Probabilistic Analysis of Radial Distribution Network
Performance with Varying Wind Speed Levels Sooraj Narayan K,
Ashwani Kumar Department of Electrical Engineering NIT
KurukshetraHaryana, India [email protected], [email protected]
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.
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