J ORNADAS TCNICAS ISA - 2012 1 OPTIMAL POWER FLOW: VOLTAGE STABILITY AND OPERATING BENEFITS Javier Vargas MarnJuan M. RamrezRosa E. Correa Gutirrez. Specialist operationResearch ProfessorResearch Professor Operation CoordinationPower Systems Mecatrnica XM, Expertos en MercadosCINVESTAV, MxicoUNAL, Facultad de Minas jvargas@xm.com.cojramirez@gdl.cinvestav.mxrecorrea@unal.edu.co Category Power System operation ABSTRACT Both technical and institutional changes suggest the need for optimal and efficient power system operation by handlingvoltageandreactiveresources.Thepaper'saimistocoordinatetheoperationbyreducingactive and reactive power losses with purposes of network's security preservation through the index of proximity to voltage instability called L-index. The impact of reducing active and reactive losses inthe security, operation cost, margins reserves and transmission capacity of network are evaluated. The approach is formulated as a multi-objective optimization problem. The results are exhibited on3, 39and190-busespowersystemstest. They show the successful of the proposition and it is encouraged to follow-up this research. KEY WORDS Active and reactive power losses, Voltage instability indexL-index, Optimization, Optimal power flow (OPF), Operation power system. INTRODUCCIN Nowadays, the deregulations of electricity markets, thelackofincentivesforinvestment,regulations regarding the care of the environment aspects, the complexityofthetransmissionsystems,have madethepowersystemoperationmorestressed. The lack of reactive power management according toanyoperatingconditioncanleadtoinstability voltageproblems,affectingtheactivepower transport.Insufficientreactivepowerresourcesin heavilyloadedsystemsarethemainreasonfor voltagecollapseVenkatesh,2000[1].Likewise, largeinterconnectedpowersystemswithahigh degreeofcomplexity,itscontrolandoperationare achallengingtask.Furthermore,interconnection networkswithlimitedcapacitylines,orweak connectivitycanleadtonaturaloscillationsdueto variationsofloads,shootdownmachines,outputs oftransmissionlinesortheproliferationof automaticcontrols(poorlytuned).Thus,boost voltage control, increase active and reactive power reserves so as to improvethe safetyand reliability networkisrequired.Itisimportantreducedthe transmissionanddistributionpowerlosses becausethisenergymaketolosemoney.Today thehighlevelofenergylossesshowsthatpower flowmanagementmustbeaddressedWysocki, 2011 [2]. During a contingency, the active power component throughalinedoesnotchangesignificantly; whereasthereactivepowercomponentmaybe changedramaticallyLeonardi,2008[3].Excessive transientvoltagevariationcancausearapid voltagecollapse,thusafactorthatmaycontribute to voltage instability, is the voltage drop due to the activeandreactivepowerflowthroughthe inductivereactanceofthetransmissionlineLiu, 2000[4].Undernormalandemergencyoperating conditions,thereactivepowermarginavailable determinesitsproximitytovoltageinstability.A greatermarginofreactivepowerimpliesabetter systemsecurityandviceversaVyjayanthi,2011 [5].Inthispaper,anoperatingstrategyis proposed,wherethepowernetworkcanbe optimizedfollowinganoptimalcriterion.For determiningoptimalsettingsforthecontrollable devices,amulti-objectiveoptimalpowerflowisa suitablemethod.Hencetheneedforproper J ORNADAS TCNICAS ISA - 2012 2 coordination among reactive power sources. Thispaperdealswithareactivepowerproblem, which is a sub-problem of the OPF calculation, and determinesthecontrollablevariables,suchas transformerstapsetting,shuntcapacitors/reactors output,reactivepoweroutputofgeneratorsand staticreactivepowercompensators,while minimizestransmissionlossesorothersuitable objectivefunctions,satisfyingagivensetof physicalandoperationalconstraints.Sincethe transformerstappositionandshunt capacitor/reactorsoutputshaveadiscretenature, whilethegeneratorsreactivepoweroutput,bus voltage magnitudes and angles, on the other hand, arecontinuousvariables,thereactivepower optimizationproblemisoriginallyformulatedas mixed-integer, nonlinear problem Momoh, 1999, [6] Ela, 2011 [7], Yan, 2011 [8], Estevam, 2010 [9]. Classicaloptimizationtechniquessuchaslinear programming,nonlinearprogramming,quadratic programming,Newtonandinteriorpointmethods Yan,2011[9],havebeenappliedforsolving OptimalReactivePowerDispatch(ORPD) problems.Thesetechniquesmayhavelimitations like: (i) need of continuous and differential objective functions,(ii)easilyconvergetolocalminima,and (iii)difficultyinhandlingdiscretevariables Jeyadevi, 2011 [10]. To overcome these limitations, robustandflexibleevolutionaryoptimization techniquessuchas,simplegeneticalgorithms Devaraj,2010[11],evolutionarystrategiesAjith, 2005[12],Deb,2001[13],evolutionary programmingCoello2001[14],Manoharan2009 [15], particle swarm optimization Baskar 2008 [16], differentialevolutionSayah,2008[17],andReal codedGeneticAlgorithms(RGA)Subbaraj,2009 [18]havebeenapplied.Recently,theORPD problemisformulatedasamulti-objective(MO) optimization problem Abido 2006 [19]. ORPDisoneofthemostcost-effectivemeasures topromotebothlossreductionandvoltageprofile withoutjeopardizingthesystemoperation.The multi-objectiveproblemthatinvolvesobjectives suchaseconomicaloperatingcondition,system securitymargin,andvoltagedeviation,reactive powersuppliesaredevelopedZhihuan,2010[20]. Especiallyatheavilyloadedoperatingpoints, preventionofvoltageinstabilityisanimportant issuethatthesystemoperatorhastomeet.In Perninge, 2010 [21], maximization of a margin from anoperatingpointtothesaddle-nodebifurcation surfaceisproposed.Likewise,ageneticalgorithm basedreactivepowerdispatchforvoltagestability improvement is presented. The minimization of the maximumofavoltageinstabilityindexL-indexof networkbuseshasbeenapproachedtoKessel 1986 [22]. Inthispaper,aGeneticAlgorithmMulti-objective NSGA-IIisusedtosolveproblem.Thealgorithm canbesummarizedasfollows:(i)Initializea population,(ii)Calculatethefitnessofeach individual,(iii)Reproducethebestindividualsto form a new population, (iv) Perform crossover and mutationoperations,(v)Returntostep2untila convergencecriterionDeb,2001[13],Deb,2002 [23].Thispaperisorganizedasfollows.Section1 describes the optimization problem. The results on test systems are shown in the Section 2. Finally the Section 3 presents the main conclusions. 1OPTIMIZATION PROBLEM FORMULATION1.1OBJECTIVE FUNCTION Usually,designoptimizationproblemsaretypically solved using an All-in-One (AiO) strategy where all objectivesandconstraintsarehandledinasingle problem.Inthispaper,theactiveandreactive powerlosses minimizations, as well as the voltage instabilityindexL-indexofallnetworkbuseshave beenapproachedbyamulti-objectivefunction Kessel1986[22].Originally,thisproblemconsists ontheoptimizationofthegeneratorterminal voltagemagnitudes, giV ,andtransformertaps positions, iTap , of the entire system, that is: ( ) min , f x u (1) Subject to, ( 0 , ) h x u = (2) ( , ) 0 g x u s (3) Wherefis the objective function;xis the vector ofdecisionvariables(giV , iTap )andu isthe vectorofcontrolvariables;( , ) h x u represents equalityconstraints(thebalanceoftheactiveand reactivepowerdescribedbythesetofpowerflow equations);( , ) g x u representsinequality constraintsofthedecisionvariables.Forasingle line, the active or reactive losses objective function is given by the following expressions: J ORNADAS TCNICAS ISA - 2012 3 ( )222 isi riVAR i i iiV VQ X I XX= =(4) 1inlVARif Q =(5) ( )222 isi riMW i i iiV VP G I GG= = (6) 2inlMWif P =(7) Where,X isthelinereactance,G istheline conductance,Iis the line current, sVand rVare voltageattheendsoftheline, sP and sQ are activeandreactivepoweratthesendingend, rPand rQ areactiveandreactivepoweratthe receiving end; ln total number lines. In a power system, the proximity to voltage stability canbeestimatedbyanindexwhichassesstwo aspects:i)avoltagestabilityindexthatdescribes when the system is close to voltage instability, ii) to drawwhichistheweakestnodeinthesystemSuganyadevia2009[24].Thisindexisableto evaluatethestabilitymarginofeachnetworkbus. Thevaluetakesavaluebetweenzero(noload) andone(voltagecollapse),thisvalueimplicitly considerstheloadeffect.Thismeansthatabus withahighL-indexvaluemeansitisvulnerable. Thus it is a practical method to identify weak areas thatrequirereactivepowersupport.TheindexL-indexiscalculatedusingthefollowingexpression Kessel1986: 31LG ji ijji F Vf L index MaxVooee= = (8) Where Lo is the set of loadbuses, Go is the set ofgeneratorbuses, jiF isthesubmatrixofthe hybrid matrixH , iVand jVare bus voltages. 1.2RESTRICTIONS Theequalityconstraints(2)aretheequationsof balance,whichimposetherestrictionofsatisfying thedemandforactiveandreactivepoweronall network buses. At the steady state operation point, thegeneratedpowerfulfillsthedemandplusthe network losses. The balance equations, consider a balanceofactiveandreactivepowerthatmust satisfy every bus, by the following equations: ( ) , 0i i iPG PD P V u + = , fori=1,2,. . . ,1n(9) ( ) , 0i i iQG QD Q V u + = , for i=1,2,. . . ,2n(10) Where 1n isthenumberofnodesinthepower system, except the slack node; 2nare all nodes in thepowersystem; GiP y GiQ aretheactiveand reactive power for thei th generator; DiPy DiQareactiveandreactiveforthei th busload; ( ) ,iP V u ( ) ,iQ V u aretheactiveandreactive power injected into thei th node, respectively. Theinequalityconstraintsreflecttheoperational limits imposed on the devices, the control and state variables.Themaininequalityconstraints considered in an OPF formulation are the following: Active and reactive power generation Limits. imin i imaxPG PG PG s s (11) imin i imaxQG QG QG s s (12) imin i imaxVG VG VG s s (13) Where iminPG, imaxPGaretheminimumand maximumactivepowerlimits, iminQG, imaxQG areminimumandmaximumreactivepowerlimits, iminVG, imaxVGaretheterminalvoltagelimits, respectively, for thei th generator. Voltage profiles Becauseofthevoltageisasafetyandquality criteriaindex,itmayincludeanadditional constrainttoimprovethevoltageprofileinthe network.Mathematically,thisconstraintcanbe specified as: mini refV V (14) Where iVrepresents the voltage magnitude at the i th loadbus, refV representsthemagnitudeof voltagereference,generallydefinedas1.0refV =J ORNADAS TCNICAS ISA - 2012 4 p.u. Limits on taps positions Transformers with tap changer are used as devices forcontrollingthevoltagemagnitude.Thesetaps are restricted within minimum and maximum limits, they are represented by: imin i imaxTap Tap Tap s s (15) Where iTapis thei th position transformer Tap, iminTap, imaxTap,aretheminimumand maximum position, respectively. Limits switchable reactive power compensation. Theswitchablestaticcompensationelementsare reactorsorcapacitors,whichhavemaximumor minimumcapabilities.Theircontributionor consumptionisdiscrete.Thelimitsofthestatic elements can be formulated as: imin i imaxYshunt Yshunt Yshunt s s (16) Where iYshunt isthecompensationusedinthe i th reactororcapacitor; iminYshunt, imaxYshunt,aretheminimumandmaximum switchable capacity. 1.3SOLUTION METHOD Asabovementioned,aGeneticAlgorithmMulti-objective NSGA-II is used to solve problem (1)-(3).Three objective functions are used: (1) f : Active power losses, (2) f : Reactive power losses, (3) f :VoltageinstabilityindexL-indexofnetwork buses.Inthispaper,functions(1) (3) f f and (2) (3) f f areusedindependently.The decisionvariablesare: giV generatorsterminal voltagemagnitudes, iTap transformerstap positions,and iYshunt switchableshunts elements. 2STUDIES CASE 2.1The 3-Bus test system The3-busestestsystemisusedassimpletest powersystem.Itconsistsof3-busesand2-synchronous machines, Figure 1. Figure 1. The 3-bus test system. TheTable1summarizedthedata,theTable2 show the line parameters and results are shown in Table 3. VolNro. Type MW MVAR MW MVAR1 SL 12 PV 1 170 03 PQ 1 200 100Bus Load Generation Table 1.Data 3-Bus Test System Line Bus from Bus to G B1 1 3 4 -52 2 3 4 -10 Table 2.Data 3-Bus line parameter Thetotaldecisionvariablesaretwo: giV for 1, 2 i =Case P Loss Q Loss Lindex G (MW) G (MVAR)Base 0.1767 0.3720 0.1401 2.1767 1.3270P Loss 0.1355 0.3049 0.1077 2.1355 1.3040Q Loss 0.1397 0.2958 0.1070 2.1397 1.2958 Table 3.Results of 3-Bus Test System Activelossreductionhasapositiveimpactin reducingthenetworkgeneration,whichreduces theoperationcostandimprovetheactiveand reactivepowerreserve.Inthisexamplethe reduction in slack generation is around 1.89 %, the reactive loss reduction has a positive impact in the voltagestability,whichcanbeobservedintheL-index.Thisindexpassesfromthebasecase 0.1401 to reactive power case 0.1070. J ORNADAS TCNICAS ISA - 2012 5 2.2The 39-Bus test system The 39-buses test system is used as the test power system.Itconsistsof39busesand10 synchronousmachines,Figure2Singapore1996 [25]. Figure 2. The 39-bus test system Thetotaldecisionvariablesare14: giV for 1, 2,...10 i = ,generatorsterminalvoltageand iTap for1, 2,...4 i = transformerstapspositions. These variables were bounded as follows: 0.90 . 1.1.ipu VG pu s s (17) 0.75 . 1.25 .ipu Tap pu s s (18) The Table 4 summarizes the results. Case P Loss Q Loss Lindex G (MW) G (MVAR)Base 0.6358 4.6059 0.2857 61.7885 20.4929P Loss 0.5110 0.5673 0.2304 61.6640 15.3192Q Loss 0.5255 0.2520 0.2297 6.6785 15.6356 Table 4.Results of 39-Bus Test System The reduction in slack generation is around 2.01 %, thenetworklossesarereducedin19.52%;the reactive power losses arereducedin 94%.These resultsasshowninDong2005[26],confirmthe factofthereducingthepowerlossesimprovethe voltagestabilityindexwithlessoperatingcost.In otherwordsitispossibletoreducethepower losses in the network without jeopardize the system voltagestabilityperformance,becauseofincrease in the active and reactive power reserve. 2.3The 190-Bus Test System The 190 buses test system, consists of 190 buses and46synchronousmachines,Figure3Ramirez-Gonzalez2010[27].Thetotaldecisionvariables are90: giV for,generatorsterminalvoltage; iTapfor1, 2,...22 i = transformerstapspositionsand iYshunt for1, 2,...22 i = thecompensationused inthereactororcapacitor.Thesevariableswere bounded as follows: 0.95 . 1.05 .ipu VG pu s s (19) 0.975 . 1.025 .ipu Tap pu s s(20) 1.5 . 2.0 .ipu Yshunt pu s s(21) 24849150656575852515553468358438554 707374717268656469667877 475789451081071065992448143808287 88 12 1051047611971096100949395101109981021031413996260616324129201318 9907991125126123192112813313211315 16 17110111 1122335122 1201211191241891172211611536127 13011811419041401751761783029 145143341861771483332180181281741731724216237164171153146147149142161381631886182184185 18339165167168170160166169179157154158159141140 144252713813626 311511371551391881351341501521874767156 Figure 3. The 190-bus test system The Table 5 summarizes the results. Case P Loss Q Loss Lindex G (MW) G (MVAR)Base 1.4255 82.9633 0.1963 111.5735 47.9873P Loss 1.3485 82.9150 0.1741 111.4965 34.7377Q Loss 1.4094 79.3213 0.1779 111.5574 27.1833 Table 5.Results of 39-Bus Test System Thenetworklossesarereducedin5.40%;the J ORNADAS TCNICAS ISA - 2012 6 reactivepowerlossesarereducedin4.39%.The powerreactivereserveisboostedin43.35%. TheseresultsasshowninVenkatesh2000[1], Wysocki 2011 [2], ratify the fact of the reducing the powerlossesimprovethevoltagestabilityindex, increasetheactiveandreactivepowerreserveat lessoperatingcost,withoutjeopardizethesystem voltagestabilityperformance.Anotherimportance aspect is at less network power losses higher is the voltageprofileinthesystem,thereforeless transmissionreactivepower,thatimprovethe active and reactive power reserve. 3CONCLUSION Anoptimalpowerflowproblemhasbeen addressedinotherkindofpapers,butinthis,itis highlightedtheimportanceofreducingnetwork losseswithoutjeopardizethesystemvoltage stability.Thepowersystemoperationwithoptimal criteriareducesthetotaloperationcostand improves the performance of transmission network. Withlessnetworkpowerlosses,higheristhe voltageprofileinthesystem,therefore,less transmissionreactivepowerthatimprovesthe active and reactive power reserve. Three objective functionshavebeensolvedbymulti-objective optimization:(i)activepowerlosses;(ii)reactive powerlosses;(iii)voltageinstabilityindexL-index of all network buses. A genetic algorithm (NSGA-II) asmulti-objectivefunctionisusedtosolvethe problem. In all cases, the verification of the steady statepreservationhasbeenmade.Thebenefits showthesuccessfulofthepropositionandis encouraged to follow-up this research. 4REFERENCIAS BIBLIOGRFICAS [1] VENKATESH, B.; SADASIVAM, G. & KHAN, M. (2000),'Anewoptimalreactivepower schedulingmethodforlossminimizationand voltagestabilitymarginmaximizationusing successivemulti-objectivefuzzyLPtechnique', PowerSystems,IEEETransactionson15(2), 844 -851. 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