advertisement

Fifteenth National Power Systems Conference (NPSC), IIT Bombay, December 2008 An Approach for Optimal Placement of UPFC to Enhance Voltage Stability Margin under Contingencies Sreekanth Reddy Donapati and M.K.Verma selection of optimal line. The sensitivity of loading factor with respect to reactive power generation at buses and reactance of the lines has been proposed in [4] to decide optimal location for the placement of Static Var Compensator (SVC) and TCSC, respectively. Two sets of sensitivity factors have been utilized together to optimally place the UPFC. The criterion for placement of UPFC suggested in [4] has ignored phaseshifter action of UPFC which may lead to inaccurate results. A voltage stability L index of load buses in coordination with minimum singular value has been proposed in [6]. The index has been computed to identify optimal location of UPFC for improving system security. A linear programming based optimal power flow algorithm for the placement of UPFC has been proposed in [7] to reduce overloads and voltage violations. However, reduction of loads and voltage violations may not always be helpful in improving voltage stability margin. Particle Swarm Optimization (PSO) technique has been used [8] to achieve maximum system loadability with minimum cost of installation. Particle swarm optimization technique has been employed in [9] to maximize the loadability of transmission system using Unified Power Flow Controller under line outages. Optimal placement of UPFC based on evolutionary programming has been suggested in [10] to enhance maximum loadability of the system. The work on UPFC placement has mainly concentrated to see its impact for the system intact case and under line outage cases. However, outage of some of the generators may also cause voltage instability in the power system. In this paper a sensitivity based approach has been presented to study impact of UPFC placement in loading margin enhancement under critical contingencies considering line as well as generator outage cases. The effectiveness of the proposed method of UPFC placement has been established on a practical 75-bus Indian system representing Uttar Pradesh State Power Corporation Network. Abstract— This paper proposes a sensitivity based technique for optimal placement of Unified Power Flow Controller (UPFC) to enhance voltage stability margin under contingencies. The sensitivity of system loading factor with respect to the reactive power flowing through lines computed for the system intact case and critical contingency cases have been used to decide optimal location for the placement of UPFC. The proposed sensitivity factor has been derived from the reactive power flow balance equation. The effectiveness of the proposed method for the placement of UPFC in voltage stability margin enhancement has been validated on a practical 75-bus Indian system representing Uttar Pradesh State Power Corporation Network. I. INTRODUCTION N recent years an instability usually termed voltage instability has been responsible for several major network collapses world-wide [1]. The actual cases of blackouts characterized by voltage depressions reported in the literature indicate that standard practice procedures such as transformer tap-changing, capacitor switching, synchronous condenser adjustment, and load shedding may aggravate an already unstable voltage profile [2]. The problem of voltage instability which may sometimes result into voltage collapse in the system, has become a matter of great concern to the utilities in view of its prediction, prevention and necessary corrections to ensure a stable operation. The advent of Flexible AC Transmission Systems (FACTS) Controllers [3] has created new opportunities for increasing power system stability margin including voltage stability margin. However, due to high cost and, for maximum enhancement in voltage stability margin, these are to be optimally placed in the system. Out of different types of FACTS controllers, Unified Power Flow Controller (UPFC) seems to be more effective in voltage stability enhancement [4] due to its ability to control series and shunt variables, simultaneously. The selection of optimal bus based on combination of continuation power flow and optimal power flow for the placement of UPFC has been suggested in [5]. However, no specific criterion has been proposed for the ____________________________ I II. UPFC MODEL In the present work, UPFC has been represented by steadystate injection model [5],[11]. The UPFC consists of two switching converters operated from a common DC link, as shown in figure-1 [12]. In this figure, the series converter of UPFC (Converter-2) has been assumed to be connected between buses i and j having voltages Vi T i and V j T j , Sreekanth Reddy Donapati (email: [email protected]) is with Reliance Infrastructure Limited, Noida, Uttar Pradesh, India. M.K.Verma (e-mail: [email protected]) is with the Department of Electrical Engineering, Institute of Technology, Banaras Hindu University,Varanasi, Uttar Pradesh, India. 541 Fifteenth National Power Systems Conference (NPSC), IIT Bombay, December 2008 In (1), variables r and Ȗ control magnitude and phase angle of respectively. Converter-2 injects an AC voltage Vs with injected voltage Vs , rmax represents maximum limit of variable controllable magnitude and phase angle in series with the transmission line. Converter-1 (shunt converter) injects or absorbs an independently controllable reactive power to bus-i. This is represented by the current, Iq. It also supplies or absorbs the active power demanded by Converter-2, through the common DC link. This is represented by the current, Ip. r. In the present work, rmax has been taken as 0.2 considering it as a reasonably high value. Vi Vi T i represents complex voltage at bus-i. The steady-state injection model of UPFC has been derived from figure-2 [5] and has been shown in figure-3. In figure -3 UPFC has been represented as controllable loads connected at buses i and j. In [4], shunt converter has been represented as a constant voltage variable reactive power source, whereas series converter has been considered as a variable reactance in the line. This model of UPFC ignores phase-shifter action of series converter. Steady-state injection model of UPFC overcomes this limitation. Figure-1: UPFC schematic diagram The UPFC circuit arrangement has been shown in figure-2. In this figure, the series converter has been represented by an AC voltage source Vs in series with a reactance X s . The shunt converter has been represented as an independently controllable reactive power Qconv 1 injected to or absorbed Figure-3: UPFC injection model III. METHODOLOGY from bus-i. In addition, this converter also supplies or absorbs real power Pconv1 to the series converter through the common DC link. The proposed sensitivity based approach for determination of the optimal location of UPFC is described below: The reactive power balance equation at bus-i can be given by: I ij and I ji represent current flowing from bus-i to ' bus-j and from bus-j to bus-i, respectively. Vi represents QG i ( QD ib O K Di S ' base sin I i ) complex voltage of a fictitious bus-i'. n Q ik ¦ V i V j Yij sin (G i G j T ij ) (2) j 1 zk where, QGi = Reactive power generation at bus –i QDib = Reactive power demand at bus-i at the base case operating point Qik = Reactive power flowing from bus-i to bus-k Ȝ = Loading factor common to all the buses KDi= Constant multiplier showing the rate of change of load at the ith bus S 'base =Mega Volt Ampere (MVA) base used for scaling to Figure-2: UPFC circuit arrangement equivalent Mega Volt Ampere Reactive (MVAR) load increase. ĭi = power factor angle of the increased load at ith bus Vi įi = Complex voltage at bus –i Yij = Gij + jBij = ij th element of the bus admittance matrix n= Total number of the buses in the system The series voltage source Vs is controllable in magnitude and phase and can be given by: Vs = r Vi e jJ (1) B where, 0 < r < rmax and 0 < Ȗ < 2ʌ 542 Fifteenth National Power Systems Conference (NPSC), IIT Bombay, December 2008 In [4], sensitivity of loading factor with respect to reactive power generation at bus-i (wO/wQGi), and sensitivity of loading factor with respect to reactance Xij of a line connected between buses i and j (wO/wXij), have been derived from reactive power balance equation (2) as: wO w QG i wO wX ij w Vi ª «1 2V i w QG Bii i « « ­§ w V j w Vi · ¸ « V j ° ¨¨ V i QG i ¸¹ QG w w « i ° © 1 « ° K Di S ' base sin I i « n ° Yij sin G i G j T ij ® « V V Y cos G i G j T ij « j 1 ° i j ij « z i °§ w G wG j · i °¨ ¸ « ¨ ° QG QG i ¸¹ w w i ¯© ¬« ¦ Vi 1 K Di S 'base sinI i X ij2 º » » ½» °» °» °» °» ¾» °» °» °» °» ¿¼ values ( of sensitivity factors computed for system intact case and critical contingency cases, priority lines for the placement of series converter of UPFC have been determined. Depending upon magnitude of (3) placement of shunt converter. If absolute value compared to (4) hand, if wO , which relates changes in loading wQik point, the factor with respect to change in reactive power flowing from bus-i to bus-k has been proposed in this work. This sensitivity factor has been obtained by differentiating reactive power balance equation (2) with respect to Qik and is given as: Y 1 [ Z 1 ( 1 X ) 1 ] ¦ wQik ª wVk wVi º Vk «Vi » Yik sin (Gi G j Tij ) wQGi ¬ wQGi wQGi ¼ ª wG wG º Vi V j Yik cos(Gi G j Tik ) « i k » ¬ wQGi wQGi ¼ (5) (6) (7) Z The sensitivity factor wO wO is greater in magnitude compared to wQki wQik wO sensitivities have been calculated for each wQ ik of the lines at a stressed point close to the maximum loadability point. The partial derivatives Vi/QGi, įi/QGi, (i = 1,…,n) in (6) & (8) can be derived for different buses from the inverse Jacobian matrix of the full Newton Raphson Load Flow (NRLF) in polar Form. An additional criterion for optimal placement of the UPFC in this work has been that UPFC should not be placed at generator buses. The placement of UPFC is a planning issue where, accuracy is important and computational speed is insignificant. Therefore, critical contingencies have been identified based on post-contingency loading margins computed using continuation power flow method [13]. In order to obtain loading margins, real power generations, real and reactive power demands have been varied as per following: PGi PGib 1 O (9) where, ­ª wV j ½ wVi º G G T sin ( ) V V Y ° ° « » i j ij i j ij n wQGi ¼ °¬ wQGi ° X ® ¾ wG j º° ª wGi j 1° »° z k ° Vi V j Yij cos( Gi G j Tij ) « ¬ wQGi wQGi ¼¿ ¯ Y K Di S 'base sin I i wO bus-i is considered as the wQki bus-k is considered as the priority bus. The loading margin (the distance between the base case operating point and the nose point) can be computed after UPFC placement at each of the candidate locations for the system intact case and critical contingency cases. The combination of priority line and priority bus producing maximum enhancement in loading margin for majority of the critical contingencies has been selected as the optimal site for UPFC placement. Since voltage instability occurs at the maximum loadability may result in inaccurate selection of priority lines. Therefore, wO wQik wO is having higher wQik priority bus for the placement of shunt converter. On the other The sensitivity factors wO/wQGi and wO/wXij have been used in [4] to determine priority buses for the placement of shunt converter and priority lines for the placement of series converter, respectively. However, the sensitivity factor wO/wXij has been obtained by neglecting the sensitivity terms relating change in complex voltages with respect to line reactance (i.e. wV k wG k and , k = 1,……., n, have been neglected). This wX ij wX ij a new sensitivity wO wO and corresponding to priority wQik wQki lines, bus-i or bus-k can be considered as priority buses for the >Vi V j cosG i G j @ wO wO and ). Based on maximum absolute value wQik wQki (8) where, PGi = Real power generation at bus-i PGib = Real power generation at bus-i at the base case operating point. PDi PDib 1 O (10) wO can be computed using (5) for wQik where, PDi = Real power demand at bus-i PDib = Real power demand at bus-i at the base case operating point each of the lines under system intact case and critical contingency cases. Each line is having two such sensitivity 543 Fifteenth National Power Systems Conference (NPSC), IIT Bombay, December 2008 QDi QDib 1 O (11), respectively. The loading margins without UPFC and with UPFC placed in priority locations for the system intact case & critical contingency cases are shown in Tables II and III. It is observed from Tables II and III that UPFC placement in line 29-38 (towards bus-29) causes maximum enhancement in voltage stability margin for system intact case and for most of the severe outage cases. Hence, line 29-38 (towards bus-29) was considered as the optimal location for UPFC placement. (11) where QDi =Reactive power demand at bus-i IV. CASE STUDIES The proposed method of placement of UPFC controller has been tested on a practical 75-bus Indian system representing Uttar Pradesh State Power Corporation Network. The 75-bus Indian system has 15 generators (at buses 1-15) and 98 transmission lines (including 24 transformers). This system has been taken from [14] with loadings reduced to 90% of original values. The loading margin for the system intact case & contingency cases (considering line and generator outages) were obtained using continuation power flow based software package UWPFLOW [15]. While running repeated load flows real power generations, real and reactive power demands were increased as per equations (9), (10) & (11), respectively. The critical contingencies were obtained based on post contingency loading margins. Based on post contingency loading margins critical contingencies were indentified to be the outages of lines 29-30, 36-37, 74-73, 23-29, 29-75, 22-25, 55-44, 26-22, 44-15( generator-15) and 16-50 in the order of relative severity. The proposed sensitivity factors wO wQik TABLE I ABSOLUTE VALUE OF wO wQik FOR TWO MOST SENSITIVE LINES – 75 BUS INDIAN SYSTEM Outage Intact System (No outage) 29-30 36-37 74-73 23-29 were calculated for all the lines using (5) at a 29-75 loading value corresponding to 90% of maximum loading value for the system intact case and for each of the critical contingencies. The absolute value of these sensitivity factors for two most sensitive lines for the intact case and critical contingency cases are shown in Table-I. It is observed from Table-I that line 29-38 (towards bus-29) has maximum value of sensitivity factor for outages of lines 23-29, 55-44, 26-22 and 44-15 (generator-15). Line 39-59 (towards bus-39) has maximum value of sensitivity factor for the system intact case and for the outage of line 74-73. Line 35-17 (towards bus-35) has maximum value of sensitivity factor for the outage of line 36-37. Line 54-28 (towards bus-54) has maximum value of sensitivity factor for the outage of lines 29-75 and 16-50. Line 43-58 (towards bus-43) has maximum value of sensitivity factor for outage of lines 29-30 and 22-25. Hence, lines 29-38 (towards bus-29), 39-59 (towards bus-39), 35-17 (towards bus-35), 54-28 (towards bus-54), 43-58 (towards bus-43) were considered as priority locations for the placement of UPFC. The loading margin for the intact system and for the critical contingency cases, with UPFC placed in each of the priority locations were calculated using repeated load flows. For obtaining maximum loadability points, starting from the base case operating point, loads were gradually increased in the steps of 0.01, until load flow diverged (loads were increased in the steps of 0.001 near the point of divergence to get more accurate estimate of loading margins). While running repeated load flows steady-state injection model of UPFC [5] was considered and real power generations, real and reactive power demands were increased as per equations (9), (10) & 22-25 55-44 26-22 44-15 (Generator -15) 16-50 Line (Towards bus) wO wQik Line (Towards bus) wO wQik 39-59 (39) 49.1434 18-71 (18) 24.590 43-58 (43) 35-17 (35) 60.388 36-19 (36) 35-41 (35) 36.448 39-59 (39) 29-38 (29) 54-28 (54) 43-58 (43) 29-38 (29) 29-38 (29) 29-38 (29) 33.771 63-55 (63) 44-45 (44) 44-45 (44) 35-17 (35) 44-45 (44) 44-45 (44) 45-44 (45) 28.098 54-28 (54) 111.808 29-38 (29) 50.475 21.331 109.61 44.458 25.244 160.02 106.40 60.21 18.105 97.686 32.495 25.178 34.04 97.686 54.517 The voltage profiles of most critical bus for intact case and for the critical contingency cases were plotted using UWPFLOW & MATLAB. Figure-4 shows the voltage profile of most critical bus for the intact system with and without UPFC controller placed in the system. The voltage profile of the most critical bus for the three most severe outage cases (viz. outage of lines 29-30,36-37,74-73) are shown in figures 5, 6 and 7, respectively. It is observed from figures 4, 5, 6 and 7 that placement of UPFC at the optimal location results in significant enhancement in voltage stability margins. 544 Fifteenth National Power Systems Conference (NPSC), IIT Bombay, December 2008 TABLE III IMPACT OF UPFC ON LOADING MARGIN (CONTINUED) (75-BUS INDIAN SYSTEM) TABLE II IMPACT OF UPFC ON LOADING MARGIN (75-BUS INDIAN SYSTEM) Loading Margin Outage Intact System (No Outage) Without UPFC Controller With UPFC in line 29-38 towards bus29 Loading Margin With UPFC in line 43-58 towards bus-43 Outage Without UPFC Controller With UPFC in line 39-59 towards bus-39 With UPFC in line 54-28 towards bus-54 With UPFC in line 35-17 towards bus-35 0.169 0.191 0.188 Intact System (No Outage) 0.17 0.19 0.18 0.18 29-30 0.013 0.029 0.033 29-30 0.01 0.03 0.03 0.01 36-37 0.038 0.045 0.042 36-37 0.04 0.043 * 0.043 74-73 0.051 0.066 0.067 74-73 0.051 0.066 0.065 0.055 23-29 0.053 0.079 0.077 23-29 0.053 0.078 0.072 0.053 29-75 0.053 0.071 0.068 29-75 0.053 0.069 0.062 0.060 22-25 0.058 0.075 0.081 22-25 0.058 0.077 0.078 0.058 55-44 0.064 0.082 0.084 55-44 0.064 0.083 0.075 0.065 26-22 0.065 0.090 0.086 26-22 0.065 0.088 0.077 0.070 0.069 0.084 0.082 0.069 0.081 0.081 0.075 0.091 0.105 0.103 0.091 0.103 0.096 0.085 44-15 (Generator -15) 16-50 44-15 (Generator-15) 16-50 *Load flow divergence Figure 5: Voltage profile of the most critical bus under line 29-30 outage for 75 -bus Indian System Figure 4: Voltage profile of the most critical bus for the intact case for 75 -bus Indian System 545 Fifteenth National Power Systems Conference (NPSC), IIT Bombay, December 2008 [4] [5] [6] [7] [8] Figure 6: Voltage profile of the most critical bus under line 36-37 outage for 75 -bus Indian System [9] [10] [11] [12] [13] [14] [15] Figure 7: Voltage profile of the most critical bus under line 74-73 outage for 75 -bus Indian System V. CONCLUSION M.K.Verma and S.C.Srivastava “ Enhancement of voltage stability margin under contingencies using FACTS controllers” Proc. of the International Conference on Power System Operation in Deregulated Regime, IT-BHU, Varanasi (India), pp. 139-149, March 6-7, 2006. H.A. Abdelsalam, G.E. M. Aly, M. Abdelkrim and K.M. Shebl, “Optimal location of the Unified Power Flow Controller in electrical power system,” Proc. of the Large Engineering Systems Conference on Power Engineering – LESCOPE-2004, Westin Nova Scotian, pp. 41-46, July 28-30, 2004. D. Thukaram, L. Jenkins and K. Visakha, “Improvement of system security with unified-power flow controller at suitable locations under network contingencies of interconnected systems”, IEE Proc.-Gener. Transm. Distrib., Vol. 152, No. 5, pp. 682-690, September 2005. Weishao and Vijay Vittal, “LP based OPF for corrective FACTS control to relieve overloads and voltage violations”, IEEE Trans on Power Systems, Vol. 21, No. 4, pp. 1832-1839, November 2006. M. Saravanan, S. Mary Raja Slochanal, P. Venkatesh, Prince Stephen Abraham. J “Application of PSO technique for optimal location of FACTS devices considering system loadability and cost of installation”, Power Engineering Conference, Singapore, Vol- 2, pp. 716-721, Nov 29- Dec 2, 2005. S.T.Jaya Christa and P.Venkatesh, “Application of Particle Swarm Optimization for optimal placement of Unified Power Flow Controllers in electrical Systems with line outages”, International Conference on Computational Intelligence and Multimedia Applications,, Sivakasi (India), Vol. 1, pp. 119-124, Dec.2007. J. Hao, L.B. Shi and Ch. Chen, “Optimising location of unified power flow controllers by means of improved evolutionary programming”, IEE Proc.-Gener. Transm. Distrib., Vol. 151, No. 6, pp.705-712, November 2004. M. Noroozian, L. Anguist, M. Ghandhari and G. Andersson, “Use of UPFC for optimal power flow control”, IEEE Trans. on Power Delivery, Vol. 12, No. 4, pp. 1629-1634, October 1997. L. Gyugyi, C. D. Schauder, S. L. Williams, T. R. Rietman, D. R. Togerson and A. Edris, “The Unified Power Flow Controller: A new approach to power transmission control”, IEEE Trans. on Power Delivery, Vol. 10, No. 2, pp. 1085-1097, April 1995. Venkataramana Ajjarapu and Colin Christy, “Continuation Power Flow: A tool for steady state voltage stability analysis”, IEEE Trans. on Power Systems, Vol. 7, No. 1, pp.416-423, February 1992. S.N.Singh and S.C. Srivastava, “Corrective action planning to achieve optimal power flow solution”, IEE Proceeedings, Part C, Vol. 142, pp. 576-582, November 1995. Software Package UWPFLOW available at http://www.power.uwaterloo.ca/~claudio/software/pflow.html. Sreekanth Reddy Donapati (b’1984) received B. Tech. degree in Electrical A sensitivity based approach has been proposed in this paper for the optimal placement of UPFC in power system to enhance voltage stability under contingencies. The sensitivity of loading parameter (O) with respect to reactive power flowing through lines has been computed to decide optimal location for the placement of UPFC. From the case studies carried out on 75-bus Indian system, a considerable increase in loading margin have been observed after UPFC placement at the optimal location. These sensitivity factors can be easily computed and are quite simple to adopt. Engineering from Bapatla Engineering College, Andhra Pradesh, India in 2006 and M. Tech. Degree from Institute of Technology, Banaras Hindu University, Varanasi, India in 2008. Presently he is working in Reliance Infrastructure Limited, Noida, India. His research interests include voltage stability studies and application of FACTS controllers. M. K. Verma (b’1965) received B. Tech. degree in Electrical Engineering from NIT, Rourkela (India) in 1989, M. Tech. degree from BIT, Sindri (India) in 1994 and Ph.D. degree from Indian Institute of Technology, Kanpur (India) in 2005. Presently he is a Reader in Electrical Engineering Department at REFERENCES [1] [2] [3] Institute of Technology, Banaras Hindu University, Varanasi, India. His Jaime De La Ree, Yilu Liu, Lamine Mili, Arun G. Phadke, and Luiz Dasilva, “Catastrophic failures in power systems: Causes, Analyses, and Countermeasures”, Proceedings of the IEEE, Vol. 93, No. 5, pp. 956964, May 2005. Clark H.K, “New challenge: voltage stability,” IEEE Power Engineering Review, pp. 33-37, April 1990. N G. Hingorani, and L. Gyugyi, “Understanding FACTS: Concepts and Technology of Flexible AC Transmission Systems”, IEEE Press, NewYork, 2000. research interests include voltage stability studies, application of FACTS controllers, power system dynamics and operation and control of modern power systems. 546