Solution of Optimal Power Flow Problem with FACTS Devices Using Grey Wolf Optimizer Algorithm

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1 Solution of Optimal Power Flow Problem with FACTS Devices Using Grey Wolf Optimizer Algorithm R.H.Bhesdadiya Dilip P Ladumor ladumordilip56@gmail.com Indrajit N. Trivedi G.E. College Gandhinagar-Gujarat, India forumtrivedi@gmail.com Pradeep Jangir pkjmtech@gmail.com Mahesh H. Pandya pandyamh@rediffmal.com Ashok Parmar abparmar80@gmail.com Abstract For the operation and planning of the power system optimal power flow is main tool. Optimal power flow is highly constrained and non-linear problem of the power system. So for the solution of OPF problem different techniques are reported in literature review. In this proposed paper we introduced a new nature inspired meta-heuristics Grey Wolf Optimization algorithm for the solution of OPF problem by FACTS device. Grey Wolf Optimizer was inspired by the hunting behavior of the grey wolves.in this proposed paper we are consider IEEE-30 bus test system for detering the effectiveness of proposed algorithm and we are considering total three different cases or three objectives. Then we compared proposed algorithm with some well-known algorithm which was reported in literature. From this analysis we realized that proposed GWO algorithm gave the best solution for all over the three cases with compared to some well-known evolutionary algorithm. Index Terms Optimal Power Flow, Grey Wolf Algorithm, Nature-inspired, Fuel Cost, Active Power Loss, Reactive Power Loss, FACTS. I. INTRODUCTION First of all, at earlier of 960s Optimal Power Flow was proposed by Dommel and Tinney [, 2]. Optimal power flow is the primary tool for the operation and planning of power system. OPF problems are highly constrained, Non-linear and non-convex problem of the power system. There are many optimal power flow problems in power system like Fuel Cost of generation, active and reactive power losses, transformer tap changing and voltage deviations.so the primary objective of OPF problem is optimization of objective function by satisfying some equality and inequality constraints simultaneously [3,4]. Now a day s new Flexible AC Transmission system (FACTs) devices is used for solution of optimal power flow problem due to the recently development in the power electronics devices. FACTs devices improve the power transfer capacity of the transmission line and maintain the stability of the system. In this Proposed paper we use two different FACTS devices for the solution of OPF problems namely SVC (Static VAR Compensator) and STATCOM (static Synchronous Compensator) [2-5]. There are many techniques are reported in literature for optimization of OPF problems. Some traditional methods which were used for optimization of OPF are Newton Based Method, Interior Point Method (IPM), Quadratic Programg (QP), Linear Programg (LP), and Non- Linear Programg (NLP), but these techniques not able to give the global solution it is used for the local solution.in recent years many evolutionary algorithms are used for optimization of OPF, some well-known techniques which is reported in literature are Genetic Algorithm (GA), Improved Genetic Algorithm (IGA) [8], Tabu Search Algorithm (TSA) [], Particle Swarm Optimization (PSO)[7] algorithm, Black-Hole Based Optimization (BHBO)[5], Biogeography Based Optimization (BBO)[2], Differential Evolutionary (DE)[8], Simulated Annealing (SA)[9],Electromagnetism Like Mechanism (EM) [3], Enhanced Genetic Algorithm (EGA)

2 [4], Modified Differential Evolutionary Algorithm, Gradient Method (GM)[8] etc. II. MODELLING OF FACTS DEVICE Up to 999 mechanical controller like Automatic Generation Control (AGC), Excitation control etc. are used for the control of Active and Reactive power and for other power flow parameters. But Now a day s new Flexible AC Transmission system (FACTs) devices is used for solution of optimal power flow problem due to the recently development in the power electronics devices. Flexible AC Transmission System (FACTs) device was first introduced by Hingorani in 999. FACTs devices improve the power transfer capacity of the transmission line and maintain the stability of the system and also improve the voltage profile of the system. In this Proposed paper we use two different FACTS devices for the solution of OPF problems namely SVC (Static VAR Compensator) and STATCOM (static Synchronous Compensator) [,2]. Static VAR Compensator (SVC) is used for improve the voltage profile during steady state and dynamic condition. SVC only exchange the reactive power it is not supply or absorb active power like STATCOM. Static Synchronous Compensator (STATCOM) is shunt connected compensator connected across the buses. It is depending on the voltage converter due to absence of passive elements so size is smaller as compare to the SVC. In STATCOM exchange of reactive power is proportional to bus voltage magnitude but in SVC it is proportional to square of bus voltage magnitude, so STATCOM is much better than compared to SVC. From the result we can observed that STATCOM gave the best performance for OPF compared to the SVC []. III. PROBLEM FORMULATION FOR OPF In OPF for imizing of some objective functions like Fuel Cost, Power Losses, Voltage Deviations etc. optimal setting [4] of Control Variable are adjusted so constraints are satisfying. Some functions are described as per follow Minimize J ( x, u ) () g( x, u ) = 0 (2) h ( xu, ) 0 (3) Where (u) is control variable, (x) is state variable, J(x, u) represents imum fuel cost, g(x, u) and h(x, u) represents Equality and Inequality constraints respectively. A. Control Variable Control variable u is set of variable and it is defined as per follow T u = PG P,,, 2 G V NG G V G Q NG C Q C T N T NT (4) Where NG, NT and NC are number of generators, number of tap changing transformer and number of static VAR compensators respectively. In above equation PG represents Active Power generation at PV bus, VG represents voltage magnitude at PV buses, T represents transformer tap setting and QC represents shunt VAR Compensations. B. State variable State variable x is defined by the following equation in OPF T x = P, V V, Q Q, S S (5) G L LNL G GNG l lnl Where NL and nl are the load bus and transmission line respectively. In above equation PG represents active power at slack bus, VL represents voltage magnitude at load buses, QG and S represents reactive power and line loading respectively. l C. Constraints There are some equality and equality constraints in optimal power flow problem. Equality Constraints Real reactive power generation constraints are considering as an equality constraints and it is described as per follow NB ( θ ) ( θ ) (6) P P V V G cos B sin + = 0 Gi Di i j ij ij ij ij j= NB ( θ ) ( θ ) (7) Q Q V V G sin B cos + = 0 Gi Di i j ij ij ij ij j= Where NB is the number of buses, Demand, power generation, P G is active power generation, G ij and P D is the total power QG is the reactive B represents conductance and susceptance between bus i and j respectively. 2. Inequality Constraints In optimal power flow problem there are some inequality constraints of physical device as follow a. Generator constraints Voltage, active power and reactive power limit of the generator is described as per follow V V V, i =,..., NG (8) Gi Gi Gi ij P P P, i =,..., NG (9) Gi Gi Gi Q Q Q, i =,..., NG (0) Gi Gi Gi b. Transformer constraint Transformer tap setting limit given by following constraint T T T, i =,..., NT () i i i c. Shunt VAR Compensator Constraints Limits of VAR compensator given by Q C Q, i =,..., i CG Q i C NG (2) i d. FACTS device Constraints In this proposed paper we use two FACTs device their imum and imum limits are given as per follow Q Q Q, i =,..., N SVCi SVCi SVCi SVC Q Q Q, i =,..., N STATi STATi STATi STAT

3 3. Security Constraints Bus voltage and line loading must be in their upper and lower limit and their constraints is given by V V V, i =,..., NL (3) S Li Li Li li S, i =,...,nl li In this paper we also consider the penalty and penalty factor is given by the following equation NG nl ( ) 2 λ S S i i + λ + s V l l i= i= NG nl ( ) 2 λ S S (4) i i + λ + s V l l i= i= Where λ P, λ V, λ s and λ V are the penalty factors and lim x is the limit value of variable x and it is given by following equation x lim > = x ; x< x x ; x x IV. GREY WOLF OPTIMIZER ALGORITHM (5) A novel nature inspired, Grey wolf optimizer algorithm [0] based on the hunting mechanism. Wolves are a member of a troop in which a number of the grey wolves is the population size or wolves that take part in hunting. Wolves in a troop are separated according to their leadership quality. Troop consists of four types of wolfs alpha, beta delta, and omega. Alpha wolfs have higher doance and decision maker in the troop and rest of wolfs have their doance decreasing sequentially as the name above written [0]. The main phase of grey wolf hunting are as follows: a. Tracking, chasing and approaching the prey. b. Pursuing, encircling, and harassing the prey unit it stops moving. c. Attack towards the prey. A. Grey Wolf Encircling Prey [5] Position updating of grey wolf and prey is shown in Fig.2 2D position vectors and their possible next locations are shown in Fig. Each of the behaviors is mathematically modelled as: The Encircling prey is calculated as following equations D = C X pt () X() (6) t X ( t ) = X p( t) A D (7) + Where, t=current iteration, X p = position vector of the prey, = X = position vector of grey wolf, AC, coefficient vectors are calculated by equation (8) and equation (9) A= 2a r a C = 2 r 2 (8) (9) Where, components of a are linearly decreased from 2 to 0 over the course of iterations and r, r2 are random vectors in [0, ]. Fig.. Best position of wolves The Hunting process is calculated as follows equation D = C X X α 2 α D = C X X β 3 β D = C X X δ δ X = X A D α 2 β 2 ( α) X = X A D ( β ) X = X A D 3 δ 3 ( δ ) (20) (2) (22) (23) (24) (25) B. Exploitation Process A method that used any information to generate a new solution that is the better than existing solution. It used in Algorithm for finding local optimum value. In exploitation process, optimal solution is find when prey is in stationary position then the grey wolf attack on the prey. In Fig.2 grey wolf attack on the prey [0]. The vector A is a random value in the interval [-2a, 2a], where a is decreased from 2 to 0 over the course of iterations. When suitable position ready to attack on the prey for find the optimal solution (exploitation process).

4 C. Exploration Process [0] In exploration process, it possible to explore the search space more efficiently & generate global optimum value that enough diversity and far from current solutions. When diverge away from the prey and again find the optimal position of prey. Fig.2. Positon of the Grey Wolves V. RESULTS AND DISCUSSION In this proposed paper we used nature inspired new developed meta heuristic Grey Wolf Optimizer algorithm for the solution of the OPF problem by FACTs devices. GWO was inspired by the hunting behavior of Grey Wolves and it was proposed by Mirjali in 204.for detere the effectiveness of proposed algorithm we consider standard IEEE-30 Bus Test system for optimization of OPF problem by the GWO algorithm. In IEEE-30 bus system Buses,2,5,8, and 3 are generator bus, at,2,5 and 30 transformer tap changer and nine VAR compensator are put at bus 0,2,5,7,20,2,23,24 and 29.in this proposed paper we used two FACTs devices SVC at bus 2 and STATCOM at bus 29. Total load demand is MW and rating of the SVC and STATCOM are in range of 0 to 0 MVAr. In this paper we are considered total five cases for solution of OPF problems. Case- In this case our main aim is to meet the load demand with imum fuel cost. As per predicted in table- and table-2 use of FACTs devices (SVC and STATCOM) gave the better result as compared to without use of FACTs device. In the fig- 3 shows the comparison for the fuel cost with and without FACTs devices. Case-2 In the second case we are consider two objectives namely Fuel Cost and Voltage Deviation simultaneously. By imizing the voltage deviation with use of FACTs devices we can improve the voltage profile.as per shown in the table-. Use of FACTs devices gave the best fuel cost and least voltage deviation as compared to without use of FACTs devices. In fig-4 shows the best solution for voltage deviation with imum fuel cost. The objective function expressed by equation as per follow. J = J + wj Cost Voltage Deviation Where w is weighting factor which is selected by user to give the importance to one from two objective function. J voltage Deviation NL = V.0 i= i Case-3 In this case we consider the voltage stability. The voltage stability is the main issue of the power system. By using FACTs devices (SVC and STATCOM) we can improve the stability of the power system. in this case we consider voltage stability with the fuel cost and objective function is given by the following equation. Here l J denote the voltage stability. From the table and figure-5 we can says that use of FACTs devices gave the best result. NG Vi Lj = HLG j =,2,... NL ji V (29) i= J = J + wj j Cost Voltage S tability Enhancement Fig.3. Convergence Curve for Best Fuel cost Fig.4. Convergence Curve for Voltage Deviation

5 Table. Optimal setting of control variable with and without FACTs devices WITHOUT SVC WITH SVC case- case-2 case-3 xase-4 case-5 case- case-2 case-3 case-4 case-5 PG PG PG PG PG PG VG VG VG VG VG VG TC($/hr) NA NA PLOSS(MW) NA NA QLOSS(MVAR) NA NA VD NA NA L NA NA Fig. 5. Convergence Curve for Voltage Stability Fig. 6. Convergence Curve for Active power loss Fig. 7. Convergence Curve for Reactive power loss In the fig-5 shows the variation in fuel cost and stability over the iterations with FACTs devices. Case-4 Losses in the transmission line is one of the major issue of OPF.in this case we consider the Active Power losses and it is denoted by the following equation. NB NB NB P = P P i Gi Di i= i= i= As per shown in the tables and fig use of FACTs device resulted imum active power losses so we can increase the power transfer capability of the line by using Flexible AC Transmission system. As per shown in fig USE of FACTs device gave the optimal solution for active power loss.

6 Table.2 Optimal setting of control variable with STATCOM WITH STATCOM case- case-2 case-3 case-4 case-5 PG PG PG PG PG PG VG VG VG VG VG VG TC($/hr) PLOSS(MW) QLOSS(MVAR) VD L Case-5 In the last case we consider the reactive Power losses and from the tables we observed that proposed GWO algorithm gave the imum reactive power losses by using FACTs devices compared to without FACTs devices. In the fig-6 shows optimal solution for reactive power over the iterations. Reactive power is described by the following equation. NB NB NB Q = Q Q i Gi Di i= i= i= CONCLUSION In this proposed paper we use nature inspired Grey Wolf Optimizer algorithm for optimization of Optimal Power Flow with and without FACTs devices. We are considered IEEE-30 Bus Test system for check the effectiveness of the facts devices for solution of OPF problem. From the result analysis we conclude that use of FACTs devices (SVC and STATCOM) gave the solution for all five cases which we are consider in this paper compared to without use of FACTs devices. By using FACTs devices, we can increasing the transfer capability of the line and improve the system stability. For the future work we can also use the TCSC and UPFC for the solution of optimal power flow problems. REFERENCE []. H.R.E.H. Bouchekara, Optimal power flow using blackhole-based optimization approach, Applied Soft Computing Xxx (204) xxx-xxx. [2]. N.M.Jothi Swaroopan, P. Somasundaram, Fuzzzified PSO algorithm for OPF with FACTs devices in interconnected power systems, Springer-verlag Berlin Heidelberg 200. [3]. Basu, M.: Optimal power flow with FACTS devices using differential evolution. Electrical Power and Energy Systems 30, (2008) [4]. Biskas, P.N., Bakirtzis, A.G.: Decentralized security constrained DC-OPF of interconnected power systems. In: IEE Proceedings Generation, Transmission and Distribution,vol. 5(6), pp (2004) [5]. Chung, T.S., Ge, S.: Optimal power flow incorporating FACTS devices and power flow control constraints. In: IEEE Conference, vol. 98, pp (998) [6]. Ge, S.Y., Chung, T.S., Wong, Y.K.: A new method to incorporate FACTS devices in optimal power flow. In: IEEE Conference, vol. 98, pp (998) [7]. Mojtaba Ghasemi, Sahand Ghavidel, Ebrahim Akbari, solving non-linear, non-smooth and non-convex optimal power flow problems using chaotic invasive weed optimization algorithm based on chaos, Energy xxx (204) -4. [8]. R.B. Squires, Economic dispatch of generation directly from power system voltages and admittances, IEEE Trans. Power Appar. Syst. 79 (3) (96) [9]. J. Carpentier, Contribution a letude du Dispatching Economique, Bull. Soc.Franc. Electr. (962) [0]. Seydali Mirjali, Sharhazad Saremi, Mohammad Mirjali, A Multi objective grey wolf optimizer A-novel algorithm for multi-objective criterion optimization 47 (206) []. A. Bhattacharya, P.K. Chattopadhyay, Application of biogeography-based opti-misation to solve different optimal power flow problems, IET Gener. Transm.Distrib. 5 () (20) [2]. A.A. Abou El Ela, M.A. Abido, Optimal power flow using differential evolutionalgorithm, Electr. Power Syst. Res. 80 (7) (200) [3]. C.A. Roa-Sepulveda, B.J. Pavez-Lazo, A solution to the optimal power flowusing simulated annealing, Int. J. Electr. Power Energy Syst. 25 () (2003) [4]. H.R.E.H. Bouchekara, Optimal power flow using electromagnetism-like mech-anism, Electr. Power Syst. Res. (203) (under review). [5]. K. Vaisakh, L.R. Srinivas, Genetic evolving ant direction HDE for OPF with non-smooth cost functions and statistical analysis, Expert Syst. Appl. 38 (20) [6]. H.R.E.H. Bouchekara, Optimal design of electromagnetic devices using a Black-Hole-based optimization technique, IEEE Trans. Magn. 49 (203) [7]. L.L. Lai, J.T. Ma, R. Yokoyama, M. Zhao, Improved genetic algorithms for optimalpower flow under both normal and contingent operation states, Int. J. Electr.Power Energy Syst. 9 (5) (997) [8]. A.G. Bakirtzis, P.N. Biskas, C.E. Zoumas, V. Petridis, Optimal power flow byenhanced genetic algorithm, IEEE Trans. Power Syst. 7 (2) (2002)

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