m6-Distrbution Load Flow analysis of distribution system.ppt

distribution system

1. Module-6
Distribution System Load
Flow
A. K. Mishra
IOE,Nepal
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2. Load Flow Solution of Radial Distribution Networks
Necessity of The separate load flow for Distribution system:
Most of the time conventional load flow methods can not be
applied to distribution systems due to following reasons:
•LimitationofG-Smethodofloadflowbecomestooslowfor
systemhavinglargenumberofbuses
•Distributionsystemshavelines/cableswithhighR/Xratio.
Thusdecouplingassumptionsarenotvalid.
•Mostofthesystemsareradialinnaturehavingsinglein-feed.
Systemshavingmultiplein-feedorultimatelyoperatedas
radialsystems.
•DistributionSystemsareunbalancedandincertainsections
carryonlysingleortwophases.Threephaserepresentationis
required.
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3. Backward & Forward Propagation Method
►Ingeneralallthemethodsusedforaradialsystemworksas
backward-forwardfashion.
►Startswithsomeassumedvoltagesateachbus,exceptthe
sourcenode.
►Inthebackwardpropagation,addsalltheloadcurrentsand
downstreambranchcurrents(computedattheassumed
voltages)tocomputecurrentintheupstreambranch.
►Startingfromthesourcenode,intheforwardpropagation,
updatesthebusvoltagesutilizingthebranchcurrents
computedinthebackwardpropagation.
►Backward-forwardpropagationcontinuestillvoltagesatall
thebusesconvergewithinpre-specifiedtolerance.
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4. Methodology-I
►Asimpleandpowerfulmethodforloadflowsolution
ofradialdistributionnetwork.
►The method is based on computation of
Bus-Injection to Branch-Current Matrix
Branch-Current to Bus-Voltage Matrix
►TheBIBCmatrixisresponsibleforthevariation
betweenthebuscurrentinjectionandbranchcurrent,
►AndtheBCBVmatrixisresponsibleforthevariation
betweenthebranchcurrentandbusvoltage.
Let’s consider an example
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5. 5/15/2024 AKM/distplng/Distribution System Load Flow 5

6. ►From the network an algorithm is developed to compute
the nodes fed by a particular branch:
►For example network
B
5= I
6
B
3 = I
4+ I
5
B
1= I
2+ I
3+I
4+I
5+ I
6
Furthermore, the Bus Injection to Branch-Current (BIBC)
matrix can be obtained as,
5/15/2024 AKM/distplng/Distribution System Load Flow 6

7. ►Branch-Current to Bus-Voltage Matrix
►The relations between the branch currents and bus voltages
is then obtained
►For example feeder it can be seen that
V
2= V
1–B
1Z
12
V
3= V
2–B
2 Z
23
V
4= V
3–B
3Z
34
Where Vi is the bus voltage of Bus i, and
Zijis the line impedance between Bus iand Bus j.
From the above the voltage at each buses can be obtained
as a function of bus 1 (substation voltage)
For example
V
4 =V
1 –B
1Z
2 –B
2Z
23 –B
3Z
34
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8. ►Thus the bus voltages can be updated as
►The above expression can be written as
[V] = [BCBV] [BIBC][I]
= [DLF] [I]
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9. ►Overall procedure:
1.Read the system configuration,physical parametersand
loads
2.Compute [BCBV] and [BIBC] Matrices
3.Assume the voltage at each bus as 1+j0
4.Compute the node currents as:
I
i(k) =[ (P
i(k) + j Q
i(k))/ V
i(k)]* {k is the iteration no.}
5.Compute [V] = [BCBV] [BIBC][I] and update voltages
6.Compute the branch real and Reactive loss as:
PL
j(k)= B
j
2
R
jand QL
j(k)= B
j
2
X
j{j is the branch no.}
7.Add these losses to the demand of sending end node of
the respective branch (j):
P
i(k)= P
i+ PL
j(k)and Q
i(k)= Q
i+ QL
j(k)
Where: P
i & Q
iare the initial (specified) load at ith Bus
8.Check V(k)-V(k-1) less than convergence criterion if
not go back to step 4 and repeat the whole procedure
9.Compute total system losses and print node voltages5/15/2024 AKM/distplng/Distribution System Load Flow 9

10. ►TheLoad-flowmethodologycouldbeemployedeither
fortheindividualFeederorforthewholesubstationat
atimeitself.
►TheSubstationtransformercouldbeincludedinthe
loadflowasalineparameterifreferenceistobe
consideredasprimaryofthesub-station.
►Itcanbeobservedthatthemethodologydescribed
canbeviewedasaspecialG-SmethodwithS/Sasa
slackbusandnoothergeneratorbuses.
►Themethodincludescomplexvariable(trigonometric
functions)duringanalysismakingprogrammingbit
complex.
►ThenumberofiterationthoughlessthanG-Smethod
butstilllargenumberofiterationrequired.
5/15/2024 AKM/distplng/Distribution System Load Flow 10

11. Methodology-II
•Themethodsderivesthevoltagemagnitudeandphase
angleexplicitlyintermsofrealandreactivepowers
fromanodeandbranchresistanceandreactance.
•Inotherword,themethodsinvolvesonlyevaluationof
asimplealgebraicexpressionofvoltagemagnitude
andnotrigonometricfunctionsareused.
•Thus,computationallythemethodsareveryefficient
andrequirelesscomputermemory.
•Maximum4to5iterationwillrequireforconvergences
forapracticaldistributionnetwork.
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12. Theoretical BackgroundLet us consider a branch of a radial distribution system as shown in the Fig. below;


Fig. : A branch of Radial distribution Feeder
In the Fig.;
1 = Sending End of branch 2 = Receiving End of branch
P2+jQ2 =Through Power at bus 2 R+jX = Branch Impedance
Then; IVQjP
*
2222 
……… (1) V
QPj
I
*
2
2
2
2


………….(2)
Also, XR
VV
I
j


 2211
2
………….(3)
P2+jQ2
R+jX 22
V
I2
1
2 11
V
5/15/2024
AKM/distplng/Distribution System Load Flow
12

13. From eq
n
(2) and (3) XjR
VV
V
QjP




 

2211
22
22
VVVRQXPjXQRP 2
2
2121
)
22
(
22
 
2121
)
22
()
22
(
2
2
 VVRQXPjXQRPV

Separating magnitude and phase 













XQRPV
RQXP
222
2
22
tan
1
12
……… (4)
And   VVRQXPXQRPV 21
2
22
2
222
2
2

 





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14. Simplifying and rearranging;   05.02
222
2
2
2
2
22
24
122  XRQPVXQRPVV     
2
45.025.02
2
2
2
2
22
2
2
22
2
1
2
221
2
QPXRVXQRPVXQRP
V















    























 VXQRPQPXRVXQRPV 1
2
2
2
2
22
1
2
22
2
2
2
22
2
1
5.05.0 … (5)
►From the above derivations, eqn(4) and eqn(5)
give the angle and the magnitude of the voltage
respectively at the receiving end bus.
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15. ►ThepreviousEquationsforvoltagemagnitudeand
phaseangleatreceivingendnodecanbewrittenin
generalizedfrom:2
1
)()( V(m2) jAjB (I)

Where; 2
)1(5.0)()2()(*)2()( mVjXmQjRmPjA 
   
2
1
2222
)2()2()()()()( mQmPjXjRjAjB 

And




In above equations,
J : is the branch number,
m1 and m2: are sending end and receiving end node respectively. 












)2(22
22
tan12
2
1
mVjXmQjRmP
jRmQjXmP
mm
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16. The load flow procedure
1.Initaillysetallthebranchrealandreactivepower
lossestozeroforallJandassumeVoltagemagnitude
as1p.uandphaseanglezero.
2.ObtaintheNodesfedbyaparticularNode(assimilar
procedureinpreviousmethod)
3.EstimateP(m2)andQ(m2)asthesumoftheloadsof
allnodesbeyondnodem2plustheloadofNodem2
itself.
4.Find|V(m2)|byexpression---I.
5.Find(m2)byexpression---II
6.FindTheRealandReactivePowerLossesofrespective
branchesas:
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17. 
 

2
2
2
2
2
2
mV
mQmPJR
JLP


 
 

2
2
2
2
2
2
mV
mQmPJX
JLQ


 7. Findnew P(m2) and Q(m2) taking into account LP(J) and
LQ(J):
8. Increase iteration No. by 1 and go to step 4.
9. Repeat steps 4to 7until convervgence is reached.
Anysuitableconvergencecriterioncanbesete.g.voltage
magnitudeatallnodescorrecttooreventherealand
reactivepowerdeliveredfromthesubstationcorrectto(less
than)afinitenumberofdecimalplaces.
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18. Radial Distribution System with
Distributed Generation
Distributed generations are represented as
►NegativePQ
Thesignoftheloads(P,Q)werejustmade
reversesothatthedirectionofpowerflow
reverses.
►PVbuses
Thegeneratorsarecapableofcontrollingthe
voltageattheiroutputterminals.
Ifthereactivepower‘Q’requiredformaintaining
constantvoltageatsuchbusesisnotwithinthe
limits,itfailstoactasgeneratingbus.Thenafter
itwillactasPQbus
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19. Distributed Generation Modeled as Negative PQ Load
►In a radial distribution feeder, the flow of current and thus
the power occurs from the buses to the loads.
►The distributed generations connected to the distribution
system are usually small fractions of the total generations
or the power flowing from the source end.
►In contrary, generation provides current and power to the
system. So, the flow of direction of current and power is
reversed.
►i.e. The buses, to which the distributed generations are
connected, are indicated as load buses but the negative
signwill carry the information that they are actually acting
as generators.
►When the distributed generators are modeled as negative
PQ load, they will have no capability of regulating their
reactive power output
►Hence, they cannot help in keeping the voltages to the
specified values at the buses where they are connected.
5/15/2024 AKM/distplng/Distribution System Load Flow 19

20. Distributed Generation Modeled as PV Model
►Inthiscase,thedistributedgenerationhasthe
capabilityofregulatingthereactivepowerwithinlimits.
►Thusvoltageofthebusatthepointofconnectioncan
becontrolled.
DerivationofReactivePowertobeGeneratedto
KeepVoltageattheSpecifiedValue
►Let’sreconsideradistributionbranch
P2+jQ2
R+jX 22
V
I2
1
2 11
V
5/15/2024 AKM/distplng/Distribution System Load Flow 20

21. V
QjP
I
*
2
22
2

 XjR
VV
I



 2211
2
From above two equations   
XjR
VVV
QjP



 221122
22








 

Z
VVVV
QjP
)()( 2221 2212
22

That is;  
Z
VV
Z
VV
Q









)sin(
)(sin( 22
12
2
21


Where,  

R
X
XRZ
ZXjRZ
1
22
tan






5/15/2024 AKM/distplng/Distribution System Load Flow 21

22. ►Ifthetotalreactivepowerconnectedtobus‘2’equals
thevaluegivenbyaboveequationeqnthevoltageat
bus‘2’willbe‘V2’.
►‘V2’canbethespecifiedvoltageatbus‘2’.
►Hence,ifthereisanyload(Qtotbranch)connectedto
bus‘2’already,thereactivepower(Qgen)thathastobe
generatedbythegeneratortokeepthevoltageatbus‘2’
equalto‘V2’isgivenby
Qgen= Qreq-Qtotbranch
Where
Qgen:reactive power to be generated
Qreq:total reactive power that has to be connected to the bus
Qtotbranch:total reactive load that is already connected to the bus
►Rest of the L.F. procedure is same
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23. LOADESTIMATION ON A
DISTRIBUTION FEEDER
►ForexistingfeederrarelytheLoadsatdifferent
nodes(mainlydistributiontransformers)is
available.
►Inadistributionsystemalmostallloadsare
estimatedbasedonthedataavailablee.g.
transformercapacitiesetc.
►Thesuitabilityofvariousmethodologiesproposed
dependsonvariousfactors,e.g.geographicaland
economicalstatusofconsumers,etc.
►Anditsquitedifferentfromeasttowestorsouth
tonorthandsoon.
5/15/2024 AKM/distplng/Distribution System Load Flow 23

24. Worldwide practiced methodologies
►Based on connected transformer capacity
►Based on consumers’ billingrecords
►Based on consumers’ numbersload(kVA)peak Feeder *
Capacityr Transformeon Distributi
)(T
)(


kVAransformerNode
kVANode (kVA) loadpeak Feeder
)nodes(kWhr all of Billing
(kWhr) billing Node
)( 

kVANode (kVA) loadpeak Feeder
)nodes(kWhr all of Consumers
number consumers Node
)( 

kVANode
5/15/2024 AKM/distplng/Distribution System Load Flow 24

25. The estimation based on Transformer
Capacity may not be practical
►Oftendistributionsystemsareillplanned
onshorttermsneeds.
►Generallytheestimateddemand not
matchinpractice
►sometimeevenestimatedandinstalleddo
notmatche.g.25kVAestimatedbut100
kVAinstalled
5/15/2024 AKM/distplng/Distribution System Load Flow 25

26. Estimation based on consumers billing
record and consumers’ numbers
►Thoughbetterbothofthesemethodslackin
informationabouttheconsumer’sclassandtheir
share.
►Foradevelopingcountrywherethestatusand
endusepatternofconsumersvarygreatly
mainlyduetoeconomicreasons.Consideration
ofdiversityalsobecomesveryimportant.
5/15/2024 AKM/distplng/Distribution System Load Flow 26

27. The proposed method considerthe
consumer classalso into account
►Themethodisbasedon
consumersbillingrecord
Theirtype
Andtheirsharing
►Intheproposedmethodsomecharacteristic
dataneedtobederivedfromthe
experimentalobservationonarealfeederin
practice.
►LeastsquareerrorhasbeenusedAsan
optimizationtool.
5/15/2024 AKM/distplng/Distribution System Load Flow 27

28. 5/15/2024 AKM/distplng/Distribution System Load Flow
Problem Formulation
►Let’s consider a particular node in a distribution
feeder as shown in fig.
The demandat L be written as;
C
k: is the contribution factor of kthtype of load at any instant
D
k: is the maximum demand of kthtype of load
►load (kW)at the point L
H L Sk
n
k
k
CD*
1


 loadtypekofLFloadtypekformonthindayseffectiveofNo
loadtypekofservedunitMonthly
thth
th
*24*.
  








 100
%
1**
1
kWhLossLV
CD
n
k
kk
28

29. 5/15/2024 AKM/distplng/Distribution System Load Flow 29
The Above Expression Can be rewritten as;
►load (kW)at the point L
►load (kVA)at the point L
►Where
collectingthecategorizedenergybillingthis(F
k)isa
knownquantityateachnode.)((kW) Load LV
1
kfactwithlvF
n
k
k

 )((kVA) Load LV
1
kpffactwithlvF
n
k
k

 24 load ith typefor month ain days effective of No.
load ith type ofkWh billingMonthly


kF

30. 5/15/2024 AKM/distplng/Distribution System Load Flow 30
►AndMultiplying factors
►Are to be known
►Forthispurposefewnodesareselectedin
experimentalfeederasmodelnodeswherereal
power(kW)andapparentpower(kVA)atLV
sideoftransformerismeasured.
►Leastsquareerrormethodhasbeenusedto
estimatetheseparametersbasedon
experimentalobservation.)
100
kWh) Loss( %
1(
)(
(k)factwithlv
LV
kLoadfactor
C
k
 )(/)
100
kWh) Loss( %
1(
)(
pf(k) factwithlv krPowerfacto
LV
kLoadfactor
C
k


31. 5/15/2024 AKM/distplng/Distribution System Load Flow 31
DETERMINATION OF THE GENERAL FACTORS
►ThefactorsdeterminedaboveincludestheLV
powerlossoftheexperimentalfeederhencecan
beusedtoestimatetheloadsofthenodesof
experimentalfeederonly.
►Oncethenodalloadsatalltheloadsin
experimentalfeederwillbedetermined;wecan
calculateLVlossas;
LVloss=Totalfeederloss-HVloss(fromloadflow)-
Transformerloss
►Dividingtheabovecalculatedfactorby
wecangetthegeneralfactorssuitabletouse
foranyfeeder100
kWh) Loss( %
1
LV


32. 5/15/2024 AKM/distplng/Distribution System Load Flow 32
APPLICATION OF THE GENERAL FACTORS FOR LOAD
CALCULATION (FOR OTHER FEEDERS)
1.Initially, assume that LV lossis equal to Total
feeder loss.
2.Calculate revised multiplying factorsfor this
feeder from general factors.
3.Calculate real and reactivepower at all nodes
using these revised multiplying factors
4.Get HV side load by adding transformer losses
and run load flow
5.Separate LV lossfrom total feeder loss
6.Repeat step 2 to 5 with this new value of %LV
loss.

33. 3 Phase Load Flow (Unbalance Condition)Z
aa
Z
bb
Z
cc
j
th
node i
th
node
Y
ag
Y
bg
Y
cg
Y
ag
Y
bg
Y
cg
Series Impedence
Z
ab
Z
ac
Z
bc
Shunt Admittance
Shunt Admittance
Model of line section k
Z
k
Y
k P
a
+jQ
a
P
b
+jQ
b
P
c
+jQ
c
Phase a
Phase b
Phase c
Three phase load model
5/15/2024 AKM/distplng/Distribution System Load Flow 33

34. Backward Propagation*
(i)
c
(i)/VS
(i)
b
(i)/VS
(i)a(i)/VS
=
(i)I
(i)I
(i)
Lc
Lb
La
Lc
Lb



















La
I 

















































(i)
c
V
(i)
b
V
(i)
a
V
sh
Y+
Mp
)p(
c
I
)p(
b
I
)p(
a
I
+
(i)
Lc
i
(i)
Lb
i
(i)
La
i
=
(m)
c
I
(m)
b
I
(m)
a
I

5/15/2024 AKM/distplng/Distribution System Load Flow 34

35. Forward Propagation






























































(m)
c
I
(m)
b
I
(m)
a
I
mcc,
Z
mcb,
Z
mca,
Z
mbc,
Z
mbb,
Z
mba,
Z
mac,
Z
mab,
Z
maa,
Z
(j)
c
V
(j)
b
V
(j)
a
V
=
(i)
c
V
(i)
b
V
(i)
a
V phases c and b a,for (j)
1-k
V - (j)
k
V = (j)
k
V
5/15/2024 AKM/distplng/Distribution System Load Flow 35

36. Where the load points are not
clearly known (e.g. LT line)
►Couldbeassumedasanuniformlydistributed
loadlongthewholeorapartofthefeeder
►Couldbeassumedasanuniformlyvaryingload
alongthewholeorapartofthefeeder
►Itcanbeshown(derived)thatauniformly
distributedloadcanbeassumedasalumpedat
l/3forpowerlossandl/2forvoltagedrop
calculation
►Thesameforuniformlyvaryingloadwouldbeat
8/15lforpowerlossand2/3lforvoltagedropcal.
5/15/2024 AKM/distplng/Distribution System Load Flow 36