optimal placement of phasor measurement unit for power ... - ijater

First we define some terms used in proposed method:1. Bus connectivity matrix: The Bus connectivitymatrix A represents bus connectivity information ofpower system network and is given in (2) for 7 bustest system.2. Isolated bus or Radial bus: The bus which isconnected to only one other bus is called as radialbus. In 7 bus test system bus 1 and 5 are the radialbuses.3. Zero injection bus (ZIB): Zero injection busses arethe busses from which no current is being injectedinto the system. If zero injection busses are alsomodelled in the PMU placement problem, the totalnumber of PMUs can be further reduced.4. Zero injection buses connected to radial buses(ZIBCRB): These are the zero injection busseswhich are connected to radial buses.5. Directly Observable buses (DOB):The busesconnected to PMU bus are called DOB. In 7 bustest system if bus 2 is the PMU bus then 1, 2,3,6,7are directly observable buses.6. Indirectly Observable buses (IOB): Buses whichare not connected to any PMU bus, but their phasorcan be found out using KCL at ZIB. In IEEE 14 bussystem bus 7 is the ZIB and it is connected to bus 4,8, and 9. Among the buses 4, 7, 8 and 9, bus 4, 7and 9 are directly observable due to PMU at bus 9.Application of KCL at bus 7 provides voltagephasor of bus 8. Bus 8 is an IOB.7. Total Observable buses (TOB): It is the sum ofDOB and IOB.Procedure for finding out optimal location of PMU:Step1. Form a bus connectivity matrix(A) from the networkdata.Step2. Find out the Isolated or Radial buses for the system.Also find buses connected to radial buses (BCRB).Step3. Remove the zero injection buses from the set ofBCRB. Select remaining buses in the set as PMU placementbus.Step4. By using PMU bus selected in step3 find indirectlyobservable buses using KCL at zero injection bus.Step5. Find out Observability index of the each buses (OIB).OIB is the number of observable buses when placing PMUon respective bus. So for each bus value of OIB is different.Step6. Find out maximum value of OIB.i.e.OIB max, andselect the bus having maximum OIB.Step7. Form a set of buses having maximum OIB. Nowremove zero injection buses from the set. If the number ofremaining buses are greater than zero go to step8,else checkwhether there is any bus in set connected to zero injectionbus connected to radial bus (ZIBCRB).If yes select that busas PMU placement bus and go to step9.If no reduce value ofmaximum OIB by one and go to Step6.else findunobservable buses(UOB) and select any bus from ZIBCRBconnected to UOB as PMU bus and go to Step9.Step8. If the number of buses found in step7 is one select thebus as PMU bus and go to step9.If the number is the morethan one check for the non zero injection bus connectivityamong the buses obtained in Step7.Step9. Find directly observable buses and indirectlyobservable buses and find out total observable buses.Step10. If TOB is equal to the total number of the systembus then system becomes completely observable. Go tostep11.Else if TOB

Radial Buses Injection BusesIEEE 118-Bus 19,73,87,111,112 5,9,30,37,38,63,64,68,71,81New England39 Bus.30.31,32,33,34,35,36,37,38.1,2,5,6,9,10,11,13,14,1719,22.The simulation results of the test systems areexplained in table number 2.Proposed method results arecompared with the PMU placement by using non-linearconstraints equation method. The last column in the table 2shows the simulation results obtained by proposed method.This column shows the optimal strategic bus locations wherePMU must be placed in order to make system fullyobservable. The result obtained by using proposed methodare compared with the the result documented in reference[15]. ( using non-linear constraints equation).Result of themethod using non-linear constraints equation are shown insecond column of table 2.The proposed heuristic approach provides minimum optimallocations of PMU buses for complete observability of thesystem.Table 2.Optimal locations of PMU for IEEE Test systems.Test System Result of [15]. Result of ProposedMethodIEEE-14 Bus 2,6,9.(three PMUs)2,6,9.(three PMUs)Test System Result of [15]. Result of ProposedMethodIEEE-30 Bus Method(a):3,5,10,12,18,23,27.(seven PMUs)Method(b):2,3,6,10,12,18,23,27(eight PMUs)2,3,10,12,15,19,27.(seven PMUs)IEEE-57 BusIEEE-118 BusMethod(a):1,6,9,15,20,25,27,32,38,47,50,53,56.(thirteen PMUs)Method (b):1,5,9,14,15,20, 25,28,32,50,53,56.(twelve PMU)Method (a):2,8,11,12,15, 19,21,27,31,32,34,40,45,49,52,56,62,65,72,75,77,80,85,86,90,94,101,105,110(twenty ninePMUs)Method (b):1,6,9,15,20,25,29,32,38,51,53,56.(twelve PMUs)2,8,11,12,15, 19,21,27,31,32,34,40,45,49,52,56,62,65,72,75,77,80,85,86,90,94,101,105,110(twenty eightPMUs)New England39 Bus system2,8,11,12,17,21,25,28,33,34,40,45,49,52,56,62,72,75,77,80,85,86,90,94,101,105,110,114(Twenty eightPMUs).Not Available. 3,8,13,16,20,23,25,29(eight PMUs).The simulation result obtained by proposed methodis compared with result of [15]. Author‟s [15] treat zeroinjection measurement in two different ways such as a)Forming non-linear constraints, b) Topology transformation.Results of the two approaches are documented in the tables5, 7 and 8. For IEEE-30 bus system method (a) givesoptimal number (seven) and their strategic location, whereasfor IEEE- 57 bus system method (b) gives the optimalnumber (twelve) and their strategic locations. It is not clearwhich method will give the optimal solution for whichsystem. For any system both the method is to be executedand compared for obtaining optimal solution. The proposedmethod provides optimal solution in all cases studied.VI. ConclusionThe problem of optimal placemat of PhasorMeasurement Unit is solved in this paper by using simpleheuristic search method to make the system completelyobservable. In this we had used simple heuristics based onthe network information for determination of minimum setof Phasor Measurment Units. The proposed methodsuccessfully overcomes the limitation of conventionalinteger programming method in producing systemindependent optimal solution when considering zeroinjection buses. The proposed method is very fast inproviding optimal solution as compared to other exhaustivesearch method. The Simulation results obtained for differentnetwork shows the effectiveness of the proposed method infinding the minimum number of PMU bus locations forcomplete observability assessment of Power Systems.Themethod is general and is applicable to all power systemnetworks.VII. References[1] A. G. Phadke, J. S. Thorp, and K. J. Karimi,StateEstimation with Phasor Measurements," IEEETransactions on Power Systems, Vol. 1, No. 1, pp.233-241, February 1986.[2] A. Monticelli, ‘State Estimation in ElectricPowerSystems: A Generalized Approach’. Boston,MA: Kluwer, 1999.ISSN NO: 2250-3536 VOLUME 2, ISSUE 2, MAY 2012 132

[3] A. Abur and A. G. Exposito, Power System StateEstimation: Theory and Implementation. New York:Mercel Dekker, 2004.[4] T. L. Baldwin, L. Mili, M. B. Boisen, and R. Adapa,“Power system observability with minimal phasormeasurement lacement,” IEEE Trans. Power Syst.,vol. 8, no. 2, pp. 707–715, May 1993.[5] R. F. Nuqui and A. G. Phadke, “Phasor measurementunit placement techniques for complete andincomplete observability,” IEEE Trans. Power Del.,vol. 20, no. 4, pp. 2381–2388, Oct. 2005.[6] B. Milosevic and M. Begovic, “Nondominatedsorting genetic algorithm for optimal phasormeasurement placement,” IEEE Trans. Power Syst.,vol. 18, no. 1, pp. 69–75, Feb. 2003[7] B. Xu and A. Abur, “Optimal placement of phasormeasurement units for state estimation,” FinalProject Report, PSERC, Oct. 2005.[8] B. Xu and A. Abur, “Observability analysis andmeasurement placement for systems with PMUs,” inproc. IEEE Power Eng. Soc. Power Systems Conf.Expo., Oct. 2004, pp. 943–946.[9] Bindeshwar Singh , N.K. Sharma , A.N. Tiwari, K.S.Verma,andS.N. Singh, “Applications of phasormeasurement units (PMUs) in electric power systemnetworks incorporated with FACTS controllers”,International Journal of Engineering, Science andTechnology Vol. 3, No. 3, 2011, pp. 64-82.[10] William Yuill, Non-Member, A. Edwards, Nonember,S. Chowdhury, Member, IEEE, and S. P.howdhury, Member, IEEE ,“ Optimal PMUplacement:A comprehensive literature review,” IEEETrans 2011.[11] B. Xu, A. Abur, “Observability Analysis andmeasurement placement for system with PMUs," inProc. 2004 IEEE Power System Conf. Expo, vol. 2,pp. 943-946.[12] Kazem Mazlumi and Hesan Vahedi , Non members,„Optimal Placement of PMUs in Power SystemsUsing Mixed Integer Non Linear Programming andBacterial Foraging Algorithm‟. ECTI Transaction onelectrical engg.Electronics,and Communications volno.9 no.1 February 2011.[13] R.Christie, Power System Test Archive, Aug. 1999.[Online].Available:http://www.ee.washington.edu/research/pstca.[14] M.A.Pai, Energy Function Analysis for PowerSystem Stability. Norwell, MA: Kluwer, 1989.[15] B.Xu and A.Abur, „Optimal Placement of PhasorMeasurement Units for State Estimation,‟ FinalProject Report,PSERC, Oct. 2005.ISSN NO: 2250-3536 VOLUME 2, ISSUE 2, MAY 2012 133