Advances in Power System Modelling, Control and Stability Analysis 2nd Edition Federico Milano
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- 6. IET ENERGY ENGINEERING SERIES 217 Advances in Power System Modelling, Control and Stability Analysis
- 7. Other volumes in this series: Volume 1 Power Circuit Breaker Theory and Design C.H. Flurscheim (Editor) Volume 4 Industrial Microwave Heating A.C. Metaxas and R.J. Meredith Volume 7 Insulators for High Voltages J.S.T. Looms Volume 8 Variable Frequency AC Motor Drive Systems D. Finney Volume 10 SF6 Switchgear H.M. Ryan and G.R. Jones Volume 11 Conduction and Induction Heating E.J. Davies Volume 13 Statistical Techniques for High Voltage Engineering W. Hauschild and W. Mosch Volume 14 Uninterruptible Power Supplies J. Platts and J.D. St Aubyn (Editors) Volume 15 Digital Protection for Power Systems A.T. Johns and S.K. Salman Volume 16 Electricity Economics and Planning T.W. Berrie Volume 18 Vacuum Switchgear A. Greenwood Volume 19 Electrical Safety: A guide to causes and prevention of hazards J.M. Adams Volume 21 Electricity Distribution Network Design, 2nd Edition E. Lakervi and E.J. Holmes Volume 22 Artificial Intelligence Techniques in Power Systems K. Warwick, A.O. Ekwue and R. Aggarwal (Editors) Volume 24 Power System Commissioning and Maintenance Practice K. Harker Volume 25 Engineers’ Handbook of Industrial Microwave Heating R.J. Meredith Volume 26 Small Electric Motors H. Moczala, J. Draeger, H. Krauss, H. Schock and S. Tillner Volume 27 AC-DC Power System Analysis J. Arrillaga and B.C. Smith Volume 29 High Voltage Direct Current Transmission, 2nd Edition J. Arrillaga Volume 30 Flexible AC Transmission Systems (FACTS) Y.-H. Song (Editor) Volume 31 Embedded generation N. Jenkins, R. Allan, P. Crossley, D. Kirschen and G. Strbac Volume 32 High Voltage Engineering and Testing, 2nd Edition H.M. Ryan (Editor) Volume 33 Overvoltage Protection of Low-Voltage Systems, Revised Edition P. Hasse Volume 36 Voltage Quality in Electrical Power Systems J. Schlabbach, D. Blume and T. Stephanblome Volume 37 Electrical Steels for Rotating Machines P. Beckley Volume 38 The Electric Car: Development and future of battery, hybrid and fuel-cell cars M. Westbrook Volume 39 Power Systems Electromagnetic Transients Simulation J. Arrillaga and N. Watson Volume 40 Advances in High Voltage Engineering M. Haddad and D. Warne Volume 41 Electrical Operation of Electrostatic Precipitators K. Parker Volume 43 Thermal Power Plant Simulation and Control D. Flynn Volume 44 Economic Evaluation of Projects in the Electricity Supply Industry H. Khatib Volume 45 Propulsion Systems for Hybrid Vehicles J. Miller Volume 46 Distribution Switchgear S. Stewart Volume 47 Protection of Electricity Distribution Networks, 2nd Edition J. Gers and E. Holmes Volume 48 Wood Pole Overhead Lines B. Wareing Volume 49 Electric Fuses, 3rd Edition A. Wright and G. Newbery Volume 50 Wind Power Integration: Connection and system operational aspects B. Fox, L. Bryans, D. Flynn, N. Jenkins, D. Milborrow, M. O’Malley, R. Watson and O. Anaya-Lara Volume 51 Short Circuit Currents J. Schlabbach Volume 52 Nuclear Power J. Wood Volume 53 Condition Assessment of High Voltage Insulation in Power System Equipment R.E. James and Q. Su Volume 55 Local Energy: Distributed generation of heat and power J. Wood Volume 56 Condition Monitoring of Rotating Electrical Machines P. Tavner, L. Ran, J. Penman and H. Sedding Volume 57 The Control Techniques Drives and Controls Handbook, 2nd Edition B. Drury Volume 58 Lightning Protection V. Cooray (Editor) Volume 59 Ultracapacitor Applications J.M. Miller Volume 62 Lightning Electromagnetics V. Cooray Volume 63 Energy Storage for Power Systems, 2nd Edition A. Ter-Gazarian Volume 65 Protection of Electricity Distribution Networks, 3rd Edition J. Gers Volume 66 High Voltage Engineering Testing, 3rd Edition H. Ryan (Editor) Volume 67 Multicore Simulation of Power System Transients F.M. Uriate Volume 68 Distribution System Analysis and Automation J. Gers Volume 69 The Lightening Flash, 2nd Edition V. Cooray (Editor) Volume 70 Economic Evaluation of Projects in the Electricity Supply Industry, 3rd Edition H. Khatib Volume 72 Control Circuits in Power Electronics: Practical issues in design and implementation M. Castilla (Editor) Volume 73 Wide Area Monitoring, Protection and Control Systems: The enabler for Smarter Grids A. Vaccaro and A. Zobaa (Editors)
- 8. Volume 74 Power Electronic Converters and Systems: Frontiers and applications A.M. Trzynadlowski (Editor) Volume 75 Power Distribution Automation B. Das (Editor) Volume 76 Power System Stability: Modelling, analysis and control A.A. Sallam and O.P. Malik Volume 78 Numerical Analysis of Power System Transients and Dynamics A. Ametani (Editor) Volume 79 Vehicle-to-Grid: Linking electric vehicles to the smart grid J. Lu and J. Hossain (Editors) Volume 81 Cyber-Physical-Social Systems and Constructs in Electric Power Engineering S. Suryanarayanan, R. Roche and T.M. Hansen (Editors) Volume 82 Periodic Control of Power Electronic Converters F. Blaabjerg, K. Zhou, D. Wang and Y. Yang Volume 86 Advances in Power System Modelling, Control and Stability Analysis F. Milano (Editor) Volume 87 Cogeneration: Technologies, optimisation and implentation C.A. Frangopoulos (Editor) Volume 88 Smarter Energy: from Smart Metering to the Smart Grid H. Sun, N. Hatziargyriou, H.V. Poor, L. Carpanini and M.A. Sánchez Fornié (Editors) Volume 89 Hydrogen Production, Separation and Purification for Energy A. Basile, F. Dalena, J. Tong and T.N. Veziroğlu (Editors) Volume 90 Clean Energy Microgrids S. Obara and J. Morel (Editors) Volume 91 Fuzzy Logic Control in Energy Systems with Design Applications in Matlab®/Simulink® I.H. Altaş Volume 92 Power Quality in Future Electrical Power Systems A.F. Zobaa and S.H.E.A. Aleem (Editors) Volume 93 Cogeneration and District Energy Systems: Modelling, Analysis and & Optimization M.A. Rosen and S. Koohi-Fayegh Volume 94 Introduction to the Smart Grid: Concepts, technologies and evolution S.K. Salman Volume 95 Communication, Control and Security Challenges for the Smart Grid S.M. Muyeen and S. Rahman (Editors) Volume 96 Industrial Power Systems with Distributed and Embedded Generation R. Belu Volume 97 Synchronized Phasor Measurements for Smart Grids M.J.B. Reddy and D.K. Mohanta (Editors) Volume 98 Large Scale Grid Integration of Renewable Energy Sources A. Moreno-Munoz (Editor) Volume 100 Modeling and Dynamic Behaviour of Hydropower Plants N. Kishor and J. Fraile-Ardanuy (Editors) Volume 101 Methane and Hydrogen for Energy Storage R. Carriveau and D.S.-K. Ting Volume 104 Power Transformer Condition Monitoring and Diagnosis A. Abu-Siada (Editor) Volume 106 Surface Passivation of Industrial Crystalline Silicon Solar Cells J. John (Editor) Volume 107 Bifacial Photovoltaics: Technology, applications and economics J. Libal and R. Kopecek (Editors) Volume 108 Fault Diagnosis of Induction Motors J. Faiz, V. Ghorbanian and G. Joksimović Volume 109 Cooling of Rotating Electrical Machines: Fundamentals, modelling, testing and design D. Staton, E. Chong, S. Pickering and A. Boglietti Volume 110 High Voltage Power Network Construction K. Harker Volume 111 Energy Storage at Different Voltage Levels: Technology, integration, and market aspects A.F. Zobaa, P.F. Ribeiro, S.H.A. Aleem and S.N. Afifi (Editors) Volume 112 Wireless Power Transfer: Theory, Technology and Application N. Shinohara Volume 114 Lightning-Induced Effects in Electrical and Telecommunication Systems Y. Baba and V.A. Rakov Volume 115 DC Distribution Systems and Microgrids T. Dragičević, F. Blaabjerg and P. Wheeler Volume 116 Modelling and Simulation of HVDC Transmission M. Han (Editor) Volume 117 Structural Control and Fault Detection of Wind Turbine Systems H.R. Karimi Volume 118 Modelling and Simulation of Complex Power Systems A. Monti and A. Benigni Volume 119 Thermal & Power Plant Control and Instrumentation: The control of boilers and HRSGs, 2nd Edition D. Lindsley, J. Grist and D. Parker Volume 120 Fault Diagnosis for Robust Inverter Power Drives A. Ginart (Editor) Volume 121 Monitoring and Control using Synchrophasors in Power Systems with Renewables I. Kamwa and C. Lu (Editors) Volume 123 Power Systems Electromagnetic Transients Simulation, 2nd Edition N. Watson and J. Arrillaga Volume 124 Power Market Transformation B. Murray Volume 125 Wind Energy Modeling and Simulation, Volume 1: Atmosphere and plant P. Veers (Editor) Volume 126 Diagnosis and Fault Tolerance of Electrical Machines, Power Electronics and Drives A.J.M. Cardoso Volume 128 Characterization of Wide Bandgap Power Semiconductor Devices F. Wang, Z. Zhang and E.A. Jones Volume 129 Renewable Energy from the Oceans: From wave, tidal and gradient systems to offshore wind and solar D. Coiro and T. Sant (Editors) Volume 130 Wind and Solar Based Energy Systems for Communities R. Carriveau and D.S.-K. Ting (Editors) Volume 131 Metaheuristic Optimization in Power Engineering J. Radosavljević
- 9. Volume 132 Power Line Communication Systems for Smart Grids I.R.S. Casella and A. Anpalagan Volume 134 Hydrogen Passivation and Laser Doping for Silicon Solar Cells B. Hallam and C. Chan (Editors) Volume 139 Variability, Scalability and Stability of Microgrids S.M. Muyeen, S.M. Islam and F. Blaabjerg (Editors) Volume 142 Wind Turbine System Design: Volume 1: Nacelles, drive trains and verification J. Wenske (Editor) Volume 143 Medium Voltage DC System Architectures B. Grainger and R.D. Doncker (Editors) Volume 145 Condition Monitoring of Rotating Electrical Machines P. Tavner, L. Ran, C. Crabtree Volume 146 Energy Storage for Power Systems, 3rd Edition A.G. Ter-Gazarian Volume 147 Distribution Systems Analysis and Automation, 2nd Edition J. Gers Volume 151 SiC Power Module Design: Performance, robustness and reliability A. Castellazzi and A. Irace (Editors) Volume 152 Power Electronic Devices: Applications, failure mechanisms and reliability F. Iannuzzo (Editor) Volume 153 Signal Processing for Fault Detection and Diagnosis in Electric Machines and Systems M. Benbouzid (Editor) Volume 155 Energy Generation and Efficiency Technologies for Green Residential Buildings D. Ting and R. Carriveau (Editors) Volume 156 Lithium-ion Batteries Enabled by Silicon Anodes C. Ban and K. Xu (Editors) Volume 157 Electrical Steels, 2 Volumes A. Moses, K. Jenkins, P. Anderson and H. Stanbury Volume 158 Advanced Dielectric Materials for Electrostatic Capacitors Q. Li (Editor) Volume 159 Transforming the Grid Towards Fully Renewable Energy O. Probst, S. Castellanos and R. Palacios (Editors) Volume 160 Microgrids for Rural Areas: Research and case studies R.K. Chauhan, K. Chauhan and S.N. Singh (Editors) Volume 161 Artificial Intelligence for Smarter Power Systems: Fuzzy Logic and Neural Networks M.G. Simoes Volume 165 Digital Protection for Power Systems, 2nd Edition S.K. Salman Volume 166 Advanced Characterization of Thin Film Solar Cells N. Haegel and M. Al-Jassim (Editors) Volume 167 Power Grids with Renewable Energy: Storage, integration and digitalization A.A. Sallam and O.P. Malik Volume 169 Small Wind and Hydrokinetic Turbines P. Clausen, J. Whale and D. Wood (Editors) Volume 170 Reliability of Power Electronics Converters for Solar Photovoltaic Applications F. Blaabjerg, A.l Haque, H. Wang, Z. Abdin Jaffery and Y. Yang (Editors) Volume 171 Utility-scale Wind Turbines and Wind Farms A. Vasel-Be-Hagh and D.S.-K. Ting Volume 172 Lighting interaction with Power Systems, 2 volumes A. Piantini (Editor) Volume 174 Silicon Solar Cell Metallization and Module Technology T. Dullweber (Editor) Volume 180 Protection of Electricity Distribution Networks, 4th Edition J. Gers and E. Holmes Volume 182 Surge Protection for Low Voltage Systems A. Rousseau (Editor) Volume 184 Compressed Air Energy Storage: Types, systems and applications D. Ting and J. Stagner Volume 186 Synchronous Reluctance Machines: Analysis, optimization and applications N. Bianchi, C. Babetto and G. Bacco Volume 191 Electric Fuses: Fundamentals and new applications, 4th Edition N. Nurse, A. Wright and P.G. Newbery Volume 193 Overhead Electric Power Lines: Theory and practice S. Chattopadhyay and A. Das Volume 194 Offshore Wind Power Reliability, availability and maintenance, 2nd edition P. Tavner Volume 196 Cyber Security for Microgrids S. Sahoo, F. Blaajberg and T. Dragicevic Volume 198 Battery Management Systems and Inductive Balancing A. Van den Bossche and A. Farzan Moghaddam Volume 199 Model Predictive Control for Microgrids: From power electronic converters to energy management J. Hu, J. M. Guerrero and S. Islam Volume 204 Electromagnetic Transients in Large HV Cable Networks: Modeling and calculations A. Ametani, H. Xue, T. Ohno and H. Khalilnezhad Volume 208 Nanogrids and Picogrids and their Integration with Electric Vehicles S. Chattopadhyay Volume 210 Superconducting Magnetic Energy Storage in Power Grids M.H. Ali Volume 211 Blockchain Technology for Smart Grids: Implementation, management and security H.L. Gururaj, K.V. Ravi, F. Flammini, H. Lin, B. Goutham, K.B.R. Sunil and C. Sivapragash Volume 212 Battery State Estimation: Methods and Models S. Wang Volume 213 Wide Area Monitoring of Interconnected Power Systems, 2nd Edition A.R. Messina Volume 215 Industrial Demand Response: Methods, best practices, case studies, and applications H. H. Alhelou, A. Moreno-Muñoz and P. Siano (Editors) Volume 217 Advances in Power System Modelling, Control and Stability Analysis, 2nd Edition F. Milano (Editor) Volume 225 Fusion-Fission Hybrid Nuclear Reactors: For enhanced nuclear fuel utilization and radioactive waste reduction W. M. Stacey Volume 238 AI for Status Monitoring of Utility Scale Batteries S. Wang, K. Liu, Y. Wang, D.-I. Stroe, C. Fernandez and J.M. Guerrero Volume 905 Power System Protection, 4 volumes The Electricity Training Association
- 10. Advances in Power System Modelling, Control and Stability Analysis 2nd Edition Edited by Federico Milano The Institution of Engineering and Technology
- 11. Published by The Institution of Engineering and Technology, London, United Kingdom The Institution of Engineering and Technology is registered as a Charity in England & Wales (no. 211014) and Scotland (no. SC038698). © The Institution of Engineering and Technology 2022 First published 2022 This publication is copyright under the Berne Convention and the Universal Copyright Convention. All rights reserved. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may be reproduced, stored or transmitted, in any form or by any means, only with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publisher at the undermentioned address: The Institution of Engineering and Technology Futures Place Kings Way, Stevenage Hertfordshire, SG1 2UA, United Kingdom www.theiet.org While the authors and publisher believe that the information and guidance given in this work are correct, all parties must rely upon their own skill and judgement when making use of them. Neither the author nor publisher assumes any liability to anyone for any loss or damage caused by any error or omission in the work, whether such an error or omission is the result of negligence or any other cause. Any and all such liability is disclaimed. The moral rights of the author to be identified as author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988. British Library Cataloguing in Publication Data A catalogue record for this product is available from the British Library ISBN 978-1-83953-575-8 (hardback) ISBN 978-1-83953-576-5 (PDF) Typeset in India by MPS Limited Printed in the UK by CPI Group (UK) Ltd, Croydon Cover image: Chris McLoughlin via Getty Images, overlaid image is the editor’s own.
- 12. Contents About the editors xix Preface to the 1st edition xxxiii Preface to the 2nd edition xxxv Part I: Modelling 1 1 Telegrapher’s equations for field-to-transmission line interaction 3 A. Borghetti, F . Napolitano, C.A. Nucci, F . Rachidi and M. Rubinstein 1.1 Transmission line approximation 3 1.2 Single-wire line above a perfectly conducting ground 5 1.2.1 Taylor, Satterwhite and Harrison model 6 1.2.2 Agrawal, Price and Gurbaxani model 10 1.2.3 Rachidi model 12 1.3 Contribution of the different electromagnetic field components 13 1.4 Inclusion of losses 13 1.5 Case of multi-conductor line 15 1.6 Time-domain representation of the coupling equations 17 1.7 Solutions with particular reference to time-domain numerical solutions 18 1.8 Application of theory to the case of lightning-induced voltages on distribution overhead lines 22 1.8.1 The LIOV code 22 1.8.2 The LIOV-EMTP-RV code 23 1.8.3 LEMP response of electrical distribution systems 29 1.9 Summary and concluding remarks 39 Acknowledgements 40 Bibliography 40 2 Reliable solutions of uncertain optimal power flow problems by affine arithmetic 45 Alfredo Vaccaro, Claudio A. Cañizares and Antonio Pepiciello 2.1 Introduction 45 2.2 Overview of existing approaches 46 2.2.1 Sampling methods 47 2.2.2 Analytical methods 47 2.2.3 Approximate methods 48 2.2.4 Non-probabilistic methods 49
- 13. viii Advances in power system modelling, control and stability analysis 2.2.5 AA-based methods 50 2.3 Mathematical background 51 2.3.1 PF analysis 51 2.3.2 Optimal PF analysis 52 2.3.3 Self-validated computing 54 2.3.4 Solving constrained optimization problems by linear AA 57 2.4 AA-based linear methods for uncertain power system analysis 61 2.4.1 Uncertain PF problems 61 2.4.2 Uncertain OPF problems 62 2.4.3 Numerical results 62 2.5 Elements of second-order AA 69 2.5.1 Uncertain power system analysis by second-order AA 72 2.5.2 Numerical results 74 2.6 Conclusion 75 Bibliography 76 3 DFT-based synchrophasor estimation processes for Phasor Measurement Units applications: algorithms definition and performance analysis 81 Mario Paolone and Paolo Romano 3.1 Literature review 82 3.2 Definitions 83 3.2.1 Signal model 83 3.2.2 Phasor 85 3.2.3 Synchrophasor 85 3.2.4 Frequency and rate of change of frequency 87 3.2.5 Phasor measurement unit 88 3.3 The discrete Fourier transform 90 3.3.1 From the Fourier transform to the DFT 90 3.3.2 DFT interpretation and relevant properties 91 3.3.3 DFT effects 93 3.3.4 DFT parameters 99 3.3.5 DFT calculation in real time 102 3.4 DFT-based SE algorithms 106 3.4.1 The Interpolated-DFT technique 107 3.4.2 The iterative-Interpolated DFT technique 114 3.5 Performance analysis of SE algorithm 116 3.5.1 The IEEE Std. C37.118 116 3.5.2 Performance assessment of the i-IpDFT SE algorithm 125 3.6 Conclusions 130 Bibliography 130 4 Modeling power systems with stochastic processes 135 Guðrún Margrét Jónsdóttir, Muhammad Adeen, Rafael Zárate-Miñano and Federico Milano 4.1 Literature review 135
- 14. Contents ix 4.2 Stochastic differential equations 137 4.2.1 Method for modeling an SDE with an analytically defined PDF and an exponentially decaying ACF 140 4.2.2 Method for modeling a SDE with an arbitrary PDF and ACF 142 4.2.3 Method for modeling SDEs with jumps 146 4.2.4 Method for modeling correlation 146 4.3 Modeling power systems as SDAEs 148 4.3.1 Initialization of stochastic power system models 149 4.3.2 Modeling stochastic perturbations in power systems 151 4.3.3 Examples 153 4.4 Time-domain integration of SDAEs 159 4.5 Stochastic power system case studies 162 4.5.1 Initialization of Irish power system models 163 4.5.2 Irish system with inclusion of wind and solar generation 165 4.5.3 Irish system with correlated load and wind generation 167 4.6 Conclusions 172 Bibliography 172 5 Detailed modeling of inverter-based resources 175 Younes Seyedi, Ulas Karaagac, Jean Mahseredjian, Aboutaleb Haddadi, Keijo Jacobs and Houshang Karimi 5.1 Introduction 176 5.2 Variable speed WT models 177 5.2.1 WT aerodynamics 177 5.2.2 Control of variable speed WTs 178 5.2.3 Wind parks with variable speed WTs 179 5.2.4 FSC WTs 180 5.2.5 DFIG WTs 188 5.3 Software implementation 191 5.4 Simulation results 194 5.4.1 FSC-based WP 194 5.4.2 DFIG-based WP 198 5.5 Conclusion 200 Bibliography 200 6 Isomorphism-based simulation of modular multilevel converters 205 Federico Bizzarri, Angelo Brambilla, Daniele Linaro and Davide del Giudice 6.1 Introduction 206 6.2 MMC models for EMT simulations: a review 209 6.2.1 Full physics, full detailed, and bi-value resistor models 211 6.2.2 Thévenin equivalent model 213 6.2.3 Switching function model 215 6.2.4 Average value model 217
- 15. x Advances in power system modelling, control and stability analysis 6.3 EMT simulation of MMCs based on isomorphism 218 6.3.1 Operating principle of the isomorphism-based approach 219 6.3.2 Dynamic partitioning in the MMC 220 6.3.3 Key features of the isomorphism-based approach 224 6.4 Validation 225 6.4.1 Simulation setting 225 6.4.2 Simulated scenarios 227 6.4.3 Analysis of simulation accuracy 228 6.4.4 Analysis of submodules variables 228 6.4.5 Analysis of simulation speed 230 6.5 Conclusions 234 Bibliography 235 Part II: Control 239 7 Optimization methods for preventive/corrective control in transmission systems 241 Massimo La Scala and Sergio Bruno 7.1 Formulation of a time-continuous dynamic optimization problem for corrective control 241 7.2 Formulation of a time-discrete static optimization problem for corrective control 244 7.3 Application to power system DAEs 247 7.3.1 Control variables 251 7.3.2 Control effort minimization 251 7.3.3 Kinetic energy cost function 252 7.3.4 Voltage penalty functions 253 7.3.5 Distance relays penalty function 254 7.4 Application of the proposed methodology for the corrective control of a realistically sized power system (test results) 256 7.5 Application to preventive control problems 261 Bibliography 264 8 Static and recursive PMU-based state estimation processes for transmission and distribution power grids 267 Mario Paolone, Jean-Yves Le Boudec, Styliani Sarri and Lorenzo Zanni 8.1 State estimation measurement and process model 268 8.1.1 Measurement model 269 8.1.2 Network observability 279 8.1.3 Process model 280 8.2 Static state estimation: the weighted least squares 281 8.2.1 Linear weighted least squares state estimator 282 8.2.2 Non-linear weighted least squares 283 8.3 Recursive state estimation: the Kalman filter 284 8.3.1 Discrete Kalman filter 284
- 16. Contents xi 8.3.2 Extended Kalman filter 288 8.3.3 Kalman Filter sensitivity with respect to the measurement and process noise covariance matrices 289 8.3.4 Assessment of the process noise covariance matrix 290 8.4 Assessment of the measurement noise covariance matrix 290 8.5 Data conditioning and bad data processing in PMU-based state estimators 297 8.6 Kalman filter vs. weighted least squares 300 8.7 Numerical validation and performance assessment of the state estimation 301 8.7.1 Linear state estimation case studies 301 8.7.2 Non-linear SE case studies 310 8.8 Kalman filter process model validation 312 8.9 Numerical validation of Theorem 8.1 313 Bibliography 314 9 Real-time applications for electric power generation and voltage control 319 Massimiliano Chiandone, Giorgio Sulligoi and Vittorio Arcidiacono 9.1 Introduction 319 9.2 Outlines of real-time system concepts 320 9.2.1 Real-time operating systems 322 9.2.2 Real-time communications 328 9.3 Voltage control 332 9.3.1 Excitation control systems 334 9.3.2 Secondary voltage control 337 9.3.3 Voltage control with distributed generation 343 9.4 Conclusions 348 Bibliography 348 10 Optimal control processes in active distribution networks 353 Mario Paolone, Jean-Yves Le Boudec, Konstantina Christakou and Dan-Cristian Tomozei 10.1 Typical architecture of ADN grid controllers 354 10.1.1 Control architecture 354 10.1.2 Controller’s actions 356 10.2 Classic computation of sensitivity coefficients in power networks 358 10.3 Efficient computation of sensitivity coefficients of bus voltages and line currents in unbalanced radial electrical distribution networks 360 10.3.1 Voltage sensitivity coefficients 360 10.3.2 Current sensitivity coefficients 363 10.3.3 Sensitivity coefficients with respect to transformer’s ULTC 364
- 17. xii Advances in power system modelling, control and stability analysis 10.4 Application examples 365 10.4.1 Distribution network case studies 365 10.4.2 Numerical validation 367 10.4.3 Voltage control and lines congestion management examples 373 10.5 Conclusions 386 Bibliography 386 11 Control of converter interfaced generation 389 S. D’Arco, A. Monti, T. Heins and J.A. Suul 11.1 Hardware structure 390 11.2 Grid-following and grid-forming control 392 11.3 Implementations for grid-following control 393 11.4 Implementations for grid-forming control 398 11.4.1 Internal frequency generation 398 11.4.2 Synchronization based on power flow 400 11.4.3 Power-frequency droop control 401 11.4.4 Emulation of generator swing equation 402 11.4.5 Single integration of power difference 402 11.5 Virtual Synchronous Machines 403 11.6 Virtual Oscillator Control 407 11.6.1 Power dispatch 409 11.6.2 Modified Andronov–Hopf oscillator 411 11.7 Concluding remarks 413 Bibliography 414 12 Combined voltage–frequency control with power electronics-based devices 417 Georgios Tzounas, Weilin Zhong, Mohammed A.A. Murad and Federico Milano 12.1 Introduction 417 12.2 Voltage-based frequency control through SVC devices 418 12.2.1 Voltage dependency of loads 419 12.2.2 Frequency control through SVC 419 12.3 Frequency control of converter-based resources through modified voltage control reference 421 12.3.1 Modified voltage control reference 421 12.3.2 DER and ESS models 424 12.4 Coupled voltage–frequency control of DERs 425 12.4.1 Control structure 426 12.4.2 Assessment metric 428 12.5 Case study I: VFC through SVC 429 12.5.1 WSCC 9-bus system 429 12.5.2 All-island Irish system 431 12.5.3 Discussion 433
- 18. Contents xiii 12.6 Case study II: FC+MRVC scheme for DERs 434 12.6.1 DERs connected to buses 2 and 3 434 12.6.2 ESS connected to bus 5 435 12.7 Case study III: FVP+FVQ control of DERs 437 12.7.1 FQ and VP control modes 439 12.7.2 Performance of FVP+FVQ control 440 12.7.3 Performance of voltage/frequency response metric 442 12.7.4 Application to aggregated power generation 444 12.7.5 Impact of resistance/reactance line ratio 444 12.7.6 Impact of DER penetration level 445 12.7.7 Impact of system granularity 446 Bibliography 448 13 Smart transformer control of the electrical grid 451 Giovanni De Carne, Marco Liserre and Felix Wald 13.1 The smart transformer concept 451 13.2 ST architectures and control 453 13.2.1 MV AC/DC converter 454 13.2.2 DC/DC conversion stage 456 13.2.3 LV DC/AC converter 457 13.3 Services provision to AC grids 458 13.3.1 Disturbance rejection 459 13.3.2 Load sensitivity identification 460 13.3.3 Voltage-based load control 464 13.3.4 Frequency-based load control 466 13.4 Enabling services for future DC grids 467 13.5 Conclusions and future outlook 469 Acknowledgment 469 Bibliography 469 14 On the interactions between plug-in electric vehicles and the power grid 473 Ekaterina Dudkina, Luca Papini, Emanuele Crisostomi and Robert Shorten 14.1 Introduction 474 14.2 Review of the state-of-the-art 475 14.2.1 Technological aspects 475 14.3 Optimized charging of the vehicles 477 14.3.1 Charging strategies 477 14.3.2 V2G and vehicle-to-everything (V2X) 479 14.3.3 Automatic adaptation of charge rates 480 14.4 Charging strategies 481 14.4.1 Uncontrolled charging 481 14.4.2 Controlled charging—centralized solutions 481
- 19. xiv Advances in power system modelling, control and stability analysis 14.4.3 Controlled charging—decentralized solutions 482 14.4.4 Controlled charging—prioritized decentralized solutions 483 14.5 Simulations 483 14.6 Research interests and future trends 489 14.6.1 Wireless power charging 489 14.6.2 Peer-to-peer energy exchange 491 14.6.3 Optimal utilization of electric charge points 492 14.6.4 Distributed ledger technologies 493 14.7 Conclusions 493 Bibliography 494 Part III: Stability Analysis 499 15 Time-domain simulation for transient stability analysis 501 Massimo La Scala 15.1 Introduction 501 15.2 Time-domain simulations and transient stability 503 15.3 Transient stability and high-performance computing 509 15.4 A new class of algorithms: from step-by-step solutions to parallel-in-time computations 512 15.5 Performances in parallel-in-time computations 520 15.6 Conclusions 523 Bibliography 523 16 Voltage security in modern power systems 527 Roberto S. Salgado, Cristian Bovo and Alberto Berizzi 16.1 Introduction 527 16.2 The power flow problem in rectangular coordinated 532 16.2.1 The power flow with SVC constraints 533 16.3 The OPF with SVC constraints 537 16.3.1 The maximum loadability with SVC constraints 538 16.3.2 Minimisation of the squared deviation of the bus voltage magnitude from a reference value 539 16.3.3 Constrained maximisation of the loadability with SVC 543 16.4 Solution of the optimisation problem 545 16.4.1 Primal-dual interior point method 545 16.4.2 Reduction of the linear system 548 16.5 Numerical results 549 16.5.1 The New England 39 buses network case 549 16.5.2 The Italian case 553 16.6 Conclusions 555 Bibliography 556
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- 21. incomprehensible to me how, if his material was at all well preserved, he could for a moment have taken them for the same thing as the big multipolar ganglion cells with large nucleus and nucleolus which lie in about the same region and were correctly described and figured by Claus but are not specially mentioned by Schewiakoff. I cannot agree with Claus, however, that their contents are composed of coarsely granular protoplasm. That which appears such by low magnification shows itself under high powers to be a beautiful network with thickenings at the nodes of the meshes, which is brought out very plainly by a cytoplasmic stain such as Lyons blue. Around the nucleus is seen a more or less well-defined clear zone. What the function of the cell is remains as unknown to me as to Claus and Schewiakoff. There is left one more point in reference to the nervous system upon which I wish to say a word. Claus and Schewiakoff both describe the wall of the crystalline sac as structureless, formed by the bare supporting lamella. The credit is due to H. V. Wilson of finding in Chiropsalmus that it has a special lining of epithelial cells, which he figures as a continuous, flattened layer. In both Charybdea and Tripedalia I find traces of the same in nuclei here and there, but whether they are the remains of a once continuous layer or not the sections do not show satisfactorily. This ends the account of what it seemed worth while to say at present upon the nervous system. In concluding, the writer wishes to express his thanks for the help afforded by Dr. Wilson’s notes, in particular on the subject of the vascular lamellæ, and desires to make especial acknowledgment of his indebtedness to Professor Brooks, whose suggestions, based upon many years of experience with the Medusæ, have been most welcome and helpful, and whose evidences of unfailing kindliness, both in Jamaica at the time the material was obtained and in Baltimore when it was being studied in the laboratory, take a most honored part in the pleasant memories associated with the work.
- 22. LITERATURE REFERRED TO. Clarke, H. J. ’78. Lucernariæ and their Allies. Washington: Smithsonian Institution. Claus, C. ’78. Ueber Charybdea marsupialis. Arb. aus d. Zool. Inst. d. Univ. Wien, Band II, Heft 2. Doflein, F. ’96. Die Eibildung bei Tubularia. Zeitsch. f. wiss. Zool., Bd. LXII, Heft 1. Haeckel, E. ’79. Das System der Medusen. Jena.—’81. Challenger Report on the Deep-sea Medusæ. Vol. IV. Hertwig, O. and R. ’78. Das Nervensystem und die Sinnesorgane der Medusen. Leipzig. Hesse, R. ’95. Ueber das Nervensystem und die Sinnesorgane von Rhizostoma Cuvieri. Zeitschr. f. wiss. Zool., Bd. LX, Heft 3. Müller, F. ’59. Zwei neue Quallen von St. Catherina (Brasilien). Abhandlungen der naturf. Gesellschaft zu Halle. Schewiakoff, W. ’89. Beiträge zur Kenntniss des Acalephenauges. Morph. Jahrb., Bd. XV, Heft 1. Wilson, H. V. Unpublished notes.
- 23. TABLE OF REFERENCE LETTERS. afr = adradial furrow. afr´ = furrow in Tripedalia that separates perradial from interrad. regions in lower half of bell. (In Charybdea the same furrow is directly continuous with afr.) ax = axis of nerve. c = concretion. cc = canal underneath ivl, connecting the two adjacent marginal pockets. ccl = circular canal. ci = cilia. cm = circular muscle. co = cornea. cp = capsule of lens. cs = covering scale of niche. csc = canal of sensory club. ct = canal of tentacle. ct´ = beginning of canals of lateral tentacles in Tripedalia. ec = ectoderm. ece = ectoderm of exumbrella. ecs = ectoderm of subumbrella. ed = distal paired eye. el = larger unpaired eye. en = endoderm. enc = endoderm of sensory club. enf = tract of nerve fibres underlying endoderm. enfl = endoderm of floor of stomach. enp = endoderm of stomach pockets. enr = endoderm of roof of stomach.
- 24. ens = endoderm of stomach. ep = proximal paired eye. es = smaller unpaired eye. fc = funnel leading into canal of sensory clubs. fp = fibre from subepithelial plexus of subumbrella. fph = filaments of phacellus. frn = frenulum. ft = funnel-shaped depression in ectoderm axial to base of tentacle. g = gelatine. gc = ganglion cell. ge = gelatine of exumbrella. go = gastric ostium. gs = gelatine of subumbrella. hvl = horizontal vascular lamella. i = interradius. if = interradial funnel of bell cavity. ifr = interradial furrow. ivl = interradial vascular lamella. l = lens. lv = lip of valve. m = bell margin. mc = mucous cell. mep = mesogonial pocket. mo = mouth. mp = marginal pocket. mp´ = smaller marginal pockets, in Tripedalia. mst = muscle of stock of sensory club. mt = muscle at base of tentacle. n = nerve. nc = network cells, in sensory club. nf = nerve fibres. nm = nematocyst.
- 25. nst = nerve of stalk of sensory club. osn = outline of sensory niche. p = perradius. pe = pedalium. ph = phacellus. pr = proboscis. r = reproductive organ. rc = remains of concretion. rcl = radial canal. rg = radial ganglion. rm = radial muscle. rn = radial nerve. rns = root of nerve of sensory club. rs? = remains of stalk (?) of sensory organ. rt = retina. s = stomach. sc = bell cavity. scl = sensory club. scn = supporting cell of nerve. se = sensory epithelium. sh = shrinkage space. sl = stalk of lens. sla = supporting lamella. sn = sensory niche. so = sensory organ in proboscis of Tripedalia. sp = stomach pocket. sph = stalk of phacellus. ss = stalk of sensory organ, in proboscis. st = stalk of sensory club. su = suspensorium. sub = subumbrella. tl = lateral tentacle. tm = median tentacle.
- 26. v = velarium. va = vacuole. vb = vitreous body. vc = velar canals. ve = edge of velarium. vfs = visual fibres, according to Schewiakoff. vg = valve of gastric ostium. vl = vascular lamella. vlc = vascular lamella connecting vls with vlm. vlm = vascular lamella of margin. vls = vascular lamella of sensory niche. vlst = vascular lamella of sensory niche at base of stalk. wc = wandering cells. w-x- y-z = successive levels of Figs. 40-43 on Fig. 5.
- 27. DESCRIPTION OF FIGURES. Fig. 1. Charybdea Xaymacana, from one of the four interradial sides. Fig. 2. The same from above. Fig. 3. The same from below, the four tentacles cut off. Fig. 4. The same cut in halves vertically (or radially) through a perradius. Fig. 5. The same out in halves vertically (or radially) through an interradius. Figs. 6-16. Diagrams of horizontal (or transverse) sections through C. Xaymacana at successive levels. Fig. 17. Tripedalia cystophora, from one of the four interradial sides. Fig. 18. The same from below. Fig. 19. The same cut in halves vertically through a perradius. Fig. 20. The same cut in halves vertically through interradius. Figs. 21-30. Diagrams of horizontal sections through T. cystophora at successive levels. (The following are of Charybdea, except when specially stated otherwise.) Fig. 31. Horizontal section through the suspensorium. Fig. 32. Diagram of a gastric ostium seen from the stomach side. Fig. 33. Diagram of a vertical section through a gastric ostium. Fig. 34. Diagram of a horizontal section through a gastric ostium.
- 28. Fig. 35. Diagram to illustrate the formation of the central and peripheral gastro-vascular systems of a Hydromedusa (a, b, and c) and a Cubomedusa (d). Fig. 36. Vertical section through the upper part of the bell, adradial, to show horizontal vascular lamella. Fig. 37. Vertical section through the perradius, to show vascular lamella of the niche of the margin. Fig. 38. Vertical section a little to one side of the last, to show same structure. Fig. 39. Horizontal section through the upper part of the sensory niche, to show vascular lamella of the niche. Figs. 40-43. Horizontal sections through the base of a pedalium at successive levels, w-x-y-z, Fig. 5, to show marginal lamella. Fig. 44. Diagram to show relations of sensory niche, of bell margin and velarium in adult Tripedalia. The velarium represented as pendant. Fig. 45. To show the same structure in a young Tripedalia. Fig. 46. Horizontal section through the last just at the margin, to compare with Fig. 29. Fig. 47. Cross-section through the nerve ring. Fig. 48. The structure of the nerve as seen by focusing at successive levels. Fig. 49. Diagram to show the relation of the nerve ring to the sensory club. Fig. 50. Horizontal section through the upper part of the sensory niche, to show passage of nerve root through gelatine of subumbrella to stalk of sensory club. Fig. 51. Vertical section through base of stalk of sensory club, to show same passage.
- 29. Fig. 52. Similar section to last, but nearer to perradius, to show sub-endodermal tract of nerve fibres. Fig. 53. Sensory organ in proboscis of Tripedalia, as seen from surface in living animal. Figs. 54 and 55. Sections of same sensory organ. Fig. 56. Vertical section through one side of proboscis, to show sensory organ attached to endoderm. (Tripedalia.) Fig. 57. Diagram of the outlines of sensory club seen from the side, by camera lucida. Fig. 58. Part of retina of larger complex eye cut radially. Figs. 59-62. Four sections in direct sequence through retinal cells transversely, larger eye. Fig. 63. Transverse section through the tips of cells of a slightly pigmented retina, larger eye. Figs. 64-66. Three transverse sections through vitreous body at different levels. All from same series, but not in direct sequence; larger eye. Fig. 67. Radial section through retina, to show fibres from the long pigment cells; larger eye. Fig. 68. Transverse section through vitreous body of Tripedalia near retina. Fig. 69. Vertical section through smaller complex eye. Fig. 70. Wandering cells, Charybdea. Fig. 71. Floating mass, from stomach pocket of Tripedalia. Fig. 72. Horizontal section through larger complex eye. (See text figure, p. 50.) CUBOMEDUSÆ. PLATE I.
- 30. Gilman Drew, del. Heliotype Co., Boston. CUBOMEDUSÆ. PLATE II. Conant & Crew, del. Heliotype Co., Boston. CUBOMEDUSÆ. PLATE III. F.S. Conant, del. Heliotype Co., Boston. CUBOMEDUSÆ. PLATE IV.
- 31. F.S. Conant, del. Heliotype Co., Boston. CUBOMEDUSÆ. PLATE V. F.S. Conant, del. Heliotype Co., Boston. CUBOMEDUSÆ. PLATE VI. F.S. Conant, del. Heliotype Co., Boston. CUBOMEDUSÆ. PLATE VII.
- 32. F.S. Conant, del. Heliotype Co., Boston. CUBOMEDUSÆ. PLATE VIII. F.S. Conant, del. Heliotype Co., Boston.
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