ELECTRIMACS 2019: Selected Papers - Volume 2 3030569691, 9783030569693

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Lecture Notes in Electrical Engineering 697

Walter Zamboni Giovanni Petrone  Editors

ELECTRIMACS 2019 Selected Papers - Volume 2

Lecture Notes in Electrical Engineering Volume 697

Series Editors Leopoldo Angrisani, Department of Electrical and Information Technologies Engineering, University of Napoli Federico II, Naples, Italy Marco Arteaga, Departament de Control y Robótica, Universidad Nacional Autónoma de México, Coyoacán, Mexico Bijaya Ketan Panigrahi, Electrical Engineering, Indian Institute of Technology Delhi, New Delhi, Delhi, India Samarjit Chakraborty, Fakultät für Elektrotechnik und Informationstechnik, TU München, Munich, Germany Jiming Chen, Zhejiang University, Hangzhou, Zhejiang, China Shanben Chen, Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai, China Tan Kay Chen, Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore Rüdiger Dillmann, Humanoids and Intelligent Systems Lab, Karlsruhe Institute for Technology, Karlsruhe, Baden-Württemberg, Germany Haibin Duan, Beijing University of Aeronautics and Astronautics, Beijing, China Gianluigi Ferrari, Università di Parma, Parma, Italy Manuel Ferre, Centre for Automation and Robotics CAR (UPM-CSIC), Universidad Politécnica de Madrid, Madrid, Spain Sandra Hirche, Department of Electrical Engineering and Information Science, Technische Universität München, Munich, Germany Faryar Jabbari, Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA, USA Limin Jia, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Janusz Kacprzyk, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland Alaa Khamis, German University in Egypt El Tagamoa El Khames, New Cairo City, Egypt Torsten Kroeger, Stanford University, Stanford, CA, USA Qilian Liang, Department of Electrical Engineering, University of Texas at Arlington, Arlington, TX, USA Ferran Martin, Departament d’Enginyeria Electrònica, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain Tan Cher Ming, College of Engineering, Nanyang Technological University, Singapore, Singapore Wolfgang Minker, Institute of Information Technology, University of Ulm, Ulm, Germany Pradeep Misra, Department of Electrical Engineering, Wright State University, Dayton, OH, USA Sebastian Möller, Quality and Usability Lab, TU Berlin, Berlin, Germany Subhas Mukhopadhyay, School of Engineering & Advanced Technology, Massey University, Palmerston North, Manawatu-Wanganui, New Zealand Cun-Zheng Ning, Electrical Engineering, Arizona State University, Tempe, AZ, USA Toyoaki Nishida, Graduate School of Informatics, Kyoto University, Kyoto, Japan Federica Pascucci, Dipartimento di Ingegneria, Università degli Studi “Roma Tre”, Rome, Italy Yong Qin, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Gan Woon Seng, School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore, Singapore Joachim Speidel, Institute of Telecommunications, Universität Stuttgart, Stuttgart, Baden-Württemberg, Germany Germano Veiga, Campus da FEUP, INESC Porto, Porto, Portugal Haitao Wu, Academy of Opto-electronics, Chinese Academy of Sciences, Beijing, China Junjie James Zhang, Charlotte, NC, USA

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Walter Zamboni • Giovanni Petrone Editors

ELECTRIMACS 2019 Selected Papers - Volume 2

Editors Walter Zamboni DIEM Università degli studi di Salerno Fisciano (SA), Italy

Giovanni Petrone DIEM Università degli studi di Salerno Fisciano (SA), Italy

ISSN 1876-1100 ISSN 1876-1119 (electronic) Lecture Notes in Electrical Engineering ISBN 978-3-030-56969-3 ISBN 978-3-030-56970-9 (eBook) https://doi.org/10.1007/978-3-030-56970-9 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, 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

Preface

ELECTRIMACS is a technical committee of IMACS as well as the name of the international conference of the TC. The conference is focused on the theory and application of modelling, simulation, analysis, design, optimisation, identification and diagnostics in electrical power engineering. The conference is a meeting point for researchers to share ideas and advances in the broad fields of electric machines and electromagnetic devices, power electronics, transportation systems, smart grids, electric and hybrid vehicles, renewable energy systems, energy storage, batteries, supercapacitors, and fuel cells. ELECTRIMACS 2019 was held in Salerno, Italy, from 21st to 23rd May 2019. Three tutorial sessions, three plenary sessions with thought leaders from academia and research centres, two forums, four technical tracks, and nine special sessions were included in the conference programme. The conference hosted 133 oral presentations of papers, selected among 169 submissions received. The review process involved at least three reviewers per paper. The main institutional sponsor of the conference is the Università degli studi di Salerno – Dipartimento di ingegneria dell’Informazione ed Elettrica e Matematica applicata (DIEM). The conference also received technical co-sponsorship from two important scientific societies: IMACS and IEEE Industrial Electronics Society (IES), and a financial co-sponsorship from Institut Français – Italia, and the Ambassade de France en Italie, in the framework of Programma CASSINI. Many industries and private companies sponsored the event or took part in the industrial exhibition. This book collects a selection of 31 papers presented at ELECTRIMACS 2019 Salerno. The papers are grouped in three thematic parts: • Renewable sources and energy storage • Smart grid and energy management • Power converters, electrical machines, devices and materials. These papers are mainly focused on electrical engineering modelling aspects and innovative applications.

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Organising Committee General Chairs Giovanni Petrone, Università degli studi di Salerno, Italy Walter Zamboni, Università degli studi di Salerno, Italy Technical Program Chairs Giovanni Spagnuolo, Università degli studi di Salerno, Italy Éric Monmasson, Université de Cergy-Pontoise, France Benoît Robyns, HEI Lille, France Ramon Blasco-Gimenez, Universitat Politécnica de Valéncia, Spain Track Chairs Federico Baronti, Università di Pisa, Italy Efstratios Batzelis, Imperial College, London, United Kingdom Pavle Boškoski, Jožef Stefan Institute, Ljubljana, Slovenia Mario Cacciato, Università degli studi di Catania, Italy Maria Carmela Di Piazza, ISSIA-CNR Palermo, Italy Seiichiro Katsura, Keio University, Japan Eftichios Koutroulis, Technical university of Crete, Greece Marie-Cécile Pera, Université de Franche-Comté, France Carlos Andres Ramos Paja, Universidad National de Colombia, Colombia Bruno Sareni, ENSEEIHT, France João Pedro Trovão, University of Sherbrooke, Canada Dmitri Vinnikov, Tallinn University of Technology Estonia Special Session Chair Ilhem Slama-Belkodja, Université de Tunis El Manar, Tunisia Local Organising Committee Gina Scorziello Raffaele Raimo Andrea Contrada Antonio Guarino Rudy Alexis Guejia Burbano Vittorio Mattei Luigi Mattia Brian Ospina Agudelo Carmine Russomando

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Scientific Committee Yacine Amara, France Federico Baronti, Italy Efstratios Batzelis, United Kingdom Ramon Blasco-Gimenez, Spain Pavle Boškoski, Slovenia Alain Bouscayrol, France Mario Cacciato, Italy Carlo Cecati, Italy Chandan Chakraborty, India Gerard Champenois, France Bruno Dehez, Belgium Louis-A. Dessaint, Canada Maria Carmela Di Piazza, Italy Christian Dufour, Canada Maurice Fadel, France Gabriel Garcerá, Spain Leopoldo García Franquelo, Spain Guillaume Gateau, France Luis Gomes, Portugal Gabriele Grandi, Italy Francesco Grasso, Italy Hamid Gualous, France Lennart Harnefors, Sweden Sergio Junco, Argentina Ðani Juriˇci´c, Slovenia Hadi Y. Kanaan, Lebanon Seiichiro Katsura, Japan Samir Kouro, Chile Eftichios Koutroulis, Greece Marco Liserre, Germany Luc Loron, France Óscar Lucía, Spain Massimiliano Luna, Italy Chengbin Ma, China Jean Mahseredjian, Canada Mariusz Malinowski, Poland Patrizio Manganiello, Belgium Sébastien Mariethoz, France Fabrizio Marignetti, Italy Bogdan Marinescu, France Pascal Maussion, France Tuomas Messo, Finland Rosario Miceli, Italy

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Éric Monmasson, France Teresa Orlowska-Kowalska, Poland Nicolas Patin, France Ruben Peña, Chile Marie-Cécile Pera, France Giovanni Petrone, Italy Serge Pierfederici, France Mircea Radulescu, Romania Carlos Andres Ramos-Paja, Colombia Nicolas Retière, France Xavier Roboam, France Benoît Robyns, France Francesco Roca, Italy Georges Salloum, Lebanon Bruno Sareni, France Manuela Sechilariu, France Ilhem Slama-Belkhodja, Tunisia Giovanni Spagnuolo, Italy João Pedro F. Trovão, Canada Maria I. Valla, Argentina Alex Van den Bossche, Belgium Philippe Viarouge, Canada Dmitri Vinnikov, Estonia Walter Zamboni, Italy Guest Editors Fisciano, Italy

Walter Zamboni Giovanni Petrone

Contents

Part I Renewable Sources and Energy Storage Data-Driven Multi-fault Diagnosis for H2 /O2 and H2 /Air PEMFCs . . . . . . . Raffaele Petrone, Didier Chamagne, Marie-Cécile Pera, and Daniel Hissel Ripple Correlation Control MPPT Scheme Applied to a Three-Phase Flying Capacitor PV System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mattia Ricco, Manel Hammami, Riccardo Mandrioli, and Gabriele Grandi Probabilistic Deconvolution of Solid Oxide Fuel Cell Impedance Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Boštjan Dolenc, Gjorgji Nusev, Pavle Boškoski, Bertrand Morel, Julie Mougin, and Ðani Juriˇci´c Development of a High Granularity Photovoltaic Model That Considers Complex Nonuniform Shadow Conditions and Different Cell Temperatures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Luis Garcia-Gutierrez, Michael Bressan, Antonino Sferlazza, Fernando Jimenez, Salvador De-Las-Heras, and Corinne Alonso Static Switch Activation Algorithm for Energy Storage System Grid-Connection and Disconnection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. Jebali-Ben Ghorbal, M. Ben Said-Romdhane, J. Arbi-Ziani, S. Skander-Mustapha, and I. Slama-Belkhodja Optimizing Scattering Behaviour of Encapsulant for Maximum PV Energy Yield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H. Goverde, I. Horvath, P. Manganiello, B. Aldalali, F. Duerinckx, A. van der Heide, E. Voroshazi, and J. Szlufcik On-Board Impedance Spectroscopy of Lithium-Ion Batteries in Electrical Vehicles: Comparative Analysis of Injected Signals and Practical Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Alexander Kuznietsov, Tilman Happek, and Aleksej Kiselev

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An Approach to the Cell-Level Diagnosis of Malfunctioning Events in PV Panels from Aerial Thermal Maps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Antonio Pio Catalano, Pierluigi Guerriero, Vincenzo d’Alessandro, Lorenzo Codecasa, and Santolo Daliento

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ECM-Based Algorithm for On-Board PEMFCs Diagnosis . . . . . . . . . . . . . . . . . 103 Ennio Andrea Adinolfi, Marco Gallo, Pierpaolo Polverino, Davide Beretta, Samuel Simon Araya, and Cesare Pianese Enhanced Kalman Filter-Based Identification of a Fuel Cell Circuit Model in Impedance Spectroscopy Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Danilo Flammia, Antonio Guarino, Giovanni Petrone, and Walter Zamboni Simplified Parameters Estimation for the Dual Polarization Model of Lithium-Ion Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Claudio Rossi, Davide Pontara, Carlo Falcomer, and Marco Bertoldi Reliability of Explicit Methods to Identify the Parameters of PV Panels with Degraded Series Resistance: An Experimental Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 G. Petrone, L.Orza, F. J. Sánchez-Pacheco, R. A. Guejia-Burbano, M. Piliougine, L. Mora-López, and M. Sidrach-de-Cardona Part II Smart Grid and Energy Management Paralleling Converters in DC Microgrids with Modified Lag I-V Droop Control and Voltage Restoration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 Daniel Zammit, Cyril Spiteri Staines, Maurice Apap, and Alexander Micallef Power Management of a Full DC Microgrid for Building Self-Consumption Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 Wenshuai Bai, Hongwei Wu, Manuela Sechilariu, and Fabrice Locment Management Strategy of an Electric Vehicle Charging Station Under Power Limitation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 Dian Wang, Hongwei Wu, Fabrice Locment, and Manuela Sechilariu Thermal Analysis of the Power Distribution System As Part of an Underwater Compressed Air Energy Storage Station . . . . . . . . . . . . . . . . . . . . . . . 203 Océane Maisonnave, Luc Moreau, René Aubrée, Mohamed Fouad Benkhoris, and Thibault Neu Automation Architecture for Multi-terminal DC Grid . . . . . . . . . . . . . . . . . . . . . . 219 Gaurav Kumar Roy, Philipp Joebges, F. Ponci, A. Monti, and Rik W. De Doncker Matrix Approach Based on Quadripole for Quality Analysis in Aircraft Electrical Power Distribution System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 Bernard Makhraz, Hubert Piquet, Xavier Roboam, and Jerome Mavier

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JADE-Based Multi-agent Decentralized Energy Management System of a Hybrid Marine-Hydrogen Power Generation System . . . . . . . . . 245 M. R. Barakat, B. Tala-Ighil, H. Gualous, and D. Hissel Modelling and Simulation of a Bidirectional SiC-Based Battery Charger for V2G Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 Giuseppe Aiello, Mario Cacciato, Alex La Cognata, Giacomo Scelba, Giuseppe Scarcella, and Alessandro Allegra Part III Power Converters, Electrical Machines, Devices and Materials Controllability Insurance of the Boost Converters Dedicated to Fuel Cell Management System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 Milad Bahrami, Jean-Philippe Martin, Gaël Maranzana, Serge Pierfederici, Farid Meibodi-Tabar, Sophie Didierjean, Jérôme Dillet, Majid Zandi, and Roghayeh Gavagsaz-ghoachani 3-D Generic Magnetic Equivalent Circuit Taking into Account Skin Effect: Magnetic Field and Eddy-Current Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 Youcef Benmessaoud, Walid Belguerras, Frédéric Dubas, and Mickael Hilairet Mathematical Procedure for Harmonic Elimination in CHB Multilevel Inverters with Variable DC Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 Concettina Buccella, Maria Gabriella Cimoroni, and Carlo Cecati Air-Gap Reluctance Function for MEC Dynamic Models of Smooth Rotor Machines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 Juliana Fernandes Cardoso, Marylin Fassenet, Christian Chillet, Laurent Gerbaud, and Lamya Abdeljalil Belhaj System-on-a-Chip Including Generic Framework of Motion Controller Using Disturbance Observer Based Acceleration Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333 Hiroki Kurumatani and Seiichiro Katsura Parseval’s Theorem Used for the Inductor Analysis in High-Frequency Boost Converters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347 A. Gutiérrez, E. Marcault, C. Alonso, J.-P. Laur, and D. Trémouilles Impedance Spectroscopy Characterization of a Graphene-Based Solar Cell with Improved Contacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363 Ilaria Matacena, Daniele Zocco, Pierluigi Guerriero, Nicola Lisi, Laura Lancellotti, Eugenia Bobeico, Paola Delli Veneri, and Santolo Daliento

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Investigation of Electrical Properties of Graphene-Based Nanocomposites Supported by Tunnelling AFM (TUNA) . . . . . . . . . . . . . . . . . . . 375 Giovanni Spinelli, Patrizia Lamberti, Vincenzo Tucci, Liberata Guadagno, Marialuigia Raimondo, and Luigi Vertuccio Weight-Function Identification for the Preisach Model of Laminated Steels Using Concentric Hysteresis Loops . . . . . . . . . . . . . . . . . . . . 389 Reza Zeinali, Dave Krop, and Elena Lomonova Enhanced Dead-Beat Predictive Control Using Power Harmonic Components for DFIG Wind System Under Asymmetrical Grid Voltage Sags. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399 M. Ghodbane-Cherif, S. Skander-Mustapha, I. Slama-Belkhodja, and A. Khan Study of Magnets and Pole Pieces Openings in Coaxial Magnetic Gearbox by Reluctance Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 Mohammed Naïdjate, Nicolas Bracikowski, Tianbo She, Luc Moreau, Xiangyu Yang, and Nicolas Bernard

About the Editors

Walter Zamboni received the PhD degree in Electrical Engineering from the Università degli studi di Napoli Federico II, Italy, in 2004. From 2016 he is Associate Professor of Electrical Engineering at the Università degli studi di Salerno, Italy, where he served as assistant professor from 2008 to 2016. He is a member of IEEE and IMACS. At present, his main scientific interests include battery modelling and SoC–SoH estimation, identification and diagnostics of batteries and fuel cells, energy and power management in systems with energy storage. He co-authored more than 80 papers published in international journals and conference proceedings, and one patent. Giovanni Petrone is Associate Professor of Circuit Theory at the University of Salerno, Italy. His research areas include analysis and design of power electronics and controls for photovoltaic, fuel cell and wind systems, tolerance analysis of electronic circuits, non-linear control techniques, wireless power transfer and identification and diagnosis of renewable sources and storage systems. He is Associate Editor of IEEE Journal of Photovoltaics and of IET Power Electronics. He is member of the editorial board of MPDI Applied Sciences journal. Since 2017, he is a senior member of IEEE. Prof. Petrone is co-author of more than 150 papers published in international journals and conference proceedings. He is also co-author of two books, two IEEE e-Learning library courses and five patents in the field of power electronics for photovoltaic applications.

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Part I

Renewable Sources and Energy Storage

Data-Driven Multi-fault Diagnosis for H2 /O2 and H2 /Air PEMFCs Raffaele Petrone, Didier Chamagne, Marie-Cécile Pera, and Daniel Hissel

Abstract Enhancing the Proton Exchange Membrane Fuel Cells’ systems (PEMFCs) life span and reliability is a sensible point for the FCs’ manufacturers. In this framework, the Health-Code project works contribute to improve the onboard monitoring and diagnostic tool for onboard state-of-health assessment to prevent improper operating conditions that can severely affect the stack performance. The diagnosed faulty conditions are the improper water management (drying and flooding), the reactants’ starvations (fuel and oxidant), and the fuel quality contaminations (poisoning). The developed methodologies are mainly based on the use of the Electrochemical Impedance Spectroscopy (EIS) measurements oriented to multi-fault detection purposes. Experimental activity was performed both on H2 /O2 PEMFC and H2 /Air PEMFC technologies. Experimental data are used for methods learning and validation, while the final tool is validated on board, directly on real systems. The developed data-driven approach is presented in this paper. Particularly, the procedure development related to the relevant features’ extraction and the algorithm learning are reported. Finally, the algorithm off-line validation results are presented.

1 Introduction Energy transition is a key challenge. From a sustainable development point of view, the improvement of the energy generation from renewable sources, and particularly the use of hydrogen as an energy vector, appears nowadays as an efficient way to face the continuous increase of energy consumption. In the framework of the “0 emission” policies, the use of stationary PEMFC systems for μ-CHP and backup

R. Petrone · D. Chamagne · M.-C. Pera · D. Hissel FEMTO-ST, CNRS, University Bourgogne Franche-Comte, Belfort, France FCLAB, CNRS, University Bourgogne Franche-Comte, Belfort, France e-mail: [email protected]; [email protected]; [email protected]; [email protected] © Springer Nature Switzerland AG 2020 W. Zamboni, G. Petrone (eds.), ELECTRIMACS 2019, Lecture Notes in Electrical Engineering 697, https://doi.org/10.1007/978-3-030-56970-9_1

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applications appears as a suited eco-friendly alternative to the common power units. Nevertheless, if nowadays the market is ready to absorb the new technology, for achieving a large-scale market penetration, the fuel cells systems (FCs) durability is still a technical hurdle. During normal operations, the FC stack voltage varies depending on the operating conditions. However, several degradation mechanisms can take place inside the FC components in case of stressed operations. When these phenomena occur, the system performances are affected, usually resulting in sensible cell voltage degradations [1–3]. As a consequence, to prevent the FC operations in stressed condition is a mandatory point. The Health-Code project aims to answer to research and industrial needs on PEMFC durability enhancement, preventing the system operation in faulty conditions. For this purpose, the main faulty operations related to the improper system management like reactants’ starvations, flooding and drying conditions, and poisoning phenomena caused if using reformed gas are investigated. The obtained dataset for method developing is presented in paragraph 2. Operating variables, such as the stack voltage, current, and temperature are commonly monitored during FCs’ operation, also in commercial applications. Particularly, this paper focus on the Electrochemical Impedance Spectroscopy (EIS)-based diagnosis [4–6]. Consequently, the system’s DC/DC converter is supported with a specific EIS board developed in the framework of the Health-Code project to perform onboard the suited EIS measurements for diagnosis. The main objective is the development of a monitoring and diagnosis tool for current state-of-health (SoH) assessment and fault detection and isolation (FDI). The data-driven approach and the algorithm development are presented in paragraph 3, while the method results and the algorithm off-line validation are illustrated in paragraph 4.

2 Experimental Activity and Dataset Creation On the basis of the EIS spectra acquired during the Health-Code project experimental activity, two different EIS dataset are obtained. Particularly, the first dataset is referred to the H2 /O2 PEMFCs’ technology and is composed of the EIS measurements performed on the Electro Power Systems (EPS) stack tests both in nominal and faulty conditions. The second dataset is referred to the H2 /Air PEMFCs technology and is composed of the EIS measurements performed on the Power System Europe A/S (BPSE) stack tests both in nominal and faulty conditions. Each dataset is divided into two parts: the first part dedicated to the algorithms training/tuning and a second part committed for methods validation and performance evaluation.

Data-Driven Multi-fault Diagnosis for H2 /O2 and H2 /Air PEMFCs

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2.1 Dataset 1 (H2 /O2 PEMFCs’ Technology) The first dataset is composed of 88 EIS spectra of which 55 are used for algorithms and models training and 33 for validation. The EIS spectra are measured on the EPS short-stacks (H2 /O2 PEMFCs’ technology) terminals on the FCLAB Research Federation test bench under normal and faulty conditions at 210 A (nominal current operation). Short-stacks are composed of eight cells, each cell having an active area of 200 cm2 . Nominal working conditions are set in according to the EPS specifications. Reactants’ pressures are fixed at the inlet to 1360 and 1420 mbar for anode and cathode, respectively. Over-stoichiometry factors are kept constant to the nominal values of 1.9 and 2.9 for hydrogen and oxygen, respectively. The stack working temperature is kept constant at 62 ◦ C in a range of ±5 degrees especially at high current values. Reactants’ relative humidity (RH) is fixed at 50% in a range of ±10%, both at cathode and anode sides. Flooding, drying, and reactants’ starvations conditions are considered as relevant stack faulty conditions. Due to the fact that reactants used in the EPS system are generated through the system electrolyzer, no CO and S poisoning tests were performed. Among the 88 spectra, 8 are referred to the nominal conditions (5 for training and 3 for validation), and 8 spectra are dedicated to the flooding conditions (5 for training and 3 for validation), while 24 spectra (15 for training and 9 for validation) are considered in case of drying, oxygen, and hydrogen starvations conditions, respectively. It is worth noting that for these last faults, three levels of intensity are considered (3 × 8=24).

2.2 Dataset 2 (H2 /air PEMFCs’ Technology) The second dataset is referred to the Ballard Power System Europe A/S (BPSE) stack tests performed both at the European Institute for Energy Research (EIFER) and in the Aalborg University (AAU) laboratories. The Ballard stacks are composed of 46 cells. Nominal working conditions are set in according to the BPSE specifications. Reactants’ pressures are fixed at the inlet to 1500 mbar, both at anode and cathode, respectively. Over-stoichiometry factors are kept constant to the nominal values of 1.5 and 2.5 for hydrogen and air, respectively. The stack working temperature is kept constant at 80 ◦ C, while the reactants’ relative humidity (RH) is fixed at 50%, both at cathode and anode sides. Globally, 111 EIS spectra are considered in dataset 2, of which 84 for training and 27 for validation. Measurements are performed both in normal and faulty conditions at the current nominal operation of 40 A. Flooding, drying, reactants’ starvations (air and hydrogen), and fuel contaminations (CO and S poisoning) conditions are considered as relevant faulty conditions.

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3 Data-Driven Approach In data-driven approaches, clustering methods are commonly used for pattern recognition. To this purpose, clusters are associated to the different faults, while data are represented by relevant features [7–10]. The method uses the EIS measurements for fault detection and stack state-of-health assessment in case of multi-failures conditions (flooding/drying, reactants’ starvation, and poisoning). The most valuable features are then selected and the feature space constructed. For this purpose, the impedance spectra are analyzed both on the Nyquist and Bode (magnitude and phase) diagrams. Finally, a classification decision-making procedure is introduced for fault detection and isolation. The features’ selection and the method training are proposed in Fig. 1. During the features’ selection phase, the EIS spectra of the training dataset are analyzed both on the Nyquist and Bode diagrams. Both geometrical parameters related to the spectra shape and physical parameters are considered. Particularly, the high-frequency resistance (also corresponding to the lowest magnitude value), the polarization resistance (also corresponding to the high magnitude value), their difference, the maximum absolute phase, and the phase slope in a frequency range between 1 and 10 Hz were considered as relevant features to define the features’ space domain [7]. The main goal of this step is to guarantee the cluster existence and unicity with the lower number of features that characterize the space dimensions. To this purpose, an automated procedure for features’ normalization and minimization, based on the variance-correlative analysis, is introduced. Once the features’ space is defined, a step-by-step Fuzzy clustering technique is adopted for the different clusters (faults) identifications. The procedure scheduled for off-line validation and onboard diagnosis is reported in Fig. 2. The results of the features’ selection procedure are summed in a reference data file. When a new EIS measurement (referred to the validation dataset or measured onboard) is available, the algorithm normalizes and projects the new spectrum’s features in the reference features’ space. The obtained new point is consequently classified and the current state of the stack identified.

4 Results and Validation The data-driven FDI results are presented in the following with respect to the different datasets. Also, if a 5D space is required for multi-fault detection and isolation, for an easier representation, the results are here visualized in a 3D space. The different levels of fault (soft, medium, and high conditions) are also identified through the different clusters.

Data-Driven Multi-fault Diagnosis for H2 /O2 and H2 /Air PEMFCs

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Fig. 1 Off-line features’ selection and space dimension optimization procedure [11]

4.1 Dataset 1 (H2 /O2 PEMFCs’ Technology) The results of the FDI algorithm validation for the dataset 1 are shown in Fig. 3. The normal operations are represented by the black points, the flooding conditions in blue, the drying conditions in red, the H2 starvation in magenta, and the O2 starvation in green. It is possible to observe that in case of the dataset 1, all the operating conditions are correctly detected and isolated (classified). The fault intensity levels (local/soft, medium, and high) are also identified. Particularly, a different direction can be noted per each fault, ensuring the correct faults’

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Fig. 2 Fault detection and isolation (FDI) procedure for off-line validation and on-field applications [11]

separation. The incipient faulty conditions states start closed to the normal condition (in black), while the distance of the different clusters increases with the fault intensities growing. In onboard applications, the decision-making procedure starts when the new EIS measurement is acquired. The new point is then classified, evaluating the conditioned probability that the new measurement can be classed in one or more clusters. In case of the new point closed to different clusters, a warning

Data-Driven Multi-fault Diagnosis for H2 /O2 and H2 /Air PEMFCs

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Fig. 3 Off-line validation results for H2 /O2 PEMFCs (dataset 1)

message is displayed. In case of the dataset 1, the 100% of detection and isolations is stated without alarms’ generation.

4.2 Dataset 2 (H2 /air PEMFCs’ Technology) The results of the FDI algorithm validation for the dataset 2 are shown in Fig. 4. Two new faulty conditions are introduced for this different technology (H2 /Air PEMFC): the CO poisoning represented with the black diamonds and the S poisoning graphed with the red diamonds. In analogy with Fig. 3, the different fault intensity levels (local/soft, medium, and high) are also identified, and different directions can be noted per each fault, ensuring the correct faults’ separation. The incipient faulty conditions states start closed to the normal condition (in black), while the distance of the different clusters increases with the fault intensities growing. However, also if the 100% of the faulty conditions are detected, incipient CO and S poisoning

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Fig. 4 Off-line validation results for H2 /air PEMFCs (dataset 2)

conditions (minor then 5 ppm) resulted very closed, generating alarms in the fault isolation (classification). In this case, due to the uncertainties introduced in clusters’ boundaries, the incipient poisoning condition is detected, but it is still not possible to distinguish between CO and S poisoning. As a higher level of poisoning is detected (major than 5 ppm), the 100% of the correct isolation is newly attained. Finally, the computational efforts of the data-driven FDI procedure are evaluated ® for a PC Windows 64-bit platform with an Intel insideTM coreTM i5 processor. A runtime included between 0.061 and 0.170 seconds is stated for the decision-making ® algorithm running in MatLab ambient (a C++ version is also available for onboard applications). Concerning memory location, the decision-making procedure needs 32 kb of ROM, while for execution, about 28 kb of RAM are used.

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5 Conclusions A data-driven approach for EIS-based monitoring and diagnosis is reported. The reference dataset for method implementation and validation are introduced. Two different PEMFCs’ technologies are considered (H2 /O2 for dataset 1 and H2 /air for dataset 2). The robustness of the methodology is successfully tested, and results are satisfying. The off-line validation test for FDI was able to group the data according to their state of health with a good precision. Particularly, the multi-faults detection capability was proved for six different faulty conditions: flooding, drying, hydrogen starvation, oxygen starvation, CO poisoning, and S poisoning. The capability to identify the level of the faulty condition (soft, medium, and high) was also proved. Computational efforts are also evaluated, requiring a runtime minor then 0.2 sec. As future work, the on-field validation test on real system is scheduled for both the technologies. Acknowledgments The research leading to these results has received funding from the European Union’s Horizon2020 Programme (H2020-JTI-FCH-2014-1) for the Fuel Cells and Hydrogen Joint Undertaking, under grant agreement n◦ 671486 – Research and Innovation Project: HEALTHCODE (Real operation pem fuel cells HEALTH-state monitoring and diagnosis based on dc-dc Converter embedded EIS). Website: http://pemfc.health-code.eu/.

References 1. R. Petrone, D. Hissel, M.-C. Péra, D. Chamagne, R. Gouriveau, Accelerated stress test procedures for PEM fuel cells under actual load constraints: State-of-art and proposals. Int. J. Hydrogen Energy 40, 12489–12505 (2015) 2. R. Borup, J. Meyers, B. Pivovar, Y.S. Kim, R. Mukundan, N. Garland, et al., Scientific aspects of polymer electrolyte fuel cell durability and degradation. Am. Chem. Soc. 107, 3904e51 (2007) 3. A. De Brujin, V.A.T. Dam, G.J.M. Janssen, Review: durability and degradation issues of PEM fuel cell components. Fuel Cells 08(1), 3–22 (2008) 4. R. Petrone, Z. Zheng, D. Hissel, M.-C. Péra, C. Pianese, M. Sorrentino, M. Becherif, N. YousfiSteiner, A review on model-based diagnosis methodologies for PEMFCs. Int. J. Hydrogen Energy 38(17), 7077–7091 (2013) 5. Z. Zheng, R. Petrone, M.-C. Péra, D. Hissel, M. Becherif, C. Pianese, N. Yousfi Steiner, M. Sorrentino, A review on non-model based diagnosis methodologies for PEM fuel cell stacks and systems. Int. J. Hydrogen Energy 38(21), 8914–8926 (2013) 6. C. Cadet, S. Jemei, F. Druart, D. Hissel, Diagnostic tools for PEMFCs: from conception to implementation. Int. J. Hydrogen Energy 39, 10613–10626 (2014) 7. R. Petrone, C. Vitagliano, M.-C. Pera, D. Chamagne, M. Sorrentino, Characterization of an H2/O2 PEMFC short-stack performance aimed to health-state monitoring and diagnosis. FC J. (2017). https://doi.org/10.1002/fuce.201700112 8. R. Petrone, E. Pahon, F. Harel, S. Jemei, D. Chamagne, D. Hissel, M.-C. Pera, Data-driven multi-fault approach for H2/O2 PEM Fuel Cell diagnosis, in IEEE VPPC, (IEEE, Belfort, 2017) 9. Z. Li, R. Outbib, D. Hissel, S. Giurgea, Data-driven diagnosis of PEM fuel cell: a comparative study. Contr. Eng. Pract. 28, 1–12 (2014)

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10. Z. Li, R. Outbib, S. Giurgea, D. Hissel, Diagnosis for PEMFC systems: a data-driven approach with the capabilities of online adaptation and novel fault detection. Ind. Electron., IEEE Trans. 62(8), 5164–5174 (2015) 11. Health-Code Project (H2020-JTI-FCH-2014-1); Deliverable 4.3: Diagnostic algorithm SW and lifetime extrapolation algorithm. Website: http://pemfc.health-code.eu/

Ripple Correlation Control MPPT Scheme Applied to a Three-Phase Flying Capacitor PV System Mattia Ricco, Manel Hammami, Riccardo Mandrioli, and Gabriele Grandi

Abstract This chapter introduces a ripple correlation control (RCC) algorithm for tracking the maximum power point (MPP) for a flying capacitor three-level three-phase photovoltaic (PV) system. Although RCC maximum power point tracking (MPPT) method has been widely used on single-phase plants, a threephase implementation based on sinusoidal carrier PWM has not been presented yet. The inherent oscillations of the PV current and voltage are employed as a perturbation for the RCC MPPT system. The proposed algorithm adopts the PV current and voltage 3rd harmonic component for estimating the power (or current) derivative, dPpv /dVpv (or dIpv /dVpv ). Firstly, referring to the carrier-based sinusoidal pulse width modulation (SPWM), the flying capacitor inverter modulation scheme is presented. Secondly, the proposed RCC MPPT method is introduced. Finally, multiple MATLAB-/Simulink-based simulations of the RCC MPPT algorithm acting on a grid-connected PV system are provided. Both steady-state and dynamic (irradiance increase and decrease) conditions present good performances.

1 Introduction Energy consumption is rapidly increasing worldwide along with concerns about global warming. For these reasons, renewable energy sources are always more employed. Among renewable energy sources (RES), PV energy has become one of the most broadly adopted. With the task to maximize the photovoltaic generation, MPPT algorithms are extensively used. Perturb and observe (P&O) algorithms [1], incremental conductance [2], constant voltage, and fuzzy logic are few of the several examples already investigated in the literature. However, these kinds of algorithms require an

M. Ricco () · M. Hammami · R. Mandrioli · G. Grandi Department of Electrical, Electronic, and Information Engineering, University of Bologna, Bologna, Italy e-mail: [email protected]; [email protected]; [email protected]; [email protected] © Springer Nature Switzerland AG 2020 W. Zamboni, G. Petrone (eds.), ELECTRIMACS 2019, Lecture Notes in Electrical Engineering 697, https://doi.org/10.1007/978-3-030-56970-9_2

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appropriate choice of the perturbation step. Even though the perturbation step and the perturbation period can be improved in order to enhance the MPPT efficiency [3–5], they are characterized by a weak maximum power point (MPP) fast-tracking capability (for instance, during sudden irradiance transients). A further method known as RCC is generally used in single-phase PV systems [6–11] because it is able to guarantee excellent performance in tracking the MPP of the PV plant. It exploits the PV inherent voltage and current oscillations (at 100Hz) to track the MPP of the PV field [8–12]. Therefore, no external perturbation signals are necessary for tracking the MPP. In [11, 13, 14], basic implementation of the RCC MPPT was proposed, employing two sets of high-/low-pass filters. In these cases, the time constants of the filters should be properly defined. A wrong choice could affect the MPPT capability of the algorithm. Then, in order to overcome this issue, a modified RCC method replacing high-/low-pass filters with the mean (moving average) function has been developed in [10]. As previously mentioned, the transient behavior of the MPPT algorithm under sudden sun irradiance variation is important. Then, the authors in [9] have proposed a hybrid RCC-constant-voltage mode controller to improve transient performance. Nowadays, multilevel inverters have gained a lot of popularity over the conventional single-/three-phase inverters [15–19]. Among the multiple benefits, one could find the improvement of the output waveforms quality, lower total harmonic distortion (THD), and smaller grid filter size [19–21]. The most relevant multilevel topologies presented in the literature are the cascaded H-bridge (CHB), the flying capacitor (FC), and the neutral-point-clamped (NPC). This kind of converters is also adopted in PV applications due to the aforementioned advantages. However, FC inverter stands out among the other topologies because of its absence of the clamping diodes and the no-need for multiple isolated DC sources (NPC). Moreover, by means of proper control, the voltage self-balancing operations of the flying capacitors can be ensured. Regarding the FC inverter, several analyses have been presented in the literature. For example, the authors in [22] have adopted a sampled data modeling approach to derive a dynamic mathematical model for a simple FC inverter. This analysis provides useful information about the circuit behavior with particular emphasis on the natural balancing property. By means of better utilization of switching states redundancy, it has been shown in [23] that it is possible to improve the inherent balancing rate for small output voltages heavily. A new PWM scheme has been proposed and analyzed in [24] by providing better balancing properties in comparison with the classical phase-shifted (PS) PWM. RCC-MPPT control schemes have been analyzed in [10] in the case of a singlephase-level doubling network (LDN) inverter having multiple input current and voltage harmonics at the dc-link (PV) side. These harmonics lead to an error in the derivative of the power (dPpv /dVpv ) when the conventional RCC-MPPT scheme is adopted. For this reason, a modified RCC-MPPT scheme working with a specific harmonic (having the largest amplitude) has been used in order to better estimate dPpv /dVpv .

Ripple Correlation Control MPPT Scheme Applied to a Three-Phase Flying. . .

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Fig. 1 PV generation system based on a flying capacitor three-level three-phase inverter

In grid-connected single-phase PV systems, many researchers have dealt with the RCC-MPPT algorithms. Considering three-phase systems, few works have been published [25]. A grid-connected three-phase FC inverter (Fig. 1) RCC-MPPT algorithm with reference to a sinusoidal carrier-based PWM modulation is presented in this chapter. In this case, a 3rd harmonic component of the PV current and voltage can be used as an external perturbation in order to track the MPP of the PV field. Fig. 1 shows the entire three-phase PV topology. The chapter is structured as follows. Firstly, the modulation principle of the adopted converter is given. Then, the proposed RCC-MPPT scheme is presented along with the main block diagram to estimate dPpv /dVpv . In section 4, simulation results are provided in both steady-state and under-sun irradiance transients. Finally, conclusions are drawn.

2 Modulation Principle for the FC Inverter Referring to SPWM operations, the modulating signals corresponding to the averaged output voltages normalized by Vpv can be written as: ⎧ (ϑ) ⎪ ⎪ uA = m sin   ⎨ uB = m sin ϑ − 2π 3   ⎪ ⎪ ⎩ uC = m sin ϑ − 4π 3

(1)

where ϑ=ωt, m is the modulation index of the inverter, and ω is the fundamental angular frequency (ω=2πf ). Employing common-mode signal injection, one might

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Fig. 2 FC converter three-level self-balancing PWM carrier-based logic

√ extend the maximum allowable modulating index from 0.5 to 0.577 (1/ 3) as it is usually done in the centered pulse width modulation (CPWM). In this chapter, the sinusoidal carrier-based modulation technique shown in Fig. 2 has been considered because it is able to ensure self-balancing capability. Indeed, it guarantees that the flying capacitor voltages spontaneously reach half of the dc-link voltage. The switching pattern Si (1) (whereas i represents each phase) can be described as: (1)

Si

= ui − |ui | + 1

(2)

The switching function (2) can be rewritten considering phase A for the adopted sinusoidal modulation (1) as: (1)

SA = m sin ϑ − m |sin ϑ| + 1

(3)

Switching functions for phase A (and similarly for phases B and C) can be obtained considering (3) and the phase displacement shown in (1). Switching function (3) in equation (4) is expressed in terms of harmonics in order to simplify the analysis in the next section. SA(1)

 ∞

2 = 1 − m + m sin ϑ + m Ak cos (kϑ) π

(4)

k=2

where Ak is the amplitude of the kth harmonic component calculated as: Ak =

1 4 , k ≥ 2, even. π k2 − 1

(5)

Ripple Correlation Control MPPT Scheme Applied to a Three-Phase Flying. . .

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3 Proposed RCC-MPPT Scheme In general, the estimation of dPpv /dVpv is calculated by multiplying the current harmonic by the voltage harmonic and integrating it over the lowest harmonic period. As demonstrated in [21], the lowest harmonic order of the PV voltage and PV current in the case of a three-phase FC inverter is the 3rd one. Then, the following equation for the RCC-MPPT is achieved:  dI  = dV Q

t

i˜pv v˜pv dt

t−T /3 t

=− 2 v˜pv

dt

I˜pv V˜pv I˜pv =− 2 ˜ Vpv V˜pv

(6)

t−T /3

The block diagram of the RCC-MPPT estimation given by (6) is depicted in Fig. 3. In this case, the concept of the moving average (MAvg) is applied over T/3 (150 Hz), being T the fundamental period. Concerning SPWM and assuming that the capacitor reactance is dominating, the amplitude of the low-harmonic PV voltage V˜ pv v˜p v i˜p v is calculated in [21] as: m Iac V˜pp ∼ = 3ω C

(7)

The amplitude of the low-harmonic PV current can be calculated based on (7) and the PV resistance at the MPP (Rpv ∼ = Vmpp /Impp ) as: I˜pp =

V˜pp ∼ m Iac = Rpv 3ω Rpv C

(8)

Fig. 3 RCC diagram for estimating dPpv /dVpv , employing the 3rd harmonic component by mean of moving average computed having one-third of switching period T/3 (150 Hz) as a subset

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Fig. 4 PV control algorithm block diagram Table 1 Circuit parameters employed in the simulation

Parameter Grid voltage (rms) AC-link inductor DC-link capacitor Flying capacitors AC fundamental frequency Switching frequency

Label Va Lf , R f C CA , CB , CC f

Value 230 V 1 mH, 3 m 2 mF 5 mF 50 Hz

fsw

3 kHz

Figure 4 depicts the whole block diagram of the PV control strategy proposed in this work. The voltage derivative of the power, dPpv /dVpv , is obtained by the RCC algorithm. Then, the reference dc-link voltage vpv * is determined by integrating the estimated dPpv /dVpv, and the grid current amplitude reference Iac * is achieved by a PI voltage regulator. This control will allow the tracking of the MPP. Finally, a dq current controller is implemented to achieve a unity power factor.

4 Simulation Results In order to evaluate the feasibility of the proposed RCC-MPPT control scheme, a three-phase grid-connected photovoltaic system (Fig. 1) has been numerically simulated in MATLAB-Simulink. The system parameters are given in Table 1. The PV array consists of 16 series PV modules and 22 PV strings connected in parallel. The parameters in standard test conditions (STC) of the considered PV modules are given in Table 2. In particular, SP-305 PV module type (96 cells, monocrystalline) has been selected for the analysis.

Ripple Correlation Control MPPT Scheme Applied to a Three-Phase Flying. . . Table 2 Specifications of the employed PV module

Parameter Open circuit voltage Short circuit current MPP photovoltaic voltage MPP photovoltaic current

19 Label VOC ISC Vmpp Impp

Value 64.2 V 5.96 A 54.7 V 5.58 A

Fig. 5 FC converter steady-state I/O waveforms: output grid voltage and current (respectively, pink and blue top traces), input PV voltage (green middle trace), and input PV current (red bottom trace) having an irradiance E = 1000 W/m2

Firstly, the input/output steady-state conditions of the considered grid-connected three-phase FC multilevel inverter, shown in Fig. 1, must be verified. The grid current and voltage are depicted in Fig. 5 (top traces), PV voltage (medium trace), and PV current (bottom trace). It is worth noting that the grid current and voltage are in phase, and the grid current is almost sinusoidal. As likely to be, dominant component oscillations at 150 Hz (3rd harmonic), in phase opposition, are present on the PV voltage and PV current. The maximum power point at sun irradiance E = 1000 W/m2 can be well tracked by the proposed RCC-

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MPPT algorithm. In this case, the maximum power point voltage Vmpp and the maximum power point current Impp are 875.2 V and 122.76 A, respectively. In the following, a sun irradiance ramp decrease is simulated to test the performance of the RCC-MPPT algorithm proposed in this chapter. The cell temperature has been considered constant and equal to 25◦ C. The irradiance starts from 1000 W/m2 and decreases linearly to 500 W/m2 in 200 ms, as shown in Fig. 6(a). The smoothed transient achieved with the proposed control strategy is depicted in Fig. 6(b) and (c), where the PV current and the PV voltage perfectly track the new MPP values under the sun irradiance ramp decrease. The grid current ia changes accordingly as depicted in Fig. 6(d). The ppv (vpv ) and ipv (vpv ) diagrams corresponding to the transient, shown in Fig. 6, are depicted in Fig. 7. The operating point moves from the first to the new MPP without any overshoots of the PV voltage. Figures 8 and 9 show the results of a sun irradiance ramp increase. In this case, the irradiance linearly increases from 500 to 1000 W/m2 in 200 ms (Fig. 8(a)). As shown in Fig. 8(b) and (c), the PV current and PV voltage perfectly track the MPP,

E (W/m 2)

1000 (a)

500 0

i pv (A)

150 100 (b)

50 0

vpv (V)

1000 (c)

800 600

ia (A)

500 (d)

0 -500

1

1.2

1.4

1.6

1.8

Time (s)

Fig. 6 Proposed algorithm (RCC-MPPT) performances on a 50% irradiance decreasing ramp transient: sun irradiance (a), input PV current (b), input PV voltage (c), and output grid current (d)

Fig. 7 Proposed algorithm (RCC-MPPT) performances on a 50% irradiance decreasing ramp transient: current-voltage (I-V) (top) and power-voltage (P-V) (bottom) characteristics

Fig. 8 Figure 12: Proposed algorithm (RCC-MPPT) performances on a 50% irradiance increasing ramp transient: sun irradiance (a), input PV current (b), input PV voltage (c), and output grid current (d)

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Fig. 9 Proposed algorithm (RCC-MPPT) performances on a 50% irradiance increasing ramp transient: current-voltage (I-V) (top) and power-voltage (P-V) (bottom) characteristics

and the grid current is sinusoidal with an increase of the amplitude correspondingly to the sun irradiance increase (Fig. 8(d)). The ppv (vpv ) and ipv (vpv ) diagrams showing the operating point are depicted in Fig. 9. It is worth noting that the new MPP is reached after the transient.

5 Conclusions In this chapter, an RCC-MPPT algorithm has been proposed and examined in detail in case of a three-phase multilevel FC PV generation system. The three-phase FC multilevel inverter introduces a 3rd-order harmonic on the PV voltage and current. Higher-order harmonics are instead completely negligible. The sinusoidal PWM modulation is presented for the adopted converter. Due to the inherent PV voltage and current oscillations, an RCC scheme has been proposed in order to track the maximum power point from the PV arrays. Since reference has been made to the third harmonic, a time window of the moving average filters in the RCC scheme has been set equal to T/3. It leads to a correct estimation of the voltage derivative of the power dPpv /dVpv . The whole PV generation scheme has been simulated in MATLAB/Simulink, and several tests have been provided to verify the effectiveness of the proposed RCC-MPPT algorithm. Both steady-state and sun irradiance variations have been considered in order to prove the good performance of the proposed control strategy.

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References 1. M.A. Elgendy, B. Zahawi, D.J. Atkinson, Assessment of perturb and observe MPPPT algorithm implementation techniques for PV pumping applications. IEEE Trans. Sustainable Energy 3(1), 21–33 (2012) 2. N. Kumar, H. Ikhlaq, S. Bhim, K.P. Bijaya, Self-adaptive incremental conductance algorithm for swift and ripple-free maximum power harvesting from PV array. IEEE Trans. Ind. Inf. 14(5), 2031–2041 (2018) 3. A. Thangavelu, V. Senthilkumar, P. Deivasundari, Linear open circuit voltage-variable stepsize-incremental conductance strategy-based hybrid MPPT controller for remote power applications. IET Power Electron. 10(11), 1363–1376 (2017) 4. P. Manganiello, M. Ricco, E. Monmasson, G. Petrone, G. Spagnuolo, On-line optimization of the P&O MPPT method by means of the system identification. IECON 2013 – 39th Annual Conference of the IEEE Industrial Electronics Society, Vienna, 2013, pp. 1786–1791 5. M. Ricco, P. Manganiello, G. Petrone, E. Monmasson, G. Spagnuolo, FPGA-based implementation of an adaptive P&O MPPT controller for PV applications. IEEE 23rd International Symposium on Industrial Electronics (ISIE), Istanbul, 2014, pp. 1876–1881 6. J.W. Kimball, P.T. Krein, Discrete-time ripple correlation control for maximum power point tracking. IEEE Trans. Power Electron. 23(5), 2353–2362 (2008) 7. C. Barth, C.N. Robert, P. Pilawa, Dithering digital ripple correlation control for photovoltaic maximum power point tracking. IEEE Trans. Power Electron. 30(8), 4548–4559 (2015) 8. A.M. Bazzi, T.K. Philip, Ripple correlation control: an extremum seeking control perspective for real-time optimization. IEEE Trans. Power Electron. 29(2), 988–995 (2014) 9. M. Hammami, G. Grandi, M. Rudan, An improved MPPT algorithm based on hybrid RCC scheme for single-phase PV systems. Proceedings of 42nd Annual Conference of the IEEE Industrial Electronics Society (IECON), Florence, Italy, 23–26 October 2016 10. M. Hammami, G. Grandi, A single-phase multilevel PV generation system with an improved ripple correlation control. Energies 10(12), 2037 (2017) 11. D. Casadei, G. Grandi, C. Rossi, Single-phase single-stage photovoltaic generation system based on a ripple correlation control maximum power point tracking. IEEE Trans. Energy Convers. 21(2), 562–568 (2006) 12. M. Hammami, G. Grandi, M. Rudan, RCC-MPPT algorithms for single-phase PV systems in case of multiple DC harmonics. Proceedings of 6th International Conference on Clean Electrical Power (ICCEP), Santa Margherita Ligure, Italy, 27–29 June 2017 13. K. Raghav, Q. Zhang, W.E. Stanchina, G.F. Reed, Z.H. Mao, Maximum power point tracking using model reference adaptive control. IEEE Trans. Power Electron. 29(3), 1490–1499 (2014) 14. E. Trishan, W.J. Kimball, P.T. Krein, P.L. Chapman, M. Pallab, Dynamic maximum power point tracking of photovoltaic arrays using ripple correlation control. IEEE Trans. Power Electron. 21(5), 1282–1290 (2006) 15. D. Suman, J. Qin, B. Bahrani, M. Saeedifard, P. Barbosa, Operation, control, and applications of the modular multilevel converter: a review. IEEE Trans. Power Electron. 30(1), 37–53 (2015) 16. E. Babaei, S. Laali, Z. Bayat, A single-phase cascaded multilevel inverter based on a new basic unit with reduced number of power switches. IEEE Trans. Ind. Electron. 62(2), 922–929 (2015) 17. N.A. Rahim, S. Jeyraj, Multistring five-level inverter with novel PWM control scheme for PV application. IEEE Trans. Ind. Electron. 57(6), 2111–2123 (2010) 18. G. Buticchi, D. Barater, E. Lorenzani, C. Concari, G. Franceschini, A nine-level grid-connected converter topology for single-phase transformerless PV Systems. IEEE Trans. Ind. Electron. 61(8), 3951–3960 (2014) 19. X. Yuan, H. Stemmler, I. Barbi, Self-balancing of the clamping-capacitor-voltages in the multilevel capacitor-clamping-inverter under sub-harmonic PWM modulation. IEEE Trans. Power Electron. 16(2), 256–263 (2001)

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20. A. Nabae, I. Takahashi, A. Hirofumi, A new neutral-point-clamped PWM inverter. IEEE Trans. Ind. Appl. IA-17(5), 518–523 (1981) 21. M. Hammami, M. Vujacic, G. Grandi, Dc-link current and voltage ripple harmonics in threephase three-level flying capacitor inverters with sinusoidal carrier-based PWM. Proceedings of 19th International Conference on Industrial Technology (ICIT), Lyon, France, 20−22 February 2018 22. M. Margaliot, A. Ruderman, B. Reznikov, Mathematical analysis of a flying capacitor converter: a sampled-data modeling approach. Int. J. Circuit Theor. Appl. 41, 682–700 (2013) 23. A. Ibrayeva, V. Ten, Y.L. Familiant, A.Ruderman, PWM strategy for improved natural balancing of a four-level H-bridge flying capacitor converter. Proceedings of Aegean Conference on Electrical Machines & Power Electronics (ACEMP), Side, Turkey, 2–4 September 2015 24. S. Thielemans, A. Ruderman, B. Reznikov, J. Melkebeek, Improved natural balancing with modified phase-shifted PWM for single-leg five-level flying-capacitor converters. IEEE Trans. Power Electron. 27(4), 1658–1667 (2012) 25. M. Hammami, M. Ricco, A. Ruderman, G. Grandi, Three-phase three-level flying capacitor PV generation system with an embedded ripple correlation control MPPT algorithm. MDPI Electron. 8(2), 118 (2019)

Probabilistic Deconvolution of Solid Oxide Fuel Cell Impedance Spectra Boštjan Dolenc, Gjorgji Nusev, Pavle Boškoski, Bertrand Morel, Julie Mougin, and Ðani Juriˇci´c

Abstract Higher exploitation of fuel cell technologies can be achieved employing effective maintenance and condition monitoring tools. Electrochemical impedance spectroscopy (EIS) is a common way for state-of-health characterisation of fuel cells. However, parameters of an equivalent circuit model (ECM) used to describe the EIS seem to be more convenient and informative. Usually, an ECM structure is selected a priori, and an optimisation problem is formulated to fit the parameters of the model and gain their corresponding point estimates. However, for more precise reasoning, better information about the parameters is desirable. This can be achieved through Bayesian inference. In this paper, Bayesian inference is employed to estimate model parameters and so to obtain the posterior marginal density functions of the model’s parameters. It is shown how point estimates may be misleading. The approach is demonstrated on solid oxide fuel cell (SOFC) short stack.

1 Introduction Fuel cells are characterised with the high efficient conversion of chemical energy from hydrogen-rich fuels into electrical energy. Sustaining the nominal conversion efficiency requires continuous monitoring of the stack’s condition. This is typically achieved through time-consuming EIS-based characterisation. Addressing this issue, this paper presents a probabilistic approach to deconvolution of EIS spectra with application to solid-oxide fuel cells (SOFCs).

B. Dolenc · G. Nusev · P. Boškoski · Ð. Juriˇci´c () Jožf Stefan Institute, Ljubljana, Slovenia e-mail: [email protected]; [email protected]; [email protected] B. Morel · J. Mougin Univ. Grenoble Alpes – CEA/LITEN, Grenoble, France e-mail: [email protected] © Springer Nature Switzerland AG 2020 W. Zamboni, G. Petrone (eds.), ELECTRIMACS 2019, Lecture Notes in Electrical Engineering 697, https://doi.org/10.1007/978-3-030-56970-9_3

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For the purpose of EIS, the fuel cells are usually perturbed with current waveforms at constant DC operating point while measuring the voltage response. The input/output data can then be used to estimate fuel cell impedance at desired frequencies employing different signal processing techniques. Conventional sinusoidal perturbation is most straightforward to implement; see, e.g. [1]. Depending on the required information, this approach may sometimes become too lengthy to be used for online condition monitoring of the system. When needed, different waveforms can be used to shorten the perturbation time. Out of all the possibilities, discrete random binary sequence (DRBS) has shown that comparable results can be obtained using only 100 s long signals [2]. No matter the measuring technique, and signal processing employed in the subsequent step, the final result comes in a form of EIS curve. Depending on the current state of the fuel cell, where state refers to specific operating condition, or health, the Nyquist curve may change. While keeping operating conditions constant, the change in the shape of Nyquist curve can be directly employed to alert the final user about ongoing degradation.

1.1 Degradation Phenomena in Solid Oxide Fuel Cells SOFCs are affected by several degradation mechanisms. The main one is thermomechanical stress due to high operating temperatures, especially during start-ups, shutdowns, and rapid load changes [3–5]. This can lead to anode/cathode delamination [6, 7]. Another major degradation phenomenon can happen on the porous Ni-doped Yttria-stabilised zirconia (YSZ) anode that may affect the fuel supply to the anode [8]. Similar effect can happen due to nickel coarsening, which is typical for the Ni-YSZ anodes [9–11]. Fuel flow can be also interrupted due to carbon deposition on the anode surface [12–14]. Finally, there is a group of the so-called poisoning effects, either due to air or fuel impurities [15, 16]. The most typical ones are the interconnect oxidation and chromium poisoning that lead to the formation of a chromium oxide scale on the steel [17]. Fuel starvation, i.e. very low concentrations of H2 and CO, may cause local oxidant environment, leading to the oxidation of Ni metal to NiO. Ni oxidation (i.e. reoxidation cycles) causes irreversible mechanical degradation of the electrolyte and electrode interface by the dimensional expansion of the anode support [18]. At a given moment, more than one degradation phenomenon can be present within the stack. The main effect of the degradation phenomena can be observed as an increase of cell losses. As the material ages, the parasitic phenomena take place inside the stack and accumulate over time. Consequently, the polarisation losses gradually increase and result in a gradual decrease in voltage. EIS can be used to quantify this change.

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1.2 Deconvolution of EIS Spectra One way of analysing EIS data is by modelling the measured Nyquist curve. This approach is often referred to as deconvolution of EIS spectra. Generally speaking, there are two approaches to the deconvolution of EIS spectra: (i) ECM modelling through non-linear optimisation and (ii) nonparametric identification of the Nyquist curve through the distribution of relaxation times (DRT) [19]. From the mathematical point of view, the above approaches are equivalent. That is, having one of the two, one can easily derive the other one [20]. Typically ECM describing fuel cell impedance is constructed as a series of RQ elements, as shown in Fig. 1. Similar observations based on the analysis of DRT curves have recently been published [21]. Having a fuel cell impedance model structure Z(j ω) = Rs +

i

Ri τi (j ω)αi + 1

(1)

the parameter identification problem can be formulated as an optimisation problem argmin c(θ ) θ

where c(θ ) denotes a loss function, which describes goodness of fit of the model with respect to measured Nyquist curve, and the θ is a vector of model parameters. Following this approach, one obtains a point estimate of parameter values. However, no information about the ‘belief’ in this estimate is provided. Having estimated also other statistical properties of the model parameters, more sophisticated and reliable diagnostics is possible. R1

R2

Rk

Q1

Q2

Qk

R0

Fig. 1 General form of the ECM using RQ-elements

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2 ECM Parameter Estimation: Bayesian Inference Bayesian inference is a probabilistic approach for estimating parameters of mathematical models. It builds on Bayes’ theorem. Given a model and data D, the posterior distribution of the model parameters θ can be estimated via Bayes rule as: p(θ |D) =

p(D|θ )p(θ ) p(D|θ )p(θ )dθ

(2)

where p(D|θ) is likelihood, p(θ) is prior and p(D|θ)p(θ )dθ is called marginal likelihood or model evidence. Selecting model structure when doing Bayesian inference is the most crucial part of the modelling procedure. Since the model structure of the fuel cell impedance is well defined, one can easily construct the likelihood function: p(D|θ) =

p(yi |θ)

(3)

i

where we assumed that measurement points i on the Nyquist curves are independent and that p(yi |θ) is defined as in Fig. 1 – see also (1):  1 −(yi − {Z(j ωi |θ}))2 p(yi |θ) = √ exp 2σ 2 σ 2π

(4)

The parameter vector θ consists of resistances Rk , time constants τk and rational exponents αk , for each of the k-th element in the ECM. In the above equation, yi denotes measured point on the Nyquist curve at frequency ωi . Note that, for the estimation of the parameters θ in (4), only one component of the complex impedance is required to successfully perform inference, hence {•} in (4). Under the assumption of low amplitude perturbation and carefully selected operating setpoint, the fuel cell under test can be considered as a linear system. Consequently, due to Kramers-Kronig relation, in the optimisation process observing either the real or imaginary part of the impedance is sufficient. The prior probabilities of parameters p(θ ) represent any knowledge that we have about the system. Typically, these are values obtained, for example, at commissioning of the system or nominal values supplied by the manufacturer. There is also an option to use the so-called uninformative priors that should be applied when such prior data is missing. For example, for parameters Ri and τi , an uninformative prior would be the truncated normal distribution. The choice of truncated normal prior is justified since these parameters always take positive values. The prior for αi parameters can be set as uniform distribution in the interval [0,1].

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Using the prior and the likelihood of the data, the posterior distribution of the model parameters can be inferred employing (2). However, for complex, models, the integral in the denominator of (2) is typically intractable. For multidimensional cases, even numerical integration is computationally not a viable solution. In such a case, a possible solution can be achieved using Markov chain Monte Carlo (MCMC) simulations. Consequently, only the proportional part of the equation (2) is required to be numerically tractable: p(θ |D) ∝ p(D|θ )p(θ).

(5)

More on MCMC methods, and Bayesian inference, can be found in [22].

3 Experimental Setup An image of experimental SOFC testing is shown in Fig. 2. The short stack was operated at CEA, in Grenoble, France, at 750 °C and at a DC current of 0.4 A/cm2 . Running on a mixture of H2/N2=0.216/0.144 Nl/h/cm2 , six planar anode-supported cells were installed in an insulated ceramic housing. Effective fuel utilisation was 77.4%. The presented results employ only a fraction of data collected throughout a durability experiment. Additional to conventional measurements, individual cell voltages were also measured throughout the experiment. Every 6 h EIS measure-

Fig. 2 Image of experimental testing installed at CEA, Grenoble

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Fig. 3 Snapshot on measurements collected during durability test. Voltages of the six cells are shown

ments were collected employing both, conventional sinusoidal excitation and using DRBS waveforms. The experimental protocol consisted of three parts, as seen in Fig. 3. There are curves in the plot, each for one of the cells. First, the stack was operated at normal operating conditions around 240 h, see step 0. Short run-in period was also observed in first 24 h. Then, high fuel utilisation experiment was employed in order to observe impact of fuel starvation on short stack. This was done in three stages – 1a 85% FU, 2a 90% FU, and 3a 95% FU. After, the stack was again operated in nominal conditions. The same protocol was repeated at around t = 600 h – 1b 85% FU, 2b 90% FU, 3b 95% FU. Note that there are two exceptional events that occurred at cca t = 700 h and t = 1200 h. These are connected with replenishing of hydrogen tanks and are denoted by F1 and F2.

4 Inference Results Measured EIS spectra from one of the cells were employed in this study. The parameters of ECM were estimated employing Bayesian approach. In particular, an ECM model (1) with i = 3, i.e. three RQ elements, was used to fit the EIS spectrum.

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Fig. 4 Posterior pfds of the model parameters

For this particular case MCMC, a slice sampler [23] available in PyMC3 package was employed. In total, 30k samples were sampled from posterior distribution (2). Results of the inference are shown in Figs. 4 and 5. Figure 4 shows posterior distribution of the model parameters. In particular, for each of the three RQ elements i ∈ {1 . . . 3}, top row shows time constants τi , second row shows resistances Ri and third row shows their corresponding αi exponents. The bottom row shows serial resistance. Note that the parameters that belong to individual RQ element are denoted with the same colour. Figure 5 illustrates how well the model (1) in combination with parameters in Fig. 4 describes the measured Nyquist curve. To be more precise, a model where maximum a posteriori (MAP) point estimate – the most probable values of the parameters are considered. The red plot denotes the model with MAP parameters, and the green shows the experimentally measured Nyqusit curve. Cleary, the model fits the experimental data rather well. In Fig. 6, we can clearly observe how point estimate of the model parameters may be misleading. Referring to Fig. 4, pay attention to τ2 parameter values – top row, second column. Note that the mean value of the τ2 is about 0.82. However, variance of the estimate is quite high, 25% to be more precise. Therefore, it is easily understood that looking at two Nyquist curves in Fig. 6, one where τ2 = 0.88, and the second where τ2 = 0.78 would show little to no difference. This can be misleading when using model parameters for diagnostic purposes as it may raise false alarms. Being aware of this may improve diagnostic stability. Note that in this comparison, only parameter τ2 is varied, the rest are equal for red and blue curves.

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Fig. 5 MAP point estimate compared to true measurement of the EIS curve. The goodness of fit is evident

Fig. 6 Comparison of two point estimates: only parameter τ2 is varied – for about 11%, the rest are the same. However, the Nyquist curves barely differ

5 Conclusions In this paper, we presented an attempt to deconvolve EIS spectrum in a probabilistic set-up. For that purpose, we employed Bayesian inference for ECM parameter estimation. The application of the approach is demonstrated on experimental SOFC 6-cell short stack, where voltages of individual cells were measured. However, only one cell was considered in this paper. The results suggest that employing statistical methods for condition monitoring purposes may be beneficial. The experimental results show that point estimates of the model parameters can sometimes be misleading. This is particularly the case for slow processes – RQ elements with large time constants – as the estimation of the Nyquist curve at low frequencies is impaired by the problems related to too long probing time of the cells.

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Acknowledgments The authors acknowledge the project L2-7663 and research core funding No. P2-0001 that are financially supported by the Slovenian Research Agency. Support from the Fuel Cells and Hydrogen Joint Undertaking (FCH JU) under grant agreement No 735918 (INSIGHT project) is gratefully acknowledged. This publication reflects the views only of the authors, and the FCH JU cannot be held responsible for any use which may be made of the information contained therein.

References 1. J. Schoukens, M. Vaes, R. Pintelon, Linear system identification in a nonlinear setting: nonparametric analysis of the nonlinear distortions and their impact on the best linear approximation. IEEE Control Syst. 36(3), 38–69 (2016) 2. P. Boškoski, A. Debenjak, B. Mileva Boshkoska, Fast Electrochemical Impedance Spectroscopy As a Statistical Condition Monitoring Tool. SpringerBriefs in Applied Sciences and Technology (Springer, Cham, 2017) 3. K. Recknagle, R. Williford, L. Chick, D. Rector, M. Khaleel, Three-dimensional thermo-fluid electrochemical modeling of planar SOFC stacks. J. Power Sources 113(1), 109–114 (2003) 4. A. Nakajo, Z. Wuillemin, J.V. Herle, D. Favrat, Simulation of thermal stresses in anodesupported solid oxide fuel cell stacks. Part I: probability of failure of the cells. J. Power Sources 193(1), 203–215 (2009). scientific Advances in Fuel Cell Systems 5. L. Liu, G.-Y. Kim, A. Chandra, Modeling of thermal stresses and lifetime prediction of planar solid oxide fuel cell under thermal cycling conditions. J. Power Sources 195(8), 2310–2318 (2010) 6. K. Park, S. Yu, J. Bae, H. Kim, Y. Ko, Fast performance degradation of SOFC caused by cathode delamination in long-term testing. Int. J. Hydrog. Energy 35, 8670–8677 (2010) 7. M. Hanasaki, C. Uryu, T. Daio, T. Kawabata, Y. Tachikawa, S.M. Lyth, Y. Shiratori, S. Taniguchi, K. Sasaki, SOFC durability against standby and shutdown cycling. J. Electrochem. Soc. 161, F850–F860 (2014) 8. D. Sarantaridis, A. Atkinson, Redox cycling of Ni-based solid oxide fuel cell anodes: a review. Fuel Cells 7(3), 246–258 (2007) 9. J.S. Cronin, J.R. Wilson, S.A. Barnett, Impact of pore microstructure evolution on polarization resistance of Ni-Yttria-stabilized zirconia fuel cell anodes. J. Power Sources 196(5), 2640–2643 (2011) 10. D. Kennouche, Y. chen Karen Chen-Wiegart, K.J. Yakal-Kremski, J. Wang, J.W. Gibbs, P.W. Voorhees, S.A. Barnett, Observing the microstructural evolution of Ni-Yttria-stabilized zirconia solid oxide fuel cell anodes. Acta Mater. 103, 204–210 (2016) 11. Y.-H. Lee, H. Muroyama, T. Matsui, K. Eguchi, Degradation of nickel–yttria-stabilized zirconia anode in solid oxide fuel cells under changing temperature and humidity conditions. J. Power Sources 262, 451–456 (2014) 12. L. Barelli, E. Barluzzi, G. Bidini, Diagnosis methodology and technique for solid oxide fuel cells: a review. Int. J. Hydrog. Energy 38, 5060–5074 (2016) 13. P. Costamagna, S. Rossi, F. Pugliese, F. Gugliotta, A. Enrico, FDI oriented simulation of an MSR reactor for application in SOFC systems. ECS Trans. 68, 3143–3150 (2015) 14. A. Greco, A. Sorce, R. Littwin, P. Costamagna, L. Magistri, Reformer faults in sofc systems: experimental and modeling analysis, and simulated fault maps. Int. J. Hydrog. Energy 39, 21700–21713 (2014) 15. S. Zha, Z. Cheng, M. Liu, Sulfur poisoning and regeneration of Ni-based anodes in solid oxide fuel cells. J. Electrochem. Soc. 154, B201–B206 (2007) 16. Z. Cheng, M. Liu, Characterization of sulfur poisoning of Ni–YSZ anodes for solid oxide fuel cells using in situ Raman microspectroscopy. Solid State Ionics 178(13), 925–935 (2007)

34

B. Dolenc et al.

17. M. Palcut, L. Mikkelsen, K. Neufeld, M. Chen, R. Knibbe, P.V. Hendriksen, Corrosion stability of ferritic stainless steels for solid oxide electrolyser cell interconnects. Corros. Sci. 52(10), 3309–3320 (2010) 18. T.-H. Lee, K.-Y. Park, J.-T. Kim, Y. Seo, K.B. Kim, S.-J. Song, B. Park, J.-Y. Park, Degradation analysis of anode-supported intermediate temperature-solid oxide fuel cells under various failure modes. J. Power Sources 276, 120–132 (2015) [Online]. Available: http://www. sciencedirect.com/science/article/pii/S0378775314019120 19. F. Ciucci, C. Chen, Analysis of electrochemical impedance spectroscopy data using the distribution of relaxation times: a Bayesian and hierarchical Bayesian approac. Electrochim. Acta 167, 439–454 (2015) [Online]. Available: http://www.sciencedirect.com/science/article/ pii/S0013468615007203 20. R.M. Fuoss, J.G. Kirkwood, Electrical properties of solids. VIII. Dipole moments in polyvinyl chloride-diphenyl systems*. J. Am. Chem. Soc. 63(2), 385–394 (1941) 21. P. Caliandro, S. Diethelm, J. Van herle, Triode solid oxide fuel cell operation under sulfurpoisoning conditions. Fuel Cells 17(4), 457–463 (2017) [Online]. Available: https://doi.org/10. 1002/fuce.201600196 22. J. K. Kruschke, Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan, Academic Press, London (2010) 23. R.M. Neal, Slice sampling. Ann. Statist. 31(3), 705–767 (200) [Online]. Available: https://doi. org/10.1214/aos/1056562461

Development of a High Granularity Photovoltaic Model That Considers Complex Nonuniform Shadow Conditions and Different Cell Temperatures Luis Garcia-Gutierrez, Michael Bressan, Antonino Sferlazza, Fernando Jimenez, Salvador De-Las-Heras, and Corinne Alonso

Abstract In this paper is the development of a high granularity photovoltaic model that considers complex nonuniform shadow conditions and different cell temperatures. The model integrates the nonuniform shading characteristics such as different areas for each cell, different direct and indirect solar irradiations for each cell, and different temperatures. The area of the shadow on the PV module is found using image processing. The bond graph formalism facilitates the representation of the energy exchange between the different parts of the PV module. This complexity justifies the effort to develop a high-granularity tool. The proposed model is validated through experimental tests under shading conditions. This work is based on previous works by the authors as García-Gutiérrez (Développement d’un contrôle actif tolérant aux défaillances appliqué aux systèmes pv, Mar 2019 [Online]. Available: http://thesesups.ups-tlse.fr/4383/; Development of an activefault tolerant control applied to PV systems. Theses, Université Toulouse 3 Paul Sabatier (UT3 Paul Sabatier), Mar 2019 [Online]. Available: https://hal.laas.fr/tel-

L. Garcia-Gutierrez () Université Toulouse III – Paul Sabatier-LAAS-CNRS,, Toulouse, France Universidad de los Andes, Bogotá, Colombia Universidad Sergio Arboleda Bogotá, Bogotá, Colombia e-mail: [email protected] M. Bressan, F. Jimenez Universidad de los Andes, Bogotá, Colombia e-mail: [email protected] A. Sferlazza Università degli Studi di Palermo, Palermo, Italy S. De-Las-Heras Universitat Politècnica de Catalunya, Terrassa, Spain C. Alonso Université Toulouse III – Paul Sabatier-LAAS-CNRS, Toulouse, France e-mail: [email protected] © Springer Nature Switzerland AG 2020 W. Zamboni, G. Petrone (eds.), ELECTRIMACS 2019, Lecture Notes in Electrical Engineering 697, https://doi.org/10.1007/978-3-030-56970-9_4

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02147149), Alonso et al (High granularity model of a photovoltaic array under complex shadow conditions. In: Electrimacs 2019, Palerme, May 2019 [Online]. Available: https://hal.laas.fr/hal-02053484), and Garcia-Gutierrez et al (Design of a global maximum power point tracking (gmppt) for pv array based on precise pv shadow model. In: 2018 7th international conference on renewable energy research and applications (ICRERA), 2018, pp 275–280).

1 Introduction In the last few years, solar or photovoltaic systems (PV) have received much attention for the ease of implementation [4]. However, the use of this source through PV array generators is affected by limits caused by the low efficiency-perm2 of conversion devices, the shadows, and the not efficient working conditions due to electrical mismatch [5]. Two kinds of shadows can be visible on PV module: the homogeneous shadows which induce a drop of PV production and the nonhomogeneous shadows such as trees, soiling drastically affect the electrical generation of PV array [6]. The shading of a PV cell or of a group of cells can lead to a phenomenon denoted as hot spot [7]. This can produce a permanent damage of the shaded cell, with a consequent reduction of the provided power despite the activation of the by-pass diodes [3, 8]. Several authors developed modeling approaches to treat the complexities arising from nonuniform environmental conditions in PV systems operation [9]. Other models were developed to understand the impact of the shadows on the PV module performances [10–12]. PV model used a system of equations and linear interpolation which usually employ simple and easy-to-use expressions. Gutierrez Galeano [13] presented the study of a simplified approach which models and analyzes the performance of partially shaded PV modules using shading ratio. This approach integrates the characteristics of shaded area and shadow opacity into the model. However, this method needs simultaneous I-V curves measurements and recording to construct the model. It is important to develop models with great details that allow to analyze and better understand the electrical behavior of PV systems. The core of this paper is the development of model allowing to represent the I-V curves of a PV module under complex shading conditions. The high level of granularity of the model permits to represent accurately the I-V curves thanks to irradiation, cell temperature, and shadow parameters. The method consists in analyzing the area of shadow and the direct and indirect radiation that receives each PV cell. Thanks to an image processing, it is easier to give an area of shadows which affects the PV module. Bond graph (BG) is used in [10] to analyze the variation of energy on each cell under complex shading conditions. This paper is organized as follows: Sect. 2 shows the proposed model of PV module including the shadow parameters. Section 3 presents the image processing to give the area of the shadow on PV module. Section 4 treats about the results of the comparison between the I-V

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curves of the model with experimental I-V curves to validate the proposed model. Section 5 shows the conclusion of the work.

2 PV Model for Complex Shading Conditions 2.1 Shaded PV Cell Model The photovoltaic effect is the conversion of light into electricity. Most of the models in the literature do not take into account the effect of the reverse bias [3, 14]. A precise model was proposed by Bishop [3, 15] which incorporates the avalanche effect as a nonlinear multiplier factor that affects the shunt resistance current term as shown below:   Vc +I Rs I = Iph − Io e Vt − 1 Vc + I Rs − Rsh



  Vc + I Rs −n 1+k 1− Vbr

(1)

where Iph is the generated photo current (A), Io is the reverse saturation current (A), Rs is the series resistance (Ω), Rsh is the shunt resistances (Ω), Vbr is the breakdown voltage (V ), and k and n are constants [4]. The photo current Iph is the electric current through a cell in function of the irradiation that receives the PV cell and its temperature as shown in the Eq. (2). Iph = IphST C

G GST C

(1 + αI (Tc − TcST C ))

(2)

where IphST C is the photo current in short circuit at the standard test condition (STC), G is the global radiation that receives the PV cell, GST C is the irradiance at STC (1000 W/m2 ), αI is the temperature coefficient given by the manufacturer of the PV module (%/°C), Tc temperature of the PV cell (C), and TcST C is the temperature on STC (25 °C). However, these equations do not take into account the shape of the shading neither the optical properties of the shadow present on PV array. The photo current in Eq. (1) depends on uniform global irradiation.

2.2 Proposed Shaded PV-Cell Model Figure 1 shows the general schematic of the proposed PV model. The model inputs represent the environmental variables such as solar irradiation, temperature, matrix

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Fig. 1 General schematic of the proposed PV module model [1]

of shadow, and the electrical parameters of PV cells. The model outputs are PV module voltage and PV module current, done variations on the load resistance [4]. The proposed model takes into account the electrical and thermal behaviors of each cell of a PV module [1]. The configuration of a cell interconnection circuit suitable for powering a given application is obtained by calculating the number of cells in series needed to generate a convenient voltage Vo (t) and the number of strings in parallel needed to produce sufficient current Io (t) see [4]. Normally, a PV panel is composed on a set of cells (e.g., 36, 60, 72) and a set of bypass diodes [1]. Direct and indirect radiations on all cells of a panel have not the same impact because of buildings or trees shades, atmosphere fluctuation, existence of clouds and daily sun angle changes [1]. The impact of the non-uniform irradiation on the production of energy depends on several aspects as cell material, magnitude of the area of shade, bypass diode placement [16], string configuration, etc. For this reason, PV module can have different values of Iph for each cell [1]. Under partial shading operation, the unshaded cells of the module receive a solar irradiation at certain level, while the shaded cells lesser irradiation. By definition, the global irradiation is composed of three radiations: the direct radiation (GD ), the diffuse radiation (Gd ), and the reflected radiation (Gf ) as shown in Eq. (3) . GT = GD + Gd + Gr

(3)

The approximation Iph ≈ Isc considers standard operating conditions with no shading. However, irradiation current depends linearly on the incident light and the area of shading, as depicted in Fig. 2. Olalla [17] showed the new relation of the photo current in function of a linear combination of the global and diffuse irradiation as seen in Eq. (4). Term 1 represents the direct solar radiation with the factor of the unshaded cell. Term 2 represents the non-direct radiation that arrives at the cell with the factor of shaded cell.

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Fig. 2 The irradiance current of a cell as a linear combination of global and diffuse light

 as   as  IphT i + (Gd + Gr ) · · Iph = GD · 1 − aT aT GST C       1

Iph

2

GD · IphT i  as  (Gd + Gr ) · IphT i as = · 1− · + G aT GST C aT  ST C      1

(4)

2

where GST C = 1000 W/m2 , aT , the total area of the cell, as , the shadow area of the cell, and IphT i the input current of each cell without shadow [1]. Equation (5) shows two attenuation factors δ1 representing the unshaded part and δ2 the shaded part [1]. δ1 =

GD as · (1 − ) GST C aT

(Gd + Gr ) as · δ2 = GST C aT

(5)

The effective input current produced by the cell is showed in Eq. (6) in the function of these factors [3]. Iph = (δ1 + δ2 ) · IphT i Iph = δ · IphT i

(6)

δ is the total attenuation factor (0 ≤ δ ≤ 1). PV cells can have different value of δ, and these modifications allow to build a shadow matrix Mδ(t) as shown in Eq. (7) see [1].

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⎡

δ11 ⎢δ ⎢ 21 ⎢ ⎢δ δ(t) = ⎢ 31 ⎢δ41 ⎢ ⎣δ51 δ61

δ12 δ22 δ32 δ42 δ52 δ62

δ13 δ23 δ33 δ43 δ53 δ63

δ14 δ24 δ34 δ44 δ54 δ64

δ15 δ25 δ35 δ45 δ55 δ65

δ16 δ26 δ36 δ46 δ56 δ66

δ17 δ27 δ37 δ47 δ57 δ67

δ18 δ28 δ38 δ48 δ58 δ68

δ19 δ29 δ39 δ49 δ59 δ69

⎤ δ110 δ210 ⎥ ⎥ ⎥ δ310 ⎥ ⎥ δ410 ⎥ ⎥ δ510 ⎦ δ610

(7)

The proposed model uses the energy flows that convert sunlight into electrical energy [3]. PV cell modeling can be done with different levels of accuracy, depending of the user’s purposes [1]. Equation (1) gives not accurate information about the effects of inherent variations on the cell performance (influenced by the uniformity of cell fabrication processes) and on the array performance [1]. In order to describe each electrical behavior of each PV cell of a PV module, the photo current term Iph is replaced by the relation shown in Eq. (6) see [1].   Vc +I Rs I = δIphT i − Io e Vt − 1 Vc + I Rs − Rsh



  Vc + I Rs −n 1+k 1− Vbr

(8)

Eq. (8) describes the behavior of the interconnection circuit of each PV cell under abnormal, but common, operating conditions, e.g., partial shadowing of the array by nearby structures at any times of the day. A complete description of the effects of electrical mismatches in real interconnection circuits requires the determination of cell operating currents and voltages. Direct measurements of the operating points of PV cells are not possible because of their encapsulation in the panel [1].

2.3 Nonuniform Shading PV Panel Model with Bypass Diode Under nonuniform conditions, PV module can see its performance decreasing because of hot spotting problem. To protect shaded PV cells from breakdown voltage, PV modules are equipped with bypass diodes [3]. The studied PV module (TE2200) has the followed specifications: 60 cells (6 × 10), multicrystalline, three bypass diodes. The electrical parameters are ISC = 8.6(A), Voc = 37.2(V ), Rs = 0.005(Ω), Rsh = 35(Ω), Vb = −30(V ), n = 3.4, k = 0.01, PMAXST C = 245(W ), and PMI NST C = 240(W ). In a string of nPV cells in series, the conditions for having bypass diode activation are:  V −Vbypass Vdiode if n < shadowed Vnon−shadowed + 1 VGk = n (9) Vshadowed −Vbypass i=1 Vcelli if n ≥ Vnon−shadowed + 1

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IGk = IC1 = IC2 = IC3 = . . . = ICn VGk is the string of series cells protected by one bypass diode, Vshadowed the voltage for shadowed cell, Vbypass the forward voltage when the bypass diode turns ON, and Vnon−shadowed the forward voltage for each illuminated cells [1]. Vmodule = VG1 + VG2 + VG3 + . . . + VGk Imodule = IG1 = IG2 = IG3 = . . . = IGk

(10)

BG uses nine basic elements or building blocks which may represent physical subsystems, components, or phenomena in every energy domains. Figure 3a shows the whole BG design of a PV module. The input parameters are the PV module temperature, the global irradiation that receives the PV module [1]. The three blocks represent 20 cells in series connected to one bypass diode. The element R corresponds to the bypass diode, and C is the parasitic capacitance [1]. MR is a variable resistance that allows to obtain the electric behavior of the PV module (I-V characteristic) varying the resistance value between [0, ∞) [1]. It is possible to obtain positive and negative variations of the resistance for achieve the responses of I = [0, ∞] and V = [VOC , Vbr ] in the complete I-V showing the avalanche effect of the PV cell in reverse bias [3]. Figure 3b shows the simulation of I-V curves in BG for different percentage of attenuation factor performed on one group of cells of a PV module [1]. If the string

(a)

(b)

Fig. 3 Shading tests simulation in BG and I-V curves results [3]. (a) PV module structure with bypass. (b) I-V curves for different delta and with diode Bypass

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voltage exceeds the transmission voltage of the bypass diode, it becomes active. Theoretically, the breakdown voltage is not reached [1]. The next part explains the different process of image processing of the shadow allowing to characterize complex shading conditions on PV modules.

3 Experimental Setup and Image Processing The experimental setup was performed in LAAS-CNRS in Toulouse, France (φ = 43.562093, λ = 1.477460). The I-V characteristics were measured through (a) I-V tracer EKO MP160, (b) PV selector EKO 510, (c) acquisition software, (d) weather station, and (e) thermal camera FLIR i-60. Two PV modules (TE2200) were used with one as reference in normal operating and the other to perform shading tests [1]. Figure 4 shows an example of complex shading (a) with the segmentation of PV cells (b) and the segmentation of the shadow area (c). A PV module is composed of 60 cells (6 × 10) with an ideal area of 156 × 156 mm. The effective area of the cell is smaller, since the cell is not a square but an octagon. The octagon is divided into four regions representing the cells C5,9; C5,10; C6,9; C6,10 [1]. To calculate the attenuation factor δ2 , it is necessary to know the irradiation received by the shaded PV cell. An approximation of the diffuse radiation was performed thanks to a planar silicon PN photodiode (BPW21R). The BPW21 has a spectral sensitivity of 10 nA/Lx. A digital camera of cellphone Huawei VNS-L31, primary camera 13 MP (f/2.0,1/3”,1.12 m) with auto focus was used to capture the image of the PV module with the shadow. The camera was placed on a tripod to record from a fixed position the shadow that affects the panel [1]. The second step consisted in treating the image thanks to the superpixel method allowing to calculate the shading area as . The process of estimation of the magnitude of shadow was performed under Matlab2017a. The complete image processing is explained as below: 1. 2. 3. 4.

The inclination of the panel is in vertical position [1]. The image is cropped to the width and height of the panel. The presence of shadow is detected using the superpixel algorithm. The image segmentation toolbox is used to isolate the shadow, food fill, and active contours.

Fig. 4 (a) PV module Photography, (b) Segmentation of PV cells, (c) Segmentation of the shadow area [1]

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5. The toolbox image region analyzer is employed to estimate the magnitude of the shadow area. Firstly, it is necessary to quantify the complete area of each selected PV cell [1]. The result of the segmentation of the whole panel to determine the area of each selected PV cell is shown in Table 1[1]. Each result value is represented in pixel numbers. The second step consists in isolating and quantifying the shadow area of the selected region on PV module. Table 2 shows the result of the segmentation of the shadow area of each PV cell [1]. Table 3 resumes the results of each affected zone of the shadow to determine the attenuation factor δ [1]. It is calculated knowing the both radiation as mentioned in Eq. (4). Table 1 Quantification of the area of each selected PV Cell [1]

Cell 5,9

5,10

6,9

6,10

Table 2 Quantification of the shadow area of each affected PV Cell area [1]

Cell 5,9 5,10 6,9

6,10

Section cell a b c,d a b c,d a b c d a b c d

Area 67362 19261 45566 66607 44272 18527 19454 45944 45783 19979 22183 45078 45226 20721

Subtotal 132189

Section cell c d c d a b c d a b c d

Area 8634 14127 17727 11997 7696 15387 14233 6147 11576 25462 25175 12048

Subtotal 22761

Total area 525963

129406

131160

133208

29724 37316

74261

Total area 164062

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Table 3 Percentage of the shadow area and attenuation factor calculation [1]

Cell 5,9 5,10 6,9 6,10

Cell area 132189 129406 131160 133208

Shadow area 22761 29724 37316 74261

as (%) 17.21 22.97 28.45 55.75

δ (%) 82.78 77.03 71.55 44.25

4 Experimentation and Results This section presents the results and the validation of the proposed model through two cases. The first one represents the model without shadow and the second one with a complex shadow on PV module.

4.1 Case 1: Validation of the BG Model in Normal Operating For this purpose, measurements of I-V curve of the reference panel are compared with the model. The test is performed the January 25, 2018, at 10:40AM with a global irradiation of 624 W/m2 and a cell temperature of 25°C. In this case, δ2 = 0 since no shadows are visible on PV module [1]. The attenuation factor δ corresponds only to the global radiation that receives PV module [1]. In this case, all the attenuation factor is fixed to 1. Figure 7 shows measurements of I-V curve of the reference panel compared with I-V curve of the model (Fig. 5). The mean square error (MSE) result is used to assess modeling accuracy based on the shading ratio. The MSE has a good accuracy around of 1.6% see [1]. The next case consists in performing a uniform shading case with various shaded PV cells [1].

4.1.1

Case 2: Validation Under Complex Shading Condition

For this purpose, two sheets of paper were placed on the surface of the panel [1] as shown in Fig. 6 with a shadow area of as = 0.5 for the one and as = 0.23 for the other. The experimentation tests were performed during February 9, 2018, at 12:06PM with a solar irradiation of 387.80 W/m2 and a cell temperature of 19 °C [4]. Depending on the characteristic of the shadow, the values of the matrix of shadow change during the day inducing some DC power losses. In function of the shadow position and its area, the attenuation factor δ is calculated and presented in the shadow matrix in Eq. (11) [1]. Figure 7 illustrated

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Fig. 5 I-V curves validation in normal operating Fig. 6 Shadow test on PV module during the February, 9th, 2018

the comparison of the model of I-V curves with the experimental I-V in normal operating and in shading conditions [1]. The MSE is 3% for the shading case. ⎡

0.5 ⎢ 1.0 ⎢ ⎢ ⎢0.77 δ(t) = ⎢ ⎢ 1.0 ⎢ ⎣ 1.0 1.0

1.0 1.0 1.0 1.0 1.0 1.0

1.0 1.0 1.0 1.0 1.0 1.0

1.0 1.0 1.0 1.0 1.0 1.0

1.0 1.0 1.0 1.0 1.0 1.0

1.0 1.0 1.0 1.0 1.0 1.0

1.0 1.0 1.0 1.0 1.0 1.0

1.0 1.0 1.0 1.0 1.0 1.0

1.0 1.0 1.0 1.0 1.0 1.0

⎤ 1.0 1.0⎥ ⎥ ⎥ 1.0⎥ ⎥ 1.0⎥ ⎥ 1.0⎦ 1.0

(11)

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Fig. 7 I-V curves validation under shading conditions [1]

5 Conclusion This paper presented a detailed model able to take into account the effect of complex shading in the current voltage curves. The area of shadow was established using to image processing. This processing consists of using a linear iterative clustering (SLIC) algorithm. Furthermore the combination of direct and indirect radiation was permitted to obtain the attenuation factor inducing the decrease of the electrical generation under complex nonuniform shadow conditions. The model was proven and validated through experimental tests during various days with an admissible error.

References 1. L.A. García-Gutiérrez, Développement d’un contrôle actif tolérant aux défaillances appliqué aux systèmes PV, Mar 2019 [Online]. Available: http://thesesups.ups-tlse.fr/4383/ 2. C. Alonso, L. Garcia-Gutierrez, M. Bressan, A. Sferlazza, F. Jimenez, S. DE-LAS-HERAS, High granularity model of a photovoltaic array under complex shadow conditions, in Electrimacs 2019, Palerme, May 2019 [Online]. Available: https://hal.laas.fr/hal-02053484 3. L.A. Garcia-Gutierrez, Development of an Active-Fault Tolerant Control Applied to PV systems. Theses, Université Toulouse 3 Paul Sabatier (UT3 Paul Sabatier), Mar 2019 [Online]. Available: https://hal.laas.fr/tel-02147149

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4. L. Garcia-Gutierrez, M. Bressan, F. Jimenez, S.D. Heras, C. Alonso, Design of a global maximum power point tracking (gmppt) for PV array based on precise pv shadow model, in 2018 7th International Conference on Renewable Energy Research and Applications (ICRERA), 2018, pp. 275–280 5. M.R. Maghami, H. Hizam, C. Gomes, M.A. Radzi, M.I. Rezadad, S. Hajighorbani, Power loss due to soiling on solar panel: a review. Renew. Sust. Energ. Rev. 59, 1307–1316 (2016) 6. Y.E. Basri, M. Bressan, L. Seguier, H. Alawadhi, C. Alonso, A proposed graphical electrical signatures supervision method to study PV module failures. Solar Energ. 116, 247–256 (2015) 7. M. Bressan, Y.E. Basri, A. Galeano, C. Alonso, A shadow fault detection method based on the standard error analysis of I-V curves. Renew. Energ. 99, 1181–1190 (2016) 8. K.A. Kim, P.T. Krein, Reexamination of photovoltaic hot spotting to show inadequacy of the bypass diode. IEEE J. Photovoltaics 5(5), 1435–1441 (2015) 9. N. Mishra, A.S. Yadav, R. Pachauri, Y.K. Chauhan, V.K. Yadav, Performance enhancement of PV system using proposed array topologies under various shadow patterns. Sol. Energ. 157, 641–656 (2017) 10. E.I. Batzelis, P.S. Georgilakis, S.A. Papathanassiou, Energy models for photovoltaic systems under partial shading conditions: a comprehensive review. IET Renew. Power Gener. 9(4), 340–349 (2015) 11. M. Bressan, A. Gutierrez, L.G. Gutierrez, C. Alonso, Development of a real-time hot-spot prevention using an emulator of partially shaded PV systems. Renew. Energ. 127, 334–343 (2018) 12. A. Mohapatra, B. Nayak, P. Das, K.B. Mohanty, A review on mppt techniques of PV system under partial shading condition. Renew. Sust. Energ. Rev. 80, 854–867 (2017) 13. A. Gutiérrez Galeano, M. Bressan, F. Jiménez Vargas, C. Alonso, Shading ratio impact on photovoltaic modules and correlation with shading patterns. Energies 11(4) (2018) [Online]. Available: http://www.mdpi.com/1996-1073/11/4/852 14. G.R. Walker, Evaluating mppt converter topologies using a matlab PV model. Aust. J. Electr. Electron. Eng. 21(1), 49–55 (2001) [Online]. Available: https://eprints.qut.edu.au/63580/ 15. J. Bishop, Computer simulation of the effects of electrical mismatches in photovoltaic cell interconnection circuits. Sol. cells 25(1), 73–89 (1988) 16. S. Silvestre, A. Boronat, A. Chouder, Study of bypass diodes configuration on {PV} modules. Appl. Energ. 86(9), 1632–1640 (2009) 17. C. Olalla, D. Clement, D. Maksimovic, C. Deline, A cell-level photovoltaic model for high-granularity simulations, in 2013 15th European Conference on Power Electronics and Applications, EPE 2013 (2013)

Static Switch Activation Algorithm for Energy Storage System Grid-Connection and Disconnection M. Jebali-Ben Ghorbal, M. Ben Said-Romdhane, J. Arbi-Ziani, S. Skander-Mustapha, and I. Slama-Belkhodja

Abstract One of the most important problems for residential rooftop photovoltaic systems with energy storage is grid voltage synchronization control under balanced grid conditions and fast and appropriate disconnection from the distribution electrical network if inacceptable voltage variation occurs. Connection and disconnection of such a system is performed through a static switch denoted as K. This chapter deals with an activation algorithm of the static switch K connecting and disconnecting a battery energy storage system (BESS) to and from the main grid. The BESS is dedicated to areas where grid is not available all the time, but where photovoltaic (PV) is available to ensure non-interruptible supply of residential loads. The BESS is connected to the grid via a DC-AC converter which hosts the proposed

M. Jebali-Ben Ghorbal · M. Ben Said-Romdhane () Ecole Nationale d’Ingénieurs de Tunis, LR11ES15 Laboratoire des Systèmes Electriques, Tunis, Tunisie e-mail: [email protected]; [email protected] J. Arbi-Ziani () Ecole Nationale d’Ingénieurs de Tunis, LR11ES15 Laboratoire des Systèmes Electriques, Tunis, Tunisie Université de Carthage, Institut Supérieur de Sciences Appliquées et de Technologie de Mateur, Mateur, Tunisie e-mail: [email protected] S. Skander-Mustapha Université de Tunis El Manar, Ecole Nationale d’Ingénieurs de Tunis, LR11ES15 Laboratoire des Systèmes Electriques, Tunis, Tunisie Université de Carthage, Ecole Nationale d’Architecture et d’Urbanisme, Sidi Bou Said, Tunisie e-mail: [email protected] I. Slama-Belkhodja Université de Tunis El Manar, Ecole Nationale d’Ingénieurs de Tunis, LR11ES15 Laboratoire des Systèmes Electriques, Tunis, Tunisie e-mail: [email protected] © Springer Nature Switzerland AG 2020 W. Zamboni, G. Petrone (eds.), ELECTRIMACS 2019, Lecture Notes in Electrical Engineering 697, https://doi.org/10.1007/978-3-030-56970-9_5

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algorithm. Fast detection of special grid conditions is first ensured, to allow a fast disconnection from the grid but keeping a good power quality for connected loads. Finally, simulation and experimental results are given to validate the effectiveness of the proposed method.

1 Introduction The need of renewable energy sources to support the main electrical grid has become a worldwide concern and among main leaders priorities. In fact, decreasing energy storage cost and technology enhancement on this field have encouraged the emergence of residential rooftop PV systems in order to support the main power grid and local load consumption [1–4]. However, due to the continuous penetration of green energy systems such as photovoltaic and wind, and especially because of their intermittent character, new issues have been raised such as power quality, grid reliability, voltage and frequency stability and generation and consumption power matching. One of the proposed solutions to deal with the last two issues is the use of energy storage system [4–6]. These systems should be able to operate into two modes, according to grid conditions: connected to the main grid or disconnected from it, which is the islanding mode. This is the reason why a synchronization control is required [7–10]. This control should lead the point of common coupling (PCC) voltages to match with grid voltages when safe conditions are verified. These conditions are set by specific standards and requirements [10, 11], and the connection/disconnection to/from the grid is ensured using a static switch [12]. The static switch allows the system protection as it should isolate the PV system, the energy storage system and local loads from the main grid if any disturbance occurs. Authors in [9] proposed a new phase locked loop (PLL) neural network controller to design the static switch, the proposed controller is able to operate in unpredictable situations; while in [13], authors proposed a design and a realization of a static switch controller for an AC microgrid without the need for extra sensors or complicated communication protocol. The chapter addresses first a fast detection method for grid voltage variation, and then proposes an algorithm to turn ON or OFF the static switch rapidly and smoothly to connect or isolate BESS and local loads to/from the PCC as shown in Fig. 1. A fast detection allows continuous energy supply of local loads and reduces use time of BESS. This chapter is structured as follows. Section 2 presents a brief description of the system under study as well as the DC-AC control strategy. Section 3 presents the proposed algorithm for fast detection of grid voltage change where simulation and experimental results are given. Section 4 details the static switch activation algorithm using the proposed method. Finally, Sect. 5 concludes the chapter.

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Fig. 1 System under consideration integrating BESS

Fig. 2 BESS without renewable energy generation

2 System Under Study For the algorithm presentation, renewable energy generation in Fig. 1 can be considered as integrated in the grid and then omitted as shown in Fig. 2. This figure focuses on part concerned by the developed algorithm, DC-AC converter, LCL filter, local residential loads, the static switch K for grid connection and disconnection, the grid with its line impedance. Two operating modes are possible, according to grid state as shown in Fig. 3. – Islanded mode (grid is absent): Loads are only supplied by the BESS. In this case, K is ON and grid currents iga (t), igb (t) and igc (t) are null. – Grid-connected mode (grid is available): It charges BESS until its limits, then supplies local loads. In this case, K is ON and grid currents iga (t), igb (t) and igc (t) are no longer equal to zero if a load is connected.

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Fig. 3 BESS operation modes. (a) Islanded mode. (b) Grid-connected mode

Fig. 4 Algorithm for K activation within DC-AC control

In grid-connected mode, as shown in Fig. 3b, the DC-AC control ensures the charging of batteries and also the monitoring of the grid to check if its quality is sufficiently good to remain connected. As no energy flows from BESS to network, anti-islanding standards like VDE-AR-NE 4105 or IEEE 1547 have not to be considered. In islanded mode, as shown in Fig. 3a, the DC-AC control ensures voltage and frequency for load supply and also grid monitoring to check if its quality is sufficiently good to connect BESS, according to EN 50160 standard. It is to note that at least 1 mn wait should be programmed since the instant when the grid quality is considered enough for connection. In grid-connected mode, LCL filter output current are controlled (i2a (t), i2b (t) and i2c (t), in Fig. 4) and the references for DC-AC control are current control considering load need and state of charges of batteries. This control is out of the scope of this chapter.

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Table 1 Operation modes and transition between modes Initial state K=0

Operation mode Islanded

Grid state Lost

To detect Grid existence

K=1

Connected

Exist

Grid loss or quality

Conditions Exist Grid PQ Synchronization No current in K

Final state K=1

K=0

In this operation mode, a fast detection of grid abnormal conditions requiring disconnection allows a better power quality for loads. In islanded mode, references are voltage ones, setting desired amplitude and frequency for loads, and DC-AC control provides LCL filter capacitor voltage control according to these references. In this mode, the control should also continuously verify grid quality and start grid synchronization to connect after the minimum required waiting time tmin . In this case, a fast detection of required grid quality for connection allows to start earlier counting tmin . Proportional resonant (PR) controllers are used for current and voltage regulation, and second-order generalized integrator (SOGI-FLL) is developed for grid synchronization. PR regulators are not discussed in this chapter, and further details can be found in [14]. Table 1 resumes for each initial state of static switch K, the corresponding operation mode, the grid state that leads to this K state and what grid change algorithm has to detect, then what conditions should be verified before changing it. In the following section, grid state detection is firstly described and then the static switch activation algorithm is given.

3 Grid Voltage Change Detection Algorithm The principle of the method is based on residual generation which is calculated from measurable quantities (here grid voltage and current through K). The residual is statistically null in healthy conditions and higher than a threshold to be defined when a grid fault occurs. Figure 5 details proposed algorithm. The idea of the developed residual is based on the fact that a continuous variable has not to have any discontinuity in normal conditions, so a very fast sampling will lead to a little variation between two consecutive samples. And the lower the sampling time is, the lower this variation will be. Hence, when a fault occurs, a discontinuity will appear and then the difference between two successive sampling will be higher than previously.

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Fig. 5 Principal of residual generation

Residual value is then analysed to decide if the measured quantity evolution is normal or abnormal. This analysis is performed based on a simple comparative test or on more sophisticate approaches like the theory of statistical decision or others. All these methods need to define a threshold. Its choice is quite sensitive: if too low, it can lead to numerous false alarms, and if too high, it can lead to no detection of small voltage magnitude faults. In this study, an analytical expression of the threshold has been established when voltage grids are sinusoidal, and its analysis is performed when a sudden change occurs in grid voltage. All the calculation details are given in [15, 16]. As the measured signal is the grid voltage here, which is assumed to be perfectly sinusoidal, this allows the use of the results given in [15, 16] without further explanations.

3.1 Residual Expression Under Normal Grid Conditions The grid voltage at the sampling kcan be expressed by (1), where Vgmand ω = 2π f are line to ground grid voltage magnitude and grid frequency, respectively. Vg (k) = Vgm sin (ωkT a )

(1)

As time acquisition Ta is much lower than grid time period, the increment defined by (2) can be approximated by (3). δk = Vgm [sin (ωkT a ) − sin (ω (k − 1) Ta )]  δk ≈ Vgm ωkT a cos

ω (k − 1) Ta 2

(2)

(3)

In normal conditions, the absolute difference between two consecutive increments, noted rk , remains very low.

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Fig. 6 Residual calculation algorithm

A simplified expression (4) is then derived based on trigonometric function simplifications rules. Its maximum value is obtained for maximum sinus value, as given in (5) 2

2

rk = |δk − δk−1 | ≈ Vgm ω Ta |sin (ω (k − 1) Ta )| 2

rk max = Vgm ω Ta

2

(4) (5)

To filter measurement noises, a final residual, noted Rk , is defined as the sum of three consecutives ones as expressed in (6). Its maximum is then as given in (7) Rk = rk + rk−1 + rk−2 2

Rk max = 3rk max = 3Vgm ω Ta

(6) 2

(7)

Figure 6 illustrates the residual algorithm. It is based on the expression of residual as expressed in (8)   r(k) = Vg (k) − 2Vg (k − 1) + Vg (k − 2)

(8)

As it is simple, low time and experimental resources consumption are required.

3.2 Residual Expression for Disconnection Decision When balanced or unbalanced grid voltage drop occurs, a peak appears on the residual waveform. During the following steady state, the residual value is related to the new grid voltage magnitude, according to (7). So, the peak residual detects any event on grid voltage, and residual value gives an indication on voltage drop level.

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As acquisition period Ta is very low (few micro seconds), only large variations will be significant and then detectable. For example, 20% voltage drop will lead to 20% drop in residual value, but 1 Hz grid frequency variation value will lead to 2% residual variation which cannot be considered as significant. Figure 7 shows simulation results carried out with PSIM software. Theoretical residual value is confirmed by these results. Impact of voltage harmonics, in the range of standards, has been investigated, and results show that peak and residual value change remains available to detect grid event and voltage drop when measured quantities is not perfectly sinusoidal, but with harmonics in the range indicated by standards. Figure 7 shows voltage waveforms and residual: in Fig. 7a, the voltage amplitude is half than in Fig. 7b and so the residual maximum also. In Fig. 7c, a voltage harmonics have been added. Since their frequency is high related to voltage fundamental frequency (10 kHz) and their amplitude low (five times lower), the

Fig. 7 Voltage waveforms and residual Ta =100 μs, f=50 Hz ,Vgm=220

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residual maximum value is not affected by these harmonics. This could be easily explained considering acquisition sampling as a filter for this high frequency signals. Figure 7d, e and f illustrates how the spike of residual depends on event instant occurrence. Since the worst case is when voltage is crossing value, Fig. 7 shows that, even if in this case, peak residual detected the event occurrence.

3.3 Experimental Results The algorithm has been integrated to the DC-AC converter control in both operation modes: grid-connected mode to detect loss of the grid and islanded to detect its recovery. Figures 8 and 9 show the experimental test bench. The AC-DC converter used is the B6U+E1CIF+B6CI (Semiteach) from SEMIKRON. Voltage and currents are sensored via LEM 55LP and LEM LV 25, respectively, as given in Fig. 9. The numerical device is STM32F4. Acquisition time is set to 100 μs. The grid voltages are measured at the output of an autotransformer as indicated in Fig. 8. In Figs. 10 and 11, residual waveforms are given for grid loss and grid recovery, respectively. As output autotransformer voltages are not perfectly sinusoidal, residual waveform in steady state is also not perfectly sinusoidal. However, residual spike appears when event occurs (even loss or recovery) and the maximum value of the residual in steady state changes with grid voltage values.

Fig. 8 Test bench principle

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Fig. 9 Experimental test bench

Fig. 10 Residual calculation algorithm at grid loss

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Fig. 11 Residual calculation algorithm at grid recovery

4 Static Switch Activation Algorithm 4.1 General Considerations First of all, grid voltage and static switch currents are measured and corresponding residual calculated. Current residual, noted rik , determines if any current is circulating through the static switch, from grid to BESS for charging operating mode. Voltage residual, noted rvk , identifies if grid voltages are present and if they meet standard requirement in terms of magnitude. All conditions for grid connection or grid disconnection should be verified before K static switch activation. In following, algorithm for each case is presented.

4.2 Algorithm for Grid Connection The operation mode is islanded one. So, the DC-AC converter control imposes LCL filter capacitor voltages equal to the references defined in (9). These references are generated by the block “reference generation” in Fig. 12. ⎧ ⎨ vcrefa (t) = 325 sin (2πf.t) ◦ vcrefb (t) = 325 sin 2πf.t − 120  ⎩ ◦ vcrefc (t) = 325 sin 2πf.t − 240

(9)

In parallel with this control, voltage residual monitors the grid state. If recovery is detected, grid connection conditions should be checked. This is performed using synchronization algorithm. Indeed, the SOGI-FLL provides grid magnitude and grid frequency. These values are compared with those provided by standard [11]. If they

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Fig. 12 Algorithm principle for activate K for grid connection

are compliant, a counter is started to verify that these conditions remain available at least 60 s as required by standard. During this time, grid connection is also checked: magnitude, frequency and phase equality of grid voltages and filter capacitor ones. This equality is performed on dq voltage components as they are DC components in the reference frame linked to grid voltage. Figure 12 illustrates the described approach.

4.3 Algorithm for Grid Disconnection In grid connection operation mode, DC-AC converter controls power exchange during charging mode and then the currents. Currents flowing through the static switch K are responsible of battery charging and or energy providing to local loads. Voltage residual monitors grid, and if an event occurs and then the residual value becomes lower than required by standard or null, disconnection could be done by the static switch K as shown in Fig. 13. Figure 14 presents the timing diagram of the implemented static switch activation algorithm. This diagram presents the computation cycles of the different functions during each sampling period.

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Fig. 13 Algorithm principle for activate K for grid disconnection

Fig. 14 Timing diagram of the implemented static switch activation algorithm

5 Conclusions This chapter presented a fast activation algorithm of a static switch used to connect and disconnect a BESS to and from the main utility grid. The proposed activation algorithm detects very quickly any grid state variation and therefore rapidly checks

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if the change conditions of the static switch state are met in order to send the appropriate activation order to the static switch. The rapid switch activation allows not only a continuity of supply of residential loads for areas where grid is not available all the time, but also a minimization of BESS use time, allowing the increase of its elements lifetime. Simulation and experimental results are presented to show the effectiveness and the rapidity of the proposed activation algorithm. Acknowledgments This work was supported by the Tunisian Ministry of High Education and Research under Grant LSE-ENIT-LR 11ES15 and funded in part by NAS and USAID under the USAID Prime Award Number AID-OAA-A-11-00012. Any opinions, findings, conclusions or recommendations expressed in this article are those of the authors alone and do not necessarily reflect the views of USAID or NAS.

References 1. M. EL-Shimya, N. Mostafab, A.N. Afandic, A.M. Sharafd, M.A. Attiaa, Impact of load models on the static and dynamic performances of grid-connected wind power plants: a comparative analysis. Math Comput Simul149, 91–108 (2018) 2. S. Lakshmi, S. Ganguly, Modelling and allocation planning of voltage-sourced converters to improve the rooftop PV hosting capacity and energy efficiency of distribution networks. IET Gener Transm Distrib 12(20), 4462–4471 (2018) 3. S. Pukhrem, M. Basu, M.F. Conlon, K. Sunderland, Enhanced network voltage management techniques under the proliferation of rooftop solar PV installation in low-voltage distribution network. IEEE J Emerg Sel Top Power Electron 5(2), 681–694 (2017) 4. M. Zeraati, M.E. Hamedani Golshan, J.M. Guerrero, Distributed control of battery energy storage systems for voltage regulation in distribution networks with high PV penetration. IEEE Trans Smart Grid 9(4), 3582–3593 (2018) 5. J. von Appen, M. Braun, Interdependencies between self-sufficiency preferences, technoeconomic drivers for investment decisions and grid integration of residential PV storage systems. Appl Energy 229, 1140–1151 (2018) 6. I. Serban, C. Marinescu, Control strategy of three-phase battery energy storage systems for frequency support in microgrids and with uninterrupted supply of local loads. IEEE Trans Power Electron29(9), 5010–5020 (2014) 7. M. Ashabani, F.D. Freijedo, S. Golestan, J.M. Guerrero, Inducverters: PLL-less converters with auto-synchronization and emulated inertia capability. IEEE Trans Smart Grid7(3), 1660–1674 (2016) 8. K. Lim, J. Choi, Seamless grid synchronization of a proportional+resonant control-based voltage controller considering non-linear loads under Islanded mode. Energies10, 10 (2017) 9. B. Nakisa, S. M. Nosratabadi, A. Rajabi, M. Dehghani, M. Molla-Ahmadi, Synchronization of a microgrid with main network through static switch based on neural network controller. 19th Conference on Electrical Power Distribution Networks, EPDC 2014, pp. 94–99, 2014 10. M. Rekik, A. Abdelkafi, L. Krichen, Synchronization of wind farm power system to utility grid under voltage and frequency variations. Int J Renew Energy Res5, 1 (2015) 11. Standard, EN50438, Requirements for Micro-Generating Plants to be Connected in Parallel with Public Low-Voltage Distribution Networks (BSI, London, 2014) 12. M. Saeedimoghadam, M. Dehghani, Static switch in microgrids. Int Res J Appl Basic Sci7(2), 95–99 (2013) 13. Y.-Y. Hong, J.-L. Gu, F.-Y. Hsu, Design and realization of controller for static switch in microgrid using wavelet-based TSK reasoning. IEEE Trans Ind Inf 14(11), 4864–4872 (2018)

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14. R. Teodorescu, M. Liserre, P. Rodríguez, Grid Converters for Photovoltaic and Wind Power Systems (Piscataway; Chichester; Hoboken, Wiley-Blackwell, 2011) 15. H. Berriri, M.W. Naouar, I. Slama-Belkhodja, Easy and fast sensor fault detection and isolation algorithm for electrical drives. IEEE Trans Power Electron 27(2), 490–499 (2012) 16. M. Jebali Ben Ghorbal, W. Ghzaiel, I. Slama-Belkhodja, Fast islanding detection of PV grid connected inverters. 2014 International Conference on Electrical Sciences and Technologies in Maghreb (CISTEM), 3–6 November, 2014, Tunisia

Optimizing Scattering Behaviour of Encapsulant for Maximum PV Energy Yield H. Goverde, I. Horvath, P. Manganiello, B. Aldalali, F. Duerinckx, A. van der Heide, E. Voroshazi, and J. Szlufcik

Abstract Nowadays, material manufacturers are engineering module materials to optimize the energy production of the PV modules. One of the elements which can be influenced is the optical scattering of a material. In this study, we quantified the effect of a scattering front encapsulant on the energy production of PV modules. First, a wavelength-dependent scattering model was developed in the ray-tracing software PVlighthouse. This model was used to find the optimal scattering conditions, looking at the photo-generated current for a glass-glass PV module with flat front surface. It was shown that a gain of +0.63 mA/cm2 can be obtained for optimal scattering conditions. The scattering is mostly beneficial when the light strikes the module surface at a perpendicular angle. The outcome of the optimization study was implemented in IMEC’s energy yield simulation framework. This framework was used to estimate the energy gain of PV module with scattering front encapsulant when installed in Kuwait’s desert. It was shown that an energy production gain of 1.8% can be expected in case of a glass-glass module with flat front surface and ARC coating.

H. Goverde () Jan De Nul Group, Taipei City, Taiwan e-mail: [email protected] I. Horvath · F. Duerinckx · A. van der Heide · E. Voroshazi · J. Szlufcik Imec (Partner in EnergyVille), Genk, Belgium e-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected] P. Manganiello Delft University of Technology, Delft, The Netherlands e-mail: [email protected] B. Aldalali College of Engineering and Petroleum, Kuwait University, Khaldiya, Kuwait e-mail: [email protected] © Springer Nature Switzerland AG 2020 W. Zamboni, G. Petrone (eds.), ELECTRIMACS 2019, Lecture Notes in Electrical Engineering 697, https://doi.org/10.1007/978-3-030-56970-9_6

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1 Introduction To tackle the worldwide challenge to provide a sustainable and economically viable energy supply, photovoltaic (PV) modules are being deployed faster than ever before, showing an astonishing annual growth reaching 95 GWp in 2017 [1]. Currently, silicon-based PV modules dominate the market, and it is expected that this will continue in the coming decade [1]. As the levelized cost of electricity of PV systems is strongly depending on the cost/Wp of the PV modules, numerous research institutes and PV module productions companies focus on improving the efficiency of silicon-based PV modules, hereby reducing the cost-price of PV devices. For a high PV energy production, one can improve the conversion efficiency of the solar cells. Another way of maximizing the yield is to optimize the module itself and, more specifically, module materials. Researches focusses on improving, e.g., the reflectivity of the backsheet, reducing the glass and encapsulant absorbance. Yield improvement could also be obtained by introducing optical scattering in the front encapsulant layer; however, not much is known about actual improvement of this feature. In this chapter, we will study the effect of optical scattering in the front encapsulant layer on the energy production of PV modules. First, we will develop a ray-tracing model which incorporates the wavelength-dependent scattering, followed by an optimization study. The ray-tracing model will then be used to simulate the energy yield for various scattering scenarios using IMEC’s energy yield simulation framework. The outcome of this study can be used by module and module material manufacturers to optimize PV modules.

2 Energy Yield Framework 2.1 General Description Framework IMEC’s PV energy yield simulation framework will form the bases to translate the scattering effect into outdoor energy yield gain. The Electrical, Optical and Thermal (EOT) modelling approach used in this chapter uses meteorological data (ambient temperature, irradiance and wind speed and direction) as input for the environmental conditions. Material properties (optical, thermal and electrical constants, thickness, etc.) and cell and module technology parameters (cell performance, temperature coefficients, EQE, etc.) serve as input to represent the PV module technology under evaluation. A full description and demonstration of this modelling approach can be found in [2, 3]. In the approach, every solar cell in the PV module is modelled individually to be able to simulate the effect of partial shading on the energy production [4]. The individual sub-models are both thermally and electrically coupled to create the model of a full module. The optical part of the model calculates the light absorption,

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heat and carrier generation in each layer of the PV module. The result is used by the thermal and the electrical parts of the model. The thermal part of the EOT model consists of an RC-equivalent thermal network that incorporates the heat capacity of each element and the conduction, convection and radiation of heat both within the module and from the module to the environment. Next to that, the thermal circuit also takes into account reduction of heat generation due to the dissipation of electrical energy in the electrical load and the thermal state of the PV module. Thermal resistances and capacities in the thermal circuit are equal to the physical value of each layer in the module. By incorporating the thermal capacity of each layer, thermal state effects are integrated. The thermal network is able to calculate the solar cell temperature as a function of illumination, ambient temperature, sky temperature, wind speed and direction, electrical operation point and thermal state. The well-known (1- or 2-) diode model is used to describe the electrical part of the PV module. Parameters of the diode model are being varied depending on solar cell temperature and illumination.

3 Intra-layer Optical Scattering 3.1 Wavelength-Dependent Scattering Optical properties of materials can be influenced by varying manufacturing parameters, composition or physical dimensions. Not only the wavelength-dependent transmittance and reflectance can be engineered, but also the internal optical scattering can be influenced by varying production parameters. Even more, the optical scattering can be varied as a function of the wavelength. An example of an encapsulant with wavelength-dependent optical scattering is displayed in Fig. 1.

3.2 Optical Scattering Model This scattering behaviour can be beneficial as it enhances the optical path and thus has the potential to reduce optical losses in the PV module. As the scattering properties of the front encapsulant can be engineered to enhance or to limit scattering, we would like to optimize this effect to obtain the highest outdoor energy yield production. As outdoor tests are time-consuming and sometimes difficult to estimate trends, we have extended the existing energy yield modelling framework to be able to estimate the effect of scattering encapsulants on the PV energy yield.

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Fig. 1 Wavelength-dependent optical scattering of PV module encapsulants, measured using absorbance, reflectance and transmittance measurements. With [red] standard EVA encapsulant, [green] standard polyolefin encapsulant and [blue] scattering encapsulant

3.3 Scattering Implementation in PVlighthouse As mentioned in Sect. 2, the energy yield model uses the layer properties in combination with the optical properties to estimate the reflectance and absorbance in each layer. For this estimation, the commercially available PVlighthouse software is being used [5]. This powerful simulation package is capable of estimating the required parameters but does not allow users to implement wavelength-dependent scattering properties; only scattering using a fixed ratio is allowed. Therefore, we implemented an artificial layer with half the thickness of the front encapsulant and provided this layer with texturing at the interface of both front layers. Figure 2 shows a snapshot of the structure used for the ray-tracing simulations. Note that we analyzed the scattering effect on a standard glass-glass module with 3.2 mm thick front and back glass (no antireflection coating), 450 μm front and back encapsulant, and 180 μm thick monofacial PERC solar cell. Furthermore, the simulation environment assumed ‘perfect mirror’ boundary conditions at the sides of the modules, and so the results are representative for cells inside the PV module. As we have a textured interface between the front encapsulant layer, varying the refractive index of the ‘second’ front layer will promote or limit scattering. The wavelength-dependent index was gradually varied using the following correlation: !  nsc (λ) = nEV A (λ) 1 + MF λf − λ

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Fig. 2 PV module structure used to perform ray-tracing simulations in PVlighthouse

with nsc (λ) the refractive index of the bottom layer, nEVA (λ) the refractive index of EVA, MF a multiplication factor, λf the highest wavelength of the interval and λ the optical wavelength. MF is varied to have various scattering modes. The input parameters (nsc (λ)) used for the optical simulations are displayed in Fig. 3.

3.4 Effect of Scattering on Photo-Generated Current Density The manipulated optical constants of the bottom layer were implemented in the ray-tracing environment. The photo-generated current density was calculated for an AM1.5 solar spectrum, perpendicular to the surface. Next to that, the ray-tracing

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Fig. 3 Refractive index for various MF values. The displayed parameters were used as optical properties of the bottom front encapsulant layer

simulations were also used to extract the optical front (reflective and escape) losses of the PV module. The simulation results for various MF constants are displayed in Fig. 4. Figure 4 shows the effect of the scattering on the photo-generated current. Up to a MF value of 0.0004, the scattering has a positive effect on the current generation. The enhanced optical path in the modules prevents that light is reflected at the rear glass layer and at the cell, resulting into a reduction of the escape losses, followed by an increase of the photo-generated current. For MF factors higher that 0.0004, the photo-generated current starts to decrease, showing an optimum in the generation profile. The decrease is caused by additional internal reflection at the artificial interface of the front encapsulant layer. The difference in refractive index between the two layers is substantial (0.7 difference at 250 nm; see Fig. 3); hence, more light is reflected at the interface leading to more front escape losses

3.5 Angular Dependency Scattering As mentioned in the section above, the scattering in the front enhances the optical path length in the PV modules resulting in less front escape losses. The PVlighthouse simulations show that there is an optimum for the scattering effect. The results were obtained by applying an AM1.5 spectrum perpendicular to the surface. It is expected that the scattering effects depend on the incident angle of the incoming light. This was investigated by varying the incident angle between 0◦ (perpendicular

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Fig. 4 Results of ray-tracing simulations for different values of MF: [top] photo-generated current and [bottom] front escape losses

to the surface) and 90◦ . The optimal scattering conditions (MF=0.0004) were implemented to demonstrate the most extreme case. Figure 5 shows the front escape losses for the standard EVA and the optimal scattering encapsulant. Note that the figure shows the absolute values; due to the angle variation, the light intensity on the modules surface decreases hereby also the absolute escape losses. To gain more insight, the relative difference between the two cases was calculated and also displayed in the bottom graph of Fig. 5. The figure shows an overall decrease of the front escape losses as a function of the incident angle. As mentioned above, this trend is caused by a reduction of energy that reaches the module surface, and therefore, the absolute total amount of energy escaped from the front is reduced. More important is the difference between the two simulation cases; this difference reduces for higher-incident angles. As discussed in the previous section, the optical scattering of the front encapsulant layer enhances the optical path in the modules and hereby improved photo-current generation. When the light hits the surface under a certain angle, inherently, the optical path is enhanced, and thus, scattering is less beneficial for situation where light has a higher angle.

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Fig. 5 Front escape losses for a PV module with a standard EVA front layer and one module with optimal scattering. The bottom part shows the relative differences between both cases

4 Energy Yield Simulation Results In the previous section, an optical scattering model in PVlighthouse was developed and used to estimate the benefits of front encapsulant with optical scattering. The simulation results showed there exists an optimal scattering condition in which the maximum photo-generated current can be obtained. In this investigation, we focussed only on the optimal current; however, this gain cannot be directly translated into energy yield gain as, e.g., a higher current also results in a higher operating temperature, followed by a reduction of conversion efficiency. Therefore, IMEC’s energy yield estimation framework was used to quantify the scattering gain. Three different scenarios were investigated: 60-cell glass-glass modules with or without ARC coating and one case with textured front glass. Layer thicknesses are equal to the situation shown in Fig. 2. For the three different scenarios, the effect of the scattering front encapsulant was tested. The optimal scattering conditions (MF=0.0004) were implemented at the different scenarios. The climate data, the year 2014 from 1 January until 31 December, recorded by Kuwait Institute for Scientific Research (KISR) at their Shagaya renewable energy park location, was used to test the potential of those modules in the MENA region. The simulated modules face south, and they are tilted at 30◦ from horizontal, which is optimal for the highest annual in-plane insolation under the latitude of Kuwait

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Fig. 6 Energy yield simulation results for the three different scenarios: glass-glass PV modules with a flat front and with or without an ARC coating and the same module with a textured front

City 29,33◦ . The ground surface albedo is assumed to be 0.2. The diffuse component of the in-plane irradiance is computed by means of the Perez model [6, 7]. The simulated energy production of a 60 cell PV modules for the different scenarios is shown by Fig. 6. Figure 6 shows that for all the scenarios, the scattering front encapsulant is improving the energy production. The highest improvement was demonstrated for the case with flat glass front and ARC coating. As in this case, the most light enters the module structure, and therefore, the scattering of the front encapsulant has in this situation the most effect on the energy production. As expected, the lowest improvement was found with the textured front case. Nevertheless, there was still a 0.7 %abs improvement demonstrated for this case. Note that comparable results were obtained for the ARC and the texturing cases. This indicates that a textured front glass can be replaced by an ARC-coated flat front glass in combination with a scattering front encapsulant. This might be beneficial for the production costs as no texturing step would be required in this process.

5 Discussion The presented results were solely based on simulation (apart from the measured scattering example behaviour of the novel encapsulant layer). Thus, the results and the optimal conditions are not linked to any real-life material or process window. The follow-up of this research will focus on validating the results and on translating the optimal scattering conditions into material properties. The study showed that scattering is mostly beneficial when the light strikes perpendicular on the PV module surface. This makes the technology extremely

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suitable for PV systems with one- or two-axis tracing devices. As those modules are always pointed towards the sun, encapsulant scattering will strongly enhance the energy production. Currently, the modelling framework is being extended to be able to quantify the scattering effect in PV systems with tracking devices.

6 Conclusions In this study, we quantified the effect of a scattering front encapsulant on the energy production of PV modules. First, a wavelength-dependent scattering model was developed in the ray-tracing software PVlighthouse. This model was used to find the optimal scattering conditions, looking at the photo-generated current for a glassglass PV module with flat front surface. It was shown that a gain of +0.63 mA/cm2 can be obtained for optimal scattering conditions. The scattering is mostly beneficial when the light strikes the module surface at a perpendicular angle. The outcome of the optimization study was implemented in IMEC’s energy yield simulation framework. This framework was used to estimate the energy gain of PV module with scattering front encapsulant when installed in Kuwait’s desert. It was shown that a yearly energy production gain of 1.8% can be expected in case of a glass-glass module with flat front surface and ARC coating. Acknowledgments Imec is a partner in EnergyVille (www.energyville.be), a collaboration between the Flemish research partners KU Leuven, VITO, imec, and UHasselt in the field of sustainable energy and intelligent energy systems. The work in this chapter was partially funded by Kuwait Foundation for the advancement of Sciences under project number P115-15EE-01. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 751159.

References 1. SolarPowerEurope, “Global Market outlook 2016–2020” 2. H. Goverde et al., Energy yield prediction model for PV modules including spatial and temporal effects, 29th European Photovoltaic Solar Energy Conference and Exhibition (EU PVSEC), pp. 3292–3296, 2014 3. H. Goverde et al., Accurately simulating PV energy production: exploring the impact of module build-up, 33rd European Photovoltaic Solar Energy Conference and Exhibition (EU PVSEC), pp. 1643–1646, 2017 4. P. Manganiello et al., A bottom-up energy simulation framework to accurately compare PV module topologies under non-uniform and dynamic operating conditions, 2017 IEEE 44th Photovoltaic Specialist Conference (PVSC), pp. 3343–3347, 2017 5. http://www.pvlighthouse.com.au/ 6. R. Perez et al., Modeling daylight availability and irradiance components from direct and global irradiance. Solar Energy 44(5), 271–289 (1990) 7. R. Perez et al., The development and verification of the Perez Diffuse Radiation Model. SAND88-7030. (1988)

On-Board Impedance Spectroscopy of Lithium-Ion Batteries in Electrical Vehicles: Comparative Analysis of Injected Signals and Practical Implementation Alexander Kuznietsov, Tilman Happek, and Aleksej Kiselev

Abstract This paper presents a fast spectroscopy of lithium-ion batteries using a modified SinC excitation signal which covers the wide frequency range within short timeframe. Power spectrum of the excitation pulse can cover frequency range of interest within given duration in the time domain. The proposed generation method allows the realisation of an impedance spectroscopy as a part of an on-board battery management system (BMS) in an electric vehicle. The current injection can be performed in a still-stand of a vehicle without influencing the movement of the motor.

1 Introduction Electrochemical impedance spectroscopy (EIS) [1] is recently one of most promising and well-investigated methods to obtain information about electrical properties of lithium-ion batteries [2]. Originally developed for laboratory analysis of cell impedances, it still has relatively less application under real operation conditions because of high expenditure of time and large amount of data to be interpreted [3]. However, it becomes important because of recently proven applicability to estimate the ageing processes in lithium-ion cells [4–6]. This fact transforms the EIS, together with an incremental capacity/differential voltage analysis, to an important diagnosis tool and increases the need to apply it for an on-board (inoperando) monitoring realised within a conventional battery management system

A. Kuznietsov () · T. Happek · A. Kiselev THM – University of Applied Sciences Mittelhessen, Friedberg, Germany e-mail: [email protected]; [email protected]; [email protected] © Springer Nature Switzerland AG 2020 W. Zamboni, G. Petrone (eds.), ELECTRIMACS 2019, Lecture Notes in Electrical Engineering 697, https://doi.org/10.1007/978-3-030-56970-9_7

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(BMS). Realisation of EIS in an on-board system faces with following problems, which are not obvious under in situ conditions but represent a crucial constraints for an in operando mode: – A laboratory typical analysis using different single-frequency signals is not realisable, and signals with continuous and constant spectrum covering the whole frequency range are needed. – The changes of battery voltage due to the injected current are very small because of low inner resistance of a battery, what makes the results very sensitive to quantisation uncertainties. An increase of injection signals levels leads to faster discharge of the battery and changes of operational conditions – To reach a good resolution in frequency domain, the observation window for the Fourier transform should be increased. Together with abovementioned fact, it leads to a significant discharge of a cell and to variation of cell properties during measurement. – The open circuit voltage of an analysed cell is changing with a state of discharge. It leads to the spreading of its spectrum and to the falsification of results in the ultralow-frequency region (millihertz) – The sampling time for a BMS should be increased to ensure correct impedance estimation in the whole frequency range between several millihertz and hundreds hertz. – On-board equipment should be able to generate test signals with a sufficient accuracy [7]. Since these requirements are partly in conflict with each other and could not be satisfied at the same time, developers often deal with a compromise solution resulting in a limited accuracy and false results. Therefore, a well-known approach of EIS should be rethought with regard to characteristic features of an on-board application under consideration of following points: – Use of signals with the sufficient information rate and without significant impact on the battery under test – An accurate generation of such signals with tools available on-board without disturbing a normal operation mode of an electric vehicle – Estimation of an impedance’s spectrum with high resolution in frequency domain. The main focus of this paper lies in the definition and properties analysis of pulselike signals which could be effectively used for an on-board impedance analysis and in the development of on-board generation scheme using a conventional inverterfed permanent magnet synchronous machine (PMSM) with DC link in closed-loop current control mode.

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2 Battery Model and Electrochemical Impedance Spectroscopy The well-known Thevenin’s model [8] shown in Fig. 1 builds the basis for an identification process. Controlled voltage source VOCV defines the state of charge (SoC) dependent open circuit voltage of the battery. RS describes input resistance (wires and connections), ohmic resistance of the electrolyte, the current collector, and the active mass [9]. The parallel RC circuit specifies the transient behaviour of the battery. This model can be complemented with an additional RC pair or nonlinear Warburg diffusion element. Though this model represents a simplest approximation at the electrical level, it is completely sufficient to investigate an effectiveness and accuracy of EIS and will be used in this paper as a prototype model. Diffusion parameters and inner resistance of the 2,5 Ah 18650 LiFePo cell, which was used for an analysis and verification of results, are listed in Table 1. The transfer function defining a complex impedance of battery can be written as follows: G(s) =

sRS RD CD + RS RD Vs (s) + VD (s) = Ibat (s) sRD CD + 1

(1)

It results to bode plot represented in Fig. 2. As it can be seen from the bode diagram, the relevant frequency region for an impedance analysis ranges from DC or several mHz up to 100 Hz. Fig. 1 Thevenin’s model of a battery

n

n

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Table 1 Parameters of the used battery model

Parameter RS RD CD

Value 0, 5 m 1 m 80 F

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1.5

Bode Diagram

× 10-3

1.4 1.3

Magnitude (abs)

1.2 1.1 1 0.9 0.8 0.7 0.6 0.5 100

101

102

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Frequency (rad/s)

Fig. 2 Impedance spectrum of used li-ion battery model

3 Comparative Analysis of Excitation Signals Used for an EIS A traditional EIS approach is based on injection of multi-sin signals resulting in a non-continuous spectrum with a resolution equals to the base frequency of an injection signal. The impedance will be calculated using following equation: Z(ωk ) =

VOCV (ωk ) − VCell (ωk ) VS (ωk ) + VDn (ωk ) = IBAT (ωk ) IBAT (ωk )

(2)

If UOCV remains strictly constant, it doesn’t impact the spectrum in an adjacent lowfrequency range, and an impedance can be calculated only using an output voltage VCell . Since the lowest-frequency component of a test signal should coincide with a smallest estimated frequency in an impedance spectrum, it should be chosen less than 1 mHz. In this case the current injection should continue about 1000 s. During this time the SoC of an analysed battery and consequently the inner impedance parameters will significantly change. Additionally, the SoC-dependent open circuit voltage of the battery will also change, causing the spreading of a spectrum and falsification of results. Figure 3 shows the spectrum leakage while discharging with 1C-Rate during 100 s. It is clearly seen that the spectrum spreads into an impedance relevant region. The necessity to enlarge an observation window to enhance the resolution and to detect a lowest impedance frequency as well as consequent impact

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0.15 DC-part of an Uocv-Spectrum

OCV [V]

0.1

Spreading due to changing Uocv 0.05

0

-0.05 0

0.5

1

1.5

2

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Frequency [Hz]

Fig. 3 Spreading of an OCV voltage spectrum

of changing UOCV represents a main operational drawback of a spectral analysis with periodic signals. It could be prevented using non-periodical signals with a continuous spectrum covering the whole region of interest independent from the width of observation window, which will define the resolution but not the lowest estimated frequency. Applying such technique makes it possible to measure the battery impedance within a significantly shorter time instant than by using periodic input signals. Nevertheless, use of such signals doesn’t solve the problem of a long observation window, required for sufficient resolution in frequency domain. Since such broadband signal have a constant energy within an observation window and the signal level should be kept high to reach sufficient voltage response, the loading of a battery will increase. It leads to the changing of object under test properties and decreases believability of spectroscopy results [10].

4 Excitation Using a Pulse Signals An impedance spectrum of a lithium-ion cell is time dependent and changes with SoC, temperature, etc. At the same time, as shown recently in [10], the properties of a battery variate during a measurement cycle and are dependent from the excitation

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Fig. 4 Impulse response of a cell describing LTI system

current. Taking this fact into account, the measurements should be as short as possible to avoid significant impedance change and as long as possible to enlarge the excitation energy and to obtain better signal-to-noise (SNR) ratio and sufficient resolution in frequency domain. Since the narrow pulses have a broadband spectrum, they can be used as a perturbation for a broadband spectroscopy [11].

4.1 Theoretical Background from the Perspective of System Theory The pulse response of a lithium-ion cell represented in Fig. 4 can be calculated as an inverse Laplace transform of the transfer function (1). The output voltage of the cell vcell (t) is a difference between a constant voltage VOCV and this function. ibat = δ(t) (Diracimpulse)

(3)

g(t) = L−1 (G(s))

(4)

vcell (t) = VOCV − g(t)

(5)

Vcell (j ω) = F(vcell (t)) = F(VOCV ) − F(g(t))

(6)

Since the F(δ(t)) = 1, the impedance spectrum can be calculated as: Z(j ω) = Vcell (j ω)

(7)

The relaxation phase of the cell is well suited to represent this case in the praxis. That is why the impedance spectrum can be obtained by loading the cell with constant current I0 during a sufficient time period to reach a steady-state condition, switching the current off and measuring the voltage response vcell (t) during complete relaxation phase. The impedance spectrum is calculated as:

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Nyquist plot of cell impedance impulse test results

8

reference

× 10-4

7

6

Im(Z), Ohm

5

4

3

2

1

0 0

0.5

1

1.5

2

Re(Z), Ohm

2.5

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Fig. 5 Estimation of an impedance spectrum using pulse excitation signal and the relaxation phase

Z(j ω) =

F(vcell (t)) I0

(8)

The main drawback of this method is an abrupt voltage change, caused by VS , directly at the beginning of the relaxation. Due to this fact, the calculated spectrum doesn’t contain the voltage change associated with RS , and this component will be not present in the impedance spectrum, as shown in Fig. 5

4.2 Signal Definition Using Requirements in Frequency Domain The approach proposed by authors of this paper is based on the inverse formulation of the excitation problem. The excitation signal should possess a constant spectrum covering not the whole frequency range, like a Dirac impulse, but a certain region

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0.8

Excitation current, A

0.6

0.4

0.2

0

-0.2

0

0.1

0.2

0.3

0.4

0.5

0.6

Time, sec Fig. 6 Excitation current with a rectangular spectrum

of interest, obtained from the magnitude response of an analysed battery: I (j ω) =

 1 0

for ω = 0 : ω0 otherwise

(9)

The desired function in time domain can be calculated using an inverse Fourier transform: i(t) = F−1 I (j ω) =

sin(ω0 t) ω0 t

(10)

The Fig. 6 shows the calculated excitation signal and demonstrates some obvious drawbacks. The signal has a jump at t = 0 which results in the falsification of the calculated impedance, as was explained for a Dirac impulse, and is bipolar. The bipolarity means that the injection should be bidirectional and should comprise both charge and discharge mode. Since the impedance of a cell is different in these modes, the results will be not correct. A simple adding of a DC signal with a magnitude equals to a magnitude of a first ripple of i(t) transforms the signal to a unipolar one but results in an additional jump at the beginning and should be avoided. The authors propose following design approach of an excitation signal:

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12

Excitation current, A

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-2

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Time, sec Fig. 7 Excitation current proposed by authors

1. Definition of a desired frequency range of interest which corresponds a passband of a battery. Taking a bode diagram and dynamical properties of the lithium ion cell into account, the authors use ω0 = 2 · π · 30. 2. Shifting an input current to the middle of an excitation period Te . 3. Adding a DC current with a magnitude IDC = SiC(3π/2) = 0, 21. This value equals the magnitude of the first negative ripple of the SiC-function. 4. Applying a Hamming window to compensate the board jumps. The resulting excitation current  i(t) = 0, 21 +    2π nTs 0, 54 − 0, 46 · cos , Te

sin(ω0 (nTs − ω0 (nTs −

Te 2 ))



Te 2)

n = 0, . . . , N − 1

(11)

is shown in the Fig. 7. It can be seen that the signal is flat and doesn’t have critical abrupt changes inside the entire observation window. The signal is absolutely integrable and has a constant magnitude spectrum in the range 0 . . . 30 Hz. Since the charge amount contained in this signal is equal to 0, 02 Ah, the operational condition due to loading the battery can be considered as constant, and a test can be performed during a short time period like a snapshot.

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5 Simulation Results The proposed approach was tested using a model of a Li-ion cell with the parameters from the Table 1. The Fig. 8 shows the Nyquist plot of a cell impedance. The signal injection was performed 100 s with the sampling time T s = 1 ms. The magnitude of the pulse was 12A what corresponds to 5C charging rate. The estimation results for impedance values obtained directly from Nyquist plot without model-based approximation are shown in Table 2. The estimation error equals to 4, 2% and can be minimised using a model-based fitting of the Nyquist plot.

6 Practical Realisation of the Injection Current Generator in an On-Board System of an Electrical Vehicle While designing an on-board impedance spectroscopy framework, an additional attention should be paid development of an injection current source, which is able

Nyquist plot of cell impedance impulse test results using proposed excitation signal

× 10

reference

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Fig. 8 Results of an impedance spectroscopy with the proposed impulse signal Table 2 Estimation results using proposed impulse signal

Parameter RS RD CD

Value 0, 5 m 1 m 80 F

Estimation result 0, 5213 m 1, 048 m 82, 2 F

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Fig. 9 Conventional field-oriented control of a PMSM in an electric vehicle

to precisely generate a required current without disturbing a regular operation of a system. The core idea of proposed approach is to involve the traction motor of the vehicle as controllable load to provide the frequency response of the vehicle battery. As motor, permanent magnet synchronous machine (PMSM) is considered, since this motor type is mostly used in electric and hybrid vehicles. The standard control strategy of a PMSM in an electric vehicle is the PI-based field-oriented control (FOC) (see Fig. 9). FOC algorithm allows to control the d- and q-axis current of the machine independently. The provided torque is either a function of the q-axis current for surface-mounted PMSM (first part of (12)) or a function of both id and iq for interior-mounted PMSM (the whole equation (12)). However, for both PMSM types, no torque will be provided, as long as iq is controlled to zero. Tem =

3 3 pΨP M iq + p(Ld − Lq )id iq 2 2

(12)

This fact allows using the motor as a flexible load for the battery by controlling iq to zero and id to some optimal pattern for frequency response calculation. The only restriction is that this diagnostic operation can be performed only when the EV is at standstill. Assuming rotational speed of the motor ωm as well as the q-axis current are zero, the equivalent circuit diagram of the drive train can be simplified as it is shown in Fig. 10. Consequently, when id is controlled to a specific value, within one PWM period Ts , inverter (represented by a switch in Fig. 10) provides an appropriate voltage vector for t = dTs , where d is the duty cycle, and subsequently switched off for t = (1 − d)Ts . As result, id increases when the switch/inverter is on and slowly decreases (flowing through the freewheeling diode of the inverter) when the switch is off. From the battery side, when the switch is on, ibat flows directly to the motor (supported by capacitor current) and charges the capacitor when the switch is

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Fig. 10 Equivalent circuit diagram of the EV drive train, assuming ωm = 0 and iq = 0

Fig. 11 D-axis current, controlled to a fixed value with appropriate battery current over two PWM periods

off (see Fig. 11). The mean value of ibat over one PWM period can be consequently calculated from the mean value of id as follows Ibat = d · Id (Fig. 12):

7 Conclusions This paper has demonstrated an on-board battery impedance measurement system that uses existing power electronics as the excitation source to measure impedance accurately at a range of frequencies of interest. The excitation signal is an impulse like one. This fact ensures the equal amount of signal energy in the entire frequency

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Fig. 12 (Top) id controlled to a sine with corresponding ibat , (middle) magnitude spectrum of id and ibat from top, (bottom) magnitude spectrum of the corresponding dc-link voltage

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range and enhances the quality of impedance measurement at the high frequencies. The total amount of discharge is very small, and the test can be fulfilled within a short time period. It prevents the changes of a battery condition during tests and spreading the spectrum of open circuit voltage which can otherwise lead to false spectroscopy results. Since the spectrum of current has the same value in an entire range and is known in advance, the spectrum of an impedance is the same as the spectrum of voltage and can be built using Fourier transform of battery voltage only. Finally an implementation approach for an on-board impedance spectroscopy using a conventional closed loop controlled PMSM was proposed.

References 1. E. Barsoukov, J.R. Macdonald, Impedance Spectroscopy: Theory, Experiment, and Applications, 2nd edn. (Wiley-Interscience, Hoboken, 2005) 2. D.I. Stroe, M. Swierczynski, A.I. Stan, V. Knap, R. Teodorescu, S.J. Andreasen, Diagnosis of Lithium-Ion Batteries State-of-Health Based on Electrochemical Impedance Spectroscopy Technique: IEEE Energy Conversion Congress and Exposition (ECCE) 2014, Pittsburgh, 14– 18 Sept 2014 (IEEE, Piscataway, 2014) [Online]. Available: http://ieeexplore.ieee.org/servlet/ opac?punumber=6926643 3. P.B. Alfred Waligo, A Comparison of the Different Broadband Impedance Measurement Techniques for Lithium-Ion Batteries (IEEE, Piscataway, 2016) [Online]. Available: http:// ieeexplore.ieee.org/servlet/opac?punumber=7835398 4. O. Kanoun, U. Troltzsch, Application of parameter extraction techniques for impedance spectroscopy, in 2005 IEEE Instrumentationand Measurement Technology Conference Proceedings, vol. 3, May 2005, pp. 2281–2286 5. C. Pastor-Fernández, K. Uddin, G.H. Chouchelamane, W.D. Widanage, J. Marco, A comparison between electrochemical impedance spectroscopy and incremental capacity-differential voltage as li-ion diagnostic techniques to identify and quantify the effects of degradation modes within battery management systems. J. Power Sources 360, 301–318 (2017) 6. A. Christensen, A. Adebusuyi, Using on-board electrochemical impedance spectroscopy in battery management systems. World Electr. Veh. J. 6(3), 793–799 (2013) 7. R.A. Nazer, V. Cattin, P. Granjon, M. Montaru, M. Ranieri, V. Heiries, Classical eis and square pattern signals comparison based on a well-known reference impedance, in World Electric Vehicle Symposium and Exposition (EVS 27), 2013 (IEEE, Piscataway, 2013), pp. 1–7 8. M. Einhorn, V. Conte, C. Kral, J. Fleig, Comparison of electrical battery models using a numerically optimized parameterization method, in IEEE Vehicle Power and Propulsion Conference, Sept 2011, pp. 1–7 9. A. Jossen, Fundamentals of battery dynamics. J. Power Sources 154(2), 530–538 (2006). Selected papers from the Ninth Ulm Electrochemical Days [Online]. Available: http://www. sciencedirect.com/science/article/pii/S0378775305014321 10. A. Barai, K. Uddin, W.D. Widanage, A. McGordon, P. Jennings, A study of the influence of measurement timescale on internal resistance characterisation methodologies for lithium-ion cells. Sci. Rep. 8(1), 21 (2018) 11. T. Saar, O. Märtens, M. Reidla, A. Ronk, Chirp-based impedance spectroscopy of piezosensors, in 2010 12th Biennial Baltic Electronics Conference, Oct 2010, pp. 339–342

An Approach to the Cell-Level Diagnosis of Malfunctioning Events in PV Panels from Aerial Thermal Maps Antonio Pio Catalano, Pierluigi Guerriero, Vincenzo d’Alessandro, Lorenzo Codecasa, and Santolo Daliento

Abstract This chapter presents an innovative approach to the cell-level diagnosis of malfunctioning events in photovoltaic (PV) panels from the processing of temperature maps taken from low-flying drones. The application of a detailed power balance equation allows deriving the electrical power generated or dissipated by each cell with a reasonable degree of accuracy. The method is tested by emulating the experimental temperature maps through accurate 3-D thermal simulations of the panel for some cases of interest.

1 Introduction It is well recognized that malfunctioning PV panels can dramatically affect both energy revenues and reliability of PV plants, the most severe case being the risk of fire related to the onset of localized overheating (hot spot) that may occur when individual cells are damaged or shaded [1, 2]. However, the identification of faults in PV plants is a challenging issue. Numerous diagnosis approaches can be found in the recent literature [3], which can be roughly classified in terms of granularity: costly high-granularity techniques exploit dedicated sensing circuits to be mounted on each PV panel [4, 5]; cheaper low-granularity methods use systems applied to the monitoring of strings, groups of strings [6, 7], or even of the entire PV plant [8]. A reliable trade-off between granularity and cost can be achieved by means of aerial thermal maps [9–13]. This strategy is based on the widely accepted opinion that the temperature is deeply related to the health status of the cells and is

A. P. Catalano · P. Guerriero () · V. d’Alessandro · S. Daliento Department of Electrical Engineering and Information Technology, University Federico II, Naples, Italy e-mail: [email protected]; [email protected]; [email protected]; [email protected] L. Codecasa Department of Electronics, Information, and Bioengineering, Politecnico di Milano, Milan, Italy e-mail: [email protected] © Springer Nature Switzerland AG 2020 W. Zamboni, G. Petrone (eds.), ELECTRIMACS 2019, Lecture Notes in Electrical Engineering 697, https://doi.org/10.1007/978-3-030-56970-9_8

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increasingly adopted, thanks to the pervasive diffusion of unmanned aerial vehicles (drones). However, it has been shown that the interpretation of thermal maps is far from trivial: simplified analyses can indeed lead to a large overestimation of malfunctioning elements. The aim of this chapter is to present a reliable diagnosis approach based on the power balance equation. Differently from prior work [10], this technique is adopted at cell level to estimate the electrical power generated or dissipated by each cell of a panel from aerial thermal maps – which is important to judge the maintenance convenience. The accuracy of the method is verified by emulating a realistic temperature field over the panel through exceptionally detailed 3-D numerical simulations; this procedure relies on the fact that – contrary to experimental maps – in this case, the powers to be assessed are known since they represent the input for thermal simulations.

2 PV Panel Under Test The panel to be thermally simulated to test the approach (Sect. 5) is a real module [14] mounted with a tilt angle β = 30◦ and oriented with an azimuth angle (positive from south to west) γ = –16◦ on the rooftop of the Department of Electrical Engineering and Information Technology in Naples, Italy (latitude φ = 40.84◦ and longitude λ = 14.25◦ ). The panel comprises 40 individual series-connected monocrystalline silicon cells gathered into two subpanels, each equipped with a bypass diode. The width, height, and thickness are W = 555 mm, H = 719 mm (including the lateral aluminum frame), and t = 34 mm, respectively. The 0.15 mmthick cells are encapsulated in a 0.95 mm-thick layer of ethylene vinyl acetate (EVA) needed to affix them to the 3 mm-thick glass cover plate and the back material, as well as to provide electrical isolation. The 1 mm-thick Tedlar backsheet is needed to prevent the entrance of water/steam. The cell area Acell was estimated to be 72.8 cm2 . Under standard test conditions (solar irradiance of 1000 W/m2 , 1.5 air mass, and cell temperature of 25◦ C), the voltage and current at the maximum power point (MPP) are 20.2 V and 2.48 A, respectively; the open-circuit voltage is 24.6 V; and the short-circuit current is 2.81 A, as reported in the datasheet. The structure of the panel with numbered cells is sketched in Fig. 1.

3 Thermal Model The power PG dissipated by each cell due to irradiance, needed for thermal simulations, was calculated by choosing June 14 (165th day of the year, under daylight saving time) at 12:00 AM as testing day/hour. The solar geography parameters were evaluated by resorting to well-known clear-sky formulations available in the literature (e.g., [15]) and are solar declination δ = 23.27◦ , true local time

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Fig. 1 Schematic representation of the panel with cell numbering

TLT = 10:57 AM, solar altitude α = 68◦ , and incidence angle of the solar rays θ = 13.65◦ (low, and thus good in terms of production). The beam (direct) and diffuse (indirect) irradiances Gb = 774.34 W/m2 and Gd = 231.92 W/m2 were calculated through the approach in [16] from the horizontal values Gbh = 739 W/m2 and Gdh = 230 W/m2 at 12:00 AM for a typical clear-sky day of June in Naples, available on the PVGIS website [17]. This implies that the total irradiance G = Gb + Gd hitting the glass is 1006.26 W/m2 . On the other hand, 5% of the irradiance is reflected (the tempered glass has a reflectivity of 0.05) so that the effective irradiance heating the cell is 0.95·G = 956 W/m2 , and the resulting PG is given by 956·Acell = 6.96 W. The absorbance of glass and EVA was neglected. The ambient temperature Tamb was also taken from [17] and amounts to 25.9◦ C. A classical relation was used for a first-order estimation of the front temperature (assumed uniform) under sunny conditions, that is, Tf ront,estimated = Tamb +

G GnomT

  ◦ · TN OCT − 20

(1)

where TNOCT = 44.4◦ C is the so-called Normal Operating Cell Temperature (NOCT) measured under open-circuit conditions at ambient temperature equal to

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A. P. Catalano et al. Table 1 Material parameters αair νair cair μair kair g εfront εback σ kglass kEVA kSi kTedlar kAl

Expansion coefficient of the air [K−1 ] Kinematic viscosity of the air [m2 /s] Specific heat capacity of the air [J/KgK] Dynamic viscosity of the air [Kg/ms] Thermal conductivity of the air [W/mK] Gravity acceleration due to Earth [m/s2 ] Emissivity of the front (glass) Emissivity of the back (Tedlar) Stephan-Boltzmann constant [W/m2 K4 ] Thermal conductivity of the glass [W/mK] Thermal conductivity of the EVA [W/mK] Thermal conductivity of silicon [W/mK] Thermal conductivity of the Tedlar [W/mK] Thermal conductivity of aluminum [W/mK]

3.4×10−3 1.557×10−5 1006.3 1.8444×10−5 2.6×10−2 9.8 0.91 [18] 0.85 [19] 5.67×10−8 1.8 [20, 21] 0.35 [20, 21] 148 [20, 21] 0.15 [20] 237

20◦ C, G = GnomT = 800 W/m2 , and wind speed of 1 m/s; Tfront,estimated was calculated to be 56.59◦ C from (1). As far as the boundary conditions (BCs) are concerned, free convection, windinduced (forced) convection, and radiant heat emitted toward the sky are considered on the panel front. Free convection and radiant heat emitted toward the ground are taken into account on the panel back, which is shielded from the wind. The side surfaces can be reasonably considered adiabatic due to their small dimensions with respect to front and back surfaces. Table 1 reports the material parameters used for the evaluation of BCs, as well as for thermal simulations (see Sect. 4).

3.1 Free Convection The free convection – which becomes significant in days with little or no wind – is determined with the following approach. The (dimensionless) Prandtl number of the air is given by Prair =

cair · μair kair

(2)

which leads to Prair = 0.7139. The (dimensionless) Grashof number on the front is given by Grf ront =

    ◦ g · cos 90 − β · αair · L3 · Tf ront − Tamb 2 νair

(3)

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L is the characteristic length of the panel, which coincides with the height H = 0.719 m only if the panel is vertical (β = 90◦ ) [22]. In (3), the following empirical strategy is adopted to account for the actual tilt angle β = 30◦ : L is set equal to H, and g is multiplied by the correction term cos(90◦ –β) [21, 23]. The nonlinear nature of the free convection was disregarded by assuming Tfront equal to the uniform value Tfront,estimated = 56.59◦ C in (3), whence Grfront = 7.84×108 . The (dimensionless) Nusselt numbers are given by [21, 23]   1  1 Grf ront · Prair 3 − (Grcr · Prair ) 3  ◦ ! 1 = 0.56 · Grcr · Prair · cos 90 − β 4

Nuf ront = Nuback + 0.14 · Nuback

(4)

where Grcr is the critical Grashof number, equal to 108 for 90◦ –β = 60◦ [21, 23]. From (4), it is found that Nufront = 100.57 and Nuback = 43.28. Finally, the heat transfer coefficients dictated by free convection are determined by (e.g., [21]) hf ront,f ree =

kair · Nuf ront kair · Nuback hback,f ree = L L

(5)

which provide 3.637 and 1.565 W/m2 K, respectively.

3.2 Forced Convection The wind-induced convection on the exposed panel front is modeled as suggested in [24], where the heat transfer coefficient hfront,forced depends on wind speed vw [m/s] and incidence angle of the wind θw (angle with respect to the normal to the panel). More specifically, (i) hfront,forced increases with vw for a given θw ; if vw is fixed, hfront,forced (ii) is higher when the panel is windward (0◦ ≤θw ≤90◦ ) and (iii) grows as θw spans from 0◦ (wind orthogonal to the panel) to 90◦ (parallel), where the maximum value is reached; and (iv) when the panel is leeward (θw >90◦ ), there is a lower cooling influence due to wind separation and reattachment. For some angles θw of interest, hfront,forced is given by  hf ront,f orced θw  hf ront,f orced θw  hf ront,f orced θw  hf ront,f orced θw  hf ront,f orced θw

◦ = 0 = 2.4 · vw + 7.9 ◦ = 45 = 2.6 · vw + 7.9 ◦ = 90 = 3.3 · vw + 7.5 ◦ = 135 = 2.2 · vw + 7.9 ◦ = 180 = 1.3 · vw + 8.3

(6)

On June 14, 2017 at 12:00 AM in Naples, the average wind velocity was estimated to be 1.5 m/s [25], and θw was assumed to be 0◦ ; as a result, hfront,forced = 11.5 W/m2 K.

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The aggregate heat transfer coefficient from the front surface of the panel is derived from the combination of the free and forced convection as [21, 26] hf ront =

" 3

h3f ront,f orced + h3f ront,f ree

(7)

giving rise to hfront = 11.62 W/m2 K. As previously mentioned, only free convection is assumed to take place on the panel back (e.g., [21]); as a result, hback = hback,f ree

(8)

which is equal to 1.565 W/m2 K.

3.3 Radiative Boundary Condition The power densities [W/m2 ] exchanged between (i) front surface and sky and (ii) back surface and ground due to radiation are accounted for through the StephanBoltzmann law (e.g., [15, 21, 27–30])   4 qf ront,rad = εf ront · Ff ront−sky · σ · Tf4ront − Tsky   4 4 qback,rad = εback · Fback−ground · σ · Tback − Tground

(9)

Ffront-sky and Fback-ground are the front-sky and background view factors, expressed as Ff ront−sky

  ◦ 1 − cos 180 − β 1 + cos β Fback−ground = = 2 2

(10)

both equal to 0.933 for β = 30◦ (the panel front “sees” very well the sky, and the back “sees” very well the ground). The radiation components front-ground and back-sky are neglected since the corresponding view factors are very small (0.067). The temperatures Tsky and Tground are assumed to coincide with Tamb . It is noteworthy that Tfront and Tback in (9) are the space-dependent outcome of the thermal simulations (Sect. 4).

4 Thermal Simulations Nonlinear 3-D thermal simulations were performed in the environment of the COMSOL software package, which relies on the finite-element method [31]. The

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mesh involves 1.8 M elements, that is, tetrahedra. Figure 2 reports the modeled panel, as obtained by removing the glass and the top EVA layer with the aim to show the cells. The BCs described in Sect. 3 were applied. Each PV cell was associated to a heat source (HS) geometrically coinciding with it. Circuit simulations [32] were exploited to determine the electrical powers to sum to the irradiance-induced counterparts so as to define the total HS powers for the thermal analysis. In particular, this evaluation was performed (i) by reducing the shunt resistance in the electrical circuit model to emulate a damaged cell and (ii) by properly lowering PG with respect to 6.96 W for a shaded cell. The thermal conductivity of silicon kSi was considered temperature-dependent according to the power law # kSi (T ) = kSi (T0 ) ·

◦

T + 273 ◦ T0 + 273

$−1.33 (11)

where T0 +273◦ C (T0 = 27◦ C) is the reference temperature in COMSOL. All other material parameters were instead assumed to be temperature-insensitive. The typical CPU time for a single simulation was found to span between 30 and 40 min on an Intel Core i7-5960X PC equipped with a 64 GB RAM. Fig. 2 (a) Geometry and (b) mesh of the panel under test in the COMSOL environment as obtained by removing the tempered glass and the top EVA layer for illustrative purposes

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5 Cell-Level Power Estimation Approach The proposed approach for the identification of the electrical powers of the individual cells relies on the following balance equation applied to the i-th cell: 0.95 · Gi · Acell = Pi +

ΔTi + Pout,i ki

(12)

where the input power corresponding to the effective irradiance 0.95·Gi impinging on the cell area Acell is compensated by three output components, namely, (i) the electrical power Pi = Vi ·Ii (positive if the cell generates, negative if the cell dissipates), (ii) the thermal power flowing vertically toward the ambient Ti /ki (Ti = Ti -Tamb , Ti being the cell temperature, estimated as an average of the temperature over the projection of the cell onto the front surface Tfront,i ), and (iii) the thermal power Pout,i flowing toward the neighboring cells. Due to the low kEVA , the lateral heat propagation is assumed to occur mainly through the glass plate; as a result, Pout,i can be evaluated from the gradient of the Tfront field as follows: % Pout,i = kglass · tglass ·

∇Tf ront · nˆ dl

(13)

Ei

where Ei is the lateral boundary of the cell, nˆ is the outward-pointing unit normal vector, and tglass = 3 mm is the thickness of the glass. Equations (12) and (13) can be exploited to assess the Pi distribution for any malfunctioning event on the basis of the mere knowledge of the temperature field Tfront , as determined by low-altitude aerial thermal images processed by edge detection filters. To this purpose, a preliminary calibration procedure has to be performed to derive the ki [K/W] map from (12) and (13) for an undamaged and sunny panel (hereinafter referred to as normal conditions), the Pi of which can be reasonably estimated from datasheet parameters. It must be remarked that the panel(s) under normal conditions enjoys an almost uniform Tfront and thus can be straightforwardly identified from the thermal images. Here, the accuracy of this strategy is verified by emulating the experimental Tfront maps through 3-D nonlinear FEM simulations performed as described in Sect. 4. In this case, the Pi map of the malfunctioning condition (to be determined by the technique) is actually known since it is given as an input to the thermal model of the panel. Prior to applying the approach, the numerical Tfront obtained over the tetrahedral grid ( 6000 top surface points) was turned into a pixel matrix (i.e., the typical camera outcome) by an in-house routine. More specifically, 1.5×1.5 mm2 pixels were considered, which are compatible with an aerial map taken by a FLIR A65 camera (with horizontal and vertical fields of view of 1.09 m and 0.87 m, respectively) from a 10 m height. The calibration procedure was carried out on a panel under normal conditions by assuming all the cells operating at the MPP, which corresponds to an evenly shared

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Fig. 3 Simulated Tfront obtained under normal conditions at the MPP: (left) COMSOL outcome; (right) average cell temperatures over the projections of the cells onto the front surface Fig. 4 ki [K/W] values computed from the calibration process

Pi = 1.188 W, estimated by a simple processing of the peak power Pmax through its temperature coefficient (both taken from datasheet) and the actual irradiance G. Figure 3 depicts the Tfront field and the average temperatures over the projections of the cells onto the glass surface, while Fig. 4 shows the computed ki map.

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Fig. 5 Simulated Tfront obtained in the case of damaged cell #3 at the MPP: (left) COMSOL outcome; (right) average cell temperatures over the projections of the cells onto the front surface

5.1 Panel with a Shunted Cell Once the ki values were determined, the approach was applied to identify the Pi distribution in a panel with a single damaged cell. The electrical power P3 to be provided to COMSOL at the MPP was estimated to be 35 mW. The resulting Tfront is shown in Fig. 5, which evidences the slightly higher temperature of cell #3 (see Fig. 1 for the cell numbering) dictated by the decrease in power production. Figure 6 illustrates the comparison between the known Pi map applied to COMSOL for the thermal simulations (shown as a reference) and the Pi map assessed by the proposed approach. It can be inferred that (i) the Pi of the normal (unbroken) cells was correctly estimated, and (ii) the dramatic P3 reduction with respect to the normal cells was predicted, although the exact value was not determined with high accuracy. This witnesses that the presented strategy can be successfully used to identify a localized fault in a panel.

5.2 Panel with a Shaded Cell In this case, cell #3 was assumed to be 20% shaded, that is, G3 = 805 W/m2 (instead of 1006.26 W/m2 ), which pushes the subpanel to bypass; under this condition, all the cells belonging to the bypassed subpanel are estimated to operate close to the MPP (Pi = 1.148 W), whereas cell #3 behaves like a load and suffers from P3 = –23.6 W, that is, it dissipates electrical power. The corresponding Tfront map is shown in Fig. 7; it is found that cell #3 is subject to hot spot (the average Tfront,3 reaches 109.1◦ C), and also the adjacent cells (mainly #2 and #4) heat up due to thermal coupling.

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Fig. 6 Electrical powers [W] of the cells for the case of damaged cell #3: (left) values fed to COMSOL for thermal simulations; (right) values determined with the proposed approach

Fig. 7 Simulated Tfront obtained in the case of partially shaded cell #3 at the MPP: (left) COMSOL outcome; (right) average cell temperatures over the projections of the cells onto the front surface

Figure 8 compares the known Pi distribution fed to COMSOL with that evaluated by the proposed technique. In this case, power P3 is estimated with a relative error of 18% primarily induced by the disregarded nonlinear nature of the radiative BC (accounted for by COMSOL), which also adversely affects the prediction of Tfront,2 and Tfront,4 . Nevertheless, a clear overview of the actual panel operation is provided:

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Fig. 8 Electrical powers [W] of the cells for the case of partially shaded cell #3: (left) values provided to COMSOL for thermal simulations; (right) values predicted with the proposed approach

for instance, it can be deduced that the subpanel is driven to bypass and thus does not limit the string current. Hence, differently from traditional diagnosis techniques, the proposed approach allows also favoring a fairly accurate estimation of the power losses in a panel, as well as the related effect on the whole plant. It must be remarked that in this case, the approach was applied by assuming that G3 is known; the Gi associated to all cells can in principle be experimentally obtained by processing visual images with edge detection filters. In the simplified case of an irradiance level considered uniform and equal to the value G = 1006.26 W/m2 computed in Sect. 3, the power loss on cell #3 would have been underestimated (P3 = –17.9 W), without drastically jeopardizing the usefulness of the approach.

6 Conclusions In this chapter, an innovative high-granularity approach to the diagnosis of PV panels based on aerial thermal images has been presented. The method relies on a power balance equation at cell level and provides the electrical power corresponding to each cell with a fairly good degree of accuracy. As a result, useful information about the health status of individual panels can be gained, and the impact of faults on the energy yield of the whole plant can be estimated, thus allowing a smart definition of the maintenance strategy. The approach was validated for the cases of a damaged

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cell and a partially shaded cell by emulating the corresponding aerial temperature maps through extremely accurate 3-D thermal simulations.

References 1. E. Kaplani, Degradation effects in sc-Si PV modules subjected to natural and induced ageing after several years of field operation. J. Eng. Sci. Technol. Rev. 5(4), 18–23 (2012) 2. M. Simon, E.L. Meyer, Detection and analysis of hot-spot formation in solar cells. Solar Energy Mater. Solar Cells 94(2), 106–113 (2010) 3. A. Livera, M. Theristis, G. Makrides, G.E. Georghiou, Recent advances in failure diagnosis techniques based on performance data analysis for grid-connected photovoltaic systems. Renew. Energy 133, 126–143 (2019) 4. F.J. Sánchez-Pacheco, P.J. Sotorrío-Ruiz, J.R. Heredia-Larrubia, F. Pérez-Hidalgo, M. Sidrach De Cardona, PLC-based PV plants smart monitoring system: field measurements and uncertainty estimation. IEEE Trans. Instr. Measure. 63(9), 2215–2222 (2014) 5. P. Guerriero, F. Di Napoli, G. Vallone, V. d’Alessandro, S. Daliento, Monitoring and diagnostics of PV plants by a wireless self-powered sensor for individual panels. IEEE J. Photovolt. 6(1), 286–294 (2016) 6. S. Vergura, G. Acciani, V. Amoruso, G.E. Patrono, F. Vacca, Descriptive and inferential statistics for supervising and monitoring the operation of PV plants. IEEE Trans. Ind. Electron. 56(11), 4456–4464 (2009) 7. P. Guerriero, L. Piegari, R. Rizzo, S. Daliento, Mismatch based diagnosis of PV fields relying on monitored string currents. Int. J. Photoenergy 2017(2), 1–10 (2017) 8. A. Drews, A.C. de Keizer, H.G. Beyer, E. Lorenz, J. Betcke, W.G.J.H.M. van Sark, et al., Monitoring and remote failure detection of grid-connected PV systems based on satellite observations. Solar Energy 81(4), 548–564 (2007) 9. P. Bellezza Quater, F. Grimaccia, S. Leva, M. Mussetta, M. Aghaei, Light Unmanned Aerial Vehicles (UAVs) for cooperative inspection of PV plants. IEEE J. Photovolt. 4(4), 1107–1113 (2014) 10. Y. Hu, W. Cao, J. Ma, S.J. Finney, D. Li, Identifying PV module mismatch faults by a thermography-based temperature distribution analysis. IEEE Trans. Device Mater. Reliab. 14(4), 951–960 (2014) 11. J.A. Tsanakas, D. Chrysostomou, P.N. Botsaris, A. Gasteratos, Fault diagnosis of photovoltaic modules through image processing and Canny edge detection on field thermographic measurements. Int. J. Sustain. Energy 34(6), 351–372 (2015) 12. S. Vergura, M. Colaprico, M.F. de Ruvo, F. Marino, A quantitative and computer-aided thermography-based diagnostics for PV devices—part II: platform and results. IEEE J. Photovolt. 7(1), 237–243 (2017) 13. S. Vergura, F. Marino, Quantitative and computer-aided thermography-based diagnostics for PV devices: part I—framework. IEEE J. Photovolt. 7(3), 822–827 (2017) 14. http://www.etsolar.com.ar/folletos/ET-M54050(50w).pdf 15. J.A. Duffie, W.A. Beckman, Solar Engineering of Thermal Processes (John Wiley & Sons, Hoboken, 1980) 16. V. d’Alessandro, F. Di Napoli, P. Guerriero, S. Daliento, An automated high-granularity tool for a fast evaluation of the yield of PV plants accounting for shading effects. Renewable Energy 83, 294–304 (2015) 17. http://re.jrc.ec.europa.eu/pvgis/ 18. G. Notton, C. Cristofari, M. Mattei, P. Poggi, Modelling of a double-glass photovoltaic module using finite differences. Appl. Ther. Eng. 25(17–18), 2854–2877 (2005)

102

A. P. Catalano et al.

19. M.D. Bazilian, H. Kamalanathan, D.K. Prasad, Thermographic analysis of a building integrated photovoltaic system. Renewable Energy 26(3), 449–461 (2002) 20. I.-R. Caluianu, F. B˘alt˘aret, u, Thermal modelling of a photovoltaic module under variable free convection conditions. Appl. Therm. Eng. 33–34, 86–91 (2012) 21. S. Armstrong, W.G. Hurley, A thermal model for photovoltaic panels under varying atmospheric conditions. Appl. Ther. Eng. 30(11–12), 1488–1495 (2010) 22. V.S. Arpaci, A. Selamet, S.-H. Kao, Introduction to Heat Transfer (Prentice Hall, Inc, Englewood Cliffs, 2000), pp. 314–315 23. Y. Jaluria, in Natural Convection, Chapter 7, p. 562 of Heat Transfer Handbook, ed. by A. Bejan, A. D. Kraus, (John Wiley & Sons, Inc., New York, 2003) 24. S. Sharples, P.S. Charlesworth, Full-scale measurements of wind-induced convective heat transfer from a roof-mounted flat plate solar collector. Solar Energy 62(2), 69–77 (1998) 25. http://www.windfinder.com/ 26. S.W. Churchill, A comprehensive correlating equation for laminar, assisting, forced and free convection. J. Am. Inst. Chem. Eng. 23(1), 10–16 (1977) 27. E. Kaplani, S. Kaplanis, Thermal modeling and experimental assessment of the dependence of PV module temperature on wind velocity and direction, module orientation and inclination. Solar Energy 107, 443–460 (2014) 28. D. Torres-Lobera, S. Valkealahti, Inclusive dynamic thermal and electrical simulation model of solar PV systems under varying atmospheric conditions. Solar Energy 105, 632–647 (2014) 29. M. Abdolzadeh, T. Zarei, Optical and thermal modeling of a photovoltaic module and experimental evaluation of the modeling performance. Environ. Progr. Sustain. Energy 36(1), 277–293 (2017) 30. L. Migliorini, L. Molinaroli, R. Simonetti, G. Manzolini, Development and experimental validation of a comprehensive thermoelectric dynamic model of photovoltaic modules. Solar Energy 144, 489–501 (2017) 31. COMSOL Multiphysics, User’s Guide, Release 5.2A, 2016 32. V. d’Alessandro, A. Magnani, L. Codecasa, F. Di Napoli, P. Guerriero, S. Daliento, Dynamic electrothermal simulation of photovoltaic plants, in Proceedings of IEEE International Conference on Clean Electrical Power (ICCEP), 2015, pp. 682–688

ECM-Based Algorithm for On-Board PEMFCs Diagnosis Ennio Andrea Adinolfi, Marco Gallo, Pierpaolo Polverino, Davide Beretta, Samuel Simon Araya, and Cesare Pianese

Abstract This work aims at implementing an advanced monitoring and diagnostic tool for μ-CHP PEM fuel cell systems running on-board. Such a tool is able to determine the FC current status (condition monitoring) to support stack failures detection. Six faults are investigated: fuel starvation, air starvation, flooding, drying, CO contamination and sulphur poisoning. The developed methodology is based on the use of the Electrochemical Impedance Spectroscopy (EIS) measurements and Equivalent Circuit Model (ECM) approach to infer on them. Experimental data from HEALTH-CODE project are exploited for training and to finally validate the modelbased algorithm. The fault detection and isolation algorithm, which works on the relevant features extracted from EIS data, is herein reported. Eventually, the offline validation results of the algorithm are presented.

1 Introduction Real-time State-of-Health (SoH) assessment of fuel cells is a challenging point for the deployment of fuel cells market [1]. Fuel cell performance is influenced by several physical phenomena. Indeed, abnormal operating conditions may induce system faults and trigger degradation mechanisms. These critical behaviours lead the research activities towards advanced monitoring and diagnostic techniques to ensure optimal system management and improve performance and durability [2–4].

E. A. Adinolfi () · M. Gallo · P. Polverino · C. Pianese Department of Industrial Engineering, University of Salerno, Fisciano, Salerno, Italy e-mail: [email protected]; [email protected]; [email protected]; [email protected] D. Beretta European Institute for Energy Research, Karlsruhe, Germany e-mail: [email protected] S. S. Araya Department of Energy Technology, Aalborg University, Aalborg, Denmark e-mail: [email protected] © Springer Nature Switzerland AG 2020 W. Zamboni, G. Petrone (eds.), ELECTRIMACS 2019, Lecture Notes in Electrical Engineering 697, https://doi.org/10.1007/978-3-030-56970-9_9

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Table 1 PEMFC system specification Ballard Power Systems Europe μ-CHP (former Dantherm Power) Commercial name μ-CHP LSN1 Application Cogeneration of heat and electricity Anode gas Reformate Cathode gas Air Efficiency 32% Auxiliary devices Reformer, heat integration, DC/AC inverter

An accurate diagnostic tool, with a reduced computational burden, should be capable of discerning a plurality of faults before the occurrence of a critical failure. Generally, for online diagnostics, grey- and black-box models are usually adopted [5]. The hereby proposed grey-box model couples a non-invasive monitoring technique, based on Electrochemical Impedance Spectroscopy (EIS), and an Equivalent Circuit Model (ECM) approach to derive significant metrics [6]. The observed analytical, coupled with a heuristic knowledge, are the basis for a reliable fault detection and isolation (FDI) design and application. The presented work describes the methodology behind the metrics extraction from EIS acquisition and the related inference for the SoH assessment. The FDI procedure is thus tested and validated against experimental data acquired on Ballard Power Systems Europe (BPSE) μ-CHP PEMFC system (see Table 1) in the framework of EU-funded FCH-JU project HEALTH-CODE.

2 Experimental Data Set Different faults can affect PEMFC during its normal functioning such as air starvation, fuel starvation, sulphur poisoning, carbon build-up on cell, cell breaks/crossover leakages, delamination and abrupt major change in fuel composition (reformer malfunction or bad fuel quality). The faults considered in this paper to investigate the change in the EIS spectra are fuel starvation, air starvation, flooding, drying, CO contamination and sulphur poisoning. The PEM stacks, supplied by BPSE, were installed on test benches and run at the EIFER and Aalborg University laboratories. The stacks were fed by air and reformed gases. The measurements were performed at three current levels (15, 25, 40 A) at both stack and single-cell levels. The frequency points of EIS acquisition are in the range of 0.5–5000 Hz. Among the experimental database of HEALTH-CODE project, the EIS spectra considered for this study relate to 40 A (nominal set point of BPSE system) at stack level. The number of available spectra (see Table 2) is 76, of which almost 2/3 is used for training (56) and 1/3 for validation (20). For a reliable diagnostic methodology, nominal conditions are used as reference. Thus, the first mandatory step is to clearly identify the EIS geometry under unfaulty

ECM-Based Algorithm for On-Board PEMFCs Diagnosis Table 2 Data set of EIS spectra used for the training and validation phases of the diagnostic approach

Operating conditions NC – nominal condition FS – fuel starvation AS – air starvation DR – drying FL – flooding CO – CO contamination SP – sulphur poisoning Total

105 Training 3 5 4 4 6 17 17 56

Validation – 3 2 2 2 7 4 20

Fig. 1 EIS spectra in nominal conditions acquired at EIFER

functioning points. The three EIS spectra in nominal conditions are presented in Fig. 1. The second step is to record and infer on faulty conditions, suitably induced in lab tests. The comparison of these latter with respect to the reference conditions provides useful information on the deviation of the characteristic features that the algorithm uses. The EIS spectra in faulty conditions are presented in the following pictures. Since the detection and isolation of poisoning faults is barely presented in literature, the data set was built in the way to mostly focus on the CO and sulphur poisoning conditions, as one can see in Table 2 and Fig. 2.

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a)

b)

c)

d)

e)

f)

Fig. 2 Experimental data set: (a) fuel starvation (decrease of stoichiometric λH2 ), (b) air starvation (decrease of stoichiometric λO2 ), (c) drying for anode side and cathode side (decrease of RH%), (d) flooding for anode side and cathode side (increase of RH%), (e) CO contamination (4-8-12-80120-160 ppm) and f) sulphur poisoning (4-6-8-10-12 ppm). Spectra acquired at EIFER (a-b-c-d-e) and AAU (e-f)

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Fig. 3 Schematic representation of diagnostic algorithm design (offline) and online application (on-board)

3 The Diagnostic Tool The on-board FDI application requires a preliminary offline training and validation phase which involves three main steps as represented in Fig. 3. The monitoring phase consists in identifying a proper circuital model whose parameters (i.e., metrics) are extracted under both nominal and faulty conditions. The statistical distribution of the reference values is exploited to define the thresholds conceived as the boundary of nominal variation region of the ECM parameters. The final step is the definition and population of a Fault Signature Matrix (FSM) which links the fault occurrence with the deviation of the parameters (i.e., symptoms) with respect to the defined threshold [7]. The online algorithm application is schematized in Fig. 4. It involves three steps. The first one consists in the parameter extraction from acquired EIS spectra on the running system. Then, the parameters are compared to the threshold defined offline (fault detection). If a deviation arises, the related symptoms is activated and is set to 1 (value=1); otherwise, it is set to 0 (value=0). The collection of the symptoms defines the fault pattern. The matching of this pattern with a unique row of the FSM isolates the fault (fault isolation) and likely locates it (anode or cathode side). So far, the on-board diagnostic tool is under testing. This paper aims at describing the general procedure aiming at extracting significative parameters and performing the detection and isolation of the faults. Offline diagnostic results are presented hereafter.

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Change detecon check with nominal behaviour 0.5 Rm

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Fig. 4 Qualitative example of on-board diagnostic algorithm operation

3.1 Equivalent Circuit Model The model-based algorithm has been designed for both PEM and Solid Oxide Fuel Cells (SOFC) technologies. The algorithm relies on proprietary patented technique, which allows high generalizability and fast fitting performance [8]. Based on the patent, a geometrical identification is performed to identify the proper initial condition of the optimization algorithm. This algorithm recognizes significant EIS points, such as the total resistance Rtot and the ohmic one RΩ (i.e., the x-axis intercepts on the Nyquist plot, Rtot >RΩ ), to roughly fit the spectrum. Then, a minimization algorithm is applied with a cost function based on the difference between both the measured real and imaginary part of the impedance and the one simulated by ECM. A suitable equivalent circuit represents the electrochemical behaviour of the stack. The goal is to properly identify the parameters of such equivalent circuit in order to use them as characteristic features on which infer for SoH assessment. So the output of the algorithm is the extraction of ECM parameters or a combination of them that can be directly associated to the specific operating condition at which the EIS spectrum was measured. The Equivalent Circuit Model here proposed is presented in Fig. 5. It is worth remarking that for the pursuit of the flexibility of the algorithm on different technologies (i.e., PEM and SOFC), some elements can be activated or deactivated as needed. The blue elements are enabled by default, being them related to the intercept at high frequencies of the first arc of the Nyquist plot. The green elements are

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Fig. 5 Scheme of the Adaptive Equivalent Circuit Model Table 3 n-dependent CPE behaviour

n value −1 0 1 0.5

Behaviour Pure inductor Pure resistor Pure capacitor Semi-infinite Warburg element

usually enabled if in the spectrum some physical parameters are recognized (e.g., the inductive element is activated if at high frequencies, positive imaginary points are observed). The purple area contains elements that shape the spectrum when additional arcs are recognized. The full circuital model presents an inductive element L in series with a resistive element R and four parallel branches. The resistive elements represent the resistance to the ions and electrons flow (ohmic resistance), whereas the inductance mainly relates to the effects of cabling. For PEMFC, the typical ECM1 constitutes of a R - Rcp1 //Cpe1 - Rcp2 //Cpe2 .The two parallel branches are representative of the phenomenon affecting both anode and cathode. The resistive elements Rcp1 and Rcp2 represent the charge transfer resistance at the electrodes. The Constant Phase Elements (CPE) model the capacitive behaviour of the electrodes according to the porous structure of PEM electrodes [9]. It is worth remarking that to ensure the high adaptability, the CPE (whose characteristic equation is presented below) is the most suitable element, being it able to turn, according to its coefficient (n), into a capacitor, a resistance or a diffusion element (i.e., Warburg), as shown in Table 3 [9].

Zcpe =

1 Please

1 Q · (ω)n

note that “-” stands for series connection while “//” stands for parallel connection.

(1)

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Table 4 EIS metrics extracted Metric R Rcp1 Rcp2 Rw ncp1 ωcp1 ncp2 ωcp2 ωw L Rtot

Unit  cm2  cm2  cm2  cm2 – rad s−1 – rad s−1 rad s−1 Henry  cm2

Description Ohmic resistance Charge transfer resistance of the high-frequency arc Charge transfer resistance of the low-frequency arc Warburg element resistance CPE coefficient of the high-frequency arc CPE characteristic frequency of the high-frequency arc CPE coefficient of the low-frequency arc CPE characteristic frequency of the low-frequency arc Warburg element characteristic frequency Inductance Total resistance

The list of the extracted parameters (or their combination) is shown in Table 4. These metrics are reliable indicators of the Fuel Cell SoH and then the basis for the FDI algorithm. The identification algorithm was applied to the whole data set (see Table 2). A comparison between the experimental and identified spectrum is shown in Fig. 6. As one can observe, the identified spectra by means of ECM parameters well follow the experimental data even at low frequencies where a third arc may show up. The quality of parameters is related to the quality of data provided by experiments and by the ECM model fitting. The algorithm has been successfully applied to the 100% of the proposed data set, providing with the related circuital parameters. For on-board purposes, the algorithm was tested on embedded board as well. The test was performed on an arm-based Raspberry Pi 3b+ model running Octave. The porting of the algorithm from MATLAB™ environment to Octave was satisfied by the comparison of the extrapolated parameters of EIS spectra acquired in nominal conditions. The porting and the on-board validation will be discussed in a future work.

3.2 Fault Detection and Isolation The parameters are then collected and analyzed via box-plot representation in order to appreciate their change with respect to the nominal boundaries (examples in Fig. 7). The horizontal red line of box plots represents the median (second quartile), the top and the bottom of boxes (in blue) are the first and third quartiles of parameter population and the end of whiskers represents the lowest datum still within 1.5 IQR of the lower quartile and the highest datum still within 1.5 IQR (interquartile range) of the upper quartile. Outliers are plotted as individual points. The green o-point are

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Fig. 6 AIR-fed technology – EIS fitting examples: (a) fuel starvation, (b) air starvation, (c) drying, (d) flooding, (e) CO contamination, (f) sulphur poisoning

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Fig. 7 Box-plot representation of parameters value, i.e., with respect to the different operating conditions. For sake of representation, only ncp2 and Fcp3 variations are reported. (a) ncp2 has change detection (value=1) only for flooding; (b) Fcp3 has change detection (value=1) for sulphur poisoning and CO contamination. Refer to Table 2 for acronyms

the values of training parameters while the magenta x-point are the test ones. The horizontal red lines represent the set threshold of each parameter. For diagnostic purpose, the change in variation gives enough information for the detection and isolation of faults. This procedure allows the definition of the threshold of the above-mentioned parameters in nominal conditions. The thresholds were set up as the first and third quartiles of parameter population corrected via a tolerance percentage.

ECM-Based Algorithm for On-Board PEMFCs Diagnosis Table 5 Fault Signature Matrix for BPSE system

FS AS DR FL CO SP

R 1 1 1 1 1 1

113 L 0 0 0 0 0 0

Rcp2 1 1 0 0 1 1

Fcp2 1 1 0 0 1 1

ncp2 0 0 0 1 0 0

Rcp3 1 0 0 0 1 0

Rtot 0 0 0 0 1 1

Table 6 Model-based FDI results Operating conditions NC FL DR FS AS CO SP Total

Tested conditions 0 2 2 3 2 7 4 20

Detections 0 2 2 3 2 7 4 20

Correct isolations 0 2 2 3 2 7 4 20

The FSM design was performed through the analysis of each ECM parameter over all the investigated operating conditions by addressing change detection with respect to nominal behaviour. The FSM structure is shown in Table 5. As one can observe, not all the extracted parameters have been used. The ones related to the high-frequency arc did not provide enough useful information for diagnostic purposes. Anyway, the matrix shows six rows pattern different to each other, as requested for the unicity of the isolation process. The test patterns (not reported for brevity) showed a full faults detection and isolation process. Results are thus summed in Table 6. Nominal spectra are not considered in data set validation set because of lack of EIS measurements at that conditions. Obviously, a large amount of data will enhance the robustness and reliability of the FSM above proposed and consequently of the whole diagnostic approach.

4 Results The diagnostic algorithm hereby proposed is able to identify the current SoH of the ® BPSE stack. The algorithm was tested in both MATLAB and Octave environment. In order to compare the algorithm results, performance indexes [10] are shown according to Table 7. Referring to Table 7, Prec(f) represents the ratio of correct detection to all diagnosed conditions, Rec(f) is defined as the ratio of the diagnosed condition to all the actually (real) occurring conditions, F1 is used for evaluating the general performance of the diagnostic method, Acc(f) is the percentage of correct

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Table 7 Performance indexes for PEMFC diagnosis [10]. For a specific condition “f”, “a” is the number of the samples assigned to f, “b” represents those samples mistakenly diagnosed as f, “c” are all samples that were not correctly diagnosed as f and “d” evaluates whether the remaining states are properly not diagnosed as f Performance indexes Precision

P rec(f ) =

Recall for fault

Rec(f ) =

F1

F1 =

Accuracy

Acc(f ) =

Error

Error(f ) =

a a+b

a a+c

2xP rec(f )xRec(f ) P rec(f )+Rec(f ) a+d a+b+c+d b+c a+b+c+d

= 1 − Acc(f ) ®

Table 8 Model-based faulty conditions results. Computational effort: MatLab ambient PC Windows x64 i7 processor 8th gen. Runtime: 1, the effect of Rs dominates and the following conditions hold: Voc Rs = Isc

γv γi (1 − γi )ln(1 − γi ) + (1 − γv )

(1 − γi )ln(1 − γi ) + γi

;

Rh → ∞

(9)

If SP R < 1, the major losses are associated to Rh , and it is calculated as follows:   Voc λ2 W −SP R · λ1 e−λ1 + λ1   Rh = ; Isc W −SP R · λ1 e−λ1 + λ1

Rs = 0

(10)

the Lambert W-function W (·) is still used, while λ1 and λ2 are given by: λ1 =

1 − γv 2γi − 1 · ; 1 − γi γi + γv − 1

λ2 =

γv 1 − γi

(11)

The remaining parameters are given by: η=

1 IMP P Rs − (Voc − VMP P ) V P Ns Vt Isc −IMP P − MP Rh ln Voc Isc − R

Iph = Isc ;

(12)

h

 Voc − ηNVocV s t e Is = Iph − Rh

(13)

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Fig. 2 Slopes calculation on the I-V curve

It is worth to note that the equation used for calculating Is does not depend on the energy gap of the semiconductor material, so it can be applied to any PV panel technology. This approach will be identified in the following as SPR method.

2.3 Esplicit Equations Based on the I-V Curves Slopes The method shown in [9, 14] is based on the consideration that the I-V slopes close to the short circuit current and open circuit voltage are strongly related to the Rh and Rs , as shown in Fig. 2. The following conditions hold: Rh0 =

V1 ; Isc − I1

Rs0 =

Voc − V2 ; I2

(14)

The Rh0 and Rs0 are coupled with other equations to derive the SDM parameters as follows: Rh = Rh0 ; η=

  Ns Vt ln Isc −

(15) VMP P + Rs0 IMP P − Voc   VMP P Rh0 − IMP P − ln Isc −

Voc Rh



; +

IMP P Isc − RVoc

h0

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 Voc − ηNVocV s t ; Is = Isc − e Rh −Voc ηV t ηN e s Vt ; Is   Rs Isc Rs ηN V s t = Is e − 1 + Isc 1 + Rh

Rs = Rs0 − Iph

This approach will be identified in the following as Slopes method.

3 Experimental System Setup To validate the methods introduced in the previous section, the PV system shown in Fig. 3 is used. It consists of a solar tracker allowing to accommodate some PV panels, pyranometers and temperature sensors. Other sensors are also available but not used in the measure of our interest. The equipment is installed on the roof of the Departamento de Fisica Aplicada II at the University of Malaga. The PV panels under test are the Isofoton I-53; the datasheet parameters are shown in Table 2. In this paper two PV panels will be analysed; they are identified in the experimental system with Panel“#18” and Panel“#30”, respectively. These panels have been in operation since 1996, which explains the degree of degradations in comparison with the datasheet parameters.

Fig. 3 Experimental setup

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Table 2 Isofoton I-53 datasheet information Parameter STC power rating [W] Voltage at maximum power [V] Current at maximum power [A] Short circuit current [A] Open circuit voltage [V] Isc temp. coeff. [A/◦ C] Voc temp. coeff. [V /◦ C] Series resistance (new panel) [Ω] Number of cells in series Cell type

Symbol PMP P VMP P IMP P Isc Voc αI βV Rs Ns Si

Value 53 17.4 3.05 3.27 21.6 0.001326 −0.07704 0.288 36 Mono

Fig. 4 SDM with additional series resistance

The series resistance degradation is emulated with an external resistance of known value added to the PV panels under test. Figure 4 shows the electrical connections of the external resistors and measurements points. The I-V curves are acquired every 3 minutes for all the day; each PV panel operated with different external resistance day by day. At the end of the measurement campaign, for each PV panel under test, the I-V curves at different irradiance and temperature conditions as well as with different additional series resistance are available. The curves that have been selected correspond to the maximum power readings in clear sky days, during the period June–July 2018, when applying irradiance conditions are close to STC. Figure 5 shows a subset of I-V curves for PV panel #30 at the same irradiance and temperature conditions with different additional series resistance. It is evident how the increase of the series resistance affects significantly the knee of the I-V curves where is located the maximum power operating point. For the PV panels under test, the temperature coefficients of Isc and Voc have been previously quantified in lab (see Table 3). They will be used for calculating the SDM parameters. These values are different to those given at the beginning, due to the degradation after 22 years of operation [15].

Reliability of Explicit Methods to Identify the Parameters of PV Panels with. . .

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Isc temp. coeff. αI [A/◦ C] Voc temp. coeff. βV [V /◦ C]

Panel #18 0.00098 −0.0689

Panel #30 0.0008 −0.0759

4 SDM Parameters Calculation and Comparison In this section the robustness and accuracy of the three methods described in the previous section will be shown. Since all methods are based on approximated equations, the reference values for the parameters P = [Rs , Rh , η, Is , Iph ] must be identified with a more accurate procedure; the MATLAB functions developed for solving nonlinear curve-fitting problems are used. They have been configured to find the parameters P by minimizing the least square error expressed as follows: N

   2 min F (P, Vpv ) − Ipv  = min F (P, V m,i ) − I mi

(16)

i=1

V m is the vector of measured voltage, I m is the vector of measured current and F (P, Vpv ) is the SDM equation in explicit form. In the following, the MATLAB approach will be identified with Fitting method. It is evident that this method, besides the use of complex MATLAB functions, processes all data of the I-V curve by increasing the computational burden.

154 Table 4 SDM parameters calculated for Panel #18

G. Petrone et al. Param. Rs [Ω] σRs [%] Rh [Ω] σRh [%] η[/] ση [%] Is [nA] σIs [%] Iph[A] σIph [%]

Fitting 0.443 0.5 120 1.9 1.33 0.4 1088 8.1 2.59 0.4

LambertW 0.545 2.6 73.6 4.4 0.948 0.1 3.1 10.5 2.567 0.4

SPR 0.00 – 162.2 18.1 1.8 1.6 50530 21.1 2.567 0.4

Slopes 0.359 30.2 249.7 2.9 1.5 6.7 9056 107 2.57 0.41

4.1 SDM Parameters Stability The first test is aimed at validating the sensibility of the methods to calculate the SDM parameters by using outdoor measurements. Indeed although have been used I-V curves acquired at very similar irradiance and the temperature conditions, each I-V curve has its peculiarity since it could be affected by different measurement noise and small fluctuation due to the environmental changes (irradiance, temperature, humidity, wind). Table 4 shows, for the panel #18, the average values of the SDM parameters and the percentage of standard deviation of each parameters calculated by considering a set of I-V curves acquired in the same environmental conditions. For all the I-V curves, the measured PV temperature is Tc = 44 ± 1◦ C, and the measured irradiance is G = 1020 ± 5[W/m2 ]. Results of Table 4 show that each method converges towards very different SDM parameters solutions; SPR and slope methods exhibit higher dispersion on Rs , Rh Is and η parameters thus less stable with respect to the I-V curve used for extracting the SDM parameters. SDM parameters calculated with the Lambert W method have similar dispersion of fitting method. The tests have been performed without additional series resistance, but similar dispersions have been obtained on degraded I-V curves.

4.2 Irradiance Dependency of Rs In this test the previous methods are applied for estimating the Rs at different irradiance levels. The I-V curves of PV panel #30 with very similar PV temperature (Tc = 33 ± 6◦ C) and for different values of added series resistance have been collected. In Fig. 6 is shown the Rs value calculated by using the I-V curves measured without adding external series resistance (ΔRs = 0). Here it is still evident that the SPR method is totally ineffective to calculate Rs, while the slopes method is not stable. Similar results are obtained by using the degraded I-V curves

Reliability of Explicit Methods to Identify the Parameters of PV Panels with. . .

LambertW Slopes SPR Fitting

0.9 0.8

Estimated Series Resistance [ ]

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0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1 200

300

400

500

600

700

800

900

1000

1100

Irradiance [W/m 2]

Fig. 6 Rs estimation at different irradiance levels (ΔRs = 0) LambertW Slopes SPR Fitting

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2

1.5

1

0.5

0 200

300

400

500

600

700

800

900

1000

1100

Irradiance [W/m 2]

Fig. 7 Rs estimation (including ΔRs = 1) at different irradiance levels

measured by adding external series resistances. Figure 7 shows the case with ΔRs = 1. In both figures is appreciated the good behaviour of the Lambert W method in comparison with the fitting method.

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4.3 Estimation of Rs Degradation As a final test, the capability of explicit methods to estimate the series resistance degradation has been verified. The values of the external series resistance ΔRs are chosen as in [16]. For each ΔRs , a set of I-V curves at similar irradiance and temperature have been collected, and the average value of the series resistance Rs has been calculated. The estimated series resistance degradation is calculated as follows: ΔRs,est = Rs − Rs0

(17)

where Rs0 is the estimated series resistance without external resistance. Figures 8 and 9 show the ΔRs,est estimated by the different methods versus the real series resistance added for the two panels under investigation. By using the results of the fitting methods as reference, it is evident that all explicit methods do not guarantee an accurate estimation of ΔRs . Although the Lambert W method exhibits an almost linear behaviour, it defects of inaccuracy in presence of strong degraded conditions.

PV panel #18

1.6 1.4 LambertW Slopes SPR Fitting

Estimated

Rs [ ]

1.2 1 0.8 0.6 0.4 0.2 0 0

0.5

Added series resistance

Fig. 8 Estimation of Rs degradation on Panel #18

1

Rs [ ]

1.5

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PV panel #30

1.6 1.4 LambertW Slopes SPR Fitting

Estimated

Rs [ ]

1.2 1 0.8 0.6 0.4 0.2 0 0

0.5

Added series resistance

1

1.5

Rs [ ]

Fig. 9 Estimation of Rs degradation on Panel #30

5 Conclusions An experimental validation of explicit methods used for the SDM parameters identification has been carried out in this paper. The analysis has been focused on the series resistance identification in presence of degraded I-V curves. The study highlighted that such methods suffer of high variability with respect to the used I-V curves, thus demonstrating that they are not too much reliable in the online diagnostic methods. Among them the method based on the Lambert W function is more stable but less accurate when the series resistance is increased. Further analysis is currently ongoing to better understand if it is possible to correct the underestimation of the series resistance so that to obtain good results without complicating the SDM parameters identification method. Acknowledgments This work has been supported by the project RTI2018-095097-B-I00 at the 2018 call for I+D+i Project of the Ministerio de Ciencia, Innovación y Universidades, Spain, by the PRIN17 (grant number 2017WA5ZT3 003) project of MIUR Italian Ministry and by FARB funds of the University of Salerno, Italy.

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References 1. E.L. Meyer, E.E. van Dyk, Assessing the reliability and degradation of photovoltaic module performance parameters. IEEE Trans. Reliab. 53(1), 83–92 (2004) 2. J.D. Bastidas-Rodriguez, G. Petrone, C.A. Ramos-Paja, G. Spagnuolo, Photovoltaic modules diagnostic: an overview, in IECON 2013 – 39th Annual Conference of the IEEE Industrial Electronics Society, Nov 2013, pp. 96–101 3. E. van Dyk, E. Meyer, Analysis of the effect of parasitic resistances on the performance of photovoltaic modules. Renew Energy 29(3), 333–344 (2004) 4. D. Sera, L. Mathe, T. Kerekes, R. Teodorescu, P. Rodriguez, A low-disturbance diagnostic function integrated in the pv arrays’ mppt algorithm, in IECON 2011 – 37th Annual Conference of the IEEE Industrial Electronics Society, Nov 2011, pp. 2456–2460 5. F. Toledo, J.M. Blanes, A. Garrigós, J.A. Martínez, Analytical resolution of the electrical fourparameters model of a photovoltaic module using small perturbation around the operating point. Renew. Energy 43, 83–89 (2012) 6. E. Batzelis, Non-iterative methods for the extraction of the single-diode model parameters of photovoltaic modules: a review and comparative assessment. Energies 12(3), 83–108 (2019) 7. C.A. Ramos-Paja, G. Petrone, G. Spagnuolo, Symbolic algebra for the calculation of the series and parallel resistances in pv module model, in International Conference on CLEAN ELECTRICAL POWER Renewable Energy Resources Impact (ICCEP), Alghero, Sardinia, 11– 13 June 2013, 2013, pp. 62–66 8. S. Cannizzaro, M.C.D. Piazza, M. Luna, G. Vitale, Pvid: an interactive matlab application for parameter identification of complete and simplified single-diode pv models, in 2014 IEEE 15th Workshop on Control and Modeling for Power Electronics (COMPEL), June 2014, pp. 1–7 9. M.S. Benghanem, S.N. Alamri, Modeling of photovoltaic module and experimental determination of serial resistance. J. Taibah Univ. Sci. 2(1), 94–105 (2009) 10. G. Petrone, C.A. Ramos-Paja, G. Spagnuolo, Photovoltaic Sources Modeling (Wiley, Chichester, 2017) 11. R.M. Corless, G.H. Gonnet, D.E.G. Hare, D.J. Jeffrey, D.E. Knuth, On the lambertw function. Adv. Comput. Math. 5(1), 329–359 (1996) 12. N. Femia, G. Petrone, G. Spagnuolo, M. Vitelli, Power Electronics and Control Techniques for Maximum Energy Harvesting in Photovoltaic Systems, 1 edn. (CRC Press, 2012), Boca Raton, Florida, USA, 2013 13. S. Cannizzaro, M. Di Piazza, M. Luna, G. Vitale, Generalized classification of PV modules by simplified single-diode models, in 2014 IEEE 23rd International Symposium on Industrial Electronics (ISIE), June 2014, pp. 2266–2273 14. S.T. Kebir, M. Haddadi, M.S. Ait-Cheikh, An overview of solar cells parameters extraction methods, in 2015 3rd International Conference on Control, Engineering Information Technology (CEIT), May 2015, pp. 1–7 15. P. Sánchez-Friera, M. Piliougine, J. Peláez, J. Carretero, M. Sidrach de Cardona, Analysis of degradation mechanisms of crystalline silicon pv modules after 12 years of operation in southern europe, Prog. Photovoltaics Res. Appl. 19(6), 658–666 (2011) 16. J.D. Bastidas-Rodriguez, E. Franco, G. Petrone, C.A. Ramos-Paja, G. Spagnuolo, Model-based degradation analysis of photovoltaic modules through series resistance estimation. IEEE Trans. Ind. Electron. 62(11), 7256–7265 (2015)

Part II

Smart Grid and Energy Management

Paralleling Converters in DC Microgrids with Modified Lag I-V Droop Control and Voltage Restoration Daniel Zammit, Cyril Spiteri Staines, Maurice Apap, and Alexander Micallef

Abstract In stand-alone or islanded DC microgrids, sharing of the load between parallel-connected converters is usually achieved using the droop control method. Two main types of droop control are used with DC microgrids: the impedance (VI) droop control method and the admittance (I-V) droop control method. Droop control permits the sharing of load between parallel-connected converters, but it creates a voltage deviation in the DC microgrid voltage. Voltage restoration control is then required to restore the DC microgrid voltage back to its preset value. This paper proposes a novel I-V droop control method using a modified lag compensator which combines voltage control and load sharing between the parallel-connected converters within the DC microgrid. The proposed control system is made up of two nested controllers: an inner Proportional Integral (PI) current controller and an outer modified lag compensator which controls the voltage and the droop. An addition outer loop is used for voltage restoration. The proposed control system was simulated using Simulink. Simulation results are shown for the operation of two Buck converters connected in parallel and sharing a common resistive load.

1 Introduction Microgrids consist of a number of distributed power generation sources, energy storage systems, and loads, forming an electrical grid system which is selfsustainable. Microgrids have the ability to operate in grid-connected mode and also in islanded mode. The islanded mode of operation provides the advantage of isolated operation in case of an electrical grid failure, and also makes the microgrid an attractive option to supply electrical energy in remote areas, where it is difficult to supply from the grid.

D. Zammit () · C. Spiteri Staines · M. Apap · A. Micallef Department of IEPC, Faculty of Engineering, University of Malta, Msida, Malta e-mail: [email protected]; [email protected] © Springer Nature Switzerland AG 2020 W. Zamboni, G. Petrone (eds.), ELECTRIMACS 2019, Lecture Notes in Electrical Engineering 697, https://doi.org/10.1007/978-3-030-56970-9_13

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WIND

AC GRID

DC DC

BATTERY STORAGE

DC

DC

AC AC

SOLAR

DC

DC

DC BUS

LOAD Fig. 1 DC microgrid

Three main types of microgrids exist, which are AC, DC, or combined ACDC microgrids. The type of microgrid considered in this literature is the DC microgrid, which has several advantages, the main being lower power loss due to less conversion stages, no issues with synchronisation; phase, or frequency, and provides separation from any voltage sags, dips, and power quality issues on the grid. A DC microgrid is shown in Fig. 1. A main area of research on DC microgrids which is presently attracting attention is the control system needed to connect and operate energy sources, energy storage systems, and various loads within the DC microgrid. The main method to achieve load sharing between converters connected in parallel within a stand-alone DC microgrid is the droop control method [1–12]. Guerrero et al. in [1] proposed a three-level hierarchical control system for microgrids. This consists of primary control including current control, voltage control, and droop, secondary control which restores deviations caused by the primary control, and tertiary control which handles the power flow between the microgrid and the electrical distribution system. In [2, 3], Zammit et al. extensively covered the design of the control system needed to operate paralleled converters within a DC microgrid. The control system has primary and secondary control levels. The primary control level consists of two nested control loops: an inner current control loop and an outer voltage control loop with droop control. The secondary control level provides a voltage restoration control loop used to obtain voltage restoration within the DC microgrid, correcting any voltage deviations caused by the droop. The droop control methods applied in [1–4] all used a constant droop resistance value, while in [5–10], adaptive or modified droop control methods were presented. However, the droop control methods in [1–10] were all based on the traditional V-I droop control method. The impedance droop method, which is also called V-I droop, is the traditional droop control method used in DC microgrids. V-I droop control was the droop control method used in [2, 3]. The V-I droop control method is applied by the introduction of a virtual resistance in an additional feedback loop. This causes a load-dependent deviation in the output voltage of the converter, achieving a loadsharing behaviour between the parallel-connected converters. The admittance droop

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control method, which is also called I-V droop, is a more recent droop method used by Jin et al. in [11, 12]. The I-V droop control method is applied by utilising the reciprocal value of the virtual resistance as a multiplying factor to obtain the current reference to the current controller from the voltage reference value. In the I-V droop control method, the outer voltage controller, generally a PI controller, is replaced with a proportional-type controller. A drawback with the I-V droop control method is that overshoots or transient oscillations may occur during start-up of the converters [11, 13]. Jin et al. in [11] introduced virtual inertia control in the DC microgrid by using an admittance-type RC-mode droop control method, which improved the transient response. This paper presents an alternative I-V droop control method aimed at eliminating the start-up oscillations. With the proposed droop control method, voltage control and droop are combined, obtained by using a modified lag compensator. A lag compensator cannot totally remove the steady-state error, so in this case, the steadystate error is used as the droop voltage deviation. In addition, by using a lag controller, the start-up oscillations can be eliminated by adjusting the bandwidth of the voltage controller. The modified lag I-V droop control method that is proposed will be tested using simulations. Since droop control causes voltage variation in the DC microgrid, voltage restoration will be applied to correct the voltage to the desired level. This paper is organised in seven sections. Section 2 provides a description of the different droop control methods, including the new proposed droop control method. The control system modelling and design are presented in Sects. 3 and 4, respectively. Section 5 contains the simulations performed to test the proposed modified lag I-V droop control method and voltage restoration. The simulation results are presented in Sect. 6, while Sect. 7 provides a conclusion with final remarks on the proposed droop control method.

2 Droop Control Load sharing between parallel-connected energy source converters in a DC microgrid operated in stand-alone or islanded mode is generally achieved using droop control. This prevents circulating currents between the parallel-connected converters, which would result if there are any differences in the converter’s output voltages. Droop control achieves this by adjusting the converter’s voltage and current control loops references. The droop control methods presented in this section, together with the control system, are based on the Buck converter since it can be considered as a basis for other converters. The Buck converter is a switching converter that produces a lower average output voltage (Vo ) than the dc input voltage (Vin ). Figure 2 shows a nonideal Buck converter, thus showing the inductor resistance RL and the equivalent series resistance of the capacitor Rc .

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L

RL + C

Vin

DC

Rc

R

Vo -

Fig. 2 Buck converter Cv

Vref + -

vo

-

PI

Voltage vdroop

Tmod

Ci

iref +

vc

PI -

iL

Gid d

1 Vm

Current

Vin sL + RL

Gvi iL + -

1+ sCRc sC

vo

vo R Rdroop

Fig. 3 Buck converter control system using V-I droop

2.1 V-I Droop Control The V-I or impedance droop can be considered as the traditional droop control method used in DC microgrid. V-I droop is used with a control system consisting of nested current and voltage loops using Proportional Integral (PI) controllers. The block diagram in Fig. 3 shows the control system for a Buck converter including the V-I droop loop. The control system consists of two nested PI controllers, one controlling the inductor current and one controlling the output voltage. V-I droop is applied by inserting an additional loop containing a virtual resistance Rdroop as shown in Fig. 3. The value of Rdroop is calculated using Eq. (1). This is graphically represented in Fig. 4. Rdroop =

Vmin − Vref Imax − 0

(1)

where Vmin is the converter minimum voltage permitted, Vref is the no load output voltage reference, and Imax is the converter maximum current. Equation (1) can also be expressed as Eq. (2): Rdroop =

εv iomax

(2)

where εv is the maximum permissible voltage deviation, and io_max is the maximum output current.

Paralleling Converters in DC Microgrids with Modified Lag I-V Droop Control. . . Fig. 4 V-I droop graphical representation

165

V Vref

Rdroop

Vmin I 0

Imax

Therefore, the converter output voltage vo can be expressed as vo = Vref − Rdroop iL

(3)

where iL is the inductor current. (Note that the output current io can be used instead of iL in the control loop).

2.2 I-V Droop Control I-V or admittance droop is another droop control method used in DC microgrids [11, 12]. In this droop control method, the voltage PI controller is replaced with a multiplier term, denoted by a constant value k, which effectively is the inverse of the droop virtual resistance Rdroop as shown in Eq. (4). The multiplier term k is multiplied to the difference between the voltage reference and the actual output voltage to obtain the current reference for the current PI controller. I-V droop is graphically represented in Fig. 5. The block diagram in Fig. 6 shows the control system for a Buck converter using I-V droop. k=

1 Rdroop

(4)

2.3 Modified Lag I-V Droop Control Comparing the I-V droop control method to the V-I droop control method, I-V droop achieves a simpler control system due to the replacement of the PI voltage controller with the multiplier term. However, this can cause transient oscillations or overshoots during start-up of the converters. In this paper, an alternative I-V droop control method is being proposed in order to reduce or eliminate these overshoots.

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Fig. 5 I-V droop graphical representation

I Imax 1/Rdroop V Vmin Vref

0 Vref + vo

k

Ci

iref +

Voltage + Droop

PI -

iL

Tmod vc

1 Vm

Gid d

Current

Vin sL + RL

Gvi iL + -

1+ sCRc sC

vo

vo R

Fig. 6 Buck converter control system using I-V droop

The proposed alternative I-V droop control method makes use of a modified lag compensator. Steady-state error is not removed by a lag compensator, and therefore, this steady-state error will be used to provide the droop voltage deviation, obtaining load sharing. This lag compensator will also offer stabilisation of the system by eliminating any start-up overshoots. With the conventional lag compensator, the DC gain is used to set the bandwidth, and the pole is placed before the zero [14]. In the proposed modified lag compensator, the DC gain is set by the multiplier term k, and the pole and zero are used to set the bandwidth, thus the term “modified.” The modified lag compensator transfer function is presented by  &  1+s ω ' z C(s) = k  s 1+ ω

(5)

p

where the value k, representing the DC gain, is the same value as the I-V droop multiplier term found by (4) and (2). ωz and ωp are the frequency locations in rad/s for the zero and pole, respectively. The block diagram in Fig. 7 shows the control system for a Buck converter using the proposed I-V droop with the modified lag compensator.

Paralleling Converters in DC Microgrids with Modified Lag I-V Droop Control. . . CvLag Vref + vo

Modified iref + Lag

Ci PI -

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iL

Tmod vc

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Gid d

1 Vm

Current

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Gvi

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iL + -

vo

vo R

Fig. 7 Buck converter control system using modified lag I-V droop Fig. 8 Buck converter small signal equivalent circuit

^ iL

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^ io

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3 Control System Modelling with Modified Lag I-V Droop The transfer functions Gid (s) and Gvi (s) can be obtained from the small signal model of the Buck converter. The design of the Buck converter, the derivation of the small signal model, as well as the derivation of the transfer functions were extensively covered in [2, 3]. The linearised small signal equivalent circuit for the Buck converter is shown in Fig. 8, which includes the inductor resistance (RL ) and the capacitor resistance (Rc ). The linearised small signal mathematical model of the Buck converter is given by (6) and (7). L

d iˆL (t) ˆ in − iˆL (t)RL − vˆo (t) = dV dt

d vˆc (t) ˆ vˆo (t) = iL (t) − iˆc (t) = C dt R

(6)

(7)

ˆ vˆo (t), and vˆc (t) are small ac variations around the quiescent where iˆL (t), iˆc (t), d, values for the inductor current, capacitor current, duty cycle, output voltage, and capacitor voltage, respectively. By considering the capacitor to be large enough to offer good decoupling for dc values, and by transforming the mathematical model equations to the s-domain, the transfer functions of the relationships between the duty cycle and the inductor current and between the inductor current and the output voltage are given by:

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Gid (s) =

Vin iˆL (s) = sL + RL dˆ

(8)

Gvi (s) =

1 + sCR c vˆo (s) = sC iˆL (s)

(9)

The current PI controller Ci (s) is as shown in (10). C(s) = KP +

KI s

(10)

where KP is the proportional gain term, and KI is the integral term. Ci (s) provides the control voltage vc from the difference between the reference inductor current iref (obtained from the combined droop and voltage controller) and the actual inductor current il . The combined droop and voltage modified lag controller, CvLag (s), is as shown in (5), which can also be represented by (11). C(s) = K

(1 + TZ s) (1 + TP s)

(11)

where K is the DC gain term set equal to the droop multiplier term k, and Tz and Tp are the inverse of the frequency locations ωz and ωp for the zero and pole, respectively. The plant transfer function Pi (s) for the current PI controller is given by Pi (s) = Tmod × Gid (s)

(12)

where Tmod is the transfer function representing the pulse width modulation stage. The duty cycle d is proportional to the control voltage vc , which is obtained from the modulation block, whose carrier has a magnitude Vm and a frequency corresponding to the converter switching frequency fs . The pulse width modulation stage can be modelled by the transfer function Tmod given by Tmod =

1 Vm

(13)

The plant transfer function Pv (s) for the modified lag (for the alternative I-V droop method case) controller is given by Pv (s) =

Ci (s)Pi (s) × Gvi (s) 1 + Ci (s)Pi (s)

(14)

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Vref CvLag + Vmgref + vmg

Cres

vres

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vo

Ci

+

Modified iref + Lag Voltage + Droop

PI iL

Current

Tmod vc

1 Vm

Gid d

iL Vin sL + R L

Gvi

1+sCR c vo sC

Converter 1

Voltage Restoration

Converter n

DC Bus

Converter 2

Fig. 9 Voltage restoration control loop

Thus, the closed-loop transfer function for the complete Buck converter and control system, including the alternative I-V droop, is given by PdmodI V (s) =

CvLag (s) Pv (s) 1 + CvLag (s) Pv (s)

(15)

Droop control provides sharing of load between parallel-connected converters, however, it causes a load-dependent output voltage deviation as can be observed from (3). The voltage deviation can be corrected by applying another PI controller to restore the microgrid voltage to the desired level. This controller will form another outer control loop common to all the converters/sources in the microgrid. This control stage is identified as secondary control in [1]. A block diagram of the voltage restoration control loop connected to all the converters within the DC microgrid is shown in Fig. 9. The voltage restoration PI controller Cres (s) is of the form shown in (10). Cres (s) provides the restoration voltage vres from the difference between the DC microgrid reference voltage Vmgref and the actual DC microgrid voltage vmg . The plant transfer function for the voltage restoration PI controller is (15) for the alternative I-V droop method.

4 Buck Converter and Control System Design To test the proposed modified lag I-V droop control method, a Buck converter and its control system was designed. The parameters for the Buck converter are listed in Table 1. The maximum percentage voltage deviation was taken to be 10% of the output voltage, thus obtaining a droop value k of 1/0.09216. The current and voltage controllers were designed using transfer functions (12) and (14), respectively. The value for Vm was taken as 100V, which is equal to the DC voltage

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Table 2 Controller values

100 V 48 V 10 kHz 2.5 kW 10% 0.5% 0.002  0.03  0.48 0.479 mH 271.25 μF

Current PI controller Current PI KP 1.144 Current PI KI 880 Lag controller Voltage lag K = k 1/0.09216 Voltage lag TZ 0.0023 Voltage lag TP 0.4 Voltage restoration PI controller Voltage restoration PI KP 0.119 Voltage restoration PI KI 7

of the energy source. Table 2 lists the values for the proportional gain term KP , the integral term KI , the DC gain K, and Tz and Tp for the controllers. The bandwidths for the current, voltage, and voltage restoration closed loops are 495 Hz, 95 Hz, and 1 Hz, respectively.

5 Simulation Matlab/Simulink was used to model two Buck converters using the parameters from Sect. 4. Simulations were performed to test the proposed modified lag I-V droop control method and compare it to the standard I-V droop control method. The simulation model was made up of two parallel-connected Buck converters sharing a resistive load to simulate converters within a simple DC microgrid. Figure 10 shows the two parallel-connected Buck converters, including the voltage restoration loop. The Simulink model for the Buck converter is shown in Fig. 11. Figure 12 shows the control system based on the modified lag I-V droop control method.

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Fig. 10 Parallel-connected Buck converters with voltage restoration

Two simulations were performed. The first simulation tested the start-up of the standard I-V droop control method and the modified lag droop control method, to perform a comparison. The second simulation was performed to test the loadsharing performance of the control system of a simple DC microgrid using the modified lag droop control method. The DC microgrid bus voltage was set to 48 V. The simulation started with initially only one Buck converter switched on, supplying a resistive load of 0.9216 . The second Buck converter was connected in parallel with the first converter after 2s to share the resistive load. The droop control of each converter adjusted the output voltage of each converter to obtain load current between the two parallel-connected converters. After 7s, the voltage restoration control loop was switched on, which started to restore the DC microgrid voltage back to 48 V.

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Fig. 11 Buck converter – Simulink model

Fig. 12 Modified lag I-V droop-based current and voltage control

6 Results The simulation tested the performance of two parallel-connected Buck converters operated using the standard I-V droop and the modified lag I-V droop control methods, with a shared resistive load of 0.9216 . Figures 13 and 14 show the start-up when I-V droop was used, while Figs. 15 and 16 show the start-up when the modified lag I-V droop control method was used. Figures 17 and 18 show the load-sharing process using the modified lag I-V droop control method, as well as the voltage restoration operation. Figures 13, 15, and 17 show the output currents for the two Buck converters (Io1 and Io2 ) and the total output current through the resistive load (Io ). Figures 14, 16, and 18 show the output voltage (Vo ). With the standard I-V droop control method one can note that during the startup of the first converter, overshoots or oscillations can occur [11, 13]. Using the

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70 Io1 Io2

60

Io

Output Current (A)

50 40 30 20 10 0 0

0.002

0.004

0.006

0.008

0.01 0.012 Time (sec)

0.014

0.016

0.018

0.02

0.014

0.016

0.018

0.02

Fig. 13 Start-up with I-V droop – output current 60

Output Voltage (V)

50

40

30

20

10

0 0

0.002

0.004

0.006

0.008

0.01 0.012 Time (sec)

Fig. 14 Start-up with I-V droop – output voltage

proposed modified lag I-V droop control method, no oscillations are present at the start-up of the converter. The results show the correct operation of the current and the combined droop-voltage control loops. The load-sharing process between the two converters started at 2s, settling in less than 2.5s. The voltage restoration controller starting at 7s corrected the output voltage in the DC microgrid back to the preset 48V in less than 1s.

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50 Io1 Io2

40

Io 30

20

10

0 0

0.05

0.1

0.15

0.2 Time (sec)

0.25

0.3

0.35

0.4

0.3

0.35

0.4

Fig. 15 Start-up with modified lag I-V droop – output current 50 45

Output Voltage (V)

40 35 30 25 20 15 10 5 0 0

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Fig. 16 Start-up with modified lag I-V droop – output voltage

7 Conclusion This paper presented an alternative droop control method for stand-alone or islanded DC microgrids. The proposed droop control method made use of a modified lag compensator which combines both the voltage controller and the droop. V-I droop and I-V droop are the two types of droop control methods used in stand-alone DC microgrids. An alternative I-V droop control method was presented in this paper,

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60 50

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Fig. 18 Output voltage with the modified lag I-V droop and voltage restoration

which made use of a modified lag controller. Simulations in Simulink/Matlab were performed to test the operation of the proposed modified lag I-V droop control method. The simulation model consisted of two parallel-connected Buck converters, sharing a resistive load. An additional outer voltage restoration loop was also applied to correct any voltage deviations caused by the droop. The I-V droop control method can offer faster operation and simpler control system when compared to the V-I droop control method, however, I-V droop can cause oscillations at the start-up of the converters [13]. The simulation results show that no start-up oscillations resulted with the proposed modified lag I-V droop control method. This resulted in a more stable response without affecting the load-sharing capability. The results also demonstrate successful operation of the control system, including load

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sharing between the two parallel-connected Buck converters, including the voltage restoration loop which corrected the microgrid voltage back to the desired voltage value.

References 1. J.M. Guerrero, J.C. Vasquez, J. Matas, L.G. de Vicuna, M. Castilla, Hierarchical control of droop-controlled AC and DC microgrids – a general approach towards standardization. IEEE Trans. Ind. Electron. 58(1), 158 (January 2011) 2. D. Zammit, C. Spiteri Staines, M. Apap, A. Micallef, Paralleling of buck converters for DC microgrid operation, IEEE International Conference on Control, Decision and Information Technologies (CoDiT2016), St Paul’s Bay, Malta. 6th–8th April 2016 3. D. Zammit, C. Spiteri Staines, M. Apap, A. Micallef, Overview of buck and boost converters modelling and control for stand-alone DC microgrid operation, Offshore Energy & Storage Symposium (OSES 2016), Valletta, Malta, July 2016 4. P. Karlsson, J. Svensson, Voltage control and load sharing in DC distributed systems, European Power Electronics Conference (EPE 2003), Toulouse, France, September 2003 5. S. Anand, B.G. Fernandes, Modified Droop controller for paralleling of DC-DC converters in standalone DC system. IET Power Electron. 5(6), 782 (February 2012) 6. B.M. Han, H.J. Kim, Operation analysis of coordinated droop control for stand-alone DC microgrid, International Conference on Renewable Energies and Power Quality (ICREPQ’14), Cordoba, Spain, April 2014 7. X. Lu, K. Sun, J.M. Guerrero, J.C. Vasquez, L. Huang, State-of-charge balance using adaptive droop control for distributed energy storage systems in DC microgrid applications. IEEE Trans. Ind. Electron. 61(6), 2804 (June 2014) 8. X. Lu, K. Sun, J.M. Guerrero, J.C. Vasquez, L. Huang, Droop-control-based state-of-charge balancing method for charging and discharging process in autonomous DC microgrids, IEEE 23rd International Symposium on Industrial Electronics (ISIE 2014), Istanbul, Turkey, June 2014 9. X. Lu, K. Sun, J.M. Guerrero, J.C. Vasquez, L. Huang, Double-quadrant state-of-charge-based droop control method for distributed energy storage systems in autonomous DC microgrids. IEEE Trans. Smart Grid 6, 147–157 (January 2015) 10. S. Peyghami, H. Mokhtari, F. Blaabjerg, Decentralized load sharing in a low-voltage direct current microgrid with an adaptive droop approach based on a superimposed frequency. IEEE J. Emerg. Select. Topics Power Electron. 5, 1205–1215 (September 2017) 11. Z. Jin, L. Meng, R. Han, J.M. Guerrero, J.C. Vasquez, Admittance-type RC-mode droop control to introduce virtual inertia in DC microgrids, IEEE Energy Conversion Congress and Exposition (ECCE), Cincinnati, Ohio, USA, 1–5 October 2017 12. Z. Jin, J.M. Guerrero, Two-degree-of-freedom admittance-type droop control for plug-and-play DC microgrid, IEEE Applied Power Electronics Conference and Exposition (APEC 2018), San Antonio, Texas, USA, 4–8 March 2018 13. D. Zammit, C. Spiteri Staines, M. Apap, A. Micallef, Alternative droop control using a modified lag compensator for paralleled converters in DC microgrids, IEEE International Conference on Control, Decision and Information Technologies (CoDiT2019), St Paul’s Bay, Malta. 23rd–26th April 2019 14. R.W. Erickson, D. Maksimovic, Fundamentals of Power Electronics, 2nd edn. (Springer, New York, 2001)

Power Management of a Full DC Microgrid for Building Self-Consumption Applications Wenshuai Bai, Hongwei Wu, Manuela Sechilariu, and Fabrice Locment

Abstract Microgrid is a small-scale power supply system that can support the intelligent energy management integrated with multisource, multi-storage, and local demand side management in multiple operational modes and most importantly make the microgrid achieve self-consumption. This paper presents an algorithm for a full DC microgrid, which combines grid-connected and islanded operational modes, with real-time demand side management optimization. Such a full microgrid consists of photovoltaic sources, a DC load, battery storage systems, a supercapacitor storage, a diesel generator, and a public grid connection, which is based on a DC common bus. The proposed real-time power management focuses on building selfconsumption and considers the power constraints imposed by the public grid as well as the sluggish dynamic of the diesel generator, self-discharging characteristic of the supercapacitor, and the load shedding optimization. The simulation results, obtained under MATLAB/Simulink, verify the real-time control algorithm can keep power balance in real time.

1 Introduction To increase the power supply efficiency and save costs, the distributed renewable energy generation is proposed. But as the renewable source is strongly influenced by weather, it generates intermittent power, which cannot be directly used by the load and is also not easy to be fully stored. Thus, a microgrid becomes an ideal technology to solve the problem. A microgrid is a power supply grid, which works in a small power range in comparison to a public grid. It can support a decentralized power management, which can also support a liberalized electricity market to save wholesale costs [1, 2]. As an internal DC power can supply most of electrical appliances, and the renewable energy source

W. Bai () · H. Wu · M. Sechilariu · F. Locment Sorbonne University – Université de Technologie de Compiègne, Compiègne, France e-mail: [email protected]; [email protected]; [email protected]; [email protected] © Springer Nature Switzerland AG 2020 W. Zamboni, G. Petrone (eds.), ELECTRIMACS 2019, Lecture Notes in Electrical Engineering 697, https://doi.org/10.1007/978-3-030-56970-9_14

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such as photovoltaic (PV) sources can directly produce DC power, a DC microgrid can increase the efficiency of power supply by decreasing the number of AC/DC converters. A hybrid microgrid can satisfy different electrical appliances, but it will be complex to control and keep power balance [3, 4]. According to system architectures, microgrid control can be divided into decentralized control and centralized control that can reach the same goal in different ways. However, decentralized control has an intrinsic advantage in flexibility. An example of decentralized control is using the multi-agent idea [5], consists of many intelligent agents which have different goals with different architectures, and will communicate with one another to reach global goals [6]. Centralized control, which is a classic control method, can make a power supply system comply with the design in detail. The real-time power management for the self-consumption plays an important role in a microgrid. In [7], a control algorithm with a centralized controller and multiple local controllers for energy management is presented, which is applied in the multiple microgrid with a main source that can support every microgrid, which can keep the main source working at a constant power by taking advantage of energy storage system in every microgrid. In [8], a power control algorithm is provided to attain effective energy management between renewable and nonrenewable sources by using the hybrid storage systems in an isolated DC microgrid, however in which the grid-connected operational mode is not considered. In [9], an energy management and control system for a microgrid based on hybrid energy resources such as wind turbine, PV, and batteries are proposed; however, it also does not consider the grid-connected operational mode. In [10], a multiobjective power management method for microgrid based on Nash bargaining solution is proposed. The proposed procedure of power management can track a unique pareto-optimal solution that introduces a fair balance among the different objective functions of the multisource microgrid. However, it does not consider sluggish dynamic and the operation period constraint of the diesel generator (DG), which always works for whole day in the test case. None of the above takes the supercapacitor (SC) self-discharging characteristic and demand side management by load shedding optimization into consideration. A full DC microgrid, which allows the grid-connected and islanded operating modes, improves the reliability of power supply by integrating the backup power in the islanded mode. This paper proposes a power management strategy of a full DC microgrid for building self-consumption, which achieves the self-consumption for the building’s electrical applications to reach the maximal usage rate of renewable energy. The constraints of PV sources, the public grid, the battery storage, the DG, and the SC are considered; meanwhile, a real-time load optimization method is applied in this paper. The rest of this paper is organized as follows: The DC microgrid modeling is presented in Sect. 2. The power management strategy is introduced in Sect. 3. The results and analyses are discussed in Sect. 4. The conclusions are given in Sect. 5.

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2 DC Microgrid Modelling The physical components of a DC microgrid are shown in Fig. 1. It consists of PV sources, a battery storage system, a public grid connection, a DG, a SC, and a DC load. All parts are connected to the common DC bus of the microgrid.

2.1 Microgrid System For keeping the power balance and common DC bus voltage stable, a proportionalintegral (PI) controller is introduced to calculate the power to be compensated by public grid and battery storage. The power balance expressed by (1), (2), and (3) is introduced to keep the common DC bus voltage vDC at the reference voltage noted ∗ : by vDC

pP I

p = pP V − pL − pP I (  ∗    ∗ = KP vDC − vDC + KI vDC − vDC p = pBS + pG − pDG + pSC

Fig. 1 Overview of full DC microgrid

(1) (2) (3)

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where pPV is the power of PV sources; pL is the DC load power; KP and KI are the PI controller coefficients; p is the compensation power by the public grid, storage, DG, and SC; pG is the public grid power; pBS is the storage power; pDG is the DG power; and pSC is the SC power.

2.2 PV Sources The PV model comes from [11], where a mathematical modelling of PV is introduced. To gain the most economic benefits, the PV should be driven by a maximum power point tracking method [4]. To reach the maximum power point, searching algorithms are required, and the mostly used are Perturb and Observe algorithm and Incremental Conductance algorithm. When the PV power is more than the microgrid needs, the system will be not stable, and the devices will be broken if out of their tolerations. Thus, a limit controller is proposed in [4], whose goal is to operate PV shedding, in case the PV power generation is over the consumption of the microgrid. pP V = pP V _MP P T − pP V _S

(4)

where pPV _ MPPT is the maximum power of PV at the standard test condition, and pPV_S is the shedding power of PV.

2.3 Public Grid Connection The public grid is a large-scale and complex power supply system. In a microgrid, it is seen as a source can supply and absorb power. The public grid power equipment must be protected from the overload by giving the power limitations for injection and supply as in (5): −PG_MAX ≤ pG (t) ≤ PG_MAX

(5)

where pG is the public grid power, which represents the power injection when pG is positive and power supply when pG is negative. The public grid power injection is limited by PG _ MAX . The public grid power supply is limited by −PG _ MAX . Therefore, when the public grid power injection and power supply are limited, it is required to operate the load shedding or PV shedding when the public grid reaches its limitations.

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2.4 Battery Storage System The battery storage system can supply and absorb power to keep the microgrid power balance. Owing to low cost and high recycling rate, lead-acid battery is the most used in a small power microgrid. To avoid overcharging and overdischarging, it is necessary to limit its state of charge (socBS ). The socBS is calculated according to (6), where CREF is the battery capacity, vBS is the battery storage voltage, and SOCBS is limited between SOCBS _ MIN and SOCBS _ MAX in (7). pBS is the battery storage power that represents battery storage charging when pBS is positive and battery storage discharging when pBS is negative. The battery storage charging and discharging powers are limited by PBS _ MAX and −PBS _ MAX , respectively, as in (8). 100% socBS (t + Δt) = socBS (t) + 3600CREF vBS

(

t+Δt

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(6)

t

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(7)

−PBS _MAX ≤ pBS (t) ≤ PBS _MAX

(8)

2.5 Diesel Generator and Supercapacitor DG is a backup source which can provide long-term support for microgrid. However, DG start-up stage presents a slow dynamic behavior. Therefore, during the period of the DG starting up, a SC is suggested to compensate the power balance because of its fast response and high-power density [12, 13]. In addition, it is assumed the DG works at duty cycle mode as in [14], where the duty cycle mode is proved to be better than a load following mode, and one hour is proposed as a good trade-off between fuel consumption and start-up frequency. The DG power pDG is limited by maximal DG supply power PDG _ MAX as given in (9). Due to the slow dynamic behavior of the DG start-up stage, the DG cannot support the microgrid until it satisfies the conditions expressed by (10), which also can prevent the converter from being broken by the peak power of the DG start-up stage. During the period between DG start-up and DG stable state given by (10), the SC compensates the microgrid to keep its power balance. 0 ≤ pDG (t) ≤ PDG_MAX )

310V < v < 340V 48H z < fDG < 52H z

(9)

(10)

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The SC power pSC is limited to its maximal SC charging power PSC _ MAX and maximal SC discharging power −PSC _ MAX as in (11). The energy of SC ESC is calculated according to SC capacitance CSC and SC voltage vSC as expressed by (12). The ESC (t) and ESC _ Rated provide the socSC (t), which can be simplified as in (13). −PSC _MAX ≤ pSC (t) ≤ PSC _MAX ESC = ESC (t) socSC (t) = = ESC _Rated

2 CSC · vSC 2

2 (t) CSC vSC 2 2 CSC vSC _Rated 2

=

(11)

(12) vSC (t) 100% vSC _Rated

(13)

As to the SC model given in [12], the SC is natural self-discharging. It should be recharged at certain time to keep its lowest energy for DG start-up compensation, and it is also necessary to define the SC recharge period. So socSC limitations are provided: SOCSC _ MIN _ MIN , SOCSC _ MIN _ MAX , SOCSC _ MAX _ MIN , and SOCSC MAX _ MAX . When PV power is enough for load demand power, the recharging start time and recharging end time are separately the time when socSC reaches SOCSC _ MAX _ MIN and SOCSC _ MAX _ MAX . The socSC minimal limitation for the SC is SOCSC _ MIN _ MIN , and the socSC minimal limitation for DG start-up compensation is SOCSC _ MIN _ MAX . When PV power is insufficient for load demand power, the recharging start time is the time when socSC reaches SOCSC _ MIN _ MAX which can keep the SC energy supporting the DG start-up.

2.6 DC Load The DC load, whose power changes according to the demand of buildings, is electrical appliances of buildings. Therefore, in order to operate the demand side management, i.e., to allow a load shedding optimization, it is necessary to assign the priority of each electrical appliance, to define the time duration of load shedding, and to define the power based on the real electrical appliances and critical loads. The purpose is to define the load power closing to the real load power by applying a load shedding real-time optimization [15], which is described in details in [16] and is formulated to the load optimization problem based on knapsack problem and solved by mixed-integer linear programming with IBM CPLEX [17]. The load power pL and the load shedding power pL _ S are given respectively by (14) and (15), where pL _ OPT is the load power after the load real-time optimization, pAVAIL is the total available power, and pL _ D is the load demand power.

Power Management of a Full DC Microgrid for Building Self-Consumption. . .

) pL =

pL_OP T if pAV AI L < pL_D pL_D if pAV AI L ≥ pL_D pL_S = pL_D − pL

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(14) (15)

The coefficient kL _ CRIT represents the percentage rate defined by the end user as the minimum amount of load demand that must be attended; it is defined by the pL _ CRIT and (16) where pL _ CRIT is the minimum power of load demand that must be attended. kL_CRI T = pL_CRI T /pL_D , kL_CRI T ∈ [0, 1]

(16)

3 Power Management Strategy The power management strategy is presented in Figs. 2 and 4. The available power block is given in Fig. 3.

3.1 Cases 1, 2, 3, and 4 The case 1, case 2, case 3, and case 4 happen when p is positive representing that the power of PV supply is more than the power sum of load demand and common

Fig. 2 Flowchart of operational power management algorithm

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Fig. 3 Flowchart of available power calculation

Fig. 4 Sub-flowchart of operational power management algorithm

DC bus compensated; meanwhile, pL is more than its critical load. In the case 1, case 2, and case 3, p can be distributed by the battery storage and public grid. The battery storage has the higher priority than public grid in the power compensation of the microgrid. When battery storage and public grid are both limited to their limitations, the PV shedding happens in case 1. The battery storage and public grid can support the p in case 2 and case 3 under their limitations. The SC recharging is triggered by the socSC in case 4. When the SC starts recharging, the p is

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the SC recharging power. The SC cannot stop recharging until socSC reaches the SOCSC _ MAX _ MAX or the SC recharging time, tSC _ CH , is more than its minimal value TSC _ MIN . The two conditions also keep the SC working at period to avoid the converters working at low efficiency.

3.2 Cases 5, 6, 7, 8, 9, and 10 The case 5, case 6, case 7, case 8, case 9, and case 10 happen when p is negative, or pL is less than its critical load. The start time of SC recharging is decided by socSC . When socSC is less than SOCSC _ MIN _ MAX , the SC starts recharging. The battery storage and public grid can support the SC recharging and pL _ D under their limitations in cases 5 and 6. The load shedding happens in case 5. The SC cannot stop recharging until socSC is more than SOCSC _ MAX _ MAX or the SC recharging time, tSC _ CH , is more than its minimal value TSC _ MIN . In case 7, case 8, case 9, and case 10, p can be distributed to the battery storage and public grid. The battery storage has the high priority than public grid in the power compensation of the microgrid. When battery storage and public grid are both limited to their limitations, the load shedding happens in case 7. When socSC is less than SOCBS _ MIN and pL is less than its critical load, the DG is turned on in case 10. The battery storage and public grid can support the p in case 8 and case 9 under their limitations.

3.3 Case 11 When the DG is turned on, the SC starts discharging to compensate the power of the sluggish dynamic of the DG till the DG can supply the stable power expressed in (10). When the DG can supply the stable power, it starts charging the SC and supplying p to keep the power balance of the microgrid until the SC finishes charging. Then the DG stops charging the SC, and it starts charging the battery and supplying p to keep the power balance of the microgrid until the battery finishes charging. When the battery finishes charging or the DG reaches its duty cycle, the DG is turned off.

4 Simulation Results and Analyses The microgrid power management is programmed in MATLAB/Simulink. The DC microgrid simulation parameters and scenario are given below.

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Values 1750 W 1000 W 80% 20% 50% 6.6 Ah 200 W 400 V 1500 W

Parameters TDG_ON_MAX SOCSC_MAX_MAX SOCSC_MAX_MIN SOCSC_MIN_MAX SOCSC_MIN_MIN SOCSC_0 PSC_MAX TSC_MIN kL_CRIT

Values 1 hour 85% 75% 45% 35% 75% 1500 W 3 min 80%

4.1 Simulation Case The weather data are recorded on 20 June 2018 at the Université de Technologie de Compiègne. The public grid is considered as a single-phase voltage power source. Load power curve is scaled according to a real daily consumption profile of the university building, which consists of 49 appliances as stated in [16]. The parameters are given in Table 1. To allow the DG start-up, in this simulation, the public grid power is limited to 200W. The DG power is limited to 1500 W to be at same level of the PV and the load demand power; the DG duty cycle is set to 1 h. The maximal power of the SC is limited to 1500 W same as the DG; the SC working period, TSC _ MIN , is constrained to be more than 3 min. kL _ CRIT is set to be 80%. The common DC bus voltage reference is 400 V.

4.2 Simulation Results The simulation is made for a time horizon from 8:00 to 17:00. From 10:00 to 14:00, the microgrid operates in islanded mode; and in the rest of time, it operates in gridconnected mode. The weather data recorded on 20 June 2018 are shown in Fig. 5. With the time increasing, the variations of the two data sets are severe at noon. The curve of the common DC bus voltage and the SOC curves of SC and battery storage are provided in Fig. 6. One notes the voltage of common DC bus oscillates around 400 V. This slight fluctuation becomes obvious when the events occur, i.e., the limitations condition of the storage and public grid, DG start-up and end-up, SC charging and discharging, PV shedding or load shedding; however, the stability of common DC bus voltage is kept. The power curves are shown in Fig. 7. At 9:58, 10:41, 11:26, and 12:34, the DG is turned on as in cases 10 and 11. At 9:31, 12:15, 13:18, 14:02, 14:42, 15:19, 15:54, and 16:28, the SC is recharged as in case 4. At 8:19 and

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Fig. 5 Weather data on 20 June 2018

Fig. 6 Curves of common DC bus voltage and SOC of storage

11:54, the load shedding happens. At 10:56, 11:49, 12:49, 14:52, and 15:44, the PV supplies more power than the power that microgrid can consume, so the PV starts being shed as in case 1.

5 Conclusions This paper presents an operational algorithm for a full DC microgrid, which combines grid-connected and islanded modes, taking the sluggish dynamic of the DG and the self-discharging characteristic of the SC into consideration. Meanwhile,

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Fig. 7 Curves of power

a demand side management is applied with a real-time load demand power optimization. The results obtained under MATLAB/Simulink show that the power management algorithm can keep the power balance and operate the building selfconsumption. The future work will focus on the techno-economic dispatching optimization.

References 1. M. Lubna, M. Basu, M.F. Conlon, Microgrid: architecture, policy and future trends. Renew. Sustain. Energy Rev. 64, 477–489 (2016) 2. M. Kumar, B. Tyagi, A state of art review of microgrid control and integration aspects, 7th India International Conference on Power Electronics (IICPE), Patiala, pp. 1–6, 2016 3. A.M.R. Lede, M.G. Molina, M.Martinez, P.E. Mercado, Microgrid architectures for distributed generation: a brief review, IEEE PES Innovative Smart Grid Technologies Conference – Latin America (ISGT Latin America), Quito, pp. 1–6, 2017 4. M. Sechilariu, F. Locment, Urban DC microgrid: intelligent control and power flow optimization (Elsevier Inc, Waltham, 2016) 5. M. Wooldridge, N.R. Jennings, Intelligent agents: Theory and practice. Knowl. Eng. Rev. 10(2), 115–152 (1995) 6. E. Amicarelli, Q.T. Tran, S. Bacha, Multi-agent system for day-ahead energy management of microgrid, 18th European Conference on Power Electronics and Applications (EPE’16 ECCE Europe), Karlsruhe, pp. 1–10, 2016. 7. R.R. Deshmukh, M.S. Ballal, H.M. Suryawanshi, G.G. Talapur, A control algorithm for energy management and transient mitigation in DC microgrid, National Power Electronics Conference (NPEC), Pune, pp. 270–275, 2017 8. P. Sanjeev, N.P. Padhy, P. Agarwal, Effective control and energy management of isolated DC microgrid, IEEE Power & Energy Society General Meeting, Chicago, IL, pp. 1–5, 2017

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9. A. Merabet, K.T. Ahmed, H. Ibrahim, R. Beguenane, A.M.Y.M. Ghias, Energy management and control system for laboratory scale microgrid based Wind-PV-Battery. IEEE Trans. Sustain. Energy 8, 145–154 (2017) 10. K. Dehghanpour, H. Nehrir, Intelligent microgrid power management using the concept of Nash bargaining solution, 19th International Conference on Intelligent System Application to Power Systems (ISAP), San Antonio, TX, pp. 1–5, 2017 11. M.G. Villalva, J.R. Gazoli, E.R. Filho, Comprehensive approach to modeling and simulation of photovoltaic arrays. IEEE Trans. Power Electron. 24, 1198–1208 (2009) 12. C. Yin, M. Sechilariu, F. Locment, Diesel generator slow start-up compensation by supercapacitor for DC microgrid power balancing, IEEE International Energy Conference (ENERGYCON), Leuven, pp. 1–6, 2016 13. C. Yin, H.W. Wu, F. Locment, M. Sechilariu, Energy management of DC microgrid based on photovoltaic combined with diesel generator and supercapacitor. Energy Convers. Manag. 132, 14–27 (2017) 14. C.Y. Yin, H.W. Wu, M. Sechilariu, F. Locment, Power management strategy for an autonomous DC microgrid. Appl. Sci. 8, 2202 (2018) 15. T.D. Khoa, L.T. Dos Santos, M. Sechilariu, F. Locment, Load shedding and restoration realtime optimization for DC microgrid power balancing, IEEE International Energy Conference (ENERGYCON), Leuven, pp. 1–6, 2016 16. L. Trigueiro dos Santos, M. Sechilariu, F. Locment, Optimized load shedding approach for grid-connected dc microgrid systems under realistic constraints. Buildings 6, 50 (2016) 17. Ibm ilog cplex optimizer. [Online]. Available: http://ibm.com

Management Strategy of an Electric Vehicle Charging Station Under Power Limitation Dian Wang, Hongwei Wu, Fabrice Locment, and Manuela Sechilariu

Abstract The rapid development of electric vehicles increases the power demand, which causes an extra burden on public grid and most importantly increases the load fluctuations to the public grid. In the proposed management strategy, a charging station is empowered by a DC microgrid, and the charging power can be limited according to power availability. Such a DC microgrid consists of electric vehicles, electrochemical storage systems, a public grid connection, and photovoltaic sources, which help to reduce greenhouse gas emissions. This paper focuses on the management strategy of an electric vehicle charging station under power limitation, presents the topology of the electric vehicle charging system, and discusses the common problems during electric vehicle charging process. The simulation results obtained under MATLAB/Simulink verify the feasibility of the management strategy that presents good performance in terms of precise control.

1 Introduction In many countries, greenhouse gas emission reduction plans have been implemented, and one of the promising solutions is the transport electrification. Electric vehicle (EV) is a transport means that emits zero greenhouse gas and produces minimal noise. The power train of the EV depends on the electric motors and battery storage, which has greater efficiency and lower operating costs compared with the traditional internal combustion engine [1]. The continuous development of lithium-ion battery and rapid charging technology will be the main driver for the EV popularity in the near future [2]. However, the current EV industry has encountered many technical limitations, such as high initial cost, limited charging facilities, limited driving range, long battery charging time, and short battery life [3]. In addition, frequent charging of

D. Wang · H. Wu · F. Locment · M. Sechilariu () Sorbonne University — Université de Technologie de Compiègne, Compiègne, France e-mail: [email protected]; [email protected]; [email protected]; [email protected] © Springer Nature Switzerland AG 2020 W. Zamboni, G. Petrone (eds.), ELECTRIMACS 2019, Lecture Notes in Electrical Engineering 697, https://doi.org/10.1007/978-3-030-56970-9_15

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electric vehicles (EVs) by grid power causes the problem of power quality as well as power system stability. Moreover, when the EV charging process is consistent with the peak load of the public grid, the impact of the charging load will be more serious [4]. The swapping of batteries is proposed in [5, 6], and optimal pricing algorithm and strategy are given [7, 8] for charging EVs. However, this increases the peak burden on public grid. The author of [4] discussed three main charging patterns of EV users from observations on measured data and proposed a novel schedule strategy based on “valley filling” concept to manage EV charging behaviors in order to relieve its impact on the grid; however, this strategy is based on probability, and it cannot completely prevent public grid overload if the charging of EVs is unscheduled. In addition, the proposed pattern-change method does not make EV users to downscale the total EV battery charging power absorbed from public grid. On the other hand, the distributed energy generation system has attracted wide attention because of its on-site power consumption, transmission investment savings, lower operating costs, and reduced power transmission losses, which improves peak performance of public grid without increasing the grid capacity [9]. Due to its simple operation and sustainability, the photovoltaic (PV) source is considered to be the most effective choice for on-site sources. However, PV power still has unpredictable properties. Thus, the energy storage system is used to complement the PV sources to overcome and sustain PV power output [10, 11]. Based on this, an EV charging station model empowered by a DC microgrid is proposed. The DC microgrid aggregates EVs, a storage system, a public grid connection, and a PV source; aims at power balancing of the system [12]; and brings some various interests [13] such as the peak power of power grid is lowered, the profits of the charging station is increased, and the EV users’ charging cost is reduced. Due to the unpredictability of the PV power, the capacity limitation of the storage, and the power limitation of the public grid, the power of an EV charging station can be limited. In addition, this power limitation is variable in different situations, according to the weather and the charging time slots. Vehicle to Grid (V2G) technology, as one of the smart grid technologies, allows bidirectional energy exchange between the EV and public grid, which has a bright development prospect brought by the EV integration in the power grid, takes advantage of the EV to improve the operation of the power system, brings many services to the power grid, and maximizes the renewable energy source integration [14, 15]. Meanwhile, EV owners could participate in V2G services in order to enjoy attractive revenue [16, 17]. Thus, a complete management strategy for an EV charging station is essential for the future V2G deployments. The main contributions of this work are (i) proposing a microgrid-based EV charging station topology and (ii) proposing a power management strategy for an EV charging station which can deal with the power availability and interact with the EV users. Following the presented considerations, the topology of the EV charging station based on a DC microgrid is described in Sect. 2. The EV charging station management strategy is introduced in Sect. 3. The simulation results and analyses are presented in Sect. 4. Conclusions and perspectives are given in Sect. 5.

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2 Topology of the Studied System The studied system is designed on the basis of a DC microgrid. As shown in Fig. 1, it is composed of the PV sources, an electrochemical storage system, a public grid connection, and an EV charging station, which includes five EV chargers.

2.1 DC Microgrid Power Supply These components are connected to the common DC bus. The electricity produced by PV sources is primarily for EV charging. Storage is an additional energy source to supply the EVs or to absorb excessive energy produced by PV sources. The public grid is used as a backup source, which allows PV sources to sell the excess energy. If PV power is lower than the power demanded by the EVs, the additional power needed to charge EVs is provided primarily by the storage and then by the public grid. In contrast, the excess energy primarily feeds the storage and then is injected

Fig. 1 The EV charging station based on a DC microgrid

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into the public grid [12, 18]. Based on the above analysis, the EVs are the only loads, as shown in Fig. 1. Since the energy efficiency may be improved by eliminating energy conversion steps, the PV is directly connected to the DC bus without a static converter.

2.2 Modeling of EV Charging The protocol of charging lithium batteries in EVs is the Constant Current/Constant Voltage (CC/CV) process [12, 19]. During the CC mode, the charging current remains constant until the voltage rises to a cutoff voltage. During the CV mode, the voltage remains constant while the current drops. This CC/CV procedure is supposed to be controlled by a battery management system already integrated into the EV battery system. When the EV just starts charging, the EV battery voltage is relatively low. If the charging current is not constant, the battery life cycle and the charger life cycle will be shortened. When the battery is nearly fully charged, the procedure goes into constant voltage phase, whose goal is to prevent the battery from overcharging. In this paper, it is assumed that three charging modes exist: the fast mode, the average mode, and the slow mode. The EV battery power pEV and its state of charge noted SOCEV for the same EV are presented in Fig. 2. In this example, the maximal charging power demanded by the fast mode PFAST _ MAX is 83 kW, the maximal charging power demanded by the average mode PAVER _ MAX is 27 kW, and the maximal charging power demanded by the slow mode PSLOW _ MAX is 7 kW.

Fig. 2 Power and state of charge during EV charging

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3 EV Charging Station Management Strategy The management strategy of the EV charging station mainly depends on the charging choice of the EV users. Different charging modes correspond to different charging costs. If the users choose the fast mode, they will save time along with relatively high fees. On the contrary, if users choose average mode or slow charge, the cost will be lower. The flowchart of the EV charging station is shown in Fig. 3, where pST _ AVA is the available power of the EV charging station. The questions for the users are listed in Table 1. The available power and options are presented in Table 2.

Fig. 3 Flowchart of the EV charge station Table 1 Question lists Sign Q1 Q2 Q3 Q4 Q5

Question Which charging mode? The fast mode, the average mode, or the slow mode. The power is insufficient for the fast mode. Which do you choose among the average mode, waiting and departure? The power is insufficient for average mode. Which do you want to choose among the slow mode, waiting and departure? The power is insufficient for any recharging mode. Which do you want to choose between waiting and departure? The EV is being charged. Do you want to stop charging and leave?

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Table 2 Available power test and options Condition pST _ AVA > PFAST _ MAX pST _ AVA < PFAST _ MAX && pST _ AVA > PAVER _ MAX pST _ AVA < PAVER _ MAX && pST _ AVA > PSLOW _ MAX pST _ AVA < PSLOW _ MAX

Option The fast mode, the average mode, or the slow mode The average mode, waiting or departure The slow mode, waiting or departure Waiting or departure

3.1 Interaction with the EV Users In order to keep the power balance in the microgrid, it is necessary to set up a power limitation for the charging station. There are three possible cases to be considered when a new EV is connected to an available charger.

3.2 Disconnect EV In the proposed EV charging station management strategy, the disconnection of the EV from the charger is always possible, permitting these users to stop charging and leave immediately.

3.3 Standby Mode The EV charger is in standby mode if the user chooses to wait for the power availability. In standby mode, the EV is not charged until the available power is enough for the chosen charging mode.

4 Simulation Results and Analyses The EV charging station management strategy simulation is performed with MATLAB/Simulink, in which the process CC/CV with three charging modes is implemented. The simulated scenario is an EV charging station based on the DC microgrid under power limitation. When an EV arrives, the user chooses the charging mode. Under the power limitation, if the charging station available power is greater than the maximal power demanded by the charging mode chosen by the user, the EV charges directly. If not, system offers options for users.

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Five EV chargers are set in the simulation model, according to the priority order, namely, from the charger 1 to the charger 5, the order from top to bottom in Fig. 1. In order to better emulate the real situation, the initial SOCEV is randomly generated in the simulation. Different users will take the charging price and charging time into account to choose the charging mode they need, and to emulate this action, the charging mode is also randomly generated.

4.1 Users’ Choice The simulation time period is from 9:00 to 18:00. In order to better analyze the simulation results, the simulation can be divided into three time slots: 9:00–11:00, 11:00–13:00, and 13:00–18:00. The number of records for the EV charging station are listed in Table 3. Output power of each charger is shown in Fig. 4, where p_charger_n is the output power of charger n. In the first time slot 9:00–11:00, six EVs arrive at the station: four EVs choose to be charged followed in turn by charging mode fast mode, fast mode, average mode, and slow mode, one EV chooses waiting, and one EV chooses departure. The power

Table 3 Number of records Number Arrive Being charged Waiting Departure

9:00–11:00 6 4 1 1

Fig. 4 Output power of each charger

11:00–13:00 5 4 1 0

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requested by charger 1 and charger 2 with peak values close to 90 kW represents that the charging mode chosen by users is fast mode. The power requested by charger 3 and charger 4 with peak values close to 30 kW indicates that the charging mode chosen by users is average mode. The power requested by charger 5 represents that the charging mode chosen by the user is slow mode. In addition, the curve shape of the power requested by charger 5 is rectangular, because the EV disconnects the charger before fully charged, while the other EVs charging curves are complete CC/CV. In the second time slot 11:00–13:00, five EVs arrive at the station: four EVs choose to be charged by average mode and one EV chooses waiting. In the third time slot 13:00–18:00, five EVs arrive at the station: four EVs choose to be charged followed in turn by charging mode average mode, average mode, average mode, and slow mode, and one EV chooses waiting. The curve shape of the power requested by charger 5 is a complete CC/CV process, which means that the EV is disconnected from the charger after being fully charged.

4.2 Disconnection As shown in Fig. 4, in the first time slot, because the user has an emergency and needs to leave immediately, the EV connected to the charger 5 disconnects the charger before fully charged. In the second time slot, the EVs connected to the charger 4, charger 2, and charger 1 disconnect respectively in order when not fully charged because of the users’ needs.

4.3 EVs on Waiting In the first time slot, after the EV connected with the charger 1 fully charged represented, the EV on waiting connected with charger 4 is starting to be charged by average mode. In the second time slot, as the EV connected with charger 4, charger 2, and charger 1 leaves urgently in order, thus pST _ AVA is greater than PFAST _ MAX , the EV connected with charger 5 on waiting is automatically starting to be charged followed by fast mode. In the third time slot, after the EVs connected with charger 1 and charger 2 fully charged, the EV on waiting connected with charger 4 is starting to be charged followed by fast mode.

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total power of the station (kW)

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180 150 120 90 60 30 0 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00

Fig. 5 Total output power of the charging station

4.4 Variable Power Limitation The PV sources, the storage, and the public grid can be considered as a multisource system imposes a total charging power limitation for EVs. Total recharging power is shown in Fig. 5. The public grid load is variable according to different time of 1 day. For example, it is considered that after 11:00, the power consumption suddenly increases because the public grid load increases. To ensure public grid power balance, therefore, the power limitation of the EV charging station is required. In order to emulate this reality, the initial power limitation of the station is 120 kW, but at 9:05, the power limitation is set to 210 kW. Thus, 120 kW can guarantee the EV charging station to provide users with one fast mode, one average mode, and one slow mode, and 210 kW can guarantee the EV charging station to provide users with two fast mode, one average mode, and one slow mode. The simulation results show that the EV charging station can operate normally under variable power limitations, which proves the effectiveness of the power management strategy.

4.5 Recording of EV Behavior The EV charging load is inherently more random than traditional power loads. For future planning and deployments of the charging station, recording of EV behavior

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21 num_arrive_N1 20 num_charging_N2 19 18 num_plein_N3 17 num_waiting_N4 16 num_departure_N5 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00

Fig. 6 Recording of EV behavior

is necessary. For example, how many EVs arrive at the charging station every day, how many EVs choose to wait when the available power of the charging station cannot meet the power demanded by the charging mode chosen by users, and how many EVs choose to leave. To continuously develop the charging station, it is necessary to adjust strategies through the recorded data to maximize benefits of the charging station. The recording of EV behavior in different situations during the simulation is shown in Fig. 6. Real-time data is recorded in the system, including total number of EVs arrived at the charging station N1 (num_arrive), total number of EVs being charged N2 (num_charging), total number of EVs fully charged N3 (num_plein), total number of EVs on waiting N4 (num_waiting), and total number of EVs choose departure N5 (num_departure). As can be seen from Fig. 6, N1 is the sum of N2, N3, N4, and N5, which satisfy (1) and is one of the ways to verify whether the system is working properly or not. N 1 = N2 + N3 + N4 + N5

(1)

As can be seen from the Fig. 6, most of the EVs arrived at the charging station choose to be charged. When the available power of the charging station is insufficient, the users are more inclined to wait, and only a small number of users choose to leave directly. Thus, the current planning of this charging station is reasonable, and the management strategy shows a significant control effect. If most of EVs arrived at the charging station choose to leave due to power

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limitation, the charging station should consider adjusting its management strategy, such as adjusting the power limitation or appropriately reducing the charging price according to the waiting time of users.

5 Conclusions In this paper, a management strategy for an EV charging station empowered by a DC microgrid under power limitation was proposed. The DC microgrid combines renewable energy like PV and prevents public grid from overloading. The proposed management strategy aims to simulate various realistic situations including the interaction with the EV users. The simulation results show in detail the management strategy of the EV charging station, such as charging modes, real-time charging power, power limitation, and especially the various options of users in case of lacking power for the EV charging, which presents excellent control effects. The spread of EVs will increase the grid load during the EV charging process. However, the expected penetration of EVs opens up the possibility for the implementation of V2G. Based on the management strategy described in this study, future research will focus on the implementation and control strategies of V2G, taking both the financial aspect and the technical aspect of the battery into account to maximize the benefits for EV owners.

References 1. K. Mahmud, G.E. Town, S. Morsalin, M.J. Hossain, Integration of electric vehicles and management in the internet of energy. Renew Sust Energ Rev 82, 4179–4203 (2018) 2. H. Weiss, T. Winkler, H. Ziegerhofer, Large lithium-ion battery-powered electric vehicles — From idea to reality, in ELEKTRO, (IEEE, Mikulov, 2018), pp. 1–5 3. K.M. Tan, V.K. Ramachandaramurthy, J.Y. Yong, Integration of electric vehicles in smart grid: a review on vehicle to grid technologies and optimization techniques. Renew Sust Energ Rev53, 720–732 (2016) 4. Q.Y. Dang, Electric Vehicle (EV) charging management and relieve impacts in grids, 9th IEEE International Symposium on Power Electronics for Distributed Generation Systems (PEDG), Charlotte, USA, pp. 1–5, 2018 5. B. Sun, X. Tan, D.H.K. Tsang, Optimal charging operation of battery swapping and charging stations with QoS guarantee. IEEE Trans Smart Grid9(5), 4689–4701 (2018) 6. M. Bashiri, N. Bahadori, Optimized plan of charging stations for management of demands: an emerging need of hybrid electric vehicle. Future Technologies Conference (FTC), San Francisco, CA, pp. 422–425, 2016 7. K. Chaudhari, A. Ukil, K.N. Kumar, U. Manandhar, S.K. Kollimalla, Hybrid optimization for economic deployment of ESS in PV-integrated EV charging stations. IEEE Trans Ind Inf 14(1), 106–116 (2018) 8. J. Tao, D. Huang, D. Li, X. Yang, C. Ling, Pricing strategy and charging management for PVassisted electric vehicle charging station. 13th IEEE Conference on Industrial Electronics and Applications (ICIEA), Wuhan, pp. 577–581, 2018

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9. B. Deng, Z. Wang, Research on electric-vehicle charging station technologies based on smart grid. Asia-Pacific Power and Energy Engineering Conference, Wuhan, China, pp. 1–4, 2011 10. M. H. F. Ahamed, U. D. S. D. Dissanayake, H. M. P. De Silva, H. R. C. G. P. Pradeep, N. W. A. Lidula, Modelling and simulation of a solar PV and battery-based DC microgrid system. International Conference on Electrical, Electronics, and Optimization Techniques (ICEEOT), Chennai, pp. 1706–1711, 2016 11. Y. Bhandari, S. Chalise, J. Sternhagen, R. Tonkoski, Reducing fuel consumption in microgrids using PV, batteries, and generator cycling. IEEE International Conference on ElectroInformation Technology, EIT 2013, Rapid City, SD, pp. 1–4, 2013 12. F. Locment, M. Sechilariu, Modeling and simulation of DC microgrids for electric vehicle charging stations. Energy8, 4335–4356 (2015) 13. O. Marcincin, Z. Medvec, Concept of charging stations for electric cars. 15th International Scientific Conference on Electric Power Engineering (EPE), Brno, pp. 169–172, 2014 14. J.Y. Yong, V.K. Ramachandaramurthy, K.M. Tan, N. Mithulananthan, A review on the stateof-the-art technologies of electric vehicle, its impacts and prospects. Renew Sust Energ Rev49, 365–385 (2015) 15. Y. Yao, W. Gao, J. Momoh, Performance optimization and evaluation of V2G in regulated and deregulated microgrid. IEEE Conference on Energy Internet and Energy System Integration (EI2), Beijing, China, pp. 1–6, 2017 16. A. A. Almehizia, J. M. Snodgrass, Investigation of V2G economical viability. IEEE Texas Power and Energy Conference (TPEC), College Station, TX, pp. 1–6, 2018 17. F. Ahmad, M.S. Alam, M. Asaad, Developments in xEVs charging infrastructure and energy management system for smart microgrids including xEVs. Sustain Cities Soc35, 552–564 (2017) 18. F. Locment, M. Sechilariu, DC microgrid for future electric vehicle charging station designed by energetic macroscopic representation and maximum control structure. IEEE International Energy Conference, Dubrovnik, Croatia, pp. 1454–1460, 2014 19. V. Bobanac, H. Pandzic, Lithium-ion batteries: experimental research and application to battery swapping stations. IEEE International Energy Conference (ENERGYCON), Limassol, pp. 1– 6, 2018

Thermal Analysis of the Power Distribution System As Part of an Underwater Compressed Air Energy Storage Station Océane Maisonnave, Luc Moreau, René Aubrée, Mohamed Fouad Benkhoris, and Thibault Neu

Abstract This paper deals with sizing and reliability of the power electronics equipment embedded in an offshore compressed air energy storage station. In this system, the power grid is distributed through a DC bus between ten identical electropneumatic power conversion units. Each unit is also divided in two parallel variable speed drive devices which operate with large power fluctuations. From a transient thermal model of IGBT modules, the thermal behaviour of power converters is described over cyclic fluctuations. Thermal results analysis shows that the sizing of the system could be considered downwards. Then, the main grid side converter sizing is discussed according to two operating configurations. Finally, considering thermal results, the temporal interleaving of the power units operation allows to reduce current rating of IGBTs as well as thermal stress of the semiconductors.

O. Maisonnave () IREENA – University of Nantes, Saint-Nazaire, France Segula Technologies, Bouguenais, France e-mail: [email protected] L. Moreau · R. Aubrée · M. F. Benkhoris IREENA – University of Nantes, Saint-Nazaire, France e-mail: [email protected]; [email protected]; [email protected] T. Neu Segula Technologies, Bouguenais, France e-mail: [email protected] © Springer Nature Switzerland AG 2020 W. Zamboni, G. Petrone (eds.), ELECTRIMACS 2019, Lecture Notes in Electrical Engineering 697, https://doi.org/10.1007/978-3-030-56970-9_16

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1 Introduction For the last decade, power electronics for variable speed operations has proven particularly effective in increasing the energy performances of renewable energy systems [1–3]. The insulated gate bipolar transistor (IGBT) technology is currently the most powerful switching component for connecting a high-power energy conversion system to the power grid. However, IGBT components can also be the most critical elements within a power conversion chain [4–6]. In fact, power converters are not usually sized to perform with large power fluctuations which lead to an important stress on the power semiconductors. That will affect reliability, lifetime and cost, especially for ocean energy systems where the marine environment limits the maintenance of power components. The studies [7–9] propose a reliability analysis of power electronics in ocean energy as wave energy converter and offshore wind turbine based on the thermal behaviour model of IGBT devices. Then, we propose in this paper a thermal analysis of the power converters as part of an offshore energy storage system operating in marine environment. The system under consideration is part of the development of a compressed air energy storage (CAES) system located in marine environment. This technology performs for storage density of a few hundred MWh of electrical energy in prospecting of local-grid support and ocean energy spreading. The system is composed of a floating platform and an underwater storage tank, Fig. 1. The barge is connected to both electrical power grid and submarine compressed air tank and includes all the electro-pneumatic conversion system. To achieve a high-power conversion, the air compression process is based on a liquid piston mechanism distributed in parallel operations. This principle of the electropneumatic energy conversion is detailed in [10]. The paper is organized as follows: Sect. 2 describes the electrical power distribution system which operates inside the floating barge. We therefore develop in Sect. 3

Fig. 1 Offshore CAES system REMORA

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the mathematical model of IGBT power losses as well as the thermal model. Then, the results on the thermal behaviours of the devices are presented and discussed in Sect. 4.

2 Description of the On-Board Power Distribution System In this study, we focus on the electrical power distribution in the platform which is shown in Fig. 2. A main low-voltage high-power inverter converts the AC power supply from the grid to a DC power supply. As mentioned below, for performances consideration, the power is distributed in the DC bus between ten identical electropneumatic power conversion units (PU). In each unit, two AC variable speed drives composed of a synchronous machine (M) and a DC/AC converter at different rated power range (low power and high power) are connected in parallel. They operate simultaneous during a cycling period to drive the compression mechanism with high efficiency. Note that for the sake of simplicity, the components of the hydropneumatic compression are not depicted in the platform architecture. Finally, the optimal management of a power unit which converters DC electrical power into compressed air leads to a dynamic and variable power flow for each electrical machine working through cycles of 3 min. This study is developed in [11].

Fig. 2 Electrical power distribution with a DC-link supply unit

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1000 LP HP 500

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The speed and torque profiles of LP (low power) and HP (high power) machines in storage mode are given in Fig. 3. Note that the system is assumed reversible, and the mechanical profiles are the same in production mode, but the machines shaft will rotate in reverse direction. The DC bus is supposed equal to 1200 V, and the main grid side converter is supplied by a AC grid with an effective value phase to phase of 690 V. In first consideration, we supposed that the 10 PUs operate identically at the same time so that the rated power of the grid converter is ten times a PU power, Fig. 4. A flux weakening mode control is established for each converter composing the ten power units in order to minimize losses of each power unit. Some examples of losses minimization control are given in [12, 13]. That leads to the rated value parameters of a PU gathered in Table 1. Besides, the main grid side converter is controlled to reach a unit power factor [14].

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Parameter Rated power Max. RMS current Max. RMS line voltage

LP value 1.1 MVA 0.92 kA 399 V

HP value 2.7 MVA 2.3 kA 391 V

Grid value 38 MVA 31.8 kA 398 V

3 Analytical Model of Power Converters In this section, a thermal design of the power converter device is proposed based on the mathematical analysis of the converter power losses and the equivalent dynamic thermal model of an IGBT module.

3.1 Converter Power Losses We assume that each power converter is a three-phase two-level-topology equipped with IGBT modules as it is shown in Fig. 5. In this case, the power losses of a module are composed of the conduction and switching losses for both IGBT and diode. The losses model is based on [15]. The conduction losses are given from the integration of forward losses over a PWM period. The expressions of these losses, PcondIGBT (t) and Pconddiode (t), are expressed in Eqs. (1) and (2). V0IGBT , V0diode , r0IGBT and r0diode are, respectively, the threshold voltage and internal resistance of both IGBT and diode. Iˆ(t) is the current peak value, m(t) the modulation factor, and cos φ stands for the power factor.

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PcondIGBT (t) = V0IGBT Iˆ(t)



m(t) 1 + cos φ 2π 8



+ r0IGBT Iˆ2 (t)

Pconddiode (t) = V0diode Iˆ(t)



m(t) 1 − cos φ 2π 8



1 m(t) + cos φ 8 3π

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+ r0diode Iˆ2 (t)



1 m(t) − cos φ 8 3π

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The switching losses are calculated from turn-on and turn-off energy losses extracted from the manufacturer data sheet. Then, Eqs. (3) and (4) express the switching losses for IGBT and diode separately. # PswIGBT (t) = fsw # Pswdiode (t) = fsw

ai bi Iˆ(t) ci Iˆ2 (t) + + 2 π 4

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ai , bi , ci , ad , and bd and cd are polynomial constant of the energy losses functions. fsw is the PWM switching frequency assumed the same for all converters, Vdc stands for the DC bus voltage, and Vcemax the voltage rating of IGBT module.

3.2 Thermal Model The thermal model of an IGBT module is presented in Fig. 5. It is based on the series connection of the impedance of each of the three layers of the device. The junction temperatures, denoted TjIGBT and Tjdiode , are the temperatures inside the chips and describe the temperature rises from the ambient temperature (Ta ) due to the losses. Considering solicitations of semiconductors, the thermal behaviour of the devices is described by a transient thermal model. As it is shown in Fig. 6, the Foster’s model is composed of the series connection of parallel RC impedances. Then, the equivalent impedance between Tj and the case temperature Tc can be written as follows: Zj −ci =

4

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(5)

i=1

The parameters Ri and τi , where τi = Ri Ci , are given by fitting the impedance curve (usually up to the order 4) extracted from the IGBT module data sheet. Rc−h is the equivalent thermal resistance of junction to case resistance of IGBT (Rc−hi ) and diodes (Rc−hd ) given in Eq. (6). Rc−h =

Rc−hi Rc−hd Rc−hi + Rc−hd

(6)

Th defines the temperature on the heat sink, and the thermal model of the heat sink is a RC parallel connection circuit. It is sized to dissipate enough heat so that the maximum junction temperature will not exceed the maximum allowed junction temperature, usually 125 °C. Finally, Ch−a is calculated from the time constant of the cooling technique using in the heat sink. Given the power involved in this

Tj

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application, we will consider a forced convection heat sink with a time constant of around 100 s [16].

4 Results In this section, we first present the results of the thermal behaviour of IGBT modules composing the conversion power unit. Then, we will analyse the behaviour of the main grid side converter according to two operating configurations of the platform.

4.1 Thermal Analysis of the Power Unit Converters Considering maximum current and rated power of the converters (see Table 1), the LP and HP converters will be equipped with IGBT modules with a voltage rating of 1700 V and a current rating of, respectively, 1600A [17] and 3600A [18]. According to the data sheets of components, a maximum temperature of 125 °C is accepted. Then, considering the ambient temperature of 25 °C, the heat sink is sized to permit a heat elevation of 100 °C in steady-state mode for the maximum total losses of IGBT and diode. The main parameters of the thermal model are gathered in Table 3, and the results on both LP and HP IGBT modules are given in Fig. 7. For each figure, the actual heat elevation of each layer of the component (solid line) is compared to the theoretical steady-state temperatures (dotted line) for which the heat sink is sized. Moreover, Table 2 compares the actual maximum temperatures and the permitted maximum temperatures. We observe that neither the first nor the second IGBT reach the temperature of 125 °C. For the LP IGBT, the temperature is lowered by 19% and 3.8% for the HP IGBT. Finally, the thermal analysis of LP and HP IGBTs shows that the cyclic power fluctuations in this application benefit the IGBTs behaviour which do not reach the steady-state temperature. Then, these results make it possible to consider forward a reduction in the power converters sizing and thus a gain on the cost of the installation.

4.2 Thermal Analysis of the Main Grid Side Converter Due to the technical limitations of IGBT ratings, it is assumed that the main grid side converter is only composed of one converter, and the high current rating is reached paralleling the IGBT modules. Then, the current distribution between parallel connection of IGBTs modules is supposed uniform. In this section, we compare the grid converter sizing and behaviour according to two configurations of the platform. The first configuration is illustrated in Fig. 4 where the ten identical power units operate simultaneous. Then, the total rated power is ten times the total

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Fig. 7 Temperatures of IGBTs modules of a power unit during a few operating cycle

R1 Device (K/kW ) LP IGBT 7.59 Diode 12.6 HP IGBT 5.06 Diode 8.43

τ1 (ms) 202 210 202.9 210

R2 (K/kW ) 1.8 2.89 1.201 1.93

τ2 (ms) 20.3 29.6 20.3 29.6

Table 2 Parameters of the thermal model of IGBT modules R3 (K/kW ) 0.743 1.3 0.495 0.866

τ3 (ms) 2.1 7.01 2.01 7.01

R4 (K/kW ) 0.369 1.26 0.246 0.839

τ4 (ms) 0.52 1.49 0.52 1.49

Rj −c (K/W ) 11 18 9 18

6

Rc−a (K/kW ) 6.8

τc−a (ms) 100 0.355 100 0.791

5.64

Max. losses (kW) 1.74

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LP

HP

TjIGBT Tjdiode Tc Th TjIGBT Tjdiode Tc Th

Steady state temp. (°C) 125 112 106 91.6 125 95.1 85.5 46.9

Actual temp. (°C) 101 89.5 83.2 69.8 121.5 91.5 81.9 43.4

213 Gain (%) 19

3.8

Fig. 8 Configuration 2: Interleaving of the 10 power units operations

power of one unit power. In that case, with 3600 A IGBT modules (the same as for HP converter), the converter needs a set of 13 IGBTs modules in parallel to create an equivalent IGBT module, namely, 78 IGBTs for the full- sized converter. Then, to decrease the number of IGBTs, the second configuration will consider a timerelated interleaving of PUs working. As it is shown in Fig. 8, each PU is moved forward according to a uniform distribution over a cyclic period of 3 min. Then, this configuration contributes to reduce significantly the total power of the grid converter, from 37 to 12 MVA, Fig. 9. Thus, the number of IGBTs is considerably reduces to a set of five IGBTs (Table 4). The thermal behaviour for each configuration is developed based on the methodology exposed in the previous section. The temperature fluctuations are shown in Fig. 10. We observe that the maximum temperatures do not exceed the maximum temperature of 125 °C in both configuration. Table 5 describes the main features of the thermal analysis. Configurations 1 and 2 have roughly the same maximum temperature; however, the difference between both behaviours is the dynamics of

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40 Config. 1

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Fig. 9 Comparison of the total power on the grid side converter according to both configurations Table 4 Parameters of the grid power converter for both configuration Config. 1 2

Max. Power (MVA) 37 MVA 14 MVA

Max. RMS current (kA) 31.8 12

Nb. IGBT in parallel 13 5

thermal fluctuations. In fact, the difference between the minimum and maximum temperature, denoted ΔTjIGBT , is around seven times lower when the PUs operating is intertwined, but the period of appearance of temperature peaks is ten times higher compared to Config. 1. However, in addition to the decrease of the rated power, the temperature variations of the chip on Config.2, lower than 10 °C, seem to be much more favourable than Config. 1 for the reliability and cost of the storage system.

5 Conclusion In the context of reliability of a storage system operating in ocean, we proposed a thermal analysis of the power semiconductors composing all the power converters of the floating platform. Based on the mathematical model of the power losses of IGBT module, a thermal model which considers the transient behaviour of devices is developed. Results on the power converters of one of the ten power units highlighted that the temperatures of the chips do not reach the thermal steady-state point. Then, it could be possible to optimize the power converters sizing by reducing either the rated current of IGBTs or the heat sink sizing. That should be contributed to reduce the global cost of the platform. On the grid side, we studied two operating configurations, and we have shown that the interleaving of the power unit operating

Thermal Analysis of the Power Distribution System As Part of an Underwater. . .

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TjIGBTmax (°C) ΔTjIGBT (°C) Peak period (s)

Config. 1

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117

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9.7 19

leads to a considerable reduction of the power converter sizing. Besides, it is resulted from a thermal analysis of the devices that the time shifting of the power units over a cycle greatly decreases the thermal fluctuations of the chips temperature. A more accurate lifetime analysis should be relevant to compare both configurations. Moreover, it should be noted the limitation assumptions on paralleling IGBT which consider a uniform current sharing between the components. Investigations on paralleling should bring forward a more accurate model of the grid side converter.

References 1. S.M. Muyeen, A. Al-Durra, J. Tamura, Variable speed wind turbine generator system with current controlled voltage source inverter. Energy Convers. Manag. 52(7), 2688–2694 (2011) 2. Y. Pannatier, B. Kawkabani, C. Nicolet, J.J. Simond, A. Schwery, P. Allenbach, Investigation of control strategies for variable-speed pump-turbine units by using a simplified model of the converters. IEEE Trans. Ind. Electron. 57(9), 3039–3049 (2014) 3. F. Blaajberg, Z. Chen, S.B. Kjaer, Power electronics as efficient interface in dispersed power generation systems. IEEE Trans. Power Electron. 19(5), 1184–1194 (2004) 4. C. Busca, R. Teodorescu, F. Blaabjerg, S. Munk-Nielsen, L. Helle, T. Abeyasekera, P. Rodriguez, An overview of the reliability prediction related aspects of high power IGBTs in wind power applications. Microelectron. Reliab. 51(9–11) 1903–1907 (2011) 5. Z. Chen, J.M. Guerrero, F. Blaajberg, A review of the state of the art of power electronics for wind turbines. IEEE Trans. Power Electron. 24(8), 1184–1194 (2009) 6. E.E. Kostandya, K. Ma, Reliability estimation with uncertainties consideration for high power IGBTs in 2.3 MW wind turbine converter system. Microelectron. Reliab. 52 2403–2408 (2012) 7. J. Sjolte, G. Tjensvoll, M. Molinas, Reliability analysis of IGBT inverter for wave energy converter with focus on thermal cycling, in 2014 Ninth International Conference on Ecological Vehicles and Renewable Energies (EVER), Monte-Carlo, pp. 1–7 (2014) 8. T. Kovaltchouk, J. Aubry, B. Multon, H. Ben Ahmed, Influence of IGBT current rating on the thermal cycling lifetime of a power electronic active rectifier in a direct wave energy converter, in 2013 15th European Conference on Power Electronics and Applications (EPE), Lille, pp. 1–10 (2013) 9. K. Ma, F. Blaabjerg, The impact of power switching devices on the thermal performance of a 10 MW wind power NPC converter. Energies 5(7), 2559–2577 (2012) 10. T. Neu, Device and method for converting and storing electric energy in the form of compressed air. Patent WO2016193322 A1 11. O. Maisonnave, L. Moreau, R. Aubrée, M.F. Benkhoris, T. Neu, D. Guyomarc’h, Optimal energy management of an underwater compressed air energy storage station using pumping systems. Energy Convers. Manag. 165, 771–782 (2018) 12. C. Mademlis, N. Margaris, Loss minimization in vector-controlled interior permanent-magnet synchronous motor drives. IEEE Trans. Ind. Electron. 49(6), 1344–1347 (2002)

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13. C. Cavallaro, A.O. DiTommaso, R. Miceli, A. Raciti., G.R. Galluzzo, M. Trapanese, Efficiency enhancement of permanent-magnet synchronous motor drives by online loss minimization approaches. IEEE Trans. Ind. Electron. 52(4), 1153–1160 (2005) 14. A. Dahbi, M. Hachemi, N. Nait-Said, M.-S. Nait-Said, Realization and control of a wind turbine connected to the grid by using PMSG. Energy Convers. Manag. 54(Suppl. C) 346– 353 (2011) 15. ABB, Applying IGBTs. Application note 5SYA 2053-04 16. L. Meysenc, M. Jylhäkallio, P. Barbosa, Power electronics cooling effectiveness versus thermal inertia. IEEE Trans. Power Electron. 20(3), 687–693 (2005) 17. ABB, 5SNA 1600N170300 HiPak IGBT Module. Data Sheet, Doc. 5SYA 1460-00, 2017 18. ABB, 5SNA 3600N170300 HiPak IGBT Module. Data Sheet, Doc. 5SYA 1414-06, 2014

Automation Architecture for Multi-terminal DC Grid Gaurav Kumar Roy, Philipp Joebges, F. Ponci, A. Monti, and Rik W. De Doncker

Abstract The multi-terminal DC (MTDC) grid is one of the solutions to accommodate the increasing distributed energy resources (DERs) capacity in the distribution grid. A MTDC grid consists of devices from different manufacturers with proprietary protocol, which is a challenge for monitoring and control of the network configuration, grid conditions and the converters. In this paper, an interoperable communication architecture with IEC 61850 is proposed, which is used to communicate with converters and devices from different manufacturers. Furthermore, the communication architecture is implemented on an MVDC demonstrator grid.

1 Introduction The multi-terminal DC (MTDC) transmission is gaining popularity in recent years because of its capability to carry high power for longer distances with multiple onshore connection points [1]. Furthermore, to reduce the spinning reserve requirement and the cost of electric power generation, a pan European multi-terminal high-voltage DC supergrid is proposed to interconnect various European countries and the regions around their borders. Hence, the generation from the different renewable energy sources can be shared [2]. The MTDC grids are an attractive solution not only for transmission system but also for distribution grid since they offer numerous advantages such as [3, 4] efficient integration of renewable energies, minimisation of multiple AC-DC conversion loss, reduction of embedded converters in grid and reduction of harmonic injection in AC grid. Therefore, it was decided

G. K. Roy () · F. Ponci · A. Monti Institute for Automation of Complex Power Systems, E.ON Energy Research Center RWTH Aachen University, Aachen, Germany e-mail: [email protected] P. Joebges · R. W. De Doncker Institute for Power Generation and Storage Systems, E.ON Energy Research Center RWTH Aachen University, Aachen, Germany e-mail: [email protected] © Springer Nature Switzerland AG 2020 W. Zamboni, G. Petrone (eds.), ELECTRIMACS 2019, Lecture Notes in Electrical Engineering 697, https://doi.org/10.1007/978-3-030-56970-9_17

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to design an MVDC network for the supply of several high-power test benches at RWTH Aachen University in Germany. The MVDC grid in the campus offers the possibility to gain experience about the challenges in the DC distribution grid. One of the challenges faced was the absence of communication standards for the DC network. Thus individual protocol channels were required for automation of the converters from different manufacturers. Furthermore, there was a requirement of including widely spaced field devices such as disconnectors, transducers and circuit breakers into the automation system. Hence the communication architecture should apply to large geographical areas for monitoring, secondary control and tertiary control applications for MVDC distribution grid. This paper describes the automation architecture for a MVDC distribution grid, which consists of three levels: the field level, bay level and station level. Furthermore, the paper describes the data exchanged between the three levels for monitoring and control of the converters. The field level consists of devices such as converter controllers, measurement transducers and circuit breakers. The field devices are connected to the Intelligent Electronic Device (IED) in the bay level, which is compatible with analogue and digital input and output. The station level consists of the SCADA centre communicating with MMS (Manufacturing Message Specification) protocol with the IED according to the IEC 61850 standard. The IEC 61850 standard is widely used in the transmission and distribution network, thus making the proposed communication architecture scalable for the future hybrid ACDC network.

2 Converter Data Model with IEC 61850 IEC 61850 is a global communication standard for the substation automation system, which defines the communication between Intelligent Electronic Devices (IEDs) and control centre [5]. The standard defines an object-oriented, hierarchical data model with semantics that provides information on the data to be exchanged as well as the mechanisms of data exchange. The standard provides Abstract Communication Service Interface (ACSI) services, which consist of a set of services such as read, write, control, reporting, logging, get directory, file transfer and response to the services [6]. The ACSI services could be implemented on an IED device which can execute applications, store measurements and exchange information with other IEDs. The IEC 61850 standardises IEDs into a hierarchical object model. The functionalities of the IED are governed by logical devices. The logical nodes are responsible for the modular programming of the IED. The data within the logical nodes are assigned data object with a specific data attribute. A logical node (LN) implementation is according to IEC 61850-5 and IEC 61850-72, contained in a logical device of an IED. The LN consists of data objects (DO) defined according to IEC 61850-7-x[7]. The logical nodes for IED in the MTDC grid can be classified into three major sections: – Basic nodes: The category consists of the basic attribute classes or logical nodes such as LLNO and LPHD. The LLNO logical node defines the communication

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protocols for the IED. The LPHD represents the physical device, and the communication properties, which is shared by other logical nodes. The converter output and input voltage, current and power are important quantities to be known for monitoring the MTDC grid. The measurements of these quantities are reported to the station level for monitoring algorithms such as state estimation and power flow of the network. The measurements are used for further advance coordinated control algorithms. Therefore, logical nodes necessary for representing the AC and DC measurements are considered for the data model design. The logical nodes representing the measurements in the AC and the DC side of the converter are MMDC and MMXU, respectively. – Control nodes: The different control strategies for DC grid power flow can be broadly grouped into constant voltage control and voltage droop control. The constant voltage control follows a master-slave scheme, whereas the droop control follows a peer-to-peer scheme. The different schemes require different control parameters to be set from the bay level or the station level. For example, the control parameters of the different variations of the droop control strategies, namely, deadband and non-deadband droop control, have to be represented as data attributes, specifying the different droop coefficients along with their band limits. The data model considers different converter topologies, filter components and types of switches employed for the operation of MTDC grids. The ZCON logical node is defined in the IEC 61850-7-420, and it has the basic system requirements regarding ratings of the converter. The logical base node has been extended with additional data objects to represent the IED converter. – Protection nodes: The converters have strict current and voltage limits, arising from their strict operational thermal limits. The different methods of protecting the converters from faults on the DC side and faults on the AC side, beyond the protection zone of the nearest AC circuit breaker, have been proposed in [20]–[22]. The methods involve measures for blocking the converter arms and coordinating with the DC and AC circuit breakers in order to isolate the converter from the external faults. Furthermore, the DC grid has to be protected from the internal faults of the converter and faults propagated from one grid to the other through the converter. Due to the lower reactance in the DC grids, the fault propagation within the DC grids is higher. Therefore, logical nodes for overcurrent protection are included in the data models that initiate the tripping of the appropriate circuit breakers isolating the converters from the grid. The logical nodes PTOC (time overcurrent protection) and PTHF (power electronic switch protection) are nodes for the protection of the converter during an over-voltage or short circuit in the system.

2.1 Automation Architecture The proposed automation architecture for MVDC grid offers flexible, interoperability and scalability for communication between SCADA centre and the field devices.

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The automation structure is divided into three levels according to IEC 61850-9-2, which is discussed below: – Process level: The process level consists of the converter controller, voltage transducers, current transducers and disconnectors. The field devices in the process level communicate with the IED through digital and analogue signals. – Bay level: The bay level is responsible for measurement, protection and secondary control of the substation. In the proposed automation architecture, the IED is responsible for the bay-level functions. The IED is implemented on NICompact Reconfigurable Input Output (RIO) processor-9024 (NI-CRIO). The IED has a scalable chassis. Hence the number of digital and analogue channels can be configured according to the application. The NI-CRIO has two Ethernet ports for communication in local area network (LAN) and wide area network (WAN). The NI-CRIO has a USB port and an RS-232 port for communication with NI-VISA software. Further protocols could be integrated into the NI-CRIO since it has a scalable chassis. – Station level: The IED can communicate with multiple control centre with MMS protocol according to IEC 61850-7. The MMS protocol is a client-serverbased architecture; hence it can send and receive data depending upon available communication infrastructure. The IED is configured as an MMS server, with the Substation Configuration Language (SCL) file defining the data model of the field devices presented in the previous section. The IED has two roles: to communicate with a client (most service models in IEC 61850 provide communication with client devices) and to send information to peer devices [8]. The server generates the server attributes according to the SCL file, and the association model provides mechanisms for establishing connections between devices. The IED communicates with the client devices such as SCADA centre through WAN. The configuration file is developed in Extensible Markup Language (XML), and the data points are addressed in the server with data bundles. The data bundles can be divided into multiple bundles corresponding to different data types, but in the automation architecture, two types of data attributes have been identified, either measurement type of data attribute or setting data attributes. The setting data attributes need to be updated on the server point since the settings can be changed from the SCADA centre.

2.1.1

Hardware Setup

The electrical network parameters of the medium-voltage DC research network shown in Fig. 1 are primarily dependent on the existing infrastructure of the various test benches to be integrated. The respective DC link voltage of the systems as well as the mains connected load of the test benches is decisive here. Figure 1 shows the wiring of the DC grid, the connection points of the medium-voltage DC grid, the Institute for Power Generation and Storage Systems (PGS), part of the E.ON Energy Research Center, the Centers for Wind Power Drives (CWD) and

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Fig. 1 Schematic grid layout and electrical parameters for the MVDC research grid

the Center for Ageing, Reliability and Lifetime Prediction of Electrochemical and Power Electronic Systems (CARL). The DC link voltage of the PGS and CWD test benches is 5 kV each. The DC link voltage of the CARL connection point has not yet been conclusively determined. However, it can be assumed that this is in the range of 380 V up to 1 kV. Hence, a modular converter approach with different output configurations on the low-voltage side will be used at this point. In order to reduce the complexity of the DC grid connection points and to be able to use commercial products for the installation of the DC converters, the DC grid voltage between the grid poles is also set to 5 kV. In this way, converters for industrial drives can be used for the DC converters, and only one converter is required on the CARL, which operates at a voltage ratio of ü = 1. The transformers for the DC mains connection points on the CWD and PGS can be designed as isolating transformers with ü = 1, which simplifies the transformer design. Due to the galvanic isolation between the DC grid and the test stands, which is ensured by the DC converters, the pole-to-pole voltage of the grid can be applied symmetrically around the earth potential. This reduces the insulation effort, and the switching of the mains current is facilitated by the lower pole-to-earth voltage. Accordingly, the medium-voltage DC network is earthed in such a way that a mains voltage of ± 2.5 kV to earth is achieved (Fig. 2). The data exchanged between the converter and the IED can be either analogue quantities or digital quantities, which is described in Table 1. The analogue measurements at the secondary and the primary side of the DAB are represented digitally as single-precision floating point format according to IEEE 754. The digital values represent status of the DAB converter, or they are used to trigger an action in the DAB converter. The data size exchanged between the converters is 19 bytes. The error flags are sent from the converter controller in the bit

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Fig. 2 Schematic grid layout and electrical parameters for the MVDC research grid Table 1 Data exchanged between station level and bay level

Table 2 Data transmitted from station level to bay level

Variable Primary voltage Primary current Secondary voltage Secondary current Idle Precharge Start Run Discharge Shutdown

Signal type Analog Analog Analog Analog Digital Digital Digital Digital Digital Digital

Variable Temperature Secondary current before capacitor Secondary current after capacitor

Data type Float Float Float Float Bit Bit Bit Bit Bit Bit Signal type Analog Analog

Data type Float Float

Analog

Float

format, which is represented in Table 2. Table 3 shows the analogue measurements sent from the converter controller to the IED for monitoring of the grid. The converter controller present in PGS, CWD, and CARL consists of the field level in the automation architecture. The converter controllers in the three location have different communication protocol to connect to IED at the bay level, which are briefly explained in this section: – CWD converter station: The converter is controlled by Texas Instrument F2833X Digital Signal Processor (DSP). The DSP communicates with the IED through serial communication at a baud rate of 9600 bits per second.

Automation Architecture for Multi-terminal DC Grid Table 3 Error status from converter controller to bay level

Table 4 Measurements between bay level and station level

Variable Voltage error in primary side Over-temperature error Over-current error

Variable Voltage magnitude at PGS converter station Voltage magnitude at CWD converter station Voltage magnitude at CARL converter station Current flow between converter station

225 Signal type Digital

Data type Bit

Digital

Bit

Digital

Bit

Signal type Analog

Data type Float

Analog

Float

Analog

Float

Analog

Float

– CARL converter station: The CARL converter station has a Multi Modular Dual Active Bridge Converter (MMC-DAB). The MMC-DAB has a master-slave control architecture, where one of the controller undertakes the role of master controller and is responsible for receiving and sending the control set points to the other controllers. A communication channel is set between the master controller and the IED. The AIX controller has the data encoded by FTDI FT2232H chip. – PGS converter station: The controller of the GE is enabled with Profibus protocol. The IED is able to communicate with the controller with chassis extension of NI-9893 module. The communication architecture between bay level and the station level is described below: – SCADA station: The IED communicates with the SCADA centre using MMS protocol in the automation architecture. Currently, the data is sent from IED to the SCADA centre, which is described in Table 4: – Data aggregation and storage: The IED stores the measurement data and the control data into Postgres database using Java Database Connectivity (JDBC) driver. The schema network topology stores the static information like the grid topology, positions of the control devices, accuracy of the different measurement devices and the different device network configurations. The schema measurement command stores the real-time measurement and control data, online state estimates and current operating set points. The schema management stores information on the diagnostic data like the fault recorder data and other execution logs. The bridge schema enables the data exchange between the schemas. One of the applications where the bridge schema would be used is to update the grid topology information in the network topology schema when the switch position status is updated in the measurement command schema. The JDBC establishes

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Fig. 3 Measurement procedure for latency characterisation

a connection with a data source, sends queries and update statements, and postprocesses the measurements. Line Impedance The line impedance needs to be uploaded by the database into the state estimation control centre. Currently the state estimation is acquiring the line parameters from the MATLAB database itself (Fig. 3).

2.1.2

Experimental Result

The automation architecture is used to monitor the MTDC campus grid which is depicted in Fig. 1. The monitoring application such as visualisation of measurement data and status of the converters, manipulating the control parameters and storing them in a database, is done by the IED from the bay level. Hence, the latency is measured for sending and acquiring the data set described in Table 1 for the converter present in CARL. The latency characterization of the measurement chain is necessary to determine the range of monitoring, protection and control applications for the IED. The latency is measured with two different methods, which is depicted in Fig. 4. In the first method, the latency of the IED to the FPGA Merkur Box controller is measured, which is termed as “Send Latency”. The second method measures the time taken for the IED to send a message packet and receive the message packet. This method has been termed as “Send+Receive Latency”. The latency measurement was characterised for 10,000 iterations. The results are

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Fig. 4 Measurement procedure for latency characterisation Table 5 Latency in milliseconds

Send and receive Send

Maximum latency 7.37 ms 5.68 ms

Minimum latency 0.07 ms 0.05 ms

Average latency 0.178 ms 0.123 ms

Table 6 Latency distribution Range (μs) 50 to 70 70 to 110 110 to 200 Over 200

Standard deviation 0.41 ms 0.39 ms Send and receive (%) 0.01 64.80 22.22 13.00

Send (%) 78.61 5.44 9.05 7.30

tabulated in Tables 5 and 6. Table 5 documents the maximum latency, average latency and the minimum latency for both the methods. Table 6 classifies the 10,000 iterations latency measurements based on the latency time. It can be seen that the proposed IED has a transfer time less than 10 ms (acquisition delay + processing delay) within the LAN infrastructure. Therefore, it meets the latency requirements for P2, P3, P4, P5 and P6 class of monitoring, protection and control application as prescribed in IEC 61850 standard.

3 Conclusion In this paper, an automation architecture is presented for making the converters of the MTDC grids interoperable. Furthermore, the data exchanges between the three levels in IEC 61850 are described as well. The hardware architecture of the

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grid in the campus is briefly described, and the implementation of the IEC 61850based architecture is explained. The latency characterization of the measurement acquisition chain is presented for one of the converter stations in the paper. The results show that the automation architecture meets the latency requirements of P2 to P6 class of monitoring, protection and control application. The monitoring platform is going to be used for power converters and their controllers. The monitoring platform will be further used for coordinated control strategies for MTDC grids. Acknowledgments The project is funded by the Federal Ministry of Education and Research (BMBF, FKZ03SF0490), Flexible Electrical Networks (FEN) Research Campus.

References 1. L. Xu, B.W. Williams, L. Yao, Multi-terminal DC transmission systems for connecting large offshore wind farms, in 2008 IEEE Power and Energy Society General Meeting – Conversion and Delivery of Electrical Energy in the 21st Century, pp. 1–7, 2008 2. A. Korompili, A. Monti, Analysis of the dynamics of DC voltage droop controller of DC-DC converters in multi-terminal DC grids, in 2017 IEEE Second International Conference on DC Microgrids (ICDCM), pp. 507–514, 2017 3. F. Mura, R.W.D. Doncker, Design aspects of a medium-voltage direct current (MVDC) grid for a university campus, in 8th International Conference on Power Electronics – ECCE Asia, 2011 4. R.A. Kaushik, N.M. Pindoriya, A hybrid AC-DC microgrid: opportunities & key issues in implementation, in 2014 International Conference on Green Computing Communication and Electrical Engineering (ICGCCEE), 2014 5. T.S. Sidhu, Y. Yin, Modelling and simulation for performance evaluation of iec61850-based substation communication systems. IEEE Trans. Power Delivery 22(3), 1482–1489 (2007) 6. P. CODE, Communication networks and systems in substations part 5: communication requirements for functions and device models, 2003 7. P. CODE, Communication networks and systems in substations part 6: Configuration description language for communication in electrical substations related to IEDS, 2003 8. P. CODE, Part 7 basic information and communication structure abstract communication service interface (ACSI), 2003

Matrix Approach Based on Quadripole for Quality Analysis in Aircraft Electrical Power Distribution System Bernard Makhraz, Hubert Piquet, Xavier Roboam, and Jerome Mavier

Abstract HVDC bus-based electrical network architectures have shown to be relevant for More-Electric Aircraft. Today, adequate standards of power quality and stability must be set and even optimized: subsequent design constraints have to allow the system integrator to guarantee the safe operation of the network, without excessive impact on the design of the equipment provided by the suppliers, especially regarding weight penalty. In this context, this chapter proposes a specific methodology to analyze the power quality constraints in an HVDC network. A matrix approach, based on quadripole analysis of the power distribution is considered. It aims at achieving a direct sensitivity analysis of any quantity (regarding its harmonic content) of any electrical network with respect to selected inputs and based on the network topology and parameters. One major advantage of this methodology is that the modeling approach is analytically developed, based on symbolic calculation. All the devices (sources, cables, filters, loads, etc.) of the system are represented as four-terminal (quadripole) devices, connected together according to the network topology. The calculations are performed at very high speed in the frequency domain. An application of this approach on a relevant aircraft electrical power distribution is shown to highlight its benefit on the path of optimizing new HVDC quality standards.

1 Introduction The More-Electric Aircraft embeds more electrical power systems aiming at minimizing both sizes and weights of components (especially in the filter device) B. Makhraz · H. Piquet · X. Roboam () LAPLACE (Laboratoire Plasma et Conversion d’Energie), Université de Toulouse, CNRS, Toulouse, France e-mail: [email protected]; [email protected] J. Mavier Airbus Operation SAS, Toulouse, France © Springer Nature Switzerland AG 2020 W. Zamboni, G. Petrone (eds.), ELECTRIMACS 2019, Lecture Notes in Electrical Engineering 697, https://doi.org/10.1007/978-3-030-56970-9_18

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by fulfilling quality and stability standards [1, 2], as well as energy management optimization by using the same power inverter to supply different loads during different flight phases [3, 4]. New distribution architecture, for instance, using HVDC buses to save weight [5] though local HVDC bus bars are used in the current state of art [6]. Using a +/−270 V DC network is a promising way to save weight as well [7]. These implications entail new challenges on the quality and the stability of the DC network [8, 9] due to the use of nonlinear loads, such as power converters [10, 11]. Interoperability between the sources and the loads falls under the responsibility of the system integrator through the HVDC standard, which defines the power quality requirements that need to be satisfied under different operating conditions. Today, standards for new distribution networks (HVDC) have to be studied and even optimized in order to avoid weight surplus. In this context, this chapter proposes an analysis methodology based on a quadripole (matrix) approach. One major advantage of this method is that the modeling approach is analytically developed, based on symbolic calculation which allows to directly analyze network couplings in the frequency domain, leading to fast and direct analysis. In this chapter, Sect. 2 introduces the four-terminal model used for all the building blocks of the HVDC network and its acausal formulation, with generalization at system level. The topology of the network is taken into account in Sect. 3, using matrix formulation. Calculations presented in Sect. 4 allow drawing the correlation and sensitivity analysis between any pair of devices (“disruptive” and “victim” devices) to evaluate the impact at the victim level of the environment pollution, especially fulfillment of standard requirements in the design of the disruptive element. An illustrative example at system level is presented in Sect. 5. Finally, an approach integrating standard’s requirements currently under study is proposed in Sect. 6.

2 Quadripole-Based model Definition 2.1 Four-Terminal Model Definition The modeling approach for quality analysis is based on representing of each component of the electrical distribution network with a four-terminal circuit (also sometimes called “two-port network”), which is represented by a “quadripole” matrix. This matrix, involving two linear equations, links currents and voltages on both sides of the concerned element as shown in Fig. 1. As the matrix representing each quadripole can have more than one format (based on the different input/output combinations of currents and voltages), the first matrix introduced in Eq. (1) is the “transfer matrix” which connects the voltage and the current on the right side with those on the left side.

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Fig. 1 Schematic representation of a generic electric quadripole



vo io





   T11 T12 vi = ∗ T21 T22 − ii

(1)

One should notice that the terms of the quadripole matrix might take into account nonlinear phenomena in the frequency domain.

2.2 Quadripole Acausal Matrix (QM) Thereafter, the linear system based on the transfer matrix is transformed into an acausal set of equations showing both variables and a zero vector, as shown in Eqs. 2 and 3. 

⎡

⎤ vo   ⎢ io ⎥ 1 0 −T11 T12 ⎥= 0 ∗⎢ ⎣ vi ⎦ 0 1 −T21 T22 0 ii ⎡ ⎤ vo   ⎢ io ⎥ ⎥= 0 [QM] ∗ ⎢ ⎣ vi ⎦ 0 ii 

(2)

(3)

For instance, Eq. (4) represents the quadripole acausal matrix (QM) of an LC filter configuration with the addition of a shunt Rd-Cd as a damping network. This configuration is represented in Fig. 2. ⎡ ⎣

10



−1

0 1 − Cp +



1 Rd + C 1 p d

⎤ vo   ⎢ ⎥ ⎦ ∗ ⎢ io ⎥ = 0 ⎣ vi ⎦ +1 0 ⎤

Lp  Lp ∗ Cp +

1 Rd + C 1 p d

⎡

ii

(4)

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Fig. 2 LC filter with Rd-Cd damping branch

2.3 System Quadripole Matrix (SQM) With the quadripole acausal matrix of each component, the “System Quadripole Matrix” is formed by gathering all of these quadripole matrices into one global matrix representing all the building blocks of the distribution network under study. In the System Quadripole Matrix, only the block diagonal terms are different from zero. For instance, the System Quadripole Matrix of an electrical distribution network that includes “n” elements looks like the matrix shown in Eq. (5) which gathers all voltage current variables of the system. ⎡

⎡

QM1 0 · · · ⎢ 0 QM2 · · · ⎢ ⎣ 0 0 ··· 0 0 0

vo1 io 1 vi1 ii1 vo2 io2 vi2 i i2 .. .

⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎢ ⎢ 0 ⎢ ⎢ 0 ⎥ ⎥∗⎢ ⎢ 0 ⎦ ⎢ ⎢ ⎢ QMn ⎢ ⎢ ⎢ ⎢ von ⎢ ⎢ ion ⎢ ⎣ vin iin

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎡ ⎤ ⎥ 0 ⎥ ⎥ ⎢ .. ⎥ ⎥=⎣.⎦ ⎥ ⎥ 0 ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

(5)

Note that the System Quadripole Matrix only integrates quadripole elements of the network without considering the topology which results from their connections; this point is considered in the following section.

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3 Structural Relationships Matrix (SRM) This second step takes into account the electrical distribution network architecture. Thereafter, structural relations are the equations that identify the connections between the different quadripoles. These relations are established using both Kirchhoff’s current (KCL) and voltage (KVL) laws. Therefore, the Structural Relations Matrix is mapped for the same variable’s vector used to define the System Quadripole Matrix.

3.1 The Number of Structural Relationships The number of structural relations depends on two factors: – The first one is “p,” the number of nodes in the network. – The second one is the number of quadripoles connected at each node. For instance, for a node connecting “k” quadripoles, the number of structural relations is one for the currents (KCL) and “k-1” for the voltages (KVLs). Therefore, the total structural relation matrix is obtained by summing all structural relations for each node of the system, as shown in Eq. (6). Total structural relations =

p

knodei

(6)

i=0

An example of electric power distribution, as shown in Fig. 3, is introduced in this section as a simple application. Two nodes are identified (#1 and #2) in a threelevel electric power distribution. The first node connects four quadripoles; the second one connects three quadripoles. In this case, the number of structural relationships is four for the first node and three for the second node, resulting in a total of seven structural relationships, as illustrated by Table 1.

4 Electrical Power System Matrix (EPSM) In order to get a matrix describing the electrical power system under analysis, both the System Quadripole Matrix and the Structural Relations Matrix, which share the same voltage-current vector, are vertically merged in Eq. (7).

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Fig. 3 Schematic representation of a simplified electric power distribution with three distribution levels

Matrix Approach Based on Quadripole for Quality Analysis in Aircraft. . . Table 1 List of the structural relationships for nodes #1 and #2

Node #1  v0 − v1 = 0  v0 − v2 = 0  v0 − v3 = 0

235 Node #2  v3 − v4 = 0  v3 − v5 = 0 i3 + i4  + i5 = 0

i0 + i1 + i2 + i3 = 0

⎡

vo1 io1 vi1 ii1 vo2 io2 vi2 i i2 .. .

⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ [EPSM] ∗ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ von ⎢ ⎢ ion ⎢ ⎣ vin iin

⎤

⎡

vo1 io1 vi1 ii1 vo2 io2 vi2 i i2 .. .

⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎥   ⎢ ⎢ ⎥ SRM ⎢ ⎥ ∗⎢ ⎥= ⎢ ⎥ SQM ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ von ⎥ ⎢ ⎥ ⎢ ion ⎥ ⎢ ⎥ ⎣ vin ⎦ iin

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎡ ⎤ ⎥ 0 ⎥ ⎥ ⎢ .. ⎥ ⎥=⎣.⎦ ⎥ ⎥ 0 ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

(7)

To go further, the aim is now to identify the “causality for the analysis” by establishing the input/output matrix related to the input variables chosen for analysis with all other variables, which can be calculated as the system’s outputs. The rank of the Electrical Power System Matrix determines the number of output variables, which are arbitrary selected. Accordingly, the input variables are the remaining system’s variables. Thereafter, the matrix connecting the inputs with the output variables is identified based on the merged Electrical Power System Matrix (Eq. (7)). Thus, the causal input-output matrix, Eq. (8), is introduced as the “Transfer Function Matrix” relating output vector with the desired input vector. Supposing that “r” is the rank of the Electrical Power System Matrix, in a system containing “m” variables (Var), which can be either voltage or current, the “Transfer Function Matrix” is derived in Eq. (8). ⎡

⎤ Varout1 ⎡ ⎤ ⎢ .. ⎥ Varin1 ⎢ . ⎥ ⎢ ⎥ ⎥ .. ⎢ Varout ⎥ = [TFM] ∗ ⎢ ⎣ ⎦ i ⎥ . ⎢ ⎢ . ⎥ ⎣ .. ⎦ Varinm−r Varoutr

(8)

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For instance, the Electrical Power System Matrix’s rank of the 24 variables example introduced in Fig. 3 is 19. Therefore, 19 variables are to be considered as output and 5 variables as input. Note that all calculations developed in Sects. 3 and 4 can be derived analytically by means of symbolic calculation solvers; for that purpose, we have selected the Matlab’s Symbolic Toolbox. In our case, the Transfer Function Matrix, in Eq. (8), is the output of the “solve” function (equations and systems solver from the Symbolic Toolbox) that solves a system of equations: it is applied for solving the Electrical Power System Matrix (Eq. (7)) considering specified output and input vectors.

5 Application The application shown in this part is a simplified HVDC electric power distribution for More-Electric Aircraft integrating +/− 270 VDC voltage bus with only two loads connected in a star configuration, as shown in Fig. 4. In this application, each load connected to the bus through an input filter associates an inverter-fed Permanent Magnet Synchronous Motor (3-Phase PMSM-1 kW). This topology is simplified in order to clarify the relevance of our modeling approach based on quadripole and frequency domain simulation and its ability to facilitate the power quality analysis. More typically, the issue is to clarify how this quadripole-based approach allows directly analyzing the influence of power quality standard requirements on the quality of waveforms (harmonic content, rms values, resonances, etc.) at the inputs/outputs of sources and loads and consequently on the weights of the connected electrical devices (especially the filters). This application case is built of three quadripoles. The source quadripole includes one capacitor (C_0=2 mF) connected to two inductors (L_0=2.8 uH) representing the harness. Equation (9) represents its quadripole matrix (QM0). 

⎤ ⎡ v0       ⎢ i0 ⎥ 1 0 − C0 L0 p2 + 1 L0 p + L0 p C0 L0 p2 + 1 0 ⎥ ⎢ = ∗⎣ C0 L0 p2 + 1 v0 ⎦ 01 −C0 p 0 i0 

(9)

On the other hand, both load quadripoles represent two different damped LC input filters which the structure is on Fig. 2 and which values after a weight optimization are(L1 = 190uH, C1 = 2.3uF, Cd1 = 0.57uF, Rd1 = 40, L2 = 306uH, C2 = 1.6uF, Cd2 = 0.7uF, Rd2 = 42) QM1 and QM2 are the same matrix as in Eq. (4). In the process developed in previous sections, the next step is to set up the System Quadripole Matrix using the three quadripole matrices (QM0, QM1, and QM2) as shown in Eq. (10).

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Fig. 4 A simplified HVDC electric power distribution for More-Electric Aircraft integrating a +/− 270 VDC voltage bus with two loads

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⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎡ ⎤ ⎢ ⎢ QM2 0 0 ⎢ ⎣ 0 QM1 0 ⎦ ∗ ⎢ ⎢ ⎢ 0 0 QM0 ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣

v2 i2 v2 i2 v1 i1 v1 i1 v0 i0 v0 i0

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎡ ⎤ ⎥ 0 ⎥ ⎥ ⎢ . ⎥ ⎥=⎣ . ⎦ . ⎥ ⎥ ⎥ 0 ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

(10)

The network of our case study is then transformed into a quadripole schematic, as shown in Fig. 5. For this n=1 node architecture associating k=3 quadripoles, the Structural Relations Matrix reflects Kirchhoff’s laws for currents (1 equation) and voltages (3−1=2 equations): v0 − v1  = 0

(11)

v0 − v2 = 0

(12)

i0 + i1  + i2 = 0

(13)

The equations above are gathered in one matrix (14).

Fig. 5 Schematic representation of a simplified HVDC electric power distribution with one source and two loads

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The aggregation of both System Quadripole Matrix with the Structural Relations Matrix gives the Electrical Power System Matrix with 12 relationships. The rank of this matrix being 9, 12−9=3 variables have to be selected as the analysis inputs and nine as outputs. For instance, choosing the source voltage and both load currents [v0 , i1 , i2 ] as the analysis input vector implies that the remaining nine variables are considered as outputs, as in Eq. (15), which sets the causality of the analysis. ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣

⎡

0 0 0 0 0 0 −1 0 1 0 0 0

v2 v2  i2 v1 v1 ’ i ’

0 0 −1 0 0 0 0 0 1 0 0 0

⎤t ⎡ v2 0 ⎢ 0⎥ ⎥ ⎢ i2 ⎥ ⎢ 0 ⎥ ⎢ v2 ⎥ ⎢ 1 ⎥ ⎢ i2 ⎥ ⎢ ⎢ 0⎥ ⎥ ⎢ v1 ⎥ 0⎥ ⎢ i1 ∗⎢ ⎢ v 0⎥ ⎥ ⎢ 1 ⎢  1⎥ ⎥ ⎢ i1 ⎥ ⎢  0 ⎥ ⎢ v0 ⎥ ⎢ 1 ⎥ ⎢ i0 ⎥ ⎢ 0 ⎦ ⎣ v0 0 i0

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎡ ⎤ ⎥ 0 ⎥ ⎥ ⎢ . ⎥ ⎥=⎣ . ⎦ . ⎥ ⎥ ⎥ 0 ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

(14)

⎤

⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎡ ⎤ ⎡ ⎤ ⎢ ⎥ M1,1 M1,2 M1,3 ⎢ ⎥ v0 ⎢ ⎥ ⎢ . .. ⎥ ∗ ⎣ ⎦ .. ⎢ ⎥=⎣ . i1 . . . ⎦ ⎢ ⎥ ⎢ ⎥ i2 ⎢ 1 ⎥ M9,1 · · · M9,1 ⎢ ⎥ ⎢ i0 ⎥ ⎢ ’ ⎥ ⎣ v0 ⎦ i0 ’

(15)

Among the capabilities of the analysis method, one can emphasize, first, the analytical (symbolic) derivation of the transfer functions (Mi,j) in the frequency domain which clarifies the analysis of main couplings (typically resonant effects, etc.) between network elements. Secondly, based on the harmonic content (magnitude and phases) of the input data (here v0,i1,i2), the harmonic content of selected outputs here (v2) can be numerically estimated to quantify the coupling analysis as displayed in Fig. 6. The electrical network of Fig. 4 was also implemented using PLECS® , a time domain simulator, in order to compare and validate the results. Each load is constituted of a power drive system here represented by a current source which

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Fig. 6 Validation (by simulation) of the load voltage v_2: blue harmonics represent the frequency domain calculation; these latter are superposed with harmonics (in red) issued from the PLECS® time simulator. Zooms are proposed at 20 kHz, 40 kHz, and 60 kHz

harmonic content represents the harmonic pollution that would be drawn by a 1 kW permanent magnet synchronous machine fed by a voltage source inverter. The simulation validation through the frequency analysis of the load voltage v2 is represented in Fig. 6, comparing both PLECS (red spectrum) and quadripole model (in blue) for a frequency range of [0; 100 kHz]: the results are completely overlaid, with a negligible difference lower than 0.4% for the main harmonics.

6 Quality Analysis Based on Power Quality Standards Civil and military aircraft manufacturers define standards, such as the MIL-STD704 for military aircraft, in order to maintain the power quality of AC and DC electric power network and to ensure interoperability at system level. These standards set the interface between sources and loads to ensure compatibility between the aircraft electric system, external power, and airborne utilization equipment. Therefore, it gives designers the specifications that they need to respect in order to

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Fig. 7 Frequency spectrum characteristics for load voltage specification

ensure that an airborne system will be compatible with the power supply provided by the aircraft manufacturer. Standards define the characteristics for different operational conditions such as power up, steady state, and reconfiguration in normal, abnormal, and emergency condition. However, no appropriate international standards are currently set to evaluate the power quality of the HVDC network, especially for recent concepts integrating +/− 270 VDC voltage distribution in aircraft [12]. In this part, the aeronautical standard’s requirements are “directly” integrated as the inputs of our analysis approach: the issue is to assess, thanks to the quadripolebased analysis method, the influence of standards on the outputs selected to be analyzed. For this purpose, we first consider that the power source and the load 1 fulfill the quality standards: “it is like if these devices would pollute at the limit ! level allowed by the quality standards.” Thereafter, v0 , i1 are then imposed as the input vectors by considering that the output voltage v0 exactly involves the frequency spectrum of Fig. 7 while the input current of the 1st load i1 has the envelope of the current requirements of Fig. 8. On the other hand, the actual emitted current pollution by the load 2 (which is under analysis) is considered as a third input.  The current i1 is replaced by the maximum current spectrum authorized by the power quality requirement as shown in Fig. 8. This current envelope represents the

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Fig. 8 Frequency spectrum characteristics for the current specification

maximum pollution that this load “may emit.” In the same way, the voltage v0 is considered as an input with the maximum voltage distortion spectrum; a typical envelope is represented in Fig. 7. Thus, the idea is to analyze the constraint on the device N◦ 2, especially its voltage v2 (shown in Fig. 8) when its network environment (source and load 1) fulfills the power quality requirements. By this way, the approach allows “directly studying” the worst-case scenario with the impact of any quality requirements on the electrical device under analysis: in Fig. 9, the output voltage of load 2 is analyzed regarding the requirements previously considered and the current pollution of the load 1. This information is relevant for the designer of the power drive system of the analyzed load.

7 Conclusion The main assets of our strategy are the capability to perform symbolic and analytical calculations in the frequency domain based on selected inputs directly showing the

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Fig. 9 Voltage v2 for a frequency range of [0; 150 kHz] when the source and the load 1 fulfill the quality requirements

main couplings on outputs: the description of the network topology and the first steps of the calculations are achieved using symbolic equations which are solved by specific symbolic calculation programs (e.g., Matlab and Maple). According to various scenarios, the mathematical relationships correlating input-output quantities can be analytically built out. In a second step, the actual implementation of each quadripole is taken into account, using the numerical values of the electrical components. Using this approach to merge electrical distribution network with aeronautical standards may simplify the power quality analysis and may be ultimately used to reconsider and even to optimize power quality requirements since integrating frequency spectrum into simulation software can be a tedious work to do. Using the proposed approach will simplify—eventually—the compliance to the requirements analysis.

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References 1. X. Liu, A. Forsyth, H. Piquet, S. Girinon, X. Roboam, N. Roux, A. Griffo, J. Wang, S. Bozhko, P. Wheeler, M. Margail, J. Mavier, L. Prisse, « Power quality and stability issues in moreelectric aircraft electrical power systems », MOET Forum EPE Conference Barcelona, Spain, 2009 2. S. Girinon, H. Piquet, N. Roux, B. Sareni, « Analytical input filter design in DC distributed power systems approach taking stability and quality criteria into account », in 2009 13th European Conference on Power Electronics and Applications, pp. 1-10, 2009 3. X. Giraud, M. Budinger, X. Roboam, H. Piquet, M. Sartor, J. Faucher, Optimal design of the integrated modular power electronics cabinet aerospace science and technology. Elsevier AESCTE (Int J Aerosp Sci Technol) 48, 37–52 (2016) 4. A. Morentin Etayo, « Methods and tools for the optimization of modular electrical power distribution cabinets in aeronautical applications », PHD Thesis of Institut National Polytechnique de Toulouse-INPT, 2017 5. X. Roboam, B. Sareni, A. De Andrade, More electricity in the air: towards optimized electrical networks embedded in “more electrical aircraft”. IEEE Ind Electron Mag 6(IV), 6–17 (2012) 6. M. Sinnett, « Saving fuel and enhancing operational efficiencies », vol. AERO Q4.07, p. 6 7. J. Brombach, A. Lücken, T. Schröter, D. Schulz, Optimizing the weight of an aircraft power supply system through a +/− 270 VDC main voltage. Przeglad ˛ Elektrotechniczny R. 88(1a), 47–50 (2012) 8. S. Girinon, C. Baumann, H. Piquet, N. Roux, Analytical modeling of the input admittance of an electric drive for stability analysis purposes. Eur Phys J Appl Phys 47(1), 11101 (2009) 9. M. Charrada, S. Girinon, H. Piquet, N. Roux, Equipments characterization methods for stability analysis of DC networks. IEEE International Symposium on Industrial Electronics, Gdansk, Poland, 2011 10. « IEEE recommended practice and requirements for harmonic control in electric power systems », IEEE Std 519-2014 Revis. IEEE Std 519-1992, p. 1-29, juin 2014 11. T. M. Blooming D. J. Carnovale, « Application of IEEE STD 519-1992 Harmonic Limits », in Conference Record of 2006 Annual Pulp and Paper Industry Technical Conference, pp. 1-9, 2006 12. I. Moir, A. Seabridge, Aircraft systems: mechanical, electrical, and avionics subsystems integration (Wiley, Hoboken, 2011) 13. M. Beltramini, L. Prisse, P. Asfaux, N. Roux, F. Richardeau, X. Roboam, F. Costa, B. Revol, Comparison of different inverter topologies and controls in terms of conducted EMI, IEEE-ICIT 2010 (International Conference on Industrial Technology), Valparaiso, Chile,14th March – 17th March, 2010

JADE-Based Multi-agent Decentralized Energy Management System of a Hybrid Marine-Hydrogen Power Generation System M. R. Barakat, B. Tala-Ighil, H. Gualous, and D. Hissel

Abstract This paper presents the decentralized JADE (Java Agent Development Environment)-based multi-agent system (MAS) oriented to the energy management and balance of the hybrid marine-hydrogen power generation system. The proposed hybrid marine-hydrogen system consists of a fixed-pitch direct drive tidal turbine, a megawatt (MW) scale proton exchange membrane electrolyzer, and fuel cell and a Li-ion battery stack. The different components are coupled together on a DC link via different topologies of power electronics converters for feeding a residential load as isolated system architecture. The MW scale electrolyzer and fuel cell systems represent the main elements of the hydrogen energy storage system. An isolated mode of operation is programmed to evaluate the MAS capability of energy management and balance considering the marine current intermittency and the demand-side variations. The proposed energy management system considers the safe operations of the electrolyzers, fuel cell, and battery by considering their constraints and dynamics.

1 Introduction Tidal energy suffers from severe seasonal, daily, and hourly variations that can limit its integration or exhibits more requirements and conditions to have the normal M. R. Barakat () Caen Normandy University, UNICAEN, Cherbourg-en-Cotentin, France Department of Electrical Power and Machines Faculty of Engineering, Helwan University, Cairo, Egypt e-mail: [email protected] B. Tala-Ighil · H. Gualous Caen Normandy University, UNICAEN, Cherbourg-en-Cotentin, France e-mail: [email protected]; [email protected] D. Hissel University of Bourgogne Franche-Comté, FEMTO-ST, FC Lab, CNRS, Belfort, France e-mail: [email protected] © Springer Nature Switzerland AG 2020 W. Zamboni, G. Petrone (eds.), ELECTRIMACS 2019, Lecture Notes in Electrical Engineering 697, https://doi.org/10.1007/978-3-030-56970-9_19

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and safe operation of isolated systems. There are different load types (household, agriculture, commercial, industrial) that define the load profiles during the day while the load profiles also change from summer to winter. The energy storage system can be considered as an energy buffer for balancing the generation-consumption power difference of the isolated power systems. The hydrogen system can meet these requirements and operating conditions. It is a clean and efficient energy carrier with an environmentally friendly nature as the only byproduct is the water with the highest energy per unit mass [1, 2]. The considered system is an active hybrid tidal-hydrogen power generation system. The expression of active power generation system has been used in the literature to describe a hybrid wind, electrolyzer, fuel cell, and supercapacitor power system [3]. The considered case study consists of a fixed-pitch direct drive marine current turbine (FPDD MCT) power generation system, an MW scale proton exchange membrane (PEM) electrolyzer, an MW scale PEM fuel cell, and the residential loads as shown in Fig. 1. The standard household load profile is selected to model an island residential loads variation that provides an isolated power system configuration. The efficient operation of this topology requires efficient energy management systems (EMS). There are three main types of management and control systems, centralized, hierarchical, and decentralized. The main difference between these systems is the responsibility of the optimization and management duties. The central systems have a master unit that feeds all the set points to the lower-level control entities. The hierarchical system distributes the management duties over the different control entities regarding the master unit for the general survey and monitoring. The decentralized has the same topology of the hierarchical with removing the master unit due to sharing the survey and monitoring duties between the control entities based on peer-to-peer communication [4]. The decentralized system is more redundant and flexible by avoiding the single point of common failure as the main disadvantage of the centralized system [4]. The multi-agent system (MAS) is a paradigm of the decentralized system that is used for energy management and control of many renewables-based systems [5, 6]. The definition and the description of the agent and the MAS have been completely presented in [7]. Many parameters must be taken into consideration for managing the hybrid tidal-hydrogen system. Consequently, the management system must have the capability of dealing with each system independently and in a reliable manner. Thus, the decentralized MAS is selected to perform the control and the management of the system under the stand-alone mode of operation. The most important question is the selection of the platform to be used for developing the MAS. There are many studies that reviewed and surveyed the different MAS platforms and compared in between [8, 9]. The more detailed and comprehensive comparison of the MAS platforms has been presented in [10]. Moreover, we have presented in [11] a detailed comparison of the different centralized and decentralized EMS systems. Based on these studies, the JADE MAS platform is selected to apply the decentralized energy management of the hybrid marine-hydrogen system as a novel EMS for this system topology. It has many advantages: an open-source Java-based software, general-purpose application, and more widely used in many applications. It is fully compliant with FIPA (Foundation of Intelligent Physical

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Fig. 1 Hybrid tidal-hydrogen active power generation system architecture

Agent) standards, and it interfaces with MATLAB [11]. The detailed description of the JADE platform has been presented in [12]. The rest of the paper is arranged as follows: the second section covers the hybrid tidal-hydrogen system modeling followed by the programming and the development of the JADE-based decentralized EMS. Then, the results of the system performance under the stand-alone mode of operation are discussed, and finally, the main conclusion is presented.

2 Hybrid Tidal-Hydrogen System Modeling The system consists of many parts that are multi-physics: mechanical, electromechanical, electrical, and electrochemical. The design of the control system requires a well and clear understanding of the relations between all the subsystems. The energetic macroscopic representation (EMR) is used to represent each subsystem that makes the whole system more readable and consequently enables the design of suitable control strategies. EMR is a graphical representation of the systems based on the physical and integral causality principles. The EMR was first developed in 2000 at the University of Lille in France to describe complex electromechanical systems. It is a very simple representation technique with a group of principles and elements [13, 14]. Since then, EMR has evolved into a more generic tool for representation, modeling, and management of the different multi-physics systems [15–19]. The EMR of the hybrid tidal-hydrogen active power generation system has been presented in our previous works [20–22]. These studies exhibit the different control strategies applied to the system MATLAB/Simulink model deduced from the proposed EMR with the help of the detailed parameters. The model represents the physical layer with the control entities that receive their setting points from the MAS-based EMS.

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3 Decentralized JADE EMS Programming and Development 3.1 JADE Platform Description

JAVA Agents

JAVA Agents

JAVA Agents

Container-1

Main Container LADT

Container-2 LADT

LADT GADT Cache

MTP

GADT Cache

GADT CT Platform

FIPA

Other FIPA Platform

JADE was initially developed in late 1998 by Telecom Italia to validate the early FIPA specifications. By 2000, the JADE platform became an open-source software distributed under the Library GNU Public License (LGPL). The main core of JADE is a Java-based set of software abstractions and tools that hid the FIPA specifications and enables the widespread of these specifications by their direct implementation. The agent paradigm in JADE is an autonomous and proactive entity that has its thread of execution and works in harmony with the other agents based on peer-topeer communication. The following paragraphs present the main architecture of the JADE platform and its classes. JADE is a fully distributed platform that consists of autonomous entities called the agents. The agent lives in a container that provides the JADE run-time and the agents hosting and execution services as a Java process. There is only one container created automatically by launching the software that is called the main container. The main container hosts the directory facilitator (DF) agent and the agent management service (AMS). The main container is the platform hub that all the other programmed containers must register with it. Consequently, it manages the container table (CT) in which all the containers register. It manages the global agent descriptor table (GADT) in which all the agents register as shown in Fig. 2. The main container has a default name of Main Container, and the others have the names of Container-1, Container-2, etc. The JADE platform has main Java classes and interfaces that implement specific and principal functions and arranged

(MPT: Message Transport Protocol, IMPT: Internal MPT, LADT: Local Agent Descriptor Table). Fig. 2 JADE main architecture [12]. (MPT Message Transport Protocol; IMPT internal MPT; LADT Local Agent Descriptor Table)

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hierarchically in the form of packages and sub-packages. One of the most important JADE services is the admin and debugging tools. The directory facilitator (DF) is one of the main debugging tools that provide the yellow pages service in which all the agents register to publish their services or searching services announced by the other agents. In addition, the sniffer agent is one of the debugging tools that surveys and monitors the conversations and the messages (agent’s communication) exchanged between a set of specified agents defined by the programmer [12].

3.2 MATLAB/Simulink-JADE Interface The development of the decentralized JADE-based multi-agent EMS requires interfacing the MATLAB/Simulink model with the JADE platform. The interface between MATLAB/Simulink and JADE requires a work-round for adding the agent options in the Simulink. A special program, called the Multi-Agent Control for Simulink (MACSim), performs the interface between MATLAB/Simulink and JADE [23]. The MACSim depends mainly on the server-client architecture where the client is the MATLAB/Simulink S-function and the server is the multi-threading program (JADE) based on C programming. The communication in between the client and the server is named a windows pipe as shown in Fig. 3. The MACSim has been extended to include Java extension (MACSimJX) that was presented for the first time in [24] to be used for the Boeing aircraft data mining and fusion. The MACSimJX program contains two main parts: the AE (Agent Environment) and the ATF (Agent Task Force). The AE represents the main interface for transferring data between Simulink and JADE. The ATF represents the different Java classes of the agents that perform the programmed tasks. Generally, the MACSimJX is an open-source program that has been utilized for many applications from the Boeing 747 data fusion and mining to the renewables (PV, wind) MAS-based energy management systems [25–27]. The software getting started and the detailed description are provided in [28, 29].

Simulink MACSim Client

Fig. 3 MACSim architecture [23]

Windows Pipes

Multi-threaded program MACSim Server

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Fig. 4 Marine-hydrogen Simulink model considering the MACSimJX client S-function

3.3 JADE-Based Multi-agent EMS Development and Programming Generally, this work represents a part of the first author Ph.D. dissertation that discusses in detail the design, the development, and the implementation of the JADE-based MAS energy management system under different operating scenarios [30]. The main objective of the proposed decentralized EMS is the energy balance between the marine current system generation (Pg ) and the load consumption (residential load, PL ). The main advantage of the JADE-based MAS over the centralized topology is the redundancy (by avoiding the single point of common failure). Each agent is responsible for managing and controlling its subsystem and communicating peer to peer to the neighbor agent for negotiation based on the JADE agent paradigm. Figure 4 shows a simplified Simulink model of the isolated system described in the second section considering the MACSimJX client as an S-function. Consequently, the MACSimJX client (S-function) forwards the generated marine current and the demand-side powers. Moreover, it is important to consider the battery and the hydrogen storage tank SOC (state of charge) as the main parameters of the energy management system. The battery SOC limits represent a safe and healthy operation. The proposed energy management system of the stand-alone mode does not consider the hydrogen tank SOC to evaluate the system performance. The different agents of the MAS are programmed to perform cooperatively a management procedure shown in Fig. 5. The performance evaluation represents the estimation of the produced hydrogen with the marine and demand profiles variations as discussed in the following paragraphs. One of the most important features of the proposed EMS is the demand-side management (DSM) based on two strategies, load shedding (valley filling) and load shifting. The proposed MAS consists of five main agents that provide the low-level control system of the Simulink model by the reference values to be tracked. The marine energy conversion system is completely controlled by the low-level control system considering the different operation modes referred to in the second section.

JADE-Based Multi-agent Decentralized Energy Management System. . .

Read SOC, Pg, PL

Pg =PL P g > PL

Yes

Yes

PFC = PEL=0 PFC =0 PEL=(Pg-PL)filtered

No PEL =0 PFC=(PL-Pg)filtered

SOC > SOCmin

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Apply Load Shifting (Connect Secondary Load) No SOC < SOCmax Yes Connect Main Load Yes

No Apply Load Shedding (Disconnect Secondary Load) Fig. 5 JADE-based isolated mode EMS flowchart

• Electrolyzer Agent It is responsible for the energy management of the electrolyzer system. Firstly, it communicates with the MACSimJX Agent Environment (AE) to search for the generation-consumption power difference. Based on the updated values of the power difference (power surplus), it filters the power difference considering the electrolyzer dynamic response that is stored in the agent arguments (its value depends on the manufacturer operation recommendations). It continuously estimates the electrolyzer operating point and feeds it back to the AE that feeds it to the Simulink model as the electrolyzer control system updated reference value. Thus, it manages the electrolyzer-consumed energy, which means the amount of the produced hydrogen, and at the same time protects the electrolyzer components from lifetime degradation (blue rectangle, Fig. 5). • Fuel Cell Agent It is responsible for the energy management of the fuel cell system. It communicates with the MACSimJX AE to search the generation-consumption power difference. Based on the updated values of the power difference (power shortage), it filters the power difference considering the fuel cell dynamic response that is stored in the agent arguments (its value depends on the manufacturer operation recommendations). It continuously estimates the fuel cell operating point and feeds it back to the AE that feeds it to the Simulink model as the fuel cell control system updated reference value. Thus, it manages the fuel cell-produced energy, which

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means the amount of the consumed hydrogen, and at the same time protects the fuel cell components from lifetime degradation (red rectangle, Fig. 5). • Battery Agent It provides the battery SOC to the JADE platform by the communication with the AE of the MACSimJX. Then, it communicates with the DSM to share the SOC and receives the power difference (yellow ovals, Fig. 5). • Demand-Side Management Agent It is responsible for implementing the demand-side management strategies [load shifting and the load shedding (filling valley)]. It communicates with the AE of the MACSimJX to receive the power difference and shares it with the battery agent to receive its SOC based on peer-to-peer communication. Consequently, it filters the power difference based on the electrolyzer and the fuel cell dynamic responses and defines the operating condition (power surplus or shortage). Based on the operation condition, it selects the DSM strategy (load shifting for power surplus and load shedding for power shortage). The amount of the shaded or shifted power is estimated based on the battery SOC to protect it from over- or undercharging/discharging (green rectangles, Fig. 5). • Hydrogen (H2) Storage Tank Agent The storage tank agent is a vital member of the proposed energy management system. It communicates with the MACSimJX AE to keep monitoring the hydrogen volume in the storage tank. Then, it starts to announce its value in the form of a periodical message (as exhibited in the system results). The hydrogen volume announcement (the periodical message) provides the system operators an alarm about the stored energy levels. Thus, it enables the decision-making even by the migration into another storage tank or changes the system configuration (gridconnected mode). The different agent’s source codes are programmed to perform the described functions and then compiled into Java class files that are added to the MACSimJX ATF (Agent Task Force) folder [26].

4 Results and Discussion Figure 6 exhibits the communication between these agents that is governed by the DF services registration and discovering. The proposed decentralized JADE-based multi-agent EMS has been tested under a marine current speed profile based on real measurements of the Alderney Race (Raz Blanchard in French) marine site. The point of measurement in the site can be considered as a bidirectional model based on its hydrodynamic model [22]. Due to the model, the measurement of 15 September 2005 is selected as it is the day of the highest tide during the year as shown in Fig. 7. The proposed JADE-based EMS can manage the energy between

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ATF

EL

FC

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Batt

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Initialization Power Difference Power Difference Updated

H2 Volume SOC H2 Updated Volume Updated SOC

DF Services Discovery Energy Balance & DSM Strategies Updated Control References Vlaues

H2 Volume Monitor

Speed

Fig. 6 JADE-based isolated mode EMS agent’s interaction

4 3 2 1 0

Marine Current Speed (m/s)

0

4

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12 Time (hr)

PMSG (rad/s)

16

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Fig. 7 Marine current and PMSG speed profiles

the marine-hydrogen system different components based on the operating conditions as shown in Fig. 8. When the marine current-generated energy is higher than the load demand, the electrolyzer is switched on converting the surplus energy in hydrogen stored in the tank. Otherwise, the fuel cell is switched on compensating the power shortage. The battery is controlled to cover the fast dynamics power for fuel cell and electrolyzer protection. The DSM agent is powerful to implement the strategies of the demand-side management (load shifting and load shedding) as shown in Fig. 9. The DSM strategies are effective to protect the battery from the overcharging and the under-discharging by limiting the battery SOC within certain limits as shown in Fig. 10. The hydrogen tank agent provides the command prompt by the hydrogen volume as periodical messages (periodical monitor). The messages are compatible with the volume of the hydrogen deduced from the Simulink model (0% SOC at

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Load

Electrolyzer 0.1

Power (MW)

2.2 1.9 1.6 1.3 1 0.7 0.4 0.1 -0.2

Fuel Cell

Battery (-Charging)

0 -0.1 0

0

4

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12 Time (hr)

18

24

16

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24

16

20

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16

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24

Fig. 8 Power profiles deduced from JADE-based EMS

Load Power (MW)

Load with out DSM

Load with DSM

1.5 0.92

1

0.84 9.6 10.2 10.8 11.4 12

0.5

0.32 0.2 1.14 1.44 1.74 2.04 2.34

0 0

4

8

12 Time (hr)

SOC

Fig. 9 DSM strategies deduced from JADE-based EMS

1.1 0.9 0.7 0.5 0.3

Over Charging

Under Discharging

0

4

8

12 Time (hr)

Fig. 10 Battery stack state of charge (SOC)

the beginning of the day) as shown in Fig. 11. The periodical messages provide the hydrogen storage tank SOC and when it is required to search a storage reserve or changing the system mode of operation.

Volume (m3)

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Negative sign = insufficient produced hydroen (indication: add reserve)

Storage Tank Pressure at 100% SOC is 30 bar

0

4

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12 Time (hr)

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Fig. 11 Storage tank hydrogen volume. Negative sign = insufficient produced hydrogen (indication: add reserve)

5 Conclusions This study presents the development of the decentralized JADE-based multi-agent EMS of the hybrid marine-hydrogen power generation system. The MAS is flexible and scalable due to the dynamic nature of the agent (e.g., appearing, registration, deregistration, freezing). As a result, the MAS has the ability to manage and optimize each subsystem separately and locally in the general frame of the whole system management. The novel proposed JADE-based EMS is applied on the MATLAB/Simulink model of the hybrid marine-hydrogen system deduced from our previous work. The developed management system is powerful to balance the energy between marine generation and the demand-side consumption (residential loads) considering their intermittency. Moreover, it provides an option of the system online monitoring that enables the system operator of decision-making.

References 1. N. Briguglio, V. Antonucci, Overview of PEM electrolysis for hydrogen production, in PEM Electrolysis for Hydrogen Production Principles and Applications, ed. by D. Bessarabov et al., 1st edn., (CRC Press, New York, 2016), pp. 1–9 2. D. Das et al., Introduction, in Biohydrogen Production Fundamentals and Technology Advances, ed. by D. Das et al., 1st edn., (CRC Press, New York, 2014), pp. 1–21 3. T. Zhou, B. Francois, Energy management and power control of a hybrid active wind generator for distributed power generation and grid integration. IEEE Trans. Ind. Electron. 58(1), 95–104 (2011) 4. G. Rohbogner, S. Fey, What the term agent stands for in the smart grid definition of agents and multi-agent systems from an engineer’s perspective, in Proceedings of the federated conference on computer science and information system (2012), pp. 1301–1305 5. Y. Eddy, H. Gooi, S. Chen, Multi-agent system for distributed management of microgrids. IEEE Trans. Power Syst. 30(1), 24–34 (2015) 6. S. McArthur et al., Multi-agent systems for power engineering applications – part I: Concepts, approaches, and technical challenges. Power Syst. IEEE Trans. 22(4), 1743–1752 (2007)

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7. S. Theiss, V. Vasyutynskyy, K. Kabitzsch, AMES – a resource-efficient platform for industrial agents, Proceedings of the IEEE International Workshop on Factory Communication Systems, 2008 8. C. Nunes et al., Comparing stability of implementation techniques for multi-agent system product lines, in Proceedings of the European conference on Software Maintenance and Reengineering, 2009, pp. 229–232 9. A. Sujil, J. Verma, R. Kumar, Multi-agent system: Concepts, platforms, and applications in power systems. Artif. Intell. Rev. 49, 153–182 (2018) 10. K. Kravari, N. Bassiliades, A survey of agent platforms. J. Artif. Soc. Soc. Simul. 18(1), 1–19 (2015) 11. M. R. Barakat, H. Gualous, D. Hissel, B. T. Ighil, Y. Slamani, Smart Micro-Grid Energy Management Strategies – A review, in The 4th International Conference on Renewable Energy: Generation and Applications (ICREGA16), Belfort, France, 8–10 February 2016, Paper ID: 143 12. F. Bellifemine, G. Caire, D. Greenwood, The JADE platform, in Developing Multi-Agent Systems with JADE, ed. by F. Bellifemine, G. Caire, D. Greenwood, 1st edn., (Wiley, Chichester, 2007), pp. 29–50 13. M. Bouscayrol, Energetic Macroscopic Representation (EMR), L2EP Lab, University Lille1, May 2011 14. D. Chrenko, Energetic macroscopic representation modeling and control of a low-temperature fuel cell system fed by hydrocarbons, Ph.D. dissertation, Dept. Electric power., Franche-Comté Univ., Belfort, France, 2008 15. A. Tabanjat et al., Fuzzy logic-based water heating control methodology for the efficiency enhancement of hybrid PV-PEM electrolyzer systems. Int. J. Hydrog. Energy 40(5), 2149– 2161 (2015) 16. J. Martinez, D. Hissel, M. Pera, M. Amiet, Practical control structure and energy Management of a Testbed Hybrid Electric Vehicle. Veh. Technol. IEEE Trans. 60(9), 4139–4152 (2011) 17. K. Agbli, D. Hissel, M. Péra, I. Doumbia, EMR modeling of a hydrogen-based electrical energy storage. Eur. Phys. J. Appl. Phys. 54 (2011) 18. L. Horrein, A. Bouscayrol, Y. Cheng, M. El. Fassi, Multiphysical modeling and description of a permanent magnet synchronous machine using energetic macroscopic representation for EV/HEV applications, in Proceedings of the 15th European Conference on Power Electronics and Applications, 2013, pp. 1–10 19. P. Delarue, A. Bouscayrol, A. Tounzi, X. Guillaud, G. Lancigu, Modelling, control, and simulation of an overall wind energy conversion system. Renew. Energy 28, 1169–1185 (2003) 20. M.R. Barakat, B. Tala-Ighil, Y. Slamani, H. Chaoui, H. Gualous, D. Hissel, Energetic macroscopic representation of a marine current turbine system with loss minimization control. IEEE Trans. Sustainable Energy 9(1), 106–117 (2018) 21. K. S. Agbli, M. R. Barakat, H. Gualous, D. Hissel, Large-scale Tidal Hydrogen Production for Fuel Cell-based EVs. Electrimacs 2017, 4–6 July 2017, Toulouse, France, Paper ID: 27 (2017) 22. M.R. Barakat, B.T. Ighil, H. Gualous, D. Hissel, Modeling of a hybrid marine current-hydrogen active power generation system. Int. J. Hydrog. Energy 44(19), 9621–9635 23. P. Mendham, T. Clarke, MACSim: A Simulink enabled environment for multi-agent system simulation. IFAC Proc. 38(1), 325–329 (2005) 24. C. Robinson, Decentralised Data Fusion Using Agents, Ph.D. dissertation, The University of York, Department of Electronics, (2008) 25. Y. Eddy, H. Gooi, S. Chen, Multi-agent system for distributed management of microgrids. IEEE Trans. Power Syst. 30(1), 24–34 (2015) 26. L. Chen, Multi-Agent System-Based Simulation of a Laboratory-Scale Microgrid, M.S. thesis, The Pennsylvania State University, The School of Science, Engineering and Technology, (2014) 27. L. Raju, R. Milton, S. Mahadevan, Multi-agent systems based distributed control and automation of micro-grid using MACSimJX, in Proceedings of the 10th International Conference on Intelligent Systems and Control, 2016, Coimbatore, India, pp. 1–6 (2016)

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28. C.R. Robinson, P. Mendham, T. Clarke, MACSimJX: A tool for enabling agent modeling with Simulink using JADE. J. Phys. Agents 4(3), 1–7 (2010) 29. C. Robinson, MACSimJX –ACSim with JADE extension, Pack A, document version 1.8, 2012, Available online. http://www.agentcontrol.co.uk/. Last access 30th April 2018 30. M. Barakat, Development of models for inegrating renewables and energy storage components in smart grid applications, Ph.D. dissertation, Electrical Engineering, Caen Normandy University, France, 2018, available online: https://pdfs.semanticscholar.org/100c / ce4ccb841905883752430f27f139cd8fce70.pdf, http://www.theses.fr/2018NORMC217#. Last checked: 04/02/2020

Modelling and Simulation of a Bidirectional SiC-Based Battery Charger for V2G Applications Giuseppe Aiello, Mario Cacciato, Alex La Cognata, Giacomo Scelba, Giuseppe Scarcella, and Alessandro Allegra

Abstract This work deals with the study of a bidirectional battery charger with SiC MOSFETs devices, from the design, modelling, and simulation stages to the realization of a laboratory prototype. The battery charger consists of a high-efficiency 5 kW single-phase bidirectional power converter suitably designed for grid-to-vehicle and vehicle-to-grid applications. It is composed of two stages: an AC/DC PFC synchronous converter and an insulated DC/DC dual active bridge modulated in phase shift. In order to optimize the design, an accurate model has been implemented, and accurate simulations have been carried out able to evaluate the system performance in several operating conditions.

1 Introduction Due to the increasing number of plug-in electric and hybrid vehicles connected to the distribution system, smart on-board and off-board bidirectional battery chargers (BBC) are becoming essential components for managing the energy flows between the vehicles and the AC mains. Recently, BBC have been also designed for vehicleto-grid (V2G) applications, as utilizing energy storage in EVs leads beyond any doubt to economic and environment benefits. Several bidirectional battery chargers have been treated in literature [1–5], in an effort to provide a compact, efficient, and cheap solution. The converter investigated in this paper is a 5 kW single-phase bidirectional battery charger based on two conversion stages: an active front-end (AFE) PWM rectifier connected to the utility grid and cascade connected to a dual active bridge (DAB) isolated converter.

G. Aiello · M. Cacciato · A. La Cognata () · G. Scelba · G. Scarcella · A. Allegra DIEEI – University of Catania, Catania, CT, Italy e-mail: [email protected]; [email protected]; [email protected]; [email protected] © Springer Nature Switzerland AG 2020 W. Zamboni, G. Petrone (eds.), ELECTRIMACS 2019, Lecture Notes in Electrical Engineering 697, https://doi.org/10.1007/978-3-030-56970-9_20

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Such architecture has been adopted for its strengths as bidirectional power flow, galvanic isolation, high efficiency in a wide operating range, and reduced size and weight due to a significant increasing of the switching frequency, thanks to the use of SiC MOSFETs power devices [6]. The connection to the utility grid is accomplished with a power factor correction (PFC). Design, modelling, and simulations have been performed to evaluate the feasibility and the performance of the considered BBC in a wide operating range.

2 Bidirectional Battery Charger Design As shown in Fig. 1, the power conversion topology investigated in this study is a single-phase SiC-based converter. The converter consists of two conversion stages. The first stage is the AFE which is connected to the grid through a LCL filter, while the second stage is realized via a DAB. Phase shift modulation has been used in the DAB stage and consists in the implementation of the control algorithm that set the phase shift between the switching signals of the two legs while maintaining the duty cycle of every switching pattern equal to 50%. During the G2V mode, the phase shift is controlled in order to let the energy flow toward the battery. On the contrary, a suitable opposite phase shift is imposed to the control signals when the converter works in V2G mode when the energy flow is directed from the battery to the AC grid.

2.1 Active Front-End Rectifier The AFE, or synchronous rectifier, is connected via a filter to the utility grid and it performs the AC/DC conversion with the power factor correction. It is a SiCbased H-bridge converter. A bipolar PWM has been implemented, whose switching frequency is fixed at fs = 100 kHz, while the modulating signal is elaborated from the knowledge of the voltage grid angle implementing a grid synchronization algorithm. The gate signals used to control the SiC MOSFETs are obtained from the current control loop.

I° Stage Active Rectifier

II° Stage DAB

LCL Filter

iac vac

Ls

io Lc

M1

M3 vdc

Cac

M5

Cdc

M7 L

HF Trafo

i2

i1 v1

M2

M4

M6

M9

Cf

v2

M8 M10

Fig. 1 Converter topology

M11

M12

vo

Battery

Modelling and Simulation of a Bidirectional SiC-Based Battery Charger for. . . Table 1 Technical specification of the filter parameters and grid operating conditions

Parameter RMS voltage grid Grid frequency fe Ls Filter parameters Cac Lc Cdc Switching frequency fsw

261 Value 230 V 50 Hz 1.5 uH 10 μF 325 μF 4 mF 100 kHz

The high switching frequency has been selected as the best compromise between power density and efficiency. Moreover, a suitable switching frequency can lead to a reduction of the passives composing the AC grid filter and the DC bus link. The LCL structure of the filter has been selected since it provides a higher attenuation of switching harmonics with lower passive element values, obtaining a smaller filter volume in comparison with other solutions [7]. The technical specification of the filter parameters, DC bus link, and grid operating conditions considered in the following analysis are listed in Table 1.

2.2 Dual Active Bridge The dual active bridge (DAB) is the DC/DC isolated bidirectional converter of the BBC. The DAB topology has been selected because of its high efficiency in a wide range of operating range [8]. It features a symmetrical structure, characterized by two full bridges connected via a high-frequency transformer used to provide the galvanic isolation [9]. The first H-bridge produces a square-wave voltage with a 50% of duty cycle in the primary side of the transformer. The second H-bridge performs the AC to DC conversion and implements the current control loop necessary to provide the appropriate current charging profile to the battery. The leakage inductance L plays a key role in the effectiveness of the power conversion. Even the DAB is realized with SiC power MOSFETs. Among the several modulation strategies suggested in literature, a single-phase shift modulation has been used to control the power exchanged between the BBC and the main grid. The phase shift (φ) is defined positive when the power flows from the grid to battery and negative when the power flows in the opposite direction. The relation between the phase shift and the delivered power is given according to [10]: P =

nV1 V2 φ (π − |φ|) 2π 2 fs L

(1)

where −90◦ < φ < 90◦ , V1 and V2 are the transformer end voltages, n is the transformer turn ratio, fs is the switching frequency, and L is the leakage inductance.

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Table 2 DAB design specifications

Parameter Nominal input voltage Vdc Nominal output voltage Vo Minimal output voltage Vo,min Output power Duty cycle Switching frequency

Value 400 V 400 V 150 V 5 kW 0.5 100 kHz

Hence, for a specific active power P, the phase shift φ that must be imposed between the input-output voltages is given by:

π φ= 2

*

 1−

 8fs L |P | 1− sgn(P ) nV1 V2

(2)

The design specifications of the DAB of the analyzed BBC are listed in Table 2.

2.3 High-Frequency Transformer The high-frequency transformer is responsible for the power transfer and for the galvanic isolation [11]. Different core geometries and materials are widespread, and the selection of the most appropriate solutions depends on the kind of application. It is well known that high frequency reduces the core dimensions, and exploiting the ferrite materials involves negligible eddy currents losses. The design method is based on the core geometry method [12, 13]. For this bidirectional converter, the EE core geometry has been chosen with N87 material [14]. This choice is related to the high switching frequency (fs = 100 kHz) and highpower density to which the transformer is subjected. The transformer characteristics are listed in Table 3.

3 Converter Modelling and Simulation Modelling of the bidirectional battery charger, with its closed control loop, has been performed in MATLAB-Simulink in order to simulate its behavior and evaluate its performances under different working conditions. The converter model includes the parasitic elements that affect each power conversion stage. The MOSFETs parameters have been taken into account as well as the dead time between each leg switch. The closed loop control block diagram for the AC/DC PFC converter is shown in Fig. 2.

Modelling and Simulation of a Bidirectional SiC-Based Battery Charger for. . .

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Vdc Vdc*

PI Vd

id* id iα

iac

PI

dq

iβ

iq

dq

PI

αβ Transport delay

αβ

iq*

θ

Vq

θ

vα

vac

θ

PLL

vβ Transport delay

dq

Vd Vq

αβ

Vd

P

id iq

θ

Vq

PQ controller

PI

Q

iq *

Q* Fig. 2 AFE PFC closed loop control block diagram

Pref

Iref

PI

Vbatt Ibatt Fig. 3 Phase shift control loop block diagram

ϕ

vcontrol

264 Table 3 High-frequency transformer parameters

G. Aiello et al. Parameter Nominal input voltage Maximum input voltage Minimum input voltage Input current Nominal output voltage Output current Switching frequency fs Efficiency η Regulation α Max operating flux density Bm Duty cycle D Maximum temperature rise Tr

Value 400 V 480 V 360 V 22 A 400 V 17.5 A 100 kHz 98% 0.15% 0.16 T 0.5 70 ◦ C

Using Park’s transformation, the regulation is implemented using the id and iq currents to control, respectively, the active and reactive power. Moreover, this control structure allows to regulate the DC voltage and the power factor. During G2V mode the AFE with power factor correction works as AC to DC converter, and it charges the battery, maintaining constant DC voltage and unitary PF. In V2G mode it discharges the battery and acts as DC/AC inverter, maintaining constant voltage on the bus DC and managing the power factor to compensate the amount of reactive power required by the grid. The control loop block diagram for the DAB is shown in Fig. 3. The required power from the converter will act on the phase shift, and by varying this reference, it will be possible to reverse the power flow. The simulation waveforms during the G2V mode are shown below. Figure 4 shows the first-stage waveforms that are the grid voltage vac and current iac with unitary power factor and the ripple of the DC voltage. The total harmonic distortion for the AC current is close to 7%. Voltage and current on the primary side of the transformer are shown in Fig. 5. The current waveform depends on the phase shift between the two transformer end voltages. The secondary side quantities are pretty similar, as the turn ratio n has been chosen equal to one. The leakage inductance L affects the power delivered in the DAB converter. Therefore, the voltage vL waveform is strictly related to the power direction. The DC output waveforms are shown in Fig. 6 in which the ripple of the voltage Vo and current Io has been highlighted. During V2G mode the power flows from the battery to the grid to satisfy the power demand. In this case the reference power is modified and it acts on the phase shift, as described before. Transition from G2V to V2G mode, during the t* instant, requires current inversion as illustrated in Fig. 7. In this case, the PF has been maintained unitary that means no reactive power demand.

Modelling and Simulation of a Bidirectional SiC-Based Battery Charger for. . .

400

vac [V] iac [A]

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100

200

50

0 -200

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0.3

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405 400 395 390

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Fig. 4 Voltage and current of the AC grid and ripple on the DC side

This inversion affects partially the total harmonic distortion of the AC grid current, with value close to 10%. The main simulation results are summarized in Table 4. In Fig. 8 you can see the efficiency of the entire power conversion system related to the output power, performed for some simulations results.

4 Battery Charger Prototype and Experimental Results The prototype of the converter has been designed and realized in order to test the performance and efficiency of this bidirectional battery charger. SiC MOSFETs have been used with voltage rating of 1200 V and current of 45 A. Modern microcontroller STM32 has been employed to generate the digital control signals that are sent to the gate via optical fiber. The microcontroller exploits the advanced internal timer, in master-slave mode, to obtain the phase shift modulation and manage the dead time in the leg switches. This allows to realize more compact and robust solutions for the entire experimental system. The experimental converter has been realized, as shown in Fig. 9, and preliminary tests have been carried out with low-power levels. This BBC is actually under test.

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v1[V]

400 200 0

-200 -400 0.39988 0.3999 i1[A]

0.39992

0.39994

0.39996

0.39998

0.4

0.39992

0.39994

0.39996

0.39998

0.4

0.39992

0.39994 Time [s]

0.39996

0.39998

0.4

20

0 -20 0.39988 0.3999 vL [V] 1000 500 0 -500

-1000 0.39988

0.3999

Fig. 5 Voltage and current on the primary side of the transformer and inductance voltage

5 Conclusions Addressing the application of single-phase bidirectional battery charger with galvanic isolation, in the paper a promising topology has been selected as the best choice in terms of high efficiency, bidirectional power flow management, and complexity. The converter accurate model has been developed and implemented

Modelling and Simulation of a Bidirectional SiC-Based Battery Charger for. . .

400

267

Iout [A]

Vout [V]

13

12.5

395

390 0.26

0.28

0.3

0.32 0.34 Time [s]

0.36

0.38

12 0.4

Fig. 6 Ripple on the DC output voltage and current

400

t*

vac [V]

iac [A]

200 0 -200 -400 0.18

0.22

0.26

0.3 Time [s]

0.34

100 50

0 -50 -100 0.4

Fig. 7 AC voltage and current from G2V to V2G mode Table 4 Simulation results Parameter RMS grid voltage Vs RMS grid current Is Average bus DC voltage Vdc Average output voltage Vo Average output current Io Input apparent power S Input active power Pac Bus DC power Pdc Output power Po Power factor PF Displacement power factor DPS Total harmonic distortion THD AFE efficiency η = PDC / Pac DAB efficiency η = Po /PDC Power efficiency ηp = Po /Pac Conversion factor ηc = Po /S

Value 230 V 22.6 A 403 V 397 V 12.4 A 5200 VA 5200 W 5030 W 4910 W 0.999 1 7% 96.7%97.6%94.42%

94.26%

η efficiency

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97,5 97 96,5 96 95,5 95 94,5 94 93,5 93 92,5 92

500

1000

1500

2000

2500

3000

Po output power Fig. 8 Efficiency vs output power

Fig. 9 Experimental prototype of the BBC

3500

4000

4500 5000

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on Simulink in closed loop also with PFC capability in order to analyze the performance and efficiency of each power conversion stage, during G2V and V2G operation mode. A converter prototype has been realized and some tests have been performed. Acknowledgments The authors wish to thank the Department of Electrical, Electronics and Computer Engineering of the University of Catania for research facilities and support provided within the framework of Departmental Research Program 2016/2018.

References 1. M. Restrepo, J. Morris, M. Kazerani, C.A. Cañizares, Modeling and testing of a bidirectional smart charger for distribution system EV integration. IEEE Trans. Smart Grid 9(1), 152–162 (2018) 2. L. Xue, Z. Shen, D. Boroyevich, P. Mattavelli, D. Diaz, Dual active bridge-based battery charger for plug-in hybrid electric vehicle with charging current containing low frequency ripple. IEEE Trans. Power Electron. 30(12), 7299–7307 (2015) 3. M.C. Kisacikoglu, M. Kesler, L.M. Tolbert, Single-phase on-board bidirectional PEV charger for V2G reactive power operation. IEEE Trans. Smart Grid 6(2), 1–9 (2014) 4. H.N. De Melo et al., A controllable bidirectional battery charger for electric vehicles with vehicle-to-grid capability. IEEE Trans. Veh. Technol. 67(1), 114–123 (2018) 5. S. De Caro, A. Testa, D.Triolo, M.Cacciato, A. Consoli, Low input current ripple converters for fuel cell power units, in European Conference on Power Electronics and Applications, EPE 2005, pp. 1–10, Dresden 6. A. Acquaviva, T. Thiringer, Energy efficiency of a SiC MOSFET propulsion inverter accounting for the MOSFET’s reverse conduction and the blanking time, in 2017 19th European Conference on Power Electronics and Applications (EPE’17 ECCE Europe), vol. 2017– January, pp. 1–9, (2017) 7. R. Baxter, N. Hastings, A. Law, E.J. Glass, Bi-directional charger of EV. Anim. Genet. 39(5), 561–563 (2008) 8. M. Jafari, Z. Malekjamshidi, J. G. Zhu, Analysis of operation modes and limitations of dual active bridge phase shift converter, in Proceedings of the International Conference on Power Electronics and Drive Systems, vol. 2015–August, no. June, pp. 393–398, (2015) 9. M. Cacciato, A. Consoli, New regenerative active snubber circuit for ZVS phase shift full bridge converter, in Conference Proceedings – IEEE Applied Power Electronics Conference and Exposition (APEC), pp. 1507–1511, 2011 10. K. Florian Krismer, Modeling and optimization of bidirectional dual active bridge DC–DC converter topologies, Thesis, no. 19177, p. 459, 2010 11. I. Transformers et al., Evaluating impedance transformers with a VNA, vol. 26, no. April, pp. 3599–3608, (2009) 12. E.L. Barrios, A. Ursúa, L. Marroyo, P. Sanchis, Analytical design methodology for Litz-wired high-frequency power transformers. IEEE Trans. Ind. Electron. 62(4), 2103–2113 (2015) 13. K. D. Hoang, J. Wang, Design optimization of high frequency transformer for dual active bridge DC-DC converter, pp. 2311–2317, (2012) 14. Epcos, Epcos, A. Epcos, E. Ag, Ferrites and accessories, no. September, pp. 6–10, (2006)

Part III

Power Converters, Electrical Machines, Devices and Materials

Controllability Insurance of the Boost Converters Dedicated to Fuel Cell Management System Milad Bahrami, Jean-Philippe Martin, Gaël Maranzana, Serge Pierfederici, Farid Meibodi-Tabar, Sophie Didierjean, Jérôme Dillet, Majid Zandi, and Roghayeh Gavagsaz-ghoachani

Abstract The lifetime of a fuel cell stack can be increased by controlling the cells separately. In such a topology, it is imperative to use a high voltage conversion ratio. The isolated step-up DC-DC converters can be a good solution but the efficiency is the major challenge. Connecting the output capacitors of classical converters like boost converters can cope with the problem of efficiency. However, the inequality of injected powers by different cells originated from the commands of the energy management system can lead to reducing the corresponding capacitor voltage. If the output capacitor voltage became lower than the corresponding converter input voltage, its controllability would be lost. An equalizer system that can send energy from the series connection to lower voltage cells is proposed in this paper to ensure the controllability of the boost converters in such a connection. The simulation and experimental results confirm the validity of the proposed equalizer.

1 Introduction Currently, the performance of polymer electrolyte membrane fuel cells (PEMFCs), in terms of power density (3.1 kW/L) and energy efficiency (60%), is sufficient to allow large-scale deployment of this technology [1–3]. On the other hand, sustainability and cost are two points that need to be improved. To improve the durability, it is possible to develop new materials more resistant but also to better

M. Bahrami () · J.-P. Martin · G. Maranzana () · S. Pierfederici () · F. Meibodi-Tabar S. Didierjean · J. Dillet Université de Lorraine, CNRS, LEMTA, Nancy, France e-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected] M. Zandi · R. Gavagsaz-ghoachani Renewable Energies Engineering Department, Shahid Beheshti University, Tehran, Iran e-mail: m\[email protected]; [email protected] © Springer Nature Switzerland AG 2020 W. Zamboni, G. Petrone (eds.), ELECTRIMACS 2019, Lecture Notes in Electrical Engineering 697, https://doi.org/10.1007/978-3-030-56970-9_21

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control the operating conditions to avoid the electrochemical instabilities that lead to irreversible damages. In a stack, cells that produce a nominal voltage of about 0.7 V are connected in series to reach a usable voltage. This architecture has the consequence that when a cell is out of order, the entire stack is unusable. Designing an electrical system called “Fuel Cell Management System” that allows controlling cells or small groups of cells independently has many advantages. For instance, when a cell starts to deteriorate, it can be relieved of some current to prevent it from degrading more. In addition, when a cell is out of order, it can be shunted and the system is able to continue to ensure the production of energy. To implement such an energy management system, a stack, which allows accessing the current of any number of cells, and a power electronic structure are crucial. The new patent obviates the first requirement and allows to access to the current of any number of cells [4]. In this paper, the classical DC-DC boost converters are used as the power electronic structure. Since the voltage of a few numbers of cells is very low and the voltage conversion ratio of a boost converter is limited in practice, the output capacitors of boost converters are connected in series. The isolated step-up DCDC converters can be also used as a response to the high voltage conversion ratio requirement. However, the efficiency improvement of such converters is the basic challenge [5, 6]. The series connection of the output capacitors can endanger the controllability of the boost converters. In such a connection, the same load current passes through all of the capacitors. Therefore, if the input power of one cell becomes lower than the required amount, the voltage of the corresponding capacitor will decrease. In this case, the controllability will be lost if the output voltage becomes lower than the input voltage. In such conditions, a voltage equalizer or a balancing system can ensure the controllability. There are many equalizers in literature. The nondissipative equalizers, which do not use the auxiliary sources, can be divided into three groups: capacitor-based [7–10], converter-based [11–21], and other type equalizers [22, 23]. A large number of switches are used to frequently connect the cells to the capacitors to equalize the cell voltages. The energy from the higher voltage cells is naturally transferred to the capacitors in one period of switching. Then in the next period, this energy is transferred to the lower voltage capacitors. As a result, they need much time to balance the voltages [7–10]. Due to the slow increase of the voltage difference between battery cells, these types of converter can equalize the voltage of battery cells with good efficiency. Many types of converterbased equalizers have been introduced in the literature. In [13] the flyback converter has been used in order to equalize the voltages and transfer the energy between the ultracapacitor and battery cells. The number of switches must be increased by increasing the number of cells. In [14] an improved push-pull converter was used to equalize the cell voltages. Due to the high equalization current in this type of converter, the speed of balancing is very high, but the number of switches must be increased by 4 times the number of cells. The worst disadvantage of the converterbased equalizers is the possibility of increasing the number of switches by increasing the number of cells. The number of switches in some converter-based equalizers depends on the cell numbers [11, 12, 14–19].

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When the difference between the cell voltages is very high, using the resonance can be dangerous for power electronic devices due to the high current peak. In the worst condition, the energy management system can command to generate no power by one cell, and as a result, a large difference between the cell voltages in the fuel cell application is possible. Therefore, a modified equalizer is proposed in this paper. The number of controlled switches is independent of the number of cells. In this paper, the performance of this equalizer is confirmed by the simulation and experimental results. The rest of this paper is organized as follows: The principals of the proposed equalizer and the operation modes are described in Sect. 2. In Sect. 3, the simulation and experimental results are presented to validate the proposed equalizer. Finally, conclusions are listed in Sect. 4.

2 Proposed Equalizer The proposed equalizer is shown in Fig. 1. The H-bridge DC-DC converter can send the energy to even- or odd-numbered cells through the transformer. CH is a film capacitor at the input of the H-bridge converter to stabilize the input voltage of

Fig. 1 Proposed equalizer topology

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this converter. In this topology, only the diodes and secondary windings increase by increasing the number of capacitors in series connection.

2.1 Operation Modes In this section, the following assumptions are considered in the operation analysis for the purpose of simplicity: 1. All the switches and diodes are considered as the ideal devices. 2. C1 and C2 are the lower voltage capacitors between the even- and odd-numbered cells, respectively. 3. Turn ratios for all secondary windings are the same and equal to m = kNN21 and k is the coupling coefficient. 4. The coupling coefficient between the secondary windings is perfect. The theoretic waveforms in steady state are shown in Fig. 2. As seen in this figure, a symmetrical square wave is imposed on the primary side of the transformer by the H-bridge converter. Due to the windings polarity and the direction of the diodes in the circuit, the odd- and even-numbered diodes can be turned on in the positive and negative sections of the square wave, respectively. All the secondary windings will have the same voltage equal to the lower voltage capacitor when one diode starts to conduct. As a result, all the other diodes are negatively biased. The different operation modes of the proposed equalizer are shown in Fig. 3. Mode 1 [t0 -t1 : Fig. 3(a)]: before t0 two switches S1 and S2 were on. At t0 , S2 is turned off and S4 is turned on. Therefore, the positive voltage is imposed on the primary side of the transformer. This voltage is induced in the secondary windings. This voltage leads to a negative voltage difference on the even-numbered diodes. Based on the reason mentioned above, only diode D1 , which connects to the lower voltage capacitor between odd-numbered capacitors, conducts current. As a result, the energy through the leakage inductance of the transformer is transferred to the capacitor C1 . Therefore, the leakage current and voltage of C1 are increased. The derivative equations of different state variables are shown in (1): ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨

Lm didtm = Lf

VC1 m

− r m im

VC1 dif dt = Vin − m  VC if −im − mR 1

⎪ dVC ⎪ ⎪ C1 dt 1 = ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ Cj dVCj = dt

iron

m PF Cj VCj

− iload

− r f if (1) − iload +

PF C1 VC1

j = 2, 3, 4

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Fig. 2 Theoretical waveforms in steady-state operation of the proposed equalizer

where L is the inductance, r is the series resistance, i is the current, m and f subscripts are used to indicate the magnetization and leakage, Riron is the shunt resistance to model the iron loss of the transformer, Vin is the input voltage at the primary side of the transformer, VCj is the voltage of Cj , PFCj is the injected power of Cellsj , and iload is the load current. Mode 2 [t1 -t2 : Fig. 3(b)]: S4 is turned off and S2 is turned on as a synchronous rectifier in this mode. Therefore, the primary side of the transformer is shortcircuited. The diode D1 continues to conduct but the current passing through it, which is proportional to the leakage current, is decreased. The derivative equations in this mode are as follows:

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Fig. 3 Different operation modes of the proposed equalizer. (a) Mode 1: t0 < t < t1. (b) Mode 2: t1 < t < t2. (c) Mode3: t2 < t < t3. (d) Mode 4: t3 < t < t4

⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨

Lm didtm =

VC1 m

dif dt

−VC1 m

Lf 

=

VC

− r m im − r f if

if −im − mR 1 ⎪ dVC1 PF C iron ⎪ ⎪ C = − iload + VC 1 ⎪ 1 dt ⎪ m ⎪ 1 ⎪ ⎪ ⎪ dVCj PF Cj ⎪ ⎩ Cj dt = VC − iload j = 2, 3, 4

(2)

j

The switching frequency is chosen in such a way that the diode D1 turns off and the leakage current is reached to the magnetizing current before the t2 . The differential equations are changed when the diode D1 is turned off (after tf ) as follows:

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⎧ ⎪ ⎪ ⎪ ⎪ ⎨

  Lm didtm = RI ron if − im − rm im   di Lf dtf = −RI ron if − im − rf if

⎪ ⎪ ⎪ ⎪ ⎩ Cj dVCj = dt

PF Cj VCj

− iload

279

(3)

j = 1, 2, 3, 4

Mode 3 [t2 -t3 : Fig. 3(c)]: S1 is turned off and S3 is turned on in this mode. The negative voltage appears on the primary side of the transformer. In other words, Vin has a negative value. This mode like mode 1 has the same effect on the evennumbered capacitors. The voltage of C2 is the lowest voltage between the evennumbered capacitors. Therefore, the diode D2 is turned on and the leakage current and the voltage of C2 start to increase. The leakage current negatively increases. The derivative equations in this mode are as follows: ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨

Lm didtm = − Lf

dif dt 

VC2 m

= Vin + VC

− r m im

VC2 m

− r f if

if −im + mR 2 ⎪ dVC2 PF C iron ⎪ ⎪ C = − − iload + VC 2 ⎪ 2 dt ⎪ m ⎪ 2 ⎪ ⎪ ⎪ dVCj PF Cj ⎪ ⎩ Cj dt = VC − iload j = 1, 3, 4

(4)

j

Mode 4 [t3 -t4 : Fig. 3(d)]: This mode is similar to mode 2 with this difference that S3 is turned off and S1 is turned on. Before the diode D2 is turned off, the differential equations of the system are as follows: ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨

Lm didtm = Lf 

dif dt

=

−VC2 m VC2 m VC

− r m im − r f if

if −im + mR 2 ⎪ dVC2 PF C iron ⎪ ⎪ C = − − iload + VC 2 ⎪ 2 ⎪ dt m ⎪ 2 ⎪ ⎪ ⎪ dVCj PF Cj ⎪ ⎩ Cj dt = VC − iload j = 1, 3, 4

(5)

j

Then, the diode D2 is turned off and the differential equations of the system change as (4). The power is transferred through the transformer to increase the voltage of lower voltage capacitors. Any losses in the transformer reduce the power that is received by lower voltage cells.

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3 Simulation and Experimental Results A simulation is made in MATLAB-Simulink by assuming the four capacitors in series and that all PEMFCs can inject the rated power of 126 W except Cells1 . Other information is summarized in Table 1. For a precise study of the balancing system, the H-bridge converter is controlled in the open-loop mode, and duty cycle is changed from 0 to 0.9 in the same time interval. Duty cycle is increased in the form of 0-0.4-0.6-0.8-0.9. It is assumed that the PEMFC connected to the first capacitor cannot inject any power but the other cells inject the nominal power (126 W). The voltage changes by increasing the duty cycle are shown in Fig. 4(b). The voltage difference between the first capacitor and the other is reduced by increasing the duty cycle. The voltage and current waveforms on the primary side of the transformer for d = 0.8 are shown in Fig. 4(a). As seen in this figure, the power can be transmitted through the transformer. For further verification of the proposed balancing system and validation of the theoretical analysis and simulation, the experiments are conducted on a laboratory prototype as demonstrated in Fig. 5. dSPACE RTI 1005 is used to receive the information and send the commands. Four programmable power supplies are used to emulate the PEMFCs. These power supplies are connected to four boost converters; the output capacitors of the boosts are connected in series. The component part number used in this prototype is listed in Table 2. The proposed balancing system connects to these capacitors. The most important objective of the proposed balancing system is to ensure the controllability of the boost converters. Like the simulation conditions, the first cell injects no power. To check the supplementary conditions in the next test, it is assumed that the second PEMFC injects no power but the others inject the nominal power (126 W). The current and voltage waveforms on the primary side of the

Table 1 Parameters of the proposed equalizer Symbol C AL N1 N2 k F

Unit μF nH/turns2 Turns Turns – kHz

Value 4700 12,500 4 1 0.98 40

RLoad VFC VC

 V V

7.5 6.3 12

Vd CH

V μF

0.8 220

Description Electrochemical Planar transformer core Primary winding turns Secondary winding turns Coupling coefficient Switching frequency of the H-bridge Resistive load Nominal voltage of FCs Nominal output voltages of boosts Drop voltage of diodes Film capacitor

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Fig. 4 Simulation results of the proposed equalizer. (a) Output capacitor voltages for the different amount of duty cycle. (b) Voltage and current waveforms on the primary side of the transformer for d = 0.8

transformer for d = 0.6 and d = 0.8 in these two experiments are shown in Fig. 6. As can be seen in this figure, reducing the voltage difference due to the increase in the duty cycle of the H-bridge converter shows its effect on the transformer current. The change in the capacitor voltages in these two experiments is shown in Fig. 7. As seen in this figure, the experimental results confirm the simulation results. As

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Fig. 5 Proposed equalizer test bench

Table 2 Component part number for the prototype FC Boost converter

Equalizer

Component Power supply Inductance Switches Capacitor Diodes Transformer H-bridge switches Capacitor

Part number TDK GENH 750 W (1 mH) IGBT Electrochemical (4700μF) STTH6004W SiC MOSFET CCS050M12CM2 Film (220 μF)

seen in this figure, the voltage of Vc1 /VC2 for the duty cycle of zero is lower than 6.3, and the controllability of the first/second boost converter is lost, but by increasing the duty cycle of the H-bridge converter, it becomes controllable in the first/second experiment.

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Fig. 6 Experimental waveforms of the current and voltage on the primary side of the transformer. (a) The first fuel cell injects no power and d = 0.6. (b) The first fuel cell injects no power and d = 0.8. (c) The second fuel cell injects no power and d = 0.6. (d) The second fuel cell injects no power and d = 0.8

4 Conclusions A new equalizer was proposed to ensure the controllability of the boost converters dedicated to implementing the fuel cell energy management system. The proposed equalizer is cost-effective because the number of switches is independent of the number of cells. A state-space model was proposed in this paper. The simulation based on this model confirms the theoretical assumptions. A test bench with four boost converters with the series connection of their capacitors was built to validate the equalizer system. The experimental voltage and current waveforms on the primary side of the transformer were in agreement with the simulation results. Therefore, the proposed model is valid. Using the proposed equalizer, the voltage changes of output capacitors by changing the duty cycle of the H-bridge converter

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Fig. 7 Experimental results of the output capacitor voltages. (a) The first fuel cell injects no power. (b) The second fuel cell injects no power

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demonstrated that when one of the capacitors is not controllable, by increasing the duty cycle of the H-bridge converter, it becomes controllable.

References 1. T. Yoshida, K. Kojima, Toyota MIRAI fuel cell vehicle and progress toward a future hydrogen society. Interface Mag. 24(2), 45–49 (2015) 2. Y. Wang, K.S. Chen, J. Mishler, S.C. Cho, X.C. Adroher, A review of polymer electrolyte membrane fuel cells: Technology, applications, and needs on fundamental research. Appl. Energy 88, 981–1007 (2011) 3. M. Matsunaga, T. Fukushima, K. Ojima, Powertrain system of Honda FCX clarity fuel cell vehicle. World Electr. Veh. J. 3(1), 820–829 (2009) 4. G. Maranzana, S. Didierjean, J. Dillet, A. Thomas, O. Lottin, Improved fuel cell. Patent n◦ : WO/2014/060198., 2014 5. T. Arunkumari, V. Indragandhi, An overview of high voltage conversion ratio DC–DC converter configurations used in DC micro-grid architectures. Renew. Sust. Energ. Rev.77(March), 670–687 (2017) 6. Q. Wu, S. Member, Q. Wang, J. Xu, A high efficiency step-up current-fed push-pull quasiresonant converter with fewer components for fuel cell application. IEEE Trans. Ind. Electron. 0046(c) (2016) 7. R. Beiranvand, Analysis of a switched-capacitor converter above its resonant frequency to overcome voltage regulation issue of resonant SCCs. IEEE Trans. Ind. Electron. 63(9), 5315– 5325 (2016) 8. R. Beiranvand, Regulating the output voltage of the resonant switched-capacitor converters below their. IEEE Trans. Ind. Electron. 64(7), 5236–5249 (2017) 9. Y. Ye, K.W.E. Cheng, S. Member, Y.C. Fong, X. Xue, S. Member, J. Lin, Topology, modeling , and design of switched-capacitor-based cell balancing systems and their balancing exploration. IEEE Trans. Power Electron. 32(6), 4444–4454 (2017) 10. Y. Shang, S. Member, B. Xia, S. Member, F. Lu, S. Member, C. Zhang, N. Cui, C.C. Mi, A switched-coupling-capacitor equalizer for series-connected battery strings. IEEE Trans. Power Electron. 32(10), 7694–7706 (2017) 11. Y. Chen, X. Liu, Y. Cui, J. Zou, S. Yang, A multi-winding transformer cell-to-cell active equalization method for lithium-ion batteries with reduced number of driving circuits. IEEE Trans. Power Electron. 31(7), 4916–4929 (2016) 12. Y. Shang, S. Member, B. Xia, S. Member, C. Zhang, An automatic equalizer based on forwardFlyback converter for series-connected battery strings. IEEE Trans. Ind. Electron. 64(7), 5380– 5391 (2017) 13. T. Anno, H. Koizumi, Double-input bidirectional DC/DC converter using cell-voltage equalizer with flyback transformer. IEEE Trans. Power Electron. 30(6), 2923–2934 (2015) 14. L. Li, Z. Huang, H. Li, J. Peng, A rapid cell voltage balancing scheme for supercapacitor based energy storage systems for urban rail vehicles. Electr. Power Syst. Res. 142, 329–340 (2017) 15. V. Yuhimenko, S. Member, G. Geula, S. Member, G. Agranovich, M. Averbukh, A. Kuperman, S. Member, Average modeling and performance analysis of voltage sensorless active supercapacitor balancer with peak current protection. IEEE Trans. Power Electron. 32(2), 1570–1578 (2017) 16. Z. Zhang, S. Member, H. Gui, S. Member, D. Gu, Y. Yang, A hierarchical active balancing architecture for lithium-ion batteries. IEEE Trans. Power Electron. 32(4), 2757–2768 (2017) 17. K. Lee, S. Lee, Y. Choi, B. Kang, Active balancing of Li-ion battery cells using transformer as energy carrier. IEEE Trans. Ind. Electron. 64(2), 1251–1257 (2017)

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18. X. Liu, J. Lv, C. Gao, Z. Chen, A novel diode-clamped modular multilevel converter with simplified capacitor voltage-balancing control. IEEE Trans. Ind. Electron. 64(11), 8843–8854 (2017) 19. H. Kang, H. Cha, A new nonisolated high-voltage-gain boost converter with inherent output voltage balancing. IEEE Trans. Ind. Electron. 65(3), 2189–2198 (2018) 20. Q. Ouyang, J. Chen, J. Zheng, Y. Hong, SOC estimation-based quasi-sliding mode control for cell balancing in lithium-ion battery packs. IEEE Trans. Ind. Electron. 65(4), 3427–3436 (2018) 21. M. Fu, C. Zhao, J. Song, A low-cost voltage equalizer based on wireless power transfer and voltage multiplier. IEEE Trans. Ind. Electron. 65(7), 5487–5496 (2018) 22. A.K. Sadigh, V. Dargahi, S. Member, K.A. Corzine, S. Member, New active capacitor voltage balancing method for flying capacitor multicell converter based on logic-form-equations. IEEE Trans. Ind. Electron. 64(5), 3467–3478 (2017) 23. M. Mazuela, I. Baraia, A. Sanchez-ruiz, Simple voltage balancing method to protect seriesconnected devices experimentally verified in a 5L-MPC converter. IEEE Trans. Ind. Electron. 65(5), 3699–3707 (2018)

3-D Generic Magnetic Equivalent Circuit Taking into Account Skin Effect: Magnetic Field and Eddy-Current Losses Youcef Benmessaoud, Walid Belguerras, Frédéric Dubas, and Mickael Hilairet

Abstract In this paper, a three-dimensional (3-D) generic magnetic equivalent circuit (MEC) in Cartesian coordinates considering the skin effect is developed. This model has been applied to a U-cored static electromagnetic device. The main objective is to compute the magnetic field behaviour in massive conductive parts (viz. aluminium) and to predict the impact of the eddy-current magnetic fields in the neighbouring nonconductive parts. The classical magnetomotive force (MMF) distribution has been modified by integrating the MMF produced by the eddy currents that occur in massive conductive regions. The eddy-current MMF was introduced by formula which derived from magnetodynamic Maxwell’s equations. Both experimental tests and three-dimensional (3-D) finite-element analysis (FEA) have been used to prove the validity of the proposed approach.

1 Introduction 1.1 Context of this Paper Different models more or less accurate taking into account spatiotemporal harmonics have been developed in the past. The importance of studying the eddycurrents topic still remains attractive in static and/or dynamic applications such as nondestructive control, permanent-magnet (PM) synchronous machines (PMSMs). Indeed, incorporating PMs in electrical machines improve really the efficiency and the behaviour of the integral quantities. However, the presence of conductive materials can consist a technical drawback in the high frequency, causing additional losses at high speed which dissipate in the heat forms, leading to the PMs degradation. Indeed, the magnetic field variation is one of the main sources of these

Y. Benmessaoud · W. Belguerras · F. Dubas · M. Hilairet () FEMTO-ST, CNRS, Univ. Bourgogne Franche-Comté, Belfort Cedex, France e-mail: [email protected]; [email protected]; [email protected] © Springer Nature Switzerland AG 2020 W. Zamboni, G. Petrone (eds.), ELECTRIMACS 2019, Lecture Notes in Electrical Engineering 697, https://doi.org/10.1007/978-3-030-56970-9_22

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losses which further affect the electromagnetic proprieties. This meant that eddy currents become essential when sizing PMSMs at high speed. In order to estimate these eddy-current losses, different modelling technics in the literature can be found based on different formulations [1]. It can be found analytical models based on the formal resolution of Maxwell’s equations [2], the finite-difference method from Maxwell’s equations where the boundary conditions (BCs) come from the FEA [3], the hybrid models [4] and the semi-analytical model based on the MEC (or reluctances network). Eddy currents can be incorporated into MEC by using magnetic reluctances, magnetic inductances, or eddy-current MMFs [5–8]. The main drawbacks of the last works can be liked to the incorporated MMFs or magnetic reluctances which don’t take into account the skin effect, and the method depends on the FEA to get the local quantities that allows computing eddy-current losses. Add to this, no models exist till now which permit to study the skin effect on the behaviour of the magnetic field over all the electromagnetic devices by applying only the MEC.

1.2 Objectives of this Paper In this paper, a new approach is proposed to incorporate the MMFs which take into account the skin effect in the semi-analytical model based on the 3-D generic MEC. In this way, it can be analysed the impact of the magnetic fields due to eddy currents occurred in massive conductive parts and over all parts of the electromagnetic devices. The performed model will be able to compute the eddy-current losses in massive conductive parts, to predict the behaviour of both magnetic field and flux density over all the electromagnetic device. The segmentation in the two axes is also allowed but not treated in this paper.

2 U-Cored Static Electromagnetic Device Figure 1 shows the two-dimensional (2-D) view of the static electromagnetic device whose experimental tests have been presented in [9]. This device is constituted by a mobile armature that allows to insert massive conductive parts (viz. aluminium) of various thicknesses. Two coils having Nt series turns are connected in parallel. It is supplied with a sinusoidal voltage. Since the magnetic circuit is not saturated, the current is then sinusoidal waveform with a maximum amplitude of Imax . The geometric and physics parameters are given in Table 1.

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Fig. 1 U-cored static electromagnetic device: (a) experimental test [9] and (b) geometrical parameters

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Y. Benmessaoud et al. Table 1 Geometrical and physical parameters Parameter, symbol [unit] Depth, d [mm] Width, w [mm] Coil height, hc [mm] Coil width, wc [mm] Coil section, Sc = hc · wc [mm2 ] Yoke height, hy [mm] Yoke length, ly [mm] Thickness of massive part, hmp [mm] Height overhang top, hot [mm] Height overhang bot, hob [mm] Electrical frequency, f [Hz] Maximal current, Imax [A] Number of turns, Nt [−] Relative permeability of massive parts in aluminium, μrmp [−] Electrical conductivity of massive parts in aluminium, σ mp [S/m] Vacuum permeability, μ0 [H/m] Relative permeability of iron core, μri [−]

Value 43 43 77 10 770 43 150 6 or 10 19 4 50 or 1600 0 to 8.2 500 1 38.46 × 106 4π × 10−7 1500

3 3-D Generic MEC Using Mesh-Based Formulation The 3-D automatic generation MEC using mesh-based formulation is already developed and explained in [10]. This provides the distributions of magnetic flux density B = {Bx ; By ; Bz } in all parts of an electromagnetic device. In [10], the MMFs associated with massive conductive parts are equal to zero because the skin effect has been neglected. The results of B were confronted with those obtained by the 3-D FEA. The computation time is divided by 3 with an error less than 1%. In the following section, it is explained the followed approach to associate the MMFs produced by the magnetic reaction field taking into account eddy-current phenomenon.

4 Developed Approach 4.1 Principle of Model Figure 2 represents the flowchart that explains the approach followed to incorporate the MMF produced by the eddy currents in massive conductive parts into the 3-D generic MEC. Firstly, it is not considered the electrical conductivity of the massive conductive parts. Hence, the 3-D generic MEC results correspond to those levied at magnetostatic application. Next, the magnetic flux density in the middle of the

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Fig. 2 Flowchart of 3-D generic MEC with the skin effect

massive conductive part will be considered to define the BCs to resolve the complex Helmholtz’s equation. At this stage, the evolution of the eddy-current magnetic field can be got. Thereafter, Hopkinson’s law will be applied to estimate the MMFs due to the magnetic field reaction caused by the massive conductive parts. Finally, these later will be incorporated into the performed 3-D generic MEC. New simulation gives the results by considering the electrical conductivity of the massive parts. Furthermore, it can be remarked that the crossing flux tube in the electromagnetic device when considering the electrical conductivity can be affected in values and length terms.

4.2 Magnetic Field Due to Electrical Conductivity in Massive Conductive Parts To estimate the MMFs with the skin effect wherever in the massive conductive part, the approach derived from the formal resolution of Maxwell’s equations by using the separation of variables method and the Fourier’s series. In quasistationary approximation, inside a linear (non)magnetic material of electrical conductivity without electromagnetic sources, the partial differential equation in magnetodynamic in terms of Hmp can be defined by [1]

∇ 2 H mp − μ · σ ·

∂H mp = 0 (Diff usion equation) . ∂t

(1)

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+ , mp mp mp = 0; Hσy ; 0 with Hσy = -In Cartesian. coordinates√ (x, z), H mp  Hσy · ej·ω·t , where j = −1 and ω = 2π · f is the electrical pulse, in massive conductive parts considering the skin effect is then governed by the complex Helmholtz’s equation, viz. mp

mp

∂ 2 Hσy ∂ 2 Hσy mp + − α 2 · Hσy = 0, ∂x 2 ∂z2

(2)

where α 2 = j · μmp · σ mp · ω. The BCs are considered homogeneous at the edges of massive conductive parts, which are equal to Hs . This value of magnetic field is defined as the normal magnetic field value crossing the middle of the massive conductive part determined by magnetostatic 3-D generic MEC, i.e. without electrical conductivity, viz. Hs = By (0, 0)/μmp . The various BCs are shown in Fig. 3. By using the separation of variables method and by applying the BCs, the 2-D general solution of Hσ y in both directions (i.e. x- and z-edges) can be written as Fourier’s series [1] mp

Hσy = Hs · fσ (x, z),

Fig. 3 BCs at edges of massive conductive parts in (x, z) coordinate system

(3a)

3-D Generic Magnetic Equivalent Circuit Taking into Account Skin Effect:. . .

fσ (x, z) =

⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ ··· +

∞  k=1,3,...

 ekz

ch(α·z)   ch α· d2

=2· 1−

⎫ ⎪ ⎪ ⎬

⎪ ekz · ch (δk · x) · cos (λk · z) ⎪ ⎭



λk δk

2 

293

  sinc λk · d2  ,  · ch δk · w2

,

(3b)

(3c)

2 mp where λk = kπ /d is the periodicity of Hσy in the z-axis, δk = α 2 + λk 2 , k are the spatial harmonic orders. mp It should be noted that Hσy is assumed to be invariant in the y-axis. Moreover, when α = 0 (viz. σ mp = 0 S/m and/or f ∼ = 0+ Hz), then fσ (x, z) = 1, thus giving mp

Hσy = Hs .

4.3 Hopkinson’s Law to Estimate the MMF Values with the Skin Effect As it is explained in the sections before, initially the MMFs associated with massive conductive parts are equal to zero. In reality, the magnetic field inside and outside the massive conductive parts is affected by electrical conductivity. Therefore, the MMFs in the massive conductive parts cannot be equal to zero. To estimate the eddy-current MMFs that occur in massive conductive parts, Hopkinson’s law on a “flux tube” in massive conductive parts is used as well as (3). So the eddy-current MMFs are defined by

mp

MMFσ (x, y) = Hs ·

! hmp y · 1 − fσ (x, z) , 2 · Nd 3

. mp j·ω·t . =  MMF · e MMF mp σ σ mp

(4a)

(4b)

Finally, MMF σ will be incorporated into the 3-D generic MEC in massive conductive parts by respecting the discretization number in the y-axis chosen in the y massive piece zone, viz. Nd 3 [see Fig. 4]. Consequently, we get new magnetic flux densities Bσ = {Bσ x ; Bσ y ; Bσ z } by considering the electrical conductivity.

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Fig. 4 2-D view of the U-cored static electromagnetic device in (a) yz-plane and (b) xz-plane

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5 Result Discussion In this section, all the results are calculated with Imax = 7.78 A at t = 0 sec and hmp = 6 mm for two values of electrical frequency (viz. 50 Hz and 1600 Hz). A very weak discretization has been imposed in the 3-D generic MEC obtaining a good approximation on the y-component of B in massive conductive parts. To improve the precision, a high discretization can be applied on the 3-D generic MEC. The validation of proposed model has been realized on the Cedrat’s Flux3D software package by using the application Harmonic State 3-D [11]. A 2-D view of the U-cored static electromagnetic device is illustrated in Fig. 4 for yz-plane [see Fig. 4(a)] and for xz-plane [see Fig. 4(b)]. The 2-D grid N◦ 1 parallel to xz-plane and the 2-D grid N◦ 2 parallel to xy-plane are presented by the dashed black bold line for various comparisons. Figure 5 represents the evolution of the y-component of B on the 2-D grid N◦ 1 with(out) the skin effect. Figure 5(a) corresponds to the magnetic flux density mp allowing to obtain the initial values of BCs (i.e. Hs to estimate MMF σ ). The Fig. 5 The y-component of the magnetic flux density on the 2-D grid N◦ 1: (a) without the skin effect and (b) with the skin effect

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Fig. 6 Evolution of Hσy in the massive conductive part for (a) f = 50 Hz and (b) f = 1, 600 Hz

results show a good agreement. Add to this, in Fig. 5(b), it can be clearly seen the deformation of the y-component of Bσ due to the electrical conductivity in massive conductive parts. Figure 6(a) illustrates more clearly the impact of the massive conductive part on the behaviour of the magnetic field, where the skin effect appears slightly at 50 Hz contrary to 1600 Hz that appears clearly as shown in Fig. 6(b). Indeed, the conductive massive part acts as a barrier to the crossing flux. Using J = ∇ × Hσ (i.e. Maxwell-Ampère), the absolute resultant current density is shown in Fig. 7. Figures 8 and 9 represent, respectively, the magnetic flux density map in terms of components (i.e. x- and y-component) on the 2-D grid N◦ 2 without and with the skin effect at 50 Hz. From these figures, the influence of the existing massive conductive part can be seen, especially the magnetic flux density values that decrease in the most parts of the device, where the maximum value for y-component goes from By = 1 T to Bσ y = 0.8 T [see Fig. 8(a) and Fig. 9(a)] and from Bx = 0.8 T to Bσ x = 0.55 T [see Fig. 8(a) and Fig. 9(a)] for x-component.

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Fig. 7 Evolution of absolute J in the massive conductive part for (a) f = 50 Hz and (b) f = 1, 600 Hz

A particular attention can be given to Bσ x , in fact that it presents a slight increase in the neighbouring region of the coil, where the x-component of magnetic flux density passes from Bx = 0.1 T toBσ x = 0.2 T. It can be noted that the massive conductive parts could affect the efficiency of the U-cored static electromagnetic device by increasing the flux leakage.

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Fig. 8 Magnetic flux density map without the skin effect on the 2-D grid N◦ 2 for (a) By and (b) Bx

6 Eddy-Current Loss Calculation The 3-D eddy-current losses results given by the 3-D generic MEC with the skin effect are confronted with those obtained by 3-D FEA and experimental tests. For the experimental acquisition, these losses are calculated by using the separation of losses method [9]. In the proposed model, the eddy-current losses in the massive conductive part can be calculated by [1]

3-D Generic Magnetic Equivalent Circuit Taking into Account Skin Effect:. . .

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Fig. 9 Magnetic flux density map with the skin effect at f = 50 Hz on the 2-D grid N◦ 2 for (a) Bσ y and (b) Bσ x

Wed =

1 σmp

(((

  Jx 2 + Jy 2 · dV ,

(5)

Vmp

where Vmp is the volume of the massive conductive part. The comparisons were performed at 50 Hz on two thicknesses in aluminium, viz. 6 mm and 10 mm. Figure 10 represents the evolution of Wed according to Imax [see Table 1]. The performed model gives a good agreement with both 3-D FEA and measurement.

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Fig. 10 Validation of eddy-current losses (3-D MEC, 3-D FEA and experimental) in conductive massive parts versus Imax at f = 50 Hz for (a) hmp = 6 mm and (b) hmp = 10 mm

7 Conclusion In this work, a new approach is proposed to analyse the influence of the eddy currents on the behaviour of the magnetic flux density over all the U-cored static electromagnetic devices. A 3-D generic MEC was used and improved taking into account skin effect in massive conductive parts. The classical MMF distribution has been modified by integrating the eddy-current MMFs in massive conductive parts, which was introduced by a formula based on the Maxwell-Fourier method and by using Hopkinson’s law. It is able to compute the eddy-current losses in massive conductive parts. The model allows to study also the segmentation in both two space

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axes. Eddy-current losses and local quantities resulted from 3-D generic MEC with the skin effect that gives good agreement comparing to both measurement and 3-D FEA. Acknowledgements This work was supported by RENAULT-SAS, Guyancourt, France. This scientific study is related to the project “Conception optimale des chaines de Traction Electrique” (COCTEL) financed by the “Agence De l’Environnement et de la Maîtrise de l’Énergie” (ADEME).

References 1. R.L. Stoll, The Analysis of Eddy Currents (Clarendon Press, Oxford, 1974) 2. Z.Q. Zhu, K. Ng, N. Schofield, D. Howe, Improved analytical modeling of rotor Eddy current loss in brushless machines equipped with surface mounted permanent magnets. IEE Proc. Electr. Power Appl. 151(6), 641–650 (2004) 3. R. Benlamine, F. Dubas, S.A. Randi, D. Lhotellier, and C. Espanet, “3-D numerical hybrid method for PM Eddy-current losses calculation: Application to axial-flux PMSMs”, IEEE Trans. Magn., vol. 51, no. 7, Jul. 2015, Art. no. 8106110 4. T. Gerlach, L. Rabenstein, A. Dietz, A. Kremser, D. Gerling, Determination of Eddy current losses in permanent magnets of SPMSM with concentrated windings: A hybrid loss calculation method and experimental verification, in Proceedings of the EVER, Monte-Carlo, Monaco, Monaco, Apr. 10–12, 2018 5. H. Gholizad, B. Funieru, A. Blinder, Direct modeling of motional Eddy currents in highly saturated solid conductors by the magnetic equivalent circuit method. IEEE Trans. Magn. 45(3), 1016–1019 (2009) 6. D. Bormann, H. Tavakoli, Reluctance network treatment of skin and proximity effects in multiconductor transmission lines. IEEE Trans. Magn. 48(2), 735–738 (2012) 7. Y. Yoshida, K. Nakamura, O. Ichinokura, A method for calculating Eddy current loss distribution based on electric and magnetic networks. IEEE Trans. Magn. 47(10), 4155–4158 (2011) 8. Y. Yoshida, K. Nakamura, O. Ichinokura, Consideration of Eddy current loss estimation in SPM motor based on electric and magnetic networks. IEEE Trans. Magn. 48(11), 3108–3111 (2012) 9. P.K. Chetangny, S. Houndedako, A. Vianou, C. Espanet, Eddy-current loss in a conductive material inserted into a U-cored electromagnetic device, in Proceedings of the VPPC, Belfort, France, Dec. 11–14, 2017 10. Y. Benmessaoud, F. Dubas, R. Benlamine, M. Hilairet, Three dimensional automatic generation magnetic equivalent circuit using mesh-based formulation, in Proc. ICEMS, Sydney, NSW, Australia, Aug. 11–14, 2017 11. Flux2D/3D, General operating instructions, Version 11.1., Cedrat S.A. Electrical Engineering, Grenoble, France, 2013

Mathematical Procedure for Harmonic Elimination in CHB Multilevel Inverters with Variable DC Sources Concettina Buccella, Maria Gabriella Cimoroni, and Carlo Cecati

Abstract In this paper, a single-phase cascaded H-bridge (CHB) multilevel inverter having s DC sources and a number of levels l = 2s+1 with s = 2n n = 1, 2, 3, . . . is considered, and a method to eliminate n + 1 harmonics and their respective multiple from its output voltage waveform is presented. The proposed procedure is compared with the conventional selective harmonic elimination (SHE) technique, and its better performances, in terms of total harmonic distortion (THD), are shown. The procedure requires low computational cost and low memory occupation, allowing real-time implementation.

1 Introduction Cascaded H-bridge (CHB) multilevel inverters have received great interest due to their superior performances [1–4]. Various selective harmonic elimination (SHE) pulse-width modulation (PWM) methods have been proposed in literature [5–10]. By applying these methods, only switching angles are regarded as unknowns of the problem. In order to increase the number of harmonics to be deleted for fixed number of levels, also DC voltage sources are regarded as unknowns, giving rise to pulse-amplitude modulation (PAM) concept [11]. Therefore, by PAM, more harmonics can be deleted without increasing the switching frequency. Compared to the SHE-PWM, the quality of output voltage in terms of harmonic content is significantly improved. It is very important to select a suitable solving algorithm or method to find the solution of the equations. Numerous techniques, such as iterative approaches [12],

C. Buccella · M. G. Cimoroni () · C. Cecati University of L’Aquila – DISIM & DigiPower srl, L’Aquila, Italy e-mail: [email protected]; [email protected]; [email protected] © Springer Nature Switzerland AG 2020 W. Zamboni, G. Petrone (eds.), ELECTRIMACS 2019, Lecture Notes in Electrical Engineering 697, https://doi.org/10.1007/978-3-030-56970-9_23

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optimization methods [13], and resultant theory [14], have been proposed. The most popular method for the solution of these nonlinear equations is the iterative one of Newton-Raphson (NR) [15]. The drawback of NR method is that the solutions set depend on the initial values and divergences may occur. In [16], the elimination of harmonics in a CHB multilevel inverter by considering the nonequality of separated DC sources has been performed by using particle swarm optimization (PSO). In [17], to solve the equations applied to a seven-level inverter, the bee algorithm (BA) has been used. Genetic algorithm (GA) techniques have been also applied to calculate solutions; they are simple methods for this optimization problem without the extensive derivation of the analytical expressions for eliminating and minimizing the harmonic content in multilevel inverter output voltage [18]. The drawbacks of the GA techniques are solutions obtained in a limited range of modulation index and randomly dependent on the chosen fitness function [19]. These methods require large computational time, especially when the number of level is high. In [20], an approach for real-time computation of switching angles using artificial neural networks (ANNs) has been presented for a CHB 11-level inverter. For CHB 5-level inverters, SHE analytical solutions can be obtained [9, 10]. In this paper, a method to eliminate n + 1 harmonics and their multiple from the output voltage waveform of a single phase CHB l-level inverter, l = 2s + 1 with s DC sources s = 2n n = 1, 2, 3, . . ., is proposed. It returns switching angles and DC voltage sources by analytically solving 2×2 linear systems, obtained by applying recursively prosthaphaeresis formulas. The proposed method allows to obtain lower total harmonic distortion (THD) of output waveforms in comparison to conventional SHE procedure. The time cost of the presented analytical algorithm is computed. Since it is very low, real-time implementation through common microprocressors or DSPs is allowed [21, 22].

2 Mathematical Model For this work, single-phase CHB l-level inverters are considered having number of levels l = 2s + 1, where s is the number of DC sources, expressed as s = 2n , n = 1, 2, 3, . . . . This means that the procedure is valid for 5-, 9-, 17-, 33-, 65and so on level inverters. The considered configuration is shown in Fig. 1. The output voltage of multilevel converter vout can be developed in Fourier series as:   s ∞

1

4 vout (ωt) = Vi cos (kαi ) sin (kωt) (1) π k k=1, 3, 5, ...

i=1

where the DC sources feeding each H-bridge are assumed equal, i.e., V1 = V2 = V3 = · · · = Vs = V

(2)

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Fig. 1 Single phase CHB l-level inverters

and depending on modulation index m. The p.u. quantity V ∗ V∗ =

V Vdc

(3)

is introduced, and a positive coefficient C is defined, such that V ∗ = Cm

(4)

π H1 4sVdc

(5)

where m=

Vdc is the rated voltage, and H1 is the fundamental harmonic amplitude. The k order harmonic Hk can be expressed as: n

2 4V∗

Hk = cos (kαi ) π k i=1

with the following conditions on the unknown switching angles:

(6)

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0 < αk
0 of the orders of harmonic to be deleted h = h(1) , h(2) , · · · , h(n) , h(n+1) in the l-level converter output waveform with l = 2 · 2n + 1, the implementation algorithm is articulated in the following steps: 1. It solves the 2 linear system: # A 2. For p = 1, . . . , n − 1, # A

(n−p)

α2i−1 (n−p) α2i

(n)

α1 (n) α2

$

# =

π h(n) π h(n+1)

$ (22)

n > 1, the following 2p systems are solved: $

# =

π h(n−p) (n−p+1) 2αi

$

(1)

, i = 1, . . . , 2p

(23)

The unknown switching angles (7) are αi i = 1, , 2 · · · , s, and they are obtained solving (23) for p = n-1. The steps of the algorithm are given in the flow chart in Fig. 2.

Mathematical Procedure for Harmonic Elimination in CHB Multilevel Inverters. . . Fig. 2 Switching angle computation procedure

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Table 1 Switching angles of single phase CHB l-level inverters

5 0.2094 0.8378

αi [rad]

l 9 0.0150 0.4338 0.6134 1.0622

17 0.1278 0.1578 0.2910 0.4706 0.5766 0.7562 0.9194 1.2050

33 0.0070 0.0369 0.1702 0.2487 0.2786 0.3497 0.4119 0.4558 0.5914 0.6353 0.6975 0.7985 0.8770 1.0402 1.0841 1.3258

5 Computational Cost and Real-Time Implementation The computational complexity Ta of the algorithm described in Sect. 3 is: Ta = Tsys

n−1

2i = (s − 1) Tsys

(24)

i=0

where Tsys is the time cost of the solution of the 2 × 2 system (22) or (23), that is, Tsys = 2Tadd + 4Tmul , where Tadd and Tmul are the time cost of the addition and multiplication operations, respectively. This computational complexity allows real-time implementation through common microprocressors or DSPs.

6 Simulated Results for Three-Phase CHB l-Level Inverters with l = 5, 9, 17, 33 The proposed procedure has been applied to single-phase CHB l-level inverters for l = 5, 9, 17, 33 when V ∗ = 1 p.u.. The obtained switching angles are summarized in Table 1 for the different levels. The obtained harmonic analyses of output voltage are shown in Figs. 3, 4, 5, and 6.

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10 8

Hn/H1 %

6 4 2 0 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 Harmonics order

Fig. 3 Harmonic analysis for single-phase CHB 5-level inverter

8 7

5 4

n

1

H /H %

6

3 2 1 0 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 Harmonics order

Fig. 4 Harmonic analysis for single-phase 9-level inverter

For variations of m, the switching angles are constant, but V ∗ varies as shown in Fig. 7. The parameter C, computed by (8), assumes the values 1.2141, 1.2453, 1.2582, 1.2674 for l = 5, 9, 17, 33, respectively. The THD% is defined by the following formula * THD% =

49  k=3, 5 ...

H1

Hk2 100

(25)

2.5

1.5

n

H /H1 %

2

1 0.5 0 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 Harmonics order

Fig. 5 Harmonic analysis for single-phase CHB 17-level inverter

2

H /H % n 1

1.5

1

0.5

0 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 Harmonics order Fig. 6 Harmonic analysis for single-phase CHB 33-level inverter 1.6 5−level 1.4 1.2

9−level 17−level 33−level

V*

1 0.8 0.6 0.4 0.2 0.3

0.4

0.5

Fig. 7 DC voltage source values

0.6

m

0.7

0.8

0.9

1

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17

THD %

15

10

5

0

5 9

17

33

65 Level

129

Fig. 8 THD% as a function of levels number

32

Output Voltage THD%

30 28 Conventional SHE

26 24 22 20

Proposed method

18 16 14 0.4

0.45

0.5

0.55

0.6

0.65 m

0.7

0.75

0.8

0.85

0.9

Fig. 9 Comparison between THD% computed by the proposed procedure and by the conventional SHE

Figure 8 gives the behavior of the THD% as a function of the number of levels. It remains constant when m varies. Figure 9 shows a comparison between THD% computed by the proposed method and by the conventional SHE. A better performance of the proposed procedure is observed.

7 Conclusions In this paper, an efficient method to eliminate n + 1 harmonics and their respective multiple in single-phase CHB l-level inverters having s DC sources, l = 2s + 1 with s = 2n n = 1, 2, 3, . . ., has been presented. The obtained results have

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shown that a high number of harmonics have been deleted, depending on the level number. Lower THD values have been obtained compared with conventional SHE. The computational cost of the proposed algorithm has been computed showing that a real-time implementation is allowed.

References 1. L. Mathe, P. Dan Burlacu, R. Teodorescu, Control of a modular multilevel converter with reduced internal data exchange. IEEE Trans Ind Inf 13(1), 248–257 (2017) 2. M.R. Islam, A.M. Mahfuz-Ur-Rahman, M. Mazharul Islam, Y.G. Guo, J.G. Zhu, Modular medium-voltage grid-connected converter with improved switching techniques for solar photovoltaic systems. IEEE Trans. Ind. Electron. 64(11), 8887–8896 (2017) 3. A. Taghvaie, J. Adabi, M. Rezanejad, A multilevel inverter structure based on a combination of switched-capacitors and DC sources. IEEE Trans. Ind. Inf. 13(5), 2162–2171 (2017) 4. J. Zeng, J. Wu, J. Liu, H. Guo, A Quasi-Resonant Switched-capacitor multilevel inverter with self-voltage balancing for single-phase high-frequency AC microgrids. IEEE Trans. Ind. Inf. 13(5), 2669–2679 (2017) 5. M.S.A.G. Konstantinou, V.G. Agelidis, A review of multilevel selective harmonic elimination PWM: formulations, solving algorithms, implementation and applications. IEEE Trans. Power Electron. 30(8), 4091–4106 (2015) 6. S.S. Lee, B. Chu, N.R.N. Idris, H.H. Goh, Y.E. Heng, Switched-battery boost-multilevel inverter with GA optimized SHEPWM for standalone application. IEEE Trans. Ind. Electron. 63(4), 2133–2142 (2016) 7. M. Balasubramonian, V. Rajamani, Design and real-time implementation of SHEPWM in single-phase inverter using generalized hopfield neural network. IEEE Trans. Ind. Electron. 61(11), 6327–6336 (2014) 8. L. He, C. Chen, Study of the phase shift plus PWM control strategy based on a resonant bridge modular switched-capacitor converter. IEEE Trans. Ind. Inf. 13(5), 2746–2755 (2017) 9. C. Buccella, C. Cecati, M.G. Cimoroni, K. Razi, Analytical method for pattern generation in five-level cascaded H-bridge inverter using selective harmonic elimination. IEEE Trans. Ind. Electron. 61(11), 5811–5819 (2014) 10. C. Buccella, C. Cecati, M.G. Cimoroni, G. Kulothungan, A. Edpuganti, A. Kumar Rathore, A selective harmonic elimination method for five-level converters for distributed generation. IEEE J. Emerg. Select. Topic Power Elec. 5(2), 775–783 (2017) 11. C. Buccella, M.G. Cimoroni, M. Tinari, C. Cecati, A new pulse active width modulation for multilevel converters. IEEE Trans. Power Electron. 34(8), 7221–7229 (2019) C. Buccella, M.G. Cimoroni, M. Tinari, C. Cecati, A new pulse active width modulation (PAWM) for multilevel converters. IEEE Trans. Power Electron, 2018, (Early Access) 12. W.M. Fei, Y.L. Zhang, X.B. Ruan, Solving the SHEPWM nonlinear equations for three-level voltage inverter based on computed initial values. IEEE Appl. Power Electron. Conf. 1084– 1088 (2007) 13. G.H. Aghdam, Optimised active harmonic elimination technique for three-level T-type inverters. IET Power Electron. 6(3), 425–433 (2013) 14. J.N. Chiasson, L.M. Tolbert, K.J. McKenzie, Z. Du, Elimination of harmonics in a multilevel converter using the theory of symmetric polynomials and resultants. IEEE Trans. Contr. Syst. Technol. 13(2), 216–223 (2005) 15. T.A. Lipo, D.G. Holmes, Pulse-Width Modulation for Power Converters Principles and Practice (IEEE Press, Piscataway, 2003) 16. H. Taghizadeh, M.T. Hagh, Harmonic elimination of cascade multilevel inverters with nonequal DC sources using particle swarm optimization. IEEE Trans. Ind. Electron. 57(11), 3678–3684 (2010)

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17. A. Kavousi, B. Vahidi, R. Salehi, M. Bakhshizadeh, N. Farokhnia, S.S. Fathi, Application of the bee algorithm for selective harmonic elimination strategy in multilevel inverters. IEEE Trans. Power Electron. 27(4), 1689–1696 (2012) 18. B. Ozpineci, L.M. Tolbert, J.N. Chiasson, Harmonic optimization of multilevel converters using genetic algorithms. IEEE Power Electron. Lett. 3(3), 92–95 (2005) 19. R. Salehi, N. Farokhnia, M. Abedi, S. Hamid Fathi, Elimination of low order harmonics in multilevel inverters using genetic algorithm. J. Power Electron. 11(2), 132–139 (2011) 20. F. Filho, H.Z. Maia, T.H.A. Mateus, B. Ozpineci, L.M. Tolbert, J.O.P. Pinto, Adaptive selective harmonic minimization based on ANNs for cascade multilevel inverters with varying DC sources. IEEE Trans. Ind. Electron. 60(5), 1955–1962 (2013) 21. C. Cecati, F. Ciancetta, P. Siano, A multilevel inverter for PV systems with fuzzy logic control. IEEE Trans. Ind. Electron. 57(12), 4115–4125 (2010) 22. M. Ahmed, A. Sheir, M. Orabi, Real-time solution and implementation of selective harmonic elimination of seven-level multilevel inverter. IEEE J. Emerg. Select. Topic Power Electron. 5(4), 1700–1709 (2017)

Air-Gap Reluctance Function for MEC Dynamic Models of Smooth Rotor Machines Juliana Fernandes Cardoso, Marylin Fassenet, Christian Chillet, Laurent Gerbaud, and Lamya Abdeljalil Belhaj

Abstract This paper presents a method which describes the air-gap reluctance for machines with smooth cylindrical rotors. The method links the air-gap reluctance model to the machine’s geometric parameters through use of the Fermi-Dirac integral as an analytical approximation of the magnetic flux waveform in the air gap. Mathematical and physical limitations of the approach are studied, and an adapted version for use in dynamic magnetic equivalent circuit (MEC) models is presented. For this study, the real rotor is replaced by an ideal smooth rotor to eliminate the spurious effects and focus the study on the air gap. The results are benchmarked against finite element (FE) simulation, showing maximum error of 1.1%. This represents an improvement of 5.6% compared to a discontinuous linear model.

1 Introduction The design of electromechanical devices and systems comprises several phases, during which multiple models of the same device have to be developed for different objectives. During the initial phase, models are required which permit fast testing with a broad range of parameters. However, in the latter stages of development, models have to be accurate and allow observation of specific phenomena. This context has favoured the evolution of distinct modelling methods such as electrical-equivalent lumped-parameter models, finite element analysis and magnetic equivalent circuits. Each one of these has been successfully employed in

J. F. Cardoso () · M. Fassenet · C. Chillet · L. Gerbaud Université Grenoble Alpes, CNRS, Grenoble INP (Institute of Engineering Université Grenoble Alpes), G2Elab, Grenoble, France e-mail: [email protected]; [email protected]; [email protected]; [email protected] L. Abdeljalil Belhaj PSA Carrières-sous-Poissy Technical Center, Carrières-sous-Poissy, France e-mail: [email protected] © Springer Nature Switzerland AG 2020 W. Zamboni, G. Petrone (eds.), ELECTRIMACS 2019, Lecture Notes in Electrical Engineering 697, https://doi.org/10.1007/978-3-030-56970-9_24

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electromechanical device analysis where application accuracy and calculation time are key factors in their selection. Since Cherry [1] demonstrated the duality between electric and magnetic circuits, the concept has been intensively explored to study devices such as transformers and electrical machines. Years later, Laithwaite [2] and Carpenter [3] formalised the use of this concept in order to describe the behaviour of electromechanical devices. The MEC method represents an interesting alternative to purely analytical or numerical modelling methods. It is a hybrid method, where a preliminary thorough study of the device electromagnetic behaviour accounts for a more sensible level of discretisation [4]. MEC allows the study of a device with satisfactory accuracy whilst maintaining computation time at moderate levels [5]. MEC has been used to study the behaviour of various electrical machines technologies such as classic induction machines [6], synchronous reluctance machines [7] and also permanent magnet synchronous machines [8]. Many studies consider static or even multi-static scenarios [9, 10] allowing the observation of saturation levels in different parts of the machine, for example. Nevertheless, in order to investigate other phenomena, torque ripple and AC losses, for instance, simulations under continuous motion are required. The main challenge in incorporating motion in these models is adequately describing flux linkage between the stator and the rotor, therein describing the air-gap reluctance behaviour. Solutions have been proposed to address this issue. A sliding line of tangent air-gap reluctances was used to model movement with success in [11, 12]. Furthermore, time-dependant linear reluctances have been used to address the problem [13]. In this paper, a new method describing the air-gap reluctance for machines with a smooth cylindrical iron rotor is introduced. Here this method is applied to the prediction of the air-gap magnetic flux waveform of an interior PMSM under continuous motion.

2 Proposed Method 2.1 Air-Gap Reluctance Behaviour The magnetic behaviour of the air gap is complex and influenced by many parameters and phenomena, for example, the size of stator teeth, the shape of the teeth ends and the length of the air gap. An air-gap reluctance network capable of adapting itself to changes in these parameters would be valuable for the purposes of sizing by an optimisation process. To achieve this, it is necessary to return to the original problem: the modelling of the magnetic flux waveform under a whole tooth. If we are able to represent this flux waveform at the rotor surface analytically, a network containing a superposition of reluctances, whose values depend on this analytical expression, would be simple to use. To achieve this, a FE simulation is performed using a rotor with infinite magnetic permeability material and a stator containing only one electrically excited tooth. The magnetic flux behaviour obtained

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Fig. 1 Air-gap magnetic flux distribution for a one excited tooth case FE simulation 2

(b)

0

(c)

0

(a)

Error (%)

M agnetic potential (mWb/m)

10

FE simulation Trapezoid model Error

–2 – 0.2

0

– 10 0.2

Rotor p osition (rad) Fig. 2 Air-gap magnetic potential waveform at the rotor surface for only one excited tooth case FE simulation, trapezoid model and deviation Table 1 Constructive parameters of modelled machine

Parameter G L Be Hb Rr Nt

Size 0.73 mm 84 mm 1.93 mm 1.03 mm 80.25 mm 48

is shown in Fig. 1, and the magnetic potential waveform at the rotor surface under this tooth is plotted in Fig. 2. The most common method used to model this waveform is the use of a trapezoid curve, also plotted in Fig. 2. This approach was evaluated for our machine start design (Fig. 12 and Table 1). The maximum error found for the trapezoid method is 6.7%. The curve seen in Fig. 2 can be divided into three distinct regions in order to better explain the phenomena behind it. The first region (a) corresponds to the increase of the magnetic flux lines passing through the air gap vertically under

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Fig. 3 Air-gap static reluctance modelling using one main path R1 (curved rectangle with radial flux direction) and two side blocks R2a and R2b (orthoradial direction of flux)

the tooth (constant induction zone = constant rise). At the ends of the tooth, the induction decreases so the curve begins to level off (region b). Finally, at the region (c), the maximum value of the magnetic potential is reached, which is related to the total flux passing from the stator tooth to the rotor. To quantify this maximum value, it is possible to create a static model of the total reluctance (RT ) of the air gap using three reluctance blocks in parallel, as shown in Fig. 3. In this paper, these reluctances are defined by: 

R1 =

ln

Rr+g Rr



 g Be 2 μ0 .L. 2.π Nt − Rr+g + Rr+g

R2a = R2b =

π 2 

μ0 .L.ln

g+H b g

(1)

.

where μ0 is the magnetic permeability of air, L is the length of the machine and Nt is the number of teeth. This paper proposes to use the Fermi-Dirac integral as a simple analytic expression to emulate the shape observed in Fig. 2. This idea was first proposed by Mariani [14] and will be formalised, applied and evaluated in this paper.

2.2 Fermi-Dirac Integral The general definition of the Fermi-Dirac integral is given by: ( Fd (θ ) =

A.θ0 1 .  .dθ ln 1 + eβ.θ0 1 + eβ.(θ−θ0 )

(2)

where A, θ 0 and β are the shaping parameters. After integration and taking into account that the expression equals zero when θ equals zero, the expression becomes:

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Fig. 4 Three identifiable regions of a Fermi-Dirac: linear (a), corner (b) and constant (c)

Fd (θ ) =

   A.θ0 1 + e−β.θ0  . β.θ + ln  . 1 + eβ.(θ−θ0 ) β.ln 1 + eβ.θ0

(3)

This expression is plotted in Fig. 4. We find again three distinct regions: a linear region (a), a constant one (c) and the corner area connecting these two (b) – bearing greater correspondence to the requirements of the application. An additional advantage is that (3) comprises only three shaping parameters: A, θ 0 and β. Despite this, in the original formulation, each region depends simultaneously on the three parameters. Therefore, the use of this expression is still too complex for applications in describing physical phenomena. This interdependence of parameters can be eliminated by simple mathematical manipulation: multiplying the expression (3) by β. In this formulation the asymptote value is equal to A. θ 0 . To further simplify the expression and its physical interpretation, the solution proposed by Mariani [14] is applied, whereby the first component of the expression remains constant and is equal to one: θ0 .β   = 1. ln 1 + eβ.θ0

(4)

   1 + e−β.θ0 1 . Fd = A. θ + .ln β 1 + eβ.(θ−θ0 )

(5)

The expression is then:

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In order to obtain the shape observed in Fig. 2, the final expression needs to be of odd parity. The final expression of the Fermi-Dirac integral taken into account in this paper is then: Fd∗ (θ )

  1 + eβ.(−θ−θ0 ) 1 . = Fd (θ ) − Fd (−θ ) − A ∗ θ = A. θ + .ln β 1 + eβ.(θ−θ0 ) 

(6)

To evaluate the fitness of the expression in representing the magnetic potential, seen in Fig. 2, FE simulations of the magnetic potential for two different stator configurations are compared to results obtained using ideal Fermi-Dirac curves. These are parameterised through a finite difference method. The results are plotted in Fig. 5. The maximum error is calculated to be 0.4% and 2% in (a) and (b), respectively. The accuracy of this method depends on the geometric parameters of the studied machine. Hence the limits of the method validity require further investigation.

2.3 Physical Interpretation After ensuring independence of the sizing parameters, the next step is to understand their influence in the overall behaviour. The function is plotted with different values of A, θ 0 and β in Fig. 6. It can be seen that parameter A sets the inclination of the linear region, the term A. θ 0 gives the asymptotic value, and the β corresponds to the sharpness of the corner region. Lower values of β correspond to a rounder corner (Fig. 6). For use in a magnetic machine model, this function must be linked to geometric parameters. The physical meaning of A, θ 0 and β must be found. As aforementioned, parameter A fixes the slope of region (a) in Fig. 2. This region corresponds to the main flux path in the air gap under the tooth. Slope A represents the rate of flux increase under a tooth: A=

μ0 .L.N I d  =  dθ ln Rr+g Rr

(7)

where μ0 is the magnetic permeability of air, L is the length of the machine, NI is the number of ampere-turns exciting the tooth, Rr is the radius of the rotor and g is the length of the air gap. The horizontal asymptotic value is determined by A. θ 0 in Fig. 2 where the asymptote corresponds to the maximum value of magnetic flux passing through the air gap: θ0 =

1 . 2.A.RT

(8)

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Fig. 5 Magnetic potential calculated by a FE simulation compared to results obtained using Fermi-Dirac for two tooth designs

RT is the total reluctance value of the air gap between one tooth and the rotor, obtained from the static reluctance model quoted in Sect. 2.1. As previously seen, β defines the corner sharpness of the Fermi-Dirac curve. In this context, this corresponds to the magnetic flux lines coming from the sidewall region of the tooth, passing through R2a and R2b and not through the main path.

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Fig. 6 Influence of β on the corner shape of the Fermi-Dirac expression

Fig. 7 Reference angles for permeance calculation

Empirically, the most suitable way found to describe the relationship between β and the sidewall reluctances is given by: β = A.R2a .

(9)

The final expression used to describe the evolution of the magnetic flux in the air-gap section under a given tooth is then:    1 + eβ.(−θ−θ0 ) 1 (W b). g (θ ) = A. θ + .ln β 1 + eβ.(θ−θ0 )

(10)

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For this expression to be independent to the magnetomotive force, A is redefined as α: α=

1 d μ0 .L  =  NI dθ ln Rr+g Rr

(H enry).

(11)

With (8), (9), (10) and (11), then:     Wb 1 + eβ.(−θ−θ0 ) 1 . p (θ ) = α. θ + .ln β A 1 + eβ.(θ−θ0 )

(12)

For a given portion of the rotor, between α 1 and α 2 (Fig. 7), the permeance to a given tooth is then: P (α1 , α2 ) = p (α2 ) − p (α1 ) (H ).

(13)

3 Limits of the Model 3.1 Mathematical Approximation The approximation made in (4) results in a physical limit to the developed model. Using the expressions presented in Sect. 2, it is possible to state in terms of the ratio R2a /R1 :  F

R2a R1

=

R2a 1 + 2.R 1  equals 1.  R2a 1+ 2.R 1 ln 1 + e

(14)

The behaviour of the expression F(R2a /R1 ) is plotted in Fig. 8 to investigate the deviation to the constant value 1. It is clearly visible that the function is incorrect for the low values of the ratio R2a /R1 . The deviation of F to unity is calculated. For an error less than 5%, R2a (side reluctance) has to be 2.3 times greater than R1 (air-gap main path reluctance). For a ratio equal to 4.0, the error is below 1.6%.

3.2 Physical Aspects Another limitation of the model arises from the definition of the total air-gap reluctance. The magnetic flux lines, which do not pass through the main flux path, were instead assumed to pass to the rotor on a curved trajectory starting from the

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F

1

1

0.9

0.8

0.7 0

2

4

6

Fig. 8 Plot of F(R2a /R1 ) Fig. 9 Magnetic flux lines when (a) g < BE and (b) g > BE

Be g

(b)

Be g

sidewall of the tooth. Under the condition the path is shorter than the gap between two teeth, Be, the flux line terminates at the rotor. This is a good approximation of the real behaviour found in the air gap with the exception of one extreme case – when the air gap is shorter than the gap between two adjacent teeth. In this case, the side reluctances R2a and R2b (Fig. 3) disappear, and the representation is no longer valid. For this method to achieve greater generalisation and applicability to a wider range of machine configurations, the definition of the side reluctances R2a and R2b needs to be more accurate and robust (Fig. 9).

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Fig. 10 Reference angles for Fermi-Dirac function application after a rotation of wt

4 How to Use This Function in MEC Dynamic Models The expression defined in (12) allows for the calculation of the magnetic permeance in the air gap in a static study. To perform a study of a MEC machine model under motion, the rotor position needs to be taken into account (Fig. 10). Then the permeance expression becomes: P (α1 , α2 , wt) = p (α2 + wt) − p (α1 + wt) (H ).

(15)

5 Application The proposed method is used to describe the air-gap reluctance blocks in an electric motor MEC model. The motor is an interior permanent magnet synchronous machine with 48 teeth (Fig. 12). The concerned constructive parameters are listed in Table 1. The computation of magnetic potential under a tooth is compared to results obtained from FE analysis yielding a maximum error of 1.1% (Fig. 11). The method is then applied to the case of a solid rotor. The motion is taken into account using the method proposed by Mariani [15] which allows for a major simplification. The overall air-gap behaviour only needs to be valid for the equivalent of a one-tooth rotation. The rest of the machine movement is then simulated by the current source displacement method. This description is made by discretising the rotor into zones and then linking each tooth to the zones with which they have an effective interaction during the one-tooth rotation time step. The magnetic flux flowing from the air gap to each rotor zone was calculated. The results obtained for zones Z1 and Z2 (Fig. 12) are plotted in Figs. 13 and Fig. 14. The magnetic flux waveforms are compared to results obtained from FE analysis

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0.061

A.θ0

–0.5 0.4

Error (%)

M agnetic potential (mWb/m)

0.8

–1

FE analysis Fdirac Error 0 0

θ0

0.109

–1.5 0.218

θ (rad) Fig. 11 Magnetic potential computation by Fermi-Dirac, FE analysis and deviation

Fig. 12 One-pole view of the modelled PMSM showing (a) rotor topology, (b) stator reluctance network and (c) air-gap reluctance model and rotor discretisation in zones

and to another Fermi-Dirac model built with a high β, to simulate a trapezoid air-gap model. The Fermi-Dirac built with the proposed method shows superior performance in both tests.

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FE analysis

MEC

=1

MEC

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= 2000

Magnetic flux (mWb)

0.135

0.11

0.08 0

10

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20

40

(°) Fig. 13 Magnetic flux curves for a solid rotor model (zone 1)

FE analysis

MEC

=1

MEC

= 2000

Magnetic flux (mWb)

0.100

0.078

0.056 0

10

30

20

(°) Fig. 14 Magnetic flux curves for a solid rotor model (zone 2)

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6 Conclusions The proposed method offers a more precise alternative to the description of airgap reluctances on electric machines MEC models incorporating motion. The magnetic potential calculations of the proposed model show only 1.1% of maximum deviation when compared to FE simulations, 5.6% less than with a discontinuous approximation. There is improvement in accuracy of magnetic flux computation. The parameters of the method can also be linked to the constructive parameters of the machine such that no external recalculation during an optimisation process is required. Acknowledgement The authors would like to thank Groupe PSA and Nidec PSA emotors for the support given to this research work.

References 1. E.C. Cherry, The duality between interlinked electric and magnetic circuits and the formation of transformer equivalent circuits. Proc. Phys. Soc. London, Sect. B 62, 101 (1949) 2. E.R. Laithwaite, Magnetic equivalent circuits for electrical machines. Proc Inst Electr Eng 114(11), 1805–1809 (1967) 3. C.J. Carpenter, Magnetic equivalent circuits. Proc Inst Electr Eng 115(10), 1503–1511 (1968) 4. V. Ostovic, A method for evaluation of transient and steady state performance in saturated squirrel cage induction machines. IEEE Trans. Energy Convers. EC-1(3), 190–197 (1986) 5. M. Amrhein, P.T. Krein, 3-D magnetic equivalent circuit framework for modeling electromechanical devices. IEEE Trans. Energy Convers. 24(2), 397–405 (2009) 6. S.D. Sudhoff, B.T. Kuhn, K.A. Corzine, B.T. Branecky, Magnetic equivalent circuit modeling of induction motors. IEEE Trans. Energy Convers. 22(2), 259–270 (2007) 7. T.J. Busch, J.D. Law, T.A. Lipo, Magnetic circuit modeling of the field regulated reluctance machine. Part II: Saturation modeling and results. IEEE Trans. Energy Convers. 11(1), 56–61 (1996) 8. C.B. Rasmussen, E. Ritchie, A magnetic equivalent circuit approach for predicting PM motor performance, in IAS ‘97. Conference Record of the 1997 IEEE Industry Applications Conference Thirty Second IAS Annual Meeting, New Orleans, vol. 1, (1997), pp. 10–17 9. Q. Yu, C. Laudensack, D. Gerling, An analytical network for switched reluctance machines with highly saturated regions, International Aegean Conference on Electrical Machines and Power Electronics and Electromotion, Joint Conference, Istanbul, 2011, pp. 250–254 (2011) 10. R. Benlamine, Y. Benmessaoud, F. Dubas, C. Espanet, Nonlinear adaptive magnetic equivalent circuit of a radial-flux interior permanent-magnet machine using air-gap sliding-line technic, in IEEE Vehicle Power and Propulsion Conference, Belfort, pp. 1–6 (2017) 11. R. Benlamine, Etude et réalisation d’une machine électrique à forte densité de couple et fort rapport de sur-couple pour des applications de la traction automobile, Thèse de l’Université de Franche-Comté, 7 juillet 2015 12. H. Dogan, L. Garbuio, H. Nguyen Xuan, B. Delinchant, A. Foggia, F. Wurtz, Multistatic reluctance network modeling for the design of permanent-magnet synchronous machines. IEEE Trans. Magn. 49(5), 2347–2350 (2013) 13. M.L. Bash, J.M. Williams, S.D. Pekarek, Incorporating motion in mesh-based magnetic equivalent circuits. IEEE Trans. Energy Convers. 25(2), 329–338 (2010)

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14. G. B. Mariani, Machine synchrone à reluctance: modèles équivalents à réseau de réluctances pour la simulation et l’optimisation. Energie électrique. Thèse de l’Université Grenoble Alpes, 29 mars 2016 15. G. B. Mariani, A. Besri, N. Voyer, C. Chillet, M. Fassenet, L. Garbuio, Modèle à base de réseau de réluctances pour machine synchrone : prise en compte du déplacement, SGE 2016, 7–9 June 2016 (2016)

System-on-a-Chip Including Generic Framework of Motion Controller Using Disturbance Observer Based Acceleration Controller Hiroki Kurumatani and Seiichiro Katsura

Abstract A system on a chip (SoC) for a motion controller using a fieldprogrammable gate array (FPGA) and ARM processors is developed, and a task-partitioning technique is presented. Motion control requires fast and real-time input and output and the FPGA is a good tool to manage them. However, flexible and complex command generations are difficult to implement. Here, the SoC FPGA is a good solution because it has processors beside the FPGA. In designing on this platform, a feedback controller achieving high robustness is on the FPGA, and a feedforward controller determining a motion is on the processor. Then, a disturbance observer (DOB), one of the 2-degree-of-freedom (DOF) controllers, and an acceleration controller are introduced to decouple these designs. The DOB is simple to design with a few parameters and then provides a general framework for motion control. Introduction of the SoC FPGA enables to attain both the high robustness and the flexible command generation.

1 Introduction The factory automation is the key-enabling infrastructure to enhance the human life [1]. Further automation is one of the challenging themes, and improvement of machine control techniques is required. For example, the machines are required to operate with intelligence and precision. The industry 4.0, giving importance on utilization of big data, is mainly to obtain the intelligence. Such an approach reduces human efforts in the factory once a framework of getting intelligence is introduced.

H. Kurumatani () · S. Katsura Keio University, Tokyo, Japan e-mail: [email protected]; [email protected] © Springer Nature Switzerland AG 2020 W. Zamboni, G. Petrone (eds.), ELECTRIMACS 2019, Lecture Notes in Electrical Engineering 697, https://doi.org/10.1007/978-3-030-56970-9_25

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On the other hands, the precision is supported by improved robust control theory and power electronics technology. This technology enables fast operation of predefined tasks with high precision, which is difficult to be attained by the human work. The combination of the intelligence and the precision eventually makes the machines substitute for expert engineers and increase production volume of quality products. In the control theory, the intelligence and the precision are attained by a feedforward controller and a feedback controller, respectively. A reference motion with the intelligence is input to the feedforward controller, and the machine tries to perform that motion. In performing the motion, the feedback controller works to suppress the error of the motion. Thus, complexity of the motion depends on the former controller, while dexterity of the motion is ensured by the latter controller. Here, since the dexterity requires to perform a precise motion within a wide bandwidth, acquiring that is very challenging. This is because the control system includes many noises such as sensor noise or discretization noise, and the wideband controller is easily affected by them. From a viewpoint of cascade control, the feedback controller should have a wider bandwidth than that of the feedforward controller. To widen the bandwidth, a field programmable gate array (FPGA)-based implementations of the motion controller [2–4] and the current controller [5–7] have been researched. In these researches, the bandwidths of the controller and signal processing units were considerably widen, and high-performance control was attained. However, due to the nature of the FPGA, complex calculations using trigonometric functions or delay buffers, which are frequently used in the control and the signal processing, take a lot of effort to implement, and hence the complex motion is difficult to be generated. These tasks are in an exclusive territory of readymade processors, which include rich ecosystems. The review [8] recommended to implement a sophisticated Kalman filter on the processor beside the FPGA. Thus, a system-on-a-chip (SoC) FPGA is a suitable platform for the motion control [9, 10]. Here, a problem is how to generate a generic framework for the motion control. Due to the nature of the systems, the processor should be in charge of having intelligence, while the FPGA should be responsible for attaining the precision. For the feedback controller, 2-degree-of-freedom (DOF) controller, which decouples tracking performance and disturbance-suppression performance, is a good tool for this architecture. By implementing this controller on the FPGA, the FPGA is able to be dedicated to disturbance suppression, without considering the feedforward controller. However, the general 2-DOF controller takes a lot of effort for implementation and tuning. Then, a disturbance observer (DOB) which is one of the 2-DOF controllers with simple structure is introduced [11]. This controller realizes acceleration control and has been showing sufficient results as the robust controller. Thus, this paper presents the generic framework for the motion controller on the SoC FPGA.

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2 Discretization Effects on Control Performance The controller is always implemented with discretization, and the amount of the noise depends on the control period. The paper explains a relation between the discretization noise and the discretization period using a generalized state-space representation: x˙ = Ax + Bu + v

(1)

y = Cx + w,

(2)

where the coefficients A, B, and C are the system matrix, input matrix, and the observation matrix and the variables x, y, u, v, and w are the state vector, the output vector, the process noise vector, and the observation noise vector, respectively. Introducing the feedforward controller K and the feedback controller F , the input is generated as: u = Kr − F y,

(3)

where r is the reference input vector. Discretized with a sampling period Td , this controller is represented as: x[k + 1] = Ad x[k] + B d Kr[k] − B d F y[k] + v[k]

(4)

= (Ad − B d F C d )x[k] + B d Kr[k] + z[k]

(5)

y[k] = C d x[k] + w[k],

(6)

where z is the noise that penetrates into the system and the subscript d denotes the coefficient matrices for the discretized representation, which are expressed as: z[k] = −B d F w[k] + v[k] ( Td eAd τ dτ B, C d = C. Ad = eAd Td , B d =

(7) (8)

0

Thus, the system is divided into the deterministic term and the stochastic term. A point to note is that the state vector and the output vector are affected by the strength of the process noise and the observation noise. The observation noise directly appears on the observed values and indirectly influences on the state values. For a linear system, a form of a noise distribution does not change when the noise passes the system and the process noise appears on the state values with scaling its strength. Because the noise which imposes on the input excites vibration of the machine, it should be reduced. An important axiom is that these strengths depend on the discretization period. Parseval’s theorem denotes the Fourier transformation is unitary and the power of a continuous signal and a sampled signal is conserved.

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In other words, the power of the discretized signal is immutable regardless of the discretization period. Here, let us consider a continuous signal whose power is Ps . Since the discretized signal can express the signal within the Nyquist frequency fN , the following equation: (

fN

Ps =

Φ(f ) df

(9)

0

is satisfied, where Φ is the power spectral density. Assuming the discretization noise is white noise, the power spectral density has a constant value Φc within whole bandwidth, and a relation between that constant value and the discretization period is expressed as: Φc = fN−1 Ps = 2Td Ps .

(10)

The power spectral density decreases 3 dB for each frequency when doubling the sampling frequency. Therefore, the noise level drops by using the fast processing system. With using this approach, the feedback gain which amplifies the observation noise can be set to a high value, and the robust controller is attained. This approach should be applied to reduce the effect of the stochastic term in (5). On the other hand, the deterministic term like the reference signal is allowed to be generated by the slow processor because it has little noise. This design concept is reflected in the task partitioning for the SoC.

3 Disturbance Observer-Based Acceleration Controller The DOB is a minimum-order observer to estimate a disturbance acting on the system. Implementing the DOB provides the robust controller while it is the simple structure. The DOB-based controller is shown in Fig. 1, where d, P , P n , and Q denote the disturbance, the plant, the nominal plant model, and the free parameter called Q filter. In practical use, the reference and the output are on the acceleration dimension. Then, this controller is called the acceleration controller. The output is expressed as: Fig. 1 DOB-based controller

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Fig. 2 Equivalent 2-DOF controller of the DOB

.−1   P P −1 y = (I − Q) + QP P −1 n n r − (I − Q)P d ≈r − (I − Q) P d,

(11) (12)

where I is the unit matrix. Due to the internal model control structure, the DOB provides robust stability and performance against fluctuation of the plant system. The disturbance suppression performance, a sensitivity function, and a complementary sensitivity function are determined by the free parameter. An equivalent block diagram of the DOB in the form of the 2-DOF controller is shown in Fig. 2. This controller is the 2-DOF controller on the acceleration dimension. Therefore, outer controllers such as a position controller, a force controller, or a hybrid controller are easily implemented [12]. This general versatility is one of the advantages to adopt the DOB. The other advantage is that implementation of this controller requires only the plant parameters and the free parameter. Owing to the general versatility and the robustness with the few design parameters, this controller is worth to be adopted for the generic framework of the motion controller.

4 Generic Framework of Motion Controller on the SoC 4.1 Block Design of FPGA SoC The DOB provides the framework of the 2-DOF controller with simple structure. Because this controller enables to design the feedforward controller and the feedback controller individually, these two blocks should be implemented on the appropriate systems; the former requires flexibility, while the latter gives importance to fast control. Moreover, the all simple feedback controllers aiming to attain the robustness or widen the bandwidth should be on the fast circuit. On the other hand, the processor should be used when the intelligence is required for the motion planning. Figure 3 shows the concept of the block design of the motion controller on the SoC. This system is composed of the processor with a chipset, including the Ethernet controller and the DDR SDRAM, and the FPGA with the input-output interfaces (I/F) to be required to construct the motion controller. In this design, the processor is devoted to execute the command generation and the signal processing, which require complex operations. Owing to embedded circuits on the processor, the processor is able to use a high-speed bulk memory and communicate with other devices. Such hard macros provide stable high-speed communication and provide

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Fig. 3 Block design of the FPGA SoC

the FPGA with rich design assets, whereas the FPGA includes the motion controller and the I/F controller to realize high-speed real-time processing. To operate the high-speed I/Fs with little jitter, the I/F controller should be on the FPGA. As discussed in Sect. 2, the input and output rates have a relationship with the noises penetrating into the control system, and these should be set high as possible when striving for the control performance. To take full advantage of the high-speed I/Fs, the motion controller also keeps the high input and output rates. Hence, the controller requiring a quick response like a feedback controller should be on the FPGA. By adopting this block design, a processor load is considerably reduced while ensuring the high robustness, and the processor cab devote resource only to the command generation. Furthermore, the command generation and the robust controller can operate with different sampling rates, and the processor can have a sufficient time to generate a complex command. As discussed in Sect. 2, the system has the deterministic term and the stochastic term, and the generation of the deterministic term does not require a high sampling rate. In many cases, since processor tasks which require the complex calculation take longer time than that of the robust controller, such a multirate control framework is effective for achieving both the versatility and the robustness.

4.2 Core of Generic Motion Controller For the motion controller on the FPGA, the paper proposes to design positionforce or angle-torque hybrid controller based on the acceleration controller. Figure 4 shows the hybrid controller, where s, K p , K d , C f , X, and F stand for the Laplace operator, the proportional gain matrix, the differential gain matrix, the force gain matrix, the position vector, and the force vector, respectively. The superscript cmd and res denote the command signal and the response signal. By dynamically setting

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Fig. 4 Hybrid controller on the FPGA

the position controller and the force controller, the controller can have any control stiffness κ [12], which is defined as: κ =−

∂F res = (QC f + (I − Q)P )−1 (s 2 I + K d s + K p ). ∂Xres

(13)

Namely, both the robust tracking controller and the compliant controller can be attained. For the position controller, P-D controller is used not to put zeros in the input-output transfer function. This is because the zeros sometimes cause the position response overshoot the command value. If zeros are required for improving the tracking performance, these can be achieved by putting zeros in a prefilter for shaping the command, namely, installing a filter: −1 2 H (s) = I + K −1 p K ds + K p s .

(14)

This filter should be applied only for differentiable commands, which are of class C 2 and whose initial values of their derivatives are zero. Owing to the lack of the design parameters, this hybrid controller is easily managed.

4.3 Realization of Real-Time System To design the real-time system, there are few problems on the FPGA, but the processor requires an additional layer to remove jitters. On the FPGA SoC, the communication between the processor and the FPGA is carried out via an advanced microcontroller bus architecture (AMBA) on the ARM processor. Although the data from the processor are downloaded to the FPGA asynchronously, these data are synchronized on the FPGA with the sampling period of the processor. Similarly, the data from the FPGA to the processor are also sampled at sampling period of the processor and are uploaded via the AMBA. Thus, the data passing the bus synchronizes with the sampler of the processor. The jitters on the input and output stages are removed with this treatment, and the real-time control is ensured on the whole system.

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5 Experiments 5.1 Hardware Setup The validity of the motion controller on the SoC FPGA is confirmed. With using a direct drive rotary motor, the angle control and the torque control were performed. Figure 5 shows (A) the SoC FPGA (ZYBO; Digilent) which has an XC7Z010-1CLG400C and a dual-core CortexTM -A9 processor, (B) the daughter board including a 16-bit D/A converter (AD5541A, Analog Devices) and a dualline receiver (26LS32AC; Texas Instruments), (C) the direct-drive motor with the arm (SGMCS-02BDC41; Yaskawa), and (D) the sponge which is used for an environment for the torque control. The direct-drive motor is driven by a designated driver (SGDV-2R1F; Yaskawa). Twenty-bit angle data of the motor is output from this driver by three pairs of differential pulses of ABZ phases. The SoC FPGA communicates with this driver with using the daughter board. Although there is no torque sensor, a reaction torque observer (RTOB) is implemented on the FPGA and used for estimation of external torque [13]. To show the validity of the SoC FPGA, a processor-based system was prepared for comparison. This system has a core processor (Intel CoreTM i7-870; Intel) and peripherals of the 16-bit D/A converter and the pulse counter using the peripheral component interconnect (PCI-3340 and PCI-6205; Interface). An operating system (Linux v.2.6.32.2) and a real-time application interface (RTAI 3.7) are installed on this system. On this platform, stable calling of the control program at every 100 μs

Fig. 5 Experimental setup

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was achieved. Because the processor should perform all the jobs such as the timing control, the calculation, and the communication, shortening the sampling time is difficult. Interface drivers for the D/A converter and the pulse counter are called from the control program, and operation frequencies synchronize with the sampling time of the control program. In these experiments, the control periods of them were set to 100 μs.

5.2 SoC FPGA Setup Controllers were implemented on the SoC FPGA based on the discussion in Sect. 4. The hybrid controller on the FPGA was implemented with the single-precision floating point number, while the command generator on the processor uses both the single-precision and the double-precision ones. Because the AMBA provides 32-bit bus, the communication between them uses single-precision one, while the internal variables on the processor uses double-precision one. A cycle time of the hybrid controller was 1 μs. The D/A converter and the pulse counter on the daughter board operated at 1 and 100 MHz. The processor was called at every 100 μs. Since the processor load is very low, the processor works stably at this operation speed.

5.3 Controller Setup On both platform, the model parameters of the DOB were set to the nominal ones, and the Q filters were designed with a second-order filter form expressed as: Q=

2 gdis 2 s 2 + 2gdis + gdis

,

(15)

where gdis is the cutoff frequency (rad) for the disturbance estimation and gdis = 400π for the SoC FPGA and gdis = 200π for the processor-based system. The acceleration control was established in the bandwidth of 200 and 100 Hz, respectively. These parameters were tuned as the motor does not start oscillating due to the system noise. On the SoC FPGA, the gain registers of the angle/torque controllers on the FPGA were connected to that of the processor, and they can be changed dynamically. In addition, RTOBs whose bandwidths were 100 Hz was implemented for the torque control on both the platform.

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5.4 Results The angle/torque control was performed in two cases. The first case is the position control when setting the gains as: ! ! Kp Kd Cf = 2500 100 0 (for both the platform) ⎧ 0.0 (0 ≤ t < 1.0) ⎨ Xcmd = 1 − cos(2π(t − 1.0)) (1 ≤ t < 3.0) , ⎩ 1 − cos(4π(t − 1.0)) (3 ≤ t)

(16) (17)

and the second one is the force control when gains are set as: ! ! Kp Kd Cf = 0 0 500 (for the FPGA SoC) ! ! Kp Kd Cf = 0 0 400 (for the processor) ⎧ ⎪ 0.0 (0.0 ≤ t < 0.5) ⎪ ⎪ ⎪ ⎪ 0.2 (0.5 ≤ t < 1.0) ⎨ F cmd = 0.2 + 0.1 sin(2π(t − 1.0)) (1.0 ≤ t < 2.0) . ⎪ ⎪ ⎪ 0.2 + 0.1 sin(4π(t − 2.0)) (2.0 ≤ t < 3.0) ⎪ ⎪ ⎩0.2 + 0.1 sin(6π(t − 3.0)) (3.0 ≤ t)

(18) (19)

(20)

Since the position command in the first case is smooth function of C 2 , the command shaping filter Hs was installed. Figures 6 and 7 are the angle response, the torque response, and tracking errors in ease case. In the first case, the motor angle tracked with little error and phase lag. Due to a friction force inherent in the motor, the tracking error becomes large as the operation speed increases. However, the high robustness was confirmed when using the SoC FPGA. Owing to the high-gain DOB, the SoC FPGA worked to suppress the angle error and showed the higher reduction of the error than the classical platform. Similarly, the motor torque tracked to the command well in the second case. Both the response shows the quick conversion against the step command, while the SoC FPGA shows the faster response. This difference comes from the magnitude of the force gains. Since the control stiffness gets small as the force gain increases, the motor became compliant to the environment, and the force response quickly converged. Also, the tracking to the sinusoidal waves were also performed well. In the low-frequency domain, there is little difference in the responses. Thus, the highgain force controller and the wideband observer result in these responses. A point to note is smallness of the noise in the control and the observation. Figure 8 shows the power spectra of the errors of the torque control. Despite the SoC FPGA having higher gain than the other one, the torque response of that controller has lower noise in the low-frequency domain. Considering that the bandwidths of RTOBs are the same, this result shows the smallness of the system noise within the control

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Fig. 6 Angle response in the case 1

bandwidth, owing to the fast controller on the FPGA. With the low-speed processor, the noise caused by the discretization makes the high-gain controller unstable. By implementing the fast 2-DOF controller on the FPGA, the low-noise robust control was achieved. In addition, the complex motion was able to be performed owing to the processor.

6 Conclusions This paper designed the FPGA SoC including the generic framework of the motion controller using the DOB-based acceleration controller. Owing to the appropriate task partitioning, both the motion versatility and the robustness were attained. Furthermore, the acceleration-based hybrid controller expands the application field of this SoC. Compared with the classical processor-based system, the task distribution on the FPGA SoC results in the reduction of the processor load and the sampling time of the controller. Furthermore, since the timer is on the FPGA, the strict real-time control is attained. Therefore, this controller can be used for

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Fig. 7 Torque response in the case 2

Fig. 8 Power spectra of the errors of the torque control

timing-critical application in industry. The FPGA SoC with the developed generic framework provides the high reliability, robustness, and flexibility in the design. Acknowledgments This work was partially supported by JSPS KAKENHI Grant Number 18H03784.

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References 1. Y. Fujimoto, T. Murakami, R. Oboe, Advanced motion control for next-generation industrial applications. IEEE Trans. Ind. Electron. 63(3), 1886–1888 (2016) 2. X. Shao, D. Sun, Development of a new robot controller architecture with fpga-based ic design for improved high-speed performance. IEEE Trans. Ind. Inf. 3(4), 312–321 (2007) 3. T.N. Shene, K. Sridharan, N. Sudha, Real-Time SURF-Based Video Stabilization System for an FPGA-Driven Mobile Robot. IEEE Trans. Ind. Electron. 63(8), 5012–5021 (2016) 4. H. Kurumatani, S. Katsura, Auxiliary circuit for velocity-acceleration estimation from position data using pipeline differentiating unit, in IEEE International Symposium on Industrial Electronics, pp. 797–802 (2018) 5. Y. Yokokura, K. Ohishi, FPGA-based broadband current control of a linear motor with Class-G power amplifiers. IEEE International Conference on Mechatronics, pp. 528–533 (2013) 6. T. Sutikno, N.R.N. Idris, A. Jidin, M.N. Cirstea, An Improved FPGA Implementation of Direct Torque Control for Induction Machines. IEEE Trans. Ind. Inf. 9(3), 1280–1290 (2013) ˇ 7. K. Jezernik, R. Horvat, M. Curkoviˇ c, Robust constant switching frequency-based fieldweakening algorithm for direct torque controlled reluctance synchronous motors. IEEE Trans. Ind. Inf. 12(4), 1272–1279 (2016) 8. F. Auger, M. Hilairet, J.M. Guerrero, E. Monmasson, T. Orlowska-Kowalska, S. Katsura, Industrial applications of the Kalman filter: a review. IEEE Trans. Ind. Electron. 60(12), 5458–5471 (2013) 9. L. Idkhajine, E. Monmasson, A. Maalouf, Fully FPGA-based sensorless control for synchronous AC drive using an extended Kalman filter. IEEE Trans. Ind. Electron. 59(10), 3908–3918 (2012) 10. J.J. Rodríguez-Andina, M.D. Valdés-Peña, M.J. Moure, Advanced features and industrial applications of FPGAs-A review. IEEE Trans. Ind. Inf. 11(4), 853–864 (2015) 11. K. Ohishi, K. Ohnishi, K. Miyachi, Torque–speed regulation of DC motor based on load torque estimation, in IEEJ International Power Electronics Conference, IPEC–TOKYO, vol. 2, pp. 1209–1216 (1983) 12. K. Ohnishi, M. Shibata, T. Murakami, Motion control for advanced mechatronics. IEEE/ASME Trans. Mechatron. 1(1), 532–537 (1996) 13. T. Murakami, F. Yu, K. Ohnishi, Torque sensorless control in multidegree-of-freedom manipulator. IEEE Trans. Ind. Electron. 40(2), 259–265 (1993)

Parseval’s Theorem Used for the Inductor Analysis in High-Frequency Boost Converters A. Gutiérrez, E. Marcault, C. Alonso, J.-P. Laur, and D. Trémouilles

Abstract Today, the tendency is to decrease the power converters size increasing the operation frequency. This requires the development of innovative methodologies for the selection and design of the associated inductors. This paper proposes a methodology for the inductor analyses and selection in power converters using Parseval’s theorem. The analysis provides a model to describe the relation between the inductor losses in the time domain and the frequency domain given the known parameters of the quality factor (Q) and the self-resonance frequency (SRF). The simulation results provide insights about the impact of the quality factor (Q) and the contribution of the inductor current harmonics to the total power losses. An experimental setup validates the proposed approach.

1 Introduction Traditional analysis of power converters requires design tools intended to deal with operation frequencies around hundreds of kilohertz. However, outstanding advances in GaN-HEMT devices enlarge the operation condition of power converters to the range of megahertz [1]. Therefore, this extended bandwidth encourages the development of innovative design methodologies to achieve a trade-off between high-frequency and high-power conditions [2]. To achieve this objective, the conventional design methodologies should integrate high-frequency design concepts. Indeed, development in power inductors searches to increase their operation frequency to be incorporated in high-frequency power converters [3, 4]. As a result, high-frequency parameters become more and more important for the selection of inductors in power converters. Usually, the most A. Gutiérrez () · E. Marcault () CEA-Tech Occitanie, Toulouse, France e-mail: [email protected]; [email protected] C. Alonso · J.-P. Laur · D. Trémouilles LAAS-CNRS, Toulouse, France e-mail: [email protected]; [email protected]; [email protected] © Springer Nature Switzerland AG 2020 W. Zamboni, G. Petrone (eds.), ELECTRIMACS 2019, Lecture Notes in Electrical Engineering 697, https://doi.org/10.1007/978-3-030-56970-9_26

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common parameters for high-frequency inductors are the self-resonance frequency (SRF) and the quality factor (Q). These parameters allow describing the inductor operation bandwidth and the associated power losses. The aforementioned parameters are few analyzed in the conventional design of power converters at level of kilohertz. However, the operation in the megahertz range encourages the development of novel methodologies to include highfrequency parameters in the design process. Indeed, the drastic advances in power semiconductors require better understand the power inductor behavior in the time domain and the frequency domain to improve the global conversion performance [5, 6]. In this context, we proposed an innovative approach using Parseval’s theorem as a means to associate the power losses in the time domain and the inductor behavior in the frequency domain. Simulation results provide insights about the impact of the quality factor (Q) and the self-resonance frequency (SRF) on the inductor current harmonics and the power losses. These results suggest a suitable trade-off between the quality factor (Q) and the power losses through feasible inductor manufacturing features. Furthermore, this paper proposes an inductor model integrating the Q and SRF parameters into a circuital converter model. Finally, experimental tests validate the proposed approach.

2 Boost Converter in High Frequency In order to develop the proposed analysis, a high-frequency boost converter is presented as an illustrative example. Figure 1 shows the designed boost converter. The switching frequency is set to 30 MHz to take advantage of advances in GaNHEMTs. This boost converter increases the voltage from 200 V to 400 V with output power of 400 W. Furthermore, the studied converter focuses on the inductor

Fig. 1 High-frequency boost converter with actual inductor and ideal associated components

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Fig. 2 Frequency behavior of Rf and Qf for an available power inductor in the market

performance considering ideal the other components to avoid their influence in the developed analysis. Figure 2 depicts the associated inductor losses Rf and its quality factor Qf . In this figure, Rf and Qf are calculated using the inductor model provided by the manufacturer. The Rf and Qf parameters depend on the actual inductor impedanceZL = |ZL |  θ L . The associated losses Rf are defined as the real part of the inductor impedance by Rf = |ZL | cos θ L . The quality factor Qf expresses the relation between the stored and dissipated energy. In an inductor, the factor Qf is given by Qf = XL /Rf = tan θ L , where XL = |ZL | sin θ L . In Fig. 2, the studied inductor L is available in the market and accomplishes the requirements of inductance and current in the range of KHz; however, it has a low performance in the range of MHz. The proposed analysis intentionally begins with this unsuitable inductor to assess and understand the influence of the high-frequency parameters in the inductor performance. This analysis is the first step to define selection criteria for high-frequency power inductors with a suitable trade-off between performance and feasibility. Figure 3 shows the simulation results comparing the inductor current in the case of an ideal inductor in series with a low resistance, well-known model, and the manufacturer model for the studied inductor. In addition, Fig. 4 illustrates the current harmonics of the inductor under analysis. Results from Figs. 3 and 4 show that the unsuitable SRF causes distortion in the inductor current given the harmonics in the capacitive region beyond of the SRF. In addition, the low Q parameter causes important power losses in comparison with the ideal inductor in series with a low resistance. These power losses in the time domain are associated with the interactions between the inductor harmonics and the inductor behavior in high frequency. Next section will discuss these interactions using Parseval’s theorem, which describes the energy conservation in the frequency and time domains.

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Fig. 3 Inductor current. Blue – ideal inductor in series with a low resistance. Red – inductor under study

Fig. 4 Current harmonics for the studied inductor

3 Parseval’s Theorem Approach As described in the previous study case, the wrong selection of the power inductor leads to low signal quality and higher losses in high-frequency power converters. As a result, the following theoretical approach provides insights about the relation between power and frequency of inductors suitable for high-frequency power converters.

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Considering the approach described in [7] and defining the inductor current and voltage, the electrical energy in an inductor is given by (

∞

UL =

−∞

(1)

iv dt

The convolution of the term iv in the frequency domain is F {iv} = I (f ) ∗ V (f ) where I (f ), V (f ) are the complex valued Fourier transforms. F denotes Fourier  transform, ∗ denotes convolution, and denotes complex conjugate. By definitions of F and convolution, (

∞ −∞

iv e−j 2π σ dt =

(

∞ −∞

I (f )V (σ − f ) df

(2)

given that (2) is valid for σ = 0, (

(

∞ −∞

where (

(

∞ −∞

iv dt =

∞ −∞

iv dt =

∞ −∞

I (f )V (f ) df

! I (f ) I (f )Z(f ) df =

(

∞ −∞

(3)

  I (f )2 Z(f ) df

(4)

given that Z(f ) = Rf + jXL is the complex impedance of the inductor and XL is an odd function [7], (

∞ −∞

( iv dt =

∞ −∞

  ! I (f )2 Rf − j XL df =

(

∞ −∞

  I (f )2 Rf df

(5)

The result in Eq. (5) illustrates the energy conservation between the time and the frequency domains. Therefore, Eq. (5) can be seen as an extension of Parseval’s theorem (Eq. (6)) [7]: (

(

∞ −∞

|h(t)|2 dt =

∞ −∞

|H (2πf )|2 df

(6)

where Parseval’s identity (Eq. (7)) defines the relation for the Fourier coefficients as 1 T

(

T /2 −T /2

|h(t)|2 dt =

∞

|Cn |2

n=−∞

therefore, the average inductor power can be expressed from Eq. (5) by

(7)

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Fig. 5 Inductor power in the time domain

Pavg =

1 T

(

T 0

PL (t) dt =

N

In2 Rf

(8)

n=0

The interpretation of Eq. (8) is that the average inductor power in the time domain can also be calculated by summing the spectral power across the frequency. As a result, the average inductor power depends on the current harmonics In and the associated inductor losses Rf from the real part of the inductor impedance in the frequency domain. The right-side criterion of Eq. (8) is applied to the designed boost converter by means of the associated inductor losses Rf and the current harmonics (see Figs. 2 and 4). The results for the average power in the time and frequency domains are summarized in Figs. 5 and 6. In Fig. 5, the average power is calculated from several periods to decrease the numerical integration error. These results agree with the expected energy conservation criterion. Figure 6 depicts the distribution of power losses in the frequency domain. Results in Fig. 6 show that harmonics higher than eight times the switching frequency Fsw have a negligible impact on the power losses. In addition, this figure allows highlighting the contribution to the power losses of the current at the switching frequency. In this case, the higher losses are given at the switching frequency Fsw despite of the very high ratio between the DC current and the current at Fsw . The relative high value of Rf explains these power losses at the switching frequency Fsw . Therefore, it is fundamental to increase the Qf factor to decrease the Rf losses at the switching frequency Fsw in order to improve the global inductor efficiency. Figure 7 shows the relation of the power losses in the time domain against the quality factor at the switching frequency Qf (Fsw ) = XL (Fsw )/Rf (Fsw ). The plot is calculated from Eq. (8) by assuming that the highest contribution to the power losses comes from the fundamental frequency at the switching frequency. To plot

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Contribution of harmonics to inductor power

Power contribution (W)

3.000 2.500

Average power = 2.000

∑ ln2 Rf = 4.2W

1.500 1.000 0.500 0.000 0

30

60

90

120

150

180

210

240

270

300

Frequency (MHz)

Fig. 6 Inductor power in the frequency domain

Fig. 7 Inductor losses and quality factor Q at the switching frequency Fsw

this figure, the SRF is assumed to be eight times the switching frequency Fsw , and the Q factor is evaluated at 30 MHz for a fixed current spectrum. Results in Fig. 7 allow concluding that increasing considerably the Q factor has low impact in the power losses since the reduction in power losses becomes negligible. Therefore, it

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is necessary an approach to the suitable selection of the Q factor. In this context, the next section will propose a circuital model to include the SRF and Q parameters in the converter design process to assess their impact in the converter performance and to further inductor selection or manufacturing.

4 Proposed Inductor Model Including SRF and Q Currently, development of power electronics requires power inductors able to operate in high frequency. Therefore, the manufacturing specifications of SRF and Q should be useful to both power converter designers and inductor manufacturers. As a result, this section provides a framework to integrate these parameters in the design of converters. Figure 8 describes a circuital model for actual inductors usually used for the circuit simulation tools. This model includes an ideal inductor L, a series resistance Rs , a capacitance parasite Cp , and a parallel losses resistance Rp . The impedance at the switching frequency Fsw in the inductor model is given by the following expression, where ωsw = 2π Fsw : Z=

1 1 Rp

+

2 LC +j ω C R 1−ωsw p sw p s Rs +j ωsw L

(9)

considering the real and imaginary parts of Z and solving for Qsw at the switching frequency, we have Qsw

  3 C L2 −Rp ωsw Cp Rs2 − ωsw L + ωsw Im(Z) p = = 2 L2 + R R Re(Z) Rs2 + ωsw p s

Fig. 8 Boost converter with inductor model

(10)

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Fig. 9 Frequency behavior of Rf and Qf for the modeled inductor

solving for Rp , Rp =

  2 L2 Qsw Rs2 + ωsw 3 C L2 + ω L − ω C R 2 − Q R −ωsw p sw sw p s sw s

(11)

The parameter Rs in Eq. (11) is known as a resistance DC or copper resistance. Additionally, the SRF is defined by the inductor resonance frequency. Thus, the Cp capacitance is given by Cp =

1 (2π ) (SRF )2 L 2

(12)

Therefore, Eq. (11) and Eq. (12) allow including in the circuital inductor model the high-frequency parameters of self-resonance frequency (SRF) and the quality factor (Qsw ) at the switching frequency Fsw . Figure 9 shows the characterization of SRF and Q parameters using the proposed model. Figure 10 depicts the simulation results for the inductor current in the boost converter considering an inductor of 8.2 μH, Q(30 MHz) = 100 and SRF = 250 MHz. The frequency distribution of power losses is plotted in Fig. 11. This figure shows that the selected inductor drastically decreases the power losses at the switching frequency. The proposed analysis for power inductors has been described through this document. The simulated results have shown a suitable trade-off between power and frequency performance. The next section will introduce the experimental setup to validate the proposed approach.

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Fig. 10 Inductor current. Blue – ideal inductor with low series resistance. Red – power inductor considering Q(30 MHz) = 100 and SRF = 250 MHz Contribution of harmonics to inductor power 1.000 0.900 Power contribution (W)

0.800 0.700

Average power =

0.600

l

2 n

Rf = 0.74W

0.500 0.400 0.300 0.200 0.100 0.000 0.0

30.0

60.0

90.0

120.0

150.0

180.0

210.0

240.0

270.0

Frequency (MHz)

Fig. 11 Inductor power distribution in the frequency domain for Q(30 MHz) = 100 and SRF = 250 MHz

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5 Experimental Results This section describes the performed tests. First, the power inductors are measured and the circuital models are validated. Then, an experimental setup allows verifying the described power equivalence between the time and frequency domains. Finally, an experimental boost converter provides results about the performance of a conventional power inductor in a relative high frequency.

5.1 Inductor Modeling and Characterization This test employs an impedance analyzer Agilent 4294A to measure the parameters of several power inductors. The impedance analyzer sweeps the frequency from 40 Hz to 110 MHz and it measures Z-θ, R-X and L-Q. Table 1 summarizes the measured and calculated parameters. Rp and Cp are calculated from Eq. (11) to Eq. (12) selecting an arbitrary Q factor. Figure 12 depicts the simulated and measured Rf (the real part of the inductor impedance) for the inductor SRP5015TA. The MAPE (mean absolute percentage error) shows a partial agreement between the experimental data and the circuital model. However, Fig. 12 allows concluding that values for frequencies farther to the selected Q have less agreement than values around the selected Q. Therefore, the circuital model can slightly lose accuracy in a wide range of frequencies.

5.2 Inductor Power in the Time and Frequency Domains In this experimental setup, a waveform generator (33612A Keysight) provides a square signal of 5Vpp to the inductor under test. The current probe (Tektronix CT2) measures the inductor current, and the active probe (RT-ZS20 R&S) measures the voltage. The oscilloscope (RTO-1044 R&S) records the waveforms and calculates the average power in the time domain and the inductor current FFT (fast Fourier transform) in the frequency domain. The test is carried out at 10 MHz and 30 MHz.

Table 1 Characterization and modeling of inductors Inductor ref. SRP5015TA-8R2M SRR1210-8R2Y 7447713082 744314850

Measure L μH Rs m 7.8 190 7.3 4.1 7.7 29 8.2 24

Q at 10 MHz 25.5 15.4 13.2 7.7

SRF MHz 24.2 21.1 29.8 35.4

Calculation Rp K Cp pF 15.3 5.6 9.1 7.9 7.2 3.7 4.3 2.5

MAPE 0.28 0.27 0.28 0.15

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10000

RF (Š)

1000

100

10

1

0

1

10

100

FREQUENCY (MHZ)

Fig. 12 Rf for inductor SRP5015TA-8R2M. Blue, measure. Yellow, simulation

The aim of this test is to validate the power equivalence using the proposed approach. Figure 13 depicts the waveforms for square signals of case (a), 10 MHz, and case (b), 30 MHz. In the case (a), the fundamental frequency is lower than the SRF. Therefore, the inductor is able to store energy as a magnetic field with relative low power loss. In contrast, the case (b) has a fundamental frequency higher than the SRF. As a result, the inductor behaves as a capacitor distorting the current signal and increasing the power loss. Figure 14 shows the inductor current FFT for the case (a). In Table 2, the contribution of each harmonic is calculated from the FFT and the measured Rf . Results from Fig. 13a and Table 2 agree with the expected correlation between the power in the time and frequency domains. Table 3 summarizes the power results for the measured inductors. These results confirm the duality between the inductor power in the time and the frequency. Indeed, the proposed approach is intended to better understand the behavior of the inductor power. However, the dissimilarity with the experimental results is mainly caused by the shifting of the SRF given the parasitic capacitance and inductance of the current and voltage probes.

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Fig. 13 Test inductor SRP5015A. (a) Test frequency 10 MHz (scale/div: 1.6 V, 1.4 mA, 4 mW, 40 ns). (b) Test frequency 30 MHz (scale/div: 1.0 V, 1.4 mA, 5 mW, 10 ns). Blue, inductor voltage. Magenta, inductor current. Brown, inductor power

5.3 Boost Converter at 1 MHz This test implements a boost converter at 1 MHz. The design uses an inductor SRR1210-8R2 given its low series resistance and favorable Q factor. The boost converter specifications are Vin = 30 V, Vout = 60 V, and Pout = 40 W. The switching frequency is set to 1 MHz to ensure harmonics lower than the SRF. A GaN-HEMT is used as a switching device. The achieved results harmonize with the theoretical framework. However, the slight deviation between the temporal and frequency responses should be overcame by improving the experimental setup decreasing the parasitic elements (Fig. 15 and Table 4). Experimental results have shown the promising perspectives for the proposed analysis of inductors for the novel generation of power converters able to operate in high power and high frequency (Fig. 16).

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Fig. 14 FFT for the inductor current (SRP5015A). Test frequency 10 MHz (scale/div: 0.4 mA, 10 MHz) Table 2 Inductor power in the frequency domain Freq. (MHz) Ph (μW)

0 0.03

10 197

30 14

50 4.8

70 2.9

90 1.7

Total 220

6 Conclusions The reported methodology has associated the analysis in the time and frequency domains for inductors in power converters using an extension of Parseval’s theorem. This analysis methodology allowed determining suitable criteria for the selection and simulation of inductors according to expected power losses. The proposed model in this work included frequency parameters of inductors in the design process of power converters. The experimental results have validated the proposed approach. However, the experimental setup should decrease the parasitic inductances and capacitances to minimize the measurement disturbances at high frequency.

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Table 3 Inductor power in the time and frequency SRP5015TA-8R2M 10 MHz 30 MHz 239 848 220 760 7447713082 10 MHz 30 MHz 285 1380 262 1140

PWR-T (μW) PWR-F (μW)

PWR-T (μW) PWR-F (μW)

SRR1210-8R2Y 10 MHz 257 235 744314850 10 MHz 299 283

30 MHz 925 857 30 MHz 818 767

Fig. 15 Experimental results for 1 MHz boost converter using the power inductor SRR1210-8R2. High – brown, inductor voltage; magenta, inductor current. Low – brown, inductor power Table 4 Inductor power in the frequency domain Freq. (MHz) Ph (mW)

0 14

1 418

2 0.4

3 11

4 0.05

5 2.7

Total 447

Acknowledgments This work has been partially funded by the Region Occitanie PyrénéesMéditerranée.

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Fig. 16 FFT for the inductor current of the boost converter (scale/div: 80 mA, 0.6 MHz)

References 1. A. Hariya, K. Matsuura, H. Yanagi, S. Tomioka, Y. Ishizuka, T. Ninomiya, Five-megahertz pwmcontrolled current-mode resonant dc-dc step-down converter using GaN-hemts. IEEE Trans. Ind. Appl. 51(4), 3263–3272 (2015) 2. M. Rodriguez, Y. Zhang, D. Maksimovic, High-frequency pwm buck converters using GaN-onSiC hemts. IEEE Trans. Power Electron. 29(5), 2462–2473 (2014) 3. A. Hilal, B. Cougo, Optimal inductor design and material selection for high power density inverters used in aircraft applications, in ESARS-ITEC 2016, (IEEE, Toulouse, 2016) 4. W. Liang, L. Raymond, J. Rivas, 3-D-printed air-core inductors for high-frequency power converters. IEEE Trans. Power Electron. 31(1), 52–64 (2016) 5. E.L. Barrios, A. Urtasun, A. Ursúa, L. Marroyo, P. Sanchis, Optimal DC gapped inductor design including high-frequency effects, in IECON 2015, (IEEE, Yokohama, 2015) 6. R. Barrera-Cardenas, T. Isobe, M. Molinas, Optimal design of air-core inductor for medium/high power DC–DC converters, in 17th IEEE Workshop on Control and Modeling for Power Electronics (COMPEL), (IEEE, Trondheim, 2016) 7. S.S. Kelkar, L.L. Grigsby, J. Langsner, An extension of Parseval’s theorem and its use in calculating transient energy in the frequency domain. IEEE Trans. Ind. Electron. IE-30(1), 42– 45 (1983)

Impedance Spectroscopy Characterization of a Graphene-Based Solar Cell with Improved Contacts Ilaria Matacena, Daniele Zocco, Pierluigi Guerriero, Nicola Lisi, Laura Lancellotti, Eugenia Bobeico, Paola Delli Veneri, and Santolo Daliento

Abstract In this paper graphene on silicon solar cells, adopting either gold contacts or graphite contacts, are characterized by means of the impedance spectroscopy analysis. Experiments are described in terms of equivalent circuit model, and lumped parameters allowing to reproduce experiments in the whole set of frequency and dc biases are given. From this analysis the C-V plot of the solar cell is extracted, and the barrier height of the graphene-silicon interface is derived.

1 Introduction Graphene-based solar cells have been proposed as low-cost photovoltaic devices [1]. In such devices, graphene is exploited to form a Schottky junction with silicon; therefore, graphene photovoltaic devices are expected to behave as metalsemiconductor (MS) solar cells, with graphene assuming the role of the metal layer. As in MS solar cells, interfaces between different materials, and microscopic phenomena taking place at such interfaces, define the overall macroscopic performance of the device. The understanding of those phenomena is of paramount importance for the effective design of the solar cell, so that a great number of characterization techniques have been proposed so far [2–8]. The most part of them rely on the occurrence of some form of charge storing, giving rise to capacitive effects.

I. Matacena () · D. Zocco · P. Guerriero () · S. Daliento Department of Electrical Engineering and Information Technology, University Federico II, Naples, Italy e-mail: [email protected]; [email protected]; [email protected]; [email protected] N. Lisi Department of Materials and New Technologies, ENEA Casaccia Research Centre, Rome, Italy e-mail: [email protected] L. Lancellotti · E. Bobeico · P. D. Veneri ENEA, Portici Research Center, Portici, Naples, Italy e-mail: [email protected]; [email protected]; [email protected] © Springer Nature Switzerland AG 2020 W. Zamboni, G. Petrone (eds.), ELECTRIMACS 2019, Lecture Notes in Electrical Engineering 697, https://doi.org/10.1007/978-3-030-56970-9_27

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Therefore, the measure of the capacitance has become the preferred electrical approach for interface characterization. Usually, specific information can be gained by exploiting the dependence of the capacitance on some measurement parameter, like the dc bias (C-V plots) or the frequency (C-f plots) [9] of the test signal. Unfortunately, the interpretation of such plots could be not straightforward and, sometimes, misleading. In fact, the overall capacitance measured at the terminals of a device is an integral information given by the sum of several concomitant phenomena, each of which governed by specific parameters. The problem is further complicated by the fact that, often, single devices embed several interfaces, all contributing to the measurable capacitance. Furthermore, all reactive phenomena that may occur in the measurement circuit (inductive phenomena, for instance) are always interpreted in terms of capacitance [10]. The consequence is that parameters extraction techniques, relying on the knowledge of the capacitance of a specific interface, could give unreliable results when applied to the overall measured signal measured by a C-V meter. Better understanding can be gained by thinking in terms of impedance [11–13] and its representation in the form of the Nyquist plots, which report the real part of the measured impedance (on the x-axis) and the imaginary part of the measured impedance (on the y-axis) as a function of both frequency and dc bias, taken as parameters. These plots can give immediate insight when interpreted in terms of equivalent circuit. At the first order, indeed, an interface can be viewed as a parallel RC (resistance capacitance) circuit, giving rise, in the Nyquist representation, to a semicircular locus of points. The more the Nyquist plot is far from the semicircular shape, the more the impedance cannot be attributable to a unique interface. In this paper a graphene-based solar cell, adopting a newly developed contact technology, is analysed by means of impedance spectroscopy and equivalent circuit representation. The new contact was made by depositing colloidal graphite onto the graphene instead of gold. The performance of this new contact technology has been compared with the standard gold-graphene contact. Equivalent circuit representation allowed distinguishing, in the overall impedance, the contribution of the graphene-silicon depletion capacitance and the contribution of either the gold-graphene contact (in one case) or the graphite-graphene contact (in the other case). The knowledge of the contribution of the sole depletion capacitance allowed the reliable extraction of both work function and barrier height of the graphene-silicon junction, while the contacts were characterized in terms of resistance. Results evidenced the superior performance of the new contact technology. The paper is organized as follows: in Sect. 2 a short overview about the fabrication of the graphene-based Schottky junctions is given; Section 3 gives details about the Nyquist representation and describes the measurements, along with their interpretation; conclusions are drawn in Sect. 4.

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2 Graphene Growth and Solar Cell Fabrication Few-layer graphene (FLG) films were grown by CVD of ethanol on Cu substrates at 1070 ◦ C [14, 15]. The CVD apparatus was a cold-wall chamber, made of a quartz tube equipped with an inductively coupled graphite susceptor heater. The heater was excited by a 3 kW (maximum power) radio frequency current source modulated by the signal of a thermocouple buried inside the graphite susceptor. This configuration presented various advantages over classic CVD system as the reduction of the contamination connected to the quartz tube ageing, fast heating and precise control on the process start/end time. After the growth, cyclododecane was used to support the films during the transfer process [16]: the Cu substrate was etched in ammonium persulphate, and then the films were rinsed in DI water before they were transferred onto different target substrate for the fabrication of the cells and for characterization purposes. After the film transfer, the substrates were heated for 60 min at 60 ◦ C to help cyclododecane sublimation and then at 90 ◦ C for 20 min for final drying. Polished Si substrates ([100]-oriented, n-doped, 1  cm), with thermally grown SiO2 layer (300 nm), were patterned to expose an active area of 0.76 cm2 . The back contact was realized by evaporating Al on the back side of the n-Si. Before the transfer of the graphene-based films, HF was used to remove native Si oxide from the active area of the cell. The graphene-based films were transferred onto the cells by scooping the floating films kept in DI water after the rinsing process. Two kinds of top contacts were realized. The first was made by standard gold deposition; the second was obtained through a colloidal graphitic glue, spread over the graphene outside the active area.

3 Nyquist Plots and Circuit Representation As widely known, Nyquist plots allow the representation of the impedance as a function of the frequency, by taking the dc bias as parameter. Figure 1a shows the complete set of measurement achieved by using a Solartron 1260 impedance analyser for the solar cell with gold contacts. For better clarity Fig. 1b only shows the measurement at dc bias 0.1 V. As can be seen, the real part and the imaginary part of the impedance are reported on the x-axis and y-axis, respectively, while each reported point corresponds to a specific frequency (the frequency was scanned with a logarithmic increment between 1 Hz and 65 kHz). What should be noted is the strongly distorted shape with respect to the semicircular shape expected for a simple MS junction, modelled by means of a parallel RC circuit. Such a distortion raised from the fact that the impedance measured at the device terminals was actually given by the superposition of several reactive behaviours, ascribable to the various interfaces forming the device.

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Fig. 1 (a) Nyquist plots for the sample with gold contacts. (b) Nyquist plot for the sample with gold contacts at V = 0.1 V

Fig. 2 Equivalent circuit model of the graphene solar cell multilayer structure

CJ

C1

C2

RJ

R1

R2

RS

In order to quantify each contribution, the overall impedance was represented by the circuit shown in Fig. 2. An automated procedure (not described in detail in this paper) was settled up to determine the minimum number of RCs needed to accurately reproduce experimental points, along with the values of the lumped parameters. In this regard, it is worth noting that some of the parameters, as the depletion capacitance, depend on bias and some others do not; hence, the identification procedure must be repeated for each bias point. One of the byproduct of this repeated procedure is, for example,

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Fig. 3 Comparison between experimentally determined real parts of the impedance (for the sample with gold contact at V = 0.1 V) and those derived from the circuit model representation of Fig. 2

Fig. 4 Comparison between experimentally determined imaginary parts of the impedance (for the sample with gold contact at V = 0.1 V) and those derived from the circuit model representation of Fig. 2

the actual dependence of the depletion capacitance on bias, from which important parameters, characterizing the junction, can be derived (see Figs. 11 and 12). The procedure operates simultaneously on Re(Z) and Im(Z) with the constraint that the values of the parameters, giving the correct shape of Re(Z), would give the correct shape of Im(Z) too. Results achieved for the sample with gold contacts are shown in Figs. 3 and 4, where the x-axis reports, as sample number, each frequency point achieved in the range 1 Hz–65 kHz. As can be seen, the match between model and experiment is almost perfect for both Re(Z) and Im(Z). This fact means that four lumped values for the resistances and three lumped values for the capacitors shown in Fig. 2 have been determined. These values are suitable to reproduce the experimental behaviour of the impedance in the whole range of the frequency.

368

30 25 Capacitance [nF]

Fig. 5 Capacitance values for the circuit model of Fig. 2 adopted to describe the impedance behaviour of the solar cell with gold contacts for every dc bias

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Cj CAu CAl

20

15 10 5 -1

2.5

Re(Z) [Ω 10-4]

Fig. 6 Resistance values for the circuit model of Fig. 2 adopted to describe the impedance behaviour of the solar cell with gold contacts for every dc bias

-0.5

0

0.5

-0.5 0 dc bias [V]

0.5

dc bias [V]

Rj R Au R Al

2

1.5 1 0.5

0 -1

The complete Nyquist plot corresponding to the circuit model of Fig. 2 can be built by composing Re(Z) and Im(Z), thus achieving the purple curve reported in Fig. 1. Figures. 1, 3 and 4 refer to one bias point only (0.1 V). The procedure was repeated for the entire set of available experiments in the range − 1 V–0.5 V, always achieving a very reliable match. All the values extracted for the capacitances and the resistances, suited to describe the behaviour of the solar cell with gold contact by means of the circuit model of Fig. 2, are reported in Fig. 5 and Fig. 6, respectively. The dominant capacitance Cj in Fig. 5 can be ascribed to the graphene-silicon interface, while the other two contributions, CAu and CAl , raised from the goldgraphene interface and aluminium-silicon interface, respectively. In principle, these latter cannot be distinguished from each other; however, it seems reasonable that the highest values come from the gold-graphene contact; this assumption is enforced by the dependence of the associated resistances RAu and RAl . Indeed, from Fig. 6 their weight can be appreciated. In particular, it is worth noting that the falling down of

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Rj and RAu at positive biases depends on the fact that we are observing differential resistances that decrease when the junctions start to inject carriers. On the other side, RAl exhibits a slight increase; this is coherent with the expected reverse biasing of the silicon-aluminium interface formed at the back contact. From Fig. 6 it can be inferred that the gold-graphene contact is the worst in terms of resistance. The same analysis described above was repeated for the solar cell with graphite contacts. The corresponding Nyquist plots, taken in a wide range of bias voltages, are shown in Fig. 7. For better clarity, Nyquist plots obtained with negative dc biases are reported in the inset in Fig. 7. The figure shows that the curves were much less distorted than those shown in Fig. 1, thus suggesting that they could have been described by a reduced set of RC couples. This fact was confirmed by the parameters extraction procedure, which identified just one dominant capacitance and only a residual contribution of the aluminium electrode of about 100 Ohm. As examples of matches, evidencing the reliability of the extraction procedure, Figs. 8 and 9 report the comparison between experimental points and model results for the real part and the imaginary part of the impedance measured on the sample with graphite contact at 0.2 V. The whole Nyquist plot achieved by combining Re(Z) and Im(Z) is shown in Fig. 10. Such a good description of the experiments held in the whole range of dc biases. The fit of the complete set of measurements allowed the extraction of the junction capacitance at fixed frequencies. In other words, the C-V plots of the Schottky barrier were derived, as shown in Fig. 11.

Fig. 7 Nyquist plots for the solar cell with graphite contacts

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Fig. 8 Comparison between experimentally determined real parts of the impedance (for the sample with graphite contact at V = 0.2 V) and those derived from the circuit model representation of Fig. 2

Fig. 9 Comparison between experimentally determined imaginary parts of the impedance (for the sample with graphite contact at V = 0.2 V) and those derived from the circuit model representation of Fig. 2

As it is widely known, this kind of plot can be exploited to derive the built-in voltage of the junction, Vbi , according to (1): 1 2 = (Vbi − V ) . 2 C (qεs ND )

(1)

 NC kT ln q ND

(2)

and the barrier height as φB = Vbi +

From (1) it can be argued that it is convenient to represent the term 1/C2 as a function of the voltage, so that the intercept of the curve with the x-axis gives the value of Vbi . Figure 12 shows such a plot. From the knowledge of Vbi , it is possible

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Fig. 10 Nyquist plot for the sample with graphite contacts at V = 0.2 V

Fig. 11 C-V plots for the solar cell with graphite contacts

Capacitance [nF]

30

10 kHz 50 kHz 65 kHz

25

20 15 10

5 -1

-0.75

-0.5

-0.25

0

-0.25

dc bias [V] to calculate the barrier height, φ B , according to (2), knowing the substrate doping concentration, ND . The figure shows both experimental points and the straight line passing through them. From this plot it was derived a barrier height of 0.7 eV [17, 18].

4 Conclusions In this paper graphene-silicon solar cells have been characterized by means of the impedance spectroscopy analysis. Experimental Nyquist plots have been reproduced by means of a proper electric circuit model, whose parameters have given physical insight about the graphene-silicon interface and on the contacts property. In

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Fig. 12 1/C2 plot for the solar cell with graphite contacts

1/C2[F-2]

3.4

3.3 3.2 3.1

3 -0.2

-0.15 -0.1 Voltage [V]

particular, it has been found that the new graphite-graphene contact allows superior performance compared with the standard gold-graphene contact.

References 1. X. Li, H. Zhu, K. Wang, A. Cao, J. Wei, C. Li, Y. Jia, Z. Li, D. Wu, Graphene-on silicon Schottky junction solar cells. Adv. Mater. 22, 2743–2748 (2010) 2. G. Luongo, F. Giubileo, L. Genovese, L. Iemmo, N. Martucciello, A. Di Bartolomeo, I-V and C-V characterization of a high Responsivity graphene/silicon photodiode with embedded MOS capacitor. Nano 7(258) (2017) 3. S. Alialy, H. Tecimer, H. Uslu, S. Altindal, A comparative study on electrical characteristics of au/N-Si Schottky diodes, with and without bi-doped PVA interfacial layer in dark and under illumination at room temperature. Nanotechnol. Nanosci. 4(3) (2013) 4. S. Daliento, L. Lancellotti, 3D analysis of the performance degradation caused by series resistance in concentrator solar cells. Sol. Energy 8, 44–50 (2010) 5. V. d’Alessandro, P. Guerriero, S. Daliento, M. Gargiulo, Accurately extracting the shunt resistance of photovoltaic cells in installed module strings, in 3d International Conference on Clean Electrical Power, ICCEP 2011, (IEEE, Ischia, 2011), pp. 164–168 6. S. Daliento, A. Sanseverino, P. Sprito, An improved model for the extraction of strongly spatial dependent lifetimes with the ac lifetime profiling technique. IEEE Trans. Electron Devices 46(8), 1808–1810 (1999) 7. P. Spirito, S. Daliento, A. Sanseverino, L. Gialanella, M. Romano, R. Carta, Characterization of recombination centers in Si epilayers after he implantation by direct measurement of local lifetime distribution with the AC lifetime profiling technique. IEEE Electron Device Lett. 25(9), 602–604 (2004) 8. S. Bellone, G.D. Licciardo, S. Daliento, L. Mele, Experimental measurements of majority and minority carrier lifetime profile in Si epilayers by the use of an improved OCVD method. IEEE Electron Device Lett. 26, 501–503 (2005) 9. S. Daliento, O. Tari, L. Lancellotti, Closed form analytical expression for the conductive and dissipative parameters of the MOS-C equivalent circuit. IEEE Trans. Electron devices 58(10), 3643–3646 (2010) 10. M. Ershov, H.C. Liu, L. Li, M. Buchanan, Z.R. Wasilewski, A.K. Jonscher, Negative capacitance effect in semiconductor devices. IEEE Trans. Electron Devices 45(10), 2196–2206 (1998)

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11. J. Bisquert, L. Bertoluzzi, I. Mora-Serao, G. Garcia-Belmonte, Theory of impedance and capacitance spectroscopy of solar cells with dielectric relaxation, drift diffusion transport, and recombination. J. Phys. Chem. 118, 18983–18991 (2014) 12. P. Yadav, K. Pandey, V. Bhatt, M. Kumar, J. Kim, Critical aspects of impedance spectroscopy in silicon solar cell characterization: A review. Renew. Sust. Energ. Rev. 76, 1562–1578 (2017) 13. A.F. Brana, E. Fornies, N. Lopez, B.J. Garcia, High efficiency Si solar cells characterization using impedance spectroscopy analysis. J. Phys. 647 (2015) 14. A. Capasso, L. Salamandra, G. Faggio, T. Dikonimos, F. Buonocore, V. Morandi, L. Ortolani, N. Lisi, Chemical vapor deposited graphene-based derivative as high-performance hole transport material for organic photovoltaics. ACS Appl. Mater. Interfaces 8, 23844 (2016) 15. L. Lancellotti, E. Bobeico, A. Castaldo, P. DelliVeneri, E. Lago, N. Lisi, Effects of different graphene dopants on double antireflection coatings/graphene/n-silicon heterojunction solar cells. Thin Solid Films 646, 21 (2018) 16. L. Lancellotti, E. Bobeico, A. Castaldo, P. Delli Veneri, E. Lago, N. Lisi, Doping of multilayer graphene for silicon based solar cells, in 6th International Conference on Clean Electrical Power (ICCEP), (IEEE, Santa Margherita Ligure, 2017), pp. 509–512 17. L. Lancellotti, E. Bobeico, M. Della Noce, P. Delli Veneri, I. Matacena, Work function determination of transparent contact for a:Si/c-Si heterojunction solar cells, in IEEE 2018 International Conference on Environment and Electrical Engineering and IEEE Industrial and Commercial Power Systems Europe, EEEIC/I and CPS Europe, 8493739, (IEEE, Palermo, 2018), pp. 1–5 18. A. Gnisci, G. Faggio, L. Lancellotti, G. Messina, R. Carotenuto, E. Bobeico, P. Delli Veneri, A. Capasso, T. Dikonimos, N. Lisi, The role of graphene-based derivative as interfacial layer in graphene/n-Si Schottky barrier solar cells. Phys. Status Solidi (a) 216(3), 1800555 (2019)

Investigation of Electrical Properties of Graphene-Based Nanocomposites Supported by Tunnelling AFM (TUNA) Giovanni Spinelli, Patrizia Lamberti, Vincenzo Tucci, Liberata Guadagno, Marialuigia Raimondo, and Luigi Vertuccio

Abstract The present study concerns the electrical properties of epoxy-/aminebased composites filled with two types of exfoliated graphite nanoparticles, i.e. partially exfoliated graphite (pEG) and carboxylated partially exfoliated graphite (CpEG), that differ in the exfoliation degree (56% and 60%, respectively) and hence for the content of carboxylate groups. The morphological analysis reveals that both graphene-based nanoparticles are homogenously dispersed within the epoxy/amine matrix. The amount of the two fillers influences the overall electrical performance of the resulting nanocomposites. In particular, it is found that the incorporation of CpEG leads to a very low percolation threshold (EPT) in the range [0.025–0.1] wt% and a relatively high electrical conductivity (about 0.096 S/m at 1.8 wt% of loading). These results are due to the higher exfoliation degree and the presence of carboxylate groups on the edges of the nanoparticles, which are responsible for weak attractive intermolecular bonds that favour the formation of the conducting network through a sort of self-assembled structure. In order to confirm this interpretation, Tunnelling Atomic Force Microscopy (TUNA) analysis is performed. In particular, the topographic mapping of the local filler dispersion of the selected nanocomposites is carried out for supporting the DC electrical results.

1 Introduction Polymer composites reinforced with nano-dimensional fillers (less than 100 nm), better known as nanocomposites, have attracted great attention in material science due to the interesting properties resulting from the synergic interaction between the two phases, i.e. polymer matrix and filler. Among the most used matrices for G. Spinelli · P. Lamberti () · V. Tucci DIEM – University of Salerno, Fisciano, SA, Italy e-mail: [email protected]; [email protected]; [email protected] L. Guadagno · M. Raimondo · L. Vertuccio DIIN – University of Salerno, Fisciano, SA, Italy e-mail: [email protected]; [email protected]; [email protected] © Springer Nature Switzerland AG 2020 W. Zamboni, G. Petrone (eds.), ELECTRIMACS 2019, Lecture Notes in Electrical Engineering 697, https://doi.org/10.1007/978-3-030-56970-9_28

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these purposes, epoxy resins stand out for their remarkable mechanical, thermal and chemical properties, easy processability, good stiffness, dimensional stability, low costs [1, 2]. Different mono-dimensional carbon-based nanostructures such as carbon nanotubes (CNTs) and carbon nanofibres (CNFs) have been extensively embedded in polymeric resin for improving its properties and in particular the electrical conductivity, thus overcoming their limitation due to the intrinsic insulating behaviour [3, 4]. More recently, bi-dimensional fillers like graphite and its derivatives such as graphene compete for many aspects with the aforementioned fillers for the development of new nanocomposites [5]. High aspect ratio combined with the exceptional electrical conductivity of graphene sheets may favour the creation of the percolating network when dispersed within polymer matrices, thus leading to conductive composites with improved electrical properties compared to traditional carbon nanotube/fibre reinforced polymeric composites [6, 7]. In particular, such materials are widely applied in different fields, especially to control the electromagnetic compatibility, to reduce EM interference or in the design of radar absorbing material (RAM) [8–10]. A flexible shield providing a high reflection against incident EM fields with shielding effectiveness up to 27 dB was developed by means of a sandwich structure based on high filled graphene/polymer composite films [11]. Moreover, graphene-based nanocomposites are attracting increasing attention for a broad range of sensors, suitable for biomedical, optoelectronic and environmental applications, due to their remarkable physicochemical properties. The amazing possibility to covalently functionalize graphene layers may allow the fitting of the sensor to the particular features of each specific application [12]. Given its high carrier mobilities for both electrons and holes, tunable band gap and unique electronic structure, graphene layers are emerging as promising candidates for a new generation of high-speed electronic devices, thus paving the way for a new postsilicon era [13]. However, despite the achievements, still many critical issues remain to be solved. Pristine graphene has poor affinity with organic polymers and tend to agglomerate. Therefore, the compliance with the manufacturing constraints and the achievement of the desired performance is not a straightforward task due to the complicated interplay of different parameters. In fact, the overall properties of the resulting nanocomposite depend on the dispersion state of graphene layers inside the polymer matrix, as well as on their mutual interaction and the interfacial bonding. Therefore, in order to fully benefit the use of such a material, an accurate knowledge of their physical, mechanical and electrical properties is required. This knowledge can be obtained by a comprehensive analysis of electrical, electromagnetic (EM), mechanical and thermal properties. A detailed investigation on the properties of epoxy resin nanocomposites filled with carbon nano-additives characterized by high surface area was performed in [14]. The present study concerns an experimental characterization of epoxy/amine-based composites filled with two types of fillers, i.e. partially exfoliated graphite (pEG) and carboxylated partially exfoliated graphite (CpEG) differing in the exfoliation degree (56% and 60%, respectively) and the presence of the carboxylate groups content on the edges of the nanoparticles. This particular choice is aimed to understand the effect of the functionalization and exfoliation degree on the physical properties of the nanocomposites. In particular,

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it has already been found that this kind of functionalization is able to promote a better polymer filler interface, which in turn determines enhancements both in the electrical and dynamic mechanical properties [8]. In order to analyse the differences in the thermal stability and morphological features of the two graphene-based nanoparticles, a preliminary study through thermogravimetric and morphological investigation by Scanning Electron Microscopy (SEM) has been carried out. The DC electrical characterization has revealed that the percolation threshold (i.e. EPT) in CpEG-based nanocomposites is lower than that of pEG-based systems and comparable to that observed in CNT-filled polymer composites; furthermore, high values of electrical conductivity are achieved with low loading percentages of filler. Tunnelling AFM (TUNA), suitable to reveal ultra-low currents ranging from 80 fA to 120 pA, is employed as innovative tool for correlating the local and microscopic topography, in terms of interconnections and conductive pathways established between graphene sheets in the resin, with the results concerning the measured macroscopic electrical properties. The interesting electrical properties shown by the graphene-based nanocomposites open the way for the development of tailored structures able to meet the ever-increasing demanding requirements in the different industrial fields. The chapter is organized as follows: Section 2 is devoted to the description of the materials used for the experimental characterization, providing some details on samples fabrication, and to the techniques applied for the different characterizations; Section 3 summarizes the main results; Section 4 provides conclusions and future perspectives.

2 Materials and Methods 2.1 Materials and Sample Preparation Exfoliated graphite particles (i.e. EG) with high surface area and an average diameter of 500 μm were prepared through an exfoliation procedure based on intercalation of natural graphite in a solution of nitric and sulphuric acids, whereas the expansion of layer spacing was obtained via heat treatment in a high temperature reactor. By varying the exposure time in the fluidized bed during the heat treatment, it is possible to tune the degree of exfoliation which, in turn, determines a different percentage of carboxylated groups on the nanoparticle edges. From this procedure, two different types of filler, i.e. partially exfoliated graphite (pEG) and carboxylated partially exfoliated graphite (CpEG) characterized by an exfoliation degree of 56% and 60%, respectively, were prepared and then used as nanofillers for the manufacturing of graphene-based nanocomposites. Epoxy resin, acting as host matrix, was prepared by mixing a tetrafunctional precursor (tetraglycidymethylene dianile, TGMDA) with a reactive diluent (1,4-butanedioldiglycidylether, BDE), which allows to reduce the moisture content, thus favouring the dispersion step of nanofillers [15, 16]. In fact, the powders of exfoliated graphite were incorporated inside the epoxy mixture

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and then dispersed with high power ultrasonic probe (Hielsher model UP200S24 kHz) for 20 min. For the hardening of the nanocomposites, two-stage curing cycles are adopted: a first one at the lower temperature of 125 ◦ C for 1 h and the following at the higher temperature of 200 ◦ C for 3 h.

2.2 Apparatus and Methods Morphological analysis on the pEG and CpEG nanofillers was carried out with a field emission Scanning Electron Microscopy (SEM) apparatus (JSM-6700F, JEOL) instrument operating at 3 kV. Thermogravimetric analysis (TGA) was performed in air by using a Mettler TGA/SDTA 851 thermal analyser. The temperature range was 25–1000 ◦ C at a heating rate of 10 ◦ C min−1 . The weight loss was recorded as a function of the temperature. The DC electrical characterization was performed on disk-shaped specimens of about 2 mm of thickness and 50 mm of diameter which are properly coated with silver paint (RS 186–3600, with volume resistivity 0.001 •cm when fully hardened) in order to reduce the effects due to surface roughness and to ensure a good ohmic contact with the measuring electrodes. The DC measurement system was composed of a multimeter Keithley 6517A with function of power supply (max ± 1000 V) and voltmeter (max ± 200 V) and an ammeter HP34401A (min current 0.1 fA). The AC properties were determined on uncoated samples by using a Quadtec7600 dielectric analyser in the frequency range of 100 Hz–1 MHz, whereas an Agilent network analyser E4991A with the appropriate dielectric text fixture (Agilent 16453A) is employed for the impedance spectroscopy in the frequency range 1 MHz–1 GHz. The conductivity mapping at nanoscale level of the etched [17] slices of nanofilled epoxy samples was performed by TUNA. The overall setup consists of a conductive AFM probe, an external power supply required to provide a potential difference between the tip and the sample holder and a current to voltage converter (trans-impedance amplifier, TIA) that converts the (analogical) current signal into voltages in digital form more suitable to be processed by a PC. More in details, in our experiments, TUNA runs with a cantilever holder and an epoxy sample filled with conductive graphene-based nanoparticles, electrically connected to an external voltage source. Atomic force microscope (AFM) images were captured at ambient conditions (30%–40% humidity) with a Dimension 3100 coupled with a Bruker NanoScope V multimode AFM controller (Digital Instruments, Santa Barbara, CA) operating in tunnelling current mode (TUNAAFM), using microfabricated silicon tips/cantilevers. The TUNA measurements were carried out through platinum-coated probes with nominal spring constants of 35 N m−1 and electrically conductive tip of 20 nm. TUNA operates in contact mode. In feedback mode, the output signal is the DC bias, adjusted to maintain the electric current set point. The adopted values of the TUNA control parameters are summarized in Table 1. Several regions of the specimens were scanned in order to obtain repeatable results. The images were analysed using the Bruker software Nanoscope Analysis 1.80 (Build R1.126200).

Investigation of Electrical Properties of Graphene-Based Nanocomposites. . . Table 1 TUNA control parameters

Parameter DC sample bias Current sensitivity Current range Samples/linesa Scan rateb

379 Value 1 V–2 V 1 nA/V 200 nA 256 0.9–1.5 Hz s−1

a Number

of data points or pixels along the X and Y axis b Rate at which the cantilever scans across the sample

3 Results and Discussion 3.1 Morphological Analysis SEM investigation of the exfoliated graphite nanoparticles (pEG and CpEG) was performed to analyse the morphology and the dispersion of each nanofiller embedded in the epoxy mixture. The SEM image of Fig. 1 shows that EG particulate looks like regularly dispersed within the resin. In particular, SEM investigation of pEG sample reveals, in different zone (top right), structures like veils of silk on the flat surface of the pin stub, whereas SEM image of the CPEG sample shows a more fluffy morphology coherently with a higher percentage of exfoliated phase.

3.2 Thermogravimetric Analysis Figure 2 shows the TGA thermograms of pEG and CpEG samples (at heating rate of 10 ◦ C min−1 ) under air atmosphere. The pEG powder shows a beginning degradation temperature of about 650 ◦ C. A two-step thermal degradation process can be observed for CpEG filler. More in details, the first stage of thermal degradation occurs at 300 ◦ C and the second one at about 650 ◦ C. The first step of the degradation process is most likely due to the removal of oxygen-containing groups and carbon oxidation, respectively. Moreover, the TGA curves indicate an amount of carboxylated groups of about 10 wt% for the CpEG.

3.3 DC Electrical Properties Figure 3 shows the variation of the DC volume conductivity, measured at room temperature, as a function of the EG filler content (wt%) for the two types of filler examined in the present study, i.e. pEG and CpEG.

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Fig. 1 Scanning Electron Microscopy (SEM) images Fig. 2 Thermogravimetric analysis under air atmosphere

The experimental results reveal significant differences in the electrical properties of the two resulting nanocomposites, especially in terms of electrical percolation threshold (EPT), i.e. the minimum filler content after which the conductivity increases sharply (by several orders of magnitude). This effect is attributed to the formation of a conductive network through the intimate connection between the neighbouring filler particles. More in details, EPT falls within the range [2÷3]%wt

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Fig. 3 DC volume conductivity of the nanocomposites versus EG weight percentage: (a) pEG and (b) CpEG type

for the pEG-based nanocomposites, whereas for the CpEG it is comprised in the narrow interval [0.025÷0.1]% wt. This last is comparable with that achieved for nanocomposites reinforced with mono-dimensional fillers, such as carbon nanotubes (CNTs) or carbon nanofibres (CNFs) [17, 18]. This means that the CpEG filler creates more easily and with lower filler amount the percolation conductive pathways through the resin compared to the pEG filler. The percolation threshold is affected by several factors such as type, functionalization, aspect ratio, dispersion state of filler, as well as different manufacturing parameters, like sonication time or curing cycles [4]. In our case, the improved electrical network achieved by using CpEG filler may be due to a higher concentration of carboxylated groups observed at the edge of graphene sheets that affects the filler/resin compatibility, while exerting an attractive intermolecular bonding between the dispersed particles (see the schematic representation shown in the inset

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of Fig. 3b). As a result, the formation of the electrical networks is favoured through a sort of self-assembled structure [8]. Above the EPT, the electrical conductivity σ can be described by a scaling law of the form: σ = σ0 (p − pc)t

(1)

where σ 0 is the intrinsic conductivity of the filler, pc is the percolation threshold and t is a critical exponent depending on the dimensionality of the percolating structure. In particular, the DC conductivity reaches the value of about 0.096 S/m at the very low loading of 1.8 wt% for CpEG reinforced composite, whereas samples of epoxy resin filled with pEG, at the same concentration, are still below the EPT. For this last system, a higher filler concentration (around 4% wt) is required in order to achieve comparable electrical conductivity values. Moreover, the parameters of the percolation law can be estimated from the best fits shown in the insets of Fig. 3a and b reporting the log-log plots of the conductivity data. In particular, the value for the exponent t can be obtained as the slope of the linear fitting. The corresponding values, i.e. 1.2 for pEG reinforced composites and 1.1 for CpEG ones, respectively, are found to agree with literature values, reflecting an effective 2D organization of the percolating structure consistent with the two-dimensional type of filler used [19]. Moreover, it is worth to note as the value of the exponent t decreases with increasing exfoliation degree of graphite since the filler evolves towards an ideal two-dimensional shape. As in the case of composites reinforced with one-dimensional fillers, also for homogenous nanocomposite based on twodimensional particles, the macroscopic DC conductivity, above the percolation threshold, can be ascribed to quantum tunnelling (see schematic of Fig. 4a), since it is verified (Fig. 5b) by the expression: ln (σDC ) ∝ p−1/3

(2)

In fact, the detection of a linear relation between the DC conductivity (in logarithmic scale) and p−1/3 is a classic methodology adopted to confirm that the electron tunnelling is the principal electrical transport mechanism in such composite systems [20, 21]. For composites whose filler loading is beyond percolation, electron tunnelling conduction takes place, which can be described by an appropriate equivalent resistance network (see schematic of Fig. 4). The resistance takes into account the characteristic parameters of this quantum phenomenon: Rtun =

h2 d exp √ Ae2 2me λ



4π d √ 2me λ h



(3)

where h is the Plank’s constant, d is the distance between strictly close particles, e is the electron charge, me is the mass of electron, λ is the height of barrier typically of few eV for epoxy resin, A is the area involved in the tunnelling phenomenon [22].

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Fig. 4 (a): Schematic of tunnelling effect and associated electrical percolation network. (b): Plot of the log of DC conductivity for sample above the EPT against p−1/3 . The dashed line is a fit of the DC data (marker) to Eq. (2)

Fig. 5 Illustration of Tunnelling AFM (TUNA) setup [25]

3.4 Tunnelling Atomic Force Microscopy (TUNA) Analysis TUNA is a highly sensitive technique through which it is possible to perform electrical characterization at nanoscale level recording ultra-low currents (< 1 pA) with a noise level of 50 fA and topographical data by moving an appropriate tip across the sample surface [23–25]. A schematic representation of a TUNA setup is shown in Fig. 6.

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Fig. 6 TUNA currents recorder in pEG and CpEG samples in (a) and (b), respectively

Figure 6 shows the TUNA micrographs and the corresponding current profiles of the 5 wt% pEG and 1.8 wt% CpEG epoxy formulations in a) and b), respectively. These concentrations were selected from those available since far above the electrical percolation threshold. The TUNA images (2.0 μm × 2.0 μm for pEG and 1.3 μm × 1.3 μm for CpEG) were collected on etched samples to partially remove the resin surrounding the graphene particles and to better observe the distribution of the nanofiller inside the host matrix. The possibility to reveal low currents (order of

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fA and pA) is due to the effective conductive paths established within the matrix, as emerges by the strong colours contrast of the TUNA current micrograph. Moreover, the previous hypothesis raised about the improved electrical network, favoured by a sort of self-assembled structures due to a higher concentration of carboxylated groups, observed at the edge of CpEG graphene particles is supported by this TUNA investigation. In fact, it is evident that the interparticle distances for CpEG filler (Fig. 6b) is considerably lower than that established between pEG inclusion (Fig. 6a). Consequently, the tunnelling resistance is reduced and the electrical properties improved both in terms of electrical percolation network and electrical conductivity as evidenced by the DC characterization.

4 Conclusions In this study, morphological and electrical properties of epoxy-/amine-based composites filled with partially exfoliated graphite (pEG) and carboxylated partially exfoliated graphite (CpEG) have been discussed. In particular, the effects of the exfoliation degree (56% and 60%, respectively) and functionalization (carboxylate groups in CpEG) on the electrical properties of the resulting composites have been investigated. For CpEG-based formulations, it has been found that the self-assembly tendency of edge-carboxylated graphene particles due to attractive interaction leads to a reduction of the EPT. The values, in the interval [0.025–0.1] %wt, are comparable with those typically achieved when one-dimensional carbon-based fillers like CNTs or CNFs are employed. In the case of bi-dimensional filler such as EG homogenously dispersed in the resin, the macroscopic DC conductivity above the percolation threshold can be associated to the tunnelling effect. Moreover, the adopted TUNA-AFM technique has proven to be really a powerful tool for measuring electric transport through the graphene-based epoxy network, thus providing a map of the nanofiller dispersion at atomic scale level inside the polymeric matrix. This technique strongly supports the DC electrical results. Acknowledgments This work was supported from H2020-SGA-FET- Graphene FlagshipGraphene Core 2, G.A.: 785219. The research leading to these results received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 760940 – MASTRO.

References 1. A. Montazeri, J. Javadpour, A. Khavandi, A. Tcharkhtchi, A. Mohajeri, Mechanical properties of multi-walled carbon nanotube/epoxy composites. Mater Des31, 4202–4208 (2010) 2. Z. Han, A. Fina, Thermal conductivity of carbon nanotubes and their polymer nanocomposites: a review. Prog Polym Sci36, 914–994 (2011)

386

G. Spinelli et al.

3. W. Zhang, A.A. Dehghani-Sanij, R.S. Blackburn, Carbon based conductive polymer composites. J Mater Sci42, 3408–3418 (2007) 4. B. De Vivo, P. Lamberti, G. Spinelli, V. Tucci, L. Guadagno, M. Raimondo, The effect of filler aspect ratio on the electromagnetic properties of carbon-nanofibers reinforced composites. J Appl Phys118, 064302 (2015) 5. T. Kuilla, S. Bhadra, D. Yao, N.H. Kim, S. Bose, J.H. Lee, Recent advances in graphene based polymer composites. Prog Polym Sci35, 1350–1375 (2010) 6. C.E. Corcione, A. Maffezzoli, Transport properties of graphite/epoxy composites: Thermal, permeability and dielectric characterization. Polym Test32, 880–888 (2013) 7. Y. Wang, J.W. Shan, G.J. Weng, Percolation threshold and electrical conductivity of graphenebased nanocomposites with filler agglomeration and interfacial tunneling. J Appl Phys118, 065101 (2015) 8. L. Guadagno, M. Raimondo, L. Vertuccio, M. Mauro, G. Guerra, K. Lafdi, B. De Vivo, P. Lamberti, G. Spinelli, V. Tucci, Optimization of graphene-based materials outperforming host epoxy matrices. RSC Adv5, 36969–36978 (2015) 9. L. Guadagno, M. Raimondo, U. Vietri, L. Vertuccio, G. Barra, B. De Vivo, P. Lamberti, G. Spinelli, V. Tucci, R. Volponi, Effective formulation and processing of nanofilled carbon fiber reinforced composites. RSC Adv5, 6033–6042 (2015) 10. T.K. Das, S. Prusty, Graphene-based polymer composites and their applications. Polym-Plast Technol Eng52, 319–331 (2013) 11. W.L. Song, M.S. Cao, M.M. Lu, S. Bi, C.Y. Wang, J. Liu, J. Yuan, L.Z. Fan, Flexible graphene/polymer composite films in sandwich structures for effective electromagnetic interference shielding. Carbon66, 67–76 (2014) 12. K.Z. Milowska, J.A. Majewski, Graphene-based sensors: theoretical study. J Phys Chem C118, 17395–17401 (2014) 13. G. Fiori, F. Bonaccorso, G. Iannaccone, T. Palacios, D. Neumaier, A. Seabaugh, S.K. Banerjee, L. Colombo, Electronics based on two-dimensional materials. Nat Nanotechnol9, 768–779 (2014) 14. P. Kuzhir, A. Paddubskaya, A. Plyushch, N. Volynets, S. Maksimenko, J. Macutkevic, I. Kranauskaite, J. Banys, E. Ivanov, R. Kotsilkova, Epoxy composites filled with high surface area-carbon fillers: optimization of electromagnetic shielding, electrical, mechanical, and thermal properties. J Appl Phys114, 164304 (2013) 15. M.R. Nobile, M. Raimondo, K. Lafdi, A. Fierro, S. Rosolia, L. Guadagno, Relationships between nanofiller morphology and viscoelastic properties in CNF/epoxy resins. Polym Compos36, 1152–1160 (2015) 16. L. Guadagno, M. Raimondo, V. Vittoria, L. Vertuccio, L. Khalid, B. De Vivo, P. Lamberti, G. Spinelli, V. Tucci, The role of carbon nanofiber defects on the electrical and mechanical properties of CNF-based resins. Nanotechnology24, 305704–305710 (2013) 17. L. Guadagno, M. Raimondo, V. Vittoria, L. Vertuccio, L. Khalid, B. De Vivo, P. Lamberti, G. Spinelli, V. Tucci, The role of carbon nanofiber defects on the electrical and mechanical properties of CNF-based resins. Nanotechnology23, 305704–305710 (2013) 18. L. Guadagno, M. Raimondo, V. Vittoria, L. Vertuccio, C. Naddeo, S. Russo, B. De Vivo, P. Lamberti, G. Spinelli, V. Tucci, Development of epoxy mixtures for application in aeronautics and aerospace. RSC Adv4, 15474–15488 (2014) 19. C.W. Nan, Y. Shen, J. Ma, Physical properties of composites near percolation. Annu Rev Mater Res 40, 131–151 (2010) 20. A. Mdarhri, F. Carmona, C. Brosseau, P. Delhaes, Direct current electrical and microwave properties of polymer-multiwalled carbon nanotubes composites. J Appl Phys103, 054303 (2008) 21. M.T. Connor, S. Roy, T.A. Ezquerra, F.J.B. Calleja, Broadband ac conductivity of conductorpolymer composites. Phys Rev B57, 2286 (1998) 22. B. De Vivo, P. Lamberti, G. Spinelli, V. Tucci, A morphological and structural approach to evaluate the electromagnetic performances of composites based on random networks of carbon nanotubes. J Appl Phys115, 154311 (2014)

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23. R.L. Harniman, J.L. Fox Oliver, W. Janssen, S. Drijkoningen, K. Haenen, P.W. May, Direct observation of electron emission from grain boundaries in CVD diamond by PeakForcecontrolled tunnelling atomic force microscopy. Carbon94, 386–395 (2015) 24. M. Raimondo, L. Guadagno, V. Speranza, L. Bonnaud, P. Dubois, K. Lafdi, Multifunctional graphene/POSS epoxy resin tailored for aircraft lightning strike protection. Compos Part B140, 44–56 (2018) 25. M. Raimondo, L. Guadagno, L. Vertuccio, C. Naddeo, G. Barra, G. Spinelli, P. Lamberti, V. Tucci, K. Lafdi, Electrical conductivity of carbon nanofiber reinforced resins: Potentiality of Tunneling Atomic Force Microscopy (TUNA) technique. Compos Part B143, 148–160 (2018)

Weight-Function Identification for the Preisach Model of Laminated Steels Using Concentric Hysteresis Loops Reza Zeinali, Dave Krop, and Elena Lomonova

Abstract This paper proposes a new methodology to obtain the weight function of the Preisach model for non-oriented laminated steels using concentric hysteresis loops. In this methodology, first the experimental weight function is obtained from measured concentric hysteresis loops, and a mathematical technique is applied to remove the existing negative values. Based on the shape of the modified weight function, a new analytic function is proposed as a weight function for the Preisach model. The proposed analytic function is more advanced than the conventional probability functions proposed in literature, such that it is able to better mimic the actual shape of the weight function. The unknown parameters of the analytic weight function are identified by minimizing the error between the Preisach model and the modified measurements. Using the proposed analytic weight function, the minimum rms error is reduced to less than 0.5%, and a decent agreement is achieved between the model and the measurement.

1 Introduction Soft-magnetic materials are one of the essential components in electromechanical energy conversion devices. Providing a low-reluctant path for the magnetic flux and high torque/force density are the main benefits of using soft-magnetic steels. On the other hand, they introduce nonlinearities to the system because of magnetic hysteresis, eddy current, and saturation effects. These nonlinearities should be considered in designing electromechanical devices, especially for high-speed and high-precision applications. Therefore, an adequately accurate magnetic material model is required to take those nonlinearities into account in the electromagnetic field computation. This problem has been explored by researchers for decades;

R. Zeinali () · D. Krop · E. Lomonova TUE – Eindhoven University of Technology, Eindhoven, The Netherlands e-mail: [email protected]; [email protected]; [email protected] © Springer Nature Switzerland AG 2020 W. Zamboni, G. Petrone (eds.), ELECTRIMACS 2019, Lecture Notes in Electrical Engineering 697, https://doi.org/10.1007/978-3-030-56970-9_29

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however there is no comprehensive magnetic material model available to describe the magnetic hysteresis and loss mechanism in soft-magnetic steels, accurately. The Preisach model can be referred to as one of the frequently used hysteresis models [1–2]. This model can be interpreted as a superposition of a finite number of shifted hysteresis operators. Each hysteresis operator only takes values of 1 or −1 depending on current and past values of the input. Each operator is multiplied by a weight value. The weight function is determined by a specific set of hysteresis loops. Mathematically, the scalar Preisach model is expressed as (( f (t) =

μ (α, β) γαβ,u(t) dαdβ,

(1)

α≥β

where μ(α, β) and γαβ,u(t) are the weight function and the hysteresis operator, respectively. The double integral of the Preisach model can be explained by geometrical means. The mathematical description and numerical implementation of the Preisach model is thoroughly discussed in literature [2–4]; therefore it is not repeated here. The driving force behind the extensive research on the Preisach model is to find an approach for accurate identification of the weight function. The weight function is usually determined by means of experimental or analytic approaches. Owing to its simple hysteresis operator, the weight function can be determined directly using a specific set of measured hysteresis loops [5–7], i.e., the experimental approach. In this identification approach, the measurement noise is amplified because of the second-order derivative of the Everett map; therefore the obtained weight function becomes noticeably unsmooth and contains spikes. A smooth weight function is desired to improve convergence, as the Preisach model is often part of a larger electromagnetic model. Furthermore, when concentric hysteresis loops are used for weight-function determination, negative values appear in the obtained weight function. Another approach which is extensively used in literature is to approximate the weight function using probability functions such as the normal, Cauchy, and lognormal distributions [8–10]. In this method, called analytic approach, the unknown parameters of the analytic function are identified by minimizing the least square error between the model and the measured hysteresis loops. The major weakness of this approach is the fact that the distribution functions never mimic the exact shape of the actual weight function and are just an approximation of the real weight function. Because of this approximation, there is always an error between the model and the measurements. In this paper, the magnetic hysteresis effect is investigated using the static Preisach model. Eddy current and excess field effects are not evaluated. The eddy current effect can be taken into account by solving the one-dimensional penetration equation describing the diffusion phenomena [11, 12]. The main aim of this paper is to propose a new methodology for identifying an accurate analytic weight function for the scalar Preisach model. For this purpose, first the experimental

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weight function is obtained from a set of measured concentric loops, and a mathematical technique is used to modify the experimental weight function by eliminating existing negative values. Then, an analytic weight function is proposed to fit the modified experimental weight function. The unknown parameters of the proposed analytic weight function are identified through an optimization process by comparing the model results with the measurements.

2 Experimental Weight Function It is a unique feature of the Preisach model that a specific set of measured hysteresis loops can be used to obtain the weight function. Either first-order reversal hysteresis loops [1] or concentric hysteresis loops [5] are used to construct a two-dimensional function, the so-called Everett map, from which the weight function is obtained by a second-order differentiation expressed as μexp (α, β) = −

∂ 2 E (α, β) , ∂α ∂β

(2)

where μexp (α, β) and E(α, β) are the experimental weight function and the Everett map, respectively. Theoretically, it is expected to achieve the same weight function when the Everett map is constructed using either first-order reversal loops or concentric ones. In other words, first-order reversal loops should be reconstructible using the Preisach model with a weight function obtained from concentric loops and vice versa. In this study, the magnetic characteristics of non-oriented steel 27 (NO27) are studied. Due to the limitation of the available measurement setup, there is no possibility to measure the static first-order reversal loops. Therefore, the measured concentric loops are used to obtain the experimental weight function of the Preisach model. An extensive set of concentric hysteresis loops is measured with the peak field strength starting from 2 A/m with steps of 2 A/m. The maximum peak field strength of the measurements is restricted to 350 A/m, where the material is close to saturation. Restricting the peak field strength reduces the number of measurements required for obtaining experimental weight function. An Epstein frame is used to carry out the measurements on strip samples of the material, cut in the rolling direction. To reduce eddy current and excess field effects, the measurements are accomplished under a quasi-static condition at which the flux density is varied with a rate of 30 mT/s. The obtained weight function is shown in Fig. 1. For a better visualization, ranges on the horizontal axes are set not to exceed ±150 A/m in this figure. As seen in the figure, the experimental weight function is unsmooth and contains spikes, which happens due to the measurement noise amplified by the second-order differentiation. Additionally, the obtained weight function contains negative values. Basically, the weight function of the Preisach model for laminated steel is not supposed to have

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Fig. 1 The experimental weight function obtained from concentric hysteresis loops for NO_27 laminated steel

Fig. 2 A set of first order reversal loops obtained from the Preisach model with the weight function shown in Fig. 1

negative values; otherwise, nonphysical hysteresis loops, at which ascending and descending branches intersect, happen for specific sets of input field strength, H. To attain a better understanding about the problem of negative values in the Preisach weight function, Fig. 2 shows a set of first-order reversal loops modeled using the obtained experimental weight function shown in Fig. 1. As seen in Fig. 2, loops 1 and 2 look normal; however in loops 3 and 4, the descending branch intersects the ascending branch. This nonphysical modeling occurs due to existence of negative values in the experimental weight function. Therefore, it is realized that it is not possible to construct accurate and physical first-order reversal loops using the classical Preisach model with a raw weight function that has been obtained experimentally from a set of concentric loops.

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Fig. 3 The modified weight function for the Preisach model of NO27 laminated steel

The weight function of the Preisach model must be nonnegative to ensure that all loops are physical and ascending and descending branches do not intersect each other. In [13], a mathematical methodology is proposed to eliminate negative values of the weight function by slight modification of the measurement data. In this method, a correction matrix with unknown elements, ei , is added to the measured ˜ The modified weight function Everett map, E, to obtain the modified Everett map, E. ˜ is determined by substituting E in (2). The modified weight function is supposed to be nonnegative. By applying a nonnegative condition to the modified weight function, a set of linear inequalities is obtained in terms of ei ’s. Then an optimization algorithm is developed to minimize the summation of squared ei ’s, while the obtained linear inequalities are satisfied. Since in this optimization problem the objective function is quadratic and the constraints are linear, quadratic programing is used to find the optimum solution [14]. The obtained modified weight function is shown in Fig. 3. For a better visualization, ranges on the horizontal axes are set not to exceed ±150 A/m in this figure. As shown in the figure, the negative values are removed as a result of applying the explained mathematical procedure. Figure 4 compares a subset of measured loops with the modified loops obtained from the modified weight function. As seen in the figure, the applied adjustment does not really change the overall loop shapes, but only introduces slight adjustments to the measured data. The applied adjustments to the small loops are more significant than the applied adjustments to the bigger loops; in other words, the bigger the loop, the minor the modification is. Although the implemented mathematical method removes the negative values successfully with a minimum change to the measurements, the obtained modified weight function is still unsmooth which results in convergence problems when the model is used in a larger electromagnetic field-solving model. To amend this problem, an analytic weight function is proposed to fit the modified weight function.

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Fig. 4 Comparison of the measured and the modified hysteresis loops

3 Analytic Weight Function One of the main advantages of the Preisach model with an analytic weight function is that the first-order derivative of the constitutive relation is smooth and continuous. This is a crucial feature to assure convergence, when the Preisach model is coupled with an electromagnetic field-solving model. By a detailed evaluation of the modified weight function, one realizes that the proposed probability functions in literature are too generic to closely fit the modified weight function locally. In this paper, a new analytic function is proposed to better fit the modified weight function. This analytic function is formulated by observing the shape of the modified weight function. Due to the symmetry, only one quarter of the weight function is considered. The weight function is decomposed into two parts, i.e., the irreversible part and the reversible part. The proposed analytic function for the irreversible part is given by μirr (α, β) =

C1 + exp



k (α, β)    + exp f2 (α,β) σ2

f1 (α,β) σ1

(3)

where C1 , σ 1 , and σ 2 are constant parameters and f1 , f2 , and k are expressed as f1 (α, β) = (β"− (s1 − 1) (α + m1 ) − m2 ) −

(−β + (s1 + 1) (α + m2 ) + m2 )2 + r,

f2 (α, β) = − (β + s2 (α + n) − n) ,

(4)

(5)

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# k (α, β) = #

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+

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  k3 α−β+m 1+exp − σ 5 5

+

k2 1+exp

α−β+m4 σ4



× $

(6)

  k4 α−β+m 1+exp − σ 6 6

The reversible part of the weight function is given by μrev (α, β) = exp



α−β σ9



   × k5 sech α+β σ  7  . +k6 sech α+β σ8

(7)

To obtain the final weight function, the irreversible and reversible parts are added. The proposed analytic weight function contains 22 unknown parameters. To identify the unknown parameters, the least square error between the modified measured loops and the modeled loops is minimized using the MATLAB optimization toolbox. All measured concentric loops are used in the optimization procedure, to have an accurate parameter identification. The rms error between the optimum model and the measurement is less than 0.5% with respect to the peak flux density of the biggest loop. Figure 5 compares some of the modeled hysteresis loops with the modified measurements. A decent agreement is obtained between the model results and the measurements. The first-order reversal loops shown in Fig. 2 are reconstructed using the Preisach model with the proposed analytic weight function. The results are shown in Fig. 6. As seen in the figure, since the weight function is nonnegative, the first-order reversal loops do not intersect anymore.

Fig. 5 The results of the Preisach model with analytic weight function versus the modified measured loops

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Fig. 6 The obtained first order reversal loops using the Preisach model with the proposed analytic weight function

4 Conclusion The weight function of the Preisach model can be either obtained directly from a specific set of measured hysteresis loops or by using an analytic function. In this study both aforementioned approaches have been combined to obtain a weight function for improving the accuracy of the Preisach model for a wide range of hysteresis loops. To do this, the experimental weight function has been determined from the measured concentric hysteresis loops. Then, a mathematical technique has been implemented to remove the existing negative values and obtain the modified weight function. Finally, based on the modified weight function, an analytic function with 22 unknown parameters has been proposed to increase the smoothness of the weight function. The unknown parameters have been identified through an optimization procedure for the Preisach model of NO27 steel. The model result with the obtained weight function has shown a decent agreement with the measured concentric loops. The large number of parameters in the proposed weight function enables it to simultaneously improve the local and global shape of the weight function.

References 1. I. Mayergoyz, Mathematical models of hysteresis. IEEE Trans. Magn. 22(5), 603–608 (1986) 2. S. Hussain, D.A. Lowther, An efficient implementation of the classical Preisach model. IEEE Trans. Magn. 54(3) (2018) 3. T. Doong, I. Mayergoyz, On numerical implementation of hysteresis models. IEEE Trans. Magn. 21(5), 1853–1855 (1985)

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4. J. Zhang, D. Torres, N. Sep�lveda, X. Tan, A compressive sensing-based approach for Preisach hysteresis model identification. Smart Mater. Struct. 25(7) (2016) 5. Z. Szabó, I. Tugyi, G. Kádár, J. Füzi, Identification procedures for scalar Preisach model. Phys. B Condens. Matter 343(1–4), 142–147 (2004) 6. Z. Szabó, J. Füzi, Implementation and identification of Preisach type hysteresis models with Everett function in closed form. J. Magn. Magn. Mater. 406, 251–258 (2016) 7. S.E. Zirka, Y.I. Moroz, P. Marketos, A.J. Moses, Congruency-based hysteresis models for transient simulation. IEEE Trans. Magn. 40(2 I), 390–399 (2004) 8. J. Fuzi, Analytical approximation of Preisach distribution functions. IEEE Trans. Magn. 39(3), 1357–1360 (2003) 9. B. Azzerboni, E. Cardelli, E. Della Torre, G. Finocchio, Reversible magnetization and Lorentzian function approximation. J. Appl. Phys. 93(10 2), 6635–6637 (2003) 10. O. Henze, W.M. Rucker, Identification procedures of Preisach model. IEEE Trans. Magn. 38(2 I), 833–836 (2002) 11. M. Petrun, S. Steentjes, K. Hameyer, D. Dolinar, One-dimensional lamination models for calculating the magnetization dynamics in non-oriented soft magnetic steel. IEEE Trans. Magn. 52(3) (2016) 12. S.E. Zirka, Y.I. Moroz, P. Marketos, A.J. Moses, Viscosity-based magnetodynamic model of soft magnetic materials. IEEE Trans. Magn. 42(9), 2121–2132 (2006) 13. M. De Wulf, L. Vandevelde, J. Maes, L. Dupré, J. Melkebeek, Computation of the Preisach distribution function based on a measured Everett map. IEEE Trans. Magn. 36(5 I), 3141–3143 (2000) 14. W. Li, X. Tian, Numerical solution method for general interval quadratic programming. Appl. Math. Comput. 202(2), 589–595 (2008)

Enhanced Dead-Beat Predictive Control Using Power Harmonic Components for DFIG Wind System Under Asymmetrical Grid Voltage Sags M. Ghodbane-Cherif, S. Skander-Mustapha, I. Slama-Belkhodja, and A. Khan

Abstract This paper focuses on an enhanced dead-beat predictive control technique for a variable speed wind system based on a doubly-fed induction generator under asymmetrical grid voltage sags. By using the proposed control strategy, the mechanical stress on the generator can be reduced by decreasing electromagnetic torque ripples. The main idea of the proposed improved control technique is to introduce a new calculation of the rotor current references for the dead-beat predictive controllers. This calculation uses power harmonic components to extract current harmonic components from the conventional rotor current references. The obtained references are used, by the dead-beat predictive controllers, to forecast the optimum voltage vector. Fast dynamic responses are ensured by using the deadbeat predictive controllers. A doubly-fed induction generator model is presented in both positive and negative reference frames to allow harmonic analysis of the wind system under the unbalanced grid voltages. A theoretical analysis is used to develop the proposed control technique. Detailed simulation tests have been conducted using the PSIM software, and the results are presented to demonstrate the effectiveness of the proposed control technique and its ability to mitigate the unbalanced operation effects.

M. Ghodbane-Cherif () · I. Slama-Belkhodja Université de Tunis El Manar, Ecole Nationale d’Ingénieurs de Tunis, LR11ES15 Laboratoire des Systèmes Electriques, Tunis, Tunisie e-mail: [email protected]; [email protected] S. Skander-Mustapha Université de Tunis El Manar, Ecole Nationale d’Ingénieurs de Tunis, LR11ES15 Laboratoire de Systèmes Electriques, Tunis, Tunisie Université de Carthage, Ecole Nationale d’Architecture et d’Urbanisme, Sidi-Bousaid, Tunisia e-mail: [email protected] A. Khan Department of Electrical Engineering, University of Cape Town, Cape Town, South Africa e-mail: [email protected] © Springer Nature Switzerland AG 2020 W. Zamboni, G. Petrone (eds.), ELECTRIMACS 2019, Lecture Notes in Electrical Engineering 697, https://doi.org/10.1007/978-3-030-56970-9_30

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1 Introduction In recent times, the interest in renewable energy sources, especially wind energy, has soared, due to the increase in the electricity costs. Doubly-fed induction generators (DFIG) are used increasingly for wind systems (WS) due to the variable speed operation, the fractional converter rating and output filter cost-effectiveness. Indeed, several substantive issues, concerning mutual influence of wind systems and power grid, are still relevant. One of the biggest issues is the voltage sags influence on DFIG behaviour that is inconceivable for grid code requirements (GCR) and low voltage ride through (LVRT) [1, 2]. In fact, the challenge is to maintain the DFIG connection to the grid during voltage sags while maintaining system stability [3–5] and also to support the grid by supplying active and reactive powers during the sags [6, 7]. Several control techniques have been proposed in the literature to enhance wind systems operation under faulty operation [8–11]. Special attention has been paid to predictive control-based techniques due to their ability to predict the future behaviour of the controlled variables [12, 13]. Many authors criticise the variable switching frequency characteristic of the model predictive control (MPC) and propose improvements in [14, 15]. In [16, 17], authors present new fault-tolerant MPC techniques. Other papers present the predictive dead-beat control as a solution as it has a constant switching frequency in spite of its sensitivity to parameters variations [18–20]. This paper proposes an enhanced predictive dead-beat control strategy for a wind system based on a DFIG under grid disturbances, particularly asymmetrical voltage sags. This control strategy provides a new method to calculate rotor current references for the dead-beat controllers. The idea of this new method is to use power harmonic values to program rotor current harmonic components, which are deduced from the original references. This paper is structured as follows. In Sect. 2, the dynamic DFIG modelling in both positive and negative sequence d − q reference frames are provided. The proposed model includes the back EMF effect. Furthermore, harmonic analysis of the DFIG behaviour under both normal operation and unbalanced grid voltage sags is investigated. Section 3 describes the basic predictive dead-beat control and Sect. 4 deals with the enhanced control strategy. In Sect. 5, simulation outcomes are presented for a 2 MW machine to verify the effectiveness of the studied control. Section 6 concludes the paper.

2 System Modelling in Case of Unbalanced Network Fault The wind system configuration adopted is exposed on Fig. 1. The converters allow power flow between the machine and the electrical network. To ensure tolerable voltage fluctuation in the common DC link, a capacitor is coupled between the two converters. The stator powers are managed by means of the rotor-side converter (RsC) control. The grid-side converter (GsC) control insures regulation of DC

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VDC

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Pr,Qr

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Control

Fig. 1 DFIG wind system overview

voltage and controls the power transit. The GsC is connected to the grid through an inductor filter.

2.1 DFIG Modelling The DFIG is modelled in a special reference frame. Indeed, system variables are decomposed into positive and negative components using symmetrical components theory [21]. As shown in Fig. 2, the positive sequence reference frame axes turn at the stator angular frequency ωs , as the negative sequence frame axes turn at the opposite angular. In the remainder of the paper, subscripts dp, qp denote the positive reference frame and dn, qn denote the negative reference frame. Hence, the dynamic DFIG model is described by Eqs. (1, 2, 3 and 4): v s _dq _p = Rs i s _dq _p +

v r _dq _p = Rr i r _dq _p +

dϕ s _dq _p dt dϕ r _dq _p dt

+j

dθs _dq _p ϕ s _dq _p dt

(1)

+j

dθr _dq _p ϕ r _dq _p dt

(2)

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Fig. 2 Positive and negative frames

βs qp

qn

dp ωsp θsp αs θsn ωsn dn

v s _dq _n = Rs i s _dq _n +

v r _dq _n = Rr i r _dq _n +

dϕ s _dq _n dt dϕ r _dq _n dt

+j

dθs _dq _n ϕ s _dq _n dt

(3)

+j

dθr _dq _n ϕ r _dq _n dt

(4)

where Rs and Rr are the phase winding resistances; vs , vr and is , ir are stator and rotor voltages and currents, respectively; ϕs and ϕr are electromagnetic flux components; and θ s and θ r are the stator and rotor grid angles, respectively. Using this DFIG modelling approach leads to the fractionation of the voltages and currents into symmetrical positive and negative sequence networks. Furthermore, (5) and (6) provide active and reactive stator powers expressions. Ps = Ps _o + Ps _cos cos (2ωs t) + Ps _sin sin (2ωs t)

(5)

Qs = Qs _o + Qs _cos cos (2ωs t) + Qs_sin sin (2ωs t)

(6)

where ωs is the stator electrical angular frequency and Ps_o , Ps_cos , Ps_sin , Qs_o , Qs_cos and Qs_sin are given by (7): ⎞ ⎛ Ps _o ⎜Q ⎟ ⎜ ⎜ s _o ⎟ ⎜ ⎜ ⎟ ⎜ ⎜ Ps _cos ⎟ ⎜ ⎜ ⎟=⎜ ⎜ Ps _sin ⎟ ⎜ ⎜ ⎟ ⎜ ⎝ Qs _cos ⎠ ⎝ Qs _sin ⎛

vs _dp vs _qp vs _dn vs _qn vs _qn − vs _dn

vs _qp −vs _dp vs _qn −vs _dn −vs _dn −vs _qn

vs _dn vs _qn vs _dp −vsqp vsqp vsdp

⎞ vs _qn ⎛ ⎞ is _dp −vs _dn ⎟ ⎟ ⎟ ⎜ vs _qp ⎟ ⎜ is _qp ⎟ ⎟ ⎟. vs _dp ⎟ ⎝ is _dn ⎠ ⎟ −vs _dp ⎠ is _qn vs _qp

(7)

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Similarly, the electromagnetic torque given in positive and negative sequence rotating reference frames is given by (8): T em = Ps

p = T emo + T emcos cos (2ωs t) + T emsin sin (2ωs t) ωs

(8)

where p corresponds to the number of pole pairs. Temo presents the constant torque component. Temcos and Temsin are the oscillating terms at twice the grid frequency.

2.2 DFIG Normal and Faulty Behaviour Expressions (7) and (8) show that oscillating terms, at twice the grid frequency, appear in both stator power and electromagnetic torque of the DFIG. Negative sequences of stator voltages and currents are the major cause of the cited additional power oscillations. Under normal operation, stator voltages are balanced, and there are no negative sequences and thus no oscillating terms neither in powers nor in the electromagnetic torque of the DFIG. However, asymmetrical disruption leads to oscillating terms Ps _ cos , Ps _ sin , Qs _ cos and Qs _ sin in active and reactive powers. Consequently, additional ripples occur at twice the electrical network frequency in the electromagnetic torque. These oscillations can lead to acoustic noise and reduce the lifetime of the rotating parts by creating vibrations in the shaft of the DFIG. In addition, as the active power is delivered to the grid from the DC link, active power oscillations lead to DC-link voltage fluctuation. Thus, asymmetrical grid voltages can decrease the performance of DFIG-based WS, so protecting actions have to be taken to overcome these adverse effects.

3 Basic Control The proposed control structure of the grid-connected DFIG is illustrated in Fig. 3. Only the rotor-side converter RsC is taken into consideration in this work. As already mentioned, the RsC controls stator powers, and this paper focuses on minimising electromagnetic torque ripples caused by stator power oscillations. The theory of field-oriented control (FOC) has been used, and the d-q rotating frame is selected such that the stator flux vector is aligned with the positive sequence daxis, in order to decouple the active and reactive powers and control them via only rotor currents. The rotor current references are generated from the expressions of stator powers. Then, the rotor currents are regulated through closed-loop control using predictive dead-beat controllers. The reference voltage signals arising from the regulation of rotor currents are applied to the space vector modulation (SVM) module that generates the switching signals for the RsC.

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Fig. 3 Basic RsC control under normal operation

3.1 Rotor Current References Calculation The expressions of the stator and rotor fluxes in the chosen synchronous reference frame are given by (9), (10) and (11): ϕs _d = Ls is _d + Msr ir _d

(9)

ϕr _d = Lr ir _d + Msr is _d

(10)

ϕr _q = Lr ir _q + Msr is _q

(11)

where Ls and Lr are the DFIG stator and rotor phase inductances, respectively, and Msr is the DFIG magnetising inductance. The orientation of the reference frame with the stator flux results in a zero flux component for ϕsq . The stator and the rotor resistances are neglected. The rotor current references for the regulation loops are expressed by (12) and (13):

Enhanced Dead-Beat Predictive Control Using Power Harmonic Components. . .

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Ls = Msr vs _q

ir _q _ref = −



vs _q ϕs _d − Qs _ref Ls

405



Ls Ps _ref Msr vs _q

(12)

(13)

3.2 Dead-Beat Controller Design The predictive dead-beat controllers, as shown in Fig. 3, regulate the rotor currents. They provide the reference voltage signals to apply to the SVM module. These controllers have to ensure the prediction criterion which is to minimise error between the predicted rotor current components ird and irq , at the (k + 1)th sampling period, and their references irdref and irqref considered at the kth one. This criterion is expressed by (14): )

ir _d [k + 1] = ir _d _ref [k] ir _q [k + 1] = ir _q _ref [k]

(14)

From the DFIG model described in (2) and (4) and using the Euler discretisation method, we obtain the prediction equations expressed by (15) and (16): vr _d [k] = a1 ir _d [k] + a2 ir _d [k + 1] − ωr ϕr _q [k]

(15)

vr _q [k] = a1 ir _q [k] + a2 ir _q [k + 1] − ωr ϕr _d [k]

(16)

where ωr is the rotor electrical angular frequency, a1 = Rr − Tσs , a2 = Tσs , σ is the leakage coefficient and Ts is the sampling period. Then, applying the prediction criterion (14) leads to the expressions of the rotor voltages references of (17) and (18): vr _d _ref [k] = a1 ir _d [k] + a2 ir _d _ref [k] − ωr ϕr _q [k]

(17)

vr _q _ref [k] = a1 ir _q [k] + a2 ir _q _ref [k] + ωr ϕr _d [k]

(18)

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4 Proposed Improved Predictive Control Using Power Harmonic Components As indicated above, in case of asymmetrical voltage sag, additional oscillations at twice the grid frequency appear in the active and reactive stator powers. Consequently, additional power ripples at the same frequency appear in the electromagnetic torque causing mechanical stress in addition to other problems described in Sect. 2.2. In order to overcome these problems, this work proposes an improved control technique under unbalanced operation. The target of this proposed control technique is to decrease shaft constraints by compensating the resulted electrical network harmonics caused by the power ones, thereby reducing the electromagnetic torque oscillations. The main idea is to establish a new computation of the references for planned controllers. The dead-beat predictive controllers are used to ensure fast dynamic responses. The projected control configuration for unbalanced electrical network is demonstrated in Fig. 4. Under an unbalanced voltage sag, the active and reactive stator powers are given by (5) and (6). To mitigate the unbalanced effect of the asymmetrical grid sag, these expressions are introduced into the terms of rotor current references (12) and (13), which lead to the references given by (19) and (20): ir _d _ref = ir _d _ref _sag + ihr _d _ref

(19)

ir _q _ref = ir _q _ref _sag + ihr _q _ref

(20)

where ihrdref and ihrqref are the double grid frequency rotor current harmonic components:      ihr _d _ref = A Qs _cos cos 2ωg t + Qs_sin sin 2ωg t

(21)

     ihr _q _ref = A Ps _cos cos 2ωg t + Ps _sin sin 2ωg t

(22)

A=−

Ls Msr vs _q

(23)

The basic idea here is to extract these components from the rotor current references, calculated previously under normal operation, to obtain the new rotor current references for the regulation loops under unbalanced operation. Consequently, new rotor current references can be expressed by (24) and (25):

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abc_άβ ir_abc

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ird + +

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irdref + irdref_sag

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θs

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Vsdp Vsdn Vsqp Vsqn

isdp isdn isqp isqn

Ps*

Qs*

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ihrqref

Pscos

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Pssin Qscos Qssin

Rotor Currents Harmonic Components Calculation

Fig. 4 Proposed enhanced control block

ir _d _ref −sag = ir _d _ref − ihr _d _ref

(24)

ir _q _ref −sag = ir _q _ref − ihr _q _ref

(25)

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5 Simulation Results and Discussion 5.1 Simulation Scenario To verify the performances of the proposed control algorithms, the following simulation scenario is adopted. Initially, the wind system is connected to the balanced grid, and the basic control using the conventional FOC with predictive dead-beat controllers is activated. Then, at t = 1s, a 30% asymmetrical voltage sag is applied to the wind system (single-phase sag in the first phase Va ). The basic control is maintained activated to show the effect of the unbalanced grid on the DFIG performances. After that, at t = 1.5s, the enhanced control is activated by injecting the double grid frequency rotor current harmonic components to obtain the new rotor current references. The proposed control scenario is illustrated in Fig. 5.

5.2 Discussion A set of simulation tests developed using the PSIM software were performed. The proposed control algorithm was applied to a 2 MW system with a four-pole doubly fed induction machine. The DFIG parameters are listed in Table 1 of the appendix. For the predictive controllers, the sampling period (Ts ) was set to 100us.

Normal operation Basic contol 0

1s

Unbalanced operation Enhanced control 1.5s

Fig. 5 Simulation control scenario Table 1 DFIG system parameters

Description Rated power (MW) Rated stator voltage (V) Rated rotor voltage (V) Rated stator current (A) Number of pairs of poles Frequency (Hz) Stator resistance (m) Rotor resistance (m) Stator inductance (mH) Rotor inductance (mH) Mutual inductance (mH)

Symbols P Vs Vr Is p fs Rs Rr Ls Lr Msr

Values 2 690 2070 1760 2 50 0.34 2.9 2.587 2.587 2.5

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ird(A) 1K 0K -1K -2K irq(A) -2K -3K -4K -5K 0.5

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Time (s) Fig. 6 dq rotor currents

Figure 6 demonstrates the temporal and frequency presentation of ird and irq . The current undulation is decreased by about 55% when the proposed enhanced control is switched. Figure 7 depicts the temporal and frequency presentation of the three-phase rotor, and Fig. 8 presents the electromagnetic torque. It can be noted that both oscillations in the rotor currents and ripples in the electromagnetic torque are significantly reduced. As shown in Figs. 7(b) and 8(b), the results examination reveals that the perturbation caused by the electrical network harmonics is notably eliminated for all machine values. Compared to conventional PI control, with the proposed control, errors between rotor currents and its references are reduced as presented in Figs. 9 and 10. These outcomes confirm the advanced performance of the enhanced algorithm in eliminating the consequence of the grid disturb, for asymmetrical electrical network faults. Moreover, it can be noted that quick dynamic system behaviour is guaranteed by the predictive controllers.

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6 Conclusions This paper presents an enhanced dead-beat control strategy to avoid unintended consequences of unbalanced grid on DFIG wind system. The objective of this paper is to improve the performance of a DFIG under unbalanced grid operation by minimising the electromagnetic torque ripples. The planned algorithm establishes an innovative process for computing the references of the rotor current, which are included to the controllers (dead-beat). Theoretical evaluation of the investigated control in healthy and faulty modes is undertaken, and presented simulation results have illustrated in exemplary fashion the effectiveness of the achieved control. Future work will concentrate on extending the control strategy, taking into account the system parameters variation.

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Tem(Nm) 20K 10K 0K -10K -20K -30K 0.5

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Time (s)

(a) Temporal Presentation Tem (Nm)

Tem (Nm) 12K

14K 12K 10K 8K 6K 4K 2K 0K

10K 8K 6K 4K 2K 0K

0

200 Frequency (Hz)

400

0

200 Frequency (Hz)

400

(b) Frequency presentation Fig. 8 Machine Tem

err_ird (A) 400 200 0 -200 -400 0

0.5

1 Time (s)

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Fig. 9 Error between measured current and reference current with dead-beat controller

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err_ird (A) 400 200 0 -200 -400 0.5

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Time (s) Fig. 10 Error between measured current and reference current with conventional PI controller

Acknowledgements This work was supported by the Tunisian Ministry of Higher Education and Research under Grant LSE-ENIT-LR 11ES15 and funded in part by NAS and USAID under the USAID Prime Award Number AID-OAA-A-11-00012. Any opinions, findings, conclusions or recommendations expressed in this article are those of the authors alone and do not necessarily reflect the views of USAID or NAS.

Appendix References 1. Z. Din, J. Zhang, Z. Xu, in A review on Low Voltage Ride-though for DFIG Based Wind Turbines. PCIM, international exhibition and conference for power electronics, intelligent motion, renewable energy and energy management, VDE Publisher, Shanghai, China, 26–28 June 2018, pp. 268–274 2. Q. Wu, Y. Sun, Grid Code Requirements for Wind Power Integration, in Wiley-IEEE Press eBook Chapters, (Wiley, Hoboken, 2018), pp. 11–36 3. Y.M. Alsmadi, L. Xu, F. Blaabjerg, A.P. Ortega, A.Y. Abdelaziz, Detailed investigation and performance improvement of the dynamic behavior of grid-connected DFIG-based wind turbines under LVRT conditions. IEEE Trans. Ind. Appl. 54(5), 4795–4812 (2018) 4. W. Tang, J. Hu, Y. Chang, Modeling of DFIG-based Wind Turbine for Power System Transient Response Analysis in Rotor Speed Control Timescale, in IEEE Transactions on Power Systems, (Iowa State University Press, Ames, 2018) 5. M.E. Hossain, A new approach for transient stability improvement of a grid-connected doubly fed induction generator–based wind generator. Wind Eng. 41, 1–15 (2017) 6. M. Zeraati, M.E. Hamedani Golshan, J.M. Guerrero, H. Golshan, Voltage quality improvement in low voltage distribution networks using reactive power. IEEE Trans. Smart Grid 10, 5057– 5065 (2018) 7. T. K. Das, Counteracting the Effects of Symmetrical and Asymmetrical Voltage Sags on DFIGBased Wind Power Systems. International Conference on Advanced Mechatronic Systems ICAMechS, 2016, pp. 79–84

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8. H. Nian, S. Member, P. Cheng, Z.Q. Zhu, Coordinated direct power control of DFIG system without phase locked loop under unbalanced grid voltage conditions. IEEE Trans. Power Electron. 31(4), 2905–2918 (2016) 9. D. Sun, X. Wang, H. Nian, S. Member, Z.Q. Zhu, A sliding-mode direct power control strategy for DFIG under both balanced and unbalanced grid conditions using extended active power. IEEE Trans. Power Electron. 33(2), 1313–1322 (2018) 10. X. Wang, D. Sun, Z.Q. Zhu, Resonant based backstepping direct power control strategy for DFIG under both balanced and unbalanced grid conditions. IEEE Trans. Ind. Appl. 53(5), 4821–4830 (2017) 11. I. Villanueva, A. Rosales, P. Ponce, A. Molina, Grid-voltage-oriented sliding mode control for DFIG under balanced and unbalanced grid faults. IEEE Trans. Sustain. Energy 9(3), 1090– 1098 (2018) 12. V. Jacomini, A.J.S. Filho, S. Member, Finite control set applied to the direct power control of a DFIG operating under voltage sags. IEEE Trans. Sustain. Energy 10, 952–960 (2018) 13. D. Sun, X. Wang, Low-complexity model predictive direct power control for DFIG under both balanced and unbalanced grid conditions. IEEE Trans. Ind. Electron. 63(8), 5186–5196 (2016) 14. S.M.A. Cruz, G.D. Marques, P.F.C. Goncalves, M.F. Iacchetti, Predictive torque and rotor flux control of a DFIG-dc system for torque-ripple compensation and loss minimization. IEEE Trans. Ind. Electron. 65(12), 9301–9310 (2018) 15. P. Kou, D. Liang, J. Li, L. Gao, Q. Ze, Finite-control-set model predictive control for DFIG wind turbines. IEEE Trans. Autom. Sci. Eng. 15(3), 1004–1013 (2018) 16. P.F.C. Gonçalves, S.M.A. Cruz, M.B. Abadi, L.M.A. Caseiro, A.M.S. Mendes, Fault-tolerant predictive power control of a DFIG for wind energy applications. IET Electr. Power Appl. 11(6), 969–980 (2017) 17. P. Goncalves, S. Cruz, L. Caseiro, M. Abadi, A. Mendes, Predictive power control of a DFIG driven by a back-To-back three-level neutral-point clamped converter. IEEE International Electric Machines & Drives Conference, IEMDC, USA, 2017 18. Y.D. Kwon, J.H. Park, K.M. Kim, K.B. Lee, Line current improvement of three-phase four-wire vienna rectifier using dead-beat control. IEEE Conference on Energy Conversion CENCON, Malaysia, 2017 19. V.T. Ha, V.H. Phuong, N.T. Lam, N.P. Quang, Dead-Beat Current Controller Based Wind Turbine Emulator. International Conference on System Science and Engineering ICSSE, Bandung, 2017, pp. 169–174 20. C. Cheng, H. Nian, X. Wang, D. Sun, Dead-beat predictive direct power control of voltage source inverters with optimised switching patterns. IET Power Electron. 10(12), 1438–1451 (2017) 21. M. Ghodbane-Cherif, S. Skander-Mustapha, I. Slama-Belkhodja, A. Khan, DFIG Analysis under Grid Voltage Sags Based on Symmetrical Components. 5th International Conference on Control Engineering & Information Technology (CEIT-2017), Proceeding of Engineering and Technology –PET, vol. 32, December 2017, pp. 21–26

Study of Magnets and Pole Pieces Openings in Coaxial Magnetic Gearbox by Reluctance Network Mohammed Naïdjate, Nicolas Bracikowski, Tianbo She, Luc Moreau, Xiangyu Yang, and Nicolas Bernard

Abstract The magnetic gearboxes have received much attention in the last few years. Their numerous advantages, such as low vibration, reduced acoustic noise, and minimum maintenance, are attracting considerable interest for sectors of a high growth like wind turbines and electric vehicles. The present paper aims to study the effect of the magnet and pole pieces opening on the torque of coaxial magnetic gears (CMGs) in order to optimize the latter. It is also about providing a fast and accurate model based on reluctance network method capable of describing the correct electromagnetic behavior of CMG. The confrontation of the obtained results to those calculated by finite element shows a good agreement while guaranteeing a considerable gain in computation time. The proposed model was adopted to optimize the CMG design using parameter-scanning method.

1 Introduction Compared with traditional mechanical gears, magnetic gears can transmit torque without mechanical contact. Thus it presents benefits: no gear wear and no need for lubrication (except for eventual bearings). Consequently, we have a significant reduction of maintenance costs. Moreover, we gain overload protection, which can avoid damage [1, 2]. In 1901, Armstrong presented a gear concept, which uses magnetic field interaction to replace the gear transmission [3]. In 1968, T. B. Martin [4] proposed the first concentric structure of three rotors. In 1973, Laing has further developed this research [5]. Various topologies are introduced in [3]. We focus this study on coaxial magnetic gearboxes. Figure 1 shows the basic structure of our coaxial magnetic gear.

M. Naïdjate () · N. Bracikowski · L. Moreau · N. Bernard IREENA Laboratory, University of Nantes, Saint-Nazaire, France e-mail: [email protected]; [email protected] T. She · X. Yang School of Electric Power, South China University of Technology, Guangzhou, China © Springer Nature Switzerland AG 2020 W. Zamboni, G. Petrone (eds.), ELECTRIMACS 2019, Lecture Notes in Electrical Engineering 697, https://doi.org/10.1007/978-3-030-56970-9_31

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Fig. 1 Quarter coaxial magnetic gearbox cross-sectional view

Permanent magnets are mounted on the surfaces of the inner rotor (pHS = 8 poles) and outer rotor (pLS = 32 poles). The ferromagnetic pieces (pFE = 20 pieces) are used for modulating flux [6]. In order to optimize the CMG performances, a fast and accurate analysis tool is required. Although finite element analysis (FEA) is usually used, however the reluctance network computation represents an interesting compromise between accuracy and quickness in an optimization process. M. Johnson et al. propose a reluctance network of CMG [7]. In a second study, they verify the proposed model with a FEA [8]. The results obtained show a good similarity with reluctance network. Another work also presents a CMG equivalent reluctance network, while taking into account the motion equation [9]. It uses this same model, associated with simplex method, to optimize the thickness of inner magnets, outer magnets, and ferromagnetic pole pieces, in order to maximize torque [10]. In our paper, we suggest optimizing the opening angle of inner magnets, outer magnets, and ferromagnetic pole pieces, in order to maximize torque. First, the reluctance network analysis (RNA) model applied to CMG is described in detail. The airgap flux density and torques of RNA were validated with FEA. Furthermore, a parameter-scanning method was adopted to optimize the inner magnet, outer magnet, and ferromagnetic angle openings, taking into account the different possible initial position of rotors.

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2 Magnetic Gearbox Modeling by Reluctance Network The dimensions of the magnetic gearbox used in this chapter are presented in Table 1. These dimensions were not selected based on a real device. The objective of this part is only to validate our model. Figure 2 shows some variables of the table. All the simulations presented in this chapter are realized in linear conditions. To get the reluctance network model, we proceed first by meshing the geometry. The mesh is a curvilinear grid. The presence of symmetry axes allows us to reduce the study of the quarter of CMG. The mesh grid is subdivided into 7 radial parts and 240 tangential parts (Fig. 3). Thus, the total number of mesh elements is 1680. The seven radial parts correspond to the seven physical layers that are inner yoke, inner magnets, inner airgap, ferromagnetic pole pieces, outer airgap, outer magnets, and outer yoke. The 240 tangential parts are an arbitrary choice. However, this number must be great enough to make an exploration step small enough for the optimization part, on the one hand, and it should avoid overlapping between different physical areas in a single mesh element, on the other hand. To build the reluctance network model, each element of the mesh is substituted by an elementary circuit (Fig. 4). The radial reluctances Rrad and tangential reluctances Table 1 Details of the gearbox dimensions Descriptions Permanent magnets of the outer rotor Permanent magnets of the inner rotor Ferromagnetic pieces of the middle rotor Magnet opening of the outer rotor Magnet opening of the inner rotor Ferromagnetic pole pieces opening External radius of the gearbox Stack length of the gearbox Radius in the middle of outer airgap Radius in the middle of inner airgap Yoke height of the inner rotor Magnet height of the inner rotor Airgap between inner rotor and middle stator Pieces height of the middle stator Airgap between middle stator and outer rotor Magnet height of the outer rotor Yoke height of the outer rotor Relative magnetic permeability of iron Relative magnetic permeability of magnet Residual magnet flux density of magnet

Names pLS pHS pFE αLS αHS αFE REXT LEXT rLS rHS W1 W2 W3 W4 W5 W6 W7 μiron μmagnet Br

Values 32 8 20 120 120 180 1500 2000 1355 1245 100 40 10 100 10 40 100 1e+4 1 1,3

Units – – – ◦ ◦ ◦

mm mm mm mm mm mm mm mm mm mm mm – – T

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Fig. 2 Heights used in the gearboxes

Fig. 3 Mesh elements of the quarter gearbox

Rtan values are calculated by the formulas (1), (2), and (3). The magnitude of flux sources ϕS is estimated by Eq. (4). It has a constant value for elements belonging to magnets and null otherwise:

down Rrad =

1 × μ

(rm r1

dr 1 1 = × × L×α×r μ L

 &  ln rm r 1

α

(1)

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Fig. 4 The elementary circuit for each element of the mesh

up

Rrad =

Rtan

1 × μ

(

1 = × μ

(

r2

1 1 dr = × × L × α × r μ L rm r2

m

α

(2)

&

& α × r 1 1 2 2 = × ×  &  L × dr μ L ln r2 r

α

r1

 &  ln r2 r

(3)

1

ϕS = Br × L × rm × α

(4)

where L is the problem depth, Br is the remanence flux density of the magnet, μ is the magnetic permeability, and α, r1 , r2 are the geometric parameters of an elementary mesh element (Fig. 4). The CMG flux densities are validated by FEA. Figures 5 and 6 illustrate radial and tangential flux density distributions in the inner airgap and the outer airgap, respectively. We observe a good concordance between the two results which validate the proposed model. The evaluation of the flux density distribution allows us to estimate the torque distribution using Maxwell tensor [11]: ΓLS (i, j ) = −2π ×

LEX rH S 2 LS LS × Brad (i, j ) × Btan (i, j ) μ0

(5)

ΓH S (i, j ) = +2π ×

LEX rH S 2 HS HS × Brad (i, j ) × Btan (i, j ) μ0

(6)

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Fig. 5 Radial, tangential flux density distributions in inner airgap

Fig. 6 Radial, tangential flux density distributions in outer airgap

where Γ HS is the torque of the high-speed rotor (inner rotor) and Γ LS is the torque of the low-speed rotor (outer rotor). j is the step index of CMG rotation, i is the division index in tangential direction, and rHS and rLS are the radii of inner and outer airgaps. Brad and Btan are radial and tangential flux density. The CMG torques are validated by FEA. Figure 7 shows the torque distribution for the initial position (j = 1). For our CMG, the inner rotor rotates four times faster than the outer rotor. This gear ratio “Gr” can be calculated using (Eq. 7): Gr =

ωH S pLS 32 = −4 =− =− ωLS pH S 8

(7)

where ωHS and ωLS are angular speeds of the inner and the outer rotors, respectively. Thereby, the rotation process is implemented in a way so one step of one increment

HS

(N.m)

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10

RNA

5

FEA

0

/4

/2

/4

/2

2 1

LS

(N.m)

-5

0 -1

(rad) spatial

Fig. 7 Torque distribution in the inner and outer rotor

in the low-speed rotor is offset by one step of four increments in the high-speed rotor in the opposite rotation sense. The distribution of the average torque for each position can be computed with relations (8) and (9). Figure 8 presents a comparison of the torque variation obtained by RNA and FEA for the inner and outer rotors for one turn of the high-speed rotor (N = 240). Fast Fourier transform has been performed on the inner and the outer torque results (Fig. 9): ΓLS (j ) = −2π

LEX rH S 2 μ0

LEX rH S 2 ΓH S (j ) = +2π μ0

)

)

 ;

N 1 LS LS × i, j Brad (i, j ) × Btan i=1 N

(8)

 ;

N 1 HS HS × B (i, j ) × Btan i, j i=1 rad N

(9)

where N is the number of divisions in tangential direction. The 40th harmonic is the ripple torque fundamental. Consequently, we can limit the number of rotation steps to six (M = 240/40 = 6). Then, the formula of the total average torque is given by ΓLS

LEX rH S 2 = −2π μ0

ΓH S

LEX rH S 2 = +2π μ0

)

)

 ; 1 M N LS LS B (i, j ) Btan i, j j =1 i=1 rad NM

(10)

 ; 1 M N H S HS B (i, j ) Btan i, j j =1 i=1 rad NM

(11)

422

Fig. 8 Torques for a quarter turn of low-speed rotor

Fig. 9 FFT for torques of a quarter turn (without offset)

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Study of Magnets and Pole Pieces Openings in Coaxial Magnetic Gearbox. . . Table 2 Comparison between RNA and FEA results

FEA RNA Proportion

 HS [N.m] 9.94e4 1.0e5 0.6%

 LS [N.m] −3.9e5 −4.1e5 5%

423 Time [s] 30 15 10−3 200,000%

Table 2 compares the results of RNA and FEA. We perceive an overestimation of 0.6% in the torque of the high-speed rotor and 5% in the torque of the low-speed rotor. We note that this precision was obtained using only 1680 elements for RNA compared to 101,270 elements in the FEA. In addition, the computation using RNA was 2000 times faster than FEA.

3 Study of Magnets and Pole Pieces Openings 3.1 Problem Introduction The aim of this study is to analyze the CMG torque variation according to the magnet opening of outer rotor (αLS ), the magnet opening of the inner rotor (αHS ), and the ferromagnetic pole pieces opening (αFE ) (see Fig. 10). The variations of each parameter give rise to a new CMG. According to Table 3 data, there are 172,800 possible CMGs (30 × 120 × 48). The torque is computed for all CMGs and for each initial position (θinit ). The initial position (θ = 0) is determined according to the relative position of the three rotors to the abscissa axis. The variation of initial position is obtained by rotating forward the outer rotor, while the inner and middle rotors always start from (θ = 0). In addition, whatever the starting initial position, the rotation of CMG rotors can be simulated by taking only the first six steps (see Fig. 9). This allows us to compute the average value of the torque. Thereby, the total number of simulations is 248,832,000 (30 × 120 × 48 × 240 × 6) performed by parameter-scanning method. The studied parameters and their variation ranges are shown in Table 3. We multiply the single pole data by pLS , pHS , and pFE to obtain the total angle opening of αLS , αHS , and αFE , respectively.

3.2 Optimization The optimization phase consists of calculating the torque for the 172,800 possible CMGs and selecting those presenting the optimal results. We note that the best initial value was investigated for each CMG. Figure 11 shows the torque variation for the inner rotor and the outer rotor and this according to the magnet opening of outer rotor (αLS ), the magnet opening of

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Fig. 10 Optimization parameters: magnet opening of low-speed rotor (αLS ), magnet opening of the high-speed rotor (αHS ), and the pole pieces opening (αFE ) Table 3 The magnet and ferromagnetic pole pieces opening angles ranges and their moving steps Parameter Single pole

All poles together

Number of steps

Low limit Step Upper limit Low limit Step Upper limit

α OUT 0.375◦ 0.375◦ 11.25◦ 12◦ 12◦ 360◦ 30

α IN 0.375◦ 0.375◦ 45◦ 3◦ 3◦ 360◦ 120

α FE 0.375◦ 0.375◦ 18◦ 7.5◦ 7.5◦ 360◦ 48

θ init 0◦ 0.375◦ 90◦

240

the inner rotor (αHS ), and the ferromagnetic pole pieces opening (αFE ) (see Fig. 10). To better analyze these results, we represent, in Fig. 12, only the best 5% that perform the optimum torque. We notice that all these optimal CMGs have a magnet opening between 320◦ and 360◦ against 120◦ to 180◦ for the ferromagnetic pole pieces opening. Table 4 provides the parameters of the CMG that give the maximum torque value. These results recommend that, for an optimal performance of a CMG, the constructor should maximize the magnet opening, while, for the ferromagnetic pole pieces opening, it should have a proportion of 30% to 50% of the maximum opening to ensure an adequate modulation of the magnetic field.

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Fig. 11 Torques versus inner magnet opening, outer magnet opening, and ferromagnetic pole pieces opening

4 Conclusion This work has investigated the effect of the magnets and pole pieces openings of a coaxial magnetic gearbox for the purpose of optimizing the torque performance. In this vein, a fast model based on reluctance network has been developed and validated by finite element calculations.

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Fig. 12 Torques for parameters that give upper than 95% of the maximum torque Table 4 CMG parameters that exhibit the optimal torque

Parameters α LS α HS α FE  LS  HS

Values 360◦ 360◦ 150◦ 838 kN.m 197 kN.m

Furthermore, due to the periodic oscillation of the torque, we can reduce significantly the simulation of the gears rotation. In our particular case, we saved 97.5% of the simulation effort.

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The evidence from this work suggests that, for an optimal performance of CMGs, the constructor should maximize the magnetic poles opening and take pole pieces opening ranges between 30% and 50% of the maximal opening.

References 1. E. Gouda, S. Mezani, L. Baghli, A. Rezzoug, Comparative study between mechanical and magnetic planetary gears. IEEE Trans. Magn. 47(2 PART 2), 439–450 (2011) 2. M. Johnson, M.C. Gardner, H.A. Toliyat, Design comparison of NdFeB and ferrite radial flux surface permanent magnet coaxial magnetic gears. IEEE Trans. Ind. Appl. 54(2), 1254–1263 (2018) 3. P.M. Tlali, R.J. Wang, S. Gerber, Magnetic Gear Technologies: A Review, in Proceedings – 2014 International Conference on Electrical Machines, ICEM 2014, 2014, pp. 544–550 4. T.B. Martin, Magnetic Transmission, 3,378,710, 1968. US patent 5. N. Laing, Magnetic Transmission, 345 650, 1972. US Patent 6. N.W. Frank, H.A. Toliyat, Gearing ratios of a magnetic gear for wind turbines, in 2009 IEEE International Electric Machines and Drives Conference, IEMDC ‘09, 2009, pp. 1224–1230 7. M. Johnson, M.C. Gardner, H.A. Toliyat, A parameterized linear magnetic equivalent circuit for analysis and design of radial flux magnetic gears-part I: Implementation. IEEE Trans. Energy Convers. 8969(c), 1–8 (2017) 8. M. Johnson, M.C. Gardner, H.A. Toliyat, A parameterized linear magnetic equivalent circuit for analysis and design of radial flux magnetic gears-part II: Evaluation. IEEE Trans. Energy Convers. 33(2), 792–800 (2018) 9. M. Fukuoka, K. Nakamura, O. Ichinokura, Dynamic analysis of planetary-type magnetic gear based on reluctance network analysis. IEEE Trans. Magn. 47(10), 2414–2417 (2011) 10. M. Fukuoka, K. Nakamura, O. Ichinokura, A method for optimizing the design of SPM type magnetic gear based on reluctance network analysis, in Proceedings – 2012 20th International Conference on Electrical Machines ICEM 2012, 2012 11. R.C. Holehouse, K. Atallah, J. Wang, A linear magnetic gear, in Proceedings – 2012 20th International Conference on Electrical Machines, ICEM 2012, 2012