Relieving Overload And Improving Voltage By The Network .

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1Relieving Overload and Improving Voltage bythe Network Contribution Factor (NCF) MethodH. Song, Student Member, IEEE, and M. Kezunovic, Fellow, IEEEAbstract--This paper introduces new Network ContributionFactor (NCF) method for relieving overload and improvingvoltage by using the network contribution information and baseload flow conditions. When line overload or low voltage occurs,irrespective if it is caused by disturbance, load increase, orwheeling, we first find the following network contribution factors:Flow Network Contribution Factor (FNCF) and VoltageNetwork Contribution Factor (VNCF). Then we choose the mostcontributing elements and change their parameters, either byline control (Thyristor Controlled Series Capacitor-TCSC, lineswitching, etc.) or bus control (shunt capacitor, Static VarCompensator-SVC, etc.). The variances of the line flow and busvoltage are calculated. The results are verified by power flowcalculation. This method can quickly find the parametercontributing to the largest variance based on the networkinformation and base load flow conditions. It can be used for redispatching load flow, solving congestion, relieving overload,improving voltage, controlling emergency, etc.Index Terms--Network Contribution Factor, CongestionManagement, Overload, Voltage Control, Emergency Control,FACTSOI. INTRODUCTIONne of the most challenging problems for a competitivepower market is that congestion may occur frequently[1].Following one or several disturbances, the over stressedsystem may have one or several lines overloaded or securityflow-gate limits violated. If the overload can not be relievedquickly and appropriately, fault may occur (i.e., line sagged totrees) and more elements will be tripped. Also, a backup relaymay operate due to the overload condition, leading tocascading outages and large area blackout as the final result[2,3,4]. In the complex and competitive power market, it isdifficult for system operators to find effective means forrelieving overload to make the maximum balance between theeconomy and security. There are examples of good and badconsequences of relieving overload during disturbances [5,6].In general, compared with generator re-dispatching andload management, transmission network control is the fastestand cheapest control for relieving overload and controllingstability. Some research results were reported on usingThis work was supported by Pserc project, “Detection, Prevention andMitigation of Cascading Events”, and in part by Texas A&M University.H. Song and Dr. M. Kezunovic are with the Department of ElectricalEngineering, Texas A&M University, College Station, TX 77843 USA (email:songjefferson@neo.tamu.edu, kezunov@ee.tamu.edu ).network switching for relieving overload condition [7,8]. Thepower flow sensitivity matrices are used to rank the candidatelines to be switched off to solve the voltage violation andoverload problems [7]. The Z-matrix method is used tocompare the changes in the Z elements due to one line beingswitched off [8]. The Optimal Power Flow (OPF) may be agood method in the regulated environment for dispatching thegeneration, adjusting the branch flow and relieving theoverload [9]. But the OPF method is not as suitable as beforein the competitive open access market.This paper presents a novel and comprehensive method ofusing network contribution factors for the purpose of relievingoverload, improving voltage, controlling emergency, etc. Itgives useful control guidance for system operators and is easyto understand and implement. Based on network parametersand base flow bus voltages, for the line flow change, the FlowNetwork Contribution Factor (FNCF) for each line parametervariance (i.e., TCSC insertion or line switching) is estimated.For the bus voltage change, the Voltage Network ContributionFactor (VNCF) for each bus shunt element variance isobtained. Given certain amount of the line flow decrease orbus voltage increase, either FNCF or VNCF is used to get thenecessary and optimal line or shunt parameter variance.This paper introduces the mathematical formulation of thenetwork contribution factor method. In Section II, both theline parameter variance and bus (shunt) parameter varianceare considered. Numerical test results are presented in SectionIII. Conclusion and references are given in Section IV and Vrespectively.II. MATHEMATICAL FORMULATIONFrom the fast decouple power flow, we know theapproximate real power equation based on the simple fact thatthe line resistance is much smaller than the reactance, ri xiP B 'θ(1)Ewhere, P, E, θ are the node real power injection,magnitude and angle of the bus voltage respectively.( B ' ) ij bij(2)where bij is the series inductance of the line i-jGiven an n-bus-l-branch system, A is the node-branchincidence matrix, Yp is the primitive branch admittance matrix,Ybs is the node shunt capacitance matrix,

2Y p diag [ y1 . yl ](3)Ybs diag [ y s1 . y sn ](4) 1 i is the sending node of branch j Aij 1 i is the receiving node of branch j 0 else Bus admittance matrix can be obtained from:Y AY p AT Ybs(5)(6)The approximate node injection can be composed from theline flows associated with this node,Pnode APline A( imag (Y p )) AT ( Eθ )(9)A. Line Parameter VarianceFor the parameter variance of line i, y i , assume that thenode injection Pnode and bus voltage magnitude E do notθvaries θ . Then(10)Since the node injection does not change, from (9) we get,A(Y1 Y1 ) AT E (θ θ ) AY1 AT Eθ(11)thus θ ( A(Y1 Y1 ) AT ) 1 ( A Y1 AT )θ(12)where Y1 diag[0 . yi . 0]From (8), we get the line flow change,new Pline Pline Pline Y1 AT ( Eθ ) (13)(Y1 Y1 ) AT ( A(Y1 Y1 ) AT ) 1 ( A Y1 AT )( Eθ )n A ji E jθ jj 1Tnn nKi A1i Aji Ejθ j . Aii Aji Ejθ j . Ani Aji Ejθ j j 1j 1 j 1(17)X 1 ( A(Y1 Y1 ) AT ) 1(18)(19)we can get the following line flow variance equations,for line k, k i , Pline k [ A1k . Ank ] X 1 Ki ( y k y i )(20)for line k, k i ,n Pline i ( Aji E jθ j / y [ A1i . Ani ]X1Ki)(y yi )j 1where'i'ij 1. Ani ] X 1 Ki(24)In general, bus impedance matrix (imaginary part) X 1doesn’t change much from the original matrix X due to theline parameter variance y i . If we assume X1 X , the FlowNetwork Contribution Factor N f will be constant except forline i.We can easily get the line flow variance, Pline k N f ,k y k yi , k 1, ,l(25)From (25) we can see that the line flow variances arerelated to three components: the Flow Network ContributionFactor N f , this line’s series inductance and admittancevariance of the line i. For each line parameter change, we canget all other line flow variances easily. Vice versa, we cancalculate the line parameter variance based on the exact lineflow change we want. This gives us a good guidance to issuenetwork control to re-dispatch the line flows:Step 1, use the base network X matrix to get N f and Pline k , so the positive or negative contribution of each lineparameter change to the line flow of interest is easily known.Step 2, choose the most contributable line, change itsparameter, get the actual N f and Pline k by using the real(15)whereX ( AY1 A )nN f ,k A ji E jθ j / yi' [ A1i Pline i Pline i . For other line flow changes, for a small sizesystem, switching off an in-service line may make a bigvariance of X , so we use real X 1 and y i' to get the actual(16) 1(23)(14)T . 0 y i ( A Y1 AT )( Eθ ) Ki yiTdefined as follows,for line k, k iN f ,k [ A1k . Ank ] X 1 KiX 1 and yi' , thus get the desired overload relieving.Step 3, run power flow program to verify the result.For the line switching, just simply assign yi yi ,since Y1 A T ( Eθ ) 0 . (22)The Flow Network Contribution Factor (FNCF) N f can befor line k, k iAssign B ' as the negative value of the imaginary part of Ymatrix,B ' imag (Y )(7)For the real power flow,Pline imag (Y p ) AT ( Eθ )(8)change much, and the bus voltage angleassignY1 imag (Y p )yi' yi yi(21)N f and Pline k . For a large size system, switching off one orseveral lines may not change X as much, so we still use thethree steps above.The above method can give quick guidance for selection ofthe parameter to change and the exact parameter variance. Thepower flow calculation can verify it to get an accurate control.B. Bus Parameter VarianceWhen shunt capacitor bank or SVC is being switchedon/off at a bus, the capacitance variance at bus i is ybs . Forreal power flow:Pline Y1 AT ( Eθ )(26)Pnode B ' ( Eθ )(27)from (26) and (27) we can getEθ ( B ' ) 1 Pnode(28)

3'' Pline Y1 AT (( Bnew) 1 ( Bold) 1 ) Pnode(29)'Since Y1 , A and Pnode are constant, B does not changemuch. The line real power flow will change, but not much, forthe variance of bus capacitance.However, based on reactive power equation of the fastdecoupled method, the reactive power Q and bus voltage Ewill change,Q B '' E(30)E Q(31) B '' EE 0 0 . . Q(32) E (B '' ) 1 (B '' ) 1 ybs E X 2 ybs EE . . 0 0 For the n-bus network with m PQ buses, B '' is m madmittance matrix, X 2 is the inverse of B '' .If we assume B '' doesn’t vary much, we can get the busvoltage magnitude variance E j ( X 2, ji E j ) y bs j 1, ,m(33)The Voltage Network Contribution Factor (VNCF) N v can bedefined as follows,N v , j X 2, ji E j , j 1, ,m(34)TABLE IBASE FLOW OF THE WSCC 9-BUS SYSTEM(100MVA BASE, VALUE: P.U.)Magnitude1-40.7164 0.2548i0.76042-71.6300 - 0.0126i1.63003-90.8500 - 0.1291i0.85974-50.4081 0.3106i0.51284-60.3062 0.0889i0.31895-7-0.8547 - 0.0193i0.85496-9-0.6014 0.0195i0.60177-80.7614 0.0503i0.76318-9-0.2414 - 0.1388i0.2785A. Cases of the Line Parameter VarianceCase 1 Insertion of TCSC at a lineIf we assume that the line flow limit of line 5-7 is 0.8 p.u.,we can see that it is overloaded at the base flow condition.Consider insertion of Thyristor Controlled Series Capacitor(TCSC) at each line (assume we have a TCSC at each line) toadjust the line flow.TABLE IIFLOW NETWORK CONTRIBUTION FACTOR (VALUE: 1E-3)(50% COMPENSATION OF A TCSC AT EACH LINE)Take an example of the WSCC 9-bus system given in Fig.1.Table I gives the base flow condition of each line in p.u.Table II presents the FNCF (Flow Network ContributionFactor) results if a TCSC with 50% compensation capacity isinserted at each of the lines 4-5, 4-6, 5-7, 6-9, 7-8 and 8-9respectively. FNCF gives the guidance for the line flowadjustment.Line FlowNote: The assumed line flow direction is from the beginning node to theending node. Negative values of real power flow of line 5-7, 6-9 and 8-9indicate that the actual flow directions are opposite to the assumed directions.III. NUMERICAL RESULTSFig. 1. WSCC 9-bus systemLineLine4-54-65-76-97-88-94-5 flow0.0928-0.1519-1.51.20.2593-0.15734-6 flow0.17570.11421.7-1.3-0.28460.17015-7 flow0.3145-0.3026-1.72.40.4759-0.29516-9 flow-0.34330.31133.21.5-0.52340.30587-8 flow0.1444-0.1371-1.31.10.12360.12498-9 flow0.2045-0.1912-1.91.40.2914-0.0972For line 5-7 flow, since its actual direction is opposite tothe assumed direction, positive value of the FNCF is neededto decrease the flow. From Table II, we can see that thebiggest positive value of FNCF for line 5-7 flow is insertionof TCSC at line 6-9. Therefore, insertion of TCSC at line 6-9will contribute the most to relieving the overload on line 5-7.Table III gives the flow changes and errors by insertingTCSC with 50% compensation capacity at line 6-9. Column 2is the line flow change based on the Network ContributionFactor from matrix X. Column 4 is the line flow change basedon the real Network Contribution Factor from matrix X1.Column 6 is the power flow result. Columns 3, 5 are errorscompared with the power flow result.

4TABLE IIILINE FLOW CHANGE FOR THE LINE 6-9 PARAMETER VARIANCE(CHANGE, FLOW VALUE: P.U., ERROR: er 0.850.08155.160.0859From Table III, we can see that the line flow changeobtained by the Network Contribution Factor method is veryclose to the power flow result. By this method, we can quicklyfind the necessary parameter change to relieve the overload,and avoid the many trials of power flow calculation.Case 2 Line SwitchingIn reality, TCSC is not installed everywhere in the network.To get an easy control of the line parameter, due to theeconomic and technological considerations, line switchingmay be more applicable for the system operators.Table IV and Table V are given to show the line flowresults of switching the line 8-9 and line 5-7 respectively.TABLE VLINE FLOWS WITH LINES DISCONNECTED (VALUE: P.U.)FlowOriginal8-9 off5-7 23051.61908-9-0.241400.6055B. Bus Parameter VarianceWe consider the bus parameter variance, caused byswitching on 0.5 p.u. (in base MVA capacity) shuntcapacitance at bus 5.TABLE VIBUS VOLTAGE MAGNITUDE VARIANCE (VALUE: P.U.)VoltageMethod 1Method 2Method 3Bus 40.01560.01630.0176Bus 50.04330.04530.0469Bus 60.01210.01260.0140Bus 70.01010.01060.0117Bus 80.00790.00820.0093Bus 90.00440.00460.0053TABLE IV. LINE FLOW CHANGES FOR LINE 8-9, 5-7 DISCONNECTED(VALUE: P.U.)FlowLine 8-9 offLine 5-7 olumns 2,3,4 are line flow changes when line 8-9 isswitched off by Flow Network Contribution Factors (obtainedfrom matrix X and X1) method and power flow methodrespectively. Columns 5,6,7 are similar except for line 5-7being switched off.We can see from Table IV that for the line switchingcontrol, the results of the Flow Network Contribution Factormethod are very accurate since they are very close to those ofthe power flow method. Since the line 5-7 carries a big flow,when this line is off, there is a big flow transfer to other lines,so other lines may be heavily loaded, as described in Table V.Thus, the line switching control to relieve overload has to becarefully used because it may result in overloading of otherlines.Method 1 uses the original matrix B '' to get the voltagevariance. Method 2 uses the new matrix B '' after switching onthe shunt capacitor. Method 3 is the power flow method. Wecan see that their bus voltage variances are very close. TheVoltage Network Contribution Factor (VNCF) method can getvoltage improvement with good accuracy.For the real line flow, switching the shunt capacitor at thebus does not cause a major change. We can see this fromTable VII.TABLE VIILINE FLOW VARIANCE (VALUE: P.U.)LineMethod 1Method Method 1 is the Network Contribution Factor method.Method 2 is the power flow method. We can see that the shuntcapacitance variance does not contribute much to real flow

5change of the line. It contributes to the variances of the busvoltage and reactive power injection.IV. CONCLUSIONThis paper introduces a novel and comprehensive methodby using Network Contribution Factors. With the aid of theFNCF and VNCF, necessary line parameter variance and busparameter variance can be calculated to adjust the line flowand bus voltage without many trials of running the power flowprogram. It can be used for re-dispatching load flow,managing congestion, relieving overload, improving voltage,controlling emergency, etc. The method is simple, fast andaccurate.V. REFERENCES[1][2][3][4][5][6][7][8][9]G.D. Irisarri, J.R. Latimer, S. Mokhtari, N. Muller, I.W. Slutsker, “Thefuture of electronic scheduling and congestion management in NorthAmerica”, IEEE Trans. Power Systems, vol. 18(2), pp. 444 – 451 May2003.C.W. Taylor, D.C. Erickson, “Recording and analyzing the July 2cascading outage [Western USA power system]”, IEEE ComputerApplications in Power, vol. 10 (1), pp. 26-30, Jan. 1997.C.W. Taylor, “Improving grid behavior”, IEEE Spectrum, vol. 36 (6), pp.40-45, June 1999.U.S.-Canada Power System Outage Task Force, “U.S.-Canada PowerSystem Outage Task Force Interim Report: Causes of the August 14thBlackout in the United States and Canada”, Nov 19, 2003, Available:http://www.nerc.comNERC Disturbance Analysis Working Group, “Peninsula FloridaDisturbance – March 12, 1996”, NERC 1996 System DisturbancesReport, Aug 2002, Available: http:// www.nerc.comNERC Disturbance Analysis Working Group, “New York Power PoolDisturbance – Aug 26 and Oct 30, 1996”, NERC 1996 SystemDisturbances Report, Aug 2002, Available: http:// www.nerc.comN. Muller, V. H. Quintana, “Line and shunt switching to alleviateoverloads and voltage violations in power networks”, in Generation,Transmission and Distribution, IEE Proceedings C, vol. 136(4), July,1989, pp. 246 –253E.B. Makram, K.P. Thorton, H.E. Brown, “Selection of lines to beswitched to eliminate overloaded lines using a Z-matrix method”, IEEETrans Power Systems, vol. 4 (2), pp. 653 – 661, May 1989.S.K. Joshi, K.N. Patel, “Real time economic dispatch”, in Proc. 2000Power System Technology, International Conf. PowerCon, vol. 3, pp.1263-1268, 2000VI. BIOGRAPHIESHongbiao Song (S'04) received his B.S. and M.S. degrees in electricalengineering from North China Electric Power University, China in 1999 and2002, respectively, and currently is a Ph.D. candidate in electrical engineeringat Texas A&M University. His research interests are power system analysis,simulation, protection, stability and control.Mladen Kezunovic (S’77–M’80–SM’85–F’99) received his Dipl. Ing. degreefrom the University of Sarajevo, the M.S. and Ph.D. degrees from theUniversity of Kansas, all in electrical engineering, in 1974, 1977 and 1980,respectively. He is the Eugene E. Webb Professor and Director of ElectricPower and Power Electronics Institute at Texas A&M University, CollegeStation, where he has been since 1987. His main research interests are digitalsimulators and simulation methods for relay testing as well as application ofintelligent methods to power system monitoring, control, and protection.Dr. Kezunovic is a Fellow of the IEEE and member of CIGRE-Paris.

Relieving Overload and Improving Voltage by the Network Contribution Factor (NCF) Method H. Song, Student Member, IEEE, and M. Kezunovic, Fellow, IEEE Abstract--This paper introduces new Network Contribution Factor (NCF) method for relieving overload and improving voltage by using the networ

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