Probabilistic Analysis of Radial Distribution Network Performance with Varying Wind Speed Levels Sooraj Narayan K, Ashwani Kumar Department of Electrical Engineering NIT KurukshetraHaryana, India soorajn14@gmail.com, ashwa_ks@yahoo.co.in AbstractThispaperpresentsananalysisofradialdistribution networkconsideringtheprobabilisticmodelingofloads, substationvoltageandintegratedwindenergysource.The impacts on the distribution network for varying wind speed levels arestudied.Thewindpowersourceisplacedonthemost optimum buses obtained from stability index calculations. A total of five scenarios for different wind speed levels are studied in this paper. The impact of wind power output on power loss reduction andvoltageprofileimprovementareobserved.Theresultsare analyzed for various wind speed levels on an IEEE 33 bus radial distribution system. KeywordsRadialDistributionNetwork,Probabilistic Modelling,WindSpeedLevels,StabilityIndex,PowerLoss Reduction, Voltage profile Improvement. I. INTRODUCTIONDuetorecentadvancesinderegulationandtheever increasing costs of power transmission, Distributed Generation (DG)israpidlyemergingasanalternativetoCentralized PowerGeneration[1].Theinexhaustiblenatureofthe renewableenergysources,namelywindandPVbasedDGs, haveledthemtobeemployedmoreandmoreforlocalized powergeneration.DuetotheintermittencyofwindandPV sources, integration of these DGs into the distribution network posessomedifficulties.Therandomnessofwindspeedand solar insolation causes the output of these generation sources to vary.Analyticalmethodshavebeenusedtomodelthese renewableresourcesasnondispatchablesourcesofpower[2]. Theprobabilisticapproachofmodelingtherenewablesources has been applied for various stages of planning [3]. Deterministic approaches to carry out distribution load flow havebeenincorporatedusingdifferentmethodologiesinthe past[4].Althoughthesemethodsprovidedaccurateresults, theyarebasedontheassumptionofthesteadystatenatureof the radial distribution system. A more realistic method is bound totakeintoconsiderationtheuncertaintyofvariousrandom variableswithinthesystem.Theloadandtheintegrated generationsourcesaregenerallyconsideredasrandom variables in the probabilistic load flow calculations.Probabilisticloadflowusingatwo-pointestimatemethod wasusedtoanalyzeadistributionsystemconsideringwind generationin[5].ProbabilisticloadflowusingMonteCarlo Simulationwasusedin[6]toassessthevoltagequalityofa distributionsystemwithdistributedgeneration.Stochastic approacheswereusedin [7] toinvestigatenetworkconstraints inapowersystemwithdistributedgeneration.Afastvoltage assessmentmethodusingprobabilisticloadflowfor distributionnetworkswithwindpowergenerationwas investigated in [8]. This paper used Latin Hypercube sampling (LHS)togeneratewindsamples.Anewloadflowalgorithm usingMonteCarlosimulationwasproposedin[9]to investigatedistributionsystemperformanceunderDG penetration.Anewprobabilisticloadflowmethodwas proposedbasedonvoltagedropcalculationfordistribution systemswithwindpowerin[10].In[11],integrationofwind power and electric vehicles were both considered to carry out a constrained probabilistic load flow of distribution systems. ThispaperfirstincorporatestheMonteCarloSimulation (MCS)methodtocarryoutprobabilisticloadflowwiththe substationvoltageandloadpowerdemandsassumedtobe randomvariables.Asamplesiteisselectedandawindpower sourceisintegratedintoselectednodesoftheradialsystem. Then,theimpactsofwindpoweradditiononthetestsystem areanalyzedbyconsideringvariouspoweroutputsofwind turbine.Thepoweroutputsvaryaccordingtothewindspeed and the probability of occurrence of that wind speed level. The rest of the paper is as follows: Section II discusses the modelingofloadpowerdemands,substationvoltagesandthe windenergysource.SectionIIIdiscussestwostabilityindex basedmethodsforfindingtheoptimumDGlocation.Section IVdealswiththeloadflowcomputationtechnique.Acasestudy wasconductedforanalyzingwindpowerintegrationimpacts ontheradialdistributionsysteminSectionV.AnIEEE33 radialbussystemwasutilizedforthispaper.Aprogramwas developed in MATLAB 7.1 for implementing the study. The programwasrunonanIntelCore(TM)i7-37703.70GHz processor. The results are analyzed and discussed in detail. II.PROBABILISTIC MODELLING A.Load Modelling Thevariabilityofloaddemandsischieflybecauseof unscheduledoutages,errorsinmeasurementorunknownload power values. The probabilistic nature of load at each bus in a distributionsystemcanbeincorporatedintoloadflowstudies by visualizing the loads as random variables distributed with a variance about a mean value. In this paper, the load demands at each bus are assumed to be random variables with Gaussian or Normal distribution [12]. (PL,) = [1c2n cxp -(PL,i-PL,i)22c2(1) where,PL,istheactiveloaddemandatbusnumberiand PL,, o are the mean and standard deviation values of each load power respectively.B.Substation Voltage Modelling Similar to the load modeling, the substation voltage is also assumed to be a random variable following normal distribution [13]. (Is) = [1c2n cxp - (vs-vs)22c2(2) where,IsisthesubstationbusvoltageandIs,oarethe meanandstandarddeviationvaluesofsubstationvoltage respectively.C.Wind Power Source Modelling Thepoweroutputfromawindturbineisgivenbythe following equation [5]. Pw = _u, : :ck1: + k2, :c< : < :P, :< : < :cou, : > :co(3) where, Pw is the power output of wind turbine in MW, : is thewindvelocityinm/s,:c isthecut-inspeedofthewind turbineinm/s,:coisthecut-outspeedofthewindturbinein m/s,:istheratedspeed ofthe windturbineinm/s, Pis the ratedpoweroutputofthewindturbineinMW,k1 = Pr:r-:ci and k2 = -k1 - :c. Windenergysource isessentiallyanintermittentsource of power.Theuncertaintyofwindturbineoutputatanylocation mainly arises due to the variation in wind speed and air density. Sincewindspeedvariesfrequently,itisconsideredtobea random variable in the radial power flow calculation. There are mainlytwoprobabilitydistributionfunctionsusedtomodel windspeed,namely,WeibullandRayleighprobability distributionfunctions.Inthispaper,theWeibulldistribution hasbeenusedtosamplewindspeed. TheWeibull distribution function is a two parameter function which isused to describe wind speed mathematically as: (I) =kc (c)k-1cxp(-c )k,u : (4) where, :isthewindspeed, kistheshapeparameterand c is the scale parameter [12]. III.OPTIMUM LOCATION FOR WIND TURBINE PLACEMENT Stability based indices have been used in the recent past to obtaintheoptimumlocationforplacingtheDGsinthe distributionsystem[14].Inthispaper,twostabilityindices havebeenutilizedtoobtainthemostoptimumlocationfor wind turbine placement in the system. A.Voltage Stability Index TheVoltageStabilityIndex(VSI)showninEq.(7)for radialdistributionsystemswasproposedbyU.Emingoluand M.H.Hocaugluin[15].Thisindexidentifiesthemostvoltage sensitive bus in the system. Fig. 1. One line diagram of a two bus distribution system. ThebuswiththeleastvalueofVSIisthemostsensitive busandtheDGistobeplacedonthatbusforvoltageprofile improvement.Thisindexisobtainedfromthetwonode distribution system shown in Fig.1. SI(r) = 2Is2I2 - I4 - 2I2(PR + X) - |Z|2(P2 -2)(7) B.Power Stability Index The Power Stability Index (VSI) shown in Eq. (8) for radial distributionsystemswasproposedbyM.M.Aman,G.B. Jasmon,H.M.MokhlisandA.H.A.Bakarin[16].Thisindex was developed considering stable node voltages. Fig.2.Onelinediagramofatwobusdistributionsystemwithactivepower support. Theindexvalueiscalculatedforeverylinei - ]inthe system. For any line i -] having the highest PSI value, the DG istobeplacedonthe]thbusofthesystem.Thisindexis obtainedfromthetwobusdistributionsystemwithactive power support shown in Fig. 2. PSI =4i](PL-PG)||v|icos(-6)]2(8) where, =os -o. IV.PROBABILISTIC LOAD FLOW Theimplementationofloadflowprocedureiscarriedout in this paper by using Monte Carlo Simulation (MCS) method. AlargenumberofwindsampleswhichareWeibull distributed can be produced using MCS. Since the relationship between wind speed and power production is known from Eq. (3),alargenumberofpowersamplescanalsobeobtained. Then, the wind speed is divided into various levels and power outputs of each level are obtained. A total of five scenarios are appliedtothetestsystem.Eachscenarioisappliedtothe candidatenodesobtainedfromVSIandPSIcalculationsand thevoltageandpowerlossvaluesaresaved.Thenumberof MCSsamplesistakenequalto15000.Fig.3showsthe flowchartforwindspeedsamplingandleveling.Fig4shows theflowchartforprobabilisticloadflowundervariouswind speedlevels.Thenodalvoltagesandbranchpowerlossesare calculated every time the loop runs. After running the loop for 15000times,themeanvaluesofnodalvoltagesandbranch power losses are saved and compared. Fig. 3. Wind speed sampling and leveling. Fig. 4. Probabilistic load flow computation. V.SIMULATION CASE STUDIES AND RESULTS ThestudieswereconductedonanIEEE33busradial distributiontestsystem[17].Thebasepowerofthesystemis 100MVAandthebasevoltageis12.66KV.Thetotal connectedactivepowerloadis3.72MWandreactivepower load is 2.30 MVAR.A.Probabilistic loadflow without wind power integration AprobabilisticloadflowusingMCSisconductedonthe testsystemconsideringloadandsubstationvoltageasrandom variables. Thenumberofsamplesfor MCS basedloadflowis setto15000.Thedatavaluesofloadateachloadbusare assumedtobetheirrespectivemeanvalues.Astandard deviationof10%issetforeachloadbus.Thesubstation voltagemeanvalueisassumedtobe1.0pu.Thestandard deviationofsubstationvoltagemodelissetto1.5%.Fig.5 showsthecomparisonofresultsobtainedfromProbabilistic Loadflow(PLF)andDeterministicLoadFlow(DLF).The resultsareincloseapproximationwiththeresultsobtained from DLF computation [17]. Fig. 5. Voltage profile for DLF and PLF. B.Optimum Bus For Wind Turbine Placement For the test system in consideration, VSI and PSI values are calculatedforzerowindpowergeneration.Fig.6showsthe variation of VSI values with bus number. The lowest VSI value of 0.66804233 is obtained for bus number 18.Similarly, Fig. 7 showsthevariationofPSIvalueswithbranchnumber.The highest PSI value of 0.01600353 is obtained for branch number 24, indicating that the DG should be placed at bus number 25. Thusthetwocandidatenodesforwindturbineplacementin this study are node number 18 and 25. Fig. 6. VSI value for each bus. Fig. 7. PSI value for each branch. START Wind speed sampling using Weibull distribution Obtain wind speed levels: Level 0, Level 1, Level 2, Level 3, Level 4 and Level 5 Obtain power output of each level STOP STARTRead static network line data, load data and wind speed parameters For 15,000 samples Update static load data with probabilistic load data Probabilistic substation voltage modeling Obtain candidate nodes for wind turbine placement using VSI and PSI Subtract wind power outputs for each level from the load power of the candidate nodes Run Deterministic Load Flow STOP 0.850.90.9511.051 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33Voltage (pu)Bus numberDLFPLF00.20.40.60.811.21 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33VSIvalueBus number00.0050.010.0150.021 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31PSI valueBranch numberC.Levels of wind speed Fortheselectedwindturbinewithparame:=11.5 m/s, :co=20 m/s and P=2.0 MW [18withWeibullparametersk=1.75andc=8.78 samplesareproducedusingMCSaccorddistribution. Since the value of shape parameteWeibulldistributionisselectedoverRayleighwindspeedsampling[19].FromEquation3arealsoproduced.ThenumberofMCSsam15000.Fig.8showsthehistogramofwind shows the histogram of power output for the 2 Fig. 8. Histogram of wind speed of the 2 MW turbine. Fig. 9. Histogram of power output of the 2 MW turbine. The 15000 wind speed samples are clustereofwindspeeds.Hence,thepoweroutputs thesewindspeedsarealsoclusteredaccordinlevels.Themeanvalueofpoweroutputof level is calculated. Then, the probability of occwind speed level is calculated by Eq. (9).prob]=Nw]1w where, prob] is the probability of occurrenlevel ], Nw] is the number of wind speed sampIwisthetotalnumberofwindspeedsampower output of each wind level is multiplied bof occurrence of that level to get that actual wiforthatlevel.TableIsummarizesthesefindtable I corresponds to zero output power fromas the wind speed is below the cut-in speed of D.WindTurbine Integration Impacts Thewindturbinepoweroutputessentianegativeloadinthedistributionsystem.ThfromLevel1toLevel5areindividuallyapsystemtoanalyzetheimpactsofwindpowradialdistributionsystems.Theeffectsareob eters:c=3m/s, 8], and for the site [12],windspeed dingtoWeibull er k is less than 2, hdistributionfor 3,powersamples mplesistakenas speedandFig.9 .0 MW turbine. ed into five levels correspondingto ngtowindspeed eachwindspeed currence of every (9) nce of wind speed ples in level ] and mples.Themean by the probability ind turbine output dings.Level0in m the wind turbine the turbine.allyappearsasa hefivescenarios ppliedonthetest werintegrationon bservedwhenthe turbineisplacedatbus18andbuvoltageprofileimprovementand carried out for both the cases. 1)PowerLossReduction: Table ofvariouswindpoweroutputson lossesofthetestsystem.Fig.10spowerlossesoneachbranchwith for the wind turbine placed at bus 1the variation of real power losses onwind speed levels for the wind turbiTABLE I.POWER OUTPUT OF TURBISPEED LEVE Level Speed Range (m/s) Mean Power Output (MW) Percentof RatPowe(%)00-300 13-50.241512.07425-80.814840.73838-11.51.557377.863411.5-152.0000100.00515-202.0000100.00AsobservedfromtableII,thelosses and reactive power losses are windturbineisplacedatbus18thanumber25.Also,themaximumpofor wind speed level 3 in both the ca2)VoltageProfileImprovement: profileofthetestsystemforvarioutheturbineisplacedatbus18.Simvoltage profile of the test system forwhen the turbine is placed at bus 25itisobservedthatmorevoltageachievedwhenthewindturbineisalso depicted in Fig. 14. For the winthereisverylittleimprovementiwind turbine placed at bus 18, windachieve the maximum voltage profilItisobservedthatbothpower profileenhancementisbetterwhen at bus 18 compared to bus 25. Fig.10.Variationofrealpowerlossesonspeed levels for the wind turbine placed at bu020406014710131619222Real power loss(KW)Branch numberus25andacomparisonof powerlossreductionis IIsummarizestheimpacts activeandreactivepower showsthevariationofreal variouswindspeedlevels 8. Similarly, Fig. 11 shows n each branch with various ine placed at bus 25. INE FOR DIFFERENT WIND ELS tage ted er Probability of occurrence Actual Power Output (MW) 0.14220 460.17490.0422 880.26920.2193 300.12070.3534 0000.22690.2413 0000.06220.1324 ereductioninrealpower more pronounced when the anwhenitisplacedatbus owerlossreductionoccurs ases. Fig.12showsthevoltage uswindspeedlevelswhen milarly,Fig.13showsthe r various wind speed levels 5. From Fig. 12 and Fig. 13, eprofileimprovementis splacedatbus18.Thisis nd turbine placed at bus 25, nvoltageprofile.Forthe d speed Level 3 is found to le improvement. lossreductionandvoltage thewindturbineisplaced neachbranchwithvariouswind us 18. 52831Level 0Level 1Level 2Level 3Level 4Level 5Fig.11.Variationofrealpowerlossesoneachbrancspeed levels for the wind turbine placed at bus 25. TABLEII.POWERLOSSREDUCTIONFORVARWIND SPEED Level Wind turbine placed at bus number 18 Wind turbus nTotal real power loss (KW) Total reactive power loss (KVAR) Total realpower loss(KW) 0211.3233143.2709211.32331204.5621138.2938209.36322180.6686121.0684201.49673167.0735111.7007196.37624178.1824119.3225200.60765191.5119128.8009205.1983Fig. 12. Voltage profile of the test system with various wthe wind turbine placed at bus 18. Fig. 13. Voltage profile of the test system with various wthe wind turbine placed at bus 25. 02040601471013161922252831Real power loss(KW)Branch number0.840.860.880.90.920.940.960.9811.021 3 5 7 9 11 13 15 17 19 21 23 25Voltage(pu)Bus number0.840.860.880.90.920.940.960.9811.021 3 5 7 9 11 13 15 17 19 21 23 25Voltage (pu)Bus number chwithvariouswind RIOUSLEVELSOF bine placed at number 25 l s Total reactive power loss (KVAR) 143.2709 2142.0644 7137.2652 2134.221 6136.7312 139.5084 wind speed levelsfor wind speed levelsfor Fig.14.Comparisonofvoltageprofilesbebus 18 and bus 25 for level 3. TheCumulativeDistributionFuin Fig. 15 and Fig. 16 show the impatthebusatwhichthewindturbinshow that on placing the wind turbinnearer to unity than it was before, reinvoltageprofile.Fig.17andFig. voltage magnitude at bus 18 and busrespectively. Fig. 15. CDF plot for level 0 and 3 for the wiFig. 16. CDF plot for level 0 and 3 for the wiFig.17.Histogramofvoltagemagnitudeatspeed. Level 0Level 1Level 2Level3 Level4 Level 527 29 31 33Level 0Level 1Level2Level 3Level 45 27 29 31 33Level 0Level 1Level 2Level 30.840.860.880.90.920.940.960.9811.021 3 5 7 9 11131517Voltage (pu)Bus nu tweenwindturbineplacementat unction(CDF)plotsshown provement in voltage profile eisplaced. TheCDFplots ne, the voltage at the bus is eferring to an improvement 18showsthehistogramof s 25 for Level 3 wind speed ind turbine placed at bus 18. ind turbine placed at bus 25. tbusnumber18forlevel3wind 71921232527293133umberWind turbine at bus number 18Wind turbine at bus number 25 Fig.18.Histogramofvoltagemagnitudeatbusnumber25forlevel3wind speed. VI.CONCLUSIONS Thispaperpresentedananalysisofprobabilisticloadflow of radial distribution systems with wind power integration. The impactsofvariouslevelsofwindspeedonthevoltageprofile andthepowerlossreductiononthetestsystemwasstudied. Thestudywasconductedonaprobabilisticperspective considering the power system components as random variables. Two stability index based methods were used to determine the location for wind turbine placement, and a comparison between thetwowasmadebasedonreducedpowerlossesandvoltage profile improvement. It was observed that the placement of the windpowersourceontheradialdistributionsystemresultsin reducedpowerlossesalongwithsignificantvoltageprofile improvement. REFERENCES [1]R.C.DuganandT.E.Mcdermont,Distributedgeneration,IEEE Ind.Applicat.Mag.,pp.19-25, Mar./Apr. 2002. [2]DuongQuocHung,N.MithulananthanandKwangY.Lee,Optimal placementofdispatchableandnondispatchablerenewableDGunitsin distributionnetworksforminimizingenergyloss,Int.J.Electr.Power Energy Syst., vol. 55, pp. 179186, February 2014. [3]SrinivasM.S,Distributionloadflows:abriefreview,IEEEPower Engineering Society Winter Meeting., vol 2, pp. 942-945, 2000. [4]Chen P, Chen Z and Bak-Jensen B, Probabilistic load flow: a review ThirdInternationalConferenceonElectricutilityderegulationand restructuring and power technologies, pp. 158691, April 2008. [5]MortezaAien,RezaRamezaniandS.MohsenGhavami,Probabilistic loadflowconsideringwindgenerationuncertainty, Engineering,Technology&AppliedScienceResearch.,vol1,pp.126-132, 2011 [6]SexauerJ.M.andMohagheghi,S.,Voltagequalityassessmentina distributionsystemwithdistributedgenerationaprobabilisticload flowapproach,IEEETransactionsonPowerDelivery,vol28,pp. 1652-1662, July 2013. [7]M.Reza,G.PapaefthymiouandP.H.Schavemaker,Anexampleof utilizingstochasticapproachforinvestigatingnetworkconstraints (congestions)onhorizontallyoperatedpowersystemswithdistributed generation, Jurnal Teknik Elektro, vol. 6, pp. 79-86, September 2006. [8]CanChen,BoomingZhangandWenchuanWu,Afastprobabilistic voltage assessment method for distribution system integrated with wind power generation, TENCON 2012 - 2012 IEEE Region 10 Conference , vol., no., pp.1-6, 19-22, Nov. 2012. [9]El-KhattamW,HegazyandY.G,SalamaM.M.A,"Investigating distributedgenerationsystemsperformanceusingMonteCarlo simulation," IEEE Transactions on Power Systems, vol.21, no.2, pp.524-532, May 2006. [10]W.CBricenoVincente,R.CaireandN.Hadjsaid,Probabilisticload flowforvoltageassessmentinradialdistributionsystemswithwind power,Int.J.Electr.PowerEnergySyst.,vol.41,pp. 27-33,October 2012. [11]VlachogiannisJ.G,Probabilisticconstrainedloadflowconsidering integrationofwindpowergenerationandelectricvehicles,IEEE Transactions on Power Systems, vol.24, no.4, pp. 1808-1817, Nov. 2009 [12]AlirezaSoroudi,MortezaAlenandMehdiEhsan,Aprobabilistic modelingofphotovoltaicmodulesandwindpowergenerationimpact on distribtuion networks, IEEE Systems Journal, vol. 6, no. 2, pp. 254-259, June 2012 [13]VichakornHengsritawat,ThavatchaiTayjasanantandNatthaphob Nimpitiwan,Optimalsizingofphotovoltaic distributedgeneratorsina distributionsystemwithconsiderationofsolarradiationandharmonic distortion,Int.J.Electr.PowerEnergySyst.,vol.39,pp.36-47,July 2012. [14]M.M.Aman,G.B.Jasmon,A.H.ABakarandH.Mokhlis,Anew approachforoptimumDGplacementandsizingbasedonvoltage stability maximization and minimization of power losses, Int. J. Energy Conversion and Management, vol. 70, pp. 202-210, June 2013 [15]EmingoluU.andHocaogluM.H.,Avoltagestabilityindexforradialdistributionnetworks,UniversitiesPowerEngineeringConference, vol., no., pp.408-413, Sept. 2007. [16]M.M.Aman,G.B.Jasmon,H.MokhlisandA.H.A.Bakar,Optimal placement and sizing of a DG based on a new power stability index and linelosses,Int.J.Electr.PowerEnergySyst.,vol.43,pp.1296-1304, December 2012. [17]RakeshRanjan&Das,SimpleandEfficientComputerAlgorithmto SolveRadialDistributionNetworks,ElectricPowerComponentsand Systems, 31:1, pp. 95-107, June 2010 [18]VestasProductsandServices,http://www.vestas.com/en/products_and_services/turbines/v110-2_0_mw#!at-a-glance.html [19]ArniS.R.SrinivasaEao,Anoteonderivationofthegenerating functionfortherighttruncatedrayleighdistribution,Int.J.Applied Mathematic Letters, vol. 19, pp. 789-794, August 2006.