SPRINGER BRIEFS IN APPLIED SCIENCES AND TECHNOLOGY Deepak Kumar Fulwani Suresh Singh Mitigation of Negative Impedance Instabilities in DC Distribution Systems A Sliding Mode Control Approach SpringerBriefs in Applied Sciences and Technology More information about this series at http://www.springer.com/series/8884 Deepak Kumar Fulwani Suresh Singh (cid:129) Mitigation of Negative Impedance Instabilities in DC Distribution Systems A Sliding Mode Control Approach 123 Deepak Kumar Fulwani SureshSingh Department ofElectrical Engineering Department ofElectrical Engineering Indian Institute of Technology Jodhpur Indian Institute of Technology Jodhpur Jodhpur, Rajasthan Jodhpur, Rajasthan India India ISSN 2191-530X ISSN 2191-5318 (electronic) SpringerBriefs inApplied SciencesandTechnology ISBN978-981-10-2070-4 ISBN978-981-10-2071-1 (eBook) DOI 10.1007/978-981-10-2071-1 LibraryofCongressControlNumber:2016947210 ©TheAuthor(s)2017 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart 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 dissimilarmethodologynowknownorhereafterdeveloped. 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 fromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained hereinorforanyerrorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerScience+BusinessMediaSingaporePteLtd. Preface RenewableenergybasedmulticonverterDCdistributionsystemsorDCmicrogrids are considered as one of the key enabling technologies, among many, towards the developmentofmodernsmartgrids.DCdistributionsystemsofferinherentbenefits ofhigherpowertransfercapacityoflines,noreactivepowerandfrequencycontrol requirements,andavoidanceofmultiplepowerconversionswhenthesourceisDC. This results in simple control structures, higher efficiency, and cost effectiveness. However, tightly regulated Point-of-Load Converters (POLCs) in a multiconverter DCdistributionsystemhavingcascadedstructurebehaveasConstantPowerLoads (CPLs)whencontrolbandwidthofloadconverterissufficientlyhigherthanthatof feeder converter, and introduces a destabilizing effect into the system. This desta- bilizingeffectofCPLs,duetotheirnegativeimpedancecharacteristics,mayleadto reduced system damping, significant oscillations in the DC bus voltage, and sometimes voltage collapse. Thismonographfocusesonthemitigationofthedestabilizingeffectsintroduced byCPLsindifferentnon-isolatedDC/DCconvertersandislandDCmicrogridusing robust nonlinear Sliding Mode Control (SMC) approach. Novel sliding mode controllers are proposed to mitigate negative impedance instabilities in DC/DC boost, buck, bidirectional buck-boost converters, and islanded DC microgrid. In each case, the condition for large-signalstabilityof theconverterfeedinga CPLis established. SMC-based nonlinear control scheme for an islanded DC microgrid feedingCPLdominatedloadisproposedtomitigatethedestabilizingeffectofCPL and to ensure system stability in various operating conditions. A limit on CPL powerisalsoestablished toensure thesystemstability.Forallproposedsolutions, simulation studies and hardware implementations are provided to validate the effectiveness of the proposed sliding mode controllers. The authors wish to acknowledge Vinod Kumar, Aditya R. Gautam, Nupur Rathore, Kumar Gaurav, Atul Agarwal, and Koyinni Deekshitha for their help.TheywishtoacknowledgeMinistryofNewandRenewableEnergy(MNRE), v vi Preface Indiaforfinanciallysupportingtheworkpresentedinthismonographunderproject no.-S/MNRE/LC/20110007.Finally,theyalsowouldliketoacknowledgepatience, encouragement, and support of their wives and children during the preparation of manuscript. Jodhpur, India Deepak Kumar Fulwani June 2016 Suresh Singh Contents 1 Introduction.... .... .... ..... .... .... .... .... .... ..... .... 1 1.1 Constant Power Loads: Sources, Behaviour and Effects..... .... 3 1.2 Stability of a Simple dc Power System with CPL .... ..... .... 6 1.3 Small-Signal Stability of Basic DC/DC Converters with CPL .... 8 1.3.1 Buck Converter.... .... .... .... .... .... ..... .... 8 1.3.2 Boost Converter ... .... .... .... .... .... ..... .... 9 1.3.3 Buck-Boost Converter... .... .... .... .... ..... .... 10 1.3.4 Bidirectional Buck-Boost Converter .... .... ..... .... 10 1.4 Stability of a DC Microgrid with CPL. .... .... .... ..... .... 12 1.5 Review of Literature.. ..... .... .... .... .... .... ..... .... 12 1.5.1 Passive Damping... .... .... .... .... .... ..... .... 12 1.5.2 Active Damping ... .... .... .... .... .... ..... .... 13 1.5.3 Feedback Linearization .. .... .... .... .... ..... .... 18 1.5.4 Pulse Adjustment... .... .... .... .... .... ..... .... 19 1.5.5 Digital Charge Control .. .... .... .... .... ..... .... 20 1.5.6 Sliding Mode Control ... .... .... .... .... ..... .... 21 1.5.7 Synergetic Control.. .... .... .... .... .... ..... .... 22 1.5.8 Passivity Based Control.. .... .... .... .... ..... .... 23 1.5.9 Power Shaping Stabilization .. .... .... .... ..... .... 23 1.5.10 Coupling Based Techniques .. .... .... .... ..... .... 24 1.5.11 State-Space Pole Placement... .... .... .... ..... .... 25 1.5.12 New Converter Topologies ... .... .... .... ..... .... 25 1.6 Motivation . .... .... ..... .... .... .... .... .... ..... .... 25 1.7 Organization of the Book... .... .... .... .... .... ..... .... 28 References.. .... .... .... ..... .... .... .... .... .... ..... .... 29 2 Stabilization of a Buck Converter Feeding a Mixed Load Using SMC.. .... .... .... .... ..... .... .... .... .... .... ..... .... 35 2.1 Mathematical Modeling of Buck Converter with Mixed Load .... 36 2.2 Sliding Mode Control Design.... .... .... .... .... ..... .... 37 2.2.1 Discontinuous SMC .... .... .... .... .... ..... .... 37 vii viii Contents 2.2.2 PWM Based SMC.. .... .... .... .... .... ..... .... 42 2.2.3 Simulation Studies.. .... .... .... .... .... ..... .... 43 2.2.4 Experimental Validation . .... .... .... .... ..... .... 48 2.3 Summary .. .... .... ..... .... .... .... .... .... ..... .... 52 References.. .... .... .... ..... .... .... .... .... .... ..... .... 53 3 Mitigation of Destabilizing Effects of CPL in a Boost Converter Feeding Total CPL .. .... ..... .... .... .... .... .... ..... .... 55 3.1 Mitigation of CPL Effects in Boost Converter Using SMC .. .... 56 3.1.1 System Modeling of Boost Converter with CPL.... .... 57 3.1.2 Design of PWM Based SMC . .... .... .... ..... .... 58 3.1.3 Existence of Sliding Mode and Stability of Surface . .... 60 3.1.4 Validation of the Proposed Controller... .... ..... .... 62 3.2 Mitigation of CPL Effects Using SMC Designed with Modified Switching Function.... .... .... .... ..... .... 68 3.2.1 Modified Switching Function . .... .... .... ..... .... 69 3.2.2 Discontinuous SMC Using Modified Switching Function .... ..... .... .... .... .... .... ..... .... 69 3.2.3 Existence of Sliding Mode with Discontinuous SMC .... 69 3.2.4 Stability of Modified Switching Surface . .... ..... .... 71 3.2.5 Real-Time Simulation Studies. .... .... .... ..... .... 73 3.2.6 Experimental Validation of the Proposed SMC..... .... 76 3.3 Summary .. .... .... ..... .... .... .... .... .... ..... .... 78 References.. .... .... .... ..... .... .... .... .... .... ..... .... 78 4 Compensation of CPL Effects in a Bidirectional Buck-Boost Converter.. .... .... .... ..... .... .... .... .... .... ..... .... 81 4.1 Compensation of CPL in a Bidirectional DC/DC Converter.. .... 82 4.1.1 Modeling of Bidirectional DC/DC Converter . ..... .... 82 4.1.2 Sliding Mode Control Design . .... .... .... ..... .... 85 4.1.3 Real-Time Simulation Studies. .... .... .... ..... .... 89 4.2 Summary .. .... .... ..... .... .... .... .... .... ..... .... 91 References.. .... .... .... ..... .... .... .... .... .... ..... .... 92 5 Robust Control of an Islanded DC Microgrid in Presence of CPL.. .... ..... .... .... .... .... .... ..... .... 93 5.1 Robust Control of a PV Based DC Microgrid ... .... ..... .... 95 5.1.1 Test System and Its Operating Modes... .... ..... .... 95 5.1.2 Mathematical Modeling of Island DC Microgrid.... .... 98 5.1.3 Sliding Mode Control Design . .... .... .... ..... .... 100 5.1.4 Stability on Switching Surface .... .... .... ..... .... 103 5.1.5 Simulation Studies and Experimental Results . ..... .... 107 5.2 Summary .. .... .... ..... .... .... .... .... .... ..... .... 112 References.. .... .... .... ..... .... .... .... .... .... ..... .... 112 Index .... .... .... .... .... ..... .... .... .... .... .... ..... .... 115 About the Authors Dr. Deepak Kumar Fulwani is working as an assistant professor in the Department of Electrical Engineering at Indian Institute of Technology Jodhpur (IITJ). He also worked at IIT Guwahati and IIT Kharagpur. He obtained his Ph.D. fromIITBombayin2009;hewasalsoawardedforexcellenceinPh.D.thesiswork in 48th convocation of IIT Bombay. His research fields include control of net- worked systems and DC micro-grid. Dr. Suresh Singh is currently a Senior Project Engineer in the Department of Electrical Engineering at Indian Institute of Technology, Jodhpur, India. He has recentlycompletedhisPh.D.fromIITJodhpurin2016.Dr.Singhhasover10years of teaching and research experience. His research interests include smart grids, AC/DC microgrids: renewable energy integration, distributed generation, DC power systems, power management in DC microgrids, sliding mode control of DC/DC power converters, constant power loads and pulse power loads in dc dis- tribution systems, power electronic converters, solar PV and wind energy systems, power system dynamics and control, real-time simulation of renewable energy systems, hardware-in-loop (HIL) and power-hardware-in-loop (PHIL). He has got several papers published in the international journals. ix