RESEARCH PAPERS APPLICATION OF METAHEURISTIC ALGORITHMS FOR OPTIMAL POWER FLOW SOLUTIONS WITH CENTRE NODE UNIFIED POWER FLOW CONTROLLER By YESHITELA SHIFERAW MARU * K. PADMA ** * Andhra University, Visakhapatnam, India. ** Department of Electrical Engineering, AU College of Engineering, Visakhapatnam, A.P, India. Date Received: 19/01/2021 Date Revised: 06/02/2021 Date Accepted: 22/03/2021 ABSTRACT This paper presents the optimal power flow solution using Multi-Population based Modified Jaya (MPMJ) algorithm with Centre-Node Unified Power flow controller (C-UPFC) FACTS device. The C-UPFC is the current and advanced FACTS device to control the flow of active power and voltage magnitude at the line and bus. The C-UPFC is the basic derivative of the original UPFC device. Still, in the C-UPFC, this device connection is inserted in series with the transmission line and connected at the transmission line's midpoint. Therefore, The C-UPFC can independently regulate active and reactive power flows at both line ends and AC voltage magnitude at line midpoint. The optimal location of the C-UPFC device in the transmission line is determined by the Analytical Hierarchy Process (AHP) method by considering the objective functions given by priority order values. Therefore, the proposed MPMJ optimization algorithm applied with C-UPFC for optimal values of total fuel cost of generation, real power loss, the total voltage deviation, and the sum of squared voltage stability index on the standard IEEE-57 bus test system. The results obtained by the proposed MPMJ algorithm are better solutions effectively in the presence of C-UPFC device and is compared with the recent algorithm reported in the literature. Keyword: Analytical Hierarchy Process, Centre-node unified power flow controller, the Fuel cost of generation, MultiPopulation based Modified Jaya algorithm, Optimal power flow. INTRODUCTION recent advancement in Computational Intelligent EOptimal Power Flow problems are strongly non-convex Techniques, deficiencies of the above deterministic and non-linear optimization problem due to certain methods are avoided. Some meta-heuristic strategies like equality and inequality constraints to satisfy objective Particle Swarm Optimization (Tehzeeb-Ul-Hassan et al., functions. There are several strategies for optimizing OPF 2012), differential evolution (El-Fergany & Hasanien, 2015), problems. Such deterministic methods, including Newton- Grey wolf optimizer (Ladumor et al., 2017), efficiency based solution, linear programming, a hybrid of linear evolutionary algorithm (Reddy et al., 2014), artificial bee programming and quadratic programming, interior-point colony algorithm (Le Dinh et al., 2013), krill herd algorithm methods, etc. used to solve OPF problems earlier (Momoh (Mukherjee & Mukherjee, 2015), mouth swarm algorithm et al., 1999). However, the key difficulties of deterministic (Mohamed et al., 2017), Mouth-Flam optimizer (Trivedi et methods are the sluggish rate of convergence. These al., 2018), novel sine-cosine algorithm (Attia et al., 2018), deterministic methods are not guaranteed for the global social spider optimizer (Nguyen, 2019), improved chaotic solution and find the local solution to the OPF problem. electromagnetic field optimization (Bouchekara, 2020), However, some of these approaches have excellent Ant Lion algorithm (Herbadji et al., 2019), Gbest Guided convergence characteristics and are primarily used in Cuckoo search algorithm (Chen et al., 2017), Animal industry to solve various optimization problems. Due to Migration Optimization (Chinta et al., 2018), Salp swarm i-manager’s Journal on Power Systems Engineering, Vol. 8 l No. 4 l November 2020 - January 2021 1 RESEARCH PAPERS algorithm (El-Fergany & Hasanien, 2020), Krill herd C-UPFC on the transmission line is determined using the algorithm (Mukherjee & Mukherjee, 2016), Multiverse Analytical Hierarchy method, based on the priority of the optimizer, chemical reaction optimization (Dutta et al., objective function ordered. 2016), since the last two decades. From the given 1. Mathematical Modelling of C-UPFC Device algorithms listed in the above literature, each algorithm has its advantage and disadvantage in terms of its control parameter, hence the parameterless optimization algorithms proposed in this paper for better optimal values of objective function and time. The C-UPFC FACTS device is modelling based on control of four parameters such as midpoint voltage magnitude, active power flow in the transmission line, reactive power flow at the sending end side, and the reactive power flow at the receiving end connected in series of the transmission The formulation of OPF is based on assigning the line at the midpoint (Alhejji et al., 2020; Ooi & Lu, 2000). generation output power, generation voltage, tap Figure 1 shows the C-UPFC consisting of three voltage changing of the transformer, reactive power device source converters connected to a common dc link compensation Var, and the FACTS device parameter. The provided by a dc storage capacitor. Two series converters operating limits of voltage, angles, and power to optimize at two ends of the lines control the systems active and the predefined objective function for the system, while reactive power, and one Shunt converter in the centre of fulfilling the operating constraints in the limits. The control of the transmission line regulates voltage magnitude. The the transformer ratio, real, and reactive power flow reduces shunt converter's basic function is to inject or absorb active the instantaneous costs and power loss (Attia et al., 2018). power demand through series converters at the common In general, the FACTS devices connection can change the dc - link to support the active power exchange resulting transmission line's parameter values, such as impedance from series voltage injection. of the line and current flow based on the compensation of Figure 2 shows the basic node point of C-UPFC devices reactive power. The FACTS devices classification can be indicated by three buses (bus, I, j, and n) to control the divided into two parts: variable impedance and voltage power flow through the transmission line. Bus i is PV type bus, source converter types. The category of variable and bus j and n are the PQ bus type. The mathematical impedance FACTS device is static var compensators (SVC), series converter model is displayed according to equation Thyristor based controlled series Capacitor (TCSC), and (1) and (2). Thyristor controlled phase shift transformer (TCPST). The Vs Is = jX s voltage source converter-based FACTS device is a static synchronous compensator (STATCOM), a unified power flow (1) Vr Ir = jX r controller (UPFC), and interline power flow controller (IPFC) (Alhejji et al., 2020; Kamel et al., 2018) etc. The Centre (2) node unified power flow controller is one of the FACTS Figure 3 shows that the current source is converted in to devices that may benefit over another multi-parameter shunt, then using Kirchhoff's Current Low at the bus (i, and n) concept. Such a system may be mounted in transmission the specified values are calculated. line in series (Ooi & Lu, 2000). By applying Kirchhoff's Current Law (KCL)at bus i: In this paper, metaheuristic TLBO, JAYA, and proposed MPMJ algorithm-based optimization techniques without and with C-UPFC device are applied to IEEE-57 bus test system and compared its performance in terms of minimization of total fuel cost of the generation, total active power loss, voltage deviation, and the sum of squared voltage stability index. The optimal location of the 2 * S s ,i ö Vi Vj æ ÷ ç Is = I ij I = ç jX s Vi ÷ ø è sp s ,i sp (3) where S ssp,i = P sp + jQ ssp,i (4) B X B Q ssp.i = Q ssp + Vm2 I mi2 + Vi 2 4 2 4 (5) i-manager’s Journal on Power Systems Engineering, Vol. 8 l No. 4 l November 2020 - January 2021 RESEARCH PAPERS Figure 1. Structure of the C-UPFC Device Figure 2. Voltage Source of C-UPFC Device Figure 3. Voltage Source of C-UPFC Device i-manager’s Journal on Power Systems Engineering, Vol. 8 l No. 4 l November 2020 - January 2021 3 RESEARCH PAPERS By assuming the converter loss ignored, the net active By applying Kirchhoff's Current Law (KCL) at bus n: * æ Vn S öV j ç÷ Ir I rsp, n I jn = ÷ ç Vn ø jX r è sp r ,n where (6) power exchange between the controller and the system is equal to zero. The shunt power to connect the system can be Psh = Pex1 Pex 2 * I se 2 æ S rsp, n ö ÷ ç I = = ÷ ç V n èø (7) sp r ,n S ssp, n = P sp + jQrsp, n (8) B X B Q ssp, n = Qrsp Vk2 I nk2 Vn2 4 2 4 (9) (14) The main function of the shunt power to balance the power flow through the converter. The injected load at the midpoint of connection Pjload = Pj Psh , Q load = Qj j (15) From Figure 4, the reactive power created using the The shunt current with considering the complex load can reactive balance power at the mid-point which described be: by Si = Vi X ( I s)* Qsh = V jVi (Gij sin d Bij cos d ij mj ) + V jVn (Gnj sin d Bnj cos d Q load (16) nj nj ) + j Sn = Vn X ( I r)* (10) * Sj = V j X ( I s+ Ir ) and current can be described in the following equation By substituting the value of Is and Ir from (1), and (2), the series injected voltage is determined according to equation (11), and (12) at the sending and receiving end. æ S ssp,i ö ç ÷ X jX s + Vi Vj Vs = ç ÷ V i ø è æ S rsp,n ö ç ÷ X jX r Vj + Vn Vr = ç ÷ V n ø è (11) (12) () Pex 2 = Re Vr ( I se 2 )* æ Psh + jQsh ö ÷ Qsh = Vj + jX sh ç çV ÷ j è ø I sh = I se1+ I se 2 (17) (18) The final model of the proposed C-NUPFC device is shown injected load (S,i Sn, Pjload) and generated reactive power (Qsh) at bus j. these all are included in the power mismatch sending and receiving end will be: () (17), (18). in Figure 4; hence C-NUPFC is characterized by the From referring Figure 2, the injected active power from the Pex1 = Re Vs ( I se1 )* Finally, by discussing Figure 1, the injected shunt voltage vector of Newton Raphson load flow solve method and update as Psp, Qssp, Qrsp and V.j 2. Mathematical Formulations of Optimal Power Flow (13) The optimum power flow issue is primarily concerned with minimizing the fuel cost of active power generations and power losses in the power system, given the system's Figure 4. Power Injected Model of C-UPFC 4 i-manager’s Journal on Power Systems Engineering, Vol. 8 l No. 4 l November 2020 - January 2021 RESEARCH PAPERS specified lower and upper limits as follows: operating limits. Ti min £ Ti £ Ti max , i = 1.....NT The optimal power problem seeks to find an optimal profile of active and reactive power generations along with voltage magnitudes in such a manner as to minimize the total operating costs of a thermal electric power system while satisfying networks security constraints. The constraint · Shunt Var compensator constraints Shunt VAR compensators must be restricted by their lower and upper limits as follows: QCimin £ QGCi £ QCimax , i = 1.....NG minimization problem can be transformed into an unconstrained one by augmenting the load flow four types of objective functions of the OPF problem are NG bi Pgi + ci )$/h is the (ai p 2 gi + Objective Function I: Min f1 = å total generation cost function i= 1 VLimin £ VLi £ VLimax , i = 1.....NL (24) Sli £ Slimax , i = 1.....nl (25) · C-UPFC FACTS device constraints VSmin £ VS £ VSmax Ni 2ViV j cos(d PL = g k [Vi 2 + V j2 Objective Function II: Min f 2 = å i -d j ) is the total real power loss 1 i= NL Vrmin £ Vr £ Vrmax ( 1) Vi Objective Function III: Min f 3 = is the total voltage å 2 Vshmin £ Vsh £ Vshmax 1 i= deviation (23) · Security constraints constraints into the objective function. Some well-known identified as below: (22) min max d £ d d s s £ s ng V Lj = 1Fij i Ð q d d å ij + i j Objective Function IV: Min f 4 = V 1 i= j (26) min max d £ d d r r £ r is the sum of the squared voltage stability index. min max d d d sh £ sh £ sh Equality Constraints The equality constraints for the proposed objective 3. MPMJ Algorithm for the Application of Optimum Power functions are as follows. Flow Solution without and with C-UPFC Device · Real power constraints In the following Figure 6, the application of the multi- n 0 PGi PDi Vi V j Yij cos(q d d å ij i + j) = 1 j= (19) · Reactive power constraints) solution of optimal power flow without and with C-NUPFC device. 4. Implementation Steps of the Proposed MPMJ Algorithm n 0 QGi QDi Vi V j Yij cos(q d d å ij i + j) = 1 j= population based modified Jaya (MPMJ) algorithm for the (20) to OPF without and with C-UPFC Device Step 1: Initialize the number of population and design variable Where jÎ [1,n] and, n=number of bus 2.1 Inequality Constraints The Multi Population-based Modified Jaya algorithm is The inequality constraints for the objective functions are as parameterless. There is no tunning parameter, only initialize follows. the number of population (N), design variable (D), and a maximum number of iteration (Itermax) for MPMJ are · Generator constraints chosen and are declared. PGimin £ PGi £ PGimax , i = 1....NG VGimin £ VGi £ VGimax , i = 1....NG (21) QGimin £ QGi £ QGimax , i = 1....NG Step 2: Declaration of data The data such as bus data, line data, tap setting of regulating transformer, load data, generator information · Transformer constraints data, and C-UPFC device locations are declared. Transformer tap settings ought to be restricted within their Step 3: Initialization i-manager’s Journal on Power Systems Engineering, Vol. 8 l No. 4 l November 2020 - January 2021 5 RESEARCH PAPERS Figure 5. Flow chart of the MPMJ Algorithm Generation count set to, iter=0, Initialize a set of random below: values for real power generation, generator voltages, PG,0=rand(0,1) (PGimax-PGimin)+PGimin, PGimin£ PGi£ PGimax, i=1,...,ng transformer tap settings, and reactive power injections of population NP within acceptable range using the equation 6 max VG,0=rand(0,1) (Vimax-Vimin)+Vimin, Vimin£ V£ , i=1,...,ng i Vi max TG,0=rand(0,1) (Timax-Timin)+Timin, Timin£ T£ , i=1,...,nt i Ti i-manager’s Journal on Power Systems Engineering, Vol. 8 l No. 4 l November 2020 - January 2021 RESEARCH PAPERS Figure 6. Flow Chart of MPMJ Algorithm for the Application of Optimum Power Flow Solution without and with C-UPFC Device i-manager’s Journal on Power Systems Engineering, Vol. 8 l No. 4 l November 2020 - January 2021 7 RESEARCH PAPERS max QG,0=rand(0,1) (Qimax-Qimin)+Qimin, Qimin£ Q£ , i=1,...,cs i Qi Step 10: For all updated solutions, if any control variable is beyond the limits, replace the values within the maximum X0=[PG,0, VG,0, QG,0] Step 4: Run the Newton-Rapson load flow without and with or minimum limits. C-UPFC device with this initial population to check the Step 11: Run the Newton-Raphson load flow method feasibility of the solution and satisfaction of equality an without and with the C-UPFC device with these modified control variables to check the solution's feasibility and inequality constraint. Step 5: Allocate the C-UPFC device on the weakest bus. The weakest bus is determined using the voltage stability index. The value of the voltage stability index approach to one or beyond one becomes a weak bus. Similarly, as the satisfaction of equality and inequality constraints. Calculate the objective function values and add the penalty functions to the objective function if the limit's volitation. bus stability index is near to zero, the system becomes Step 12: For each solution, compare the objective function stable, and no need for compensation. from the previous values and the updated solution. Accept Step 6: Define the objective function to be optimized individually, given below. The objective functions are fuel the updated solution is that the values are better than the previous values. Otherwise, keep the previous solution cost of generation, total real power loss, voltage stability Step 13: The program terminates if the termination criterion index, and voltage deviation. Initialize the number of is achieved, else the program continues from step 8. control variables (n) and population size (m), the maximum 5. Result and Discussion number of iterations, and the maximum and minimum The proposed comparison techniques of optimal power limits of control variables. flow solutions are evaluated using the IEEE-57 bus system. ng f1 = F ( PG ) = bi PGi + ci ) (ai PGi2 + å i= 1 Nl 2Vi V j cos(d d f2 = PL = g k [Vi 2 + V j2 å i j )] 1 i= 2 NL f3 = VD = ( Vi 1) å Bus systems have 7 generators in buses 1, 2, 3, 6, 8, 9, and 12, seventeen off-nominal tap-ratio transformers in branches 19, 20, 31, 35, 36, 37, 41, 46, 54, 58, 59, 65, 66, 71, 73, 76 and 80 and three shunt VAR compensation in buses 18, 25 and 53 (Le Dinh et al., 2013). The single line diagram has been seen in Figure 5.The proposed method i= 1 is tested under normal operating conditions. Under this V 1f4 = Lj = Fij i Ð q d d å ij + i j Vj 1 i= operating condition, the optimal power flow simulations ng Step 7: Run the power flow program for each candidate solution without using the C-UPFC device for all objective functions. Step 8: Identify the best and worst solutions among the candidate solutions. Step 9: Based on the value of best and worst conditions, modify all the candidate solutions, the proposed multi population-based modified Jaya algorithm modifications expressed using equation (2). Based on the flow chart of multi-population, and pseudo-code of multi-population, divide the population into sub-population, compare the are carried out without using the C-UPFC device at five selected lines. Finally, the overall best location of the CUPFC device is obtained using the Analytical Hierarchy Process (AHP) method. In each case study, each objective function is optimized individually. Also, the obtained results are compared with those reported in the literature. The case studies for simulation are as follows under normal operating conditions: Case I: Single-objective optimization without C-UPFC device Case II: Single-objective optimization with C-UPFC device at the selected locations new solution with the old solution for each sub-population, Case III: Application of AHP methods for determination of and finally identify the best discarded the worst solution. the optimal location of C-NUPFC device 8 i-manager’s Journal on Power Systems Engineering, Vol. 8 l No. 4 l November 2020 - January 2021 RESEARCH PAPERS 5.1 Case I: Single-Objective Optimization without C-UPFC proposed MPMJ algorithm reaches the best solution within Device a few numbers of iterations under all objective functions. There is a lot of optimization algorithm in the literature This shows the convergence reliability of the proposed review to solve the optimal power flow solution. In this MPMJ algorithm. paper, compare to the TLBO, JAYA, and proposed MPMJ Figure 8 (a) shows the convergence of fuel cost of algorithm in terms of getting optimal values of the generation of the IEEE 57-bus test system under normal objective functions (minimizing of fuel cost of the operating conditions. The minimum costs obtained using generator, minimizing of active power loss, the sum of TLBO, JAYA, and proposed MPMJ algorithms are voltage deviation improvement, and enhancement of 41167.56$/hr, 41159.25$/hr, and 41158.16$/hr, voltage stability index on the bus), and convergence respectively. Figure 8(b) shows the convergence of total characteristics for the IEEE-57 bus system. In each case real power loss of the IEEE 57-bus system under normal study, 10 test runs were performed for solving the OPF operating conditions. The minimum power losses obtained problems. using TLBO, JAYA, and proposed MPMJ algorithms are Figures 8(a)-8(d) shows the total fuel cost of generation, 0.1520p.u, 0.1481pu and 0.148pu respectively. Figure 8(c) active power losses, the sum of bus voltage deviation, and shows the convergence of the sum of voltage deviation of voltage stability index for the original power system without the IEEE 57-bus system under normal operating conditions. connecting any C-UPFC device for the IEEE-57 bus system. The minimum sum of voltage deviation obtained using It is seen from Figures 8(a)-8(d), it can be observed that the TLBO, JAYA, and proposed MPMJ algorithms are 1.0111p.u, Figure 7. IEEE-57 Bus Network Single Line Diagram i-manager’s Journal on Power Systems Engineering, Vol. 8 l No. 4 l November 2020 - January 2021 9 RESEARCH PAPERS 0.856pu and 0.7011pu respectively. Figure 8(d) shows the in the transmission system is anticipated to increase in the convergence of the voltage stability index of the IEEE 57- future because of utility deregulation and power wheeling bus system under normal operating conditions. The requirement. The utilities need to operate their power minimum of voltage stability index obtained using TLBO, transmission system much more effectively, increasing their JAYA, and proposed MPMJ algorithms are 0.2651, 0.2578 utilization degree. Because of the power electronic and 0.2463, respectively. Figure 8(a)-8(d) shows that the switching capabilities in terms of control and high speed, proposed MPMJ algorithm reaches the best solution within more advantages have been done in areas of FACTS a few numbers of iterations under all objective functions of devices, and the presence of these devices improve the the IEEE 57-bus system without C-UPFC device. performance of the power system. To get the maximum Table 7 summarized all objective function results in benefit, selecting the best location of FACTS devices plays comparisons with recent literature. From the comparison an important role. provided in Table 7, the proposed MPMJ result is better than The proposed MPMJ algorithm is applied for solving the the costs, power loss, voltage deviation and the sum of optimal power flow problems subjected to different squared voltage stability index obtained by the algorithms equality and inequality constraints with the location of the mentioned in the literature. C-UPFC device in the selected buses under normal 5.2 Case II: Single-objective Optimization with C-UPFC operating conditions. The selected locations of C-UPFC are Device At The Selected Locations the lines 9-13,9-12,56-41,9-10 and 54-55. These locations Nowadays, the need for flexible and fast power flow control (a) are taken based on the first five maximum voltage stability (b) 4 proposed MPMJ JAYA TBLO Sumof voltage variation (pu) 3.5 3 2.5 2 1.5 1 0.5 0 20 40 60 80 Number of Iteration (c) 100 120 140 150 (d) Figure 8. Convergence Characteristics of the (a) Fuel Cost of Generation without C-UPFC Device (b) Total Active Power Loss without C-UPFC Device (c) Total Active Power Loss without C-UPFC Device (d) The Sum of Squared Voltage Stability Index without C-UPFC Device 10 i-manager’s Journal on Power Systems Engineering, Vol. 8 l No. 4 l November 2020 - January 2021 RESEARCH PAPERS index of the lines from the transmission line steady-state problem cannot obtain a solution that satisfies other values. The value of the voltage stability index at lines 9- objective functions. Hence, for achieving a result that 13,9-12,56-41,9-10, and 54-55is0.1747, 0.1667, meets some objectives, it is necessary to use the Analytical 0.1652,0.1649, and 0.1402, respectively. The line stability Hierarchy Process method. Thus, after solving the OPF index for all the transmission line is shown in Figure 9. problem for different alternatives of the objective The proposed MPMJ algorithm is applied for solving the OPF functions/attributes, these values are given as input to AHP problem with four different objective functions. In each methods to select the best C-UPFC installation in the IEEE case study, four sets of 10 test runs were performed for 57-bus test system. solving the OPF problems under normal operating 5.3 Case III: Application of AHP Methods for conditions. All the solution satisfies the constraints on Determination of the Optimal Location of C-UPFC Device reactive power generation limits and line flow limits. To get the optimal operation of the power system within the Table 1 gives the total fuel cost of generation, total real constraint, the selection of the best location of FACTS power loss, the sum of squared voltage stability index, and devices plays an essential role in the process of the power the voltage deviation with the C-UPFC device at the system. Therefore, different techniques are explained in the selected locations for IEEE-57 bus. Table 1 shows that each literature to select the best position of FACTS devices. Still, candidate bus has given minimum attributes (objective the methods are their advantages, and the disadvantages function value) as the best value than optimization without depend on the system optimal operation. In this paper, the the C-UPFC device. Also, from Table 1, it can be observed Analytical Hierarchy Process (AHP) is used to select the C- that under normal conditions, the optimal value for the cost UPFC FACTS device best position since the AHP methods of generation is 41096.7$/hr at line 54-55, and the optimal considered all the four objectives of fuel cost of the value for power loss is 0.1016pu at line 9-13, the optimal generator, active power loss, the bus voltage deviation, value for the sum of squared voltage stability index is and the sum of squared voltage stability index. 0.220pu at line 56-41, an optimal value for the voltage Thus, the AHP method is applied to differentiate the best deviation is 0.58pu at line 56-41. With this, one can say that alternative out of five considered alternatives. The optimal under normal conditions, optimal values of four attributes power flow solution is displayed in Table 1 for five weakest are obtained at different alternatives. Therefore, it is tough lines using the proposed MPMJ algorithm, since as to differentiate the best option from considered five compared in Table 6 with TLBO, and JAYA algorithm, alternatives that operate the power transmission system proposed MPMJ algorithm-based result is the most more effectively and efficiently. It is also clear that optimal. The OPF results with the C-UPFC device are shown considering a specific objective function in the OPF in Table 1, used as a decision matrix for the system and Figure 9. Line Stability Index for the IEEE-57 Bus System i-manager’s Journal on Power Systems Engineering, Vol. 8 l No. 4 l November 2020 - January 2021 11 RESEARCH PAPERS Alternatives Attributes Attributes From line To line Fuel Cost ($/h) Power Loss (pu) VSI VD (pu) Objective Fuel Cost ($/h) Power Loss (pu) VSI VD (pu) 9 9 56 9 54 13 12 41 10 55 41104.1 41106.8 41098.4 41101.3 41096.7 0.1016 0.1340 0.1120 0.1240 0.1046 0.229 0.231 0.220 0.2321 0.221 0.645 0.609 0.58 0.601 0.608 Fuel cost Power loss VSI VD 1 0.5 0.5 0.5 2 1 0.5 0.5 2 2 1 0.5 2 2 2 1 Table 2. Pairwise Comparison Matrix for Attributes for IEEE-57 Bus Table 1. OPF Results And Decision Table for the AHP Method for IEEE-57 bu values of the sum of voltage deviation attribute. then given as an input to the AHP method. From Table 1, Table 3 is the attributes weight matrix, and a normalized one or two alternatives give the best value when principal eigenvector called a priority vector or weight compared to optimization with C-UPFC located at other matrix of the attributes. Since it is normalized, the sum of all alternatives. It is challenging to differentiate the best attributes in the priority vector is 1, and the Priority vector alternatives out of considered five alternatives that operate shows relative weights among the things that we compare. the power transmission system more effectively and Table 3 shows that 39.05% of priority is given to the cost efficiently. It is also clear that considering a specific attribute, 27.61% priority is given to the power loss attribute, objective function in the OPF problem cannot obtain a 19.53% priority is given to the voltage stability index, and solution that satisfies other objective functions. Hence, for 13.81% is given to the sum of voltage deviation attributes. achieving a result that meets some objectives, it is Table 3 shows that the total fuel cost of generation is the necessary to use Analytical Hierarchy Process methods. essential criterion or attribute. The second most important Thus, after solving the OPF problem for different alternatives criterion is the total real power loss. The third most important of the objective functions, and these values are given as criterion is the voltage stability index and the least input to AHP methods to select the best location for C-UPFC importance given to the voltage deviation attribute. This installation in the IEEE-57 bus test system. weight matrix or eigenvector determines the relative The pairwise comparison matrix shown in Table ranking of alternatives under each criterion. 2determines the preference of each attribute over Since it is normalized, the sum of all attributes in the priority another. In pairwise comparison Table 2, diagonal vector is one, and the Priority vector shows relative weights elements are taken as 1, which means objectives are of among the things that we compare. This shows that the equal importance. The upper diagonal elements of the considered preference matrix or pairwise comparisons are matrix have been taken by giving preferences to the acceptable because the degree of consistency or attributes, and the lower diagonal elements of the matrix Consistency ratio is 0.0454, which is smaller than 10%, have been taken as a reciprocal of the upper diagonal where the consistency is acceptable. Random elements of the matrix. In upper diagonal elements of the Consistency index (RCI) is 0.9. matrix, the first-row second column is taken as 2 which Table 4, shows the relative ranking of alternatives under five means that the cost attribute is the intermediate values of objective functions: the minimization of fuel cost of the the power loss attribute, the first row third and fourth columns are taken as 2 that means that cost attribute is the intermediate values of the voltage stability index and voltage deviation attributes. Similarly, the second-row third column is taken as 2, which means the power loss attributes the intermediate values of the voltage stability index attribute. The second-row fourth column is taken as 2, which means the power loss attribute is the intermediate 12 Objective Weight-Age Fuel cost Power loss VSI VD 0.3905 0.2761 0.1953 0.1381 Subjective measurement of attributes Assigned values Eigen value Consistency index Consistency ratio 4.1213 0.0404 0.0454 Table 3. Weight Matrix and Value of Attributes for IEEE-57 Bus i-manager’s Journal on Power Systems Engineering, Vol. 8 l No. 4 l November 2020 - January 2021 RESEARCH PAPERS From bus To AHP Ranking Algorithms CPU Time (s) 56 54 9 9 9 41 55 13 12 10 2 1 4 5 3 DE(Basu, 2011) RCGA (Basu, 2011) ALC-PSO (Singh et al., 2016) KHA (Mukherjee & Mukherjee,2016) OKHA (Mukherjee & Mukherjee,2016) Proposed MPMJ 689.9 874.9 680.12 671.2 654.11 607.3 Table 4. Weakest Bus Ranking by AHP Methods for IEEE- 57 Bus Table 5. Proposed MPMJ Computational Time Comparison generator, minimizing the sum of voltage deviation, enhanced from 0.242pu by TLBO to 0.233pu by JAYA, and minimizing active power loss, and enhancing the voltage 0.221pu by proposed MPMJ Algorithm. stability index by the AHP method. Therefore, the AHP method under normal operating conditions gives the alternative line 54-55 for the C-UPFC location to the IEEE-57 bus system. So, it is considered an optimal location for CUPFC device among the lines considered for the system, which gives the highest benefits to the power system operation in terms of performance parameters. The convergence time for the OPF results without and with the C-UPFC device under normal operating conditions are also given in Table 6. The convergence characteristic of each objective function with C-UPFC at line 54-55 is shown in Figures 10(a)-10(d), which shows smooth convergence to the optimum value without any abrupt oscillations for the best run under normal operating conditions respectively. From Table 6, under normal load case, it is clear that the Tables 5 shows that the optimal the computational time control setting corresponding to the OPF with cost comparison of the proposed MPMJ algorithm with recent minimization with the C-UPFC device at line 54-55. The literature for IEEE-57 bus system without C-UPFC device. As optimized fuel cost value using TLBO, JAYA and proposed seen from the result, the proposed MPMJ algorithm MPMJ algorithm is 41116.34$/h, 41100.72$/h, and converged with less computational time. 41096.7$/h, respectively. The total active power loss enhancement from 0.1203pu by TLBO to 0.1163pu by JAYA, and 0.1046pu by proposed MPMJ algorithm. The sum of voltage deviation improved 0.786pu by TLBO to 0.716pu by JAYA, and 0.608 pu by proposed MPMJ algorithm. Similarly, the minimum voltage stability index is Algorithm TLBO Performance Parameters Fuel cost ($/hr.) Real power loss(pu) ∑Voltage deviation(pu) L-index CPU time (s) Fuel cost ($/hr.) Real power loss(pu) JAYA ∑Voltage deviation(pu) Proposed MPMJ L-index CPU time (s) Fuel cost ($/hr.) Real power loss(pu) ∑Voltage deviation(pu) L-index CPU time (s) Cost According to the simulation result from Figure 11 to Figure 14 comparison analysis was shown for the techniques TLBO, JAYA, and proposed MPMJ algorithm without FACTS device for each generator's generated power, active power loss in the transmission line, voltage magnitude at the load bus. Power Loss Voltage Deviation L-Index without with without with without with without with 41167.56 0.172 1.22 41116.34 0.164 1.109 43000 0.1502 2.0595 42367 0.1203 1.980 43248 0.19 1.0111 42154 0.185 0.786 44080 0.20 2.04 42056 0.194 1.983 0.4871 628.3 41159.25 0.162 1.13 0.410 638 41100.72 0.155 1.101 0.312 696.5 43908 0.1481 2.043 0.28 708 42353 0.1163 1.936 0.368 620.6 43228 0.189 0.8561 0.3364 635 42133 0.1837 0.716 0.2651 621.5 43040 0.198 2.012 0.242 630 42006 0.190 1.863 0.4671 617.3 41158.15 0.1601 1.111 0.404 624 41096.7 0.152 1.09 0.302 685.5 43906 0.148 2.022 0.287 698 42340 0.1046 1.907 0.3632 609.6 43216 0.178 0.7011 0.3346 620 42125 0.1741 0.608 0.2578 610.5 43030 0.188 1.986 0.233 618 41984 0.1815 1.842 0.4571 607.3 0.40 615 0.3011 663.5 0.285 680 0.3582 602.5 0.3336 614 0.2463 608.4 0.221 616 Table 6. Performance Parameters Comparison for IEEE 57-Bus Test System without and with C-UPFC Device at line 54-55 i-manager’s Journal on Power Systems Engineering, Vol. 8 l No. 4 l November 2020 - January 2021 13 RESEARCH PAPERS (a) (b) (c) (d) Figure 10. (a). Convergence characteristics of the fuel cost of generation without C-UPFC device (b). Convergence characteristics total active power loss without C-UPFC device (c). Convergence characteristics of voltage deviation without C-UPFC device (d). Convergence characteristics of sum of squared voltage stability index without C-UPFC device Figure 11. Variation of Generated Power for the IEEE-57 Bus System 14 Figure 12. Variation of Voltage Magnitude at the Load Bus for the IEEE-57 Bus System i-manager’s Journal on Power Systems Engineering, Vol. 8 l No. 4 l November 2020 - January 2021 RESEARCH PAPERS conditions. Similarly, the bus's voltage angles were compared in Figure 14, and the angles maintain the values within the minimum and maximum limits for normal operating conditions. Conclusion This paper solves optimal power flow with the C-UPFC FACTS device's inclusion using the proposed MPMJ algorithm. The proposed algorithm compares and presents Teaching Learning-based optimization and JAYA algorithm without Figure 13. Variation of Active Power Loss in the Line for the IEEE-57 Bus System and with C-UPFC FACTS device considering different objective functions under normal operation for system performance improvement. Also, the performance of the proposed algorithm compared with another algorithm in recent literature. The Centre-Node Unified Power Flow Controller (C-UPFC) is a flexible system capable of regulating the corresponding voltage magnitude, phase angle and line impedance individually. Analytical Hierarchy Process methods distinguish the best location for C-UPFC devices from considered locations in system output parameters. The suggested solution was Figure 14. Variation of Voltage Magnitude at the Load Bus for the IEEE-57 Bus System successfully and efficiently applied to find optimal control According to the result, the obtained result using proposed test systems have been presented for illustration purposes. MPMJ optimization technique achieved better than the In general, it was observed through the present case of variables settings. The simulation results on the IEEE-57 bus others. Figure 12 shows that the load bus voltages and the optimal power flow solution with and without C-UPFC percentage of voltages change are maintained within device that the proposed MPMJ algorithm provides their minimum and maximum limits (from -10% to +10%), accurate results with less computational effort, time and ensuring the system's security under normal operating optimal results. Algorithm AMO (Chinta et al., 2018) SSA (El-Fergany & Hasanien, 2020) MSA (Mohamed et al., 2017) MVO CRO (Dutta et al., 2016) ICEFO (Bouchekara, 2020) CKHA (Mukherjee & Mukherjee, 2015) MOALO (Herbadji et al., 2019) FCGCS (Chen et al., 2017) AGO with UPFC device (Alhejji et al., 2020) AGO with C-UPFC device (Alhejji et al., 2020) TLBO JAYA Proposed MPMJ Fuel Cost ($/h) Real Power Loss (mw) Voltage Deviation (p u) L-Index 41679.83 41672 41673.72 41678.084 NR 41706.1117 41660.4657 41623.1352 41666.6316 NR NR 41167.56 41159.25 41158.16 15.955 11.321 15.0526 15.1751 25.3584 15.72 15.45 14.81 NR 11.1153 10.708 15.02 14.81 14.8 0.7582 0.7569 NR NR 1.1796 0.6798 0.7247 0.830 0.7507 0.7596 0.7076 1.0111 0.8561 0.7011 NR 0.259 0.27481 NR 0.5784 0.2740 NR NR 0.2742 0.2336 0.2266 0.2651 0.2578 0.2463 Table 7. 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His area of research includes power system optimization, application of FACTS device in power system, and power system protection and coordination. K. Padma received the B.Tech degree in electrical and electronics engineering from SV University, Tirupathi, India in 2005, M.E, and Ph.D degree from Andhra University, Visakhapatnam, India in 2010, and 2015. She is currently working as an Assistant Professor in the department of electrical engineering, AU College of engineering, Visakhapatnam, A.P, India. Her research interest includes power system operation, and control, power system analysis, power system optimization, soft computing applications and FACTS. i-manager’s Journal on Power Systems Engineering, Vol. 8 l No. 4 l November 2020 - January 2021 17