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International Conference on Advancements in Electronics and Power Engineering (ICAEPE'2011) Bangkok Dec., 2011 Identification of Unified Power Flow Controller Location underLine Outage Contingencies Dr. Shobha Shankar1, Dr. T. Ananthapadmanabha2, The increase in power flows and environmental constraints have forced electric utilities to install new equipment to enhance networkoperation.The continuous and fast improvement of power electronicstechnology has made flexible AC transmission systems (FACTS) a promising concept for power system applications. The IEEE definition of FACTS is “Alternating Current transmission system incorporating power electronic-based and other static controllers to enhance controllability and increase power transfer capability”.With the application of FACTS technology, power flow along transmission line can be more flexibly controlled. Among a variety of FACTS controllers, UPFC is one of the most interesting and potentially the most versatile. It can provide simultaneous and independent control of important power system parameters: line active power flow, line reactive power flow, impedance and voltage. It offers the necessary functional flexibility for the combined application of phase angle control with controlled series and shunt compensation. From the literature, it is clear that most of the work on UPFC belongs to two areas namely i)UPFC modeling and integration into power flow solutions and ii) control actions for effective operation of UPFC [1]-[10]. Because of the considerable costs of the FACTS device, it is important to ascertain the location for placement of these devices suitable for various network contingencies. Many static models are proposed and incorporated into the existing load flow model in the literature.The sending and receiving ends of the UPFC are decoupled. The former is transformed into a PQ bus while the latter is transformed into a PV bus. The active and reactive power loads in the PQ bus and the voltage magnitude at the PV bus are set at the values to be controlled by the UPFC. The method is simple but works only if the UPFC is used to control voltage magnitude, active power and reactive power simultaneously [11]. The UPFC is modelled as a series reactance together with a set of active and reactive nodal power injections at each end of the series reactance. The UPFC injection model is implemented into a full Newton-Raphson program by adding the UPFC power injections and their derivatives with respect to the AC network state variables, i.e. nodal voltage magnitude and angles, at the appropriate locations in the mismatch vector and Jacobian matrix. The original dimensions of the mismatch vector and Jacobian matrix are not altered at all. The series voltage source parameters voltage magnitude and angle are adjusted manually in order to achieve a power flow solution [12]. The UPFC Abstract:With the increased loading of existing power transmission system and the tendency towards maximizing economic benefits has led power system utilities to run close to the limits of stable operation. The increase in power flows and environmental constraints have forced electric utilities to install new equipment to enhance network operation. This paper presents an approach for identifying optimal location of Unified Power Flow Controller under line outage contingencies. Fuzzy approach is used to combine the effect of voltage stability margin indicated by Minimum Singular Value of load flow Jacobian matrix (MSV) and voltage change to identify the optimal location. With unified power flow controller at optimal location, the voltage stability margin of the system is enhancedand voltage profiles are improved. The proposed method is tested with simulated condition on 24 bus 400 kV Southern grid of India. Keywords: Line Stability Index, Minimum Singular Value, Voltage Change Index, Voltage Stability Margin Index I. INTRODUCTION P OWER system security forms an integral part of modern energy management systems, but its implementation is still a challenging task to power system engineers. Steadystate security assessment enables the operating personnel to know which system disturbances or contingencies may cause limit violations and force the system to enter into emergency state. The studies on assessing the static voltage stability margin of a system have revealed that, the system reaches to the proximity of voltage collapse due to an excessive loading of a bus or due to a sudden line outage in the system. In both the cases it is the excessive line flows through a particular line which exceedthe static stability limit and results in pushing the system to voltage collapse. Hence, under these conditions, if a Unified Power Flow Controller (UPFC) comes into operation with appropriate control parameters, it is possible to enhance the line flow capacity of few such lines and thereby avoiding the possible voltage collapse.With the increased loading of existing power transmission system and the tendency towards maximizing economic benefits has led power system utilities to run close to the limits of stable operation. 1 Dr. Shobha Shankar is with Department of Electrical and Electronics Engg., Vidyavardhaka College of Engineering, Mysore, India. (phone: 94484 88697, fax: 0821 2510677, e-mail: [email protected]) 2 Dr. T. Ananthapadmanabha is with Department of Electrical and Electronics Engg.,The National Institute of Engineering, Mysore, India. (e-mail: [email protected]) 122 International Conference on Advancements in Electronics and Power Engineering (ICAEPE'2011) Bangkok Dec., 2011 power flow model is completely general. The UPFC state variables are incorporated inside the Jacobian and mismatch equations, leading to very robust iterative solutions. It controls active and reactive power simultaneously as well as voltage magnitude. It can also be set to control one or more of the parameters in any combination or to control none of them. A set of analytical equations has been derived to provide good UPFC initial conditions. The algorithm exhibits quadratic or near quadratic convergence characteristics [13]. There are several methods in the literature for finding locations of FACTS device in vertically integrated power system. However, very little work has been reported in the area of identifying suitable location of UPFC with static considerations under various network contingencies.K.S. Verma et al have developed sensitivity based approach for suitable location of UPFC with static point of view, for congestion management. The location of UPFC with high sensitive factor is considered as the best location, as it indicates more loss reduction in the system [14]. B. Venkatesh and H.B. Gooi have proposed a model of UPFC and its inclusion in polar form of fast decoupled power flow algorithm. The optimal siting of UPFC devices leads to reduction of operating costs [15]. Mehmet Tumay et al have developed complete power injection model of UPFC including both the series injection branch and shunt exciting branch in rectangular form [16]. D. Thukaram et al have selected suitable locations of UPFC using voltage stability index (Lindex) of load buses and minimum singular value [17]. Lucio Ippolito et al have proposed a methodology based on genetic algorithm to identify the optimal number and location of UPFC devices by minimizing generation costs, line overload and the costs of installation and maintenance of UPFC devices [18]. Line stability is used for tasks (i) and (ii) and fuzzy approach which combines voltage change index and voltage stability margin index is used for task (iii). Minimum singular value of load flow Jacobian matrix is computed for monitoring the enhancement in voltage stability margin. A. Line Stability Index LS index = L ij = P r / P r(max) = Real power transferred from node i to node j Maximum real power that can be transferred (1) LS index is capable of identifying critical line outages and possible lines for installing UPFC. B. Voltage Change Index The Voltage Change Index quantifies the improvement in the bus voltage profile after incorporating UPFC at the selected location in the system. It is defined as: 𝑉𝑉𝑉𝑉𝑉𝑉 = ∑𝑛𝑛𝑖𝑖=1 �𝑉𝑉𝑖𝑖𝑤𝑤 −𝑉𝑉𝑖𝑖𝑜𝑜 � 𝑉𝑉𝑖𝑖𝑜𝑜 (2) where, n is the number of buses, 𝑉𝑉𝑖𝑖𝑜𝑜 is bus voltage profile without UPFC and 𝑉𝑉𝑖𝑖𝑤𝑤 is bus voltage profile with UPFC. C. Voltage Stability Margin Index The voltage stability margin index quantifies the improvement in the voltage stability margin indicated by the Minimum Singular Value of modified Jacobian matrix (MSV) after incorporating UPFC at the selected location in the system. It is defined as �𝑀𝑀𝑀𝑀𝑀𝑀 𝑊𝑊 −𝑀𝑀𝑀𝑀𝑀𝑀 𝑂𝑂 � 𝑉𝑉𝑉𝑉𝑉𝑉𝐼𝐼 = 𝑀𝑀𝑀𝑀𝑀𝑀 𝑜𝑜 (3) where MSVo is the MSV without UPFC in the system andMSVw is the MSV with UPFC incorporated in the system. The criteria for selection of best location for installation of UPFC are enhancement in voltage stability margin and improvement in the voltage profile. The Line Stability Index is used to screen down the possible locations for installing UPFC. Further fuzzy approach is used to combine the effect of voltage stability margin indicated by Minimum Singular Value of load flow Jacobian matrix (MSV) and voltage change to select the optimal location. The proposed method is tested with simulated condition on 24 bus 400 kV Southern grid of India. The validity of the proposed method is verified with the results of [14]. P III.FUZZY BASED OPTIMAL LOCATION OF UPFC The fuzzy approach computes fuzzy rank coefficient with Voltage Change Index rank (VCIrank) and Voltage Stability Margin Index rank (VSMI rank) as inputs to the Fuzzy Inference System (FIS). The VCI and VSMIrank are expressed in fuzzy set notation. The fuzzy rank coefficient is also divided into different categories. The fuzzy rules are used to evaluate the fuzzy rank coefficient for each UPFC location. Based on fuzzy rank coefficient, synergized rank is obtained. Lower the fuzzy rank coefficient; lower the synergized rank and the best location of UPFC. The Fuzzy Inference Structure is tested in MATLAB 7 Fuzzy Toolbox. II.METHODOLOGY FOR OPTIMAL LOCATION OF UPFC The methodology involves i) Short listing of line outage contingencies ii) Possible lines for incorporating UPFC iii) Optimal location of UPFC with enhancement of voltage stability margin and improvement in bus voltage profiles. A. VCI Rank The VCIrank is divided into three categories using fuzzy set notation: low (1-3), medium (3-5) and high (5-7). The membership functions for all the linguistic terms are taken as trapezoidal function. 123 International Conference on Advancements in Electronics and Power Engineering (ICAEPE'2011) Bangkok Dec., 2011 Defuzzification: ‘centroid’ Fig. 1 Membership function for 3 linguistic variables of VCI rank B.VSMI Rank The VSMI SUM rank is divided into three categories using fuzzy set notation: low (1-3), medium (3-5) and high (5-7). The membership functions for all the linguistic terms are taken as trapezoidal function. Fig. 4 Fuzzy surface for the proposed model The fuzzy rules for evaluation of fuzzy rank coefficient are given in the Table I Rule No. 1 2 3 4 5 6 7 8 9 TABLE I FUZZY IF-THEN RULES VCI rank VSMI rank Fuzzy Rank Coefficient Low Low Low Low Medium Low Low High Medium Medium Low Low Medium Medium Medium Medium High High High Low Medium High Medium High High High High Based on fuzzy rank coefficient synergized rank list is prepared. The location of UPFC with lowest synergized rank is the best location. The proposed fuzzy approach not only takes into account the improvement in the voltage profiles but also enhancement in the voltage stability margin. Fig. 2 Membership function for 3 linguistic variables of VSMI rank C. Fuzzy Rank Coefficient The Fuzzy Rank coefficient is divided into three categories using fuzzy set notation: low (1-3), medium (3-5) and high (57). The membership functions for all the linguistic terms are taken as trapezoidal function. VCI rank Fuzzy Inference System Fuzzy rank coefficient VSMI rank Fig. 5 Fuzzy Inference System for optimal location of UPFC E.Procedure For a given system, critical line outage contingencies are identified. a) Load flow analysis is carried out for a precontingency system to obtain bus voltage profiles. b) Minimum Singular Value of the load flow Jacobian matrix is computed. c) For each critical contingency, the LS index value is calculated for each of the lines. d) Lines having high values of LS index are selected as possible locations of UPFC. e) UPFC is installed in each one of the selected line and Fig. 3 Membership function for 3 linguistic variables of Fuzzy Rank coefficient D. Fuzzy Inference System Type: ‘Mamdani’ And method: ‘min’ Or method: ‘max’ Implication method: ‘min’ Aggregation method: ‘max’ 124 International Conference on Advancements in Electronics and Power Engineering (ICAEPE'2011) Bangkok Dec., 2011 Voltage Change Index and Voltage Stability Margin Index are computed for all the critical contingencies. f) VCI obtained for all the contingencies for a specific location of UPFC are added to get VCI SUM . g) Voltage Stability Margin Index computed for all the contingencies for a specific location of UPFC are added to get VSMI SUM . h) The UPFC locations are ranked separately based on VCI SUM and VSMI SUM . i) Using Fuzzy-If-Then rules, fuzzy rank coefficient is obtained and further synergized rank is obtained and the location with lowest synergized rank is the best location of the UPFC. 6 DLO 7 DLO 8 DLO 9 DLO 10 DLO 9 8 8 14 5 8 21 15 12 14 10 9 11 23 8 14 9 8 8 17 Simulations are carried out to compute LS index values for all the lines under these contingencies. The lines having maximum LS index are (12-17), (17-19), (5-6) and (5-8). They are the possible locations for installing UPFC in the system. UPFC is installed at each of these selected lines and VCI and VSMI are computed. Further VCI rank and VSMI rank list is prepared which are given as inputs to the Fuzzy Inference System. Table III and IV shows the VCI rank and VSMI rank for possible locations of UPFC under selected contingencies. F. UPFC equivalent circuit The UPFC equivalent circuit for steady state model as shown in fig 6. is used in the evaluation of system performance under network contingency. TABLE III VCI RANK FOR ALL POSSIBLE LOCATIONS OF UPFC: 24 BUS EHV SYSTEM Contingencies 5-8 12-15 21-19 12-14,10-11 9-8,8-14 12-14,10-9 9-8,8-17 11-23,8-14 VCI SUM VCI Rank Fig. 6 UPFC equivalent circuit The equivalent circuit consists of two ideal voltage sources, V CR = V CR (cosθ CR +j sinθ CR ) V VR = V VR (cosθ VR +jsinθ VR ) where V VR and θ VR are the controllable magnitude (V VRmin ≤V VR ≤ V VRmax ) and angle (0 ≤ θ VR ≤ 2Л) of the parallelvoltage source. The magnitude V CR and angle of the series voltage source are controlled between limits (V cRmin ≤V cR ≤ V cRmax ) and angle (0 ≤ θ cR ≤ 2Л), respectively[13]. For the placement strategy line outage contingencies considered are shown in Table II. TABLE II LIST OF LINE OUTAGE CONTINGENCIES: 24 BUS EHV SYSTEM Type of no. contingency From bus To bus 1 SLO 5 8 2 SLO 12 15 3 SLO 21 15 4 SLO 21 19 6 DLO 12 14 10 11 VCI UPFC in (17-19) 0.0769 ……….. …………. 1.5081 0.8373 2.1314 -0.7874 -0.1564 3.6099 4 values UPFC in (5-6) …………. 0.1420 1.0674 2.1519 1.1258 2.5977 -0.8372 -0.2570 5.9906 2 UPFC in (5-8) ………….. 0.1225 1.1300 2.3540 1.1742 2.6402 -0.6557 0.4654 7.2306 1 TABLE IV VSMI RANK FOR ALL POSSIBLE LOCATIONS OF UPFC : 24 BUS EHV SYSTEM VSMI values ContinUPFC in UPFC in UPFC in UPFC in gencies (12-17) (17-19) (5-6) (5-8) 5-8 0.0329 -0.2341 ………….. …………. 12-15 0.1644 ………….. 0.1492 -0.4837 21-19 0.0619 ………. 0.1422 -0.4356 12-14,10-11 -0.5761 -0.2403 0.4378 -0.2010 9-8,8-14 0.2014 -0.3917 -0.0880 -0.6404 12-14,10-9 -0.4943 0.2485 0.7166 -1.0751 9-8,8-17 0.4269 -0.3826 -0.2800 -0.5848 11-23,8-14 -0.4377 -0.1511 -0.2540 -0.6010 VSMI SUM -0.6203 -1.1515 0.8218 -4.0219 VSMI Rank 2 3 1 4 IV. TEST RESULTS Contingency UPFC in (12-17) 0.1083 -0.0530 0.8599 1.5343 0.4753 1.7467 -1.4145 0.8550 4.1120 3 Based on fuzzy If-Then rules fuzzy rank coefficient and synergized rank is obtained. Table V shows fuzzy rank coefficient and synergized rank. The location of UPFC with highest rank is the best location which provides improvement in bus voltage profiles and enhancement in voltage stability margin. 125 International Conference on Advancements in Electronics and Power Engineering (ICAEPE'2011) Bangkok Dec., 2011 TABLE V SYNERGIZED RANK FOR ALL POSSIBLE LOCATIONS OF UPFC: 24 BUS EHV SYSTEM UPFC Locations VCI Rank VSMI Rank Fuzzy Rank Coefficient Synergized Rank 12-17 17-19 5-6 5-8 3 4 2 1 2 3 1 4 2.72 3.40 1.60 2.50 3 4 1 2 Rank-3 contingency (12-14, 10-9) At base load condition without UPFC the power loss is 84.59 MW. At bus number 24, the minimum voltage is 0.835 p.u. and MSV of the system is 0.1276. After installing UPFC at (5-6) the voltage stability margin has increased to 0.4738 and the voltage at bus number 24 has increased to 1.06 p.u. The system losses have reduced to 83.63 MW. From Table V, it can be observed that locations (5-8), (5-6), and (12-17) have been ranked as 1, 2 and 3 respectively according to VCI rank. Similarly, (5-6), (12-17) and (17-19) are ranked as 1, 2 and 3 respectively based on VSMI rank. Based on fuzzy rank coefficient, synergized rank list is prepared and accordingly (5-6) is ranked as the first best location and (5-8) as next best location. UPFC is installed at (5-6) and voltage profiles are computed for selected critical contingencies namely (5-8), (12-15), (21-19), (12-14, 10-11), (9-8, 8-14), (12-14, 10-9), (9-8, 8-17) and (11-23, 8-14). Fig. 7 to 10 shows the bus voltage profile for selected contingencies with UPFC located at (5-6). Voltage Profile for (12-14, 10-9) Contingency Voltage Magnitude in p.u. 1.1 1.05 1 without UPFC 0.95 with UPFC in 5-6 0.9 0.85 0.8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Bus Number Fig. 9 Voltage Profile for Rank-3 Contingency Less Critical contingency (12-15) At base load condition without UPFC the power loss is 50.857MW. At bus number 7, the minimum voltage is 0.991 p.u. and MSV of the system is 0.53. After installing UPFC at (5-6) the voltage stability margin has increased to 0.6091 and the voltage at bus number 7 has increased to 1.0258 p.u. The system losses have reduced to 50.609 MW. Rank-1 Contingency (9-8, 8-17) Without UPFC at base load condition the power loss is 130.579 MW. At bus number 7, the minimum voltage is 0.925 p.u. and MSV of the system is 0.271. After installing UPFC at (5-6) the voltage stability margin has increased to 0.347 and the voltage at bus number 7 has increased to 0.9488 p.u. The system losses have reduced to 84.84MW. Voltage Profile for (9-8,8-17) Contingency Voltage Profile for 12-15 Contingency 1.08 1.08 1.04 1.02 1 Voltage Magnitude in p.u. Voltage Msgnitude in p.u. 1.06 without UPFC 0.98 with UPFC in 5-6 0.96 0.94 0.92 0.9 0.88 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 1.06 1.04 1.02 without UPFC with UPFC in 5-6 1 0.98 0.96 Bus Number 0.94 1 Fig. 7 Voltage Profile for Rank-1 Contingency 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Bus number Rank-2 Contingency (11-23, 8-14) At base load condition without UPFC the power loss is 88.27 MW. At bus number 23, the minimum voltage is 0.849 p.u. and MSV of the system is 0.358. After installing UPFC at (5-6) the voltage stability margin has increased to 0.4492 and the voltage at bus number 26 is increased to 0.8626 p.u. The system losses have reduced to 11.1647 MW. Fig. 10 Voltage Profile for Rank-7 Contingency TABLE VI COMPARISON OF RESULTS: 24 BUS EHV SYSTEM Voltage Profile for (11-23, 8-14) Contingency 1.1 Voltage magnitude in p.u. 2 1.05 Line section Fuzzy rank coefficient Synergized rank Sensitivity factor (b i k) 5-6 5-8 12-17 1.6000 2.5000 2.7200 1 2 3 -0.9318 -0.6823 -0.5134 Best UPFC location 1 2 3 1 The location of UPFC obtained from the proposed method is verified by finding total loss sensitivity factor (b i k) with respect to voltage as proposed in [14]. It is found from Table VI that concurrent results are obtained from fuzzy approach and sensitivity factor method. without UPFC 0.95 with UPFC in 5-6 0.9 0.85 0.8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Bus Number Fig. 8 Voltage Profile for Rank-2 Contingency 126 International Conference on Advancements in Electronics and Power Engineering (ICAEPE'2011) Bangkok Dec., 2011 [7] V. CONCLUSIONS The Unified Power Flow Controller (UPFC) is very expensive device, therefore it is important to ascertain the location for placement of UPFC which is suitable for various contingencies. In this paper, an effective but simple placement strategy for UPFC is proposed. The method uses Line Stability index which is sensitive to line flow to screen down the possible locations for UPFC. Further Voltage Change Index and Voltage Stability Margin Index are combined using fuzzy approach to determine optimal location of UPFC. The method guarantees improvement in voltage profile and enhancement in voltage stability margin. [8] [9] [10] [11] REFERENCES [1] [2] [3] [4] [5] [6] [12] Xuan Wei, Joe H. Chow, B. Fardanesh and Abdel-Aty Edris, “A Dispatch Strategy for a Unified Power-Flow Controller to Maximize Voltage-Stability-Limited Power Transfer”, IEEE Transactions on Power Delivery, Vol. 20, No. 3, pp. 2022-2029, July 2005. Kalyan K. Sen and Eric J Stacey, “UPFC- Unified Power Flow Controller: Theory, Modeling and Applications”, IEEE Transactions on Power Delivery, Vol. 13, No. 4, pp. 1453-1460, October 1998. S. Tara Kalyani and G. Tulasiram Das, “Simulation of Real and Reactive Power Flow Control with UPFC Connected to a Transmission Line”, Journal of Theoretical and Applied Information Technology, pp. 16-22, 2008 C. D. Shauder, L.Gyugyi, S. L. Williams, T. R. Rietman, D. R. Torgerson and A. Edris, “The Unified Power Flow Controller: A new Approach to Power Transmission Control”, IEEE Transactions on Power Delivery, Vol. 10, No. 2, pp. 1085-1097, April 1995. K. R. Padiyar and A. M. Kulkarni, “Control Design and Simulation of Unified Power Flow Controller”, IEEE Transactions on Power Delivery, Vol. 13, No. 4, pp. 1348-1354, October 1998. A. J. F. Keri, A. S. Mehraban, S. Lombard, A. Elriachy and A. A. Edris, “Unified Power Flow Controller (UPFC) : Modelling and Analysis”, IEEE Transactions on Power Delivery, Vol. 14, No. 2, pp. 648-654, April 1999. [13] [14] [15] [16] [17] [18] 127 L. Gyugyi, “Unified Power Flow Control concept for flexible AC transmission systems”, IEE Proceedings-C, Vol. 139, No. 4, pp. 323-331, July 1992. H. Ambriz-Perez, E. Acha, C. R. Fuerte-Esquivel and A. De la Torre, “Incorporation of a UPFC model in an optimal power flow using Newton’s method”, IEE Proceedings Generation Transmission Distribution, Vol. 145, No. 3, pp. 336-344, May 1998. Samina Elyas Mubeen, R.K. Nema and Gayatri Agnihotri, “Power Flow Control with UPFC in Power Transmission System”, PWASET, Vol.30, pp. 955-959, July 2008. C. R. Fuerte-Esquivel and E. Acha, “Unified Power Flow Controller: a critical comparision of Newton-Raphson UPFC algorithms in power flow studies”, IEE Proceedings Generation Transmission Distribution, Vol. 144, No. 5, pp. 437-444, September 1997. A. Nabavi-Niaki and M. R. Iravani, “Steady-State and Dynamic models of Unified Power Flow Controller (UPFC) for Power System Studies”, IEEE Transactions on Power System, Vol. 11, No. 4, pp. 1937-1943, November 1996. M. Noorzian, L. Anguist, M. Ghandhari and G. Anderson, “Use of UPFC for Optimal Power Flow Control”, IEEE Transactions on Power Delivery, Vol. 12, No. 4, pp. 1629-1634, October 1997. C.R. Fuerte-Esquivel, E.Acha and H.Ambriz-Perez, “A Comprehensive Newton-Raphson UPFC Model for the Quadratic Power Flow Solution of Practical Power Networks”, IEEE Transactions on Power Systems, Vol. 15, No. 1, pp. 102-109, February 2000. K. S. Verma, S. N. Singh, H. O. Gupta, “Location of unified power flow controller for congestion management”, Electric Power Systems Research, No. 58, pp.89-96, 2001. B. Venkatesh, H. B. Gooi, “Optimal Siting of Unified Power Flow Controllers”, Electric Power Components and Systems, No. 34, pp. 271-284, 2006. Mehmet Tumay, A. M. Vural, K. L. Lo, “The effect of unified power controller location in power systems”, Electrical Power and Energy Systems, No. 26, pp. 561-569, 2004. D. Thukaram, L. Jenkins and K. Vishaka,“ Improvement of System Security with Unified Power Flow Controller at Suitable Locations under Network contingencies of Interconnected Systems”, IEE Proc.-Generation Transmission Distribution, Vol. 152, No.5, pp.682-690, September 2005. Lucio Ippolito, Antonio La Cortiglia, Michele Petrocelli, “Optimal allocation of FACTS devices by using multi-objective Optimal Power Flow and Genetic Algorithms”, International Journal of Emerging Electric Power Systems, Vol. 7 Issue- 2, Article 1, 2006.