Operation and Control in Power Systems Prof.P.S.R.MURTY B.Sc.(Engg.)(Hans.)ME., Dr.- lng (Berlin),F.I.E.(India) Life Member - ISTE (Formerly Principal O.U. College of Engineering & Dean, Faculty of Engineering, O.U.Hyderabad) BSP BSPublications === 4-4-309,GirirajLane,SultanBazar, Hyderabad - 500 095 A.P. Phone:040- 23445688 Copyright 2008, by Publisher No part of this book or parts thereof may be reproduced, stored in a retrieval system ortransmittedinanylanguageorbyanymeans,electronic,mechanical, iphotocopying,recordingorotherwisewithoutthepriorwrittenpermissionof the Published by: SSP BSPublications 4-4-309, Giriraj Lane,Sultan Bazar, Hyderabad - 500 095 A. P. Phone: 040 - 23445688,Fax:91+40-23445611 e-mail: contactus@bspublications.net Printed at Adithya Art Printers Hyderabad. ISBN:978-81-7800-181-0 Contents 1Introduction 2Load Flow Analysis 2.1Bus Classification...............................................................................................9 2.2Modelling for Load Flow Studies ......................................................................10 2.3Gauses - Seidel Iterative Method ......................................................................13 2.4Newton - Raphson Method..............................................................................16 2.4.1Rectangular Coordinates Method .....................................................17 2.4.2The Polar Coordinates Method ........................................................19 2.5Sparsity of Network AdmittanceMatrices ........................................................22 2.6Triangular Decompostion ..................................................................................23 2.7Optimal Ordering ...............................................................................................25 2.8Decoupled Methods ...........................................................................................27 (xiI) Contents 2.9Fast Decoupled Methods ..................................................................................27 2.10Load Flow Solution Using Z Bus......................................................................29 2.10.1BusImpedance Formation ............................ ~..................................29 2.10.2Addition of a Line to the Reference Bus ..........................................29 2.10.3Addition ofaRadial Line and New Bus...........................................30 2.10.4Addition of a Loop Closing Two Existing Buses in the System......30 2.10.5Gauss - Seidel Method Using Z-bus for Load Flow Solution .........31 2.11Load Flow Solution with Static Load Model....................................................32 2.12Comparision of VariousMethodsfor Power Flow Solution .............................33 Questions............................................................. ................ .......... .......... ........71 Problems......................... ................... .... ..... ................................... .................72 3Economic Operation of Power Systems 3.1Characteristicsof SteamPlants........................................................................86 3.2Input OutputCurves.........................................................................................87 3.3The Incremental Heat Rate Characteristic........................................................88 3.4The IncrementalFuelCost Characteristic........................................................88 3.5Heat Rate Characteristic ....................................................................................89 3.6IncrementalProductionCostCharacteristics...................................................89 3.7Characteristics of HydroPlants........................................................................90 3.8IncrementalWaterRateCharacteristics ............................................................91 3.9IncrementalProduction CostCharacteristic .....................................................92 3.10Generating Costsat Thermal Plants ..................................................................93 3.11Analytical Form forInput-Output Characteristics of Thermal Units ................93 3.12Constraints in Operation ....................................................................................94 3.13Plant Scheduling Methods .................................................................................96 3.14Merit Order Method ..........................................................................................97 3.15EqualIncremental Cost Method: Transmission Losses Neglected ..................97 3.16Transmission LossFormula - B.Coefficients ..................................................99 3.17Active Power Scheduling ................................................................................. 103 3.18PenaltyFactor.................................................................................................. 106 3.19Evaluation ofl for Computation ....................................................................... 107 (xfu)Contents 3.20Hydro Electric Plant Models............................................................................ 119 3.21Pumped StoragePlant ...................................................................................... 120 3.22Hydro Thermal Scheduling.............................................................................. 120 3.23Energy Scheduling Method .............................................................................. 121 3.24Short TermHydroThermalScheduling ........................................................... 125 3.24.1Method of Lagrange Multipliers (losses neglected) ........................ 125 3.24.2Lagrange Multipliers Method Transmission Losses Considered.... 126 3.24.3Short TermHydro ThermalScheduling using B-CoefficientsforTransmission losses .......................................... 127 Questions........................................................................................................ 151 Problems........................................................................................................ 152 4Optimal Load Flow 4.1Reactive Power Control for Loss Minimization ............................................... 155 4.2Gradient Method for Optimal Load Flow ......................................................... 156 4.3Non - Linear Programming .............................................................................. 157 4.4Lagrange Function for Optimal Load Flow..................................................... 158 4.5Computational Procedures................................................................ _............. 159 4.6Conditions for Optimal Load Flow ................................................................... 159 4.7Implementation of optimal conditions .............................................................. 161 Questions........................................................................................................ 168 Problems........................................................................................................ 169 5Unit Commitment 5.1Cost Function Formulation.............................................................................. 171 5.2Constraints forPlant Commitment Schedules ................................................. 173 5.3Priority - List Method ...................................................................................... 174 5.4DynamicProgramming .................................................................................... t:z5 5.5Unit Commitment by Dynamic Programming................................................. 177 Questions........................................................................................................ 180 Problems........................................................................................................ 180 Contents 6Load Frequency Control 6.1Speed Governing Mechanism.......................................................................... 183 6.2SpeedGovernor ................................................................................................ 183 6.3Steady State Speed Regulation ......................................................................... 185 6.4Adjustment of Governor Characteristics......................................................... 185 6.5Transfer Function of Speed ControlMechanism............................................ 186 6.6TransferFunctionof aPowerSystem............................................................ 188 6.7TransferFunction of theSpeedGovernor ....................................................... 190 6.8Governing of Hydro Units ................................................................................ 191 6.9Penstock TurbineModel.................................................................................. 193 6.10ModalforaSteam Vessel ................................................................................ 196 6.11Steam Turbine Model ...................................................................................... 197 6.12Reheat TypeSteam Turbine Model .................................................................. 198 6.13Single Control Area ........................................................................................... 199 6.14The basicsof LoadFrequency Control........................................................... 200 6.15Flat Frequency Control.................................................................................... 201 6.16Real Power Balance for Load Changes ............................................................ 202 6.17Transfer Function of a Single Area System ..................................................... 203 6.18Analysis of Single Area System ........................................................................ 205 6.19DynamicResponseof Load Frequency ControlLoop.................................... 208 6.20ControlStrategy ............................................................................................... 209 6.21PIDControllers................................................................................................ 212 6.22The optimal Control Problem ........................................................................... 222 6.23The Linear Regulator Problem......................................................................... 222 6.24Matrix Riccati Equation .................................................................................... 224 6.25Application of Modern Control Theory ............................................................ 224 6.26Optimal Load Frequency Control - Single Area System .................................. 225 Contents 6.27Optimal Control for Tandem Compound Single Reheat Turbine -GeneratorSystem ............................................................................................. 229 6.28Optimal Control of HydroSpeed GoverningSystem ....................................... 232 6.29A Review of Optimal Control ........................................................................... 235 6.30Load Frequency Controlwith RestrictionsontheRateof Power Generation '".................... : ..................................................................... 236 6.31Load Frequency Controlusing Output Feedback ............................................ 237 6.32Load frequencyControl and EconomicDispatch ............................................ 238 Questions......................................................................................................."39 Problems........................................................................................................ 240 7Control of Interconnected Systems 7. 1InterconnectedOperation ................................................................................. 241 7.2FlatFrequency Controlof InterconnectedStations ......................................... 241 7.3Flat Tie-Line and Flat Frequency Control ........................................................ 244 7.4Tie-Line Bias Control ........................................................................................ 247 7.5Complete Tie-Line Bias Control....................................................................... 250 7.6Two Area System - Tie-LinePower Model ..................................................... 253 7.7Block Diagram for Two Area System .............................................................. 254 7.8Analysis of Two Area System .......................................................................... 255 7.9DynamicResponse ........................................................................................... 257 7.10Tie-Line Bias Control- Implementation ........................................................... 266 7.11The Effect of Bias Factor on System Regulation............................................ 267 7.12Scope forSupplementary Control .................................................................... 269 7.13State Variable Model for a Three Area System ................................................. 269 7.14State Variable Model fora Two Area System ................................................... 274 7.15State Variable Model for a Single Area System................................................ 275 7.16Model Reduction and Decentralised Control .................................................. ,284 Questions........................................................................................................ 287 Problems........................................................................................................ 288 (XVl) Contents 8Voltage and Reactive Power Control 8.1Impedance andReactivePower ....................................................................... 289 8.2System Voltageand ReactivePower ................................................................ 293 8.3ReactivePower Generation bySynchronousMachines .................................. 294 8.4Effect of Excitation Control ............................................................................. 295 8.5Voltage Regulation and Power Transfer ........................................................... 296 8.6Exciter and Voltage Regulator.......................................................................... 297 8.7Block Schematic of Excitation Control ............................................................ 299 8.8Static Excitation System.................................................................................. 300 8.9Brushless Excitation Scheme........................................................................... 301 8.10Automatic Voltage Regulators for Alternators .................................................. 302 8.11Analysis of Generator Voltage Control ............................................................. 303 8.12Steady State Performance Evaluation .............................................................. 306 8.13Dynamic Response of Voltage Regulation Control ........................................... 306 8.14Stability Compensation for Voltage Control..................................................... 307 8.15Stabilizing Transformer .................................................................................... 307 8.16Voltage Regulators............................................................................................ 309 8.17ieee Type1 Excitation System......................................................................... 310 8.18Power SystemStabilizer .................................................................................. 313 8.19Reactive Power Generation by TurboGenerator ............................................. 314 8.20SynchronousCompensators ............................................................................ 314 8.21Reactors315 8.22Capacitors315 8.23Tap---ChangingTransformers........................................................................... 316 8.24Tap-Staggering Method ................................................................................... 317 8.25Voltage Regulation and Short Circuit Capacity ................................................. 318 8.26Loading Capability ofa Line ............................................................................. 320 8.27Compensation inPower Systems ..................................................................... 320 (xviI) Contents 8.28Load Compensation .......................................................................................... 321 8.29StaticCompensators........................................................................................ 328 8.30SteadyStatePerfonnanceof Staticvarcompensators................................... 331 8.31Overvoltages on Sudden Lossof Load ............................................................ 334 8.32Voltage Dips ...................................................................................................... 335 8.33SubsynchronousResonance ............................................................................ 337 Questions........................................................................................................ 343 Problems........................................................................................................ 344 9Introduction to Advanced Topics 9.1FactsControllers .............................................................................................. 346 9.1.1Series Controllers ............................................................................ 346 9.1.2Shunt Controller .............................................................................. 347 9.1.3Series - Series Controllers .............................................................. 347 9.1.4Series - Shunt Controllers.............................................................. 348 9.1.5PowerFlowControl...................................................................... 348 9.1.6Static Var Compensator(SVC)........................................................ 349 9.1.7Unified Power Flow Controller ....................................................... 349 9.1.8Advantages due toFACTSdevices ................................................. 349 9.2Voltage Stability................................................................................................ 350 9.3Power Quality ................................................................................................... 352 9.3.1Power Quality Index ....................................................................... 353 9.3.2Voltage Sags.................................................................................... 353 9.3.3Rectifier Loads ................................................................................ 355 9.3.4Flicker............................................................................................. 355 9.3.5Power Acceptability or Voltage Tolerance ....................................... 356 9.3.6Solutions to Power Quality.problem ............................................... 356 9.4Data Base for Control ....................................................................................... 357 9.5State Estimation ................................................................................................ 358 9.6PowerSystemSecurity .................................................................................... 360 (xviii) Contents 9.7SteadyStateSecurity Assessment................................................................... 361 9.8Application to Outage Studies.......................................................................... 362 9.9Pattern Recognition Methods ........................................................................... 363 9.10PowerSystemControlCentres ........................................................................ 365 9.11LevelDecomposition in Power Systems......................................................... 367 9.12NetworkAutomation ........................................................................................ 368 9.13LoadPrediction................................................................................................. 369 9.14Load Prediction using Matereological Data ...................................................... 371 9.15Spetral Expansion Method ................................................................................ 376 9.16Prediction by ScalingaStandard Load .......................................................... 377 9.17Short - Term Load Forecasting Using ExponentialSmoothing ....................... 378 9.18Peak Power Demand Prediction ....................................................................... 378 9.19State Estimation in Load Forecasting ............................................................... 379 9.20Generating Capacity Reliability and Outage Probabilities ................................. 380 Questions........................................................................................................ 386 Objective Questions ..........................................................................387 Answers to Objective Questions ......................................................400 References .........................................................................................401 Index.................................................................................................407 1INTRODUCTION Elecricalenergyisthemostpopularformof energy,becauseitcanbetransportedeasilyat highefficiencyandreasonablecosts.ThomasEdison,establishedthefirstpowerstationin 1882 at New Yorkcity,UnitedStates of America.Thelower Manhattan area wassuppliedDC power from this station.Underground cables were usedfor distribution.At Appelton, Wisconcin the first water wheel generator wasinstalled.Under Edison's patents several companies started functioninginUSA.However, these companies could supply energy tosmalldistances due to I2Rpowerlossbeing excessiveatlowvoltagedistribution. In1885,WililiamStanleyinventedthetransformer.whichrevolutionizedtheAC transmission.Theinventionof inductionmotorin1888byNnikolaTeslacauseddramatic changeinelectricalpower consumptionthroughACreplacingmanyDCmotorloads. ItisnowanacknowledgedfactthatHVandEHVtransmissionalonecanreduce substantially the losses andbulk power transmissionis feasible at these voltages.Nevertheless, itisalsowellestablished thatHVDCisconvenient andmoreeconomicalfromoperation and controlpoint of viewunder certaincircumstances suchasatdistancesof morethan500kms. A detaileddiscussionof this aspectisnotwithinthepurviewof thisbook. InIndia, twothirdof theelectricalpower generatedisfromcoalbasedpower stations. Of therest,about24%comesfromhydroelectric,8.7%fromGasfiredplants,2.4%from nuclearpowerplants.Atthetimeof independence,thepercapitaconsumptionof electric 2OperationandControlinPowerSystems energy was1.3units.It isnow about 3unitswhile China'sper capita consumptionisabout 6 units.Developedcountrieshavepercapitaconsumptionsof ashighas8,500units.This shows the great disparity that exists between the richandthepoor countries.However,Indian Power Sector hasundergonerevolutionarychanges.Whilein1947theinstalled capacity was at1300MW,todayithassurpassed1,00,000MW.InIndia,NuclearPowerhasatargetof 350 GW,andHydroPower isestimatedat84GWbyCEA. InIndia regionalandnationalpower grids are established tofacilitate transfer of power withinandacrosstheregionswithreliability,securityandeconomyonsoundcommercial principles.ThePowerGridCorporationwasestablishedinAugust1991anditstartedits commercialoperationsfrom1992-93.Itisoneof thelargesttransmissionutilitiesinthe world.Thepower gridisanISO9001company withcomplete capabilityin ACtransmission upto 765kVlevelandHVDC transmissionupto 500kV.Challenging jobs inoperation and maintenance of the national demand which is expected to reach a peak value of 114000 MW by 2006 are undertaken byPower Grid Corporation.Power Gridis also engaged inactivities such asunifiedloaddispatchwhichfacilitatesclosemonitoringof gridwithrealtimedatafor economicdispatchof power betweenthefiveregionalgridsandstates. Planning,design, operation, control and protection of power systems requires continuous andcomprehensive the current states andremedialcontrol, if any,needed. Manual computation of power flows isexrremely time consuming even for very simple networks. In1929,ACnetworkanalyzer,ananalogcomputerwasdevised.Mostof theearlysystem studieswereperformedonthenetworkanalyzer. TheIndianPower GridSystem isdividedintofiveregionalgrids.Thesouthern region comprises of Andhra Pradesh, Tamilnadu,Karnataka,Kerala andPondichery.AlltheseState ElectricityBoardsareintegratedforoperationintoSouthernRegionalElectricityBoard. Likewise,other boardsareformed.EachstatehasinterStateandInterRegionallinks.For example Andhra Pradesh and Maharastra have a tie-line at Ramagundam - Chandrapur 400 kV link at Chandrapur. In a similar way Andhra Pradesh has tie-line connections with Orissa, Madhaya Pradesh, Tamilnadu and Karnataka. The stipulated system frequencyinIndiais50Hz.Since, thereisdeficit of generation inthesouthernregion,theoperatingfrequencygoesto48.5Hz.Stateslike,Maharastra, Madhyapradesh,andOrissa operate at50to52Hz.Andhra Pradeshimportspower through HVDCbacktobacksystematChandrapurthroughthe400kVACdoublecircuitlinefrom Chandrapur-Ramagundam.In a similar way, through the HVDC back to back system at Gajuwaka power istransmittedvia 400..kVJaypore-Gajuwaka doublecircuit AClinefromOrissa. While,wehave dealt with thefrequencyscenario,itisworthwhile, tolook at the other performance index of electric power, the voltage profile.400 kVlines have their voltage falling to340.3kVatCuddapah,220kVlinesreaching160.8kVatSullurpetand132kVlines operating at 95.8 kVat Nagarkurnool. Introduction3 From the above, it can be seen that there isvery heavy demand for electric power in this areas seriously compromising the power quality.While more generation is needed to be added continuously a thoroughknowledge of variousaspectsinvolvedinthestudy of power system operation and controlisvery essentialfor electricpower engineers.This book isdedicated to this task in a manner that students of power engineering grasp theessentialconceptsinvolved inoperation andcontrol. Thesystemvariablesarecontinuouslychanginginbothmagnitudeandnumber.The system never reaches asteadystate so astopermit anyteststobecarriedout onit,so thatits dynamicbehaviour canbeascertained.Inpractice,itrequiresbothcontinuousanddiscrete controls.Thespreadof thepowersystemsovervastgeographicalareascontributestoits vulnerabilitytoenvironmentalchanges.Thesystem'sdynamicsextendsoverabroadband widthrangingfrommicrosecondstoseveralminutes. Planning operationandcontrolof isolatedorinterconnectedpower systemspresenta largevarietyof challengingproblems,thesolutionof whichrequiresapplicationof several mathematicaltechniques fromvariousbranches of it.Knowledgeof optimization techniques and optimal controlmethodsisveryessentialtounderstandthemultilevelapproach thathas been very successfully utilized.Variousmathematical techniques that needed to be applied are explained at the appropriate places while dealing withthe subject. Models for analysis and control Powersystemengineeringisabranchwherepracticallyalltheresultsof moderncontrol theory can be applied.Such an application willresult ineconomy, better quality of service and theleast inconvenience under abnormalsituations,bothanticipatedandunforeseen. Control system design, in general, for its analytical treatment, requires the determination of a mathematicalmodelfromwhichthecontrolstrategy canbederived.Whilemuchof the controltheory postulates that a modelof the systemisavailable.It isalsonecessary to have a suitabletechniquetodeterminethemodelsfortheprocesstobecontrolled.Thus,itis requiredtomodelandidentifypowersystemcomponentsusingbothphysicalrelationships andexperimentalornormaloperatingdata.Theobjectiveof systemidentificationisthe determination of a mathematical model characterizing the operation of a system insome form. Theavailableinformationiseithersystemoutputsorsomefunctionsof outputswhichmay contain measurementnoise.Theinputsmaybeknownfunctionsappliedforthepurposeof identification,orunknownfunctionswhichitmaybepossibletomonitorsomehow,ora combination of both. The identified modelmaybein theformof differential equations, difference equations, transferfunctions,etc. Even though allsystems are nonlinear to some extent,the assumption of alinear model leadstosimplermodelswhichcanyieldmeaningfulresultswithfairlygoodaccuracy.A system may be classified as stationary or nonstationary.During theperiod of operation, when 4OperationandControlinPowerSystems controls are implemented, the system is normally assumed to be stationary.The system equations may be formulated either in the continuous mode or in the discrete mode.While measurements andpredicted values areavailable at discreteintervals, continuousrepresentationisthemost familiarmode.Transformationfromcontinuous todiscreteformulationisastraight forward process.A power systeminvariably,isstochasticinnaturesince the loaddemandisthemost uncertainaspectintheoperationof it.Inaddition,measurementuncertainty,errors,non availability of readings,etc.allcontribute toitsstochasticnatureinthe model.Inmost of the power systemstudies only adeterministicmodelisassumed,but when the situation demands theprobabilisticmodelisalsoused.Amodernpowersystemrequiredidentificationof the modeland optimizationof thesamewithreferencetoaperformance criterionwithcomputer predictive,adaptive,noninteracting,sampled-data controlforefficient operation. Variousmodelsthat areneededinanalysisandfor controlare discussedandpresented throughout thebook. Chapter2dealswithloadflowstudies.Theyareperformedtodeterminevoltages, active and reactive powers, etc. at various points in the network for different operating conditions subject to the constraints on generator capacities and specified net interchange between operating systems and severalother restraints.Loadflowsolution isessentialfor continuous evaluation of theperformanceof thepowersystemssothatsuitablecontrolmeasurescanbetakenin caseof necessity.Inpracticeitwillberequiredtocarryoutnumerousloadflowsundera varietyof conditions. Economicsystemoperation canbedefinedinamoregeneralsenseasmaking thebest useof theresources available,subject toavarietyof requirementsover anydesiredperiodof time.Economicpowersystemoperationdealswiththemeansandtechniquesforachieving minimumoperating cost tosupply a givenpredictedloaddemand.It maybepointedout that extensiveresearchhasbeencarried outinthisfieldcovering topicssuchaseconomy of fuel, maintenance and overhaul schedules of equipment, starting and shut-down of generating plants, scheduling of generation todifferentunits,exchange of power betweenneighbouring utilities and a wide range of problems related to hydrogeneration, like water usage, policies for different types of hydro plants (reservoir, pondage, run-off river and pumped storage) and their integration withthesystem,bothhydraulicallyandelectrically.Differentcombinationsof thermaland hydrogenerating plants giverise todifferentcost structures.Also,fora given combination of plants, the operational requirement of scheduling generating plants to supply the predicted load demandandsubsequentformulationof loadingpatterntobeimposedonindividualunits committed to service to minimize the cost of supplying a given load is another important aspect of theproblem.Ingeneral,theorderingorcommittingplanttooperateononehandand loadingof plantinoperationontheother are thetwofacetsof theeconomicoperation,both consideredseparatelyinChapter 3 and4. The division ismainly fromthe period_of time over which cost minimization is affected. Theloading of plantinoperation'isrelatedto'Costminimizationovershortperiodsof time. Introduction5 Thisproblemiscalledinstantaneous,staticoroptimalpointminimization.Committingof plants to service, by comparison, relates tolarger periods of time and gives rise to a variational form ofthe problem in which the minimization required is that ofthe time integral of operating costsovertheperiodforwhichprogrammesof plant(unit)commitment areformulated. A division of scheduling studies related to operation and control can be made as foHows: SchedulingproblemTime IPeriod (a)Long-range scheduling forplant maintenance andMonth /Year forshort termavailability orresources (b)Short termscheduling forunitcommitment andIDay/2Weeks unithourlyenergyschedules (c)Economic allocation of generation to operating unitsMinutes (d)Tie-lineinterchange,systemfrequencycontrolSeconds . (e)Plant andunit controlContinuous InChapter5optimalloadflowproblemandcertainguidelinestoobtainanoptimal solution are presented,but theinformationisonly at anintroductory level. There areseveralproblems associatedwithhydrothermalcombined operationsuch as: 1.Fuel ordering, i.e., given the operating pattern over the period of interest (say two weeks), determine the station fuelrequirements and the optimal fuelprocurement policy. 2.Plantorderingorunitcommitment,i.e.,theschedulingof thestartupandshut down of generating units,a dynamic optimization problem. 3.Hydrothermalscheduling,i.e.,theoptimaluseof availablewatertocoordinate withthe thermalgeneration, a dynamic optimizationproblem,etc. The economic objective of a schedule canbeassumedeither bytheprofit fromenergy sales or by the cost of energyproduction.If theloads arefixed,thenboth the criteria result in the same schedule.However,under morerealistic circumstances,i.e., whenloadisa function ofa voltage, the two criteria yield different optimal policies.Minimization of production costs istaken generaHyas thecriterion foreconomicoperation. Eachminimizationproblemissubjecttoanumberof constraintsarisingfromthe characteristicsof plantsandtheirsafeoperatingconditionsandfromtherequirementsof technically favourable operating conditions in the transmission system interconnecting various power stations.Therequirementsof securityaresuperimposedontheseconstraints.Added tothesearetherequirementsof marginalorreservegeneratingcapacityinexcessof the minimum necessary to supply a predictedload demand to complement the probabilistic nature of loadpredictedandtocoverunforeseenoperationaloccurrences.Awidenumberof formulationsandanalyticalsolutiontechniqueshavebeenpursuedinthisdirection.A few importantmethodsonlyare discussedinChapters 3,4andS. 6OperationandControlinPowerSystems Thedisturbancestowhichapowersystemissubjectedcanberoughlyclassifiedas smallscaleandlargescaledisturbances.Slowlyvaryingsmallmagnitudechangescanbe effectivelycontrolled,usinggovernors,exciters,etc.Thecontrolof thesystemfrequency using speed governors and supplementary controls is discussedin detailinChapter 6 under the title "Loadfrequencycontrol" Powersystemsareofteninterconnectedtoimprovereliabilityandqualityof power supply to the consumer, to reduce the spinning reserverequirements of individual systems and forsimilar other advantages.Theoperating state of apower system canbedividedintofour modes:. 1.Nonnalmode 2.Preventivemode 3.Emergencymode,and 4.Restorativemode. In the nonnal mode of operation, the system has to maintain scheduled voltages, frequency and load flow profile maintaining the scheduled tie line power flows.In this mode of operation controlisrequired to I.Maintain scheduled voltages andfrequency 2.Maintain scheduled tie-line flows, and 3.Obtain economic generation Inthe emergencymodeof operation,i.e.,whenthecontingencyhasoccurred,control isrequired to I.Maintain the specified frequency,and 2.Maximize the amount of load demandbeing met. During the restorative mode of operation, the systemisbrought fromemergency mode of operation into either nonnalmode or preventive mode. Themostimportantaspectinanymodeof operationisthematchingbetweenload demandandgeneration.Thefrequencydeviationof thesystemisadirectmeasureof the mismatch between the total generation and combined load demand.It is only when the frequency ismaintained at the rated value that the generation balances the load demand.An accelerating frequency means that the generation is high while a decelerating freqttency indicates insufficient generation. Atransmissionlinemaybeaconnectionbetweenageneratingstationtoasystemor maybeaninter-tiebetweentwolargesystems. Assumingthelinelossestobenegligible,itcanbeprovedthatamoreor lessnatural way of operating a transmissionlinewouldbetoseek tomaintainthevoltagelevelsthrough regulating the reactive power flow and to provide for the variations of the active power demand IntrtJduction7 byallowing the phase angle between the two end voltages 0,to change.Thisisbrought about by adjusting the throttle ofthe prime movers inthe generating stations at one end or both ends of theline.Thepewer transfer over thelineisgivenby p=VsVRSino XL where V s andV R aresending endandreceiving endvoltagemagnitudesrespectively. Byslowlyincreasingtheload,themaximumpowertransfercanbeobtainedwhen o ~90.Further, increase inload willnot increase the power transmitted, but instead decreases it.This point is referred to as the static stability limit or static transmission capacity of the line. This capacity can, of course,beincreasedbyincreasing thevoltagemagnitudes,but there are limitsfor thisincrease. Theincrementalincreaseintransmittedpower~ pcausedbyasmallincrement~ oin thephaseangleisameasureof theelectricalstiffnessof thetransmissionline.Thequantity ( ~ )isalso called synchronizing coefficient. Itcanbeseenthatthetransmissioncapacitycanbeincreasedalsobyreducingthe effectivereactance of the line.Thiscanbeachievedbyparalleling thelines,usingbundled conductorsorinsertingseriescapacitors. The analysis,operationandcontrolof interconnectedpower systemsorsimplyareas arediscussedcomprehensivelyinChapter7.Theobjectiveof systemvoltagecontrolisto maintainasatisfactoryvoltageprofileinthesystemduringbothperiodsof maximumand minimumloadings.A detailedanalysisof excitation controlandmeans adoptedforreactive power generationinaddition tosynchronous machinearepresentedinChapter 8. Variousdevicessuchastapchangers,reactors,capacitors,inductionregulatorsstatic var compensatorsetc.,arediscussedinChapter8.Theroleof apowersystemstabilizeris alsopresented. InChapter9,certainadvancedtopicsthatarerelatedtooperationandcontrolare introduced.Theseare,state estimation,FACTScontrollers,Voltagestability,Power quality, load prediction, energy control centers etc.The inclusion of the topics andthe presentation of the information isbynomeans exhaustive. 2LOADFLOW ANALYSIS LoadFloworPowerFlowisthesolutionforthePowerSystemunderstaticconditionsof operation.LoadFlow studies areundertakentodetermine: I.The lineflows 2.Thebusvoltages andsystemvoltageprofile 3.Theeffectof changesincircuitconfiguration,andincorporatingnewcircuitson systemloading 4.The effect of temporary loss of transmission capacity and (or) generation on system loading andaccompaniedeffects 5.The effect of in-phaseandquadratureboostvoltagesonsystemloading. 6.Economicsystemoperation 7.systemtransmissionlossminimization 8.Transformer tapsettingsforeconomicoperationand 9.Possibleimprovementstoanexistingsystembychangeof conductorsizesand systemvoltages. For the purpose of loadflow studies, a single phase representation of the power network isusedsincethesystemisgenerallybalanced.Whensystemshadnotgrowntothepresent size,networkswere simulated onnetworkanalyzersforpower flowstudies.These analyzers LoadFlowAnalysis9 areof analoguetype,scaleddownminiaturemodelsof powersystemswithresistances, reactances, capacitances, autotransformers, transformers, loads, and generators.The generators are just supply sources operating at a much higher frequency than 50Hz tolimit the size of the components.Theloads arerepresentedbyconstant impedances.Meters areprovided on the panelboard for measuring voltages,currents, andpowers.Theloadflowsolutionisobtained directlyfrommeasurementsforanysystemsimulatedontheanalyzer. With the advent of the modern digital computer possessing large storage and high speed, the mode of loadflow studies have changed fromanalog to digitalsimulation. A largenumber of algorithmsaredevelopedfordigitalpowerflowsolutions.Someof thegenerallyused methodsaredescribedinthischapter.Themethodsbasically distinguishbetween themselves in the rate of convergence, storage requirement and time of computation. The loads are generally representedbyconstantpower. Inthenetworkateachbusornodetherearefourvariablesviz. (i)Voltage magnitude (ii)Voltage phase angle (iii)Realpower and (iv)Reactivepower. Out of these four quantities two of them are specified at each bus and the remaining two aredeterminedfromtheloadflowsolution.Tosupplytherealandreactivepowerlossesin lineswhichwillnotbeknowntilltheendof thepower flowsolution,a generator bus,called slack or swing bus isselected.At this bus, the voltage magnitude andits phase angle arespecifiedsothattheunknownpowerlossesarealsoassignedtothisbusinadditionto balanceof generationif any.Generally,at allother buses,voltagemagnitudeandrealpower are specified.At allloadbuses the realand thereactiveload demands are specified.Table 2.1 illustrates thetypes of busesandtheassociatedknownandunknownvariables. 2.1Bus Classification Table 2.1 BusSpecified variablesComputed variables Slack - busVoltagemagnitude anditsphase angleRealand reactive powers Generator busMagnitudesof busvoltagesandrealVoltage phase angle and (PV - bus or voltagepowers (limit on reactive powers)reactive power. controlledbus) LoadbusReal and reactive powersMagnitudeandphase angleof busvoltages 10OperationandControlinPowerSystems 2.2Modelling for Load Flow Studies Bus admittance formation Consider thetransmissionsystemshowninFig.2.1. Fig.2.1Threebustransmissionsystem The line impedances joining buses1,2 and 3 are denoted by z12'Z 22and z31respectively. The corresponding lineadmittances areY12'Y22and Y31 The totalcapacitive susceptancesatthebusesarerepresentedbyYIO'Y20andY30' ApplyingKirchoff's currentlawateachbus Inmatrixfrom where II=VIYIO+ (VI- V2) YI2+ (VI- V3)YI3 12=V2 Y20+ (V2 - VI) Y 21+ (V2 - V3)Y23 13=V3Y30+ (V3 - VI) Y 31+ (V3 - V2)Y32 lll] f' +!I' +y" 12_.Y12 13-YI3 lVI][YII V2 ==Y2I V3YJI YII==YIO+ YI2+ YI3 Y22 =Y20+ YI2+ Y23 Y33 =Y30+ YI3+ Y23 YI2 Y22 Y32 - YI2 Y 20+ Y 12+ Y 23 - Y23 y"]n Y23'~ 2 Y333 - Y13] - Y23x Y30+ YI3+ Y23 Load FlowAnalysis are the self admittances formingthediagonalterms and Y12=Y21 =-YI2 Y13 =Y31 =-YI3 Y 23=Y 32=-Y23 11 arethemutualadmittancesformingtheoff-diagonalelementsof thebusadmittance matrix.For ann-bussystem,theelements of thebusadmittancematrixcanbewrittendown merelybyinspectionof thenetworkas diagonal terms n YII= YiO+ LY,k k=1 k ..i off and diagonalterms Y.k =-Y.k If thenetwork elements have mutualadmittance (impedance), theaboveformulaewi\l notapply.Forasystematicformationof they-bus,lineargraphtheorywithsingular transformationsmaybeused. System Model for Load Flow Studies The variable andparameters associatedwithbusi anda neighboring bus k arerepresentedin the usualnotationas follows: Bus admittance, Y.k =I Y ikI exp je .k=I Y .kI (Cos q.k+ jsine.k) Complexpower, S.= p.+ jQ.= Vi[\ Using the indices G andL for generation andload, p.= PG - PLi = Re[Vi[.J Q.= QG.- QL.= 1m[Vi1.1] Thebuscurrentisgivenby IBus =YBUS.VBUS Hence,fromeqn.(2.3)and(2.4)fromann-bussystem I ~=P,- jQ IY~ IV,.=IIV,+ LY,k V k Ik=1 k .. 1 ..... (2.1 ) ..... (2.2) ..... (2.3) ..... (2.4) ..... (2.5) ..... (2.6) ..... (2.7) 12OperationandControlinPowerSystems andfromeqn.(2.7) ..... (2.8) Further, n P,+ jQ, =V,L Y i ~V: ..... (2.9) k=1 Inthepolarform n P,+ jQ,=LlV,Vk Y,klexpj(o,-Ok-e,k)..... (2.10) k=1 so that n P,==LlV,Vk Yiklcos(o,-Ok-e,k) ..... (2.11 ) k=1 and n Q,==LlV,Vk Y,k Isin (0,-Ok-e,k)..... (2.12) k=1 i =1,2,.....n;i -:t:- slackbus Thepower floweqns.(2.11)and(2.12) arenonlinear anditisrequiredto solve 2(n-1) such equations involving 1V,I,0"P,and Q,at each bus i for the load flowsolution.Finally, the powers at theslackbusmaybecomputedfromwhichthelossesandallotherlineflowscan beascertained.V-matrixinteractivemethodsarebasedonsolutiontopowerflowrelations usingtheir currentmismatchatabusgivenby n L\I,=I,- L Y,kV k k=1 or using thevoltagefrom L\I L\V.==-' IYII ..... (2.13) ..... (2.14) Theconvergenceof theiterativemethodsdependsonthediagonaldominanceof the busadmittancematrix.Theself-admittancesof thebuses,areusuallylarge,relativetothe mutual admittances and thus,usually convergence is obtained.Junctions of very high andlow series impedances andlarge capacitances obtained in cable circuits long,EHV lines, series and shuntcompensationaredetrimentaltoconvergenceasthesetendtoweakenthediagonal dominanceinthe V-matrix.The choice of slackbuscanaffectconvergence considerably.In LoadFlowAnalysis13 difficult cases,itispossible to obtain convergencebyremoving theleast diagonally dominant rowandcolumnof Y.Thesalientfeaturesof theV-matrixiterativemethodsarethatthe elementsinthesummationtermsineqn.(2.7)or(2.8)areontheaverageonly threeevenfor well-developedpower systems.Thesparsityof theV-matrixanditssymmetryreducesboth thestoragerequirementandthecomputationtimeforiteration(sec.4).Foralarge,well conditioned system of n-buses, the number of iterations required are of the order of n and total computing time varies approximatelyasn2 Insteadof usingeqn(2.6),onecanselecttheimpedancematrixandrewritethe equation as v= y-I 1= Z.I..... (2.15) The Z-matrixmethodisnotusuallyverysensitive tothechoice of theslackbus.It can easilybeverifiedthattheZ-matrixisnotsparse.Forproblemsthatcanbesolvedbyboth Z-matrix and V-matrixmethods,the formerarerarelycompetitive with the V-matrixmethods. 2.3Gauses - Seidel Iterative Method Inthismethod,voltagesatallbusesexcept attheslackbusareassumed.Thevoltageatthe slackbusisspecifiedandremainsfixedat thatvalue.The(n-I)busvoltagerelations. V=_Iv] IYVL.Ikk IIIk=1 k",] ..... (2.16) i =I, 2,.....n;i 7=slackbus are solved simultaneously for an improved solution.Inorder to accelerate'the convergence, all newly-computed values of bus voltages are substituted ineqn. (2.16).The bus voltage equation of the(m+I )thiterationmaythenbewrittenas ..... (2.17) Themethodconvergesbecause of theloosemathematical coupling between the buses.Therateof convergenceof theprocesscanbeincreasedbyusing accelerationfactors tothesolutionobtainedaftereachiteration.Afixedaccelerationfactora(I::;a::;2)is normallyusedforeach voltagechange, AV= aAS: I VjYII ..... (2.18) 14OperationandControlinPowerSystems Theuseof theaccelerationfactoramountstoa linear extrapolationof VI'For a given system,itisquite oftenfoundthat a near-optimalchoice of aexists assuggestedinliterature over -arangeof operatingconditions.Eventhoughacomplexvalueof aissuggestedin literature,itismoreconvenient tooperatewithrealvalues givenby ..... (2.19) Alternatively,different acceleration factorsmaybeusedforrealandimaginary parts of thevoltage. Treatment of a PV - bus The method of handling a PV -bus requires rectangular coordinate representation for the voltages. Lettering ..... (2.20) Wherev;andv;'are therealandimaginary components of Vithe relationship. '2"2112 V+v::;V IIIschedules ..... (2.21) mustbe satisfied, sothat thereactivebus power requiredto establish the scheduled bus voltagecanbecomputed.Theestimatesof voltagecomponents,v;(m)andV;-(m)after m iterationsmustbeadjustedtosatisfyeqn.(2.21).ThePhaseangleof theestimatedbus voltage is [ "Cm)1 oem)= tan-I I'em) Vi ..... (2.22) Assuming that the phase angles of the estimated and scheduled voltages are equal;.then the adjusted estimates of V'(m)andV;'cm)are ICm)-IV Is:Cm) vi(new)- I Scheduiedcosul ..... (2.23) and "(m)_II.(m) vi(new)- VlscheduledsmBj ..... (2.24) These values are used to calculate the reactive powerQ\m) . Using these reactive powers andvoltagesa new estimateV lm+l)is calculated.The flowchart for computing thesolution of loadflowusing gauss-seidelmethodisgiveninFig.2.2. Load FlowAnalysis15 Whilecomputing thereactivepowers,thelimitsonthereactive sourcemustbetaken into consideration.If the calculated value of the reactive power is beyond limits. Then its value is fixed at the limit that is violated and itisnolonger possible to hold the desired magnitude of the bus voltage,thebusistreated asaPQbusorloadbus. Yes VCm) =_1 [