Load flow methods Load flow methods in Radial systemin Radial system

OutlineOutline

DefinitionDefinition MethodsMethods Gauss-SeidelGauss-Seidel Newton-RaphsonNewton-Raphson Distflow Distflow Direct approachDirect approach Decoupling compensationDecoupling compensation

Discussion and ConclusionDiscussion and Conclusion

What is load flow?What is load flow? Given specific quantities, determine the Given specific quantities, determine the

behavior of bus voltage and power flows behavior of bus voltage and power flows Important way to analysis any power systemImportant way to analysis any power system

What is load flow?What is load flow?

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Characteristics of distribution Characteristics of distribution systemsystem

Radial or weakly meshed structureRadial or weakly meshed structure Multiphase and unbalanced operationMultiphase and unbalanced operation Unbalanced distribution loadUnbalanced distribution load Extremely large number of branches and nodesExtremely large number of branches and nodes Wide-ranging resistance and reactance valuesWide-ranging resistance and reactance values

Gauss-Seidel methodGauss-Seidel method Slow iterative problem-solving techniqueSlow iterative problem-solving technique Use a full matrixUse a full matrix Require a large number of processorsRequire a large number of processors

Gauss-Seidel method Gauss-Seidel method

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1

Gauss-Seidel methodGauss-Seidel method

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Gauss-Seidel methodGauss-Seidel method Comparably slow convergance rateComparably slow convergance rate matrix is sparse and can’t be invertedmatrix is sparse and can’t be inverted Usually solve for linear power systemUsually solve for linear power system

Newton-Raphson methodNewton-Raphson method Solve nonsquare and nonlinear problemsSolve nonsquare and nonlinear problems Relatively high iterationRelatively high iteration Require a good initial guess of the solutionRequire a good initial guess of the solution

Newton-Raphson methodNewton-Raphson method

Active power cost optimizationActive power cost optimization Active power loss minimizationActive power loss minimization Minimum control-shiftMinimum control-shift Minimum number of controls rescheduledMinimum number of controls rescheduled

Newton-Raphson methodNewton-Raphson method First order First order

Second orderSecond order

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2

Newton-Raphson method Newton-Raphson method Y=Yij;Y=Yij; i=n(p-1)+k;i=n(p-1)+k; J=n(q-1)+1;J=n(q-1)+1;

S is three phase bus complex power vectorS is three phase bus complex power vector E is diagonal three phase bus voltage matrixE is diagonal three phase bus voltage matrix Y is complex conjugation of three phase bus admittance Y is complex conjugation of three phase bus admittance

matrixmatrix

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Newton-Raphson methodNewton-Raphson method Very complicatedVery complicated Lead to partial derivations of nonlinear compleLead to partial derivations of nonlinear comple

x x It is involved Jacobian -J complex formIt is involved Jacobian -J complex form It has relatively slow convergence timeIt has relatively slow convergence time

DistFlow methodDistFlow method Don’t require the admittance matrix Don’t require the admittance matrix

calculationcalculation Use a set of recursive equations Use a set of recursive equations Estimating the power loss reduction due to a Estimating the power loss reduction due to a

branch exchange.branch exchange.

DistFlow methodDistFlow method Basic equationBasic equation

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DistFlow methodDistFlow method Pi represents the real powerPi represents the real power Qi represents reactive powerQi represents reactive power Vi represents voltage magnitudesVi represents voltage magnitudes

DistFlow methodDistFlow method Had a greater speed of convergence and fewer Had a greater speed of convergence and fewer

iterations to obtain an optimal solutioniterations to obtain an optimal solution Minimize the feeder lossesMinimize the feeder losses Make it possible for the power industry to Make it possible for the power industry to

supply energy in the most cost effective supply energy in the most cost effective mannermanner

Still need to reconfiguration of the networkStill need to reconfiguration of the network

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Direct approachDirect approach Bus injection to branch-current matrix (BIBC)Bus injection to branch-current matrix (BIBC) Branch-current to bus-voltage matrix (BCBV)Branch-current to bus-voltage matrix (BCBV)

Direct approachDirect approach Accuracy: Accuracy: They both have almost same They both have almost same

accuracy as Gauss-Seidel accuracy as Gauss-Seidel Performance:1.Performance:1. BCBV has more efficiency, BCBV has more efficiency,

especially when the network size increases. especially when the network size increases.

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Direct approachDirect approach 2.The normalized time increases since the 2.The normalized time increases since the

network increase the nonzero terms of the network increase the nonzero terms of the BIBC and BCBV metricsBIBC and BCBV metrics

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Decoupling compensationDecoupling compensation

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Sequence Decoupling compensation Newton-Sequence Decoupling compensation Newton-Raphson (SDCNR)Raphson (SDCNR)

Sequence Decoupling Compensation Fast Sequence Decoupling Compensation Fast Decoupling (SDCFD)Decoupling (SDCFD)

Decoupling compensationDecoupling compensation Use to analysis both normal and abnormal Use to analysis both normal and abnormal

three phase power system steady state three phase power system steady state operationoperation

Computation accuracy and speed improvedComputation accuracy and speed improved Convergence reliableConvergence reliable Simplify computation procedureSimplify computation procedure Positive-sequence impedance of generatorPositive-sequence impedance of generator

ConclusionConclusion Introduce Some load flow LF-methods Introduce Some load flow LF-methods Some other methods:Some other methods: Bus-impedanceBus-impedance Fast decouplingFast decoupling

Unique features of each LF-methodUnique features of each LF-method How to use these methodsHow to use these methods

Questions?Questions?

ReferenceReference

1:A parallel Gauss-Seidel algorithm for sparse power system matrices1:A parallel Gauss-Seidel algorithm for sparse power system matricesKoester, D.P.; Ranka, S.; Fox, G.C.;Koester, D.P.; Ranka, S.; Fox, G.C.;Supercomputing '94. ProceedingsSupercomputing '94. Proceedings14-18 Nov. 1994 Page(s):184 - 193 14-18 Nov. 1994 Page(s):184 - 193 2: Newton-Raphson method in complex form [power flow analysis]2: Newton-Raphson method in complex form [power flow analysis]Hieu Le Nguyen;Hieu Le Nguyen;Transmission and Distribution Conference, 1996. Proceedings., 1996 IEEETransmission and Distribution Conference, 1996. Proceedings., 1996 IEEE15-20 Sept. 1996 Page(s):591 - 595 15-20 Sept. 1996 Page(s):591 - 595 3:A comparison of load flow analysis using DistFlow, Gauss-Seidel, and optimal lo3:A comparison of load flow analysis using DistFlow, Gauss-Seidel, and optimal load flow algorithmsad flow algorithmsGilbert, G.M.; Bouchard, D.E.; Chikhani, A.Y.;Gilbert, G.M.; Bouchard, D.E.; Chikhani, A.Y.;Electrical and Computer Engineering, 1998. IEEE Canadian Conference onElectrical and Computer Engineering, 1998. IEEE Canadian Conference on Volume 2,  24-28 May 1998 Page(s):850 - 853 vol.2 Volume 2,  24-28 May 1998 Page(s):850 - 853 vol.2

4:A direct approach for distribution system load flow solutions4:A direct approach for distribution system load flow solutionsJen-Hao Teng;Jen-Hao Teng;Power Delivery, IEEE Transactions onPower Delivery, IEEE Transactions onVolume 18,  Issue 3,  July 2003 Page(s):882 - 887 Volume 18,  Issue 3,  July 2003 Page(s):882 - 887

5:Fast three phase load flow methods5:Fast three phase load flow methodsXiao-Ping Zhang;Xiao-Ping Zhang;Power Systems, IEEE Transactions onPower Systems, IEEE Transactions onVolume 11,  Issue 3,  Aug. 1996 Page(s):1547 - 1554 Volume 11,  Issue 3,  Aug. 1996 Page(s):1547 - 1554