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ZOO4 International Conference onPower SystemTechnology - POWERCON2004Singapore,21-24 November 2004

Distribution System Load Flow usingObject-Oriented MethodologyM.P.Selvan, tudent Member, IEEE, and K.S.Swarup,Senior Member, IEEE

AbsWct- Distribu tion System hns been analyzed in thispaperusing Objed-Oriented Approach. The important contribution ofthis paper b the development of sofiware objects for variousdistribution system components in such s way that they can bereused in most of the distribution system analysis programs. Thedesign, proposed in this paper, is used for developing load flowanalysis program. Object-OdentedDesign re plicates the physicalsystem strumre exactly In the software. T h e extensibility of theobjeet-oriented design is exploitedto extend the radial load flowanalysis module for performing the load flow analysis o f weaklymeshed system by deriving fe w specialized objects from thefundamental objects used for radial load flow. Modeled objectsare implemented in C-H, an object-oriented programminglanguage, and tested with various test systems, The resultsobtained for 69-bus radial system and 33-bus weakly meshedsystem are provided. Tbia design is being extendedfor developingload flow analysis module for %phase unbalanced distributionsystem and distribution system with d ispersed generations.

Index Terms- Distribution System, Object-Oriented Design,Load flow analysis,Radial and Weakly meshedsystem.1. INTRODUCTION

OAD FLOW analysis is a steady state analysis of powerL ystem, which provides information about the currentstate of the system for a given generation and load conditions.Load flow analysis is a basic function in both the EnergyManagement System (EMS) and the Distribution ManagementSystem OM S ) [l]. Distribution load flow is mandatory forperforming short circuit calculations in distribution systemsince the load currents are not small compared to short circuitcurrent an d cannot be neglected. Distribution load flowanalysis also plays an important role in contingency analysisto study the effect of outage of feeders. Results of thedistribution load flow program are being used for thereconfigumtion of' eeders to minimize the real power loss.Distribution system is usually radial or near radial (weaklymeshed) in nature in order to simplify the over currentprotection. In an electrical distribution system that operatesradially, evefy segment of the system gets its power tiom onlyone substation, with a unique path fiom it to the associatedsubstation. This pdth involves feeders, switches, transformers,etc. The RIX ratios of branches in a distribution system are

M.P. Selvan i s with the Department of Electrical Engineering, IndianInstitute ofTechnology, Madras, INDIA. (E-mail: selv"p@ yahoo.comj.KS.Swarup is with the Department of Electrical Engineering, IndianInstitute of Technology, Madras, INDIA. (phone: 914-22578404, fax: 91-44-22570509; e-mail: !;[email protected]).

relatively high compared to a transmission ystem. This makesthe distribution system ill conditioned. Literature confirms thatthe conventional Newton Raphson method and the fast-decoupled power flow algorithm and their modifications arenot suitable for solving the load flow problem of such ill-conditioned system [2f[3]. Several methods and solvingalgorithms have been proposed in the literature for distributionload flow analysis, which can be essentially classified intothree categories: direct methods, backward I forward sweepmethods and Newton-Raphson based methods. Backward andforward sweep algorithm exploits the radial nature o f thedistribution system and it is computationally more efficient[4][5]. Distribution system consists ofseveral components ofdifferent types. Representation of these components insoftware is an importanttask since the software model of thecomponents decides the capability of the analysis tool.Escalating power demand and expanding distribution networkmake the operation of Distribution Management System@MS) more complex. Modern Distribution ManagementSystem requires distributed computing and revision of existingDMS application software. Reliable and flexible software arerequired in DMS to meet the forthcoming computationrequirements [6]. Traditional programming methodologies,which are based on functional decomposition, are not abIe torepresent the components in flexible and reusable manner. Inpower engineering research field object-oriented approach hasbeen accepted as a feasible alternativeto traditional proceduralprogramming development due to its advantages over othermethodologies 17-1 11. In object-oriented approach thedecomposition of problem domain is based on the physicalnature. of the components rather thanbased on their functions.Object-OrientedProgrammiag (OOP) enerally leads to moreflexible, modular and reusable code. The strengths of Object-Oriented Methodology (OOM) are exploited well by theefforts involved during the analysis and design phases ratherthan 60m he actual implementation [12]. Researchers haveexploited the features of the OOM or developing applicationsoftware for transmission systems. Little amount of focus isalso given to the Object-Oriented modeling of distributionsystem software [13]. Losi and Russo [I41 proposed a methodbased on Newton Fbphson algorithm for object-oriented loadflow. This paper proposes a new object-oriented softwaremodeling of distribution system components. Object modelinghas been done in such a way that they can be reused indifferent distribution analysis functions. Compensation baseddistribution load flow algorithm, proposed by Shirmohammadiet al. [4], is the most appropriate technique for the proposed

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object-oriented software mode1 and data structure because ofits less complication. A balanced single-phase approach hasbeen implemented for radial distribution system and extendedfor weakly meshed system. It is observed that the extension ofthe load flow analysis program of radial system to weaklymeshed system becomes much effortless due to the advantagesof object-oriented design. The developed program using theproposed design has been tested on a 10-bus, 23 kV [15], 33-[181 distribution systems.bus, 12.66 kV [16], 6 9 - b ~ , 2.66 kV [17] and IEEE-37 bUS

U. DISTRIBUTION SYSTEMDistribution system consists of several components andgenerally radial in nature. Fig.1 shows the single line diagram

of a typical radial distribution system. RadiaI distributionsystem is fed at a single node called Root node, marked as Rin Fig.1. Singlemain and several lateral feeders are there in adistribution system. Feeders are composed of branches, whichmay be a transformer, a switch, a transmission line sectionor acable. Usually a bus is connected with two branches and it i ssending end bus for one branch and receiving end bus foranother branch, Fork node i s a bus to which more than twobranches are connected and marked as F in Fig.1. A bus,which is connected to only one branch is called Terminal nodeMT0

?-Pi1 ll 13Fig.1 Single line diagram o f a typical radial distributionsystem

and marked as T. he bus numbers are marked with boldletters and the branch numbers are marked with italic letters.Afeeder section may start either h m he root node or eom afork node and terminate either at a fork node or at a terminalnode.Distribution loadflow Problem

The power generated by the generators and the powerconsumed by the load and losses are essentially to be balancedfor a steady state operation of the power system. Themathematical equations describing the power balance aretermed load flow or power flow equations. The load flowanalysis is the determination of steady state conditions of Qpower system for a specified power generation and loaddemand, The radial nature and high R/X ratio of thedistribution system makes it ill-conditioned. Literatureco nf ms that the conventional Newton Raphson method andthe fast-decoupled power flow algorithm and theirmodifications are not suitable for solving the load flowproblem of such ill-conditioned system. Some efficientalgorithms for solving the load flow problem of a radialdistribution network are exploiting the radial nature of thesystem. One of such efficient algorithms based oncompensation technique has been used for the implementation

of object-oriented design. This method uses the fundamentalKirchoffs Currrent Law (KCL) and Kirchoff s VoItage Law(KVL) for solving the load flow problem. The steady stateequivalent circuit of any branch j in a feeder can berepresentedas shownin Fig.2.

I l - t l

Fig.:! Steady state equivalentcircuit of a branch jThe j* branch is characterized by 7 variables such asbranch current I ~ J ,esistance r,, reactance xj, sending andreceiving bus voltages Vi.1 andVi, the currents of the load andshunt devices connected at the receiving bus ILJand Ish, andthe current leaving the receiving bus (i.e. the current of thej+l* branch) Ihj+l. Load flow is a problem of finding thesteady state value of the bus voltage magnitude and angle bysolving the equations relating the current injections.In. OBJECT-MODELINGOR DISTRIBUTIONYSTEM

A. Object-Oriented Analysis (OOA)The fundamental problem domain objects have beenidentified in the Object-Oriented Analysis phase. Domainanalysis is the best way to identify the objects. By analyzingthe distribution system we can come up with the physicallyexisting components such as feeder, bus, transformer,transmission line, switch, source, load and shunt devices(shunt capacitor) etc. to be. modeled as s o h a r e objects. The

distribution system itself cafl be modeled as an object since itis a composition of other physically existing objects. Everysoftware object has prime attributes that represent the physicalcharacteristics of the object, data processing and dataaccessing methods that define the interfaces of the object.B. Object-i%?nfed Des& (000)

Object-Oriented Design involves the design of identifiedobjects and the establishment of their relationships. Thissection deals with the design of the folIowing objects:

1) LoadLoad i s a basic component in electric power system, whichconsumes power. In reality load is an object, which isconnected at the node where the electric power is fed. Thispaper models the Iond as a software object by abstracting itspower and voltage ratings asprime attributes.2) Shunt devicesShunt devices (capacitors) are used in the distributionsystem to provide reactive power support. They are alsousually connected at the nodes. Shunt devices are modeled inthe program as objectsshunt. The prime attributesof the shuntdevices are their constant admittance, which is calculated fromthe reactive power and voltage ratings of the devices.

3) BMSBus is a junction point (node) where different elements

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such as line, transformer, load and shunt devices areconnected. Existing physical buses have been modeled assoftware object Bus. Bus number, voltage magnitude, angleand the references of the devices connected to the bus are theprime attributes. Several specialized classes have been derivedfiom the base class of object bus.

4) BranchBranch is considered as an object and its abstraction is adevice connected between two buses. Transmission line,transformer, cable and switch are the specializationsof objectbranch.5) FeederFeeder carries power from the substation to the consumerpremises. In reality, feeder is divided into several sections.Each section may be either a transmission Line or transformer.Feeder is modeled as a software object, which is anaggregationof branches.6) Dishibufiun ,ystemDistribution system itself can be abstracted as an objectsince it is a composition of other physically existing objectssuch asbus, feeder. transformer and load etc.

Establishing the relationship between the objects is the nextstep in the design phase. The most important relationships arespecialization (is a), association (has a), and aggregation@art 08. The diagrammatic representation of theserelationships is shown in Fig.3. Triangle shape ( A ) indicatesspecialization or inheritance relationship. Connectionsrepresented by filled circles ( 0 ) indicate the associationrelationship between objects. Connections between objects,represented by diamond shape (0) t one-end and filledcircles ( ) at the other-end,indicate the aggregationof simpleobjects to form a complex object [19]. The associationrelationship describes the physical connection between theobjects. Transformer is a specialized object of branch withzero resistance and tap settings. Switch is a special branchwith zero impedance.

Fig. 3 Class diagramfor radialdistributionsystem

Design Extensionfur Weak& Meshed systemWeakly meshed system, which is generally created undermaintenance or emergency operation, is a radial distributionsystem with few loops. Loops are fomed by tie lines. Usuallyfor analysis, the weakly meshed system is converted into aradial system by breaking the loops and introducing a dummy

bus for each loop at the loop break point. Two new soRWai-eobjects, dummy bus and tie have been derived to model theweakly meshed system.7) Dummy busDummy bus is introduced at the loop break points. Dummybus is an object of a special class derived fkom the class ofobject bur. It is a speciaIbus created by a parent bus object atthe loop break point. The parent bus object is one of the primeattributes of the object dummy bus. A dummy bus and itsparent bus together form a loop break point.8) TieTi e is derived from he class feeder. Tie is a feeder havingsingle branch, which makes a loop. Since we arebreaking theloop and introducing a dummybus, tie lines can be considered

as a feeder starting at B node and terminating at the durnmybus.Fig.4 shows the extended class diagram with new classes forweakly meshed system.New classes are shown by thick lines.

Fig. 4meshedswtemExtended class diagram of Fig. 3 to accommodate weakly

C. Object-OrientedProgramming (UOP)Object-Oriented Programming is the final phase of object-oriented methodology in which implementation is carried out.The proposed design is implemented in C-H programminglanguage. Classes have been developed for every designedobjects using Bottom-Up approach, which gives an easeimplementation. Class inheritance is used to implement thespecialization relationship. Association relationship isimplemented with the help of pointers. Each branch has twopointers to point its sending and receiving end buses. Everyfeeder has two pointers to address its starting and terminalnodes. Everybus has an array of pointers to point the branchesconnected to it. A method of distribution system object called

establkhlinh0 establishes the association relationship. Thismethod serves two purposes. First, replicates the physicalstructure of the system in the computer memory byestablishing the physical connection between the objects.Second, serves the purpose of navigation from one object toanother object. The aggregation relationship is implementedby containership. The classes, which are already developed bythe authors for various power system analysis programs, suchas sparse matrix, vector, linear system solver and complexhave also been reused in this application. This ensures thereusability of the object-oriented design.

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W . BJECT-ORIENTED DISIWBTJTION LOAD FLOWThe present work assumes that the 3-phase distributionsystem is balanced and can be represented by a single linediagram and the line to ground capacitance at distribution

voltage level are small enough o neglect. Compensation basedalgorithm, which has both forward sweep and backwardsweep, is used to develop the distribution load flow analysisprogram using the designed objects. During backward sweepthe branch currents are calculated and during forward sweepbus voltages are calculated.

First, do the above calculations for the feeders terminatingat the terminal node. Then do for the remaining feeders thatare terminating at the fork node. This branch currentcalculation begins at the last branch and terminates at the firstbranch of each feeder as shown by the thick lines in FigS.2) Forward sweep3 . Calculatethe nodal voltages using equation (5).v =Vtl -z.Ik l (5 )

zj - impedance of the jm ranchasa- _ _ _SS . Forward sweep starts from the feeder connected to the rootnode and continues to the feeders emanating fiom thisfeeder and so on as shown by dotted lines in Fig.5.4. Check for convergence. Find the mismatch betweenthe calculated load power and the specified load power atall buses. If the absolute value of he mismatch at all buses

ar e less than certain tolerance value, then stop the iteration.Otherwise continue the backward and forward sweeping.Due to the advantagesof object oriented design the forwardand backward sweeping calculations are done locally withinthe feeder object. Actually feeder object completes its task bycommunicatingwith the bus and branch objects.

B S I- - - -S 3 ~+Back ward Sweep - -bForwardSweep

Fig. Backward and Forward SweepsA . Akorifhm or Radial con$guration

1) Backwardsweep1. Calculate the net nodal current injections using equation(1).

wherek - iterationnumber1;Is,jI , j - Load current at bus j

1 = Is,j- ;,j 4- (1)

- Net current injection at bus j- Injected current by any source s at bus j

k

1.(2) 2 .S,,j - Complex load powerI . - Current of the shunt device connected atbussh ik

j= Y*+jv;- (3)L,,Admittance of the shunt element

2. Calculate th e branch current in all feeders usingequation(4).1; (4), j = Ib , j+ l -k

whereI:,,+] - current in the j+ l branch or current leavingIir,j+t= 0 if the bus j s the terminal node ofa feeder

the j~ bus.3.5.e - emanating feeder sections from the fork node 6.

= if the bus j is the fork node, 4.c

B. Akorithm fo r weaRly meshedsystemEach loop in a mesh network can be opened by adding adummy or fictitiousbus. The breakingpoint of a loop is calledloop break point (LBP). The current flowing through thebranch that makes a loop can be simulated by injecting thesame current at the LBPs. Thus, by adding some dummybuses, it is possible to convert a mesh network into a radialnetwork. In this case, the number of dummy buses should be

same as the number of Ioops in the original network. Thus, heload flow problem of a mesh network can be solved using thetechnique of radialnetwork, but a proper calculationof currentinjections at the LBPs is required. Algorithm for solving theweaklv meshed network is as follows:Make the network radial by breaking the loop andintroducing a dummy bus for each loop.Form the loop break point impedance matsix ZDiagonal blockZap,i,= s u m of branch impedances in loop imdiagonal blockZ,,, = sum of the impedances of branches common toloops i and jThe sign is positive if the loops have same direction andnegative if they have opposite direction.

This can be cakulated by current injectionmethod. nject1 p.u. and -1p.u. current at the loop break points aftershort-circuitingall the loads and source, hen measure thevoltages at all the loop break points.These voltages willform one column of the ZBp,This can be done by theradial load flow, which converges in a single iteration atthe absence of loads. Object-oriented design makes thisstraightforward by communicating with the objects.Calculate theLU actors o f ZBp.Start the loop iteration.Inject zero current at all loop break pointsDo radial load flow,

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7.8.

9.10.

Calculate break point voltage vector V B p ~Update the breakpoint current injections using equation(6 ) .[IL] = [ G ] + [ G P ] (9where, [A&] = [ZBp - [V:+,] (7)[aip] an be calculated using the LU factors of thematrix ZBP.Inject the calculated current at LBPs and repeat fiom step6 .Continue the above steps till the Convergence.

v. hPLEMENTATIONAND RESULTSThe proposed design has been implemented in Ctbprogramming language. The developed program has beencompiled using Microsoft Visual C+ 6.0 compiler, in aPentium IIl machine. Every class has a method to establishlinks (associative rdationship) with the objects of other class.A method of object Bus called injecrcurrent() will injectthe ament at the loop break points, which simulates thecurrent flowing through the loop. The methods d o f o ~ a r d c u l ~ l a r i o n s ( )and dobackwardcalculut i~~()fobject Feeder perform the forward sweep and backwardsweep computations. A method of object Branch,findcurrent() calculates the branch current during backwardsweep. Th e method updotevoltuge() updates the voltage ofthe receiving end bus during forward sweep. The developedprogram has been tested on a 10- bus, 23 kV,33-bus, 12.66

Fig. 6 69-bus Radial DistributionSystem

TABLE IBUSVOLTAGEMAGNllVDESOFTHE69-BUS RADIAL SYSTEM

Voltage Voltage VoltageMagnitude Bus Magnitude Magnitude- o. - No. .inp.u.

Radial Fadial RadialSyStetD system system

Bus

0123456789101112131415161718192021

~I .woo0.99990.99990.99980.99900.99010.98080.97860.97750.47250.97140.96820.96530.96240.95950.95890.95810.95800.95760.95730.95680.9568

23242526272829303132333435363738394041424344

0.95660.95640.95640.95630.99990.99980.99970.99970.99960.99940.99900.99890.99990.99980.99960.99950.99950.99880.99860.99850.99850.9984

4647484950515253545s565758596061626364656667

0.99980.99860.99470.99420.97860.97850.97470.97140.96690.96260.94010.929 I0.92480.91980.91240.91210.91170.90980.90930.97130.97130.967922 0.9567 45 0.9984 68 0.9678

TABLE UBUSVOLTAGEMAGN~TCT~ESF Tl633-BUSSYSTEM W T E i 5 MESHES--oltaEe Mamitude VoltaneSystem System system System0 1.0000 1.0000 17 0.9131 0.9541

1 0.9970 0.9971 18 0.9965 0.99532 0.9829 0.9863 19 0.9929 0.98073 0.9755 0.9826 20 0.9922 0.97664 0.9681 0.9791 21 0.9916 0.97296 0.9462 0.9702 23 0.9727 0.97007 0.9414 0.9691 24 0.9694 0.96268 0.9351 0.9658 25 0.9477 0.97019 0.9293 0.9654 26 0.9452 0.968910 0.9284 0.9654 27 0.9337 0.963711 0.9269 0.9655 28 0.9255 0.960312 0.9208 0.9621 29 0.9219 0.957113 0.9185 0.9609 30 0.9178 0.953914 0.9171 0.9606 31 0.9169 0.953415 0.9158 0.9588 32 0.9166 0.953616 0.9137 0.9552

5 0.9497 0.9711 22 0.9794 0.9807

kV, 69-bus 12.66 kV and IEEE 37-bus distribution systems.Fig. 6 hows the 69-bus istributionsystem. able I providesthe magnitude of the voltage of all buses in the 69-bus radialdistribution system. These results are exactly in agreementwith the results published in the Ref. [ 5 ] . Fig.7 shows the 33 -busdistribution system with 5 loops. The systemdata is givenin the appendix. The thick lines are tie lines, which make theloops. Table II gives magnitude of the voltage of all buses inth e 33-bus system for both radial and weakly meshedconfiguration with total system load of 3715 kW and 2300kVar.Fig.7 33-busDistribution System with 5 Meshes

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VI. CONCLUSION [I91 J.Rumbaugh, MBlaha, W.Pennerhoi, F.Eddy, W.Loreosen,ObjectOrientedModeling und Design, Prentice Hall,EnglewoodCliffs, NewThe proposed object-oriented design for distributionsystem J ~ ~ .gives more flexibility and extensibility for developingDistribution Management System analysis programs. Theproposed design has been used for developing load flowd y s i s program for radial distribution system and extendedfor weakly meshed system. The robustness of the developedprogram has been tested with various test cases and it isobserved that the results were in exact agreement with theresults reported in the literature. Extension of the proposedobject-oriented design for unbalanced load flow analysis andother DM S functionsis currently under implementation.

m. REFERENCESW.R.Casse4 ?Distribution Management Systems: f~~~c t io n sndpaybac!?, IEEE lkamactions on Power Systems,Vol. 8,No. 3, AugustHsiao-Dong Chiang, A decouplcd load flow method for distributionpower networks: algorithms, analysis and convergencestudy,ElechicdPowerondEnergy System, Vol. 13, No.3, June 1991, pp.130-138.M.H.Hque, Efficient load flow method for distribution syztema withradial or mesh co~guration, IEE Proceedings Generation.Tramission, Distribution,Vol.143, No.], January 1996,pp.33-38.D.Shirmohammadiet al, A compensation basedpower flow methodforweakly mashed distribution and lransmission nehvorks, IEEETransactions on Power Sysfem, Vo1.3, N0.2, May 1988, pp.753-762.B.Venkatesh and R.Ranjan, Data Structure for radial distributionsystem load flow analysis,IEE Proc.-Gener.Trans. Distrib., Vol. 150,No. l,lanuary2003,pp.101-106.T.E.Dy-Liacco,Modem Control Centers and Computer Networking,IEEE Computer Applications in Power, Vol. 74, October 1994, pp.17-

1993, pp.796-801.

??*& .[7] Andreas F.Neyer, Felix F.Wu an d Karl Imhof, Object-Orientedlrogrammhg for Flexible Software: Example of a Laad Flow, IEEE

Tmnsuctionson PaverSystem,V01.5,No.3,August 1990,pp. 689-696.[SI B.Hakavik and A.T.Holen, Tower System Modeling and SparseMatrixOperationsusing Object-OrientedProgammicg,IEEE Tramucfwm nPower System, Vo1.9,No. 2, May 1994, pp. 1045-1051.T.S.Dillon and E.Chang, Solution of Power System Problems throughthe use of the Object-Oriented Paradigm,Elechical Power & Energy

Sysiemr, o1.16, No.3, 1994, pp.157-165.[lo] E.Z.Zhou, Object-Oriented Programmiug, c and Power SystemSimulation, IEEE Tronroclionr on Power Sysfem, Vol.11, No.1,February 1996,pp.206-215.[ I 1 1 Shubha Pandit, S . k S o m a n and S.A.Khaparde, Design of GenericDud Sparse Linear System Solver in C-H for Power SystemAnalysis, IEEE Transactions on Power Sysrem, Vol. 16, No.4,November 2001, pp.647-652.[12] Jun Zhu and David L. Lubkcman, Object-OrientedDevelopment of

Software Systems for Power System Simulations, IEEE Pumactionson PowerSysrems,Vol.12, No. 2, May 1997,pp.1002-1007.[13] J.Britton,An open, abject-based model as the basis of an architecturefor distributioncontrol centers, IEEE Trunsuctionron Power System,Vol. 7,No. , November 1992, pp.1500-1508.[I41 A.Losi, M.Russo, Object OrientedLoad Flow for Radial and WeaklyMeshed DistributionNetworks, IEEE Trunsoctiom on Power Systems,

[I51 J.J.Giainger and S.H.Lee, Capacity release by shunt capacitorplacement on distribution feeders: A new voltage-dependentmodel ,IEEE Transactions on Power Apparutw and Sysfems, VoLPAS-lOI,NOS,May 1982, pp.1236-1244.[I61 M.E.Baran and Felix F.Wu, Network r e c o n f p t i o n in distributionsystems for loss reduction and load balancing, IEEE Truwuctionr onPower Delivev, Vo1.4, No.2, April 1989, pp. 1401-1407.[I71 M.E.Baran and Felix F.Wq Optima1 capacitor placement of radialdistribution systems, IEEE Transactions on Power Delivery, Vo1.4,No.1, January 1989, pp. 725-734.[I81 M.Shahidehpour an d Yaoyu Wang, Communicution und Control inEiecrric Power Systems -Applicoiions of Puralkl ond DbtributedProcessing,IEEE ress,John Wiley& Sons, 003.

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Vol. 18,No.4, November 2003, pp . 1265-1274.

m. APPENDIXTABLE Ill33-Bus RADIAL S y s m DATA

Branch From To R i n X i nNo. Bus Bus Obms O h EndBusP &V Q W a r )1 0 1 0.0922 0.0470 i00 602 I 2 0.4930 0.2511 90 403 2 3 0.3660 0.1864 120 804 3 4 0.3811 0,1941 60 30

5 4 5 0.8190 0.7070 60 206 5 6 0.1872 0.6188 200 100789101112131415161718192021222324

6789I O111213141516118192022223

789IOI I12131415161718192021222324

0.71141.03001.04400.I9660.37441.46800.54160.59100.74631.28900.73200.16401.50420.40950.70890.45120.89800.8960

0.23510.74000.74000.06500.12381.15500.71290.52600.54501.72 100.57400.15651.35540.47840.93730.30830.70910.701

200 10060 2060 2045 3060 3560 35

120 8060 1060 2060 2090 4090 4090 4090 4090 4090 50420 200420 20 025 5 25 0.2030 0.1034 60 2526 25 26 0.2842 0,1447 60 2527 26 27 1.0590 0.9337 64 2028 27 28 0.8042 0.7006 120 7029 28 29 0.5075 0.2565 200 60030 29 30 0.9744 0.9630 150 70

31 30 31 0.3105 0.3619 210 10032 31 32 0.3410 0.5302 60 40TAB= IV33-BusMESHEDSYSTEMIELINESDATA

Ri l l X i nie From Toohms ohmsNo. Bus Bus2 . m o 2.00007 202 8 14 2.0000 2.0000

3 11 21 2.0000 2.00004 17 32 0.5000 0.50005 24 28 0.5000 0.5000

IX.BIOGRAPHIESM. . Selvan (S, 2002) is a doctoral candidate in the Department of ElectricalEngineering, Indian Institute of Technology Madras, India. His areas ofinterest are Computer Methods in Power Systems, Object OrientedMethodologyand DesignApplicationsto Power system.KS. Swarup (S 87, M 92 , SM 002) is with the Departmentof ElectricalEngineering, ndian Institute ofTechnologyMadras, India.Prior tojoining hedepartment as visiting faculty, he held pasitions at the Mitsubishi ElectricCorporation, Osaka, Japan, and Kitami Institute of Techoology, Hokkaido,Japan,as visiting research scientist and visiting professor,respectively during1992 to 1999. His areas of research are AI, knowledge-based systems,computational intelligence, sol? computing and object modelingan d design ofelectric power systems.

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