The Essentials of Power System Dynamics and Control PDF
Preview The Essentials of Power System Dynamics and Control
Hemanshu Roy Pota The Essentials of Power System Dynamics and Control The Essentials of Power System Dynamics and Control Hemanshu Roy Pota The Essentials of Power System Dynamics and Control 123 Hemanshu RoyPota Schoolof Engineering andInformation Technology TheUniversity of NewSouthWales Canberra,ACT Australia ISBN978-981-10-8913-8 ISBN978-981-10-8914-5 (eBook) https://doi.org/10.1007/978-981-10-8914-5 LibraryofCongressControlNumber:2018936646 ©SpringerNatureSingaporePteLtd.2018 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 orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. 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 authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictionalclaimsinpublishedmapsandinstitutionalaffiliations. Printedonacid-freepaper ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSingaporePteLtd. partofSpringerNature Theregisteredcompanyaddressis:152BeachRoad,#21-01/04GatewayEast,Singapore189721,Singapore May the winds, born from the shining sky electricity, protect us and give us happiness. Preface Every aspect of the power system is undergoing a transformation, and the existing dynamicalrepresentationofthepowersystemwillchange.Engineersfromdiverse background, often working in one specialised area of the interconnected power system,arecontributingtothischange.Theabilitytoaccuratelymodeltheexisting complexinterconnectedpowersystemdynamicswithonlyafewsimpledifferential equations has been a fascinating intellectual achievement. The work of the engi- neerswhoareattheforefrontoftransformingthepowersystemwillhaveahigher impact if the new contributions rest on and are connected with the existing foun- dations of power system dynamics. This book is written for students or practising engineers with a background in science or engineering. It is self-contained, starting from phasor analysis and leading the reader to the design of automatic voltage regulators and power system stabilisersforsynchronousgenerators.Itincludesfundamentalsofthelinearcontrol systems that enable the design of the controllers. Historically speaking, initially dynamic models for synchronous machines were developed for analysis and immediately after that they were successfully used for voltage and frequency reg- ulation. A solid understanding of power system dynamics is obtained from com- pleting themodel, analysis, design,and then model refinementcycle. Inthis book, the reader is guided through the entire cycle. The simplification in modelling the power system dynamics is achieved by partitioning the dynamics into fast and slow dynamics. The fast dynamics, also knownasthestatororthetransmissionsystemdynamics,isassumedtobeinsteady state during each integration time-step of the slow dynamics, also known as rotor dynamics. Although mathematically straightforward, it is important to understand the steady-state analysis of the slow dynamics. This analysis, also known as the power flow or load flow analysis, is introduced in Chap. 1. A simple technique to solve for the nonlinear steady-state solution is given so that the reader gets a completeappreciationoftheproblem.Manyadvanced methods existforloadflow vii viii Preface solution, but an understanding of those methods is not necessary for a deep understanding of power system dynamics. Magnetic energy is the intermediate energy storage mechanism during the conversion between electrical and mechanical energy. Magnetic circuits can be easily understood in analogy with electrical circuits. Although magnetic circuits have a much smaller linear range, once properly formulated, it is not difficult to include the nonlinear characteristics during the numerical integration process. The firstchaptercoversacomprehensiveanalysisofthemagneticcircuitofthree-phase rotating machines which leads to the principle of operation of synchronous and induction machines. The dynamics of generators with moving parts has coupled mechanical and electrical dynamic equations. The mechanical dynamics is often equivalent to a mass–spring system driven by the difference between the input mechanical power and the output electrical power. The electrical output power is a function of the generator angular position and terminal voltage, and this couples the mechanical and electrical dynamics of the rotating electrical generators. In most situations, a first-order differential equation accurately represents the voltage dynamics. In Chap. 2, a detailed method is presented that shows how the third-order dynamic equations, for each generator, are coupled to form interconnected system dynamic equations.Thischapteriscompleteinallthedetails,andeveryequationisderived fully. The reader is encouraged to derive each expression using symbolic compu- tationsoftwareorusingthepaper-and-pencilmethod.Thefundamentalprincipleis very simple, but the confidence that this simple principle can lead to such com- plicated models will only sink in if the reader derives each expression and gets convinced that only one simple principle, Faraday’s law of induced electromotive force, has such far-reaching consequences. Algebraic transformation using matrix algebra plays an important role in the simplified transient analysis models, and the complete derivation includes all the matrix manipulation required to arrive at the final simple model. Chapter 2 extendsthe simple transient model, accurate intheorder ofhundreds of milliseconds, by adding additional dynamics to make it accurate for tens of milliseconds time frame. Once the understanding of a single coil dynamics is understoodwell,itissimplyamechanicalprocesstokeepaddingadditionalcoilsto the model to obtain the so called sub-transient model. The chapter further derives the block diagrams used by commercial power system analysis software to model rotating machines. These models are parameterised both in terms of open-circuit and short-circuit time constants. The author has used symbolic manipulation soft- ware to derive these results, and the reader is also strongly urged to use similar software,especiallysincehigh-qualityopen-sourcesymbolicmanipulationsoftware is available. Chapter 3 covers essential linear systems analysis for the design of classical controllers, using frequency domain techniques, for voltage regulation and oscil- lationdampingofrotatinggenerators.Inthischapter,detailedderivationsaregiven sothatthereaderisabsolutelyclearwhatisfrequencyresponseandwhyisitsucha wonderfultoolforthedesignofrobustcontrollers.Almostallclassicaldesigntools Preface ix are covered in this chapter giving enough information about the utility of the method. With the availability of open-source software tools such as octave and Scilab, this chapter does not detail how to draw various plots for analysis, but it emphasises on what the tools fit in the design process. Power system analysis is done with the nonlinear models, but control design is moreconvenientwiththelinearisedmodels.Chapter3givescompletederivationof allthelinearisedmodels.Althoughexpressionsforthelinearisedmodelsaregiven, here again the reader is urged to derive the models themselves so that they have definiteexpressionswhichtheycanownandfurtheruseitforcontroldesignwitha full understanding. Automaticvoltageregulator(AVR)isanessentialcomponentofgenerators,and almost all the commercially available AVRs can be designed using frequency domain techniques covered in Chap. 3. In Chap. 4, AVR design is covered from simple fixed gain controllers to complex multiple-loop proportional–derivative– integral (PID) controllers. The control specifications are given in terms of steady-state error, bandwidth, and phase-margin, and the lag-lead compensator designisusedtosatisfythesecontrolspecifications.Thesemethodshavebeenused to design and implement AVRs for commercial synchronous generators. There is no inherent mechanical damping in the interconnected system, and the electrical transients couple with the mechanical dynamics to provide damping. Chapter5coversadetailedanalysisofthemagnitudeandsignofthedampingdue to feedback mechanism used for AVRs. Often the damping due to electrical tran- sientsisnotenough,andinthosesituations,apowersystemstabiliser(PSS)isused to increase the damping. The design of PSS is also done using frequency domain methods. Chapter 5 covers the design of the classical PSS, and it completes the model, analysis, and design cycle. Althoughthisbookcoverstheessentialsofpowersystemdynamicswithrotating generators,thesameideasareapplicabletostaticgenerators,suchasphoto-voltaic solar generators. The material in this book will enable researchers to integrate generator models of the emerging renewable resources-based generators to inter- connected power systems and do control design considering the dynamics of the entire power systems. Theessentialsinthisbookhavebeenverycarefullychosentoprovidesufficient depthtothereadersothatitiseasytointegratethedynamicsofemergingdevices. Theauthoremphasisesthatthefullbenefitfromthisbookcanonlyberealisedifthe reader derives the expression in this book. I have taught a ten-week forty-lecture course based on this book thrice to engineerswithdiversebackground,andasaresult,somerefinementhasbeendone andtheauthorsincerelyhopesthatitwillhelpengineersfromdiversebackgrounds tobecomeproductivepowersystemengineers.Ashorterversionofthiscoursehas been also taught twice to practising power system consultants. I have incorporated most of the feedback that I received during the course. IthankmyformerPh.D.studentswhohaveshapedmuchofthematerialinthis book by asking questions and giving me an idea of the difficulties faced by a beginningresearcherintheareaofpowersystemdynamics.IthankDr.C.S.Kumble x Preface and Mr. Prahlad Tilwalli for engaging me as a consultant and giving me the satisfaction of observing the performance of the controllers designed using the methodsinthisbookoncommercialsynchronousgenerators. Canberra, Australia Hemanshu Roy Pota Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Sinusoidal Steady-State. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 RL Circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.2 Phasor Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Real and Reactive Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.1 P and Q Sign Convention. . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.2 Real and Reactive Power Balance. . . . . . . . . . . . . . . . . . 8 1.3 Load Flow Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3.1 Three-Phase to Single-Line Diagram. . . . . . . . . . . . . . . . 10 1.3.2 Circuit Analysis Versus Power Systems Analysis. . . . . . . 11 1.3.3 Bus Types. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.3.4 Single Machine Infinite Bus . . . . . . . . . . . . . . . . . . . . . . 14 1.3.5 N-Bus System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.4 Magnetic Circuits and Inductance . . . . . . . . . . . . . . . . . . . . . . . . 21 1.4.1 An Inductor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.4.2 Rotating Machine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.5 Electromechanical Energy Conversion . . . . . . . . . . . . . . . . . . . . . 27 1.5.1 Plunger-Spring System. . . . . . . . . . . . . . . . . . . . . . . . . . 29 1.5.2 Rotor-Spring System . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 1.6 Rotating Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 1.6.1 Synchronous Machine . . . . . . . . . . . . . . . . . . . . . . . . . . 33 1.6.2 Induction Machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 1.7 Essential Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 1.7.1 Complex Number Algebra . . . . . . . . . . . . . . . . . . . . . . . 37 1.7.2 Per Unit System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 1.7.3 Circuit Theory in a Nutshell. . . . . . . . . . . . . . . . . . . . . . 38 xi
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