Advanced Technologies, Systems, and Applications V: Papers Selected by the Technical Sciences Division of the Bosnian-Herzegovinian American Academy of Arts and Sciences 2020 [1st ed.] 9783030547646, 9783030547653

Table of contents :
Front Matter ....Pages i-x
Front Matter ....Pages 1-1
Partial Configuration Spaces as Pullbacks of Diagrams of Configuration Spaces (Amy Q. H. Li, Ismar Volić)....Pages 3-31
Front Matter ....Pages 33-33
Smart Sarajevo—Analysis of Smart Home System (Emir àaljić, Samir Avdaković)....Pages 35-48
Western Balkans Green-Deal: Zero Emissions by 2050 (M. Brkljača, M. Tabaković, M. Vranjkovina, Dž. Ćorović, L. Dedić, M. Krzović et al.)....Pages 49-62
Biomass Potential Monitoring System as a Tool for Exchange and Comparing Findings from Different Sectoral Studies (Mirza Ponjavic, Almir Karabegovic, Slavoljub Stanojevic, Sanja Celebicanin)....Pages 63-83
Cost Analysis of Photovoltaic and Battery System for Improving Residential Energy Self-consumption (Amer Aščerić, Marko Čepin, Boštjan Blažič)....Pages 85-105
Machine Learning Based Electrical Load Forecasting Using Decision Tree Algorithms (T. Hubana, E. àemić, N. Laković)....Pages 107-116
Comparative Analysis of World’s Energy Prices Versus Those in Bosnia and Herzegovina—Crude Prices and Impact on Profitability of Oil Sector (Sanel Halilbegovic, Mirza Saric, Nedim Celebic, Amna Avdagic)....Pages 117-128
Identification on Dominant Oscillation Based on EMD and Prony’s Method Approach (M. Muftic Dedovic, Adnan Mujezinović, N. Dautbasic)....Pages 129-138
The Hybrid EMD-SARIMA Model for Air Quality Index Prediction, Case of Canton Sarajevo (M. Muftic Dedovic, Samir Avdaković, Adnan Mujezinović, N. Dautbasic)....Pages 139-150
Influence of a Photovoltaic Power System Connection to Power System Voltage Stability (Nedis Dautbašić, Tatjana Konjić, Ermin Ahatović, Majda Đonlagić, Dina Fejzović)....Pages 151-168
Front Matter ....Pages 169-169
Nonlinear Static Analysis of a Railway Bridge (Aljoša Skočajić, Naida Ademović)....Pages 171-184
Automatization of the Ranking Process of the Land Consolidation Projects (Marinković Goran, Mirko Borisov, Nikolina Mijić, Trifković Milan, Lazić Jelena)....Pages 185-199
Correlation Between the Ionosphere Anomalies and the Earthquake in Albania M6.4R (Medžida Mulić, Randa Natraš, Slavica Matić, Jasmin Ćatić)....Pages 201-214
Front Matter ....Pages 215-215
On the Impact of Body Forces in Low Prandtl Number Liquid Bridges (B. àeta, D. Dubert, J. Massons, P. Salgado Sánchez, J. Porter, Jna. Gavald`et al.)....Pages 217-227
Analysis of Contact Mechanics Problems of Pipes Using a Finite-Volume Method (Muris Torlak, Elvedin Kljuno)....Pages 229-238
A Contribution to Modeling and Computer Simulation of Species Spread in Natural Environments (Muris Torlak, Vahidin Hadžiabdić, Sadjit Metović)....Pages 239-251
Front Matter ....Pages 253-253
The Influence of System Factors on QoE for WebRTC Video Communication (Maida Balihodžić, Jasmina Baraković Husić, Sabina Baraković)....Pages 255-267
Multidimensional QoE Prediction of WebRTC Video Communication with Machine Learning (Amna Karadža, Jasmina Baraković Husić, Sabina Baraković, Srđan Nogo)....Pages 269-283
The Smart Greenhouse System Based on the the Mobile Network and IoT (Zehra àabić, Una Drakulić, Edin Mujčić)....Pages 285-298
Smart Musical Fountain (Minela Selmanović, Una Drakulić, Edin Mujčić)....Pages 299-310
Towards Development of Comprehensive Framework for Evaluation of Potential Consequences of Cyber-Attacks (Igor Ognjanović, Ramo àendelj, Ivana Ognjanović)....Pages 311-319
Optical Network Security Attacks by Tapping and Encrypting Optical Signals (Anis Maslo, Nermin Sarajlić, Mujo Hodžić, Aljo Mujčić)....Pages 321-332
Front Matter ....Pages 333-333
Multiple Linear Regression Model for Predicting PM2.5 Concentration in Zenica (Zinaid Kapić)....Pages 335-341
Physical and Cognitive Therapy Enhancement Using Game-Based Learning (Belma Ramic-Brkic, Marijana Cosovic, Edin Begic)....Pages 343-359
Determining Sentiment of Tweets Using First Bosnian Lexicon and (AnA)-Affirmative and Non-affirmative Words (Sead Jahić, Jernej Vičič)....Pages 361-373
Quantifier Elimination in Fields and Application in Geometry (Mirna Udovicic)....Pages 375-396
Workpiece Measurement Device—Workpiece Height Classification (Ermin Podrug, Slobodan Lubura)....Pages 397-405
Implementation of Single-Phase Phase-Locked Loop with DC Offset and Noise Rejection Using Fuzzy Logic Controller (Nihad Ferhatović, Srđan Lale, Jasmin Kevrić, Slobodan Lubura)....Pages 407-421
Air Quality Prediction Using Machine Learning Methods: A Case Study of Bjelave Neighborhood, Sarajevo, BiH (Emina Džaferović, Kanita Karađuzović-Hadžiabdić)....Pages 423-434
Naive Website Categorization Based on Text Coverage (Aldin Kovačević, Zerina Mašetić, Dino Kečo)....Pages 435-448
Front Matter ....Pages 449-449
Conceptual Wind Turbine Prototype Design and Performance Testing (Đanis Kadrić, Emir Nezirić, Ernad Bešlagić)....Pages 451-458
Sustainable Transition of District Heating Networks—Upgrading the Performance of DH System Tuzla and Integration of RES Modules (Anes Kazagic, Dominik Rutz, Ajla Merzic, Dino Tresnjo, Jasenko Fazlic, Suljo Saric et al.)....Pages 459-476
Manipulating Epoxy resin’s Electrical Conductivity Using Carbon Nanotubes (F. Ustamujić, Ž. Husnić)....Pages 477-487
Simulation of Solar Assisted Solid Desiccant Cooling System (Haris Lulić, Adnan Đugum)....Pages 489-500
Pipe Stress Analysis Using an Analytical and a Finite-Volume Method (Elvedin Kljuno, Muris Torlak)....Pages 501-512
Sizing of a Micro-cogeneration System of One Residential Building in Sarajevo (S. Metović, S. Oglečevac, N. Hodžić)....Pages 513-523
Physical and Numerical Modeling of Water Flow Through Coanda-Effect Screens (Hajrudin Dzafo, Sadzit Metovic, Ejub Dzaferovic)....Pages 525-538
Numerical Structural Analysis Using Combined Finite Elements: A Case Study of Electric Bicycle Design (Matej Pezer, Adis J. Muminovic, Elmedin Mesic, Nedim Pervan)....Pages 539-553
Product Development and Design: A Bicycle Stand Case Study (Mehridzana Popovac, Tarik Klinac, Adis J. Muminovic, Isad Saric)....Pages 555-569
An Overview of Research Irregularities Regarding Water Regimes and Environmental Effects in the Design of Small Hydropower Plants in Bosnia and Herzegovina (Azra Tanović, Edin Kasamović, Hajrudin Džafo)....Pages 571-580
Back Matter ....Pages 581-582

Citation preview

Lecture Notes in Networks and Systems 142

Samir Avdaković · Ismar Volić · Aljo Mujčić · Tarik Uzunović · Adnan Mujezinović   Editors

Advanced Technologies, Systems, and Applications V Papers Selected by the Technical Sciences Division of the Bosnian-Herzegovinian American Academy of Arts and Sciences 2020

Lecture Notes in Networks and Systems Volume 142

Series Editor Janusz Kacprzyk, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland Advisory Editors Fernando Gomide, Department of Computer Engineering and Automation—DCA, School of Electrical and Computer Engineering—FEEC, University of Campinas— UNICAMP, São Paulo, Brazil Okyay Kaynak, Department of Electrical and Electronic Engineering, Bogazici University, Istanbul, Turkey Derong Liu, Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, USA; Institute of Automation, Chinese Academy of Sciences, Beijing, China Witold Pedrycz, Department of Electrical and Computer Engineering, University of Alberta, Alberta, Canada; Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland Marios M. Polycarpou, Department of Electrical and Computer Engineering, KIOS Research Center for Intelligent Systems and Networks, University of Cyprus, Nicosia, Cyprus Imre J. Rudas, Óbuda University, Budapest, Hungary Jun Wang, Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong

The series “Lecture Notes in Networks and Systems” publishes the latest developments in Networks and Systems—quickly, informally and with high quality. Original research reported in proceedings and post-proceedings represents the core of LNNS. Volumes published in LNNS embrace all aspects and subfields of, as well as new challenges in, Networks and Systems. The series contains proceedings and edited volumes in systems and networks, spanning the areas of Cyber-Physical Systems, Autonomous Systems, Sensor Networks, Control Systems, Energy Systems, Automotive Systems, Biological Systems, Vehicular Networking and Connected Vehicles, Aerospace Systems, Automation, Manufacturing, Smart Grids, Nonlinear Systems, Power Systems, Robotics, Social Systems, Economic Systems and other. Of particular value to both the contributors and the readership are the short publication timeframe and the world-wide distribution and exposure which enable both a wide and rapid dissemination of research output. The series covers the theory, applications, and perspectives on the state of the art and future developments relevant to systems and networks, decision making, control, complex processes and related areas, as embedded in the fields of interdisciplinary and applied sciences, engineering, computer science, physics, economics, social, and life sciences, as well as the paradigms and methodologies behind them. Indexed by SCOPUS, INSPEC, WTI Frankfurt eG, zbMATH, SCImago.

More information about this series at http://www.springer.com/series/15179

Samir Avdaković Ismar Volić Aljo Mujčić Tarik Uzunović Adnan Mujezinović •

•

•

•

Editors

Advanced Technologies, Systems, and Applications V Papers Selected by the Technical Sciences Division of the Bosnian-Herzegovinian American Academy of Arts and Sciences 2020

123

Editors Samir Avdaković Faculty of Electrical Engineering University of Sarajevo Sarajevo, Bosnia and Herzegovina

Ismar Volić Department of Mathematics Wellesley College Wellesley Hills, MA, USA

Aljo Mujčić Faculty of Electrical Engineering University of Tuzla Tuzla, Bosnia and Herzegovina

Tarik Uzunović Faculty of Electrical Engineering University of Sarajevo Sarajevo, Bosnia and Herzegovina

Adnan Mujezinović Faculty of Electrical Engineering University of Sarajevo Sarajevo, Bosnia and Herzegovina

ISSN 2367-3370 ISSN 2367-3389 (electronic) Lecture Notes in Networks and Systems ISBN 978-3-030-54764-6 ISBN 978-3-030-54765-3 (eBook) https://doi.org/10.1007/978-3-030-54765-3 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 This work is subject to copyright. All rights are solely and exclusively licensed 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, expressed 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

About This Book

The papers in this collection are centred around the theory and practice of a wide variety of advanced technologies. They cover the latest developments in computing, networking, information technology, robotics, complex systems, communications, energy, mechanical engineering, civil engineering, geodesy, and other subjects. These papers were selected for presentation at the conference 12th Days of Bosnian-Herzegovinan American Academy of Arts and Sciences (BHAAAS) that was supposed to be held in Mostar, Bosnia, and Herzegovina in June 2020 but was postponed due to the coronavirus pandemic. However, because of the high quality of the submissions, BHAAAS’ division of technical and natural sciences decided to create this special volume despite the postponement. The editors would like to extend special gratitude to all the chairs of the planned symposia of the 12th Days of BHAAAS for their dedicated work in the production of this volume: Jasmin Kevrić, Zerina Mašetić, Dželila Mehanović (Computer Science); Anes Kazagić, Hajrudin Džafo, Izet Smajević (Mechanical Engineering); Tarik Uzunović, Asif Šabanović, Jasmin Kevrić (Mechatronics, Robotics, and Embedded Systems); Mirza Šarić, Tarik Hubana, Maja Muftić Dedović (Advanced Electrical Power Systems); Mirza Pozder, Naida Ademović, Medžida Mulić (Civil Engineering and Geodesy); Adnan Mujezinović, Muris Torlak (Computer Modelling and Simulations for Engineering Applications); Aljo Mujčić, Edin Mujčić (Information and Communication Technologies).

v

Contents

Applied Mathematics Partial Configuration Spaces as Pullbacks of Diagrams of Configuration Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Amy Q. H. Li and Ismar Volić

3

Power Systems Smart Sarajevo—Analysis of Smart Home System . . . . . . . . . . . . . . . . . Emir Šaljić and Samir Avdaković

35

Western Balkans Green-Deal: Zero Emissions by 2050 . . . . . . . . . . . . . M. Brkljača, M. Tabaković, M. Vranjkovina, Dž. Ćorović, L. Dedić, M. Krzović, M. Skenderović, T. Hubana, and Samir Avdaković

49

Biomass Potential Monitoring System as a Tool for Exchange and Comparing Findings from Different Sectoral Studies . . . . . . . . . . . Mirza Ponjavic, Almir Karabegovic, Slavoljub Stanojevic, and Sanja Celebicanin Cost Analysis of Photovoltaic and Battery System for Improving Residential Energy Self-consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . Amer Aščerić, Marko Čepin, and Boštjan Blažič

63

85

Machine Learning Based Electrical Load Forecasting Using Decision Tree Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 T. Hubana, E. Šemić, and N. Laković Comparative Analysis of World’s Energy Prices Versus Those in Bosnia and Herzegovina—Crude Prices and Impact on Profitability of Oil Sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Sanel Halilbegovic, Mirza Saric, Nedim Celebic, and Amna Avdagic

vii

viii

Contents

Identification on Dominant Oscillation Based on EMD and Prony’s Method Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 M. Muftic Dedovic, Adnan Mujezinović, and N. Dautbasic The Hybrid EMD-SARIMA Model for Air Quality Index Prediction, Case of Canton Sarajevo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 M. Muftic Dedovic, Samir Avdaković, Adnan Mujezinović, and N. Dautbasic Influence of a Photovoltaic Power System Connection to Power System Voltage Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 Nedis Dautbašić, Tatjana Konjić, Ermin Ahatović, Majda Đonlagić, and Dina Fejzović Civil Engineering and Geodesy Nonlinear Static Analysis of a Railway Bridge . . . . . . . . . . . . . . . . . . . . 171 Aljoša Skočajić and Naida Ademović Automatization of the Ranking Process of the Land Consolidation Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 Marinković Goran, Mirko Borisov, Nikolina Mijić, Trifković Milan, and Lazić Jelena Correlation Between the Ionosphere Anomalies and the Earthquake in Albania M6.4R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 Medžida Mulić, Randa Natraš, Slavica Matić, and Jasmin Ćatić Computer Modelling and Simulations for Engineering Applications On the Impact of Body Forces in Low Prandtl Number Liquid Bridges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 B. Šeta, D. Dubert, J. Massons, P. Salgado Sánchez, J. Porter, Jna. Gavaldà, M. M. Bou-Ali, and X. Ruiz Analysis of Contact Mechanics Problems of Pipes Using a Finite-Volume Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 Muris Torlak and Elvedin Kljuno A Contribution to Modeling and Computer Simulation of Species Spread in Natural Environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 Muris Torlak, Vahidin Hadžiabdić, and Sadjit Metović Information and Communication Technologies The Influence of System Factors on QoE for WebRTC Video Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 Maida Balihodžić, Jasmina Baraković Husić, and Sabina Baraković

Contents

ix

Multidimensional QoE Prediction of WebRTC Video Communication with Machine Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 Amna Karadža, Jasmina Baraković Husić, Sabina Baraković, and Srđan Nogo The Smart Greenhouse System Based on the the Mobile Network and IoT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 Zehra Šabić, Una Drakulić, and Edin Mujčić Smart Musical Fountain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 Minela Selmanović, Una Drakulić, and Edin Mujčić Towards Development of Comprehensive Framework for Evaluation of Potential Consequences of Cyber-Attacks . . . . . . . . . . . . . . . . . . . . . 311 Igor Ognjanović, Ramo Šendelj, and Ivana Ognjanović Optical Network Security Attacks by Tapping and Encrypting Optical Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 Anis Maslo, Nermin Sarajlić, Mujo Hodžić, and Aljo Mujčić Computer Science Multiple Linear Regression Model for Predicting PM2.5 Concentration in Zenica . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 Zinaid Kapić Physical and Cognitive Therapy Enhancement Using Game-Based Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 Belma Ramic-Brkic, Marijana Cosovic, and Edin Begic Determining Sentiment of Tweets Using First Bosnian Lexicon and (AnA)-Affirmative and Non-affirmative Words . . . . . . . . . . . . . . . . 361 Sead Jahić and Jernej Vičič Quantifier Elimination in Fields and Application in Geometry . . . . . . . 375 Mirna Udovicic Workpiece Measurement Device—Workpiece Height Classification . . . . 397 Ermin Podrug and Slobodan Lubura Implementation of Single-Phase Phase-Locked Loop with DC Offset and Noise Rejection Using Fuzzy Logic Controller . . . . . . . . . . . . . . . . 407 Nihad Ferhatović, Srđan Lale, Jasmin Kevrić, and Slobodan Lubura Air Quality Prediction Using Machine Learning Methods: A Case Study of Bjelave Neighborhood, Sarajevo, BiH . . . . . . . . . . . . . 423 Emina Džaferović and Kanita Karađuzović-Hadžiabdić Naive Website Categorization Based on Text Coverage . . . . . . . . . . . . . 435 Aldin Kovačević, Zerina Mašetić, and Dino Kečo

x

Contents

Mechanical Engineering Conceptual Wind Turbine Prototype Design and Performance Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451 Đanis Kadrić, Emir Nezirić, and Ernad Bešlagić Sustainable Transition of District Heating Networks—Upgrading the Performance of DH System Tuzla and Integration of RES Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459 Anes Kazagic, Dominik Rutz, Ajla Merzic, Dino Tresnjo, Jasenko Fazlic, Suljo Saric, Mustafa Music, and Izet Delalic Manipulating Epoxy resin’s Electrical Conductivity Using Carbon Nanotubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477 F. Ustamujić and Ž. Husnić Simulation of Solar Assisted Solid Desiccant Cooling System . . . . . . . . . 489 Haris Lulić and Adnan Đugum Pipe Stress Analysis Using an Analytical and a Finite-Volume Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501 Elvedin Kljuno and Muris Torlak Sizing of a Micro-cogeneration System of One Residential Building in Sarajevo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513 S. Metović, S. Oglečevac, and N. Hodžić Physical and Numerical Modeling of Water Flow Through Coanda-Effect Screens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525 Hajrudin Dzafo, Sadzit Metovic, and Ejub Dzaferovic Numerical Structural Analysis Using Combined Finite Elements: A Case Study of Electric Bicycle Design . . . . . . . . . . . . . . . . . . . . . . . . . 539 Matej Pezer, Adis J. Muminovic, Elmedin Mesic, and Nedim Pervan Product Development and Design: A Bicycle Stand Case Study . . . . . . . 555 Mehridzana Popovac, Tarik Klinac, Adis J. Muminovic, and Isad Saric An Overview of Research Irregularities Regarding Water Regimes and Environmental Effects in the Design of Small Hydropower Plants in Bosnia and Herzegovina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571 Azra Tanović, Edin Kasamović, and Hajrudin Džafo Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581

Applied Mathematics

Partial Configuration Spaces as Pullbacks of Diagrams of Configuration Spaces Amy Q. H. Li and Ismar Voli´c

Abstract Partial configuration spaces are a version of ordinary configuration spaces where some points are allowed to coincide. We express these spaces as pullbacks of diagrams of ordinary configuration spaces and provide some examples where the limit coincides with the homotopy limit. We also indicate how one might use calculations in cohomology to show that the limit is the homotopy limit in general. Keywords Configuration spaces · Partial configuration space · Diagrams · Limits Homotopy limits · Subspace arrangements

1 Introduction Let P1 , …, Pk , M be smooth manifolds and let Link(P1 , . . . , Pk ; M )

(1)

be the space of link maps of P1 , …, Pk in M, namely the space of k-tuples of smooth maps (f1 : P1 → M , . . . , fk : Pk → M ) such that the images of the fi are disjoint (topologized as the subspace of the space of maps Map(P1  · · ·  Pk , N )). These spaces appear, among other places, in recent work on intersection theory [8], study of generalizations of Milnor invariants [7], and homotopy-theoretic models for homotopy string links [10]. One way to study the space Link(P1 , . . . , Pk ; M ) is via manifold calculus of functors [5, 12]. This approach has already yielded useful information [4, 9]. The idea is to associate a Taylor tower of approximations to the space Link(P1 , . . . , Pk ; M ) and study it in a piecemeal way. The building blocks for the stages of the Taylor A. Q. H. Li (B) · I. Voli´c Department of Mathematics, Wellesley College, Wellesley, MA, USA e-mail: [email protected] I. Voli´c e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. Avdakovi´c et al. (eds.), Advanced Technologies, Systems, and Applications V, Lecture Notes in Networks and Systems 142, https://doi.org/10.1007/978-3-030-54765-3_1

3

4

A. Q. H. Li and I. Voli´c

tower are link maps of unions of points, i.e. Link(n1 ∗, . . . , nk ∗; M ).

(2)

In fact, the spaces of homotopy string links, which are some of the simplest (yet still very interesting) examples of spaces of link maps are built out of these in a straightforward fashion [10]. Getting a handle on the topology of spaces of link maps of points is therefore central in understanding the functor calculus point of view on general spaces of link maps. The goal of this paper is to realize spaces of link maps of points as pullbacks of fairly simple diagrams of configuration spaces. Since configuration spaces are well-understood, the hope is that this would translate into new understanding of the topology of link maps of points and hence general link maps. The point of view we take is that Link(n1 ∗, . . . , nk ∗; M ) is homeomorphic to the space of n1 + n2 + · · · + nk points in M where the first n1 do not have to be distinct, the second n2 do not have to be distinct, and so on, but points in different clusters are not allowed to coincide. We will denote this space by Conf(n1 , n2 , . . . , nk ; M ) (see Sect. 2 for precise definitions). For most of our results, the requirement that M be a manifold is not necessary, so we will consider Conf(n1 , n2 , . . . , nk ; X ) where X is any space. This space is familiar from algebraic geometry as it can be regarded as a complement of a  subspace arrangements where some diagonals have been removed from the space X nl . Let Star(n) be the category with objects 0, 1, . . . , n and non-identity morphisms j → 0, j = 0. Then take the product category Star(n1 ) × Star(n2 ) × · · · × Star(nk ). Its elements are thus k-tuples (i1 , i2 , . . . , ik ), 0 ≤ ij ≤ nj , and non-identity morphisms are generated by (i1 , i2 , . . . , ij−1 , ij , ij+1 , . . . , ik ) −→ (i1 , i2 , . . . , ij−1 , 0, ij+1 , . . . , ik ), ij = 0. (3) Now consider the functor P from this product category to the category of spaces that sends (i1 , i2 , . . . , ik ) maps to Conf(l; X ), the ordinary configuration space of l points in X , if this k-tuple contains exactly l non-zero entries. The morphisms are sent to projection maps that forget a point (Sect. 4 has the details). Our main result is the following. Theorem 1.1 The limit (or pullback) of the diagram P is homeomorphic to Conf(n1 , n2 , . . . , nk ; X ). It would be more useful, from an algebraic topology point of view, if we could show that partial configuration spaces are the homotopy limits of diagrams of ordinary configuration spaces. This is because homotopy limits are homotopy invariant while limits are not. Theorem 1.1 is an indication that this might be true and we will

Partial Configuration Spaces as Pullbacks of Diagrams …

5

provide some examples where the limit and the homotopy limit are indeed equivalent in Sect. 5.2 (most notably for the space Conf(n, 1, ..., 1; M ) in Example 5.7). In addition, we will in Sect. 5.3 outline a strategy for proving the general case that combines the Goresky-MacPherson machinery for calculating the cohomology of complements of subspace arrangements with the cohomology spectral sequence associated to the diagrams P. The diagram P has cubical diagrams as its building blocks. Namely, given an element (i1 , i2 , . . . , ik ) in Star(n1 ) × Star(n2 ) × · · · × Star(nk ), one can look at the category of objects under it. This gives a cubical diagram (see Definition 3.5); for example, (2, 0, 1, 3) gives (0, 0, 1, 3)

(2, 0, 1, 3) (2, 0, 0, 3) (2, 0, 1, 0)

(0, 0, 0, 3) (0, 0, 1, 0)

(2, 0, 0, 0)

(0, 0, 0, 0)

Applying P to this cube produces a cube of configuration spaces with projection maps between them. The (homotopy) limit of such a cube is a configuration space in the initial slot of the cube. Diagram P can thus be thought of as gluing cubical diagrams of configuration spaces along faces, and this gluing corresponds geometrically to taking products of configuration spaces and gluing them along some of the configuration points. This will be illustrated in some of the examples in Sect. 5.2. Some other possible further directions of investigation are: • The projection maps in the P(Star(n1 ) × Star(n2 ) × · · · × Star(nk )) do not have to be to one fewer points. One can declare that, depending on how many zeros (or non-zeros) there are in the tuple (i1 , i2 , . . . , ij−1 , ij , ij+1 , . . . , ik ), the projection is to some other number of factors. This would lead to more complicated conditions in the limit about which points can collide and which cannot. It would be desirable to show that, given any subspace arrangement, there is a way to write it as the homotopy limit of an appropriate diagram. • Another generalization would be to capture the requirement that, within each cluster of ni points, only up to ri of them are allowed to collide. This would then have bearing on the study of r-immersions via functor calculus and, in turn, on some recent Tverberg-like results in combinatorial topology. In particular, the most important object there is the space of r-immersions of k points in M , namely the configuration space of k points where no more than r − 1 are allowed to be the same. It would be very useful to have a diagrammatic description of these spaces. • Some ideas in this paper seem in some sense dual to those in [13]. The authors of that paper realize complements of subspace arrangements as (homotopy) colimits of diagrams where spaces are subspaces of the arrangement complement and maps are inclusions. Everything is governed by the combinatorics of the poset that

6

A. Q. H. Li and I. Voli´c 

prescribes how the diagonals are removed from X nl to get an arrangement. It would be desirable to flesh out the potential duality between the two constructions.

2 Partial Configuration Spaces For X a space, let Conf(k; X ) be the configuration space of k points in X, i.e. Conf(k; X ) = {(x1 , x2 , . . . , xk ) ∈ X k : xi = xj when i = j}. This is the space X k with all the diagonals xi = xj removed. For example, if X = R, then Conf(2; R) is homeomorphic to the plane R2 with the diagonal x1 = x2 removed. Configuration spaces are well-understood for many X (for an overview, see [1]). One way to generalize configuration spaces is to allow some of the points to coincide. For example, consider Conf(4; X ) and label an arbitrary point in it by (x1 , x2 , x3 , x4 ). This configuration space is homeomorphic to X 4 with all diagonals removed. Suppose we allowed x1 to coincide with x2 and x3 to coincide with x4 . This corresponds to adding back in the diagonals x1 = x2 and x3 = x4 . The space described above will be denoted by Conf(2, 2; X ), where this notation means the first pair of points can coincide, the second pair of two points can coincide, but points between different pairs cannot. More generally, we make the following definition. Definition 2.1 Let Conf(n1 , n2 , . . . , nk ; X ) be the partial configuration space of n1 + n2 + · · · + nk points in X, i.e. Conf(n1 , n2 , . . . , nk ; X ) = {(x11 , x21 , . . . , xn11 , x12 , x22 , . . . , xn22 , . . . , x1k , x2k , . . . , xnkk ) ∈X

k

l=1

nl

: xia = xjb when a = b}.

As mentioned in the Introduction, Conf(n1 , n2 , ..., nk ; X ) can be thought of as a complement of a subspace arrangement, a notion familiar from algebraic geometry. A special case of Definition 2.1 is the ordinary configuration space since Conf(1, 1, ..., 1; X ) = Conf(k; X )

(4)

(1 repeats k times). An important feature of configuration spaces is that, when X is a manifold M , the projection map Conf(k; M ) −→ Conf(k − 1; M ) that forgets a point is a fibration [2]. However, this is not true for partial configuration spaces. Consider, for example, the projection

Partial Configuration Spaces as Pullbacks of Diagrams …

7

Conf(2, 1; Rn ) −→ Conf(2; Rn ) (x11 , x21 , x12 ) −→ (x11 , x21 ) The preimage of a point (x11 , x21 ) where the two coordinates coincide is a sphere S n−1 , but if the two coordinates are different, the preimage is the wedge S n−1 ∨ S n−1 . Since the preimages over different points are not homotopy equivalent, the map cannot be a fibration. This basic observation makes partial configuration spaces much harder to study than ordinary configuration spaces.

3 Star Diagrams and Limits 3.1 Star Categories We will assume the reader is familiar with the basics of category theory. Here is the main category we will need. Definition 3.1 Let Star(n) be the category whose objects are elements of n = {0, 1, . . . , n} and whose (non-trivial) morphisms are arrows from j = 0 to 0. Of interest to us are the products of k star diagrams, Star(n1 ) × Star(n2 ) × · · · × Star(nk ), consisting of objects (i1 , i2 , . . . , ik ), where ij ∈ {0, 1, . . . , nj }. The (non-trivial) morphisms are generated by the maps from (i1 , . . . , ij−1 , ij , ij+1 , . . . , ik ) to (i1 , . . . , ij−1 , 0, ij+1 , . . . , ik ), where ij = 0. Example 3.2

Star(n) =

n

1

2

.. .

0

3

6

5

4

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A. Q. H. Li and I. Voli´c

Example 3.3

Star(3) × Star(2) = 3

1

1

0

× 0 2

=

2 (1, 1)

(1, 0)

(1, 2)

(0, 2)

(3, 2)

(0, 0)

(3, 0)

(0, 1)

(3, 1)

(2, 1)

(2, 0)

(2, 2)

Definition 3.4 A small category I is an inverse system if there is a degree function deg : Ob(I) → N such that if m : i → i is a non-identity morphism in I, then deg(i) > deg(i ). This means that the objects of I can be drawn in “levels” according to degree, say from higher to lower degrees, and the non-identity morphisms will then all point downward. Categories Star(n1 ) × Star(n2 ) × · · · × Star(nk ) are inverse systems because they have a degree function where the degree of an object corresponds to the number of nonzero entries in its indexing tuple. The other category that is relevant here provides the building blocks for the products of star categories. Definition 3.5 An n-cube P(n) is the poset of subsets of n = {1, ..., n}, i.e. its objects are subsets of n and non-identity morphisms are inclusions.

Partial Configuration Spaces as Pullbacks of Diagrams …

9

Example 3.6 The 3-cube P(3) can be represented as ∅

{1} {2}

{3}

{1, 2} {1, 3}

{2, 3}

{1, 2, 3}

Category Star(n1 ) × Star(n2 ) × · · · × Star(nk ) can be realized as n1 n2 · · · nk kcubes glued along some faces. For example, Star(3) × Star(2), as pictured in Example 3.3, can be thought of as 3 × 2 = 6 2-cubes (squares) glued along some faces. More examples can be found in Sect. 5.2.

3.2 Limits of Inverse Diagrams One notion that is central for us is that of a diagram. Recall that a category is small if the classes of objects and morphisms are both sets. Let Top be the category of topological spaces. Definition 3.7 A diagram of spaces is a functor from a small category I to Top. By abuse of notation, we often say “diagram” when we mean the image of I. Category I is called the indexing category. We will also speak of the shape of the diagram, and, by abuse of notation, this might refer to either the shape of I or its image. Sometimes our diagrams will have based spaces as their target, and the morphisms are then sent to based maps of spaces. The two most important examples for us are the following. Example 3.8 A star diagram of spaces is a functor S from Star(n) to Top. For example, the functor S : Star(3) −→ Top j −→ Xj

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A. Q. H. Li and I. Voli´c

can be represented as a 3-star X1

X0

X3

X2

Example 3.9 A cube of spaces is a functor C from P(n) to Top. For example, the functor C : P(3) −→ Top S −→ XS can be represented as a 3-cube X1

X∅ X2 X3

X12 X13

X23

X123

(Here we abbreviate subsets S in the subscripts by writing them without braces or commas.) Definition 3.10 The limit, or pullback of  a diagram X : I → Top, i → Xi , denoted by limI X , is the subspace of the product i∈I Xi consisting of tuples (xi ) such that xj and xk are in the same tuple iff there is a morphism f such that f (xj ) = xk . Thus limI Xi is the subspace of the product of all the spaces in the diagram consisting of tuples that are “compatible” with respect to the maps in the diagram. In other words, if two points in a tuple in the limit are mapped to the same space, their images must be the same. This means that the product need not be taken over all the spaces in the diagram but only over the “initial” spaces, namely those that are not the image of any map. For an inverse system such as Star(n1 ) × Star(n2 ) × · · · × Star(nk ), the situation is even more straightforward since such initial spaces can be easily characterized. More precisely, given an inverse system with bounded degree (automatically true for a finite diagram), another degree function d on Ob(I) can be defined by: • All objects that are not codomains for any non-identity morphisms are labelled dˆ = 1.

Partial Configuration Spaces as Pullbacks of Diagrams …

11

• An object x is labelled dˆ = l if l − 1 = max{dˆ (y) : y maps (non-trivially) to x}. • Define the degree d of each object to be n + 1 − dˆ , where n is the largest value of dˆ in the inverse system. Under this degree function, each object of degree l < n has morphisms mapping into it from objects of degree j ∈ {l + 1, . . . , n}. Having an inverse system (with bounded degree) is necessary to define this new degree function because otherwise it is possible the maximum would not exist. Proposition 3.11 The limit of an inverse diagram with bounded degree is homeomorphic to a subset of the product of the objects of highest degree d . Proof The inverse diagram F(I) sends i to Xi . The limit is  L = (x1 , x2 , . . . , xk , . . . , xj−1 , xj , xj+1 , . . . ) ∈



 Xi

i

where if f : Xp → Xq and g : Xr → Xq then f (xp ) = g(xr ) = xq for all p, q, r. Suppose Xj is of degree less than n. Then there is a map h : Xk → Xj where Xk has degree n. We will show that L is homeomorphic to the set L =

⎧ ⎨ ⎩

(x1 , x2 , . . . , xk , . . . , xj−1 , xj+1 , . . . ) ∈

 i=j

⎫ ⎬ Xi

⎭

with the same conditions on maps. This homeomorphism is given by p : L −→ L

(x1 , x2 , . . . , xk , . . . , xj−1 , xj , xj+1 , . . . ) −→ (x1 , x2 , . . . , xk , . . . , xj−1 , xj+1 , . . . ) and r : L −→ L (x1 , x2 , . . . , xk , . . . , xj−1 , xj+1 , . . . ) −→ (x1 , x2 , . . . , xk , . . . , xj−1 , h(xk ), xj+1 , . . . ). Note that p ◦ r is the identity on L, and since h(xk ) = xj , the composition r ◦ p is the identity on L . Thus L ∼ = L . We can continue to remove objects of degree less than n from the product of all Xi and preserve this homeomorphism. Therefore L is homeomorphic to the set ⎧ ⎫ ⎨  ⎬ S = (x1 , x2 , . . . , xk , . . . ) ∈ Xi ⎩ ⎭ d (i)=n

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A. Q. H. Li and I. Voli´c

given by projecting points in L onto the coordinates corresponding to objects of degree n. Example 3.12 Consider the following inverse diagram. X1

X2

X3

f2

f1

f3

X6 f7

f6

X4

X5

f5

X8

X7 f8

X9

In this case the objects of highest degree are X1 , X2 , X3 , X4 , X5 . The limit is  L = (x1 , x2 , x3 , x4 , x5 , x6 , x7 , x8 , x9 ) ∈

9 

 Xi

i=1

where f1 (x1 ) = f2 (x2 ) = x6 , f5 (x4 ) = x7 , f6 (x6 ) = x8 , and f7 (x6 ) = f3 (x3 ) = f8 (x7 ) = x9 . Define p:

9 

Xi −→

i=1

5 

Xi

i=1

(x1 , x2 , x3 , x4 , x5 , x6 , x7 , x8 , x9 ) −→ (x1 , x2 , x3 , x4 , x5 ). Consider the set S = p(L). From any point (x1 , x2 , x3 , x4 , x5 ) ∈ S, we reconstruct the original point in L by defining r:

5 

Xi −→ L

i=1

(x1 , x2 , x3 , x4 , x5 ) −→ (x1 , x2 , x3 , x4 , x5 , f1 (x1 ), f5 (x4 ), f6 (f2 (x2 )), f3 (x3 )). So this is a homeomorphism between S and L.

4 Main Result Consider the functor P : Star(n1 ) × Star(n2 ) × · · · × Star(nk ) −→ Top

(5)

where the k-tuple (i1 , i2 , . . . , ik ) is mapped to the configuration space Conf(l; X ), with X a space and l the number of nonzero entries in (i1 , i2 , . . . , ik ). The morphism

Partial Configuration Spaces as Pullbacks of Diagrams …

13

(i1 , . . . , ij−1 , ij , ij+1 , . . . , ik ) −→ (i1 , . . . , ij−1 , 0, ij+1 , . . . , ik ) is sent to the following map: If (i1 , . . . , ij−1 , ij , ij+1 , . . . , ik ) has l nonzero entries, then suppose ij is the ath nonzero entry. Then take the projection map a : Conf(l; X ) −→ Conf(l − 1; X ) (x1 , . . . , xa−1 , xa , xa+1 , . . . , xl ) −→ (x1 , . . . , xa−1 , xa+1 , . . . , xl ). Our main result is the following: Theorem 4.1 The limit of the diagram P from (5) is homeomorphic to the partial configuration space Conf(n1 , n2 , ..., nk ; X ). To make bookkeeping clearer, we will write P((i1 , i2 , . . . , ik )) = Conf(δi1 , δi2 , . . . , δik ; X )(i1 ,i2 ,...,ik ) , where δij = 0 if ij = 0 and δij = 1 if ij = 0. These configuration spaces are of course really just ordinary configuration spaces since Conf(δi1 , δi2 , . . . , δik ; X ) = Conf(k; X ), where k is the number of δij ’s that are 1 (see (4). Before we provide the proof of Theorem 4.1, we will illustrate it with some examples. Recall that in the partial configuration space Conf(n1 , n2 , . . . , nk ; X ), we have n1 points (in what we will refer to as the first coordinate) which can coincide with one another, n2 points (in the second coordinate) which can coincide with one another, etc., but the points that belong to different coordinates cannot coincide. Example 4.2 Here we show that Conf(3, 2; X ) is the limit of P(Star(3) × Star(2)). Consider the diagram P(Star(3) × Star(2)) in Fig. 1. The subscript on each configuration space refers to the object that maps to it (see Example 3.3). The maps are projection maps, where π1 (x, y) = y and π2 (x, y) = x. To find the limit of this diagram, it suffices by Proposition 3.11 to look at the product of the initial spaces: Conf(1, 1; X )(1,2) × Conf(1, 1; X )(2,2) × Conf(1, 1; X )(3,2) × Conf(1, 1; X )(1,1) × Conf(1, 1; X )(2,1) × Conf(1, 1; X )(3,1) and consider what compatibility restrictions are placed on a point in the limit (which is a subspace of this product). A point in the limit has coordinates ((x, y)(1,2) , (x, y)(2,2) , (x, y)(3,2) , (x, y)(1,1) , (x, y)(2,1) , (x, y)(3,1) ).

14

A. Q. H. Li and I. Voli´c Conf(1, 1; X)(1,1) π2

π1

Conf(1, 0; X)(1,0) π2

π1

Conf(1, 1; X)(1,2) π1

π2

Conf(0, 1; X)(0,2) Conf(1, 0; X)(3,0)

Conf(1, 1; X)(3,2)

π2

π1

π1

Conf(0, 0; X)(0,0) Conf(1, 1; X)(3,1) π2

π1

π1

Conf(0, 1; X)(0,1) π2

π1

π1

Conf(1, 1; X)(2,1) π2

Conf(1, 0; X)(2,0) π2

Conf(1, 1; X)(2,2)

Fig. 1 P (Star(3) × Star(2))

Since Conf(1, 1; X )(1,2) , Conf(1, 1; X )(2,2) , and Conf(1, 1; X )(3,2) all map to Conf(0, 1; X )(0,2) under π1 , we have (y)(1,2) = (y)(2,2) = (y)(3,2) . (We are continuing to write parentheses around single letters since the double subscripts that appear later will be easier to read that way.) Similarly, we have (y)(1,1) = (y)(2,1) = (y)(3,1) , (x)(1,2) = (x)(1,1) , (x)(2,2) = (x)(2,1) and (x)(3,2) = (x)(3,1) . Thus a point in the limit can be written as ((x)(1,2) , (x)(2,2) , (x)(3,2) , (y)(1,2) , (y)(1,1) ). Notice that each of the (x)(i,j) came from different configuration spaces, so they are free to coincide. Similarly, each of the (y)(i,j) came from different configuration spaces, so they are free to coincide. However, we know that (x)(i,j) = (y)(i ,j ) for any i, j, i , j . This is because (x)(i,j) = (x)(i,j ) = (y)(i,j ) = (y)(i ,j ) .

(both come from Conf(1, 1; X )(i,j ) )

Since we have a set of three coordinates that can coincide with one another, a set of two coordinates which can coincide with one another, but coordinates in different sets cannot coincide, this limit is homeomorphic to Conf(3, 2; X ). Example 4.3 In this example, we determine the limit of P(Star(n1 ) × Star(n2 ) × Star(n3 )). We need only consider the product of copies of Conf(1, 1, 1; X )(i1 ,i2 ,i3 ) where i1 , i2 , i3 are all nonzero (Proposition 3.11).

Partial Configuration Spaces as Pullbacks of Diagrams …

15

Consider the following subdiagram of P(Star(n1 ) × Star(n2 ) × Star(n3 )): Conf(1, 1, 1; X )(1,2,1)

Conf(1, 1, 1; X )(1,1,1) p3

p3

Conf(1, 1, 0; X )(1,1,i3 )

Conf(1, 1, 0; X )(1,2,i3 ) p2

p1

Conf(0, 1, 0; X )(i1 ,1,i3 )

p2

Conf(1, 0, 0; X )(1,i2 ,i3 )

p1

Conf(0, 1, 0; X )(i1 ,2,i3 )

Points map through the diagram as follows: (x1 , x2 , x3 )(1,1,1)

(x1 , x2 , x3 )(1,2,1)

p3

p3

(x1 , x2 )(1,1,i3 ) p1

(x)2 (i1 ,1,i3 )

(x1 , x2 )(1,2,i3 ) p2

p2

(x)1 (1,i2 ,i3 )

p1

(x)2 (i1 ,2,i3 )

For instance, we have that (x1 )(1,i2 ,i3 ) must be equal for all nonzero i2 , i3 . This is true for any fixed i1 . By symmetry, for every fixed i2 , we have that (x2 )(i1 ,i2 ,i3 ) are equal for varying nonzero i1 and i3 , and for every fixed i3 , we have that (x3 )(i1 ,i2 ,i3 ) are equal for varying nonzero i1 and i2 . All coordinates (x1 ) which are labelled with (1, i2 , i3 ) are mapped to (x1 )1 . Similarly, for a fixed i1 , all entries (x1 )(i1 ,i2 ,i3 ) are mapped to (x1 )i1 . For a fixed i2 , any coordinate (x2 )(i1 ,i2 ,i3 ) is mapped to (x2 )i2 . For a fixed i3 , all entries (x3 )(i1 ,i2 ,i3 ) are mapped to (x3 )i3 . This map is a homeomorphism from the limit to the set L = {((x1 )1 , (x1 )2 , . . . , (x1 )n1 , (x2 )1 , (x2 )2 , . . . , (x2 )n2 , (x3 )1 , (x3 )2 , . . . , (x3 )n3 )}. The map from L back to the limit is given by inserting (x1 )1 into the entries (x1 )1,i2 ,i3 , for all i2 , i3 , inserting (x2 )1 into the entries (x2 )i1 ,1,i3 , for all i1 , i3 , and so on. Note that each (x1 )i1 in L comes from a different configuration space. Thus any (x1 )i1 is free to coincide with (x1 )i1 . This is true for the sets of (x2 )i2 and (x3 )i3 respectively. However, (x1 )i1 cannot coincide with (x2 )i2 for any i1 , i2 for the following reason: (x1 )(i1 ) = (x1 )(i1 ,i2 ,i3 )  = (x2 )(i1 ,i2 ,i3 ) = (x2 )(i2 ) .

(the two points come from (x1 , x2 , x3 )(i1 ,i2 ,i3 ) ∈ Conf(1, 1, 1; X )i1 ,i2 ,i3 )

The same argument holds for any pair in {(x1 )i1 , (x2 )i2 , (x3 )i3 }. Since elements in {(x1 )i1 } can coincide with each other, elements in {(x2 )i2 } can coincide with each other, elements in {(x3 )i3 } can coincide with each other, but elements in different coordinates must be different, we see that the limit is homeomorphic to Conf(n1 , n2 , n3 ; X ).

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A. Q. H. Li and I. Voli´c

Proof of Theorem 4.1 To determine the limit of P(Star(n1 ) × Star(n2 ) × · · · × Star(nk )), it suffices by Proposition 3.11 to look at the product of the initial spaces. Consider the following subdiagram: Conf(1, 1, . . . , 1; X)(i1 ,i2 ,...,ik )

pk

Conf(1, 1, . . . , 0; X)(i1 ,i2 ,...,ik )

pk−1

···

p2

Conf(1, 0, . . . , 0; X)(i1 ,i2 ,...,ik ) p2

.. . pk−1

Conf(1, 1, . . . , 0; X)(i1 ,i2 ,...,ik ) pk

Conf(1, 1, . . . , 1; X)(i1 ,i2 ,...,ik )

The limit is a subset of the product of Conf(1, 1, . . . , 1; X )(i1 ,i2 ,...,ik ) where the i1 , i2 , . . . , ik are nonzero. For a fixed i1 , we have (x1 )(i1 ,i2 ,...,ik ) = (x1 )(i1 ,i2 ,...,ik ) in the limit. Similarly, for a fixed ij , we have that (xj )(i1 ,i2 ,...,ij ,...,ik ) = (xj )(i1 ,i2 ,...,ij ,...,ik ) . Analogously to Example 4.3, this means that, for each coordinate (xj ), we have nj points which are free to coincide. However, when j = l, we have that (xj )(i1 ,...,ij ,...,il ,...,ik ) = (xj )(i1 ,...,ij ,...il ,...,ik ) = (xl )(i1 ,...,ij ,...il ,...,ik ) = (xl )(i1 ,...,ij ,...il ,...,ik ) . So we have a set of n1 + n2 + · · · + nk points where the first n1 points are free to coincide, the second n2 points are free to coincide, etc., but points in different coordinates cannot coincide. Therefore the limit is homeomorphic to Conf(n1 , n2 , . . . , nk ; X ).

5 Homotopy Limits of Products of Star Diagrams As we have shown, partial configuration spaces are limits of ordinary configuration spaces, but limits are not homotopy invariant. That is to say, if we were to change the spaces in a diagram to homotopy equivalent spaces, the limit of the diagram could change. It would thus be more useful if we could show that partial configuration spaces are homotopy limits of ordinary configuration spaces, but this appears to be significantly harder to prove. In this section, we will provide a few examples where the limit is indeed the homotopy limit and then outline the beginnings of a strategy for proving this in general.

Partial Configuration Spaces as Pullbacks of Diagrams …

17

5.1 Homotopy Limits It would take us too far afield to define the homotopy limit holimI X of a diagram X : I → Top precisely. Suffice it to say that this is a “fattened up” version of limI X that consists of compatible points up to coherent homotopies, and these homotopies are part of the data. Details and examples can be found in [11, Chap. 8]. The “fattening up” gives the homotopy limit its homotopy invariance (see [11, Theorem 8.3.1]). In fact, for our purposes, it will be enough to know the definition of the homotopy limit of a particularly simple diagram. Definition 5.1 For a diagram f

g

X −→ Z ←− Y of spaces, the homotopy limit (or homotopy pullback) is f

g

holim(X → Z ← Y ) = {(x, α, y) : α(0) = f (x), α(1) = g(y)} ⊂ X × Map(I , Z) × Y .

(6) While the limit is the set of points in X and Y that agree on the nose in Z, homotopy limit is a fattened up version of this in the sense that the images of the points in M and Y do not necessarily agree, but paths between those images are also kept track of. For more on homotopy limits of diagrams of this shape, see [11, Sect. 3.2]. There is a canonical map a : lim X −→ holim X I

I

(7)

given by regarding the on-the-nose compatibility of the points in the limit as being constant homotopies in the homotopy limit (see [11, Eq. (8.2.1)]). Under favorable circumstances, this map is a (weak) equivalence, and the limit is hence homotopy invariant. One situation when this occurs is when I has an initial object, namely an object that has a unique morphism to all other objects. Proposition 5.2 Suppose I is a small category with initial object i0 and F : I → Top is a functor. Then lim F ∼ = F(i0 ) and holim F  F(i0 ). I

I

The limit statement in the above is immediate from the definition. For the proof of the homotopy limit statement, see, for example, [11, Proposition 9.3.4]. Another familiar situation when (7) is an equivalence is when the category I is a Reedy category and the diagram indexed on it is fibrant. Reedy categories have a notion of degree on them (see [6, Definition 15.1.2] or [11, Definition 8.4.4]). Our indexing categories, namely products of categories Star(n), are readily seen to be Reedy. Indeed, one easily identifies Star(n) as a Reedy category and products of Reedy categories are Reedy [6, Proposition 15.1.6].

18

A. Q. H. Li and I. Voli´c

Fibrancy means that the natural map from each space to the limit of everything it maps to is a fibration (see, for example, [6, Sects. 15.10 and 19.9] or [11, Sect. 8.4]). Diagrams of configuration spaces of points in a manifold that are indexed on Star(n) turn out to be fibrant. Namely, consider the following diagram indexed on Star(n) (see Example 3.2) where k ≥ 1: Conf(k; M ) S = Conf(k; M )

Conf(k − 1; M )

Conf(k; M )

(8)

··· The maps are projections that forget some point (it does not have to be the same point). Proposition 5.3 The diagram S is fibrant, and hence lim S −→ holim S. I

I

Proof For a diagram of this shape, the fibrancy condition reduces to observing that all the maps are fibrations, which projections of configuration spaces in manifolds are [2]. However, our diagrams P indexed on products of categories Star(−) are not fibrant. For example, in P(Star(n1 ) × Star(n2 )), we have squares Conf(2; M )

Conf(1; M )

Conf(1; M )

Conf(0; M )  

where the maps from Conf(2; M ) are projections to the two points. The limit of Conf(1; M )

Conf(1; M )

Conf(0; M )  

is Conf(1; M ) × Conf(1; M ). However, the map Conf(2; M ) −→ Conf(1; M ) × Conf(1; M ),

(9)

Partial Configuration Spaces as Pullbacks of Diagrams …

19

which is an inclusion (Conf(2; M ) is Conf(1; M ) × Conf(1; M ) with the diagonal removed), is not a fibration. Fibrancy is a sufficient, but not a necessary condition for the limit to be equivalent to the homotopy limit. Indeed, in the square (9), limit and the homotopy limit are equivalent (and are equivalent to Conf(2; M ); see Proposition 5.2). We therefore cannot rely on fibrancy to establish the equivalence of the limit and homotopy limit of P. We record one more useful result. Namely, a diagram F : I × J → Top can be regarded as a diagram of diagrams in two ways – as an I-diagram of J diagrams and vice versa. In other words, we can fix a j ∈ J or an i ∈ I to get diagrams F(I × j) or F(i × J ), and then let j or i vary to get diagrams of those diagrams. We can also take the limit or the homotopy limit for each j ∈ J or i ∈ I, and then take the limit or the homotopy limit of the resulting diagrams of (homotopy) limits. The following says that the way in which we do this does not matter. Proposition 5.4 For I and J small categories and a diagram F : I × J → Top, there are canonical homeomorphisms lim F ∼ = lim lim F ∼ = lim lim F

I×J

and

I

J

J

I

holim F ∼ = holim holim F ∼ = holim holim F I×J

I

J

J

I

For proofs of these statements, see [11, Theorem 7.5.3 and Proposition 8.5.5]. These results of course extend to diagrams indexed over arbitrary finite products of small categories. Unfortunately, it is not in general true that limits and homotopy limits commute; this is a consequence of the fact that limits are not homotopy invariant and are not in general equivalent to homotopy limits.

5.2 Examples Here are a few simple examples where the limit and the homotopy limit of P(Star(n1 ) × Star(n2 ) × · · · × Star(nk )) agree. Example 5.5 We can recover the usual configuration space of points in X as follows. Consider 1 1 1 Star(1)k =

× 0

× ··· × 0

0

20

A. Q. H. Li and I. Voli´c

This category can be pictured as a k-cubical diagram. For example, when k = 3, we get (1, 1, 1) (1, 1, 0) Star(1)3 =

(1, 0, 1) (0, 1, 1)

(1, 0, 0) (0, 1, 0)

(0, 0, 1)

(0, 0, 0)

Then Conf(3; X )

π3

Conf(2; X )

π2

Conf(2; X )

π1

P= Conf(2; X )

π2 π1

π1

π2

π2

Conf(1; X )

π1

(10)

Conf(1; X ) Conf(0; X ) ∼ =

Conf(1; X )

Here πi means the projection that forgets the ith configuration point. Since Conf(3; X ) is the initial space in the cube P, it is the limit and the homotopy limit of this diagram by Proposition 5.2. The same argument holds for Star(1)k instead of Star(1)3 . Hence holimP  Conf(k; X ) = Conf(1, 1, ..., 1; X ). Star(1)k

Example 5.6 This example illustrates the notion that products of star diagrams are obtained by gluing cubical diagrams. Namely, take (1, 1, 1) (1, 0, 1)

1 1

Star(2) × Star(1) = 0 ×

1

×

2

0 2

(1, 1, 0)

=

(0, 1, 1)

(1, 0, 0) (0, 1, 0)

(0, 0, 1)

0

(0, 0, 0) (2, 1, 0)

(2, 1, 1) (2, 0, 1)

This indeed looks like two 3-cubes glued along a face. Then

(2, 0, 0)

Partial Configuration Spaces as Pullbacks of Diagrams … π3

Conf(3; X )

P=

Conf(2; X )

π2

Conf(2; X )

π1

π2

Conf(2; X )

π1

π1

π3

Conf(3; X )

π2

π1

π2

π2

Conf(1; X )

π1

Conf(1; X ) π1

Conf(1; X )

π1

21

Conf(0; X ) ∼ =

Conf(2; X )

π2

π2

Conf(2; X )

(11)

Conf(1; X )

We can easily verify Theorem 4.1 in this case: The limit is the subspace of Conf(3; X ) × Conf(3, X ) (product of two initial spaces) consisting of tuples (x1 , y1 , z1 , x2 , y2 , z2 ) such that (x1 , y1 ) = (x2 , y2 ). A point in the limit can thus be represented by (x, y, z1 , z2 ), where x and y cannot equal z1 or z2 nor each other, but z1 and z2 can. But this gives a point in Conf(2, 1, 1; X ). Hence lim

Star(2)×Star(1)2

P∼ = Conf(2, 1, 1; X ).

When X is a manifold, this is also the homotopy limit, as will be explained in Example 5.7 where a more general example is treated. The gluing of cubes has a geometric interpretation since the limit can be thought of as two copies of Conf(3; X ) glued along Conf(2; X ) via projections onto the first two points. There are also natural projection maps Conf(2, 1, 1; X ) −→ Conf(2, 1; X ) Conf(2, 1, 1; X ) −→ Conf(1, 1, 1; X ) = Conf(3; X ) These can be realized in the diagram as maps to the limits of subdiagrams obtained by restricting the category Star(2) × Star(1)2 to various subcategories. For example, restricting to 1 1 1 1 0 1 × 0

× 0

×

and 0

2

× 0

0

gives the two 3-cubes whose limits are their initial spaces, namely the two copies of Conf(3; X ). The maps from the limit of the entire diagram to these limits of two subdiagrams are precisely the two projections Conf(2, 1, 1; X ) −→ Conf(3; X )

22

A. Q. H. Li and I. Voli´c

where one of the first two points is forgetten. Example 5.7 Now let X = M be a manifold and consider 1 1 Star(m) × Star(1) = m k

2 ×

0

1 × ··· ×

0

0

··· Then by Proposition 5.4, lim

Star(m)×Star(1)k

P∼ = lim

lim P.

Star(m) Star(1)k

But, from Example 5.5, this is equivalent to lim holim P.

Star(m) Star(1)k

Since the homotopy limit over Star(1)k is Conf(k; M ), we thus have that ⎛ ⎜ ⎜ ⎜ ⎜ ∼ P = lim ⎜ lim ⎜ Conf(k; M ) Star(m)×Star(1)k ⎜ ⎜ ⎝

Conf(k; M )

Conf(k − 1; M )

⎞ ⎟ ⎟ ⎟ ⎟ Conf(k; M ) ⎟ ⎟ ⎟ ⎟ ⎠

··· The projection maps all forget the same point, and the limit is readily seen to be Conf(m, 1, ..., 1; M ) (we also know this from Theorem 4.1). But this diagram is fibrant because of Proposition 5.3. Thus the limit is equivalent to the homotopy limit and we finally have holim

Star(m)×Star(1)k

P  Conf(m, 1, ..., 1; M )

(where 1 repeats k times). Example 5.6 is of course a special case of this as long as we set X to be a manifold in that example.

Partial Configuration Spaces as Pullbacks of Diagrams …

23

5.3 Cohomology of the Products of Star Diagrams One strategy of showing that limits of products of star diagrams P(Star(n1 ) × Star(n2 ) × · · · × Star(nk )) are equivalent to their homotopy limits would be to compare the following: 1. Compute the cohomology groups for the partial configuration spaces; 2. Apply the cohomology functor to P and compute the colimit of the resulting diagram (in the category of chain complexes). The hope is that the cohomology groups in (1) and the colimits in (2) are isomorphic. But since we know that the limits of the diagrams P are partial configuration spaces, this would give evidence that the limits we computed are homotopy equivalent to the homotopy limits. In the next two subsections we give an initial indication of how (1) and (2) might be computed in the case X = Rn .

5.3.1

Cohomology of Partial Configuration Spaces

We provide a simple example of a computation of a cohomology group of a partial configuration space in Rn . To do this, we will use the Goresky-MacPherson result (Theorem 5.11) that describes the cohomology of complements of subspace arrangements in Rn . The idea is to illustrate how this machinery might be useful in computing the cohomology of arbitrary partial configuration spaces (we have not seen any such explicit computations in the literature). Definition 5.8 An affine subspace arrangement A = {A1 , . . . , Al } ⊆ Rn is a collection of affine proper subspaces of Rn . Such an arrangement is central if all the Ai are linear subspaces. Consider the subspace arrangement A = {Ai : Ai is a 2-diagonal} ⊆ (Rn )k (a 2diagonal is the subset obtained by setting two of the coordinates equal to each other). It is clear that this arrangement is central. Let VA =

l 

Ai

i=1

and MA = (Rn )k \ VA . Then MA = Conf(k, Rn ). To express a partial configuration space as a complement, we set A to be some, but not all 2-diagonals in the ambient space (see Example 5.13).

24

A. Q. H. Li and I. Voli´c

Definition 5.9 Given an affine arrangement A in Rn , the intersection semilattice LA is the collection of all non-empty intersections Ai1 ∩ · · · ∩ Aij where 1 ≤ i1 < · · · < ij ≤ t ordered by reverse inclusion, i.e. x ≤ y if and only if y ⊆ x. The partial order on LA allows us to define the open interval (x, y) = {z ∈ LA : x < z < y} in LA . Definition 5.10 The ordered complex ((x, y)), denoted by (x, y), is the simplicial complex whose vertices are z ∈ (x, y) and p-simplices are the chains x0 < · · · < xp in (x, y). i (x, y) for the ith reduced simplicial homology group of (x, y) with integer Write H  i (x, y) for the ith reduced cohomology group. The following result coefficients, and H by Goresky and MacPherson [3] relates the cohomologies of the complement MA to the homologies of the elements in the lattice. Theorem 5.11 For every affine arrangement A in Rn , we have that  i (MA ) ∼ H =



ˆ x) codim(x)−2−i (0, H

x∈LA ; x>0ˆ

where 0ˆ = Rn . Note that 0ˆ is the bottom element of the lattice LA since it contains all the subspaces, and for a central arrangement we have a top element 1ˆ which is the origin. The original proof of Theorem 5.11 by Goresky and MacPherson can be found in [3], and an elementary proof by Ziegler and Živaljevi´c can be found in [13]. Example 5.12 Here is a warmup calculation involving an ordinary configuration space of two points. Figure 2 shows the subspace lattice for Conf(2; Rn ). Its subspace arrangement is the diagonal x1 = x2 in (Rn )2 , represented by {12} in the lattice. Then 0ˆ is (Rn )2 and 1ˆ is the origin in (Rn )2 . The codimension of an element x in the lattice for Conf(k, Rn ) is n(k − c(x)) where c(x) is the number of components of the partition defining the element. In this case, A is the partition {12}, referring to x1 = x2 , and there are 2 coordinates total,

ˆ1 {12} ˆ0 Fig. 2 Intersection lattice for Conf(2, Rn )

Partial Configuration Spaces as Pullbacks of Diagrams …

25

so codim(A) = n(2 − 1) = n. The codimension of 1ˆ = 0 is 2n. By Theorem 5.11, we have that n−2−i (0, ˆ {12}) ⊕ H 2n−2−i (0, ˆ 1). ˆ  i (Conf(2; Rn )) = H H ˆ {12}) = ∅ and (0, ˆ 1) ˆ as a single point. By convention, the only nonWe view (0, trivial reduced homologies of ∅ is Z in degree −1. There are no nontrivial reduced homologies for a point. Thus we have that n−2 (0, ˆ A) ⊕ H 2n−2 (0, ˆ 1) ˆ  0 (Conf(2; Rn )) = H H 2n−2 (∗) n−2 (∅) ⊕ H =H  Z n=1 = 0 n>1

 n−1 (Conf(2; Rn )) = H −1 (0, ˆ A) ⊕ H n−1 (0, ˆ 1) ˆ H n−1 (∗) −1 (∅) ⊕ H =H = Z. Example 5.13 Figure 3 shows the subspace lattice for Conf(2, 2; Rn ). Each node is labeled by the partition which defines the diagonal which is removed from (Rn )4 to construct the configuration space. For example, {13}{2}{4} refers to the diagonal x1 = x3 , where x2 , x4 are free. This partition has 3 components and there are 4 coordinates used to define a point in Conf(2, 2; Rn ), so its codimension is n(4 − 3) = n. The cohomology groups are given by  i (Conf(2, 2; Rn )) ∼ H =



n−2−i (∅)⊕ H

4 times



2n−2−i (2 points) ⊕ H 3n−2−i (0, ˆ {1234}) ⊕ H 4n−2−i (0, ˆ 1). ˆ H

6 times

ˆ {1234}) and (0, ˆ 1) ˆ are harder to compute. However, The homology groups for (0, we can compute the cohomologies in degree 0 and n − 1, since for n > 1 we have ˆ {1234}) 3n − 2, 2n − 1 > 1 and 4n − 2, 3n − 1 > 2, so the homology groups for (0, ˆ 1) ˆ are trivial in those degrees. We have and (0,  0 (Conf(2, 2; Rn )) ∼ H =

 4 times

n−2 (∅) ⊕ H



2n−2 (2 points) ⊕ H 3n−2 (0, ˆ {1234}) ⊕ H 4n−2 (0, ˆ 1) ˆ H

6 times

= 0,

which corresponds to the fact that Conf(2, 2; Rn ) is path connected, so its (unreduced) cohomology in degree 0 is Z. Then we have

26

A. Q. H. Li and I. Voli´c ˆ1 {1234}

{123}{4}

{134}{2}

{124}{3}

{13}{2}{4}

{14}{2}{3}

{234}{1}

{13}{24}

{23}{1}{4}

{14}{23}

{24}{1}{3}

ˆ0

Fig. 3 Intersection lattice for Conf(2, 2, Rn ) 

 n−1 (Conf(2, 2; Rn )) ∼ H =

−1 (∅) ⊕ H

4 times = Z4 .



n−1 (2 points) ⊕ H 2n−1 (0, ˆ {1234}) ⊕ H 3n−1 (0, ˆ 1) ˆ H

6 times

Example 5.14 Figure 4 shows the subspace lattice for Conf(3, 2; Rn ). A point in Conf(3, 2; Rn ) looks like (x1 , x2 , x3 , x4 , x5 ), where x1 , x2 , x3 cannot coincide with x4 or x5 . Thus our subspace arrangement consists of the diagonals in (Rn )5 where x1 = x4 , x1 = x5 , x2 = x4 , x2 = x5 , x3 = x4 , x3 = x5 . These are represented by the ˆ We label these nodes A. nodes in the first level above 0. The rest of the nodes in the intersection lattice represent thinner diagonals which contain these 2-diagonals. The second level of nodes above 0ˆ (label them B) represent 3-diagonals of the form {abc}{d }{e} . Note that the 3-diagonal {123} is missing (there are 9 nodes rather than 10) in the lattice, because x1 = x2 = x3 is allowed in Conf(3, 2; Rn ). The third level of nodes above 0ˆ (label them C) represent 2-diagonals of the form {ab}{cd }{e} (which have the same codimension as nodes on the second level). The fourth level (label them D) is 4-diagonals of the form {abcd }{e}, and the fifth level (label it E) is the thin 5-diagonal. Thus the cohomologies are given by  i (Conf(3, 2; Rn )) ∼ H =

 6 times

⊕



ˆ A) ⊕ n−2−i (0, H

 9 times

ˆ B) ⊕ 2n−2−i (0, H



ˆ C) 2n−2−i (0, H

5 times

ˆ D) ⊕ H 4n−2−i (0, ˆ E) ⊕ H 5n−2−i (0, ˆ 1). ˆ 3n−2−i (0, H

5 times

ˆ D), (0, ˆ E), and (0, ˆ 1) ˆ are harder to compute. But Again, the homology groups for (0, the cohomology for Conf(2, 2; Rn ) in degree 0 is Z, because all of the homologies in the equation above are trivial for i = 0. The cohomology in degree n − 1 for n > 1 is given by:

Partial Configuration Spaces as Pullbacks of Diagrams …

27

ˆ1 •◦ •◦

•◦

•◦

◦•

◦ •

•

•

◦•

◦•

•

•◦

◦•

•◦

•

•

◦•

•◦

◦•

•

◦•

•◦

•

•

•

•

ˆ0

Fig. 4 Intersection lattice for Conf(3, 2, Rn ). We omit labels on nodes for clarity

 n−1 (Conf(3, 2; Rn )) ∼ H =



−1 (∅) ⊕ H

6 times

⊕





n−1 (2 points) ⊕ H

9 times



n−1 (2 points) H

5 times

ˆ D) ⊕ H 3n−1 (0, ˆ E) ⊕ H 4n−1 (0, ˆ 1) ˆ 2n−1 (0, H

5 times

= Z6 .

 n−1 (Conf(n1 , n2 , . . . , nk ; Rn )) It is not hard to see that, in general, the rank of H is n1 · n2 . . . nk .

5.3.2

Colimits of Products of Star Diagrams of Cohomology Groups

In this section we will provide some easy computations of the colimit of products of star diagrams of cohomology groups in lower degrees for the partial configuration spaces discussed in the previous section. To tackle the general case, one could work with the cohomology (or homotopy) spectral sequence for the products of star diagrams of configuration spaces P(Star(n1 ) × Star(n2 ) × · · · × Star(nk )). The spectral sequences are easy to set up since, as discussed in Sect. 3, these diagrams are inverse diagrams. The cosimplicial model for the diagrams, which would in turn give rise to the spectral sequence has, in degree zero, the space  n1 n2 ···nk

Conf(n1 + n2 + · + nk ; X ).

28

A. Q. H. Li and I. Voli´c

The two cofaces are made from projection onto one fewer point. In the next degree, there is the product of configuration spaces with one fewer points, with cofaces again coming from projections, etc. Since this would be a finite cosimplicial space (as diagram is finite), the cohomology spectral sequences associated to it would converge to its totalization. Furthermore, since configuration spaces are rationally formal, it is likely that these spectral sequences would in fact collapse at E 2 rationally. For our examples, we will apply the cohomology functor to a couple of diagrams of configuration spaces and compute the colimit. As is well-known, the nontrivial cohomology groups of Conf(2; Rn ) (also denoted by Conf(1, 1; Rn )) are Z in degrees 0 and n − 1. The nontrivial cohomology for Conf(1; Rn ) ∼ = Rn is Z in degree 0. Since n Conf(0; R ) is a point, it has cohomology Z in degree 0. Also recall that, given abelian groups A, B, C, the colimit (or pushout) of the diagram g

A

C

f

B is the disjoint union B ⊕ C with f (a), g(a) identified for all a ∈ A. Example 5.15 The diagram whose limit is Conf(2, 2; Rn ) is given in Fig. 5. Applying the cohomology functor, we in degree zero get a copy of Z everywhere in the diagram, and the maps are isomorphisms. To find the colimit, we can proceed iteratively: First take the colimit of each of the rows Z

Z

Z

which is Z ⊕ Z. But the generators are identified, so this is isomorphic to Z. We can thus replace the rows of Z’s by single Z’s to get Z Z Z Conf(1, 1; Rn )(1,1)

π2

π1

Conf(0, 1; Rn )(0,1)

Fig. 5 P (Star(2) × Star(2))

π2

Conf(0, 0; Rn )(0,0)

π2

π1 π2

Conf(1, 0; Rn )(2,0)

Conf(1, 1; Rn )(1,2) π1

π1 π2

π1

Conf(1, 1; Rn )(2,1)

Conf(1, 0; Rn )(1,0)

Conf(0, 1; Rn )(0,2) π1

π2

Conf(1, 1; Rn )(2,2)

Partial Configuration Spaces as Pullbacks of Diagrams …

29

Z

0

Z

0

0

0

Z

0

Z

Fig. 6 H n−1 (P (Star(2) × Star(2)))

The colimit of this is again Z. For cohomology groups in degree n − 1, we get the diagram in Fig. 6. To find the colimit, we first take the colimit of the subdiagrams Z

Z and 0

0

0

0

which are Z2 and 0, respectively. Then we replace the subdiagrams in Fig. 6 to get Z2 0 Z2 whose colimit is Z4 . This agrees with the result in Example 5.13. Example 5.16 The diagram of cohomology groups for Conf(3, 2; Rn ) in degree 0 is given in Fig. 7. To find the colimit, first take the colimit of the subdiagram Z Z Z

Z

which is Z ⊕ Z ⊕ Z, with the generators in each Z identified. Then we take the colimit of Z ← Z → Z which is Z as in the previous example. The diagram of cohomology groups for Conf(3, 2; Rn ) in degree n − 1 is given in Fig. 8. The colimit of the diagram in that figure can be found by first taking the colimit of the subdiagrams

30

A. Q. H. Li and I. Voli´c

Z

0 and

0 Z

Z

0 0

0

which are Z3 and 0 respectively, and then taking the colimit of Z3

0

Z3

which is Z6 . This agrees with the result in Example 5.14. Acknowledgements The authors would like to thank Franjo Šarˇcevi´c for suggestions and corrections. The second author would like to thank the Simons Foundation for its support.

Z Z Z Z Z

Z Z

Z Z

Z

Z

Z

Fig. 7 H 0 (P (Star(3) × Star(2)))

Z 0 Z 0 Z

0 0 Z

Fig. 8 H n−1 (P (Star(3) × Star(2)))

0 Z 0

Z

Partial Configuration Spaces as Pullbacks of Diagrams …

31

References 1. Cohen, F.R.: Introduction to Configuration Spaces and Their Applications. Available at https:// www.mimuw.edu.pl/~sjack/prosem/Cohen_Singapore.final.24.december.2008.pdf 2. Fadell, E., Neuwirth, L.: Configuration spaces. Math. Scand. 10, 111–118 (1962) 3. Goresky, M., MacPherson, R.: Stratified Morse theory. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) (Results in Mathematics and Related Areas (3)) 14. Springer, Berlin (1988) 4. Goodwillie, T.G., Munson, B.A.: A stable range description of the space of link maps. Algebr. Geom. Topol. 10, 1305–1315 (2010) 5. Goodwillie, T.G., Weiss, M.: Embeddings from the point of view of immersion theory II. Geom. Topol. 3, 103–118 (electronic) (1999) 6. Hirschhorn, P.S.: Model categories and their localizations. In: Mathematical Surveys and Monographs, vol. 99. American Mathematical Society, Providence, RI (2003) 7. Koschorke, U.: A generalization of Milnor’s μ-invariants to higher-dimensional link maps. Topology 36(2), 301–324 (1997) 8. Klein, J., Williams, B.: Homotopical intersection theory, iii: Multirelative intersection problems. arXiv:1212.4420 (2012) 9. Munson, B.A.: A manifold calculus approach to link maps and the linking number. Algebr. Geom. Topol. 8(4), 2323–2353 (2008) 10. Munson, B.A., Voli´c, I.: Cosimplicial models for spaces of links. J. Homotopy Relat. Struct. 9(2), 419–454 (2014) 11. Munson, B.A., Voli´c, I.: Cubical homotopy theory. New Mathematical Monographs, Vol. 25. Cambridge University Press, Cambridge (2015) 12. Weiss, M.: Embeddings from the point of view of immersion theory I. Geom. Topol. 3, 67–101 (electronic) (1999) 13. Ziegler, G.M., Živaljevi´c, R.T.: Homotopy types of subspace arrangements via diagrams of spaces. Math. Ann. 295(3), 527–548 (1993)

Power Systems

Smart Sarajevo—Analysis of Smart Home System Emir Šalji´c and Samir Avdakovi´c

Abstract In addition to being designed to raise the quality of life to a higher level, smart homes are also designed to monitor real-time electricity consumption and optimally operate to reduce electricity bills. This paper presents how electric vehicles can be integrated into smart home energy management both in the form of a consumer and in the form of a storage system. Modeling and analysis of the smart home system based on the mixed integer linear programming (MILP) allows electrical vehicle charging and discharging processes to be sophisticatedly controlled, while meeting domestic electricity demand with additional focus on the fluctuating supply of decentralized energy sources such as photovoltaic panels. At the same time, the charging of the electric car is guaranteed to the level that is predetermined by the user himself. The selected location for the smart home is in Sarajevo, Bosnia and Herzegovina. This smart home system includes a photovoltaic power plant, an electric vehicle and a battery. Real data for the consumption of households in the city of Sarajevo were used for analyzes. Bosnia and Herzegovina is a medium-developed country with a relatively low economic standard. However, the results of the analysis show that despite the relatively unfavorable economic environment and low standard, the implementation of smart home system would pay off over a period of about 11 years. Keywords Smart home · Vehicle-to-Grid technology · Battery · PV system · Resource optimization · MILP

1 Introduction The development of advanced technologies in the field of electricity production, electric vehicles, energy storage systems, information and communication technologies, etc., in recent years has made the basis for the development of smart systems. We E. Šalji´c (B) · S. Avdakovi´c Faculty of Electrical Engineering, University of Sarajevo, Sarajevo, Bosnia and Herzegovina e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. Avdakovi´c et al. (eds.), Advanced Technologies, Systems, and Applications V, Lecture Notes in Networks and Systems 142, https://doi.org/10.1007/978-3-030-54765-3_2

35

36

E. Šalji´c and S. Avdakovi´c

can look at smart systems at the level of cities, parts of networks, or increasingly smart homes today. Smart homes should be designed to raise the quality of life to a higher standard while monitoring real-time electricity consumption and operating optimally to reduce electricity costs. The smart home system today should have its own PV production, electric car, and electricity storage system that would “correct” the difference in production and consumption. Mathematically described smart home resources are presented in the work [1]. Techno-economic feasibility of the construction of photovoltaic powerplant at the selected location is displayed in the work [2]. In addition to the infrastructure that would underpin smart homes, they also need appropriate optimization models or control units that would be integrated into the whole system. There is a lot of literature for optimized home energy management approaches, which can generally be classified as mixed integer linearprogramming (MILP) [3], prediction model [4], dynamic programming (DP) [5], stochastic dynamic programming (SDP) [6] etc. The optimal operation of a smart home with PV system, home battery and electric vehicle with V2G technology is discussed through solving the MILP model in [7]. The optimal arrangement of household appliances was developed in [8] together with a strategy based on power limitation, where the model was developed using MILP. The MILP model of the smart home management system (SHEMS), as well as the predicted neural network (ANN) housing load with additional wavelet transformation (WT), are described in [9] for different price signals. Taking into account the housing load, the size of the PV and energy storage systems, a model was created within MILP in [10]. It is clear that MILP modeling has been widely adopted both to create effective load scheduling strategies for SHEMS and to determine the optimal size of individual resources. However, several studies have simultaneously analyzed the optimal resource dimensions and their optimal use strategy using MILP modeling in [11], an optimization strategy was developed for the efficient operation of household load according to dynamic tariff models. In addition, connecting the EV to a home network can be useful for cutting peaks during critical periods, which is also shown in [12]. A research paper [13] demonstrates the possibility of scheduling devices in a smart home taking into account dynamic electricity prices and plans for the use of electrical devices. The model in [7] considers the price of electricity and the maximum power allowed by the grid, but neglects the possibility of a two-way flow of energy from the resource with the grid, which can be of great financial benefit. Modeling and analysis of smart home system based on the mixed integer linear programming (MILP) are presented in this paper. The selected location for the smart home is in Sarajevo, Bosnia and Herzegovina. This smart home system includes a photovoltaic power plant, an electric vehicle and a battery. Real data for the consumption of households in the city of Sarajevo were used for analyzes. Bosnia and Herzegovina is a medium-developed country with a relatively low economic standard. However, the results of the analysis show that despite the relatively unfavorable economic environment and low standard, the implementation of smart home system would pay off over a period of about 11 years.

Smart Sarajevo—Analysis of Smart Home System

37

2 Materials and Methods SHEMS is a central component, as shown in Fig. 1, and provides scenarios where technologies can be observed and controlled according to their current state. The smart home has PV panels installed and the power of one panel is 280 W. There are 6 such panels on the roof and together they have an installed power of 1680 W. Following characteristics of the PV panels are: NOCT (45 ± 2 °C), efficiency ηr e f (18.35%), dimensions A (1650 mm × 991 mm × 35 mm) and Pmax at NOCT (205 W). The power of the PV system is determined by the following equation for the period of 24 h [1]:

Fig. 1 The structure of a nanogrid modeled smart home

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PP V (t) = η P V (t) · ηinv · A · I (t)

(1)

where the inverter efficiency is set to ηinv = 0.95, and η P V is the hourly efficiency of the PV panel and can be expressed as the following equation [2]:    η P V (t) = ηr e f · 1 − m · T (t) − Tr e f

(2)

m = 0.005 for further calculations, A—total area of photovoltaic system I (t)—Solar irradiation at time t. Equation that calculates the approximate temperature of the panel depending on the solar irradiation [14]:  T (t) = Tamb (t) +

N OC T − 20◦ 800

 · I (t)

(3)

where T (t)—panel temperature at time t, Tamb (t)—ambient temperature at time t and I (t)—Solar irradiation at time t. The location coordinates of the selected smart home and the optimum fixed panel angles for the given location are: North latitude (43,864), North longitude (18,393), Altitude (624 m), Tilt angle (33°), Azimuth angle (−8°). Since the calculations are made with real data, two days from the year 2016 are taken into account for illustrative purposes. The first one is 1.8.2016 which should be a representative day for the summer. The second day is 29.12.2016 which should be a representative day for winter. Figure 2 shows the solar irradiation for the indicated days over 24 h [15]. Due to the large amount of data, not all results will be displayed (such as ambient temperature and approximate panel temperature, panel efficiency over 24 h for 1000 Solar irradiation (Wm-2)

900

29. decembar

1. august

800 700 600 500 400 300 200 100 0 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5 6 Time (h)

Fig. 2 Solar irradiation for the indicated days during 24 h

Smart Sarajevo—Analysis of Smart Home System

1.4

39

29. december

1. august

Power (kW)

1.2 1 0.8 0.6 0.4 0.2 0 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5 6 Time (h) Fig. 3 Total photovoltaic system power produced during 24 h

selected days, etc.). The calculation of the total power output of the photovoltaic system is shown in Fig. 3. The analyzed smart home has an EV charging station that supports vehicle-togrid (V2G) technology as well as the vehicle itself, so that EV becomes an integral part of the smart home, both in the form of load and in the form of electricity storage system according to the instructions of the energy management system. The characteristic vehicle technical data that are important for proper modeling and used in this work are: Maximum engine power 60 kW, Maximum speed—130 km/h, EV battery usable capacity—16 kWh, Approximate range—95 km, Connector—Type 2 (Europe), Maximum Charging Power—3.7 kW (AC). The goal of a large number of problems is optimization, maximizing utility, or minimizing costs within given constraints. These problems are solved by some form of linear programming. In this paper, the problem is set as a mixed-integer linear programing (MILP) problem [3, 7, 8]. That means, in addition to the variables that have a solution that belongs to the set of real numbers, there are variables that can only have an integer solution. Furthermore, all integer variables in this work are further limited in such a way that they can only have values of 0 or 1, in other words they are declared as binary variables. The main task of the model is to minimize the electricity bill on a daily basis. Electricity bill is the difference between the energy purchased from the grid and the energy sold to the same grid. The price of electricity is time dependent. The MILP model made for this work has the objective function: DB =

24   t=1

 Pgrid,buy (t) ∗ t ∗ αbuy (t) − Pgrid,sell (t) ∗ t ∗ αsell (t)

(4)

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E. Šalji´c and S. Avdakovi´c

In Eq. (4) two optimization variables can be found: Pgrid,buy (t) and Pgrid,sell (t) · Pgrid,buy (t) is the total power purchased from the grid at the moment t and Pgrid,sell (t) is the total power sold to the grid. αbuy (t) and αsell (t) are electricity prices at the moment t, while t is the time step and in this model it has a value of 1 h. The formed MILP model has a total of 27 time-dependent constraints and they are valid for 17 optimization variables in total that are also time-dependent.

3 Case Study and Discussion The focus of this paper is on the optimization of energy resources. In order to use resources effectively, they should be planned one day in advance and based on load forecast and tomorrow’s weather. Then, SHEMS distributes the power of production of each resource and the consumption of each load so that all resident requirements are met and cost is kept to a minimum. In addition, a management strategy is also formed based on the dynamic price of electricity and the constraints set by the EV, the battery and the grid itself.

3.1 Scenario In this scenario, solar irradiation data and ambient temperatures for summer and winter days in Sarajevo were taken. Also in this scenario, the electric vehicle is disconnected from the home grid at 7:00 and reconnected at 18:00. In this way, going to work is simulated. Home battery storage capacity is set to 1.5 kWh and maximum charging and discharging power of this storage station is set to 0.5 kW. The buying price of electricity is shown in Fig. 4 while the selling price in this modeling has a constant value of 0.109 KM.

3.2 Results The MILP model was tested in GAMS v.25.1.3 using the CPLEX v.12 solver. The results of the optimization problem are: Representative summer day (1.02 KM), Representative winter day (1.32 KM). As smart homes are supposed to be an integral part of smart grids, a daily cost calculation has also been made when grid power is limited, because it is a phenomenon that can occur. In the original calculation, the maximum grid power is 10 kW, while in the new scenario it is 3 kW. The new results of the optimization problem are: Representative summer day with limited grid power to 3 kW (1.12 KM), Representative winter day with limited grid power to 3 kW (1.43 KM). What can be noticed immediately with the grid power limitation is that the minimum daily bill has increased. The increase in percent for the summer day is

Smart Sarajevo—Analysis of Smart Home System

41

0.18 0.16

Winter

Summer

KM/kWh

0.14 0.12 0.1 0.08 0.06 0.04 0.02 0

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5 6

Time (t) Fig. 4 The buying price of electric energy for 24 h for the household [16]

8.847%, while for the winter day it is 7.676%. Figures 5 and 6 show the optimal use of resources graphically. Figure 5 is the optimal solution for a summer day without power limitation, while Fig. 6 is the optimal solution for a winter day without power limitation. Figures 7 and 8 show the optimization results when the maximum grid power is set to 3 kW. The setting of the simulation parameters considered the situation of emptying the electric vehicle battery by 50% in the period when the vehicle is not connected to 5 4.5 4 Power (kW)

3.5 3 2.5

EV battery used for home purposes Home battery used for home purposes PV energy used for home purposes Power retrieved from the grid Home load Home load with charging load

2 1.5 1 0.5 0 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5 6 Time (h)

Fig. 5 Optimal use of resources for the selected summer day

Power (kW)

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E. Šalji´c and S. Avdakovi´c

5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

EV battery used for home purposes Home battery used for home purposes PV energy used for home purposes Power retrived from the grid Home load Home load with charging load

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5 6 Time (h) Fig. 6 Optimal use of resources for the selected winter day

4 3.5 Power (kW)

3 2.5 2

EV battery used for home purposes Home battery used for home purposes PV energy used for home purposes Power retrived from the grid Home load Home load with charging load

1.5 1 0.5 0 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5 6 Time (h)

Fig. 7 Optimal use of resources for the selected summer day with the maximum power the grid can provide set to 3 kW

the smart home grid. Assumed that the EV consumed the energy from the battery only for driving, the approximate distance traveled is 47.5 km. For the same journey, a car with a gasoline 1.0 engine and a consumption of 4.5 l/100 km [17] consumes 2.1375 l of gasoline. At current fuel prices in Bosnia and Herzegovina 2.37 KM/l [18] the mentioned car need 5.05 KM of gasoline for the calculated EV kilometers. Furthermore, if the home from the model was only powered from the grid, the cost for the winter day would be 3.03 KM, and for the summer day 2.18 KM. So, without a home battery, PV system and SHEMS, while using the mentioned car with the gasoline engine, resident should pay a total of 8.08 KM for the considered winter

Smart Sarajevo—Analysis of Smart Home System

43

3.5 3

Power (kW)

2.5 2 1.5

EV battery used for home purposes Home battery used for home purposes PV energy used for home purposes Power retrived from the grid Home load Home load with charging load

1 0.5 0

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5 6 Time (h)

Fig. 8 Optimal use of resources for the selected winter day with the maximum power the grid can provide set to 3 kW

day and a total of 7.23 KM for the summer day. The savings for the selected winter day without power limitation is 6.757 KM or 83.63%. The savings for the selected summer day without power limitation is 6.21 KM or 85.89%. Figures 9 and 10 show the results of optimal selling and buying amounts of electric energy for the defined summer and winter day for the case without grid power limitation. With the combination of GAMS and MATLAB software, optimal values were calculated for the whole year. Figure 11 shows the annual results of optimal smart home behavior for 2016.

Electrical energy (kWh)

5 4 3

Buying electrical energy from the grid Selling electrical energy to the grid

2 1 0 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5 6 Time (h)

Fig. 9 Display of buying and selling electricity during 24 h on a summer day

Electrical energy (kWh)

44

E. Šalji´c and S. Avdakovi´c

5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

Buying electrical energy from the grid Selling electrical energy to the grid

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5 6 Time (h)

Fig. 10 Display of buying and selling electricity during the 24 h for a winter day

Fig. 11 Annual discharge of both home and EV battery discharge power as well as PV system power and home load power without recharging the same batteries

A shorter economic analysis of the implementation of such a system in real term was made. We have the following prices EV (40,000 KM), average cost of a home lithium-ion battery (600 KM/kWh), indicative price of the PV system (1200 KM/kW), and price for setting up SHEMS (3000 KM). The estimated annual bill for the year 2016 with the help of the developed SHEMS system is 771.5 KM. It should be emphasized that this bill also includes the total cost of using an EV. If

Smart Sarajevo—Analysis of Smart Home System

45

the home do not have the described SHEMS system and its components, the annual electricity bill alone would be 180.3 KM higher, or 951.8 KM in total. For the daily 47.5 km that the EV is making contained in the annual bill of 771.5 KM, a car with a petrol 1.0 engine of similar power, requires approximately 782 l of fuel per year. At current fuel prices, the total cost of gasoline is 1854 KM per year. This means, the total cost of the mentioned car with petrol engine in the described scenario and home electricity consumption for 2016 without SHEMS is 2805.8 KM. Furthermore, it should be taken into account that maintaining an electric car requires about 50% less compared to a petrol engine car. Within 4 years, about 2500 KM should be given for the petrol version and about 1300 KM for the electric version of the same car [19], therefore the savings on an annual basis in terms of regular servicing and maintenance amount to approximately 300 KM. Finally, the total savings that a modeled smart home and electric vehicle can generate is 2334.3 KM per year. If we calculate the selling price of the car with petrol engine, the total investment for equipping the home is approx. 26,000 KM. When the investment is divided by the total annual savings caused by the described smart home and an electric car, we get the information that after the 11th year the investment is worthwhile. It should be noted that this is based on current electricity and fuel prices in Bosnia and Herzegovina and is assumed to be fixed over the timespan. Table 1 shows the annual bills and behavior of a smart home for three cases: 1. Modeled smart home with official data, 2. Same smart home with a stronger PV system, and 3. Same smart home with twice the price of selling electricity. What can be noticed is that with the described input data, the SHEMS system forces the smart home to operate on the same principle as the reversible hydroelectric power plant. This effect is quite noticeable when the price of selling electricity is twice the official price. Then SHEMS buys even more energy from the grid to sell it in the end at a higher price in the right moment. It should be noted that SHEMS aims to minimize the financial cost to the homeowner, while always fulfilling all energy requirements without compromising the quality of experience. In the case of a stronger PV system, a higher amount of energy is produced compared to the other two cases and all excess power is immediately sent to the grid. The reason that the EV’s battery energy amount has not changed much from the first case is that in moments of the strongest Sun, the EV is not connected to the home microgrid. Further, the maximum potential of the 1.5 kWh home battery was used in the moments of the strongest Sun in the first case so that its stored energy did not change significantly in the case of a larger amount of solar energy. Higher amounts of stored home battery energy and stored EV battery energy are noticeable in the third case, since the full potential of battery storage in the evenings of the day was not utilized in the first case due to lack of financial motivation.

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Table 1 Annual bills and smart home behavior for three cases: 1. Modeled smart home with official data, 2. Same smart home with a stronger PV system, and 3. Same smart home with twice the price of selling electrical energy (kWh)

PV = 1.68 (kW) λsell = 0.109 (KM/kWh)

PV = 5.60 (kW) PV = 1.68 (kW) λsell = 0.109 (KM/kWh) λsell = 0.218 (KM/kWh)

House consumption

7538

7538

7538

EV consumption for driving

3073.68

3073.68

3073.68

Production of PV

2550

8500

2550

Taken from the network

11,559.87

10,553.22

15,188.73

Taken from the network HT

1386.07

997.22

4314.45

Taken from the network LT

10,173.80

9556

10,804.28

EV (battery capacity 16 kWh—online from 6:00 p.m. to 7:00 a.m.) Total energy taken from the microgrid

6795.62

6764.96

9854.43

Losses due to self-discharge

27.03

29.02

31.35

Total discharge energy

3508.81

3477.70

6410.36

Energy delivered to the grid (energy sold)

2046.40

2005.29

4647.98

Energy delivered for home needs

1286.97

1298.53

1441.87

Home battery (1.5 kWh capacity) Total energy taken from the microgrid

868.60

936.68

1195.67

Losses due to self-discharge

4.75

4.90

6.22

Total discharge energy

820.42

884.95

1129.66

Energy delivered to the grid (energy sold)

330.46

341.26

854.70

Energy delivered for home needs

448.94

449.45

218.47

Annual electricity bill (km)

771.5

116.9

218.0

Annual electricity bill for a house without SHEMS, EV, PV and storage (instead of EV, the cost of a car with a petrol engine with the same amount of kilometers driven is added) (KM)

951.8 + (1854 + 300) = 3105.8

Smart Sarajevo—Analysis of Smart Home System

47

4 Conclusion In this paper, a smart home is modeled and analyzed using real data from Sarajevo. This data implies hourly values of electricity consumption, hourly values of temperatures and other metrological data. The smart home has an integrated 1.68 kW PV system, an electric vehicle and a battery for storing electric energy. For the various conditions analyzed, SHEMS minimized electricity costs by making decisions based only on home load information. However, as a smart home must be part of a future smart grid, it must be able to both communicate and interact with the smart grid. Therefore, a scenario is presented in the paper where the power of the grid supplying the smart home is limited. This causes an increase in overall costs, however, analyzes with a constraint of this type must be feasible in order to be able to establish a smart grid at all. The techno-economic analysis of the considered system shows that the investment for this smart home system would pay off in about 11 years in the environment described. The relatively large payback period of the investment is the result of extremely low electricity prices in Bosnia and Herzegovina, which is a result of the country’s low standard and poor economic development. However, the development of smart cities will certainly be a challenge for the scientific and professional community in Bosnia and Herzegovina. A favorable regulatory framework, the availability of technologies and market prices are likely to intensify development in this area in Bosnia and Herzegovina in the future.

References 1. Lorestani, A., Ardehali, M.M., Gharehpetian, G.B.: Optimal resource planning of smart home energy system under dynamic pricing based on invasive weed optimization algorithm (2016) 2. Musi´c, M., Avdakovi´c, S., Skopljak, A., Ademovi´c, A., Turkovi´c, E., Hasanbegovi´c, O.: Tehno—ekonomskaopravdanostizgradnjefotonaponskeelektranenaodabranojlokaciji (2012) 3. De Angelis, F., Boaro, M., Fuselli, D., Squartini, S., Piazza, F., Wei, Q.: Optimal home energy management under dynamic electrical and thermal constraints. IEEE Trans. Ind. Inf. (2013) 4. Sun, C., Sun, F., Moura, S.J.: Nonlinear predictive energy management of residential buildings with photovoltaics & batteries. J. Power Sources (2016) 5. Muratori, M., Rizzoni, G.: Residential demand response: dynamic energy management and time-varying electricity pricing. IEEE Trans. Power Syst. (2016) 6. Munkhammar, J., Widn, J., Rydn, J.: On a probability distribution model combining household power consumption, electric vehicle home-charging and photovoltaic power production. Appl. Energy (2015) 7. Erdinc, O.: Economic impacts of small-scale own generating and storage units, and electric vehicles under different demand response strategies for smart households. Appl. Energy (2014) 8. Paterakis, N.G., Erdinc, O., Bakirtzis, A.G., Catalao, J.P.S.: Optimal household appliances scheduling under day-ahead pricing and load-shaping demand response strategies. IEEE Trans. Ind. Inf. (2015) 9. Paterakis, N.G., Tascikaraoglu, A., Erdinc, O., Bakirtzis, A.G., Catalao, J.P.S.: Assessment of demand-response-driven load pattern elasticity using a combined approach for smart households. IEEE Trans. Ind. Inf. (2016)

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10. Erdinc, O., Paterakis, N.G., Pappi, I.N., Bakirtzis, A.G., Catalao, J.P.: A new perspective for sizing of distributed generation and energy storage for smart households under demand response. Appl. Energy (2015) 11. Chen, Z., Wu, L., Fu, Y.: Real-time price-based demand response management for residential appliances via stochastic optimization and robust optimization. IEEE Trans. Smart Grid (2012) 12. Li, X., Hong, S.: User-expected price-based demand response algorithm for a home-to-grid system. Energy (2014) 13. Chen, X., Wei, T., Hu, S.: Uncertainty-aware household appliance scheduling considering dynamic electricity pricing in smart home. IEEE Trans. Smart Grid (2013) 14. Ross, R.G.: Flat-plate photovoltaic array design optimization (1980) 15. Photovoltaic Geographical Information System. https://re.jrc.ec.europa.eu/pvg_tools/en/tools. html (2019) 16. Offical Website: Elektroprivreda Bosne i Hercegovine. https://www.epbih.ba/ (2019) 17. Wiki Automotive Catalog. https://www.auto-data.net/en/volkswagen-up-1.0-60hp-17897 (2019) 18. Vanjskotrgovinskakomora BIH. https://www.komorabih.ba/wp-content/uploads/2019/10/cij ene-goriva-2019-41.pdf (2019) 19. JutarnjiList—AUTOKLUB. https://www.jutarnji.hr/autoklub/ak-specijali/e-mobilnost/uspore dba-troskova-auto-na-struju-isplativ-nakon-125000-kilometara/8649611/ (2019)

Western Balkans Green-Deal: Zero Emissions by 2050 ´ M. Brkljaˇca, M. Tabakovi´c, M. Vranjkovina, Dž. Corovi´ c, L. Dedi´c, M. Krzovi´c, M. Skenderovi´c, T. Hubana, and Samir Avdakovi´c

Abstract Following the recent European Commission strategic growth plan called the EU Green Deal that intends to make the Europe the first climate neutral continent by 2050, this research analyzes the possibility of achieving zero emissions in the European Western Balkans—Albania, Bosnia and Herzegovina, Kosovo, North Macedonia, Montenegro and Serbia. By using the existing official data for population, GDP and energy consumption, linear regression is used for the forecasts by 2050. With the current generation data and energy forecasts, the analysis presented in this paper demonstrates the replacement plan of the coal-based power plants with the renewable energy sources (wind, solar and biomass energy), by 2050. The multicriteria decision-making analytical hierarchy process is used to determine the locations of the renewable energy-based power plants in the Western Balkans. The annual energy outputs of the potential renewable energy-based power plants are calculated by using the official irradiance and wind databases and official reports from the national power grid operators. The results demonstrated that the Western Balkans Green Deal can be achieved by 2050 with the number of suitable locations for renewable energy sources, but with high investment costs that are justified by the main goal—zero emissions. Keywords Green Deal · Green energy in Western Balkan · Bosnia and Herzegovina · Serbia · Montenegro · North Macedonia · Kosovo · Albania

´ M. Brkljaˇca (B) · M. Tabakovi´c · M. Vranjkovina · Dž. Corovi´ c · L. Dedi´c · M. Krzovi´c · M. Skenderovi´c · S. Avdakovi´c Faculty of Electrical Engineering, University of Sarajevo, Sarajevo, Bosnia and Herzegovina e-mail: [email protected] T. Hubana Institute of Electrical Power Systems, Graz University of Technology, Graz, Austria © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. Avdakovi´c et al. (eds.), Advanced Technologies, Systems, and Applications V, Lecture Notes in Networks and Systems 142, https://doi.org/10.1007/978-3-030-54765-3_3

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1 Introduction In January 2020, the European Commission adopted a strategic growth plan called the EU Green Deal that would make Europe the first “climate-neutral continent” by 2050 [1]. European countries outside the European Union such as the Western Balkan countries should also be involved in this to realize such plan. Based on the European Union’s decision, the objective of this study is to construct basis of the Green Deal for the energy sector of the mentioned countries facing major difficulties in terms of environmental protection. The latest official research shows that thermal power plants located in Bosnia and Herzegovina, Serbia, Montenegro, North Macedonia and Kosovo pollute the same as all thermal power plants in the EU, causing up to 3000 premature deaths, 8000 cases of bronchitis as well as other chronic diseases a year [2]. Accordingly, radical changes in the energy sector are required. To this end, this study will develop a plan to replace all existing thermal power plants with power plants that use renewable sources. Furthermore, these countries, as well as the rest of the world, record an increase in electricity demand and it is necessary to meet these needs by including additional electricity production capacities. The decision on site selection for the construction of new power plants depends on a number of different factors: techno-economic, social, geographic and environmental. Thus, the selection of locations requires multi-criteria decision-making. This study will apply an analytical hierarchy process (AHP) and develop a decision support system. Given the wide scope of the research and very complex topic, this paper does not consider some important aspects such as power control in a grid with predominant renewable energy sources, heating issue in cities that are currently heated by thermal power plants, reliability and security of the power grid and the need for investment in the expansion of transmission networks. Observed region has significant capacities for the construction of new hydropower plants which were also not considered in this paper. As the countries of the Western Balkans are part of Europe and on the path of joining the EU they have to be prepared to replace their conventional energy sources with renewables, in order to comply with the European future plans. Many researches have been conducted over the years on topic of renewable energy potential of the region. Lalic et al. [3], Karakosta et al. [4] and Golušin et al. [5] all agree on the high potential for RES but low production due to a number of political, legislative and financial constraints. Paper [5] goes on to claim that wind energy is a priority for the region. Koçak and Sarkgüne¸ ¸ si [6] explore the correlation between RES and economic growth and concludes that RES consumption could lead to economic growth in Balkan and Black Sea countries. Karakosta et al. [7] used SWOT analysis to show that Western Balkans countries helped by the Intelligent Energy Europe Programme co-financing could potentially export RES energy and overcome the fragmented electricity system of the past two decades. Papapostolou et al. [8] and Mesfun et al. [9] have used methodological approach for assessment of the opportunities and risks of implementation of RES electricity in the region.

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As already mentioned, the analytic hierarchy process is a decision making tool for choosing the best among several alternatives based on specific criteria. AHP has been revised and explained in detail by Saaty [10] who expanded it further mathematically in 2003 [11]. Robles et al. [12] have used this method to assess the best source of renewable energy in Colombia and the Caribbean region. Budak et al. [13] used the AHP to analyze the number of cities around the world and concluded that most sustainable energy source for one city might be least sustainable for another. Kaya and Kahraman [14] and Solangi et al. [15] have used AHP along with VIKOR method. Research [14] found the most suitable energy source and locations in Istanbul, while [15] used a similar approach to determine the best cities in Pakistan for installation of solar PV power projects. Weiss et al. [16] also studied various zones on the coastal area of Brazil in estimation of production of suitable zones.

2 Theoretical Background 2.1 Photovoltaic Systems The photovoltaic system is a system composed of one or more solar panels combined with an inverter or other electrical and mechanical components that use solar energy to produce electricity. Measurements that describe the sun’s radiation are: irradiation (W/m2 )—strength of the solar radiation per unit of the surface; insolation (Wh/m2 )— quantity of the solar energy that has been absorbed by a certain surface during a certain time; solar constant is a mean yearly irradiation on the upper layer of Earth’s atmosphere. Exploitation of solar energy for electricity production can be done in two ways: using solar-thermal power plants, and by directly transforming solar energy into electric energy using photovoltaic (solar) cells [17]. By photovoltaic conversions we refer to the direct transformation of solar energy into electrical energy through the photoelectric effect. The power provided by the photovoltaic cell is given by the formula:   qV d (1) P = U ∗I = U I F − I0 e kT + I0 where I F —is the current of PV current source; I D —current through a diode of PV electrical circuit; k—Boltzmann constant; VD —voltage on the diode; I0 —reverse saturation current; T—temperature of the PV cell, U—PV cell voltage, I—current through the PV cell.

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2.2 Wind Power Wind is abundant, easily accessible and a clean source of energy. According to the World Wind Energy Association (WWEA), the current share of wind energy in total world electricity production is above 5%. Further forecasts for the development of wind energy are very optimistic and, in all variants, represent wind farms as very important sources of electricity in the future. World’s leading country in terms of the installed power capacities is China, which at the end of 2004 had only 769 (MW) installed, while having more than 217 GW according to the most recent data (2019). The leader in Europe is Germany with a total installed power capacity of 59 (GW), which corresponds to 20% of its electricity needs [18]. Wind kinetic energy is transformed into the mechanical energy of rotational motion by a wind turbine. The equation for wind power on a wind turbine is: Pv =

1 ρC p Av 3 2

(2)

where ρ—average air density; C p —Betz coefficient, which determines the ratio of wind speed at the inlet and outlet of the turbine; A—Surface formed by the turbine blades; v—Wind speed. The basic precondition when choosing a location is a reliable knowledge of wind energy resources at the location of a potential wind farm. This criterion is important since the power depends on the third degree of wind speed. Analysis of statistical indicators, such as wind rose, mean annual wind speed, wind speed histogram and wind speed probability density function, is required. Important local factors are the shape of the terrain and the roughness of the earth’s surface. Another important criterion is the possibility of connection to the grid infrastructure, economic profitability, and number of spatial, environmental and other conditions for the construction of wind farms. Modern turbines generally have a diameter of 40–90 m with a nominal power of 500 kW–2 MW, but larger are available too. The largest wind turbine manufacturer is Denmark’s Vestas, which has a 20.3% market share, followed by China’s Goldwind with 13.8% and Spain’s Siemens Games with 12.3% [19].

2.3 Biomass Biomass presents a biodegradable part of products, waste and residues of agricultural production (plant and animal origin), forestry and related industries. Energy from biomass comes in solid, liquid (e.g. biodiesel, bioethanol, biomethanol) and gaseous state (e.g. biogas, biomass gasification gas and landfill gas). The main advantage in the use of biomass as an energy source it is their great potential. For this purpose, planted crops and waste materials in the agricultural and food industries can be used. Biomass is the only renewable energy source that can be used indefinitely to

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produce electricity, heat and liquid fuels. In the past decade, the number of traditional coal-based power plants were successfully transformed in the biomass power plants. Currently, some of the largest biomass power plants in the world are in the range of 140–749 MW [19].

2.4 Analytical Hierarchy Process In engineering, the problem of multicriterial decision-making is often encountered, for which different methods are used. One of the methods is the method of analytical hierarchy process (AHP) which will be used in this study to compare the locations for the construction of power plants, and later for their selection, i.e. ranking. The AHP is one of the most useful mathematical tools for analyzing complex decisions with multiple alternatives based on multiple criteria. The first step in solving the problem is the process of defining the problem and setting a clearly defined goal. Initially, it is necessary to break down a complex problem into a hierarchy of more easily understandable problems that can be separately analyzed. After forming structured and transparent hierarchy, the elements are evaluated by comparing the two elements with each other in terms of their influence on the element that is in the formed hierarchy above them. Since the essence of AHP is the human assessment, not just basic information related to an issue, when comparing, in addition to using concrete data on the elements, decision makers can also use a personal opinion on the significance of individual elements. The aim is to convert descriptive ratings into numerical values that can be further processed and compared at the overall problem’s level. To each element priority is assigned. This allows for the comparison of elements that are completely different and incompatible at first glance. The last step of the process involves calculating the numeric priorities for each of the alternatives set. The procedure described above can be presented with a flowchart that is displayed in Fig. 1. The hierarchical structure of AHP consists of a goal, below which on the first level, there are criteria for evaluation and alternatives are on the last level [10]. The AHP method uses the matrix for ranking and comparison of alternatives and criteria for the assessment. Within the matrix, you do not type standard units, but numeric values from the Saaty scale. It is convenient to mention that Saaty also developed the AHP method, and the table was retrieved from one of his studies [10, 21]. This scale contains nine numerical ratings that allow you to distinguish between the intensity of the relation between the individual elements of the hierarchical structure by comparing them in pairs. The table provides explanations for definitions associated with odd numbers, while even numbers are predicted to be their intermediate values. In the AHP method, the axiom of reciprocity is valid, i.e. if alternative 1 has one of the attributed values from the Saaty scale when compared to alternative 2, then alternative 2 has a reciprocal value when compared to alternative 1. The same applies when comparing criteria.

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Fig. 1 Analytical hierarchical process flowchart [20]

Calculating the weight of the criteria is done based on comparisons in pairs by forming a priority relation matrix. In doing so, the values of the estimated priority ratio of the two different criteria are placed in the ith row and jth column of the matrix in place of ai j according to the Saaty scale. If ai j is greater than 1 then the ith criterion is more important than the jth criterion, if ai j is equal to one, then the criteria are equally important and if ai j is less than 1 then the jth criterion is more important than the ith criterion. Elements ai j and ai j based on the axiom reciprocity meet the limitation: ai j · a ji = 1

(3)

After the formation of this matrix, a normalized comparison is made in pairs by dividing each element with the sum of the elements of the column to which they belong, i.e.: ai j ai j = m k=1

ak j

(4)

where m—number of criteria. Based on this, the weight of the criteria w is calculated as follows: m wj =

k=1

m

aik

(5)

Consistency check in the AHP method is possible and performed on the basis of the consistency index (CI) and the consistency ratio (CR). They are calculated by the following relations:

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CI =

55

λmax − n n−1

(6)

CI RI

(7)

CR =

where n—number of alternatives; λmax —eigenvalue and R I —random consistency index. The values of the RI indexes are obtained from the table of average random consistency index values [20] based on the number of alternatives n. The eigenvalue of a consistent matrix is equal to the order n: λmax = n

(8)

For ideal consistency C I = 0, but less inconsistency can be tolerated within these limits: 0 < C R < 0.1 [11]. When consistency is within the limits 0 < C R < 0.1 it is not necessary to repeat the procedure and it is considered to be sufficiently accurate. If an inconsistency exceeds 0.1, the comparison matrix would be inconsistent, it is necessary to investigate the reasons why there was an unacceptably high inconsistency of assessments and remove the cause by partially repeating the comparison process in pairs. If, even after such a recurrence, a consistency of less than 0.1 is not obtained, the procedure would be completely discarded and must be done from scratch. In this paper, this method will be applied to a concrete example of the sites’ ranking for the construction of power plants.

3 Methodology 3.1 Electricity Forecast Model According to World Bank database [22], there is enough data to adequately forecast electricity consumption by 2050. The forecast of electricity consumption was done by a linear trend, as the available data shows approximate linear growth. Accordingly, the trend that foresees an increase in electricity consumption has the following form: Wi = a + b · Ti

(9)

where Wi —electricity consumption in year T; Ti —time expressed in the whole number of years compared to the initial year; a—consumption in the initial year; b—constant annual increase in consumption. Constants a and b are determined based on the following relations:

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n n n Wi · i=1 Ti2 − i=1 Ti · i=1 Ti · Wi n n a= n · i=1 Ti2 − ( i=1 Ti )2 n n n Ti · Wi i=1 Ti · i=1 Wi − n · n n i=1 2 b= 2 ( i=1 Ti ) − n · i=1 Ti n

i=1

(10) (11)

3.2 The Power Plants Locations Selection Process The first step of power plant locations selection process is stating the problem and determining an objective goal. As mentioned earlier, the Western Balkan countries are currently facing problems in the field of electricity generation, so the aim is to impose the integration of renewable energy power plants to achieve sustainable development. This study will look at locations that have been intuitively considered. The next step of this process is setting up the criteria. Selected locations will be ranked based on criteria that include techno-economic, social and environmental aspects: • energy source potential (implies the sustainability, i.e. the supply of electricity sources for the continuous supply of the final consumer), • infrastructure (refers to the technical resources of the area), • price, • impact on the environment and • job creation. Based on these criteria, the following step of the process, constructing the hierarchy, can be conducted. To solve the specific problem in this study, the ranking of locations for the construction of power plants, the hierarchy of the decision-making structure is set up as shown in Fig. 2. After the pairwise comparisons are made, for all locations and five presented criteria, the ranking system is set up. For this purpose, a software package Expert Choice 11 is used. The results of sites’ ranking for the construction of power plants will be presented below, obtained using the Expert Choice 11 program, and based on the evaluations of the nine authors of this research.

4 Result and Discussion Data on electricity consumption per capita and total population in the Western Balkans, available in the World Bank Database, was used to estimate current electricity consumption in the Western Balkan countries. In order to estimate the total electricity consumption by 2050, it was necessary to make a forecast of the changes in this data. Table 1 shows the forecast concerning population, which is conducted

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Fig. 2 Decision structure hierarchy for the observed problem

Table 1 Population forecast for 10 years periods Year

2020

2030

2040

2050

Albania

2,835,590

2,681,660

2,527,731

2,373,801

Bosnia and Herzegovina

3,294,317

3,146,257

2,998,198

2,850,138

Kosovo

1,834,069

1,777,911

1,721,754

1,665,597

North Macedonia

2,103,054

2,139,380

2,175,705

2,212,030

Montenegro

626,066

634,254

642,442

650,630

Serbia

6,970,385

6,684,614

6,398,843

6,113,072

according to the model in Sect. 3.1. Data from 1960 to 2018 was used for all countries except Serbia, where data is available from 1990. Based on the data, further estimates of the population have been conducted until 2050, and as it can be seen, there is a decline in the number of inhabitants in all countries. Consumption per capita by 2050 was also estimated by using the model from Sect. 3.1. Table 2 shows the results of this forecast. Table 2 Electric power consumption per capita for 10 years periods (kWh per capita) Year

2020

2030

2040

2050

Albania

2774.75

3568.05

4361.34

5154.64

Bosnia and Herzegovina

4319.81

5557.56

6795.3

8033.05

Kosovo

3579.14

4503.45

5427.77

6352.08

North Macedonia

4067.61

4594.21

5120.81

5647.41

Montenegro

3475.45

4074.26

4657.82

5226.68

Serbia

4393.43

4480.31

4567.19

4654,07

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Table 3 Total GWh consumption in Western Balkan countries for 10 years periods (GWh) Year

2020

Albania Bosnia and Herzegovina

2030

2040

2050

6982.89

8516.57

9869.90

11,144.19 16,888.73

12,855.76

14,412.20

15,520.73

Kosovo

5193.45

6403.04

6513.13

7332.31

North Macedonia

7405.66

8204.02

8805.26

9631.95

Montenegro Serbia

2175.86

2584.12

2992.37

3400.63

29,927.17

33,333.64

32,744.47

34,496.93

Total electricity consumption by 2050 was primarily estimated based on electricity consumption per capita and the total population of all Western Balkan countries in this period, which is presented above. However, some unrealistic estimates were observed, and were finally corrected by considering the GDP forecast, which was also made based on data from the World Bank Database. This modification was done according to the model used in [23]. The final forecast of electricity consumption in the Western Balkan countries is shown in Table 3. Since the Green Deal implies abandonment of thermal power plants, it is necessary to determine the electricity production from coal sources. To make the model representative, values for the last three years available in the World Bank Database were used and the average was calculated and shown in the first column of Table 4. Other data required for the calculation were obtained previously, so the total consumption in 2015 is shown in the second column, and the estimate of electricity consumption in 2050 in the third column. The final step in estimating is to add the difference of total electricity consumption to the values of the first column from 2050 and 2015. This is shown in the fourth column in Table 4. Table 4 Total electricity needed from renewable sources for countries to become climate-neutral Country

Electricity production from coal-based sources in 2015

Total electricity consumption in 2015

Electricity consumption estimate in 2050

Total electricity needed to be provided from renewable sources

Albania

0

6015.00

11,144.19

5129.19

Bosnia and Herzegovina

7602.37

11,924.00

16,888.73

12,567.11

North Macedonia

4845.64

6755.00

9631.95

7722.59

Kosovo

5200.82

4633.00

7332.31

7900.13

Serbia

21,942.99

28,462.00

34,496.93

27,977.92

Montenegro

845.86

1943.46

3400.63

2303.03

Total (GWh)

40,437.69

59,732.46

82,894.74

63,599.97

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Table 5 Total energy production from each kind of renewable sources Country

Wind power energy

Solar power energy

Biomass power energy

Energy from residential rooftops

Total

Albania

2467.03

2668.12

0

772.9

5908.05

Bosnia and Herzegovina

10,497.82

1031.52

1038

485

13,052.34

Kosovo

5468.99

761.52

1365

390

7985.51

North Macedonia

5378.48

2159.74

0

215

7753.22

Montenegro

1111.25

1043.33

0

390

2544.58

Serbia

12,549.26

4657.22

9591.18

1342.12

28,140.39

Total

37,472.83

12,321.45

11,994.18

2822.12

65,384.09

Since it is realistic to expect that the level of distributed generation in the future will be considerably higher than today, it is considered that the solar panels with 10 kWp of power are installed on 10% of buildings with one and two households. The information regarding the number of buildings is from [24–28]. The second preposition is transferring some of the thermal block within these countries into biomass fueled blocks to reduce their pollution, so they can stay operative up to 2050. Besides the amount of energy that would be obtained from household rooftops and blocks that were converted into biomass fueled blocks, additional more than 200 locations are analyzed in order to fulfill the rest of the energy requirements. With the AHP methodology, that was described in previous sections, 81 wind and 74 solar power plants were left, which will cover the amount of energy needed by 2050. The annual energy production for each power plant is calculated by using the PVGIS and Global Wind Atlas databases for solar and wind power plants respectively. The amount of energy that is to be provided by different renewable energy sourced are shown in Table 5. The locations of these plants in each country are presented in Fig. 3. Based on the AHP methodology results, every location was given a priority coefficient, which represents a number that is less than 1, but presents the priority level for that power plant. Few examples of locations of power plants are shown in Table 6. The sum of all priority coefficients from each location in a country is equal to 1. The locations that were given lowest coefficients were eliminated from the study, since the energy needs can be satisfied with the reduced list of the analyzed power plants. In this manner, only the most appropriate plant locations and sizes are taken into consideration. Based on the information gathered, the countries that would have least effort in completing the Green Deal 2050 are Montenegro and Albania. With their access to the sea there are plenty of locations in that area that are proposed because of the good wind and sun conditions. On the other hand, Kosovo is the country that is powered mostly on thermal power plants and with its small area, was the hardest to

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Fig. 3 Approximate locations of solar power plants in the Western Balkans

Table 6 Examples of renewable power plants from each country with their corresponding coefficients Country

Resource

Coordinates

Estimated yearly production (GWh)

Coeff.

Albania

Wind

42.3125°, 19.8374°

577.74

0.183

North Macedonia

Wind

40.9949°, 21.1734°

590.00

0.064

Bosnia and Herzegovina

Solar

43.3161°, 17.7271°

137.35

0.211

Kosovo

Biomass

42.6764°, 21.0866°

1365

1

Montenegro

Solar

42.2820°, 19.2660°

141.74

0.104

Serbia

Biomass

44.6721°, 20.1624°

3734.16

0.33

Albania

Solar

40.6530°, 19.3710°

307.43

0.111

Serbia

Wind

44.2491°, 22.2075°

469.80

0.031

Kosovo

Wind

42.6068°, 21.4365°

304.70

0.045

find enough locations to compensate the amount of energy needed by 2050, but with converting some of the thermal blocks into biomass fueled, not many locations were needed. Serbia, which has the largest population and the largest power consumption is also challenging to compensate. Wind power plants which are proposed by the AHP method are localized in the Southern area of Serbia because that is where the wind power is most stable and powerful. The solar power plants are mostly proposed in the Northern parts due to the plain terrain. North Macedonia was also

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easy to compensate because of the low consumption increase in 2050. The locations are evenly distributed across North Macedonia because of the great wind and sun potential.

5 Conclusion This research has provided an in-depth study of the energy transition in developing countries which are: Bosnia and Herzegovina, Serbia, Montenegro, Albania, North Macedonia and Kosovo. That makes significant contributions to the qualitative studies of the green energy. There are very few studies on this subject, whether at the international or regional level because it is considered as a modern topic in today’s world. Therefore, this research will contribute to the existing body of knowledge in the field of green energy and sustainable development through renewable energies such as wind power, solar power and biomass. Choice of locations for renewable energy sources is a complex decision-making problem. This research used the analytic hierarchy process (AHP) to prioritize a set of criteria such as technical, economic and environmental criteria. The analysis shows that the technical and economic criteria were the most relevant for multicriteria decision-making. After calculating the required energy for individual countries and ranking locations according to the AHP analysis, the right amount of power is obtained in order to cover energy needs by 2050. South-Eastern Europe has a huge potential for developing green energy, with its mountains and plains enabling wind power, its large number of sunny days a year, and the inhabitants of its many cities keen on sustainable development. These countries are still heavily dependent on ageing coal-fired thermal power plants and suffer from high levels of air pollution. Since the Western Balkans is a priority region for the EBRD, this time could be an auspicious period for advancing a clean-energy transition in Southeastern Europe.

References 1. European Commission: ec.europa.eu, 11 Dec 2019. [Online]. Available: https://ec.europa. eu/info/sites/info/files/european-green-deal-communication_en.pdf (2019). Accessed 14 Apr 2020 2. Matkovi´c Pulji´c, V., Jones, D., Moore, C., Myllyvirta, L., Gierens, R., Kalaba, I., Ciuta, I., Gallop, P., Risteska, S.: Chronic coal pollution. In: HEAL, CAN Europe, Sandbag, CEE Bankwatch Network, Europe Beyond Coal, Brussels (2019) 3. Lalic, D., Popovski, K., Gecevska, V., Popovska Vasilevska, S., Tesic, Z.: Analysis of the opportunities and challenges for renewable energy market in the Western Balkan countries. Renew. Sustain. Energy Rev. 15(6), 3187–3195 (2011) 4. Karakosta, C., Flouri, M., Dimpopoulou, S., Psarras, J.: Analysis of renewable energy progress in the Western Balkan countries: Bosnia–Herzegovina and Serbia (2012)

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Biomass Potential Monitoring System as a Tool for Exchange and Comparing Findings from Different Sectoral Studies Mirza Ponjavic, Almir Karabegovic, Slavoljub Stanojevic, and Sanja Celebicanin

Abstract For planning and reporting purposes, many countries have established official statistics on the available biomass potential. These databases are a useful source for designing new studies, but often existing studies are also used. The findings from various sectoral studies may be heterogeneous in terms of diversity reference units, age of the data, its reliability and precision, which prevents their further use. Because such databases, i.e. biomass potential monitoring systems, allow the biomass data entry, verification, quality and reliability assessment for a specific geographical area, they can serve as a tool for exchange and comparing findings from different sectoral studies. This paper presents an approach for the conversion of the findings from the sectoral study into the biomass potential monitoring system, using the database and atlas monitoring system of biomass potential in Bosnia and Herzegovina as a test case. Keywords Biomass potential monitoring system · Animal waste · Web Atlas · Sustainable development

M. Ponjavic International Burch University, Francuske revolucije bb, 71210 Ilidza, Bosnia and Herzegovina A. Karabegovic (B) Faculty of Electrical Engineering, University of Sarajevo, Zmaja od Bosne, 71000 Sarajevo, Bosnia and Herzegovina e-mail: [email protected] S. Stanojevic Directorate of National Reference Laboratories, Batajnicki drum 7, deo br. 10, 11186 Beograd, Serbia S. Celebicanin Veterinary Faculty, University of Sarajevo, Zmaja od Bosne 90, 71000 Sarajevo, Bosnia and Herzegovina © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. Avdakovi´c et al. (eds.), Advanced Technologies, Systems, and Applications V, Lecture Notes in Networks and Systems 142, https://doi.org/10.1007/978-3-030-54765-3_4

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1 Introduction The Sustainable Development Goals [1] set by the United Nations in 2015 relate to three dimensions of sustainable development (economic, social and environmental) and include 169 targets for poverty, food security, gender equality, water, energy, climate change, industrial development and global partnerships. They are supported by indicators to measure progress towards achieving them and governments of all countries (both developed and developing ones) have a responsibility to integrate them into national policies, strategies and plans and monitor their implementation [2], taking into account their national circumstances [3]. For planning and reporting purposes, many countries have established official statistics on the use of biomass, but often lack up-to-date information on its untapped potential. Some sources rely on research using remote sensing and LiDAR methods [4], mapping suitable areas [5] or soil and land cover types mapped in GIS [6], but this mainly serves to estimate the biomass potential of plant origin at wide scale. Developed countries such as the US [7], Canada, the EU [8], and many others have databases on the different types and origins of biomass. For their original establishment, apart from statistical sources, findings from various studies using different methodologies have been used, taking into account differences in the biomass potential estimation calculations. It is often the case that for a new study, in addition to these databases, findings from previous sectoral studies that may be heterogeneous are used. This heterogeneity may be related to the diversity in the reference units, the age of the data, their reliability and precision, which prevents their further use. For the purpose of sharing and comparing such findings, in this paper, we propose an approach with the conversion of quantitative data on the potential of biomass into an existing reference database according to the methodology it already uses. Such converted data can then be used, if appropriate, for further analysis in the new study. Because such databases, i.e. biomass potential monitoring systems, allow the biomass data entry, verification, quality and reliability assessment for a specific geographical area, we find that they can serve as a tool for exchange and comparing findings from different sectoral studies, in addition to the basic purpose for official biomass statistics. The results from these studies can be mapped and validated in the system using the same unique methodology, and used to update the data or analyse them further. As a case for testing this approach, this paper uses the atlas for biomass potential monitoring in Bosnia and Herzegovina (BiH), established by experts from the German Centre for Biomass Research (DBFZ) and with the assistance of experts from BiH. Biomass as a feedstock for industrial production and as a renewable energy source plays a significant role in the economy of Bosnia and Herzegovina (BiH). About 43% of BiH is covered by forests, while land used for agricultural production occupies approximately the same percentage of the area [9]. The wood processing industry, as well as the growing market for the production of high-quality wood fuels (pellets,

Biomass Potential Monitoring System as a Tool for Exchange …

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Fig. 1 Sankey diagram, biomass resources in BiH from 2015. Source Report on Biomass Potential Monitoring in Bosnia and Herzegovina, 2019 [11]

briquettes and wood chips), in 2010 accounted for about 3% of total gross domestic product (GDP) in BiH [10] and 11% in exports with a growing trend [11]. The Biomass Potential Monitoring System in Bosnia and Herzegovina is based on the systematization and entry of initially collected data from various sources into the biomass resource database [12]. It supports the geospatial presentation of available biomass quantities through the Biomass Potential Atlas (https://atlasbm. bhas.gov.ba/). Biomass is grouped into agricultural biomass (exclusively by-products for 13 categories) and forest biomass (basic products and by-products in the woodprocessing industry for 10 categories) according to the categorization and definition of recognized biomass types [13]. Based on the investigated 23 categories of biomass, the data collected showed that the biomass potential in BiH in 2015 was between 10.3 (minimum value) and 10.4 million tonnes of dry matter (maximum value) (Fig. 1). The Feasibility Study on Animal By-Products and Animal Waste (ABP/AW) Management [14] can serve as a valuable source of data on the potential of animal biomass in BiH. Particularly useful results in the context of the availability of biomass potential of animal origin, provided by this study, are estimates of current and future amounts of animal by-products generated. In that sense, it describes the methodology for calculating the structure of livestock, analyses trend and forecasts the short- and long-term quantities of these by-products. These forecasts were used to locate processing and collection facilities [15], determining transportation capacity [16], treatment technology, and ABP/AW processing capacity. Statistics data sets, stratified by animal species and distributed by levels of administrative division in BiH (entities, cantons, municipalities), are used for calculation and spatial (cartographic) presentation of ABP/AW quantities for all three risk categories (classified according to EC Regulation 1069/2009) [16]. Based on the available statistics and the developed prediction model, total amount of solid manure generated for 2020 is estimated at around 20 million tonnes per year. The reference year for the calculation is 2017.

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Initial values and accompanying trends in the model are based on livestock statistics, slaughterhouse data, meat imports and exports [17–20] and calculated livestock structure for previous years. Considering all of the above, this paper presents an approach for the conversion of the findings from the described sectoral study on animal by-products and animal waste into a biomass potential monitoring system, using the example from BiH as a case study. For the Biomass Potential Monitoring System in BiH, this approach can serve as a modus operandi and facilitate downloading of data from certain similar sectoral studies, thus enabling the correction and updating of the database, i.e. improving its quality and completeness. Also, when creating similar sectoral studies, monitoring systems, with the described approach, can serve as a tool to exchange and compare findings on the potential of biomass from other sectoral studies, and from various literary sources.

2 Methods The scheme shown in Fig. 2 describes the methodological approach of computing biomass potential for animal by-products, conversion the results into the Biomass Potential Monitoring System and comparison of results. Within the first phase, the categorization and the model used to calculate the quantities of animal-by-product origin were initially determined. The next phase, concerning the conversion results in the monitoring system, involves mapping categories from the sectoral study in biomass types from the system and calculation values of key information about the biomass potential followed by calculation flowcharts

Fig. 2 The steps of the conversion and comparison of results from the sectoral study with key information of the monitoring system

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and the assessment of the calculation elements quality. After conversion of the results, through the following phase, existing values from the monitoring system and new converted values from the sectoral study are compared by individual types of biomass. The quality of calculation elements is assessed, and the impact of the biomass potential in relation to another total biomass potential is analysed. Finally, the mapping of biomass potential a mapping system for spatial decision-making is performed at the same stage, ending with a conclusion.

3 Case Study: Conversion of ABP/AW Sector Study Findings into Biomass Potential Monitoring System BiH Regulation EC 1069/2009 prescribes the conditions under which the animal byproducts and animal waste (ABP/AW) may be safely removed in order to exclude the risks to human and animal health [16]. In this context, the Feasibility Study on ABP/AW Management in BiH offered technological, technical and organizational solutions for the disposal and use of this biogenic material based on the estimation of quantities for particular categories of its risk. Besides the possibility of using the material, the energy potential of using these by-products is significant, and should therefore be included in the Biomass Potential Monitoring System in BiH. In order to ensure proper conversion of their quantities, it is necessary to recognize the relationship between their categories and methods of calculation, and to perform their proper mapping. After the conversion, it is possible to calculate the values of key information for each mapped category and compare them with existing equivalent values in the monitoring system.

3.1 Categorization of Animal By-Products and Animal Waste According to the definition given in Regulation EC 1069/2009, animal by-products are parts of the animal body or whole carcasses of animals, products of animal origin, or other products derived from animals not intended for human consumption [21]. Animal by-products and animal waste in BiH are mainly generated during slaughtering of animals for human consumption, during the production of products of animal origin in dairy factories, in animal husbandry during animal production (technological mortality, manure and during the eradication of diseases as consequence of implementation of disease control measures). The main generators are farms, slaughterhouses or meat cuttings, processors and meat products producers, small scale farms, backyard farms and small rural holdings [22]. Regardless of their source and quantities, they pose a potential risk to public and animal health and threatens the environment, in particular with regard to Transmissible Spongiform Encephalopathy

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(TSE), pollution by dioxins and various exotic diseases [22–24]. These ABP/AW degradation products directly or indirectly pollute the environment [25]. According to EC Regulation 1069/2009, animal waste is classified into one of three categories (according to the level of risk). Category 1 consists of brains of ruminants, parts their intestine, spinal cord and similar tissue of ruminants. The dead animals are classified in category 2 or category 1 (if it is found that they have died from the disease such as Bovine Spongiform Encephalopathy (BSE), TSE, or zoonosis). The content of the digestive tract and manure also fall into category 2, while category 3 consists of low risk materials which can be treated in a rendering machine, composted, and used for the production of biogas or pet food [26].

3.2 Calculation of Animal By-Products and Animal Waste Quantities The ABP/AW distribution analysis is conducted by statistics data sets on livestock, livestock balance and number of slaughtered animals obtained from competent institutions for statistics [25, 27]. The total quantities of different categories of animal by-products are assessed by calculating the conditional heads, livestock units (LSU), using the standard methodology and multiplying the obtained values with the literature data on the expected technological mortality of animals during primary production [28–30]. Data on the theoretical values of waste resulting from the slaughter of different animal species and categories have been taken from the literature and used to calculate the expected amount of waste that occurs when slaughtering different animal species and categories of livestock [31, 32]. Table 1 summarizes the aggregate quantities of animal by-products/animal waste (ABP/AW) for Bosnia and Herzegovina (including its entities and Brcko District) calculated on the basis of available statistics from previous years (2012, 2013, 2014, 2015 and 2016) with a prediction in 2017 and 2020 [14]. The last one is the year in which the animal waste management infrastructure should be started in full capacity [16]. Table 1 shows the by-product quantities for all three categories by risk level, with the digestive tract (DTC) and manure contents, belonging to category 2, shown separately in Table 1 because of their specific utilization and biomass classification. Also, these quantities are shown individually for each animal species in Table 2 [14]. Quantities for all these categories as well as animal species are calculated for all municipalities in BiH.

7,205,625

44,801

Total (without manure)

Total manure

32,350

Category 3

6812

9550

Category 2

7,198,813

2901

Category 1

Manure (Cat. 2)

2017

Category/year

DTC (Cat. 2)

Federation of BiH

Level of aggregation

7,096,163

7,089,387

6776

51,045

37,159

11,022

2864

2020

12,580,869

12,566,964

13,905

46,842

33,084

10,075

3682

2017

Republika Srpska

12,389,197

12,375,930

13,267

48,362

34,238

10,381

3743

2020

120,621

120,495

126

559

399

120

40

2017

Brcko District

Table 1 ABP/AW quantities predicted in 2017 and 2020 on the bases of available statistics (in t/year) [14, 16]

118,767

118,663

104

606

200

361

45

2020

19,906,115

19,886,272

20,843

92,201

65,833

19,745

6623

2017

19,604,137

19,583,990

20,147

100,014

71,597

21,764

6652

2020

Bosnia and Herzegovina

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Table 2 Quantities of manure including digestive tract content (DTC) for individual animal species in BiH [14] Animal species

Poultry

Sheep

Goat

Cattle

Pig

Predicted number of animals in 2017 using statistics

21,045,201

1,008,986

75,322

445,055

514,944

Number of animals by modela

46,547,687

1,051,889

93,988

444,597

1,778,650

Calculated quantities of manure including DTC in tonnes per year

2,159,169

1,686,050

148,767

8,208,609

7,704,517

a The

model is based on statistics, literature data on the expected values of reproductive characteristics of the average herd of an animal species, analysis of data on the number of animals slaughtered, import/export ratios, and average meat consumption in BiH

3.3 Conversion of Results to Biomass Potential Monitoring System Conversion of ABP/AW quantities involves mapping categories from the sectoral study with biomass types in the monitoring system, encoding the calculation elements used to calculate key information, and creating calculation flowchart and assessment the quality of the data used. During the development and establishment of the Biomass Potential Monitoring System in BiH, a categorization of biomass types (total of 23 types) was made and aggregation levels were selected to adapt the approach to the situation in BiH. For each biomass investigated, the key information was calculated using calculation elements of different origins and dynamics to summarize individual data and calculate biomass potential. Finally, all calculation elements and key biomass information are stored in the database. This database uses an online atlas to visualize the results in different spatial units (municipality, entity, canton and state). To reflect the trend in resource availability over time, a timeframe from 2012 to 2017 was selected, and quantities for 2017 were used due to time overlap (between the system and the sectoral study). In the process of creating the biomass monitoring system methodology, as well as developing databases and on-line atlas, mostly publicly available data (e.g. official and publicly available statistics or publications) and open source software have been used to facilitate platform updates, data collection, monitoring and verification [11].

3.4 Categories of Animal Origin Biomass Mapping and Calculation Elements Coding Table 3 shows the biomass categories of animal origin recognized in the monitoring system according to Brosowski et al. [12]. From a total of 23 existing biomass categories from the monitoring system, 7 categories were identified related to manure

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Table 3 Mapping categories from the study on ABP/AW management to the BPMS [11–13] Category in the sectoral study

Biomass type in monitoring system

Definition of biomass type (in the monitoring system)

Code

Cattle manure and content Cattle slurry of digestive tract (DTC) (ABP/AW Category 2)

Liquid manure from cattle farming

CAS

Pig manure and DTC (ABP/AW Category 2)

Pig slurry

Liquid manure from pig farming

PIS

Cattle manure and DTC (ABP/AW Category 2)

Cattle manure

Manure (solid) from cattle farming

CAM

Pig manure and DTC (ABP/AW Category 2)

Pig manure

Manure (solid) from pig farming

PIM

Poultry manure and DTC (ABP/AW Category 2)

Poultry manure

Manure (solid) from poultry POM (and chicken) farming

Sheep manure and DTC (ABP/AW Category 2)

Sheep manure

Manure (solid) from sheep farming

SHM

Goat manure and DTC (ABP/AW Category 2)

Goat manure

Manure (solid) from goat farming

GOM

ABP/AW Category 1 ABP/AW Category 2 (without manure and content of digestive tract) and ABP/AW Category 3

Epizootic animals, fallen animals, blood, heart, lungs Bristles, skin, hooves, heads Horns, bones, stomach, intestines

Residues from slaughter, not OME meat processing. Different Categories (Cat. 1: epizootic animals. Cat. 2: fallen animals. Cat. 3: usable for human alimentation: blood, heart, lung). In addition: bristles, skin, hooves, heads, horns, bones, stomach, intestines

[11]. Also, Table 3 shows a category which is not in the monitoring system, but it is identified using the specification from monitoring system developed by DBFZ [13]. The way of geocoding the calculation elements used to compute key information has been taken from the methodology of monitoring biomass potential [11, 12]. It was used a code consisting of 15 characters (letters and numbers) with the meaning described in Table 4. For example, geocode BA003WIOME01001 refers to total quantity of all categories animal by-products (without manure and DTC) used as element for theoretical potential calculation “residues from breeding animals and slaughterhouses (offal and meat processing)” biomass type (belonging to industrial residua sector) in Brcko District as administrative unit of Bosnia and Herzegovina. In this way, each element in the monitoring system is described by unique geocode and can be represented spatially.

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Table 4 Coding of calculation elements in the monitoring system [11, 12] Code part for

No. of characters

Meaning

Example

Description

Country

2 letters

National level

BA

Bosnia and Herzegovina

Administrative unit

3 figures

Spatial level

003

District Brcko

Sector

2 letters

Biomass categorization

WI

Industrial residues (waste) sector

Biomass

3 letters

OME

Residues from breeding animals and slaughterhouses (offal and meat processing) biomass type

Key information

2 figures

Calculation element

3 figures

Biomass potential calculation

01

Theoretical potential

001

Total quantity of ABP/AW Categories 1, 2 and 3, without manure and digestive tract content (DTC)

3.5 Key Information and Calculation Flowcharts Brosowski et al. [12] propose 10 key information for the determination of biomass potential (Table 5). These ten key information items are presented in tonnes of dry matter (t DM) to ensure the comparability of individual biomasses. In this way, the supply and use of raw materials can be described for all sectors. All calculated relevant quantities in the sectoral study, which are in different units of measurement, should be expressed using these units. For this conversion, the same coefficients were used to calculate the dry matter content of the individual categories as used in the monitoring system Table 5 Key information for biomass potential [11, 12]

ID

Key items of information

1

Theoretical biomass potential

2

Technical biomass potential

3

Not mobilizable

4

Data situation unclear

5

Material use

6

Energetic use

7

Material or energetic use

8

Use not differentiable

9

Technical biomass potential used

10

Mobilizable technical biomass potential

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Table 6 Dry matter content in manure and slaughterhouse wastes (including animal breeding deaths) [11, 33, 34] No

Category of biomass

The ratio of water and dry matter (literature) [33]

Adapted coefficients for the dry matter content [34]

1

Cattle slurry

87.5%/12.5%

0.10

2

Cattle manure

77.3%/22.7%

0.25

3

Pig slurry

87.5%/12.5%

0.05

4

Pig manure

72.4%/27.6%

0.25

5

Sheep manure

63.4%/36.6%

0.30

6

Goat manure

63.4%/36.6%

0.30

7

Poultry manure

55%/45%

0.50

8

Epizootic animals, fallen animals, blood, heart, lungs; bristles, skin, hooves, heads, horns, bones, stomach, intestines

81.2%/18.8% (20–25% dry matter) [35] MBM (meat and bone meal) to 25%; fat to 15%; water 60–65% [14]

MBM 0.20 [35] FAT 0.15 [14]

(Table 6, column “Adapted coefficients for the dry matter content”), except for the eighth category relating to animal by-products from farming, meat production and processing. Also, for calculating the potential for the first seven types of biomass (manure and DTC) in Table 6, the same calculation flow and specific excretion per animal (EA) were used, specifically for large animal (LA) (dairy cows, sows, breeding sheep) and other animal categories (OA) (Table 7), as used in the monitoring system [11, 36]. For the biomass potential related to other animal by-products from farming, meat production and processing (Table 6, biomass type no. 8, belonging to the industrial residues sector), the calculation shown in Table 8 was used [11]. In order to visualize the individual calculation steps, calculation flowcharts were created for the mapped types of biomass of animal origin (Fig. 3). In this way, the flow of calculation of each biomass potential of animal origin is visualized and understood. It is also possible to use another way of comprehensible visualization of the findings applying the Sankey diagrams (example in Fig. 1) [12].

3.6 Data Quality To analyse and compare the quality of the data [11, 12] used in the calculation of the biomass potential of animal origin, their sources were considered. Official statistics have played a key role in modelling the forecasts in the Study on ABP/AW Management and, therefore, in calculating the theoretical potential of these types of biomass (e.g. data on the number of animals and the number of animals slaughtered), so their credibility has been taken into account. In addition to statistics at national,

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Table 7 Specific excretion per animal and key information for biomass types related to manure [36] Specific excretion per animal/biomass type

Poultry manure

Sheep manure

Goat manure

Cattle manure

Pig manure

Cattle slurry

Pig slurry

EA-LA (tonnes per year)

0.06

0.58

0.69

10

1.8

18.6

6.1

EA-OA (tonnes per year)

0.06

0.36

0.69

6

1.1

11.1

3.7

Ratio LA/OA in %

100/0

70/30

100/0

60/40

20/80

60/40

20/80

Key information t DM Theoretic potential

1,396,431

162,201

19,456

933,654

551,381

693,571

371,738

Technical potential

226,312

0

0

36,531

89,823

19,966

48,139

Not mobilizable

1,170,119

162,201

19,456

897,123

461,559

673,605

323,598

Mobilizable tech. potential

226,312

0

0

36,531

89,823

19,966

48,139

municipal, cantonal or entity level, the study used data from national and international literature as well as expert estimates of these values. Therefore, these data sources include: statistics, literature and expert assessment (shown on the right side of the calculation diagram in Fig. 3, “Source of data” column). In the case of literature, domestic and international literature was consulted to determine the values that are applicable in the context of BiH. Where data were not available in statistics or literature, mainly expert assessment relevant to the establishment of the monitoring system (e.g. for dry matter content) was used for mapping and conversion of biomass types. The quality of the above data sources is indicated as follows: “very good” (green), “good” (yellow) and “bad” (red) [12]. The statistics, as well as the literature that is applicable in the context of BiH [11] without the need for adaptation, are labelled “very good”. Expert assessments, depending on how well founded they are, or how much additional information was available to determine this expert assessment, are designated as “very good” or “good”. Expert assessments are otherwise considered to be of poor quality due to their nature.

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Table 8 Calculation used for biomass potential from other animal by-products (ABP/AW without manure and DTC) [11] ID

Key item

Calculation used

1

Theoretical biomass potential

Theoretical potential = (total quantity of ABP/AW Categories 1, 2 and 3, without manure and digestive tract content) * dry matter content (%)/100 Dry matter content (%) = MBM content (%) + fat content (%)

2

Technical biomass potential

Technical potential = quantity of 3rd ABP/AW category ABP/AW processing facilities and infrastructure do not exist so that Category 1 and Category 2 quantities are disposed of by alternative means of destruction

3

Not mobilizable

Not mobilizable = theoretical potential − technical potential − data situation unclear

4

Data situation unclear

Unknown value

5

Material use

Material use = (quantity of 3rd ABP/AW category used for leather industry, pet food production, human nutrition and other industries) * dry matter content (%)/100 Dry matter content (%) = MBM content (%) + fat content (%)

6

Energetic use

Unknown value

7

Material or energetic use

Unknown value

8

Use not differentiable

Unknown value

9

Technical biomass potential used

Technical potential used = material use + energetic use + material or energetic use + use not differentiable

10

Mobilizable technical biomass potential

Mobilizable potential = technical potential − technical potential used

Fig. 3 Part of calculation flowchart (theoretic biomass potential calculation). Source Report on Biomass Potential Monitoring in Bosnia and Herzegovina, 2019 [11]

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4 Result and Discussion After conversion of the quantities for the mapped types of biomass, the values from the sectoral study [14] and the monitoring system [11] are compared and their differences are discussed in the context of the methods used and the data quality of the calculation elements. In order to assess the relevance of the identified amounts of biomass potential of animal origin from the study, it is necessary to analyse the impact of their unused portion relative to the rest of the total biomass potential at national level for 2017. For the purposes of geo-visualization and exploratory analysis of potential biomass quantities for mobilization, it is possible to use an existing biomass atlas or other mapping system with appropriate functionality. The advantages and potential of applying the described approach in the paper are outlined in the conclusion after this section.

4.1 Comparison of the Sectoral Study Results with the Monitoring System Findings By applying the same parameters related to the calculations of certain key information in the monitoring system to the values of the mapped biomass types from the sectoral study, it is provided their comparability. This allows checking the quality of individual sets of data from these two sources and possible corrections. Table 9 compares key information of individual biomass categories. Significant discrepancies were observed between the values from the study [14] and the monitoring system [11], for the biomass types of pig slurry and poultry manure. These discrepancies were due to the difference in manure quantities for these animal species in the developed model (used in the study) compared to the original statistics (used in the monitoring system) (illustrated in Table 2, first and second rows). Should it be decided to accept these values from the study as relevant and start using them in the monitoring system, they could represent an upper limit (maximum) for the potentials of these biomass types. The values for the other types of biomass (Table 9) are relatively well matched, so this is an additional control, making the calculations and expert assessments more reliable. In addition to the national level, calculations are also provided at the entity, cantonal and municipal levels.

4.2 Applied Methodologies and Data Quality Both approaches used to calculate quantities for biomass types of animal origin, in the monitoring system and the sectoral study, are identical in terms of using the same common statistical elements. The difference in methodologies is reflected in the use

Cattle slurry

Study

693,571

19,966

673,605

19,966

Biomass category

Quantities

Theoretical potential

Technical potential

Not mobilizable

Mobilizable potential

20,317

685,447

20,317

705,765

System

48,139

323,598

48,139

371,738

Study

Pig slurry

14,334

96,355

14,334

110,689

System

0

162,201

0

162,201

Study

Sheep manure

0

156,666

0

156,666

System

0

19,456

0

19,456

Study

Goat manure

0

20,832

0

20,832

System

226,312

1,170,119

226,312

1,396,431

Study

Poultry manure

108,193

559,400

108,193

667,593

System

Table 9 Comparison of results from the study on ABP/AW management [14] with findings from the monitoring system [11] at the national level (quantities are given in t DM)

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of different literature sources for modelling and calculation the values of parameters relevant for the quantification of these types of biomass. Furthermore, although the aim of both approaches is to quantify the amounts of this biomass, their purpose is different and therefore the way in which the available data are used is different. Specifically, the goal of the monitoring system is to investigate and quantify the unused potential of biomass for its mobilization. On the other hand, the aim of the Study on ABP/AW Management, in this context, is to identify the quantities of ABP/AW in accordance with Regulations EC 1069/2009 and 142/2011 for their safe disposal and management that excludes risks to human and animal health. As this is a sector study, a more detailed analysis of the available statistics reliability has been conducted, and several aspects of their use combined with literature data and expert assessment have been considered. The observed discrepancies in the entity statistics are compensated by the development of model whose application mainly led to an increase in ABP/AW quantities related to the number of pigs and poultry. Regarding the quality of the data sources [12] used in the sectoral study and for conversion the calculation elements of the mapped biomass types, it is at the level of the data quality used in the monitoring system. The use of identical initial datasets, as well as parameters taken from the literature, implies the same quality of data.

4.3 Determination of Animal By-Products Biomass Potential Impact As the values regarding the use of the technical potential are not known, the impact of biomass potential [12] of animal by-products from farming, meat production and processing (type of biomass no. 8 in Table 6) in this case can only be determined in theoretical terms (Table 10). In this context, the diagram in Fig. 4 presents its theoretical potential in relation to other types of biomass in the monitoring system. Also, the diagram presents biomass types from the study [14] whose values differ significantly from the corresponding values in the monitoring system [11] (pig slurry and poultry manure—box with dashed line). Their deviation indicates the importance of monitoring the biomass potential of animal by-products and animal waste. Figure 1 shows the total maximum potential for all 23 biomass types investigated in BiH for the reference year 2015 with a value of about 10.4 million t DM. In 2017, an amount of DM 6.9 million was recorded (https://atlasbm.bhas.gov.ba/). The establishment of the ABP/AW management infrastructure would release additional biomass potential which, in 2017, would theoretically be 32 thousand t DM from slaughterhouse waste (including animal breeding deaths) and 1.022 million t DM from ABP/AW altogether (slaughterhouse waste, animal breeding deaths, manure and digestive tract content). Compared to other quantities of biomass (Fig. 4), this would be 0.4% and 14.8% respectively of the total balance of theoretical potential of

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Table 10 Key information for the biomass potential of animal by-products at national level for 2017 [14] Key information

Biomass quantity in tonnes

Dry matter conversion coefficient (MBM)

Dry matter conversion coefficient (FAT)

Biomass quantity in t DM (MBM)

Biomass Total quantity in quantity in t DM (FAT) t DM

Theoretical potential

92,201

0.20

0.15

18,440

13,830

32,271

Technical potential

65,833

0.20

0.15

13,167

9875

23,042

Not mobilizablea

26,368

0.20

0.15

5274

3955

9229

Mobilizable potentialb

65,833

0.20

0.15

13,167

9875

23,042

a The quantities of biomass that cannot be used currently, because it is not established infrastructure

for ABP/AW management quantities of biomass that can be used, but further research is needed to determine how much of this amount is already being used and how

b The

Fig. 4 Theoretic biomass potential from animal by-products and animal waste [14] compared to other types in Bosnia and Herzegovina [11]

biomass in BiH, which represents a significant impact. Only the theoretical potential of manure and digestive tract content, in this impact analysis, is 990 thousand t DM. Taking into account the conversion factor of 16.5 GJ/t DM, this quantity corresponds to 16,335 TJ or 390.2 ktoe in primary energy supply, i.e. 20% of the expected amount of energy from renewable sources for 2020 (the total goal is 1940.5 ktoe) [11].

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Fig. 5 User environment of the online biomass potential atlas

4.4 Biomass Potential Mapping Monitoring of biomass potential includes identification, collection and input, i.e. processing of relevant data related to the assessment of biomass potential in forestry and agriculture in BiH. A part of the monitoring system presents publicly available data through an online platform/atlas that can be updated regularly (Fig. 5). It serves as a source of relevant data for policy makers to create decisions that will lead to sustainable use of biomass for energy purposes. The database linked to the online atlas contains information on relevant biomass data and appropriate sources at the state, cantons, entities, Brcko District and municipalities levels in BiH [11]. All data updated in the database are automatically visualized on the geoportal of the biomass potential atlas. The user environment of the atlas is based on best practice for creating online interactive maps [37–39], most of all to be simple and easy to understand (Fig. 5).

5 Conclusion In this paper, the biomass categories were mapped from the Study on ABP/AW Management to the Monitoring Biomass Potential System in BiH and the results are offered for the purpose of expanding and updating database and online atlas. The

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findings of this paper, in addition to the results that can be used in the manner stated above, have multiple benefits. The described approach can be applied to download data from other sectoral studies, thus allowing the database to be updated, but also, when designing new studies, monitoring systems can serve as a tool for sharing and comparing findings on biomass potential with other models, databases and literary sources. The results of the sectoral study were compared with the values of biomass potential from the monitoring system and the observed differences were discussed. These differences are related to two types of biomass (pig slurry and poultry manure), whose values (if accepted as reliable) can also be used in the monitoring system. The impact analysis for the converted values of the mapped biomass types from the study into the monitoring system pointed out the importance of biomass potential from animal by-products and the need to establish an ABP/AW management infrastructure as soon as possible. The impact, in respect of all types of biomass investigated in the monitoring system, for slaughterhouse waste alone is 0.4%, and for ABP/AW altogether is 14.8% of the total balance of theoretical biomass potential in BiH. In order to determine more precisely the available technical potential for mobilization of these types of biomass, it is necessary to determine how much and how it is already being used. Using an online atlas facilitates access to biomass potential data, and by geovisualization, the data becomes more comprehensible and easier for mutual comparison. With the development of web mapping systems with a wide range of tools for display and analysing biomass databases, it is expected that the monitoring system will be more widely applied in the context of making spatial decisions regarding the mobilization of unused biomass potential. In further research, it is necessary to examine in more detail the possibilities of applying a cartographic system (such as the Atlas of Biomass Potential) with functional extension for decision support, specifically for comparison findings from different sectoral studies, and their analysis and spatial presentation.

References 1. United Nations: The Sustainable Development Agenda (2015) 2. Hák, T., Janoušková, S., Moldan, B.: Sustainable development goals: a need for relevant indicators. Ecol. Indic. (2016) 3. Stafford-Smith, M., Griggs, D., Gaffney, O., Ullah, F., Reyers, B., Kanie, N., Stigson, B., Shrivastava, P., Leach, M., O’Connell, D.: Integration: the key to implementing the sustainable development goals. Sustain. Sci. (2017) 4. Matasci, G., Hermosilla, T., Wulder, M.A., White, J.C., Coops, N.C., Hobart, G.W., Zald, H.S.J.: Large-area mapping of Canadian boreal forest cover, height, biomass and other structural attributes using Landsat composites and lidar plots. Remote Sens. Environ. (2018) 5. Houri, A., Machaka-Houri, N.N.: Agave lechuguilla as a potential biomass source in arid areas. J. Sustain. Dev. Energy Water Environ. Syst. 4(1), 89–93 (2016) 6. Havlíˇcková, K., Weger, J., Šedivá, J.: Methodology of analysis of biomass potential using GIS in the Czech Republic. Acta Univ. Agric. Silvic. Mendelianae Brun. LVIII(5) (2010)

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7. Milbrandt, A.: A Geographic Perspective on the Current Biomass Resource Availability in the United States. Technical Report, NREL/TP-560-39181 (2005) 8. Elbersen, B., Startisky, I., Hengeveld, G., Schelhaas, M.-J., Naeff, H., Böttcher, H.: Atlas of EU biomass potentials. Biomass Futures (2012) 9. Agency for Statistics of Bosnia and Herzegovina: Gross Domestic Product of Bosnia and Herzegovina, Production Approach, First Results (2017) 10. BiH Economic Planning Directorate: Bosnia and Herzegovina Report on Development (2013) 11. Pfeiffer, A., Krause, T., Horschig, T., Avdibegovic, M., Custovic, H., Ljusa, M., Comic, D., Mrkobrada, A., Mitschke, T., Mutabdzija Becirovic, S., Ponjavic, M., Karabegovic, A., Brosowski, A.: Report on Biomass Potential Monitoring in Bosnia and Herzegovina (2019) 12. Brosowski, A., Krause, T., Mantau, U., Mahro, B., Noke, A., Richter, F., Raussen, T., Bischof, R., Hering, T., Blanke, C., Müller, P., Thrän, D.: How to measure the impact of biogenic residues, wastes and by-products: development of a national resource monitoring based on the example of Germany. Biomass Bioenergy 127 (2019) 13. Brosowski, A., Thrän, D., Mantau, U., Mahro, B., Erdmann, G., Adler, P., Stinner, W., Reinhold, G., Hering, T., Blanke, C.: A review of biomass potential and current utilisation—status quo for 93 biogenic wastes and residues in Germany. Biomass Bioenergy 95 (2016) 14. Ministry of Foreign Trade and Economic Relations of Bosnia and Herzegovina: Feasibility study on the management of animal by-products and animal waste (ABP/AW) in Bosnia and Herzegovina (2018) 15. Ponjavic, M., Celebicanin, S., Stanojevic, S.: Geoprostorna multikriterijalna optimizacija lokacije za objekte infrastrukture upravljanja animalnim otpadom, Peti naucno strucni skup „5.juni—Svjetski dan zastite okolisa“ (2017) 16. Ponjavic, M., Celebicanin, S., Stanojevic, S., Gazdic, M.: Defining optimal locations of establishment and transportation routes for treatment and storage of animal waste. AGROFOR Int. J. 3(1) (2018) 17. Agency for Statistics of Bosnia and Herzegovina: Statistical Areas: Agriculture, Environment and Regional Statistics, Statistical Reports (2018) 18. Federal Bureau for Statistics: Statistical Yearbooks 2013, 2014, 2015, 2016 19. Republic of Srpska Institute of Statistics: Statistical Yearbooks 2013, 2014, 2015, 2016 20. Ministry of Foreign Trade and Economic Relations of Bosnia and Herzegovina: Agriculture and Rural Development, Livestock Production (2018) 21. European Commission: Regulation no 1069/2009 of the European Parliament and of the Council of 21 October 2009 Laying Down Health Rules as Regards Animal By-Products and Derived Products not Intended for Human Consumption and Repealing Regulation (EC) no 1774/2002 (Animal By-Products Regulation). Brussels (2019) 22. Gagi´c, A.: Animalni otpad u Bosni i Hercegovini—Znaˇcaj, porijeklo, kategorije i koliˇcine, Nauˇcno-struˇcni skup sa medunarodnim sudjelovanjem “Upravljanje animalnim otpadom i održivi razvoj”. In: Proceedings, Academy of Sciences and Arts of Bosnia and Herzegovina (2012) 23. Pearson, A.M., Dutson, T.R.: Inedible Meat By-Products. Elsevier Applied Science, London and New York (1992) 24. Feiner, G.: Meat Products Handbook. Woodhead Publishing Limited, Cambridge, England (2006) 25. Sannik, U., Pitk, P., Lepasalu, L., Soidla, R., Põldvere, A., Saar, R., Tänavots, A., Poikalainen, V.: Calculation model for the assessment of animal byproduct resources in Estonian meat industry. Agron. Res. 13(4) (2015) 26. Oreopoulou, V., Russ, W.: Utilization of By-Products and Treatment of Waste in the Food Industry. Springer (2007) 27. Sannik, U., Pitk, P., Lepasalu, L., Poikalainen, V.: Tool for the assessment and prediction of animal by-product resources. Waste Biomass Valor. (2016) 28. Kuˇcevi´c, D.: Tehnologija govedarske proizvodnje—praktikum (Technology of Cattle Production—Practicum). Agricultural Faculty, University of Novi Sad, Serbia (2015) 29. Uremovi´c, Z.: Govedarstvo. National and University Library, Zagreb, Croatia (2004)

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30. Eurostat Statistics Explained: Glossary: Livestock Unite (LSU) (2013) 31. Rede, R., Petrovi´c, L.J.: Tehnologija mesa i nauka o mesu. Faculty of Technology, University in Novi Sad, Serbia (1997) 32. Vukovi´c, I.: Osnove tehnologije mesa. Veterinary Chamber of Serbia, Belgrade, Serbia (1998) 33. Goletic, R., Kubat, S., Berisa Fazlagic, A.: Stajski otpad sa peradarskih farmi—od problema do iskoristivog resursa, Institut za zdravlje i sigurnost hrane. Zenica, Bosnia and Herzegovina (2019) 34. Bayerische Landesanstalt für Landwirtschaft: Basisdaten (2013) 35. Kricka, T., Voca, N., Jurisic, V.: Alkalna hidroliza kao alternativna metoda sanacije klaoniˇckog ˇ otpada. Casopis za procesnu tehniku i energetiku u poljoprivredi 12(1–2), 15–18. National Society for Process Engineering and Energy in Agriculture, Novi Sad, Serbia (2008) 36. Biomass Potential Mapping in Bosnia Herzegovina—Biomass Atlas. Agency for Statistics of Bosnia and Herzegovina (2019) 37. Karabegovic, A., Ponjavic, M.: Integration and interoperability of spatial data in spatial decision support system environment. In: MIPRO 2010—33rd International Convention on Information and Communication Technology, Electronics and Microelectronics, Proceedings, pp. 1266– 1271 (2010) 38. Karabegovic, A., Ponjavic, M.: Geoportal as interface for data warehouse and business intelligence information system. In: Mach-Król, M., Pełech-Pilichowski, T. (eds.) Advances in Business ICT. Advances in Intelligent Systems and Computing, vol. 257. Springer, Cham (2014) 39. Karabegovic, A., Ponjavic, M.: Online atlas as decision support system for biomass potential assessment. In: 2020 19th International Symposium INFOTEH (2020)

Cost Analysis of Photovoltaic and Battery System for Improving Residential Energy Self-consumption ˇ Amer Ašˇceri´c, Marko Cepin, and Boštjan Blažiˇc

Abstract Constant decrease of photovoltaic and battery system prices imposes the need for cost–benefit analysis of using combined photovoltaic and battery system for own consumption of generated and stored electric energy. Furthermore, European Union promotes increasing self-consumption by reducing feed-in tariffs for electric energy feed into the power grid. The objective of this paper is to provide a cost–benefit analysis of combined photovoltaic and battery system for certain household based on household annual load profile and annual irradiation profile considering the price of equipment, electricity feed-in tariff and retail price. The paper describes dependency of self-consumption indicators on installed photovoltaic power and battery capacity based on simple battery dispatch algorithm. Provided analysis show that investment in improving self-consumption is becoming attractive economical solution. Keywords PV system · Battery energy storage system · Self-consumption · Smart household

1 Introduction Increasing awareness of global warming and the depletion of conventional energy sources has led to an expansion of the use of renewable energy sources. Worldwide installed capacity of renewable energy sources (RES) is in sustained growth. This kind of expansion continues to be driven mostly by new installations, producing electric energy from solar and wind energy. These accounted for 84% of all new facilities installed in 2018, finally pushing the overall share of hydro to just under 50% of the world’s renewable installed capacity [1]. Technological developments A. Ašˇceri´c (B) Public Enterprise Elektroprivreda BiH d.d., Sarajevo, Bosnia and Herzegovina e-mail: [email protected] ˇ A. Ašˇceri´c · M. Cepin · B. Blažiˇc Faculty of Electrical Engineering, University of Ljubljana, Ljubljana, Slovenia © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. Avdakovi´c et al. (eds.), Advanced Technologies, Systems, and Applications V, Lecture Notes in Networks and Systems 142, https://doi.org/10.1007/978-3-030-54765-3_5

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and a decrease in production costs are factors that are highly contributing to the fast spread of solar and wind energy. Due to the financial benefits, most of installed photovoltaic (PV) power plants were maximizing energy feed into the power grid, without use for own consumption. Further increase of installed PV systems on rooftops of residential and commercial buildings will increase and complicate the problem of predicting variations in power and voltage, which will affect the stability and power quality of the low voltage network. However, in recent years many European countries have been advocating policies through feed-in limitation or feed-in tariff reductions supporting self-consumption [2, 3]. Of the total installed PV capacity in Germany (40 GW), 90% are production units of individual power less than 30 kW [4]. As a result of the difference between PV feed-in tariffs and the price of electrical energy taken from the network, the use of the PV system for its own consumption becomes an attractive option versus the sale of the produced energy. Of course, special attention should be paid to the limited simultaneity of PV production and household consumption. One solution to increasing self-consumption is to move suitable loads into periods of PV production surplus using demand side management [5]. The PV system with an additional battery system provides further opportunities for increasing self-consumption. Energy storage batteries are already used in the distribution system, most commonly on the consumer side, to store surplus production, reduce energy exchange with the grid, and maintain the distribution system within operating limits [6]. The use of batteries provides the ability to store excess production so it can be used in periods of production shortages. In this way, energy consumed from the grid is reduced, which leads to greater autonomy of household supply. When using batteries with a capacity of 0.5–1 kWh per kW peak (kWp) of installed PV system power self-consumption increases from 13 to 24% compared to the case without batteries [7]. Research has shown that in the long run, a PV battery system will be more economically viable than PV system alone [8]. Improving household self-consumption, by combining PV system with battery energy storage, electrical energy cost can be reduced even if different electricity price mechanisms are used [9]. The objective of this research is to consider economic benefits of improving household self-consumption. Therefore, annual data of solar irradiation and power demand were obtained. The used dispatch algorithm for household PV battery system is presented in Sect. 2 as well as the effect of PV installed power and the usable battery capacity size on self-consumption indicators. The third section contains the results of conducted cost analysis and a discussion of the results. The last section presents conclusions of this work.

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Fig. 1 Annual PV system production at selected location in p.u.

2 Simulation Model 2.1 Input Data Solar irradiation data is required to simulate the production of the PV system. For the purposes of this paper, hourly solar irradiation data was obtained from PVSOL software for the city of Mostar, Bosnia and Herzegovina. For the observed location, yearly solar energy density is 1526.2 kWh/m2 . Based on data from the PVSOL PV production profile in per unit (p.u.) was obtained (Fig. 1). Capacity factor of considered PV system is 0.1881. Based on the measurement of the observed household load profile was formed, which is shown in Fig. 2. It is assumed that investing in improving self-consumption is more cost effective for household with high yearly consumption. Annual consumption of an observed household is 14.447 MWh.

2.2 Algorithm The household load profile is characterized by peaks during the day as a result of the behavior of the household and the use of domestic appliances. The energy produced by a PV system that can be directly consumed by load is used on-site. If the generated PV power is greater than the load at the observed moment, the energy surplus is stored in the battery until the maximum state of charge (SOC) is reached. If the battery usable capacity is full, excess energy is feed into the grid. If the load is greater than the PV generation power, the battery will be discharged until the minimum SOC is reached. If the battery do not contain enough energy to satisfy demand, then the rest is consumed from the grid. Battery discharging to the grid and

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Fig. 2 Annual load profile of household

charging battery from the grid is not considered in this paper. This algorithm has been adopted to encourage self-consumption and reduce energy consumed from the grid. The conceptual scheme of considered PV battery system is shown in Fig. 3.

Fig. 3 PV-battery system conceptual scheme

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Charging and discharging of the battery was modeled using a simple battery dispatch algorithm described with Eqs. (1)–(5) for each timestep t. The maximum discharge power of battery Pmax_dis for individual timestep depends on the maximum power that battery can give at each timestep Pmax_bat and state of charge. The maximum charge power of battery Pmax_ch for individual timestep depends on the maximum power that battery can accept Pmax_bat , battery maximum usable capacity CAPbat and state of charge. Power of battery discharge Pdis for individual timestep depends on maximum possible discharge power of battery Pmax_dis , load Pload and PV production power PPV for that timestep. Likewise, the power of battery charge Pch for individual timestep depends on maximum possible charge power of battery Pmax_ch , load Pload and PV production power PPV for that timestep. At each timestep SOC is calculated. Total of battery discharge energy and battery charge energy is calculated as a sum of discharge and charge battery energies, respectively, for each timestep. Invertor efficiency ηinv and battery efficiency ηbat were taken into consideration.   S OC Pmax_dis = min Pmax_bat , ηbat t   C A Pbat − S OC Pmax_ch = min Pmax_bat , t    Pload Pdis = min Pmax_dis , max 0, − PP V ηinv    Pload Pch = min Pmax_ch , max 0, PP V − ηinv S OC = S OC + Pch t −

Pdis t ηbat

(1) (2) (3) (4) (5)

Battery SOC, load demand and PV production determine whether energy will be exchanged between household and grid or not. For each timestep following power balance equation must be satisfied: Pgrid = Pload − PP V ηinv − Pdis ηinv +

Pch ηbat

(6)

The used dispatch algorithm for energy management is shown in Fig. 4. Difference between PV production power PPV and load Pload is marked as P.

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Fig. 4 Household PV battery system dispatch algorithm

2.3 Indicators Based on the defined simulation model and the input data, the simulation of household PV battery system for different PV and battery size was performed. To evaluate the simulation results, it is necessary to define certain indicators. Self-consumption rate is described as a ratio of energy self-consumed ESC and energy produced from PV system EPV . Self-consumed energy is a sum of energy consumed directly from the PV system and battery discharge energy. Self-consumption rate SCR is given by following expresion [10]: T T PSC (i) E SC i=1 PSC (i)t = T = Ti=1 SC R = E PV i=1 PP V (i)t i=1 PP V (i)

(7)

Self-sufficiency rate SSR represents the share of self-consumed energy in total energy demand. Self-sufficiency rate is described by following expresion [11]: SS R =

E SC E demand

T

=

i=1 PSC (i)t T i=1 Pload (i)t

T = Ti=1 i=1

PSC (i) Pload (i)

(8)

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The number of storage cycles of a battery can be compared to evaluate battery usage [12]. The number of storage cycles nC can be estimated as the ratio of discharge energy on the DC side of the battery Edis and usable battery capacity CAPbat by following expresion: nC =

E dis C A Pbat

(9)

2.4 Assumptions In simulation, several assumptions have been made. There is no direct exchange of energy between battery and grid. So battery can only be charged with PV produced energy and battery can only be discharged to satisfy load demand, if PV production is not sufficient. The efficiency of an inverter is set to 97% and the efficiency of the battery system to 90%.

2.5 Results Indicators mentioned in section Indicators describe the behavior of the PV battery system based on several factors. Therefore, a sensitivity analysis is required to quantify them. The effect of variation in installed PV power and battery capacity on the value of the mean annual self-sufficiency rate is shown in Fig. 5, while the effect on the self-consumption rate is shown in Fig. 6. Installed PV power and usable battery Fig. 5 Self-sufficiency rate

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Fig. 6 Self-consumption rate

capacity are normalized to the annual load demand of a household. So installed PV power is expresed as kWp of PV system per MWh of consumption (kWp/MWh) and usable battery capacity is expressed as kWh of usable battery capacity per MWh of consumption (kWh/MWh). In this way, it is possible to make analysis independent of annual consumption while neglecting the difference in load profiles. Figure 5 shows that small installed PV power results in small self-consumption. The reason is that small installed PV power implies a small amount of PV generated energy. Considering Eq. (7) consequence of that is the small value of SSR. Figure 6 shows that a small amount of PV generated energy is easily self-consumed, so for small installed PV power, SCR have a high value. With an increase in installed PV power there is an increase in self-sufficiency rate and a decrease in self-consumption rate. With increasing installed PV system power over 1 kWp/MWh SSR tends to saturate because the surpluses of PV production cannot be used for direct consumption or battery charging after reaching maximum SOC. On the other hand SCR shows a tendency to saturate just after 2.5 kWp/MWh of installed PV system power. This is because with increasing installed PV system power generated energy from the PV system also increases which results in increase of energy transferred to the grid. According to Eq. (8) SCR decreases with an increse of PV generated energy which cannot be consumed on-site or used for charging the battery. Both indicators (SSR and SCR) have higher values with larger battery capacity. Anyway, an increase of battery capacity over 2 kWh/MWh have a small effect on SSR and SCR. For the observed household load profile, an SSR of 40% without the use of batteries is achieved at 0.41 kWp/MWh. Considering that the annual consumption of the observed household is 14,447 MWh, this is achieved at 5.92 kWp installed PV power. SCR of 40% without the use of batteries is achieved at 0.69 kWp/MWh or 9.97 kWp for considered household load profile. The additional use of batteries with a useful capacity of 2 kWh/MWh SSR and SCR will increase to 0.64 and 0.93 respectively. Further increases in useful battery

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capacity do not result in a significant increase in SSR and SCR. This is due to the fact that the larger batteries only partially discharge overnight and are not discharged the next morning. A suitable useful battery capacity would be equal to the average consumption from sunset to sunrise. Battery size should be selected based on the nominal PV power and electricity demand of the observed household. In addition to SSR and SCR, the number of storage cycles of the battery was compared for different installed PV power and battery sizes. As can be seen in Fig. 7, the number of storage cycles of the battery has a strong connection to the battery capacity as well as installed PV power. Batteries combined with low installed PV power have only a few cycles per year. The reason is that with small PV installed, there is rarely a surplus of production over consumption, which would charge the batteries. With the increase of installed PV power, the production surplus also increases, and therefore the number of cycles increases. Bigger PV system power than 1 kWp/MWh does not contribute to an annual number of storage cycles, regardless to battery capacity. Most cycles are available for low capacity batteries. So they reach the maximum number of charges faster or have a shorter life span than larger capacity batteries. This indicates that the battery life is conditioned by the configuration of the system. The PV system of 1 kWp/MWh and battery system of 1 kWh/MWh of usable battery capacity charges and discharges roughly once a day. Considering the self-consumption of the PV battery system, it is necessary to look at the amount of energy exchanged between the observed system and the grid. Figure 8 shows the dependency of energy exchange on installed PV power and usable battery capacity. Increasing installed PV power to value at which minimum energy exchange is obtained results in decreasing of exchanged energy as a self-consumed energy is bigger and energy consumed from grid is smaller. Increasing installed PV power over the value at which minimum energy exchange is obtained increases exchanged energy as more PV generated energy is transferred to the grid. In the case of using an additional battery system, for storing surplus PV generation, the Fig. 7 Number of battery storage cycles

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Fig. 8 Energy exchanged with the grid

exchange of energy between household and grid decreases. The reason for this is that battery contributes to the increase of energy self-consumed, so less energy is consumed from the grid. Increasing in battery capacity further decreases exchanged energy. Anyway, increase of battery capacity over 2 kWh/MWh have a small effect on decreasing energy exchanged with the grid. For oversized battery it’s utilization is low, which leads to unnecessary costs. Effect of installed PV power and battery capacity on energy consumed from grid and energy feed into the grid can be seen in Figs. 9 and 10, respectively. Figures 8, 9 and 10 show energy exchanged between household and grid normalized to annual household consumption. It should be noted that the presented results depend on the technology used, input data, simulation model, limitations. Of course, load demand and PV generation have a special influence on the indicators shown. Nonetheless, the results presented can Fig. 9 Energy consumed from the grid

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Fig. 10 Energy feed into grid

provide an indicative assessment of the indicators for the PV battery household system.

3 Cost Analysis of the PV Battery System After energetic consideration of household self-consumption, cost analysis of installed PV system and battery capacity should be provided. The objective is to achieve a smaller annual electricity cost than retail price. The annual cost is defined in Eq. (10). It consists of three parts: the investment cost of PV system, the investment cost of the battery system and annual operational cost. Fixed costs are equivalent annual investment cost of PV CPV_inv_a given by Eq. (11) and equivalent annual investment cost of battery system Cbat_inv_a given by Eq. (12), while the variable cost is annual operation cost Cop_a described by Eq. (13). In this paper, power grid is considered as zero investment generator producing electricity at retail price. Likewise, the price of energy feed into the grid should be taken into account. Cannual = C P V _inv_a + Cbat_inv_a + Cop_a

(10)

C P V _inv_a = C P V PP V _install C R FP V

(11)

Cbat_inv_a = Cbat C A Pbat C R Fbat

(12)

Cop_a = C P Vop

T  i=1

PP V (i)t + Cbatop

T  i=1

(Pch (i) + Pdis (i))t

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+ Cbuy E f r om grid − Csell E togrid − C P Vsub

T 

PP V (i)t

(13)

i=1

Meaning of marks used in Eqs. (11)–(13) are: CPV —PV system price (e/kWp) PPV install —installed power of PV system (kWp) CRFPV —capital recovery factor of PV system Cbat —battery price (e/kWh) CAPbat —battery capacity (kWh) CRFbat —capital recovery factor of battery system CPvop —operational cost of PV system (e/kWh) Cbatop —operational cost of battery system (e/kWh) Cbuy —price of electric energy consumed from grid (e/kWh) Efromgrid —energy consumed from grid (kWh) Csell —price of energy feed into grid without subsidy (e/kWh) Etogrid —energy feed into grid (kWh) CPvsub —subsidy price of PV energy produced (e/kWh). Capital recovery factor CRF, which is calculated based on interest rate i, lifetime of PV system NPV and lifetime of battery system Nbat , is given by following expresions: C R FP V =

i(i + 1) N P V (i + 1) N P V − 1

(14)

C R Fbat =

i(i + 1) Nbat (i + 1) Nbat − 1

(15)

The effect of installed PV power and usable battery capacity on mean electricity costs on a yearly basis without subsidy is shown in Fig. 10. As can be seen in Fig. 11 there is small reduction of electricity cost in case that small power PV system is used. Otherwise investment in PV battery system with current prices of PV and battery systems have no contrubution on reducing electricity cost. So calculations were made for three scenarios in reference to PV and battery systems price as well as reducing of feed-in tariffs. Scenario 1 represents current prices, while scenario 2 and scenario 3 represent medium-term and long-term price estimate.

3.1 Assumptions For each of the three scenarios price of the PV system, battery system and feed-in tariff is defined. Values used for feed-in tariff, PV and battery system for considered scenarios are shown in Table 1. Lifetime of PV system is set to 20 years, while a lifetime of the battery system is set to 10 years. Considered interest rate is 4%. For

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Fig. 11 Mean annual electricity price without subsidy

Table 1 Parameters of considered scenarios

Category

Scenario 1

Scenario 2

Scenario 3

PV system cost (e/kWp)

1500

1200

900

Battery system cost (e/kWh)

1500

1000

500

Feed-in tariff (e/kWh)

0.20815

0.08

0.02

Bosnia and Herzegovina household retail electricity price is 0.06882 e/kWh, which is not realistic price and is encouraged by the state. Therefore, for the purpose of this paper retail price of 0.206 e/kWh will be used which is the European average [13]. Used PV generated selling price is 0.05564 e/kWh without subsidy. The current subsidy price is 0.20815 e/kWh, which is very high. The annual operational cost of the PV system is 0.05 e per installed kWp. For battery system annual operational cost is 0.005 e per kWh of charged and discharged energy. Scenarios were implemented on household with PV installed power of 1 kWp/MWh and usable battery capacity of 1 kWh/MWh.

3.2 Scenario 1 Currently, due to goals set by the European Union on the promotion of the use of energy from renewable sources feed-in tariff is set very high [14]. High feed-in tariff is motivating for investment in renewables with the aim to maximize the energy feed into the grid and thus the investor’s profit. Figure 12 show the effect of installed PV power and usable battery capacity on mean annual electricity cost. As could be

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Fig. 12 Mean annual electricity price (scenario 1)

expected bigger PV system power results in a decrease of electricity cost. Due to bigger feed-in tariff than electricity buying price, the producer can provide bigger revenue of feed-in energy than the expence of energy consumed from the grid for large enough PV system. Therefore the negative price is obtained. Figure 13 shows that for PV power of 1 kWp/MWh and usable battery capacity smaller than 1.9 kWh/MWh mean annual electricity price is smaller than retail price. Figure 14 shows that for PV power larger than 0.45 kWp/MWh and usable battery capacity of 1 kWh/MWh mean annual electricity price is smaller than the retail price. The effect of different installed PV power and usable battery capacity on mean annual electricity cost is shown in Fig. 15. As can be seen in Fig. 15, current feed-in tariffs are convenient for making a profit and not reducing expenses for electricity consumption. This has a contra effect on the increase of self-consumption because Fig. 13 Electricity price structure as a function of usable battery capacity considering installed PV power of 1 kWp/MWh (scenario 1)

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Fig. 14 Electricity price structure as a function of installed PV power considering usable battery capacity of 1 kWh/MWh (scenario 1)

Fig. 15 Mean annual electricity price as a function of installed PV power and usable battery capacity (scenario 1)

it is stimulating to feed all produced energy of the PV system into the grid and not to invest in the battery system as it only reduces profit.

3.3 Scenario 2 So the current feed-in tariff system support investment in building PV power plants but does not contribute to the increase of self-consumption. Due to this in near future, tariffs should be reduced [3]. Scenario 2 considers a medium-time estimate

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for feed-in tariff, PV and battery system price as well as the effect that have on selfconsumption. Figure 16 represents graphical representation of how PV and battery system size effect mean annual cost for pricing used in scenario 2. Comparing Figs. 12 and 16: it is obvious that with system configuration considered in scenario 2 negative mean annual cost (profit) is not achieved. Looking at the mean annual price structure for installed PV system power of 1 kWp/MWh (Fig. 17) it can be concluded that usable battery capacity less than 1.35 kWh/MWh results in smaller mean annual electricity price than retail price. Figure 18 shows how installed PV power effect mean annual electricity price for input parameters defined for scenario 2. Battery system of usable capacity 1 kWh/MWh should be combined with a PV system of installed power above 0.6 kWp/MWh in order to achieve a smaller electricity price than retail price. Fig. 16 Mean annual electricity price (scenario 2)

Fig. 17 Electricity price structure as a function of usable battery capacity considering installed PV power of 1 kWp/MWh (scenario 2)

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Fig. 18 Electricity price structure as a function of installed PV power considering usable battery capacity of 1 kWh/MWh (scenario 2)

Feed-in tariff reduction in proportion to the price of PV and battery system will result in increasing self-consumption. Economical benefit will not be making a profit on feeding renewable energy into the grid, but the reduction of electricity expenses (Fig. 19). Fig. 19 Mean annual electricity price as a function of installed PV power and usable battery capacity (scenario 2)

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Fig. 20 Mean annual electricity price (scenario 3)

3.4 Scenario 3 The development of PV and battery technology and improvement of the production process will lead to further reduction of PV and battery system prices. Proportionally feed-in tariff income should further decrease. Scenario 3 considers a long-term estimate of feed-in tariff value, price of PV and battery system. Figure 20 shows the behavior of mean annual electricity cost depending on installed PV power for different values of usable battery capacity. Minimum electricity cost is obtained in a range of 0.3–0.7 kWp/MWh depending on usable battery capacity. Bigger battery capacity allows larger PV system in order to minimize mean cost. Looking at electricity price structure depending on usable battery capacity while the installed PV system power is 1 kWp/MWh it can be concluded that for usable battery capacity under 1.5 kWh/MWh mean annual electricity price is under retail price (Fig. 21). Figure 22 shows that exploitation of a battery system with 1 kWh/MWh of usable capacity can reduce household expenses if installed PV power is in range between 0.4 and 1.7 kWp/MWh. Electricity price for the household which is exploiting PV battery system depends on installed PV and battery size. In case of the feed-in tariff of 0.02 e/kWh as well as price of 900 e/kWp of installed PV system and 500 e/kWh of usable battery capacity such dependency is presented in Fig. 23. Figure 24 shows effect of PV and battery price on annual mean electricity price in case that there is no feed-in tariff subsidy for installed PV power of 1 kWp/MWh and battery capacity of 1 kWh/MWh. As can be seen, smalller annual mean electricity cost, compared to retail price (0.206 e/kWh), will be achieved if battery cost is under 900 e per kWh of usable battery capacity and installed PV power cost is under 1450 e/kWp.

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Fig. 21 Electricity price structure as a function of usable battery capacity considering installed PV power of 1 kWp/MWh (scenario 3)

Fig. 22 Electricity price structure as a function of installed PV power considering usable battery capacity of 1 kWh/MWh (scenario 3)

4 Conclusion Battery system can store surpluses of produced PV energy and enables it’s usage in periods of PV energy shortage. So battery system combined with PV system contribute to increase of self-consumption. The analysis showed that PV and battery size have high impact on degree of self-consumption. It should be emphasized that too small as well as oversized PV or battery size have less contribution on improving self-consumption. For oversized battery capacity it’s utilization is low, which leads to unnecessary investment costs. On the other hand, batteries with small capacity don’t have a significant impact on self-consumption because in that case displaced load is low. A similar conclusion stands for the PV system. Small installed PV power

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Fig. 23 Mean annual electricity price as a function of installed PV power and usable battery capacity (scenario 3)

Fig. 24 Mean annual electricity price as a function of installed PV system power cost and usable battery capacity cost

has a marginal contribution to self-consumption, while oversized PV power doesn’t increase self-consumption energy. Cost-optimal system configuration of PV battery system for household highly depends on costs of PV and battery system as well as retail price and feed-in tariff. Considering feed-in tariff reduction policy and trend of decreasing PV and battery cost, installing combined PV and battery system with goal of self-consumption energy increase is becoming an attractive economical solution.

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References 1. IRENA: Renewable Energy Capacity Highlights (2019) 2. Castillo-Cagigal, M., et al.: PV self-consumption optimization with storage and active DSM for the residential sector. Sol. Energy 85(9), 2338–2348 (2011). https://doi.org/10.1016/j.sol ener.2011.06.028 3. European Commission: Best practices on renewable energy self-consumption. J. Chem. Inf. Model. 53(9), 1689–1699 (2015). https://doi.org/10.1017/CBO9781107415324.004 4. Bayram, I.S.: Energy storage sizing and photovoltaic self-consumption in selected households in Qatar. In: 2018 8th International Conference on Power and Energy Systems ICPES 2018, pp. 229–233 (2019). https://doi.org/10.1109/ICPESYS.2018.8626964 5. Zong, Y., Mihet-Popa, L., Kullmann, D., Thavlov, A., Gehrke, O., Bindner, H.W.: Model predictive controller for active demand side management with PV self-consumption in an intelligent building. In: IEEE PES Innovative Smart Grid Technologies Conference Europe, pp. 1–8 (2012). https://doi.org/10.1109/ISGTEurope.2012.6465618 6. Bayram, I.S., Ustun, T.S.: A survey on behind the meter energy management systems in smart grid. Renew. Sustain. Energy Rev. 72, 1208–1232 (2017). https://doi.org/10.1016/j.rser.2016. 10.034 7. Luthander, R., Widén, J., Nilsson, D., Palm, J.: Photovoltaic self-consumption in buildings: a review. Appl. Energy 142, 80–94 (2015). https://doi.org/10.1016/j.apenergy.2014.12.028 8. Weniger, J., Tjaden, T., Quaschning, V.: Sizing of residential PV battery systems. Energy Procedia 46, 78–87 (2014). https://doi.org/10.1016/j.egypro.2014.01.160 9. Zhou, L., Zhang, Y., Lin, X., Li, C., Cai, Z., Yang, P.: Optimal sizing of PV and bess for a smart household considering different price mechanisms. IEEE Access 6, 41050–41059 (2018). https://doi.org/10.1109/ACCESS.2018.2845900 10. Farinet, D., Maurer, M., Vacca, L., Spataru, S.V., Stroe, D.I.: Battery lifetime analysis for residential PV-battery system used to optimize the self consumption—a Danish scenario. In: 2019 IEEE Energy Conversion Congress and Exposition ECCE 2019, pp. 6693–6698 (2019). https://doi.org/10.1109/ECCE.2019.8912280 11. Weniger, V.Q.J., Bergner, J., Tjaden, T.: Economics of residential PV battery systems in the self-consumption age. In: 29th EU-PVSEC, Sept 2014, pp. 3871–3877. https://doi.org/10.4229/ EUPVSEC20142014-7DO.14.3 12. Werner, C., Gerlach, A., Beckel, O.: Photovoltaic with residential energy storage: an overview on economics, system design and politics (2012) 13. Gfk Belgium Consortium: Study on ‘Residential Prosumers in the European Energy Union’. JUST/2015/CONS/FW/C006/0127. Framework Contract EAHC/2013/CP/04”, May 2017, pp. 1–234. https://doi.org/JUST/2015/CONS/FW/C006/0127 14. The European Commission: Renewable Energy Progress Report, COM (2019) 225 Final, pp. 1– 16 (2019)

Machine Learning Based Electrical Load Forecasting Using Decision Tree Algorithms T. Hubana, E. Šemi´c, and N. Lakovi´c

Abstract With the development of electricity markets, accurate load forecasting of the electricity demand plays an important role in power system strategy management. Electrical load forecasting is challenging due to the nonlinearity of its influencing factors, even with the detailed knowledge of the operated system. Also, with the dynamic changes in the electricity market, forecasting errors can be very expensive for the power utilities. On the other hand, machine learning methods coped with the nonlinear data and demonstrated their applicability over the past decade. In this research, a machine learning model is proposed to be used for the electrical load forecast. The proposed method is based on regression decision trees, where the best one is chosen between 68 different tested regression trainers. Data used for the purpose of training and testing are real historical load and temperature data from the Bosnia and Herzegovina. The results reveal that the proposed method presents a promising forecasting method with satisfied accuracy. This paper contributes to the existing body of knowledge by testing and comparing the existing forecasting method used by the power system operator with the proposed machine learning method whose utilization does not require a detailed knowledge of the operated system and its properties. Keywords Machine learning · Artificial intelligence · Load forecast · Power system · Decision tree

1 Introduction Electrical load forecasting is important for utility owners, power system managers, energy planners and power system operators. Electrical load forecasting divides into T. Hubana (B) Graz University of Technology, Graz, Austria e-mail: [email protected] E. Šemi´c · N. Lakovi´c Public Enterprise Elektroprivreda of Bosnia and Herzegovina, Sarajevo, Bosnia and Herzegovina © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. Avdakovi´c et al. (eds.), Advanced Technologies, Systems, and Applications V, Lecture Notes in Networks and Systems 142, https://doi.org/10.1007/978-3-030-54765-3_6

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three distinct categories: long-term forecasting, medium-term forecasting and shortterm forecasting. Long-term forecasting is oriented to predicting multi-year trends in electrical load which impacts the decisions regarding infrastructure investment. This requires a lot of contextual information regarding governmental policy, economic growth and industrial activity within the country of interest [1]. Medium-term forecasting takes week to month periods into consideration [2], while short-term forecasting focuses on the electrical load forecasting on a day to day basis. In this paper, short-term electrical load forecasting is considered. Electrical load forecasting is an important part in the field of power systems and it plays a very crucial role when it comes to economic aspects of managing the power system and production capacities [3]. The importance of accurate electrical load forecasting is especially emphasized in countries with relatively underdeveloped industry such as Bosnia and Herzegovina, where electrical load is highly dependent on and population activities [4] and habits during the day. Also, models for electrical load forecasting on a daily basis are found to be dependent on weather conditions due to the strong correlation between weather variables and electrical load [5]. Accurate electrical load forecasting allows better energy planning and management and ensures optimal supply. Load forecast techniques generally can be classified into two categories: parametric and nonparametric techniques [5]. The parametric techniques are based on the assumptions that sampled data follow a probability distribution based on a fixed set of parameters and include linear regression, exponential smoothing, auto regressive moving average (ARMA), etc. While non-parametric techniques which consist mainly of Artificial Intelligence—have flexible parameter sets which may increase or decrease depending on new information. Such examples include Support Vector Machine (SVM), Artificial Neural Networks (ANN), Machine Learning (ML) and others. These techniques, however have different strengths and weaknesses as pertaining to the research problem at hand [5]. Electrical load forecasting on a daily basis needs to account for the large number of behavioral variations and is a non-linear problem [2]. Artificial intelligence algorithms have been used extensively in the last decade to solve non-linear problems [6–12] in electrical power systems. These techniques have also proved to be important and extremely useful in forecasting electrical load in the short term for more effective operation of the grid by the power system operators. In this paper, Machine Learning (ML) technique is used to forecast electrical load. Advances in computers have allowed these traditionally expensive methods to be used on vast datasets where patterns may be obscured by the noise or the scale of the data. Patterns can be used to form models to make predictions on new data [1]. Between different machine learning methodologies, decision trees have emerged as the ones with promising accuracy when it comes to electrical load forecasting [13–15]. The introduction section is followed by theoretical background that gives a brief overview of the concept of machine learning and decision tree algorithms. After a description of the proposed methodology, the results are presented and discussed. Finally, the conclusion and the future research directions are given.

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2 Theoretical Background 2.1 Machine Learning A machine learning task is the type of prediction or inference being made, based on the problem or question that is being asked, and the available data. Machine learning tasks rely on patterns in the data rather than being explicitly programmed [16]. Examples include classification, regression, and structured prediction [16]. However, supervised learning is the machine learning task of learning a function that maps an input to an output based on example input–output pairs [17]. It infers a function from labeled training data consisting of a set of training examples [18]. In supervised learning, each example is a pair consisting of an input object (in this paper a vector) and a desired output value (in this paper numerical value). A supervised learning algorithm analyzes the training data and produces an inferred function, which can be used for mapping new examples. This requires the learning algorithm to generalize from the training data to unseen situations in a “reasonable” way [17, 18]. For the forecasting methods, regression algorithms demonstrated the best fit. Regression algorithms model the dependency of the label on its related features to determine how the label will change as the values of the features are varied. The input of a regression algorithm is a set of examples with labels of known values. The output of a regression algorithm is a function, which can be used to predict the label value for any new set of input features [16].

2.2 Decision Tree Algorithms Decision tree algorithms present an important part of the machine learning, especially when it comes to regression models. Decision tree algorithms create a model that contains a series of decisions: effectively a flow chart through the data values. Features do not need to be linearly separable to use this type of algorithm, and features do not need to be normalized, because the individual values in the feature vector are used independently in the decision process. Boosted decision trees are an ensemble of small trees where each tree scores the input data and passes the score onto the next tree to produce a better score, and so on, where each tree in the ensemble improves on the previous [16]. The decision tree building algorithm is based on determination and the classification of objects by testing the values of their properties. It builds the tree in a top down fashion, starting from a set of objects and a specification of properties. At each node of the tree, a property is tested using the criterion called gain below. The information entropy theory that underpins this criterion can be given in one statement: The information conveyed by a message depends on its probability and can be measured in bits as minus the logarithm to the base two of that probability. A decision tree structure is shown in Fig. 1.

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Fig. 1 Decision tree structure

  Supposed a set of S and f r eq C j , S standing for the number of cases in S belonging to the class C j , the information entropy is [19]:      k  f r eq C j , S f r eq C j , S in f o(S) = − · log2 |S| |S| j=1

(1)

After T has been partitioned in accordance with the n outcome of a test X. the expected information requirement can be found as the weighted sum over the subsets, as [19]:  n    Ti    in f o X (S) = −  T  · in f o(Ti )

(2)

i=1

The quantity: gain(X ) = in f o(T ) − in f o X (S)

(3)

Measures the information that is gained by partitioning T in accordance with the test X. The gain criterion selects a test to maximize this information gain. But this gain criterion has strong bias in favor of tests with many outcomes. It can be rectified by a kind of normalization:    n    Ti   Ti      split_in f o(S) = −  T  · log2  T  i=1

(4)

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which represents the potential information generated by dividing T into n subsets. Now a new gain criterion is gain_ratio(X ) =

gain(X ) split_in f o(X )

(5)

which express the proportion of information generated by the split that appears helpful for classification.

3 Methodology For the purpose of data preparation, historical data about load consumption and air temperatures are collected. The hourly load data from the largest power system operator (around 700,000 customers) in Bosnia and Herzegovina for the period from 2015 to 2020 are used. Besides that, the hourly air temperatures for the 5 largest cities in this supplied area that make the largest part of the consumption are collected as well. By using this data, other characteristic values are calculated and associated with each hour load. As a result, each hour load value has 22 properties that reflect the scenario when that load value occurred, and in that way help the machine learning algorithm to learn better. These inputs include: • • • • •

Data about date, hour, weekdays and school days, Data about electricity tariff and loads from previous periods, Previous day temperatures in 5 large cities, Current temperatures in 5 large cities, Data about holidays (e.g. religious).

Outputs that are used in the learning process are the hourly load values. All data used in the learning process are real measured data from the power system operator and the Federal hydrometeorological institute from Bosnia and Herzegovina. Therefore, the inputs for the learning process consisted of 43,032 vectors with 22 values. Correspondingly, the 43,032 outputs were associated with each vector. The machine learning process is conducted in Microsoft Visual Studio, by using the ML.NET Model Builder [16]. The ML.NET Model Builder provides a visual interface to build, train, and deploy custom machine learning models. By using the ML.NET Model Builder, different machine learning algorithms are explored and the one that suits the scenario best, is chosen.

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4 Results and Discussion For the purpose of this research paper, different regression models are used in order to estimate the electrical load according to the presented inputs. During the machine learning process in the ML.NET Model Builder, 68 different models were explored in order to choose the best one for the formulated problem. The results of the 3 best models are shown in Table 1. As shown in Table 1, FastTreeTweedieRegression proved to have the best results. It presents the decision tree regression model using Tweedie loss function. This trainer is a generalization of Poisson, compound Poisson, and gamma regression. The Tweedie boosting model follows the mathematics established in [20]. However, in order to test the trained algorithm, the new data will be used to prove the practicality and compare it to current estimation models used by the power system operator. Because of that, the measured data from the December 2019 were excluded from the training data. These data will be used to test and visually compare the proposed method with the existing forecasting methods. The real load forecasts that were used in December 2019 are also obtained from the dispatch center (DC) of the power system operator. These forecasts are made by the experienced engineers that have a detailed knowledge of the operated system. The comparison of the forecast methods with real measured data is shown in Fig. 2. In this scenario, the data between 02.12.2019 and 08.12.2019 are used for evaluation. The average error of the machine learning based algorithm is 2.45%, while Table 1 Top 3 models explored Trainer

R2

Absolute loss

Squared loss

RMS loss

FastTreeTweedieRegression

0.9859

9.3032

195.5376

13.9835

FastTreeRegression

0.9858

9.5738

196.0959

14.0034

LightGbmRegression

0.9855

9.7608

200.8976

14.1738

Fig. 2 Comparison of forecast models with measured models during one week

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the error of the DC forecast is 2.92% for the analyzed week time span. The hourly forecast error for both methods is shown in Fig. 3. However, since the forecast error varies from hour to hour, and day to day, the machine learning algorithm is in some scenarios better, and in some scenarios worse that the DC forecasting method. A comparison of forecast models with measured models during one daily load forecast (on 06.12.2019), is shown in Fig. 4. In this scenario, the forecast error of the machine learning method is 1.17%, while the forecast error of the existing DC method is 2.60%. The hourly forecast error for the analyzed day is shown in Fig. 5. The presented comparative results for the machine learning based load forecasting show that the algorithm can be used with an accuracy close to the DC forecasts (in some cases even better). This means that the algorithm can be used without a detailed

Fig. 3 Hour forecast error during the analyzed week

Fig. 4 Comparison of forecast models with measured values for one day

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Fig. 5 Hour forecast error during the analyzed day

knowledge of the operated system and experience in the area of load forecasting. Also, since the algorithm is developed in Microsoft Visual Studio with the ML.NET Model Builder, the algorithm can be easily integrated and used in other software solutions.

5 Conclusion The aim of this paper is to design the electrical load forecasting model which will achieve satisfactory accuracy in electrical load forecasting process for each hour of the day. A boosted decision tree machine learning model for the electrical load forecast is proposed in this paper. The accuracy of electrical load forecasting data affects the process of operational management of power system and production capacities which implies financial consequences for the power system operator. During the design of the proposed model and the training, an effort has been made to account as many parameters that affect the consumption behavior as possible. Using historical data of electrical load, air temperature, and other parameters that affects consumption behavior, the proposed method shows that it can forecast electrical load with an accuracy which is very close to accuracy achieved by an engineer with years of experience. While this accuracy is worse in some cases and better in other cases than accuracy achieved by experienced engineer, it can be at a very satisfactory level. The proposed method for electrical load forecast can be extended with additional input parameters that affects the level of electrical load for every hour of the day in order to obtain even more accurate data in the electrical load forecasting process. In addition, in order to improve the accuracy of the obtained data, it is recommended to retrain algorithm with new obtained data after a certain period. The proposed method for

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electrical load forecast, with continuous improvements, can become a very useful tool in the process of energy planning and operational management of the power system and production capacities.

References 1. Scott, D., Simpson, T., Dervilis, N., Rogers, T., Worden, K.: Machine learning for energy load forecasting. J. Phys. Conf. Ser. (2018) 2. Warrior, K.P., Shrenik, M., Soni, N.: Short-term electrical load forecasting using predictive machine learning models. In: 2016 IEEE Annual India Conference, INDICON 2016 (2017) 3. Abera, F.Z., Khedkar, V.: Machine learning approach electric appliance consumption and peak demand forecasting of residential customers using smart meter data. Wirel. Pers. Commun. (2020) 4. Madhavi, K.S.L., et al.: Advanced electricity load forecasting combining electricity and transportation network. In: 2017 North American Power Symposium, NAPS 2017 (2017) 5. Alagbe, V., Popoola, S.I., Atayero, A.A., Adebisi, B., Abolade, R.O., Misra, S.: Artificial intelligence techniques for electrical load forecasting in smart and connected communities. In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (2019) 6. Šari´c, M., Hubana, T., Begi´c, E.: Fuzzy logic based approach for faults identification and classification in medium voltage isolated distribution network. In: Hadžikadi´c, M., Avdakovi´c, S. (eds.) Advanced Technologies, Systems, and Applications II. IAT 2017. Lecture Notes in Networks and Systems, vol. 28 (2018) 7. Hubana, T., Saric, M., Avdakovic, S.: Approach for identification and classification of HIFs in medium voltage distribution networks. IET Gener. Transm. Distrib. 12(5) (2018) 8. Hubana, T., Šaric, M., Avdakovic, S.: High-impedance fault identification and classification using a discrete wavelet transform and artificial neural networks. Elektroteh. Vestn./Electrotech. Rev. 85(3) (2018) 9. Hubana, T., Šari´c, M., Avdakovi´c, S.: Classification of distribution network faults using HilbertHuang transform and artificial neural network. In: Avdakovi´c, S. (ed.) Advanced Technologies, Systems, and Applications III. IAT 2018. Lecture Notes in Networks and Systems, vol. 59 (2019) 10. Hubana, T.: Transmission lines fault location estimation based on artificial neural networks and power quality monitoring data. In: Proceedings—2018 IEEE PES Innovative Smart Grid Technologies Conference Europe, ISGT-Europe 2018 (2018) 11. Hubana, T., Šari´c, M., Avdakovi´c, S.: New approach for fault identification and classification in microgrids. In: Avdakovi´c, S., Mujˇci´c, A., Mujezinovi´c, A., Uzunovi´c, T., Voli´c, I. (eds.) Advanced Technologies, Systems, and Applications IV—Proceedings of the International Symposium on Innovative and Interdisciplinary Applications of Advanced Technologies (IAT 2019). IAT 2019. Lecture Notes in Networks and Systems, vol. 83 (2020) 12. Šemi´c, E., Hubana, T., Šari´c, M.: Distributed generation allocation in low voltage distribution network using artificial neural network. In: EUROCON 2019—18th International Conference on Smart Technologies (2019) 13. Yu, X., et al.: Load forecasting based on smart meter data and gradient boosting decision tree. In: Proceedings—2019 Chinese Automation Congress, CAC 2019 (2019) 14. Xie, Z., Wang, R., Wu, Z., Liu, T.: Short-term power load forecasting model based on fuzzy neural network using improved decision tree. In: iSPEC 2019—2019 IEEE Sustainable Power and Energy Conference: Grid Modernization for Energy Revolution, Proceedings (2019)

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15. Khan, A.R., Razzaq, S., Alquthami, T., Moghal, M.R., Amin, A., Mahmood, A.: Day ahead load forecasting for IESCO using artificial neural network and bagged regression tree. In: Proceedings—2018, IEEE 1st International Conference on Power, Energy and Smart Grid, ICPESG 2018 (2018) 16. Machine Learning Tasks—ML.NET | Microsoft Docs 17. Russel, S., Norvig, P.: Artificial Intelligence—A Modern Approach, 3rd edn. (2012) 18. Mohri, M., Rostamizadeh, A., Talwalkar, A.: Foundations of Machine Learning, 2nd edn. (2018) 19. Ding, Q.: Long-term load forecast using decision tree method. In: 2006 IEEE PES Power Systems Conference and Exposition, PSCE 2006—Proceedings (2006) 20. Yang, Y., Qian, W., Zou, H.: Insurance premium prediction via gradient tree-boosted Tweedie compound poisson models. J. Bus. Econ. Stat. (2018)

Comparative Analysis of World’s Energy Prices Versus Those in Bosnia and Herzegovina—Crude Prices and Impact on Profitability of Oil Sector Sanel Halilbegovic, Mirza Saric, Nedim Celebic, and Amna Avdagic

Abstract This research serves the purpose of determining the effect that the crude oil price has on the financial performance of oil companies in the Federation of Bosnia and Herzegovina, during the period of 2014–2018. A knowledge gap is easily detectable since the crude oil price was rarely or never used as an independent variable in relation to the financial performance ratios of oil companies in the Federation of BiH. Additionally, similar studies focus on more popular regions such as United States and Asia. The firm’s performance is measured by standard set of profitability ratios, such as profit margin, return on asset and return on equity, using the information from audited annual financial reports. Results presented at the end of the research are expected to help and guide individuals, companies, population and/or government into understanding how oil companies in Bosnia and Herzegovina behave compared to the movement of global crude oil market prices. Since no similar research was previously conducted in the country or a region, it can serve as a contribution model for other developing or transition markets. Keywords Crude oil price relation · Energy sector profitability · Return on assets · Return on equity · Profit margin

1 Introduction This research is written for every stakeholder in the energy sector, more precisely in the oil and gas industry, more specifically in the relationship between crude oil prices and the financial performance of oil companies. This research investigates the financial profitability of oil companies by studying profit margins of oil companies in relation to the movement of the crude oil price on the global market as one of the S. Halilbegovic · N. Celebic · A. Avdagic International Burch University, Sarajevo, Bosnia and Herzegovina M. Saric (B) Public Enterprise Elektroprivreda of Bosnia And Herzegovina, Mostar, Bosnia and Herzegovina e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. Avdakovi´c et al. (eds.), Advanced Technologies, Systems, and Applications V, Lecture Notes in Networks and Systems 142, https://doi.org/10.1007/978-3-030-54765-3_7

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leading energy types. Volatility of the crude oil price influences market and financial position of oil companies. Constant industrial growth allows crude oil to gain on its value and significance of reserves. As seen with electricity, and deregulation of energy sector, household electricity prices have increased considerably, mainly due to decarbonization, switching to renewable resources. Similar situation is expected in the oil and gas sectors which are considered a heavy polluter. Most of the Western European countries have declared that they will reach net zero carbon emissions by the end of 2050. Such feats will have significant impacts on oil in the Euro market, via additional restrictions, taxes and levies [1]. Energy Community Treaty is the most important international obligation that affects the energy sector. Signed on October 25th, 2005, the community has been tasked with creating a stable and legal market, single regulatory space for trading, security of supply, improving energy efficiency and developing market competition. Unfortunately, political structure and the complexity of government administration has caused BiH to violate the contracted obligations. Commercially profitable oil reserves are still not discovered, however, there are several different types of research conducted and the area of Dinarides has been claimed as a prospective area for exploration. Unfortunately, BiH currently does not have the means or power to engage process of crude oil excavation, until then country remains primarily import focused. All the imported crude oil is processed in refineries “Brod” and “Modrica” both of which are owned by Optima Group and none are in the Federation of Bosnia and Herzegovina [2] (Fig. 1). Petroleum products retail network is mainly structured with many small retailers with less than 5 petrol station and those make up for closely 75% of the market. Fig. 1 Oil market structure in Bosnia and Herzegovina, 2015 (estimate)

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Highest consumption is present in the transport sector with diesel and motor gasoline used the most. According to Worldometers’ “Oil Consumption by country”, Bosnia and Herzegovina is ranked as 117th in the world by oil consumption, which accounts for less than 0.1% of the world’s total consumption and is estimated to the amount of 97,103,871 barrels/day. In 2016, consumption per capita is estimated to be 0.43 gallons/day. The daily deficit is noticeable in this country as its daily consumption is around 35,000 barrels/day whereas Bosnia and Herzegovina is only able to produce between 250 and 300 barrels/day. In order to partially cover this deficit country is forced to import crude oil and its products. Slightly less than 18,500 barrels/s are imported into the country [3]. The research results can be used to prove that crude oil price is an indicator to consider while handling financial performance in Oil and Gas Industry. An interesting factor is introduced in this research and that is how the market for oil products in Bosnia and Herzegovina is heavily dependent on imports. Having this in mind as well as the existence of so-called “free forming of price” makes Bosnia and Herzegovina a very interesting area for conducting this research. The financial performance of the firm is a broad subject. It can be measured with several different ratios such as return on equity (ROE), return on assets (ROA), earnings before interest and taxes (EBIT). The size of the firm plays a big role in financial performance, as the movement of crude oil can be extreme. Only bigger companies can withstand the change and adapt to the new price, due to lower chance of bankruptcy, lower transaction costs and lower operating risk as the smaller companies are unable to use as much debt as the bigger ones. Lameiras (2012) conclusion on the performance of Eurozone companies is that the oil and gas sector have the highest profitability. This type of industry tends to profit the most in the periods when the price of crude oil rises [4]. It is expected from the Balkan region, which is highly import based, to profit from oil price declines, however the effect of the decline is different among Balkan countries because of the different share in total merchandise imports. The period of 2014–2016 is highly in favor of oil-importing countries rather than exporting ones. Most of the Balkan countries are oil importers. Crude oil is a specific resource as it heavily relies on supply–demand but being one of the most valuable resources for the industry it also relies on the geopolitical situation. Annually, Bosnia and Herzegovina use nearly 1 million metric tons of crude oil and its products for the needs of transportation, industrialization, etc. About 60% of that amount is used in the region of the Federation of Bosnia and Herzegovina. In reality, 600,000 million is only the figure of what is published and could be significantly higher [5]. Research conducted by Rados, introduced a hypothesis “Crude oil price on the global market is mainly determined by the supply–demand” to confirm how one of the highest oil production areas such as Saudi Arabia, Iran, Russia, etc. from the period of 1990– 2013 have an impact on crude oil prices. Interesting results showed how by focusing solely on the Brent model in the North Sea, it excludes OPEC countries from the assumption that they are the main influent on the pricing. By focusing on specific areas, researchers have realized that even if some countries increased their production,

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the price of crude oil would still increase which is against the common logic behind the supply–demand model. Based on the research results, it can be concluded the multiple factors influence the pricing of crude oil and that solely relying on the supply–demand can prove highly inaccurate [6]. According to available data, Bosnia and Herzegovina have very little domestic oil and natural gas production. This country heavily relies on importing these types of commodities. The country has failed to address governance and control of the petroleum sector on the national level. Additionally, it lacks in requirements and preferences of local industry involvement. Bosnia and Herzegovina do not have a national oil company. Therefore, it exclusively focuses on oil companies that operate within the country. Similar issues occur in the neighboring countries, excluding Italy. Mediterranean countries generally have poorer petroleum sector performance in comparison with North Sea countries. This is due to the inadequate administrative design model [7]. The year 2014 can be marked as a period of increase in oil production which, as a result, caused a slight drop in the crude oil price. Such event causes consumers of oil products to buy them at a significantly smaller amount of money, which then allows them to increase their spending habits and ultimately increase macroeconomic activity. Activity generates growth in the economy, especially in countries such as China or members of the European Union.

2 Literature Review The aim of this research is to test the profitability of oil companies based on the movement of crude oil prices on the global market. The market of the focus is in the region of the Federation of Bosnia and Herzegovina. It is presumed that this market is not highly competitive and could be labeled as a monopolistic. The idea behind this comes from the behavior of the companies which are experiencing changes in crude oil price. Media in BiH often reports how companies strictly follow increases in crude oil prices and are quick to adjust the oil product prices, while on the other hand, when the crude oil prices drop, companies are reluctant to act accordingly. Profit is the main goal of each company and competing in the market for goods is a means to reach that goal. Research requires a distinction between oil-producing companies and oil companies that resell and/or refine crude oils into different, more widely useful oil products. This type of distinction is important for theoretical reasons. For retail firms and refineries, an increase in crude oil prices is an increase in the input prices. If anything, a negative profit margin and gas price relationship can be expected. For a vertically integrated firm, oil is both input and output. Therefore, an increase in crude oil price is an increase in profits from the products sold at that moment, but on the other hand, input price will also be higher if some of that inputs are purchased rather than being self-produced [8]. Global decline in oil prices has significant financial, macroeconomic and policy implications. The decline has the potential to support growth, reduce inflationary and

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fiscal pressures in most of the oil-importing countries. On the other hand, for the oilexporting countries, a sharp drop in oil prices will expose those countries to a reduction in economic activity, weaker fiscal and external positions. However, commodity prices, including oil, are prone to errors for being volatile. This unpredictability is often amplified by the geopolitical tensions. All of these are the factors that indirectly influence the oil companies. None of these can make a significant impact on the company as per se, but if left unmonitored, consequences can be noticeable [9]. According to research by Tamuleviˇciene, profit and profitability analysis carries the significance of this research, as profit is the ratio that defines the company’s activity the best. It is related to other activity ratios, such as assets, equity, liabilities, expenses, etc. Achieving a high profit should be every company’s goal, therefore, performing a profit analysis and seeking an increase in profit is a crucial step for every company [10]. Bosnia and Herzegovina, as a transitional economy, is one of the poorest countries in Europe. Addressing the impact of oil prices, more specifically decline of those prices has less direct, but significant, substantial and largely beneficial indirect effect. Many positive outcomes come from the fall of crude oil prices such as reduction of agricultural commodity outcomes even with only reduced transport costs. Since this topic can be wide to cover, we have decided to only focus on how oil companies behave and address those changes [9]. The research purpose is to determine if there is a significant relationship between financial performance and crude oil prices. The study will serve the purpose of assessing the impact on financial performance based on the crude oil price change. In addition to assessing, this study will try to bring forth any types of patterns or anomalies within the comparison. Based on the current pricing behavior of the oil companies, we expect to see a positive relationship between the change of crude oil prices and the financial performance of oil companies. Table 1 content serves as an exemplary result of the consequences created by the change in crude oil prices. Most of the Balkan countries profited from the oil price decline in the period of 2013–2014. It is important to emphasize that the drop in the prices is different among each country of Balkan, due to different percentages of total imports being the crude oil product imports. Research is expected to raise awareness of how crucial this commodity in today’s day and age is. Reflecting on several of the strongest and richest countries in the world and understanding how much they’re expanding their oil and gas market shows how little is done in Bosnia and Herzegovina. The government of the Federation of BiH has signed a contract with Table 1 Import of crude oil products in USD and % change Country

2014

2018

% difference

Bosnia and Herzegovina

$701,879,369.00

$364,448,294.00

−48

Croatia

$1,418,780,310.00

$1,524,954,397.00

7

Serbia

$1,105,711,832.00

$1,418,725,154.00

28

Montenegro

$1,814.00

$17.00

−99

Total

$3,226,373,325.00

$3,308,127,862.00

3

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IHS Global as an expert consultant company to prepare a tender for an exploration and exploitation concession. This is one of the big steps the government has taken in the last few years regarding the involvement in the Oil and Gas Industry [11]. In 1990 Bosnia and Herzegovina adopted the Law of Private Economy, which as a result has stimulated the growth of just over 800 gas stations. Most of these gas stations are now closed due to irrational investments. Competitiveness amongst those oil companies was expressed and a significant number of them are operating at their profitability limit. The Law of Private Economy is also the main cause of significant differences in oil product prices between the cities in the Federation of Bosnia and Herzegovina. While the country has deregulated the market, distributors were as a result able to compete for the most competitive price on the market. This situation led to the point where distributors were setting the most favorable price for them, by making sure they never go below a certain point, which ultimately is ironic since they have made the market regulated again [12]. Through this research, we try to evaluate financial performance of the oil industry in the Federation of Bosnia and Herzegovina. Based on the relationship between profitability and crude oil price change, research offers new evidence for the oil industry in Bosnia and Herzegovina. Evidence is going to be in the fashion of statistical and real data of oil companies. The main contribution of this study serves as a guide and basis for any similar research type which will be more thorough.

3 Methodology and Analysis Through this research, authors try to analyze the financial performance of the oil industry in the Federation of Bosnia and Herzegovina. Based on the relationship between profitability and crude oil price change, research offers new evidence for the oil industry in Bosnia and Herzegovina. Evidence is going to be in the fashion of statistical and real data of oil companies. The main contribution of this study serves as a guide and basis for any similar research type which will be more thorough. From the literature review and based on the aim of this research, the following hypothesis can be derived: H1: The Crude Oil Prices are positively related with the financial profitability performance of oil companies in Federation of Bosnia and Herzegovina. For the purpose of this research we have introduced average crude oil prices (COP), per year in the period between 2014 and 2018 as well as return on asset (ROA), return on equity (ROE) and profit margin (PM) of 22 oil companies in the area of Federation of Bosnia and Herzegovina into SPSS program. In order to accurately calculate return on asset, return on equity and profit margin, audited and verified financial information have been provided by the Financial Information Agency (FIA) (Tables 2 and 3). Results that came from SPSS proved how the main hypothesis, H1, cannot be supported as there is an insignificant impact of crude oil prices on the financial profitability of oil companies in the Federation of Bosnia and Herzegovina. The

2014—COP $93.17

Hifa Petrol

Selex

3.10

−18.60

−2.90

Proming doo

Rafinerija Nafte-Brod

4.90

3.00

1.50

Petrol BH

5.60

6.20

1.90

1.50

Orman

6.20

36.00

3.70

10.20

Oil AC

27.40

36.60

0.90

3.60

36.70

0.40

19.20

16.20

Oilmer doo

5.40

15.00

Nestro

Neskovic

0.60

0.30

10.20

Hifa Oktan

Nahonal-Gas doo

7.50

Hifa doo

0.40

12.50

Hifa Oil

KG Oil

15.30

Green Oil

41.40

−17.10

−6.10

G-Petrol

2.90

29.50

0.90

1.20

0.70

3.10

4.60

2.20

9.90

0.40

0.40

3.20

0.50

2.90

2.00

9.50

−3.60

0.00

−25.90

−63.70 0.20

0.60

1.00

PM %

24.10

6.10

ROE%

0.10

28.80

Butmir Oil

El-Tarik Benzinske

1.80

7.20

Antunovic

ROA%

Almy

Oil company

4.70

0.70

0.90

1.50

8.50

3.00

9.20

5.30

15.00

1.10

0.80

12.90

2.30

6.60

12.50

7.00

2.20

0.00

−9.20

6.70

3.50

ROA%

2015—COP $48.72

Table 2 Results of crude oil prices on financial performance of oil companies (2014–2016)

9.60

0.20

3.20

2.80

10.00

5.50

29.20

22.80

36.60

1.50

7.60

39.80

3.50

15.50

17.00

35.60

5.60

0.10

−24.20

23.70

12.20

ROE%

4.40

6.10

0.90

0.50

4.00

4.10

1.90

2.40

9.90

0.90

0.80

4.80

3.60

3.10

2.50

2.80

1.00

0.00

−10.00

0.90

2.10

PM %

2016—COP $43.58

0.70

−8.60

1.00

5.70

3.70

1.30

7.50

0.00

10.70

0.70

0.40

10.80

3.70

6.60

8.80

9.30

1.40

0.30

−20.30

7.50

4.60

ROA%

1.50

−57.10

3.30

8.50

4.40

2.80

25.20

0.10

22.10

0.90

3.20

41.40

5.40

25.10

13.00

30.00

3.70

0.70

−86.50

23.90

16.50

ROE%

(continued)

0.60

−85.40

1.00

2.00

2.10

2.30

2.00

0.00

7.40

0.60

0.30

4.60

7.90

3.30

2.60

3.90

0.70

0.20

−34.10

1.30

2.90

PM %

Comparative Analysis of world’s Energy Prices … 123

Terex

Oil company

Table 2 (continued)

2014—COP $93.17

6.40

ROA% 7.10

ROE% 4.80

PM %

2015—COP $48.72 3.20

ROA% 3.50

ROE% 3.10

PM %

2016—COP $43.58 3.20

ROA% 3.50

ROE%

3.10

PM %

124 S. Halilbegovic et al.

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125

Table 3 Results of crude oil prices on financial performance of oil companies (2017–2018) Oil company

2017—COP 50.84 ROA (%)

2018—COP 64.9

ROE (%)

PM (%)

ROA (%)

ROE (%)

PM (%)

Almy

5.70

23.10

3.70

4.40

20.00

2.90

Antunovic

5.30

14.10

0.70

4.00

10.10

0.60

Butmir Oil

−8.70

−43.60

−12.10

62.50

76.80

503.30

El-Tarik Benzinske

1.00

1.90

0.60

0.40

0.80

0.20

G-Petrol

1.40

4.10

0.60

3.20

8.30

0.90

Green Oil

2.50

6.70

1.40

1.40

4.00

0.60

Hifa Oil

6.40

14.90

2.00

7.50

17.80

1.90

Hifa doo

7.60

28.50

3.70

5.40

20.10

2.50

Hifa Oktan

2.70

5.90

7.90

2.20

6.10

8.70

Hifa Petrol

10.00

32.00

4.10

6.90

38.50

2.80

KG Oil

0.40

2.80

0.30

0.30

2.80

0.30

Nahonal-Gas doo

1.50

2.10

1.10

12.70

21.40

5.80

Neskovic

13.20

25.80

8.40

12.10

25.40

8.10

Nestro

3.70

14.60

1.60

−1.10

−3.60

−0.40

Oil AC

7.90

23.40

2.30

5.80

18.80

1.90

Oilmer doo

1.40

3.00

2.50

2.40

4.30

4.80

Orman

2.20

2.70

1.10

10.20

12.20

4.30

Petrol BH

3.70

5.60

1.30

3.40

5.40

1.10

Proming doo Rafinerija Nafte-Brod

0.40 -2.00

1.40 – 13.70

0.50

-19.00

-30.10

-12.80

-17.50

-1.70

-11.60

-18.20

Selex

1.70

3.90

1.60

1.70

4.00

1.30

Terex company

2.20

2.50

2.40

2.90

3.60

3.20

null hypothesis is introduced into this research as a by product of the rejected main hypothesis. The null hypothesis states H0: The crude oil prices do not have a positive relationship with the financial profitability performance of the oil companies in the Federation of Bosnia and Herzegovina. In order to gather more information as to why the main hypothesis was rejected, authors have created 3 alternative secondary hypotheses listed below. Instead of the financial profitability performance of oil companies, each alternative hypothesis is expected to prove the effect of crude oil prices on return on asset, return on equity, and profit margin as a separate, standalone values. H1a: Crude oil prices have strong and positive effects on return on assets. H1b: Crude oil prices have strong and positive effects on return on equity.

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Table 4 Crude oil price effect on Return on assets, SPSS output

Model 1

Unstandardized coefficients

Standardized coefficients

B

Beta

t 0.510

0.611

−0.012

−0.150

0.881

(Constant) Crude oil price

Std. Error 1.862

3.648

−0.009

0.058

Sig.

H1c: Crude oil prices have strong and positive effects on profit margin. Crude Oil Price was introduced in SPSS as an independent variable over which return on asset, return on equity and profit margin will be tested for dependability. On the first run to test why the main hypothesis failed, we tested the crude oil price effect on oil company’s return on asset. Results from SPSS show a negative impact of crude oil price on return on asset as shown in Table 4. In this case, assets decreased by 0.12 for each increment of the crude oil price by 1 unit. As significance is larger than 0.05, authors can confirm that there is no statistical impact of crude oil price on return on asset in this period for the selected oil companies. As hypothesis H1a is rejected, we introduced alternative null hypothesis, H1a0: Crude oil prices do not have strong and positive effects on return on assets. The first test confirms that secondary hypothesis H1a0 is supported and H1a is rejected based on the results. Following the principles of the first test, we proceeded to test the following alternative hypothesis, H1b. As shown in Table 5, the crude oil price effect on return on equity is negative. Besides being negative it is insignificant. Again, as in the previous testing, Sig. is larger than the margin 0.05 which makes H1b unsupported, therefore we introduced alternative null hypothesis, H1b0 that is supported by the results of this test. H1b0: Crude oil prices do not have strong and positive effects on return on equity. Lastly, we have conducted tests in order to confirm the remaining alternative hypothesis: H1c. In the last test shown in Table 6 we have realized that profit margin is being impacted by the crude oil price change more than return on asset and return on equity; however, it is still statistically insignificant to be labeled as in direct relationship with crude oil prices changes. Per results from the Table 6, hypothesis H1c is rejected and we have introduced alternative null hypothesis H1c0: Crude oil prices do not have strong and positive effects on profit margin. Table 5 Crude oil price effect on Return on equity, SPSS output Unstandardized coefficients

Standardized coefficients

B

Std. Error

Beta

t

(Constant)

10.783

13.855

0.778

0.438

Crude oil price

-0.004

0.222

−0.002

−0.019

0.985

Model 1

Sig

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127

Table 6 Crude oil price effect on Profit margin, SPSS output Unstandardized coefficients

Standardized coefficients

B

Std. Error

Beta

(Constant)

−27.072

32.853

Crude oil price

0.223

0.524

Model 1

0.036

t

Sig

−0.824

0.411

0.424

0.672

Based on the information introduced into SPSS and the results that came through testing, we concluded that the main hypothesis, H1, as well as all alternative hypotheses, H1a, H1b and H1c, were rejected and all null hypotheses, both main and alternative ones are supported.

4 Conclusion In the region of Federation of Bosnia and Herzegovina, change of crude oil price has insignificant effect on profitability of Oil companies; this can be due to the political system, monopolistic behavior of the market, etc. Additional variables should be introduced in new researches in other to precisely point why financial performance is not affected by the crude oil price changes. Main hypothesis is rejected based on the conducted tests and null hypothesis is supported. Energy sector in Bosnia and Herzegovina is stepping towards total deregulation to stop monopoly over certain sectors. Country does not have its own natural gas extraction; therefore, it highly depends on import from Russia through Beregovo-Horgos-Zvornik import route and furthermore is limited by the distribution network only present in Sarajevo, Zenica, Zvornik and Visoko. Oil is mostly imported through refinery Brod on the Croatian border via Adriatic oil pipeline JANAF. However, even though gas and oil as mostly imported, the country is exporter in electricity. More than half of its electricity generation is made up of hydropower, while remaining percentage comes from lignite power plants [13]. Limitations were created for the purpose of this study. First is the time period as a constraint, a longer period allows more data to be taken into consideration which results in more detailed research. The second delimitation is of a geographical kind, analyzing Oil companies in the Federation of Bosnia and Herzegovina. As a last limitation for this research 22 oil companies from the Federation of Bosnia and Herzegovina were taken into consideration. This research was able to find a research gap in the fact that the crude oil price was never used as a variable that could affect the financial returns of oil companies in the Federation of BiH. In addition, the Federation of BiH was never the main topic of previous literature; authors of those researches focused on the oil and gas industry in general or in different regions. Most of them used North America or the Asia– Pacific region. The findings of this research paper could permit the creation of other hypotheses. The main practical contribution of this research paper is the knowledge of

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the negative relationship between the crude oil price and the financial performance of oil companies in the Federation of BiH during the period of 5 years between 2014 and 2018. Based on the results and information used, we suspect that the debt level, size of the company, political influence and/or monopolistic behavior of the market could be the reason why crude oil price alone has no influence on financial performance. All of these can be variables introduced in new research conducted in this region.

References: 1. Ktena, A., Panagakis, G., Hivziefendic, J.: A study of the retail electricity prices increasing trend in European electricity markets. In: 60th International Scientific Conference on Power and Electrical Engineering of Riga Technical University (RTUCON), IEEE RTUCON2019, Latvia, 7–9 Oct 2019 2. Okvirna energetska strategija Bosne I Hercegovine do 2035.godine (2018) 3. Oil Consumption by Country, Worldometers. https://www.worldometers.info/oil/oil-consum ption-by-country/. Accessed Mar 2020 4. Manikom, O., Guillermet, C.: International Oil Companies’ Financial Performance and Crude Oil Prices in the Eurozone from 2004 to 2013. Umea School of Business and Economics (2014) 5. Drusko, D.K.: Shema naftne mafije, Bhdani (2000) 6. Rados, K.: Kretanje cijene nafte na svjetskom trzistu I njene determinante, Sveuciliste u Splitu Ekonomski Fakultet (2016) 7. Doric, B., Dimovski, V.: Managing petroleum sector performance—a sustainable administrative design. Economic research-Ekonomska istrazivanja (2018) 8. Ford, S.G.: An investigation into the relationship of retail gas prices on oil company profitability. Appl. Econ. 43(27), 4033–4041 (2011) 9. Baffes, J., Kose, A.M., Ohnsorge, F., Stocker, M.: The Great Plunge in Oil Prices: Causes, Consequences, and Policy Responses. Australian National University (2015) 10. Tamuleviˇciene, D.: Methodology of complex analysis of companies’ profitability, Entrepreneurship and sustainability issues. Int. J. (2016) 11. Dragojlovic, M.: Federation BiH (Bosnia & Herzegovina) Searches for Oil Reserves, Independent Balkan. News Agency (2019) 12. Administrator LogisticMag, Da li je trziste nafte u BiH van kontrole drzave? (BiH), Logistic magazine (2018) 13. The energy sector in Bosnia and Herzegovina, Bankwatch Network (2019)

Identification on Dominant Oscillation Based on EMD and Prony’s Method Approach M. Muftic Dedovic, Adnan Mujezinovi´c, and N. Dautbasic

Abstract In this paper, the application of the Prony’s method based on Empirical Mode Decomposition (EMD) and Ensembled Empirical Mode Decomposition (EEMD) for identification of dominant modal parameter, oscillation frequency, is presented. The validation of the methods are done on real frequency signal obtained from FNET/GridEye, GPS-synchronized wide-area frequency measurement network obtained during tornado outbreak in Southeastern U.S. According to many studies and reports, the values of dominant modal parameters from such event, are already known, and have been used to compare method performance and accuracy of results. Firstly, EMD and EEMD are performed over the frequency time series to obtain intrinsic mode functions IMFs, on which the Prony’s method for frequency oscillation extraction is further applied. In addition, according to obtained results the proposed methods have proven to be reliable for identification of the model parameters of low-frequency oscillation in power systems. Keywords Dominant oscillation mode · EMD · EEMD · Prony’s method · FDR

1 Introduction Low-frequency electromechanical oscillations are common in power systems. The electric power system will by its nature enter a period of oscillations, responding to changes within the system itself and adapting to new operating conditions. In power systems there is a constant problem of stability, because power systems are continuously exposed to various disturbances, such as generation trip, line trip, etc. [1]. So it would be useful to implement automatic systems in power systems that could prevent the propagation of the initial disturbance through the system and its cascading decay. To prevent such adverse events, monitoring, protection and control systems based on phasor measurement units (PMUs) are being intensively developed and M. M. Dedovic (B) · A. Mujezinovi´c · N. Dautbasic Faculty of Electrical Engineering, University of Sarajevo, Sarajevo, Bosnia and Herzegovina e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. Avdakovi´c et al. (eds.), Advanced Technologies, Systems, and Applications V, Lecture Notes in Networks and Systems 142, https://doi.org/10.1007/978-3-030-54765-3_8

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implemented in power grids to provide GPS-synchronized measurements at a high sampling rate (typically, 30 samples per second), Wide Area Monitoring Protection and Control (WAMPC) systems. Unlike existing SCADA systems, WAM systems provide on-line representation of system dynamic states based on PMU technology. The PMU gives a more complete picture of electromechanical dynamic processes in power systems. The architecture of these systems is based on PMUs, with a central data acquisition system (PDC) and telecommunications infrastructure. The basic functions of these systems are real-time monitoring of the system, safer system operation and alarm in case of dynamic occurrences in the system, assistance in planning the drive, monitoring of power flows, etc. [2]. According to that in this paper for identification of the model parameters of low-frequency oscillation in power systems, frequency signal obtained from FNET/GridEye is used. A single phase Phasor Measurement Unit (PMU) known as a Frequency Disturbance Recorder (FDR) with precise time information provided by the Global Positioning System is used to collect synchronized voltage, angle, and frequency measurements at 100 ms intervals. FNET system provides frequency measurement data from 2004 over North American and also worldwide power grids and consists of around 150 FDRs installed in the United States and another 50 installed worldwide [3]. In this paper for implementation of proposed methodology are used frequency measurements at 10 samples per second provided from FNET/GridEye for April 27, 2011 when tornado outbreak caused severe impacts on power transmission systems in the southeast U.S. For Eastern Interconnection area there are about 70 FDRs and for this paper one oscillation event during that tornado outbreak is analysed [4]. In literature can be found many papers with different approaches and methods applied for identification of dominant oscillator modes in power systems during severe disturbance events. Herein the signal processing techniques for estimation of power system oscillations are emphasized. In [5] can be found implementation on Fourier spectrum analysis and in [6, 7], power system modes are calculated with the aid of Prony’s analysis using transient data. Also Matrix pencil method is widely used in estimation of the electromechanical modes using measured transient data [8]. Algorithms based on the nonstationary signal analysis in order to extract inter area oscillations, such as Hilbert-Huang transform (HHT) technique can be found in [9–11]. Also wavelet transform (WT) is very useful tool for detection and classification of power system transients, quality events [12, 13] and enable the time and the frequency domain representation of the signals providing non-stationary power system signals assessment. Application of the discrete WT (DWT) and continuous WT (CWT) for analysis of the low-frequency oscillations of power systems can be found in [14, 15]. This paper is organized as follows. In introduction, the Wide Area Monitoring System and FNET/GridEye system are explained and brief literature review on techniques used for identification of low frequency electromechanical oscillations is given. In second section are described power system oscillations, classifications and oscillations of interest for this paper. In third section is described applied

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methodology. The fourth section is reserved for results presentation and finally some conclusion remarks are given in fifth section of this paper.

2 Power System Oscillations Power system oscillations usually contain multiple frequency components (modes), which are determined by generator inertia, transmission line impedance, governor and excitation control, etc. For generators close to each other (in the same area), the electric link between generators are relatively strong. The oscillations between these generators tend to be at relatively higher frequencies. Also, generators in the same area can also oscillate against generators in the neighbouring areas. This type of oscillation is called inter-area oscillation and the frequency is called inter-area modes. Generator groups in different areas are connected through long distance transmission lines, therefore, the electric link is relatively weak. Oscillations (modes) in power systems can be divided into local modes and interarea modes. Local mode oscillations are associated with electrically “close” groups of generators and generally observed at frequencies above 1 Hz. Some of the causes for occurrence of local modes are inadequate tuning of control systems such as exciters, HVDC converters, SVCs, etc.On the other hand, inter-area modes are oscillations associated with the flow of power between “electrically far” areas and generally observed at frequencies between 0.1 and 1 Hz. During some severe events in large interconnections, groups of generators in one area swinging against another group of generators in another area and inter-area oscillations occur across weak or heavily loaded transmission paths [16]. In this paper the basis of consideration are inter-area oscillations, and for analysis and identification of dominant mode, the frequency oscillations occurred during tornado outbreak in Southeastern U.S are taken. In 2011, the worst tornado outbreaks ever recorded caused widespread power outages. More than 300 power transmission towers supporting around 100 transmission lines were destroyed by the storm. For further analyses and application of proposed methods for identification of oscillator mode from 70 FDRs one oscillation event during the outbreak is taken [17]. On Fig. 1 is presented frequency oscillation during tornado outbreak in Southeastern U.S. for bus UsTnKnoxsolar770. Also, on Fig. 1 can be seen that the rang of interest for analyze the frequency components of the denoised signal is between 17 and 25.3 s. Thus, the time interval from 17 to 25.3 s is chosen to be analyzed by the proposed methods.

3 Applied Methodology In this section methodology and steps of EMD, EEMD and Prony’s methods are briefly explained.

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EMD Empirical Mode Decomposition (EMD) is a technique used to decompose a given signal into a set of elementary signals called Intrinsic Mode Functions (IMF). This technique is part of the Hilbert-Huang transformation. EMD contains Hilbert spectral analysis with simultaneous frequency calculation. Each IMF must meet two conditions. The first is that the extreme number (min and max) of zero points should be equal to or differ only by one. The second condition is that the mean value of the envelope at any point for the IMF is zero. The EMD algorithm can be explained in four steps. The first is to find all the local extremes and create an upper and lower envelope using a cubic spline (eup (t) i elow (t), e (t)+elow (t)) , after that respectively). Then the mean value is calculated by: m (t) = ( up 1

2

h 1 (t) is calculated by the expression h 1 (t) = x(t) − m 1 (t). These steps should be repeated until h 1 (t) satisfies a set of predefined stop criteria for the IMF function: c1 = h 1k . If h 1 (t) does not meet the criteria for the existence of the IMF, the previous procedure is repeated and determines h 11 (t) as a new signal: h 11 (t) = x(t) − m 11 (t) where m 11 (t) represents the mean value of signal h 1 (t) upper and lower envelope. The last step is to calculate the residual of the signal by repeating the calculation of the mean values of eup (t) and elow (t) k times to obtain n IMFs and residual, and the new signal is then: x(t) =

n  i=1

ci (t) + rn (t) =

q  i=1

ci (t) +

p  j=q+1

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n 

ck (t) + rn (t)

(1)

k= p+1

where q < p < n, and ci (t) is the i-th IMF, c j (t) are the components representing the properties of the array and ck (t) and rn (t) are the final residuals, the non-sinusoidal components [18, 19].

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EEMD The EEMD algorithm is new denosinig technique based on EMD. To overcome the problem of identifying modal aliasing caused by signal discontinuity in the EMD process, Huang proposed a research-based method of noise-assisted decomposition. This method mainly uses the IMF component as the average signal value and uses the white noise signal spectrum to evenly distribute the signals of different scales to the appropriate reference scale. Each IMF is added in advance with a finite amplitude white noise signal and EMD decomposition is performed to obtain the average IMF value. So it can be expressed by Eq. (2), xi (t) as independent signals of different scales is obtained by adding an distributed noise signal to the original signal x(t). xi (t) = x(t) + n i (t), i = 1, 2, . . . , N

(2)

The EEMD algorithm is widely used in power systems for signal decomposition, significantly reducing the chance of mode mixing and preserving the dyadic property. More about this method, as well as its application can be found in [20, 21]. Prony’s method Prony’s method is developed by Gaspard Riche de Prony, in 1795 [22]. In his original work, he suggested that equally sampled data could be approximated by exponential functions, and described how to obtain information from time series. Prony’s method allows the adjustment of complex exponential functions of any nature (pure sinusoids, exponentially decreasing or increasing functions) on lower fixed data samples. Prony’s method belongs to the group of parametric methods. Its advantage is the precise estimation of signal components parameters: frequency, amplitude and phase, as well as coefficients suppression. The method consists in presenting the signal as a linear combination of exponential functions, which for real signals can be expressed by the relationship. xˆn =

p/2 

2ak e[αk (n−1)T ] cos[2π f k (n − 1)T + θk ]

(3)

k=1

where are: n = 1, 2, . . . , N ; N —signal length (number of samples); p—number of exponential components (model order); T —sampling period (s); ak —amplitude of the k-th; αk - damping factor (s−1 ); f k —sinusoidal frequency (Hz); θk —initial phase of the sinusoidal component (rad). The Prony’s method is computationally complex and requires inversion of large matrices, calculation of roots of high order polynomials, etc. There may also be

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problems with the numerical stability of solutions. This method is also known for its sensitivity to noise contained in the signal. Despite these drawbacks, there are many attempts in the literature to use the method for identification of dominant oscillator modes in power systems. Furthermore, on Prony’s method and its application in identification of dominant modes can be found in the literature [23, 24]. According to sensitivity to noise contained in the signal, before performing Prony’s method on selected frequency time series from Fig. 1f or estimating fundamental frequency, firstly EMD and EEMD are adopted for denoising the signal in order to obtain components of the time series and to remove signal trend. It is well known that noise with SNR greater than 10 dB does not affect the original signal, according to that before performing EEMD it is calculated SNR for analyzed frequency signal and is greater then 10. So for implementation of EEMD and comparison of its performance with the EMD method an SNR of 5 dB is added to original frequency signal. After EMD application over frequency signal from selected bus, three IMFs are obtained and residual. On Fig. 2 are presented IMF1, IMF2 and IMF3. After EEMD application over frequency signal from selected bus, three IMFs are obtained and residual. On Fig. 3 are presented IMF1, IMF2 and IMF3. Also, on Fig. 4 can be seen th e reconstructed frequency signal from IMFs obtained after application of EMD (a) and EEMD (b) approaches. It can be seen from Figs. 2, 3 and 4 that IMFs containing the important information of the signal such as, frequencies and corresponding phases and amplitudes are used to reconstruct the signal so that the noisy components are discarded. Prony’s method is applied on each IMF obtained after EMD and EEMD approaches (Figs. 2 and 3). Also, Prony’s method is applied on reconstructed signal Fig. 2. IMFs obtained by EMD IMF1

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obtained by summing all IMFs received from each method (signals from Fig. 4). Among the obtained IMFs, the first and second IMFs extracted in this process (EMD and EEMD) capture the high and middle frequency components and noise of the input signal. Finally, the last IMF extracted by EMD and EEMD define the low frequency components of the input and might contain useful information of inter-area oscillation.

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Fig. 5 Scalogram of the actual measured signal

4 Results The results obtained after application of EMD-Prony’s method and EEMD-Prony’s method are compared to the actual values of inter-area oscillation frequency for bus UsTnKnoxsolar770 on one oscillation event during tornado outbreak. In [4] offline demonstration using FNET data are presented, and dominant oscillation mode for this bus is 0.197 Hz. Also, in order to validate obtained results on Fig. 5 is presented scalogram of frequency from Fig. 1. On this scalogram can be seen that dominant frequency for this time series corresponds to actual values of 0.197 Hz. Since the inter-area band is 0.1 to 0.8 Hz, after all calculations, the best results are obtained by performing Prony’s method on IMF 3 from EMD and EEMD process. On Fig. 6 are presented obtained oscillation modes according to applied method EMD-Prony (a) and EEMD-Prony (b). In Table 1 are pointed out the identification results of measured data in terms of mode, frequency, amplitude, damping and order of applied methods. From results presented on Fig. 6 and Table 1 can be concluded that both methods give satisfactory results according to dominant oscillation mode actual value obtained from [4].

5 Conclusion This paper proposed the application of Prony’s method based on EMD and EEMD for identification of dominant modal parameter, oscillation frequency. The time series taken for analysis is the oscillation from one bus during a major disturbance in Southeastern U.S. The dominant oscillatory mode for this bus is adopted from FNTE/GridEye system and has been used to compare the performance and results from applied methods. According to results this paper has shown the efficiency of using Prony’s method based on EMD and EEMD for estimating fundamental frequency, amplitude and damping of a power system signal. EMD and EEMD

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-30 a)

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Table 1 The identification results of measured data Methods

Mode

Frequency/Hz

Amplitude

Damping

Order

EMD-Prony

1

0.2014

0.011

0.371

27

EEMD-Prony

1

0,1963

0.014

0.345

27

methods are used for denoising a noisy power system signal as Prony’s method is very much sensitive to noise. The results from both methods are near correct but slightly accurate using EEMD-based Prony because of some limitations of EMD method discussed above.

References 1. EPRI: Interconnected Power System Dynamics Tutorial, EPRI, Final Report Third Edition TR-107726-R1, January 1998 2. Terzija, V.: Wide area monitoring protection and control—WAMPC. In: IET-UK International Conference on Information and Communication Technology in Electrical Sciences (ICTES 2007), Tamil Nadu, pp. 1–7 (2007) 3. Zhang, Y.: Frequency Monitoring Network (FNET) Data Center Development and Data Analysis. Ph.D. dissertation, University of Tennessee (2014)

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4. Rosso, A.: Demonstration of a novel synchrophasor-based situational awareness system: wide area power system visualization. On-line Event Replay and Early Warning of Grid Problems (2012) 5. Kakimoto, N., Sugumi, M., Makino, T., Tomiyama, K.: Monitoring of inter area oscillation mode by synchronized phasor measurement. IEEE Trans. Power Syst. 21(1), 260–268 (2006) 6. Hauer, J., Demeure, C., Scharf, L.: Initial results in Prony analysis of power system response signals. IEEE Trans. Power Syst. 5(1), 80–89 (1990) 7. Shim, K., Nam, H., Lim, Y.: Use of Prony analysis to extract sync information of low frequency oscillation from measured data. Eur. Trans. Electr. Power 21(5), 1746–1762 (2011) 8. Guoping, L., Quintero, J., Venkatasubramanian, V.: Oscillation monitoring system based on wide area synchrophasors in power systems. In: Bulk Power System Dynamics and Control— VII. Revitalizing Operational Reliability, iRE Symposium, pp. 1–13 (2007) 9. Laila, D.S., Messina, A.R., Pal, B.C.: A refined Hilbert-Huang transform with applications to inter area oscillation monitoring. IEEE Trans. Power Syst. 24(2), 611–620 (2009) 10. Echeverria, J., Crowe, J., Woolfson, M., Hayes-Gill, B.: Application of empirical mode decomposition to heart rate variability analysis. Med. Biol. Eng. Comput. 39(4), 471–479 (2001) 11. Battista, B.M., Knapp, C., McGee, T., Goebel, V.: Application of the empirical mode decomposition and Hilbert-Huang transform to seismic reflection data. Geophysics 72(2), H29–H37 (2007) 12. Zhengyou, H., Shibin, G., Xiaoqin, C., Jun, Z., Zhiqian, B., Qingquan, Q.: Study of a new method for power system transients classification based on wavelet entropy and neural network. Int. J. Electr. Power Energy Syst. 33(3), 402–410 (2011) 13. Oleskovicz, M., Coury, D.V., Felho, O.D., Usida, W.F., Carneiro, A.A., Pires, L.R.: Power quality analysis applying a hybrid methodology with wavelet transforms and neural networks. Int. J. Electr. Power. Energy Syst. 31(5), 206–212 (2009) 14. Avdakovic, S., Nuhanovic, A., Kusljugic, M., Music, M.: Wavelet transform applications in power system dynamics. Electr. Power Syst. Res. 83(1), 237–245 (2012) 15. Bruno, S., De Benedictis, M., La Scala, M.: “Taking the pulse” of power systems: monitoring oscillations by wavelet analysis and wide area measurement system. In: Power Systems Conference and Exposition, 2006. PSCE ’06.2006 IEEE PES, pp. 436–443 (2006) 16. Kundur, P.: Power system stability and control. Information on the state of air quality in the Sarajevo Canton for 2018. McGraw Hill, Ministry of Physical Planning, Construction and Environmental Protection 1994. [email protected] 17. http://fnetpublic.utk.edu/sample_events.html 18. Huang, H.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H., Zheng, Q., Yen, N.C., Tung, C.C., Liu, H.H.: The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. Lond. A 454, 903–995 (1998) 19. Dedovic, M.M., Avdakovic, S., Dautbasic, N.: Impact of air temperature on active and reactive power consumption—Sarajevo case study. Bosanskohercegovaˇcka elektrotehnika 20. Hao, Q.: Application of Prony algorithm based on EEMD for identifying PSS parameters. IOP Conf. Ser. Earth Environ. Sci. 440, 032129 (2020). https://doi.org/10.1088/1755-1315/440/3/ 032129 21. Wu, Z., Huang, N.E.: Ensemble empirical mode decomposition: a noise-assisted data analysis method. Adv. Adapt. Data Anal. 1, 1–41 (2009) 22. Chao, B.F., Gilbert, F.: Autoregressive estimation of complex eigenfrequencies in low frequency seismic spectra. Geophys. J. R. Astr. Soc. 63, 641–657 (1980) 23. Arpanahi, M.K., Kordi, M., Torkzadeh, R., Alhelou, H.H., Siano, P.: An augmented Prony method for power system oscillation analysis using synchrophasor data. Energies 12, 1267 (2019). https://doi.org/10.3390/en12071267 24. Tasnim, K.N., Hasan, M.T., Reza, M.S.: Empirical mode decomposition based Prony’s method for fundamental and harmonics analysis of power system. In: 2019 International Conference on Electrical, Computer and Communication Engineering (ECCE), Cox’s Bazar, Bangladesh, 2019, pp. 1–6. https://doi.org/10.1109/ECACE.2019.8679300

The Hybrid EMD-SARIMA Model for Air Quality Index Prediction, Case of Canton Sarajevo M. Muftic Dedovic, Samir Avdakovi´c, Adnan Mujezinovi´c, and N. Dautbasic

Abstract The aim of this paper is to calculate the Air Quality Index (AQI) for each pollutant during a single year for Canton Sarajevo. After obtaining the Air Quality Index for all pollutants during an observed year, the calculation of the total Air Quality Index is given. Based on the collected hourly measured values of pollution concentrations for the period from 2014 to 2018 using the hybrid EMD-SARIMA model, the values of the Air Quality Index for 2019 are forecasted. After obtaining the prediction results for the model, four different measures were taken to identify the performance of the model. The Mean Absolute Percentage Error MAPE of 6.66 (%) shows highly accurate model performance forecasts. The model is created and performance of the proposed model has been tested in the MATLAB. Keywords Hybrid model · EMD-SARIMA · Air Quality Index · Forecast · Pollutants

1 Introduction Monitoring of air quality in Sarajevo Canton is performed in accordance with the requirements of the Rulebook on the method of air quality monitoring and definition of polluting substance types, limit values and other air quality standards (“OG FBiH”, no. 1/12) for the needs of the Ministry of Physical Planning and Urban Development of Sarajevo Canton by the Public Institution Institute for Public Health of Sarajevo Canton. The aim is to provide continuous monitoring of pollutants throughout the year in the Canton of Sarajevo in order to protect the health of citizens and the environment through timely information on the state of air quality. Based on trends in monitoring the air pollution indicators, the competent institutions receive information on the basis of which plans can be made for the long-term improvement of the existing air quality status and the rehabilitation of the existing state. Also, air quality M. M. Dedovic (B) · S. Avdakovi´c · A. Mujezinovi´c · N. Dautbasic Faculty of Electrical Engineering, University of Sarajevo, Sarajevo, Bosnia and Herzegovina e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. Avdakovi´c et al. (eds.), Advanced Technologies, Systems, and Applications V, Lecture Notes in Networks and Systems 142, https://doi.org/10.1007/978-3-030-54765-3_9

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monitoring enable prompt and timely treatment in cases of excessive air pollution [1]. Air pollution is a direct consequence of the uncontrolled emission of pollutants from motor vehicles under conditions of public transport and the use of alternative and solid fuels for household heating in relation to natural gas or renewable electricity [2]. Also, it is very important to know the values of pollutant concentrations and AQI ahead. There are different methods for predicting the concentration of air pollution. Some methods are simpler than others, but provide lower quality results and vice versa. Better predictions are those that use several different assessment methods using the advantages of some methods where others show shortcomings, all in order to achieve more accurate air quality forecasts. According to that, in literature can be found many approaches for forecasting the pollution, such as Atmospheric Dispersion Modelling System, ADMS [3], the most popular statistical method Artificial intelligence, AI [4–6], Artificial neural network, ANN [7–9], Adaptive neuro-fuzzy, ANF [10], HF Hybrid forecast as statistical method [11], Autoregressive integrated moving average and ARIMA with a seasonal difference called SARIMA [4]. Also commonly used methods for pollution prediction are Adaptive neural network fuzzy inference system, ANFIS [12], Empirical mode decomposition, EMD [13], Support vector regression, SVR [14], Fuzzy c–Means algorithm, FCM [15] and Genetic algorithm, GA optimization procedure, mainly used to select input variables [5]. In this paper hybrid EMD-SARIMA model is implemented for forecasting of Air Quality Index. Model creation and all calculations are done in the MATLAB software package.

2 Theoretical Background The Air Quality Index (Index, AQI) represents the value of the state of the observed pollutants measured at a single measuring station presented in a simple and easily understandable way for most people. There is no universal formula for the presentation and calculation of air quality indices and in many countries local specifics are taken into account when calculating the Index. The AQI with a numerical value also includes a recommendation on adjusting the activity of the air population, as well as a note on the risks for individual population groups according to the state of the air quality at a given moment. This recommendation is drafted or endorsed by the competent health institutions in Bosnia and Herzegovina. The numerical value of the Index is expressed in the range of 0–500 and is divided into six qualitative categories. The numerical value of the Index does not represent the concentration of a single pollutant (pollutants) or the set of pollutants (pollutants) expressed in a standard unit of measure (microgram, milligram, ppb, ppm …) and is expressed in whole numbers. The proposal for the Bosnia and Herzegovina Index is modelled on the EPA’s Air Quality Index, with minor changes [16]. These changes imply the following: all

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concentration values in the formula for the Index calculus are expressed in micrograms (particulate matter, sulphur dioxide, nitrogen oxides and ozone), or milligrams (carbon monoxide). The limit values for concentrations of individual pollutants are rounded to the nearest integer and approximate to the prescribed values in the applicable regulations on air quality monitoring in Bosnia and Herzegovina. A significant change from the US model is that when two or more pollutants have measured concentrations corresponding to the Unhealthy or Very Unhealthy Index categories, the measurement point index is automatically transferred to the next category by adding 50 index numbers (when two or more pollutants in the Unhealthy category), or 100 index numbers (when two or more pollutants are in the Very Unhealthy category). When concentrations of two or more pollutants are within the “Dangerous” category, a value up to 100 index points is added, with the maximum total number of Index values not exceeding 500. The numerical value of the Index is calculated for each pollutant to be measured at each measurement site (sulphur dioxide, PM10 and PM2.5 particulate matter, carbon monoxide, ozone, nitrogen dioxide). Calculation of the index for pollutants calculated on the basis of concentrations in the last 24 h is performed if there have been at least 18 h measurements in the past 24 h. Calculation of the index for pollutants calculated on the basis of concentrations in the last 8 h is performed if there have been at least 6 hourly measurements in the past 8 h [17]. The numerical value of the Index for each pollutant is calculated using the mathematical formula, as follows: I =

(AQ I max − AQ I min ) · (Ci − C O N C min ) + AQ I min (C O N C max − C O N C min )

(1)

where are: AQ I max —the index breakpoint corresponding to C O N C max ; AQ I min —the index breakpoint corresponding to C O N C min ; C O N C max —the concentration breakpoint that is ≥Ci ; C O N C min —the concentration breakpoint that is ≤Ci ; Ci —the pollutant concentration. This is the only changeable value in Eq. (1) [17] Table 1 shows the ranges of certain pollutants to which the relevant qualitative categories of the Index apply. Furthermore, for the collected hourly values for certain pollutants in the range from 2014 to 2018, Indices were calculated individually, and time series of Indices were determined for each year. The calculation methodology is shown on Fig. 1. So first the input data were collected, hourly values for certain pollutants, on the basis of these values, the average daily values of certain pollutants were calculated. Equation (1) was applied to the time series obtained in order to obtain the Index of each pollutant. From the possible Indices for each pollutant in a given year, the maximum value of the Index was identified for each day regardless of the type of pollutant, and a time series of the Index with the highest values is obtained, representing the overall Air Quality Index for the observed year. AQ I = max(AQ I P M 2,5 , AQ I P M 10 , AQ I S O 2 , . . . )

(2)

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Fig. 1 Air quality index calculation methodology based on the measured values of pollutants for a given year

As example, on Fig. 2 are presented the calculated Air Quality Index of all measured pollutants NO2 , O3 , PM10 , SO2 , and calculated overall AQI for 2015.

3 Methodology and Results In this paper, the hybrid method EMD-SARIMA [18] is used to predict the Air Quality Index. In this methodology, the EMD method is first used to decompose the original time series of the Air Quality Index into independent components called IMF (intrinsic mode functions). More about this method, description, and implementation steps can be found in the literature [19, 20]. The main purpose of decomposition is to distinguish modes based on different signs and to improve prediction accuracy. Using the EMD method, original nonlinear and nonstationary time series are decomposed into a limited number of IMFs. After the decomposition step, each IMF is modelled with the SARIMA model for more accurate predictions. Finally, predictions from the SARIMA model are collected to produce prediction results from the hybrid EMDSARIMA model. The detailed procedure of the EMD-SARIMA modelling frame is shown in the Fig. 3. Based on the collected values of pollutant emissions and the calculated Air Quality Indices, Fig. 4 shows the Air Quality Index for the period from 2014 to 2018, and this part of the data represents the first set of data, input data for the model. The second set of data represents the values of the Air Quality Index for 2019. These daily values of the Index will also be forecasted. On Fig. 5 is presented the Air Quality Indices for 2019. Original time serie of Air Quality Index for 2019 is obtained from [21]. Thus, the first step is to decompose the original time series of the Air Quality Index from 2014 to 2018 into components (IMFs) and residual. After decomposition,

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nine IMFs were obtained, and one residue, shown in Fig. 6. The high frequency components are identified from IMF 1 to IMF 4, and the low frequency components are identified from IMF 5 to IMF 9. The last component is the residual representing the trend of the original time series. The next step that needs to be done is the identification of the SARIMA model, its seasonal and non-seasonal parameters. To use SARIMA there are three steps, definition of the model, fitting the defined model and making a prediction with the fit model. More about this prediction method, description, and implementation steps can be found in the literature [22]. Following the standard SARIMA process of parameter identification, based on stationary series, autocorrelation (ACF) and partial autocorrelation (PACF) are examined to determine the best combinational order of the SARIMA model for each data set. Possible models are selected: Sarima (1, 1, 0) (1, 1, 0)12 Sarima (1, 1, 0) (0, 1, 1)12 Sarima (0, 1, 1) (1, 1, 0)12

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Sarima (0, 1, 1) (0, 1, 1)12 Once the framework model is identified, the next step is to achieve the most effective parameter estimates. Then, based on the ARIMA model, the seasonal and non-seasonal parameters are identified by autoregression (AR), differencing (I) and moving average (MA). Furthermore, by applying the Bayesian information criterion [23], the model with the smallest error is identified and has the following parameters: Sarima (0, 1, 1) (0, 1, 1)12 After selecting the most suitable SARIMA model, the next step is to model all IMFs and the residual using the proposed model. On Fig. 7 are presented original and forecasted time series of the Air Quality Index for 2019 year, blue line represents the original time serie, whale the time serie of the Air Quality Index after the application of the hybrid EMD-SARIMA prediction model for 2019 is shown in orange. Also, on Fig. 8 are presented original and forecasted time series of the Air Quality Index for one month in 2019, the month of January. It is essential to conclude from the presented analysis is the number of days with exceeded allowable values in accordance with the qualitative categories of the Index,

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presented in the Table 1. All Index values above 100 were considered unhealthy for human, and the number of days with values over 100 from the original time series was 81. After applying the hybrid model and prediction of the Index time series for 2019 and identifying values greater than 100, a number of 79 days is established. After obtaining the prediction results for the model, the four different measures are taken to identify the performance of the model (Table 2). Mean Absolute Error-MAE: M AE =

m  1  xt − x t  m t=1 

(3)

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Table 2 Measures for model performance identification MODEL

MAE

MSE

RMSE

MAPE

Hibryd EMD-SARIMA

5.59

61.22

7.82

6.66

Root Mean Square Error-MSE: MSE =

m 2 1  xt − x t m t=1 

(4)

Mean Square Error-RMSE: RMSE =

√

MSE

(5)

Mean Absolute Percentage Error-MAPE:   m  1  xt − x t  M AP E = (100), xt = 0   xt m t=1  

(6)

What can be seen from the table are the values of various measures to identify the proposed EMD-SARIMA hybrid model for predicting the time series of the Index for 2019, based on the time series of the Index for the period from 2014 to 2018. The value for the mean absolute error is 5.59, the root mean square error is 61.22, and the mean square error is 7.82. According to Klobas (2011) [24], the mean absolute percentage error of MAPE less than 10% shows highly accurate model performance forecasts, for the mentioned hybrid model the obtained value of this measure to identify model performance is 6.66 (%). Therefore, based on the already known values, time series of the AQI for 2019, the actual number of days with exceeded values is 81 days (AQI higher then 100—unhealthy). Based on the forecasted values, time series of the AQI for 2019 in Sarajevo Canton, 79 days with exceeded values are obtained. This data also confirms good hybrid models performance for AQI prediction.

4 Conclusion The aim of this paper is to present results of Air Quality Index forecast for one year ahead. Based on model input data, calculated Air Quality Index in Sarajevo Canton for the period from 2014 to 2018, the Air Quality Index for 2019 is forecasted. There are different methods for pollution and AQI prediction. The proposed hybrid EMD-SARIMA method for Air Quality Index forecast, can become a very useful tool in the process of predications. The advantages of this method are high accuracy

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in predicting AQI, which can be inferred from the mean absolute percentage error of less than 10% showing highly accurate model performance forecast.

References 1. Information on the state of air quality in the Sarajevo Canton for 2018. Ministry of Physical Planning, Construction and Environmental Protection. [email protected] 2. Air quality in Sarajevo Canton—website of the Ministry of Physical Planning. Construction and environmental protection KS. www.kvalitetzraka.ba 3. Riddle, A., Carruthers, D., Sharpe, A., McHugh, C., Stocker, J.: Comparisons between FLUENT and ADMS for atmospheric dispersion modelling. Atmos. Environ. 38, 1029–1038 (2004) 4. Rahman, N.H.A., Lee, M.H., Suhartono, Latif, M.T. Artificial neural networks and fuzzy time series forecasting: an application to air quality. Qual. Quant. 49, 2633–2647 (2015) 5. Grivas, G., Chaloulakou, A.: Artificial neural network models for prediction of PM10 hourly concentrations, in the Greater Area of Athens. Greece. Atmos. Environ. 40, 1216–1229 (2006) 6. Elangasinghe, M.A., Singhal, N., Dirks, K.N., Salmond, J.A.: Development of an ANN–based air pollution forecasting system with explicit knowledge through sensitivity analysis. Atmos. Pollut. Res. 5, 696–708 (2014) 7. Bai, Y., Li, Y., Wang, X., Xie, J., Li, C.: Air pollutants concentrations forecasting using back propagation neural network based on wavelet decomposition with meteorological conditions. Atmos. Pollut. Res. 7, 557–566 (2016) 8. Mishra, D., Goyal, P.: NO2 forecasting models Agra. Atmos. Pollut. Res. 6, 99–106 (2015) 9. Kurt, A., Oktay, A.B.: Forecasting air pollutant indicator levels with geographic models 3 days in advance using neural networks. Expert Syst. Appl. 37, 7986–7992 (2010) 10. Song, Y., Qin, S., Qu, J., Liu, F.: The forecasting research of early warning systems for atmospheric pollutants: A case in Yangtze River Delta region. Atmos. Environ. 118, 58–69 (2015) 11. Silibello, C., D’Allura, A., Finardi, S., Bolignano, A., Sozzi, R.: Application of bias adjustment techniques to improve air quality forecasts. Atmos. Pollut. Res. 6, 928–938 (2015) 12. Kosko, B.: Neural Networks and Fuzzy Systems: A Dynamical Systems Approach to Machine Intelligence. Prentice Hall, Upper Saddle River (1992) 13. Qin, S., Liu, F., Wang, J., Sun, B.: Analysis and forecasting of the particulate matter (PM) concentration levels over four major cities of China using hybrid models. Atmos. Environ. 98, 665–675 (2014) 14. Drucker, H., Burges, C.J.C., Kaufman, L., Smola, A., Vapnik, V.: Support vector regression machines. Adv. Neural Inf. Process. Syst. 9, 155–161 (1997) 15. Cortina-Januchs, M.G., Quintanilla-Dominguez, J., Vega-Corona, A., Andina, D.: Development of a model for forecasting of PM10 concentrations in Salamanca. Mexico. Atmos. Pollut. Res. 6, 626–634 (2015) 16. Technical Assistance Document for the Reporting of Daily Air Quality—the Air Quality Index; U.S. Environmental Protection Agency (2016) 17. https://www.fhmzbih.gov.ba/latinica/ZRAK/AQI-metodologija.php 18. Nai, W., Liu, Lu., Wang, S., Dong, D.: An EMD-SARIMA-based modeling approach for air traffic forecasting. Algorithms 10, 139 (2017). https://doi.org/10.3390/a10040139 19. Dedovi´c, M.M., Avdakovi´c, S.: A new approach for df/dt and active power imbalance in power system estimation using Huang’s empirical mode decomposition. Int. J. Electr. Power Energy Syst. 110, 62–71 (2019) 20. Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H., Zheng, Q., Yen, N.-C., Tung, C.C., Liu, H.H.: The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. London A 454(1971), 903–995 (1998)

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21. https://aqicn.org/ 22. Bai, L., Wang, J., Ma, X., Lu, H.: Air Pollution forecasts: an overview. Int. J. Environ. Res. Publ. Health 15, 780 (2018) 23. Bošnjak, R. (2019). Forecast of time series using Scikit-learn software libraries. Graduation Thesis. Retrieved from https://urn.nsk.hr/urn:nbn:hr:168:765650 24. Baggio, R., Klobas, J.: Quantitative methods in tourism. Channel View Publication, BristolBuffalo-Toronto (2011)

Influence of a Photovoltaic Power System Connection to Power System Voltage Stability Nedis Dautbaši´c, Tatjana Konji´c, Ermin Ahatovi´c, Majda Ðonlagi´c, and Dina Fejzovi´c

Abstract In this paper the influence of photovoltaic (PV) power system connection on power flows and voltage stability using the DIgSILENT Power Factory software package are presented. If PV system is well dimensioned, it could improve voltage in a distribution node, but it also could have many negative impacts to the power system. There are three basic criteria for connecting a PV system to a distribution network: rapid voltage changes, high harmonic generations and flickers. The analysis was performed on a part of the real distribution system. The system consists of transformer stations 35/10 kV and 10/0.4 kV, consumers connected to low voltage level (0.4 kV), cables and overhead lines. Four cases were examined: normal conditions, connection of 10 kW PV power system, 20 kW PV power system and connection of 6 PV power systems with total power of 100 kW. Keywords Photovoltaic power system · Voltage stability · Distribution system · Q-V curve · V-P curve

1 Introduction Technology development and modern way of life result in increasing electricity demand. Well-known limits of conventional power systems and their negative impact to environment made the renewable’s growth increasing. Climate changes and high prices of fossil fuels lead to increase the number of laws and regulations to encourage and commercialize the renewable [1, 2]. Some basic advantages of renewables are: an ability of a long-term exploitation, low variable expenses and small impact to the environment. One of very attractive renewable is solar energy. The photoelectric effect has known for over 100 years, but its application to electricity production was limited due to insufficient technological development at the beginning. The commercial application of photovoltaic systems N. Dautbaši´c (B) · T. Konji´c · E. Ahatovi´c · M. Ðonlagi´c · D. Fejzovi´c Faculty of Electrical Engineering, University of Sarajevo, Sarajevo, Bosnia and Herzegovina e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. Avdakovi´c et al. (eds.), Advanced Technologies, Systems, and Applications V, Lecture Notes in Networks and Systems 142, https://doi.org/10.1007/978-3-030-54765-3_10

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started in 1960s for satellite power supplies, but their growth have begun in later decades. In the 1980s the photovoltaic cells were widely used for some small batteries for calculators, watches, radios and many other electronic devices [3, 4]. The photovoltaic system is based on semi-conductor elements which price on the market has been decreased since last ten years. This part is tightly connected to some other electronic devices used in combination with photovoltaic systems [3]. According to data from 2019, some leading countries in using PV systems are: Japan (55.5 GW installed), Germany (47.72 GW installed) and China (22.79 GW installed), then Italy, USA, India, UK, Australia, France and South Korea following [5]. The renewables, such as PV systems, wind power systems, fuel cells and small hydro power systems are increasingly used for a distributed generation in order to avoid the conventional power systems negative effects to the environment. On the other hand, a large number of distributed generation units connected to system cause many different problems, as described in [1]: • Some voltage value changes in network, depending of generation, load and bidirectional power flow; • An appearance of some voltage transients caused by generator’s connecting and disconnecting; • An increase of a short-circuit current value; • Power losses depending of generation and load values; • An influence to power system quality and reliability; • Some distributive power network protection devices need to be re-installed, due to bidirectional power flow. The connection of a PV system to a power network is studied in [4] as well as the distribution system management and some geographical, topological and meteorological factors. Variability of solar energy depending on weather conditions makes PV systems stochastic, so their integration to power system represent the real challenge. Connection of the photovoltaic panels to power system cause many problems, such as power quality problems and influences to electrical power system management, regulation and stability. Because of some economic reasons, modern power systems usually reach their stability limits, so the correct drive depends of the photovoltaic system connection analysis [6]. In general, system stability is an ability of the system to reach the stationary state after a disturbance, and in electrical power system it’s divided to angle, frequency and voltage stability. Each of these three stabilities refers to both small and big disturbances. The ability of synchronous machines to stay synchronized is represented through the angle stability. The frequency stability represents the ability of power system to keep the nominal frequency after a disturbance, and the voltage stability refers to voltage values staying within the prospected range [7, 8]. Electrical power system is considered to be unstable if the voltage value of any bus in the system is under the critical value, which may cause the system collapse during the maximum load [9].

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The voltage and angle stability of a micro-network with some renewables connected is analyzed in [9]. The optimization of the micro-network is done by using HOMER, and the model of the network is made in DIgSILENT [10]. These results show that renewables could improve the voltage levels in distributive power network nodes if these generation units were controllable. The problem of low voltage values is solved, and dynamic reactive power absorbing disables some high voltage values. All generator units connected to the network are pretty stable, considering their angle stability. Main problem occurs while connecting some synchronous generators to the network, due the slow reaction of an existing protection system, so the solution lays in its reconstruction in some places of the network [10]. The influence of a PV system to Bangladesh power system is shown in [11]. The results presented in [11] suggest that photovoltaic system connected to a power network have some positive effects against the voltage collapse, and the transient stability of a whole system is improved as well. Improving the voltage stability of the system by connecting the photovoltaic generators is also tested in urban distribution network of New Toshka. Using a PV curve and voltage stability index in voltage stability analyzes was presented in [12]. Some positive influences of photovoltaic generators to voltage stability were also concluded. These results showed an improvement of the voltage stability index and decrease of the power losses. Some different parameters of the photovoltaic systems, such as temperature, irradiation and load changes are analyzed in [13]. Dynamic voltage stability of a distribution system is shown in [14], considering the intermittency of the Sun radiation, a photovoltaic system penetration level and some unexpected situations such as load value increasing or an interruption of a transmission line. According to a simulation of connecting 0.5 MVA photovoltaic power system to the power system, it is shown that the voltage is stable during the high level of photovoltaic system penetration, but its value decreases under the allowed value by increasing the load. In case of a transmission line interruption the voltage collapse occurs, so the photovoltaic system has no influence to the voltage stability. This simulation is made by using DIgSILENT Power Factory software [6]. As shown in [15], a static voltage stability is influenced by location, power and a way of connecting the photovoltaic system to a network. The photovoltaic system can be concentrated in one place or contained of some different units in some different areas of the power system. Some minor photovoltaic units connected to various power system spots near loads affect the power system voltage stability better than the centralized ones [16]. An influence of controlling the photovoltaic unit to power system voltage stability is also shown in [15]. It’s shown that the photovoltaic control by a power factor has a negative influence to the system, unlike the systems controlled by voltage. Moreover, the influence of STATCOM and SVC is also tested, and it’s shown that STATCOM compensators insure more stable system in case of some large photovoltaic systems connecting. Photovoltaic system connection to an unfavorable location may cause a serious degradation of power system voltage stability, as shown in [17]. CPFLOW algorithm

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is used for voltage stability analysis due to its many advantages, such as calculation speed or numeric availabilities near the voltage collapse value. Numeric results show that high penetration level of the photovoltaic system affects positively the voltage stability in general. Using a genetic algorithm (GA) in photovoltaic system voltage stability is analyzed in [18]. Comparing a standard PI controller and a genetic algorithm based one is shown in a MATLAB/Simulink model, and it’s concluded that the genetic algorithm controller gives better results. The reactive power from photovoltaic system can be used for the power system voltage stability improvement, as explained in [19]. The main aim of this paper is to investigate influence of PV systems to voltage stability in real distribution network throughout different scenarios. The analyses have been done in DIgSILENT Power Factory. The paperwork organization is shown below: • Chapter 2 contains some theoretical principles of photovoltaic system, connection criteria for PV system integration to a distribution network and their influence to a distribution network. • Chapter 3 elaborates a term of a power system stability in general and represent their classification. • Chapter 4 presents results of software simulations obtained by different connections of photovoltaic system(s) to a real distribution system.

2 Photovoltaic System A basic unit of each photovoltaic system is a photovoltaic cell made of some semiconducting materials, mainly a pure silicon or germanium. A disposal of some used PV cells occurs as a serious problem [3]. In order to increase the output power of the system, PV cells are practically connected to some series and parallel PV modules. Serial connection of the PV cells results a higher value of an output voltage, and the current value stays the same through each cell. In case of parallel connecting, the voltage value stays the same between the contacts of each cell, and the output current value gets higher. PV modules are usually made of 36 (an output voltage is 12 V) or 72 cells (an output voltage is 24 V) [20]. More PV modules represent one PV panel. Due to a small-scale output power, comparing to some conventional power systems, PV panels are usually connected to a distribution system. A classical distribution system was passive, which means that power flow direction was from a substation to end users. In case of PV systems connections, the power flow gets bidirectional.

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2.1 Some Basic Criteria for Connecting a PV System to a Distribution Network If well dimensioned, PV system could make the distribution node voltage levels improve, but they also have many negative impacts to the power system. They can cause a disruption of some power quality parameters due to their power electronic parts. There are three basic criteria for connecting a PV system to a distribution network, according to [20]: rapid voltage changes (RVCs), high harmonic generations (HHG) and flickers.

2.2 Influence of a PV System to a Distribution Network Connecting a PV system to a distribution network makes the power flow bidirectional, which means that the distribution network gets active. Some voltage levels, power losses and protection system settings are changed as well. Power flow are important for planning future expansion of power systems. The principal information obtained from the power flow study is the magnitude and phase angle of the voltage at each bus, and the active and reactive power flowing in each line. PV systems are designed to generate an active power to the power system, so the voltage magnitude of some near-by buses could increase due to a lack of a reactive power. Power flow and voltage fluctuations are mutually connected. A location of a PV system in power system also plays a great role in power flow regulation. Distributed generations, especially PV systems, are decentralize and usually are located close to end-users. Therefore, power losses could be decreased and power system became more efficient. Some potential malfunctions and disturbances in power system inside the PV power system switchgear could be solved by setting some protection devices to a circuit breaker situated in a bus coupler bay, in agreement with some given technical criteria. The power system protection is mostly enabled by some existing over current protection system settings, whereas the PV panels usually don’t cause an increasing of a short-circuit current value. Some special criteria for connecting a PV systems to a network refer to power quality parameters given in [21]. PV power systems are connected to power network through a DC/AC converter (inverter) which switching causes a voltage and current harmonic distortion. A high harmonic generation disrupts the power quality parameters in general, so the THD (total harmonic distortion) of the PV system has to be well tested and accordant followed the technical recommendations.

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3 Power System Stability A serious factor that ensures the safe operation of power systems is their stability. Definition of power system stability according to [20] is: Power system stability is the ability of a system to, for a given initial operating state, regain a state of operating equilibrium after being subjected to a physical disturbance, with most system state variables within the boundary limits that practically ensure the integrity of the whole system. The system is stable if it maintains a state of operating equilibrium under normal operating conditions and if after the occurrence of disturbances it can reach a new satisfactory equilibrium state [20]. The power system is a nonlinear system in which the operating conditions change continuously, and when a disturbance occurs, the stability depends on the initial operating state, the system configuration and the nature of the disturbance.

3.1 Power System Disturbances Classification In power systems, a disturbance can be defined as a change or series of changes in the values of one or more state variables, or one or more operating quantities of the system. Disturbances that lead to loss of stability of power systems can be different in nature and can be divided according to intensity and probability [22]. According to the intensity, the disturbances are divided into: • Small disturbances—refer to slow and continuous load changes, to which the power system is constantly exposed in operation and constantly adapts to them, changing its equilibrium state through a series of stable modes. • Major disturbances—refer to rapid and major systemic disturbances caused by sudden causes, such as short circuits, atmospheric discharges, natural disasters, etc. Designing a power system with respect to stability for every possible outage of an element in the network is impractical and uneconomical. Power system design according to outages is always based on the choice of the most probable possible outage. According to the probability of occurrence, the disorders are divided into expected and unexpected. The dynamic characteristic of the system implies the way the system responds to disturbances, such as line outage, generator shutdowns, atmospheric discharges, short circuits, etc. The time response of a system is one of the most important classifications of its dynamic characteristics [22].

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3.2 Power System Stability Classification The problem of power system stability is divided into different categories based on several factors, namely: angle, voltage and frequency stability. Since the topic of this paper is related to voltage stability, the basic theoretical assumptions of voltage stability are given below.

3.2.1

Voltage Stability and Voltage Collapse

The phenomenon of voltage stability arose as a consequence of connecting power systems with large interconnections. Connecting more systems leads to the good techno-economic properties of the system, and eliminates criticality regarding the angle stability, as well as criticality of the problem of frequency regulation. Voltage instability is basically a local problem, however it can initiate a series of events that lead to progressive and uncontrolled voltage drop in most of the system, with voltages drop below the acceptable boundary limits. This phenomenon is called voltage collapse [23]. Voltage collapses occur during the following events: • a sharp increase in the active and/or reactive load of the system, • loss of local production in the predominantly consumer part, • long transmission line failure, which transfers active or reactive power to a part of the system with bad voltage conditions. 3.2.2

Maximum Power, Critical Voltage and Critical Current

Figure 1 shows a simplified transmission system, which is most commonly used to explain voltage stability. From the system presented, the relations for current, phase voltage, and active and reactive power on the consumer can be determined: P = 3V f I cos ϕ =

2 3E 2f Z cos ϕ 3Z Iks cos ϕ = ZL F ZL F

(1)

Q = 3V f I sin ϕ =

2 3E 2f Z sin ϕ 3Z Iks sin ϕ = ZL F ZL F

(2)

Fig. 1 A simplified transmission system scheme

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where P Q Ef Vf I ϕ Z L ∠β Z ∠ϕ Iks F

active power delivered to the load, reactive power delivered to the load, voltage source, load bus voltage, current in the line, power angle, impedance of the line, impedance of the load, three phase short-circuit current and impedancecoefficient.

Voltage Vcrit and current Icrit correspond to the maximum transmission power, and are called the critical voltage and critical current, respectively. The calculation of critical values of voltages and currents is done by including Z /Z L = 1 in the V f and I modules expressions: Vcrit = √

Ef Ef = 2(1 + cos(β − ϕ) 2 cos β−ϕ 2

(3)

Iks Iks = 2(1 + cos(β − ϕ) 2cos β−ϕ 2

(4)

Icrit = √

Maximum values of active and reactive power using (3) and (4) are obtained as: Pmax = 3Vcrit Icrit cosϕ = =

ZL

cosϕ 2[1 + cos(β − ϕ)]

3E 2f

cosϕ   Z L 4cos2 β−ϕ 2

Q max = 3Vcrit Icrit sinϕ = =

3E 2f

3E 2f

sinϕ   Z L 4cos2 β−ϕ 2

(5) 3E 2f ZL

sinϕ 2[1 + cos(β − ϕ)] (6)

3.3 P-Q, V-P I Q-V Curves Changes in active and reactive power in the power system affect the voltage stability of entire system. Stability is best described by using P-Q, V-P and Q-V characteristics.

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The equations of the area connecting the variables P, Q and V, in the space of p-q-v coordinates can be written in the following form:   v 4 + (2q − 1)v 2 + p 2 + q 2 = 0

(7)

Real solutions of this equation are given by:  v=

1 −q ± 2



1 − q − p2 4

(8)

P-Q curves are obtained for v = const, V-P curves are obtained for q = const and Q-V curves are obtained for p = const. For each point (p, q) there are two voltage values, the first one is in the range of higher voltage values and represents a stable case, while the second solution represents an unstable case. Considering Eq. (7) for the case v = const, P-Q curves are obtained. V-P static characteristics are obtained from relation (7), for q = const. They represent the dependence of the voltage at the consumer and the active power injected on the consumer bus. If the first derivative by v of Eq. (7) is equal to zero, the geometric locations the absolute maximum transmission power points is obtained. Q-V curves are developed for bus that are considered more susceptible to voltage instability and are often the most efficient analysis method. The Q-V curves show the dependence of the change in reactive power to the voltage variations at the buses, i.e. how much additional reactive power needs to be injected into the bus in order to keep the voltage of that bus within the limits. The equation of the Q-V characteristic is obtained by solving (7) by q.

4 Voltage Stability Analysis The analysis of photovoltaic system connection on the voltage stability was performed on the part of the real distribution network Biha´c, using the DIgSILENT Power Factory software. The observed distribution system is powered from the substation 35/10 kV, 2.5 MVA. The distribution network is radial, consists 21 transformers 10/0.4 kV, 21 consumers, 64 buses and 41 lines. Each consumer in the network is connected to 0.4 kV. Four cases were investigated: • • • •

normal conditions, connection of 10 kW PV power system, connection of 20 kW PV power system and connection of 6 PV power systems with total power of 100 kW.

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4.1 Voltage Stability in Normal Conditions V-P and Q-V characteristics and sensitivity factors of voltage stability dv/d P and dv/d Q were used for the analysis of voltage stability of the observed system. Previously, the power flow calculation was performed, which showed that all bus voltages are within the allowable limits. Table 1 shows the sensitivity factors of the voltage stability of the five buses with the highest value of the sensitivity factor and the five buses with the lowest value of the sensitivity factor in normal conditions. From Table 1 it is possible to conclude that in the analyzed system the bus marked with S16 on 0.4 kV is the weakest and has the highest value of the sensitivity factor. Therefore, the S16 bus is the most critical bus in the system. Also, it is noticed that the buses closest to the reference bus (C1, A1, S1, B1) have the lowest value of the sensitivity factor, so they are the most stable, in terms of voltage stability. By calculating the V-P characteristics using the PV Curves Calculation option, it was also determined that the most critical bus is S16 0.4 kV. The V-P curve for this bus is shown in Fig. 2. The stability limit for the critical bus is represented by the point at the bottom of the V-P curve shown in this figure. The voltage limit value is 0.433 p.u. for a load of 2.15 MW. Considering that the load in the system is significantly lower than 2.15 MW, and that the voltage collapse requires a load 12 times higher than the load in normal operation. It can be concluded that the system is stable in terms of voltage stability. The load required for the voltage to fall below the limit of 0.9 p.u. is 0.726 MW. As the operating point of the bus is 0.206 MW for a voltage of 0.975 p.u., a stability reserve of 1.95 MW is determined. For the analyzed critical bus S16 0.4 kV, the Q-V curve is shown in Fig. 3. The curve minimum (0.409 MVAr) represents the limit of voltage stability. Table 1 Sensitivity factors of voltage stability in the system in normal conditions

Bus

Voltage (kV)

dv/d P

dv/d Q

S16

0.4

0.44423151

0.52413824

S34

10

0.26206185

0.154219

S17

0.4

0.25305685

0.14885999

S36

10

0.2526042

0.14859372

S35

10

0.25260395

0.14859357

C1

10

0.00530979

0.0239292

A1

10

0.00530978

0.02392914

S1

10

0.00530974

0.02392897

B1

10

0.00530973

0.02392893

B1

0.4

0.00530881

0.02392477

Influence of a Photovoltaic Power System …

161

1.2 1

V (p.u.)

0.8 0.6 0.4 0.2 0

0

0.5

1

1.5

2

2.5

P (MW) Fig. 2 V-P characteristics of critical bus S16 0.4 kV in the system in normal conditions

0.2 0.1

Q (MVAr)

0 -0.1 -0.2 -0.3 -0.4 -0.5 0

0.2

0.4

0.6

0.8

1

1.2

V (p.u.)

Fig. 3 Q-V characteristics of critical bus S16 0.4 kV in the system in normal conditions

4.2 Connection of the Photovoltaic Power System to the Critical Bus In this chapter two cases, 10 and 20 kW photovoltaic power system connection system to the critical bus S16 is analyzed. The nominal power of the analyzed photovoltaic power system and the injected power to the network are shown in Table 2. The part of the system model where the photovoltaic power system was connected is shown in Fig. 4. By connecting a 10 kW photovoltaic power system to the critical bus in the system in terms of voltage stability, the analysis showed that even after connecting the power

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Table 2 Analyzed cases of the connected power system

Power system Nominal power Power factor Active power (kVA) (kW) FN 1

15

1

10

FN 2

30

1

20

Fig. 4 Connection of a photovoltaic power system to a critical bus

system, the critical bus is still S16 0.4 kV. The stable part of the V-P characteristic for this bus is shown in Fig. 5. Compared this V-P characteristic to the V-P characteristic of the critical bus in normal conditions, no significant difference is noticeable. Thus, the stability limit is shifted by an additional 50 kW compared to the case without a connected photovoltaic power system. In the case the voltage reaches prescribed limits of 0.9 p.u. from the V-P characteristic, the power is 0.763 MW. Compared to the case without a connected 1.2

V (p.u.)

1 0.8 0.6 0.4 0.2 0 0

0.5

1

1.5

2

2.5

P (MW) Fig. 5 V-P characteristic of the critical bus in a system after the connection of a 10 kW photovoltaic power system

Influence of a Photovoltaic Power System …

163

photovoltaic power system, it can be concluded that the bus can be loaded with an additional 37 kW while the voltage value does not fall below the prescribed limit. Figure 6 shows the Q-V characteristic of the bus S16 0.4 kV. Comparing the obtained Q-V curve with the Q-V curve before the connection of the photovoltaic power system, it can be noticed that the curves coincide. It can be concluded that the analyzed photovoltaic power system, as a source of active power, does not affect the Q-V curve of the critical bus. In the case of 20 kW photovoltaic power system connection, the results of the analysis showed that even after connecting the power system, the critical bus is S16. The V-P characteristic of the critical bus in this case is shown in Fig. 7. Compared to the previously analyzed cases, it can be noticed that there is no significant difference in the V-P characteristics. The bus can be loaded by 53 kW more than in the case without a connected power system, until the voltage collapse, which means that the 0.2

Q (MVAr)

0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 0

0.2

0.4

0.6

0.8

1

1.2

V (p.u.)

Fig. 6 Q-V characteristic of the critical bus in a system after the connection of a 10 kW photovoltaic power system

1.2 1

V (p.u.)

0.8 0.6 0.4 0.2 0 0

0.5

1

1.5

2

2.5

P (MW)

Fig. 7 V-P characteristic of the critical bus in a system after the connection of a 20 kW photovoltaic power system

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Table 3 V-P curve points in a system without a connected power system, with a connected 10 kW and with a connected 20 kW photovoltaic power system Power (MW) At the curve knee At the voltage of 0.9 p.u. System in normal conditions

2.15

0.726

System with connected 10 kW PV power system 2.2

0.763

System with connected 20 kW PV power system 2.203

0.764

stability reserve is higher. The ratio of the power of the knee curve, and the power with the voltage value of 0.9 p.u. in the case without connection of photovoltaic system, and with connected 10 kW and 20 kW power system are shown in Table 3.

4.3 Integration of Six Photovoltaic Power Systems to the Distribution System Dispersed production from photovoltaic power systems was analyzed, with six power systems of different power, at different locations. Table 4 shows the nominal powers, the buses to which they are connected, and the injected active powers of these photovoltaic power systems. The total injected power is 100 kW, and the locations of the power systems connection are shown in Fig. 8. Obtained results show that the critical bus in the system in terms of voltage stability is still the bus S16. Figure 9 shows the V-P characteristic of the critical bus S16. The V-P characteristic of the critical bus in a system without connected photovoltaic power systems is shown in blue, while the V-P characteristic of the critical bus in a system with six connected PV power systems is shown in red. It is noticeable that the system can be loaded for an additional 106 kW. Load factor in this case it is 0.827 MW, which is 101 kW more than the system without connected PV power systems. Figure 10 shows the Q-V curve of the bus S16. In the observed system with six connected PV power systems, the system has Table 4 Characteristics of connected photovoltaic power systems Photovoltaic power systems

Connection location

Voltage (kV)

Nominal power (kVA)

Power factor

Active power (kW)

FN 1

S16 0.4 kV

0.4

10

1

8

FN 2

S11 10 kV

10

30

1

20

FN 3

S21 10 kV

10

50

1

40

FN 4

C1 0.4 kV

0.4

15

1

12

FN 5

S9 0.4 kV

0.4

15

1

10

FN 6

S15 0.4 kV

0.4

15

1

10

Influence of a Photovoltaic Power System …

165

Fig. 8 Distribution system model with connected photovoltaic power systems

1.2 1

V (p.u.)

0.8 0.6 0.4 0.2 0 0

0.5

1

1.5

2

2.5

P (MW)

Fig. 9 V-P characteristic of a critical bus in a system with six connected photovoltaic systems

a larger reactive power reserve, which is calculated as the difference between the reactive power at the operating point and the reactive power at the knee of the curve and amounts to 0.435 MVAr.

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Q (MVAr)

0 -0.1 -0.2 -0.3 -0.4 -0.5 0

0.2

0.4

0.6

0.8

1

1.2

V (p.u.)

Fig. 10 Q-V characteristic of a critical bus in a system with six connected photovoltaic power systems

5 Conclusion The connection of a photovoltaic power system to the distribution network in stationary conditions affects the power flows in the network, voltage conditions and losses of active and reactive power in the network. Influence of the connected power system depends on its injected power to the network and its location in the network. Also, the influences are reflected in the change of the power quality, protection and stability of the distribution network. One of the main influence is voltage increase in the connection point to the distribution network. In the case of a fault, the photovoltaic power system does not contribute to the short-circuit current, because it is connected to the network via a converter, so it cannot develop currents higher than the rated ones. Potential problems could be caused by harmonic distortion, which is caused by the operation of a DC-AC converter. The production of photovoltaic systems is limited exclusively to the period of the day, when the loads are the highest, so significant power system production can have a very favorable effect by reducing daily peak loads, and thus can significantly reduce active power losses in the network. Especially in the case when the consumption is closer to the power system than to the power transformer station, the impact of the photovoltaic power system is positive. The paper analyzes the influence of photovoltaic power system connection on power flows and voltage stability using the DIgSILENT Power Factory software package. The analysis was performed on a part of the real distribution system. Four cases were examined: normal conditions, connection of 10 kW PV power system, 20 kW PV power system and connection of 6 PV power systems with total power of 100 kW. Prior to the connection of PV power systems, due to low load and oversized elements of the system, there are high power losses in the system amounting to 7.7%

Influence of a Photovoltaic Power System …

167

of total consumption. The system proved to be voltage stable, whose critical bus is located at the end of the radial line. Second case is the connection of a 10 kW PV power system to a critical bus. Connected PV power system improves the voltage conditions in the part of the system around the connection point, and does not increase the voltage above the prescribed limits. In terms of voltage stability, the PV power system has a positive effect on the voltage stability of the system and the critical bus, but the impact is not significant due to the low installed power of the PV power system. The third analyzed case is the connection of a 20 kW PV power system to a critical bus. By increasing the power of the connected PV power system, the impact on power flows and voltage stability becomes more significant. The photovoltaic power system improves the voltage conditions in the part of the system around the connection point and reduces the losses of active and reactive power. Also, the impact on voltage stability is positive. By increasing the power of the connected photovoltaic power system, the stability reserve of the critical bus increases. However, as the PV power system is connected to a 0.4 kV voltage level, the power of the connected photovoltaic power system is limited, so that its impact on power flows and stability in the system is small. The fourth analyzed case is the connection of six PV power systems evenly distributed in the distribution network, which is a dispersed production with a large share of photovoltaic power systems. It was concluded that, due to dispersed production, the voltage conditions in the system were significantly improved, and the losses of active and reactive power were reduced due to the reduction of power flows. The voltage stability of the system with a high share of production from PV power systems is significantly improved and the stability reserve is increased, which is shown on the V-P and Q-V characteristics of the critical bus. Future work should consider variations of the number, total power and connection location of the PV power systems in distribution network and their influence on voltage stability. The influence of the of PV power systems control mode on voltage stability is also of interest. Furthermore, analysis of the system during a day taking into account variations of end users load profiles, behavior of new elements in the network (electrical vehicles, storage) and PV system production are interesting too.

References 1. Bloem, J.: Distribution Generation and Renewables-Integration and Interconnection. Copper Development Association Institution of Engineering and Technology Endorsed Training Provider (2007) 2. Tehniˇcka preporuka za prikljuˇcenje i pogon distribuiranih generatora, Izdanje br. 3, Javno preduze´ce ELEKTROPRIVREDA BOSNE I HERCEGOVINE, Decembar (2013) 3. Alinjak, T., Jakši´c, D., Pavi´c, I.: Model solarne elektrane u proraˇcunima tokova snaga. Hrvatski ogranak Medunarodne elektrodistribucijske konferencije, Sveti Martin na Muri (2012) 4. Hudson, R., Heilscher, G.: PV Grid integration—system management issues and utility concerns. In: PV Asia Pacific Conference (2011)

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5. IsolarWorld, Top 10 leading countries in Global Solar Power Generation in (2019). https:// www.isolarworld.com/blog/Top-ten-leading-countries-in-solar-power-generation/ 6. Kamaruzzaman, Z.A., Mohamed, A., Shareef, H.: Effect of grid-connected photovoltaic systems on static and dynamic voltage stability with analysis techniques—a review. Przegl˛ad Elektrotechniczny. ISSN 0033-2097, R. 91 NR 6/2015 7. Machowski, J., Bialek, J., Bumby, J.: Power System Dynamics: Stability and Control, 2nd edn. Wiley, New York (2008) 8. Duncan Glover, J., Sarma, M.S., Overbye, T.J.: Power System Analysis and Design, 5 edn. Cengage Learning (2012) 9. Kundur, P., Paserba, J., Ajjarapu, V., Andersson, G., Bose, A., Canizares, C., Hatziargyriou, N., Hill, D., Stankovic, A., Taylor, C., Van Cutsem, T., Vittal, V.: Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions. IEEE Trans. Power Syst. 9(3), 1387–1401 (2004) 10. I. Vidakovi´c, I., Miloševi´c, D.: Voltage and angle stability in microgrid. Infoteh-Jahorina, vol. 15 (2016) 11. Khan, M.M.S., Arifin, M.S., Haque, A., Al-Masood, N.: Stability analysis of power system with the penetration of photovoltaic based generation. Int. J. Energy Power Eng. 2(2), 84–89 (2013). https://doi.org/10.11648/j.ijepe.20130202.18 12. Abdelraheem, H., Salah, K., Loai, S.N., Abdel-Moamen, M.A.: Voltage stability improvement of New Toshka network with high penetration of photovoltaic generations. Int. J. Power Eng. Energy (IJPEE) (2017) 13. Xue, Y., Manjrekar, M., Lin, C., Tamayo, M., Jiang, J.N.: Voltage stability and sensitivity analysis of grid-connected photovoltaic systems. Power and Energy Society General Meeting. IEEE (2011) 14. Kamaruzzaman, Z.A., Mohmed, A.: Dynamic voltage stability of a distribution system with high penetration of grid-connected photovoltaic type solar generators. J. Electr. Syst. 12–2, 239–248 (2016) 15. Shah, R., Mithulananathan, N., Bansal, R., Lee, K.Y., Lomi, A.: Influence of Large-scale PV on voltage stability of sub-transmission system. Int. J. Electr. Eng. Inf. 4(1) (2012) 16. Youssef, E., El Azab, R.M., Amin, A.M.: Influence study of concentrated photovoltaic location on voltage stability. Int. J. Smart Grid Clean Energy 4(3) (2015) 17. Suampun, W.: Voltage stability analysis of grid-connected photovoltaic power systems using CPFLOW. In: 2016 International Electrical Engineering Congress, iEECON2016, 2-4 March 2016, Chiang Mai, Thailand (2016) 18. Mostafa, A.E.E.A., Bahgaat, N.K., El Sayed, M.E., Othman, E.S.A.: Voltage stability for a photovoltaic system connected to grid by using genetic algorithm technique. Int. J. Grid Distrib. Comput. 10(4), 33–42 (2017) 19. Abdel-Aziz, E.Z., Ishaq, J., Al-Khulayfi, A.M., Fawzy, Y.T.: Voltage stability improvement in transmission network embedded with photovoltaic systems. In: 2016 IEEE International Energy Conference (ENERGYCON) (2016) 20. Hanjali´c, S., Smaka, S., Hela´c, V.: Proizvodnja elektriˇcne energije 1. Elektrotehniˇcki fakultet, Univerzitet u Sarajevu, Sarajevo (2019) 21. Leši´c, M., Konji´c, T.: Power quality field measurements on photovoltaic system. In: Hadžikadi´c, M., Avdakovi´c, S. (eds.) Advanced Technologies, Systems, and Applications II. IAT 2017. Lecture Notes in Networks and Systems, vol 28. Springer, Cham (2018). Online ISBN978-3319-71321-2 22. Anderson, P.M., Fouad, A.A.: Power System Control and Stability. Wiley, New York (2002) 23. Taylor, C.W.: Power System Voltage Stability. McGraw Hill (1994)

Civil Engineering and Geodesy

Nonlinear Static Analysis of a Railway Bridge Aljoša Skoˇcaji´c and Naida Ademovi´c

Abstract One of the facilities which are crucial for each nation’s infrastructure are bridges. Therefore, it is necessary to take into account the effects of earthquakes when designing bridge structures. Static nonlinear methods (e.g. pushover method) are very useful for the first preliminary check of the structure. In recent years pushover analysis has become one of the most practical tools for nonlinear analysis of bridges due to its simplicity and rapidness on one hand and acceptable accuracy of obtained results on the other hand. Software SAP 2000 enables a simple and rather easy approach for determination of the nonlinear hinge properties with the application of either user-defined or automated-hinge models as concentrated hinge models or distributed plastic behavior models using fiber elements. This paper presents the difference in the results of nonlinear static analysis for three different models of plastic hinges for a characteristic railway reinforced concrete bridge. Keywords Railway bridge · Nonlinear analysis · Pushover · Plastic hinge · Fiber plastic hinges

1 Introduction One of the facilities which are crucial for each nation’s infrastructure are bridges. An earthquake as a natural phenomenon can cause catastrophic consequences, causing devastating damage and loss of human life. Therefore, it is necessary to take into account the effects of earthquakes when designing structures. Assessment of bridges exposed to earthquake action can be conducted in various ways. It goes without saying, that the most accurate method for the assessment of structures exposed to earthquake action is the nonlinear dynamic analysis. However, as any other method, besides its positive implications, it has its difficulties and flaws [1] and limitations A. Skoˇcaji´c (B) · N. Ademovi´c Faculty of Civil Engineering, University of Sarajevo, Patriotske lige 30, 71000 Sarajevo, Bosnia and Herzegovina e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. Avdakovi´c et al. (eds.), Advanced Technologies, Systems, and Applications V, Lecture Notes in Networks and Systems 142, https://doi.org/10.1007/978-3-030-54765-3_11

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have been identified for application by the practical engineers [2].For an adequate application of the time history analysis, it is necessary to obtain a set of site-specific ground motions that are well-matched with the seismic hazard spectrum of the site in question. This is not an easy task as explained and emphasized by Boomer and Acevedo [3]. The difficulty is seen in the insufficient or inadequate guidance in the seismic codes, computational time and time effort which highly depends on the type of the plastic hinge which is used, and due to its complexity, it is very difficult to find a mistake which may occur in the modeling process. On the other hand, static nonlinear methods (e.g. pushover method) even though they do not take time as a variable, are very useful for the first preliminary check of the structure. This is a very simple and quick procedure with an acceptable accuracy of obtained results [4]. The benefits of this method have resulted in a more frequent implementation of the pushover analysis in practice as means of nonlinear analysis of regular and irregular highway bridges [5]. Assessment and investigation of the bridges have been done by various researchers in the recent years [6–14] which was introduced and implemented in several design codes like Eurocode 8 [15], different guidelines like ATC-40 [16], FEMA-273 [17], FEMA-356 [18], ATC-55 [19], and ASCE/SEI 41-06 Standard [20]. The result of a pushover method is the capacity curve which gives insight into the stiffness, strength, and ductility of a given structure. The definition of plastic hinges can be different from lumped to distributed plasticity models [ [4]] and they can be automated-hinge or user-defined hinge models. By reviewing the literature, it was noted that not many investigations were conducted regarding the application of various hinge types on bridges and comparisons of obtained capacity curves.

2 Linear Static and Modal Analysis Modeling of the bridge’s structure was done with the application of the SAP 2000 program which is one of the most frequent software used in the bridge design. The design of the bridge was done according to the Eurocodes (Eurocode 2, Eurocode 8). The use of FEM analysis and the design of the deck and the pier for the ultimate limit state and serviceability state was done, including the second-order effects for the seismic analysis. The next step was the determination of the eigenmodes and eigenfrequencies of the bridge. The most important dynamic characteristics of railway bridges are their natural frequencies which characterize the extent to which the bridge is sensitive to dynamic loads. The natural frequency of railway bridge structures depends on the span, boundary conditions, modulus of elasticity of the bridge material, moment of inertia of the bridge, and the mass of the bridge per unit length.

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173

3 Nonlinear Static Pushover Analysis By applying nonlinear static analysis, it is possible to monitor the locations of potential hinges of the system, thus creating the conditions for the desired fracture mechanism to be formed on the structure. The preferred fracture mechanism is one which, with the smallest rotation in the plastic joints, enables the highest global ductility of the structure. The behavior of the plastic hinges is described by the moment-curvature relationship (M − κ). In this specific case, three different models were made. Frame elements were used to model the system, and the plastic joints were joined at the ends of the pier, i.e. at 0.05 and 0.95 relative lengths of the pier. The cross-section for model 1 was created using a rectangular section, while models 2 and 3 were created using the Section Designer. Model 1—User-Defined plastic hinge properties—In this case, the user defines the moment-curvature relationship as well as the axial-moment contact surface of the potential plastic hinge and introduces this in software SAP2000. In this case the M − κ relation was determined analytically and the compression axial force in the pier was taken into account. In this case, the concentric plastic behavior model was used. Model 2—Automated plastic hinge properties—For this model, the momentcurvature relationship and the axial moment interaction surface of the potential plastic hinges are determined by the software SAP2000 as defined in [18]. The concentric plastic behavior model was used in this model as well. Model 3—Distributed plastic behavior model using fiber elements—In this case, fiber plastic hinges are used to define the plastic behavior caused by the interaction of normal force and bending moment along with the linear element. The cross-section is discretized into a series of axial fibers extending along the plastic hinge. These plastic hinges are elastic-plastic and consist of a group of material points. Each material point represents a cross-section of the same material. The moment - rotation curve (M − ) of the plastic hinges is not predetermined but is calculated during the analysis from the stress–strain relationship (σ–ε) of material points. During the last two decades, widespread experimental and analytical research was conducted in material modeling for concrete and steel. According to these investigations, different values for the limit strains have been suggested in various codes. In the standards, usually, simplifications are used for formulas and various expressions. However, some of the models have been accepted by the practical engineers and one of them in Mander’s model [21]. This model has been applied for concrete confined by reinforcing bars (ties or spirals) of any shape, however, with certain modifications, it can as well be used for concrete-filled steel tubes as well as for various sections with confined concrete. Other models for confined concrete can be used which were developed by Kent and Park [22], then upgraded by Scott et al. [23]. A polynomial expression for stress–strain relation of rectilinear confined high-strength concrete was proposed by Yong et al. [24], while [25] proposed a stress–strain relationship based on the detailed experimental campaign. For high-strength concrete confined by

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various types of transversal reinforcement [26] defined a three-branch stress–strain model. In this case, the Mander’s confined concrete and unconfined concrete model was used (Fig. 1), and for reinforcing steel the Simple model was applied (Fig. 2). According to Mander, confined and unconfined concrete are differentiated by the compressive strength and ultimate strain. The reason for this is the presence of transverse reinforcement. Confined concrete has increased maximum compressive strength and ductility than unconfined concrete (Fig. 1). A simple model of reinforcing steel is used for reinforcing steel. The simple model is defined by four zones: linear elastic, yield plateau, strain hardening and softening zone [27]. Fig. 1 Mander’s models of confined and unconfined [21]

Fig. 2 Parameters of reinforcing steel material [27]

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4 Case Study The proposed location of the bridge is Sarajevo, Bosnia and Herzegovina. It is a twospan bridge of 17.5 m each, with a total length of 35 m (Fig. 3a) and the cross-section of the railway bridge is shown in Fig. 3b. The material properties of the bridge are indicated in Table 1. The modeling of the bridge was done with frame elements. The span and the pier are connected by constraint elements to achieve their interaction, as well as the end of the span to the supports. Two supports were used to support the span, one of which is longitudinally and transversely moveable, while the other is moveable only in the longitudinal direction (Fig. 4).

Fig. 3 a Elevation view of the bridge. b Cross-section of the superstructure [28]

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Table 1 Material properties of the bridge structure Clear length (m)

Column

Deck

5.00

35.00

Shape

Rectangular

Rectangular

Dimensions

360 × 90 cm

630 × 100 cm

Compressive strength (MPa)

30

35

Size and number

64  28

(In the middle of the span) 90  28; (above the pier) 158  28

Modulus of elasticity (MPa)

200

200

Yield strength (MPa)

550

550

Longitudinal reinforcement

Transverse reinforcement Type

Hoop

Hoop

Size and number

14, 3

(In the middle of the span) 4 14/20 (above the pier) 4 16/10

Spacing (cm)

15

(In the middle of the span) 20 (above the pier) 10

Modulus of elasticity (MPa)

200

200

Yield strength (MPa)

550

550

Within plastic hinge

Yes

No

Length (cm)

50

–

Lap splice

Fig. 4 Extruded view of the 3D model railway bridge [28]

Nonlinear Static Analysis of a Railway Bridge Table 2 Modal periods and frequencies

177

Mode

Period (s)

Frequency (Hz)

1

0.288

3.46

Fig. 5 The first eigenmode [28]

In the first phase of the numerical analysis, the modal analysis was performed to determine the modes and (fundamental) periods of free vibration. The first mode is in the longitudinal direction. The modal participating mass ratio for the first mode is 99.63%. The first eigenmode is shown in Fig. 5, while the values of the first three eigenfrequencies and periods are presented in Table 2. In the second phase of the numerical analysis, the static analysis was performed for the design purposes and to determine the behavior of the structure under self-weight and live load as per Eurocode 2. The design of the structure was done according to the Ultimate Limit State, while deflection check and crack width were done in the Serviceability Limit State design. In the final stage of the analysis, a nonlinear pushover analysis was performed. It was anticipated that the pier will be subjected to inelastic behavior under a severe earthquake loading. In that respect, the position of the plastic hinges in the piers was placed at the base immediately adjacent to the contact of the foundation with the pier, and at the top immediately adjacent to the contact of the span with the pier. The offset is limited to 2% of the total height of the structure as per [19], which for this case gives a value of T = 10 cm. For approximate determination of the strain-based target T displacement Eq. (1) was used, as provided in [29] and it reads:    T =  y + φt − φ y · L p · L

(1)

where y is the yield displacement of the bridge pier, φt , φ y are target and yield curvature, respectively, L is the pier height and L p is the plastic hinge length. As the plastic joints appear in the piers of the bridge structures, the reinforcement of the pier is presented in Fig. 6. As stated previously the plastic hinges were modeled in three different ways. In the following subsections, the models are explained with a commentary on the obtained results.In the pushover analysis the FEMA procedure was followed with uniform acceleration.

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Fig. 6 Cross-section of the substructure [28]

4.1 Model 1 In the first model,a rectangular cross-section of the pier was used and only one material was selectedthe Mander’s confined concrete. The behavior of the plastic hinges is presented in the form of the M − κ relation, which was obtained analytically (Fig. 7). The obtained pushover curve is presented in Fig. 8. The structure behaves linearly until 3168.95 kN, after that the structure, goes into a nonlinear range with the formation of plastic hinges. The maximum force reached at the limit of 10 cm is equal to 3704.87 kN (Fig. 8).

Fig. 7 M – κ relations [28]

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Fig. 8 Pushover curve for model [28]

4.2 Model 2 For the creation of the cross-section in the model 2 Section designer was used. In this case, multiple materials may be considered in the modeling, like confined concrete (shown in yellow), unconfined concrete (shown in blue), and reinforcing steel shown in dots (Fig. 9). The result of the pushover analysis using the plastic hinges as defined in Model 2 is presented in Fig. 10. The elastic region, in this case, reduced for 35.63 kN in comparison with Model 1. A larger hardening can be seen in Model 2 in relation to Model 1 which can be explainedby the introduction of all three materials in the crosssection. The nonlinear behavior in Model 2 starts at the shear force of 3122.32 kN

Fig. 9 Cross-section model 2

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Fig. 10 Pushover curve for model 2 [28]

and a higher shear force was obtained at the displacement of 10 cm compared to Model 1.

4.3 Model 3 To obtain a more accurate representation of plasticity and nonlinear behavior along with the member length Model 3 used a distributed plasticity model with the application of fibrous plastic hinges that simulate the propagation of plasticity along with the element, as opposed to concentric plastic hinges where plastic behavior occurs at only one point. The length of the plastic joint is equal to the height of the section, which is equal to 0.9 m.The cross-section was modeled using a section designer, taking into account confined concrete (shown in yellow), unconfined concrete (shown in blue), and reinforcing steel shown in dots as presented in Fig. 11. The cross-section is divided into 2500 fibers. Each fiber has its σ − ε diagram (Fig. 12). The pushover curve resulting from Model 3 is presented in Fig. 13. The structure behaves linearly until 1760.95 kN, after that the structure, goes into a nonlinear range with the formation of plastic hinges. The maximum shear force reached at the limit of 10 cm is equal to 3816.42 kN. The slope changes drastically after 2 cm indicating a rapid decrease in the stiffness and the structure goes into a nonlinear range.

Nonlinear Static Analysis of a Railway Bridge

Fig. 11 Cross-section Model 3

Fig. 12 Cross-section model 3

Fig. 13 Pushover curve using model 3 for plastic hinges [28]

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Figure 14 compares the capacity curves obtained from the three models. It is noticeable that the pushover curves for Model 1 and Model 2 on one hand, and the curve for Model 3 on the other, differ significantly in terms of initial stiffness. Models 1 and 2 which are (concentric plastic behavior models) possess a linear response until the yielding point of the material as per FEMA356 [19]. On the other hand,Model 3, in which a distributed plasticity model is applied, consists of a large number of fibers, each of which has a separate stress–strain (σ − ε) relation. Since the force-displacement ratio is calculated based on the analysis of the σ − ε diagram of each fiber individually, nonlinearity occurs even before the yielding of the material (Fig. 14). Considering the shear force at a displacement of 10 cm, it can be concluded that the difference very small, less than 2% (Table 3).

Fig. 14 Comparison of pushover curves [28]

Table 3 Shear force Models of plasticity

Base force (kN)

Difference (%)

Concentric plastic behavior model (Model 1)

3704.87

1.84

Concentric plastic behavior model (Model 2)

3816.43

1.15

Distributed plastic behavior model—fiber (Model 3)

3773.02

–

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5 Conclusion The conclusion of the study may be summarized as follows: 1. The capacity curve depends on the plastic hinge properties, the amount of longitudinal and transverse reinforcement and their design. 2. The results of the pushover analysis using plastic hinges with a concentric plastic behavior model (Model 1 and 2) give approximately the same results except for the hardening part. 3. The results of pushover analysis using plastic hinges with a distributed plastic behavior model (Model 3) differ in the initial stiffness with respect to the models with concentrated plastic hinges. 4. Comparing the pushover curves, a bigger variation is seen regarding the initial elastic behavior, and formation of the first plastic hinges, whereas the shear forces at the displacement of 10 cm are quite similar in all cases.

References 1. Goel, R.K., Chopra, A.K.: Response to B. Maison’s discussion of “Evaluation of modal and FEMA pushover analysis: SAC buildings. Earthq. Spectra 21(1), 277–279 (2005) 2. Priestley, M.J.N., Seible, F., Calvi, G.M.: Seismic Design and Retrofit of Bridges. Wiley, New York (1996) 3. Boomer, J.J., Acevedo, A. B.: The use of real earthquake accelerograms as input to dynamic analysis. J. Earthq. Eng. 8 (Special Issue 1), 43–91 (2004) 4. Shattarat, N.K., Symans, M.D., McLean, D.I., Cofer, W.F.: Evaluation of nonlinear static analysis methods and software tools for seismic analysis of highway bridges. Eng. Struct. 30(5), 1335–1345 (2008) 5. Shatarat, N., Shehadeh, M., Naser, M.: Impact of plastic hinge properties on capacity curve of reinforced concrete bridges, Hindawi Adv. Mater. Sci. Eng. Volume 2017. Article ID 6310321, 1–13 (2017). https://doi.org/10.1155/2017/6310321 6. Isakovic, T., Fischinger, M.: Higher modes in simplified inelastic seismic analysis of single column bent viaducts. Earthq. Eng. Struct. Dynam. 35, 95–114 (2006) 7. Paraskeva, T., Kappos, A., Sextos, A.: Development and evaluation of a modal pushover analysis procedure for seismic assessment of bridges. Earthq. Eng. Struct. Dyn. 1269–1293 (2006)s 8. Casarotti, C., Pinho, R.: Seismic response of continuous span bridges through fibrebased finite element analysis. Earthq. Eng. Eng. Vibr. 5, 119–131 (2006) 9. Casarotti, C., Pinho, R.: An adaptive capacity spectrum method for assessment of bridges subjected to earthquake action. Bull. Earthq. Eng. 5, 377–390 (2007) 10. Pinho, R., Casarotti, C.: S, Antoniou, A comparison of single-run pushover analysis techniques for seismic assessment of bridges. Earthq. Eng. Struct. Dynam. 36(10), 1347–1362 (2007) 11. Pinho, R., Monteiro, R., Casarotti, C., Delgado, R.: Assessment of continuous span bridges through nonlinear static procedures. Earthq. Spectra 25(1), 143–159 (2009) 12. Isakovic, T., Nino Lazaro, M.P., Fischinger, M.: Applicability of pushover methods for the seismic analysis of single-column bent viaducts. Earthq. Eng. Struct. Dyn. 37(8), 1185–1202 (2008) 13. Paraskeva, T.S., Kappos, A.J., Sextos, A.G.: Extension of modal pushover analysis to seismic assessment of bridges. Earthq. Eng. Struct. Dynam. 35(10), 1269–1293 (2006)

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14. MuntasirBillah, A.H.M., ShahriaAlam, M.: Seismic fragility assessment of concrete bridge pier reinforced with superelastic shape memory alloy. Earthq. Spectra 31(3), 1515–1541 (2015) 15. CEN.: Eurocode 8: Design of structures for earthquake resistance, Part 1: general rules, seismic actions and rules for buildings. Technical Report EN1998-1, European Committee for Standardization (2005) 16. ATC.: Seismic evaluation and retrofit of concrete buildings. Technical Report ATC-40, Applied Technology Council, Redwood (1997) 17. FEMA.: NEHRP guidelines for the seismic rehabilitation of buildings. Report FEMA-273 (Guidelines) and Report FEMA274 (Commentary), Washington (1997) 18. FEMA.: Prestandard and commentary for the seismic rehabilitation of buildings. Technical Report FEMA 356. American Society of Civil Engineers for the Federal Emergency Management Agency, Washington (2000) 19. FEMA.: Improvement of nonlinear static seismic analysis procedures, Applied Technology Council (ATC-55 Project) FEMA 440, Federal Emergency Management Agency, Washington, DC, USA, 2005. ASCE, Seismic rehabilitation of existing buildings, Technical Report ASCE/SEI 7- 05, American Society of Civil Engineers (2005) 20. ASCE.: Seismic Rehabilitation of Existing Buildings. ASCE/SEI Standard 41-06 2006. 21. Mander, J.B., Priestley, M.J.N., Park, R.: Theoretical stress-strain model for confined concrete. J. Struct. Eng. 114(8), 1804–1826 (1988) 22. Kent, D.C., Park, R.: Flexural members with confined concrete. J. Struct. Div. Proc. Am. Soc. Civ. Eng. 97(ST7), 1969–1990 (1971) 23. Scott, B.D., Park, R., Priestley, M.J.N.: Stress-strain behavior of concrete confined by overlapping hoops at low and high stress rates. J. Am. Concr. Inst. 79, 13–27 (1982) 24. Yong, Y.K., Nour, M.G., Nawy, E.G.: Behavior of laterally confined high-strength concrete under axial loads. J. Struct. Eng. 114(2), 332–351 (1989) 25. Bjerkeli, L., Tomaszewicz, A., Jensen, J.J.: Deformation properties and ductility of highstrength concrete. In: High-Strength Concrete: Second International Symposium, pp. 215–238. American Concrete Institute, Detroit (1990) 26. Li, N., Park, R., Tanaka, H.: Constitutive behavior of high-strength concrete under dynamic loads. ACI Struct. J. 97(4), 619–629 (2000) 27. Wang, Z., Wang, J., Lui, T., Zhang, F.: Modeling seismic performance of high-strength steelultra-highperformance concrete piers with modified Kent-Park model using fiber elements. Adv. Mech. Eng. 8(2), 1–14 (2016) 28. Skoˇcaji´c, A.: Dynamic Analysis of a Reinforced Concrete Railway Bridge. Master thesis, University of Sarajevo, Faculty of Civil Engineering (2020) 29. Karim, M.R.A., Huang, Z.: A new damage-control target displacement procedure for direct displacement-based design of circular reinforced concrete Bridge pier. Int. J. Saf. Secur. Eng. 9(3), 249–260 (2019)

Automatization of the Ranking Process of the Land Consolidation Projects Marinkovi´c Goran, Mirko Borisov, Nikolina Miji´c, Trifkovi´c Milan, and Lazi´c Jelena

Abstract In recent years in the countries of Southeastern Europe, it has been an increasing demand and launch of complex land consolidation projects. If we consider the complicated process of such activities but also the particular restriction of financial resources, it raises the fundamental question which is how to implement land consolidation projects in these conditions and which cadastral municipalities to give priority. For this research, it has been used and applied appropriate mathematical models which are: TOPSIS (The Technique for Order of Preference by Similarity to Ideal Solution), ELECTRE (Elimination et Choix Traduisan la Real), SAW (Simple Additive Weighting) and AHP (Analytical Hierarchical Process) method. For the cadastral municipalities ranking purposes, it has been created special logarithm and software which can significantly contribute to the economic process, regarding the process of the automatization of the land consolidation projects. Additionally, the results which have been achieved justify the application of the mathematical models, not only in Serbia but also in the region where are at the moment a lot of the land consolidation projects. Keywords Land consolidation · Project ranking · Methods · TOPSIS · ELECTRE · SAW · AHP M. Goran · M. Borisov · L. Jelena Faculty of Technical Sciences, Novi Sad, Serbia e-mail: [email protected] M. Borisov e-mail: [email protected] L. Jelena e-mail: [email protected] N. Miji´c (B) Faculty of Earth Sciences and Engineering, Miskolc, Hungary e-mail: [email protected] T. Milan Faculty of Civil Engineering, Subotica, Serbia e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. Avdakovi´c et al. (eds.), Advanced Technologies, Systems, and Applications V, Lecture Notes in Networks and Systems 142, https://doi.org/10.1007/978-3-030-54765-3_12

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1 Introduction Land consolidation represents a planned process that is done arranging land parcels and ownership over them [1]. According to the Law on Agricultural Land of the Republic of Serbia, land consolidation is defined as a process that encompasses planning, organizational, legal, economic and technical measures that are implemented to consolidate and improve natural and ecological conditions. The main objective of land consolidation is to consolidate agricultural holdings into as few welldesigned plots as possible, to improve primary agricultural production and improve its development [2]. Land consolidation is essential for ensuring the economic sustainability of rural areas, facilitating environmental management as well as rationalizing urban growth [3–7]. According to [8, 9] land consolidation has proven to be a useful tool in creating better living conditions in rural and urban areas and in improving the sustainable use of resources and thus has been defined as a particular type of instrument for rural development and the development of modern agriculture. Also, according to [10–16] land consolidation represents an essential approach to sustainable development, which from the original objective of increasing arable land, has become an essential instrument for the comprehensive management and development of urban and rural areas. During the time, land consolidation has been adapted to progressively more complex land development goals [17]. Increasing the quality of life in rural areas must include concrete activities, such as the promotion of agricultural production, employment, infrastructure, public goods, housing and natural resources [18, 19]. It is necessary to create values that will attract the locals to stay in rural areas and find sufficient opportunities for their development there, and one of the ways is the realization of land consolidation projects. According to research conducted in Spain [20], for several decades, it has found that the adverse effects of emigration from rural areas are smaller in areas where land consolidation has taken place than in areas where land consolidation has not carried out. This result is of great importance because it indicates that the effects of land consolidation cannot be measured solely by economic parameters. Still, that land consolidation adds some new value to rural life. Land consolidation can significantly improve the level of land fragmentation. However, factors are limiting the more widespread use of land consolidation, which are dominated by economic factors. The cost of land consolidation projects is quite high [21, 22]. Other factors limiting the effectiveness of land consolidation are the intense opposition of landowners. Reference to agricultural land and reluctance to abandon heritage, it is necessary in the case of slowing land consolidation or even make it impossible [4, 23–26]. Also, relevant factors include policies, law and regulations that determine the conditions for conducting a land integration process [24–26]. Considering the importance and benefits that land consolidation projects bring to the development of the area, and limited financial resources for the realization of the projects themselves in Serbia as well as in the countries of Southeastern Europe, it is clear that those cadastral municipalities in which there is a greater

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need to regulate land territory must be selected to rank the cadastral municipalities according to specific criteria. The most common issue by this problem methods is the analysis of several criteria according to which it is possible to make a ranking based on real data on cadastral municipalities, but that should have been collected from relevant institutions (Republic Geodetic Authority, Department of Statistics, Municipalities, etc.). If we consider the important characteristics and positive effects of land consolidation projects it is clear that the imperative is precisely the unambiguous decision-making, provision of funds and setting priorities in the selection of regions and cadastral municipalities for the regulation of agricultural land by land consolidation [27–29]. Namely, in the last few years, papers dealing with the problem of applying different criteria in analysis in the process of initiating land consolidation projects are increasingly being found in the scientific and professional literature. For example, these criteria have been applied in the Republic of Serbia [30–33] in the Republic of Croatia [34] as well as in the Republic of Slovakia [6]. With the BZIR, the topic is very current in the future are expected increased use of methods of the different criteria analysis in the process of ranking the cadastral municipality or the development of agricultural land by land management. If we consider all these criteria, there is a need for automating the process of ranking. This paper will deal with the problem of the ranking of cadastral municipalities to start projecting and the consolidations, with an emphasis on the use of four methods for decision making: TOPSIS (The Technique for Order of Preference by Similarity to Ideal Solution), ELECTRE (Elimination et Choix Traduisan la Real), AHP (Analytical Hierarchical Process), and SAW (Simple Additive Weighting). In doing so, the essential task of the paper is to define a ranking model. Because of a more efficient selection of the best solutions for the ranking of the cadastral municipality and arranging a farmland LR, was applied software tool MATLAB. The result of this research work is the methodology and technology of the algorithm or application is in the procedure of the automation process of ranking the land redistribution projects.

2 Materials and Methods 2.1 Materials In order to rank cadastral municipalities in the Municipality of Vrbas, Republic of Serbia (test example for software evaluation), data on the status of estates and parcels in the analyzed cadastral municipalities were collected. The data has been taken from several relevant institutions, such as the Republic Geodetic Authority, the Ministry of Agriculture of Forestry and Water Management, the Ministry of State Administration and Local Self-Government, the Institute for Statistics and the Local Government Unit of Vrbas. Due to the complexity of the problems in the research collected vast

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amounts of data which are from the cadastral municipalities, so the fields the research will be quite different.

2.2 Ranking Model for Land Consolidation Projects To formulate a ranking model, it is necessary to define the goal, criteria and alternatives. The model aims to rank the cadastral municipalities (alternative—7 cadastral municipalities) in the Municipality of Vrbas is to determine the order of priorities for the regulation of agricultural land by the land consolidation in the mentioned municipality. The approach, which is presented in the paper [27], has been used to define the optimization model. Defining the model is done through several steps: • • • •

Defining target functions (criteria); Defining the weight of individual criteria; Defining a decision matrix for cadastral municipality ranking; Application of mathematical model TOPSIS, ELECTRE, SAW and AHP method.

2.3 Defining Target Functions (Criteria) Several indicators indicate the effects of land consolidation projects [6, 33, 34], which directly influence the selection of ranking criteria. In order to determine the optimal cadastral municipality and ranking them for the realization of land consolidation projects in the Municipality of Vrbas, the selection of criteria in this research relies on the analysis of numerous scientific literature (Chap. 1 of this paper), as well as on previous research of the authors of this paper [28–31, 33, 35]. For the ranking of cadastral municipalities, the following criteria have been defined in this paper: f 1 : Share of arable agricultural land in the total area of the cadastral municipality; f 2 : Share of state property in total land area; f 3 : The size of the land in the state of property which will be released; f 4 : Average plot area in a suburban area; f 5 : Number of parcels per property list; f 6 : Average size of ed estates in a suburban area; f 7 : Number of holders with an area greater than 5 ha; f 8 : Condition of diameter; f 9 : Condition of consolidation. The Weight of individual criteria is defined When there are several different criteria in making a decision that does not have the same importance, they need to be assigned those weights (weighting factors, and values) that reflect their relative importance. The weights serve to define the importance of the participation of particular criteria in the decision to choose the most suitable alternative solution to the problem. In this paper, the criterion weights

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Table 1 The decision matrix The goal

Max

Max

Max

Min

Max

Max

Max

Min

The unit

%

%

%

ha

br/ln

ha

%

n.n

Min n.n

Alternative/criterion

f1

f2

f3

f4

f5

f6

f7

f8

f9

Backo Dobro Polje

98.06

27.02

6.58

2.01

2.24

4.51

3.00

5.00

5.00

Kosanˇci´c

93.36

68.35

4.04

1.14

3.72

4.25

2.00

1.00

1.00 1.00

Kucura

98.98

6.39

1.98

0.83

3.24

2.70

10.00

1.00

Ravno Selo

98.31

6.96

2.33

1.73

1.99

3.44

6.00

5.00

5.00

Savino Selo

96.70

19.35

16.68

0.83

3.64

3.02

2.00

1.00

1.00

Vrbas

97.35

9.86

11.73

2.15

2.21

4.75

8.00

5.00

5.00

were determined using the AHP consensus model. The mathematical model of the applied method has been described in many papers [36], so its detailed description is omitted here. Defining a decision matrix for cadastral municipality ranking After assigning weights to the criteria, a decision matrix will need to be formed. Table 1 shows the decision matrix for the ranking of the municipalities in the territory of the municipality of Vrbas, for the regulation of agricultural land by comminution. A mathematical model of the methods used Mathematical models of different criteria methods have been described in many scientific and professional papers [30, 32–34, 36] their more detailed description is omitted here.

2.4 Development of Software for Ranking Land Consolidation Projects As it has been already mentioned, the basic idea in this work is to create an application—software solution within the software tool MATLAB, which is implemented by the methods above for decision making. MATLAB is a fourth-generation numerical computing and programming language environment developed by MathWorks. Also, MATLAB makes it easy to manage, and process matrices, display functions and modelling implement algorithms create graphical user interfaces and connect to programs written in other languages, including C, C++, C#, Java, Fortran, and Python. All four methods were implemented in the planned application: TOPSIS, ELECTRE, SAW and AHP. When starting the application, it opens with the window shown in Fig. 1. The main window of the application consists of three panels, namely: • the input of the data; • calculating the rank of alternatives;

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Fig. 1 The main application windows

• graphical representation of the results. The application contains verification systems and notifies the user of the type of error in case: • an attempt whose Entered matrix performance goals or criteria by weight; • an attempt is made to select a method for multicriteria analysis, and the input data is not stored; • an attempt is made to calculate the rank of the alternatives, and the input data is not saved; • an attempt is made to calculate the rank of alternatives without the multi-criteria analysis method previously selected. The Input Panel allows the data to be loaded into the application via a Microsoft Excel document. Three documents need to be created, where one will enter the performance matrix, the other the weighting factors of the criteria, and the third objective of the criteria. The Microsoft Excel documents provided must comply with the appropriate entry form shown in Tables 1, 2 and 3. The first lines of Microsoft Excel documents refer to the names of the cadastral municipality ranking criteria. In the first column, be provided for on the alternative names, “This contrasts” or “The aim of” depending on which form is to be filled. Entering this textual information provides transparency and understanding of the result. Any number of alternatives and criteria can be entered. By loading the documents prepared in this way, the main window looks like Fig. 2.

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Table 2 Obtained rank cadastral municipalities in individual methods An alternative

TOPSIS

ELECTRE

SAW

AHP

Backo Dobro Polje

7

4

6

7

Kosanˇci´c

4

5

3

3

Kucura

1

1

1

1

Ravno Selo

6

6

7

6

Savino Selo

2

2

2

2

Vrbas

5

7

5

5

Zmajevo

3

3

4

4

If the spreadsheet in the Microsoft Excel document is larger than the panel space, a slider will appear that allows viewing all the data entered. Data cannot be modified in the application, and this is only possible in Excel. Once the input data is loaded, it must be saved in the workspace MATLAB-a, clicking on “Sa guard data input”. Input data must be forwarded to the workspace MATLAB functions method could be made (Figs. 3, 4 and 5). The Alternate Rank Ranking panel allows the user to select one of four methods for multicriteria analysis from the drop-down list. The implementation of TOPSIS, ELECTRE, SAW and AHP methods was done through m-functions according to their mathematical models. After the input is passed to MATLAB’s workspace, selecting the method from the drop-down list triggers the corresponding m-function. Pressing the “Calculate alligator rang” appear in the resulting solution, numerically and graphically. In addition to the numerical representation, the application also provides a graphical representation of the intensity of alternatives, and therefore the rank of alternatives. Press “Compute alligator rang” appear in the resulting solution.

3 Results In the first step, according to the procedure described above, the decision matrix, weight coefficients and criterion goals were bundled into the software and using the procedure described above, a ranking is made according to all the selected methods. The output window showing the results and graphical representation of the ranking by the selected methods is given in Figs. 6, 7, 8 and 9. Based on the results obtained from the ranking of cadastral municipalities using TOPSIS, ELECTRE, SAW and AHP methods, a comparative analysis was performed. Table 2 gives the summary overview of the obtained rank cadastral municipalities in individual methods, and Table 3 shows the differences between the ranks of the methods used.

–

–

–

2

–

Savino Selo

Vrbas

Zmajevo

1

Kosanˇci´c

Ravno Selo

3

Backo Dobro Polje

Kucura

Topsis-ELECTRE

An alternative

1

–

–

1

–

1

1

TOPSIS-SAW

1

–

–

–

–

1

–

TOPSIS-AHP

Table 3 Pregression of obtained cadastral municipality rankings by individual methods

1

2

–

1

–

2

2

ELECTRE-SAW

1

2

–

–

–

2

3

ELECTRE-AHP

–

–

–

1

–

–

1

SAW-AHP

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Fig. 2 Display of the loaded input data in the software

Fig. 3 The form for entering criteria weights

Fig. 4 The form for entering matrix performance

Fig. 5 The form for entering the criteria goals

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Fig. 6 Ranking results—TOPSIS method

Fig. 7 Ranking results—ELECTRE method

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Fig. 8 Ranking results—SAW method

Fig. 9 Ranking results—AHP method

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4 Analysis and Discussion of the Results When prioritizing one project from a group of land consolidation projects, the decision-maker (Municipality) faces the problem of having multiple factors that influence the final decision. It is often the case that there is a conflict between the criteria, i.e. that individual ranking according to different criteria gives different ranking rankings of future land consolidation projects. Making a decision based on only one, and not considering all the criteria, brings with it the question of correctness, and such a decision is incomplete and unbiased. To make the right decision, all relevant criteria must be taken into account and respected. The problem is most easily solved by the application of already inevitable methods of multicriteria analysis. Multi-criteria analysis methods are an excellent instrument with which it is possible to incorporate all the criteria in the final decision, a TOPSIS, ELECTRE, AHP and SAW methods would represent the only part of many methods that are used in the world. The results of the ranking of municipalities as expected gave different ranks of alternatives. Reasons should be sought in different mathematical models, on the one hand, and a significant (or very small) disproportionate value of the same criterion for particular alternatives, on the other. The rankings of the individual alternatives obtained by different methods in most cases, overlapped and, to a lesser extent, differed. The differences in the ranking of cadastral municipalities obtained by TOPSIS, SAW andAHP methods do not exceed one. Significant differences were also observed when comparing the rankings obtained by the ELECTRE method with those obtained by other methods, such as ranking cadastral municipalities Baˇcko, prepared using the methods TOPSIS, AHP and ELECTRA to differ in 3 positions. It should also be emphasized that a comparative analysis of the time required to determine the ranks was carried out, using the software created and using standard procedures. The standard ranking procedure, using these four methods, requires several hours of work, while the ranking of the created software is completed in less than ten minutes.

5 Conclusion The great importance of land consolidation projects and the interest of states to financially assist agricultural development has made the process of choosing the appropriate municipalities and cadastral municipalities in which agricultural land to be regulated by land consolidation quite complex. The state financial resources must be appropriately targeted at the most vulnerable cadastral municipalities, i.e. those where the effects of land consolidation would be most significant. The decision on

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the choice of the cadastral municipality must be made objectively, which is achieved by multi-criteria analysis, one of the mathematical fields that have recently played a significant role in decision-making in general. It is necessary to consider, through a series of criteria, all alternatives, that is, possible cadastral municipalities for initiating land consolidation projects. The criterion targets seeking the optimal value, or a maximum or minimum, and after the application of the algorithm for selecting one or more, the best solutions. For multi-criteria analysis, which was used in this work to the case in Serbia, chosen from the same in the four methods of multi-criteria analysis, TOPSIS, ELECTRA, SAW and AHP, which are detailed mathematically processed, and then implemented in software, using a programming language, and the statistical software MATLAB. The main aim of this study was to be created in the software MATLAB is, using TOPSIS, ELECTRE, AHP and SAW method, do the ranking cadastral municipalities in the municipality of Vrbas, of agricultural land and land management performs analyzes and the results obtained, as well as, the time necessary for computation using standard procedures and application of created software. In this purpose, nine criteria functions were proposed and defined by which seven cadastral municipalities of Vrbas municipality will be ranked. The proposed criteria functions are of a quantitative and qualitative type. Qualitative data is written on defined scales. Selected criteria may vary depending on the decision-maker. Each criterion also defines the goal to which that criterion aims. The importance of the criteria, that is, the weighting factors, is assigned by the subjective method. The cadastral municipalities in the municipality of Vrbas were ranked by the defined ranking model, using the mathematical model TOPSIS, ELECTRE, SAW and AHP methods in the created software. Based on the rank, it has been identified which cadastral municipalities have priority in the regulation of agricultural land by consolidation. A comparative analysis of the results of the two methods was also performed. The software created and used is the basis for further development and potential refinement by adding new methods and specific functional solutions that would make it easier for decision-makers to process. The use of the created software has enabled fast, economical and efficient work on the development of cadastral municipalities for the regulation of agricultural land by land consolidation.

References 1. Wang, J., Yan, S., Guo, Y., Li, J., Sun, G.: The effects of land consolidation on ecological connectivity based on ecosystem service value: a case study of the Da’an land consolidation project in Jilin province. . J. Geogr. Sci. 25(5), 603–616 (2015). https://doi.org/10.1007/s11 442-015-1190-y 2. Trifkovic, M., Marinkovic, G., Ilic, B., Pejicic, G., Lazic, J.: Land consolidation and irrigation case study of the Municipality of Velika Plana. Arch. Techn. Sci. 14(1), 35–45 (2016)

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Correlation Between the Ionosphere Anomalies and the Earthquake in Albania M6.4R ´ c Medžida Muli´c, Randa Natraš, Slavica Mati´c, and Jasmin Cati´

Abstract A strong earthquake (EQ) of the magnitude 6.4° on the Richter’s scale occurred in Albania on 26/11/2019 at 02:54 UT with an epicenter near Durres. The earthquake is triggered by deformations of the tectonic plates in the fault zone and caused human casualties and huge material damage. Scientific studies have been conducting during recent decades, using different methods of geophysical research to find a way to forecast earthquakes for avoiding human losses and infrastructure damages. TEC (Total Electron Content) values in the ionosphere are estimated using observation of radio signal propagating from Global Navigation Satellite Systems (GNSS). The values of TEC are estimated by Ciraolo methodology using observation data of the Albanian Positioning Services and of the European Permanent Network (EPN). For the reduction of space weather impact on the GNSS observations, data of EPN stations out of EQ affected area are used, which radius is estimated by Dobrovolsky formula. The geomagnetic indices Dst and Kp are used to distinguish the disturbed state of the ionosphere what is reflected by the TEC anomalies related to the geomagnetic activities. Results show a detailed analysis of the VTEC values but also differences dVTEC between GNSS stations inside and outside of the earth preparation zone (EPZ). Results indicate that the occurrence of anomalous VTEC values in GNSS station located in the EPZ are statistically significant and can be attributed to the seismic impact, as they are not noticeable in the ionospheric signature of station Istanbul that is outside the EPZ. Keywords Earthquake · Space weather · Ionosphere anomalies · TEC · GNSS ´ c M. Muli´c (B) · J. Cati´ Faculty of Civil Engineering, University of Sarajevo, Sarajevo, Bosnia and Herzegovina e-mail: [email protected] R. Natraš Department of Aerospace and Geodesy, Technical University of Munich, Munich, Germany e-mail: [email protected] S. Mati´c GBM Group, Sarajevo, Bosnia and Herzegovina e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. Avdakovi´c et al. (eds.), Advanced Technologies, Systems, and Applications V, Lecture Notes in Networks and Systems 142, https://doi.org/10.1007/978-3-030-54765-3_13

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1 Introduction A strong earthquake (EQ) of the magnitude (M) 6.4 on the Richter (R) scale, and the intensity of VIII on the Mercalli scale, hit the Albanian port Durrës on November 26, at 02:54:11.39 am UT. The epicenter was located at latitude 41° 30 50 N, longitude 19° 31 34 E, at the depth of 22 km. The quake killed more than 30 people, severely damaged hundreds of buildings, and left thousands homeless [1]. Geoscientists study earthquakes by many different methods. One of methods is tracking changes in the upper atmosphere (ionosphere), but results are still often blurred due to the complexity in the lithosphere-seismoionosphere system. The observations of the radio signals broadcasted by the Global Navigation Satellite Systems (GNSS) [2], such as the American GPS (Global Positioning System), Russian GLONASS (Global naya navigatsion naya sputnikovaya sistema) are routinely used in geodesy and land surveying for the navigation and precise positioning [3]. These space-based radio systems of the military and civil user infrastructure have many other applications, and among the many ones is the remote sensing of the atmosphere, i.e. its parts, ionosphere [4, 5] and the troposphere such as meteorology [6, 7] and weather forecasting [8, 9]. This case study presents an investigation of the anomalies in the ionosphere in time of the earthquake near Durres of the magnitude 6.4 Richter scale, that was occurred on 26/11/2019. This strong earthquake M6.4 R, at the depth 22 km with the epicenter about 20 km from the coastal city of Durrës was preceded by several weaker earthquakes (M < 3R). The seismic shock of M 6.4 R was followed by a series of earthquakes (Fig. 1) mostly of weaker magnitude than 3R, and only a few of magnitude between 4 and 5, but these earthquakes occurred at shallower depths, [10]. Visualization of the earthquake’s epicenter location is available on Fig. 1 [11] and a photo illustrating the severely damaged buildings in Durrës is on Fig. 2.

Fig. 1 Map with location of the epicenter of the earthquakes, magnitude 6.4 Richter on 26/11/2019 (the biggest red circle)—Epicenter was around 20 km to north from Durrës at a depth of 22 km [11]

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Fig. 2 Photo of the heavy damaged buildings in Durrës [12]

The motivation for this study is to investigate TEC anomalies before and after the strong earthquake during the condition of the calm ionosphere, i.e. without presence of strong geomagnetic storms and other space weather issues. Space weather can make analyses of possible impact from lithosphere-ionosphere coupling difficult or impossible. The impacts of space weather are hard to minimize from the data and they disable conclusions about lithosphere-seismo-ionospheric coupling, as it was described in [13, 14], but also in all other TEC anomalies investigation in which authors participated. The investigation has been done primarily by analyzing Total Electron Content (TEC) within the ionosphere estimated from GNSS observations [15, 16]. TEC data, obtained from GNSS receivers, was widely used in last decades to detect seismo-ionospheric anomalies. TEC is quantity that describes number of electrons on the GNSS signals’ path in the ionosphere, which affect signals’ propagation and consequently impact positioning applications. TEC variability and the impact on geodetic coordinate’s accuracy is studied in [17, 18]. This case study is conducted by analyzing the variability of the TEC values estimated from the observations recorded at the continuously operating GNSS stations: Durrës and Tirana (Albania), Sarajevo (Bosnia and Herzegovina), and Istanbul (Turkey).

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Table 1 GNSS stations, their latitudes and longitudes, distances from EQ epicenter and radius of EPZ GNSS station

Latitude

Longitude

Distance to EQ epicenter in km

EQ preparation zone (EPZ) in km

Durres (DURR)

41° 19 5.25 N

19° 26 40.43 E

10

565

Tirana (TIRA)

41° 19 46.49 N

19° 48 59.00 E

40

565

295

565

798

565

51

26.57

Sarajevo (SRJV)

43°

Istanbul (ISTA)

41° 1 39.58 N

N

18°

24

21.48

E

29° 0 47.29 E

2 Methods and Data 2.1 Earthquake Preparation Zone The case on the lithosphere-ionosphere coupling refers to the EQ of the magnitude 6.4 Richter scale, occurred on 2019/11/26 at 02:54:11.39 am UT with epicenter near Durres at location: latitude 41.4593° N, longitude 190.4418 E, at depth 22 km [10]. The radius of the earthquake preparation zone (EPZ) was estimated by Formula (1) [19]: ρ = 100.43M

(1)

where ρ is radius of the earthquake preparation zone in km, and M is magnitude of earthquake, on Richter scale. Information on the stations’ locations, distance from the epicenter and radius of the EPZ is presented in Table 1. The radius of the EPZ is quite large, 565 km. GNSS stations were selected by their distance from the earthquake’s epicenter in a way to have stations inside and outside the EPZ. Station DURR was just 10 km away from the epicenter, which makes it the closest available GNSS station to the epicenter. Station TIRA is the second nearest station to the epicenter, but its distance to the epicenter is 4 times larger than at station DURR. Station SRJV was a bit further from the epicenter with near 300 km, but still inside of the EPZ. One station outside the EPZ was GNSS station ISTA. It was away from the EPZ for 233 km.

2.2 VTEC Estimation and Analysis GNSS observation (GPS + GLONASS) for the estimation of the TEC values for stations SRJV (Sarajevo, Bosnia and Herzegovina), ISTA (Istanbul, Turkey) are available at the European Permanent Network (EPN) [20] and GPS data of stations DURR (Durres) and TIRA (Tirana) are part of the ALBAPOS (Albanian Positioning

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Service) available at the web site of the Institute of Geo-Sciences, Energy, Water and Environment (IGEAWA) [21] working under umbrella of the Polytechnic University of Tirana. All GNSS data used for estimation of TEC were collected by dual-frequency receivers of geodetic quality. The ionosphere was approximated with the singlelayer model [22] with the assumption that all free electrons were concentrated in an infinitely thin layer at a fixed height of 400 km above the Earth’s surface. Carrier phase GNSS measurements of GPS and GLONASS satellite systems were applied. Biases were determined and reduced from the measurements. TEC calibration was performed by the Ciraolo methodology [23] for every 5 min. TEC values were converted to its vertical equivalent, i.e. VTEC (vertical TEC). VTEC time series were analyzed for the two weeks before and two weeks after the earthquake (EQ). To investigate EQ-induced ionosphere anomalies, common statistical analysis is applied [24] using lower (LB) and upper bounds (UB) (μ ± 2σ) to detect VTE anomalies with confidence level of 95%, where μ represents median of 15-day VTEC before the day of the earthquake, and σ is standard deviations of VTEC during 15 days before the earthquake. The comparison of VTEC values between different stations is carried out to detect possible local ionosphere anomalies. Detailed analyses are carried out to distinguish different anomalies, especially because of a fact that some geomagnetic activity might be present within the period of earthquake preparation, in spite that period of study is approaching to solar minimum.

2.3 Space Weather Analysis Parameters of space weather such as: data of solar wind, interplanetary magnetic field and geomagnetic indices are applied to characterize effect of space weather on the Earth, as well as possible space weather-induced disturbances in the ionosphere. Data of solar wind speed (Vsw) and the vertical component of the interplanetary magnetic field (IMF) are collected from OmniWeb interface of Goddard Space flight center of NASA [25]. Indices of geomagnetic field (GMF Kp and Dst is obtained from the German Research Centre for Geosciences [26] and World Data Center for Geomagnetism in Kyoto, respectively [27].

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3 Result and Discussion 3.1 Analysis of the Indices of Solar and Geomagnetic Activities Solar index R (sunspot number) showed that the period of analysis is characterized with almost no sunspots on Sun’s surface (Fig. 3). This is no surprise since that was the period of the solar minimum because solar cycle 24 approaches to its end [28]. During solar minimum, the number of sunspots is minimum or there are no sunspots at all. It is the period of the least solar activity in the 11-year cycle of the Sun. Also, another solar proxy, F10.7 solar radio flux confirms the low level of solar activity, where the value of 80 sfu can already be considered as solar minimum. The speed of the solar wind was most of the time between 300 km/s to 400 and 450 km/s. From 21/11/2019 there is an increase in the solar wind to 600 km/s. The reason for this is a stream of solar wind which flown from a sprawling coronal hole in the sun’s atmosphere. The high-speed solar wind stream affected Earth’s magnetic field and caused moderate disturbances in the geomagnetic field. Dst index reached a minimum of around −30 and Kp was mostly around 3. There were no geomagnetic storms. Observed conditions on Sun’s surface, solar wind and in the geomagnetic field for study period show the following: • solar activity was close to minimum, • the geomagnetic field was mostly quiet, Fig. 3 Indices of solar and geomagnetic activity (from up to bottom): sunspot number (SN), solar radio flux F10.7 in sfu (solar flux units), solar wind (Vsw) plasma speed in km/s, Dst (disturbance storm time) in nT (nano Tesla), Kp (Quiet Kp < 3, Moderate 3 ≤ Kp < 4, Active 4 ≤ Kp < 5, Storm Kp ≥ 5) for period 11/11/2019–11/12/2019. Dark red dot-line indicates the occurrence of the earthquake in Durres of magnitude 6.4 Richter

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Fig. 4 VTEC variabilities for all stations from 11/11/2019 to 02/12/2019. Red dotted line indicates time of the main seismic occurrence

• moderate disturbances in geomagnetic field resulted from the solar wind blowing from coronal holes, • disturbances in geomagnetic field lasted mostly short time intervals and were not strong, • effect of such disturbances to the mid-latitude ionosphere should not be major or considerable.

3.2 Analyses of the VTEC Maximum daily VTEC values that normally occur around local noon, show variations from mostly 4 to maximum 13 TECU before the seismic event and from 3 to mostly around 10 TECU during 2 weeks after the seismic event including the day of seismic shock near Durres (Fig. 4). The highest values occurred at the station in Istanbul, on 11/11/2019, i.e. 15 days before the EQ. Next high VTEC values are showed for the stations Tirana and Durres on the day preceding the earthquake. Minimum TEC values, what normally occur before a sunrise, are between 3 and 6 TECU for all stations. Generally, GNSS VTEC values reflect mostly quiet ionosphere, which is in line with the analysis of the space time conditions, and the fact that the solar minimum is approaching. Differences between VTEC daily values are in range of few (mostly 2–3) TECU. Higher VTEC values at all stations are observed during 15 days before the seismic event and lower values during 15 days after the event including the day of the EQ. Some earlier studies showed VTEC up the 40 TECU and more in the same solar cycle 24, but during different phase of solar cycle, i.e. near solar maximum. This solar cycle characterized as the smallest and weakest in recent history, [28]. Differences in the VTEC values at all stations were analyzed. Differences in VTEC variations for GNSS stations located in Durres and Tirana, which are close to the epicenter, vary mostly from 0 to 1TECU (Fig. 5). But, it is noticed that the

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Fig. 5 Differences dVTEC between GNSS stations close to the EQ epicenter: Durres and Tirana

differences dVTEC between GNSS stations in Durres and Tirana during the day before the earthquake exceeded 1 TECU. It was negative, which means that higher ionization was at station TIRA. During the day of seismic event difference again reached 1 TECU. This time it was positive, which indicates that ionization was higher at station DURRE than at station TIRA. Differences between TECs exceeded 1 TECU also within four other days within two weeks preceding the main seismic shock. On 14/11/2019 there is one outlier that reached more than 2 TECU. This outlier can be attributed to biases occurred during VTEC processing or to data gaps in GNSS observations. Differences in ionization are of the small intensity, but they might be related to the seismic preparation’s activities and be reflected slightly differently in the ionosphere above the stations accordingly to the epicenter. A similar detailed analysis of VTEC value differences was performed also on other GNSS stations. Differences in VTEC variabilities between GNSS station in Durres and GNSS station in Istanbul, (which is out of area of seismic preparation zone) are presented at Fig. 6, where several elements for the analyses are graphically shown: differences of dVTEC between station Durres and Istanbul, VTEC mean, upper and lower bounds, UB and LB, respectively. Anomalies in dVTEC time series are observed (Fig. 6) during the two weeks before and after the main earthquake. Values of the dVTEC are over the UB on the day before the EQ. Also, anomalies are noticeable on the 3rd , 4th and 5th day before the EQ. Minor anomalies are observed during the 7th , 8th and 9th day before the EQ, but larger anomalies are evident on the 11th , 12th , 13th , 14th and 15th day prior the 26/11/2019. In the weeks after EQ, small differences in dVTEC values were observed on the day the earthquake occurred, and on 5th , 7th , 14th and 15th day after the EQ. It is noticeable that dVTEC significantly exceeds UB on the 8th day after the earthquake. Figure 4 shows that VTEC at station ISTA during the night between 7th and 8th day after the EQ reached very low values, which looks more like outlier.

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Fig. 6 Differences dVTEC between stations Durres and Istanbul from 11/11/2019 to 11/12/2019

The dVTEC values recorded as exceeding the lower limit of LB are as follows: a low ionization trend was observed on the day of the EQ’s occurrence and one day after, although the anomalous values of dVTEC were not statistically significant. However, on the 3rd , 5th , 11th , 14th and 15th day before the earthquake, the anomalies were of statistically significant intensity. Within the weeks after EQ, dVTEC values went below LB on days 4th , 5th , and 7th , 8th and 10th day after the EQ. The presented analysis of dVTEC differences indicates that the occurrence of the anomalous VTEC values in GNSS station DURR that is located in the EPZ earthquake preparation zone could be attributed to the influence of seismic processes, as they are not noticeable in the ionospheric signature of station Istanbul outside the EPZ. This claim is supported by the presentation of the dVTEC values between GNSS stations in Sarajevo and Istanbul (Fig. 7). The latter is outside the impact zone of Fig. 7 Differences dVTEC between stations Sarajevo and Istanbul from 11/11/2019 to 11/12/2019

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the earthquake because it is almost 800 km away, and the radius of the impact area, i.e. EPZ is 565 km. Differences in dVTEC exist, but are not statistically significant, which can be understood because, although Sarajevo is located within EPZ but almost 300 km away from the epicenter. It is interesting to note that a general trend of the low ionization above all three GNSS stations in the earthquake’ impact zone (Tirana, Durres and Sarajevo) is observed on the day when the earthquake occurred and the days after, but also trend of increased ionization within three days for all three station and 5 days for DURA and TIRA preceding the event. Also, to mention trend of the higher ionization during days from 12 to 15th days before the EQ. These trends are illustrated here at example of the differences dVTEC between GNSS station in Durres and Istanbul (Fig. 8). Similar graphics are shown for other two stations (Figs. 9 and 10). Fig. 8 Differences of VTEC between station Durres, the closest to EQ epicenter, and Istanbul outside of the EPZ. Differences can be partly attributed to the VTEC variability because of the differences in the station’s location, but another part of the variability could be due impact of the seismic processes during earthquake preparation and setting down afterward

Fig. 9 Differences dVTEC between Tirana (~40 km from epicenter) and Istanbul which is out of the EPZ. Trends of the differences are like ones at the other stations

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Fig. 10 Differences of VTEC between Sarajevo (295 km away from epicenter) and Istanbul which is out of EPZ. Trend of the differences are like ones at stations Durres and Tirana, but of the lower intensity

Differences dVTEC at Figs. 8, 9 and 10 could be attributed in first place to the differences in VTEC of stations location and secondly to the seismic activities. Figure 8 shows that difference is mostly about 1 TECU during the night and 2 TECU during the day. This can be attributed to regular spatial VTEC variability. Other peaks could be due to local source of ionization such as seismic activity. Such peaks to 3 TECU are visible about 5 days before the EQ and 14th and 15th day before the EQ. Similar situation can be seen at Fig. 9. There is also additional peak visible on 9th day before the EQ, on both Figs. 8 and 9 it is visible that in days before the EQ higher ionization (peaks) was at station DURR and TIRA (positive values of differences), while on the day of the EQ and one day after the EQ ionization is higher at station ISTA (VTEC difference has mostly negative values). These changes in ionization could be attributed to processes within the lithosphere during earthquake preparations and tectonic activities during the seismic shock and short after it, see Figs. 9 and 10. Understandably, the EPN GNSS station SRJV, due to its greater distance from the epicenter showed anomalies of the smaller intensity.

4 Conclusion The observations of the Global Navigation Satellite Systems, that is routinely used in the navigation and precise positioning in geodesy and land surveying have many other applications. One among the many is remote sensing of the atmosphere, i.e. its parts, ionosphere and the troposphere. This case study describes investigation of the anomalies in the ionosphere in time of the earthquake occurrence, and weeks before and after seismic shock. Total electron content that is estimated from GNSS observation data is used as the ionospheric state parameter.

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The research was focused on the strong earthquake of magnitude 6.4 on the Richter scale, with the epicenter at a depth of 22 km, located to the north not far from the Albanian port of Durres, which occurred on November 26, 2019. The results showed that the vertical equivalent of the TEC value or VTEC did not behave completely in accordance with the usual daily variations during the study period. On the day of the earthquake and in the periods of two weeks preceding and two weeks after the earthquake, anomalies in the behavior of TEC values were recorded. Analyzes of the space weather parameters of showed that the ionosphere was not under the physical influences of extreme disruptive events from space, i.e. space weather in the Earth–Sun system, since this research has been done for the period when the solar minimum is approaching. The period of this investigation was mostly characterized with quiet conditions in the IMF and GMF. This is in accordance with prediction of solar minimum occurring around spring or summer 2020, what is reflected in the space weather analyses. This follows that the anomalies in the VTEC time-series cannot be attributed to influences of space weather. The results presented detailed analysis of the VTEC values and VTEC differences dVTEC between GNSS stations, that were located near the epicenter (Durres and Tirana), or a further GNSS station in Sarajevo, that was 295 km far away, but still belonged to the earthquake preparation zone, which radius was 565 km. One GNSS station located in Istanbul (789 km far away from epicenter), outside of the EPZ but on the similar geographic latitude is used for the comparison of VTEC anomalies. Results indicates that the occurrence of anomalous VTEC values in GNSS station located in the EPZ are statistically significant and could be attributed to the influence of seismic processes, as they were not noticeable much in the ionospheric signature of station Istanbul outside the EPZ. The study should be extended to other GNSS stations located at similar latitudes but outside the EPZ for deeper problem research. Besides that, the research should be extended to the other atmospheric parameters for the research period, such as a temperature for example. In addition, applying artificial intelligence techniques to distinguish different ionospheric anomalies would be useful.

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6. Zhao, Q., Yao, Y., Yao, W., et al.: Real-time precise point positioning-based zenith tropospheric delay for precipitation forecasting. Sci. Rep. 8, 7939 (2018). https://doi.org/10.1038/s41598018-26299-3 7. Dousa, J., Vaclavovic, P.: Real-time zenith tropospheric delays in support of numerical weather prediction applications. Adv. Space Res. 2014(53), 1347–1358 (2014) 8. Tabakovi´c, A., Krdžali´c, D., Muli´c, M.: GNSS meteorologijaiistraživanjeparametaratroposfere. Geodetskiglasnik, br. 46 V49, str. 91–110. Sarajevo (2015) 9. Ding, W., Teferle, F.N., Kazmierski, K., Laurichesse, D., Yuan, Y.: An evaluation of real-time troposphere estimation based on GNSS precise point positioning. J. Geophys. Res. Atmos. 122, 2779–2790 (2017). https://doi.org/10.1002/2016JD025727 10. Monthly Bulletin of the Seismology: Institute of Geosciences, energy, water and environment. Polytechnic University of Tirana. November 20919, No. 5 (2019). Available online at: https:// www.geo.edu.al/skedaret/bul112019.pdf 11. Watcher: Portal of the relevant news on data relevant for Earth. Available online at: https:// watchers.news/2019/11/27/29-dead-after-m6-4-quake-in-albania-which-experts-say-likelystruck-on-blind-fault/(12.04.2020) 12. Oslobodenje.News. Available online at: https://www.oslobodjenje.ba/vijesti/bbc-news/zemljo tres-u-albaniji-najmanje-24-mrtvih-650-povredenih-510191(12.04.2020) 13. Horozovic, D., Natras, R., Mulic, M.: Impact of geomagnetic storms and ionospheric disturbances on mid-latitude station’s coordinates using static and kinematic PPP. EGU General Assembly 2018, Vienna, Austria, 8–13 April 2018; Symposium G 1.3—High-precision GNSS: methods, open problems and geoscience applications, EGU2018–9009; board number x3.116 (2018). Available online at: https://presentations.copernicus.org/EGU20189009_presentation. pdf 14. Muli´c, M., Natraš, R.: Ionosphere TEC variations over Bosnia and Herzegovina using GNSS data. In: Cefalo, R., Zielinski, J.B., Barbarella, M. (eds.) New advanced GNSS and 3D spatial techniques, applications to civil and environmental engineering, geophysics, architecture, archeology and cultural heritage. In: Lecture Notes in Geoinformation and Cartography, pp. 271–283. Springer International Publishing AG2018 (2017). https://doi.org/10.1007/9783-319-56218-6_22 15. Pulinets, S., Ouzounov, D.: Lithosphere-atmosphere-ionosphere coupling (LAIC) model: an unified concept for earthquake precursors validation. J. Asian. Earth. Sci. 41(4–5), 371–382 (2011) 16. Natras, R., Mulic, M.: Geodetic remote sensing of ionosphere in relation to space weather and seismic activity in B&H. In: Freymueller, J., Sánchez, L. (eds.) International Symposium on Advancing Geodesy in a Changing World. International Association of Geodesy Symposia, vol. 149. Springer, Cham (2018). https://doi.org/10.1007/1345_2018_49 17. Natras, R., Horozovic, D., Mulic, M.: Strong solar flare detection and its impact on ionospheric layers and on coordinates accuracy in the Western Balkans in October 2014. Springer Nat. Appl. Sci. 1(1), 49 18. Natraš, R., Krdžali´c, D., Horozovi´c, D., Tabakovi´c, A., Muli´c, M.: GNSS ionospheric TEC and positioning accuracy during intense space and terrestrial weather events in B&H. GeodetskiVestnik 63(1) (2019) 19. Dobrovolsky, I.R., Zubkov, S.I., Myachkin, V.I.: Estimation of the size of earthquake preparation zones. Pure Appl. Geophys 117, 1025–1044 (1979) 20. EPN—European Permanent Network. Available online at: https://www.epncb.oma.be/(15.03. 2020) 21. IGEAWA—Institute of Geo-Sciences, Energy, Water and Environment. Available online at: https://www.geo.edu.al/newweb/?fq=gps&gj=gj1 22. Schaer, S.: Mapping and predicting the Earth’s ionosphere using the Global Positioning System. Ph.D. thesis, Bern University, Bern (1999) 23. Ciraolo, L., Azpilicueta, F., Brunini, C., Meza, A., Radicella, S.M.: Calibration error on experimental slant total electron contents (TEC) 506 determined with GPS. J Geod 81(2):111–120 (2007)

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Computer Modelling and Simulations for Engineering Applications

On the Impact of Body Forces in Low Prandtl Number Liquid Bridges B. Šeta, D. Dubert, J. Massons, P. Salgado Sánchez, J. Porter, Jna. Gavaldà, M. M. Bou-Ali, and X. Ruiz

Abstract The influence of different body forces on the frequencies of the oscillatory regime in liquid bridges of molten silicone is studied. To do so, three different gravity levels are applied: the first related with Earth gravitational acceleration, the second with International Space Station reboosting maneuvers and the third with zero gravitational acceleration. In addition, different Marangoni numbers are considered in order to compare the influence of bulk body forces on them. Finally, a short study of the possible impact of the relationship between length and diameter of a liquid bridge on the number of instability modes is presented. Keywords Liquid bridges · Marangoni convection · Molten silicone · Oscillatory instability · Mode number

1 Introduction The high-temperature containerless floating zone growth technique enables one to obtain high quality single crystals with less contamination, more homogeneity and higher purity [1]. However, despite these theoretical advantages, buoyancy driven convection generated by the thermal distribution inside the furnace could induce striations in the growing front [2]. To avoid these kinds of micro-inhomogeneities, low gravity environments seem to be an idoneous solution. However, even in these places, the dependence of surface tension on the temperature and concentration gradients along any liquid–gas interface inevitably leads to thermocapillary and solutocapillary B. Šeta (B) · D. Dubert · J. Massons · Jna. Gavaldà · X. Ruiz Universitat Rovira I Virgili, Tarragona, Spain e-mail: [email protected] P. S. Sánchez · J. Porter ETSIAE, Universidad Politécnica de Madrid, Madrid, Spain M. M. Bou-Ali Mondragon Unibersitatea, Mondragon, Spain © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. Avdakovi´c et al. (eds.), Advanced Technologies, Systems, and Applications V, Lecture Notes in Networks and Systems 142, https://doi.org/10.1007/978-3-030-54765-3_14

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Marangoni convection. Both convection mechanisms are independent of gravity and can also induce inhomogeneities in the resulting crystals [3]. To anticipate and avoid these types of problems, the characterization of the different flow regimes established in the melt has, for a long time, been a priority. To do so, a number of theoretical and 3D numerical studies have been proposed, using a simplified approach referred to as the half-zone model. This simplified model considers two coaxial circular disks of equal diameter, at different temperatures, in such a way that a thermal gradient is established on the cylindrical volume that joins them. This approach is different than a full zone model as only half of the space between rods in real floating zone growth configurations is simulated. In some sense, this model is restricted by one degree of freedom, as we impose only a hot rod on top fixing also its temperature. Free surface represents interface between surrounding air and molten silicone. The use of this computational model incase of molten silicon has an additional advantage since low Prandtl melts are opaque and highly reactive, which makes difficult to do any systematic experimental research. The characterizations mainly proposed until now in the literature focused on the determination of the first and second bifurcation points, as well as the complex flow structures beyond them as a function of the wave number of the instability [4–7]. Using the above-mentioned half-zone model, the aim of the present 3D numerical work will cover different complementary aspects. We will concentrate on the impact of different gravity conditions on the base case flow g = 0. These conditions cover the gravitational environments existing on the International Space Station on Earth labs. In case of the International Space Station (ISS) a real reboosting will be presented in order to fix a threshold impact during the most dangerous gravitational situation [8, 9]. Similar changes in buoyancy levels reported in the half-zone literature are only related with the reversing of the buoyancy flow by interchanging the temperature conditions between the top and bottom disks. In these cases, the flow is stabilized if the heating comes from above and destabilized if gravity is reversed. Also, in case of heating from above, the critical Marangoni number of the first bifurcation is larger, the flow structures are different and the critical wave number smaller [10]. Mention finally that, for simplicity, neither curvature [11] nor heat losses have been considered here [12].

2 Materials and Methods The thermophysical properties of the silicon melt are presented in Table 1 [7]. The plot of half-zone used is shown in Fig. 1. In this figure T is the basic (mean) temperature and it is the same as T0 in the numerical model, while T the temperature difference between hot and cold plates. The system dynamics are described by Eqs. (1)–(3) where u represents the velocity → g vector, ρ0 the density at the reference temperature T0 , μ is the dynamic viscosity, − is the vector of gravitational acceleration and p the hydrostatic pressure (difference between total and hydrodynamic pressures). At the top and bottom of the domain

On the Impact of Body Forces in Low Prandtl Number Liquid Bridges Table 1 Thermophysical properties of silicon-melt [7]

Property

219

Symbol

Value

ρ0

2.53 × 103

μ

8.89 × 10−4

Thermal conductivity (W/mK)

λ

67

Specific heat (J/kg K)

CP

1 × 103

α

2.65 × 10−5

Thermal surface tension gradient (N/mK)

σT

−2.8 × 10−4

Thermal expansion coefficient (1/K)

βT

9.1 × 10−4

Density

(kg/m3 )

Dynamic viscosity (kg/ms)

Thermal diffusivity

(m2 /s)

Fig. 1 Numerical model of half-zone with corresponding axes

(see Fig. 1) we have imposed no-slip impermeable boundary conditions and fixed temperatures. In addition, on all walls zero gradient of pressure have been considered. On the free surface, the adiabatic condition imposes a zero temperature gradient, while the Marangoni conditions are used for velocity (shear stress balance on the cylindrical free surface). To numerically resolve the model, an OpenFOAM solver has specifically been adapted for this purpose [13]. ∇ • u = 0(1)

(1)

1 ∂u → + (u · ∇)u = − ∇ p + ν∇ 2 u + − g [1 − βT (T − T0 )] ∂t ρ0

(2)

∂T + (u · ∇)T = α∇ 2 T ∂t

(3)

The numerical mesh consisted in 33,320 cells, non-uniformly distributed along the three axes. Mesh is refined in z direction close to the hot and cold plates, as it is

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expected to have strong gradients of temperature and strong Marangoni flow. Also and for the same reasons the mesh has been refined in circumferential and radial direction, closer to the free surface. Time discretization scheme used in the work is Crank-Nicolson scheme of second order accuracy. Although it can be sometimes susceptible and produce numerical oscillations with small enough time step (from 10−4 to 10−3 in this work) we ensure that oscillations are truly physical ones. Notice that the nondimensional numbers characterizing the problem are the Prandtl and Marangoni numbers as well as the aspect ratio between length and diamμC eter of liquid bridge. The Prandtl number is defined as Pr = λ p and in the present case of silicone melt is 0.0132. Note that in liquid metals the Prandtl number is, in general, very low meaning that even for very small temperature gradients oscillatory motion can appear in the melt. The Marangoni number is defined as Ma = TμαLσT and the aspect ratio A = Ld , where L is length of liquid bridge and d is diameter. A complementary nondimensional number which parametrizes the ratio between 2 , buoyancy and surface tension forces is the dynamic Bond number,Bo = βT σρgL T where σT is gradient of surface tension. Further in the paper, Bond number will be useful in comparison of results with and without gravitational acceleration.

3 ISS Acceleration Signal The raw accelerometric signal selected here corresponds to the ISS reboosting maneuver performed on 23rd of May 2019 [14]. These maneuvers are mandatorily used to correct the changes in attitude. During this period (of approximately 20 min) the ISS g-levels abruptly increase, mainly in the reboosting direction (XA ), from 10−6 g to 0.1–0.2 × 10−3 g (or 1–2 mm/s2 , maxima g-levels detected in the ISS). The data used here were recorded by the 121f03 SAMS sensor, with sampling rate of 500 Hz and cut-off frequency of 200 Hz, located in the Destiny module. The signal was downloaded freely thanks NASA PIMS from its website [15]. In order to adapt the real signal to the specific simulation conditions (time step of 0.005 s corresponding to a 200 Hz) a mathematical manipulation based on two procedures was needed. The first one relates to resampling the signal from 500 to 200 Hz and the second one consists in filtering the signal by using the denoising tool [16]. In the latter, a Symlet 8 mother wavelet function was used with a decomposition level fixed at 11. These conditions imply that the resulting denoised signal was filtered at low frequencies under 1 Hz. Figure 2 plots the three acceleration components of the signal, in m/s2 , once the mathematical manipulation has been performed. The strongest acceleration corresponds with in x direction (see Fig. 2).

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Fig. 2 Resampled and denoised SAMS 121f03 signal of the ISS reboosting period (23rd of May 2019). The rectangle indicates the simulation period used

4 Results and Discussion The critical Marangoni number for the onset of oscillations ina wide range of Prandtl numbers can be expressed as [17]: Ma C = 2000Pr 0.6

(4)

This implies that, for the present thermophysical properties, the critical value is approximately Ma C ≈ 150. Equation (4) is somewhat incomplete as it does not take the aspect ratio A in consideration. This number was shown to be important not only for the onset of oscillations but also for the number of flow modes [18]. However, despite the incompleteness of the previous expression (4), the simulations performed here below the critical number, Ma = 83.19(T = 1.4K , L = 0.5cm), confirms a stable thermal flow against oscillations while that the simulation made above this critical threshold, Ma = 166(T = 1.4K, L = 1cm), clearly shows an oscillatory behavior (see Fig. 3). In addition, some studies in microgravity and Earth laboratories showed that in case of low Prandtl number, the second Marangoni transition is characterized by the change from an oscillatory flow characterized by a single frequency to another one with multiple frequencies [19, 20]. In the present case, the Fourier transform analysis of thermal signals shows a single sharp peak in case of Ma = 166(T = 1.4 K, L = 1 cm) which increases for Ma = 357(T = 3 K, L = 1 cm). Another increase to Ma = 588(T = 5 K, L = 1 cm) reveal a multiple frequency response beyond the second bifurcation. Those results can be seen from Fig. 4.

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Fig. 3 Oscillatory mode for the case Ma = 166

Fig. 4 Dominant frequencies for different gravity levels and Marangoni numbers

Neither ISS’s reboosting nor gravity had any effect in thermal signals for simulated time in cases Ma = 166(T = 1.4 K, L = 1 cm) and 357(T = 3 K, L = 1 cm), while in the case of Ma = 588(T = 5 K, L = 1 cm) there was a significant difference between zero g and Earth levels. In addition, as it can be seen from Fig. 5, again there is almost negligible difference for simulated time between zero g and the ISS’s reboosting levels. It is expected that differences arise for larger simulation times in the case of higher Marangoni numbers. These results agree with the fact that the magnitude of the Bond number is low. Such low Bond number is expected because the quite short height of the liquid bridge (1 cm). Remember that if the Bond number is very small, the surface tension forces dominate, and hence there is no big impact of gravity levels before turbulent state.

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Fig. 5 Temperature oscillations with Ma = 357 and Ma = 588

The oscillations seen in Fig. 5 were observed in liquid bridges of diameter (d) 2 cm and length (l) 1 cm, aspect ratio of A = 0.5. The observed flow corresponds to mode m = 2. At this respect, and in order to see the transition of modes with different aspect ratios [16], we have changed the length of liquid bridge to 0.5 and 2 cm. Figure 6 plot iso-lines of temperature revealing the number of modes. All cases are calculated for g = 0. For A = 1, the longest bridge, mode one m = 1 is observed. In case A = 0.5, m = 2, while in the case of A = 0.3 the number of modes changes to three (m = 3). Finally with aspect ratio A = 0.25, number of modes is four (m = 4). Figure 7 presents the vortices related with the formation of the temperature field. All those sections from Fig. 6 and Fig. 7 are taken on the midplane with respect to z axis and the patterns are consistent with those explained in Ref. [21]. Also, the mechanism of the standing wave oscillation is illustrated on Fig. 8, where it can be seen the beginning of oscillation (left) and the end (right). If we take a cross-section in another direction (x) then another aspect of the Marangoni convection is revealed. As can be seen from Fig. 8, there is a convective movement from the hot top to the cold bottom plates along the free surface, while in the middle of the half-zone, a strong flow upwards exists. In the case of oscillations, this flow is not axisymmetric, but oscillates, creating moving vortexes from one side to another (Fig. 9).

5 Conclusion The influence of different gravity level on the oscillatory regime in liquid bridges of molten silicone for flow regimes after the first bifurcation point is studied here. Results indicate that, for low Marangoni values near the above-mentioned point and Earth laboratories, there is a small impact on oscillations, while reboosting do

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Fig. 6 Midplane temperature patterns for A = 1 (m = 1, top left), A = 0.5 (m = 2, top right), A = 0.3 (m = 3, bottom left) A = 0.25 (m = 4, bottom right), red-hot; blue-cold

not affect them at all. However, as soon as the second bifurcation point is surpassed, frequencies on the Earth laboratories are quite different and gravity level plays significant role. Even reboosting show some difference for a relatively short simulated time, with tendency to make even bigger impact as the experiment runs. On the other hand, fixing a gravity level at zero g, Marangoni flow modes and their dependence on the aspect ratio is also investigated. The tendency reported in previous literature is confirmed here. Smaller aspect ratio exhibits more modes.

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Fig. 7 Midplane velocity field for A = 1 (m = 1, top left), A = 0.5 (m = 2, top right), A = 0.3 (m = 3, bottom left) A = 0.25 (m = 4, bottom right)

Fig. 8 Midplane temperature patterns at the beginning (left) and middle of oscillation (right) for the case A = 0.25 (m = 4), red-hot; blue-cold

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Fig. 9 Velocity field for the four different cases considered in the cross section vertical plane revealing the complex nature of Marangoni convection in liquid bridges; A = 1 (m = 1, first row left), A = 0.5 (m = 2, first row right), A = 0.3 (m = 3, second row) A = 0.25 (m = 4, third row) Acknowledgements This work was supported by the Universitat Rovira i Virgili (URV) grant number DLRF4741.

References 1. Riemann, H., Luedge, A.: Floating zone crystal growth. In: Crystal Growth of Si for Solar Cells. Springer, Berlin (2009)

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2. Muiznieks, A., Virbulis, J., Lüdge, A., Riemann, H., Werner, N.: Floating zone growth of silicon. In: Handbook of Crystal Growth. Bulk Crystal Growth: Basic Techniques, vol. II, Part A. Elsevier, Amsterdam (2015) 3. Rost, H.J., Luedge, A., Riemann, H., Kirscht, F., Schulze, T.W.: Float zone (FZ) silicon: a potential material for advanced commercial solar cells? Cryst. Res. Technol. 47, 273–278 (2012) 4. Leypoldt, J., Kuhlmann, H.C., Rath, H.J.: Three-dimensional numerical simulation of thermocapillary flows in cylindrical liquid bridges. J. Fluid Mech. 414, 285–307 (2000) 5. Yasushiro, S., Sato, T., Imaishi, N., Yoda, S.: Three dimensional Marangoni flow in liquid bridge of low Pr fluid. Space Forum 6, 39–47 (2000) 6. Lappa, M., Savino, R., Monti, R.: Three-dimensional numerical simulation of Marangoni instabilities in non-cylindrical liquid bridges in microgravity. Int. J. Heat Mass Transf. 44, 1983–2003 (2001a) 7. Huang, H., Zhu, G., Zhang, Y.: Effect of Marangoni number on thermocapillary convection in a liquid bridge under microgravity. Int. J. Therm. Sci. 118, 226–235 (2017) 8. Jurado, R., Pallarès, J., Gavaldà, J., Ruiz, X.: On the impact of the ISS reboosting maneuvers during thermodiffusion experiments of ternary liquid systems: Pure diffusion. Int. J. Thermal Sci. 132: 186–198 (2017) 9. Jurado, R., Pallarès, J., Gavaldà, J., Ruiz, X.: Effect of reboosting manoeuvres on the determination of the Soret coefficients of DCMIX ternary systems. Int. J. Thermal Sci. 142, 205–219 (2019) 10. Lappa, M., Imaischi, N.: 3D numerical simulation of on ground Marangoni flow instabilities in liquid bridges of low Prandtl number fluid. Int. J. Numer. Methods Heat Fluid Flows 13, 309–339 (2003) 11. Shevtsova, V.: Thermal convection in liquid bridges with curved free surfaces: Benchmark of numerical solutions. J. Cryst. Growth 280, 632–651 (2005) 12. Melnikov, D.E., Shevtsova, V., Yano, T., Nishino, K.: Modeling of the experiments on the Marangoni convection in liquid bridges in weightlessness for a wide range of aspect ratios. Int. J. Heat Mass Transf. 87, 119–127 (2015) 13. OpenFOAM user guide 14. Hb_vib_vehicle_Progress_71P_Reboost_2019-05-23.pdf. https://gipoc.grc.nasa.gov/wp/ pims/handbook/ 15. NASA PIMS website: https://gipoc.grc.nasa.gov/wp/pims/acceleration-archives/ 16. Jurado, R., Gavaldà, J., Simón, M.J., Pallarés, J., Laverón-Simavilla, A., Ruiz, X., Shevtsova, V.: Some considerations on the vibrational environment of the DSC-DCMIX1 experiment onboard ISS. ActaAstronautica 129, 345–356 (2016) 17. Yang, Y.K., Kou, S.: Temperature oscillation in a tin liquid bridge and critical Marangoni number dependency on Prandtl number. J. Cryst. Growth 222, 135–143 (2001) 18. Lappa, M., Savino, R., Monti, R.: Three-dimensional numerical simulation of Marangoni instabilities in liquid bridges: influence of geometrical aspect ration. Int. J. Numer. Meth. Fluids 36, 53–90 (2001b) 19. Nakamura, S., Hibiya, T., Imaishi, N., Hirao, K., Nishizawa, S., Hirata, A., Mukai, K., Yoda, S., Morita, T.S.: Temperature fluctuations of the Marangoni flow in a liquid bridge of molten silicon under microgravity on board the TR-14 rocket. J. Crystal Growth 207, 55–61 (1989) 20. Croll, A., Muller, S.W., Nitsche, R.: The critical Marangoni number for the onset of timedependent convection in silicon. Mater. Res. Bull. 24, 995 (1989) 21. Hibiya, T., Nakamura, S.: Fluid flow in silicon melt with free surface. Adv. Space Res. 24(10), 1225–1230 (1999)

Analysis of Contact Mechanics Problems of Pipes Using a Finite-Volume Method Muris Torlak and Elvedin Kljuno

Abstract A finite-volume Method (FVM) is tested for application to contact problems of linearly elastic bodies, aiming at analysis of pipes exposed to local stress and strain increase triggered by their contact with supports or foundation. The implemented numerical algorithm is verified by comparison of the numerical results with the analytical ones in case of a pressurized thick-walled pipe, as well as in a Hertzian contact of a solid cylinder and a rigid flat foundation. The algorithm is demonstrated in case of a thin-walled pipe lying on a rigid foundation, and the results are discussed. Keywords Contact mechanics · Pipes · Numerical methods · Finite-volume method

1 Introduction Contact problems in solids are a wide set of problems dealing with stress and deformation analysis in and around the contact zone of solid bodies. The most problems of this type have no exact analytical solution in a closed format practically relevant conditions. For engineering purposes a number of models have been developed to predict the main quantities such as the size of the contact area, the depth of the penetration, and the maximum contact pressure with respect to the applied force. Problem of two elastic bodies in contact was first described by Hertz in 1881 [1], whose theory is still widely used in engineering practice. The theory is derived emanating from the following assumptions, which define the so-called Hertzian contact problems: (a) the bodies in contact have continuous, non-conforming shapes, with parabolic pressure distribution in the contact zone, implying that the bodies in contact have M. Torlak (B) · E. Kljuno Mechanical Engineering Faculty, University of Sarajevo, Vilsonovo šetalište 9, 71000 Sarajevo, Bosnia and Herzegovina e-mail: [email protected] E. Kljuno e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. Avdakovi´c et al. (eds.), Advanced Technologies, Systems, and Applications V, Lecture Notes in Networks and Systems 142, https://doi.org/10.1007/978-3-030-54765-3_15

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parabolic shapes, (b) the curvature radii of the bodies in contact are large compared with the size of the contact zone, (c) the dimensions of the bodies in contact are large compared with the size of the contact zone, (d) friction in the contact zone and adhesion between the contacting bodies are neglected—only compressive normal stress exists, no tensile and no tangential stress, (e) usual linear elasticity assumptions, such as those on small strains and homogeneous, isotropic material. Description of Hertz model can be found in many textbooks, such as [2, 3]. Beside this, a number of models both of Hertzian and non-Hertzian contact have been proposed and used, such as the Greenwood-Williamson model [4] for rough surfaces, or the Johnson-Kendall-Roberts model [5] and the Derjaguin-Muller-Toporov [6] model for problems including adhesion. The earliest models assumed ideally elastic bodies in the contact, without consideration of interaction on an atomic level. The newest models are more advanced and more complex, such that they consider the impact of adhesion forces on the major parameters of the contact. Detailed analysis of displacement, stress and strain distribution in practically relevant conditions (arbitrary shapes, various material properties, surface quality, boundary conditions etc.) can be performed using advanced numerical methods, such as finite-element, finite-difference or boundary-element methods. In last decades strong advances are achieved in analysis of solid mechanics using finite-volume methods, which are primarily used for calculation of heat transfer and fluid flow. Although the finite-volume methods are used in a variety of stress analysis problems including linear elastic, non-linear thermo-elasto-plastic, incompressible and viscoelastic material behavior, see for example [7–9], their application in analysis of contact problems is very limited [10–16]. The most contact problems include nonlinear effects: geometric ones due to dependence of the contact area on the applied load, physical ones due to friction on the contact surfaces, or material ones due to frequently encountered large local stresses in the contact area. Finite-volume methods include iterative solution process, e.g. driven by necessity to resolve convection in fluid flow problems, providing a suitable framework for implementation of contact detection and treatment of boundary conditions at the contact surfaces. This paper presents some test results of application of a finite-volume method to stress and strain analysis of contacting solid bodies with corresponding treatment of boundary conditions, while these change in the course of solution depending on applied load, and herewith local stress distribution or indentation depth in the contact zone. The goal is to explore applicability of the method in analysis of stress and strain distribution in pipes arising during their contact with supports or foundations, in order to prevent possible failures.

2 Method In this work the finite-volume method developed by Demirdži´c and Muzaferija [7] is used, which emanates from the momentum balance written in integral form:

Analysis of Contact Mechanics Problems of Pipes …





− → σ · d S +

ρ ud V = V

231

S



fV d V,

(1)

V

where ρ is the material density, u is the displacement vector, V is the volume of the − → considered element of the material, σ is the stress tensor, S is the surface bounding − → the considered volume, and f v is the vector of volume forces distributed over the observed part of the space. The solution domain of Eq. (1) is formed by a computational mesh, consisting typically of a set of polyhedral cells in 3D or polygonal cells in 2D. Equation (1) is solved for displacement components. At the final stage, the strains and stresses can be calculated from displacement fields. The numerical method including the details on the mathematical model, the discretization procedure and the solution of resulting linear algebraic equations are given in the original work [7]. It is worth noticing that, unlike in finite-element methods, this method employs the centroids of cells as computational points, while the boundary conditions applying on a corresponding part of surface S are implemented through appropriate discretized form of the surface integral in Eq. (1). They are defined either through imposed displacements or through imposed tractions on the boundary surface Sb . The contact problems are practically focused on treatment of variable boundary conditions. In general case, during the contact of bodies with arbitrary shapes, the contact zone shape and size vary with applied force or applied indentation depth, and cannot be determined explicitly prior to the calculation. This means that the regions on the bodies’ surfaces, where the distinct boundary conditions are to be applied (contact case and no-contact case), have to be sought in the course of the calculation. In this study, algorithms for contact detection and corresponding selection of appropriate boundary conditions, originally investigated in [10] on rectangular shapes, are further developed and tested. They assume that the geometric data of surfaces of the bodies in contact as well as the position of the initial contact point are known in advance. Two approaches are implemented in the numerical algorithm, as illustrated in Fig. 1. Depending on the case analyzed and herewith the contact algorithm chosen, either Fig. 1 Boundary conditions applied after contact detection: imposed displacements in the contact zone, traction-free otherwise (left) and applied displacement guess in the contact zone, predicted using the imbalance of the external load and the calculated stress distribution over the surface; traction-free outside the contact zone (right)

F

F 1

1

σ b = 0, τ b = 0

σ b = 0, τ b = 0 σ yy(x)

x 2 uib= d(x)=(rb1-rb2)y

d

2 uib= f(F,σ yy)

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(a) the relative displacement of the other body, see Fig. 1 (left), or (b) the resultant pressure force on the contact side, see Fig. 1 (right), is imposed only in the contact zone detected by position comparison of the bodies’ surface points. In the case (b), the detailed pressure distribution over the contact zone cannot be defined, since it is not known in advance. In both cases, outside the detected contact zone, the traction-free condition is used. The employed solution procedure is iterative, providing the necessary framework for prediction and correction of the unknown contact area conditions. In the case (a), the algorithm searches for the boundary faces which are beyond the foundation border, where the displacements corresponding to the local indention depth are imposed; otherwise the traction-free condition is used. In the case (b) only the external force is prescribed and the local displacements in the contact zone, after sufficiently small initial guess, are corrected iteratively, using the difference of the external and the internal force calculated in the contact zone. After that, the balance of the prescribed external force and the calculated inner forces at the contact zone is tested.

3 Results 3.1 Thick-Walled Pipe This case is used for verification and validation of the numerical method and its implementation in the own computer program for stress and strain analysis. Analysis of stress and strain in a cross section of a pipe can be done in 2D assuming plane-strain model when the pipe is sufficiently long. Analytical solution of stress distribution for the case of uniformly distributed internal and external pressure can be found in a number of books, such as [2]: σrr = C1 +

C2 C2 , σθθ = C1 − 2 , r2 r

(2)

where the coefficients C1 and C2 are defined as: C1 =

Ri2 Pi − Ro2 Po (Po − Pi )Ri2 Ro2 , C = . 2 Ro2 − Ri2 Ro2 − Ri2

(3)

From Eqs. (2)–(3) and the stress–strain relationship, the relation for distribution of radial displacement can also be found by integration along the pipe radius. In the test example, a pipe with the inner radius of 0.5 m and the outer radius of 1 m is considered. The elasticity modulus of 210 GPa and the Poisson ratio of 0.3 are adopted. The pipe is exposed to the internal pressure of 1 MPa, while the outer surface is traction-free. Distribution of the calculated radial displacements across

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Fig. 2 Radial displacements of a thick-walled pipe across the thickness: convergence of numerical results with mesh refinement

Fig. 3 Radial stress distribution in a thick-walled pipe across the thickness: convergence of numerical results with mesh refinement (left) and comparison of the numerical results obtained on two different profile lines on structured mesh, and with an unstructured mesh with the same typical mesh spacing (right)

the pipe wall thickness are shown in Fig. 2, while the distribution of the radial stress component is shown in Fig. 3. Agreement of the numerical results with the analytical solution is seen, revealing convergence of the results achieved with successive mesh refinement.

3.2 Hertzian Contact of a Cylinder and Rigid Flat Foundation In this example, deformation of a linearly elastic cylinder pressed against a rigid flat foundation is considered. This problem can be approximately described by Hertzian

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theory of non-adhesive elastic contact, within the limits of the theory assumptions. One body, the cylinder, has only one, finite radius of curvature, while the other radius (along the cylinder axis) is infinite. The other body, a flat foundation, has infinitely large curvature radii. Since rigid, its elasticity modulus can be described as infinitely large. In such a case, the following formulae can be derived [1–3] for indentation depth d:   4F 1 − ν 2 , d= π El

(4)

where F is the external force pressing the bodies in contact, ν is the Poisson’s ratio, E is elasticity modulus and l is the length of the cylinder. The half-width of the contact zone a (which has elliptical shape in the more general case of contact of two paraboloids or spheres) is:  √ rF 2  2 a = rd = √ , 1−ν El π

(5)

where r is the radius of the cylinder. The maximum pressure in the contact zone p0 is:  EF 1 p0 =   (6)  rl . π 1 − ν2 In the case presented here, the outer radius of the cylinder is 1 m. Assuming 2D plane strain model, the cylinder is regarded as infinitely long, but all calculations are done with the unit length. The values of the elasticity modulus of 2 GPa and the total external force acting on the cylinder 100 MN (applied as uniformly distributed body forces over the entire cross section) are adopted so that the deformation in the contact zone is sufficiently large to be visualized. The Poisson ratio is 0.3. For simplicity reasons, the computational mesh is created as a single annular block, leaving a small hole in the center. Its radius is 1% of the outer one, so that its effect on the stress and strain distribution in the contact zone is regarded as negligible. Both algorithms for application of contact boundary conditions are applied: the one with prescribed indentation depth (d was calculated in advance using Eq. (4)), and the one with imposed integral normal force on the contact side of the cylinder, here supposed to be equal to the external load with opposite sign. The calculated pressure distribution in the contact zone over the horizontal distance from the cylinder axis is shown in Fig. 4 (left). Both algorithms show consistent behavior with nearly the same results. Although the trend of the numerically calculated pressure variation agrees well with the analytical one, a certain deviation in magnitude is observed (about 6%) which can be addressed to differences between the model setup and one of the Hertzian theory assumptions. The external load and

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Fig. 4 Pressure distribution in the contact zone, depending on the distance from the central contact point (left). History of the calculated displacement and normal force during solution process (right)

the elasticity modulus in the model setup presented here were adopted anticipating relatively large indentation depth, which increases geometrically nonlinear effects. The Hertzian theory assumes sufficiently small displacements and small contact zone compared to typical body dimensions neglecting non-linear effects. The histories of calculated displacement and the force in the contact zone using the algorithm with imposed resultant force in the contact zone is shown in Fig. 4 (right). The maximum indentation depth in the contact zone of 0.0557 m is obtained, while the analytical solution (4) predicts the value of 0.0579 m. The difference is less than 4%. Overall force balance equations must be satisfied at any cross-section with the normal in x and y directions. The stress σ yy integrated over any plane with the normal in the direction y must be equal and must provide the total force applied, which is satisfied. Distribution of the normal stress σ yy and the effective von Mises-stress over the cylinder cross section is shown in Fig. 5. It is worth noticing that the boundary of the original computational mesh is circular, but Fig. 5 shows the results on the mesh

Fig. 5 Distribution of the normal stress σ yy in the cylinder loaded by volume forces (left) and the effective von Mises-stress in the cylinder loaded by concentrated force (right)

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deformed after the calculation in order to visualize the deformation in the contact zone better (without magnification). Note that the two depicted cases have different type of external force: distributed body force over the cross section (left) and concentrated force on the top of the cylinder (right). However, its resultant value is the same. Figure 5 (right) is showing relatively high values of the effective stress at the edges of the top area, where the force is applied over a small surface area, and around the bottom contact area, where an equivalent no-slip condition is applied. Since the normal and the shear stress are not addable and influence yielding in different manners, where the shear stress has higher impact, several hypotheses can be used depending on materials that are in contact, more precisely whether the materials are plastic or brittle. Here, the effective stress is calculated according to von Mises’ hypothesis, and it is a mathematical combination of the normal and the shear stress components: σe f f =



2 − σ σ + 3τ 2 . σx2x + σ yy xy x x yy

(7)

The effective stress, according to (7), shows significant influence of the shear stress, which is relatively high at the edges of the top and the bottom area, and that is the reason for the high effective stress in Fig. 5 (right) in those areas.

3.3 Elastic Thin-Walled Pipe on a Rigid Foundation Having considered verification of the method as acceptable and results of the contact algorithm as satisfactory, performance of the solution algorithm is further tested in a case of thin-walled pipe pressed against the flat, horizontal, rigid foundation. The inner and outer radius of the pipe are 0.95 m and 1 m, respectively. The model is considered in 2D so it has the unit length. The elasticity modulus of 1 MPa and the Poisson’s ratio of 0.3 are adopted. The external load of 30 kN is uniformly distributed over the inner side of the pipe cross-section, directed downwards. Unlike in both previous cases, the pipe wall is exposed to local bending caused by the contact force acting on the pipe bottom. As a consequence, the convergence rate turns out to be slower, exhibiting sometimes severe stability problems. Partly, this is caused by bending effects in thin-wall structure, a problem which has already been discussed in literature [17, 18]. In addition to that it seems that the external pressure acting on the contact surface is prone to develop temporary “numerical” buckling which triggers sudden changes in the intermediate forces and displacements, so that careful selection of under-relaxation factors is needed in order to keep the solution process stable. Figure 6 (left) shows distribution of the normal stress over the horizontal distance from the pipe axis in the contact zone between the pipe wall and the foundation. As compared to the case with the full cylinder, the normal stress variation is not monotone and reveals two extreme values, nearly symmetrically located with respect to the pipe

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Fig. 6 Distribution of the normal stress σ yy (left) and effective von Mises-stress σ ef (right) in the contact zone of the thin-wall pipe

axis. The extreme values of the normal stress give rise considerably to the effective stress, whose distribution near the contact zone is shown in Fig. 6 (right). It is worth noticing that the maximum effective stress does not appear exactly on the contact surface, but within the material, slightly away from the contact surface.

4 Conclusions Generally speaking, problems of contact mechanics have no exact analytical solution, such that there is a need for approximate modeling to predict contact stresses analytically. Several analytical models have been developed to predict the most important factors of the elastic bodies contact, such as the maximum contact pressure, contact area and the depth of the deformation. However, all analytical models include approximations, such that numerical solutions can have advantages in the accuracy of predicting the major parameters and to provide the stress distribution around the contact area. A finite-volume method was used to develop own program and predict the components of the stress and the effective stress distribution in the case of elastic contact of solid cylinder with a rigid foundation and a thin walled pipe with a rigid massive foundation. The developed numerical algorithm is verified and validated using cases of stress analysis of a pipe when there is an analytical solution, such as the case of thick-walled pipe loaded with internal pressure. The results of the stress analysis via numerical method were compared with the results of the analytical models showing acceptable agreement, with relatively small deviations.

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References 1. 2. 3. 4. 5. 6. 7.

8. 9. 10. 11.

12.

13.

14. 15.

16.

17. 18.

Hertz, H.: Über die Berührung fester elastischer Körper. Z. Angew. Math. 92, 156–171 (1881) Timoshenko, S., Goodier, J.N.: Theory of Elasticity. McGraw-Hill (1951) K.L. Johnson: Contact Mechanics. Cambridge University Press (1985) Greenwood, J.A., Williamson, J.B.P.: Contact of nominally flat surfaces. Proc. R. Soc. Lond. A 295, 300–319 (1966) Johnson, K.L., Kendall, K., Roberts, A.D.: Surface energy and the contact of elastic solids. Proc. R. Soc. Lond. A 324, 301–313 (1971) Derjaguin, B.V., Muller, V.M., Toporov, Y.P.: Effect of contact deformations on the adhesion of particles. J. Colloid Interface Sci. 53(2), 314–326 (1975) Demirdži´c, I., Muzaferija, S.: Numerical method for coupled fluid flow, heat transfer and stress analysis using unstructured moving meshes with cells of arbitrary topology. Comput. Methods Appl. Mech. Eng. 125(1–4), 235–255 (1995) Demirdži´c, I., Martinovi´c, D.: Finite volume method for thermo-elasto-plastic stress analysis. Comput. Methods Appl. Mech. Eng. 109(3–4), 331–349 (1993) Cardiff, P., Demirdži´c, I.: Thirty years of the finite volume method for solid mechanics. arXiv: 1810.02105 [math.NA] (2018) Torlak, M.: Application of finite volume method to problems of contact mechanics. Diplomathesis, University of Sarajevo, Mechanical Engineering Faculty (1998) Jasak, H., Weller, H.G.: Finite volume methodology for contact problems of linear elastic solids. In: Proceedings of 3rd Congress of Croatian Society of Mechanics, pp. 253–260, Dubrovnik, Croatia (2000) Taylor, G., Breiguine, V., Bailey, C., Cross, M.: An augmented Lagrangian contact algorithm employing a vertex-based finite volume method. In: Proceedings of the 8th Annual Conference of the Association for Computational Mechanics in Engineering, ACME 2000, London, UK (2000) Cardiff, P., Ivankovi´c, A., FitzPatrick, D., Flavin, R., Karaˇc, A.: Development of a finite volume methodology for linear elastic contact problems. In: Proceedings of the IWCMM, Limerick, Ireland (2011) Cardiff, P., Karaˇc, A., Ivankovi´c, A.: Development of a finite volume contact solver based on the penalty method. Comput. Mater. Sci. 64, 283–284 (2012) Cardiff, P., Karaˇc, A., FitzPatrick, D., Flavin, R., Ivankovi´c, A.: Development of a hip joint model for finite volume simulations. J. Biomech. Eng. 136, 1–8 (2014). https://doi.org/10.1115/ 1.4025776 Berge, R.L., Berre, I., Keilegavlen, E., Nordbotten, J.M., Wohlmuth, B.: Finite volume discretization for poroelastic media with fractures modeled by contact mechanics. Int. J. Numer. Methods Eng. 12, 644–663 (2020) Wheel, M.A.: A finite volume method for analyzing the bending deformation of thick and thin plates. Comput. Methods Appl. Mech. Eng. 147, 199–208 (1997) Torlak, M.: A finite-volume method for coupled numerical analysis of incompressible fluid flow and linear deformation of elastic structures. PhD thesis, TU Hamburg-Harburg (2006)

A Contribution to Modeling and Computer Simulation of Species Spread in Natural Environments Muris Torlak, Vahidin Hadžiabdi´c, and Sadjit Metovi´c

Abstract In this paper, analogy of heat- or mass-transfer problem and progression of species in natural environments is used. Time-dependent spatial distributions of species in a given population (such as microbes, bacteria, viruses or herewith infected individuals etc.) are described by time-dependent convection-diffusion equation, which is widely used in analysis of a number of physical, engineering or environmental problems. In the presented example, a finite-volume method is used for its numerical solution. The source term is calibrated using the available recorded data on the species concentration development in the beginning stage. The integral results of the proposed model are compared with another, integral model (SIR) based on ordinary differential equations. Calculated spatial distributions for three different modeling cases are given. Keywords Modeling · Computer simulation · Species · Partial differential equations · Disease spreading

1 Introduction Analysis of dynamics of biological species spread in natural environments requires a variety of mathematical tools. Typically, these tools involve model creation, solving the corresponding equations, usually including or derived from ordinary or partial differential equations, statistical analysis and others. A considerable number of models used for this purpose is described by ordinary differential equations, usually delivering integral analysis of the variations in time, while the spatial distributions remain unresolved. The spatial models of biological species in natural environments due to growth or flow-induced transport in aquatic ecosystems, e.g. plankton populations in the ocean under complex turbulent flows, M. Torlak (B) · V. Hadžiabdi´c · S. Metovi´c Mechanical Engineering Faculty, University of Sarajevo, Vilsonovo šetalište 9, 71000 Sarajevo, Bosnia-Herzegovina e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. Avdakovi´c et al. (eds.), Advanced Technologies, Systems, and Applications V, Lecture Notes in Networks and Systems 142, https://doi.org/10.1007/978-3-030-54765-3_16

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can be described by partial differential equations, such as used for heat or mass transfer, transport of species in fluids, semiconductor physics and other problems. The reaction–diffusion–advection equation is also used to model some of the problems, e.g. bacterial chemotaxis or migration of population. On the other hand, simulations of some spreading phenomena, such as epidemics, usually consider variation of the sought variables (e.g. number of infected people) in time. There is a number of different models used for this (SIR, SIRS, SIS, SEIR, MSEIR etc.) [1–3]. The problems are analyzed for a given part of space, e.g. for a country or for a city, but without detailed information about spatial variation of the characteristic quantities and their interaction. In this paper solution of the time-dependent convection–diffusion equation applied to spread of infectious disease, observing temporal and spatial variation of the number of infected individuals is tested. The problem is solved first using one of the frequently employed models, SIR model. Then the analogy between the heat-transfer problem and the disease spread is outlined, and finally numerical solution of the convection– diffusion model for disease spread is demonstrated.

2 Modeling by Ordinary Differential Equations In a large number of cases, spread of infectious diseases is described by a system of non-linear, mutually coupled differential equations. The basic model of this kind, which is probably mostly used, is the SIR (Susceptible-Infected-Recovered) model [1]. The model emanates from the following assumptions: a closed population under consideration consists of three groups of individuals: susceptible, infected and recovered ones (S, I, R, respectively), and its total number is constant; a recovered individual cannot be re-infected; the rate of transmission of the disease is proportional to the number of possible communications between susceptible S and infected I individuals; the recovery rate is proportional to the number of infected. The unknown quantities are the number of susceptible, infected and recovered individuals which are variable in time. The model is mathematically described as follows: dS − β S I, dt dI = β S I − ν I, dt

(1)

dR = ν I, dt where β and ν are positive parameters. The parameter β describes the transmission rate. The parameter ν describes the recovery rate and it is the reciprocal value of the

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average recovery time. The model described by Eq. (1) is suitable for simulations of relatively fast disease development, so that assumption on the constant total number of individuals in the observed time is valid. Beside this one, there are many other models in use [2, 3] with different degrees of complexity introduced to provide appropriate accuracy and reliability of predictions in different disease scenarios. The model given by Eq. (1), as well as other similar models from the same class, describe the considered population in integral way: only variations in time are observed, and they do not contain any information about distribution of the quantities of interest in space. This lack of spatial variations is one of the drawbacks of the models based on time-dependent ordinary differential equations.

3 Convection–Diffusion Equation In this work time-dependent convection–diffusion equation is used for analysis of infectious-disease development both in time and space. This type of equation is very frequently used in analysis of a number of physical and engineering problems, such as heat transfer or transport of species in a continuous medium. Very robust and efficient numerical solution methods are available since decades, delivering a good framework for application to analysis of temporal variation and spatial distribution of species in other systems with the same or similar behavior. One of such application fields could be spread of viruses which cause infectious diseases in a population, where the number of infected persons would be the primary quantity of interest. The equation is written here in integral form: ∂ ∫ ρcφd V + ∂t V

 S

ρ vcφd S =



 S + ∫ q + d V − ∫ q − d V. k ∇φd V

(2)

V

S

Equation (2) describes temporal and spatial variation of the unknown quantity φ within a part of space, which is bounded by a closed surface S and whose size is expressed by the volume V. The first term describes the local rate of change of the unknown quantity φ. The second term describes convective transport through the boundary S, which may be applied to directed transport of the individuals at relatively large distances (in the further text also denoted as “convection”). The third term is the diffusion term, which is here used to describe “undirected” transport and spread of the quantity φ in the intermediate vicinity of the considered part of space (in the further text also denoted as “diffusion”). The last two terms describe local production and destruction rate, or simply local sources and sinks of the considered quantity. In case of modeling of chemical processes they describe the reaction effects. The quantities ρ, c, and k are the properties describing behavior and response of the specific medium in the considered part of space. In heat transfer problem, they describe the density, the specific heat capacity, and the thermal conductivity of the material, respectively.

242 Table 1 Analogy between the quantities in heat transfer and disease spread

M. Torlak et al. Variable

Heat transfer

Disease spread

φ

Temperature

Specific number of infected personsa

V S

Volume

Populated area

Surface/area

Border/widthb

ρ

Density

Population density

c

Specific heat capacity

Resistance to disease

ρ v S

Mass flux of the transporting medium

Transportationc

k

Thermal conductivity

Local transmission capability

q+

Specific heat source rate Production rate

q−

Specific heat sink rate

a Fraction

Destruction rate

of the total population or concentration of the infected

persons that S may be described in different ways. It may also be a number of neighboring “points”, such as contact persons or neighboring places/towns c This quantity describes the net number of persons moving from one place to the other b Note

Assuming analogy between the convective-diffusive transport and disease spreading, as described in Table 1, Eq. (2) can be used to simulate the temporal and spatial development of the disease. Clearly, the results depend on the input data. While the geographic data (area, border length, population density) can be estimated with sufficient accuracy, the values such as production or destruction rate can be estimated only roughly, while the resistance to disease, the transportation, and the local transmission rate must be assumed since the detailed data on these effects are in a large number of cases not available. When Eq. (2) is written in differential form (as a partial differential equation), finite-difference methods can be used for its solution. This is, however, difficult to process on complex geometries, so finite-element or finite-volume methods are usually preferred choice. In this work a finite-volume method, such as described in [4], is implemented in own computer program [5] and used for solution of Eq. (2). The procedure is here described just briefly, and the details can be found in the aforementioned literature. The considered part of space is divided into a set of cells of polyhedral shapes, typically hexahedra or tetrahedra. In plane two-dimensional domains, they reduce to polygons, quadrilaterals and triangles, respectively; the volume integrals reduce to the integrals over the polygon area, while the surface integrals reduce to the integrals along their boundaries. The cells do not penetrate into each other and there are no voids between them. For each cell in the set Eq. (2) is discretized, yielding

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thus a system of non-linear algebraic equations to be solved for the quantity φ at the computational points. In the method applied here, the computational points are located at the cell centroids. The discretization include approximation of the volume and the surface integrals by midpoint rule and assumption of linear variation of the variables in space. Consequently, the variable values required on the surface S are obtained by linear interpolation, except in case of strong convection where other techniques might be required (such as upwind schemes) in order to promote stability. Similarly, the required gradients at the surface S are approximated by central differencing scheme, while the gradients at the computational points are obtained by least-square-method in accordance with the assumed linear spatial variation of the variables. The time derivative is approximated by a backward differencing scheme, typically a 1st- or 2nd-order accurate one. The solution process is iterative, allowing temporary linearization of the equations in the system as well as explicit treatment of the numerical correction terms. Due to suitable matrix structure of the linearized system, in each iteration systems are solved by one of the methods for unstructured: preconditioned BiCGSTAB for non-symmetric matrices when the convection is included or preconditioned CG method for symmetric matrices. The iterations are repeated where the algebraic systems are recalculated, assembled and solved in turn, until prescribed tolerance level is reached.

4 Spread of COVID-19 Disease in Bosnia-Herzegovina The models described by Eqs. (1) and (2) are applied to simulation of COVID-19 disease development in Bosnia-Herzegovina in the spring 2020. The total population in Bosnia-Herzegovina is 3.8 million people. The parameters adopted for simulation using SIR model, Eq. (1), are explained as follows. Assuming that one infected individual infects the others every three days, the transmission rate β = 1/3 is used. The recovery rate υ is described as reciprocal value of the required recovery time. Typically, recovery takes from 14 to 28 days. Here the value of the recovery rate of 1/25 = 0.04 is assumed. Since this is an initial-value problem, as described by Eq. (1), the results depend strongly on the initial values of the susceptible and the infected individuals. Their precise estimation is frequently difficult, not rarely it is impossible, and usually these values are not known in advance. In the present simulation we use a guess with 1 initial infected person and the entire population being susceptible, i.e. 3.8 million people. The time step size is 1 day. Explicit Euler method is used to approximate the differential equations. In Fig. 1 the results of the simulation are compared with the public recorded data. The vertical axis shows the data as fraction of the total population. The two plots show two different periods, 20 days and 40 days after the first recorded case, for better visibility. In the first 20 days of the disease spread the agreement of the simulated and the real data on the infected individuals is clear, and the trend can be described approximately by an exponential function, or by a polynomial of the 3rd order, given

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Fig. 1 Number of the infected and the recovered individuals in Bosnia-Herzegovina: comparison of the SIR model with the real recorded data

by Eq. (3) later in the text. In the next 20 days, the real data show more-or-less linear increase, while the simulation still predicts exponential growth. The change in trend of the real data is probably caused by strict measures for disease-spread prevention (contact prevention, social distance, isolation) which are imposed relatively early, about 7–15 days after the first recorded case. Without these measures the development of the number of infected individuals would be much faster and probably it would also follow exponential-growth pattern. The overall disease development predicted by the SIR model for a theoretical case corresponding to the conditions under which this model is derived and the assumptions applying to the adopted model parameters is given in Fig. 2. According to these results, the maximum number of the infected individuals, about 64.5% of the total population, would be reached after 65 days. After that an asymptotic decay is seen. The currently available data (in April 2020, 45 days of disease development) show that the real number of infected individuals still increases following nearly linear pattern. According to the data given in [6], the total number of infected persons in BosniaHerzegovina after 40 days of disease development (on April 14th, 2020) is 1037, which delivers a rate of about 26 newly infected persons per day on average, or about 6.8 × 10−6 new infected individuals per day as a fraction of the total population. According to the same data, the increase of the number of infected individuals in the first 20 days can be described approximately by a polynomial of 3rd degree: Fig. 2 Overall development of the number of infected and recovered individuals in Bosnia-Herzegovina according to the SIR model

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I ≈ 0.03663t 3 − 0.40647t 2 + 1.91293t + 0.12343,

245

(3)

where t is the time in days. If we consider the entire country as the system under observation which is isolated from its environment, so there is no “diffusive” or “convective” transport (surface integrals in Eq. (2) are neglected, since transport across the boundaries is neglected), the source term for this period can be estimated from the approximate equation: ∂I ∂φ V =c ≈ q+V ⇒ ∂t ∂t 3 · 0.03663t 2 − 2 · 0.40647t + 1.91293 c. q+ ≈ 55130 ρc

(4)

After the first 20 days, the available statistical data reveal quite linear increase of the number of infected persons, which implies that the source is constant, i.e. does not vary with time or with the number of infected persons. The value of the source is estimated to be: ρc

1 ∂φ ≈ q + = 7.9 × 10−4 2 , ∂t km day

(5)

with ρ equal to 69 persons/km2 and c set to 1 for simplicity. This estimation presumes uniform distribution of the source q+ over the entire area of the country. In reality, the source is not uniform, but concentrated in a certain number of locations (typically, large cities and towns). In simulations conducted in this work, the source term q+ is defined in the distinct circular regions, defined around 7 cities: Banja Luka, Zenica, Mostar, Konjic, Biha´c, Sarajevo, and Tuzla, considered to be important due to the relatively large number of infected persons at the beginning of the disease, as well as due to the relatively high population density. In agreement with previously given conclusions on character of the source term for the entire country, the source term in the affected regions around the mentioned 7 cities is defined as variable in time following the expressions given in Eq. (4) for the first 20 days, and constant after that. The values of numerical coefficients in these expressions are, however, adapted to keep the same value of the total source in the entire country. The magnitude of the sources is not the same for each city. It is distributed in accordance with the public, registered data in the beginning period of the disease by assignment of the appropriate weighting factors. The destruction term q− in Eq. (2) can describe reduction of the number of infected persons, for example including the number of recovered individuals. In this work, however, it is not taken into account since the attention is paid to the progress of infection. The boundary conditions are given as Dirichlet boundary conditions, described by the number of the infected persons. Here, it is assumed to be equal to zero along all country borders.

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Fig. 3 Computational mesh and the results of simulation with variable source term in Eq. (2). The SIR model results and the real data are given for comparison

Figure 3 shows the computational mesh covering the total area of BosniaHerzegovina. The mesh resolution is increased in the regions with higher expected concentration of infected individuals (left). The calculated results obtained solving Eq. (2) without “convective” and “diffusive” transport by the described finite-volume method are given as well, denoted by “numerical method” (right). By neglecting the convective and the diffusive term in Eq. (2), the model simulates the case with completely prevented local contacts among individuals and suppressed distant motion, which would otherwise trigger undirected and directed spatial spread, respectively. Only the increase of the number of infected individuals caused by local sources is obtained, as expected. The simulation results are compared with the results of the previously described SIR model setup as well as with the real data. Their agreement with the real data is obvious. This is expected, since the source term in Eq. (2) is fit to the available real data set, while in SIR model it is defined as proportional to the product of the number of susceptible and infected people in the whole domain.The idea behind this procedure is to calibrate the model to a real case in its beginning stage, in order to be able to provide results of later development as accurate as possible. The spatial distribution of the number of infected individuals calculated for the cases: (a) without “convection” and “diffusion”, (b) with “diffusion” only, where the diffusion parameter (local transmission capability) is set to 10, and (c) with “diffusion” and “convection” driven by fictitious velocity, randomly generated to fit transportation capacities from 0 to 100 individuals per day, per km of the boundary width are shown in Figs. 4, 5 and 6, respectively. In all cases, the source functions are the same, as previously discussed. The calculated concentrations of the infected individuals φ (the number of infected individuals divided by total population) for all three cases are shown by color spectra corresponding to the logarithmic scale, from 10–6 to 10–1 , for three instants of time: after 30, 60 and 90 days. In case (a) all regions with non-zero sources remain isolated, since there are no mixing processes which would be caused by “convection” or “diffusion”. The concentration of the infected individuals increases with time due to the existence of

A Contribution to Modeling and Computer Simulation … Fig. 4 Spatial distribution of the concentration of the infected persons, case (a)

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248 Fig. 5 Spatial distribution of the concentration of the infected persons, case (b)

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A Contribution to Modeling and Computer Simulation … Fig. 6 Spatial distribution of the concentration of the infected persons, case (c)

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sources. The total number of infected individuals (the integral of concentration over population in the considered area) and herewith the average concentration over the entire area follow the corresponding curve in Fig. 3 (right). In case (b) a certain spreading of the regions with sources is seen which increases with time. Some of the regions, which are separated at the beginning but close to each other, merge after sufficiently long time. Due to increase of the area covered by the infected persons, the local maximum concentration in the infected regions is not as high as in case (a). Due to transportation effects across the local, inner boundaries (in randomly generated directions), the spreading in case (c) is not smooth and not equally distributed in all directions. The covered area seems to be larger than in case (b), and is larger than in case (a). Correspondingly, the local maximum concentration is reduced in the most parts. However, at some places, the additional local maxima of concentration may arise, induced by transported infected individuals, such as in the north-west area, quite close to the border. Depending on the observed level of the concentration of infected individuals, merging of the infected areas may be seen. In the presented example, the convective transport is calculated using randomly generated velocities, and herewith transportation directions and intensity at the beginning of simulation.

5 Conclusions In this paper, variation of species in time and space within a given population is calculated solving time-dependent convection–diffusion equation using a finitevolume method. The simulation is demonstrated in analysis of spread of individuals infected by SARS-CoV-2 virus, and herewith spread of COVID-19 disease in BosniaHerzegovina. Unlike usually used models based on ordinary differential equations only, the mathematical model presented here includes convective and diffusive terms describing directed remote and undirected intermediate transport of infection, respectively. This choice is motivated by capability of these terms to describe variations of the observed variable in space (species concentration i.e. fraction of infected individuals in the given population). The presented results are plausible. The available public data on disease spread in the beginning period are used to calibrate the source terms. The calculated integral values of the number of infected individuals show a good agreement with the publicly reported values. The results show different responses in spatial spread for three different cases, illustrating scenarios of complete isolation, undirected intermediate contacts, and arbitrary contacts including transportation effects. As expected, the results show clearly larger spread in case of allowed contact/communication between the affected regions, undirected or directed. More detailed and accurate analysis of spatial spread requires exact input data, such as distribution of transportation directions and intensity, or spatial variation in population density, so further research is required in order to collect the necessary data for appropriate modeling of these effects. Additionally, in future research the source and the sink term (production and

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destruction terms) could be expanded in order to account for other effects, such as variation of number of recovered individuals, birth rate, deceased individuals etc., or the present model can be combined with one of the SIR-like models in order to take these quantities into account.

References 1. Kermack, W.O., McKendrick, A.G.: A contribution to the mathematical theory of epidemics. Proc. R. Soc. 115(772), 700–721 (1927) 2. Hethcote, H.W.: The mathematics of infectious diseases. SIAM Rev. 42(4), 599–653 (2000) 3. Vynnycky, E., White, R.: An Introduction to Infectious Disease Modelling. Oxford University Press, Oxford (2010) 4. Ferziger, J.H., Peri´c, M.: Computational Methods for Fluid Dynamics. Springer, Berlin (2002) 5. Torlak, M., Hadžiabdi´c, V.: Solving linear wave equation using a finite-volume method in time domain on unstructured computational grids. In: Avdakovi´c, S., (ed.) Advanced Technologies, Systems, and Applications III, Proceedings of the International Symposium on Innovative and Interdisciplinary Applications of Advanced Technologies (IAT 2018), vol. 1, Lecture Notes in Networks and Systems, vol. 59, pp. 347–356, Springer (2019) 6. https://github.com/CSSEGISandData/COVID-19/tree/master/csse_covid_19_data. Access date Apr. 19 2020

Information and Communication Technologies

The Influence of System Factors on QoE for WebRTC Video Communication Maida Balihodži´c, Jasmina Barakovi´c Husi´c, and Sabina Barakovi´c

Abstract Web Real-Time Communication (WebRTC) is a relatively new technology which enables peer-to-peer communication between web browsers in real time. In order to survive in a competitive market, it is important to satisfy customer expectations, provide expected Quality of Service (QoS) and certain levels of Quality of Experience (QoE). This paper examines the influence of three system factors, i.e., delay, jitter, and Central Processing Unit (CPU), on the QoE of WebRTC video communication. The QoE metrics were collected by questionnaire and statistically analyzed using Friedman’s test and Pearson correlation. The statistical analysis has shown a statistically significant impact of considered system influence factors on QoE. Keywords WebRTC · QoE · System factors · Video communication · Statistical analysis

1 Introduction In recent years, many voice and video applications that enable faster dissemination of information have been created due to the rapid expansion of the Internet and the technologies that use the Internet to transmit the data [1]. However, one of the problems with such applications is that a lot of them are supported by specific Operating System (OS), so users of different mobile device models with different OSs cannot use the same application to communicate or have to find a specific one that fits each M. Balihodži´c · J. Barakovi´c Husi´c (B) Faculty of Electrical Engineering, University of Sarajevo, Sarajevo, Bosnia and Herzegovina e-mail: [email protected] S. Barakovi´c Faculty of Transport and Communications, University of Sarajevo, Sarajevo, Bosnia and Herzegovina American University in Bosnia and Herzegovina, Tuzla, Bosnia and Herzegovina © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. Avdakovi´c et al. (eds.), Advanced Technologies, Systems, and Applications V, Lecture Notes in Networks and Systems 142, https://doi.org/10.1007/978-3-030-54765-3_17

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mobile device. In order to overcome these problems, Web Real-Time Communication (WebRTC) is introduced. WebRTC is an open-source project that provides peer-to-peer communication between browsers with the help of Application Programming Interfaces (APIs). It is used to transmit information using browser without installation of new application or any upgrades [2]. Use of browser provides easier communication, which attracts new users who do not have much knowledge of computers and mobile devices, while those who are more experienced save time as there are no new upgrades and big changes of settings [3]. The benefits of implementing WebRTC can be grouped into five categories: (i) cost reduction, (ii) ease of use, (iii) security, (iv) fast time to market, and (v) simplified device integration. There are some limitations, which can be grouped into six categories: (i) signaling, (ii) presence, (iii) authentication, (iv) address book integration, (v) ringing notification, and (vi) native push notifications [4]. WebRTC underpins a number of Over The Top (OTT) services including social networks, such as Google Hangouts, Facebook WhatsApp calling features, Twitter calling options, etc. A number of operator services have been implemented based on WebRTC technology. AT&T has exposed telco services to web developers via JavaScript and Representational State Transfer (RESTful) APIs utilizing WebRTC gateways to its IP Multimedia Subsystem (IMS) backend platforms. Telefónica’s TokBox uses WebRTC to provide live video communication services to customers of all sizes, from independent developers to global enterprises. Orange Libon incorporates WebRTC into an existing mobile Voice over IP (VoIP) service (similar to Viber or Skype) [4]. The important challenge is associated with insurances of QoS parameters such as jitter and delay, which are important for real-time voice and video transmission, as well as for maintaining conversation continuity. Efforts to improve the QoS parameters are essential to increase QoE that determines customer satisfaction with a specific service. According to the QoE definition presented in [5], “QoE is the degree of delight or announce of the user of an application or service. It results from the fulfillment of his or her expectations with respect to the utility and/or enjoyment of the application or service in the light of the user’s personality and current state”. QoE can be decomposed into perceptual features. QoE feature is a perceivable, recognized and namable characteristic of the individual’s experience of a service which contributes to its quality [5]. Exploring the factors that influence the QoE is essential for telecommunications companies to maintain services and position in the market. In this regard, Influence Factor (IF) is any characteristic of a user, system, service, application, or context whose actual state or setting may have influence on the QoE for the user. IFs may be grouped in three categories, i.e., Human IFs (HIFs), System IFs (SIFs), and Context IFs (CIFs) [5]. SIFs refer to properties and characteristics that determine the technically produced quality of an application or service. The SIFs may be divided into four sub-categories: (i) content-related SIFs referring to the content type and content reliability, (ii)

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media-related SIFs referring to media configuration factors, (iii) network-related SIFs referring to data transmission over a network, and (iv) device-related SIFs [5]. The aim of this paper is to analyze the impact of selected SIFs on QoE for WebRTC-based video communication. In addition to our previous work [6–9], we have considered three network-related SIFs, i.e., jitter, delay, and Central Processing Unit (CPU). In this paper, the QoE was expressed using a Mean Opinion Score (MOS) of 1 (“Bad”) to 5 (“Excellent”). The QoE metrics were collected by questionnaire and statistically analyzed using Friedman’s test and Pearson correlation. It is expected to exit a statistically significant impact of considered SIFs on QoE in the context of WebRTC video communication. The remainder of the paper is organized as follows: Sect. 2 provides the related work considering the influence of system factors on QoE and QoE features for various video services. Section 3 describes the research methodology. In Section 4 are presented results and discussion. Finally, Sect. 5 concludes the paper.

2 Related Work A large number of studies have considered QoE and QoE features related to IFs in the context of various services. SIFs seems to be the most commonly analyzed IFs, which most affect the final satisfaction ratings. In this regard, we have selected 20 papers and analyzed them considering SIFs and their influence on QoE in the context of various services types [10–29]. Table 1 shows the percentage representation of considered service types, QoE IFs (as independent variables), and consideration of QoE features (as dependent variables). Video was used as a service type in 50% of the reviewed papers. All three categories of QoE IFs were examined as independent variables in the following manner. The most analyzed HIFs were previous experience (30%) and age (10%). The CIFs was mainly considered in terms of interactivity (35%) and task context (35%), while the SIFs were explored in terms of bit rate (45%), packet loss (40%), video resolution (30%), and delay (20%). The meta-analysis of related work has shown that the most frequently considered SIFs were bit rate and packet loss. It is observed that bit rate affects perceived quality [10, 12, 14, 15, 19, 28], enjoyment [10, 15, 19], and satisfaction [10, 15, 19, 28]. Packet loss affects satisfaction [15–17, 25], perceived quality [11, 12, 14–17, 25], and discomfort [18]. Video resolution and screen size affect perceived quality [20, 21, 29], enjoyment [20], and ultimate user satisfaction [10, 13, 16, 25], while delay affects satisfaction [17, 22, 26], discomfort [22], and enjoyment [17, 22]. Jitter affects satisfaction [17] and has an impact to enjoy. The most commonly examined QoE features were: perceived video quality (60%), perceived quality (55%), perceived audio quality (50%), enjoyment, while using the service (50%), efficiency in completing the task (50%), satisfaction with the service (40%), complexity of using the service (25%), and involvement in content (15%).

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Table 1 Meta-analysis of related work considering service types, QoE IFs, QoE features, analysis methods, and scale type

Service type

QoE IFs

References

N

P (%)

Video

[11, 13, 15–17, 21, 25–28]

10

50

Video conference

[10, 12–14, 18, 29]

6

30

Audio

[15, 16, 23, 25]

4

20

Online games

[19, 20, 22]

3

15

Previous experience

[10, 12, 13, 19, 22, 24]

6

30

Age

[10, 26]

2

10

Emotional state

[21]

1

5

Interactivity

[13, 15, 18–20, 23, 29]

7

35

Task context

[10, 15, 18–20, 22, 27]

7

35

Technical context

[23]

1

5

Physically context

[27]

1

5

Bit rate

[10, 12, 14, 15, 19, 20, 25, 28, 29]

9

45

Packet loss

[11, 12, 14–18, 25]

8

40

Video resolution

[14, 16, 20, 21, 25, 29]

6

30

Delay

[17, 22, 24, 26]

4

20

Frame rate

[19, 20, 25]

3

15

Display size

[10, 20]

2

10

Content

[26, 28]

2

10

Type of device [10]

1

5

Video constrast

[10]

1

5

Turbidity

[21]

1

5

Complession

[28]

1

5

Mlbs

[11]

1

5

Jitter

[17]

1

5

[10–12, 14–17, 20, 21, 24, 25, 29]

12

60

Perceived quality

[15–19, 22, 23, 25–28]

11

55

Perceived audio quality

[10–12, 14–17, 24, 25, 29]

10

50

Enjoyment

[10, 13, 15, 17, 19, 20, 22, 23, 25, 27]

10

50

Efficiency

[12, 13, 17–21, 23, 27, 28]

10

50

Satisfaction

[10, 13, 15–18, 22, 23]

8

40

Human

Context

System

QoE features

Perceived video quality

(continued)

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Table 1 (continued) References

Analysis method

N

P (%)

Complexity

[12, 17–19, 23]

5

25

Involvment

[18, 22, 25]

3

15

Annoying

[22]

1

5

ANOVA

[14, 15, 17–19, 22, 24, 25]

8

40

Regression analysis

[10, 12, 16]

3

15

Pearson’s correlation

[28, 29]

2

10

Spearman rank correlation

[28]

1

5

CPLEX

[20]

1

5

MANOVA

[21]

1

5

Scale type ACR

12

60

MOS

[11, 12, 15–22, 27, 29] [10, 13, 22, 26, 28]

5

25

Likert

[14, 24]

2

10

Legend ACR (Absolute category rating); ANOVA (Analysis of variance); IF (Influence factor); MANOVA (Multivariate analysis of variance); MOS (Mean opinion score); N (Number); P (Percentage); QoE (Quality of experience)

In addition, Table 1 shows the methods used for analysis and related scales that are found in the related work. It can be observed that the most commonly used scales were Absolute Category Rating (ACR) (60%) and MOS (25%). The 5-point scale was used in 65% of the considered studies. The analyses were mainly based on the following statistical methods: Analysis of Variance (ANOVA) (40%), regression analysis (15%), Pearson’s correlation (10%), as well as Spearman rank correlation (5%), CPLEX (5%), and Multivariate Analysis of Variance (MANOVA) (5%). According to related work, we have selected jitter, delay, and CPU as SIFs to be analyzed in the experimental part of this paper. This combination of SIFs has not been analysed in considered related work [10–29]. Based on the abovementioned, the research methodology has been defined and described in the next section.

3 Research Methodology 3.1 Objective and Hypotheses The objective of this paper was to analyze the impact of selected SIFs on QoE for WebRTC video communication. Jitter, delay, and CPU were selected as SIFs to experimentally investigate their individual influence on QoE in the given context.

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In order to determine the impact of different SIFs on the QoE, the following hypotheses have been set: H1: The change of QoE in context of WebRTC video communication, which is induced by alteration in CPU, is not statistically significant. H2: The change of QoE in context of WebRTC video communication, which is induced by alteration in delay, is not statistically significant. H3: The change of QoE in context of WebRTC video communication, which is induced by alteration in jitter, is not statistically significant. The intention was to determine the individual impact of each and every SIF (i.e., CPU (H1), delay (H2), jitter (H3)) on QoE. Therefore, it was necessary to set a total of 3 hypotheses. If hypotheses were merged into one integral, it would not be possible to ensure the validity of the reported statistical analysis used to test them. Since ANOVA presumptions were not satisfied, Freidman’s test was used and Pearson correlation coefficients were calculated.

3.2 Experiment Design According to recommendation ITU-T P.805 [30], free conversation task was chosen for the experiment, since conversation tasks are the most appropriate method for measuring the effect on the acceptability of certain system failures, such as delays. A total of 260 experiments were performed as described below (13 scenarios × 20 participants). We have created 13 scenarios as presented in Table 2. Three different Table 2 Description of scenarios

Scenario

Delay (ms)

Jitter (ms)

CPU (%)

1

0

0

0

2

200

0

20

3

200

100

20

4

200

200

20

5

300

0

20

6

300

100

20

7

300

200

20

8

200

0

10

9

200

100

10

10

200

200

10

11

300

0

10

12

300

100

10

13

300

200

10

Legend CPU (Central processing unit); ms (milliseconds)

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SIFs were combined with different levels, i.e., delay (2 levels), jitter (3 levels) and CPU (2 levels). Each and every scenario was conducted by 20 participants, which means that each participant made 13 video calls. Also, scenarios were not played sequentially, so participants did not know if the next scenario would be better or worse than the previous one. Each participant was asked to read instructions for participating in the experiment [31, 32] and asked to sign a consent to participate in the survey. Subsequently, the participant was asked to complete the questionnaire about demographic data (i.e., age, gender, occupation, educational level, physical disabilities, information about the experimental environment, and the used mobile device). At the end of each scenario, the participant completed an evaluation questionnaire to rate the considered performance using the MOS scale. A subjective user study involved 20 participants, which meets the minimum sample size according to the recommendation ITU-T P.920 [33], i.e., 16 participants. Ages of participants were between 15 and 47 years, where the highest percentage of participants (80%) belongs to the age group of 18–27 years. Of the all participants, 40% were male and 60% were female. The largest percentage of participants were students (70%), followed by employees (25%) and unemployed participants (5%). The highest percentage were with the bachelor degree (55%), followed by high-school degree (35%), and master degree (10%). Participants had no previous experience with WebRTC. The experiments were conducted at home (70%) and college (30%). Half of the participants used a laptop (50%), while the other half used their mobile devices (50%). The most commonly used mobile device was Samsung (80%), Huawei (10%), and LG (10%).

4 Results and Discussion To interpret experiment results, we planned to use ANOVA. The collected data was tested to determine whether they satisfy the presumptions of ANOVA (i.e., normally distributed variables, independent observations, and homogeneity) [34]. In order to assess the assumption that data is normally distributed, we firstly plotted the histogram of CPU-related data and presented it in Fig. 1. It can be observed that data was not normally distributed as required for repeated measures ANOVA. Normal distribution is necessary for ANOVA, but since the data did not satisfy that condition, we used a Friedman’s test instead. The Friedman’s test is available in the SPSS Statistics tool [35]. The Friedman’s test was performed to examine whether jitter, delay, and CPU had the statistically significant influence on QoE for WebRTC video communication. As shown in Table 3, there is a statistically significant difference in QoE depending on which CPU level was used during video call, χ2 (1) = 64.2, p < 0.05, the same applies for delay χ2 (1) = 54.73, p < 0.05, and jitter χ2 (2) = 66.14, p < 0.05.

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Fig. 1 Histogram of CPU data

Table 3 The Friedman’s test results Test statistics

N

Chi-square

df

Asymp. Sig

CPU

120

64.2

1