AbstractThispaperproposesabackward/forwardsweep method to
analyze the power flow in radial distribution systems. The
distributionsystemhasradialstructureandhighR/Xratios.Sothe
newton-raphsonandfastdecoupledmethodsarefailedwith distribution
system. The proposed method presents a load flow study
usingbackward/forwardsweepmethod,whichisoneofthemost effective
methods for the load-flow analysis of the radial distribution
system. By using thismethod, powerlosses foreach busbranch and
voltagemagnitudesforeachbusnodearedetermined.Thismethod
hasbeentestedonIEEE33-busradialdistributionsystemand effective
results are obtained using MATLAB.
KeywordsBackward/Forwardsweepmethod,Distribution system, Load flow
analysis. I.INTRODUCTION OADflowstudiesareperformedonPowerSystemsto
understand the nature of the installed network. Load flow
isusedtodeterminethestaticperformanceofthesystem.A
power-flowstudyusuallyusessimplifiednotationsuchas a
one-linediagram and per-unitsystem,andfocuseson various forms of AC
power (i.e.: voltages, voltage angles, real
powerandreactivepower).Itanalyzesthepowersystemsin
normalsteady-stateoperation.Thedistributionnetworks
becauseofthesomeofthefollowingspecialfeaturesfallin the category of
ill-condition. Radial or weakly meshed networks High R/X ratios
Multi phase, unbalanced operation Unbalanced distributed load
Distributed generationDuetotheabovefactorstheNewtonRaphsonandother
transmissionsystemalgorithmsarefailedwithdistribution
network.Sothebackwardforwardsweepingmethodis
introducedtoanalyzethedistributionnetwork.Thismethod
donotneedJacobianmatrixunlikeNRmethods.However,
conventionalbackwardforwardsweepmethodisnotuseful for modern active
distribution networks.Tripathyetal.[1]presentedaNewtonlikemethodfor
solvingill-conditionedpowersystems.Theirmethodshowed
voltageconvergencebutcouldnotbeefficientlyusedfor optimal power
flow calculations. The conventional Newton Raphson (NR) and fast
decoupled loadflow(FDLF)methodsareinefficientinsolvingsuch
systems.Eventhoughwithsomeadvancementsinthe
S.GaneshiswiththeDepartmentofElectricalandElectronics Engineering,
Chandy College of Engineering, Thoothukudi, Anna University,
Chennai, TamilNadu, India (email: [email protected]).
Newton-RaphsonMethodstherobustnessoftheprogramis obtained but still
the computational time is large enough [2]. The distribution power
flow involves, first of all, finding all
thenodevoltages.Fromthesevoltages,itispossibleto
computecurrentdirectly,powerflows,systemlossesand
othersteadystatequantities.someapplications,especiallyin
thefieldsofoptimizationofdistributionsystem,and
distributionautomation(i.e.,VARplanning,network
optimization,stateestimation,etc.),needrepeatedfastload flow
solutions. [3] Aradialnetworkleavesthestationandpassesthroughthe
networkareawithnonormalconnectiontoanyothersupply. The
Forward-Backward Sweep Method (FBSM) in [4] is easy to program and
runs quickly. The method is designed to solve
thedifferentialalgebraicsystemgeneratedbytheMaximum Principle that
characterizes the solution [5].
TheNewton-Raphsonmethodanditsvariantshavebeen
developedspecificallyfortransmissionsystemswhichhavea
meshedstructure,withparallellinesandmanyredundant paths from the
generation points to the load points. Typically,
adistributionsystemoriginatesatasubstationwherethe electric power
is converted from the high voltage transmission system to a lower
voltage for delivery to the customers
[6].A.AugugliaroandL.Dusonchetproposedanimproved
Backward/Forwardsweeploadflowalgorithmforradial
distributionsystemswhichincludesthebackwardsweepand
thedecomposedforwardsweep.BackwardsweepusesKVL and KCL to obtain
the calculated voltage at each upstream bus [7].The properties of
the backward/forward sweep method with
differentlineX/Rratiosandtheconvergenceconditionsare explained by
E.Bombard, E. Carpaneto [8]. The convergence
theoremforabasictypeofoptimalcontrolproblemis explained in
[9].Chiang [10] had also proposed three different algorithms for
solvingradialdistributionnetworksbasedonthemethod proposed
byBaranandWu.He had proposed decoupled,fast
decoupled&veryfastdecoupleddistributionload-flow
algorithms.Infactdecoupledandfastdecoupleddistribution load-flow
algorithms proposed by Chiang [10] were similar to that of Baran
and Wu [11]. GoswamiandBasu[12]hadpresentedadirectmethodfor solving
radial and meshed distribution networks. However, the main
limitation of their method is that no node in the network is the
junction of more than three branches, i.e.one incoming and two
outgoing branches. Jasmon and Lee [13] had proposed a new load-flow
method for obtaining the solution of radial distribution networks.
They J. A. Michline Rupa, S. Ganesh Power Flow Analysis for Radial
Distribution System Using Backward/Forward Sweep Method LWorld
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haveusedthethreefundamentalequationsrepresentingreal
power,reactivepowerandvoltagemagnitudederivedin [13].The majority
of power flow algorithms used in industry is
newton-raphsonmethodanditsvariantsthathavebeen
developedspecificallyfortransmissionsystemswhichhavea
meshedstructure,withparallellinesandmanyredundant
pathsfromthegenerationpointstotheloadpoints[14].The
Gauss-Seidelpowerflowtechniquehasalsoshowntobe extremely
inefficient in solving large power system [15].
Inthispaperaforwardbackwardsweepingmethodis proposed to solve the
radial distribution system. The proposed
methodistestedbytaking33busradialdistributionsystems.
Thebackwardforwardsweepingmethodsolvesarecursive
relationofvoltagemagnitudes.Theloadflowwillberunin
MATLABforsolvingtheequations.Themathematical formulation of the
proposed load flow method isdescribed in the following section. II.
DISTRIBUTION SYSTEMAn electricpowerdistributionsystem
isthefinalstagein thedelivery of
electricpower;itcarrieselectricityfromthe
transmissionsystemtoindividualconsumers.Primary
distributionlinescarrythemediumvoltagepowerto
distributiontransformerswhichis locatednearthecustomer's premises.
Distribution transformers again lower the voltage to the
utilizationvoltage ofhouseholdappliancesandtypically
feedseveralcustomersthrough secondary distributionlinesat this
voltage. A. Types of Distribution System Distribution networks are
divided into two types, a)Radial Distribution System b)Ring Main
Distribution System Generallytheringmainsystemismoreexpensive than
the radialsystembecausemoreswitchesandconductorsare required
toconstruct theringmain system.Itisnotpreferred when the generation
is at low voltage and its construction cost also high. Due to the
above factors the radial system is used in distribution system.B.
Radial Distribution System
Separatefeedersareradiatefromasinglesubstationand
feedthedistributorsatonlyoneendiscalledradialsystem. Radial
distribution is the type of power distribution where the
powerisdeliveredfromthemainbranchtothesubbranches then it split out
from the sub-branches again as seen in Fig. 1,
wherethepoweristransferredfromrootnodeandthenitis split at L1. The
radial structure implies that there are no loops
inthenetworkandeachbusisconnectedtothesourcevia
exactlyonepath.Itisthecheapestbuttheleastreliable
networkconfiguration.TheRadialdistributionsystemis widely used in
sparsely populated areas.
Aradialnetworkleavesthestationandpassesthroughthe
networkareawithnonormalconnection toanyothersupply.
Thisistypicalinlongrurallineswithisolatedloadareas.In
thistypeofRadialDeliveryNetwork(RDN)eachnodeis connected to the
substation via at least one path. Fig. 1 Radial distribution
network Thefollowingcriterionisassumedfornodeandline numbering:
1.Thenodesarenumberedsequentiallyinascendingorder
proceedingfromlayertolayer,insuchawaythatany
pathfromtherootnodetoaterminalnodeencounters nodes numbered in the
ascending order. 2.Each branch starts from the sending bus (at the
root side) and is identified by the number of its (unique) ending
bus. [8] Themainadvantageofradialnetworkisitssimple construction,
low initial cost, useful when generation is at low
voltage.Radialnetworkispreferredwhenthestationis located at the
centre of the load. Fig. 2 Single line diagram III.FORMULATION OF
THE PROBLEM ThePowerflowsinadistributionsystemarecomputedby
thefollowingsetofsimplifiedrecursiveequationsderived from the
single-line diagram shown in Fig. 2. The power flow
analysiscanbeusedtoobtainthevoltagemagnitude,power lossesof
the33bussystem.Theobjectivefunctionistofind the power flow. , (1) ,
(2) where Realpowerflowingoutofbus; Reactive power flowing out of
bus; Real load power at bus k+1; Reactive load power at bus k+1 The
power loss in the line section connecting buses k and k+1 may be
computed as , 1 (3) , 1 (4) World Academy of Science, Engineering
and TechnologyInternational Journal of Electrical, Computer,
Energetic, Electronic and Communication Engineering Vol:8, No:10,
2014 1544 International Scholarly and Scientific Research &
Innovation 8(10) 2014International Science Index Vol:8, No:10, 2014
waset.org/Publication/10000126 Where, 1
RealpowerLossinthelinesection connectingbuseskandk+1;,
1-Reactivepower Loss in the line section connecting buses k and
k+1. Thetotalpowerlossofthefeeder,,maythenbe determined by summing
up the losses of all line sections of the feeder, which is given as
,, 1 , 1 (5) ,, 1 , 1(6) where,, 1 TotalRealPowerLossintheline
section;,, 1-TotalReactivePowerLossinthe line section [16].
IV.BACKWARD/ FORWARD SWEEP METHOD
Letusconsideraradialnetwork,thebackward/forward
sweepmethodfortheload-flowcomputationisaniterative
methodinwhich,ateachiterationtwocomputationalstages
areperformed:Theloadflowofasinglesourcenetworkcan be solved
iteratively from two sets of recursive equations. The first set of
equations for calculation of the power flow through
thebranchesstartingfromthelastbranchandproceedingin the backward
direction towards the root node. The other set of equations are
forcalculating thevoltage magnitude and angle of each node starting
from the root node and proceeding in the forward direction towards
the last node.A. Forward Sweep
Theforwardsweepisbasicallyavoltagedropcalculation
withpossiblecur-rentorpowerflowupdates.Nodalvoltages
areupdatedinaforwardsweepstartingfrombranchesinthe first layer
toward those in the last. The purpose of the forward
propagationistocalculatethevoltagesateachnodestarting fromthefeeder
sourcenode.Thefeeder substationvoltageis
setatitsactualvalue.Duringtheforwardpropagationthe
effectivepowerineachbranchisheldconstanttothevalue obtained in
backward walk. B. Backward Sweep
Thebackwardsweepisbasicallyacurrentorpowerflow
solutionwithpossiblevoltageupdates.Itstartingfromthe
branchesinthelastlayerandmovingtowardsthebranches connected to the
root node .The updated effective power flows
ineachbranchareobtainedinthebackwardpropagation
computationbyconsideringthenodevoltagesofprevious
iteration.Itmeansthevoltagevaluesobtainedintheforward
pathareheldconstantduringthebackwardpropagationand updated power
flows in each branch are transmitted backward
alongthefeederusingbackwardpath.Thisindicatesthatthe
backwardpropagationstartsattheextremeendnodeand proceeds towards
source node. Itiswellknownthatthereexistthreemainvariantsofthe
forward/backwardsweepmethodthatdifferfromeachother
basedonthetypeofelectricquantitiesthatateachiteration,
startingfromtheterminalnodesandgoinguptothesource node (backward
sweep), are calculated.
1.Thecurrentsummationmethod,inwhichthebranch currents are
evaluated;2.The power summation method, in which the power flows in
the branches are evaluated;
3.Theadmittancesummationmethod,inwhich,nodeby node, the driving
point admittances are evaluated. In other
terms,thethreevariantsoftheB/Fmethodsimulatethe
loadswithineachiteration,withaconstantcurrent,a
constantpowerandaconstantadmittancemodel.Inthe forward phase, the
three variants are identical since, based
onquantitiescalculatedinthebackwardphase,thebus
voltagesarecalculatedstartingfromthe sourcenodeand going towards
the ending nodes. Voltages are then used to update, based on the
dependency of loads on the voltage,
thequantitiesusedinthebackwardsweepinorderto
proceedtoiteration.Theprocessstopswhena convergence criterion is
verified. Bycomparingthecalculatedvoltagesinpreviousand
presentiterations,thesuccessiveiterationisobtained.The
convergencecanbeachievedifthevoltagemismatchisless
thanthespecifiedtolerancei.e.,0.0001.Otherwisenew
effectivepowerflowsineachbrancharecalculatedthrough
backwardwalkwiththepresentcomputedvoltagesandthen the procedure is
repeated until the solution is converged.
Thebackward/forwardsweepmethodisnowreformulated
inawaysuitablefortheanalysisoftheconvergenceofthe
iterativeprocess.ConsiderFig.2,abranchisconnected between the nodes
k and k+1.The effective active ( ) and
reactive()powersthatofflowingthroughbranchfrom
nodek'tonodek+1canbecalculatedbackwardsfromthe last node and is
given as, , ,,(7) , ,,(8) where , , and
areloadsthatareconnectedatnodek+1, and
aretheeffectiverealandreactivepowerflows from node k+1.
Thevoltagemagnitudeandangleateachnodeare
calculatedinforwarddirection.Consideravoltage at nodekand
atnodek+1,thenthecurrent flowingthroughthebranchhavinganimpedance,
connected between k and k+1is given as, (9)
Themagnitudeandthephaseangleequationscanbeused recursively in a
forward direction to find the voltage and angle respectively of all
nodes of radial distribution
system.Initially,aflatvoltageprofileisassumedatallnodesi.e.,
1.0pu.Thebranchpowersarecomputediterativelywiththe World Academy of
Science, Engineering and TechnologyInternational Journal of
Electrical, Computer, Energetic, Electronic and Communication
Engineering Vol:8, No:10, 2014 1545 International Scholarly and
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updatedvoltagesateachnode.Intheproposedloadflow
method,powersummationisdoneinthebackwardwalkand voltages are
calculated in the forward walk.
Fig.3givesthedetailedoperationofthepowerflow calculation using
backward forward sweeping algorithm. Fig. 3 Flow chart for backward
forward sweep method V. TEST SYSTEM
TheproposedbackwardForwardsweepalgorithmis applied to IEEE 33bus
network. The test system contains five
tieswitchesand32sectionalizingswitches.Fig.4showsthe
33bustestsystem[17].Inthenetworksectionalizeswitches (normally
closed) are numbered from 1 to 32 and tie-switches
(normallyopen)arenumberedfrom33to37.Theproposed method is also used
to find power flow. TodemonstratetheefficiencyofthebackwardForward
sweep algorithm, the proposed method is tested on the 33bus system.
The details of the 33bus system are given below: Number of buses33
Number of branches37 Number of tie lines5 Tie linesS33, S34, S35,
S36, S37 Total real power3715 KW Total reactive power2300 KVAR Fig.
4 33- bus system TABLE I BRANCH LOSSES OF 33BUS SYSTEM Bus
ConnectionReal power loss(KW)Reactive power loss(KVAR) 1-29.174.67
2-337.319.0 3-415.57.92 4-514.47.34 5-629.325.3 6-71.264.15
7-83.751.24 8-94.142.97 9-103.532.50 10-110.540.18 11-120.870.28
12-132.652.08 13-140.720.95 14-150.350.31 15-160.280.20
16-170.250.33 17-180.050.04 2-190.000.00 19-200.830.75
20-210.100.11 21-220.040.05 3-230.000.00 23-242.812.22
24-251.100.86 6-260.000.00 26-272.931.49 27-289.908.73
28-296.855.97 29-303.381.72 30-311.051.04 31-320.100.12
32-330.010.02 Set flat voltage (1 p.u) for all nodes Compute
effective real and reactive power flows of all branches using
backward propagation Update node voltages and phase angles using
forward propagation Is load flow Converged? Compute branch power
loss, total system loss and print the result Stop Start Read line
data and load data yes No World Academy of Science, Engineering and
TechnologyInternational Journal of Electrical, Computer, Energetic,
Electronic and Communication Engineering Vol:8, No:10, 2014 1546
International Scholarly and Scientific Research & Innovation
8(10) 2014International Science Index Vol:8, No:10, 2014
waset.org/Publication/10000126
Thevoltage,realandreactivepowerlossesof33bus
systemisobtainedbyusingthebackwardforwardsweep method.The power
lossforeachbranch isshown inTableI.
Thevoltagemagnitudeatdifferentnodesofthissystemis
givenbyTableII.Theminimumvoltageofproposedsystem is 0.9136 p.u at
node 18. TABLE II NODE VOLTAGE OF 33BUS SYSTEM BusNo: Bus
Voltage(p.u) 1 1 2 0.9974 3 0.9851 4 0.9782 5 0.9714 6 0.9548 7
0.9517 8 0.9469 9 0.9397 10 0.9334 11 0.9325 12 0.9308 13 0.9239 14
0.9213 150.9191 160.9174 17 0.9146 18 0.9136 19 0.9965 20 0.9917 21
0.9907 22 0.9894 23 0.981624 0.9762 25 0.9715 26 0.9529 27 0.9504
28 0.9392 29 0.9312 30 0.9275 31 0.9189 32 0.9177 330.9168 The
performance of the proposed methodology is shown in Table III.
TABLE IIIPERFORMANCE OF THE PROPOSED METHODOLOGY Total real power
losses(KW) Total reactive power losses(KVAR) Minimum Voltage(P.U)
203.65102.600.9136 V.CONCLUSION The performance of the
backward/forward sweep method of
radialnetworkshasbeenpresented.Thebackwardand
forwardpropagationiterativeequationcarries thedistribution
powerflow.Byusingbackwardpropagationthepowerof
eachbranchhasbeencalculated.Thevoltagemagnitudesat
eachnodearecalculatedinforwardpropagation.The
iterationshavefastconvergenceability.TheresultsforIEEE 33bustest
systemhavebeentabulated.Itwasfound thatthe
proposedloadflowmethodissuitableforfastconvergence characteristics
and radial structure. REFERENCES
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J.AMichlineRupareceivedtheB.EdegreeinElectricalandElectronics
EngineeringfromSRREngineeringCollege,Chennai,AnnaUniversity,
Tamilnadu,India,in2013andsheisdoingMasterofEngineering(Power
SystemsEngineering)inChandyCollegeofEngineering,Thoothukudi,
Tamilnadu, India S. Ganesh obtained hisB.E. in
ElectricalandElectronics Engineeringin Dr.
SivanthiAdithanarCollegeofEngineeringTiruchendur,AnnaUniversity,
Tamilnadu, India, in 2009 and did his Master of Engineering (Power
Systems Engineering)inSt. Josephs Engineering College,Anna
University,India,in 2013. He is working as an Assistant Professor
in the department of Electrical
andElectronicsEngineering,ChandyCollegeofEngineering,Thoothukudi,
Tamilnadu,India.Hisareasofinterestarenetworkreconfiguration,power
quality, smart grid and renewable energy World Academy of Science,
Engineering and TechnologyInternational Journal of Electrical,
Computer, Energetic, Electronic and Communication Engineering
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