the disturbance rejection of

70

3 Modeling and Control of Inverter-Interfaced Wind Farms

the DC voltage control loop as shown in Fig. 3.4. As described in Sect. 2.4.1.2 of Chap. 2, the inner current control loop is designed to achieve a first-order response with time constant τi . The DC voltage controller Kv (s) is designed based on the symmetrical optimum criterion given in [12].

3.3.2 Isolated Mode of Control In this mode the wind farm is connected to isolated loads. An example of this can be a microgrid in a remote location, which has no connectivity with the main grid. In this case, in the absence of any grid support, the voltage magnitude and frequency at the PCC depend on the wind farm. Unlike the grid-connected mode, in this case MPPT cannot be followed due to the fact that the generated power by the wind farm should match with the load demand. The GSC performs the same DC voltage and reactive power control as in the previous mode, while the RSC is responsible for building up and controlling the AC voltage at the PCC as described in the next section.

3.3.2.1

RSC Control

The DFIG should generate a constant voltage and frequency at its terminal. Since it is not connected to power grid, its flux is no longer determined by the grid voltage and should be regulated by rotor excitation current. A common control strategy for a DFIG-based wind farm feeding an isolated load was proposed in [14] and is usually referred to as the direct flux control approach. The q-axis of the rotating reference frame is aligned with stator flux vector as in grid-connected mode. Thus the d-axis stator flux, λds , is equal to zero. Similar relationships hold for voltages, currents, and fluxes as described in the model with the tie-reactors. Figure 3.8 shows the control scheme of a DFIG feeding an isolated load. As shown in Fig. 3.8, using the plant equations described under grid-connected mode and applying appropriate feed-forward terms, two PI controllers in the inner ∗ and v ∗ for RSC. current control loop are used to generate the commands vdt qt From (3.27) the d-axis reference current is given by the following relationship: Lss ids Lm

(3.44)

dims 1 + σs + ims = iqr + vqs dt Rs

(3.45)

∗ idr =−

From Eqs. (3.25) and (3.26) we have: 

where σs =

Lss −Lm Lm

Lss Rs



vs

ids

ims

im* s

Rs

L ss / L m

1

s

vqs

s

i

-

-

iqr idr

* dr

iqr* sl

o

L fr

sl

Fig. 3.8 Isolated DFIG-based wind farm control scheme

vs*

r

VW

r _ dfg

Lrr

ir

-

vdc

I ext

Qg

s li p

v

L2m ims Lss * dt

vqt*

L fr idr

L fr iqr

Lrr

R fr vt

Qs

Ps

C

v

s

* qg

vd*g

I dc

L fg idg

L fg iqg

vds

vqs

-

Kip

vg

is

2

ig

R fg L fg

idg iqg

1 s

* iqg

-

K pp

el

Ploss

Pdc

K v (s )

3 Vd 2

* Qgsc

-

-

r _ d fg

vdc

* vdc

0

-

vs

s

2

2

3.3 Control Strategy of DFIGs 71

72

3 Modeling and Control of Inverter-Interfaced Wind Farms

Equation (3.45) shows that iqr can be used to control ims . In Fig. 3.8, a PI s controller is shown, which controls ims and uses 1+σ Rs vds as a feed-forward term. The outer loop of this controller maintains a desired terminal voltage magnitude. As shown in Fig. 3.8, the stator flux angle θo is derived directly by integrating demanded angular frequency ωel = 2π 60rad/s. Therefore, the angle needed for the decoupled current controls in the RSC is derived from:  (3.46) θslip = ωel dt − θr where θr is the rotor angle measured by an encoder as shown in Fig. 3.8. The inner current control loops are exactly the same as in grid-connected mode.

3.3.2.2

GSC Control

The control structure of GSC in DFIG’s isolated mode of control uses a rotating frame in which the q-axis is oriented along the terminal voltage vector position and is similar to the grid-connected mode, which was described in Sect. 3.3.1.2. One of the complications in GSC-side control in direct flux control mode arises from the challenge of determining the stator terminal voltage vector position. In this mode, aligning the voltage vector using a PLL is not recommended due to the presence of harmonics when there is no grid voltage support. As proposed in [14], the angle θs that approximately determines the position of the terminal voltage vector Vs with respect to a stationary reference frame could be derived from: θs = θ0 +

π 2

(3.47)

where θ0 is the angle obtained from the free-running integrator described in RSC control. The inner and the outer loops function similar to the grid-connected mode.

3.4 Full-Converter-Based Wind Energy System Type 4 wind turbine generators (WTGs) are variable speed wind turbines with synchronous or asynchronous generators connected to the grid through a full-scale power converter. There are two generic models of Type 4 WTGs, Type 4A where the aerodynamic and mechanical parts are neglected and Type 4B, which includes a 2-mass mechanical model assuming constant aerodynamic torque. Generic models are simplified low-order representations of WTGs. The generic model is comprised of a combination of three different models, which are model representing generator and converter dynamics, model for wind aerodynamics and turbine, and model representing real and reactive power control [2]. In the absence of standard guidelines

3.5 PMSG-Based Direct-Drive WTG Model

73

for development of these generic models, different approaches have been used in adopting generic model of type 4 WTG [3]. These models are suitable for studying the dynamic stability of the system. Reference [3] uses the basic structure of generic type 4 wind turbine model proposed by Western Electricity Coordinating Council (WECC) and proposes modifications, which makes it appropriate for frequency regulation studies by including pitch control and addition of available power lookup to determine mechanical power in aerodynamic model. Reference [19] discusses the generic model of Type 4 WTG considering a point-to-point offshore HVDC transmission. It discusses issues concerning coordinated HVDC and wind farm control and the need of a communication link, and presents two control schemes for such system configuration. It mostly presents block diagrams for modeling and control in simulation software. In [16], authors propose an EMT-type model for full converter-based externally excited synchronous generator. Reference [17] proposes application of a neutral point diode clamped (NPC) converter for a gearless variable speed synchronous generator wind energy system. Considering the higher voltage and current capacities of NPCs, this can be useful for modern larger turbines. The schematic of a Type 4 wind energy system was illustrated in Fig. 1.3d. The used machine could be wound-rotor synchronous generator with high number of poles, permanent magnet synchronous generator, or squirrel cage induction generator. The stator is connected to grid via a converter system which adjusts the frequency of stator circuit excitation to allow a variable rotor speed. In this type of system, the gearbox can be omitted if a high number of poles is used so that the machine spins at the slow turbine speed and generates an electrical frequency lower than that of the grid. Such direct-drive wind generating units are widely used for OWFs. Following is the modeling and control of a Type 4 WTG based on permanent magnet synchronous generator (PMSG) [4].

3.5 PMSG-Based Direct-Drive WTG Model 3.5.1 Generator-Side Converter Control The stator voltage of the PMSG in rotating d-q reference frame can be described with the following equations [4]: vsd = −Rs isd − Ls didtsd + Ls ωr isq di vsq = −Rs isq − Ls dtsq + Ls ωr isq + ωr ψ

(3.48)

where Rs and Ls are generator resistance and inductance, ωr is the generator speed, and ψ is the permanent magnet flux. Using (3.48) one can control the d and q current channels by vsd and vsq . The electromagnetic torque of the machine can be regulated using isq with the following equation: Te =

3 pψisq 2

(3.49)

74

3 Modeling and Control of Inverter-Interfaced Wind Farms

R

vdc d dt

L

Grid

DC Link

PWM

i sd*

PI

-

v sd

i sd -

PI

i sq* -

PI

v sq -

i sq

Fig. 3.9 Generator-side converter control scheme

where p is the number of machine’s pole pairs. Figure 3.9 shows the block diagram of the generator side converter. As it can be seen from Fig. 3.9 two PI controllers can be used to control the d and q channel currents with proper feed-forwards to ∗ is used to control torque, i ∗ can be set to improve dynamic response. While isq sd zero to minimize resistive losses. Chinchilla et al. [4] proposes that d-axis reference current can be used to minimize core losses by minimizing stator flux. The following equation describes stator flux: ψs =

(Ls isq )2 + (ψ + Ls isd )2

(3.50)

∗ can be found via: An optimum value for isd

min(Σploss ) = min(pf e + pcu + pmech + prect )

(3.51)

The derived optimum value is tabulated as a function of generator speed indicated as f (ωr _meas) in Fig. 3.9.

3.5.2 Grid-Side Converter Control The grid-side converter is also controlled based on decoupled vector concept. Figure 3.10 shows the control structure of this converter. For this converter q and d

3.5 PMSG-Based Direct-Drive WTG Model

75

R

vdc

L

Grid

DC Link

PWM

V

* dc

-

PI

i d* -

id

V dc

Q

vd

PI

i q*

*

-

3 vd 2

vq

PI

-

iq

Fig. 3.10 Grid-side converter control scheme

channels can be used to control the reactive power and DC-link voltage, respectively. The grid voltage components can be expressed by Chinchilla et al. [4]: vd = vid − Rid − L didtd + ωLiq di

vq = viq − Riq − L dtq − ωLid

(3.52)

where vid and viq are converter voltage components, and R and L are the grid resistance and inductance, respectively. Having the d axis of the rotating frame locked to the grid voltage vector, we have: P = 32 vd id Q = 32 vd iq

(3.53)

As it can be seen from (3.53) one can use current components to control real and reactive power. The active power control for grid-side converter is used to regulate DC-link voltage indirectly (see Fig. 3.10).

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3 Modeling and Control of Inverter-Interfaced Wind Farms

References 1. Anderson, P.M., Bose, A.: Stability simulation of wind turbine systems. IEEE Trans. Power Apparatus Syst. PAS-102(12), 3791–3795 (1983) 2. Aziz, A., Amanullah, M., Vinayagam, A., Stojcevski, A.: Modelling and comparison of generic type 4 WTG with EMT type 4 WTG model. In: 2015 Annual IEEE India Conference (INDICON), pp. 1–6 (2015). https://doi.org/10.1109/INDICON.2015.7443139 3. Aziz, A., Amanullah, M.T.O., Stojcevski, A.: Modelling and analysis of type 4 wind turbine generator system for utilization in frequency regulation studies. In: 2015 Australasian Universities Power Engineering Conference (AUPEC), pp. 1–6 (2015). https://doi.org/10.1109/ AUPEC.2015.7324817 4. Chinchilla, M., Arnaltes, S., Burgos, J.C.: Control of permanent-magnet generators applied to variable-speed wind-energy systems connected to the grid. IEEE Trans. Energy Convers. 21(1), 130–135 (2006). https://doi.org/10.1109/TEC.2005.853735 5. Datta, R., Ranganathan, V.T.: Variable-speed wind power generation using doubly fed wound rotor induction machine-a comparison with alternative schemes. IEEE Trans. Energy Convers. 17(3), 414–421 (2002) 6. Heier, S.: Grid Integration of Wind Energy Conversion Systems. Wiley, Chichester (2006) 7. Kazmierkowski, M.P., Krishnan, R., Blaabjerg, F.: Control in Power Electronics, Selected Problems. Academic press, Amsterdam (2002) 8. Kundur, P.: Power System Stability and Control. The EPRI Power System Engineering Series. McGraw-Hill, New York (1994) 9. Liserre, M., Cardenas, R., Molinas, M., Rodriguez, J.: Overview of multi-MW wind turbines and wind parks. IEEE Trans. Ind. Electron. 58(4), 1081–1095 (2011) 10. Mei, F.: Small-signal modelling and analysis of doubly-fed induction generators in wind power applications. Ph.D. thesis, Imperial College London, 2008 11. Muyeen, S.M., Tamura, J., Murata, T.: Stability Augmentation of a Grid-Connected Wind Farm. Springer, Dordrecht (2009) 12. Nicolau, V.: On PID Controller Design by Combining Pole Placement Technique with Symmetrical Optimum Criterion. Mathematical Problems in Engineering. Hindawi Publishing Corporation, Cairo, pp. 1–8 (2013) 13. Pena, R., Clare, J.C., Asher, G.M.: Doubly fed induction generator using back-to-back PWM converters and its application to variable-speed wind-energy generation. IEE Proc. Electr. Power Appl. 143(3), 231–241 (1996) 14. Pena, R., Clare, J.C., Asher, G.M.: A doubly fed induction generator using back-to-back PWM converters supplying an isolated load from a variable speed wind turbine. IEE Proc. Electr. Power Appl. 143(5), 380–387 (1996) 15. Song, Y.D., Dhinakaran, B.: Nonlinear variable speed control of wind turbines. In: Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328), vol. 1, pp. 814–819 (1999) 16. Trevisan, A.S., El-Deib, A., Gagnon, R., Mahseredjian, J., Fecteau, M.: Field validated generic EMT-type model of a full converter wind turbine based on a gearless externally excited synchronous generator. IEEE Trans. Power Delivery pp. 1–1 (2018). https://doi.org/10.1109/ TPWRD.2018.2850848 17. Yazdani, A., Iravani, R.: A neutral-point clamped converter system for direct-drive variablespeed wind power unit. IEEE Trans. Energy Convers. 21(2), 596–607 (2006). https://doi.org/ 10.1109/TEC.2005.860392 18. Yogarathinam, A., Kaur, J., Chaudhuri, N.R.: Impact of inertia and effective short circuit ratio on control of frequency in weak grids interfacing LCC-HVDC and DFIG-based wind farms. IEEE Trans. Power Delivery 32(4), 2040–2051 (2017) 19. Zeni, L., Morgans, I., Hansen, A.D., Serensen, P.E., Kjœr, P.C.: Generic models of wind turbine generators for advanced applications in a VSC-based offshore HVDC network. In: 10th IET International Conference on AC and DC Power Transmission (ACDC 2012), pp. 1–6 (2012). https://doi.org/10.1049/cp.2012.1980

Chapter 4

Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC Transmission

Abstract This chapter presents three case studies relating challenges of interfacing doubly fed induction generator (DFIG)-based onshore wind farms in weak AC grids with line-commutated converter (LCC) HVDC. The first study focuses on modeling and analysis of the impact of inertia and effective short circuit ratio on control of frequency in such weak grids. In the second study, coupling between frequency dynamics of the AC systems on both inverter and rectifier side of LCC-HVDC with the rectifier station operating in frequency control is studied, along with the presence of large DFIG-based wind farms on the weak rectifier-side grid. The third study illustrates the effectiveness of converting conventional generators to synchronous condensers to improve frequency dynamics in weak grid systems following loss of infeed from a wind farm. The effectiveness of secondary frequency control through LCC HVDC is also investigated.

4.1 Introduction LCC HVDC technology is more suitable for transmitting power from very large wind farms over long distances to load centers. As of today, VSC technology cannot match the power rating and efficiency of LCC. For example, in the USA, the onshore wind energy potential is mostly concentrated in the Mid-West region, which is shown in Fig. 1.1. This region is far from the load centers in the east and west, requiring long distance transmission of power. Both the US Department of Energy (DoE) report [28] and the Joint Coordinated System Plan (JCSP) report [18] preferred LCC HVDC systems were proposed to transmit power from these wind farms to the load centers in the east. A recent example is the Rock Island Clean Line project [4] that proposes to deliver 3500 MW of wind power from North-East Iowa to Illinois and other states to the east using a 500-mile overhead Line-Commutated Converter (LCC)-based HVDC system. VSC technology was not chosen due to the high power rating of the wind farms. The plan is to connect the rectifier-side wind farms to two 345-kV substations in the local AC grid [10]. The closest substation is the OBRIEN substation located 6 km away. The other one is substation RAUN situated 97 km away from the rectifier station. © Springer Nature Switzerland AG 2019 N. R. Chaudhuri, Integrating Wind Energy to Weak Power Grids using High Voltage Direct Current Technology, https://doi.org/10.1007/978-3-030-03409-2_4

77

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4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . .

This implies that local AC grid in the rectifier-end of LCC-HVDC is “weak” in nature. Due to the remote geographical location of wind resources, this is becoming increasingly commonplace around the globe. There are two measures to quantify the “weakness” of a grid—Effective Short Circuit Ratio (ESCR), and Effective DC Inertia Constant (Hdc ). These measures were described in Sect. 1.6 Chap. 1. Typical weak grids have ESCR less than 2.5 and Hdc less than 2.0 [9]. For the Rock Island Clean Line project, the remote location of substations leads to the reduction of ESCR. On the other hand, relatively lesser number of synchronous generators in the local grid can lead to a low inertia system. This is becoming more serious as the conventional (coal, nuclear, etc.) generating plants are getting displaced by inverterinterfaced wind generators. For example, between 2002 and 2016, 531 coal-fired plants were shut down in the United States, which represents approximately 59 GW of generating capacity [29]. This chapter focuses on three case studies relating different challenges of integrating wind farms interfaced with weak AC grids in the rectifier-side of LCC HVDC transmission systems. 1. Control of frequency in weak grids interfacing LCC-HVDC and onshore DFIGbased wind farms is challenging. In the first study, the focus will be on the development of fundamental understanding of the impact of Hdc and ESCR on control of frequency in such weak systems. To that end, a comprehensive modeling and stability analysis framework of a weak grid that interfaces an LCCHVDC station and a DFIG-based wind farm will be presented. However, the inverter-side AC grid is modeled as an ideal voltage source. Therefore, the effects of coupling between the rectifier-side and the inverter-side frequency dynamics cannot be studied using such models. This is the subject matter of the next study. 2. In the second study, the coupling between frequency dynamics of the AC systems on both inverter and rectifier side of LCC-HVDC with the rectifier station operating in frequency control will be presented, along with the presence of large DFIG-based wind farms on the weak rectifier-side grid. To develop a deeper understanding of the frequency dynamics, a simplified four-state nonlinear model is presented, which reveals a strong coupling between frequency and AC voltage at the HVDC rectifier terminal. A firing angle correction strategy is presented to decouple frequency–voltage interactions. This improves the frequency dynamics on the rectifier side. One issue however is that the rectifier-side AC system is modeled by a single generator and a single wind farm, which limits the scope of this study. The next case study overcomes this limitation. 3. In the final study, a proposal of using phased-out coal-fired generation as synchronous condensers (SC)1 in a power system with weak interconnection to large DFIG-based wind farms exporting energy to remote load centers through the LCC-HVDC transmission is investigated. The frequency nadir (i.e., the minimum post-contingency frequency) and the rate of change of frequency

1 Synchronous

condensers are synchronous motors without a mechanical load.

4.2 Case Study I: Impact of Inertia and Effective Short Circuit Ratio on. . .

79

(RoCoF) in such systems following disturbances like loss of generation due to a single-point failure are analyzed. LCC-HVDC rectifier is used for secondary frequency control in the weak AC system. At the beginning of each case study, we will elaborate on the relevant literature. This will be followed by mathematical modeling, simulation studies, analysis, and concluding remarks leading to the logical progression towards the next topic.

4.2 Case Study I: Impact of Inertia and Effective Short Circuit Ratio on Frequency Dynamics Literature in the area of wind energy interconnection using HVDC can be broadly divided into two groups—offshore wind farm (OWF) integration and onshore wind farm integration. A lot of work has been done on the OWFs connected to LCCHVDC delivery systems [2, 3, 14, 23, 31–34, 38, 39]. References [32–34] presented control coordination of OWFs and LCC-HVDC system transporting wind energy to the onshore grid. Here, the DFIG operates in isolated control mode, which was described in Sect. 3.3.2 of Chap. 3. Li et al. in [31] presented the damping enhancement and mitigation of the power fluctuations of a DFIG-based OWF. The DFIG operates in grid-connected mode and the LCC-HVDC rectifier in current control mode—see Chaps. 3 and 2, respectively. The DFIG maintains the AC terminal voltage instead of regulating the flux. This is challenging in absence of voltage support at the PCC. Also, in absence of a separate source/sink of power, it is difficult to coordinate the current control in LCC HVDC with the power tracking of DFIG. Bozhko et al. [2, 3] and Zhou et al. [38, 39] introduced a STATCOM in the offshore platform for providing voltage support at the PCC. DFIG-based wind farms and their controls are represented functionally using controllable current sources. The inverter station of LCC HVDC was also modeled simply by a DC voltage source [2, 3]. Although these assumptions simplify the model to a great extent, it cannot simulate interaction of DFIG’s control loops with the rest of the system and limits the scope of case studies involving disturbance in the HVDC inverter-side. Reference [14] proposed operation of LCC-HVDC rectifier in frequency control mode. The authors presented an analytical formulation, which helped design the LCC-HVDC frequency controller. To achieve analytical solution, certain simplifying assumptions were made: converter commutating reactance is neglected and the inverter-side is represented by a DC voltage source. There are proposals of using hybrid HVDC systems to send power from OWFs to the onshore grid where the offshore converter is LCC and the onshore station employs a selfcommutated current source converter [38, 39]. As described in Sect. 1.3.2 of Chap. 1, the LCC HVDC demands significant real estate due to the presence of capacitor banks and filters. Although inclusion of a STATCOM as proposed in [38, 39] improves the system operation, it needs more real estate. In the offshore environment, space comes at a premium since building

80

4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . .

platforms is quite expensive. As a result, LCC-HVDC technology is never used in OWF installations. In contrast, VSC HVDC requires significantly low footprint and is preferred for OWFs. Literature on DFIG-based onshore wind farms connected to LCC HVDC systems includes [15, 17, 35, 37]. A very strong grid in the rectifier-side was considered by Yin et al. in [35] where a synchronous generator is connected to the terminal of the LCC-HVDC station. Some papers [15, 17] focused on deriving frequency support from DFIG-based wind farms to the AC grid in the inverter-side. This is performed through the LCC HVDC transmission system. Like some of the papers mentioned before, reference [37] oversimplified the inverter model and represented it by a DC voltage source. In [36] onshore wind farms connected to weak grid was considered where the impact of ESCR and Hdc on the system performance was analyzed. Based on [36], in this study a comprehensive modeling and stability analysis framework is presented, which reveals how ESCR and Hdc affects the frequency control in a progressively weak system in addition to the negative interaction between the “generator speed-HVDC PLL-frequency controller” mode and the “DFIG-GSC Controller” mode. The approach is based on nonlinear state-space modeling for such systems. Also, a stability analysis framework that can perform root-cause analysis of dynamic performance and analyze interaction of various control loops in the system with the variation of system parameters is presented. The case study is organized as follows: first, the nonlinear state-space averaged phasor model of the LCC-HVDC and the DFIG-based wind farm with their controllers is benchmarked against a detailed model in EMTDC/PSCAD [22]. Following this, the frequency dynamics in a progressively weak grid is analyzed using modal participation factor, eigenvalue-sensitivity, and root locus analysis. The regulation of frequency is improved in a very weak grid through systematic design of the HVDC frequency controller and modal interaction analysis. Finally, the performance of the controller under different operating points is presented.

4.2.1 State-Space Averaged Phasor Model of the System A nonlinear state-space averaged phasor model of a power system with a DFIGbased wind farm connected to an LCC-HVDC is derived in the form of the following Differential and Algebraic Equations (DAEs): x˙ = f (x, u, z) 0 = g (x, u, z)

(4.1)

where x, u, and z are the state-variables, input variables, and algebraic variables, respectively. Figure 4.1 shows the schematic of the LCC-HVDC with its rectifier operating under current control (CC) and inverter operating under extinction angle

4.2 Case Study I: Impact of Inertia and Effective Short Circuit Ratio on. . .

81

control. This figure also shows the schematic of a DFIG-based wind farm with its components and controls, which is connected to the rectifier station PCC. The PCC is a part of an AC grid modeled by an ideal source behind impedance Zgrid . LCC-HVDC The state-space averaged model of LCC-HVDC was derived in Sect. 2.2.2 of Chap. 2. The state-variables x, input variables u, and the algebraic variables z in the LCC-HVDC model can be summarized as:  T x = Idr xr1 Idi xi1 vdm , T  u = Id∗ γi∗ , T  z = Eacr Eaci

(4.2)

DFIG-Based Wind Farm The state-space averaged model of DFIG-based wind farms was presented in Sect. 3.2.2 of Chap. 3. As shown in Fig. 4.1, the wind farms uses PLL2. The working principle of a PLL based on [25] was described in Sect. 2.4.1.2 of Chap. 3. The phasor model of the PLL is shown in Fig. 4.2. This model was used for P LL2. The state-equations are described in Eq. (4.3). θ˙ˆi = −Kp_pll θˆi + xpll(i) + Kp_pll θi + ω0 x˙pll(i) = −Ki_pll θˆi + Ki_pll θi

(4.3)

The state-variables x, input variables u, and the algebraic variables z in the model of DFIG-based wind farm along with its controls are: 2  e i  ωr_dfg ωt θtw iqs ids eqs ds ms vdc iqg idg xrr1 xrr2 xg1 · · ·  T x= ∗ x xg2 θˆ2 xpll(2) iqg v

T    ∗ 2 ∗ Qgsc θi , Vw vs∗  vdc   z = |vs | vqs T

u=



(4.4)

∗ and x are the state-variables of the DC-link voltage controller with gain Here, iqg v Kdc . The AC network, AC system static loads, the capacitor banks and filters are modeled algebraically, as described in Sect. 2.2.2 in Chap. 2. It is important to validate the accuracy of the phasor model before using it for analysis. One way to do this is to compare its response with a detailed model built in a commercial EMT-type platform like EMTDC/PSCAD [22], as described next.

I dc

GSC

MPPT and Stator DC voltage and reactive power control voltage control

Inner current Control loops

PWM

Inner current Control loops

RSC

Qg

DC Link

Qs

PWF , QWF

0

vs

PLL2

PCC

Pgrid

caps & filters

r r

Vdr

I dr

K ir xr1

Kprpr

Ldc 2

1 s

Cdc

Rdc 2

AC grid G1

-

I dr

I

Ldc 2

Vdm

Rdc 2

Rectifier current controller

-

Rectifier

Z grid

tapr

Phvdc

* d

Vdi

I di

-

i

Min over a cycle

Kii

xi1

K pi

tapi

1 s

Ti :1 Eaci

i

i

-

* i

K di I d* I di

caps & filters

Vgi

Inverter extinction angle controller

i

Inverter

Fig. 4.1 Schematic of DFIG-based wind farm connected to LCC-HVDC in an AC grid is modeled using an ideal source behind an impedance. The HVDC rectifier station operates in a constant control mode

Stator flux and Flux angle calculations

DFIG

Ps

PGSC QGSC

r

Wind turbine

VW

Eacr

82 4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . .

4.3 Dynamic Model Representing Weak AC System

∠

ωt

K p _ pll

θi θˆi

-

vs

θ0( i )

83

K i _ pll

ωˆ i

1 s x pll (i ) ω 0 = 1

1 s

θˆi

Fig. 4.2 Phasor model for the ith PLL [25]

4.2.2 Validation Using Detailed Model The dynamic response of the state-space averaged model developed in the previous section was compared against a detailed three-phase model in EMTDC/PSCAD that considers switched model of converters. The AC grid connected to the PCC (see Fig. 4.1) in this simulation was modeled using an ideal source behind an impedance. Three disturbances were considered for comparing the response of these two models: Test 1: Response following a step-reduction in the current order of the rectifier controller, which excites the LCC-HVDC dynamics is shown in Fig. 4.3. Test 2: Response following a step-reduction in the wind speed, which excites the wind farm dynamics is shown in Fig. 4.4. Test 3: The system response can be seen in Fig. 4.5 after a pulse change in rectifier-side grid voltage is applied. A comparison of the dynamic response from the averaged model and from the EMTDC/PSCAD model shows that they match reasonably well.

4.3 Dynamic Model Representing Weak AC System The weak AC grid in the rectifier side is modeled using a dynamic representation with low ESCR and Hdc . The schematic of the AC system connected at the PCC of the DFIG-based wind farm and the LCC-HVDC is shown in Fig. 4.6. The synchronous generator G1 is represented by a sixth-order subtransient model, which neglects the stator transients. The excitation system is represented by an IEEE DC1A type model and a turbine-governor is also considered for the generator. The state-space representation of generators, governors, and exciters can be found in standard textbooks like [13].

84

4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . .

Idr [kA]

2

Detailed Model Averaged Model

1.9

γi [deg]

αr [deg]

32

30

16

15 15

15.05

15.1

15.15

15.2

15.25

15.3

time [s] Fig. 4.3 Test 1: Dynamic response of the system following a step-reduction in the current reference of the rectifier current controller. Response in γi is delayed by a cycle following the disturbance due to the minimum-over-a-cycle measurement of γi in the feedback signal, see Fig. 2.2. Source: Yogarathinam et al. [36]. Reproduced with permission of IEEE

4.4 LCC-HVDC Frequency Controller The operating mode of LCC-HVDC rectifier station is changed from constant current control to constant frequency control as shown in Fig. 4.6. This type of control was proposed in [14]. The inverter-side still operates in constant extinction angle control mode. The rectifier side frequency controller facilitates two important objectives: 1. Ensures stability in the frequency dynamics, provided the frequency controller is designed appropriately, and 2. Ensures that the power generated by the wind farm (PW F ) and the AC grid (Pgrid ) flow through the HVDC rectifier to the AC system on the inverter-side. 3. Ensures stable operation of the P LL in strong AC grid scenario as well (discussed in Sect. 4.6). The frequency is estimated at the rectifier bus using P LL1, which has the same structure shown in Fig. 4.2. Usually, the rectifier PLL is also used to calculate

4.4 LCC-HVDC Frequency Controller

85

Ptur [M W ]

1200

Detailed Model Averaged Model 1000

PW F [M W ]

800 1000

850

700

slip

-0.12 -0.16 -0.2

15

20

25

30

time [s] Fig. 4.4 Test 2: Dynamic response of the system following a step-reduction in wind speed (Vw ). Source: Yogarathinam et al. [36]. Reproduced with permission of IEEE

the zero crossing points of the voltage waveform and thus generate the firing pulses from the firing angle command. The nonlinear averaged phasor model cannot consider such zero-crossing points of the voltage waveform. A PI compensator is used to generate the firing angle αr for the rectifier to maintain constant frequency. Due to the introduction of frequency controller, the state-space model of the LCC-HVDC described in Sect. 2.2.2 in Chap. 2 requires modification by replacing the state-variable xr1 with a new state-variable xrf shown in Fig. 4.6. The state equation for Idr will also be modified as shown in Eq. (4.5). x˙rf = ω∗ − ωˆ  √       6 2 1 + 2R R 2 dc cr Idr − vdm + I˙dr = − Ldc Ldc π Ldc    ∗ × (BTr tapr ) Eacr cos αr0 + Kpf ω − ωˆ + Kif xrf

(4.5)

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4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . .

αr [deg]

31

Detailed Model Averaged Model

30 29

Eacr [kV ]

28 390

385

Pdi [M W ]

380 1010 1000 990 15

15.05

15.1

15.15

15.2

15.25

15.3

time [s] Fig. 4.5 Test 3: Dynamic response of the system following a step-reduction in rectifier side grid voltage (Vgr ). Source: Yogarathinam et al. [36]. Reproduced with permission of IEEE

4.5 Analysis of Frequency Dynamics in a Progressively Weak System The objective of this section is to develop a deeper understanding of the frequency dynamics of the system shown in Fig. 4.6 through modal analysis when the system is made progressively weaker by decreasing Hdc and ESCR of the AC grid with reduction of Hgrid and increase of Zgrid , respectively. The AC system frequency f is determined by the angular speed ω of the synchronous generator G1 . A power-balance equation at the PCC, neglecting losses, leads to PW F + Pgrid = Phvdc . With the q-axis aligned to the stator flux and with  ≈ L i ω [14], one can write: an approximation Eacr ≈ vds m ms dω 3Lm ims = dt 2Hgrid +

 √

1 2Hgrid

 2 1  − (BTr tapr Idr cos αr ) + idW F ω π 2   3   3 (1 − ω) 2 vqs iqW F + Pmgrid + Xcr BIdr + 2 π Rgov

(4.6)

I dc

MPPT and Stator voltage control

GSC

PWF , QWF

DC voltage and reacve power control

Inner current Control loops

PWM

Inner current Control loops

RSC

Qg

DC Link

Qs

0

vs

PLL2

PCC

Eacr

Pgrid

caps & filters

ˆ

PLL1

Z grid

tapr r

r

Vdr

I dr Cdc

Rdc 2

Kif

1 xrf s

K pf

Ldc 2

G1

H grid

Dynamic Model of AC grid

Ldc 2

Vdm

Rdc 2

Recfier Frequency controller

r0

Recfier

ˆ

Vdi

I di

*

-

i

xi1

K pi

Kii

Min over a cycle

tapi

Ti :1 Eaci

1 s

caps & filters

Vgi

Inverter exncon angle controller

i

Inverter

i

-

i * i

Fig. 4.6 Schematic of DFIG-based wind farm connected to LCC-HVDC in an AC grid represented by a dynamic model. Values of Zgrid can be gradually increased and Hgrid can be reduced to simulate a progressively weak AC system. The HVDC rectifier station operates in a constant frequency control mode

Stator flux and Flux angle calculaons

DFIG

Ps

PGSC QGSC

r

Wind turbine

VW

Phvdc 1: Tr

4.5 Analysis of Frequency Dynamics in a Progressively Weak System 87

88

4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . .

where Pmgrid is the mechanical power input to G1 , Rgov is the governor droop   coefficient, iqW F /idW F are q/d-axis components of total wind farm current iW F with the q-axis aligned to the stator flux. This approximate expression is used for qualitative understanding that the dynamics in ω is influenced by the dynamics of LCC-HVDC, wind farm, synchronous generator and their respective controllers, including the PLLs. The modal analysis that follows does not use such an approximation. To perform modal analysis, the state-space averaged model developed in Sects. 4.2.1 and 4.4, which was expressed in a compact form in Eq. (4.1), is linearized around an operating point (x0 , u0 , z0 ), see Appendix 2, and expressed in state-space form as: Δx˙ = AΔx + BΔu + τ Δz

(4.7)

where Δx and A are the state-vector and the state-matrix, respectively. The right (φi ) and the left (ψi ) eigen vectors corresponding to the eigenvalues λi , i = 1, 2, . . . , n satisfy: Aφi = λi φi , ψi A = λi ψi

(4.8)

The kth element of the right eigenvector φi measures the activity of the state variable Δxk in the ith mode while that of the left eigenvector ψi weighs the contribution of this activity to the ith mode [13]. Participation factor are the elements of the participation matrix, P denoted by pki = φki ψik . For modal analysis of frequency dynamics in the progressively weak AC system, a three-step approach was proposed in [36]: Step I Modal participation analysis was performed to figure out the nature and the root cause of the dynamic response of frequency in a strong AC grid. Attention was paid to identify the modes with high participation from the dynamic state ω and the dynamic state xrf of the frequency controller. Since the frequency controller works based on the frequency ω, ˆ estimated by P LL1, it is important to identify the modes with high participation from the states of P LL1. Similarly, dynamic states of P LL2 should also be considered in this study. Step II Eigenvalue-sensitivity analysis with respect to Hdc and ESCR of the AC system was performed to evaluate how the above-mentioned modes are impacted by a progressively weak system. Eigenvalue sensitivity is considered as a very important measure in the area of small signal stability, and has been used in various applications in the past. The first-order eigenvalue sensitivity is given by [5]: ∂A ψi ∂Γ φi ∂λi = ∂Γ ψi φi

(4.9)

4.5 Analysis of Frequency Dynamics in a Progressively Weak System

89 ψ

ΔA

φ

i where Γ is a system parameter. The sensitivity was approximated by iψΔΓ where i φi ΔA denotes the change in the state-matrix corresponding to a small change in parameter Γ .

Step III Root locus analysis was performed to observe the eigenvalue movement as the system is made progressively weaker by gradual reduction in Hdc and ESCR.

4.5.1 Results and Analysis For the test system shown in Fig. 4.6, Steps I and II were performed assuming a strong nominal system with Hdc = 5.85 s and ESCR = 4.37. Remark Note that the calculation of ESCR considered only the AC grid and the AC switchyard of LCC rectifier station. It does not consider the DFIG-based wind farm in ESCR calculation. The following are the key observations from Table 4.1, which summarizes these results: • The eigenvalue-sensitivity was computed by reducing the parameters Hdc and i ESCR. Therefore, a positive ∂σ ∂Γ indicates eigenvalue moving towards left and a ∂ωdi positive ∂Γ indicates a reduction of the value ωdi . • The states ω, θˆ1 , and xrf participate primarily in a low frequency mode −0.20 ± j 0.98. As observed from Eq. (4.6), Hgrid , and therefore, Hdc has direct impact on this mode. This is verified from the eigen-sensitivity values shown in Table 4.1. When Hdc is reduced, the real part becomes slightly more negative and the imaginary part increases significantly. This eigenvalue has a negligible sensitivity w.r.t. the ESCR. • The mode −273.47±j 605.28 that is dominated by the dynamic-state θˆ1 of P LL1 is highly sensitive to change in ESCR and moves towards right with an increase in frequency when ESCR is reduced. Therefore, stability of such PLL-modes should be evaluated for weak systems.

Table 4.1 Modal participation and eigenvalue sensitivity analysis for strong system: nominal Hdc = 5.85 s, ESCR = 4.37, Kpf = 0.754, Kif = 7.54, ΔΓ < 0, i.e. parameters were reduced [36] Dominant States G1 : ω , PLL1 : θˆ1 , Freq Controller : xr f PLL1 : θˆ1 PLL1 : xˆpll(1) PLL2 : xˆpll(2) GSC : iqg , xg1

Modes λi = σi ± j ωdi −0.20 ± j0.98 −273.47 ± j605.28 −527.40 ± j531.44 −533.10 ± j533.24

Hdc

∂ σi ∂Γ

ESCR

Hdc

∂ ωdi ∂Γ

ESCR

0.18 0.01 −0.64 0.02 0.12 −84.80 −0.17 −61.44 0.00 −0.01 0.00 2.85 0.00 −0.00 0.00 −0.00

−516.01 ± j1357.78 −0.11 72.51

−0.15 −490.69

90

4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . . Hdc = 5.85 to 1.35, ESCR = 4.37

Hdc = 5.85, ESCR = 4.37 to 0.17 2500

3

2000 2

1500 1000

1

jω

500 0

0 -500

-1

-1000 -1500

-2

-2000

(a) -3 -2

-1

-0.5

0

Hdc = 5.85 to 1.35 and ESCR = 4.37 to 0.17

jω

2500

-1500

2 1.5

1000

1

500

0.5

0

0

-500

-0.5

-1000

-1

-1500

-1.5 (d)

-2500

σ

0

-2

(c) -1000

-500

Hdc = 5.85 to 1.35 and ESCR = 4.37 to 0.17

1500

-2000

-1000

2.5

2000

-1500

(b)

-2500 -1.5

-500

0

-2.5 -1.5

-1

σ

-0.5

0

Fig. 4.7 Eigenvalue-movement with reduction in Hdc and ESCR that renders the system progressively weaker. (a) only Hdc is reduced from 5.85 to 1.35 s while ESCR remains unchanged at 4.37. (b) only ESCR is reduced from 4.37 to 0.17 while Hdc remains unchanged at 5.85 s. (c) Hdc is reduced from 5.85 to 1.35 s and ESCR is reduced from 4.37 to 0.17 simultaneously. (d) zoomed view of subplot (c). Source: Yogarathinam et al. [36]. Reproduced with permission of IEEE

• The states xpll1 and xpll2 of P LL1 and P LL2 participate in one pair of poles each, which are very close to each other and are insensitive to the changes in system strength. In Step III, the values of Hgrid and ESCR are reduced to analyze a progressively weaker system. Figure 4.7 shows the movement of the eigenvalues of interest. Figure 4.7a highlights the movement of the mode −0.20 ± j 0.98 with reduction in Hdc from 5.85 to 1.35 s while ESCR remains unchanged at 4.37. As shown in Fig. 4.7b, the eigenvalues −273.47 ± j 605.28 move towards right and its frequency increases when ESCR reduces to 0.17. There is another mode −516.01 ± j 1357.78 that moves a lot towards left and then turns back towards right at very low ESCR. Participation factor analysis confirms that this is a wind farm GSC mode, which is shown in Table 4.1.

4.5 Analysis of Frequency Dynamics in a Progressively Weak System

91

Finally, both Hdc and ESCR were reduced simultaneously to 1.35 and 0.17, respectively, which makes the system very weak. The loci of the eigenvalues corresponding to this change is shown in Fig. 4.7c, d. It should be noted that these movements are all in line with the expectations from Table 4.1.

4.5.2 Improving Control of Frequency in Very Weak System The system shown in Fig. 4.6 with Hdc = 1.35 s and ESCR = 0.17 can be considered a very weak AC system. The control of the frequency of this weak AC system is improved considering the design of appropriate controller parameters. To that end the following systematic procedure is adopted: Step A: Determine Critical Modes Impacted by Hdc and ESCR Two such modes are −0.20 ± j 0.98 and −273.47 ± j 605.28, which moved to −0.35 ± j 2.27 and −105.41 ± j 793.58, respectively, following the reduction in Hdc to 1.35 s and ESCR to 0.17, see Fig. 4.7c, d. Step B: Determine Dominant Participating States in Those Modes Modal participation factor analysis was performed on all the states of the system and the dominant participating states in the modes of interest from step A are listed in Table 4.2. It can be seen that dominant states in the poorly damped mode are from G1 : ω, P LL1 : θˆ1 , Freq Controller: xrf . The dominant states participating in the other mode is a combination of states from DFIG, GSC, GSC current controller, and PLL1. Step C: Select Candidate Controllers Using Eigenvalue Sensitivity Eigenvalue-sensitivity analysis with respect to different controller parameters was performed for these modes of interest, which are shown in Table 4.2. Sensitivities with significant order of magnitudes are highlighted. The following are the key observations: • It can be seen that the real-part of poorly damped 0.36 Hz mode has high sensitivity w.r.t. Kpf and Kif . Increasing Kpf and decreasing Kif will improve the damping of this mode. A closer look at the values corresponding to the imaginary part reveals that a decrease in Kif decreases the modal frequency, whereas such a change is insignificant when Kpf is changed.

Table 4.2 Modal participation & eigenvalue sensitivity analysis for a very weak system: nominal Hdc = 1.35 s, ESCR = 0.17, Kpf = 0.754, Kif = 7.54, ΔΓ < 0, i.e. parameters were reduced [36] ∂ω

∂ σi di Dominant Modes ∂Γ ∂Γ λi = σi ± j ωd Kp f Ki f Kp pll Kdc Ki f Kp pll Kdc Kp f States −0.35 ± j2.27 −0.18 0.22 0.00 0.00 0.02 0.75 0.0 0.00 ω , θˆ1 , xr f iqs , iqg , eds , θˆ1 , xg1 −105.41 ± j793.58 122.65 −2.06 38.05 −32.15 −150.36 −1.27 153.30 244.27

92

4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . .

jω

Kpf = 0.754 to 3.77, Kif = 7.54

Kpf = 0.754, Kif = 7.54 to 0.038

800

800

600

600

400

400

200

200

0

0

-200

-200

-400

-400

-600 -800

-600

(a)

-800

jω

-150

-100

-50

0

50

-150

3

3

2

2

1

1

0

0

-1

-1

-2

(b) -100

-50

0

50

-2

(c)

(d)

-3

-3 -1.5

-1

σ

-0.5

-1.5

-1

σ

-0.5

Fig. 4.8 Movement of eigenvalues with: (a), (c) increase in Kpf , and (b), (d) decrease in Kif . Source: Yogarathinam et al. [36]. Reproduced with permission of IEEE

• Parameters Kpf and Kif appear to be the best choice for improving frequency dynamics in the system. However, sensitivity of the other eigenvalue −105.41 ±  , θˆ , x j 793.58 with dominant participation from iqs , iqg , eds 1 g1 reveals negative interaction with the mode −0.35 ± j 2.27 that has a dominant participation from ω, θˆ1 , xrf . This is clear from the opposite signs of the sensitivities, e.g. −0.18 vs 122.65 for Kpf and 0.22 vs −2.06 for Kif . Step D: Design Frequency Controller Using Root-Locus Method The controller parameters Kpf and Kif are designed using root-locus method while utilizing the eigenvalue sensitivity information from Step C. The following steps are followed: • The value of Kpf was increased by 5 times while keeping Kif constant at 7.54. As shown in Fig. 4.8c, this improves the damping of the −0.35 ± j 2.27 mode with insignificant change in modal frequency. However, Fig. 4.8a shows that the mode −105.41 ± j 793.58 crosses into the right-half of s-plane.

4.5 Analysis of Frequency Dynamics in a Progressively Weak System

93

Vw [m/s]

13.4 13.2

Kif = 7.54, Kpf = 0.754 Kif = 0.038, Kpf = 0.754 Kif = 1.508, Kpf = 1.319

13 12.8 0

2

4

6

8

10

12

14

16

f [Hz]

60.1 60 59.9 59.8 0

2

4

6

8

10

12

14

16

18

20

PW F [M W ]

990 980 970 960 0

2

4

6

8

10

12

14

16

time [s] Fig. 4.9 Dynamic response of the system following a pulse-change in wind speed. Gray trace: response with Kif = 7.54, Kpf = 0.754. Black trace: Kif = 0.038 s, Kpf = 0.754. Dotted trace: Kif = 1.508, Kpf = 1.319. Source: Yogarathinam et al. [36]. Reproduced with permission of IEEE

• Figure 4.8d shows that a decreasing Kif to 0.038 while keeping Kpf constant at 0.754 moves the dominant pole −0.35 ± j 2.27 towards the left and also decreases its frequency, which is in agreement with the eigenvalue sensitivity figures mentioned in Table 4.2. It is also verified from Fig. 4.8b that this change has hardly any impact on the movement of other poles. Thus Kpf = 0.754 and Kif = 0.038 are chosen as the designed values. The performance of the frequency controller is compared against the response with the nominal values, i.e. Kpf = 0.754 and Kif = 7.54. The time-domain simulations were performed using the nonlinear averaged phasor model. A pulsechange in the wind-speed Vw is created in the test system shown in Fig. 4.6. Even though a wind pulse is unrealistic, it is nevertheless useful to study how pole position affects overall system dynamics. The dynamic performance of the system following this disturbance is shown in Figs. 4.9 and 4.10. With a reduction in Vw , the wind farm power output PW F drops and as the wind velocity increases, it comes back to pre-disturbance value. No oscillation is observed in PW F since the RSC controls the DFIG speed very tightly to ensure MPPT.

94

4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . .

Idcr [kA]

2.02 2

Kif = 7.54, Kpf = 0.754 Kif = 0.038, Kpf = 0.754 Kif = 1.508, Kpf = 1.319

1.98 1.96 0

2

4

6

8

10

12

14

16

0

2

4

6

8

10

12

14

16

0

2

4

6

8

10

12

14

16

αr [deg]

24 23.5 23 22.5

Pgrid [M W ]

90 80 70 60

time [s] Fig. 4.10 Dynamic response of the system following a pulse-change in wind speed. Gray trace: response with Kif = 7.54, Kpf = 0.754. Black trace: Kif = 0.038, Kpf = 0.754. Dotted trace: Kif = 1.508, Kpf = 1.319. Source: Yogarathinam et al. [36]. Reproduced with permission of IEEE

Responses denoted in gray trace correspond to the case with Kif = 7.54, Kpf = 0.754, where the 0.36 Hz-mode is clearly visible in the frequency of the system since the generator speed ω has the highest participation in that mode (Fig. 4.9). The same mode is observable in the oscillations of Idcr , αr , and Pgrid (Fig. 4.10). Following the design procedure mentioned before, the values of Kif and Kpf are set to 0.038 and 0.754, respectively, which improves the damping of the concerned mode from 15% to 58%. The dynamic response with this design is shown with black traces in Figs. 4.9 and 4.10, which confirms a much better damping. It can be observed from Fig. 4.9 that this design leads to a larger dip in frequency (59.8 Hz) compared with the case with poorer damping. To address this issue, the value of Kpf was increased and Kif decreased simultaneously. Figure 4.11 shows the eigenvalue movement when Kpf was increased from 0.754 to 1.319, and Kif is reduced from 7.54 to 1.508. As shown in Fig. 4.11b, this ensures that the −105.41 ± j 793.58 mode does not become unstable while a 50% damping-ratio is achieved for the poorly damped mode, see Fig. 4.11c. The dotted traces in Figs. 4.9 and 4.10 show the dynamic performance with this design

4.6 Performance Across Operating Points: Inclusion of Pitch Controller

95

Kpf = 0.754 to 1.319, Kif = 7.54 to 1.508 2000 500

jω

1000

0

0

(a)

-1000

(b)

-500

-2000 -1500

-1000

-500

0

-120

-100

-80

-60

σ 2

-40

-20

σ

0.52

0.4

0.28

0.2

2.5 0.13

0.06

0.7

1

jω

0.5

(c) 0.5

-1 0.88 -2

2 1.5

1 0.88 0

0

1 1.5

0.7

-1.8

0.52 -1.6

-1.4

0.4 -1.2

0.28 -1

σ

-0.8

0.2 -0.6

0.13 -0.4

2

0.06 -0.2

2.5 0

Fig. 4.11 Movement of eigenvalues with (a) increase in Kpf to 1.319 and simultaneous decrease in Kif to 1.508; (b), (c) zoomed view of (a). Source: Yogarathinam et al. [36]. Reproduced with permission of IEEE

following a pulse disturbance in the wind speed. Improvement in the frequency-dip is clearly visible from the nonlinear time-domain simulation.

4.6 Performance Across Operating Points: Inclusion of Pitch Controller The performance of the frequency controller is evaluated under different operating points by varying the ESCR and the wind speed when pitch angle controller is included in the model. • Different ESCR scenarios: Figure 4.12 shows the system response following a pulse disturbance in Vw with increasing ESCR. The response of frequency and Idcr is similar to the previous case (Figs. 4.9 and 4.10) when pitch controller was not included.

96

4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . .

f [Hz ]

60.1 60

ESCR = 0.52 ESCR = 2.10 ESCR = 4.37

59.9 59.8 0

2

4

6

8

10

12

14

16

18

20

I dcr [kA]

2.02 2 1.98 1.96 0

2

4

6

0

2

4

6

8

10

12

14

16

8

10

12

14

16

αr [deg]

25

24

23

time [s] Fig. 4.12 Dynamic response of the system after pulse change in wind speed with different ESCR values. Gray trace: response with ESCR = 0.52; dotted trace: ESCR = 2.10; Black trace:ESCR = 4.37. Source: Yogarathinam et al. [36]. Reproduced with permission of IEEE Table 4.3 Variation of modes of interest with different operating points: nominal Hdc = 1.35 s, ESCR = 0.52, Kpf = 1.319, Kif = 1.508 [36]

Dominant states ω, θˆ1 , xrf i qs , i qg , eds , θˆ 1 , x g1

Modes Vw = 12.4 m/s −0.997 ± j 1.673 −75.28 ± j 620.0

Vw = 12.8 m/s −1.009 ± j 1.683 −66.88 ± j 649.0

Vw = 13.2 m/s −1.002 ± j 1.646 −59.07 ± j 679.0

Vw = 13.8 m/s −0.972 ± j 1.594 −51.94 ± j 710.0

Vw = 14.3 m/s −0.949 ± j 1.565 −45.640 ± j 742.4

• Different wind speed conditions: When the wind speed is varied the corresponding modes of interest are listed in Table 4.3. It reveals that all the modes are stable without much deviation in the damping ratio of the critical low frequency mode. To validate the findings of frequency-domain analysis the following timedomain simulations have been carried out:

4.7 Case Study II: Coupled Frequency Dynamics of Rectifier and Inverter-Side. . .

97

Vgi [kV ]

250 250

200

200

(a)

γ[deg]

0.1

0.16

0

0.18

0.2

0.22

25 20 15 10

(b) 0.12

0.14

0.16

0.18

0.2

0

0.22

1

2

0.24

1

3

0.26

2

0.24

4

5

0.28

3

0.26

0.3

4

5

0.28

0.3

1040 1000 960

1040 1020 1000 980 960

0

1

2

3

4

5

(c) 0.1

f [Hz]

0.14

25 20 15 10 0.1

P di [M W ]

0.12

0.15

0.2

0.25

0.3

60.4 60.2

(d)

60 0

2

4

0.35 Vw = 12.4m/s Vw = 13.2m/s Vw = 14.3m/s

6

8

10

12

14

time [s] Fig. 4.13 Dynamic response of the system following the disturbance in inverter-side grid voltage (Vgi ). Gray trace: response with Vw = 12.4 m/s; dotted trace:Vw = 13.2 m/s; Black trace:Vw = 14.3 m/s. (the zoomed view of Vgi , γ , Pdi along with their overall view in (a), (b), and (c)). Source: Yogarathinam et al. [36]. Reproduced with permission of IEEE

Inverter-side disturbance: The dynamic response of the system after a large disturbance on the inverter-side grid voltage (Vgi ) leading to overfrequency scenario at different wind speeds is shown in Fig. 4.13. Performance under fault: When a three-phase high impedance self-clearing fault occurs at the rectifier-side AC system, the system response under different wind speeds can be seen in Fig. 4.14. The frequency controller appears to work effectively for different operating conditions and disturbances in the system.

4.7 Case Study II: Coupled Frequency Dynamics of Rectifier and Inverter-Side AC Grids As described before, quite a few papers presented research on offshore wind farms (OWFs) connected to LCC-HVDC delivery systems [2, 3, 14, 23, 31–34, 38, 39]. Also, a few papers [15, 17, 35, 37] reported research on the interconnection of DFIG-based wind farms with LCC-HVDC systems for onshore applications. In the case study I presented earlier, which was reported in [36], the rectifier station was

4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . .

Vdi [kV ]

98

500

Vw = 12.4m/s Vw = 13.2m/s Vw = 14.3m/s

490 480 0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

γ[deg]

22 20 18

f [Hz]

16

60 59.6 0

2

4

6

8

10

12

14

time [s] Fig. 4.14 Dynamic response of the system following a high impedance self-clearing fault at rectifier-side AC system with ESCR = 0.52. Gray trace: response with Vw = 12.4 m/s; dotted trace: Vw = 13.2 m/s; Black trace: Vw = 14.3 m/s. Source: Yogarathinam et al. [36]. Reproduced with permission of IEEE

operated with a constant frequency control and the impacts of low Hdc and ESCR were studied. However, the inverter-side AC grid was modeled as an ideal voltage source. Clearly, none of the papers have studied the effects of coupling between the rectifier-side and the inverter-side frequency dynamics. This case study reported in [30] aims to analyze the coupling between frequency dynamics of the two AC systems interacting through LCC-HVDC. As shown in Fig. 4.15, the inverter-side AC grid is a relatively strong system whereas the rectifier side is interfaced with a weak AC system and a DFIG-based wind farm. The HVDC rectifier station operates in the frequency control mode as in reference [36]. To that end, a simple four-state nonlinear model is derived, which is representative of the real power–frequency (P − f ) interaction. Comparing response of the four-state model with the full-order model a coupling phenomenon between the real powerfrequency (P − f ) and reactive power-voltage (Q − V ) channels is observed. This complex P − f and Q − V interaction affects both the rectifier and the inverterside AC grids through the LCC HVDC transmission system. Such interactions were found to negatively impact the frequency dynamics of the AC systems. Reference [30] proposes a firing angle correction strategy to solve this issue. This method uses certain feedforward signals to reduce the sensitivity of the real power with respect to AC voltage at the LCC-HVDC converter terminals. This helps in decoupling the P − f and Q − V interactions and improves the frequency dynamics

4.8 Full-Order Model of the System

99

of the system. Nonlinear time-domain simulations are performed to validate the effectiveness of the correction strategy. Linearization of the fourth-order model leads to certain fundamental insights on frequency dynamics. Especially, the interaction between the frequency dynamics on the rectifier and the inverter-end AC systems are analytically quantified. It also reveals that the synchronizing and the damping torque contribution of the rectifierside generator gets altered when frequency droop control is used in the DFIG-based wind farm.

4.8 Full-Order Model of the System The test system under consideration is shown in Fig. 4.15. This system is a modified version of the test system used in the previous case study. A full-order nonlinear state-space averaged phasor model of this power system is derived using the DAEs that represent each component. The rectifier and the inverter-side AC systems include synchronous generators G1 and G2 , which are represented using sixth-order subtransient models along with turbines, governors, and IEEE DC1A exciters. For this study, an inertia constant HG1 of 1.5 s and an ESCR of 0.52 are considered to represent a weak rectifier-side AC system, while an inertia constant HG2 of 7.0 s is assumed for representing a strong inverter-side AC grid that also includes a load center as shown in Fig. 4.15. The rectifier-side AC system includes a DFIG-based wind farm represented by an aggregated model. The wind farm considers a two-mass wind turbine model, a fourth order subtransient model of induction machine, and grid-side and rotor-side converters represented by averaged models along with inner current control loops. In addition, DC-link dynamics and the converter tie-reactor dynamics are also taken into account. Details of this model were described in Sect. 3.2.2 of Chap. 3. The LCC HVDC converters are represented by standard algebraic models, while the DC transmission line is modeled by differential equations as described in Sect. 2.2.2 of Chap. 2. The rectifier station operates in a frequency control mode, where the controller parameters Kpf = 0.0008 and Kif = 0.0007 are chosen, see Fig. 4.15.

4.8.1 Four-State Nonlinear Model A four-state nonlinear model is presented to help develop a deeper understanding of the interaction between frequencies of the rectifier-side and the inverter-side AC grids. In addition, a complex frequency-voltage coupling phenomenon that is propagated to both the grids through LCC-HVDC is explained with the help of the four-state model. Other applications will also be presented in later sections, none of which can be achieved with the full-order model.

Inner current control loops

DC voltage and reactive power control

MPPT or droop and stator voltage control

GSC

Inner current control loops

PWM

I dc

2

PWF , QWF

0

PLL2

-

PLL1

PI

tapr

PG1

r

Z grid

Governor

G1

0 r

r

Dynamic model of weak AC grid

Rectifier frequency controller

*

caps & filters

Vdr

I dr

H G1

Ldc 2

i

i

Vdi

I di

PI

Min over a cycle

Ldc 2

Vdm

Rdc 2

i

i

Inverter

caps & filters

tapi

Ti :1 Eaci

Inverter extinction angle controller

* i

Tmech1

Cdc

Rdc 2

PL

PG 2

G2

Governor

Dynamic model of AC grid

HG2

Tmech 2

Fig. 4.15 Schematic of the DFIG-based wind farm connected to LCC-HVDC in a weak AC grid represented by a dynamic model. Dynamic model of the inverter-side AC grid is also considered

Stator flux and flux angle calculations

RSC

Qg

DC Link

Qs

Ps

PGSC QGSC

r

DFIG

Total inertia = HWF

Wind turbine

VW

Eacr

Rectifier

-

PHVDC _ IN 1 : Tr

PHVDC _ OUT

100 4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . .

4.8 Full-Order Model of the System

101

The following assumptions are made while deriving the four-state nonlinear model: • AC network equations are not considered. Instead, real power balance equations obeying the network structure are considered. • The AC system losses including losses in the lines, transformers, DFIG, and both the generators are neglected. • It is assumed that the fast-acting power electronic control of the DFIG tracks the reference electrical torque instantaneously. • Only the swing dynamics of the synchronous generators are considered. • The PLL dynamics and the DC line dynamics of LCC-HVDC are neglected, and only DC line resistance is considered. • The inverter-side control is assumed to tightly regulate the extinction angle at a constant value. With the above assumptions, the derivation begins from the power balance equations at PCC in the rectifier side and the load bus on inverter side as shown in Fig. 4.15, PG1 + PW F = PH V DC_I N

(4.10)

PG2 + PH V DC_OU T = PL where PG1 , PG2 , and PW F are the real power output of generators G1, G2, and the wind farm, respectively; PH V DC_I N /PH V DC_OU T are the real power entering/leaving the HVDC rectifier-side/inverter-side AC systems; and PL is the real power consumption at the load center in the inverter-side AC grid. Considering the swing dynamics of the two synchronous machines and substituting powers PG1 and PG2 based on the above power balance equations, ω˙ 1 = = ω˙ 2 = =

1 2HG1 ω1 (Pmech1 − PG1 ) ω∗ −ω1 1 2HG1 ω1 Tmech1 ω1 + Rgov1 1 2HG2 ω2 (Pmech2 − PG2 ) ω∗ −ω2 1 2HG2 ω2 Tmech2 ω2 + Rgov2

+ PW F − PH V DC_I N + PH V DC_OU T − PL

 (4.11) 

Here, ω∗ is the synchronous speed, ω1 and ω2 are the rotor speeds, Rgov1 and Rgov2 are governor droop coefficients, Pmech1 and Pmech2 are mechanical power input, Tmech1 and Tmech2 are mechanical torque input, and HG1 and HG2 are the inertia constants of generators G1 and G2 , respectively. State variables ω1 and ω2 represent the angular frequencies of the rectifier and inverter AC grids. In order to obtain the expression for the wind farm electrical power output, it is assumed that the reference electrical torque (Te = Kopt ωr2 ) for DFIG is tracked instantaneously by the fast-acting controls. Therefore, PW F = Te ωr = Kopt ωr3 Kopt being the constant for MPPT as mentioned in Sect. 3.3.1 of Chap. 3. Moreover, the mechanical dynamics of the wind farm can be represented by the following equation:

102

4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . .

ω˙ r =

1 2HW F

[Ttur (Vw , ωr ) − Te ]

(4.12)

Here, HW F is the total inertia of the rotor and the turbine, and the mechanical torque input Ttur depends on wind speed Vw and rotor speed ωr . The expressions for the DC voltages are given by Vdr = V¯or Eacr cos αr − Rcr Idr Vdi = V¯oi Eaci cos γi − Rci Idi √

(4.13)

√

r tapr i tapi where V¯or = 3 2BT and V¯oi = 3 2BT , and αr is the firing angle of the π π rectifier, and γi is the extinction angle of the inverter. Since γi is assumed to be constant, let V¯oi Eaci cos γi = Vi and for simplicity let Rcr −Rci +Rdc = RH . Other notations are standard and were explained in Sect. 2.2.2 of Chap. 2. Furthermore, αr is obtained from the frequency controller in the rectifier station as shown in Fig. 4.15. Therefore we have

αr = αro + Kpf (ω∗ − ω1 ) + Kif xrf

(4.14)

where xrf is the integrator state, and Kpf and Kif are the proportional and integral gains of the PI controller. The expression for DC current is obtained as Idr = Idi =

(V¯or Eacr cos αr − V¯oi Eaci cos γi ) (V¯or Eacr cos αr − Vi ) = Rcr − Rci + Rdc RH (4.15)

From the above, the expressions for HVDC power input PH V DC_I N and power output PH V DC_OU T shown in Fig. 4.15 are obtained as 2 PH V DC_I N = Vdr Idr = Idr V¯or Eacr cos αr − Rcr Idr

=

(V¯or Eacr cos αr − Vi ) ¯ Vor Eacr cos αr RH −

(V¯or Eacr cos αr − Vi )2 Rcr 2 RH

2 PH V DC_OU T = Vdi Idi = Vi Idi − Rci Idi

=

(V¯or Eacr cos αr − Vi ) Vi RH −

(V¯or Eacr cos αr − Vi )2 Rci 2 RH

(4.16)

Finally, upon replacing the expressions for powers in (4.11) and the expression for electrical torque in (4.12) and including the state equation of rectifier frequency controller, the four-state nonlinear model can be summarized as:

4.9 Application I: Revealing Voltage-Frequency Coupling Phenomenon

ω˙ 1 =

103

 1 ω∗ − ω1 Tmech1 ω1 + + Kopt ωr3 2ω1 HG1 Rgov1

(V¯or Eacr cos αr − Vi ) ¯ Vor Eacr cos αr RH  (V¯or Eacr cos αr − Vi )2 + R cr 2 RH  1 ω∗ − ω2 ω˙ 2 = Tmech2 ω2 + 2ω2 HG2 Rgov2 −

ω˙ r =

+

(V¯or Eacr cos αr − Vi ) Vi RH

−

 (V¯or Eacr cos αr − Vi )2 R − P ci L 2 RH

 1  Ttur (Vw , ωr ) − Kopt ωr2 2HW F

x˙rf = ω∗ − ω1

(4.17)

In this study, the following applications of the four-state nonlinear model will be presented: • Application I: Reveal voltage-frequency coupling phenomenon • Application II: Derive firing-angle correction strategy • Application III: Develop analytical insight and energy bound on frequency deviation

4.9 Application I: Revealing Voltage-Frequency Coupling Phenomenon Upon deriving the full-order model and the reduced four-state model, two experiments are performed, which reveals a voltage-frequency coupling phenomenon that arises when LCC-HVDC is regulating the frequency in a weak grid. For these experiments, a pulse variation in wind speed as shown in Fig. 4.16a is considered as disturbance. Figure 4.17 shows the variations in Eacr and Eaci observed in the fullorder model due to this disturbance. In experiment-I, the four-state model assumes Eacr and Eaci to be constant since variations in these variables are small. Noting that the four-state model adequately captures the dynamics in the P − f channel, it is expected to faithfully represent the frequency deviations. However, it will be observed from experiment-I that the frequency dynamics obtained from the full-order model, which is expected to follow the four-state model’s frequency

power, (MW) power, (MW) frequency, (Hz)

Vw , (m/s)

104

4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . .

13.4

13.5

(a)

13.2 13

13

wind speed 0

12.8 60.1

1

2

60

(b)

59.9

f1 full-order

59.8

f2 full-order

f1 four-state

f2 four-state

985 980

(c)

975

PW F full-order

970

PW F four-state

965 1065 1060

(d) PHV DC

1055 0

5

PHV DC

full-order

IN

10

15

IN

20

four-state 25

30

time, (s) Fig. 4.16 Experiment-I: Comparison between the four-state nonlinear model and the full-order model responses following a pulse change in the wind speed. Source: Vennelaganti and Chaudhuri [30]. Reproduced with permission of IEEE

241.55

368.35

(b)

(a) 368.3

241.5

368.25

Eaci , (kV)

Eacr , (kV)

Eacr full-order

368.2 368.15

Eaci full-order

241.45

241.4

241.35

368.1 368.05

241.3 0

10

20

time, (s)

30

0

10

20

30

time, (s)

Fig. 4.17 Variations in the voltages at rectifier and inverter AC buses during the disturbance in wind speed, as obtained from the full-order model. Source: Vennelaganti and Chaudhuri [30]. Reproduced with permission of IEEE

4.9 Application I: Revealing Voltage-Frequency Coupling Phenomenon Fig. 4.18 Schematic of simulation experiment-II considering variations of Eacr and Eaci from full-order model and feeding as input to four-state nonlinear model

Four-state nonlinear model

Vw

Eacr

105

,

1

2

Comparison plot

Eaci

Full-order nonlinear model

,

1

2

dynamics, actually does not match. Moreover, the rectifier-side frequency variation is worse compared to the four-state model. It is logical to assume that such a deterioration in the frequency dynamics of the full-order model could be arising from the variations in Eacr and Eaci , which in turn can be treated as disturbance input negatively affecting the performance of the rectifier-side frequency regulator. To prove the above assertion, in experiment-II, these variations are fed from the full-order model to the four-state model as shown in Fig. 4.18. It will be shown that the same unfavorable frequency dynamics are also observed in four-state model upon introducing these disturbances. Finally, based on these experimental results three conclusions will be drawn.

4.9.1 Experiment-I: Without Eacr and Eaci Variations in Four-State Model Since the variations in Eacr and Eaci are small, both are assumed to be constant at their pre-disturbance steady state values in the four-state model. Figure 4.16b shows the frequency dynamics of the four-state nonlinear model in comparison with the unfavorable full-order model dynamics. Note that this unfavorable dynamics is particularly in relations to the frequency nadir, which is of major concern to the system operators. Despite the good match in the variation of PW F (Fig. 4.16c), there is discrepancy in power flowing through HVDC at the rectifier as shown in Fig. 4.16d. Therefore, this HVDC power discrepancy could be the reason behind an unfavorable frequency dynamics in the full-order model, which could be caused by the variations in Eacr and Eaci . To verify this, experiment-II is performed as described next.

4.9.2 Experiment-II: With Eacr and Eaci Variations in Four-State Model In this experiment, the variations of Eacr and Eaci that are obtained from the fullorder model are fed to the four-state nonlinear model as shown in Fig. 4.18. It can

4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . .

frequency, (Hz)

106

(a) 60

f1 f2 f1 f2

59.9 59.8

full-order full-order four-state four-state

power, (MW)

1068

(b)

1066 1064 1062

PHV DC PHV DC

1060 1058 1056

0

5

10

15

20

IN IN

full-order four-state 25

30

time, (s) Fig. 4.19 Experiment-II: Similar unfavorable frequency dynamics as in the full-order model is obtained from the four-state model when the voltage variations are fed back from the full-order to four-state model as shown in Fig. 4.18. Source: Vennelaganti and Chaudhuri [30]. Reproduced with permission of IEEE

be seen from Fig. 4.19a that the unfavorable frequency dynamics of the full-order model are replicated by the four-state nonlinear model. Also, power flowing into the HVDC rectifier shows similar variations, see Fig. 4.19b. This implies that feeding the disturbances, i.e., Eacr and Eaci variations into the four-state model, affects the frequency regulator in the four-state model in the same way as the full-order model.

4.9.3 Analysis of Voltage-Frequency Coupling Three important points can be concluded from the above experiments especially for a weak grid with low inertia constant and low ESCR, 1. The frequency dynamics of the system are governed by Eqs. (4.11), which are dependent on the real powers. However, the HVDC real power is sensitive to voltage variations at the rectifier and inverter buses. The voltage variations depend on the reactive power flow. The reactive power consumed by the HVDC rectifier depends on αr , which in turn is dependent on ω1 . Therefore, the P − f and the Q − V dynamics are strongly interdependent in such weak grids and this complex coupling phenomenon is transferred to both AC grids via HVDC. 2. As observed from Fig. 4.16, the frequency deviation in the rectifier side is much less in the four-state model, which considers only the P − f dynamics as compared to the full-order model. Clearly, unfavorable frequency dynamics are

4.10 Application II: Firing Angle Correction Strategy

107

caused by the complex coupling phenomenon explained above. Therefore, it is logical to conclude that desired dynamics of rectifier-side frequency can be achieved for a given set of frequency controller gains of HVDC if the P − f and the Q − V dynamics can be decoupled by some means. 3. The decoupling would involve desensitization of real power going into HVDC rectifier from the rectifier and inverter bus voltage variations. This can be achieved by a correction strategy, which is described next.

4.10 Application II: Firing Angle Correction Strategy In order to decouple the P − f and the Q − V dynamics, a firing angle correction strategy is required. The aim is to make a correction to firing angle αr such that the HVDC power becomes insensitive to the Eacr and Eaci variations. In case of the four-state model with the assumption of constant rectifier and inverter AC voltages equal to their respective nominal values, the HVDC power at the rectifier-end is given by   0 cos α ∗ − V 0 V¯or Eacr r i ∗ 0 PH V DC_I N = cos αr∗ V¯or Eacr RH   0 cos α ∗ − V 0 2 V¯or Eacr r i − Rcr (4.18) 2 RH 0 is the nominal voltage at the rectifier bus. Also, V 0 = V¯ E 0 cos γ 0 , where Eacr oi aci i i 0 is the nominal voltage at the inverter bus and γi0 is the constant where Eaci extinction angle maintained at the inverter-end. αr∗ is the firing angle output of the frequency controller at rectifier. It can be argued that PH∗ V DC_I N is the desired rectifier-side power, which is insensitive to the variations in Eacr and Eaci . In actual case, due to variations in Eacr and Eaci , for any αr the rectifier-side power is given by 2 PH V DC_I N = Vdr Idr = Idr V¯or Eacr cos αr − Rcr Idr

(4.19)

Equating the above expression to PH∗ V DC_I N and solving for αr , we obtain a firing angle, which when input to HVDC ensures that the rectifier-side power is PH∗ V DC_I N . It implies that this power is insensitive to voltage variations at rectifier and inverter buses. Upon solving, the expression for αr is obtained as  αr = cos

−1

2 PH∗ V DC_I N + Rcr Idr Idr V¯or Eacr

 (4.20)

108

4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . .

* r

* PHVDCIN _

Power calculation

I dr

( )2

Rcr

cos

-

1 r

Vor

Eacr

*

PI

Firing angle correction

r

* r

* r

r

0 r

-

Rectifier frequency controller Fig. 4.20 Schematic of the firing angle correction strategy with αr∗ , Eacr , and Idr as input

The control block diagram of the firing angle correction strategy along with the rectifier frequency controller is presented in Fig. 4.20. Only locally measured signals Eacr and Idr are used—there is no need to communicate Eaci from the remote inverter station.

4.10.1 Results and Analysis 4.10.1.1

Effectiveness of the Correction Strategy

Figure 4.21a shows the reduction of the nadir and improved tracking of the rectifierside frequency when the firing angle correction is applied. The same disturbance in wind speed as shown in Fig. 4.16a is considered and the same PI controller gains are used in both cases. Figure 4.21d shows the variation in the controller output αr∗ and the actual firing angle αr , which is obtained by adding the correction term Δαr to the controller output, see Fig. 4.20. Figure 4.22 shows the frequency dynamics in the rectifier and the inverter side following a self-clearing fault in the rectifier-side AC system. Also, plots of Eacr and Eaci are shown in Fig. 4.23 for more clarity. It can be observed that the firing angle correction strategy is quite effective in improving the tracking performance of the rectifier-side frequency controller. It can be seen that the improvement in the response of the rectifier-side frequency comes at an expense of slightly worse nadir of the frequency in the inverter-side AC system. However, a careful look at the response of f2 reveals that firing angle correction brings this frequency back to the nominal value faster following both disturbances.

f1 , (Hz)

4.10 Application II: Firing Angle Correction Strategy

109

60

with correction four-state without correction

59.9 59.8

(a)

f2 , (Hz)

1065

PHV DC

IN ,

59.95

(MW)

60

(b)

59.9

(c)

1060 1055

αr , (deg)

19.2

αr* before correction αr after correction

19

(d)

18.8 0

5

10

15

20

25

30

time, (s) Fig. 4.21 Improved rectifier frequency dynamics obtained by implementing the firing angle correction strategy in the full-order model as shown in Fig. 4.20. Response from the four-state model with constant Eacr and Eaci is also shown. Source: Vennelaganti and Chaudhuri [30]. Reproduced with permission of IEEE

60.1

frequency, (Hz)

60 59.9

f1 f2 f1 f2

59.8 59.7

with correction with correction without correction without correction

59.6 59.5 0

5

10

15

20

time, (s) Fig. 4.22 Improved rectifier-side frequency dynamics following a self-clearing fault in the rectifier-side AC grid upon implementing the firing angle correction strategy. Source: Vennelaganti and Chaudhuri [30]. Reproduced with permission of IEEE

110

4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . . 243

380

(b)

(a) 242

370

Eaci , (kV)

Eacr , (kV)

375

365 360

241

240

Eaci full-order

Eacr full-order 239

355 350

238 0

0.5

1

1.5

0

time, (s)

0.5

1

1.5

time, (s)

Fig. 4.23 Voltage variations after self-clearing fault in the rectifier-side AC system: (a) at the rectifier bus and (b) at the inverter bus. Rectifier is equipped with the firing angle correction control. Source: Vennelaganti and Chaudhuri [30]. Reproduced with permission of IEEE

4.10.1.2

Modeling Adequacy of Four-State Model

Figure 4.21 shows a good match between the response of the four-state model with constant Eacr and Eaci , and the response of the full-order model with firing angle correction for wind speed variation. Also, a good match in frequency dynamics as shown in Fig. 4.24b is obtained following a change in real power consumption at the rectifier bus highlighted in Fig. 4.24a. Similarly, a good match as shown in Fig. 4.24c is obtained following a 10% reduction in generation on the rectifier side. Therefore, the four-state model can adequately capture the frequency dynamics of the full-order system for disturbances like wind speed variations, generation and load changes, when the full-order or the actual system is equipped with the firing angle correction strategy. However, for large disturbances like AC-side fault, DCside fault, and loss of generation a detailed modeling is essential. Nonetheless, the frequency dynamics is improved even for disturbances like AC-side fault, see Fig. 4.22, by implementation of the correction strategy, which is inspired by the four-state model. From now on, unless otherwise stated, all the time-domain responses will be presented from the full-order nonlinear model equipped with firing angle correction.

4.11 Application III: Analytical Insight and Energy Bound on Frequency Deviation The four-state nonlinear model can be linearized to develop fundamental analytical insights that are not obtainable from the full-order linear model. The

4.11 Application III: Analytical Insight and Energy Bound on Frequency. . .

111

load, (MW)

38

load variation 36

(a) 34

frequency, (Hz)

0

0.5

1

1.5

2

2.5

60 59.99 59.98 59.97

f1 f2 f1 f2

full-order full-order four-state four-state

f1 f2 f1 f2

full-order full-order four-state four-state

(b)

frequency, (Hz)

59.96 60 59.9 59.8

0

5

10

15

20

(c)

25

time, (s) Fig. 4.24 Model validation for two scenarios. (1) Load change: (b) comparison of frequency deviation in the rectifier and the inverter-end following a change in real power consumption at the rectifier bus shown in (a). (2) Generation change: (c) comparison of frequency deviation in the rectifier and the inverter-end following a 10% step reduction in G1 ’s torque at t = 0.1 s. Source: Vennelaganti and Chaudhuri [30]. Reproduced with permission of IEEE

four-state model is representative of the full-order system when the latter is equipped with firing angle correction.

4.11.1 Analytical Insight I: Decoupling of Rectifier-Side Frequency Dynamics from Inverter-Side Disturbance The nonlinear state equations of the form x˙ = f (x, u) are linearized around the nominal operating point to obtain a linear state-space model of the form, x˙ = Ax + Bu. For linearization, torque references of both the generators, load on the inverter side, and wind speed are considered as input. Therefore, x and A are obtained as ⎡

⎤ ⎡ ∗  K Δω1 a11 + a11 pf ⎢ Δω2 ⎥ ⎢ a  Kpf 21 ⎥ ⎢ x=⎢ ⎣ Δωr ⎦ ; A = ⎣ 0 Δxrf a41

0 a22 0 0

 K ⎤ a13 a14 if  K ⎥ 0 a24 if ⎥ a33 0 ⎦ 0 0

(4.21)

112

4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . .

Also, u and B are obtained as ⎡ ⎤ ΔTmech1 b11 0 0 ⎢ 0 b22 0 ⎢ ΔTmech2 ⎥ ⎢ ⎥ u=⎢ ⎣ ΔVw ⎦ ; B = ⎣ 0 0 b33 ΔPL 0 0 0 ⎡

⎤ 0 b24 ⎥ ⎥ 0 ⎦

(4.22)

0

The expressions for the terms in the A and B matrices are presented later. The dependence of the terms of A matrix on the proportional (Kpf ) and the integral (Kif ) gains of the frequency controller at the rectifier station is shown. From the locations of zeros in the A and the B matrices, we can develop the following fundamental insights: • The dynamics of ω1 is dependent on ω1 , ωr , and xrf , which are not affected by variations in ω2 . Therefore, disturbances on the inverter side does not directly affect ω1 , unless Eaci is so much out of range that the firing angle correction strategy fails. • Based on the above, since changes in Tmech2 and PL cause variation in ω2 , they do not affect the dynamics of ω1 . Notably, dynamics in ω2 is dependent on ω1 and xrf . Therefore, as far as the frequency dynamics is concerned, the firing angle correction is allowing a one-way propagation of disturbance from the rectifier side to the inverter side, while firewalling the return path. • The above is not true for LCC-HVDC when traditional current order control is present at the rectifier-side. In presence of sufficient reactive power compensation and traditional current control in the rectifier-side, there will be no one-way coupling from the rectifier-side frequency dynamics to the inverter-side. This is well-known, and can be found from literature; one of the early examples being [12].

4.11.2 Analytical Insight II: Per-Unit Energy Bound on Frequency Deviation From the matrices A and B, transfer functions between Δω1 and ΔVw , and between Δω2 and ΔVw are derived as Δω1 (s) ΔVw (s)

=

Δω2 (s) ΔVw (s)

=

b33 a13 s    ∗ −a  K  (s−a33 ) s s−a11 11 pf −a41 a14 Kif  a K ) b33 a13 (a21 s+a24 41 if





∗ −a  K  (s−a22 )(s−a33 ) s s−a11 11 pf −a41 a14 Kif



(4.23)

Using the transfer functions we can determine the H∞ norm, which gives us a bound on the per unit (pu) energy of the variation in frequencies of the rectifierside and inverter-side grids for a unit variation in energy of the wind speed in m/s.

4.11 Application III: Analytical Insight and Energy Bound on Frequency. . . Table 4.4 Per-unit energy bound on Δω1 and Δω2 for different PI gains [30]

PI gains, pu Kpf = 0.0004, Kif = 0.00035 Kpf = 0.0008, Kif = 0.0007

113

Bound: Δω1 0.0161 0.0088

Bound: Δω2 0.0656 0.0656

101

102

Magnitude (dB)

0 -50 -100

Δω2 (s)/ΔVw (s) Δω1 (s)/ΔVw (s)

-150

Phase (deg)

-200 180 0 -180 -360 10 -3

10 -2

10 -1

100

Frequency (rad/s) Fig. 4.25 Bode plot of the transfer functions from wind speed to ω1 and ω2 . Source: Vennelaganti and Chaudhuri [30]. Reproduced with permission of IEEE

Table 4.4 shows that the pu energy bound on Δω1 is lower when higher gains are used for the frequency controller while the pu energy bound on Δω2 remains unchanged. Also, Fig. 4.25 shows the bode plot of the two transfer functions with nominal values of Kpf and Kif . Please note that frequency-domain analysis is now being considered. Therefore, the input, which is the wind speed variation is in frequencydomain i.e., the Fourier transform of the wind speed variation, is taken into account. Also notice that the energy bound (H∞ norm) on the variation in ω2 is the DC gain Δω2 (s) (maximum magnitude) of the transfer function ΔV . This shows that: w (s) • Very low frequency (less than 0.1 Hz) variations in wind speed affects the rotational kinetic energy of the generator on the inverter side, while the rectifier frequency remains unaffected. • A crossover around 0.1 Hz frequency is observed. This implies wind speed fluctuations at higher than 0.1 Hz frequency will affect f1 more than f2 . Figure 4.26 shows that the rectifier-side frequency dynamics improves when higher PI gains are used, see Table 4.4. The same pulse change in the wind speed as in Fig. 4.16a is applied as the disturbance. However, a high gain controller leads

114

4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . .

60.02

frequency, (Hz)

60 59.98 59.96

f1 f2 f1 f2

59.94 59.92

low gains low gains high gains high gains

59.9 59.88 0

10

20

30

40

50

time, (s) Fig. 4.26 Effect of increasing PI gains (Table 4.4) in the frequency controller at the rectifier station: response from full-order model with firing angle correction. Source: Vennelaganti and Chaudhuri [30]. Reproduced with permission of IEEE

to higher loop transfer function, which negatively impacts the robust stability due to system noise, and uncertain and un-modeled plant dynamics when operating conditions change. Also, it leads to higher control effort. Moreover, this does not improve the inverter-side frequency dynamics. In order to improve the frequency dynamics on both the grids by using low PI gains, droop control of wind farm is considered, which is described next.

4.11.3 Analytical Insight III: Droop Control of Wind Farm Usually, frequency droop control in wind farms will need a deloaded operation. However, with the frequency controller at the rectifier station maintaining the frequency at a constant value in steady state—the frequency droop control is effective only under dynamic condition. Therefore, it is not essential to operate the wind farm in deloaded condition. For implementing the droop control, the electrical torque reference of the DFIG is modified as Te∗ = Kopt ωr2 +

ω∗ − ω1 Rwind

(4.24)

where Rwind is the wind droop constant. In the full-order model ω1 is measured using the PLL located at the DFIG bus, which usually measures angle of the voltage for DFIG controls. Also, for the four-state model the wind farm electrical power

4.11 Application III: Analytical Insight and Energy Bound on Frequency. . .

115

output is modified as PW F = Te∗ ωr and the updated four-state nonlinear equations are obtained as ' w ∗ − w1 1 w˙ 1 = + Kopt wr3 Tmech1 w1 + 1 2w1 HG1 Rgov1 w1∗ − w1 (V¯or Eacr cos αr − Vi ) ¯ − Vor Eacr cos αr Rwind RH ( (V¯or Eacr cos αr − Vi )2 + Rcr 2 RH ' w ∗ − w2 1 w˙ 2 = Tmech2 w2 + 2 2w2 HG2 Rgov2 +wr

+

(V¯or Eacr cos αr − Vi ) Vi RH

( (V¯or Eacr cos αr − Vi )2 − Rci − PL 2 RH   w1∗ − w1 1 2 w˙ r = Tmech (Vw , wr ) − Kopt wr − 2HW F Rwind x˙rf = w1∗ − w1

(4.25)

Upon linearization we get the A matrix as ⎡

1 ∗ + a   a11 11 Rwind + a11 Kpf ⎢  a21 Kpf ⎢ A=⎢ 1  a31 ⎣ Rwind a41

0 a22 0 0

⎤  K a13 a14 if  K ⎥ 0 a24 if ⎥ ⎥ a33 0 ⎦ 0 0

(4.26)

while B, x, and u remain the same. The expressions for the terms in the A and B matrices are presented below (superscript “0” denotes nominal condition): ∗ a11

 a11



 3  2 ω10 + Kopt ωr0 − Id0 V¯or Eacr cos αr0 + Rcr Id0 Rgov1  1  = −a14 =− Id0 V¯or Eacr sin αr0 2HG1 ω10  2Rcr Id0 V¯or Eacr sin αr0 (V¯or Eacr )2 sin 2αr0 + − 2RH RH 1 =−  2 2HG1 ω10



116

 a11

4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . .

=−

ωr0 2HG1 ω10

  a21 = −a24 =

a22  a31

; a13 =

 2 3Kopt ω20

1 2HG2 ω20 RH

2HG1 ω10   Vi V¯or Eacr sin αr0 − 2Rci Id0 V¯or Eacr sin αr0



ω20 =− + Id0 Vi − Rci (Id0 )2 − PL0 0 2 R 2HG2 (ω2 ) gov2    ∂Tmech (Vw , ωr )  1 0 =  0 0  − 2Kopt ωr 2HW F ∂ωr Vw ,ωr 1



1 1 ; b22 = 2HG1 2HG2    ∂Tmech (Vw , ωr )  −1  0 0  ; b24 = 2H ω0 ∂Vw G2 2 Vw ,ωr

a41 = −1; b11 = b33 =

1 2HW F

∗  a11 = a11 + a11

1 Rwind

  + a11 Kpf ; a14 = a14 Kif

   a21 = a21 Kpf ; a24 = a24 Kif ; a31 = a31

1 Rwind

Also as explained in Sect. 4.11.1, based on the zeros in the A matrix, HVDC is acting as a one-way firewall thereby, protecting the rectifier-side grid from the disturbances in the inverter-side grid. With this, the following insights can be derived: • In the previous case, dynamics of ωr was decoupled from other dynamic states. In presence of droop control, the wind farm’s rotor dynamics gets coupled with ω1 and in turn with the rectifier station PI controller dynamics as well. This is 1  due to the term a31 Rwind appearing in the A matrix. 1  • A term a11 Rwind is appearing in the A matrix, which could improve the dynamics of ω1 . Improvement in ω1 could possibly improve the dynamics of ω2 as well. Note that this improvement in the dynamics is obtained without the deloaded operation of the wind farm.

In the case of droop control of wind farm, from the matrices A and B, transfer functions between Δω1 and ΔVw , and between Δω2 and ΔVw are derived as Δω1 (s) ΔVw (s) Δω2 (s) ΔVw (s)

= =

b33 a13 s [s(s−a11 )(s−a33 )−sa13 a31 −(s−a33 )a14 a41 ] b33 a13 (a21 s+a24 a41 ) (s−a22 )[s(s−a11 )(s−a33 )−sa13 a31 −(s−a33 )a14 a41 ]

(4.27)

Note that by setting a31 to “0,” transfer functions presented in (4.23) are obtained.

4.12 Results and Analysis

117

4.11.4 Analytical Insight IV: Synchronizing and Damping Torque The state variable xrf is obtained by integration of ω∗ −ω1 , so Δxrf represents Δδ of  K Δδ the machine. Therefore, from the first row of the A matrix, we have 2HG1 a14 if 1  as the additional synchronizing torque and 2HG1 a11 Kpf Δω1 as additional damping 1  torque from the rectifier frequency control, and 2HG1 a11 Rwind Δω1 as another additional damping torque from frequency droop control of wind farm—see Fig. 4.27. The increase in damping torque contribution from G1 in presence of droop control will further enhance damping, which will be shown later.

4.12 Results and Analysis In order to improve the frequency dynamics in both the grids, droop control of wind farm is considered in this section. As before, the results are demonstrated using the full-order model equipped with firing angle correction strategy. Lower gains of the frequency controller were chosen when droop control is used, so as to match the frequency nadir in the rectifier side in the absence of droop, see Table 4.5.

1

Tewind

TDwind

TePI

TDPI

TSPI

Te0

PI D

T

TD0

wind D

T

TS0

TSPI

2HG1a14 Kif 2HG1a11K pf 1 2 H G1a11 Rwind

1 1

1

1

0 e PI e wind e

T - Electrical torque with current control of HVDC T - Electrical torque with frequency control of HVDC T - Electrical torque with droop control of wind farm Fig. 4.27 Impacts of frequency control of rectifier station and frequency droop control of wind farm on damping torque and synchronizing torque of G1 . Source: Vennelaganti and Chaudhuri [30]. Reproduced with permission of IEEE Table 4.5 Damping torque coefficients Kd of G1 [30]

PI gains, pu Kpf = 0.0001333, Kif = 0.0001167 Kpf = 0.0008, Kif = 0.0007

Rwind 5 No droop

Kd 14.5299 10.3209

118

4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . .

f2 , (Hz)

f1 , (Hz)

αr , (deg)

19.2

no droop (Kpf = 8 × 10−4 , Kif = 7 × 10−4 ) with droop (Kpf = 1.333 × 10−4 , Kif = 1.167 × 10−4 ) (a)

19 18.8

60.02 60 59.98 59.96 59.94 59.92

(b)

60

(c)

59.95 59.9 0

10

20

30

40

50

60

time, (s) Fig. 4.28 Frequency dynamics due to pulse reduction in wind speed, presenting improvement on both inverter and rectifier sides dynamics upon implementation of the frequency droop control in wind farm. Source: Vennelaganti and Chaudhuri [30]. Reproduced with permission of IEEE

Figure 4.28 presents the dynamics following a pulse reduction in wind speed, as shown in Fig. 4.16a. It can be seen from Fig. 4.28b that the frequency nadir on the rectifier side is the same with and without frequency droop control of wind farm. However, Fig. 4.28c shows that the frequency nadir on the inverter side is improved with the implementation of the frequency droop control of the wind farm. Similar observations can be made when fluctuating wind speeds as shown in Fig. 4.29a is considered. This is because the frequency nadir is of more concern than the frequency overshoot to the system operators as it directly affects underfrequency tripping. Therefore, a zoomed portion of the rectifier-side frequency nadir is presented in Fig. 4.29c to prove that the nadir is almost the same with or without frequency droop control. However, frequency dynamics on the inverter side (Fig. 4.29d) is improved with frequency droop control of wind farm. Lower PI gains are used in presence of frequency droop control. As a result, the variations in firing angle (αr ) is less when droop control is applied, see Figs. 4.28a and 4.29b. Figure 4.30 shows the frequency deviation following a high impedance selfclearing fault in the rectifier-side AC system. Although during the fault the responses are the same, after the fault is cleared, the frequency excursion on both the rectifier side and inverter side is more contained in presence of frequency droop control as shown in the zoomed part of Fig. 4.30. Figure 4.31 shows different system variables following the fault. Improved system damping is observed from PG2 as well as f2 in Fig. 4.30 in presence of droop control. This is in line with damping torque analysis of Sect. 4.11.4 and calculated values of Kd presented in Table 4.5. Note that the source of system damping is the damping torque contribution from generators.

f1 , (Hz)

αr , (deg)

Vw , (m/sec)

4.13 Case Study III: Displaced Conventional Generation Converted to. . .

119

13.6

(a) 13.4

f luctuatingwindspeed

13.2 19.2 19 18.8 18.6 18.4 18.2 60.1

(b) no droop(Kpf = 8e-4, Kif = 7e-4) with droop(Kpf = 1.333e-4, Kif = 1.167e-4) (c)

60

f2 , (Hz)

59.9

(d)

60.1 60 59.9 0

5

10

15

20

25

30

35

40

time, (s)

Fig. 4.29 Frequency dynamics due to fluctuations in the wind speed. Improvement on inverterside dynamics, upon implementation of the frequency droop control in wind farm. Source: Vennelaganti and Chaudhuri [30]. Reproduced with permission of IEEE

In this case, damping torque contribution from G1 increases in presence of droop control, thereby improving the system damping ratio. This gets reflected in the entire system response, which is not just confined to the rectifier-side. As a result, improvement is also observed in the inverter-side response, like PG2 and f2 .

4.13 Case Study III: Displaced Conventional Generation Converted to Synchronous Condensers In the previous case studies, the rectifier-side AC system was represented by a single generator and a single wind farm. The limitations of such a model are: 1. it does not represent the feeders connecting the wind farm and the HVDC station, 2. it cannot represent the case of outage of a part of the wind farm due to a singlepoint failure, and 3. it cannot represent the multi-modal characteristics of a multi-machine power grid and its load distribution.

120

4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . .

60.1

frequency, (Hz)

60 60.1

59.9

60.05 59.8 60 59.95

59.7

f1 f2 f1 f2

59.6

no droop 59.9 no droop with droop with droop

2

4

6

8

10

12

59.5 0

5

10

15

20

25

time, (s) Fig. 4.30 Improvement in frequency dynamics following a rectifier-side self-clearing fault with the implementation of frequency droop control in wind farm. Improved damping in f2 is observed with droop. Source: Vennelaganti and Chaudhuri [30]. Reproduced with permission of IEEE

This motivates case study III, which is based on reference [11], and is discussed next. As described in case studies I and II, the rectifier-side AC grid experiences serious issues including large rate of change of frequency (RoCoF), frequency nadir [19], and voltage instability following faults or disturbances near the converter PCC. Voltage oscillations might be observed when wind farms try to tightly regulate terminal voltages in a weak grid. In addition, following a fault, excessive line charging current coupled with low power transfer can give rise to overvoltage cascading [4, 7, 10, 20, 21, 24]. A reasonable solution to this problem is installation of synchronous condensers (SCs) [1, 2, 8, 21, 24, 27]. Synchronous condensers are synchronous motors without a mechanical load. It can consume or generate reactive power as needed by controlling its excitation system, which can enhance system’s short circuit capacity and improve voltage stability. If a flywheel is connected to the rotor shaft of the synchronous condenser, it can also contribute towards system inertia. As a result, the frequency dynamics can be improved as well. However, synchronous condensers are usually very expensive. For instance, in the Guadalupe Station and the Blackwater Station upgrade project in Public Service Company of New Mexico (PNM), the installation cost of synchronous condensers constituted more than 60% of the total project cost [1].

PG1 , (MW) PHV DC

IN ,

(MW) PW F , (MW)

4.13 Case Study III: Displaced Conventional Generation Converted to. . .

121

1000 1050 900

1000

800

950

(a) 0

0.5

1

1070 1060

no droop (Kpf = 8e-4, Kif = 7e-4) with droop (Kpf = 1.333e-4, Kif = 1.167e-4)

1050 1040

140 120 100 80 60 40

1000 500

(b)

(c)

0

0.5

1

PG2 , (MW)

0 790

(d)

780 770 0

5

10

15

time, (s)

Fig. 4.31 Variation in powers of: (a) Wind farm, (b) HVDC rectifier-side input, (c) Rectifier-side generator, and (d) Inverter-side generator following a rectifier-side self-clearing fault. Improved damping in PG2 with droop is observed. Source: Vennelaganti and Chaudhuri [30]. Reproduced with permission of IEEE

One solution has been proposed in literature, which takes into account conversion of phased out synchronous generators to synchronous condensers [6, 21, 26, 27]. This is quite relevant in today’s grid where a significant number of coal-fired plants are getting shut down. This can be an effective alternative in reinforcing the grid while renewable resources are integrated. This is already turning into practice in utility industry. For example, the FirstEnergy Eastlake plant in Ohio, USA converted two generating units to synchronous condensers [26]. Different aspects of conversion of such decommissioned coal-fired plants to synchronous condensers have been presented in [27]. In complex scenarios like Rock Island HVDC project [10], where wind farms are connected to a weak AC grid transferring power through LCC-HVDC, studies have been reported on using synchronous condensers at the converter bus. In general, such studies have taken into consideration only time-domain aspect. Although useful, it cannot provide insights provided by a frequency-domain analysis. This case study focuses on a more practical scenario involving multiple large remote wind farms transmitting power through LCC-HVDC system to the remote load centers. A weak grid interfaces these wind farms in the rectifier side. Instead of

122

4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . .

representing the AC grid with a single AC generator, a multi-machine system with transmission lines and load centers have been taken into account. Shutting down of conventional generation and modifying it to synchronous condenser is studied. A severe contingency of loss of a wind farm following a fault and tripping of a feeder is studied. The study involves analysis of RoCoF and frequency nadir. To improve the frequency dynamics secondary frequency control is imposed in the weak AC system through the LCC HVDC rectifier. Time-domain and frequency-domain analyses are used to compare different scenarios. Root-cause analysis is performed to develop deeper insights into the root-cause of the frequency dynamics.

4.14 Effect of Synchronous Condenser on System Performance In order to understand the system performance with the conversion of coal fired plant as synchronous condenser, an important aspect to be taken into account is the effect of its location on the inertial support it provides. To that end, the synchronous generator representing the weak AC grid in Fig. 4.6 is converted to a synchronous condenser. We separately model two wind farms, which are connected to the PCC using two feeders, while the HVDC rectifier station operates under frequency control mode. The test system is shown in Fig. 4.32. The process of integrating synchronous condensers for load flow analysis is no-trivial, which is described next.

4.14.1 Load Flow Analysis Considering Synchronous Condenser Load flow study is an essential part of power system planning. It is also the first step before doing the dynamic simulation. In this case, all the generator buses including the buses connected to wind farms are assumed to be PV buses. The bus at which the synchronous condenser is connected is assumed as the slack bus. The mechanical power at the synchronous condenser shaft (Pm(sc) ) should be zero and the power injection at its terminal should be a small negative number indicating power consumed to supply the machine’s losses. To ensure this, the power injected at the synchronous condenser-bus, which is a slack bus, is computed from load flow. Then, Pm(sc) is calculated using the steady-state equations of the synchronous   machine. The calculated Pm(sc) could be either positive or negative. If Pm(sc)  ≤ ε—a predetermined threshold, the total power generated by the wind farms is increased or decreased by Pm(sc) . If there are m wind farms, then the power injected by the ith wind farm is changed by Pm(sc) /m, i.e. PW F i = PW F i +

Pm(sc) m

DFIG

DFIG

RSC

RSC

DC Link

I dc

DC Link

I dc

GSC

GSC

PCC

feeder

PWF 2,QWF 2

feeder

PWF 1,QWF 1

Pgrid

caps & filters

ˆ

PLL1

tapr

Z grid

r

Rectifier

Cdc

Rdc 2

1 xrf s

K pf Kif

Ldc 2 Ldc 2

Vdm

Rdc 2

G2

Decommissioned coal power plant

Rectifier Frequency controller

r0

r

Vdr

I dr

ˆ

Vdi

I di

*

-

i

xi1

K pi

Kii

Min over a cycle

tapi

Ti :1 Eaci

1 s

caps & filters

i

-

Vgi

Inverter extinction angle controller

i

Inverter

i * i

Fig. 4.32 Schematic of two DFIG-based wind farms connected to LCC-HVDC in an AC grid represented by a single synchronous generator. The synchronous generator is converter to a synchronous condenser. The LCC-HVDC rectifier station is operating in constant frequency control mode

Wind Farm 2

VW 2

Wind Farm 1

VW 1

Eacr

Phvdc

1: Tr

4.14 Effect of Synchronous Condenser on System Performance 123

124

4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . .

The AC and the DC loadflow are solved with the new values of real power. The process is continued till when all of ΔPr/i =  iteration   the (k + 1)th    (k+1)  (k+1) (k)  (k)   Pr/i − Pr/i  , ΔQr/i = Qr/i − Qr/i , and Pm(sc)  falls below predetermined thresholds.

4.14.2 Results and Analysis

Eacr [p.u]

Time-domain simulations are performed under two conditions: with increasing distance of the converted synchronous condenser and with increasing inertia of synchronous condenser, which can be done by adding a flywheel [8]. Figure 4.33 shows that the effect of location of synchronous condenser on frequency nadir and RoCoF is negligible when the distance from the PCC shown in Fig. 4.32 is increased from 10 to 70 km. This study considers a self-clearing fault at the PCC. The real power output of the synchronous condenser Psc is close to zero before and after the disturbance. During the disturbance, the rotor of the synchronous condenser slows down to release kinetic energy, which results in positive value

3 2 1

δ[deg]

0

0.4

0.6

0.8

1

1.2

1.6

1.8

2

SC 10km SC 50km SC 70km

-4 -6 1

2

3

4

5

6

7

8

0.2

0.3

9

10

60 57.6 57.5 57.4

59 58 0

PSC [p.u.]

1.4

-2

0

f [Hz]

0.2

1

2

3

4

5

0.4 6

7

10 5 0 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

time[s] Fig. 4.33 Effect of synchronous condenser location from point of common coupling on frequency nadir. Source: Kaur and Chaudhuri [11]. Reproduced with permission of IEEE

Vdf g [pu]

4.14 Effect of Synchronous Condenser on System Performance

125

2 1 0 0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.35

0.4

0.45

4

5

6

0.5

Vsc [pu]

2 1.5 1

F req[Hz]

0.15

0.2

0.25

0.3

2

3

0.5

60 55 50

QW F [pu]

0

1

7

self clearing Hsc = 2.05s (WF2 outage) Hsc = 6.20s (WF2 outage)

10 5 0 -5 0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

time[s]

Fig. 4.34 Effect of synchronous condenser inertia following self-clearing fault resulting in loss of WF2 on frequency nadir and RoCoF. Response following self-clearing fault with Hsc = 2.15 s is also shown for comparison. Source: Kaur and Chaudhuri [11]. Reproduced with permission of IEEE

of Psc . Since the rotor slows down, it results in a negative value of power angle δ. Results indicate that the retired coal-fired plants within this distance can be converted to synchronous condensers to effectively provide inertial support. One problem however is the voltage overshoot at the PCC following the clearance of the fault. In a separate study, the frequency nadir with a self-clearing fault at the WF2 terminal followed by the outage of WF2 is shown in Fig. 4.33. The terminal voltage and the reactive power output of WF2 denoted by Vdfg and QW F are also shown in this figure. By increasing the inertia of synchronous condenser, the frequency nadir can be improved. In addition, the rate of change of frequency is also improved which can be observed from Fig. 4.34. To analyze the system performance in terms of frequency nadir and RoCoF, it is essential to have a detailed model of the AC grid where one of the decommissioned plants is converted to a synchronous condenser while the rest are still in operation instead of having just a synchronous condenser without any other generating unit except wind farms. The study system with a detailed representation of the AC grid on the rectifier side of the LCC-HVDC is considered next.

126

4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . .

4.15 Test System with Detailed Model of Weak AC Grid Figure 4.35 shows a schematic of the test system. A 4-machine, 2-area system [13] is considered to model a regional AC grid connected to a distant substation denoted by bus 13. The transmission line connecting this AC grid to the substation is modeled with an impedance Zgrid of j0.2pu. This is representative of low short circuit capacity at the substation. Two wind farms are considered as before, which are modeled and controlled as described in Sect. 3.2.2 of Chap. 3. These wind farms are connected to the substation, which is considered as the PCC. Two feeders, each of 50 km length, are used to interconnect the wind farms. An LCC-HVDC transmission system transports the power from the wind farms to distant load centers. The synchronous generators are represented by sixth-order subtransient models. Each generator is equipped with an IEEE DC1A type excitation system and a turbine-governor. Further, to represent a grid with progressively reducing inertia, the MVA ratings of the synchronous generators in this system are reduced while proportionately reducing their power output. To keep the net power output same at the generator buses, the remaining real and reactive powers were supplied by negative constant power loads, which represent simplified wind farm models at these locations. In effect, this is representative of replacing coal-fired plants with wind generation in the regional grid.

4.16 Challenges and Proposed Solutions The weak grid negatively affects the rate of change of frequency (RoCoF) and frequency nadir following any disturbance. In the case study where the weak AC grid was represented by one equivalent generator, the multi-modal characteristics of a multi-machine power grid and its load distribution could not be modeled. The major challenge is to improve the frequency dynamics of such a weak system under severe conditions like loss of generation. Following a loss of generation, traditional governors work under off-nominal frequency. In such a weak system, the off-nominal value can be lower than 59 Hz and recover very gradually due to slow automatic generation control (AGC) action. This can trigger under-frequency load shedding (UFLS)—typical threshold for UFLS in the USA being 59.5 Hz. One approach to provide inertial support, short circuit power, and reactive power support is to have SCs installed at the PCC. However, the installation of SCs to serve this purpose may not be cost-effective as pointed out in [1]. The approach presented in here is to convert the retired or decommissioned coal-fired power plants into SCs. These SCs can improve the frequency nadir and RoCoF under severe faults or loss of generation. One of the challenges facing this idea is that the SCs may participate in the poorly damped mode of the system. To solve the issue of a large and persistent frequency deviation risking UFLS, the HVDC rectifier station can be used for providing secondary frequency support, which was proposed in [11]. The

DFIG

DFIG

RSC

RSC

DC Link

I dc

DC Link

I dc

GSC

GSC

12

vs12

18

vs18 feeder

PCC

16

feeder

PWF 2,QWF 2

17

PWF 1,QWF 1

Pgrid

ˆ

G1

G2

1

Z grid

r

Cdc

Rdc 2

1 xrf s

K pf Kif

Ldc 2 Ldc 2

Vdm

Rdc 2

-

K

1 ir x r1 s

K pr

-

7

9

10 11

-

tapi i

xi1

K pi

Kii

Min over a cycle

Eaci

Ti :1 14

1 s

caps & filters

15

4

3

G4

G3 and

and

i

-

Vgi

Inverter extinction angle controller

i

Inverter

Dynamic Model of weak AC grid

8

*

I d*

Vdi

I di

ˆ I dr

Rectifier current controller

5 6

-

r

Rectifier Frequency controller

r

Vdr

I dr

r0

Rectifier

Decommissioned 2 coal power plant

and

caps & filters

PLL1

tapr

Phvdc 1: Tr

i * i

Fig. 4.35 Schematic of two DFIG-based wind farms connected to LCC-HVDC in an AC grid represented by a 4-machine 2-area system. The LCC-HVDC rectifier operates either in a current control mode or in a frequency control mode. One of the synchronous generators G2 is converted to a synchronous condenser

Wind Farm 2

VW 2

Wind Farm 1

VW 1

13

Eacr

4.16 Challenges and Proposed Solutions 127

128

4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . .

following section compares the performance of the HVDC rectifier in traditional current control with the frequency control method.

4.17 Results and Analysis To study the effectiveness of the proposed solutions, the test system shown in Fig. 4.35 is considered. The system stability and performance are analyzed in two ways: frequency-domain analysis and time-domain analysis.

4.17.1 Frequency-Domain Analysis Modal analysis has been performed to understand the interaction of system modes, especially the inter-area mode, in different operating conditions mimicking a gradual change in power system with reduction of coal-fired plants and increased penetration of local wind farms to replenish load demand. These changes are considered under different control modes of HVDC rectifier-side converter, i.e., current control mode and frequency control mode. Each analysis has been done considering two scenarios: with and without converting a retired plant to synchronous condenser. The eigenvalue analysis is performed considering five operating conditions: (1) Base Case: when all the generators are operating with full rating. (2) When G2 is decommissioned while the rest of the generators still operate with maximum capacity. To replenish local load, extra power is imported from the wind farms (i.e., from bus 13 to bus 7 in Fig. 4.35). (3) When G2 is retired and the inertia of the grid is progressively reduced due to partial replacement of generation at buses 1, 3, and 4 by wind farms. This reduction is done in three steps: each generator’s (except retired G2) output is reduced from full power to two-third, half and one-third of the rated value, respectively. While the remaining one-third, half and two-third power has been added from local wind farms modeled as negative constant power loads.

4.17.1.1

Without Converting G2 into Synchronous Condenser

Figures 4.36 and 4.37 show the movement of the critical modes of the system when HVDC rectifier is in constant current (CC) control and frequency control mode, respectively. It can be observed that the modal frequency of a couple of electromechanical modes keep increasing with a progressive reduction of system inertia from case (1) to (3) described above. It can also be observed that the lowest frequency electromechanical mode is moving towards right.

4.17 Results and Analysis

129

1000

All G full P no G2 rest full P no G2 rest 2P/3 no G2 rest P/2 no G2 rest P/3

8

800 6 600 4

400

2

jω

jω

200 0 -200

0 -2

-400 -4 0.5 -600

(c)

-0.5

(a)

-1000 -600

0

-6

-800

-400

-200

(b)

-8

-0.6

0

-8

-0.4

-6

-0.2

-4

0

-2

0

σ

σ

Fig. 4.36 (a): Eigenvalue plot without synchronous condenser when rectifier-side is at current control; (b): and (c): Zoomed inter-area modes. Source: Kaur and Chaudhuri [11]. Reproduced with permission of IEEE 1000

All G full P no G2 rest full P no G2 rest 2P/3 no G2 rest P/2 no G2 rest P/3

8 800 6

400

4

200

2

jω

jω

600

0 -200

-2 0.5

-400

-4 0

-600

-6

-800 -1000 -600

0

(a) -400

-200

σ

0

-8

-0.5

(c) -0.6

-6

-0.4

-0.2

-4

0

-2

(b) 0

σ

Fig. 4.37 (a): Eigenvalue plot without synchronous condenser when rectifier-side is at frequency control; (b): and (c): Zoomed inter-area modes. Source: Kaur and Chaudhuri [11]. Reproduced with permission of IEEE

130

4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . .

4.17.1.2

With G2 Converted to Synchronous Condenser

In presence of G2 converted to synchronous condenser, the same exercise was performed. As shown in Figs. 4.38 and 4.39, a mixed eigenvalue movement is observed progressively from case (1) to (3). Further insight can be developed from the frequency-domain approach through participation factor analysis of the weakest system where the MVA rating of generators: G1, G3, and G4 are one-third of the base case rating while the rest of the power is coming from local wind farms modeled as negative loads; and G2 is retired. We only focus on the modes relevant to the frequency dynamics of the system, i.e. where the dynamic states like generator speeds and PLL states have the highest participation. Tables 4.6 and 4.7 show the critical modes of the system without converting G2 to synchronous condenser. Under both control schemes, there are two modes, which have participation from the rotor speed of all the synchronous machines. Tables 4.8 and 4.9 show the changes in modes after including the converted synchronous condenser. Comparing the different control schemes after converting G2 to synchronous condenser, the low frequency mode present in CC control (−0.3659 ± j 0.0582) shown in Table 4.8 is eliminated in Table 4.9, instead a welldamped high-frequency mode (−554.35 ± j 508.22) of the HVDC-PLL appears. The effect of including synchronous condenser on the frequency nadir and the RoCoF in such systems following disturbances like loss of generation due to a single-point failure is considered next.

1000

All G full P no G2 rest full P with SC rest 2P/3 with SC rest P/2 with SC rest P/3

8

800

6

600 4

400

2

jω

jω

200 0 -200

0 -2

1

-400 -4 -600

0

-6

-800 (a)

-1000 -600

-400

-200

σ

0

-8

(c) -1 -0.4

-6

-0.3

-0.2

-4

-0.1

σ

0

-2

(b) 0

Fig. 4.38 (a): Eigenvalue plot with synchronous condenser when rectifier-side is at current control; (b): and (c): Zoomed inter-area modes. Source: Kaur and Chaudhuri [11]. Reproduced with permission of IEEE

4.17 Results and Analysis

131

1000

All G full P no G2 rest full P with SC rest 2P/3 with SC rest P/2 with SC rest P/3

8

800

6

600 4 400 2

jω

jω

200 0 -200

0 -2 2

-400

-4

-600

0

-6

-800 (a) -1000 -600

-8

(c)

-2 -1

-400

σ

-200

0

-8

-0.5

-6

(b)

0

-4

σ

-2

0

Fig. 4.39 (a): Eigenvalue plot with synchronous condenser when rectifier-side is at frequency control; (b): and (c): Zoomed inter-area modes. Source: Kaur and Chaudhuri [11]. Reproduced with permission of IEEE Table 4.6 Modal participation analysis for weak system without synchronous condenser (CC control) [11]

Table 4.7 Modal participation analysis for weak system without synchronous condenser (frequency control) [11]

Dominant states G4 : ω4 , G3 : ω3 G1 : ω1 , G4 : ω4 , G3 : ω3 G1 : ω1 , G3 : ω3 , G4 : ω4 P LL(GSC1) : xˆpll , ωˆ Dominant states G4 : ω4 , G3 : ω3 G3 : ω3 , G4 : ω4 , G1 : ω1 G1 : ω1 , G3 : ω3 , G4 : ω4 P LL(GSCi ) : xˆpll(i) , ωˆ i P LL(H V DC) : xˆpll , ωˆ

Modes λi = σi ± j ωdi −0.8110 ± j 8.4242 −0.2492 ± j 6.2501 −0.3511 ± j 0.4305 −533.1 ± j 533.2395

Modes λi = σi ± j ωdi −0.8109 ± j 8.4243 −0.8408 ± j 1.1332 −0.2777 ± j 6.25012 −533.1 ± j 533.2395 −545.5223 ± j 499.0775

4.17.2 Time-Domain Analysis In order to analyze the effect of including synchronous condenser on frequency dynamics, it is essential to conduct time-domain analysis. For the time-domain analysis, the performance of the system under different control schemes of HVDC

132

4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . .

Table 4.8 Modal participation analysis for weak system including synchronous condenser (CC control) [11] Dominant states G1 : ω1 , SC : ωsc G3 : ω3 , G4 : ω4 , SC : ωsc , G3 : ω3 , SC : ωsc , G1 : ω1 , G3 : ω3 , SC : ωsc , G3 : ω3 , G4 : ω4 , G1 : ω1 P LL(GSC1) : xˆpll , ωˆ

Modes λi = σi ± j ωdi −1.0208 ± j 7.2503 −0.8202 ± j 8.4200 −1.0257 ± j 1.9119 −0.3659 ± j 0.0582 −0.6866 ± j 5.0232 −533.1 ± j 533.2395

Table 4.9 Modal participation analysis for weak system including synchronous condenser (frequency control) [11] Dominant states G1 : ω1 , SC : ωsc G3 : ω3 , G4 : ω4 , SC : ωsc , G1 : ω1 , G3 : ω3 , SC : ωsc , G4 : ω4 , G4 : ω4 , G3 : ω3 , SC : ωsc , G1 : ω1 P LL(GSC) : xˆpll(i) , ωˆ P LL(H V DC) : xˆpll , ωˆ

Modes λi = σi ± j ωdi −1.0288 ± j 7.2602 −0.8201 ± j 8.4200 −1.0203 ± j 1.9127 −0.6866 ± j 5.0196 −1.0068 ± j 0.6093 −533.1 ± j 533.2395 −554.3481 ± j 508.2163

rectifier is considered following the outage of one of the wind farms. The simulations were carried out for the weakest system for which the participation factor analysis was conducted.

4.17.2.1

Constant Current Control Scheme

Without Synchronous Condenser Conversion During the pre-fault conditions, the major portion of the local loads at bus 7 is supplied from the remote wind farms, which is around 297 MW, while 13 MW was flowing through the tie-lines from bus 7 in Fig. 4.35. The tie-lines are extremely lightly loaded in this case. This could be the reason behind the presence of a well-damped inter-area mode in the system. However, in the post-contingency conditions, the direction of power flow through the tie-lines is reversed and increased up to 185 MW. The same pre- and post-contingency conditions were examined after converting G2 into synchronous condenser at bus 2. In this case as well, during the pre-fault case the tie-lines are lightly loaded while wind farms are supplying power to the local loads near the PCC. However, with the loss of generation from one of the wind farms, the tie-line power is reversed and increased to around 197 MW. Due to the stiff current control of rectifier, extra power is needed to be delivered from the other side of the tie-line.

4.17 Results and Analysis

133

(b)

(a)

60

NO SC (No G2) with SC

fSC [Hz]

fG1 [Hz]

60

59.5

59.5

59

59 (c)

(d)

60

fG4 [Hz]

fG3 [Hz]

60

59.5

59

59.5

59 0

5

10

15

20

25

30

time[s]

0

5

10

15

20

25

30

time[s]

Fig. 4.40 The effect of outage of WF-1 on frequency nadir with and without considering synchronous condenser when HVDC rectifier-side is under Current control. (a) Frequency of G1, (b) Frequency of synchronous condenser, (c) Frequency of G3, (d) Frequency of G4. Source: Kaur and Chaudhuri [11]. Reproduced with permission of IEEE

Figure 4.40 shows the frequency dynamics of the system following a 5-cycle three-phase fault at bus 17 resulting in the loss of WF-1 producing 300 MW. It shows a marginal improvement in frequency nadir after including the synchronous condenser. However, the inclusion of synchronous condenser leads to poorly damped inter-area oscillations. Issues involving SCs have been documented in literature—examples include upgradation of the New Zealand HVDC bipole from 600 to 1240 MW [16]. It is difficult to analyze the system behavior in frequencydomain following the loss of generation.

4.17.2.2

Frequency Control Scheme

Without Synchronous Condenser Conversion In the post-contingency case, since the HVDC rectifier is at frequency control, the power flowing through the HVDC is changed. In other words, LCC-HVDC works as a frequency dependent load. During the post-fault condition, the power flowing through the HVDC link is decreased. Although the direction of tie-line power flow is reversed, it remains lightly loaded at around 5 MW to feed the local loads at the PCC.

134

4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . . 60.4 (a)

60 59.8 59.6

No SC (No G2) with SC

59.4 59.2

60 59.8 59.6 59.4 59.2

(c)

(d)

60.2

60

60

fG4 [Hz]

fG3 [Hz]

60.2

(b)

60.2

fSC [Hz]

fG1 [Hz]

60.2

59.8 59.6 59.4 59.2

59.8 59.6 59.4 59.2

0

10

20

30

time[s]

40

50

0 59.2 Hz

59.09 Hz 10

20

30

40

50

time[s]

Fig. 4.41 The effect of outage of WF-1 (Fig. 4.35) on frequency dynamics with and without considering synchronous condenser when HVDC rectifier-side is under frequency control mode. (a) Frequency of G1, (b) Frequency of synchronous condenser, (c) Frequency of G3, (d) Frequency of G4. Source: Kaur and Chaudhuri [11]. Reproduced with permission of IEEE

With Synchronous Condenser Conversion Figure 4.41 shows the frequency dynamics with the loss of generation from WF-1 following three-phase fault at bus 17. As shown in Fig. 4.41, compared to the system without synchronous condenser, frequency nadir of the system is improved with the addition of synchronous condenser. Moreover, the issue faced by the current control scheme with the addition of synchronous condenser is eliminated. Since HVDC rectifier controls the frequency, the power flowing through the HVDC reduces after the loss of generation. The major advantages of this control are: 1. Due to frequency control, HVDC acts as a frequency-dependent load, which helps improve frequency dynamics following the loss of generation. 2. The issue of operating the wind farms at off-nominal frequency under slow AGC action is eliminated as the secondary frequency control action of HVDC brings it back to the nominal value.

4.17 Results and Analysis

135

Appendix 1 In an alternative form, the induction machine and the RSC dynamics can be modeled as follows (q-axis aligned with stator flux): i˙qs =



Rr + Kpr ωel Rs − σ Lrr Lss





iqs

Kpr Lm + − σ Lrr Lss



Rr + Kpr σ Lrr

 ims

  Lm Kir  Lm Kpr ωel Kvc |vs | − vs∗  − xrr1 − vqs Lss σLr Lss σ Lrr Lss   Kopt Kpr 1 2 Rr + Kpr Lm Kir ids − = xrr2 − ω σ Lrr Lss σ Lrr Lm σ Lrr ims r_dfg   2 eqs ωel ω Kmrr  =  ω i − L − f r r_dfg qs 2 Lf r Kmrr a aTr ω +1 +

i˙ds  e˙qs

aLs



2 R Lf r Kmrr s + R2 − aLs

 e˙ds

i˙ms



 ids +

 2 Lf r Kmrr  + sl eds aLs

 2 Lf r Kmrr Kmrr vdt − vds − aLs a   2 eds ωel ω Kmrr  L =  ω i − − f r r_dfg ds 2 Lf r Kmrr a aTr ω +1 aLs     2 R 2 Lf r Kmrr Lf r Kmrr s  − R2 − + sl eqs iqs − aLs aLs  2 Lf r Kmrr Kmrr vqt + vqs + aLs a    ωel  Rs iqs + vqs =− Lm

where  vdt = Kir xrr2 + Kpr −sl ω

 

2 Lss Kopt ωr_dfg

L2m ims

 − idr

 L2 σ Lrr + Lf r iqr + m ims Lss



(4.28)

136

4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . .

    vqt = Kir xrr1 + Kpr ims + Kvc vs∗  − |vs | − iqr   +sl ω σ Lrr + Lf r idr Lss = Ls + Lm ,

Lrr = Lr + Lm

Kmrr = Lm /Lrr , σ = 1 − L2m /(Lss Lrr ), 2 R2 = Kmrr (Rf r + Rr ),

idr = −

Lss ids , Lm

Ls = Lss − Lm /Kmrr a = 1 + (Lf r /Lrr ) Tr = Lrr /(Rf r + Rr ) iqr = ims −

Lss iqs Lm

Kopt = 0.5ρπ R 5 CP opt /λ3opt The DC link and the GSC (q-axis aligned with vs ) can be modeled as described below:  3  vdt idr + vqt iqr + vdg idg + vqg iqg C       Rfg + Kpg Kig Kpg ∗ iqg + xg1 + i =− Lfg Lfg Lfg qg    ∗     2Qgsc Rfg + Kpg Kig Kpg idg + xg2 − =− Lfg Lfg Lfg 3vqs

2 v˙dc =−

i˙qg i˙dg

(4.29)

(4.30)

Note that vqg and vdg can be expressed as:   ∗ − iqg − ωLfg idg + vqs vqg = Kig xg2 + Kpg iqg   2Q∗gsc vdg = Kig xg1 + Kpg − − idg + ωLfg iqg + vds 3vqs

(4.31)

The state equations of the RSC and the GSC current control loops are shown in Eq. (4.32).    x˙rr1 = ims + Kvc Vs∗  − |vs | − iqr   Lss Kopt 2 x˙rr2 = ω − idr L2m ims r_dfg   ∗ − iqg x˙g1 = iqg   2Q∗gsc − idg x˙g2 = − 3vqs

(4.32)

4.17 Results and Analysis

137

Appendix 2 DFIG Parameters (pu) on 1.667 MVA, 575 kV Base Ls = 0.1714, Rs = 0.00706, Lm = 2.904, Lr = 0.1563 Rr = 0.005, C = 0.7477,

Ht = 3.5 s,

Hg = 4.55 s

Lf r = 4.752, Rf r = 0.0761, Lfg = 2.311, Rfg = 0.0338 Csh = 0.09 pu s/elect rad, Ksh = 0.3 pu/elect rad, λopt = 10.5

LCC-HVDC Parameters Bi = 2,

Br = 2,

Cdc = 26 µF,

Xci = 13.2062 , Xcr = 13.0956 

Ldc = 1.1936 H, tapi = 1,

Rdc = 5 , tapr = 1

AC Grid (Dynamic Model) Parameters (pu) on 900 MVA, 20 kV Base [13] Xd = 1.8,

Xq = 1.7,

Xl = 0.2,

X q = 0.55, X d = 0.25, X q = 0.25,

Xd = 0.3 Ra = 0.0025

 = 8.0 s, T  = 0.4 s, T   Td0 d0 = 0.03 s, T q0 = 0.05 s q0

State-Space Averaged Model Variables The following are the state variables, input variables, and the algebraic variables obtained when the state-space model is linearized around the operating point (refer Table 4.2).

138

4 Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC. . .

State Variables, x0 θˆ2 = 0.046 pu, xrr1 = −0.020, xpll(2) = 0, iqs = 8.340 pu ids = 4.532 pu, xrr2 = 0.045,

xrf = 0,

ims = 3.962 pu,

2 = 5.928 pu, i vdc qg = 0.951 pu, idg = 0,

θtw = 2.683 rad.

ωt = 1.180 pu, xg1 = 0.005,

xg2 = 0,

ωr−dfg = 1.18 pu

 = 0.908 pu, x = 0.036, eqs i1

∗ = 0.951 pu Idr = 2 A, iqg

 = 0.292 pu, x = 0.030, eds r1

Idi = 2 A, vdm = 504.5 kV

Input Variables, u0   Id∗ = 2 A, vs∗  = 0.817 pu, Vw = 13.2 m/s, θ2 = 0.046 pu,  ∗ 2 Q∗gsc = 0, vdc = 5.928 pu, γi∗ = 0.263 rad. Algebraic Variables, z0 |vs | = 1.035 pu, vqs = 1.035 pu, Eacr = 367.0 kV, Eaci = 231.8 kV, αr0 = 367.0 kV

Pitch Angle Control The parameters of the pitch angle controller (Fig. 4.42) are: Kpp = 1 deg, Kip = 40 deg s−1 Fig. 4.42 Schematic of the pitch angle (β) controller [15]

K pp

r dfg r dfg

K ip s

References

139

Parameters for Case Study II Inverter-side system: HG2 = 7.0 s, Rgov2 = 0.005 (Hz/pu−MW), PL = 1700 MW, nominal PG2 = 774.01 MW and rating of G2 = 900 MW. Acknowledgements Results reported in this chapter are developed based on research papers [11, 30, 36] published from my group, which are reproduced with permission of IEEE. Graduate students involved in producing these results are Mr. Amirthagunaraj Yogarathinam, Ms. Jagdeep Kaur, and Mr. Sai Gopal Vennelaganti. Most of the research material was produced with support from NSF grant award ECCS1656983.

References 1. Blackwater-four corners 128 MW transmission service request: transmission service facilities study report. PNM, Public Service Company of New Mexico, Albuquerque, NM (2014) 2. Bozhko, S.V., Blasco-Gimenez, R., Li, R., Clare, J.C., Asher, G.M.: Control of offshore DFIGbased wind farm grid with line-commutated HVDC connection. IEEE Trans. Energy Convers. 22(1), 71–78 (2007) 3. Bozhko, S., Asher, G., Li, R., Clare, J., Yao, L.: Large offshore DFIG-based wind farm with line-commutated HVDC connection to the main grid: engineering studies. IEEE Trans. Energy Convers. 23(1), 119–127 (2008) 4. Clean Line Energy. http://www.rockislandcleanline.com/site/home 5. Condren, J.E., Gedra, T.W.: Eigenvalue and eigenvector sensitivities applied to power system steady-state operating point. In: Proceedings of the 45th Midwest Symposium on Circuits and Systems (2002) 6. Deecke, A., Kawecki, R.: Usage of existing power plants as synchronous condenser. PRZEGLAD ELEKTROTECHNICZNY 10, 64 (2015) ‘ 7. ElMehdi, A., Momen, A., Johnson, B.K.: Dynamic reactive compensation requirements at the rectifier end of an LCC HVDC link connected to a weak AC system. In: 2014 North American Power Symposium (NAPS), pp. 1–6 (2014) 8. Giulio, A.D., Giannuzzi, G., Iuliani, V., Palone, F., Rebolini, M., Zaottini, R., Zunino, S.: Increased grid performance using synchronous condensers in multi in-feed multi-terminal HVDC system. In: 2014 Cigre’ session papers and proceedings (2014) 9. Guide For Planning DC Links Terminating at AC Locations Having Low Short-Circuit Capacities, Part I: AC/DC Interaction Phenomena. CIGRE’ and IEEE Joint Task Force Report, vol. 68. CIGRE’ Publication (1992) 10. Hernandez, A., Majumder, R., Galli, W., Bartzsch, C., Danis, D., Chaudhry, A.: Facilitating bulk wind power integration using LCC HVDC. In: Rock Island Exhibit 2.19, CIGRE’ US National Committee 2013 Grid of the Future Symposium 11. Kaur, J., Chaudhuri, N.R.: Conversion of retired coal-fired plant to synchronous condenser to support weak AC grid. In: 2018 IEEE PES General Meeting, Portland, OR (2018) 12. Klein, M., Rogers, G.J., Kundur, P.: A fundamental study of inter-area oscillations in power systems. IEEE Trans. Power Syst. 6(3), 914–921 (1991). https://doi.org/10.1109/59.119229 13. Kundur, P.: Power System Stability and Control. The EPRI Power System Engineering Series. McGraw-Hill, New York (1994) 14. Li, R., Bozhko, S., Asher, G.: Frequency control design for offshore wind farm grid with LCCHVDC link connection. IEEE Trans. Power Electron. 23(3), 1085–1092 (2008) 15. Lingling, F., Zhixin, M., Osborn, D.: Wind farms with HVDC delivery in load frequency control. IEEE Trans. Power Syst. 24(4), 1894–1895 (2009)

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16. Martin, D., Wong, W., Liss, G., Arnlov, B., Jonsson, T., Gleadow, J., de Silva, J.: Modulation controls for the New Zealand DC hybrid project. IEEE Trans. Power Deliv. 6(4), 1825–1830 (1991) 17. Miao, Z., Fan, L., Osborn, D., Yuvarajan, S.: Wind farms with HVdc delivery in inertial response and primary frequency control. IEEE Trans. Energy Convers. 25(4), 1171–1178 (2010) 18. Midwest ISO, PJM, SPP and TVA: Joint coordinated system plan 2008. Technical report (2008). http://www.jcspstudy.org/ 19. Miller, N.W., Shao, M., Pajic, S., D’Aquila, R.: Eastern frequency response study, DE-AC3608GO28308. NREL, National Renewable Energy Laboratory, Golden, CO (2013) 20. Miller, N.W., Shao, M., Pajic, S., D’Aquila, R.: Western wind and solar integration study phase 3 - frequency response and transient stability: executive summary. NREL, National Renewable Energy Laboratory, Golden, CO (2014) 21. Miller, N.W., Leonardi, B., D’Aquila, R.: Western wind and solar integration study phase 3A: low levels of synchronous generation. NREL, National Renewable Energy Laboratory, Golden, CO (2015) 22. PSCAD/EMTDC v. 4.2.1, Manitoba HVDC Research Centre, Winnipeg, MB, Canada 23. Ran, L., Xiang, D., Hu, L., Abbott, K.: Voltage stability of an HVDC system for a large offshore wind farm with DFIGs. In: The 8th IEE International Conference on AC and DC Power Transmission, ACDC, pp. 150–154 (2006) 24. Schmall, J., Huang, S.H., Li, Y., Billo, J., Conto, J., Zhang, Y.: Voltage stability of large-scale wind plants integrated in weak networks: an ERCOT case study. In: 2015 IEEE Power Energy Society General Meeting, pp. 1–5 (2015) 25. Se-Kyo, C.: A phase tracking system for three phase utility interface inverters. IEEE Trans. Power Electron. 15(3), 431–438 (2000) 26. Slattery, C., fogarty, J.: Synchronous condenser conversions at firstEnergy Eastlake plant. In: Rock Island Exhibit 2.19, CIGRE US National Committee 2015 Grid of the Future Symposium (2015) 27. Turbine-generator topics for power plant engineers: converting a synchronous generator for operation as a synchronous condenser. EPRI, Palo Alto, CA. (2014). 3002002902 28. U.S. Department of Energy: 20% wind energy by 2030: increasing wind energy’s contribution to U.S. electricity supply. Technical report (2008) 29. U.S. Department of Energy: Staff report to the secretary on electricity markets and reliability. Technical report (2017) 30. Vennelaganti, S.G., Chaudhuri, N.R.: New insights into coupled frequency dynamics of AC grids in rectifier and inverter sides of LCC-HVDC interfacing DFIG-based wind farms. IEEE Trans. Power Deliv. 33(4), 1765–1776 (2018) 31. Wang, L., Wang, K.H.: Dynamic stability analysis of a DFIG-based offshore wind farm connected to a power grid through an HVDC link. IEEE Trans. Power Syst. 26(3), 1501–1510 (2011) 32. Xiang, D., Ran, L., Bumby, J., Tavner, P., Yang, S.: Coordinated control of an HVDC link and doubly fed induction generators in a large offshore wind farm. IEEE Trans. Power Deliv. 21(1), 463–471 (2006) 33. Yin, H., Fan, L.: Modeling and control of DFIG-based large offshore wind farm with HVDClink integration. In: North American Power Symposium (NAPS), pp. 1–5 (2009) 34. Yin, H., Fan, L., Miao, Z.: Coordination between DFIG-based wind farm and LCC-HVDC transmission considering limiting factors. In: IEEE 2011 EnergyTech, pp. 1–6 (2011) 35. Yin, H., Fan, L., Miao, Z.: Fast power routing through HVDC. IEEE Trans. Power Deliv. 27(3), 1432–1441 (2012) 36. Yogarathinam, A., Kaur, J., Chaudhuri, N.R.: Impact of inertia and effective short circuit ratio on control of frequency in weak grids interfacing LCC-HVDC and DFIG-based wind farms. IEEE Trans. Power Deliv. 32(4), 2040–2051 (2017). https://doi.org/10.1109/TPWRD.2016. 2607205

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37. Zhang, M., Yuan, X., Hu, J., Wang, S., Ma, S., He, Q., Yi, J.: Wind power transmission through LCC-HVDC with wind turbine inertial and primary frequency supports. In: IEEE Power Energy Society General Meeting, pp. 1–5 (2015) 38. Zhou, H., Yang, G.: Control of DFIG-based wind farms with hybrid HVDC connection. In: IEEE 6th International Power Electronics and Motion Control Conference, IPEMC, pp. 1085– 1091 (2009) 39. Zhou, H., Yang, G., Wang, J.: Modeling, analysis, and control for the rectifier of hybrid HVdc systems for DFIG-based wind farms. IEEE Trans. Energy Convers. 26(1), 340–353 (2011)

Chapter 5

Power System Restoration Using DFIG-Based Wind Farms and VSC-HVDC Transmission Systems

Abstract This chapter focuses on restoration of AC grids using doubly fed induction generator (DFIG)-based wind farms and voltage source converter (VSC) HVDC systems. During the black-start process, the system becomes extremely weak and study of restoration following a blackout becomes challenging due to a wide bandwidth of interest. A “Hybrid” simulation platform that allows representation of a portion of the grid using detailed three-phase electromagnetic transient (EMT)type models and the rest of the grid by phasor model is described to simulate the black-start process. The results from the Hybrid and the non-Hybrid simulations are compared. Finally, a phasor-measurement unit (PMU)-assisted restoration process involving DFIG-based wind farms and VSC-HVDC link is presented using the Hybrid simulation platform.

5.1 Introduction Failures in power systems in the past have led to large blackouts, which have cost the economy billions of dollars and affected societies around the world. Following a blackout, during the early stages of restoration, an AC grid remains extremely weak in nature. This is due to the lack of generating resources in the grid providing voltage and reactive power support combined with dearth of inertia in the system providing adequate frequency stabilization. Restoration methods that can reduce the downtime following such massive outages are important since they help reduce the negative impact and its cost. History of blackouts in the recent past has shown that HVDC links can help stop the propagation of blackout. They have a “firewall” effect stemming from the DC transmission. Especially, a VSC-HVDC has the capability to operate in an isolated/islanded mode, which was described in Sect. 2.5 of Chap. 2. In this mode, the converter station can impose self-generated AC voltage—given that it has a charged DC bus. Since HVDC transmission systems stop blackouts from reaching the AC grid at the other end of the link, the healthy AC system can help keep the DC bus charged. A few important steps in system restoration include transformer charging, transmission line charging, and cold load pickup, which can © Springer Nature Switzerland AG 2019 N. R. Chaudhuri, Integrating Wind Energy to Weak Power Grids using High Voltage Direct Current Technology, https://doi.org/10.1007/978-3-030-03409-2_5

143

144

5 Power System Restoration Using DFIG-Based Wind Farms and VSC-HVDC. . .

be performed by the VSC stations operating in isolated mode, while the healthy AC system supplies the required power. Such capabilities have been demonstrated in [14, 17, 30] using EMT-type models for small-scale systems. During the North-East blackout of 2003, the 330-MW VSC-HVDC link across Long Island Sound, also known as cross-sound cable (CSC), was started up under an emergency order from the US Department of Energy [12] to facilitate the black-start process. The most significant role during system restoration is played by the generators that help build system voltage, charge equipments and transmission lines, and pick up loads. These units are called the “black-start” units, which are designated a priori. Although a growing portion of generation in modern power grid comes from wind farms, so far only conventional generators have been considered as black-start units for power system restoration [1]. In case of a blackout, the black-start units start charging transmission lines and transformers so that the non-black-start units could also start up and connect to the grid. Based on the North American Electric Reliability Corporation (NERC) definition, black-start units (BSU) are generators with the ability to start without any outer support from the grid-like hydroelectric units [15]. Gas turbine-based plants can also be profitably used in system restoration as black-start units [5]. Simultaneously, cold loads could be picked up by these generating units based on related considerations including generation and transmission capacities, the priority of loads to be picked up, and stability considerations. There are general approaches for system black start which are employed based on the scale of blackout, and availability of resources and outer support. If wind farms are also used as black-start units, they will be able to help achieve faster restoration. One key aspect is that advanced wind forecasting tools need to be integrated in this process. Since wind forecast can alter with time, the “blackstart unit” designated wind farms will change too. Restoration of microgrids has been studied in [6, 18, 28], which involve renewable resources. In these papers, the AC voltage is first established by solar PV, battery storage, or diesel generation before the wind resource is connected. This disqualifies wind generator as a blackstart unit per NERC definition [15]. Restoration of bulk power system is quite different compared to microgrid restoration. Research in the area of transmission system restoration involving wind generation is relatively new [2, 25–27, 31]. References [25, 31] presented very preliminary results; [26] is focused on the static aspects of restoration; [2] needs battery energy storage in the DC link of the wind unit; and [27] utilized a diesel generator before connecting the wind unit. In reference [11], it was shown that a DFIG-based wind farm can be effectively used for such purpose by means of a seamless control transition and autonomous synchronization approach. No energy storage system is necessary for this method. Hence, it complies with the NERC definition [15] of black-start unit. This restoration strategy uses DFIG-based wind farms without any conflict with their normal operation or any major deviation from current widely manufactured and used DIFGbased wind turbine systems. Wind farms can generally be operated when connected to power grid or when feeding isolated loads. There are different control schemes for the operation in these two modes. Chapter 3 described two widely known control schemes for DFIG-based wind farms in grid-connected and isolated modes

5.2 Black-Start Process Using DFIG-Based Wind Farms

145

of operation. In the proposed strategy, one of the two control schemes is used to start up a DFIG-based wind farm in isolated mode. In this mode, the wind farm can energize transmission lines and pick up local or remote loads, while the rest of the system is restored by other sources. An “autonomous synchronization” method will be presented, which can be utilized to connect the wind farm feeding the isolated load to the rest of the grid and switch its control structure to grid-connected mode. The details of this restoration approach are described later, and nonlinear hybrid simulation studies are presented to validate its performance. In this chapter, first the black-start process using a DFIG-based wind farms is described. Following this, the VSC-HVDC controls for black start are presented. Next, the motivation behind using a hybrid co-simulation platform proposed in [10] for system restoration studies is laid out, and the hybrid simulation architecture is presented. The hybrid co-simulation is first performed to demonstrate restoration of a portion of a reasonably large system. The portion of the system under restoration includes a VSC-HVDC connection, two conventional (synchronous) generators, multiple transmission lines, transformers, different loads, and a remote grid, which are represented by an EMT-type model in PSCAD [22]. The rest of the system consisting a 20-bus 5-generator network is simulated as a phasor model in PSSE [23]. A comparison with non-hybrid simulation is also carried out at this stage. Following this, a DFIG-based wind farm is introduced in the portion of the test system under restoration, which replaces one of the conventional generators. System restoration is then aided by the DFIG-based wind farm, and the effectiveness of the presented strategies is verified through hybrid simulation. Picking up of loads of different compositions including constant impedance, constant power, and nonlinear rectifier load is demonstrated. ETRAN PLUS [9] is used for the simulation platform, which facilitates exchange of data between the two types of models.

5.2 Black-Start Process Using DFIG-Based Wind Farms Selected wind farms can be equipped with the control systems presented later and be designated as black-start units. In addition to the considerations mentioned in [26], one can envision that the wind farms used during restoration will be a subset of those wind farms designated as black-start units in the planning stage. During the restoration process, accurate wind forecast tools should be used by the system operators to determine which units can be chosen for this purpose. The black-start process using wind farms is discussed in detail in the following sections.

5.2.1 Step I: DC Bus Pre-charging Controls A challenge in operating an isolated DFIG-based wind farm is that it requires a charged DC bus. In the absence of a grid, this can be ensured by installing a

146

5 Power System Restoration Using DFIG-Based Wind Farms and VSC-HVDC. . .

battery in each wind turbine, which could be used to charge the DC bus capacitor in the start-up stage. This will need additional investment and pose maintenance challenges. To avoid this, a mechanism is needed to retain the charge in the DC bus capacitor when the grid voltage support is lost following a blackout. Figure 5.1 shows the RSC and the GSC of DFIG connected via the DC link. Without loss of generality, let us assume that the flow of power in the DC link is from RSC to GSC, which can be determined from the direction of flow of the DC-link current Idc in Fig. 5.1. When loss of grid voltage is sensed, switching of GSC is stopped. This will cause an immediate rise in the DC-link voltage. However, switching in RSC is continued to allow the capacitor to discharge through it, which causes a gradual decrease in DC voltage. When the DC voltage comes back to its rated value, switching of RSC is stopped. If power flows from GSC to RSC, the described process should be reversed. It can be observed from the results in Fig. 5.2 that the strategy can successfully restore the voltage to its rated value within a short time period and maintain a pre-charged DC bus. At t = 7.0 s, the wind farm is disconnected from the grid and remote loads by opening the breaker. The switching of the GSC stops immediately. This causes the DC bus voltage to increase as shown in Fig. 5.2b. However, switching of RSC continues to reduce the voltage. When the DC voltage is back at its rated value, RSC switching is stopped. Obviously, the DC bus capacitor will slowly discharge. If wind energy is available, the DFIG-based wind farm designated as black-start unit will start operating in the direct flux control mode to self-support the DC bus, charge transmission line, and pick up remote loads, which is described next.

5.2.2 Step II: Self-Supporting DC Bus, Line Charging, and Load Pickup At the beginning of the restoration process, using the pre-charged DC bus in Step I, the wind farm can self-support the DC bus by regulating the voltage. It can also perform line and transformer charging, and load pickup. The size of load pickup should be determined by calculating the wind farm capacity based on wind forecast. These loads are not necessarily local but can be located far from the wind farm as shown in Fig. 5.1. In this step, the DFIG-based wind farm operates in direct stator flux control mode and builds up the terminal voltage vt . As shown in Fig. 5.1, in this control mode the switch S2 is in position  0 . The details of this control mode, also called the “isolated mode,” were described in Chap. 3 in Sect. 3.3.2. The only difference is that in this chapter, the d-axis of the reference frame is aligned with the stator flux vector for the RSC controls shown in Fig. 5.1. As shown in Fig. 5.1, the GSC is also regulated based on vector control strategy where the d-axis of the rotating frame is aligned with the voltage Vt at PCC. It can be seen in Fig. 5.1, the d-component of the current is used for controlling

PI

ims

* ims

-

-

vt

L i

PI

K vc

2

1

ims

2 m ms

Lss K opt

Lss / L m

Flux esmaon

vt

-

r

iqs

vt*

r

s

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5.2 Black-Start Process Using DFIG-Based Wind Farms 147

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5 Power System Restoration Using DFIG-Based Wind Farms and VSC-HVDC. . .

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Fig. 5.3 The DFIG-based wind farm is disconnected from the grid at t = 7.0 s followed by the application of DC bus pre-charging control and isolated operation for a self-supporting DC bus

the DC-link voltage and the q-component controls the reactive power. Therefore, at this stage the DFIG operates to maintain the self-supporting DC bus. After the DC bus pre-charging process, the wind farm starts operating in isolated mode to support the DC bus and prevent its discharging. As shown in Fig. 5.3, at t = 10.0 s the DFIG converters start operating in direct flux control mode with an open terminal, which results in some transients in the DC-link voltage. It can be seen that the wind farm can control the DC bus voltage at its rated value. Since there is no load connected to the wind farm, it only feeds the losses of generators, converters, and step-up transformers in this condition. This power is a very small fraction of the wind farm capacity and hence, it is necessary to have pitch angle control in order to prevent the rotational speed of turbines from increasing beyond a certain limit. The method of pitch angle control was discussed in Sect. 3.2.4 of Chap. 3. After building up the PCC voltage vt , the wind farm can charge the transmission line and pick up remote loads shown in Fig. 5.1. It should be kept in mind that

5.2 Black-Start Process Using DFIG-Based Wind Farms

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cold loads consume significantly higher power compared to the nominal condition. Therefore, the amount of load pickup should be carefully planned. Moreover, transmission line charging involves transients. Therefore, DFIG controls should be able to withstand those transients. Assuming that the rest of the AC grid will also undergo restoration process in parallel, the objective now is to synchronize the wind farm to the rest of the grid, which is described next.

5.2.3 Step III: PMU-Enabled Autonomous Synchronization When the grid on the other side of the breaker shown in Fig. 5.1 is restored, it is likely that the voltage on each side of the breaker differs in phase. Therefore, a synchronization method is necessary before this breaker is closed. Figure 5.4 shows the synchronization mechanism. In this context, the following points should be noted: • The phase of the voltage of the islanded system charged by the wind farm is determined by integrating the rated frequency ωel shown in Figs. 5.1 and 5.4, which is performed by digital control systems. Due to a finite resolution, its frequency could be slightly different from the rest of the grid—let us denote this by ωel + Δω. As a result, there is a time-varying phase difference between voltage vectors on the two sides of the breaker denoted by Vl and Vg in Fig. 5.4. • The goal is to align the voltage vector V l with that of V g using the controls of the wind farm.

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5 Power System Restoration Using DFIG-Based Wind Farms and VSC-HVDC. . .

Since V t and V l have the same frequency ωel + Δω, their phase difference (θt − θl ) is constant, which depends on the transmission line impedance and the current iW F . As shown in Fig. 5.4, before synchronization, the space vectors can be represented with respect to a rotating voltage reference frame aligned with V g . Mathematically: V g = Vg V l = Vl ej (θl −θg ) = Vl ej ϕ(t) V t = Vt ej (θt −θg ) = Vt ej γ (t)

(5.1)

Let us assume that PMUs are installed in the remote substation where the breaker is located, which can measure the phase difference ϕ(t). All substations are equipped with standby power supply for operating essential equipment during outages, which will ensure that PMUs operate under a blackout. As shown in Figs. 5.1 and 5.4, let the phase difference ϕ(t) be communicated to the wind farm using dedicated fiber-optic channels with a 20-ms latency, which in turn will be continuously subtracted from the free-running integrator angle θ0 , eventually controlling θt . As shown in Fig. 5.4, this process shifts V t by a phase angle ϕ(t) and aligns vector V l with V g . Let to be the time when synchronization begins, and let Ts be the sampling time of the PMU. After attaining steady state, we have V g = Vg V l = Vl ej (Δω (t−t0 )/Ts Ts ) V t = Vt ej (Δω (t−t0 )/Ts Ts +θt −θl )

(5.2)

where x represents floor of x. Since ΔωTs is quite small, V g and V l are almost in-phase.

5.2.4 Step IV: Hot-Swapping When the autonomous synchronization process is complete, and the voltages V l and V g on two sides of the circuit breaker in the remote substation shown in Fig. 5.1 are in the same phase, the breaker is closed. The breaker status is communicated to the DFIG-based wind farm, which in turn performs the “Hot-Swapping” operation by changing the position of the switch “S2 ” to position “1” as shown in Fig. 5.1. This modifies the RSC and GSC controls to conventional grid-connected mode [21] described in Sect. 3.3.1 in Chap. 3. The only difference is that for RSC controls the d-axis is aligned with the stator flux vector position. The flux is estimated by

5.3 VSC-HVDC Controls for Black-Start

151

measuring the PCC voltage vt and the stator current is , see Fig. 5.1, and the d-axis is locked with the estimated flux vector by PLL1. For the GSC controls, PLL2, shown in Fig. 5.1, is used to align the d-axis of the rotating frame with the voltage vt at PCC. A few noteworthy points regarding “Hot-Swapping” are: • PLL1 and PLL2 runs from the beginning of the DFIG operation, although the output of the PLLs is used only after the “Hot-Swapping.” • The approach does not require switching of any dynamic states of the controllers. This ensures a seamless transition.

5.3 VSC-HVDC Controls for Black-Start A bipolar VSC-HVDC system with metallic return is considered. It is assumed that the rectifier is connected to a system unaffected by the blackout and operates in reactive power and DC voltage control mode using traditional vector control [29], which was described in Sect. 2.4.2 of Chap. 2. Figure 5.5 shows the control scheme of the positive pole VSCs (identical with negative pole) in the inverter side, which is assumed to be connected to the blacked-out AC system. Initially, the inverter operates in AC voltage and frequency control mode to energize the blackedout system. As shown in Fig. 5.5, the AC voltage is controlled using magnitude of modulating signal, while the phase angle comes from an integrator shown in Fig. 5.5. Please refer to Sect. 2.5 of Chap. 2 for more details. After the AC system is synchronized with a generating unit, the control mode is shifted to AC voltage and real power control mode. AC voltage is controlled in the same fashion, and the phase of the modulating signal is used for power control. At some stage of the restoration process, the power flow through the HVDC line might reverse as will be evident in the case study, described next.

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Fig. 5.5 VSC-HVDC controls for the positive pole of the inverter. Notations carry standard meanings unless stated otherwise

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5 Power System Restoration Using DFIG-Based Wind Farms and VSC-HVDC. . .

5.4 Hybrid Simulation Platform Power system planners traditionally use software tools that are based on positive sequence, fundamental frequency phasor models. Examples of a few commercial power system planning software are PSLF [13], PSSE [23], and DIgSILENT [7]. System planners make sure that the grid’s reliability standards are met. However, the history of blackouts has shown us that it is very important to develop a system restoration plan following such events so as to reduce the downtime. Although infrequent, the cost of blackouts in the USA, e.g., the Western Electricity Coordinating Council (WECC) blackout in 1996, the 2003 blackout in the Eastern Interconnection, and large blackouts that took place in 2012 in India runs into billions of dollars. Therefore, the research on system restoration is highly important. Unfortunately, traditional planning software tools may not be adequate for simulating restoration of large systems. One of the reasons behind this is the wide range of bandwidth of interest for the system restoration including phenomena with small time constants like transformer inrush current, voltage fluctuations, long line switching along with relatively slower phenomena including inertial and frequency support, and different system stability challenges. This gets even more complicated when the black-start process assisted by voltage source converter (VSC)-based high voltage DC (HVDC) links is considered. When an HVDC link, especially VSC-HVDC, interconnects two asynchronous AC systems, it acts as a “firewall” against the propagation of blackouts. This implies that the blackout taking place in one AC area cannot propagate into the other. During the North-East blackout of 2003, the 330-MW VSC-HVDC link across Long Island Sound, also known as cross-sound cable (CSC), was started up under an emergency order from the US Department of Energy [4]. The CSC was used to restore service to Long Island, although it was not equipped with black-start controls. This link was also instrumental in stabilizing system voltage as lines, transformers, etc., were energized, generators were synchronized, and cold loads were picked up. The dynamic voltage restoration capability was very important in riding through these transients [4]. Soft start-up of a long line using VSC-HVDC is studied in reference [16]. Reference [17] uses the soft-start method described in [16] and studies black start using VSC-HVDC for a small system with two generators and three loads. The simulations were conducted in EMTDC/PSCAD platform. Simulating a large system in an EMT-type platform is computationally prohibitive and unnecessary. A “hybrid” co-simulation platform [10] can be used in system restoration application for large power grids that will have the ability to capture faster transients in a certain region of the grid, while the rest of the system is modeled in the phasor domain. The need for hybrid co-simulation is described next in further detail.

5.6 Hybrid Simulation Architecture

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5.5 Need for Hybrid Co-simulation Dynamic simulation of power grid restoration is essentially a “system-level” problem. However, it is unique in the sense that unlike traditional planning simulations, the dynamic response of interest during restoration has a wide range of time constants. Challenges during restoration stem from: (a) frequency, angle, and voltage stability issues that can be represented by phasor models, and (b) faster transients like transformer inrush and long line switching currents that demands EMTP-type representation. None of the previous studies done on VSCHVDC assisted system restoration [14, 17, 30] have considered a medium or large system in their simulation-based studies. The tasks performed by a VSC-HVDC link during system restoration include transformer energization, line energization, generator synchronization, system inertia and frequency control, cold load pickup, etc. Different restoration functionalities of the HVDC system have been presented using EMTDC/PSCAD [22]-type models [14, 17, 30]. Although the simulation run time of such models is manageable in a small-scale system, it becomes unrealistic when considering large power grids. ETRAN [8] is a software that has been widely used by system planners under such circumstances. The software converts a user-defined section of the large power system model in phasor domain in PSSE [23] into a detailed three-phase dynamic model in EMTDC/PSCAD. It represents the rest of the power system by ideal voltage sources behind an equivalent Ybus network that retains the short circuit capacity (SCC) as viewed from the boundary nodes. Unfortunately, such a representation has two drawbacks: 1. It does not have any dynamic representation of the rest of the power system. 2. It cannot allow the simulation of system restoration of the rest of the grid or a portion thereof. Herein comes the motivation for a “hybrid” simulation in handling this problem where the rest of the power grid in phasor domain will be retained and co-simulated along with the detailed three-phase model in EMTDC/PSCAD. Such a hybrid simulation will be able to capture different time constants of interest. The hybrid simulation architecture is described next in detail.

5.6 Hybrid Simulation Architecture A hybrid simulation approach was proposed in [10] in which the HVDC link and a region surrounding it was represented using a detailed three-phase EMT-type model. The reason is that the influence of HVDC in initiating system restoration is limited up to a certain boundary of the network, beyond which, the focus of research is into optimal resource allocation subject to the system’s static and dynamic constraints. The DFIG-based wind farm is also represented in the same platform. The rest of the

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5 Power System Restoration Using DFIG-Based Wind Farms and VSC-HVDC. . .

DFT Update voltage PSCAD PSCAD phase, b oundary boundary frequency bus bus VSC-HVDC, DFIG, and surrounding buses (3-phase EMT model)

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Fig. 5.6 (a) Hybrid simulation architecture. The updation of data from PSCAD/EMTDC to PSSE and vice versa takes place at a sampling rate, which is equal to the integration time step that is larger among the two platforms. ETRAN library components: (b) “ETRANPlus-Com,” (c) “AutoLaunch,” and (d) “chan-import”. Source: Farsani et al. [10]. Reproduced with permission of IEEE

system is modeled by its phasor equivalent in which the network will be represented by the algebraic model (Ybus ) and the generators by their subtransient dynamic models. In the boundary between these two regions, the three-phase variables are converted into equivalent phasors and this information is exchanged between the models. The hybrid simulation architecture is shown in Fig. 5.6a. The detailed threephase model runs in EMTDC/PSCAD platform using time step of the order of microseconds, and the rest of the system runs with time step of the order of milliseconds in PSSE [23] platform—simultaneously. The interface between these two platforms is provided by ETRAN-PLUS [9]. There are specific points in performing such hybrid simulations. It should be noted that generator, turbine, and exciter components which are converted to PSCAD from PSSE require a detailed dynamic model. These dynamic models are specified in dynamic model file (i.e., the .dyr file), which includes dynamic details of every component in a PSSE simulation case. User should refer PSCAD to this file by adding its address in these components’ settings. One complication in the process of preparing a hybrid simulation case arises from choosing the proper bus to connect

5.7 Case Study I

155

generator model in PSSE simulation and problem of how to keep lines between boundary bus and other buses as they are. When a portion of system is converted from PSSE to PSCAD, the lines connected to boundary bus are not converted to PSCAD and they will not exist in PSSE simulation either. A practical approach is to create an additional bus in PSSE simulation which connects to the boundary bus by an ideal connection and connect boundary bus-connected transmission lines to this new bus. The generator model, which should be added to PSSE simulation after deleting the converted portion should also be connected to this additional bus. Such an approach solves the discussed problems without making any practical change to the study case. It should be noted that specific versions of Fortran compiler should be used by PSCAD in order for this hybrid simulation platform to work. Intel Fortran V.15 has been used effectively in the simulations, which will be presented later.

5.7 Case Study I As shown in Fig. 5.7, a 31-bus 4-area power system with 8 generators is considered in this work. A bipolar VSC-HVDC link connects area #3 to area #4. A phasor model of area#1, #2, and #3 was built in PSSE software. A portion of area #3 was then converted to equivalent PSCAD model using ETRAN, see Fig. 5.7. A detailed switched model of the VSC-HVDC link was built in PSCAD connecting area #4 to area #3. The response of two types of models is compared: non-hybrid model and hybrid model, which are described next.

5.7.1 Non-hybrid Model In a non-hybrid simulation platform, the system outside the detailed three-phase model is represented by a voltage source behind an impedance that retains the short circuit capacity (SCC) of the system model viewed from the point of intersection. This is performed using the ETRAN [8] software. Since the non-hybrid model does not have any representation of the dynamics of the phasor model, it will not be adequate for dynamic simulation during the restoration process. To overcome this challenge, the hybrid simulation architecture will be used for this system.

5.7.2 Hybrid Model As mentioned in Sect. 5.6, in the hybrid model the representation of the phasor model is retained. The phasor model in PSSE is interfaced with the detailed threephase model in PSCAD using the ETRAN-PLUS software. Figure 5.7 shows the test system in a hybrid simulation platform.

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156 5 Power System Restoration Using DFIG-Based Wind Farms and VSC-HVDC. . .

5.8 Simulation Results

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5.8 Simulation Results Let us consider a scenario where blackout occurred in a portion of area #3 shown in Fig. 5.7. The goals are: (a) to restore that portion of the system with the help of the VSC-HVDC link, and (b) to pick up an additional 200-MW load connected to bus 154 (marked in red in Fig. 5.7) and supply a portion of the load from generators G1 and G2 in the restored area. It was assumed that the blackout could not propagate to area #4 since the DC link was acting as a “firewall.” Initially, all the breakers are assumed to be open. First, the dynamic behavior of the non-hybrid and the hybrid simulation is compared when the first objective (a) is considered, which is described next.

5.8.1 System Restoration: Non-hybrid vs Hybrid Simulation The same restoration sequence is used for both simulations, and identical control parameters are used. The results are shown in Figs. 5.8 and 5.9. In these figures, Pvsc is the power output of one of the VSCs in converter station #2, P22−bus is the power flowing through the line interfacing the phasor model and the detailed model, f denotes the frequency measured at bus 6, and Vac is the AC voltage at bus 2. The timing of the breaker reclosure is shown in Fig. 5.7 and will not be repeated here. The steps followed for the system restoration are described next:

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5 Power System Restoration Using DFIG-Based Wind Farms and VSC-HVDC. . . Non-Hybrid

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Step I: Soft-Start [t = 0.2–1 s] During this stage, converter #1 is in Vdc − Q control and converter #2 is in Vac − f control mode. As shown in Fig. 5.8a, b, the AC voltage at bus 2 is ramped up gradually using AC voltage control illustrated in Fig. 5.5. This method of energization of long line and transformers prevents inrush currents under no-load condition [17]. Step II: Pick-Up Auxiliary Load of G1 [t = 3 s] Auxiliary equipment of G1 which are modeled as a 56-MW load is picked up using the power flowing from area #4 through the HVDC link. Step III: Synchronizing Generator G1 [t =3.8 s] Generator G1 is connected to system after synchronization. Step IV: Load 1 Pick-Up [t = 6 s] Load 1, which is a 100-MW load connected to bus 6 is connected. This load is fed by VSC-HVDC, and G1 is still a floating source at this stage. It could be seen that as expected, the non-hybrid and the hybrid models produce the same dynamic response up to this point since BR10 is open. Step V: Closing BR 10 [t = 11.2 s] At this step, the part of the system, which is modeled in PSSE in hybrid simulation and as a source in non-hybrid simulation is connected to the rest by closing BR10 after synchronization. Significant oscillations can be seen in power output of VSCs and power flow to bus 6 from bus 3020 (Fig. 5.7). Figure 5.9c shows the zoomed view of frequency during this event. It can be observed that the dynamic response of frequency substantially differs when the hybrid simulation is considered. Figure 5.8e, f also shows the direction and the dynamic behavior of the power flowing into the detailed model is quite different in the hybrid simulation from the non-hybrid simulation. Similar observations can be made from Fig. 5.8c, d for the power output of the VSC-HVDC.

5.8 Simulation Results

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Step VI: HVDC Mode Switch [t = 20 s] The control mode of converter #2 VSCs, which was in AC voltage and frequency control mode is switched to AC voltage and power control mode as described in Sect. 5.3. Step VII: Power Ramping [t = 21–24 s] In this step, the power output of G1, which was primarily floating is ramped up to 40 MWs and simultaneously the power output of each of two VSCs in station #2 has been ramped down by 20 MW. Step VIII: Synchronizing Generator G2 [t = 25 s] G2 is connected to the system after synchronization as a floating generator. Step IX: Load 2 Pickup [t = 30 s] The 50-MW load at bus 2 is connected to the system. Since VSCs are in power control mode at this stage, this load is fed from the rest of the system. Results from this section emphasize the importance of using a hybrid simulation in such studies. Although the control schemes and parameters have resulted in a desirable black-start process, if the exact model of a large system is used in the study, the outcome is significantly different. In the next section, the focus will be on the other objective, i.e., load pickup at bus 154, which cannot be studied using the non-hybrid model.

5.8.2 Additional Load Pickup: Hybrid Simulation In this study, a 200-MW load has been picked up at bus 154 at t = 30 s. Prior to picking up the load, the sequence of events and their timing from Steps I–V are identical to what was described in the previous section. The rest of the sequence is described as follows: Step VI: 200 MW Load Pickup [t = 30 s] At t = 30 s, the 200-MW load is connected at bus 154. As it is shown in Fig. 5.10a, the power flow from the portion of system modeled in PSSE is reduced following oscillations from around 230 to 50 MWs. At the same time, the power output of each HVDC pole has increased to more than 50 MW, see Fig. 5.10c. Step VII: HVDC Mode Switch [t = 38 s] The control mode of converter #2 VSCs, which was in AC voltage and frequency control mode is switched to AC voltage and power control mode as described in Sect. 5.3. Step VIII: [t = 39–42 s] From t = 39 to 42 s, the same process of ramping down the power output of HVDC and increasing power output of G1 is done as described in the previous section. Step IX: Synchronizing Generator G2 [t = 42.5 s] G2 is connected to network at t = 42.5 s as a floating source.

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Fig. 5.10 Hybrid simulation: dynamic response for simulating additional load pickup in 22-bus test system shown in Fig. 5.7. Source: Farsani et al. [10]. Reproduced with permission of IEEE

Step X: Power Ramping [t = 50–56 s] In the last step from t = 50 to 56 s, power output of G1 is increased by 80 MW and G2 by 45 MW as seen in Fig. 5.10e, f in order to supply the power needed for the 200-MW load. During this process, the power output of each HVDC pole is also reduced by 20 MWs using power control. It is easily seen in Fig. 5.10a that through this process power flow reverses and starts flowing into the PSSE-side segment of the system. The power flow in two tie lines shown in Fig. 5.7 in the phasor model is highlighted in Fig. 5.10b, d. This dynamic response observed in the hybrid simulation paradigm cannot be simulated in the non-hybrid counterpart. Hybrid simulation is a powerful tool in restoration studies where a detailed model of HVDC system is needed besides the need for simulation of a large power system, which cannot be performed in a three-phase EMT environment like PSCAD. With the ETRAN PLUS-based hybrid simulation tool, the impact of load pickup or disturbances in large system during the restoration can also be studied. In the next case study, a DFIG-based wind farm will be used as a black-start unit in this hybrid platform.

5.9 Case Study II The test system shown in Fig. 5.7 is slightly modified for this case study. Synchronous generator G1 is replaced by a DFIG-based wind farm in addition to some modifications in loads. The modified test system is shown in Fig. 5.11. As before, a part of area 3 in the 27-bus network is under blackout, while the remote grid is healthy. The portion of the blacked-out system connected to the remote healthy grid through the HVDC transmission system is shown in dark gray, which is presented

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by a detailed 3-phase model in PSCAD [22]. The rest of the 3-area network, which is healthy, is shown in light gray and is represented in a phasor framework in PSSE [23].

5.9.1 Simulation Results Assuming that blackout occurred in the area shown in Fig. 5.11, the purpose is to perform restoration process in this area using both the DFIG-based wind farm and the VSC-HVDC link, simultaneously. The wind farm starts operating in the flux control mode and picks up remote loads marked as Load 1. In parallel, the VSC-HVDC link charges lines #1 and #2, and the transformers using a softstart process described in [30] and picks up Load 2 followed by Loads 3 and 4. When the two terminals of the circuit breaker BR4 are live, the process of autonomous synchronization and Hot-Swapping are performed and the wind farm is connected to the rest of the grid. The details of the restoration process are described next. Wind Speed Fluctuations Let us assume availability of wind energy based on forecast at the location of the wind farm. Figure 5.12a shows the wind speed profile during the period of system restoration. A slow decline, sharp reduction and increase, and random fluctuations in the wind speed have been considered to evaluate the performance of the restoration strategy under challenging circumstances. Load Composition Different types of loads have been considered for reflecting the load diversity. These include constant impedance, constant power, and nonlinear loads.

wind speed and pitch angle

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time [s] Fig. 5.13 Build up of (a) magnetizing current and (b) terminal voltage of DFIG-based wind farm during line charging and simultaneous remote load pickup. Source: Farsani et al. [11]. Reproduced by permission of the Institution of Engineering & Technology

Voltage Buildup, Line Charging, and Load Pickup by Wind Farm [t = 0.0–12.0 s] The wind farm starts its operation in flux control mode using the pre-charged DC bus and builds up the voltage at its terminal using the outer voltage control loop in ∗ . Figure 5.13 shows the RSC control shown in Fig. 5.1, which in turn generates ims magnetizing current and terminal voltage build-up by the wind farm, while charging the 345-kV, 50-km line (line #3) and simultaneously picking up a remote load at bus 8 in Fig. 5.11. The load consists of three components: (a) a 100-MW and 35-MVAr constant impedance load, (b) a 20-MW and 10-MVAr constant power load, and (c) a 100-MW nonlinear rectifier load. It can be seen from Fig. 5.13b that the terminal voltage reaches its rated value in about 6.0 s and the load power consumption shown in Fig. 5.14b steadily increases, while the DC-link voltage (Fig. 5.14a) is tightly regulated by the GSC controls. Additional loads at bus 8 were picked up in the following sequence: (1) at t = 8.5 s: a 20-MW resistive load, (2) at t = 9.5 s: a 20-MW resistive load, (3) at t = 11.0 s: a 10-MW, 10-MVAr constant impedance load, and finally (4) at t = 12.0 s: a 20-MW, 5-MVAr constant power load. Figure 5.13 shows the load power consumption increases in steps, while the DC bus voltage controller demonstrates good tracking performance. The wind speed profile throughout this process is higher than the wind farm’s rated wind speed of 13.5 m/s, which results in the variation in pitch angle β as shown in Fig. 5.12b. The simulations considered a Bergeron Model representation of transmission line. The cold load model follows reference [3]. At the beginning, the active power consumption is about 2.7 pu. The power consumption stays at that level for about 2.0 min and then gradually decreases to 1.2 pu over a 20-min time interval. The power consumptions indicated in this study are the maximum values consumed at the beginning.

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DC link voltage and power consumption in remote loads

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Fig. 5.14 (a) DC-link voltage of the DFIG-based wind farm and (b) the power consumed by the remote loads at bus 8 picked up by the wind farm. Source: Farsani et al. [11]. Reproduced by permission of the Institution of Engineering & Technology

Voltage Buildup, Line Charging, and Load Pickup by VSC-HVDC [t = 0.2–12.0 s] Simultaneously, on the VSC-HVDC side, converter #1 starts operating in Vdc − Q control and converter #2 in Vac −f control mode. The AC voltage at bus 2 is ramped up gradually during 0.2–1.0 s, while charging line #1, which is 190-km long and the transformers between buses 6 and 7, and 6 and 3. At t = 2.0 s, a constant power 56MW, 14-MVAr load is picked up at bus 7 by closing BR2 followed by the pickup of Load 3 at t = 4.0 s, which is a constant power load consuming 50 MW and 37 MVAr. Figure 5.15 shows the comparison of voltage build up at bus 8 from the wind farm and at bus 7 from VSC-HVDC. Synchronization and Generation Ramp Up [t = 4.5–12.0 s] Synchronous generator G2 is synchronized and connected at t = 4.5s and its power output is gradually ramped up to 100 MW during t = 6.0–12.0 s. Also, the healthy portion of the 3-area 6-machine grid, modeled in phasor framework in PSSE [23], is synchronized and connected to bus 6 of the blacked-out portion modeled in PSCAD [22] by closing BR3 at t = 11.0 s, see Fig. 5.11. Figure 5.16 shows the power output of generator G2, the 20-bus system, and the positive pole of the VSC-HVDC station. This figure also shows power flow in one of the tie lines inside the 20-bus system which is indicated in Fig. 5.11. It can be seen from Fig. 5.16b that the power flowing through VSC-HVDC line reverses during this phase. Remark on Coordination Requirement Proper allocation of black-start resources, order of line charging, and load pickup is an optimization problem in system restoration. Optimized resource allocation is performed to assure the fastest and most economical restoration process. Different methods have been proposed to solve this optimization problem for black-start purpose [19, 24]. It is obvious that

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build up of phase-a voltage in both sides of BR4

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Fig. 5.15 Comparison of voltage build up in phase at (a) bus 8 from the wind farm and (b) at bus 7 from VSC-HVDC. (c) Overlapping zoomed view. Source: Farsani et al. [11]. Reproduced by permission of the Institution of Engineering & Technology

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Fig. 5.16 Power flow: (a) from 20-bus system to bus 6, (b) out of positive pole VSC station, (c) out of generator G2, and (d) from bus 153 to bus 3006. Source: Farsani et al. [11]. Reproduced by permission of the Institution of Engineering & Technology

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mdqg

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time [s] Fig. 5.17 Dynamic performance while connecting the breaker BR4 without synchronization process: (a) phase difference between voltages in both sides of breaker BR4. (b) DC-link voltage of DFIG. (c) GSC modulating signals. Source: Farsani et al. [11]. Reproduced by permission of the Institution of Engineering & Technology

in a practical scenario, for the test system used in this study, the operators decide on the timing of conventional generator synchronization and its power output based on capacity of the healthy grid, VSC-HVDC system, and optimization considerations. Autonomous Synchronization of DFIG [t = 10.0–14.0 s] Figure 5.17 shows the dynamic response of the system when the auto-synchronization is not enabled and BR4 is closed at t = 14.0s when the phase difference ϕ(t) between voltages v7a and v8a , shown in Fig. 5.19, is around 90◦ . Over-modulation in GSC and unacceptable transients in the DC-link voltage are observed. Now, the autonomous synchronization process is enabled at t = 10.0 s, which shows its effectiveness. Figure 5.18a shows that the phase difference between voltages from both sides of BR4 changes slowly before t = 10.0 s, which can be explained by the wind farm-side frequency, which is slightly less than the gridside frequency due to the finite resolution of numerical integration as highlighted in Fig. 5.18c. It can be seen from Fig. 5.18 that this process can successfully change the phase of voltage on DFIG side of BR4 so that the two voltages have the same phase. In Fig. 5.19, the two instantaneous voltage waves are shown to gradually synchronize. Remark on Communication Latency Since restoration is a critical application, a dedicated fiber-optic channel with very high bandwidth is preferred, which will be solely used to communicate the PMU data packets. Considering such a small data transfer requirement, the communication latency is expected to be as low as 5.0 µs per km [20]. Figure 5.18a shows the effect of a 10-ms communication latency. Clearly, the phase difference has multiple zero crossings at which the breaker

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closure can take place without any transients. The effect of 20-ms latency in the communication channel was studied, which led to a similar conclusion. Breaker Closure and Hot-Swapping [t = 14.0 s] At this stage, BR4 is closed and the DFIG-based wind farm control is switched to grid-connected mode. Figures 5.20 and 5.21 show GSC and RSC decoupled currents, before and after Hot-Swapping.

5 Power System Restoration Using DFIG-Based Wind Farms and VSC-HVDC. . .

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time [s] Fig. 5.20 (a) DFIG GSC d-axis current and (b) DC-link voltage during closure of BR4 at t = 14.0 s and Hot-Swapping. Source: Farsani et al. [11]. Reproduced by permission of the Institution of Engineering & Technology

RSC decoupled currents [a]

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Fig. 5.21 DFIG RSC currents in d and q reference frames during closure of BR4 at t = 14.0 s and Hot-Swapping. Source: Farsani et al. [11]. Reproduced by permission of the Institution of Engineering & Technology

It is obvious that in both modes these currents are controlled at their reference values and a seamless transition occurs during mode switch at t = 14.0 s. HVDC Control Mode Swapping [t = 30.0 s] At t = 30.0 s, converter #2 of the HVDC link, which was in AC voltage and frequency control mode is switched to AC voltage and real power control mode, see Fig. 5.5. Figure 5.16b shows that the power flowing through the HVDC transmission system is maintained at around 100 MW flowing into the remote grid.

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Acknowledgements Results reported in this chapter are developed based on research papers [10, 11] published from my group, which are reproduced with permission of the Institution of Engineering & Technology (IET) and IEEE. Graduate student involved in producing these results is Mr. Pooyan Moradi Farsani. Most of the research material was produced with support from NSF grant award ECCS1656983.

References 1. Adibi, M.M., Borkoski, J.N., Kafka, R.J.: Power system restoration - the second task force report. IEEE Trans. Power Syst. 2(4), 927–932 (1987) 2. Aktarujjaman, M., Kashem, M., Negnevitsky, M., Ledwich, G.: Black start with DFIG based distributed generation after major emergencies. In: International Conference on Power Electronics, Drives and Energy Systems, 2006 (PEDES ’06), pp. 1–6 (2006) 3. Angeholm, E.: Cold load pickup. Department of Electric Power Engineering, Chalmers University of Technology (1990) 4. Bahrman, M., Bjorklund, P.E.: The new black start: system restoration with help from voltagesourced converters. IEEE Power Energy Mag. 12(1), 44–53 (2014) 5. Barsali, S., Poli, D., Pratico, A., Salvati, R., Sforna, M., Zaottini, R.: Restoration islands supplied by gas turbines. Electr. Power Syst. Res. 78(12), 2004–2010 (2008) 6. Dang, J., Harley, R.G.: Islanded microgrids black start procedures with wind power integration. In: 2013 IEEE Power Energy Society General Meeting, pp. 1–5 (2013) 7. Digsilent. http://www.digsilent.de/ 8. E-TRAN, ELECTRANIX Corporation, Winnipeg, Canada. http://www.electranix.com/ETRAN/ 9. E-TRAN PLUS, ELECTRANIX Corporation, Winnipeg, Canada. http://www.electranix.com/ software/e-tran-plus/ 10. Farsani, P.M., Chaudhuri, N.R., Majumder, R.: Hybrid simulation platform for VSC-HVDCassisted large-scale system restoration studies. In: 2016 IEEE Power Energy Society Innovative Smart Grid Technologies Conference (ISGT), pp. 1–5 (2016) 11. Farsani, P.M., Vennelaganti, S.G., Chaudhuri, N.R.: Synchrophasor-enabled power grid restoration with DFIG-based wind farms and VSC-HVDC transmission system. IET Gener. Transm. Distrib. 12(6), 1339–1345 (2018) 12. Feltes, J.W., Grande-Moran, C., Duggan, P., Kalinowsky, S., Zamzam, M., Kotecha, V.C., de Mello, F.P.: Some considerations in the development of restoration plans for electric utilities serving large metropolitan areas. IEEE Trans. Power Syst. 21(2), 909–915 (2006) 13. GE PSLF. http://www.geenergyconsulting.com/practice-area/software-products/pslf 14. Jiang-Hafner, Y., Duchen, H., Karlsson, M., Ronstrom, L., Abrahamsson, B.: HVDC with voltage source converters - a powerful standby black start facility. In: IEEE/PES Transmission and Distribution Conference and Exposition (T&D), 2008, pp. 1–9 (2008) 15. Kafka, R.J.: Review of PJM restoration practices and NERC restoration standards. In: 2008 IEEE Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century, pp. 1–5 (2008) 16. Li, G., Zhao, C., Zhang, X., Li, G.: Research on “soft start-up” of VSC-HVDC in power system restoration after blackouts. In: 2007 2nd IEEE Conference on Industrial Electronics and Applications (2007) 17. Li, S., Zhou, M., Liu, Z., Zhang, J., Li, Y.: A study on VSC-HVDC based black start compared with traditional black start. In: 2009 International Conference on Sustainable Power Generation and Supply (SUPERGEN ’09), pp. 1–6 (2009) 18. Li, J., Su, J., Yang, X., Zhao, T.: Study on microgrid operation control and black start. In: 2011 4th International Conference on Electric Utility Deregulation and Restructuring and Power Technologies (DRPT), pp. 1652–1655 (2011)

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19. Liu, Y., Fan, R., Terzija, V.: Power system restoration: a literature review from 2006 to 2016. J. Mod. Power Syst. Clean Energy 4(3), 332–341 (2016) 20. Nordell, S.: Network latency - how low can you go? http://www.lightwaveonline.com/articles/ print/volume-29/issue-6/feature/network-latency-how-low-can-you-go.html 21. Pena, R., Clare, J.C., Asher, G.M.: Doubly fed induction generator using back-to-back PWM converters and its application to variable-speed wind-energy generation. IEE Proc. Electr. Power Appl. 143(3), 231–241 (1996) 22. PSCAD/EMTDC v. 4.2.1, Manitoba HVDC Research Centre, Winnipeg, MB, Canada 23. PSS/E, Program Operation Manual. SIEMENS Power Technologies, New York, USA 24. Qiu, F., Wang, J., Chen, C., Tong, J.: Optimal black start resource allocation. IEEE Trans. Power Syst. 31(3), 2493–2494 (2016) 25. Seca, L., Costa, H., Moreira, C.L., Lopes, J.A.P.: An innovative strategy for power system restoration using utility scale wind parks. In: 2013 IREP Symposium-Bulk Power System Dynamics and Control - IX (IREP), Rethymnon, pp. 1–8 (2013) 26. Sun, W., Golshani, A.: Harnessing renewables in power system restoration. In: 2015 IEEE PES General Meeting, Denver, pp. 1–8 (2015) 27. Tang, Y., Dai, J., Wang, Q., Feng, Y.: Frequency control strategy for black starts via PMSGbased wind power generation. Energies 10(3), 358 (2017) 28. Thale, S., Agarwal, V.: A smart control strategy for the black start of a microgrid based on PV and other auxiliary sources under islanded condition. In: 2011 37th IEEE Photovoltaic Specialists Conference (2011) 29. Yazdani, A., Iravani, R.: Voltage-Sourced Converters in Power Systems: Modeling, Control, and Applications. Wiley, Oxford (2010) 30. Zhou, M., Li, S., Zhang, J., Liu, Z., Li, Y.: A study on the black start capability of VSC-HVDC using soft-starting mode. In: IEEE 6th International Power Electronics and Motion Control Conference, 2009 (IPEMC ’09), pp. 910–914 (2009) 31. Zhu, H., Liu, Y.: Aspects of power system restoration considering wind farms. In: International Conference on Sustainable Power Generation and Supply (SUPERGEN 2012), pp. 1–5 (2012)

Chapter 6

Integration of Wind Farms Using MTDC Grids: Frequency Support Perspective

Abstract Provision of frequency support through multiterminal DC (MTDC) grids from one asynchronous AC area to the other is presented. Weak AC areas with low inertia need such frequency support following contingencies like loss of generation. Principle of operator-prescribed ratio-based frequency support contribution is discussed, which can quantify the extent of such contribution. In addition, the concept of ratio-based selective participation from different areas based on existing contractual obligations is highlighted as a mechanism for future ancillary service markets. Extraction of inertial and primary frequency support from both onshore and offshore wind farms is discussed in the context of VSC MTDC and hybrid MTDC grids, where the latter consist of both VSC and LCC converters.

6.1 Introduction In the previous chapters, the focus was on interfacing wind farms in a weak AC grid using point-to-point HVDC links. In a grand scale, there are multiple envisioned projects for integrating offshore wind and onshore renewable resources to PanEuropean AC grid through multiterminal DC (MTDC) grids. As described before, the onshore renewable resources, especially wind farms are located in remote areas, which have weak interconnection to AC grids. For offshore wind farms (OWFs), there exist no offshore AC grids that can provide voltage support. Both for remote onshore and deep-sea offshore wind farms, point-to-point HVDC interconnections can be used to transmit power to distant load centers. However, one of the major concerns has been the loss of infeed due to a single-point failure in the wind farm energy delivery system, in other words following an (N − 1) contingency, which can jeopardize the stability of distant AC systems with load centers. As opposed to multiple point-to-point HVDC links connecting individual wind farms to the remote load centers, an MTDC grid can avoid such system reliability issues by rerouting power from other sources. There are many other advantages associated with the MTDC grid systems that were described in Sect. 1.4 in Chap. 1. MTDC grid systems are complex in terms of their operation and control. Different aspects of these systems have been already studied and are still being © Springer Nature Switzerland AG 2019 N. R. Chaudhuri, Integrating Wind Energy to Weak Power Grids using High Voltage Direct Current Technology, https://doi.org/10.1007/978-3-030-03409-2_6

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actively researched. The focus here will be limited to the challenge of providing frequency support through MTDC grids. The frequency dynamics in an AC system can be divided into three regimes—(a) inertial, (b) primary frequency, and (c) secondary frequency. In an AC grid the inertia of the synchronous generators is the primary source of inertial support; the governors act towards primary frequency regulation; and AGC action provides secondary frequency control. More precisely, the inertial and primary frequency support regimes will be the topic of interest in this chapter. Unlike AC grids, the MTDC grid system interfacing surrounding AC grids acts as a “firewall,” which means that these AC grids are “asynchronous” in nature. The MTDC grid by default does not allow the transfer of frequency support through it. Therefore, special mechanisms are required to channel such support from one asynchronous AC area to the other. Another challenge is the quantification and control of these contributions since certain areas might not be willing or it might not be feasible to provide support for certain magnitude. As inverterinterfaced renewable energy resources replace conventional generation, this results in reduction of system inertia. Hence, the importance of frequency support provision is becoming more important and has given rise to frequency regulation market [31] in AC systems. It can be envisaged that future AC-MTDC systems will also have such frequency regulation market structures, where the frequency support contribution from one asynchronous AC area to the other needs to be quantified and controlled based upon contractual obligation.

6.2 Methods of Frequency Support in AC-MTDC Systems Provision of primary and secondary frequency support through MTDC grids has been studied in different papers. Researchers have followed two philosophies— methods that require communication [2, 3, 11, 12, 15, 19, 20, 33, 34] and communication-free approaches [14, 17, 30, 35, 40, 41]. The first category of methods where communication among converter stations is required can be further classified into distributed and centralized architectures. For example, the distributed PI controllers proposed in [2, 3, 7] require exchange of information from the neighboring asynchronous areas. Another example is reference Kirakosyan et al. [15] where frequency regulator in a centralized architecture is proposed, which is dependent on remote communication. The idea is to modify the reference voltage to bring back the DC voltage to its nominal value following a disturbance. Of late, model predictive control (MPC) [4] has found application in this area. A centralized primary and secondary frequency regulation architecture based on MPC was proposed in [19]. The proposed architecture relies on remote measurements communicated from multiple locations and uses Kalman filter for state estimation. Effect of latency in sending the feedback signals was also taken into account. Some of the researchers have proposed communication-free approaches to derive frequency support from asynchronous AC areas containing wind farms. For

6.2 Methods of Frequency Support in AC-MTDC Systems

173

example, [30] presented a mechanism to derive frequency support from wind farms connected to a point-to-point HVDC link, which does not required communication. In [35], this concept was expanded and applied to an MTDC system. The problem of extracting frequency support from OWFs connected to the MTDC grid was investigated. The idea in [30, 35] is to indirectly communicate the onshore frequency information to the offshore location by means of DC grid voltage. To that end, the onshore converters operate two modes—“normal” operating mode and “disturbed” operating mode. In the “normal” mode, the onshore stations operate in power– voltage (P –V ) droop control. When the frequency deviation in the onshore grids fall outside a deadband, the “disturbed” mode kicks in. In this mode, the onshore converters operate in frequency–voltage (f –V ) droop. As a result, the DC voltage deviation at the onshore station becomes proportional to the frequency deviation in the corresponding area. This change in DC voltage affects the voltage of the offshore node almost instantly. The converter station connected to the OWF also operates in f –V droop, which reacts to the DC voltage change and alters the frequency of the offshore AC system. This in turn extracts frequency support from the OWF. Li et al. [17] presented design insights and further improvement to the strategy proposed in [35]. One issue is that when a step change in power reference takes place at the onshore converter station, the “disturbed” operating mode is activated and the power reference change will not occur. In [33], frequencies of onshore AC systems are communicated to the MTDC terminal connected to the OWF. The frequency of the AC system connected to the OWF is varied as a weighted sum of the frequencies of the onshore AC grids. Determining these weights however is not straightforward. They will be dependent on the topology of the DC network. Advantages of this method over the communication-free approach (apart from step change in power) should be established to justify reliance on extensive communication of frequency from each onshore area to each offshore area. Literature on communication-free frequency support also includes [14, 17, 40, 41]. One idea is to control VSC to emulate a virtual synchronous generator, which can provide inertial and primary frequency support [40]. An adaptive voltage-droop coefficient as a function of frequency deviation has been proposed by Wang et al. [41], which results in a characteristic similar to the P –V –f droop. Another (N − 1) contingency, which can lead to large frequency deviation, is converter outage. Following such an outage, the converter powers can be optimally redistributed to minimize the frequency deviation [14]. References [36, 37] proposed frequency support based on local frequency measurement at the converter stations. However, this scheme is not completely communication-free. This is due to the use of common DC-link voltage-droop control that uses communication of the DC voltage from a particular node in the DC grid to each converter station. The concept of “inertial coupling matrix” was introduced in [9]. The matrix represents the interaction between steady state frequencies in the asynchronous AC areas as a function of the governor droop, DC voltage-droop, and frequency-droop coefficients.

174

6 Integration of Wind Farms Using MTDC Grids: Frequency Support Perspective

Another important aspect is that the DC voltage droop and the frequency droop in a converter station in the DC grid interact with each other. The steady-state values of the DC voltages and AC-side frequency impact each other, which has been studied in [1, 32]. For example, the steady-state values of frequencies in the presence of local P –V –f droop control have been studied [32]. Research in this area has gone beyond understanding the interplay of DC voltage and frequency-droop controls—ideas to negate the influence of DC voltage droop on frequency-droop control have also been explored. One approach [1] is to calculate the effective frequency-droop constant at a converter connected an AC area based on the assumption that frequency deviation in other areas can be neglected. This assumption can lead to issues when other AC areas provide frequency support, which in turn leads to deviation in frequencies in those areas. Nonetheless, this idea was extended to an integration method [26] and receding horizon control [27, 28] for negating the influence of voltage-droop control. MPC has also been applied as an extension of the same strategy with the objective of minimizing the frequency nadir [29]. So far the focus in [27–29] has been on a test system with two synchronous AC areas connected by an MTDC grid—one providing frequency support to the others. From a frequency support standpoint, the MTDC grid can be viewed as an equivalent point-to-point HVDC connection. It becomes challenging when more than two asynchronous AC areas become involved in frequency support. Techniques proposed in [27–29] require to be tested in such systems.

6.2.1 Ratio-Based Selective Frequency Support It is understandable that in an AC-MTDC grid with multiple asynchronous AC areas, frequency support from one area to the other would likely be governed by frequency regulations markets in the future. In such a market, there should be a provision of “selective” participation, i.e., all AC areas might not be willing to participate. Moreover, there can be restrictions on participation of certain areas following a particular contingency depending on its severity. Such restrictions might be imposed by the capability of a particular area to provide frequency support. Extensive offline planning studies can dictate these limitations and provide guidance to system operators. Moreover, there should be a mechanism to quantify the contribution of the areas towards frequency support. This is crucial for the future frequency regulation market in such systems. More importantly, this allows the system planners and operators lay out an allowable range of frequency deviation for each area. One measure can be the post-contingency ratios of frequency deviations among different asynchronous areas. The idea of “selective power routing” was first proposed in [37]. In this approach, common DC voltage-droop control as in [5, 6] was employed. Under nominal condition, only voltage droop is considered. Therefore, the AC systems keep operating asynchronously most of the time. When an area requires frequency support assistance, the corresponding converter sends a distress signal to the other

6.3 Chapter Outline

175

areas through existing communication channels used for common DC voltagebased droop control [9], see Option III in Sect. 2.6.4 of Chap. 2. The distress signal contains two types of information: the affected area and the type of disturbance, i.e., AC-side disturbance or converter outage. Such basic information does not consume any additional bandwidth and is needed to be sent only for a short time. This signal can be sent using the existing fiber-optic communication channels embedded in the DC cables, which are being used for the common DC voltage-droop scheme. DC cables can also be used for communicating this signal by leveraging power line carrier communication (PLCC). In this context, it should be mentioned that PLCC is a well-established technology for the AC transmission lines. The AC lines are employed to carry both data and electric power simultaneously. This can eliminate the need for installing new communication infrastructure. However, PLCC through DC lines is still being researched [23]. Theoretically, it is possible to communicate data by modulating the power or voltage reference. To be more specific, communication of distress signal should not be an issue since only minimal information needs to be sent. Upon receipt of the distress signal, a converter station selectively participates in frequency support based upon contractual obligation or other considerations. One approach for quantifying frequency support contribution from the AC areas is to use a ratio-based requirement. In this method, a certain ratio among the frequency deviations in different areas can be attained following a disturbance. This requirement was first introduced in the context of steady-state deviations in [39]. This was further extended in [36, 37] by requiring a prescribed ratio among the frequency deviations of the asynchronous areas even during the dynamic conditions. The concept of ratio-based inertial support was also introduced in [36]. Different approaches for frequency support through MTDC proposed in the literature are summarized in Table 6.1.

6.3 Chapter Outline The organization of this chapter is as follows: 1. Frequency support in asynchronous AC-MTDC system: First, frequency support principles in asynchronous AC-MTDC systems based on the ratio-based selective philosophy will be detailed. Ratio-based inertial and primary frequency support following AC-side disturbances will be analyzed in detail. A strategy for reducing frequency deviation following DC-side disturbances will also be elaborated. Converter outage will be considered for the DC-side disturbance. 2. Frequency support in asynchronous AC-MTDC system with offshore wind farm: Based on the frequency support mechanisms for general asynchronous AC systems, OWFs will be considered in one of the AC areas. The controls of OWF will be modified to emulate the behavior of an asynchronous AC system. This will enable implementation of the ratio-based scheme to extract frequency support from OWFs.

176

6 Integration of Wind Farms Using MTDC Grids: Frequency Support Perspective

Table 6.1 Existing literature on frequency support through MTDC grids [36] Category Communicationbased frequency Support

References [2, 3, 7] [19]

[15] Phulpin et al. [30]-based works

[35]

[33]

Communicationfree MPC based

[27, 28]

Communicationfree frequency support

[40]

[29]

[41] [17]

Comments Implemented distributed PI controllers requiring communication from neighboring asynchronous areas Centralized MPC-based controller for primary and secondary frequency support using Kalman filter for state estimation Suggested to modify DC voltage reference to bring the voltage back after disturbance Extended the communication-free mechanism proposed in [30] to provide frequency support from OWF to onshore AC areas via MTDC grid Overcame limitations of [35] by explicitly communicating the onshore frequencies to offshore MTDC WF terminal and providing only inertial support from OWF Nullified the effect of voltage droop on frequency-droop coefficients Extended [27, 28] and proposed a strategy to limit the frequency nadir MTDC converters are emulated as synchronous generator to extract frequency support Adaptively changed the voltage-droop coefficients based on frequency deviation Presented design insights and improved performance of [35] for a specific system

3. Frequency support in asynchronous AC-H-MTDC system with offshore and onshore wind farm: The concept of hybrid-MTDC (H-MTDC) was introduced briefly in Sect. 1.4 of Chap. 2, which considers LCC converter for integrating onshore wind farms and VSCs to integrate OWFs. Modeling and control options of such grids will be briefly introduced and a case study involving frequency support in such systems will be presented.

6.4 Topic I: Frequency Support in Asynchronous AC-MTDC System For AC-side disturbances, the frequency droop is activated with values that are predesigned to provide desired primary frequency support. The desired frequency support is defined based upon steady-state frequency deviations [37, 39]. However, it will be shown that this procedure does not ensure the best dynamic performance. Next, a dynamic approach is presented, where the instantaneous frequency variations of the areas that are not the origin of the disturbance are estimated using

6.5 Study System: Full-Order Model

177

approximate models that will be derived in Sect. 6.6. Upon estimation, the converter located at the affected area (i.e., the area where disturbance occurred) uses MPC [4] in order to ensure a desired frequency dynamics with a single-point actuation [37]. For a better inertial support provision, an inertial-droop controller is introduced [36]. A new design procedure is presented and conditions on droop coefficients are derived to achieve a ratio-based requirement. Finally, for converter outages, the power references are modified in a way that the DC power redistribution does not or minimally affect the AC-side frequencies. Insights in terms of limiting factors for power redistribution and effects of these limiting factors are also highlighted.

6.5 Study System: Full-Order Model A test system, which consists of three asynchronous AC areas connected to a four-terminal bipolar MTDC grid with metallic return network, is considered as shown in Fig. 6.1. From a reliability standpoint and to transfer higher levels of power, a bipolar MTDC system is much better compared to a monopolar MTDC. A comprehensive full-order model is used for simulation studies where state-space averaged model is used to represent the two-level VSC-based converter stations. Standard vector control strategy with inner current control loops is assumed. The

PG4 700 MW

AC Area #1

G4

15

10

2

9

3

7

8

11 17

3

G3

700 MW

2

4

12

PG2

G2

Pinv16 16 300 MW

Pinv17 900 MW

Slack

1

PG1 700 MW

PL10 2500 MW QL10 -250 MVAr

G1

P L9 1500 MW Q L9 -100 MVAr 1

Slack

4

Slack

G6

G5 6

AC Area #3

14

13 5

Prect14

Prect13

300 MW

900 MW

AC Area #2

Fig. 6.1 Schematic of the bipolar MTDC grid with metallic return (single line diagram) connected to three AC areas

6 Integration of Wind Farms Using MTDC Grids: Frequency Support Perspective

PI

pre-disturbance value

PCgi 2 DCg max

kvgi ( V

Pvgi

)

2 DCg min

kvgi ( V

)

/4

/4

2 2 (VDCgcom VDCgref )/4

fi

Pf max

Switch

kvgi

Prefgi

0

* I dgi

p (positive-pole) or n (negative-pole)

k fgi

Switch

Pf min

-

g

-

178

f0

Distress Signal for AC-side Disturbances

Fig. 6.2 Representation of the power–frequency–voltage-droop control of an aggregation of the converter stations belonging to the same pole connected to the ith AC area. Frequency droop (in gray) is activated in participating converters when an AC area requests frequency support through distress signal

DC transmission lines are modeled using one π -section. A standard representation of the AC system, where all the generators are represented by sixth-order subtransient models equipped with type DC-1A excitation systems, is considered. Real power loads of constant current and reactive power loads of constant impedance characteristics are assumed. Further details of the system modeling can be found in Sect. 2.6 of Chap. 2 and system parameters can be found in [9]. The control structure proposed in [37], which will be described in more detail in the later sections, is shown in Fig. 6.2 in a compact form. In the next section, a simplified N th-order model of the system comprising N asynchronous AC areas is presented, which forms the basis for the ratio-based selective frequency-support methodologies.

6.6 N th-Order Model of the System In order to develop a deeper understanding of the coupling between the autonomous power sharing of the DC grid and the frequency dynamics of the AC grids, a simplified N th-order nonlinear model is required. This model forms the basis for various control strategies that are presented in the later sections. The following assumptions are made while deriving the N th-order nonlinear model: (1) The DC lines’ inductive and capacitive dynamics, and the DC power losses are neglected. However, the effect of voltage-droop control is considered. (2) The dynamics of the inner current control loop and the outer droop loop are neglected, i.e., instantaneous tracking is assumed for the converters.

6.6 N th-Order Model of the System

179

(3) The AC system losses are neglected and only the effective swing dynamics of the synchronous generators are considered. This model with the stated assumptions is a simplified representation of the fullorder model, which can closely capture the frequency dynamics in the AC-MTDC system. It is derived to gain better insight into the frequency support phenomena and to analytically design control parameters according to the response criteria. The inductive and capacitive dynamics of the DC lines and the speed of the converter controls are neglected since they are too fast compared to the frequency dynamics. The swing dynamics of machines is considered as it is the most important factor in determining the frequency variations. Implication of these assumptions will be presented in Sect. 6.7.5 when compared against simulation results of full-order model of Sect. 4.8. Let us formulate the positive and negative-pole converter powers of the ith-AC grid (Fig. 6.2). Based on the “selective power routing concept,” which is presented in the later sections, only some of the converters would have frequency droop activated. However, for now, the N th-order model is derived assuming voltage and frequency droops are active in all the converters. 2 2 PCgi = Prefgi + kfgi Δfi + kvgi (VDCpcom − VDCpref )/4

(6.1)

where g = p represents the positive-pole variables; g = n represents the negativepole variables. Δfi = f0 − fi denotes frequency deviation; kfgi is the effective frequency-droop coefficient; and kvgi is the effective voltage-droop coefficient. These are effective droop coefficients, i.e., they are obtained by summing up corresponding droop coefficients of all the VSCs interfaced with the ith AC grid. For example, in the test system considered, see Fig. 6.1, area #1’s effective positive-pole voltage-droop coefficient is obtained by the summation of positivepole voltage-droop coefficients of converters 2 and 3. Therefore, PCgi and Prefgi represent the actual and reference, respectively, for the net power going into the ith area through the pole “g.” Variables VDCgcom and VDCgref are the measured and reference common DC voltages from the MTDC “g”-pole network, respectively. This voltage measured from a common node in the DC grid (for the study system, DC bus of station#1 is the common node) is communicated to all the converters for autonomous power sharing [8, 9]. By summing up the “g”-pole converter powers in all the areas, we get, N ) k

PCgk =

N ) k

Prefgk +

N )

kfgk Δfk + (

k

N ) k

2 2 kvgk )(VDCgcom − VDCgref )/4

(6.2) Upon rearranging the terms, we have, N )

2 (VDCgcom

2 − VDCgref )/4

=−

k

N N ) ) Prefgk + kfgk Δfk − PCgk k

k

N ) k

kvgk

(6.3)

180

6 Integration of Wind Farms Using MTDC Grids: Frequency Support Perspective

The terms

N )

PCgk represent power loss in the “g”-pole of the MTDC network.

k

By replacing the voltage error in Eq. (6.1), we get the effective “g”-pole converter power of the ith-AC grid as, N )

PCgi = Prefgi + kfgi Δfi − kvgi

N N ) ) Prefgk + kfgk Δfk − PCgk

k

k

k

N )

(6.4)

kvgk

k

To include the frequency dynamics into the derivation, we consider real power balance equation of the ith AC grid, PGi − PLi + PCpi + PCni = 0

(6.5)

Here, the convention is that the converter power flows from MTDC grid to AC grid. Also, PGi and PLi are the total generation and total load in the ith AC grid, respectively. Next, we consider the following per-unitized swing equation and replace PGi , i.e., the generator power output from the power balance equation, 2HGi fi f˙i = Pmechi − PGi = PMi + kgovi Δfi − PLi + PCpi + PCni

(6.6)

where HGi is the “effective inertia constant” and kgovi = 1/Rgovi is the “effective inverse governor droop constant.” These constants are obtained by summing up all the individual generator’s inertia constants and the inverse of the governor droop coefficients in the ith AC grid, respectively. Similarly, PMi is the “effective mechanical power input,” which is the total mechanical power input of all the generators in the ith AC grid. Upon replacing PCpi and PCni in Eq. (6.6) from Eq. (6.4) and upon rearranging terms, we finally get, ⎞

⎛

kfpi kf ni ⎟ ⎜ 2HGi fi f˙i = ⎝kfpi + kf ni + kgovi − kvpi ) − kvni ) ⎠ Δfi N N kvpk

N )

−kvpi

−kvpi

N )

k

kfpk Δfk kf nk Δfk k=i k=i vni ) Mi N N ) kvpk kvnk k k N N N N ) ) ) ) Prefpk − PCpk Pref nk − PCnk k k k k vni N N ) ) kvpk kvnk k k

−k

+P

−k

kvnk

k

− PLi + Prefpi + Pref ni

(6.7)

6.7 AC-Side Disturbance: Primary Frequency Support

181

By putting the above in a matrix–vector form for N areas, we have Eq. (6.9). In a compact from, we have, 2H ◦ f ◦ ˙f = KΔf + ΔP

(6.8)

where “◦” denotes a “Hadamard product.” Also, unless otherwise stated, from now on matrices and vectors will be denoted using “bold” symbols. ⎡

⎡ ⎤ ⎤ 2HG1 f1 f˙1 Δf1 ⎢ ⎢ . ⎥ ⎥ .. ⎣ ⎦ = K ⎣ .. ⎦ . 2HGN fN f˙N ΔfN ⎡

N )

Prefpk −

N )

PCpk

N )

Pref nk −

N )

⎤ PCnk

⎢ k k −kvn1 k ) ⎢ PM1 −PL1 + Prefp1 + Pref n1 −kvp1 k ) N N ⎢ kvpk kvnk ⎢ k k ⎢ ⎢ .. +⎢ . ⎢ N N N N ⎢ ) ) ) ) ⎢ Prefpk − PCpk Pref nk − PCnk ⎢ k k k k −kvnN ⎣ PMN −PLN + PrefpN + Pref nN −kvpN N N ) ) kvpk

k

⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

kvnk

k

(6.9) Vector ΔP is zero during steady-state conditions. The frequency dynamics resulting from both AC-side disturbances and DC-side disturbances can be represented by introducing variations in ΔP. For example, load or generation changes in the ith AC grid can be represented by varying ΔPi (ith row in ΔP). In contrast, a DC-side disturbance like converter loss would require changing all the elements of the vector ΔP. The generic N th-order bipolar model addresses the following: (1) It enables consideration of contingencies like converter outages as will be presented in Sect. 6.11. (2) The generic bipolar framework with metallic return network can be used for future research on unbalance in the DC-side, ground current control, and so on. A monopolar model cannot address these issues.

6.7 AC-Side Disturbance: Primary Frequency Support In this section, the concept of “selective power routing” and a “static design approach” for the droop coefficients based on the N th-order model is presented. This approach is also applicable for monopolar MTDC system. In fact, the bipolar system is reduced to an equivalent monopolar representation for applying this method.

182

6 Integration of Wind Farms Using MTDC Grids: Frequency Support Perspective

6.7.1 Selective Power Routing Concept Selective power routing is the ability of the MTDC network to selectively modify converter power to provide ancillary or emergency services. This concept, originally proposed in [37], allows the participation of certain AC areas connected to those converters based upon pre-existing contracts through a market mechanism or under the directive of the reliability coordinator in an emergency scenario. As shown in Fig. 6.2, upon occurrence of an AC-side disturbance, a distress signal is sent from the affected area. The affected area seeks provision of frequency support from other areas through this distress signal. It was proposed in [37] that the distress signal will be sent when the magnitude of the rate of change of frequency (RoCoF) in that area crosses a threshold. The threshold can be determined based on requirements of the system operators. A threshold of 80 mHz/s was assumed in [37]. Therefore, from the distress signal, all the converters understand which area is affected. Depending on which area needs support, some areas would like to participate in frequency support and some do not. This could be due to predefined operation rules or economic constraints or due to the area’s capabilities. For example, Area#3 could be a nonparticipating when there is disturbance in Area#2. However, for a disturbance in Area#1, Area#3 could be a participating area (Fig. 6.1). Let Np be the number of non-participating areas and Enp denote the set of such areas. One approach to ensure that no additional power is delivered from these areas is to set the droop coefficients of the non-participating areas to zero, i.e., kvpi = kvni = 0 for all, i ∈ Enp . However, due to the presence of voltage droop, losses in the MTDC network are shared among all the areas. Setting the droop coefficients zero could make ΔPvgi non-zero ∀i ∈ Enp , see Fig. 6.2 and Eq. (6.9). To avoid this while achieving a seamless turnoff of voltage droop, ΔPvgi is held at the pre-disturbance value as shown in Fig. 6.2. This ensures that the non-participating areas continue to share the same loss in the MTDC network, which they were sharing in the pre-disturbance condition. Therefore, the frequency of the non-participating areas remains unaffected. Note that, the stations connected to these areas are no longer operating in DC voltage-droop control, but in constant power control mode. For the participating areas, the frequency-droop control is activated, see Fig. 6.2. For the participating areas, we propose to activate the frequency-droop controllers, see Fig. 6.2. If inertial support is provided by the area, then inertial droop can also be enabled. The coefficients of these controllers are predetermined and are designed offline to meet a ratio-based requirement, which can be prescribed by the system operators. Figure 6.3 summarized the controller within the framework of the hierarchal AC-MTDC control. During nominal conditions only voltage-droop control is considered (mode (i)). Following a disturbance, based on the information from the distress signal, inertial–frequency–voltage droop (mode ii) is activated for participating areas and constant power control (mode iii) is activated for nonparticipating areas.

6.7 AC-Side Disturbance: Primary Frequency Support Fig. 6.3 Proposed controller within the framework of the hierarchal AC-MTDC control: Outer control loop is chosen based on mode of operation and information carried by distress signal. For participating areas, predesigned droop coefficients, which ensures a prescribed ratio-based criterion, are used

183

Power and Voltage References by System Operators Power and Voltage References (i) or (ii) or (iii) based on distress signal

Control Objectives (i) Nominal Mode Voltage-droop Control

(iii) Non-participating Area Constant Power Control

(ii) Participating Area Inertial, Frequency and Voltage Droop Control

Current References Inner Current Control Loop

Modulation Index Inverter Switching Control

6.7.2 Characteristic Features of Selective Power Routing (1) Asynchronous operation in the nominal conditions: In nominal conditions, the frequency-droop control is kept inactive and only the voltage-droop control is activated. Since the AC systems operate under quasi-static condition, most of the disturbances are not serious enough to require assistance from other AC areas. Therefore, in nominal conditions, frequency-droop control is kept inactive. (2) Frequency-droop option in all areas: Following a disturbance that is large enough to request assistance from other areas, the ability to turn on and off the frequency-droop control enables us to choose participating and nonparticipating areas. This “selectivity” is required as participating and nonparticipating areas are not fixed and can vary depending on where the disturbance occurred. Therefore, the option for frequency droop is maintained in each converter station. (3) Non-participating areas in power control mode only during the frequencysupport process: Based on where the disturbance occurred non-participating areas are chosen and their controls switch from voltage droop to constant power control. By maintaining their powers at the pre-disturbance values, non-participation from them is ensured. During the nominal condition, the nonparticipating areas are operated in voltage-droop control instead of constant

184

6 Integration of Wind Farms Using MTDC Grids: Frequency Support Perspective

power control. This is helpful as constant power control tends to negatively affect system stability. Moreover, it helps in sharing power loss and also helps in sharing the burden following a converter outage. (4) Ability to ensure a specified performance among participating areas: The participating areas are operated in P –V –f droop control whose frequencydroop coefficients are designed to achieve certain performance requirements. This leads to a specific structure, which can be used to meet the system operators’ requirements as illustrated next. To retain this structure, the voltage droops cannot be deactivated in the participating areas.

6.7.3 Monopolar Representation of Nth-Order Model The N th-order model can be further reduced to a monopolar representation. From this representation, an approach is presented next to design the frequency-droop coefficients that meet the system operators’ requirements. To ensure zero current flow through the metallic return path under normal operation, the droop coefficients and power references of the positive and negative poles of a converter station are made equal in this model. This means, kfpi = kf ni = kf i /2; kvpi = kvni = kvi ; and Prefpi = Pref ni = Pref i /2 are to be satisfied. Since AC-side disturbances do not lead to unbalance in the DC-side, the bipolar system can be treated using an equivalent monopolar representation. Equation (6.8) can now be rewritten as, 2H ◦ f ◦ ˙f = KN Δf + ΔP. Here, the matrix KN is given by Eq. (6.10). ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ KN = ⎢ ⎢ ⎢ ⎢ ⎢ ⎣

kf 1 + kgov1 − kv2 kf 1 −) N kvk

kv1 kf 1 N ) kvk

k kf 2

v1 −) N

k

kf 2 + kgov2 −

k

.. .

−

kvN kf 1 N ) kvk k

.. . −

−

···

kv2 kf N −) N kvk

kvk

k

kvN kf 2 N ) kvk

kv2 kf 2 N ) kvk

⎤

kv1 kf N N ) kvk

···

k

k

k

..

.

.. .

· · · kf N + kgovN −

k

kvN kf N N ) kvk

⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

k

(6.10)

6.7.4 Static Design of Frequency-Droop Coefficients The value of frequency-droop coefficients can be designed based on the steadystate deviation in frequencies of the participating areas. The required steady-state deviations could be governed by the prescription of the system operators. As an example, consider the scenario wherein AC-side disturbance occurs only in Area#1 (ΔP1 = 0). Let Nr be the number of areas participating in frequency support. For

6.7 AC-Side Disturbance: Primary Frequency Support

185

simplicity, let us index the areas in a way so that all the non-participating areas are concatenated to the end. Also assume that the system operators want to ensure a predefined ratio among the post-disturbance steady-state frequency deviations of the participating AC areas. Let the desired ratio be r1 :r2 : · · · :rNr . Then the postdisturbance steady-state frequency deviations are given by, ⎤T ⎡ ⎢ ∗ ∗ ∗ Δf = ⎢ ·· ⎣ r1 Δf r2 Δf · · · rNr Δf  0 ·

1×Nr

⎥ 0⎥ ⎦

(6.11)

1×Np

Assuming that the frequency deviations reach the expected ratio in steady state, the monopolar representation gives, ⎡ ⎡ ⎤ ⎤ r1 Δf ∗ −ΔP1 ' ( .. ⎢ 0 ⎥ ⎢ ⎥ KNr 0 ⎢ ⎢ ⎥ ⎥ . ⎢ . ⎥= ⎢ ⎥ ⎣ .. ⎦ 0 Nkp ⎣ rN Δf ∗ ⎦ (6.12) r

 0 0 KN 

 −ΔP

Δf

Since the voltage-droop control and frequency-droop control of non-participating areas are disabled, the off-diagonal matrices of KN in Eq. (6.12) are 0. Matrix KNr (size Nr ×Nr ) can be obtained by replacing “N ” by “Nr ” in the KN matrix presented in Eq. (6.10). This is consistent with the understanding that only participating areas are responsible for frequency deviation. The matrix Nkp is diagonal in nature. However, as seen from Eq. (6.12) the matrix Nkp does not play any role in frequency deviation for this scenario. Therefore, re-writing (6.12) gives us, ⎡ ⎤ r1  T ⎢ ⎥ (6.13) KNr ⎣ ... ⎦ Δf ∗ = −ΔP1 1 0 · · · 0 r Nr Upon summing all the row equations in (6.13), all the kf i ’s cancel out due to the structure of KNr matrix and Δf ∗ can be expressed as, Δf ∗ = −ΔP1 /

Nr )

rk kgovk

(6.14)

k

Eliminating Δf ∗ and ΔP1 from Eqs. (6.13) and (6.14) gives us the condition that the set of frequency-droop coefficients ({kf 1 , · · · , kf Nr }) of the participating areas should obey in order to achieve the prescribed ratio. ⎡ ⎤ r1 Nr  T ⎢ ⎥ ) (6.15) KNr ⎣ ... ⎦ = rk kgovk 1 0 · · · 0 r Nr

k

186

6 Integration of Wind Farms Using MTDC Grids: Frequency Support Perspective

From the row operation of replacing 1st row by sum of all rows, and upon rearranging terms in (6.15), we get, ⎡

0

0 Nr )

⎢ ⎢ r1 kv2 −r2 kvk ⎢ ⎢ k=2 ⎢ . .. ⎢ . ⎢ . . ⎢ ⎣ r1 kvN r r2 kvN r

···

0

···

rNr kv2

..

.

· · · −rNr

⎤

⎡

⎤

0

⎥⎡ k ⎤ ⎢ ⎥ Nr ) ⎢ r k ⎥ ⎥ f1 ⎢ 2 gov2 kvk ⎥ ⎥⎢ ⎥ ⎥ ⎢ kf 2 ⎥ ⎢ ⎥ k ⎥⎢ . ⎥ = ⎢ ⎥ .. .. ⎥⎣ . ⎦ ⎢ ⎥ ⎢ ⎥ ⎥ . . . ⎢ ⎥ ⎥ Nr Nr ) ) ⎣ ⎦ kf N r ⎦ rNr kgovN r kvk kvk

k=N

k

(6.16) Equations (6.14) and (6.16) hold two valuable insights, which are stated below, 1. The frequency deviation solely depends on the disturbance (ΔP1 ), effective inverse governor droops of all the participating areas (kgovi ), and the desired ratio of frequency deviation (ri ). The values of frequency-droop coefficients do not directly influence steady-state frequency deviations. Instead, the frequencydroop coefficients redistribute the governor droop availability to achieve a certain ratio of steady state frequency deviation, see (6.14). 2. Since the matrix in (6.16) has a rank of Nr − 1, we have multiple solutions for Nr frequency-droop coefficients ({kf 1 , · · · , kf N r }), which achieve the same desired frequency deviation ratio. Since there are multiple solutions, we choose an arbitrary value for a frequencydroop coefficient and solve for the remaining frequency-droop coefficients using Eq. (6.16). We also perform small-signal stability analysis on the full-order model described in Sect. 6.5 to ensure the stability of the system.

6.7.5 Simulation Results In order to validate the design method under ideal conditions, first the controller is applied on the N th-order model without considering any transmission delay for the distress signal. Figure 6.4a shows the frequency dynamics following a 20% step-reduction in power output of generator G6 (Fig. 6.1) at t = 1.0s. Here, the frequency-droop coefficients are designed to achieve a prescribed ratio of 1 : 1.5 : 2 among the post-disturbance steady-state frequency deviations, see Table 6.2. The steady-state frequency deviations are exactly in the prescribed ratio as shown in Fig. 6.4b. In contrast, Fig. 6.5a–c shows the frequency dynamics, ratios among the frequency deviations of generators G6, G5, and G1, and positive-pole DC voltages as obtained from the full-order model. The full-order model represents a non-ideal realistic scenario. Moreover, a transmission delay of 100 ms is considered for communicating the distress signal in the full-order model. The difference between the obtained ratios and prescribed ratios in Fig. 6.5b is due to the fact that the strategy is built on a simple N th-order model, which has certain assumptions (see, Sect. 6.6).

frequency, (Hz)

6.7 AC-Side Disturbance: Primary Frequency Support

60

Area#2

Area#1

Area#3

(a)

59.9 59.8 59.7 2.5

ratio

187

(Δf3 /Δf1 )

(Δf2 /Δf1 )

2

(b) 1.5 5

10

15

20

25

30

35

40

time, (s) Fig. 6.4 Ideal response from N th-order model with a 20% reduction in generation of G6 in Area#3 (with a prescribed ratio of 1 : 1.5 : 2): (a) frequency dynamics and (b) ratios among frequency deviations. Source: Vennelaganti and Chaudhuri [37]. Reproduced with permission of IEEE Table 6.2 Frequency-droop coefficients of positive-pole (same for negative-pole) used for different scenarios of simulation studies [37] Area #1 kf 1 (MW/Hz) (positive-pole) Distressed area Area#2

Area#2

Area#3

Prescribed ratio (r1 :r2 :r3 ) Traditional frequency droop [9] (no ratio) All areas participate Area#3 doesn’t participate All areas participate

Area #2 kf 2 Area #3 kf 3 (MW/Hz) (MW/Hz) (positive-pole) (positive-pole)

Station#2 Station #3 Station #4 50.00 50.00

Station #1 50.00

50.00

1:1:1

15.63

15.63

224.83

50.00

1:1:NaN 50.00

50.00

209.15

–

1:1.5:2

101.06

76.21

150.00

101.06

However, the N th-order model enabled the strategy, which delivered a response in a realistic scenario that is close to the desired performance. From this point on, unless otherwise stated, only full-order model is used for simulation studies. Figure 6.6a shows the variation of frequencies due to a 10% step-reduction in generator G5 (Area#2) power output with a traditional frequency-droop control as reported in [9]. In this case, there was no transmission of distress signal and frequency-droop controllers were always kept active with values presented in Table 6.2. In contrast, for the same disturbance in Area#2, Fig. 6.7a shows a better

6 Integration of Wind Farms Using MTDC Grids: Frequency Support Perspective

frequency, (Hz)

188

60

Area#1

Area#2

Area#3

(a)

59.9 59.8 59.7

ratio

59.6 2.5 2

(ΔfG5 /ΔfG1 )

(ΔfG6 /ΔfG1 )

1.5

(b)

VDCp , (KV)

352

station#1

station#2

station#3

station#4

(c)

350 348

0

5

10

15

20

25

30

35

40

time, (s)

VDCp , (KV) frequency, (Hz)

Fig. 6.5 Non-ideal response from full-order model with a 20% reduction in generation of G6 in Area#3 (with a prescribed ratio of 1 : 1.5 : 2): (a) frequency dynamics, (b) ratios among frequency deviations of G6, G5, and G1, and (c) positive-pole DC voltage. Source: Vennelaganti and Chaudhuri [37]. Reproduced with permission of IEEE

Area#1

60

Area#2

Area#3

(a)

59.8 59.6 59.4

station#1

352

station#2

station#3

station#4

(b)

350 348 346 0

5

10

time, (s)15

20

25

Fig. 6.6 Full-order model response following a 10% reduction in generation from G5 of Area#2 with traditional frequency-droop control [9] (Table 6.2). Source: Vennelaganti and Chaudhuri [37]. Reproduced with permission of IEEE

VDCp , (KV)

frequency, (Hz) VDCp , (KV) frequency, (Hz)

6.7 AC-Side Disturbance: Primary Frequency Support

189

Area#1

60

Area#2

Area#3

(a)

59.9 59.8 59.7 354

station#1

station#2

station#3

station#4

352

(b)

350 348 346

Area#1

Area#2

Area#3

60

(c) 59.8 59.6 354

station#1

station#2

station#3

station#4

352

(d)

350 348 346 0

5

10

15

20

25

time, (s) Fig. 6.7 Full-order model response following a 10% reduction in generation from G5 of Area#2 for two scenarios: (a, b) all areas participate and (c, d) Area#3 doesn’t participate (see, Table 6.2). Source: Vennelaganti and Chaudhuri [37]. Reproduced with permission of IEEE

response when the frequency-droop coefficients are designed based on this method with an objective to achieve the same frequency deviation in all areas. In a separate study, following the same disturbance in Area#2, Fig. 6.7c shows the frequency dynamics, when Area#3 does not participate in frequency support. The prescribed ratios and frequency-droop coefficient values for both the studies are presented in Table 6.2. As described before, due to the difference between the N th-order and the full-order model, the frequency deviations are close, but not exactly the same. Figure 6.8 shows the dynamics of converter powers with and without participation of Area#3. Consequently, the frequency of Area#3 shown in Fig. 6.7c and the converter power in Area#3 (station#1) shown in Fig. 6.8a remain unchanged. Additionally, Fig. 6.7b, d shows the DC voltages with and without participation of Area#3, respectively. These voltages are in range of DC voltages obtained from traditional frequency-droop control (Fig. 6.6b). Even though this method ensures approximate convergence to the desired frequency ratio, this does not ensure the desired dynamic performance. For example, the frequency nadir in Figs. 6.5a, 6.7a, c could be improved. To that end, an MPCbased dynamic approach is presented in the next section.

190

6 Integration of Wind Farms Using MTDC Grids: Frequency Support Perspective

station#1

-150

Postive-pole Power PCp , (MW)

-160

(a)

all areas participate Area#3 does not participate

450 440

station#2

(b)

station#3

(c)

station#4

(d)

430 150 140 130 -410 -430 -450 0

5

10

15

20

25

time, (s) Fig. 6.8 Converter power dynamics from full-order model following a 10% reduction in generation of G5, when all areas participate (solid trace) and when Area#3 does not participate (dotted trace). Source: Vennelaganti and Chaudhuri [37]. Reproduced with permission of IEEE

6.8 AC-Side Disturbance: Inertial and Primary Frequency Support MPC [4] has been applied at the converter of the affected area [37], with an aim to provide inertial support, thereby achieving the desired performance in dynamic and steady-state frequency variations. Additionally, the concept of selective power routing was also extended to this strategy. First, MPC without frequency-droop control is considered to verify its effectiveness in providing inertial support. Next, MPC along with the frequency-droop control, where the droop coefficients are designed based on the desired primary frequency regulation needs, is explored. Both schemes do not require communication of frequency measurements.

6.8.1 MPC Without Frequency Droop In this scheme, the voltage-droop control is still functional and the frequency-droop control remains inactive. Indexing the affected area as Area#1, its converter control structure is modified such that the effective converter power becomes, 2 2 PC1 = Pref 1 + u + kv1 (VDCcom − VDCref )/4

(6.17)

6.8 AC-Side Disturbance: Inertial and Primary Frequency Support

191

Here, u is the control input to the plant obtained from MPC. With this controller the plant model can be described as,  2Hp ◦ fp ◦ ˙fp = KNr k =0:∀i Δfp fi ' (T −kvNr kv1 −kv2 1− ) · · · Nr N N )r )r (6.18) + u k k k vk



k

vk

k

+ ΔP1 0 · · · 0

T

vk

k

Here, Hp and fp are the inertia and frequency vectors, respectively, formed only by the participating areas. To perform MPC, the ability to foresee the frequency trajectories of all participating areas as a function of control input u is essential. Using the above plant model (6.18), actuating at the converter of Area#1, the trajectories of all the participating frequencies except that of Area#1 can be estimated as a function of u. Since ΔP1 is unknown f1 is also unknown. However, the frequency of Area#1 can be measured in real time at the terminal of the converter. Therefore, based on the model of the plant in (6.18) and the past trajectory of frequency of Area#1, ΔP1 is estimated using the model reference adaptive control [4] architecture as shown in Fig. 6.9. The desired response criterion is that the ratio r1 : r2 : · · · : rNr has to be maintained among frequency deviations for the entire post-disturbance period. Then the post-disturbance frequency deviations of participating areas are given by, T  (6.19) ΔfP = r1 Δfs r2 Δfs · · · rNr Δfs where fs is the reference frequency. In order to obtain the dynamical equation governing the reference frequency fs , (6.19) is substituted in the plant model (6.18) and all rows in the plant model are added following the substitution. This gives us,  Nr  Nr   0 0 ˙ 2 rk HGk fs fs = rk kgovk Δfs + ΔP1 (6.20) k

f1

fˆ1

PI

k

P1

u

Reference generator

Plant Model

fs

[ fˆp ]

MPC

u

Fig. 6.9 MPC and estimation of ΔP1 using model reference adaptive control

[ fp] Plant

192

6 Integration of Wind Farms Using MTDC Grids: Frequency Support Perspective

frequency, (Hz)

60 59.9

(a)

59.8

Area#1 actual Area#1 estimate

59.7 60.002 60 59.998 59.996

60 59.9

Area#2 actual Area#2 estimate

59.8

1

1.02

(b)

frequency, (Hz)

power, (MW)

59.7 0

-85 -90 -95 -100

-50

actual ΔPm in Area#2 estimated ΔPm in Area#2 2

4

(c)

-100 60 59.9

(d)

59.8

Area#1 actual Area#1 estimate Area#2 actual MPC reference Area#3 actual

59.7 0

5

10

15

20

25

time, (s) Fig. 6.10 Frequency dynamics along with disturbance and frequency estimation using scheme in Fig. 6.9 following a 10% change in generation of G5 of Area#2 with a prescribed ratio of 1 : 1. Source: Vennelaganti and Chaudhuri [37]. Reproduced with permission of IEEE

In MPC, an optimization algorithm tries to find u that minimizes the sum of squares of errors between the estimated frequency deviations, Δfˆi , of participating areas and the reference frequency deviation multiplied by corresponding ratio ri for “M” future time steps. Hence, the objective function is given by, Nr ) M ) (ri Δfs [k] − Δfˆi [k])2 . i

k

For simulation studies, the same disturbance as in the previous section is chosen, where Area#3 is a non-participating area. The MPC actuation is located in Area#2 (i.e., converter station #4), where the disturbance occurred. As mentioned before, frequency droop is not activated in the participating areas. The delay in transmission of the distress signal is still considered to be 100ms. To validate the effectiveness of this scheme, two scenarios are considered. For one scenario, the desired ratio (r1 : r2 ) is chosen as 1 : 1 and for the other, desired ratio is chosen as 1 : 2.

frequency, (Hz)

6.8 AC-Side Disturbance: Inertial and Primary Frequency Support

fG1

60

fˆ1

r1 f s

fG5

193

r2 f s

fG6

(a) 59.8 59.6 59.4

ratio

2.5

(b) 2

ΔfG5 /ΔfG1

ΔfG5 /Δfˆ1

reference

1.5 0

5

10

15

20

25

time, (s) Fig. 6.11 Response following 10% change in generation of G5 of Area#2 (with a prescribed ratio of 1 : 2): (a) frequency dynamics, (b) ratio between frequency deviations of G5 and G1. Source: Vennelaganti and Chaudhuri [37]. Reproduced with permission of IEEE

Figure 6.10 shows the frequency dynamics with MPC for a desired ratio of 1 : 1 and the accuracy of estimated frequencies of Areas#1 and #2, and the disturbance within Area#2 using the architecture shown in Fig. 6.9. Figure 6.10a, b shows the approximate and exact matching of the actual and estimated frequency of Area#1 and Area#2, respectively. Future values of frequency of Area#2 are estimated for implementation of MPC, see Fig. 6.9. Figure 6.10c shows almost exact matching of the actual and estimated disturbance in Area#2, i.e., 10% step reduction mechanical input of G5. Since MPC aims to match the trajectories of estimated frequencies to that of the reference frequency, Fig. 6.10d shows the trajectory matching of estimates to that of the MPC reference frequency (fs ). Also, frequency of non-participating Area#3 remains undisturbed. In comparison to frequency dynamics in the case of frequencydroop control with selective power routing, see Fig. 6.7c, the frequency dynamics improved significantly. Figure 6.11 shows the frequency dynamics for a prescribed ratio of 1 : 2 between Area#1 and Area#2. The estimated frequency of Area#1 and actual frequency of Area#2 are exactly tracked to their corresponding references. However, there is a slight difference between reference frequency and actual frequency of Area#1. As explained before, this is due to error in estimation. The error is reflected in the ratio plot, see Fig. 6.11b. Remark From Eq. (6.17), “u” can be interpreted as modification to power reference. Consider a simple scenario, where all the participating areas are identical. Let, the aim be achieving equal post-disturbance steady-state frequency deviations. In the

194

6 Integration of Wind Farms Using MTDC Grids: Frequency Support Perspective

v2 case of two participating areas, this aim is achievable with u = −ΔP1 kv12k+k , v2 refer to Eq. (6.18). In case of more than two participating areas, given a generic set of voltage-droop coefficients, there exists no “u” that attains this aim. In other words, power redistribution to achieve equal frequency trajectories using a singlepoint actuation is not possible with more than two participating areas. 

6.8.2 MPC with Frequency Droop One way to partially overcome the shortcoming of single-point actuation is to addressing the steady-state response criteria by using frequency droop, which are designed to maintain the prescribed ratio as discussed before. MPC works in conjunction with the selective frequency-droop control to try achieve the ratio during dynamic condition. Therefore, we obtain the new plant model as, 2Hp ◦ fp ◦ ˙fp = KNr Δfp ' kv1 −kv2 1− ) ··· Nr Nr ) + kvk kvk  T + ΔP1 0 · · · 0 k

k

−kvNr Nr ) kvk

(T u

(6.21)

k

The plant specified above still has the problem described before. However, the steady-state frequency deviations will converge to the desired ratio based on the design of the frequency-droop coefficients. In addition, the MPC will ensure that the Nr ) M ) objective function (ri Δfs [k] − Δfˆi [k])2 is minimized. Therefore, this method i

k

tries to obtain the best possible dynamics from a single point of actuation. To validate the efficacy of the presented method, the same disturbance, i.e., 10% step reduction in G5 torque input is considered. In this case, all the areas are participating with the desired ratio being 1 : 1 : 1. Note that, apart from frequency of Area#1, frequency of Area#3 is also estimated at converter of Area#2. The estimation results are similar to the previous scenario and are not repeated. Figure 6.12a shows the frequency dynamics of all the areas along with the MPC reference frequency (fs ). The initial frequency trajectories of all the areas are not tracked as efficiently as observed in the previous case with just two participating areas. This is expected, because from a single actuation, power redistribution to achieve equal frequency trajectories is not possible. However, in comparison to just frequency-droop control, see Fig. 6.7a, the frequency dynamics have improved, especially in terms of frequency nadir. Additionally, the positive-pole DC voltages shown in Fig. 6.12b are well within the acceptable limits. However, some spikes in voltages are observed due to the action of the MPC controller. A plausible explanation is that the plant model of the MPC controller is based on a simple N th-order model, which is an approximate representation of the actual plant corresponding to a realistic full-order model.

6.9 Inertial-Droop Control: Modified N th-Order Model

frequency, (Hz)

Area#1

Area#2

195

Area#3

MPC reference

60

(a) 59.9 59.8 59.7

VDCp , (KV)

354

station#1

station#2

station#3

station#4

352

(b)

350 348 346 0

5

10

15

20

25

time, (s) Fig. 6.12 Dynamic response following 10% change in generation of G5 in Area#2 upon applying MPC along with frequency-droop control designed according to Sect. 6.7. Source: Vennelaganti and Chaudhuri [37]. Reproduced with permission of IEEE

6.9 Inertial-Droop Control: Modified N th-Order Model The inertial support provided through MPC is not complete in nature. As mentioned before, since the actuation is only from one location, the desired performance cannot be achieved when there are more than two participating areas. For example, in Fig. 6.12a, the initial frequency trajectories of all the areas are not tracked as efficiently as observed in the previous case with just two participating areas. Moreover, the formulation becomes complicated if the requirement is to have specified ratio of frequency deviations among the participating areas for the entire post-disturbance duration, i.e., have a specific ratio among frequency deviations during the dynamic and steady-state conditions. In order to improve the inertial support, reference [36] proposed to add an inertial-droop over and above the frequency-droop controller as shown in Fig. 6.13. Here, like kfgi , the term hgi is the inertial-droop coefficient. For the AC-MTDC systems with the decentralized inertial-droop controllers a modified N th-order model can be derived that is similar to the N th-order model in Sect. 6.6. With the same assumptions as stated in Sect. 6.6, the derivation begins by formulating the “g”-pole converter powers of the ith-AC grid when voltagedroop, decentralized inertial-droop, and decentralized frequency-droop controllers are activated in all areas (see Fig. 6.13). 2 2 PCgi = Prefgi + kfgi Δfi − 2hgi fi f˙i + kvgi (VDCgcom − VDCgref )/4

(6.22)

6 Integration of Wind Farms Using MTDC Grids: Frequency Support Perspective

PI

PCgi kvgi ( VDCg ) 2max / 4

Pvgi

pre-disturbance value

Prefgi

kvgi ( VDCg ) 2min / 4

fi

Pf max

Switch

0

kvgi

k fgi

Switch

-

* I dgi

p (positive-pole) or n (negative-pole)

Pf min

2 2 (VDCgcom VDCgref )/4

k fgi 2hgi

Distress Signal for AC-side Disturbances

-

g

-

196

f0

fi

Fig. 6.13 Representation of the power–frequency–inertial–voltage-droop control of an aggregation of the converter stations belonging to the same pole connected to the ith AC area. Frequency–inertial-droop control (in gray) is activated in participating converters when an AC area requests frequency support through distress signal

Going through the similar process of summing all the converter powers and rearranging terms, we get, N )

2 (VDCgcom

2 − VDCgref )/4

=−

k

kfgk Δfk −2

N )

N N ) ) hgk fk f˙k + Prefgk − PCgk

k

k N )

k

(6.23)

kvgk

k

By replacing the voltage error in Eq. (6.22), we get the effective “g”-pole converter power of the ith AC grid as, PCgi = Prefgi + kfgi Δfi − 2hgi fi f˙i N  N N N ) ) ) ) ¯ ˙ −kvgi kfgk Δfk − 2 hgk fk fk + Prefgk − PCgk k

where k¯vgi = kvgi /

k N )

k

(6.24)

k

kvgk is the normalized voltage-droop coefficient of the “g”-

k

pole connected to the ith AC grid. In order to include the frequency dynamics into the derivation, we replace PCpi and PCni in Eq. (6.6) from Eq. (6.24) and by rearranging terms, we finally get, ¯ ˙ 2[HGi + (1 −k¯vpi )hpi + (1 −  kvni )hni]fi fi  N N ) ) −k¯vpi 2hpk fk f˙k − k¯vni 2hnk fk f˙k k=i

k=i

¯ + (1 − k¯vpi )k = [kgovi  fpi + (1 −  kvni )kf ni ]Δf i N N ) ) −k¯vpi kfpk Δfk − k¯vni kf nk Δfk + ΔPi k=i

k=i

(6.25)

6.10 Ratio-Based Inertial and Primary Frequency Support

197

where ΔPi is given by, ΔPi = PMi − PLi + Prefpi + Pref ni N  N  N N ) ) ) ) ¯ ¯ −kvpi Prefpk − PCpk − kvni Pref nk − PCnk k

k

k

(6.26)

k

By representing Eq. (6.25) in a compact matrix–vector form, we have, ‘2H(f ◦ ˙f) = KΔf + ΔP

(6.27)

Here, “◦” denotes a “Hadamard product.” Also, unless otherwise stated, from now on matrices and vectors will be denoted using “bold” symbols. The matrices H and K have similar structures whose elements are given by,  H (i, j ) =  K(i, j ) =

HGi + (1 − k¯vpi )hpi + (1 − k¯vni )hni if i = j if i = j −k¯vpi hpj − k¯vni hnj

kgovi + (1 − k¯vpi )kfpi + (1 − k¯vni )kf ni if i = j if i = j −k¯vpi kfpj − k¯vni kf nj

(6.28)

This similar structure is achieved due to the specific form of inertial-droop controller in Eq. (6.24). This structure will be used in designing the inertial and frequency-droop coefficients in the next section. The ith element of vector ΔP is ΔPi from (6.26). This vector is zero during steady-state conditions. The frequency dynamics resulting from both AC-side disturbances and DC-side disturbances can be represented by introducing variations in ΔP. For example, load or generation changes in the ith AC grid can be represented by varying ΔPi . In contrast, a DC-side disturbance like converter loss would require changing all the elements of the vector ΔP.

6.10 Ratio-Based Inertial and Primary Frequency Support In this section, a new ratio-based performance requirement for frequency support and design of inertial and primary frequency-droop coefficients to achieve that requirement are presented. The design of droop coefficients is based on the modified N th-order model. As before, the scheme described in this section is also applicable for monopolar MTDC system. Selective power routing as proposed in Sect. 6.7 is applied in this case as well. As shown in Fig. 6.13, upon occurrence of an AC-side disturbance, a distress signal is sent from the affected area. As before, it is assumed that the affected AC area sends the distress signal when the magnitude of the rate of change of frequency (RoCoF) in that area crosses 80 mH z/s. Based on the location of disturbance, participating and non-participating areas react accordingly.

198

6 Integration of Wind Farms Using MTDC Grids: Frequency Support Perspective

For non-participating areas, a seamless turnoff of voltage droop is achieved by holding the ΔPvgi as shown in Fig. 6.13 to the pre-disturbance value. This ensures that the non-participating areas continue to share the same loss in the MTDC network, which they were sharing in the pre-disturbance condition. Therefore, the frequencies of the non-participating areas remain unaffected. For the participating areas, the inertial and frequency-droop controllers, see Fig. 6.13, are activated. The coefficients of these controllers are designed to meet a new ratio-based requirement, which can be prescribed by the system operators. Next, the modified N th-order model presented in the previous section is reduced to a specific form to aid the design process. ⎡

HG1 + (1 − k¯v1 )h1 −k¯v1 h2 ⎢ −k¯v2 h1 HG2 + (1 − k¯v2 )h2 ⎢ HN = ⎢ .. .. ⎣ . . −k¯vN h2 −k¯vN h1 ⎡

··· ··· .. . · · · HGN

kgov1 + (1 − k¯v1 )kf 1 −k¯v1 kf 2 ⎢ ¯ −kv2 kf 1 kgov2 + (1 − k¯v2 )kf 2 ⎢ KN = ⎢ .. .. ⎣ . . ¯ ¯ −kvN kf 2 −kvN kf 1

⎤ −k¯v1 hN ⎥ −k¯v2 hN ⎥ ⎥ .. ⎦ . + (1 − k¯vN )hN

··· ··· .. . · · · kgovN

⎤ −k¯v1 kf N ⎥ −k¯v2 kf N ⎥ ⎥ .. ⎦ . ¯ + (1 − kvN )kf N (6.29)

6.10.1 Monopolar Representation of Modified Nth-Order Model In general, to ensure zero current flow through the metallic return path under normal operation, the droop coefficients and power references of the positive and negative poles of a converter station are made equal. This means, hpi = hni = hi /2; kfpi = kf ni = kf i /2; kvpi = kvni = kvi ; and Prefpi = Pref ni = Pref i /2 are to be satisfied. As before, since AC-side disturbances do not lead to unbalance in the DCside, we can treat the bipolar system using an equivalent monopolar representation. Equation (6.27) can now be rewritten as, 2HN (f◦˙f) = KN Δf+ΔP. Here, the matrices HN and KN are given by Eq. (6.29).

6.10.2 Design of Inertial and Frequency-Droop Coefficients The inertial-droop coefficients along with frequency-droop coefficients determine the frequency dynamics of the participating areas. The aim here is to design these coefficients to achieve a new ratio-based requirement that can be prescribed by the

6.10 Ratio-Based Inertial and Primary Frequency Support

199

system operators. According to this requirement, the frequency deviations of the participating areas must have a prescribed ratio at all time after the disturbance. Let Nr be the number of participating areas. Let the prescribed ratio be r1 : r2 : · · · : rNr . Without loss of generality, the indexing of areas is done such that the area with AC disturbance is indexed as Area#1 (ΔP1 = 0) and that the nonparticipating areas are concatenated to the end. This way of indexing will simplify the description of the design process. We introduce a variable f ∗ as the “base frequency” and Δf ∗ as the deviation in base frequency from its nominal value f0 . The expected post-disturbance frequency deviations at any time after disturbance are given by, ⎤T

⎡

⎥ ⎢ Δf = ⎣ r1 Δf ∗ r2 Δf ∗ · · · rNr Δf ∗ 0 · · · 0 ⎦

 

(6.30)

1×(N −Nr )

1×Nr

Substituting the above in monopolar representation of the N th-order model along with the assumption that fi f˙i ≈ ri f0 f˙∗ leads to, ⎡

⎤ r1 f0 f˙∗ .. ⎢ ⎥ HNr 0 ⎢ ⎥ . 2 ⎢ ⎥ 0 Nhp ⎣ rN f0 f˙∗ ⎦ r

 0 HN

 '

(

˙

⎡f◦f ⎤ ⎤ ⎡ r1 Δf ∗ ΔP1 ' ( .. ⎢ ⎥ ⎢ 0 ⎥ KNr 0 ⎢ ⎥ ⎥ ⎢ . = ⎢ ⎥+⎢ . ⎥ 0 Nkp ⎣ rN Δf ∗ ⎦ ⎣ .. ⎦ r

 0 0 KN

 

(6.31)

ΔP

Δf

Since the voltage-droop, the inertial-droop, and the frequency-droop controllers of non-participating areas are disabled, the off-diagonal matrices of HN and KN in Eq. (6.32) are 0. Matrices HNr and KNr (size Nr × Nr each) can be obtained by replacing “N ” by “Nr ” in the HN and KN matrices presented in Eq. (6.29). The matrices Nhp and Nkp are diagonal in nature. However, as can be observed from Eq. (6.31) these matrices do not play any role in frequency dynamics. Therefore, re-writing Eq. (6.31) gives us, ⎡

⎤ ⎡ r1 ⎢ ⎥ ⎢ 2HNr ⎣ ... ⎦ f0 f˙∗ = KNr ⎣ r Nr

⎤ ⎡ ⎤ r1 1 .. ⎥ Δf ∗ + ⎢ .. ⎥ ΔP ⎣.⎦ 1 . ⎦ r Nr

0

(6.32)

200

6 Integration of Wind Farms Using MTDC Grids: Frequency Support Perspective

From the structure of HNr and KNr , and using the fact that

Nr )

k¯vk = 1, it is easy

k

to see that upon summing all the row equations in (6.32), we get,  2

Nr )

 rk HGk

f0 f˙∗ =

k

 Nr )

 rk kgovk Δf ∗ + ΔP1

(6.33)

k

This equation determines the base frequency deviation dynamics to which the frequencies of all the participating areas are proportional to. Also, notice that the base frequency is independent of the inertial and frequency-droop coefficients. Note that Eq. (6.30) holds true if and only if Eq. (6.32) holds true. Therefore, our goal is to obtain the set of Nr inertial-droop coefficients ({h1 , · · · , hNr }) and Nr frequency-droop coefficients ({kf 1 , · · · , kf Nr }) of the participating areas such that Eq. (6.32) holds true for the entire post-disturbance period. We begin this process by applying a boundary condition on (6.32) and (6.33), as described next. Boundary Condition We consider the instant t = t0 (say) at which the disturbance occurs. Since f ∗ is a state variable, Δf ∗ (t0+ ) = 0. Therefore, Eqs. (6.32) and (6.33) reduce to, ⎡ ⎤ ⎡ ⎤ r1 1 ⎢ ⎥ ⎢ ⎥ 2HNr ⎣ ... ⎦ f0 f˙∗ (t0+ ) = ⎣ ... ⎦ ΔP1 (t0+ ) 0   r Nr N )r rk HGk f0 f˙∗ (t0+ ) = ΔP1 (t0+ ) 2

(6.34)

k

Eliminating ΔP1 (t0+ ) and 2f0 f˙∗ (t0+ ) from the above equations we get the following constraint: ⎡ ⎤ ⎡ ⎤ 1 r1 Nr ⎢ .. ⎥ ⎢ .. ⎥ ) (6.35) HNr ⎣ . ⎦ = ⎣ . ⎦ rk HGk r Nr

0

k

Constraint (6.35) by itself ensures that the prescribed ratio is maintained among the initial slopes of the frequencies. Expansion to Entire Post-Disturbance Time-Horizon Now, we impose constraint (6.35) on the continuous time Eq. (6.32) to obtain further constraints on frequency-droop coefficients. This gives us, ⎡ ⎤ ⎡ 1 Nr ) ⎢ ⎥ ⎢ 2( rk HGk )f0 f˙∗ ⎣ ... ⎦ = KNr ⎣ k

0

⎤ ⎡ ⎤ r1 1 .. ⎥ Δf ∗ + ⎢ .. ⎥ ΔP ⎣.⎦ 1 . ⎦ r Nr

0

(6.36)

6.10 Ratio-Based Inertial and Primary Frequency Support

201

From Eqs. (6.33) and (6.36), we can obtain a constraint on frequency-droop coefficients as follows: ⎡ ⎤ ⎡ ⎤ 1 r1 Nr ⎢ .. ⎥ ⎢ .. ⎥ ) KNr ⎣ . ⎦ = ⎣ . ⎦ rk kgovk (6.37) k

0

r Nr

Therefore, if the constraint (6.35) along with constraint (6.37) are satisfied, then the prescribed ratio-based criterion will be met for the entire duration of the postdisturbance period. Remark Instead of starting with the initial boundary condition at t = t0 , obtaining constraint (6.35), and deriving constraint (6.37) from that, we can start from the final boundary condition (t → ∞) to first obtain constraint (6.37) from which constraint (6.35) can be derived. In that process, we will discover that constraint (6.37) independently ensures that the post-disturbance steady-state frequency deviations are in the prescribed ratio.  Now, we shall try to solve for the droop coefficients that obey constraints (6.35) and (6.37). However, from the row operation of replacing the 1st row by sum of all rows, and upon rearranging terms in (6.35) and (6.37) we get, ⎡ ⎤ 0 ⎡ ⎤ ⎢ ⎥ N h1 ⎢ r H )r k ⎥ ⎢ ⎢ h2 ⎥ ⎢ 2 G2 k vk ⎥ ⎥ ⎢ ⎥ ⎥ (6.38) RK ⎢ . ⎥ = ⎢ . ⎢ ⎥ .. ⎣ .. ⎦ ⎢ ⎥ ⎢ ⎥ Nr ) ⎣ ⎦ hN r rNr HGN r kvk k

⎡ ⎡

⎤

0

⎤

⎢ ⎥ Nr ) ⎢ r k ⎥ k ⎢ ⎥ 2 gov2 vk ⎢ ⎥ ⎢ ⎥ k ⎢ ⎥ ⎢ ⎥ RK ⎢ = ⎥ ⎢ .. ⎥ ⎣ ⎦ ⎢ ⎥ . ⎢ ⎥ Nr ) ⎣ ⎦ kf N r rNr kgovN r kvk kf 1 kf 2 .. .

(6.39)

k

where matrix RK is given by, ⎡

0

0 N )r

⎢ ⎢ r1 kv2 −r2 kvk ⎢ ⎢ k=2 RK = ⎢ .. ⎢ .. ⎢ . . ⎢ ⎣ r1 kvN r r2 kvN r

···

0

···

rNr kv2

..

.

· · · −rNr

.. . Nr ) k=N

⎤

kvk

⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

(6.40)

202

6 Integration of Wind Farms Using MTDC Grids: Frequency Support Perspective

Fig. 6.14 Proposed offline design scheme for obtaining the coefficients that ensure the ratio-based criterion and stability of the full-order model

for disturbance in Area#i Based on Market Mechanism or Grid Code System Operators Provide Ratios

Repeat till Stable

Ratios and Participation of Areas

Solve for Droop Coefficients Satisfying Constraints (17) and (19)

choose a set of droop coefficients Small Signal Stability Analysis on Full-order Model

Unstable

Stable End

Since the matrix RK has rank Nr − 1, Eqs. (6.38) and (6.39) have multiple solutions. Therefore, there are multiple sets of Nr inertial-droop coefficients and Nr frequency-droop coefficients that satisfy constraints (6.35) and (6.37), respectively. Before choosing a particular solution set, small-signal stability analysis needs to be performed to ensure the stability of the full-order system. Figure 6.14 summarizes the offline design process of the droop coefficients that are determined for a disturbance in the ith-Area based on the prescribed ratios and participation areas chosen by system operators.

6.10.3 Simulation Results of Modified N th-Order and Full-Order Models For simulation studies, additionally, Area#4 is added to the system presented in Fig. 6.1 [9]. The generator G7 model parameters are the same as G6 of Area#3. Furthermore, a constant impedance load of 900 MW is added at bus#19 (Fig. 6.15). For theoretical validation under ideal conditions, first the scheme is simulated in the N th-order model without considering any transmission delay for the distress signal. A 20% reduction in generation of G7 (Fig. 6.15) is considered as a AC-side disturbance at t = 5s in Area#4. Area#3 is chosen to be a non-participating area and droop coefficients are designed for a prescribed ratio of 1 : 1.5 : 2 (r1 : r2 : r4 ). Figure 6.16 illustrates the stability analysis for two sets of droop coefficients

6.10 Ratio-Based Inertial and Primary Frequency Support

PG4

AC Area #1

G4

700 MW

203

15

10

2

9

3 7

8

11 17

3

G3

700 MW

2

4

12

PG2

G2

Pinv16 16 300 MW

Pinv17 900 MW

Slack

1

PG1 700 MW

PL10 2500 MW QL10 -250 MVAr

G1

P L9 1500 MW Q L9 -100 MVAr 1

Slack

4

Slack

G5

G6 14

6

AC Area #3

13 5

Prect14

Prect13

300 MW

1100 MW

AC Area #2

G7 Slack

18

20 19

PL19 AC Area #4

Pinv18

5

200 MW

900 MW

Fig. 6.15 Schematic of the bipolar MTDC grid with metallic return (single-line diagram) connecting 4 asynchronous AC areas

satisfying Eqs. (6.35) and (6.37), one set (kf 1 = 404.24; kf 2 = 152.4; kf 4 = 300) leading to a stable system, while the other set (kf 1 = −395.7; kf 2 = −114.2; kf 4 = 100) making the system unstable. Figure 6.17a shows the frequency dynamics of all areas. Note that frequency of Area#3 did not get affected since it is a non-participating area. Figure 6.17b shows that the frequency deviations are indeed obeying the designed ratio for the entire post-disturbance period. Now, we simulate the same scenario in full-order model of 4-area-asynchronous system including a transmission delay of 100 ms for the distress signal. Figure 6.18a shows the frequency dynamics wherein Area#3 is non-participating. The Area#1 frequency plot contains closely overlapping traces from 4 generators, which are indistinguishable. Since the disturbance is not from Area#1, the inter-area mode was not excited. The ratio among the participating areas is approximately maintained

204

6 Integration of Wind Farms Using MTDC Grids: Frequency Support Perspective

20 15 10 5 0 -5 -10 -15 -20 -0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Fig. 6.16 Small-signal stability analysis on full-order model illustrating two sets of droop coefficients satisfying Eqs. (6.35) and (6.37), one set leading to a stable system and another set to an unstable system. Source: Vennelaganti and Chaudhuri [36]. Reproduced with permission of IEEE

60 59.8 59.6 59.4 59.2 2

1.5 0

5

10

15

20

25

30

35

40

45

50

Fig. 6.17 Ideal response from N th-order model with 20% reduction in generation of G7: (a) frequency dynamics and (b) ratios among frequency deviations. Source: Vennelaganti and Chaudhuri [36]. Reproduced with permission of IEEE

to the prescribed values as shown in Fig. 6.18b. Note that fGi is the frequency corresponding to generator Gi . Apart from the transmission delay of distress signal, a major reason for full-order model to deviate from the N th-order model’s response is the slow reference tracking by the outer loop of converter control. The outer

frequency, (Hz)

6.11 DC-Side Disturbance: Converter Outage

Area#1

60

Area#2

ratio

Area#3

Area#4

(a)

59.8 59.6 59.4 59.2 2.5

VDCp , (KV)

205

(ΔfG5 /ΔfG1 )

(ΔfG7 /ΔfG1 )

2

(b)

1.5 352

station:

#1

#2

#3

#4

350

#5

(c)

348 346 0

5

10

15

20

25

30

35

40

45

50

time, (s) Fig. 6.18 Non-ideal response from full-order model with 20% reduction in generation of G7: (a) frequency dynamics, (b) ratios among frequency deviations of G7, G5, and G1 and (c) positivepole DC voltage. Source: Vennelaganti and Chaudhuri [36]. Reproduced with permission of IEEE

droop loop with a PI controller, as shown in Fig. 6.13, cannot be made faster due to stability issues [9]. On the other hand, the effect of the control strategy on DC voltage dynamics is fairly insignificant as shown in Fig. 6.18c. Figure 6.19 shows the variations in converter power as obtained from the full-order model. Since, Area#3 is non-participating, its MTDC converter power (station#1) is held constant, see Fig. 6.19a. At t = 5s there is an increase in power of station#5 to compensate for the step reduction in generation of G7. In response to the increased power in station#5, all other stations except station#1 reduced their powers. Due to inertial and frequency-droop controller designs, these power changes resulted in frequency deviations as shown in Fig. 6.18a, which approximately follows the ratio-based criterion. Similarly, an expected response is obtained for a design ratio of 1:1:1:1 following a 30% reduction in generation of G6 simulated in full-order model as shown in Fig. 6.20.

6.11 DC-Side Disturbance: Converter Outage In this section converter outage, which is a DC-side disturbance, is studied specific to the case of bipolar MTDC with metallic return. However, a similar solution can also be applied to monopolar MTDC. First, the converter loss problem along with

206

6 Integration of Wind Farms Using MTDC Grids: Frequency Support Perspective -150 -152 -154 450 440 430 150 140 130

-560 -580 150

100 0

5

10

15

20

25

30

35

40

45

50

frequency, (Hz)

Fig. 6.19 Power in each of the converter stations as obtained from full-order model following a 20% reduction in generation of G7. Source: Vennelaganti and Chaudhuri [36]. Reproduced with permission of IEEE 60

Area#1

Area#2

Area#3

Area#4

59.9

(a)

59.8 59.7

VDCp , (KV)

352

(b)

350 348

station:

346 0

5

10

15

#1 20

#2 25

#3 30

35

#4 40

#5 45

50

time, (s) Fig. 6.20 Response following 30% reduction in generation of G6 simulated in full-order model: (a) frequency dynamics and (b) positive-pole DC voltage

its constraints is described. Next, the solution, i.e., to modify the reference power set points obeying the constrains is described. Finally, simulation results showing the effectiveness of this method are shown.

6.11 DC-Side Disturbance: Converter Outage

207

6.11.1 Converter Outage Problem and Its Constraints Following a converter outage in a positive or negative-pole circuit, the lost converter power would be distributed among the remaining converters according to their voltage-droop coefficients, thereby resulting in change of power flow among the AC areas. The net power change of the AC area that lost the converter is almost equal and opposite in direction to the sum of net power change of the other AC areas. Therefore, frequency regulation following converter outage is a problem of redistribution of power to negate the net change of power in all AC areas. However, the redistribution of power is constrained by the following factors: (i) converter rating, (ii) transmission capability of DC lines, and (iii) in some configurations, transmission capability of AC lines. It is straightforward to see that constraints (i) and (ii) occur while changing the power reference set points. Constraint (iii), on the other hand, occurs in situations where there are more than one converter station connected to same AC area. In these scenarios, the power set points modification can be constrained by the capacity of AC tie-lines. For converter outage studies, let us consider the system with three areas, which is show in Fig. 6.1. For explanation purpose consider loss of negative pole of converter station#3. When that converter is lost due to outage, the power it used to carry is shared based on voltage droop among other negative-pole converters. From Fig. 6.22a it is clear that loss of roughly 150 MW from station #3 created an increase of 50 MW in the remaining negative-pole stations. This is the first limitation, for this distribution to occur the converters and DC lines must have enough ratings. Frequency-droop control does not account for these constraints and therefore, is not the best way to provide frequency support following a converter outage. Reference [8] presents a way to address the converter rating issue. However, it does not ensure power redistribution to attain minimal frequency deviation. Therefore, a solution that takes these constraints into account and acts to minimize the frequency deviations is presented next.

6.11.2 Proposed Solution to Converter Outage Problem At each converter station, a look-up table holding different predefined power reference changes that are to be made corresponding to different N − 1 converter outage scenarios is incorporated (see, Fig. 6.21). System operators will provide these reference changes based on offline planning studies. The process of obtaining these reference changes for an operating condition is described next. Following a converter outage, a distress signal is sent to all other converters as shown in Fig. 6.21. Therefore, all converters have the knowledge of which converter is out and from the look-up table the corresponding power reference change is applied. The same strategy can be extended to DC line outages if the information regarding the line outage can be communicated to all converters and corresponding reference change to be made is predetermined and saved in the look-up table. However,

208

6 Integration of Wind Farms Using MTDC Grids: Frequency Support Perspective look up

table

Prefgi

kvgi ( VDCg )2min / 4

kvgi 2 2 (VDCgcom VDCgref )/4

fi

Pf max

Switch

0

pre-disturbance value

Pvgi

Distress Signal for Converter Outage

k fgi

Switch

Pf min Distress Signal for AC-side Disturbances

-

PI

PCgi kvgi ( VDCg ) 2max / 4

k fgi 2hgi

-

* I dgi

p (positive-pole) or n (negative-pole)

-

g

f0

fi

Fig. 6.21 Representation of the power–frequency–voltage-droop control of an aggregation of the converter stations belonging to the same pole connected to the ith AC area. For converter outage, Pref gi is altered from look-up table based on the outage (as obtained from distress signal)

obtaining a set of power references post-line outage, such that these references minimize the frequency deviations, is a significantly more involved process. A constrained optimization problem respecting system stability and other mentioned constraints can be solved offline for predetermining the references changes, details of which are outside the scope of this paper and will be addressed in our future work. In this paper, the following simple three-step process is used for predetermining the power reference changes for a converter outage. Step-I: If there is no constraint violation, the power reference set points are modified such that there is no net power change from each converter station. This means change of power in one pole is compensated by change of power in another pole at the same converter station. Therefore, the unaffected pole at the converter station where the outage took place would have to carry twice the power it was carrying before the outage occurred. Typically, the headroom of this converter is the most critical of all constraints. Step-II: If there is constraint violation in Step-I due to the insufficiency of headroom in the unaffected pole at the converter station where outage took place, first, the available headroom in that converter is utilized. Next, if there are two or more stations connected to the AC area where the outage occurred, both the poles of the unaffected converter stations are used to nullify the net power change in that AC area. Step-III: If there is constraint violation in Step-II due to the insufficiency of headroom in the unaffected converter stations connected to the DC and/or AC area where outage occurred or due the insufficiency of the transmission capacity of the AC system, Step-III is implemented. The power reference set points of the unaffected converter stations connected to the AC area where outage occurred are modified to minimize the net power change in that AC area till there are no constraint violations.

6.11 DC-Side Disturbance: Converter Outage

209

Step-I would result in almost no disturbance in frequency dynamics since there is no net power change at every converter. Similarly, Step-II would also ensure no steady-state frequency deviation. However, it might create other issues due to change in the AC network power flow. Step-III, on the other hand, ensures least possible steady-state frequency deviation in the post-contingency condition. However, steady-state frequency deviation is inevitable due to net power change in all the AC areas. In addition, like Step-II, Step-III could also cause inter-area oscillations.

6.11.3 Simulation Results For converter outage studies, we consider the system with three areas, which is show in Fig. 6.1. Figure 6.22 shows results when Step-I is performed following the outage of negative pole in converter station#3. Figure 6.22a shows the distribution of power

Neg Power, (MW)

500

0

station#1 station#2 station#3 station#4

(a)

station#1 station#2 station#3 station#4

(b)

Pos Power, (MW)

-500 400 200 0 -200 -400

Frequency, (Hz)

-600

Area#1 Area#2 Area#3

60.05

(c)

60

59.95 0

5

10

15

20

25

time, (s) Fig. 6.22 Simulation results for outage of negative-pole at station#3 (Fig. 6.1): (a) the distribution of negative-pole powers, (b) the redistribution of positive-pole powers using Step-I, and (c) almost no disturbance in frequencies

210

6 Integration of Wind Farms Using MTDC Grids: Frequency Support Perspective

Fig. 6.23 Simulation results for major outage of negative-pole at station#2 (Fig. 6.1): (a) the distribution of negative-pole powers, (b) the redistribution of positive-pole powers using StepIII, (c) positive-pole DC voltages, and (d) frequency dynamics with the presented methodology. Source: Vennelaganti and Chaudhuri [37]. Reproduced with permission of IEEE

among the negative-pole converters following the converter outage according to the voltage-droop control. Figure 6.22b shows the change of power in the positivepole converters to nullify the change of power in the negative-pole converters. As expected from Step-I, we see almost no change in the frequencies of all areas as shown in Fig. 6.22c. A major contingency scenario of the outage of negative pole of station#2 carrying 450 MW is considered. Each of converter stations #2 and #4 is assumed to have a rating of 600 MW and the converter stations #1 and #3 are assumed to have a rating of 275 MW per pole. Constraints in the AC and the DC transmission systems are not considered for this case study. Sufficient headroom is not available to have a redistribution of power like in Step-I and Step-II. As a result, Step-III is implemented in this scenario. Figure 6.23a shows the

6.13 Study System

211

distribution of power among the negative-pole converters following the converter outage according to the voltage-droop control. Note that the power reference of the negative pole of station#3 is modified to ensure that it carries rated power. Figure 6.23b shows the change of power in the positive-pole converters to nullify the net change of power in those AC areas to the extent that is possible. Since it is not completely nullified due to exhaustion of headrooms, Fig. 6.23d shows non-zero frequency deviation in post-contingency steady-state condition. In contrast, the same outage resulted in an unstable system with the frequency-droop coefficients proposed in [9]. Inter-area oscillations from Area#1 gets transmitted into the DC voltages shown in Fig. 6.23c. This stems from a slow power tracking loop with a low-gain PI controller in Fig. 6.21, which is required to ensure stability [9].

6.12 Topic II: Frequency Support in Asynchronous AC-MTDC System with Offshore Wind Farm The provision of primary and secondary frequency support through MTDC grid especially in the presence of OWFs is one of the challenging aspects in its operation. In future grids, as the generation shifts from conventional generation to renewables, the renewables would inevitably have to provide some frequency support for a stable operation of the grid. An approach that attempts to provide frequency support by maintaining the ratio-based requirement presented above was explored in [36]. The scheme based upon the modified N th-order system, which was developed earlier, forms the basis of the approach presented in this chapter. Modifications are made to the controls of OWF in order to emulate the AC-MTDC system with OWF as an N -asynchronous-area MTDC system. This enables us to implement the aforementioned strategy to extract frequency support from OWF. To prove the effectiveness of this, the scheme along with the modified OWF’s control is implemented in the full-order model consisting 3 asynchronous areas and an OWF (Fig. 6.24).

6.13 Study System Figure 6.24 shows the test system chosen for the validation of the presented control strategies, which consists of 4 asynchronous AC areas connected to a 5-terminal bipolar MTDC grid with metallic return network. This is the same test system shown in Fig. 6.15, except that the generator in Area#2 is replaced by an OWF. All the converters except converter station 4 have similar control structure as that of Fig. 6.13.

212

6 Integration of Wind Farms Using MTDC Grids: Frequency Support Perspective

PG4

AC Area #1

G4

700 MW

15

10

2

9

3 7

8

11 17

3

G3

700 MW

2

4

12

PG2

G2

Pinv16 16 300 MW

Pinv17 900 MW

Slack

PL10 2500 MW QL10 -250 MVAr

1

PG1 700 MW 1500 MW

G1

P L9 Q L9 -100 MVAr 1

Slack

4

G5

G6 14

6

AC Area #3

13 5

Prect14

Prect13

300 MW

1100 MW

OWF

G7 Slack

18

20 19

PL19 AC Area #4

Pinv18

5

200 MW

900 MW

Fig. 6.24 Schematic of the bipolar MTDC grid with metallic return (single-line diagram) connecting 3 asynchronous AC areas and OWF

6.14 Inertial and Primary Frequency Support with OWFs Previously, a strategy to share the inertial and primary frequency reserves among N asynchronous AC areas in response to an AC-side disturbance was presented and validated. Modification of the power reference of the OWF enables us to employ same strategies to extract inertial and primary frequency support from OWFs. Let us consider a system where an OWF is connected to an (N − 1)asynchronous-area MTDC grid. Here, the wind farm is represented by an aggregated ∗ ) as functional model, which takes wind velocity (Vw ) and power reference (PW F input and incorporates the turbine–generator rotor dynamics. This model is generic and accommodates both doubly fed induction machine and full-rated converter machine in grid-connected mode. The rotor dynamics can be described as follows: ∗ )/ω 2HW F ω˙ r = (Ptur (Vw , ωr ) − PW r F

(6.41)

6.14 Inertial and Primary Frequency Support with OWFs

213

Here, ωr is rotor speed in the aggregated model of OWF; HW F is the combined machine and turbine inertia constant. The wind turbine characteristics are introduced through the nonlinear function Ptur (Vw , ωr ), which takes wind velocity and rotor speed as input. Due to the fast acting converter controls of wind generator, ∗ we assume that the reference power PW F is equal to output power PW F . In [38], it was shown that such simplifying assumptions in the wind farm model do not compromise the accuracy of frequency dynamics when compared with the response obtained by considering the details of vector controls in the wind farm.

6.14.1 Wind Farm Controller for Emulating the N th-Order Model Typically, the voltage and frequency of the point of common coupling (PCC) to which the OWF is connected are established by the corresponding MTDC converter station [33, 35]. This allows the operation of the OWF in grid-connected mode wherein, power output can be controlled to achieve a specific task, for example, maximum-power-point tracking, DC voltage-droop control, and so on. To exploit the aforementioned degree of freedom, in this paper, we take a similar approach as presented in [35]. The converter connected to OWF establishes the AC voltage and sets the offshore grid frequency (foff ) as a function of the error in common DC bus voltage. This relationship is given by, Δfoff = M[

2 2 VDCpcom −VDCpref 4

+

2 2 VDCncom −VDCnref 4

(6.42)

]

Here, M is a scaling factor, which is set based on allowable offshore AC frequency deviation and typical maximum DC voltage error. The voltage and frequency control in a block diagram of the offshore MTDC converter is shown in Fig. 6.25a. In order to extract and control the frequency support from OWF using the strategy developed in the previous section, the entire AC-MTDC system with OWF should behave like an N -asynchronous-area AC-MTDC system. This means, the power output of the equivalent monopolar MTDC converter connected to OWF should be of the form (6.24). In our case, neglecting the offshore AC grid losses, we have, PCwf = −PW F . Here, PW F is the power output of the wind farm and PCwf is the OWF’s MTDC converter power. Therefore, our objective is to control PW F to obtain a form similar to (6.24). To that end, we propose that the frequency term in the expression of PW F will be obtained by emulating frequency dynamics of the synthetic synchronous generator as shown in Fig. 6.25b. Therefore, the OWF power reference is given by, ∗ = −(P PW ref wf + kf wf Δfem − 2hwf fem f˙em + F

Δfoff M

)

(6.43)

6 Integration of Wind Farms Using MTDC Grids: Frequency Support Perspective

Vac

-

PLL

Identical controller for each pole

-

---

foff n

p

mabc / p / n

PWM

mn mp

2 2 (VDCncom VDCnref )/4

M

1

2 2 (VDCpcom VDCpref )/4

s mmax

-

214

PI

Vac Vac*

mmin

(a) Wind Farm MTDC Converter Controls: Emulation of Synthetic Synchronous Generator Dynamics

1

-

* PWF

Pe 0

f em

s

-

fem

kem

2 H em

f0

Reference Reference Calculation Calculation

1

M

(b) Wind Farm Controls:

PWF

PLL

foff PWF

Fig. 6.25 Controls of: (a) MTDC converter connected to OWF and (b) OWF

wherein Pref wf is set such that its magnitude is less than the maximum power that can be extracted at that wind speed. This means that the OWF is operated under a “de-loaded” condition. Also, fem is obtained by emulating the following dynamics at the OWF: 2Hem fem f˙em = kem Δfem + (Pe0 − PW F )

(6.44)

In pre-disturbance nominal condition, Δfem has to be set to 0. This implies Pe0 should be the pre-disturbance nominal power output of the wind farm, which is Δf equal to the pre-disturbance nominal value of −(Pref wf + Moff ). The parameters Hem and kem are chosen based on the available kinetic energy and headroom in deloaded operation, respectively. The higher the values, lesser is the margin of stability of the OWF’s rotor dynamics. The stability concern with higher values of these parameters is out of the scope of this paper, and will be addressed in the future

6.15 Topic III: Frequency Support in Asynchronous AC-H-MTDC System. . .

215

work. Conservative values of these parameters should be chosen, i.e., Hem should be designed to be less than HW F .. Now that the dynamics of the AC-MTDC system with OWF is similar to the N -asynchronous-area system, the following can be claimed: 1. The parameters, Hem and kem contribute towards the total inertial capacity and total frequency-droop capacity of the interconnected MTDC system, see Eq. (6.33). 2. For an AC-side disturbance, the coefficients hwf and kf wf along with other droop coefficients of the MTDC grid can be designed to achieve a certain ratio among the frequency deviations of onshore AC grids and Δfem . 3. Larger the ratio of Δfem to Δf ∗ , larger is the inertial and frequency-droop support provided by the OWF. Thus, the emulation provides means to quantify and control the inertial and frequency support extracted from the OWF.

6.14.2 Simulation Results of Full-Order Model with OWF The simulation results are presented for a case where the prescribed ratio is such that maximum frequency deviation occurs in the emulated frequency (fem ) of OWF. This means that majority of the support is coming from the OWF. In this case, the AC-side disturbance is a 10% increase in load at bus #19 in Area#4 (Fig. 6.24) at t = 0.5 s. As in the previous section, a delay of 100 ms is assumed for transmission of the distress signal. Area#3 is chosen to be a non-participating area. The prescribed ratio, however, is 1 : 20 : 1 (r1 : r2 : r4 ). This implies Δfem = 20ΔfG7 = 20ΔfG1 . Figure 6.26a shows the frequency dynamics, wherein frequencies of all the onshore AC areas are well contained, while the emulated frequency of the OWF absorbed most of the disturbance. This is translated into OWF supplying most of the change in load, see PW F from Fig. 6.27a. Despite a major change in the DC power flow, the DC voltages are not greatly affected, see Fig. 6.26b. The turbine dynamics, on the other hand, is quite slow. The rotor speed slowly decreases as Ptur slowly catches up with PW F , see Fig. 6.27a, b. The speed reduction increases Ptur because, for a constant power reference, de-loaded operating point is on the right side of the maximum power point. Note that in this case we assumed that there is enough headroom in the OWF to absorb the power of AC-side disturbance.

6.15 Topic III: Frequency Support in Asynchronous AC-H-MTDC System with Offshore and Onshore Wind Farm The motivation behind interconnecting onshore wind farm through LCC-HVDC and OWFs using VSC-HVDC was presented in Sect. 1.4 of Chap. 1, it is imperative that the onshore wind farms and the OWFs should be connected through an MTDC

216

6 Integration of Wind Farms Using MTDC Grids: Frequency Support Perspective

fem

VDCp , (KV)

frequency, (Hz)

Area#1

Area#3

Area#4

60

(a)

60 59.5 59.95

59

1 58.5 352

#1

station:

2

3

#2

4

#3

5

#4

#5

350

(b)

348 346 344 0

5

10

15

20

25

time, (s)

power, (pu)

Fig. 6.26 Response following a 10% increase in load at bus #19 (Fig. 6.24) simulated in full-order model with OWF: (a) frequency response along with emulated frequency and (b) positive-pole DC voltage. Source: Vennelaganti and Chaudhuri [36]. Reproduced with permission of IEEE 12

Ptur (Vw , ωr )

PW F

(a)

11.5

speed, (elec-rad/s)

11 500

rotor speed (ωr ) (b)

480 0

10

20

30

40 time, (s)

50

60

70

80

Fig. 6.27 OWF turbine response following a 10% increase in load at bus #19 simulated in fullorder model with OWF (Fig. 6.24). Source: Vennelaganti and Chaudhuri [36]. Reproduced with permission of IEEE

grid that consists of both LCC and VSC-HVDC stations. Modeling of VSC-MTDC is well-understood and was briefly introduced in Chap. 2. This model needs to be modified in order to integrate LCC-HVDC. MTDC grids with both LCC and VSC converters are known as hybrid-MTDC or H-MTDC. A few papers have been published on the hybrid-MTDC concept. All of these papers [13, 24, 25, 42] consider integration of offshore WFs using VSCHVDC, while the onshore converters are LCC based that are connected to strong

6.16 Modeling Bipolar H-MTDC Grid

217

onshore grid system. In [18] a 4-terminal hybrid MTDC system with two wind farms was proposed where the VSCs serve as the rectifier at the wind farm-side and the LCC as inverter at the grid-side. The VSCs are controlled to establish the AC voltage for the wind farm whereas the LCCs are in the DC voltage-current droop control. The authors also studied a comprehensive control strategy for wind farms and LCC to provide short-term frequency support to the AC power grid. The combined advantages of conventional CSC-HVDC system and novel VSCHVDC system for the large-scale interconnection of distributed wind farms were studied in [25]. This study was limited to analysis under normal operating condition of the system and did not consider any fault scenarios or outage of converters. The practicality of hybrid MTDC transmission system for the grid interconnection issue of wind farms was analyzed in [10]. The utilization of hybrid MTDC to strengthen the transient stability of the AC grid was presented in [21]. The proposed hybrid MTDC architecture utilizes LCC and VSC-HVDC technologies to transfer geothermal power over a long distance and interconnecting intermittent wind generation to a relatively weak AC grid, respectively. The small-signal stability analysis of a hybrid MTDC system was presented in [22]. It was shown in [22] that the HVDC stations could negatively impact the small-signal stability of the hybrid MTDC system with an AC grid. As a solution, proper tuning of power oscillation damping controller with appropriate selection of input and output signals was presented in [24]. In [42], a hybrid MTDC simulation model consisting of a CSC inverter, a CSC rectifier, and a VSC inverter was developed. The paper also demonstrated the system start-up, system normal operations, and system faults in the DC links as well as the AC systems using simulation studies. A synchronverter-based control technique for integrating distributed generation using hybrid MTDC was proposed in [13]. The synchronverter proposed in this work improves the traditional synchronverter performance to achieve secondary frequency control, and is able to limit its current under fault conditions. This paper also proposes a novel steady-state control strategy involving active voltage feedback control for the hybrid MTDC system. Next, modeling of H-MTDC grid is briefly presented.

6.16 Modeling Bipolar H-MTDC Grid The configuration of a bipolar H-MTDC grid with the provision of metallic return is shown in Fig. 6.28 for the ith and the j th converter stations where one is an LCC station and the other is a VSC station. The DC transmission system is modeled using a cascaded π -section model, where the number of π -sections can be chosen as a compromise between accuracy and computational complexity. This model is generic enough to include: (1) different grounding options, (2) fault in the DC network, and (3) asymmetry in the DC grid following the outage of a converter station or a line. It is developed building upon the models described in Sect. 2.6 of Chap. 2.

Fig. 6.28 The ith (LCC) and the j th (VSC) converter stations in the H-MTDC grid connected in bipole configuration with metallic return network

218 6 Integration of Wind Farms Using MTDC Grids: Frequency Support Perspective

6.18 Frequency Support in H-MTDC Grids

219

Figure 6.29 shows the block diagram of the model in a positive sequence, fundamental frequency phasor framework. Unlike the VSC terminal, the LCC converter station is modeled as a controllable voltage source in the DC-side g with magnitude Vd where superscript g stands for positive/negative poles. Let us g consider an LCC rectifier terminal. The value of Vd (Fig. 6.28) is given by: g Vd g

√ 3 2 3 g = B × T × tapg × Vg × cos α g − Xc × B × Idc π π

(6.45)

√

where Vd0 = 3 π 2 B × T × tap g × Vg , B is the number of bridges, T is the transformer turns ratio, tapg is the tap ratio, Vg is the AC-side grid voltage, and Xc is the commutating reactance. g The current injection vector from the LCC terminal I¯g is given by:  g I¯g

= conj

P g + j Qg V¯g

 (6.46)

 g   V g g where P g = Vd × Idc , Qg = P g tan cos−1 V dg d0

6.17 Control Strategies in H-MTDC Grids Control strategies of converter stations in VSC-MTDC grids are well-established. On the contrary, control strategy of H-MTDC stations is still being researched actively. One possible approach is described here. Table 6.3 shows different converter stations and their possible control functions. The LCC converter stations connected to onshore wind farms control frequency as shown in Fig. 6.31. LCC inverter stations will be working in the autonomous power sharing mode to regulate DC current Idc as shown in Fig. 6.30. Please note that this is in contrast with the extinction angle control for LCC inverter station applied in Chap. 4. VSC stations connected to OWFs will operate in AC voltage frequency (Vac − f ) control mode with DC voltage droop as shown in Fig. 6.25a. Other VSC stations will operate in the Vdc − P − f droop mode, as shown in Fig. 6.21.

6.18 Frequency Support in H-MTDC Grids The frequency support principles as described before can be applied in this case. The OWFs can be controlled as shown in Fig. 6.25b. The onshore wind farms can also be controlled in the same manner, see Fig. 6.31. Ratio-based inertial and primary frequency support can be applied as described before.

Fig. 6.29 Block diagram of the model in a positive sequence, fundamental frequency phasor framework. The reference frames marked as Re − I m is the network reference frame rotating at synchronous speed. Reference frames marked as Xi − Yi rotate with a speed proportional to the local frequency. Connection between WF model and VSC station is not shown for clarity

220 6 Integration of Wind Farms Using MTDC Grids: Frequency Support Perspective

6.18 Frequency Support in H-MTDC Grids

221

Table 6.3 Converter stations and possible control strategy Converter station LCC connected to WF

VSC connected to WF

Control strategy Vdc − f droop or remote freq droop P − Vdc − f droop sharing in Idc control mode Vac /Vdc − f droop

VSC rectifier (other) VSC inverter

P − Vdc − f droop P − Vdc − f droop

LCC inverter

Remarks Acts as “slack” bus, transmitting WF power – Acts as “slack” bus, transmitting WF power – –

look up

table

Prefgi

kvgi ( VDCg ) 2min / 4

kvgi 2 2 (VDCgcom VDCgref )/4

fi

Pf max

Switch

0

pre-disturbance value

Pvgi

Distress Signal for Converter Outage

k fgi

Switch

Pf min Distress Distress Signal Signal for for AC-side Disturbances

-

PI

PCgi kvgi ( VDCg ) 2max / 4

k fgi 2hgi

-

p (positive-pole) or n (negative-pole)

-

g

f0

fi

Fig. 6.30 Representation of the power–frequency–voltage-droop control of an aggregation of the LCC inverter stations belonging to the same pole connected to the ith AC area. For converter outage, Pref gi is altered from look-up table based on the outage (as obtained from distress signal)

An alternative to this approach is to explicitly communicate the frequency of the particular AC area that needs support. This approach is described next. 1. LCC-HVDC terminal connected to onshore wind farm controls frequency as shown in Fig. 6.31. The frequency reference is modified by measuring frequency deviation from a remote AC system, which requires frequency support from the wind farm. This is shown in a dotted box in Fig. 6.31. A fraction of that frequency deviation can be compensated by the wind farm, which is determined by Kf rq . This emulates the frequency pattern of the grid of interest [36]. This way, the burden of frequency support of a particular AC system can be allocated to a certain wind farm in a certain proportion. 2. The rest of the VSC and LCC-HVDC stations are operated as mentioned before.

r

Inner current Control loops

RSC

Inner current Control loops

GSC

DC voltage and reactive power control

PWM

Idc

DC Link

MPPT & Stator voltage control

DFIG

Ps Qs= Qg Pg,Q g

Pgrid

Rgrid + j Xgrid

Very low inertia (weak) AC grid

G1

Hgrid

PLL2

PSC

f*

fi

PLL1

-

HSC

M1

Synchronous Condenser

P*WF calculation

Vs

PGSC QGSC = 0 Kfrq

M

Hf(s)

Phvdc

i

Vndc

Vnd

from j th converter station

Communicaon channel

fj

-

f*

2 2 VDCncom VDCnref /4

2 2 VDCpcom VDCpref /4

i th converter station

n L dci

Vpdc

Vpd

p L dci

Fig. 6.31 DFIG-based wind farm with overall control blocks. The wind farm is interconnected with LCC-HVDC, which controls system frequency. Supplementary control input Δf can be used for frequency support to the other AC grids connected to the H-MTDC grid. Inertia of very weak AC grid (and synchronous condenser, if needed) will impact the frequency dynamics

Stator flux and Flux angle calculations

θr

encoder

Wind turbine

Pt

Pitch Controller

222 6 Integration of Wind Farms Using MTDC Grids: Frequency Support Perspective

6.19 Simulation Results

Generation/ load change Converter loss/ DC line outage

223 Fiber optic channels in cables and power -line comms for OH lines can be used Kfrq determines the fraction of frequency support burden to be supplied by WFs See Fig. 10 for details

Under/Over-frequency event in AC system

f signal communicated to HVDC converter stations

HVDC Converter changes local frequency by Kfrq f

DFIG’s power reference is changed using droop control

Reduced frequency deviation in AC system

P-Vdc-f droop at converter stations increase/decrease P for frequency support

Turbine mechanical power input is changed to match electrical output

Turbine pitch controller changes pitch angle to maintain same rotor speed

Fig. 6.32 Flowchart demonstrating the sequence of events and the frequency support scheme

3. DFIGs operate in traditional control mode as shown in Fig. 6.31. The power ∗ shown in Fig. 6.31 can be derived as mentioned before. The reference signal PW F pitch controller operates with a pitch angle that leads to a suboptimal speed of operation so that more power can be extracted at the same wind speed condition to extract frequency support. The sequence of events and control actions that will deliver frequency support is shown in Fig. 6.32. Following an under/over-frequency even in a remote AC grid, the frequency deviation is measured and communicated to the wind farm location. The HVDC converter station changes the frequency of the local grid to mimic the condition in the remote AC grid. The wind farms operating under a de-loaded condition changes the power reference command using a frequencydroop mechanism to extract higher/lower power output. The pitch control works to change the pitch angle and increase/decrease the wind power captured by the blades. Finally, the other asynchronous AC areas and OWFs will provide inertial and primary frequency support through the mechanisms outlined before.

6.19 Simulation Results The alternative approach mentioned above is used in a hybrid MTDC system with an onshore wind farm connected to a weak AC system is shown in Fig. 6.33. This consists of a 4-terminal bipolar H-MTDC grid with metallic return network where converter station #1 is an LCC station and the rest are VSC stations. Station #1 interfaces an onshore DFIG-based wind farm connected to a weak AC grid. Converter stations #2 and #3 are connected to a 4-machine 2-area AC system [16]. In this model the DFIG-based onshore wind farm is represented in detail as mentioned in Chap. 3. Station #2 is chosen as the converter station from which the common DC voltage is communicated. A linearized model was derived from this. Figure 6.34a shows the variation of a critical eigenvalue with respect to the short circuit ratio (SCR) of the

224

6 Integration of Wind Farms Using MTDC Grids: Frequency Support Perspective 1

G1

PG2 700 MW

PG1 700 MW

7

G2

slack

8

2

G5 9

5

16

13

PL9 1500 MW Q L9 -100 MVAr 3

Pinv16 300 MW

4

Prec13 900 MW

2

Pinv17 900 MW

1

LCC

15

Rgrid + j Xgrid PL10 2500 MW QL10 -250 MVAr

G6

17

Very low inera (weak) AC grid

10 4

11

Remote onshore Wind Farm

G4 PG4 700 MW

12

Hgrid

3

slack

G3 Fig. 6.33 A 4-terminal bipolar H-MTDC grid with metallic return network. Station #1 interfaces an onshore DFIG-based wind farm connected to a weak AC grid

weak AC grid. To that end, the impedance Rgrid + j Xgrid shown in Fig. 6.33 is changed. When the SCR is as high as 140, the mode is real. It becomes a complex mode and moves towards the right-half-plane as the SCR reduces to as low as 1.4. When the effective inertia constant Hdc , defined in Eq. (1.2), is reduced from 1.0 to as low as 0.02, the critical eigenvalue moves towards right and then changes its course at extremely low values of Hdc .

6.19 Simulation Results

225

0.2 SCR = 1.4

0.6

H dc = 1.0

0.15 0.4 0.1 0.2

jω

jω

0.05 0

H dc = 0.02 0

SCR = 140 -0.05

-0.2

-0.1 -0.4 -0.15 (a) -0.2 -0.2

(b)

-0.6 -0.18

-0.16

σ

-0.14

-0.12

-0.4

-0.3

-0.2

-0.1

σ

Fig. 6.34 (a) Variation of a critical eigenvalue with respect to the SCR of the weak AC system. (b) Variation of a critical eigenvalue with respect to the effective inertia constant of the weak AC system

For the wind farm controls, the torque reference is modified using the relation ΔTref = − R1 Kf rq Δf . Movement of a critical eigenvalue with the change in droop constant R is shown in Fig. 6.35a. A reduction of droop coefficient will result in higher frequency support from the wind farm. However, this might lead to instability. Similarly, as observed from Fig. 6.35b, a higher value of Kf rq will change the frequency reference of the LCC station by a larger amount, thereby increasing the frequency support. Unfortunately, this might lead to instability in the system. Such a conflicting requirement demands appropriate design of these parameters. In Fig. 6.36, an under-frequency event is created by increasing the loads at buses 9 and 10 (Fig. 6.33). Frequency support from the wind farm is shown to reduce the frequency deviation in the 4-machine system. R = 0.1 and Kf rq = 0.15 have been used. Pitch angle θ is reduced to increase the power output from the wind farm. In Fig. 6.37, an over-frequency event is created by decreasing the loads at buses 9 and 10 (Fig. 6.33). Frequency support from the wind farm is shown to reduce the frequency deviation in the 4-machine system. R = 0.1 and Kf rq = 0.15 have been used. Pitch angle β is increased to reduce the power output from the wind farm.

jω

0.5

R = 0.001

R = 0.5

0 (a) -0.5 -0.1

-0.09

-0.08

-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

-0.02

-0.01

σ

jω

0.5

K frq = 1.0

K frq = 0.01

0 (b) -0.5 -0.1

-0.09

-0.08

-0.07

-0.06

-0.05

-0.04

-0.03

σ Fig. 6.35 Movement of eigenvalues with (a) reduction in the droop coefficient R and (b) increase in the parameter Kf rq

G1 − G4

G5 60

no droop with droop

59.98

freq, Hz

freq, Hz

60

59.96

no droop with droop

59.95

59.9

59.94

0

10

20

30

40

0

50

10

G6 10

no droop with droop

59.998

30

40

50

WF

θ, deg

freq, Hz

60

20

59.996

no droop with droop

9.9 9.8

59.994 9.7 59.992

0

10

20

30

time, s

40

50

0

10

20

30

time, s

Fig. 6.36 Frequency support from the wind farm following an under-frequency event

40

50

References

227

G1 − G4

G5 60.15

freq, Hz

freq, Hz

60.06 60.04 60.02

no droop with droop

60.1 60.05

no droop with droop

60

60 0

10

20

30

40

50

0

10

G6

20

30

40

50

WF

60.008

θ, deg

freq, Hz

10.3 60.006 60.004 60.002

no droop with droop

60 0

10

20

30

time, s

40

10.2 10.1 no droop with droop

10 50

0

10

20

30

40

50

time, s

Fig. 6.37 Frequency support from the wind farm following an over-frequency event

Acknowledgements Results reported in this chapter are developed based on research papers [36, 37] published from my group, which are reproduced with permission of IEEE. Graduate student involved in producing these results is Mr. Sai Gopal Vennelaganti. Most of the research material was produced with support from NSF grant award ECCS1656983.

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Appendix A

Space Phasor and dq Reference Frame

A.1 Introduction This Appendix includes a brief description of space phasor and transformations used to transfer abc, αβ, and dq reference frames. An extensive discussion about space phasors, stationary, frames and rotating frames can be found in [29] in Chap. 5.

A.2 Space Phasor A three-phase AC system can be represented, analyzed, and controlled using the concept of space phasors. Assume that fa (t), fb (t), and fc (t) are three signals of arbitrary waveforms that satisfy the following equation: fa (t) + fb (t) + fc (t) = 0

(A.1)

Then their corresponding space phasor F¯ (t) also known as space vector is defined as: F¯ (t) = Fα (t) + j Fβ (t)  2π 4π 2  j0 e fa (t) + ej 3 fb (t) + ej 3 fc (t) = 3

(A.2)

F¯ (t) is a complex function of time and Fα (t) and Fβ (t) are the real and imaginary components, respectively. In terms of real valued signals we can write: 

⎡ ⎤  f (t) 2 ⎣ a ⎦ Fα (t) = C fb (t) Fβ (t) 3 fc (t)

© Springer Nature Switzerland AG 2019 N. R. Chaudhuri, Integrating Wind Energy to Weak Power Grids using High Voltage Direct Current Technology, https://doi.org/10.1007/978-3-030-03409-2

(A.3)

231

232

A Space Phasor and dq Reference Frame

where, C is: ' C=

1 1− −√12 √2 0 23 − 23

( (A.4)

In case the space phasor is known, one can find the corresponding three phase signals by:   fa (t) = Re F¯ (t)e−j 0   2π fb (t) = Re F¯ (t)e−j 3   4π fc (t) = Re F¯ (t)e−j 3

(A.5)

In terms of the real-valued components Fα (t) and Fβ (t) , the corresponding signals are given by: ⎤ ⎤ ⎡ 1 √0   fa (t) ⎥ Fα (t) ⎣ fb (t) ⎦ = ⎢ ⎣ − 12 2√3 ⎦ Fβ (t) fc (t) − 12 − 23   Fα (t) = CT Fβ (t) ⎡

(A.6)

where, C T is the transpose of C defined in (A.4).

A.2.1 dq-Frame Representation of a Space Phasor Assuming a space phasor as F¯ = Fα + j Fβ , the αβ to dq-frame transformation is defined as:   fd + jfq = fα + jfβ e−j ε(t)

(A.7)

The dq to αβ-frame transformation is achieved by multiplying both sides of (A.7) by e−j ε(t) . Hence we have:   fα + jfβ = fd + jfq ej ε(t)

(A.8)

A.2 Space Phasor

233

Based on Euler’s identity ej (.) = cos(.) + j sin(.), we can rewrite (A.7) as: 

   fα (t) fd (t) = R [ε(t)] fq (t) fβ (t)

(A.9)

where, 

cos ε(t) sin ε(t) R [ε(t)] = − sin ε(t) cos ε(t)

 (A.10)

Also, (A.8) can be rewritten as: 

     f (t) fα (t) f (t) = R −1 [ε(t)] d = R [−ε(t)] d fβ (t) fq (t) fq (t)

(A.11)

where, R −1 [ε(t)] = R [−ε(t)] =



cos ε(t) − sin ε(t) sin ε(t) cos ε(t)

 (A.12)

A direct transformation from the abc to dq-frame can be obtained by: 

⎡ ⎤  fa (t) 2 fd (t) = T [ε(t)] ⎣ fb (t) ⎦ fq (t) 3 fc (t)

(A.13)

where,    ⎤ cos [ε(t)] cos ε(t) − 2π cos ε(t) − 4π 3 3   ⎦  T [ε(t)] = R [ε(t)] C = ⎣ 4π sin ε(t) − sin [ε(t)] sin ε(t) − 2π 3 3 ⎡

(A.14) Similarly, direct transformation from dq to abc-frame can be obtained by: ⎡

⎤   fa (t) ⎣ fb (t) ⎦ = T [ε(t)]T fd (t) fq (t) fc (t)

(A.15)

Index

A AC-MTDC systems, frequency support asynchronous AC-MTDC system (see Asynchronous AC-MTDC system) communication-based methods, 172 communication-free approaches, 172–173 DC-link voltage-droop control, 173–174 frequency-droop controls, 174 inertia, 172 inertial coupling matrix, 173 inverter-interfaced renewable energy resources, 172 literature on, 175, 176 onshore converters, modes, 173 primary frequency, 172 ratio-based selective frequency support, 174–175 secondary frequency, 172 AC-side voltages, 36 Asymmetric bipolar MTDC grid model, 46–48 Asymmetric bipole structure, 26 Asymmetric monopole structure, 26 Asynchronous AC-MTDC system AC-side disturbance inertial and primary frequency support (see Inertial and primary frequency support) primary frequency support (see Primary frequency support) simulation results, 186–190 DC-side disturbance, converter outage (see Converter outage, DC-side disturbance)

desired frequency support, 176 full-order model bipolar MTDC grid with metallic return, 177 converter power dynamics, 189, 190 non-ideal response, 186, 188 power–frequency–voltage-droop control, 178 10% step-reduction, 187–189 inertial-droop control, modified N th-order model, 195–197 N th-order model assumptions, 178–179 bipolar model, 181 DC-side disturbance, 181 effective inertia constant, 180 effective inverse governor droop constant, 180 “g”-pole converter powers, 179–180 Hadamard product, 181 ideal response, 186, 187 monopolar representation, 184 positive and negative-pole converter powers, 179 with offshore wind farm, 215–217 bipolar MTDC grid with metallic return, 211, 212 inertial and primary frequency support (see Inertial and primary frequency support) with onshore wind farm, 215–217 Atlantic Wind Connection project, 2 Average-value models (AVMs), 27

© Springer Nature Switzerland AG 2019 N. R. Chaudhuri, Integrating Wind Energy to Weak Power Grids using High Voltage Direct Current Technology, https://doi.org/10.1007/978-3-030-03409-2

235

236 B Bay Link, 2 Bergeron model, 163 Black-start process DC bus pre-charging controls, 145–148 hot-swapping, 150–151 line charging, 148, 163 load pickup, 149, 163 PMU-enabled autonomous synchronization, 149–150 self-supporting DC bus, 146, 148 voltage buildup, 149, 163 VSC-HVDC system, 151

C Carrier waveform, 35, 36 CIGRE’ benchmark HVDC system, 28 Converter outage, 50–51 Converter outage, DC-side disturbance bipolar MTDC, 205 problem and constraints, 207 solution, 207–209 simulation results, 209–211 “Cut-in” speed, 3 “Cut-out” speed, 3

D DC line fault, 50 DC line outage, 50 Delmarva Energy Link, 2 Department of Energy (DoE) report, 1 DFIG-based wind energy system components, 57, 58 control architecture, 57, 58 DC bus dynamics, 64 grid-connected mode of control GSC control, 68–70 RSC control, 65–68 GSC tie-rector dynamics, 64 isolated mode of control GSC control, 72 RSC control, 70–72 machine slip, 62 model neglecting tie-reactors, 62 model with tie-reactors, 62–64 pitch controller, 58 power system restoration autonomous synchronization, 166 black-start process, 145–151 breaker closure, 166–167

Index communication latency, 166–167 control schemes, 145 hot-swapping, 167, 168 hybrid simulation platform (see Hybrid simulation platform) load composition, 162 test system configuration, 160, 161 wind speed fluctuations, 162 rotational speed, 61 rotor current, 58 schematic diagram, 57, 58 stator synchronous frequency, 61 turbine pitch control, 64–65 wind turbine model and characteristics, 59–61 Differential and algebraic equations (DAEs), 28, 80 Doubly fed induction generator (DFIG) topology, 4, 5

E Effective DC Inertia Constant (Hdc ), 22, 78 Effective short circuit ratio (ESCR), 22, 78, 80, 89, 90, 95, 96 EMTDC/PSCAD platform, 152 ETRAN, 153 ETRAN-PLUS, 154

F Firing angle correction strategy control block diagram, 108 effectiveness, 108–110 HVDC power, 107 P − f and Q − V dynamics, 107 rectifier-side power, 107 Four-state nonlinear model assumptions, 101 droop control of wind farm, 114–118, 120 expressions for DC voltages, 102 firing angle correction strategy, 107–110 frequency dynamics, 117–120 frequency nadir, 118 frequency-voltage coupling phenomenon, 99 mechanical dynamics, 101 modeling adequacy, 110, 111 per-unit energy bound, 112–114 power balance equations, 101 rectifier-side frequency dynamics, 111–112 reference electrical torque, 101 synchronizing and damping torque, 117

Index system variables, 118, 121 voltage-frequency coupling phenomenon, 103–107 Frequency-domain model, 27 Frequency droop control, 114–118, 120 Frequency-voltage coupling phenomenon, 99 Full-converter-based wind energy system, 72–73 Full-order model bipolar MTDC grid with metallic return, 177 converter power dynamics, 189, 190, 205, 206 DAEs, 99 four-state nonlinear model assumptions, 101 droop control of wind farm, 114–118, 120 expressions for DC voltages, 102 firing angle correction strategy, 107–110 frequency dynamics, 117–120 frequency nadir, 118 frequency-voltage coupling phenomenon, 99 mechanical dynamics, 101 modeling adequacy, 110, 111 per-unit energy bound, 112–114 power balance equations, 101 rectifier-side frequency dynamics, 111–112 reference electrical torque, 101 synchronizing and damping torque, 117 system variables, 118, 121 voltage-frequency coupling phenomenon, 103–107 non-ideal response, 186, 188 with offshore wind farm, simulation results, 215 power–frequency–voltage-droop control, 178 rectifier-side AC system, 99 small-signal stability analysis, 202, 204 standard vector control strategy, 177 state-space averaged phasor model, 99 10% step-reduction, 187–189 30% reduction, 205, 206

G Grid-connected mode, VSC controls, 33, 34 AC-side voltage control, 44–45 DC-side voltage control, 42–44

237 real and reactive power control controller structure, 40–42 “current mode” control, 37 hierarchical control structure, 37 KVL equations, 37 plant dynamics, 39, 40 space phasor, 37 two-level VSC, 37, 38 Grid-side converter (GSC), 5, 68–70, 72 H High-voltage direct current (HVDC) systems AC vs. DC transmission break-even distance, 6–8 cost vs. transmission distance, 6–7 HVDC lines crossing over near Wing, North Dakota, USA, 7, 8 345-kV AC transmission lines, 7, 9 underground or subsea cable transmission, 8 categories, 25 DC transmission configurations, 26 LCC (see Line-commutated converter (LCC)-based HVDC) mass-spring-damping model, 27 monograph, 22–23 MTDC electric power grids Hydro-Quebec-New-England interconnection, 20, 21 monograph, 22–23 Nanao project, 20, 21 vs. point-to-point HVDC, 17 renewable resources, 19 single-line diagram, 17, 18 supergrid, 19 three-terminal SACOI interconnections, 20–21 Zhoushan project, 19–20 point-to-point HVDC links, 17, 18 VSC (see Voltage source converter (VSC)-based HVDC) vs. wind farms, 1 HVDC systems, see High-voltage direct current systems Hybrid MTDC grid modeling bipolar H-MTDC grid configuration, 217–219 control strategies, 219, 221, 222 frequency support DFIG-based wind farm, 219, 221, 222 sequence of events and control actions, 223

238 Hybrid MTDC grid modeling (cont.) simulation results critical eigenvalue variation, 223, 225 4-terminal bipolar H-MTDC grid, 223, 224 movement of eigenvalues, 225, 226 over-frequency event, 225, 227 torque reference,225 under-frequency event, 225, 226 Hybrid simulation platform additional load pickup, 159–160 architecture, 154 31-bus 4-area power system, 155, 156 commercial power system planning software, 152 detailed three-phase EMT-type model, 153 dynamic models, 154 EMTDC/PSCAD type models, 152, 153 ETRAN, 153, 154 ETRAN-PLUS, 154 PSSE simulation, 154, 155 system-level problem, 153 system restoration, 155–159

I Inertial and primary frequency support MPC with frequency droop, 194 without frequency droop, 190–194 with offshore wind farm full-order model, simulation results, 215 turbine–generator rotor dynamics, 212 wind farm controller with N th-order model, 213–216 wind turbine characteristics, 213 ratio-based inertial and primary frequency support bipolar MTDC grid with metallic return, 202, 203 converter power, full-order model, 205, 206 ideal response, N th-order model, 203, 204 inertial and frequency-droop coefficient design, 198–202 monopolar representation, 198 non-ideal response, N th-order model, 203–205 non-participating areas, 198 participating areas, 197 selective power routing, modified N th-order model, 198

Index small-signal stability analysis, full-order model, 202, 204 30% reduction, full-order model, 205, 206 Inertial coupling matrix, 173 Insulated-gate bipolar-junction transistor (IGBT), 12, 13 Islanded mode, VSC controls, 45–46

J Joint Coordinated System Plan (JCSP) report, 1

L LCC technology, see Line-commutated converter technology Linear time-invariant (LTI) state-space model, 27 Line-commutated converter (LCC)-based HVDC, 2 AC grid (dynamic model) parameters, 137 DFIG parameters, 137 dynamic model, 83, 87 ESCR, 80, 89, 90, 95, 96 fault energy and DC fault current, 11 filter design, 11 frequency controller candidate controllers, 91–92 critical modes, 91 eigenvalue sensitivity analysis, 91 modal participation, 91 objectives, 84 root-locus method, 92–95 zero crossing points, 85 frequency-domain analysis eigenvalue analysis, 128 with synchronous condenser, 130–132 without synchronous condenser, 128–129 frequency dynamic analysis AC system frequency, 86 eigenvalue-sensitivity analysis, 88–89 governor droop coefficient, 88 inverter-side AC grid and rectifier, 97–100 mechanical power input, 88 modal participation analysis, 88 power-balance equation, 86 root locus analysis, 89 full-order model (see Full-order model) Graetz bridge, 8–10 Hdc , 80, 89, 90

Index induction machine and RSC dynamics, 135–136 inverter station, 79 mercury arc valves, 8 modeling philosophies, 27–28 monograph, 22 offshore wind farm integration, 79 onshore wind farm integration, 79, 80 pitch angle controller parameters, 138 performance under fault, 97, 98 wind speed conditions, 96–97 schematic, 28, 29 STATCOM, 79 state-space averaged phasor model AC network interface, cap bank and filters, 32–33 algebraic variables, 138 DAEs, 80 DC line model, 30 DFIG-based wind farm, 81, 83 differential and algebraic equations, 28 dynamic response, 83–86 input variables, 138 inverter control, 31, 32 rectifier control, 30, 31 schematic diagram, 80, 82 state variables, 138 station model, 28, 30 synchronous condensers frequency nadir, 126 installation, 120–122, 126 load flow analysis, 122, 124 results and analysis, 124–125 RoCoF, 126 root-cause analysis, 122 test system, 122, 123 synchronous generators, 80, 126, 127 three-phase 12-pulse bridge, 10–11 thyristor valves, 8–9 time-domain analysis constant current control scheme, 132–133 frequency control scheme, 133–134 UHVDC systems, 11–12 vs. VSC, 16, 17 Line-commutated converter (LCC) technology, 8, 25

M Mass-spring-damping model, 27 Maximum power point tracking (MPPT), 5, 60

239 Model predictive control (MPC) with frequency droop, 194 without frequency droop, 190–194 Modified N th-order model inertial-droop control, 195–197 selective power routing, 198 Modular multi-level converter (MMC), 14–15 Modulating signal, 35, 36 MPC, see Model predictive control Multiterminal DC (MTDC) grids, 2 AC grid systems, unified model, 48, 50 asymmetric bipolar model, 46–48 contingencies, 50–51 converters control options, 51–53 droop control strategies, 52 DC cable network, dynamic model, 48, 49 frequency support, AC system (see AC-MTDC systems, frequency support) H-MTDC grid modeling bipolar H-MTDC grid configuration, 217–220 control strategies, 219, 221 frequency support, 219, 221–223 simulation results, 223–227 Hydro-Quebec-New-England interconnection, 20, 21 monograph, 22–23 Nanao project, 20, 21 vs. point-to-point HVDC, 17 renewable resources, 19 single-line diagram, 17, 18 supergrid, 19 three-terminal SACOI interconnections, 20–21 Zhoushan project, 19–20

N Nacelle, 3 NERC, see North American Electric Reliability Corporation New Jersey Energy Link, 2 Non-hybrid simulation platform, VSC-HVDC controls short circuit capacity, 155 system restoration, 157–159 North American Electric Reliability Corporation (NERC), 144 N th-order model assumptions, 178–179 bipolar model, 181

240 N th-order model (cont.) DC-side disturbance, 181 effective inertia constant, 180 effective inverse governor droop constant, 180 “g”-pole converter powers, 179–180 Hadamard product, 181 ideal response, 186, 187, 203, 204 monopolar representation, 184 non-ideal response, 203–205 positive and negative-pole converter powers, 179 wind farm controller with, 213–216 O Offshore wind farms (OWFs), 79 de-loaded condition, 214 direct-drive wind generating units, 73 frequency support, 173, 211 full-order model (see Full-order model) inertial and primary frequency support, 212–215 LCC-HVDC delivery systems, 97 MTDC grid, 173 N -asynchronous-area AC-MTDC system, 211, 213, 215 power reference, 213 VSC technology, 2 P Pan-European supergrids, 19 Phase-locked loop (PLL), 40–41 PMSG-based direct-drive WTG model generator-side converter control, 73–74 grid-side converter control, 74–75 PMU-enabled autonomous synchronization, 149–150 Point of common coupling (PCC), 36 Point-to-point HVDC links, 17, 171 Power balance, 42 Power system restoration autonomous synchronization method, 145 DFIG-based wind farm autonomous synchronization, 166–168 black-start process, 145–151 breaker closure, 167 communication latency, 166–167 control schemes, 145 hot-swapping, 167–168 hybrid simulation platform (see Hybrid simulation platform) load composition, 162

Index test system configuration, 160, 161 wind speed fluctuations, 162 early stages of, 143 firewall effect, 143 VSC-HVDC controls black-start process, 151, 164–166 hybrid simulation platform (see Hybrid simulation platform) line charging, 163, 164 load composition, 162 load pickup, 164, 165 non-hybrid simulation platform, 155, 157–159 synchronization and generation ramp up, 164, 165 voltage buildup, 164, 165 wind speed fluctuations, 162 wind forecasting tools, 144 Primary frequency support frequency-droop coefficients of positive pole, 186, 187 static design, 184–186 selective power routing concept characteristic features, 183–184 hierarchal AC-MTDC control framework, 182, 183 non-participating areas, 182 participating areas, 182 pre-disturbance value, 182 RoCoF, 182 threshold, 182 voltage-droop control, 182

R Rate of change of frequency (RoCoF), 126, 182 Rock Island Clean Line project, 77 Root-locus method, 92–95 Rotor-side converter (RSC), 5, 65–68, 70–72

S Selective power routing characteristic features, 183–184 hierarchal AC-MTDC control framework, 182, 183 non-participating areas, 182 participating areas, 182 pre-disturbance value, 182 RoCoF, 182 threshold, 182 voltage-droop control, 182

Index Sinusoidal pulse-width modulation (SPWM), 33, 35 Small-signal models, 27 Space phasor dq-frame transformation, 232–233 real-valued components, 232 space vector, 231 three phase signals, 232 State-space averaged phasor model, LCC-HVDC AC network interface, cap bank and filters, 32–33 DC line model, 30 differential and algebraic equations, 28 inverter control, 31, 32 rectifier control, 30, 31 station model, 28, 30 Submodules (SMs), 14–15 Symmetric bipole structure, 26 Symmetric monopole structure, 26 T Telephone influence factor (TIF), 11 Total harmonic distortion (THD), 11 Turbine-generator rotational dynamics, 61 Turbine pitch control, 64–65 U Ultra high voltage DC (UHVDC) transmission system, 11–12 V Voltage-frequency coupling phenomenon desensitization of real power, 107 Eacr and Eaci variations, 103–106 frequency dynamics, 106 and full-order model responses, 103, 104 P − f and Q − V dynamics, 106, 107 reactive power, 106 without Eacr and Eaci variations, 105 Voltage source converter (VSC), 25 Atlantic Wind Connection project, 2 self-commutating devices, 12 Voltage source converter (VSC)-based HVDC, 2 controls grid-connected mode (see Gridconnected mode, VSC controls) islanded mode, 45–46

241 full-bridges, 13–14 half-bridge, single-phase, two-level VSC, 12, 13 IGBTs, 12, 13 key features, 16 vs. LCC, 16, 17 MMC, 14–15 monograph, 22 power system restoration black-start process, 152, 164–165 hybrid simulation platform (see Hybrid simulation platform) line charging, 164, 165 load composition, 162 load pickup, 164, 165 non-hybrid simulation platform, 155, 157–159 synchronization and generation ramp up, 164, 165 voltage buildup, 164, 165 wind speed fluctuations, 162 structure, 33, 34 submodules, 14–15 three-phase 2-level 6-pulse bridge configuration, 13, 14 two-level VSC modeling, 33, 35–36 VSC, see Voltage source converter

W Western Electricity Coordinating Council (WECC), 73, 152 Wind energy potential, US onshore and offshore, 1, 2 Wind energy technologies, see Wind turbine–generator systems Wind sensors, 3 Wind turbine–generator systems asynchronous generator and converter, 4, 5 constant-speed wind power system, 3–5 DFIG topology, 4, 5 gearless synchronous generator and converter, 4, 5 mechanical interface, 6 synchronous machine, 6 torque-speed characteristics, 5, 6 variable-speed wind power system, 4, 5 wind turbine components, 3