modern-power-systems-analysis-d-p-kothari-i-j-nagrath-

nrp ://nIgnereo.mcgraw-n||Lcom/sites/O07o 4g4gg4 u t i l r l r u w E tiF r -'J----u;; DaEir-4iE va s Rm Anllueis- o'co- € ryrrr Trlrutr tgrl, il In simplelanguage,the book providesa modernintroductionto power systemoperation,controland analysis. FT rt- 9 -A- Key Features of the Third -- frvt New chapters added on = ) .PowerSystemSecurity ) StateEstimation TI ) Powersystemcompensationincludingsvs and FACTS ) Load Forecasting srd r o€ ) VoltageStability - New appendiceson : -o o=, > MATLABand SIMULINKdemonstratintgheiruse in problemsolving. oI r - ) Realtimecomputercontrolof powersystems. Third Editior; LFf' rllf rJ(\\ (^Jr*Il-l t d^,.f.!l lJ Nagrath From the Reviewen., The book is verycomprehensivew, ell organised,up-to-dateand (above all) lucidand easyto followfor self-study.lt is ampiy illustratedw1h solved examplesfor everyconceptand technique. lMr iltililttJffiillililil ll--=i

Modern PorroerSYstem Third Edition

About the Authors Modern Power System Analysis D P Kothari is vice chan cellor,vIT Universit y,vellore. Earlier,he was Professor,Centre for Energy Studies,and Depufy Director (Administration) Third Edition dfEfIeonenlrdglgoEiraiwennneeeIsaernfgtrrsoiyRtnmiStgMuctButIoeTdIloT,lieefSMgsT,(ee1eP,c9liNblh9aoan5nugo-ir.9plnAo7ueg)r,fa.yAeEDn,lualdeosrPwltlhirreaiio.nrl iHflcaftlei.hapHhezaae-lI(snsl :osugtbiigrttoua7atit-nin.god\"e8nnd1)E,9hVtngihsigs9eivB)nH,eehEesee,avrdwMsa(oraIEanfsytdhaaaRi aenve)dci,gseppiinrothiotnnDrfag.el D P Kothari jiTKonruocarltunhndsaaiirlensing/cthsoPa,nosTfwepherueerbonslrciyyseshsatee.nHdmd/epEprnehrgosaibesnlneeatemeurdsit4nh5goo0,rfeEpdElea/lccepotcer-tircrasicuMitnhaMocnarheacidtnhimoeinnsoe,arse2l,/aet2nh,/deap.no,iwnat1een5rrdns.bayoBtsiooateknsmsiac,l Vice Chancellor Electrical Engineering. His researchinterestsinclude VIT University optimisation,reliability and energyconservation. power systemcontrol, Vellore I J Nagrath is Adjunct Professor,BITS Pilani and retired as professorof Former Director-Incharge, IIT Delhi Electrical Engineeringand DeputyDirectorof Birla Instituteof Technology Former Principal, VRCE, Nagpur Mua1nn9aid5cvh6eSi'rncsHeiieetsyn2cho/eaef,s,PRPcialooaja-wnasie.utrhHt hsaeyonisrnoteebd1msta9eEi5vnn1eegardiannhldeisseMurBcSincEgefr,sionssmifgEuntbllhaeolecsotUrkaiscnnaidwvl ehEs.iyrncistghtyeinimnoecfselWruaindni\"gedsf.crEsooylmensscteittnhrmiinecs: Modelling and Analyns. He has also puulistred ,\"rr.ui I J Nagrath prestigiousnationaland internationajlournats. researchpapers in Adjunct Professor, and Former Deputy Director, Birla Ins1i1y7\"of Technologt and Science Pilani Tata McGraw Hill Education private Limited NEWDELHI McGraw-Hill Offices New Delhi Newyork St Louis San Francisco Auckland Bogot6 Caracas KualaLumpur Lis bon London Madrid Mexicocity Milan Montreal SanJuan Santiago SingaporeSydney Tokyo Toronto

Information contained in this work has been obtained by Tata McGraw-Hill, from Preface to the Third Edition sources believed to be reliable. However, neither Tata McGraw-Hill nor its authors guaranteethe accuracyor completenessof any information published hereiir, and neittier Sincethe appearanceof the secondedition in 1989,the overall energysituation Tata McGraw-Hill nor its authors shall be responsiblefor any errors, omissions,or has changed considerablyand this has generatedgreat interest in non- damages arising out of use of this information. This work is publi'shed-with the conventionaland renewableenergy sources,energyconservationand manage- understandingthat Tata McGraw-Hill and its authorsare supplying information but are ment,power reforms andrestructuringand distributedarrddispersedgeneration. not attempting to renderenginecringor other professionalservices.If such seryicesare Chapter t has been therefore,enlargedand completely rewritten. In addition, required, the assistanceof an appropriate professional should be sought the influencesof environmentalconstraintsare also discussed. TataMcGraw-Hill The present edition, like the earlier two, is designedfor a two-semester courseat the undergraduatelevel or for first-semesterpost-graduatestudy. O 2003,1989,1980T, ataMcGrtrwI{ill EducationPrivateI-imited Modern power systemshave grown larger and spreadover larger geographi- Sixteenthreprint2009 cal areawith many interconnectionbs etweenneighbouringsystems.Optimal RCXCRRBFRARBQ planning,operationand control of such large-scalesystemsrequireadvanced computer-basedtechniquesmany of which areexplainedin the student-oriented No part of thispublicationcanbe reproducedin anyform or by any -\"un, and reader-friendlymannerby meansof numericalexamplesthroughoutthis withoutthe prior writtenpermissionof the publishers book. Electric utility engineerswill also be benefittedby the book as it will pisreapmaerentahbelmetomsoerlef-astduedqyu'.Iahteelwytoidfearcaenthgeeonfetwopcihcasfllaecnigliteast.Tehsveesrstyaleriloesf ewlerictitniogn This editioncanbe exportedfrom India only by thepublishers, of chaptersand sectionsfbr completion in the semestertime frame. TataMcGraw Hill EducationPrivateLimited Highlights of this edition are the five new chapters.Chapter 13 deals with ISBN-13: 978-0-07-049489-3 power system security. Contingency analysis and sensitivity factors are ISBN- 10: 0-07-049489-4 described.An analyticalframeworkis developedto control bulk power systems in sucha way that securityis enhancedE. verythingseemsto havea propensity Publishedby TataMcGrawHill EducationPrivateLimited, to fail. Power systemsareno exception.Powersystemsecuritypracticestry to 7 WestPatelNagat New Delhi I l0 008, typesetin TimesRomanby ScriptMakers, control and operatepower systemsin a defensivepostureso that the effects of Al-8, ShopNo. 19, DDA Markct,PaschimVihar,NewDelhi ll0 063 andprintedat theseinevitable failures are minimized. GopaljeeEnterprisesD,elhi ll0 053 Chapter 14 is an introductionto the useof stateestimationin electricpower Coverprinter:SDR Printcrs systems.We have selectedLeast SquaresEstimationto give basic solution. External system equivalencingand treatmentof bad data are also discussed. The economics of power transmissionhas always lured the planners to transmit as much power as possible through existing transmission lines. Difficulty of acquiring the right of way for new lines (the corridor crisis) has always motivated the power engineersto develop compensatorysystems. Therefore,Chapter 15 addressescompensationin power systems.Both series and shuntcompensationof linqs have beenthoroughly discussed.Conceptsof SVS, STATCOM and FACTS havc-beenbriefly introduced. Chapter 16 covers the important topic of load forecasting technique. Knowing load is absolutelyessentialfor solving any power systemproblem. Chapter17 dealswith theimportantproblemof voltagestability.Mathemati- cal formulation, analysis, state-of-art, future trends and challenges are discussed.

Wl Preracero rne lhlrd Edrtion MATLAB andSIMULINK,idealprogramfsor powersystemanalysisare includedin thisbookasanappendixalongwith 18solvedexampleisllustrating Preface to the First theirusein solvin tive tem problems.The help rendered Mathematicaml odellingand solutionon digital computersis the only practical approachto systemsanalysis and planning studiesfor a modern day power by Shri Sunil Bhat of VNIT, Nagpur in writing this appendixis thankfully system with its large size, complex and integrated nature. The stage has, therefore,been reachedwhere an undergraduatemust be trained in the latest acknowledged. techniquesof analysisof large-scalepowersystemsA. similar needalsoexists in the industrywherea practisingpower systemengineeris constantlyfacedwith Tata McGraw-Hill and the authors would like to thank the following the challengeof therapidly advancingfield. This book hasbedndesignedto fulfil this needby integratingthe basicprinciplesof power systemanalysisillustrated reviewersof this edition: Prof. J.D. Sharma,IIT Roorkee; Prof. S.N. Tiwari, throughthe simplestsystemstructurewith analysistechniquesfor practicalsize systemsI.n this book large-scalesystemanalysisfollows asa naturalextension MNNIT Allahabad;Dr. M.R. Mohan, Anna University, Chennai;Prof. M.K. of the basicprinciples.The form andlevel of someof the well-knowntechniques are presentedin such a manner that undergraduatescan easily grasp and Deshmukh,BITS,Pilani;Dr. H.R. SeedharP, EC,Chandigarh;Prof.P.R.Bijwe appreciatethem. andDr. SanjayRoy, IIT Delhi. The book is designedfor a two-semestercourseat the undergraduatelevel. With a judicious choice of advancedtopics,some institutionsmay also frnd it While revising the text, we have had the benefit of valuable advice and useful for a first coursefor postgraduates. suggestionsfrom many professors,studentsand practising engineerswho used The readeris expectedto havea prior groundingin circuit theory andelectrical machines.He should also have been exposedto Laplace transform, linear the earlier editions of this book. All theseindividuals have influenced this differential equations,optimisation techniquesand a first course in control theory. Matrix analysisis appliedthroughoutthe book. However,a knowledge edition.We expressour thanksand appreciationto them. We hopethis support/ of simple matrix operationswould suffice and these are summarisedin an appendixfbr quick reference. responsewould continuein the future also. The digital computerbeing an indispensabletool for power systemanalysis, D P Kors[m computationalalgorithmsfor various systemstudiessuchasload flow, fault level I J Nlcn+rn analysis,stability, etc. have beenincludedat appropriateplacesin the book. It is suggestedthat wherecomputerfacilities exist, studentsshouldbe encouraged to build computerprograms for thesestudiesusing the algorithmsprovided. Further, the studentscan be asked to pool the various programsfor more advancedandsophisticatedstudies,e.g.optimal scheduling.An importantnovel featureof the book is the inclusionof the latestand practicallyusefultopicslike unit commitment, generationreliability, optimal thermal scheduling,optimal hydro-thermalschedulingand decoupledload flow in a text which is primarily meantfor undergraduates. The introductory chapter contains a discussionon various methods of electricalenergygenerationandtheir techno-economicomparisonA. glimpseis giveninto thefutureof electricalenergy.The readeris alsoexposedto theIndian power scenariowith facts and figures. Chapters2 and3 give the transmissionline parametersandtheseareincluded for the sakeof completnessof the text. Chapter4 on the representatioonf power systemcomponentsgivesthe steadystatemodelsof thesynchronoums achineand the circuit modelsof compositepower systemsalong with the per unit method.

preface ro rhe Frrst Edition Contents W Preface to First Edition vn Chapter5 deals with the performanceof transmissionlines. The load flow problemis introducedright at this stagethroughthe simple two-bussystemand 1. Introduction I basicconceptsof watt andvar control areillustrated.A brief treatmentof circle 1 . 1 A Perspective I concept of load flow and line compensation. ABCD constants are generally well 1 . 2 Structureof Power Systems I0 covered in the circuit theory course and are, therefore, relegated to an appendix. 1 . 3 ConventionalSourcesof Electric Energy I3 Chapter 6 gives power network modelling and load flow analysis, while r . 4 RenewableEnergy Sources 25 Chapter 7 gives optimal system operation with both approximate and rigorous treatment. 1 . 5 Energy Storage 28 1 . 6 Growth of Power Systemsin India 29 Chapter 8 deals with load frequency control wherein both conventional and 1 . 7 EnergyConservbtion 3I modern control approaches have been adopted for analysis and design. Voltage control is briefly discussed. r . 8 Deregulation 33 Chapters 9-l l discuss fault studies (abnormal system operation). The 1 . 9 Distributed and DispersedGeneration 34 synchronous machine model for transient studies is heuristically introduced to 1 . 1 0EnvironmentalAspectsof Electric Energy Generation 35 the reader. 1 . 1 1PowerSystemEngineersandPower SystemStudies 39 T . I 2Use of Computersand Microprocessors 39 Chapter l2 emphasisesthe concepts of various types <lf stability in a power 1 . 1 3ProblemsFacing Indian Power Industry and its Choices 40 system. In particular the concepts of transient stability is well illustrated through the equal areacriterion. The classical numerical solution technique of the swing References 43 equation as well as the algorithm for large system stability are advanced. 2. Inductance and Resistanceof Transmission Lines 45 Every concept and technique presented is well supported through examples employing mainly a two-bus structure while sometimes three- and four-bus 2 . 1 Introduction 45 illustrations wherever necessary have also been used. A large number of 2.2 Definition of Inductance 45 unsolved problems with their answers are included at the end of each chapter. 2.3 Flux Linkages of an Isolated These have been so selected that apart from providing a drill they help the reader develop a deeper insight and illustrate some points beyond what is directly Current-CtrryingConductor 46 covered by the text. 2.4 Inductanceof a Single-PhaseTwo-Wire Line 50 2 . 5 ConductorTypes 5I The internal organisation of various chapters is flexible and permits the 2.6 Flux Linkages of one Conductorin a Group 53 teacher to adapt them to the particular needs of the class and curriculum. If 2 . 7 Inductanceof CompositeConductorLines 54 desired, some of the advanced level topics could be bypassed without loss of 2 . 8 Inductanceof Three-PhaseLines 59 continuity. The style of writing is specially adaptedto self-study. Exploiting this 2 . 9 Double-CircuitThree-PhaseLines66 fact a teacher will have enough time at his disposal to extend the coverage of 2 . 1 0BundledConductors 68 this book to suit his particular syllabus and to include tutorial work on the 2 . l I Resistance 70 numerous examples suggestedin the text. 2 . r 2 Skin Effect and Proximity Effect 7I The authors are indebted to their colleagues at the Birla Institute of Problems 72 Technology and Science, Pilani and the Indian Institute of Technology, Delhi for the encouragement and various useful suggestionsthey received from them References 75 while writing this book. They are grateful to the authorities of the Birla lnstitute of Technology and Science, Pilani and the Indian Institute of Technology, Delhi 3. Capacitance of Transmission Lines 76 for providing facilities necessary for writing the book. The authors welcome any constructive criticism of the book and will be grateful for any appraisal by 3.1 Introduction 76 the readers. 3.2 Electric Field of a Long StraightConductor 76 I J NlcRArH D P KorHlnr

fW . contents . 3.3 PotentialDiff'erencebetweentwo Conductors 6.4 Load Flow Problem 196 of a Group of ParallelConductors 77 6.5 Gauss-SeidelMethod 204 6.6 Newton-Raphson(NR) Method 213 3.4 Capacitanceof a Two-Wire Line 78 6.7 DecoupledLoad Flow Methods 222 3.5 Capacitanceof a Three-phaseLine with EquilateralSpacing B0 UnsymmetricalSpacing BI 6.9 Controlof Voltage Profile 230 3.7 Effect of Earth on TransmissionLine capacitance g3 Problems 236 J\" .oo rl vt - ltel -ln- l(Jo ora \\rlvr . l^l-, /r. yl D^t--^---. )20 (vloollled) IIYJEIETLLCJ LJ7 3.9 BundledConductors 92 7. Optimal System Operation 242 Problems 93 7.I Introduction 242 1.2 Optimal Operation of Generatorson a Bus Bar 243 References 94 7.3 Optimal Unit Commitment (UC) 250 7.4 ReliabilityConsiderations 253 4. Representation,of Power System Components 95 1.5 OptimumGenerationScheduling 259 128 7.6 Optimal Load Flow Solution 270 4.1 Introduction g5 t84 7.7 OptimalSchedulingof HydrothermaSl ystem 276 4.2 Single-phaseSolutionof Balanced Problems 284 Three-phaseNetworks 95 References 286 4.3 One-LineDiagramand Impedanceor 8. Automatic Generation and Voltage Control 291'l ReactanceDiagram 98 8.1 Introduction 290 4.4 Per Unit (PU) System 99 8.2 Load FrequencyControl (SingleArea Case) 291 4.5 ComplexPower 105 8.3 Load FrequencyControl and 4.6 SynchronousMachine 108 4.7 Representatioonf Loads I2I EconomicDespatchControl 305 8.4 Two-Area Load FreqlrencyControl 307 Problems 125 8 . 5 Optimal (Two-Area) Load FrequencyControl 3I0 References 127 8 . 6 AutomaticVoltage Control 318 8 . 7 Load FrequencyControl with Generation 5. Characteristics and Performance of power 321 Transmission Lines Rate Constraints(GRCs) 320 8 . 8 SpeedGovernor Dead-Bandand Its Effect on AGC 5.1 Introduction 128 8.9 Digital LF Controllers 322 5.2 ShortTransmissionLine 129 8 . 1 0DecentralizedControl 323 5.3 Medium TransmissionLine i37 5.4 The LongTransmissioLnine-Rigorous Solution I 39 Prohlents 324 5.5 Interpretationof the Long Line Equations 143 References 325 5.6 FerrantiEffect 150 5.1 TunedPowerLines 151 9. Symmetrical Fault Analysis 327 5.8 The EquivalentCircuit of a Long Line 152 5.9 Power Flow througha TransmissionLine I58 9.1 Introduction 327 5 .1 0 Me th o d so l ' V o l ra g eC o n trol 173 9.2 Transienton a TransmissionLine 328 9.3 ShortCircuit of a SynchronouMs achine Problems 180 References 183 (On No Load) 330 9.4 ShortCircuit of a LoadedSynchronousMachine 339 6. Load Flow Studies 9.5 Selectionof Circuit Breakers 344 6.1 lntrotluction 184 6.2 NetworkModel Formulation I85

rffi#q confenfs I' 9.6 Algorithm for ShortCircuit Studies 349 9.7 Zsus Formulation 355 Problems 363 References 368 Symmetrical Com 12.10MultimachineStabilitv 487 10.1 Introduction 369 Problems 506 10.2 SymmetricalComponentTransformation370 References 508 10.3 PhaseShift in Star-DeltaTransformers 377 10.4 SequenceImpedancesof TransmissionLines 379 13. Power System Security 10.5 SequenceImpedancesand SequenceNetwork 13.1 Introduction 510 of PowerSystern 381 13.2 SystemStateClassification 512 10.6 SequenceImpedancesand Networks of 13.3 SecurityAnalysis 512 13.4 ContingencyAnalysis 516 SynchronousMachine 381 13.5 SensitivityFactors 520 10.7 SequenceImpedancesof TransmissionLines 385 13.6 Power SystemVoltage Stability 524 10.8 SequenceImpedancesand Networks References 529 of Transformers 386 10.9 Constructionof SequenceNetworks of 14. An Introduction to state Estimation of Power systems 531 a Power System 389 l4.l Introduction 531 Problems 393 I4.2 Least SquaresEstimation: The Basic References 396 Solution 532 ll. Unsymmetrical Fault Analysis 397 14.3 StaticStateEstimationof Power 433 Systems 538 11.1 Introduction 397 11.2 SymmetricalComponentAnalysis of I4.4 Tracking StateEstimation of Power Systems 544 14.5 SomeComputationaCl onsiderations 544 UnsymmetricalFaults398 14.6 External SystemEquivalencing 545 , 11.3 Single Line-To-Ground(LG) Fault 3gg I4.7 Treatmentof Bad Dara 546 14.8 Network observability and Pseudo-Measurementss49 11.4 Line-To-Line(LL) Fault 402 14.9 Application of Power SystemStateEstimation 550 11.5 Double Line-To-Ground(LLG) Fault 404 11.6 Open ConductorFaults 414 Problems 552 11.1 Bus ImpedanceMatrix Method For Analysis References 5.13 of UnsymmetricaSl huntFaults 416 Problems 427 15. Compensation in Power Systems 550 References 432 15.1 Introduction 556 12. Power System Stability 15.2 LoadingCapability 557 15.3 LoadCompensation 557 12.1 Introduction 433 15.4 Line Compensation 558 12.2 Dynamics of a SynchronousMachine 435 15.5 SeriesCompensation 559 12.3 Power Angle Equation 440 15.6 ShuntCornpensators 562 12.4 Node Elimination Technique 444 I5.7 ComparisonbetweenSTATCOM and SVC 565 I2.5 SimpleSystems 451 15.8 FlexibleAC TransmissionSystems(FACTS) 566 12.6 Steady StateStability 454 15.9 Principleand Operationof Converrers 567 12.7 Transient Stability 459 15.10FactsControllers 569 I2.8 Fq'-ralArea Criterion 461 References 574

16. Load Forecasting Technique 16.1 Introduction 575 16.2 ForecastingMethodology 577 timation of Averageand Trend Terms 577 16.4 Estimationof PeriodicComponents 581 1 6 . 5 Estimationof y., (ft): Time SeriesApproach 582 1 6 . 6 Estimationof StochasticComponent: Kalman Filtering Approach 583 16.7 Long-TermLoad PredictionsUsing EconometricModels 587 r 6 . 8 ReactiveLoad Forecast 587 References 589 17. Voltage Stability 591 11.1 Introduction 591 I.T A PERSPECTIVE 17.2 Comparisonof Angle and Voltage Stability 592 17.3 ReactivePowerFlow and Voltage Collapse 593 Electric energy is an essentialingredient for the industrial and all-round 11.4 MathematicalFormulationof developmentof any country.It is a covetedform of energy,becauseit can be generatedcentrallyin bulk and transmittedeconomicallyover long distances. Voltage StabilityProblem 593 Further, it can be adaptedeasily and efficiently to domesticand industrial 11.5 Voltage StabilityAnalysis 597 applications, particularly for lighting purposesand rnechanicalwork*, e.g. 17.6 Preventionof VoltageCollapse 600 drives.The per capitaconsumptionof electricalenergyis a reliableindicator ll.1 State-of-the-Art,Future Trends and Challenses 601 of a country's stateof development-figures for 2006 are615 kwh for India and 5600 kWh for UK and 15000kwh for USA. References 603 Conventionally,electricenergyis obtainedby conversionfiom fossil fuels Appendix A: Introduction to Vector and Matrix Algebra 605 (coal,oil, naturalgas),andnuclearand hydro sourcesH. eatenergyreleasedby burning fossil fuels or by fissionof nuclearmaterialis convertedto electricity Appendix B: Generalized Circuit Constants 617 by first convertingheatenergyto the mechanicaflorm througha thermocycle and then convertingmechanicalenergy throughgeneratorsto the electrical Appendix C: Triangular Factorization and Optimal Ordering 623 form. Thermocycleis basicallya low efficiencyprocess-highestefficiencies for modernlargesize plantsrangeup to 40o/ow, hile smallerplants may have Appendix D: Elements of Power System Jacobian Matrix 629 considerably lower efficiencies. The earth has fixed non-replenishablere- sourcesof fossil fuels and nuclear materials,with certain countries over- Appendix E: Kuhn-Tucker Theorem 632 endowedby natureand othersdeficient.Hydro energy,thoughreplenishable,is alsolimited in termsof power.The world's increasingpowerrequirementscan Appendix F: Real-time Computer Control of power Systems 634 only be partially met by hydro sources.Furthermore,ecologicaland biological factorsplace a stringentlimit on the useof hydro sourcesfor power production. Appendix G: Introduction to MATLAB and SIMULINK 640 (The USA has already developed around 50Voof its hydro potential and hardly any furtherexpansionis plannedbecauseof ecologicalconsiderations.) Answers to Problems x Electricity is a very inefficient agentfor heatingpurposes,becauseit is generatedby Index the low efficiency thermocyclefrom heat energy. Electricity is used for heating purposesfor only very special applications, say an electric furnace.

with the ever in__c_r__e_a_-s-^iDngper capitaev^n,vet6rJgyvcuorrnJLsuurlpm[ruplttionailtnlud gexxpopnognnllea ntially Introduction rising population, technologists already r* the end of the earth,ss nocn - fuel trhei ss of a. uc tr.cIensf-*aT. chte,woei lc ac nr ins iosloofn intense pollution in their programmes of energy development.Bulk power dllfreanwinslaatbtelentionto th e 1970shas dramatically generatingstations are more easily amenableto control of pollution since centralizedone-point measurescan be adopted. tor generationof electricity. In terms of bulk electric energy generation,a consumptionon a worldwidebasis.This figure is expectedto rise as oil supply distinct shift is taking placeacrossthe world in favour of coalLJin particular for industrial usesbecomesmore stringent.Transportationcan be expectedto go electric in a big way in the long run, when non-conventionalenergy Cufiailment of enerry consumption resourcesare we[ developedor a breakthroughin fusion is achieved. mlTeheveealne,swnoehfrircgehydctuhocinsinspgulatmhnipsettliecoavnenolnf.oTmthaoefsfdoterddve.evTleohlpeoirnpegcicdsoc, iounnrrftanrictertis,e,aoshnnaetsheeadltorotehfaiencrdlhyrawenaadyc,shhaaenvcadel To understandsomeof the problems that the power industry faces let us catoomninestnteaitnniestlisyfytdothraethwireeuirfpfooterntestmhtoeinrgaeixsmpeeitlhlriioeeninrscle.evsoeoflfotcfhoeeunrdeseregv,ye-ipnloropddeoudicnctgoiou,nnottoritpehrs\"oyavninddeegebudaastroidc briefly review some of the characteristic featuresof generation and transmis- againstobsoletetechnology. sion.Electricity, unlike water and gas, cannotbe storedeconomically (except in very small quantities-in batteries),and the electricutility can exerciselittle rntensification of effofts to develop alternative sources of control over the load (power demand) at any time. The power system must, therefore,be capableof matching the output from generatorsto the demand at anytime at a specifiedvoltageandfrequency.The difficulty encounteredin this task can be imagined from the fact that load variationsover a day comprises three components-a steady component known as base load; a varying componentwhose daily patterndependsupon the time of day; weather,season, a popular festival, etc.; anda purely randomly varying componentof relatively small amplitude. Figure 1.1showsa typical daily load curve.The characteris- tics of a daily load curve on a grossbasis are indicatedby peak load and the time of its occurrenceand load factor defined as enerw including unconventional sources like solan tidal averageload = lessthan unity energy, etc. maximum (peak)load Distant hopesarepitched on fusion energybut the scientific and technological 100 pardovvaidneceasnhainveexahlaounsgtibwlaesyotuorcgeooifnetnheisrgrye.gAarbdr.eFauks-itohnrowuhgehninhathrenecsosnevdecrosuioldn from solar to electricenergy could pr*io\" anotheranswerto the world,s B steeplyrising energyneeds. Recyclingr of nuclear wastes EBo Fast breederreactortechnologyis expectedto provide the answerfor extending c nuclear energyresourcesto last much longer. o D e velopm ent an d applicati on of an ttpollu tion techn ologries tr dInevtehliospreedgcaorudn, tthrieesdwehveelroepbiyngthceoyucnatrnieasvaolrideagdoyinhgavtehrtohueghextahme pplheaosfesthoef cAmr*nev'uDnaac'ttrhueyrrwibyinae.hglTyisleeoh'Ansetfdtsiiste5mhs0eieaosytpnteciarmashobraajlseetv;ecsemstebe,ahvcdtoececwrnoraipenalcvuslsoeutumfrmo,nacrptryattihineocfnsoanworrratrirlybteleesufsacrs,ecorwvegilcaesasreolldnrle'ibdoodeguialyas,sosgsnhhaediossgraahtthranleyegdnecdmosoeoitdapfedelcaxlnoenpdaceaollclbfiatsleetfshtd.eietoro2nnl2eaa0xbs0tlte :6o 6 0 E l+o xo Fig. 1.1 Typicaldailyloadcurve The average load determines the energy consumption over the day, while the peak load along with considerations of standby capacity determines plant capacity for meeting the load.

gA.eAsnhienirgadlhhival ovideaaudroftaiamarcecdtuodevrJrln,vh; eteurnrhliipsr(xyasa,wvwi nrrherJgidcirhmrawoowrhe*nenengn\";e6mrr1,go#iyl rlureo\"me;,&n\"a;''e.;g;ir\"i.vigr,e;ii;nylii;,,*jiinil'jsnntauflfla,i'tiuon\".n I pdemoixstwceteearrcns. oscPnehoniwgehectrviooofnlta,arpggleraternaaatnjaildysumsdinnisjgasticiogknhinlto\"gt\"uor,F*ahtanpl\",ear\"ifoahdc\"st\"ios\"ritsera;vt;'a;e\"p*cr-j-u;in;a,&:t;e\"vP;dti#rhJuJrropurwgehrlvoicnsg , n , . uI * I ' , i | To:try:\"n9d.:.o\"_lTlth:efu:n,_itsTprjo_d.u:clleTadn:1dt1he,r:e::fo.\"reo1n:t,h1€.tuj:eiljc:h::a.r,gj:ejas:n*dTth:ej wages I of Tthaer.isfftasttriounc.tsutareffms. aybe suchasto influencetheloadcurveandto improve i s\"j:9.fi\",.:'' | Tariff should consider the pf (power factor) of the load of the consumer. ] If it is low, it takes more current for the same kWs and hence Z and D Diversity Factor i i;;;;.i.\" and distribution) losses are conespondingly increased.The drhiisvisiddbeeny,ndrea,*\"dst*hies-uum-o-fiin;d#iv\"id#umUaalHxim:fufdimeTmTanfoid,nst1he\"cfofn\"s:u\"mil:efrfsi,:Ii :::#m::r*,':_::\"i.,*':J\"i:f[f1\"tHf,z.%j,\"f\".l,'i,\".\"dirT13:H$:::T\"g*l\"Y\"riiil:''J.:],fff;ffi::_f'iJi*\"\",1:t.r;iff; ::::*1\":i\"\"1\".:1t:,i1.\";'f.t:;;:3,\"\"':?\";:ffii\"T,\"-jTi,ffiHtr:;'3f;:xll#1rJ,ffi?,1?Til'jli[l,i\"ftfHi\":tsJ,'?tr\"J;ii:.\"e::u.1n9'ictd,v.riv\"detrnarniutsv\"mtoitsr's,pi\"or'aniont;rt.f;J'a;u\";th;;eidl.e;m;;a;;n;d\"irls-T\"ff;;i\"? ,;\"'11'f,;: -- * i -:,':T\":.-\"::i,\"\":\"^::::\":--\":J ma ptfhpaenraelteyc:,la:lfu\"esTem:la:y_b^e,im:Tp_ol se;i;tdf1of;n:tYhe_cTon;^;s\":u\"*m;;'e-r-. more.Luckily, rhefactoris muchhighertrranunity, f-;;#; i lil loads. I tlil , \"il*t, (iiD the consumermay be askedto use shuntcapacitorsfor improving the A high diversity factor could be obtained bv; I po*er factor of his installations. 1' Giving incentivesto farmers and/or someindustriesto use electricity in tuhrue rnuiEgihrrt ourr UligBhI|Lr rloaaod ppeefrloioosd.s. 2 using daylight saving as in many other counfies. Llg4\" 1'1 L------ 3' staggering the offrce timings A factory to be set up is to have a fixed load of 760 kw gt 0.8 pt. The electricrty board offeri to supplJ, energy at the following alb;ate rates: 4' Having different time zones in the country like USA, Australia, etc. L 5' oudHfneapivkteiVnonoAgdftheeendtnwrteeoomfran-gacpyttnaohcdrroetsinnmtussastuareeixmfafdimdefduroien.mfsqoukwmWedhneeitmuctltyiohamn3aepdcreseohnc:neaoslnuimzsmeauekmtore\"esOh,rai.pisluocsfthoatuor'pg*\"ahely.odg*o;\"a?, ntfto\"a.tminu\"o\"u\"tuso\"ntir,.t (a) Lv supply at Rs 32ftvA max demand/annum + 10 paise/tWh plant capacity foctor i I (b) HV supply at Rs 30/kvA max demand/annum + l0 paise/kwh. rne lrv switchgear costs Rs 60/kvA and swirchgearlossesat full load amount to 5qa- Intercst depreciation charges ibr the snitchgear arc l29o of the capital cost. If the factory is to work for 48 hours/week, determine the more e.conomical tariff. - Actual energyproduced 7@ m a x i m u m p o s s i b l e e ' m -s o f u t i o n M a x i m u m d e m a n d = 0 3 = 9 5 0 k v A @asedon instarelptant capaciiyy Loss in switchgear= 5% _ Average demand .. InPut dematrd= j-950 = 1000 kvA Installedcapacity of switchgear= 60 x 1000= Rs 60,000 Plant usef(tctor I Annual char\"goesston degeciation= 0.12x 60,000= Rs 7,200 ' Annual fixed chargesdue to maximum demandcorrespondingto tariff (b) _ _ --_ AxctTuaimleen(-ei.nrgh.yop-ur,o:r-sd)uthc-\"e-pd(lkuWnrhh)^ plant i = 30 x 1.000= Rs 30,000 capacity(kw) b;i\" il;;ti\"\" Annual running chargesdueto kwh consumed Tariffs = 1000x 0.8 x 48 x 52 x 0.10 oT+fhcethxceokpsWotwohf)erepoleeurctatprnuicntp;ubomwd,weehprieesrnendo4sorimns aathllryeixgmeivaaexcnilmabruygmethdfe_eme,xfap,\"nrdeoosiisnfiifot,i'nrin\"(aas\"+ypr\"iDe.a-x\"*akWno = Rs 1.99.680

Introduction WI I t .'.600+0.03 4E-too-o.r3dE= o Total charges/annum= Rs 2,36,gg0 dP dP Max. demandcorrespondingto tariff(a) j 950 kVA or dE=3m dP Annual running chargesfor kWh consumed l\"' d E = d P x t =950x0.8x48x52x0.10 = Rs t,89,696 From triangles ADF and ABC, 5,00,000-P_ 3000 Total= Rs 2,20,096 5,00,000 8760 Therefore, tariff (a) is economical. P = 328,say 330MW Capacityof thermalplant= 170MW Energy generatedby thermal plant = 1 7 0 x 3 0 0 0 x 1 0 0 0 ttIAhhoeiasrrdemlgodaiauold.rnaTbhthiyaoesnsceacotutmsrintvasgexaucirmpeanuaamsbgeuednnaedesmesraaru:tnmindegodsftyo5s0bte0emMa,wWtrhiaiacnhtgaliesr.opTaahdretlfyaucthitlyoitdryroohf aa5sn0tdovpoma.Trethreyet = 255 x106kwh Energy generatedby hydro plant = 1935x i06 kwh Total annual cost = Rs 340.20 x 106/year Hydro plant: Rs 600 per kw per annum and operatingexpensesat 3p per kWh. overalgl eneratiocons=t ###P x 100 Thermal plant: Rs 300 per kw per annumand operatingexpensesat r3p = 15.53paise/kWh ea Determinethe tionchoysdt proepr rkTW!,h.rheenergygenerateadnnuallyby ch, and overall :gfefinlye:rfa Solution Total energy generatedper year = 500 x 1000 x 0.5 x g760 A generatingstationhasa maximum demandof 25 MW, a load factor of 6OVo, a plant capacity factor of 5OVo,and a plant use factor of 72Vo.Find (a) the - 219 x 10' kwh daily energy produced, (b) 'the reservecapacity of the plant, and (c) the maximum energy that could be produceddaily if the plant, while running as Figure 1.2 shows the load duration per schedule,were fully loaded. curve. Since operatingcostof hydro plant is low, the baseload would be supplied I Solution from the hydro plant and peak load from 500,000- P the thermal plant. Load factor = averagedemand m a x i m u md e m a n d Ler the hydro capacity be p kW and the energy generaredby hydro plant E 0.60 = averagedemand kWh/year. 25 Thermal capacity= (5,00,000_ p) kW B Hours afoo Average demand= 15 MW Thermal energy = (2lg x107_ E) kwh 0 Annual cost of hydro plant Plant capacity factor = averagedemand ;#;;..0\".,,, =600P+0.03E Fig. 1.2 Loaddurationcurve l5 Annual cost of thermarplant = 300(5,00,000- p) + 0.r3(zrg x r07_ n) 0 . 5 0= installedcapacity Total cost C = 600p + 0.038 + 300(5,00,000_ p) Installedcapacity= +0=.5 30 MW + 0.t3(219 x 107_ E) For minimum cost, 4Q- = 0 dP

Introduction N Reservecapacity of the plant = instalredcapacity - maximum demand I =30-25=5MW The annualload factor of the total plant = 1 . 0 7 5 x 1 0 E x 1=060135%o Daily energyproduced= flver&g€demandx 24 = 15 x 24 20,000x 8760 =360MWh CommentsThe various plant factors, the capacity of base and peak load Energycorrespondintog installedcapacityper day units can thus be found out from the load duration curve. The load factor of =24x30_720MWh than that of the base load unit, and thus the axlmum energy t be produced cosf of power generation from the peak load unit is much higher than that from the baseload unit. _ actualenergyproducedin a day plant usefactor i' -;;;'\"-;. -- -l* -i \" = :09.7 = 5ooMWh/day There are threeconsumersof electricity having different load requirementsat 2 different times.Consumer t has a maximum demandof 5 kW at 6 p.m. and a demandof 3 kW at 7 p.m. and a daily load factor of 20Vo.Consumer2 has From a load durationcurve, the folrowing data are obtained: a maximum demandof 5 kW at 11 a.m.' a load of 2 kW at 7 p'm' and an Maximum demandon the sysremis 20 Mw. The load suppliedby the two averageload of 1200 w. consumer 3 has an averageload of I kw and his maximum demandis 3 kW at 7 p.m. Determine:(a) the diversityfactor, (b) units is 14 MW and 10 MW. Unit No. 1 (baseunit) works for l00Voof the the load factor and averageload of eachconsumer,and (c) the averageload time, and Unit No. 2 (peakload unit) only for 45vo of the time. The energy and load factorof the combinedload. g e n e r a t e d b y u n iIt i s 1 x 1 0 8 u n i t s , a n d t h a t b y u n izt i s 7 . 5 x 1 0 6 u n i t s . F i n d the load factor, plant capacityfactor and plant use factor of each unit, and the Solution MD5KW 3kw LF load factor of the total plant. (a) ConsumerI at6pm ZOVo Solution MD5KW atTpm Averageload Consumer2 at 11 am 1\\2kW Annual load factor for Unit 1 = 1 x 1 0 8 x 1 0 0:81.54V o MD3KW 2kw Average load 14,00x0 8760 Consumer3 atTpm 1kw atTpm The maximumdemandon Unit 2 is 6 MW. Maximum demand of the systemis 8 kW at 7 p'm' Annual load factor for Unit 2 = 7 . 5 x 1 0x61 0 0 = 14.27Vo 6000x 8760 sum of the individual maximum dernands= 5 + 5 + 3 = 13 kw Loadfactor of Unit 2 for the time it takesthe load DiversitYfactor = 13/8= 7.625 7.5x106x100 (b) ConsumerI Averageload 0'2 x 5 = I kW, LF= 20Vo 6 0 0 0x 0 . 4 5 x 8 7 6 0 Consumer2 Averageload 1.2kW, LF= l'2*1000-24Vo = 3I.7I7o 5 Since no reserveis available at Unit No. 1, its capacity factor is the Consumer3 Averageload I kW, I 100-33.3Vo sameas the load factor,i.e. 81.54voA. lso sinceunit I has beenrunning LF= 5x throughoutthe year, the plant use factor equalsthe plant capacityfactor i . e .8 1 . 5 4 V o . (c) Combinedaverageload = I + l'2 + l = i . 2 k W Annual plant capacityf'actorof Unit z = 100 = 8'567o Combinedload factor = + x 1 0 0= 4 0 V o lloPxggx 7 6 o x l o o Plant use factor of Unit 2 = 1 0 7.5x106x100 = 01 9. 027 o Load Forecasting x0.45x8760x1 0 As power plant planning and constructionrequire a gestationperiod of four to eight yearsor evenlonger for the presentday superpower stations,energy anrl load demandfnrecastingplays a crucialrole in power systemstudies.

ffiil,ftffi| ModernpowerSyslemnnatysis I This necessitatelsong rangeforecasting.while sophisticatedprobabilistic lntroduction methodsexist in literature[5, 16, 28], the simple extrapolationtechnique is quite adequatefor long range forecasting.since weatherhas a much more system(gtid,area) to another.A distributionsystemconnectsall the loads in influence on residentialthan the industrial component,it may be better to a particularareato the transmissionlines. prepareforecast in constituentparts to obtain total. Both power and energy For economicaal ndtechnologicarl easons(which will be discussedin detail uru ractorsrnvolved re ng an involved electricallyconnectedareasor regionalgrids (also called power pools). Each processrequiring experienceand high analytical ability. areaor regionalgrid operatestechnicallyand economically independently,but theseare eventuallyinterconnected*to form a national grid (which may even Yearly forecastsare basedon previous year's loading for the period under form an internationalgrid) so that eachareais contractuallytied to other areas considerationupdatedby factors such as generalload increases,major loads in respectto certaingenerationand schedulingfeatures.India is now heading and weathertrends. for a nationalgrid. In short-term load forecasting,hour-by-hour predictions are made for the The siting of hydro stations is determinedby the natural water power sourcesT. he choiceof site for coalfired thermalstationsis more flexible. The decadeof the 21st century it would be nparing2,00,000Mw-a stupendous following two alternativesare possible. task indeed.This, in turn, would require a correspondingdevelopmeniin coal resources. l. power starionsmay be built closeto coal tnines(calledpit headstations) T.2 STRUCTURE OF POWER SYSTEMS and electric energy is evacuatedover transmission lines to the load Generatingstations,transmissionlines andthe distributionsystemsare the main centres. componentsof an electricpower system.Generatingstationsand a distribution systemareconnectedthroughtransmissionlines,which alsoconnectone power Z. power stationsmay be built close to the load ceutresand coal is * 38Voof the total power required in India is for industrial consumption.Generation transportedto them from the mines by rail road' of electricityin India was around 530 billion kWh in 2000-2001 A.D. compared to less than 200 billion kWh in 1986-87. In practice,however,power stationsiting will dependuponmanyfactors- technical, economical and environmental.As it is considerablycheaper to transport bulk electric energy over extra high voltage (EHV) transmission lines than to transportequivalentquantitiesof coal over rail roqd, the recent trends in India (as well as abroad)is to build super (large) thermal power stations near coal mines. Bulk power can be transmitted to fairly long distancesover transmissionlines of 4001765kV and above.However, the country's coal resourcesare locatedmainly in the easternbelt and some coal fired stationswill continueto be sitedin distantwesternandsouthernregions. As nuclearstationsare not constrainedby the problemsof fuel transport and air pollution, a greater flexibility exists in their siting, so that these stationsarelocatedclose to load centreswhile avoidinghigh densitypollution areasto reducethe risks, howeverremote,of radioactivityleakage. *Interconnectionhas the economic advantageof reducing the reserve generation capacity in eacharea.Under conditionsof suddenincreasein load or loss of generation in one area,it is immediately possibleto borrow power from adjoininginterconnected areas.Interconnectioncauseslargercurrentsto flow on transmissionlinesunderfaulty condition with a consequent increase in capacity of circuit breakers. Also, the centres.It providescapacity savingsby seasonael xchangeof power betweenareas having opposing winter and summer requirements.It permits capacity savings from time zones and random diversity. It facilitates transmissionof off-peak power. It also gives the flexibility to meet unexpectedemergencyloads'

:p^l:ayInnftts.Ins(idnical,uaadsniondfg.onnotuhwcel,erasacb.roo).2uat3l7vi5sovtfohrooemffeumleeorcsftortilrcypmhoyowdsretorosuftsatehtdieoissnrgseaeannmdeZpravlatoen.dctinso,mtthheeefrrrmoemaslt substationw, herethe reductionis to a rangeof 33 to 132kV, dependingon the transmissionline voltage. Some industriesmay require power at thesevoltage a O Generatinsgtations .qi-aji, '-qff-9-a,at 11kV- 25kv level. The next stepdownin voltageis at the distributionsubstation.Normally, two Transmissiolnevel T i e l i n e st o (220kv - 765 kV) othersystems distribution voltagelevels are employed: Large l. The primary or feedervoltage(11 kV) consumers 2. The secondaryor consumer voltage (440 V three phase/230V single Smalcl onsumers phase). Fig. 1.3 schematic diagram depicting power system structure The distribution system, fed from the distribution transformer stations, suppliespower to ttre domesticor industrial and commercialconsumers. Thus, the power system operatesat various voltage levels separatedby transformer.Figure 1.3 depicts schematicallythe structureof a power system. Though the distribution system design, planning and operation are subjects of great importance,we are compelled,for reasonsof space,to exclude them from the scopeof this book. 1.3 CONVENTIONAL SOURCES OF ELECTRIC ENERGY Thermal (coal, oil, nuclear) and hydro generationsare the main conventional sources of electric energy. The necessity to conserve fosqil fuels has forced scientists and technologists across the world to search for unconventional sourcesof electric energy. Some of the sourcesbeing explored are solar, wind and tidal sources.The conventional and someof the unconventionalsourcesand techniquesof energy generationarebriefly surveyedhere with a stresson future trends, particularly with referenceto the Indian electric energy scenario- Ttrermal Power Stations-Steam/Gas-based The heatreleasedduring the combustionof coal, oil or gas is usedin a boiler to raise steam.In India heat generationis mostly coal basedexceptin small sizes, becauseof limited indigenous production of oil. Therefore, we shall discussonly coal-fired boilers for raising steamto be used in a turbine for electric generation. The chemical energy stored in coal is transformed into electric energy in thermal power plants. The heat releasedby the combustion of coal produces steamin a boiler at high pressureand temperature,which when passedthrough a steamturbine gives off someof its internal energy as mechanicalenergy. The axial-flow type of turbine is normally used with severalcylinders on the same shaft. The steamturbine acts as a prime mover and drives the electric generator (alternator). A simple schematicdiagram of a coal fired thermal plant is shown in Fig. 1.4. The efficiency of the overall conversionprocessis poor and its maximum value is about4OVobecauseof the high heatlossesin the combustiongasesand

E rt^-r^-- h-.-^- ^ rntroduction Effi coaofnfodliitnnhgec'olTaorhlgienegsqtuetoaawnmteiptrysoowofer hriensattoat rtieaojnesoctrtpeeeadrmtaotleathskoeencinothnetdheRenacsnaeksrwienheoifccyhdcihrleae,scmttocoobdneifdigeeidnvestoenr perhaps increase unit sizes to several GWs which would result in better generatingeconomy. Air and thermal pollution is always presentin a coal fired steam plant. The rfttuiehunsherianbelgsianstteeetsaasdtemtoseaftmsea\\tovahfvtfmiaes'ytbrivsslteriihtDtzeeherdhew,ianhnarsirrsgde.hdbuteueirtsreitonrn'ne.plpadro.alstiornsrti.citbuahrlleeIelnyateupscerrenebxinsapinsnaeuelncrfefwdaiclehidaeeenrnnbdeecyriyttgeaiyimssn) poeceebxaxrptantaa;tu;in;bnredee.edidbinw\"tycuhirtirhre\"oera.uhsgesehtaderttnahibn\"meyg COz,SOX, etc.) are emitted via the exhaustgasesand thermal pollution is due osfskttmtsuuohoohnhwannreao-ovhii2Tlirettoccinims.s5nonnkkpt0eeocvgacctStnaifoloraMcariaaanonafakntnWtnncelhpbaelbdcmeeaesaesewbcleuhdisieaeztniannivytoxregcysstgiaspl'atshtetotenTeae)uesrfar,tnhlpasmtialzsehdeuaotegeedeinwllteooll|cuiuaaapvohtnflrsstrtrnofeeligeoyohmd.nctesihniAltonguaoreoge,conhcnnnuarccupsheigttnaaotdubrarrldiprd.oealmgndeeditwnsectihefniiadintofteilpghiilseicforclstiseiishontcsseosteoasuoonuaftslcfcccnupsgthshayieeaepotia.iragcvremsionTipnkrinlonziaahJikfgflefoinrro\"icoglyalmiwooanikeKllweanwyaaarcfsrtarthoeusgatgat,fqeheptbedn.ulksrayvtouaTicchcarntgrsohaeeiniiteios\"tlyzyt[eyixita3ieouns(pcog]s*wnagerfte\"otoihrihh,eutnfeudeiedpocbuauorthcolrfnerlcuar}secuieovarbmtomutsomprocrcag.eespouohyvsLn.alnrfeiosTdaebca1oraahseetpgphu0niirtrseeeaosned0,rrr to the rejected heat transferred from the condenserto cooling water. Cooling towers are used in situations where the stream/lake cannot withstand the thermal burden without excessivetemperaturerise. The problem of air pollution can be minimized through scrubbers and elecmo-staticprecipitators and by resorting to minimum emission dispatch [32] and Clean Air Act has already been passedin Indian Parliament. Fluidized-bed Boiler The main problem with coal in India is its high ashcontent (up to 4OVomax). To solve this, Jtuidized bed combustion technologyis being developed and perfected.The fluidized-bedboiler is undergoingextensivedevelopmentandis being preferreddue to its lower pollutant level and better efficiency. Direct ignition of pulverized coal is being introducedbut initial oil firing supportis needed. Cogeneration Stack uAEh Step-up Considering the tremendousamount of waste heat generatedin tlbrmal power transformer generation,it is advisableto save fuel by the simultaneousgenerationof 10-30kv / electricity and steam(or hot water) for industrial use or spaceheating. Now C o o l i r r gt o w e r called cogeneration,such systemshave long beencommon, here and abroad. -Condenser Currently, there is renewedinterestin thesebecauseof the overall increasein Burner energy efficiencieswhich are claimed to be as high as 65Vo. Cogeneration of steam and power is highly energy efficient and is Preheated air Forced particularlysuitablefor chemicals,paper,textiles,food, fertilizer andpetroleum mill draft fan refining industries.Thus theseindustriescan solveenergyshortageproblem in a big way. Further,they will not haveto dependon the grid power which is not Flg. 1.4 schematicdiagramof a coarfiredsteamprant so reliable. Of coursethey can sell the extra power to the governmentfor use cgpcjreoeonmnIdnesmuriactiiIsetenosdsdriuosiuasenne,veidtedinirsanaitzltr1euTo9rrtibsoo7orm0(gsnabeenatnhadyere.srlyatBaft1hiotro2arssr0rteaw0tts5iMnHo0dwfe0i5an) 0veM0yslwi.mMEEiWltfeefsocdurtcrtpsiabcepyaaraltrtshcheieLetoyrinmmp.Teiatotoreldmuddaniseyi(s;vtBsiebHmhlloaeEaodcLxusi)mbrrrDheueaeemnsrnt. in deficient areas.They may aiso seil power to the neighbouringindustries,a conceptcalled wheelingPower. 19,500MW -and As on 3I.12.2000,total co-generationpotentialin India is actual achievementis 273 MW as per MNES (Ministry of Non-Conventional Energy Sources,Governmentof India) Annual Report 200H1. There are two possible ways of cogenerationof heat and electricity: (i) Topping cycle, (ii) Bottoming cycle. In the topping cycle, fuel is burnt to produce electrical or mechanicalpower and the waste heat from the power generationprovidesthe processheat.In the bottomingcycle, fuel first produces processheat and the waste heat from the process6sis then used to produce power.

H I f-osCsiol-aflu-feirlepdlapnltasn; ttshesshearinecelunvdiero\"namciednrtaailnp\"roabnledmthsew,i,tghreseonmheouosthee,e,rffteypcet.s of The oldest and cheapestmethod of power generationis that of utilizing the Gas Turbines potential energy of water. The energy is obtained almost free of nrnning cost and is completely pollution free. Of course, it involves high capital cost With increasing availability of natural gas uangladesh)primemoversbasedon gas turbines have been developedon the requires a long gestation period of about five to eight years as compared to lines similar to those used in aircraft. Gas combustion generateshigh four to six yearsfor steamplants. Hydroelectric stationsare designed,mostly, temperatures and pressures, so that the efficiency of the las comparable to that of steamturbine. Additional advantageis that turbine is as multipurpose projects such as river flood control, storage of irrigation and exhaust gas drinking water, and navigation. A simple block diagram of a hydro plant is from the turbine still has sufficient heat content, which is used to raise steam given in Fig. 1.6. The vertical difference betweenthe upper reservoir and tail to run a conventional steam turbine coupled to a generator. This race is called the head. combined-cyclegas-turbine(CCGT) plant. The schernaticdiagram is called plant is drawn in Fig. 1.5. of such a Surgechamber Headworks Spillway Valve house Reservoir Pen stock Powerhouse Generator Tailracepond Steam Fig. 1.6 A typicallayout for a storagetype hydro plant Fig.1.5 CCGTpowerstation Hydro plants are of different types suchas run-of-river (use of water as it comes), pondage (medium head) type, and reservoir (high head) type. The pc2ae0srmieooidnfsugCotaeCf ssGtsifmTuoprepptltlhayoeninttasthetkeameasrmcpaattrifuoaernsbo.tifnsTatehan.erLyt uooencfmiat2lec-r3sagtnoemtrnaainckgyeef.outarpnttkhoseIJTgrVasgouoturvre\"burilnio-eua\"dafnoudrraesbdhooiunrtt reservoir type plants are the ones which are employed for bulk power generation.Often, cascadedplants are alsoconstructedi,.e., on the sa.mewater CCGT unit produces55voof CO2producedby a coal/oil-firedplant. Units stream where the dischargeof one plant becomesthe inflow of a downs6eam are now available for a fully automatedoperation for 24h or to meet the peak plant. demands. The utilization of energy in tidal flows in channets has long been the subject of researeh;Ttrsteehnical and economic difficulties still prevail. Some In Delhi (India) a CCGT unit6f 34Mw is installed at Indraprasthapower of the major sites under investigation are: Bhavnagar,Navalakhi (Kutch), Station. Diamond Harbour and Ganga Sagar. The basin in Kandala (Gujrat) has been estimated to have a capacity of 600 MW. There are of course intense siting There are culrently many installationsusing gas turbinesin the world with problems of the basin. Total potential is around 9000 IvftV out of which 900 100 Mw generators.A 6 x 30 MW gas turbine station has already beenput MW is being planned. up in Delhi. A gas turbine unit can also be usedas synchrono.r,.ornp\"nsator A tidal power station has been constructedon the La Rance estuary in to help maintain flat voltage profile in the system. northern France where the tidal height rangeis 9.2 m and the tidal flow is estimatedto be 18.000 m3/sec. Different types of turbines such as Pelton. Francis and Kaplan are used for storage,pondageand run-of-river plants, respectively.Hydroelectricplants are

W -- ModernpowersystemAnarvsis t daily load demandcurve. Someof the existingpumpedstorageplantsare I100 MW Srisailemin Ap and 80 MW at Bhira in Maharashtra. p=gpWHW Nuclear Power Stations where W = dischargem3ls through turbine With the end of coal reservesin sight in the not too distantfuture, the immediate p = densiry1000kg/m3 practicalalternativesourceof large scale electric energygenerationis nuclear steoonuethrrcgeeyua.Iscnecfoaoucfnt,ntstuhfcoelredoaenrvleeynlo3epVregodoycffootuhr nepttrooiewtaselhrpaogvweeneaerlrrgeaeatnidoeynsr.awIntiitocInnhwdeiidtaho, vnaeutrcpilnereaasrbesitngatt,witohaniyss 11= head(m) 8 = 9.81mlsz at Tarapur (Maharashtra),Kota (Rajasthan),Kalpakkam(Tamil Nadu), Narora Problemspeculiarto hydro plant which inhibit expansionare: (UP) and Kakrapar (Gujarat). Several other nuclear power plants will be 1. Silting-reportedly Bhakra dead storagehas silted fully in 30 years commissionedby 20I2.In future,it is likely thatmoreandmorepower will be 2. Seepage generatedusing this important resource (it is plannedto raise nuclear power 3. Ecological damageto region generationto 10,000MW by rhe year 2010). 4. Displacementof human habitationfrom areasbehind the dam which will When Uranium-235is bombardedwith neutrons,fissionreactiontakesplace fill up and becomea lake. rreelaecatsioinngonfefuistrsoinosnianngdmheoaret eanteormgys.oTfhe2s3e5nUe.Iuntroonrdstehretnhpaat rthticeipfraetsehinlythreelecahaseind 5. Thesecannotprovidebaseload, mustbe usedfor peak.shavingandenergy naecurittriocnasl bvealaubel-eTtohefirsesfioornet,hfoerutrhaenriuemacatitoonmtso,tbheeisrusspteaeindesmd,nuusct bleeairefduuecl eroddtos savingin coordinationwith thermalplants. India alsohasa tremendouspotential (5000MW) of having largenumberof micro (< 1 Mw), mini (< 1-5 Mw), and,small (< Himalayan region, Himachal, up, uttaranchal and 15 Mw) Mrl plants in mustbe embeddedin neutronspeedreducingagents(like graphite,hqavy water, JK which must be fully etc.) called moderators.Forreaction control, rods made of n'eutron-absorbing exploitedto generatecheapand cleanpowerfor villages situatedfar awayfrom the grid power*. At present500 MW capacityis und\"r construction. material (boron-steel)are usedwhich, when insertedinto the reactor vessel, control the amount of neutron flux thereby controlling the rate of reaction. In areaswheresufficienthydro generationis not available,peakload may be However,this rate canbe controlledoniy within a narrowrange.The schemadc, handled by meansof pumped storage.This consists of un ,rpp\". and lower diagramof a nuclearpower plant is reservoirs and reversibleturbine-generatorsets, which cun ulio be used as 'uclear reaction is transportedto a shown in Fig. 1.7.The heit releasedby the motor-pump sets.The upper reservoir has enoughstoragefor about six hours heat exchangervia primary coolant (coz, of full load generation.Such a plant actsas a conventionalhydro plant during water,etc.). Steamis then generatedin the heatexchanger,which is used in a the peak load period, when production costsare the highest.The iurbines are conventionalmanner to generateelectric energyby meansof a steamturbine. driven by water from the upperreservoirin the usualmanner.During the light load period, water in the lower reservoiris pumped back into the ipper one Various types of reactorsare being used in practicefor power plant pu{poses, so as to be ready for use in the next cycle of the peak ioad p.rioo. rn\" viz., advancedgas reactor (AGR), boiling generatorsin this period changeto synchronousmotor action and drive the water moderatedreactor.etc. water reactor (BwR), und h\"uuy turbineswhich now work as pumps.The electricpower is suppliedto the sets from the general power network or adjoining thermal plant. The overall Controrl ods efficiency of the sets is normarly as high ut 60-7oEo. The pumped srorage scheme,in fact, is analogousto the chargingand discharging or u battery. It Fuelrods_ has the added advantage that the synchronousmachin\", tu1 be used as synchronouscondensersfor vAR compensationof the power network, if required.In-a way, from the point of view of the thermal sectorof the system, * Existing capacity (small hydro) is 1341 MW as on June 200I. Total estimated potentialis 15000MW. Waterintake

ModernPo*\", systemAn\"tysis iiiriociucrion - W require that they be normally located away from populatedareas. CANDU reactor-Natural uranium(in cixideform), pressurizedheavywater Demerits moderated-is adopted in India. Its schematic diagram is shown in Fig. 1.8. Nuclear reactors produce radioactive fuel waste, the disposal Containment poses serious environmentalhazards. Fig. 1.8 CANDUreactor-pressurizheedavywaterrnoderated-adopteidn 2. The rate of nuclearreaction can be lowered only by a small margin, so India that the load on a nuclear power plant can only be permitted to be marginally reduced below its full load value. Nuclear power stations The associatedmerits and problems of nuclear power plants as compared must, therefore, be realiably connectedto a power network, as tripping to conventionalthermal plants are mentionedbelow. of the lines connecting the station can be quite seriousand may required Merits shutting down of the reactor with all its consequences. 1. A nuclearpower plant is totally free of air pollution. 3. Because of relatively high capital cost as against running cost, the 2. It requireslinle fuel in terms of volume and weight, and thereforeposes. nuclear plant should operate continuously as the base load station. Wherever possible, it is preferable to support such a station with a no transportationproblems and may be sited, independentlyof nuclear pumped storageschemementioned earlier. 4. The greatestdangerin a fission reactoris in the caseof loss of coolant in an accident.Even with the control rods fully loweredquickly called scrarn operation, the fission does continue and its after-heatmay cause vaporizing and dispersalof radioactive material. The world uranium resourcesare quite limited, and at the presentrate may not last much beyond 50 years.However, there is a redeemingfeqture.During the fission of 235U,some of the neutrons are absorbedby lhe more abundant iitssotiospe23283U8U)cleonnrvicehrteindguritantioumplcuotonntaiuinmso(n\"nlyUa),bowuht3icVhooinf 23sUwhile uranium itself is a most of fissionablematerial and can be extractedfrom the reactorfuel wasteby a fuel reprocessingplant. Plutonium would then be used in the next generation reactors (fast breeder reactors-FBRs), thereby considerablyextending the life of nuclearfuels. The FBR technologyis being intenselydevelopedas it will extend the availability of nuclear fuels at predicted rates of energy consumptionto severalcenturies. Figure 1.9 shows the schematicdiagram of an FBR. It is essentialthat for breeding operation, conversionratio (fissile material generated/fissilematerial consumed) has to be more than unity. This is achieved by fast moving neutronsso that no moderatoris needed.The neutronsdo slow down a little through collisions with structural and fuel elements.The energy densitylkg of fuel is very high and so the core is small. It is therefore necessarythat the coolant should possessgood thermal propertiesand hence liquid sodium is used.The fuel for an FBR consistsof 20Voplutonium phts 8Vouranium oxide. The coolant, liquid sodium, .ldavesthe reactor at 650\"C at atmospheric pressure.The heat so transportedis led to a secondarysodium circuit which transfers it to a heat exchangerto generatesteam at 540'C.

t_ Mr r toy dy vprrrn. pnrrrar errolam Anal.,^l^ r vrrvr vyglgttl nttdtvsts with a breeder reactor the release of plutonium, an extremely toxic suitedfor India,with poor qualitycoal,inadequarheydropotentiaiilentiful amtaKAtenarlipeaxal,pkwekoraiummldaelnmotnaalgkfaessitdthbeeareenenudvceirrroetneamsrpteorenwataeclrrcpoolran(FsniBtd.TFeRrBa)Rti(o4tne0scmMhoWnso)tlsohtgraiysin,-gbeenetn. built reservesof uranium(70,000tons)andthorium,and many yearsof nuclear engineeringexperience.The presentcost of nuclear \"*f..l\"J wlm coal-ttred power plant, can be further reduced by standardisingpl4nt conventional thermal plants. designand shifting from heavy wate,r eactorto light water reactortechnology. - Core Typical power densities1MWm3) in fission reactor cores are: gas cooled 0.53, high temperaturegas cooled 7.75, heavy warer 1g.0,boiling iut., Zg.O, Coolant pressurizedwater 54.75, fast breederreactor 760.0. Containment Fusion Fig. 1.9 Fastbreeder eactor(FBR) Energy is producedin this processby the combination of two light nuclei to An important advantageof FBR technologyis that it can also use thorium form a single heavier one under sustainedconditions of exiemely high (as fertile material) which gets convertedto t33U which is fissionable.This temperatures(in millions of degreecentigrade).Fusion is futuristic. Genera- holds great promisefor India as we have one of the world's largestdeposits tion of electricity via fusion would solve the long-tenn energy needsof the of thoriym-about 450000tons in form of sanddunesin Keralu una along the world with minimum environmental problems. A .o--\"i.iul reactor is GopalpfurChatrapurcoastof Orissa.We have merely 1 per cent of the world's expectedby 2010 AD. Consideringradioactive wastes,the impact of fusion reactorswould be much less than the fission reactors. In caseof successin fusion technologysometimein the distantfuture or a breakthroughin the pollution-free solarenergy,FBRs would becomeobsolete. However, there is an intense need today to develop FBR technology as an insuranceagainstfailure to deveropthesetwo technologies. \\ In the past few years, serious doubts have been raised.about the safety claims of nuclearpower plants.Therehavebeenas many as 150neardisaster nuclear accidents from the Three-mile accident in USA to the recent Chernobyl accidentin the former USSR.There is a fear.that all this may pur the nuclearenergydevelopmentin reversegear.If this happenstherecould be serious energy crisis in the third world countries which have pitched their hopeson nuclear energy to meet their burgeoningenergy needs.France(with 78Voof its power requirementfrom nuclearsources)and Canadaare possibly the two countrieswith a fairty clean recordof nuclear generation.India needs to watch carefully their design, constructionand operating strategiesas it is committed to go in a big way for nuclear generation and hopes to achieve a capacity of 10,000 MW by z0ro AD. As p.erIndian nuclear scientists,our heavy water-basedplants are most safe.But we must adoptmore conservative strategiesin design,constructionand operationof nuclearplants. World scientistshave to adopt of differentreaction safetystrategy-may be to discover additives to automatically inhibit feaction beyond cr;ii\"at rather than by mechanicallyinsertedcontrol rods which have possibilitiesof several primary failure events. Magnetohydrodynamic (MHD) Generation In thermal generation of electric energy, the heat released by the fuel is converted to rotational mechanical energy by means of a thermocvcle. The

ModerPnoweSr ystemAnatysis Introduction w ry I mechanicalenergy is then used to rotate the electric generator.Thus two stagesof energy conversion are involved in which the heat to mechanical volcanic regionscan be utilized. Since the pressureand temperaturesare low, energy conversionhas inherently low efficiency. Also, the rotating machine has its associatedlossesand maintenanceproblems.In MHD technology, the efficiencyis even less than the conventionafl ossil fuelledplants,but the cornbustionof fuel without the need for mechanicalmoving parts. capital costsare less and the fuel is availablefree of cost. In a MHD generator,electricallyconductinggas at a very high temperature I.4 RENEWABLE ENERGY SOURCES is passed in a strong magnetic fleld, thereby generatingelectricity. High temperature is needed to iontze the gas, so that it has good eiectrical To protect environmentand for sustainabledevelopment,the importanceof conductivity.The conductinggas is obtainedby burning a fuel and injecting renewableenergysourcescannotbe overemphasizedIt. is an establishedand a seeding materials such as potassium carbonate in the products of acceptedtact that renewableand non-conventionaflorms of energywill play combustion. The principle of MHD power generationis illustrated in Fig. an increasinglyimportant role in the future as they are cleanerand easier to 1.10.Abotrt 50Voefficiency can be achievedif the MHD generatoris operated use and environmentallybenign and are boundto becomeeconomicallymore in tandem with a conventionalsteamplant. viable with increaseduse. Gas flow Becauseof the limited availability of coal, there is considerableinterna- at 2,500'C tional effort into the developmentof alternative/new/non-conventionaUrenew- able/cleansourcesof energy. Most of the new sources(someof them in fact Strongmagnetic have been known and used for centuries now!) are nothing but the field manifestationof solar energy, e.g., wind, sea waves, oceanthermalenergy conversion (OTEC) etc. In this section,we shall discussthe possibilitiesand F i g .1 .1 0 T h ep ri n c i p loef MH Dpow ergenerati on potentialitiesof various methods of using solar energy. Though the technologicalfeasibility of MHD generationhas been estab- Wind Power lished, its economicf'easibilityis yct to be demonstratedl.ndia had starteda research and developmentproject in collaboration with the former USSR to Winds are essentiallycreatedby the solar heatingof the atmosphereS. everal install a pilot MHD plant basedon coal and generating2 MW power. In attemptshave been made since 1940 to use wind to generateelectric energy Russia,a 25 MW MHD plant which usesnatural gas as fuel had been in and developmentis still going on. However, technoeconomicfeasibility has operation for someyears.In fact with the developmentof CCGT (combined yet to be satisfactorilyestablished. cycle gas turbine) plant, MHD developmenthas been put on the shelf. Wind as a power source is attractivebecauseit is plentiful, inexhaustible Geothermal Power Plants and non-polluting.Fnrther, it does not impose extra heat burden on the environment.Unlbrtunately,it is non-steadyand undependableC. ontrol In a geothermalpower plant, heat deep inside the earth act as a source of equipmenthas beendevised to start the wind power plant wheneverthe wind power. There has been someuse of geothermalenergy in the form of steam speedreaches30 kmftr. Methods have also been found to generateconstant coming from undergroundin the USA, Italy, New Zealand,Mexico, Japan, frequencypower with varying wind speedsand consequentlyvarying speeds Philippines and some other countries.In India, feasibility studies of 1 MW of wind mill propellers. Wind power may prove practical for small power station at Puggy valley in Ladakh is being carried out. Another geothermal needsin isolatedsites.But for maximum flexibility, it shouldbe used in field has beenlocatedat ChumantangT. here are a number of hot springsin conjunctionwith other methodsof power generationto ensurecontinuity. India, but the total exploitableenergypotentialseemsto be very little. For wind power generation,there are three types of operations: Ttre presentinstalled geothermalplant capacity in the world is about 500 MW and the total estimatedcapacityis immenseprovidedheatgeneratedin the 1. Small, 0.5-10 kW for isolatedsinglepremises i 2. Medium, 10-100 kW for comrnunities 3. Large, 1.5 MW for connectionto the grid. The theoreticalpower in a wind streamis given by P = 0.5 pAV3W where p = densityof air (1201 g/m' at NTP) V _ meanair velocity (m/s) and A = sweptarea(rn\").

2. Rural grid systemsarelikely to be 'weak, in theseareas.since Introduction retatrvelylow voitagesupplies(e.g. 33 kV). Tota lsolar ener gypot ent iailn I ndiais 5 x lO ls kwh/ yr . Up r o 31. t 2. 2000. 3. There are alwaysperiods without wind. 462000solar cookers,55 x10am2solar thermai systemcollector area,47 MW MaIhnarIansdhiatr,aawnidnTdampoilwNear dpul,awnhtserheawviendbebelonwisnasttaslpleededinsofG3u0jakrmatf,trodruisrisnag, of SPV power, 270 community lights, 278000 solar lanterns(PV domestic (cDtso7oueUnmcbeV.ems2opse0)our.0'nbO0dsnitisnatgnh1wtei2aow6lrah7ldnoMdlfewig,is,tuhraeethrwoeisuinbn1dud4lpk40o50ow00f0eM0rwwphMo,ictwehr.nhitesiTabhlinoueflkTiInnaosdmftiaaiwlllhehNadiacsdhcbaueip-se(an6icn0eit%syEt)iaum. sraTootpheneed lighting units),640 TV (solar),39000PV streetlights and 3370 warer pumps MW of grid connected solar power plants were in operation. As per one estimate[36], solarpower will overtakewind in 2040 and would becomethe world's overall largest source of electricity by 2050. Direct Conversion to Electricity (Photovoltaic Generation) This technologyconvertssolarenergyto the electricalform by meansof silicon wafer photoelectriccells known as\"Solar Cells\". Their theoreticalefficiency is about 25Vobut the practical value is only about I5Vo. But that doesnot matter as solar energy is basically free of cost. The chief problem is the cost and Solar Energy maintenanceof solarcells. With the likelihood of a breakthroughin the large scaleproductionof cheap solar cells with amorphoussilicon, this technology hbaT6ave0hani0enidlWgaa,fibtvr/erlehenera2afosogbfrseucetooivntnsehcltriye,adnleaocancrnrtt-paueawsaxorblhtlvaaaaocrulfkusesettn-ihbeveealnreagerdniyreadgsyryce,codcoeamennnipvssdleiiedtdcytelep,roolaeynupbi doyuleynla.Iluitratttnhahiodar'sen,sha-stfaihruszeeryvefaae.Oacdrtyenvmartioohsnswetpaa,ohgbitteheooireusifcrt amcenonodnesdrittgiistmyiofcponoorsnregvtalerenercstatbitrolieycniintrtoeyggdttehhuneaceeteortlaehf tcetihotreenicnc,caheolraflglolelyrecmnrtiegotcnihneraigovtnueedgcdchh. oTnenhoffcelioecrgienefitncoraatretpali,ornhondaobcrflenosmemosslpsaeairnxreagisntstiev,otrehlgaleyyr may competewith conventionalmethodsof electricity generation,particularly e c o n o m i c a lm e a n s . as conventionafluels becomescarce. Solar energy could, at the most, supplementup to 5-r0vo of the total energydemand.It has been estimatedthat to produce1012kwh per year, the necessarycellswould occupy about0.l%oof US land areaasagainsthighways which occupy 1.57o(in I975) assumingI07o efficiency and a daily insolation of 4 kWh/m'. .\\ In all solarthermalschentess, torageis necessarybecauseof the fluctuating natureof sun's energy.This is equallytrue with many otherunconventional At present, two technologiesare sourcesas well as sourceslike wind. Fluctuatingsourceswith fluctuating energyto the electrical form.-'Inone being developedfor conversion of solar loads complicatestill further the electricitysupply. technology,collectorswith concentrators fldceaa'aoinrrarenTggrfseerhrnnoimaeedemntepseadrlotraboeilbenyxraelitecrenraeedipgcsentoaoocgdtwnoeiiannamecsegbrhpt3elrteieu0reoietcnviwmfttgefiuevidtcrteerieiofemw[fsi1ngicnipc5teuvhey]nlotreig\"atieovoretsiatunnrgtirugneeeep\"rshtnlbeaiutieurgitgohreih\"alnadssteapiectnnlseeag2Joalpe0luaemict0gcastfhtrkliorino(wcir7cgui.ti0lettyely0T.alte'rgHyhCaceeao)ctnrnwtksieodcicenrihovaagteyeptsibrmpoeo,ornrfewoat.ihtctnioeelvwduaroeacihtlythvaeieiorasaesnt . Wave Energy ]'here is a 10 MW installationof such a tower by the SouthernCalifornia The energyconientof seawavesis very high. In India, with severalhundreds EdisonCo' in USA using 1818planernirrors, eachi of kilometersof coastline, a vastsourceof energyis available.The power in racliationto thc raisecbl oiler. m x 7 m reflectingdirect the wave is proportionalto the squareof the anrplitudeand to the period of the motion.Therefore,rhe long period(- 10 s), largeamplitude(- 2m) waves Electricity may be generatedfrom a Solar pond by using a special .low are of considerable interest for power generaticln, with energy fluxes temperatureh' eatenginecoupledto commonly averagingbetween50 and 70 kW/m width of oncoming wave. Borek in Israel proclucesa steady1 an electricgeneratorA. solar Though the engineeringproblemsassociatedwith wave-powerare formidable, of abo u t$ O.tO /k w h . 50 kW fiorn 0.74 hectareat a the amountof energythat can be harnessedis large and developmenwt ork is in progress(alsoseethe sectionon HydroelectricPowerGenerationp, age17). Sea wave power estimatedpoterrtialis 20000 MW. pond at Ein Ocean Thermal Energy Conversion (OTEC) busb arcost Solarpower potential is unlimited,however,total capacityof about 2000 The ocean is the world's largest solar coilector. Temperaturedifference of MW is being planned. 2O\"Cbetween\\,varrn,solar absorbingsurfacewater and cooler 'bottorn' water

ffiffi| ModemPow'esrystemAnatysis lntroduction can occlrr.This can providea continuallyreplenishedstoreof thermal energy solar.The most widely usedstoragebatteryis the lead acid battery.invented which is in principle availablefbr conversion to other energy forms. OTEC by Plantein 1860.Sodiuttt-sulphubrattery(200 Wh/kg) and othercolrbina- refers to the conversionof someof this thermal energyinto work and thence tions of materialsarea-lsobeing developedto get more output and storageper unit weisht. 50,000Mw. A proposedplant using seaiemperaturedifferencewould be situated25 km Fuel Cells cast ol'Mianii (USA), wherethe temperatureclil'l'eroncise 17.5\"C. A fuel cell convertschemicalenerry of a fuel into electricityclirectly,with no intermediatecotnbustioncycle. In the fuel cell, hyclrogenis supplied to the Biofuels negativeelectrodeand oxygen (or air) to the positive.Hydrogenand oxygen are combined to give water and electricity. The porous electrodesallow The material of plants and animals is called biomass, which may be hydrogenions to pass.The main reason';rhy fuel cells are not in wide use is transformed by chemical and biological processesto produce intermediate their cost (> $ 2000/kW). Global electricity generatingcapacityfrom full cells biofuels sttch as methanegas, ethanol liquid or charcoal solid. Biomass is will grow fromjust 75 Mw in 2001ro 15000MW bv 2010.US. Germanvand burnt to provide heat for cooking, comfort heat (spaceheat), crop drying, Japanmay take lead for this. tactory processesand raising steamfor electricity productionand transport.In I ndia p o te n ti aIl' ttlb i o -E n e rg yi s 1 7 0 00MW andthatfbr agri cul tunrwl i rstci s Hydrogen Energy Systems about 6000 MW. There are about 2000 community biogasplants and tamily size biogas plants are 3.1 x 106.Total biomasspower harnessedso far is Hydrogen can be used as a medium for energy transmissionand storage. 222 MW. Electrolysisis a well-establishecdommerciapl rocessyieldingpurehydrogen. Ht can be convertedvery efficiently back to electi'icityby rneansof fuel ceils. Renewableenergyprogrammesare specially designedto meet the growing Also the useof hydrogena.sfuel for aircraftand automcbilescould encourase energy needs in the rural areas for prornoting decentralizedand hybrid its large scaleproduction,storageand distriburion. dcvelopmentst.las to stem growing migration of rural populationto urban areasin searchof betterliving conditions.It would be through this integration 1\"6 GROWTH OF POWER SYSTEII{S IN INDIA of energy conservationefforts with renewable energyprogrammesthat India would be able to achievea smoothtransition from fossil fuel economy to India is fairly rich in natural resourceslike coal and lignite; while sorneoil sustainablerenewableenergybasedeconomy and bring \"Energy for ali\" for reserveshavebeendiscoveredso far. intenseexplorationis beingundertakeri ec;uitableand environrnentafrl iendlysustainabledevelopment. in vitriousregitlnsof thc country.India has immensewaterpowerl.csources alsoof whichonly around25Tohaveso farbeenutilisecii,.e.,oniy 25000t\\,IW 1.5 ENERGY STORAGE has so far beencommissionedup to the end of 9th plan.As per a recentreport of tlreCEA (CcntlalFlectricit,vAuthority),the totalpotentialof h1,dropower 'l'hereis a lol ol problenrin storingclectricity in largc quantities.Enclgy is 84,040Iv{Wat ('L't%load factor.As regardsnuclearpower,India is cleflcient wliich can be convertedinto electricitycan be storedin a number of ways. in uranium,but hasrich depositsof thorir-imrvhichcan be utilisedat a future S t or ag eo f a n y n a tu rei s l ro w e v e rv ery costl y arrcilts cconomi csmust be clatc in l'astbrccclorrci.tctor.sS.ince indepcndcncct,hc coulltry has nnde worked out properly. Various options available are: pLrmpedstorage,c:onl- tremendousprogressin the developmenot f electricenergyandtodayit has the pressedair, heat,hydrogengas,secondarybatteriesf,lywheelsand supercon- largestsystemamong the developingcountries. d u c t i n gc o i l s . When lndia attainedindependencet,he installeclcapacity was as low as As already mentioned, gas turbines are normally used for meeting peak 1400 MW in the early stagesof the growth of power system,the major portion loads but are very expensive.A significant amount of storage capable of of generationwas through thermal stations,but due to economicalreasons. instantancoususewould be betterway of meetingsuchpeakloads,and so far hydro developmentreceivedattentionin areaslike Kerala,Tamil Nadu. Uttar the most importantway is to havea pumpedstorageplant as discussedearlier. Pradeshand Punjab. Other methods are discuss-edbelow very briefly. In the beginningof the First Five Year Plan (1951-56),the rotal installed Secondary Batteries capacitywasaround2300 MV/ (560 MW hydro, 1004MW thermal,149 MW through oil stations and 587 MW through non-utilities).For transportingthis Large scalebattery use is almostruled out and they will be used for battery powered vehiclesand local fluctuating energy sourcessuch as wind mills or

Introduction HE FI power to the load centres,transmissionlines of up to 110 regions of the country with projectedenergyrequirementand peak load in the were constructed. year 2011-12 [19]' Five Plan, Indiioa osrtoarrrtcertdgcrecnncerrearitingnuclearpower' At the During the Fourth units were comrnissionedin April-May water reactorsof American design.By Tarapur i\\uclear Plant 2 x 210 MW . This stationusestwo boiling Northern region 308528 (49674) .,. MW* 9 Westernregion commissionedbY 2012. and future projection for 2011- 299075 The growth of generatingcapacityso far (46825) 2012 A.D. are given in Table 1'1' Tabte1.1 Growthof Installedcapacityin lndia(ln MW) Year Hydrtt Nuclear Thermal DieseI Total 398 1970-7t 6383 420 7503 r4704 1978-79 l 1378 890 t6372 =2700 MW 28640 1984-85 t4271 1095 27074 renewable 42240 2000-01 25141 2720 71060 101630 \\'./ Pattern of utlization of electrical energy in 1997-98 was: Domestic {O.6g\\o,commercia6l .9 17o, inigation 30.54Voi,ndustry 35'22Voand othersis Fig. 1.11 Mapof Indiashowingfive regionapl rojecteednergyrequiremenint MkWhandparkloadin MW for year2011-12' 6chefisio.yrr6ssduTc5,trnooso75tnwro0bssyi.e0etiIadcttnMshesisc,ergtWeultleefhdr-axboestrpiunussnefere,efebtcisuoctotcferif-oen.gdrtEntehootanneuicunertmhecraalpmpaentoljaoaaeowrrinnrwpnettplamirsaro'spenoBwrectrasHeoce,nrirEtaonigpiLlrgmeilzaflotieehnsfpsastsipinss\"ieoo.sqptawnuaulearermiaedpnranemetstgbiqneseosuniiop2niltpefrg0memrer0saaaqe,4dnupun-oulo0iitpu'f,wv5amtTi'eczoaetr'dulnttlruartaeo'yrBnrbvHsBseoinfErIosILEtrethmh'Ltsese-'- The emphasisduring the SecondPlan (1956-61) was on the developmentof basic ancl heavy inclustriesand thus there was a need to step up power generation.The total installedcapacity which was around3420 MW at the end of tn\" First Five year Plan became5700 MW at the end of the SecondFive year plan. The introductionof 230 kv transmissionvoltagecame up in Tarnil world. T.7 ENERGY CONSERVATION Energy conservationis the cheapesnt ew sourceof energy'we shouldresort to variousconservationmeasuressuchas cogeneration(discussedearlier), and

,r32 I Modernpower SvstemAnalvsis lntroduction use energy efficient motors to avoid wasteful electric uses.We can achieve Load Management considerableelectricalpower savingsby reducingunnecessaryhigh lighting levels,oversizedmotors,etc.A 9 W cornpactfluorescentlamp (CFL) may be As mentionedearlier by various 'load management'schemes.It is possibleto used insteadof 40 w fluorescenttube or 60 w lamp, all having the same shift demanrlaway frorn peak hours (SectionI .1.). A more direct method lu would be the control of the load either through rnodified tariff structurethat a year.Everyoneshouldbe madeawarethroughprint or electronicmediahow encourage consumptionlevelscanbe reducedwithout any essentialowering of comfort. schedulesor direct electrical control of appliancein the form of remote timer Rate restructuringcan have incentivesin this regard.There is no conscious- controlled on/off switches with the least inconvenience io the customer. nesson energy accountabilityet etndno senseof urgencyas in developed Various systems for load rnanagementare described in Ref. [27]. Ripple countries. control has been tried in Europe. Remote kWh meter reading by carrier sysremsis being tried. Most of the potential for load control lies in the Transmissionand distributionlossesshoulclnot exceed2OVoT. his can be domestic sector. Power companies are now planning the introduction of achievedby employing series/shunct ompensation,power factor improvement system-wideload managementschemes. methods, static var compensators,HVDC option and FACTS (flexible ac technology) devices/controllers. 1.8 DEREGULATION Gas turbirre combined with steam turbine is ernployed for peak load For over one hundredyears,the electricpower industryworldwide operatedas shaving. This is more efficient than normal steam turbine and has a quick a regulatedindustry. In any areatherewas only one company oI government automated starl and shut doivn. It improves the load factor of the steam agency (mostly state-owned)that produced,transmitted,distributed and sold staflon. electric power and services.Deregulationas a conceptcame in early 1990s.It brought in changesdesignectio enc<.rutagceompetition. Energy storage can play an important role where there is time or rate mismatchbetweensupplyand demandof energy.This hasbeen discussedin Restructuring involves disassemblyof the power industry and reassembly Section 1.5. Pumpedstorage(hyclro)schemehas beenconsicleredin Section into anotherform or functional organisation.Privatisation startedsale by a 1.3. governmentof its state-ownedelectricutility assetsa, nd operatingeconomy, to private companies.In some cases,deregulationwas driven by privatization Industry needs.The state wants to sell its electric utility investment and changethe rules (deregulation)to make the electric industry more palatablefor potential In India where most areashave large number of sunny days hot water for investors,thus raising the price it could expectfrom the sale. Open accessrs bath arrdkitchen by solarwaterheatersis becomingcommon for commercial nothing but a common way for a govenlmentto encouragecompetition in the buildings,hotels evenhospitals. electric industry and tackle monopoly. The consumer is assuredof good quality power supply at competitive price. In India where vastregionsaredeficient in electricsupply and,aresubjected to long hours of power sheddingmostly random, the use of small diesel/petrol The structurefor deregulationis evolved in terms of Genco (Generation generatorsand invertersare very conmon in commercialand domesticuse. Company),Transco(TransrnissionCompany)and ISO (IndependentSystem Theseare highly wastefulenergydevices.By properplanned maintelance the Operator).It is expectedthat the optimal bidding will help Gencoto maximize downtime of existing large stationscan be cut down. Plant utilization factors its payoffs. The consumersare given choice to buy energy from different retail of existingplants mustbe improved.Maintenancemust be on schedulerather energy supplierswho in turn buy the energyfrom Genco in a power market. than an elner-qencyM. aintenancemanpower training should be placed on war (independentpower producer, IPP). footing. These actionswill also improve the load factor of most power stations,which would indirectly contribute to energyconservation. The restructuringof the electricity supply industry that norrnally accompa- nies the introduction of competiiion providesa fertile ground for the growth of embeddedgeneration,i.e. generationthat is connectedto the distribut-icn systemratherthan to the transmissionsystetn. The earliestreforms in power industrieswere initiated in Chile. They were followed by England, the USA, etc. Now India is also implementing the restructuringL. ot of researchis neededto clearlyunderstandthe power system operation under deregulation. The focus of, researchis now shifting towards

W Modernpo*\", Syster Anulyri, Introduction finding the optimal bidding methodswhich take into accountlocal optimal Therearealready32 million improved chulhas.If growing energyneedsin the dispatch,revenueadequacyand market uncertainties. rural areasare met by decentralisedand hybrid ener-qysystems(distributed/ dispersedgeneration)t,his can stem growing migrationof rural populationto India has now enactedthe ElectricityRegulatoryComrnission'sAct, 1998 urban areasin searchof betterliving conditions.Thus, India will be able to and the Electricity (Laws) AmendmentAct, 1998.Theselaws enablesetting uo of able-energy based econolny iind bring \"Energy for all\" for equitable, State Electricity RegulatoryComrnissions(SERC) at srate level. 'fhe main environment-friendlya, nd sustainabiedevelopment. purposeof CERC is to promoteefficiency, economy and competition in bulk electricity supply. orissa, Haryana,Andhra Pradesh,etc. have startedthe 1.10 ENVIRONMENT/\\L ASPECTS OF ELECTRIC ENER,GY processof restructuringthe power sectorin their respectivestates. GENERATION 1.9 DISTRIBUTED AND DISPERSED GENERATION As far as environmentaal nd healthrisks involvedin nuclearplantsof various kinds are concernedt,hesehave already'beendiscussedin Section1.3. The DistributedGeneration(DG) entailsusinglnany srnallgeneratorsof 2-50 MW problernsrelatedto largelrydroplantshavealsobeendwelleduponin Section output,installedat variousstrategicpointsthroughout he area,so that each 1.3.Therefore,we shall now focus our attentionon fossil fuel plant including providespower to a small numberof consumersnearby.Thesemay be solar, g a s - b a s e dp l a n t s . mini/micro hydel or wind turbine units, highly efficient gas turbines,small combincdcycle plitnts,sinccthcsearo the rnostccon<lnricaclhoiccs. Conversion of clne lornr ol' energy or anotherto electrical tortn has unwantedside effectsand the pollutants generatedin the processhave to be Dispersedgenerationreferesto use of still smaller generatingunits, of less disposed off. Pollutants know no geographical boundary, as result the than 500 kW output and often sizedto serveindividual homesor businesses. pollution issuehas becomea nightmarishproblemand strong nationaland Micro gas turbines,fuel cells,diesel,and small wind and solar PV senerators international pressuregroups have sprung up and they are having a definite makeup this category. impacton the developmenot f energyresourcesG. overnmentaal wareneshsas creatednumerouslegislationat national andinternationalevels,w[ich power Dispersedgenerationhas been usedfor clecadesas an emergencybackup engineershave to be fully conversantwith in practiceof their professionand power source.Most of theseunits are usedonly fbr reliability reinfbrcement. survey and planning of large power projects.Lengthy, time consuming Now-a-daysinverters are being increasinglyused in domestic sectoras an proceduresat governrnenltevel, PIL (public interestlitigation)and demonstra- emergencysupplyduring black outs. tive protestshave delayedseveralprojectsin severalcountries.This has led to favouringof small-sizeprojectsand redevelopmenotf existing sites.But The distributed/dispersedgeneratorscan be stand alone/autonomousor with the increasinggap in electricdernandandproduction,our country has to grid connecteddepending upon the requirement. move forward fbr severallarge thermal, hydro and nuclearpower projects. At the time of writing this (200i) therestill is and will probablyalwaysbe E ntphasisis lr cinglaid on cor ] scr vilt ioirst sucsc. ur t uilt nenotf t r ansnt issit t n some economy of scale f-avouringlarge generators.But the margin of losses, theft, subsidizedpower supplies and above all on sustainable economydecreasedconsiderablyin last 10 years[23]. Even if the power itself devektpnrenlwittr uppntpriata technolog-)w' hercver feasible. It has to be c t ls t sa b i t rtttl rcth i tnc c n (r' aslta ti o np o wcr,therei s no nccd < tftransrni ssi on particularly assuredthat no irreversible damageis causedto environment lines, and perhapsa reducedneedfbr distribution equipmentas well. Another which wouid affect the living conditions of the future generations.Irreversible maior advantageof dispersedgene.rationis its modularity, porlability and damageslike ozonelayerholesand global warmingcausedby increasein CO2 relocatabilityD. ispersedgeneratoraslsoincludetwo new typesof tbssilfuel in the atmosphereare alreadyshowing up. units-fuel cells and microgasturbines. Atmospheric Pollution The main challengetoday is to upgradethe existing technologiesand to proniotedeveloprnentd, emonstrations,calingup and cornmercializatioonf We shall treat here only pollutrorras causedby thermalplants usingcoal as new and emerging technologiesfor widespreadadaptation.In the rural sector feedstock. Certain issuesconcerning this have already been highlighted in main thrust areasare biomassbriquetting,biomass-basedcogeneration,etc. In Section 1.3. The fossil fuel based generatingplants fonn the backboneof solar PV (Photovoltaic),large size solar cells/modulesbased on crystalline power generation in our country and also giobally as other options (like siliconthin films needto be developedS. olarcellsefficiencyis to be improved nuclear and even hydro) have even strongerhazardsassociatedwith them. to 15%too be of useat commercialevel.Otherareasaredeveloprnenotf high eificiency inverters.Urban and industrialwastesare usedfor variousenergy applicationsincluding power generationwhich was around 17 Mw in 2002.

wf f i_f f i | tr vr ^iro^u- -ernrno^ .w. .-^e- ru^ .y, -sr t- e- mAa -n- ar .i-y- ,sts lntroduction Also it shouldbe understoodthat pollutionin large cities like Delhi is caused Oxides of Carhon (CO, COt) more by vehicrtlar traffic and their emission.In Delhi of courseInderprastha and Badarpurpower stationscontributetheir sharein certain areas. CO is a very toxic pollutantbut it getsconvertedto CO'.,in the openatmosphere (if available) surroundingthe plant. On the other handCO2 has beenidentified Problematic pollutants in emission of coal-basedgeneratingplants are. developingcountries. a2 Ifydrocarbons a NO.r,nitrogen oxides During the oxidation process in cornbustioncharnbercertain light weight o CO hydrocarbon may be formed. Tire compounds are a major source of photochemicalreactionthat adds to depleti,rnof ozone layer. a coz Particulates (fIY ash) . Certainhydrocarbons Dust content is particularly high in the Indian coal. Particulatescome out of o Particulates the stack in the form of fly ash. It comprisesfine particlesof carbon, ash and Though the accountthat follows will be general,it needsto be mentioned other inert materials.In high concentrations,thesecausepoor visibility and herethat Indian coal has comparativelylow sulphur content but a very high respiratorydiseases. ashcontent which in some coals may be as high as 53Vo. A brief accountof various pollutants,their likely impact and methods of Concentrationof pollutants can be reducedby dispersalover a wider area abatementsare presentedas follows. by use of high stacks.Precipitators canbe usedto removeparticlesas the flue gasesrise up the stack.If in the stack a verticalwire is strung in the middle Oxides of Sulphur (SOr) and charged to a high negative potential, it emits electrons.These electrons are capturedby the gasmoleculestherebybecomingnegativeions. Theseions Most of the sulphur present in the fossil fuel is oxidized to SO2 in the acceleratetowards the walls, get neutralized on hitting the'walls and the combustionchamberbefore being emittedby the chimney. In atmosphereit particles drop down the walls. Precipitatorshavehigh efficiency up to 99Vofor gets further oxidized to HrSOo and metallic sulphateswhich are the major large particles,but they have poor performancefor particles of size less than sourceof concernas thesecan causeacid rain, impaired visibility, damageto 0.1 pm in diameter.The efficiency of precipitatorsis high with reasonable buildings and vegetation. Sulphate concenffationsof 9 -10 LElm3 of air sulphurcontentin flue gasesbut dropsfor'low sulphurcontentcoals;99Vofor aggravateasthma,lung and heart disease.It may also be noted that although 37o sulphur and 83Vofor 0.5Vosulphur. sulphur does not accumulatein air, it does so in soil. Fabric filters in form of bag lnuses have also been employed and are Sulphuremissioncan be controlledby: located before the flue gasesenter the stack. o IJse of fuel with less than IVo sulphur;generallynot a feasiblesolution. Thermal Pollution o LJseof chemical reaction to remove sulphur in the form of sulphuric Steam fronr low-pressureturbine has to be liquefied in a condenser and acid, from combustionproductsby lirnestonescrubbersor fluidized bed reduced to lowest possible temperatureto maximize the thermodynamic combustion. efficiency. The best efficiency of steam-cyclepracticallyachievableis about 4\\Vo.It meansthat60Voof the heatin steamat thecycleend must be removed' . Removing sulphurfrom the coal by gasificationor floatationprocesses. This is achievedby following two methods' It has been noticed that the byproduct sulphur could off-set the cost of sulphurrecovery plant. 1. Once throughcirculation through condensecr ooling tubesof seaor river water whereavailable.This raisesthe temperatureof water in thesetwo Oxides of Nitrogen (NO*) sourcesand threatenssea and river life around in sea and downstream in river. ThesE,are serious environmentalobjections and many times Of theseNOz, nitrogenoxides,is a majorconcernas a pollutant.It is soluble cannot be overruled ard also there may be legislation againstit. in water and so has adverseaff'ecton human health as it entersthe lungs on inhaling and combining with moisture converts to nitrous and nitric acids, 2. Cooling tov,ersCool water is circulatedrottnd the condensertube to which danngethe lungs.At ievelsof 25-100 partsper million NO, can cause remove heat from the exhaust steam in order to condenseit. The acutebronchitis and pneumonia. Emissionof NO_,can be controlledby fitting advancedtechnologyburners which can assuremore completecombustion,thereby reducingtheseoxides from being emitted.Thesecan also be removedfrom the combustionproducts by absorptionprocessby certainsolventsgoing on to the stock.

fGfif-rfffuiid MociernPowerSysteqAnaiysis lntrcCuction sEfEfiF I T.TT POWER SYSTEMENGINEERSAND POWER SYSTEM STUDIES circulatingwater gets hot in the process.tt is pumpedto cooling tower The power systemengineerof the first decadeof the twenty-first century has and is sprayedthrough nozzlesinto a rising volume of air. Someof the water evaporatepsrovidingcooling.The latentheatof wateris 2 x 106 J/kg and coolingcan occur fast,But this has the disaclvantagoef raising u n o e s t r a o t e Jt e v e l s l n t h c s u l r f t l u n d l n ga r e a s . abreastof the recent scientific advancesand the latest techniques.On the planning side, he or she has to make decisionson how much electricity to coursethe water evaporatedmust be macleup in the systemby adcting generate-where, when, and by using what fuel. He has to be involved in constructiontasksof greatmagnitudeboth in generationand transmission.He fresh waterfrom the source. has to solve the problemsof planning and coordinatedoperationof a vast and complex power network, so as to achieve a high degreeof economy and Closed cooling towerswhere condenr;atfelows through tubcsanclair is reliability. In a country like India, he has to additionallyface the perennial problem of power shortagesand to evolve strategiesfor energyconservation blown in thesetubesavoidsthe humidityproblembut at a very high cost.In and load management. India only v,et towersare being used. For planningthe operation,improvementandexpansionof a power system, Electromagnetic Radiation from Overhead Lines a power systemengineerneedsload flow studies,short circuit studies,and stability studies.He hasto know the principlesof economicload despatchand Biological effectsof electromagneticradiation from power lines and even load frequency control. All theseproblemsare dealt with in the next few cables in closeproximity of buildings have recently attractedattentionand chapters after some basic concepts in the theory of transmission lines are have also causedsomeconcern.Power frequency(50 or 60 Hz) and eventheir discussed.The solutionsto these problems and the enormouscontribution harmonics are not consideredharmful. Investigationscarried out in certain madeby digital cornputersto solve the planningand operationapl roblemsof power systemsis also investigated. advanced countrieshave so far proved inconclusive.The electrical and electronicsengineers,while being aware of this controversy,must know that I.I2 USE OF COMPUTERS AND MICR.OPROCESSOiTS many other environmentalagentsaremoving aroundthat can causefar greater harm to humanhealththan does electromagneticradiation. As a pieceof information it may be quotedthat directly underan overhead line of 400 kV, the electricfield strengthis 11000V/m and magnericflux density (dependingon current) may be as much as 40 ptT. Electric field strengthin the rangeof 10000-15000 v/m is consideredsafe. Visual and Audible Impacts Jlhef irst rnethoslirl solvingvariouspowcr systemprobleniswereAC and DC network analysersdevelopedin early 1930s.AC analyserswere usedfor load These environmentalproblems are causedby the following factors. florv and stability studieswhereasDC were preferredfor short-circuitstudies. l. Right of way acquiresland underneathN. ot a seriousproblernin India AnaloguecompLrterws ere developedin 1940sand were usedin conjunc- at present.Could be a problem in future. tion with AC networkanalyserto solve variousproblemsfor off--linestudies. In 1950s many analoguedevices were developedto control the on-line 2. Lines convergingat a large substationmar the beautyof the lanclscape tunctions such as genelationr--ontrolI,i'equencyand tie-line controt. around. Undergroundcablesas alternativeare too expensivea proposi- tion exceptin congestecclity areas. The 1950salso saw the adventof digital computerswhich were first used to solve a.load flow problem in 1956.Power systemstudiesby computers 3' Radio interference(RI) has to be taken into accountand counteredbv gave greaterflexibility, accuracy,speedand economy.Till 1970s,there was varlous means. a widespreaduse of computersin systemanalysis.With the entry of micro- processorsin the arena,now, besidesmain frame compLltersm, ini, micro and 4. Phenomenonof corona (a sort of electric dischargearoundthe high personalcomputersare all increasinglybeingusedto carry out variouspower tensionline) producesa hissingnoisewhich is aucliblewhen habitation systern studies and solve power system problems for off-line and on-line is in close proximity. At the to'wersgreat attention must be paid to applications. tightness of joints, avoidanceof sharp edgesand use of earth screen shielding to lirnit audible noiseto acceptablelevels. Off-line applications include research,routine evaluation of system performanceand dataassimilationand retrieval.It is mainly usedfor planning 5' Workers inside a power plant are subjectedto various kinds of noise and arralysing some new aspectsof the system. On-line and real time (particularlynear the turbines)and vibration of floor. To reducethis applicationsinclude data-loggingand the monitoring of the system state. uoise to tolerable level foundations and vibration filters have to be designedproperly and simulation studiescarried out. The worker nlust be given regularmedical examinationsand sound medical advice.

-r-y-tr-f-i\\r----- tutodernpowerSvstemAnaivsis '.1g.r.,'\"\" A large central computer is used in central load despatchcentres for F cc<ln<lmiacndsecurccontrolof'largcintegratedsystemsM. icroprocessorasncl computersinstalledin generatingstationscontrol variouslocal processes uch severalsuper thermal stationssuch as at Singrauli (Uttar Pradesh)F, arakka as startingup of a generatorfrom the cold state,etc.Table 1.2depictsthe time (WestBengal),Korba (MadhyaPradesh)R, arnagundam(AndhraPradesh)and Neyveli (Tamil Nadu), Chandrapur(Maharashtra)all in coal mining areas, 2000 MW*. Manv more superthermal microprocessorss.ome of theseproblemsare tackled in this book. plants would be built in future. Intensivework must be conductedon boiler furnaces to burn coal with high ash content. Nationai Thennal Power T a b l e1 . 2 Corporation(NTPC) is in chargeof theselarge scalegenerationprojects. Tirne scale Control Problems Hydro power will continue to remain cheaperthan the other types for the Milliseconds Relayingand systemvoltagecontrol and next decade.As mentioned earlier, India has so far developedonly around excitation control 2 s-5 minutes AGC (Automatic generationconrrol) l87o of its estimatedtotal hydro potentialof 89000 MW. The utilization of 10 min-few hours ED (Economicdespatch) Securityanalysis this perennialsourceof energy would involve massiveinvestmentsin dams, - do- UC (Unit commitment) few hours-l week M a in t c r r a n c cs c h e d Lirnl g channelsand generation-transrnissiosnystem.The Central Electricity Author- I m o n t h- 6 m o n t h s Systernplanning I yr- 10 years (modification/extension) ity, the PlanningCommissionand the Ministry of Power arecoordinatingto work out a perspectiveplan to developall hydroelectric sourcesby the end of this century to be executed by the National Hydro Power Corporation (NHPC). NTPC has also startedrecentlydevelopmentof hydro plants. Nuclear energy assumesspecialsignificancein energy planningin India. Becauseof limited coal reservesand its poor quality, India hasno choice but 1.13 PROBLEMS FACING INDIAN POWER INDUSTR.Y to keep going on with its nuclearenergy plans. According to the Atomic AND ITS CHOICES EnergyCommission,India's nuclearpower generationwill increaseto 10000 MW by year2010.Everythingseemsto be set for a takeoff in nuclearpowel' The electricity requilements of .[ndia have giown tremendously anC the productionusing the country's thorium reservesin breederreac\\tootrhse.r non- demand has been running ahead of supplyl Electricity generation and In India, concerted efforts to develop solar energy and t r ans m i s s i opnro c c s s cisn In d i a a rc v c ry i neffi ci cnti n c< l l npari sowni tl r those of somedevelopedcountriesA. s per oneestimatei,n India generatingcapacity conventionasl ourcesof energyneedto be emphasizeds,o that the growing is utilized on an averagefor 360t)hoursout of 8760 hclursin a year,r,vhilein Japanit is rrsedlbr 5 t00 hours.ll' the utilizationlactor could be increascdi,t clemancclan be met and depletingfbssil fuel resourcesmay be conserved.To shouldbe possibleto avoid power cuts.The transmissionloss in 1997-98 on a nationalbasiswas 23.68Voconsistingof both technicallossesin transmis- meetthe energyrequirement,it is expectedthat the coal productionwill have sion lines ancltransfonnersa,nd also non-technicallossescausedby energy to be ipclcascdto q)orcthan .150nrilliontottsitt 200'+-2005 lts cotttpltrcdto thefts and metersnot being read correctiy.It should be possibleto achieve considerablseavingby leducingthis lossto 1570by the end of theTenthFive 180 million tonnesin 1988. Year Plan by r-rsingwell known ways and nreansand by adooting sound A number of 400 kV lines are operating successfullysince 1980s as commercial practices.Further, evcry attempt should be made to improve systemload factorsby flatteningthe load curve by giving proper tariff mentionedalreaclyT. his was the firsi stepin workingtowardsa nationalgrid. incentives and taking other administrativem.easuresA. s per the Central Electricity Authority's (CEA) sixteenthannual power survey of India report, There is a need in future to go in for even higher voltages(800 kV). It is the all India load factorup to 1998-99was of the order of 78Vo.Infuture it is likely to be 7I7o.By 200i,5.07 lakhof villages(86Vo)havebeenelectrified expecredrhat by the year 2Ol1-12,5400 ckt krn of 800 kV lines and 48000 and 117 lakh of pumpsetshave been energized. ckt kni gf 400 kV lines would be in operationA. lso lines may be sericsand Assuminga very modestaverageannualenergygrowth of 5Vo,India's electricalenergy requirementin the year 2010 will be enormouslyhigh. A shunt compensatedto carry huge blocks of power with greaterstability. There difficult and challengingtask of planning,engineeringand constructingnew power stationsis imrninentto rneetthis situation.The governnlenht as bLrilt is a needfor constructingHVDC (High VoltageDC) links in the country since DC lines can carry considerablymore power at the samevoltageand require fewer conductors.A 400 kV Singrauli-Vindhyachal of 500 MW capacity first HVDC back-to-backschemehasbeencommissionedby NPTC (National point-to-point bulk power Transmission Corporation) fo-l+lowed by first distanceof 91-5km EHVDC transmissionof 1500 MW at 500 kV over a from Rihandto Delhi, PowerGrid recentlycommissionedon 14'Feb.2003 a 'k NTPC has also built sevengas-basedcombinedcycle power stationssuch as Anta and Auraiya.

t 2000 MW Talcher-Kolar + 500 kV HVDC bipole transmissionsystem thus real time control of power system.It may also be pointedout that this book will enabling excesspower from East to flow to South. 7000 ckt km of + 500 kV also help in training and preparingthe largenumber of professionalstrained in HVDC line is expectedby Z0ll-I2. computeraidedpower systemoperationand control that would be required to handlev At the time of writing, the whole energy sce is so clouded with future. However, certain trends that will decide the future developmentsof REFERECNES electric power industry are clear. Books Generally,unit sizewill go further up from 500 MW. A higher voltage(7651 1200kV) will come eventuallyat the transmissionlevel. There is little chance l. Nagrath,I.J. and D.P. Kothari, Electric Machines,Tata McGraw-Hill. New Delhi. for six-phasetransmissionbecomingpopularthoughthereare few suchlines in 3rd edn, 1997. USA. More of HVDC lines will do-. in operation.As populhtion has already touched the 1000 million mark in India, we may see a trend to go toward 2. Eilgerd,O.1., Basic Electric Power Engineering,Reading,Mass., 1977. undergroundtransmissionin urban areas. 3. Kashkari,C., Energy ResourcesD, emandand Conservationwith SpecialReference Public sectorinvestmentin power has increasedfrom Rs 2600 million in to India, Tata McGraw-Hill, New Delhi, 1975. the First Plan to Rs 242330million in the SevenrhPlan (1985-90). Shortfall in the Sixth Plan has been around 26Vo.There have been serious power 4. Parikh,Kirit, .sacondIndia studies-Energy, Macmillian, New Delhi, 1976. shortagesand generationand availability of power in turn have lagged too 5. Sullivan,R.L, Power SystemPlanning,McGraw-Hill, New york, 1977. much from the industrial, agricultural and domestic requiremeni. Huge amountsof funds (of the order of Rs. 1893200million) will be requiredif we 6. S. Krotzki, B.G.A. and W.A. Vopat, Power Station Engineeringand Economy, have to achievepower surplusposition by the time we reachthe terminal year McGraw-Hill,New York. 1960. to the XI Plan (201I-2012). Otherwiseachievinga rargetof 975billion units of electric power will remain an utopian dream. 7. Car,T.H.,ElectricPowerStationsv, olsI andlI, ChapmanandHall,London, 1944. 8. CentralElectricity GeneratingBoard, Modern Power Station Practice, 2nd edn, Power grid is planning creation of transmissionhighways to conserve Right-of-way. Strongnationalgrid is being developedin phasedmanner.In ' PergamonL, 976. 20Ol the interregionalcapacitywas 5000 MW. It is Lxpecredthat by 2OlI-12, it will be 30000 Mw. Huge investmentis plannedto the tune of us $ 20 9t Golding,E.W., The Generationo.fE' lectricitlt b1tWind Power,Ctnpman and Hall, billion in the coming decade.presenrfigures for HVDC is 3136 ckt km, 800 kV is 950 ckt km, 400 kV is 45500 ckt krn and.220/132kv is 215000 L o n d o n ,1 9 7 6 . i ckt km. State-of-theart technologieswhich are, being usedin India currently are HVDC bipole, HVDC back-to-back, svc (static var compensator), 10. McMillan, J.T., et. al., Energy Resoorcesand Supp\\t, Wiley, London, 1976. FACTs (Flexible AC Transmissions) devices etc. Improved o and M I L Bennet,D.J., The ElementsoJ'NuclearPoveer,Longman,1972. (Operation and Maintenance) technologieswhich are being used tgday are 12. Berkowitz,D.A:,. Power Generationand Environmentalchange, M.I.T. press, hotline maintenance,emergencyrestoration system, thermovision scanning, etc. CambridgeM, ass., 1972. Because of power shortages,many of the industries, particularly power- 13. SteinbergM, .J. and T.H. Smith, Econonr-loadingof Power Plants and Electric intensive ones,have installed their own captivepower plants.* Curcently20Vo SystemsW, iley, New York, 1943. of electricity generatedin lndia comesfrom the captive power plants and this is bound to go up in the future. Consortiumof industrial .onru-.rs should be 14. Power System Planning and Operations:Future Problemsand ResearchNeeds. encouragedto put up coal-basedcaptive plants. Import should be liberalized E P R I E L - 3 7 7 - S R ,F e b r u a r y1 9 7 7 . to support this activity. 15. Twidell,J.w. and A.D. weir, RenewubleEnergyResourcesE, . and F. N, spon, London.1986. 16. MahalanabisA, .K., D.P. Kothari and S.l. Ahson, ConxputeAr ided Power,S),srenr Analysisand Control, Tata McGraw-Hill,New Delhi, 1988. 17. RobertNoyes(Ed.), Cogenerationof Steamand Electric Power,NoyesDali Corp., usA, 1978. 18. weedy, B.M. and B.J. cory, ElectricPower svstems,4thedn,wiley, New york, 1998. 19. cEA 12 Annual survey of PowerReport,Aug. 1985; l4th Report,March l99l; 16thElectricPower Surveyof India,Sept2000. x Captive dieselplants (and small diesel setsfor commercial and domestic uses) are 20. Kothari, D.P. and D.K. sharma (Eds), Energy En.gineeringT. heoryand practice, very uneconomicalfrom a national point of view. Apart from being lower efficiency S. Chand,2000. plants they use diesel which should be conservedfor transportationsector. 21. Kothari, D.P. and I.J. Nagrath, Basic Electrical Engineering,2nd edn, Tata McGraw-Hill,New Delhi, 2002.(Ch. 15).

ffiffi N4oderpnowerSystemAlqtysis , 20. Kothari, D.P. and D.K. Sharma(Eds), EnergyEngineeringT. heoryand practice, j S. Chand,2000. ^a 21. Kothari, D,P. and I.J. Nagrath, Basic Electrical Engineering, 2nd edn, Tata McGraw-Hill, New Delhi, 2002.(Ch. l5). 22. Wehenkel,L.A. AutomaticLearning Techniquesin Power Systems,Norwell MA: Kiuwer, i997. 23. Philipson,L and H. Lee Willis, (JnderstandingElectric Utilities and Deregulation, MarcelDekkerInc, NY. 1999. Papers 24. Kusko, A., 'A Predictionof Power SystemDevelopment,1968-2030', IEEE SpectrumA, pl. 1968,75. 25. Fink, L. and K. Carlsen,'OperatingunderS/ressand Strain',IEEESpectrum,Mar. r978. 26. Talukdar,s.N., et. al., 'Methodsfor AssessingenergyManagementoptions', IEEE Trans.,Jan. 1981,PAS-100,no. I, 273. 27. Morgen, M.G. and S.N. Talukdar, 'Electric Power Load Management: some Technological,Economic,Regularity and Social Issues',Proc. IEEE, Feb. L979, vol.67,no.2,241. 28. SachdevM, .S.,'LoadForecasting-BibliographyI,EEE Trans.,PAS-96, 1977,697. 29. Spom, P., 'Our Environment-Options on the Way into the Future', ibid May 1977,49. 2.I INTRODUCTION 30. Kothari D.P., Energy ProblemsFacing the Third World, Seminar to the Bio- The four parameterswhich affect the performance of a transmissionline as an Physics Workshop,8 Oct., 1986 Trieste Italy 31. Kothari, D.P,'Energy systemPlanningand Energy conservation',presentedat eiflfllieffffmiirlfe\"?#n;#rt or-,f'r\"-a*L.p-r-Lo*'i.+\"w.r,+-e,++;^rhi^S;an;#y.cr;s\"ra;rr;ttri;e;cnrqmr\"A\"lainnir\"eceJoewininh.aiirdtcaiumhuiceuiistte,aor.nsndo,avcrteme1o',reanch'llgaltyenhpddtaeuarucldaceitanitnntoeacsealnemncaaedkintsa,dhrlseeleriesnoovstiviesosnettsagranr'lechninetci'heseearn d YYIV Nntinnnl fnnvontinn sn v^ JF tltlrlLt r, Nr \\Iw^ r 'w, ynv- lt ht lil , IE -wk u , lI OQO , 7QL 32. Kothari, D.P. et. a1.,'Minimization of Air Pollution due to Thermal Plants'. ,I1E (India), Feb. 1977,57, 65. 33. Kothari, D.P, and J. Nanda,'Power Supply Scenarioin India' 'Retrospectsand Prospects',Proc. NPC Cong., on Captive Power Generation,New Delhi, Mar. i\"; th\" ,\"ri., imPedanceof the line' Inductar,c. ;;f; the most dominant 1986. i, line parameterfrom a power system 34. NationalSolarEnergyConventionO, rganisedby SESI,1-3Dec. 1988,Hyderabad. 35. Kothari, D.P., \"Mini and Micro FlydropowerSystemsin India\", invited chapterin engineer,sviewpoi nthte. Atrsawnsems hisasilol snceaepiancliatyt eofr cahlianpet' e r s , i t i s t h e i n d u c t i v e reactancewhich limits the book, Energy Resourcesand Technology,ScientificPublishers,1992,pp 147- 158. 36. PowerLine, vol.5. no. 9, June2001. 2,2 DEFINITION OF INDUCTANCE 37. United Nations.'Electricity Costsatxd Tariffs: A GeneralStudy; 1972. Voltage inducedin a circuit is given by 38. Shikha,T.S. Bhatti and D.P. Kothari,\"Wind as an Eco-friendlyEnergy Sourceto meet the Electricity Needs of sAARC Region\", Proc. Int. conf. (icME 2001), , =VY (2.r) BUET, Dhaka,BangladeshD. ec. 2001,pp 11-16. 39. Bansal,R. C., D.P. Kothari & T. S. Bhatti, \"On Someof the Design Aspectsof \", ,ti\" flux linkagesof the circuitin weber-turns(Wb-T)' Wind EnergyConversionSystems\",Int. J. of Energy Conversionand Managment, Vol. 43, 16,Nov. 2002,pp.2175-2187. This can be written in the form di., (2.2) drb di 40. l). P. Kothari and Amit Arora, \"Fuel Cells in Transporation-BeyondBatteries\", , e= ,-:L-:v Proc.Nut. Conf. on TransportatioSn ystemsI,IT Delhi, April 2002, pp. 173-176. dt dr dr 41. Saxena,Anshu, D. P. Kothari et al, \"Analysisof Multimedia and Hypermediafor anceof the circ'lit in henrys' which in ComputerSimulationand Growtft\",EJEISA,UK, Vol 3, 1 Sep 2001, 14-28. nearmagneticcircuit, i'e'' a circuit Ies vary linearly with current such that

+f ,,il Modernpo**, Syrtm An\"lyri, lnductancaend Resistancoef TransmissioLnines ffffi or - L=!H I (2.3) ,---f\\-]y A= LI ,'.rt t, -?5 tl li \\\\ e.4) -l-l- where ) and I arc the rms values of flux linkagesand current respectively. ir' i+----r 1 \\t. i ! These are of coursein phase. \\ t.rtt- I t'l Replacing + Eq.(2.1) by ir, we get the steadystateAC volrage drop -ir-.\" r1/ i due to alternatingflux linkagesas Y= jwLI = jt^r) V e.5) -On similar lines,the mutualinductancebetweentwo circuitsis defined asthe flux linkages of one circuit due to current in another,i.e., M r rnL= )t, (2.6) Fig. 2.1 Fluxlinkagesdueto internafllux (cross-sectionvailew) , Iz The voltagedrop in circuit 1 due to current in circuit 2 is where V, = jwMnlz = 7tl\\12 V (2.7) H, = magnetic field intensity (AT/m) The conceptof mutualinductanceis requiredwhile consideringthe coupling /y = current enclosed(A) betweenparallellines and the influenceof power lines on telephonelines. By symmetry,H, is.constantand is in direction of ds all alongithe circular 2.3 FLUX LINKAGES OF AN ISOTATED CURRENT. path. Therefore,from Eq. (2.8) we have CARRYTNG coNqucroR 2rryH,=1, (2.e) Assrrmino rrniform crrrrenf dcnsifv* Transmissionlines arecomposedof parallel contluctorswhich, for all practical ,' \" = (- ) t :[ 4 ), (2.10) purposesc, an be consideredas infinitely long. Let us first developexpressions for flux linkagesof a long isolatedcurrent-canying cylindricat conductor with \\r rr' ) \\r \") returnpath lying at infinity. This systemforms a single-turncircuit, flux linking FromEqs.(2.9)and(2.10),we obtain which is in the form of circularlines concentricto the conductor.The total flux can be divided into two parts,that which is internal to the conductor and the Ht,.=)2!T- r \" AT/m (2.rr) flux externalto the conductor.Such a division is helpful as the internal flux The flux density By, y metresfrom the centreof the conductorsis progressivelylinks a smalleramountof currentaswe proceedinwards towards the centreof the conductor,while the externalflux alwayslinks the total current Bu=pHu=:z+rnzttIr- Wb/m2 (2.r2) insidetheconductor. wherep is the permeability of the conductor. Flux Linkages due to Internal Flux Considernow an infinitesimal tubular elementof thicknessdy and length one metre. The flux in the tubular element dd = Bu dy webers links the fractional Figure 2.1 shows the cross-sectionavl i,ew of a long cylindrical conductor trrrn(Iril - yzly'l resulting in flux linkagesof carrying current 1. *For power frequency of 50 Hz, it is quite reasonableto assumeuniform current The mmf round a concentricclosed circular path of radius y internal to the density. The effect of non-uniform current density is consideredlater in this chapter conductoras shown in the figure is while treating resistance. {nr.ds =Iy (Ampere'slaw) (2,8)

ModernPqwer SystemAnalysis lnductancaend Resistancoef rransmissioLnines tf-fi.$ The flux dd containedin the tubular elementof thicknessdy is (2.r3) Integrating,we get the total internalflux lin dd = +dy Wb/m lengthof conductor ^^,=I#fdy:ffwat^ (2.14) The flux dQbeing externalto the conductorlinks all the current in the conductor which together with the return conductor at infinity forms a single return, such For a relative permeability lf,, = | (non-magneticconductor), 1t = 4n x that its flux linkagesare given by l0-'[Vm. therefore d)=1 x d 6' = FI d , 2n y f- (2.1s) Therefore, the total flux linkages of the conductor due to flux between points ^rn =T*10-/ wb-T/m and P, and Pr is Lint= ]zxto-7 rVm (2.16) \\,\" = ,|1p DD' \"t2,t,nnf'.vdy - -t\"- I ln \"n2 wb-T/m 2r Dr Flux Linkage due to Flux Between Two Points External to Conductor where ln standsfor natural logarithm*. SinceFr=I, F = 4t x10-7 Figure 2.2 showstwo pointsP, and Prat distancesD, and Drftoma conductor -n (2.r7) which carriesa cunent of 1 amperes.As the conductoris far removedfrom the return current path, the magneticfield external to the conductoris concentric ) r z= 2 x l}- t l ln =DLr wb/ m circles around the conductorand therefore all the flux betweenP, and Pr lines The inductanceof the conductor contributedbv the flux included between within the concentriccylindrical surfacespassingthrough P, and P2. points P, and Pr is then Lrz = 2 x I0-1fn -? fV* (2.18) Dl or L,LnL = 0.461 los.D' mH,/km (2.1e) \"Dl Flux Linkages due to Flux up to an External Point Let the externalpoint be at distanceD from the centre of the conductor.Flux linkages of the conductordue to externalflux (from the surfaceof the conductor up to the externalpoint)is obtainedfrom Eq. (2.17)by substitutinE D t = r and Dz = D, i'e', ).*,= 2x70-1 lln D (2.20) r Total flux linkages of the conductor due to internal and externalflux are )= )in,* )\"*, Fig.2.2 Fluxlinkagesdueto fluxbetweenexternapl ointsPI, P2 = I x 1 o - 7 + Z x r o - :I.I n 2 2r Magnetic field intensityat distancey from the conductoris H'. , = Z I r y AT/m *Throughout the book ln denotes natural logarithm (base e), while log denotes r logarithm to base 10.

W ModernPowersystgmAnalysis -- lnductancaendFlesistanaoef TransmissiLoinnes li$Bfr f-- =- .2^x- t[ +- 4r n 2 ) To start with, let us considerthe flux linkagesof the circuit causedby current 1 0 - , / r ) in conductor 1 only. We make three observationsin regard to these flux x ro_7t1\" *J_r, linkages: 1. External flux from 11to (D - ,) links all the current It in conductor 1. I-et ,t - ,r-r/4 = 0.7788r 2. External flux from (D - r) to (D + rr) links a current whose magnitude progressivelyreducesfrom Irto zeroalong this distance,becauseof the \\ = 2 x ro4rh + wb-T/m (2.Zra) effect of negative current flowing in conductor 2. rl 3. Flux beyond (D + 12)links a net cunent of zero. For calculating the total inductance due to current in conductor 1, a Inductance of the conductor due to flux up to an external point is therefore simplifying assumptionwill now be made. If D is much greaterthan rt and 12 (which is normally the casefor overheadlines),it canbe assumedthat the flux L= 2x 1o-n7 Ir w^ (z.zrb) from (D - r) to the centre of conductor 2 links all the current ^Irand the flux from the centre of conductor2 to (D + rr) links zero current*. Here r' can be regarded as the radius of a fictitious conductor with no Based on the above assumption,the flux linkagesof the circuit causedby current in conductor 1 as per Eq. (2.2Ia) are internal inductancebut the sametotal inductanceas the actual conductor. 2.4 INDUCTANCE OF A SINGLE.PHASE TWO.WIRE LINE Considera simpletwo-wire line composedof solid round conductorscarrying ) r = 2 x 1 0 - 7 1 ,l n - L (2.22a) currents1, and 1, as shownin Fig. 2.3.|n a single-phaseline, r\\ 11+Ir= Q The inductance of the conductor due to current in conductor 1 only is then Lt= 2 x 10-7l\" + (2.22b) f'1 Iz= - It Similarly, the inductanceof the circuit due to current in conductor 2 is ' Lz=2x10-7h D r,2 . (2'23) rloinc rha crrncrrrnsifinn f! ahr vev ^nv ^r^e^ t r n fhe flrrx linkaoes and likewise fhe indttcfances vurrrE ruv usrvrr of the circuit causedby currentin eachconductorccnsideredseparatelymay be addedto obtain the total circuit inductance.Therefore,for the completecircuit L= Lt+ 4= 4 x 10-'ln FVm (2.24) D-rz If r/r= r'z= /; then D L= 4 x 10-'ln D// Wm (2.25a) D+rz L - 0.92t log Dlr' mHlkm (2.zsb) Fig. 2.3 Single-phastewo-wirelineandthe magneticfielddueto currentin conducto1r only Transmission lines are infinitely long comparedto D in practical situations It is important to note that the effect of earth's presenceon magneticfield and therefore the end effects in the above derivation have been neglected. geometry* is insignificant.This is so becausethe relative permeabilityof earth is aboutthe sameasthat of air and its electricalconductivitv is relativelvsmall. 2.5 CONDUCTOR TYPES *The electric field geometry will, however, be very much affected as we shall see So far we have considered transmission lines consisting of single solid later while dealing with capacitance. cylindrical conductors for forward and return paths.To provide the necessary flexibility for stringing,conductorsusedin practicearealways strandedexcept *Kimbark [l9] has shownthat the resultsbasedon this assumptionare fairly accurateevenwhen D is not muchlarger than 11and12.

52 | Vodern PowerSystemAnalysis I rl nrerlLr r Lr n.+vatnca ^l t t u t t c^ ^t-'ft t u ant t^'^sl ^t.l^'-l-a- t l u g u^ tt r I- ^l-a l l s-r-n^ :l-s s l-o! n- , r. l*| -^ \" fo, .r.ry small cross-sectionalareas.Stranded conductors are composed of Unes ! 5.* strands of wire, electrically in parallel,with alternatelayers spiralled in 2.6 FIUX LINI{AGES OF ONE CONDUCTORIN A GROUP opposite direction to prevent unwinding. The total number of strands(M) in concentrically strandedcables with total annular spacefilled with strandsof As shown in Fig. 2.5, considera group of n pnallel round conductorscarrying phasor currents Ip 12,-, I, vvhose sum equals zero. I)istances of these uniform diameter(rD is given by N=3x'-3x+l (2.26a) lt ult,..t un. us oDtam where x is the number of layerswhereinthe single central strandis counted as an expression for the total flux linkages of the ith conductor of the group the first layer.The overall diameter(D) of a strandedconductoris consideringflux up to the point P only. P-(2x-r)d (2.26b) o Aluminium is now the most commonlyemployedconductormaterial.It has (, n the advdntagesof being cheaperand lighter than copper though with less 3 conductivity and tensile strength.Low density and low conductivity result in 2 larger overall conductordiameter,which offers anotherincidentaladvantagein high voltage lines. Increaseddiameterresults in reduced electrical stressat - conductor surfacefor a given voltage so that the line is coronafree. The low 4 tensile strengthof aluminium conductorsis made up by providing central I strandsof high tensilestrengthsteel.Sucha conductoris known as alurninium Fig. 2.5 Arbitrargy roupof n parallerl oundconductorcsarryingcurrents conductor steelreinforced(ACSR) and is most commonly usedin overhead The flux linkagesof ith conductordue to its own current1,(selflinkages)are given by [see F,q.(2.21)] transmissionlines. Figure 2.4 showsthe cross-sectionavliew of an ACSR conductor wrth 24 strandsof aluminium and 7 strandsof steel. Steelstrands )ii= 2 x 10-7t, h! Wb-T/m (2.27) ri The flux linkages of conductor i due to currentin conductor7 1rlf\"r to Eq. ( 2 . 1 7 ) li s 5,,= 2 x l;-il,fn a Wb-T/m (2.28) Dij Aluminium whereDu is the distanceof ith conductor from 7th conductorcarrying current strands 1r.From F,q. (2.27) and by repeateduse of Eq. (2.28), rhe rotal flux linkages of conductor i due to flux up to point P are Fig.2.4 Cross-sectionvailewof ACSR-7steelstrands2, 4 aluminiumstrands )i = Xir + )iz + ... + )ii *... * )in In extra high voltage (EHV) transmissionline, expandedACSR conductors are used.Theseare provided with paperor hessianbetweenvariouslayers of =2x rca(r,t'* + 4' u D!,-z + . . . +1 ,l,n D i strandsso as to increasethe overall conductordiameterin an attemptto reduce electrical stressat conductor surfaceand prevent corona. The most effective \\^ Dt rl. way of constructingcorona-freeEHV linesis to provide severalconductorsper phase in suitable geometrical configuration.These are known as bundled +...+ In conductorsand are a common practicenow for EHV lines. The above equation can be reorganizedas )i = 2xro'[[r, h+ +hn[*.+ I,m]+..+ + (/, ln D r + I r h D z + . . . + I i k D , + . . + I n ^ O , ) But, I, - - (1, + Iz +... + In-).

lnductanec anrl ,Frl as raqi or rruagn a a u^ ir TI -r-a- ^l l-s-m! l s s f . Llnes f.. on k,...i<Er Substiiuti'g for /n in the secondterm of Eq.(2.29)and simplifying, we have - I --- u, Applying Eqa . (/ 12-l3A0\\ t )^ rc or filamenr i of conductorA, weobtainits flux I f/ tintages )i' = 2 * t o - tIlt , m l * L,h L_.+...+r1na, L(' Dir'-\"\"'Diz\"\"''''^'rti zxfir ! h+a6J-a...*rnl*...*rn I * I,ln =e+. ..*li ln at- - 2 x t o -4^7,,l ( . . . * I , - r 1 n' D4r -)t1)) t\" ] -* 6^^-' J - 1 |. .\" .' *' l'nr t ) \\ Dir, Diz, D,^, ) In order to accountfor total flux linkagesof conductor i, let the point p now =2x lo-716 (P,r:D,r,...D,t Wb_T/m recedeto infinity. The terms suchas ln D1/Dn,etc. approachln t = o. Also for (D,rD,r.. .D,,.. .D,n)r'\" the sakeof symmetry,denoting ,.{^ D,,,-wi have The inductance-offilament f is then li= z x 1orI trn** r' r ' , ' ! - + 1-\", l--n- - 1 L i = ]7-! / : 2nx70-t,n (Dn'\"' D,,\"' ' D,^')1/^' FVm (2.3r) n ( D , r D , r . . . D , ,. D ' * U Dt D,2 Dii +...+I^t\" wb-r/m (2.30) Theaverageinductanceof thefilamentsof compositeconductoAr is +) L u u , =L t + L 2 + 4 + \" ' + L n 2.7 INDUCTANCE OF COMPOSITE CONDUCTOR LINES Sinceconductora is co#posedof n filamentselectricallyin parallel,its inductancies We arenow readyto study the inductanceof transmissionlines composedof , _ L u , , _ \\+ 12+...+L, compositeconductor sF. uture 2.6 showssuch a single-phaselin e comprising _A =- compositeconductorsA and B with A havingn paraliel filamentsandB having .*pr\"f,rionforrir\"#i\"t indu*ancefromEq.(2.31)i\"E;. mt parallelfilaments.Though theinductanceof eachfilament will be somewhat *ru\"rorr:rr\"rh\" 3'::r', udniftfteorremn)t,(itthiesisrruefsfiicsiteanntlcyeawscicllubraeteefqouaaslisf ucmon.tedhuact tthoerdciaumrreentetirssaerqeucahlolysdeinvtiodebde l ( D n ,. . .D rj , . . . D r . , ) . . . ( D ^.,. .p r j ,. . . D , ^ , ) . . . among the filamentsof each compositeconductor.Thus, eachfilament of A is taken to carry a current I/n, (Dnr.,..Dnj,... Dr^,17r/ntn return current of - Ihnt. while each filament of conductor B carries the L e = 2 x 1 0 - 7l n [ ( D n . .D. u. . .D r n ) . . . ( D i t . . n4, .t . Htm (2.33) oo o (Dnt... Dni ...D rn)]r,n' 2 2l I 11?x-.::ir:l :f ,he,arsumeonfrthelogarithmin Eq.(2.33i)s rhem,nth o r) t:?,T,:!u\"^.]:-tl-*'ocf onducAtotimr i'ri\"L.il \"il\"#il#:ili:ffi; m yl:f#lr,1\"\"1:#i) *: jr:lr* nrpyrnod2u.cittntehrtompfnerzpta,i;ndtso;\";f;i.i\"_;;,;;ir;frjf\"\"f,if,isitlsil:; setof T:l of CompositceonductoAr I!:::::1li:*Ti:r{. rnl denominaisrdoerfin\"uo,;;;w;;:;;:;,1;::; lf Fig.2.6 single-phasleineconsistinogf two compositeconductors G!:{MKDr,i\"s-lai:lst:ot:cya?lled ofcondutocrA,and,sauureviat;e, ; \"r';#;;;\":::\"* geometric mean radius (GMR). \"J In terms of the above symbols,we can write Eq (2.33) as

56 ,1 todern FowerSystemAnalysis Inductanceand Resistanceof TransmissionLines I L t = 2 x 1 0 - 7 h+ - I i l m srngrelayer oI alurrunlum conductorshownin Fig. 2.8 is 5.04cm. The diameterof eachstrandis 1.6g cm. Dr.t (2.34a) Determinethe 50 Hz reactanceat I rn spacing;neglectthe effectof the central strand of steel and advancereasonsfor the same. '^ ^Hn^ Solution The conductivity of steelbeing much poorer than thatof aluminium and the internal inductance of steelstrandsbeing p-times that of aluminium Note the similarityof the aboverelation with Eq. (2.22b),which gives the strands,the currentconductedby the centralstrandsof steelcanbe assumedto be zero. inductanceof oneconductorof a single-phaseline for the specialcaseof two solid, round conductors.In Eq. (2.22b) r\\ is the self GMD of a single Diameterof steelstrand= 5.04 -2 x 1.68= 1.68cm. conductor andD is the mutual GMD of two single conductors. Thus, all strands are of the samediameter, say d. For the arrangement of strandsas given in Fig. 2.8a, The inductanceof the composite conductor B is determinedin a similar Dtz= Drc= d manner,andthe total inductanceof the line is Drt= Dn= Jld L= Le+ Ln (2.3s) Du= 2d A conductor is composedof sevenidentical copper strands,each having a Dr= (l(+)- dTil,eilf') radius r, as shownin Fig. 2.7. Frnd the self GMD of the conductor. -- D^^= 2..fir Fig.2.7 Cross-sectioonf a seven-strancdonductor (a) Cross-sectionof ACSR conductor Solution The self GMD of the sevenstrandconductoris the 49th root of the (b) Line composedof twoACSR conductors 49 distancesT. hus Fig.2.8 D, = (V)7 (D1zD'ruDrp r)u (zr)u )t'on Substitutingthe valuesof various distances, p..- ((tJ.7788r)7(2212x 3 x 22f x 22rx 2r x 2r)u)t'o' u, s _- 2 r(3 (0 .7 7 8 8))tt7_ 2.t77r 6U+e

I M o d e r nP o w e r S v s t e mA n a l v s i s lnductanceand Resistanceoi TransmissionLines 5t I Substitutingd' = 0.7188dand simplifying The self GMD fbr side A is D , = l . l 5 5 d = 1 . 1 5 5x 1 . 6 8= 1 . 9 3c m D ^ = D s i n c eD > >d D,A= ((DnD nD n)(DztDzzDn)(D3tDtrDtr))''e Here. D,, = Doc= Dat= 2.5 x 10-3x 0.7788m Substitutingthe valuesof variousinterdistancesand self distancesin D16,we L= 0 . 4 6 t t o\"e 1P - 0.789mH /km get 1.9 3 D,A= (2.5 x 10-3x 0.778U3x 4a x 8\\tte = 0.367m Loop inductance- 2 x 0.789 = 1.578mHlkm Similarly, ; ; ; , ; ,I;Loop reactance= 1.578x 314 x 10-3 - 0.495ohms/lcm The arrangemenot f conductorsof a single-phasetransmissionline is shownin D, B= ( ( 5 x 10- 3x 0. 778q2, 4') t 'o Fig.2.9, whereinthe forwardcircuit is composedof threesolid wires 2.5 mm = 0 . 1 2 5m in radius and the return circuit of two-wires of radius 5 mm placed symmetricallywith respectto the forward circuit. Find the inductanceof each Substitutingthe values of D^, D6 andDr, in Eq. (2.25b),we get the various side of the line and that of the completeline. inductancesas Solution The mutual GMD betweensidesA and B is L^^ = 0.46 1 l o\"s 8'8 = 0.635mHlkm 0.367 D.= ((DMD$) (Dz+Dz) 1D3aD3))tt6 L .D = 0.4 61 to-e 8'8 = 0.85 mH/<m 0J25 L = Lt + Ln = 1.485mH/km If the conductorsin this problem are each composedof seven identical strandsas in Example2.1, the problemcanbe solvedby writing t[e conductcr self distancesas Dii= 2'177rt where r, is the stranciraciius. 2.8 INDUCTANCE OF THREE.PHASE LINES ()z 4m So far we have considered only single-phaselines. The basic equations developedcan,however,be easilyadapledto the calculationof theinductance l i of three-phaselines. Figure 2.10 showsthe conductorsof a three-phaseline with unsymmetricasl pacing. 4m \"s (' t\"l ' It I SideA Side B Dn Dzs Fig. 2.9 Arrangemenotf conductorfsor Example2.3 From the figure it is obviousthat D t q = D z q = D z s - D . u = J O am Fig. 2.10 Cross-sectionavl iew of a three-phaseline with unsymmetricasl pacing Drs=Dy = 10m D ^ = (6 8 2x 1 0 0 )l /6= 8.8 m

Ugdern Power SystemA lnductanceand Resistanceof TransmissioLnines Assumethat thereis no neutralwire, so that But, 1, I I, = - /n, hence (D\"D'trDt')''' Ir,+Ir+ Ir-0 Ao=2 x 10-7Iok Unsymmetrical spacingcausesthe flux linkagesandthereforethe inductanceof eachphaseto be differentresultingin unbalancedreceiving-endvoltageseven r'a en senolng-e tages and llne currents are balanced. AIso voltages will be D\"o (DtzDnDrr)t''- equivalenetquilateraslpacing induced in adjacentcommunication lines even when line currents are balanced. This problem is tackled by exchanging the positions of the conductors at regular intervais aiong the line such that each conductor occupies the original position L o = 2 x t 0 - 7h + = 2 x f O - ?f n { : r F V m (2.36) of every other conductor over an equal distance. Such an exchange of conductor f'oD, positions is called transposition. A complete transposition cycle is shown in This is the samerelation as Eq. (2.34a) where Dn,= D\"o, the mutual GMD Fig.2.11. This alrangementcauseseach conductor to have the same average betweenthe three-phaseconductors.lf ro = 11=, r6t we have inductance over the transposition cycle. Over the length of one transposition Lo= LO=L, It is not the presentpracticeto transposethe powerlinesat regularintervals. cycle, the total flux linkages and hence net voltage induced in a nearby However,an interchangein the positionof theconductorsis madeat switching stationsto balancethe inductanceof the phases.For all practicalpurposesthe telephone line is zero. dissynrnrctrcyanbc neglectcdandthe inductanccof an untransposelcinl e can be taken equal to that of a transposedline. 1b If ttre spacingis equilateral,then D\"o= D and Fig.2.11 A completetranspositiocnycle L o = 2 x l 0 - 7 mIra f m n (2.37) To find the averageinductanceof eachconductorof a transposedline, the If ro = 11,= r,-, it follows from F,q. (2.37) that flux linkages of the conductorare found for eachposition it occupiesin the iransposecciycie. appiying Eq. (2.s0) to conciuctora of Fig. z.lI, for section Lo= Ltr= L, 1 of the transpositioncyclewhereina is in position1, b is in position2 and c is in position3, we get ) u r= 2 x t o - r,f, , r \"* I I,,m]-*l ( I n- 1 j * o - r r , r , Show that over the length of one transpositioncycle of a power line, the total flux linkagesof a nearby telephoneline are z,erof,trr balancedthree-phase \\\" ''r, \" Dr, Dt,) currents. For the second section 'x to-- ?( [rk\" | * 16tnb|: \\ + . '' t\" ],;i wuv- Fotrhetr,ira,\".* := (bl) c i'-) )o3= z x ro - 7r\"1h !ft',, 1\" 6t n*+ r.,nlu-zlr / *o-rr- D, \\7 \\ c'l Average flux linkages of conductor a are - 1 u rctlI,,h!r,,tn +1.ln () (DnDrDlt)t/3 \\4, (Dt2D2.)3t)t/3 T2 F19.2.12 Effectof transpositionon Inducedvoltageof a telephoneline

62 | Modern Power Svstem Anatrrqic. lnductanceand Resistanceof TransmissionLines solution Referring to Fig. 2.r2, the flux linkagesof the conductor r, of the (ii) third and multiple of third harmoniccurrenrsunder healthy .ondirion, telephoneline are where rc-7 , \" ^ * + 1 , l n t\"* Wb-T/m(2.38) 1,,(3)+IoQ)+ I,(3)= 31(3) *.1 The harmonicline currentsare troublesomein two wavs: Similarly, (i) Inducedernf is proportionalto the frequency. (ii) Higher frequenciescome within the audiblerange. ) t 2 = 2 x t o t l, \" L n5 * r- 6o -t- n+ * 1 . 1 n +l w b\"_v r i' 'mt (2.3s) Thus thereis needto avoid the presenceof suchharmoniccurrentson power \" ( Do z Du , D,, ) Iine from considerationos f the performanceof nearbytelephonelines. It has been shown abovethat voltageinducedin a telephoneline running The net flux linkagesof the telephoneline are parallel to a power line is reducedto zero if the power line is transposedand ),= ),t- )tz provided it carries balanced currents. It was also shown that ptwer line transpositionis ineffectivein reducingthe inducedtelephoneline uoitug. when = 2 x to-rt(\" h D:, * 16tn? *r\"\" ,-\"+D)\" ) wb-rim(2.40) power line currents are unbalancedor when they contain third harmonics. rheemfinduce,d\" ,n!,.,\"p'#ir\"t* Power line transpositionaparrfrom beingineffectiveintroducesmechanicaland \"3Jti, insulationproblems.It is, therefore,easierto eliminateinduced voltagesby E,= Zrf),\\lm transposingthe telephoneline instead.In fact, the readercan easilyverify that even when the power line currents are unbalancedor when t-h\"y cgntain tccfhjaanrnndecceeeeralllnlbaadattiilaooarnnnedtcooteheadeslrngoeorafeotdatratecekionexntppdelhiantaitcoosenfews.tC,ihthoe),nhfslauiesrxqmunloieonnntkrta.vl\"ygeu,ter.hyrse.dnlsautesrefgrwteeohqbiuIceoehc,naa1cur6ieesasemn,tidufhle1tpirrpre.elSesisuseocnahft. harmonics,the voltage induced over completetranspositioncycle (called a maybe verytroublesome. barrel) of a telephoneline is zero.Someinducedvoltagewill alwaysbe present on a telephoneline running parallel to a power line becausein actu4l practice lf the power line is f'ully transposedwith respectto the telephoneline transpositionis nevercompletelysymmetrical.Therefore,when the lines run parallel over a considerablelength,it is a good practiceto transposeboth power ),,= )\" (I)* 4, (tr)* ),,(III) and telephone lines. The two transposition cyeles ^re staggered.and the 3 telephoneline is transposedover shorterlengthscomparedto the power line. where),r(I), )/r(II) ancl),,(III) are the flux linkagesof the threetranspositionsectionsof the power line. the telephoneline r, in i,.\"rp,\"i- u fI Writing for ),,(l), ,\\/2(II)and ),r([l) by repeareduseof Eq. (2.3g),we have A three-phase5,0 Hz,15 km long line hasfour No. 4/0 wires(1 cm dia) spaced horizontally 1.5m apartin a plane.The wires in orderarecarryingcurrents1o, Similarly, A,t= 2 x l0-/(tn+ 16+1,,)ln Iu and I, and the fourth wire, which is a neutral, carries ,\".o iu..\"nt. The (DntDutD,.itt3 currents are: =2x104(1,+.Ib+1,)ln Io= -30 + 750 A (Dn2Db2D,,r)t,, Iu= -25 + j55 A I\"= 55- j105 A ) r = 2 x 1 0 - 7 1 1+, I t , + I , )' l n ( D \" 2 D b 2 D , ) r t : (2.4r) The line is untransposed. (DorDarD,r)r,, (a) From the fundamentalconsideration,find the flux linkagesof the neutral. Also find the voltageinduced in the neutralwire. If Io + Iu + I, = 0, ), = 0, i.e. voltage inducedin the telephoneloop is zero (b) Find the voltage drop in each of the three-phasewires. over one transpositioncycle of the power line. - It may be notedherethat the condition Iu+ Iu+ I, = 0 is not satisfiedfor (i) rpwer frequencyL-G (line-to-groundfault) currents.where Io+ Iu* Ir=J[o

64 I ModernPower SystemAnalysis lnductanceand Resistanceof TransmissionLines I t abcn In2 (. 1 ,r\"n.'f(') ln Dlrl (:; (:) ln2 t-r.s n.-'-.-t--1.5 m-l*- r.sn1-l s e 4 r s c a ulated below: Fig.2.13 Arrangemenotf conductorfsor Example2.5 voltage p o Solution (a)From Frg.2.I3, Avo = j2xra-lx3r4x rs x rd(6 !9e (-30+j50)+0.6e3(-25+is5)) D o n = 4 .5 m, D b n= 3 m, D rn = 1.5 m = - (348.+6 j204) V Flux linkagesof the neutral wire n are -( I' + 1 ^ l n 1' * l l n ' r\\ ) - = 2 x 1 0 - 7 11 - l n lwb-T/m \\\" Don \" Drn D,n) A single-phase50 Hz power line is supportedon a horizontalcross-ann.The spacing between the conductorsis 3 m. A telephoneline is supported Substitutingthe valuesof D,,n,Dg, and D,.n,andsimplifying, we get symmetricallybelow the power line as shownin Fig. 2.14. Find the mutual inductancebetweenthe two circuits and the voltageinducedper kilometre in the An=- 2 x lO-' 0.51 I, + 1.1Iu + 0.4051\")Wb-Tim telephoneline if the currentin the power line is 100A. Assume the telephone Since I, = - (Io+ I) (this is easily checkedfrom the given values), Iine current to be zero. 2,, = - 2 x l0-' (1.1051o+ 0.695I) Wb-T/m Solution Flux linkaeesof conductor Z, The voltage inducedin the neutral wire is then Vn= jw),nx 15 x 103V ) , r = 2 x I o - 7( , r n t - l 6 t ) = 2 x ro-1I h D' = - j 3 1 4 x 15 x 103x Z x 10-7(1J05Io+0.695I) y \\ Dt D r ) D1 or Vn = - j 0 .9 4 2 (1 .105Io + 0.695I) V Flux linkages of conductor 7, Substitutingthe valuesof 1, and 16,and simplifying Vn= 0.942x 106= 100 V \\,2= 2 x 10-71lnD' (b) From Eq. (2.30),the flux linkages of the conductor a are D^ ( r I r\\ ) o =2 x r o - ?r [, r nlr*' o r\"u r n* * r rn*2D)| wu-r- \\ D The voltagedrop/metrein phasea canbe writtenas a v , , = 2 x r 0 - 7 i w ( , - r n I + 1'^' l n l * 1 - lcn I ) tr,o \\.\" f'o D 2D) Since Ir= - (lr,+ Iu), and furthersincero= rb= rr= r, the expressionfor AVo canbe written in simplified form \\)d/ Avo= 2 x to-ty,(r, rn!* romz) v/m I,'-Yt'- \\-l-l Similarly, voltage drop/petre of phasesb and c canbe written as \" l*-O.et Fig.2.14 Powerandtelephonelinesfor Example2.6 AVo=2 x r;a iulbo#_ Total flux linkage of the telephonecircuit A V , = 2x t o t / , ( 1 ,f n2 + 1 , \" + ) ) , = \\ , r - \\ r z = 4 x 1 0 - ' l l n D2 Dr Using matrix notation,we can presentthe result in compact form

66 iI Modernpower SystemAnalysis lnductaneaend Resistanceof TransmissioLnines A4pt=4 x tl-i n ! Ul^ eachother. (The readercantry other configurationsto verity that thesewill lead Dl to low D..) Applying the methodof GMD, theequivalentequilateralspacingis D rn (DnbDbrD.n)''t (2.42) a andb in sectionI of the D r = Q . 1 2+ 2 \\ t / 2 = ( 5 . 2 I ) t / 2 transpositioncYcle D2= (L92 + Z\\r/2 = (7.61)t/2 = (DpDp)rr+- 7DP)tt2 Dt,=mutual GMD betweenphasesb and c in section 1 of the v or t' = o .g 2 r b s- (Jsf)t\"= \\ 5 2 1) transpositioncYcle 0 . 0 7 5 8m H / k m = (DP)r;z Voltage inducedin the telephonecircuit V,= jttMr,I D,o=mutual GMD betweenphasesc and a in sectionI of the lV,l = 314 x 0.0758x l0-3 x 100 _ 2.3,/9 Vlkm r- transPositioncYcle = (2Dh)v2 2.9 DOUBI\"E.CIRCUIT THREE.PHASE LINES Hence D\"o 2rt6Drt2pr/3htt6 (2'43) It is commonpracticeto build double-circuithree-phaselinesso asto increase It uray be noteclhere that D\"u t'eurainsthe sallle in each section of the transmissionreliability at somewhatenhancedcost. From the point of view of transpositioncycle, as the conductorsof eachparallelcircuit rotatecyclically, rrowertransferfrom one end of the line to the other (seeSec. 12.3),it is so do D,,h, Dbrand D,.,,.The reader is advisedto verify this for sections2 and desirableto build the two lineswith aslow an inductance/phasaespossible.In 3 of the transpositioncycle in Fig' 2'15' order to achievethis, self GMD (D\") should be made high and mutual GMD Self GMD in section1 of phase a (i.e.,conductorsa and a/) rs (D') should be made low. Therefore,the individual conductorsof a phase shouldbe kept asfar apartaspossible(for high self GMD), while the distance Drr,= (r'qy'q)t'o= (r'q)'/z respectiverv'i betweenphasesbe kept as low as permissible(for low mutual GMD). SerGr MD\"t *;:;=' Figure2.15showsthethreesectionsof thetranspositioncycleof two parallel ,*;;';:^':'ffi'1'are circuit three-phaselines with vertical spacing (it is a very commonly used configuration). Drr= (y'qr'q)'''= (r'q)''t cb'b Equivalent self GMD D, = (Dr,,DrbD,,)rt3 = (r')t''qtt3hrt6 (2.44) Becauseof the cyclic rotation of conductorsof eachparallel circuit over the transpositioncycle,D. alsoremainsthe samein eachtranspositionsection.The readershould verify this for sections2 and3 in Fig. 2.15. The inductancePer Phaseis o o\\ 0 , D',n L = 2 x 1 0 - 7l o Section 3 Ds Section 1 Section2 = z x ,ot ,n't'u'|l'ltl\"tlt)u (r')t'' qr/3hrt6 Fig. 2.15 Arrangementof conductorsof a double-circuit hree-phaseline = 2 x 1 0 - 7 h ( 2,,u(q')\"'[a)\"' ] rvpnur.rrn(2.4s) [' \\r') \\q) It may be noted here that conductors a and a' in parallel compose phase a and sirnilarly b and b'compose phase b and,c and c'compose phasec. in order The self inductanceof eachcircuit is givenby to achieve high D\" the conductors of two phases are placed diametrically ( 2 ) ' ' 'p opposite to each other and those of the third phase are horizontally opposite to Lr= 2 x 10-7ln r

Equation(2.45) cannno\\,v be written as lnductanceand Resisianceof TransmissioLnines L= ! ' ^ c[.2 * 2 x r o - 7(rt n) ' ^ l 8-10 timesthe conductor'sdiameter,irrespectiveof the numberof conductors u in the bundle. [ , \" , ,r.ou, = +M) tt,d dl ,(t, di I where M is the mutual inductancebetweenthe two circuits. i.e. \\r-.\\ / - d /-\\ (} ---1-) \\_.. d M = z x 1 o -^7( z \\ ' ' ' F i g . 2 . 1 6 Configurationof bundledconductors \\q ) This is a well known result for the two coupled curcuits connected in parallel (at similar polarity ends). (f \")= o. aml, -] s = 0.4m\"\" - s = 0 .4 m ! . /\\ , I ou', be) I On' \"\\ ' '/^' :' 6 / rf h >>o,[ L l-l unaM '--+0i.,e.themutuairmpedancbeetweetnhecucuits l-_- d =7 m---*]*- d =7 m--- >l \\q ) I : becomes zero. Under this condition 0\"- IJ 2D Fig.2.17 Bundledconductotrhree-phasleine L=I x 1 ' ln \"'; (2.47) Further, because of increased self GMD- line inductance is reduced considerablywith the incidental advantageof increasedtransmissioncapacity The GMD method,though applied above to a particular configuration of a of the line. any configurationas long as the circuits are double circuit, is valid for electricallyparallel. While the GMD method is valid.for fully transposedlines, it is commonly appliedfor untransposedlines and is quite u.rrrui\" for practical purposes. s2. r v1 n sEvl rl rTrl-.rtrrrr.rq . L r r : r n AAr? Find the inductive reactancein ohms per kilometer at 50 Hz of a three-phase tetJM,rUUl-L,t(S bundledconductorline with two conductorsper phaseas shownin Fig. z.ri. All the conductorsare ACSR with radii of 1.725cm' ascccfproleIoelierotobemfmirapnwtuatiiihcspadftnrceoehelaruadoerradencalmllyccotedtcbteipooosman'eayCrhsnrtgbfsoiotoafoowEeh-esnrsanmtehpHocwaeithnpivVocssgeceahohf*rvearleRo.dloicenc1ltnnuiwaeraos0teotphgnichrascmtoeheeobgr.hnimaHaenfeesmarnngoatscgwaasocrwelecaeannmnovcoeednpd[eafvri1ioettreuecl1baterannhsroeii],nnrctmeerhtgoalrfshbcoaiadcenneeaonrsoiicadlsselddnstmih.ettnccwhahnuidomeononeeunrcntvwucoaemokodoenntnnspnhulbbiattosctsecaheei,iafmittlrgadtrncoyotwpeiuetor(ofotefsuamrnhanctapewbdhiecobn\"nsoiaet.ntltsp,uyitterocihpacptsbronle3acafhuytevsi,cnhacn0er.giestebCtgn0rrh<eneorg0rielels.icuoouritkTsneisupfnosvchuassef/gactilmhnsetdolftdohodclanoiifinrengrsaadfmieceorttsouarbosNinsvrcenue'udiooTctagznvopeclepastedrri,ates)ttasrhloihiigebeotnniefecsedylnyd - Even thoughthe power linesarenot normallytransposed(exceptwhen they omtifoeTntthhhseeoillbdbuuiussnntdrsdalteliteleludufsiannuilraeFlylsliygsac'cc2ooc.nm1udr6pua.rtTcisethefooesrrstcwwuaoilrltr,heptinhrnatrwecthteiilecol arnblofupotnuuddrriplvecoiodasnereedseu.rqucutloyarllsytaraarmrnasonpngogestdheinedcT.cohonendfGiugcMutroDar-s enter and leave a switching station), it is sufficiently accurate to assume complete transposition(of the bundles as well as of the conductorswithin the bundle) so that the methodof GMD can be applied' The mutual GMD betweenbundles of phasesa and b Dob=@ @+ s) (d- i d)rt4 Mutual GMD betweenbundles of phasesb and c Dh, = D,,,,(bY sYmmetrY) Mutual GMD betweenbundlesof phasesc uruJa D,n = Qd (2d + s ) (2d - t)Zd)tt+ D,o= (DrPaPro)t't = @f@ + s)z(d- s)2(2a+ i(Zd - t))tt\" = GQ)6Q .q26.0)2(14.4)(13.6))','',2 = 8 . 8 1m The more the number of conductorsin a bundle, the more is the self GMD'

70 I n llarlarn Dnre,o' erra+^- ^ -^r-,^. D .,= (r' s r' r)' ' o =(rk)r/z= (0.77ggx 1.725x l 0-2 x 0.4\\t/z lnductanceand Resistanceof TransmissionLines = 0 .0 7 3m A = cross-sectionaal rea,ln2 Inductivereactanceper phase The effective resistancegiven by Eq. (2.48) is equalro the DC resistanceof the conductor given by Eq. (2.49) only if the current distribution is uniform 8.8r throughoutthe conductor. 0.073 r small changesin temperature,the resistanceincreaseswith temperature in accordancewith the relationship = 0.301ohm/km In mostcasesi't is sufficientlyaccurateto usethe centreto centredista'ces R,= R (1 + oor) (2.s0) betweenbundlesratherthan mutual GMD betweenbundlesfor computingD\"n. with this approximation,we have for the examplein hand where R = resistanceat temperature0\"C Drn=exTxl4yrrt-g.g2m ao = temperaturecoefficient of the conductorat 0\"C Xr= 3I4 x 0.461x 1 0 - 3l o\"s 8'82 Equation (2.50) can be used to find the resistanceRo at a temperature /2, if 0.073 resistanceRr1at temperature tl is known = 0.301ohmlkm ( 2 . s1 ) tcehoxeanTcedhtxuumacsmettohtphlreiloenadiepn'Iwpt hriitosahxnianidmsn, ttearhuqteemcuteiievvqtaeuhltioeovdnacy(ltoeoi emnnltcphlliaensarueelrmtwihsoeitlsilicnbtthdhaauesvcisestai)vsmdei ner=greelae7accctmoat nanndaccuenoedcvftacoalourlbinenudaenus.dcFtltheooedrr 2.T2 SKIN EFFECT AND PROXIMITY EFFECT diameter(for sametotal cross-sectionaalrea)as JT x 1.i25 cm The distribution of current throughout the cross-sectionof a conductor is Xr= 314x 0.461x l0-3 6n (7x7 xl4)t/3 uniform only when DC is passingthrough it. on the contrary when AC is flowing througha conductor,the currentis non-uniformlydistributedover the = 0 .5 3 1o h m /k m 0.7799x J2 xl.725x 10-3 cross-sectionin a mannerthat the current densityis higherat the surface of the conductor comparedto the current density at its centre.This effect becornes This is 7-6'4rvohigherthan the colrespondingvalue for a bundledconductor Inorepronouncedas frequencyis increasedT. his phenonlenoins cilled stirr ilil itil vA ' -A\\ci do liriaund. lu\" J -^l-r^l o- -u. rt' ir o w e r qffect.It causeslargerpower lossfor a given rms AC thanthe loss when the reactance of a bundled conductor Sairr€vaiueof DC is flowing ihroughthe conciuctorC. onsequentlyth, e effective liuirit€c line conductor esistanceis morefbr AC thenfbr DC. A qualitativeexplanationof the phenomenonis as follows. increasesits transmissioncapacity. Imagine a solid rottnd conductor (a round shape is considered for 2.TT RESISTANCE convenienceonly) to be composedof annularfilamentsof equalcross-sectional area. The flux linking the filaments progressively decreasesas we move ccnTooehnngosslueiigddcheeterrteidhnideng.trcmaoonnsstrtmicbiaussstieioosnnl'iitonfiesleitnhceoenmroeasmiinsyt,stahoneucprecrtoeeossefenlricnieeeosfplilonineweeirmrelpsoiessdstaa.Tnnhccueemscuawsnht bibleee towardsthe outer filamentsfbr the simple reasonthat the flux inside a filament The effectiveAC resistanceis given by doesnot link it. The inductivereactanceof the inraginaryfilamentstherefore decreasesoutwards with the result that the outer filamentsconduct more AC O_ averagepowerlossin conductorin watts than the inner filaments (filaments being parallel). With the increase of ohms (2.48) frequencythe non-uniformity of inductive reactanceof the filaments becomes more pronounced,so also the non-uniformity of currentdistribution.For large where 1is the rms current in the conductoiin amperes. solid conductors the skin effect is quite significant even at 50 Hz. The Ohmic or DC resistanceis given by the formula analytical study of skin effect requiresthe use of Bessel'sfunctions and is beyond the scopeof this book. R'n -' 'n\"l ohlns (2.49) A Apart fronl the skin effect, non-uniformityof currentdistributionis also causedby proximity eJJ'ecct.onsider a two-wire line as shownin Fig. 2.1g. where p = resistivity of the conductor,ohm_m Each line conductorcan be divided into sectionsof equalcross-sectionaat rea / = length,m (say threesections).Pairsaat, bbt andc, ct can form threeloopsin parallel. The

72 I M o d e r nP o w e rS y s t e mA n a i y s i s Inductanceand Resistancoef TransmissioLnines | b t flux linking loop aat (and thereforeits inductance)is the least and it increases somewhatfor loops bbt and ccl. Thus the density of AC flowing through the conductorsis highestat the inneredges(au') of theconductorsandis the least at the outer edges(cc').This type of non-uniform AC current distribution Decomes more pronounceo as me olstance Detween conouctors ls reouceo. LlKe skin effect, the non-uniformity of current distribution causedby proximity effect also increasesthe effective conductor resistance.For normal spacing of Fig.p-2.5 overhead lines, this effect is always of a negligible order. However, for undergroundcableswhereconductorsarelocatedcloseto eachother,proximity 2.6 Two three-phaselinesconnectedin parallelhaveselt'-reactanceosf X, and X2. If the mutual reactancebetweenthem is Xp, what is the effective etfect causesan appreciableincreasein effectiveconductorresistance. reactancebetweenthe two endsof the line? Fig. 2.18 2.7 A single-phase50 Hz power line is supportedon a horizonralcross-arm. The spacing between conductorsis 2.5 m. A telephoneline is also Both skin and proximity effects depend upon conductor size, fiequency, supportedon a horizontalcross-armin the samehorizontalplane as the distance between conductors and permeability of conductor material. power line. The condttctorsof the telephrlncline are of solid copper spaced0.6 m between centres.The distance between the nearest PROBLEIVSI conductorsof the two linesis 20 m. Find the mutualinductancebetween thecircuitsand the voltageperkilometreinducedin theteiephoneline for 2 . 1Derive the formula for the internal inductancein H/m of a hollow 150A currentflowing over the power line. r;onductohr avinginsideradiusr, andoutsideradiusr, andalsodetermine the expressionfor theinductancein H/rn of a single-phaseline consisting 2.8 A telephoneline runsparallelto an untrasposedthree-phasteransmission of the hollow conductorsdescribed above with conductors spaced a line, as shown in Fig. P-2.8.The power line carriesbalancedcurrent of distanceD apart. 400 A per phase.Find the mutual inductancebetweenthe circuits and calculatethe 50 Hz voltageinducedin the telephoneline ptsrkm. 2 . ? Calculatethe 50 Hz inductive reactanceat I m spacingin ohms/km of a cable consistingof 12 equal strandsarounda nonconductingcore. The abc hb diameterof eachstrandis 0.25 cm and the outsidediameterof the cable i s 1 .2 5c m . (r (r (, ,. 2 . 3 A concentriccableconsistsof two thin-walled tubesof meanradii r and lL 15m ---*1rn.__ It respectivelyD. erive an expressionfor the inductanceof the cable per unit length. f^ 5m---+++--5m---f - 2 . 4 A single-phas5e0 Hz circuit comprisestwo single-corelead-sheathed Fig. P-2.8 Telephoneline parallelto a power line cableslaid sideby side;if the centresof the cablesare 0.5 m apart and each sheathhas a mean diameterof 7.5 cm, estimatethe longitudinal 2.9 A 500 kV line has a bundling arrangement of two conductors per phase voltage induced per km of sheathwhen the circuit carries a current of as shown in Fic. P-2.9. 800A. Fig.P-2.9 500kV,three-phasbeundledconductolrine 2.5 Two longparallelconductorscarrycurrentsof + 1 and- 1.Whatis the magnetifcieldintensitay t a pointP, shownin Fig. P-2.5? Computethe reactanceper phaseof this line at 50 Hz Each conductor carries50Voof the phasecurrent.Assumefull transposition.

lgq er1-tgryg.f!yg!U_An4ygp Inductanceand Resistanceof TransmissionLines 2.10 An overheadline 50 kms in lengthis to be constructedof conductors2.56 REFERNECES cm in diameter,for single-phasetransmissionT. he line reactancemust not exceed31.4 ohms.Find the maximum permissiblespacing. l. Electric'ttl Transrnission and Distributiort Book, Westinghouse Electric and Manufacturing Co., East Pittsburgh, Pennsylvania, 1964. 2.11In Fig. P-2.1I which depictstwo three-phasceircuitson a steeltowerthere 2. Waddicor, H., Principles of Electric Power Transmission, 5th edn, Chapman and cal cenre tlnes. Hall, London, 1964. three-phasecircuit be transposedby replacing a by b and then by c, so that the reactancesof the three-phasesare equaland the GMD methodof 3. Nagrath, I.J. and D.P. Kothari, Electric Machines, 2nd edn, Tata McGraw-Hill, reactancecalculationscan be used.Each circuit remainson its own side New Delhi, 1997. of the tower. Let the self GMD of a singleconductorbe 1 cm. Conductors a and at and other correspondingphase conductorsare connectedin 4. Stevenson,W.D., Elements of Power System Analvsis,4th edn, Mccraw-Hill, New parallel. Find the reactanceper phaseof the system. York, 1982. I o c' 5. Edison Electric Institute, EHV Transmission Line Reference Book, 1968. 6. Thc Aluminium Association, Aluminium Electrical Conductor Handboo,t. New C) York, 1971. 4 m i-----z.sm ---j 1. Woodruff. L.F., Principles of Electric Pov,er Trun.snissiorr,John Wiley & Sons, I ob c )b ' New York, 1947. 1 om - -l 8. Gross, C.A., Power System Analysis, Wiley, New York, 1979. l-4 m l- 9. Weedy, B.M. and B.J. Cory Electric Power Systems,4th edn, Wiley, New york, I r.___zsm___l 1998. I ') 10. Kimbark, E.W., Electrical Transmission of Power and Signals, John Wiley, New .) York, 1949. Fig. P-2.11 Paper I l. Reichman.J., 'Bundled Conductor Voltage Gradient Calculations,\" AIEE Trans. 1959,Pr III. 78: 598. )-.12 A double-circuit three-phaseline is shown in Fig. P-2.I2. The conductors a, a/l b, bt and c, c/ belong to the same phase respectively. The radius of each conductor is 1.5cm. Find the inductance of the double-circuit line in mH/km/phase. ab lt a/ b/ [\\.r_./ (_) () a )l l \\..,_/ -l i'1m - i - 1 m - lI - 1 m >l< 1 m - l - , r I I Fig. P-2.12 Arrangemenotf conductorfsor a double-circuthitree-phasleine 2.13 A three-phaseline with equilateralspacingof 3 m is to be rebuilt with horizontalspacing(.Dn = ZDn - ZDrr).The conducrorsare to be fully transposed.Find the spacingbetweenadjacentconductorssuch that the new line has the sameinductanceas the original line. 2.14 Find the self GMD of threearrangernentsof bundledconductorsshownin Fig. 2.16in termsof thetotalcross-sectionalreaA of concluctor(ssame in each case)and the distanced betweenthem.

Capacitanceof TransmissionLines t V , \"= 6 e a v: 6 - - - q - d v V tL r| .', ),,, r L /t'\\V Fig. 3.1 Electricfield of a lclngstraightconductor 3.1 INTRODUCTION As the potential difference is independent of the path, we choose the path of integration as PrPP2 shown in thick line. Since the path PP2lies along an The capacitancetogetherwith conductanceforms the shunt admittanceof a equipo',entral,Vrris obtained simply by integrating along PyP, t.e. transmissionline. As mentionedearlierthe conductanceis the result of leakage over the surfaceof insulatorsand is of negligible order. When an alternating v r zl =: , ' t r a v : h t \" ? u (3.1) voltageis appliedto the line, the line capacitancderawsa leadingsinusoidal currentcalled the charging current which is drawnevenwhen the line is open 3.3 POTENTIAL DIFFERENCE BETWEEN TWO CONDUCTORS circuited at the far end.The line capacitancebeingproportionalto its length,the OF A GROUP OF PARALLEL CONDUCTORS chargingcurrentis negligiblefor lineslessthan 100km long.For longerlines the capacitancebecomesincreasinglyimportantand hasto be accountedfor. Figure3.2 showsa group of parallelchargedconductorsI.t is assumedthat the conductorsare far removedfrom the ground andare sufficiently removedfrom 3.2 ELECTRIC FIELD OF A LONG STRAIGHT CONDUCTOR eachother-i,.e. the conductorradii aremuchsmallerthanthe distancesbetween them.The spacingcommonly usedin overheadpower transmissionlines always Imaginean infinitely long straightconductorfar removedfrom other conductors meetstheseassumptions.Further, theseassumptionsimply that the chargeon (including earth) carrying a unifbrrn charge of 4 coulomb/metrelength.By eachconductorremainsuniformly distributedaroundits peripheryand length. symmetry,the equipotentialsurfaceswill be concentriccylinders,while thelines of electrostaticstresswill be radial. The electric field intensitv at a distancev nn from the axis of the conductoris i,o --- ,= Q v/^ 2nky Fig. 3.2 A group of parallelchargedconductors whereft is the permittivity* of the medium. As shownin Fig. 3.1 considertwo pclintsP, andP, locatedat clistanceDs, and Dr respectively from the conductor axis. The potential difference Vn (betweenP, and Pr) is given by * In SI units the pennittivity of free space is ko = 8.85 x 10-12 F/m. Relative permittivity for air is ft, = klko = 1.

7S 'l M o d e r np o w e r S y s t e mA n a l y s i s Capacitanceof TransmissionLines l' .-^ or The potentialdifferencebetweenany two conductorsof the group can then be r| - 79 obtainedby adding the contributionsof the individual chargedconductors:by 0.0121 repeatedapplication of Eq. (3.1). so, the potential difference between Cot log (D / (ror)ttz) trtF/km (3.4b) conductorsa and b (voltagedrop from a to b) is *lcln tn+. qotn*;. n,h++.. qn\" +) v (3.2) The associatedline charging current is (3.4c) I,= ju.Co6Vnu Allvn (3.5) Each term in Eq. (3.2) is the potentialdrop from a to b causedby chargeon one of the conductors of the group. Expressionson similar lines could be \"O___l [__{b written for voltage drop betweenany two conductorsof the group. (a) Line-to-linecapacitance If thechargesvary sinusoidally,so do the voltages(this is the casefor AC transmissionline), the expressionof Eq. (3.2) still applieswith charges/metre lengthandvoltagesregardedas phasorquantities.Equation(3.2) is thus valid for instantaneousquantitiesand for sinusoidal quantitiesas well, wherein all chargesand voltagesare phasors. 3.4 CAPACITANCE OF A TWO.WIRE LINE l---r )o Considera two-wire line shownin Fig. 3.3 excitedfrom a single-phasesource. i..-- The line developsequalandoppositesinusoidalchargeson thetwo conductors which can be representedas phaso$ QoNd qb so that eo = _ eu. c\", Cnn C.n=Cbr=2C\"a (b) Line-to-neutralcapacitance Fig. 3.4 ll *---- - --J As shown in Figs. 3.a @) and (b) the line-to-line capacitancecan be equivalentlyconsideredastwo equalcapacitanceiss senes.The voltageacross l the lines dividesequallybetweenthe capacitancessuchthatthe neutralpoint n is at the groundpotential.The capacitanceof eachline to neutralis thengiven Fig. 3.3 Cross-sectionavl iew of a two_wireline by The potential difference Vo6 can be written in terms of the contributions C,= Co,=Cb,= 2Cou= pflkm (3.6) made by qo and q6 by use of Eq. (3.2) with associatedassumptions (i.e. Dlr is ,!#A large and ground is lar away). Thus, The assumptionisnherentin the abovederivationare: (i) The chargeon the surfaceof eachconductoris assumedto be uniformly V' , = , l ; t ( n \" h*D\" ^ + ) (3.3) distributed,but this is strictly not correct. 0 t ) If non-uniforrnityof chargedistributionis takeninto account,then Since Qr,= - qu, we have C, 0.0242 pFkm (3.7) v o b =! + m L r-c[ 2nLr(+ ( 4 - , ) \" ' ) \\4r' ) ) 27rk rorb The line capacitance Cnhis then lf D/2r >>1, the aboveexpressionreducesto that of Eq. (3.6)andthe error causedby the assumptionof uniform chargedistributionis negligible. - Qo In (D / (ror)ttz1 F/m length of line Q.aa) (ii) The cross-sectionof both the conductorsis assumedto be circular, while \"ab Vot in actual practice strandedconductorsare used.The use of the radius of the circumscribingcircle for a strandedconductorcausesinsignificanterror.

q0 | Modernpb*gl Jysteq 4!gly..!s s1^-4 es TLg' - 3.5 CAPACITANCE OF A THREE-PHASE LINE WITH a (3.14b) EOUILATERAL SPACING (3.1s) For air medium (k, = l), ,,=#ffi p,Flkm Figure3.5 showsa three-phasleine composedof threeiclenticacl oncluctorosf 1o (line charging) = ju,CnVnn \\D Vac,/ Vab+ Vac=2 rt cos 30\" V\"n =3V\"n A a/ \\_-/b ,''h Fig. 3.5 cross-sectionof a three-phaseline with equilateralspacing t1 \" ,\" Using Eq. (3.2) we can write the expressions for Vu,,and V,,..as ,\"I vub= 6 2 * t1,t,nt , r, ,, +) (3.8) I \\V'o *(0\" I Vca 1 30 I v n , =i ! * ( n \" 6 P -t q 1 , t n # * r ,^ r j ) I Adding Eqs. (3.8)and (3.9),we get Itvun (3.e) IF n\". v,,t*, v,,=, ,'oolrr,,,, D + (qu'l ,1),t,, ; ] ( 3r.0 ) v\", vb Since there ilre no othcr chargesin the vicinity, thc sunr of'clrar_{eson the three 6D !b conductorsis zero. Thus q6 * Qr=- Qu,which when substitutedin Eq. (3.10) vields Vr Fig. 3.6 phasordiagramof barancetdhree-phasveortages V,,hI Vn=, !+ r\" 2 (3.11) 3.6 CAPACITANCE OF A THREE.PHASE LINE WITH UNSYMMETRICAL SPACING zTTk r from the With balanced three-phase voltages applied to the line, it follows phasor diagrarn ol'I,rig. 3.(r that VouI Vor= 3Von (3.r2) Substituting for (Vot,+ V,,,) trom Eq. (3.12) i n E q . ( 3 . 1 1 ) ,w e g e r v^_- 4o tn2 (3.13) For the first,sectionof the transpositioncycle 27Tk r follows as v o b= +zT(vec\\o t r n ! *r q u r-t'n f + The capacitance of line to neutral immediately /- Qo 2 Tlc D r z e , r r n} ) (\\ 3 . r 6 a ) \" Von ln (D/r) (3.l 4a) Dr ,)

.l ModernPowerSystemAnalysis E2' I Capacitanceof TransmissionLines Im t *lr\"ho-3L+aatnL t D rn = (D nDnDT)tl3 (3.18) r' /o ,-=- l f i l ( ^ trn^ ;D*\"nn,' r, \" , t j (3.1e) l (3.20) Fig. 3.7 Cross-sectionof a three-phaseline with asymmetricalspacing n , * ) (fullytransposed) Adding Eqs. (3.18)and (3.19),we get For the second section of the transposition cycle ') - t e.zt+\" l vot # vo, = *r(, / r ^,\\, 6 2rt r ( q-t - r q\") r n t f %) uzt utz) (3.16b) zTrK\\ f As per Eq. (3.12) for balancedthree-phasevoltages For the third sectionof the transpositioncycle V n ti V o r = ' 3 V n n v o b =|z-i.'(! r\\ \" r l n -&r-* q6rtn-!-i e,tt\"+l (3.16c) and also (qu + qr) = - qo Dy Dr,) Use of theserelationshipsin Eq. (3.20) leadsro If the voltage drop along the line is neglected, Vno is the same in each l/o^.n.-- Qo ln D\"n (3.2r) transposition cycle. On similar lines three such equations can be written for Znk-\" r Vbr= Vut,I -120. Thrce more equations can be written equating to zero the summation of all line chargesin each section of the transposition cycle. From The capacitanceof line to neutralof the transposedline is then giveh by these nine (independent) equations, it is possible to determine the nine unknoWn charges. The rigorous solution though possible is too involved. C\". = 3s-: -2nk F/m to neutral (3.22a) Von ln (D\"o/ r) With the usual spacing of conductors sufficient accuracy is obtained by assuming Forairmedium'o;= \\-n\" -='u--ut- D ,o / r ) p,F/km to neutral (3.22b) Qat= Qa2= Qa3= Q\"i Qut= Qaz= Quz= Qo, log ( 4ct= Q,'2=4,3= 4r' (3.t7) It is obvious that for equilateralspacingD,, = D, the above (approximate) formula gives the exact resdlt presentedearlier. This assumptionof equaicharge/unitlength of a line in the threesectionsof the transpositioncycle requires,on the other hand, three diff'erentvalues of Vnu The line charging currentfor a three-phaseline in phasor form is designatedas Vo61,Vo62andVoo,in the three sections.The solution can be Io Qine charging) = jut,,Vnn Alkm (3.23) considerablysimplified by taking Vouasthe averageof thesethreevoltages,i.e. v , q , @ v g ) =! { v , , u r + v o u r + v o o z ) 3.7 EFFECT OF EARTH ON TRANSMISSION LINE J CAPACITANCE I l- ( D t z D ? t D.y1 * o \" r' ) r or '/ nb= q1aln' 'n [ ' nI D t 2 D 2 3 D 3)t In calculatingthe capacitanceof transrnissionlines,the presenceof earthwas 6 ,, ) \"' \\ ignored, so far. The effect of earth on capacitancecan be convenientlytaken into accountby the methodof images. + q ^ l ( DrrD r ^ D ^ ,\\ 1 nl -:ll Method of Images \\ DnDnD3t )) The electric field of transmissionline conductorsmustconforrnto the presence of the earth below. The earthfor this purposemay be assumedto be a perfectty