Improved optimal power flow for a power system incorporating wind power generation by using Grey Wolf Optimizer algorithm

POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 16 |NUMBER: 4 |2018 |DECEMBER Improved Optimal Power Flow for a Power System Incorporating Wind Power Generation by Using Grey Wolf Optimizer Algorithm Sebaa HADDI, Omrane BOUKETIR, Tarek BOUKTIR Department of Electrical Engineering, Faculty of Technology, University of Setif, El Bez, 19000 Setif, Algeria [email protected], [email protected], tarek.b[email protected] DOI: 10.15598/aeee.v16i4.2883 Abstract. In this paper, an efficient Grey Wolf Optimizer (GWO) search algorithm is presented for solving the optimal power flow problem in a power system, enhanced by wind power plant. The GWO algorithm is based on meta-heuristic method, and it has been proven to give very competitive results in different optimization problems. First, by using the proposed technique, the system independent variables such as the generators’ power outputs as well as the associated dependent variables like the bus voltage magnitudes, transformer tap setting and shunt VAR compensators values are optimized to meet the power system operation requirements. The Optimal power flow study is then performed to assess the impact of variable wind power generation on system parameters. Two standard power systems IEEE30 and IEEE57 are used to test and verify the effectiveness of the proposed GWO method. The obtained results are then compared with others given by available optimization methods in the literature. The outcome of the comparison proved the superiority of the GWO algorithm over other meta-heuristics techniques such as Modified Differential Evolution (MDE), Enhanced Genetic Algorithm (EGA), Particle Swarm Optimization (PSO), Biogeography Based Optimization (BBO), Artificial Bee Algorithm (ABC) and Tree-Seed Algorithm (TSA). Keywords Grey Wolf Optimizer (GWO), grey wolves, OPF problem. 1. Introduction Optimal power flow problem has been studied for many years and has become one of the most important means used for adjusting optimal settings of power systems. Therefore, it has received more attention from many researchers throughout the world [1]. Several optimization techniques have been used to solve this problem, in order to find the optimal solution for operational objective functions in a power system, such as fuel cost, voltage profile and voltage stability enhancement. Some methods are based on nonlinear programming, quadratic programming, Newton techniques and interior point. These methods have many drawbacks, such as high complexity, convergence to local optimum and sensitivity to initial conditions [2]. Intelligent search methods such as meta-heuristic optimization techniques have been introduced to overcome some optimization problems encountered with classical methods. The most popular ones are; Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Simulated Annealing (SA), Evolutionary Programming (EP), Artificial Bee Colony algorithm (ABC), Ant Colony Optimization (ACO), Differential Evolution (DE). Based on these original methods new derived techniques have been obtained and used in OPF problem as in ABC [3], EGA [4], gradient method and General Algebraic Modeling System (GAMS) [5], Efficient Evolutionary Algorithm (EEA) [5], Evolving Ant Direction Differential Evolution (EADDE) [6], Differential Search Algorithm (DSA) [7], CSA [8], Krill Herd Algorithm (KHA) [9], Simulated Annealing (SA) [10], Interior Search Algorithm (ISA) [11], Enhanced Genetic Algorithm (EGA) [12], BBO [13], PSO [14], Gravitational Search Algorithm (GSA) [15], Genetic evolving ant direction PSODV hybrid algorithm (PSODV) [16], Real Coded Biogeography-Based Optimization RC-BBO [17] and Evolutionary Algorithm (EA) [18]. Most of these methods are recently extensively used in solving global optimization searching problems and have been giving promising results beside that they c 2018 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 471 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 16 |NUMBER: 4 |2018 |DECEMBER have attractive characteristics, such as easy implementation and fast convergence [18]. A common drawback to meta-heuristic methods is that, in general, the optimization performance is highly dependent on fine parameter tuning. However, the proposed approach outperforms these methods in term of convergence speed to the best solution. Moreover, the use of OPF is extended to include the study of renewable energy systems like wind power, which becomes more and more useful in recent power networks, and many studies are made to integrate this natural power efficiently to a power system. Ranjit and Jadhav in [19], as well as Maskar et al. in [20], presented a study of OPF problem in a system incorporating wind power sources, using modified ABC algorithm named Gbest guided ABC algorithm; the method showed good results for fuel cost optimization case, and voltage profile enhancement, then under wind condition the total operating cost is optimized efficiently, compared to other methods. The method presented some benefits concerning reserve coefficient adjustment when considering imbalance cost of wind power. Meanwhile, Shanhe et al. [21] presented a new economic dispatch technique based on PSO-GSA algorithm for a power system including two wind power sources; the method was tested on a six generators’ system connected with two stochastic wind power sources. The test yielded good results compared with other results found in the literature with different methods especially for cost and emission reduction. Panda and Tripathy [22], and Mishra and Vignesh [23] introduced another OPF algorithm based on security constrained OPF solution of wind-thermal generation system using modified bacteria foraging algorithm. The method was tested on the same system stated in [18], in which the wind power variability was modelled incorporating conventional thermal generating system. Recent works in [19], [24] and [25] presented better results and faster convergence characteristics using Grey Wolf Optimizer algorithm. Grey Wolf Optimizer (GWO) algorithm mimics the behaviour of grey wolves in nature by simulating their leadership hierarchy, through haunting, searching for, encircling, and attacking the prey [26]. The present paper aims to investigate the efficiency of GWO algorithm, as a new meta-heuristic population-based algorithm. It presents a solution to the OPF problem of a power system incorporating wind power generation. The rest of the paper is organized as follows; after the introduction, the OPF problem formulation is given in Sec 2. Subsec. 2.2. deals with the OPF problem incorporating wind power. Section 3. presents the GWO algorithm and associated simulation steps for solving the OPF problem. In Sec. 4. simulation results using GWO algorithm are presented and analysed. Section 5. concludes the study. 2. OPF Problem Formulation 2.1. Optimal Power Flow The objective of conventional OPF problem is to minimize fuel cost for power generation by determining a set of control variables while satisfying system equality and inequality constraints. The OPF problem is formulated by [27]: min f(x, u),(1) s·tg(x, u)=0,(2) h(x, u)≤0,(3) where [~x]: is the vector of dependent variables consisting of slack bus PG1, load bus voltage VL, generator reactive power outputs QG, and transmission line loading SL. This vector is expressed by: XT= [PG1, VL1, ..VND, QG1, ..QGN , Sl1, ..SlNL ],(4) where ND,NG and NL are number of load buses, number of generators, and number of transmission lines, respectively. [~u] is the vector of independent variables consisting of generator voltages VG, generator real power outputs PGexcept at the slack bus PG1, transformer tap settings TP, shunt VAR compensation QC. This vector is expressed by: ~uT=[VG1, ..VNG, .PG2..PGN , TP1, ..TPNT , QC1, ..QCNC ], (5) where: NG,NT, and NC are the number of thermal generators, regulating transformers, shunt compensators, respectively. 1) Fuel Cost Optimization The function ffrom Eq. (1) concerned in the OPF study represents the total generation cost formulation and it is as: f(Pgi) = NG X i=1 aiP2 gi +biPgi +ci($/h).(6) When considering valve effect, the function f; is rewritten as: f(Pgi) = NG P i=1 aiP2 gi +biPgi+ +ci|di(sin(ei(Pgi min −Pgi ($/h), (7) where: ai,bi,ci,diand eiare fuel cost coefficients of ith thermal generating unit. c 2018 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 472 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 16 |NUMBER: 4 |2018 |DECEMBER 2) Voltage Profile Improvement The aim of this objective function is to minimize the load bus voltage deviations from the reference value which is 1 per unit; this function is expressed by: VD = NP Q X i=1 |Vi−Vref |,(8) where: VD represents the voltage deviation in (p.u); Viis the ith load bus voltage; and Vref is the reference voltage which is taken here to be 1 p.u, and thus the objective function Eq. (6) becomes as follows: f(Pgi) = NG P i=1 (aiP2 gi +biPgi +ci)+ +w NP Q P i=1 |Vi−1|, (9) where: wrepresents a weighting factor selected by the user; many works are choosing wto be 100 in order to keep the variable within the designed limits, as in [1] and [15].The OPF equality constraint such as the active power balance equation is expressed by: NG X i=1 PGi =Pd+Pl,(10) where: Pdrepresents the load of the system, and Plis the total active power loss. 3) OPF Incorporating Inequality Constraints In order to handle the inequality constraints of dependent variables, including slack bus real and reactive power, load bus voltage magnitudes and transmissions line loading; the problem is transformed into unconstrained OPF problem by penalizing these quantities using the penalty function defined as: h(xi) =      (xi−ximax)if x>ximax, (ximin −xi)2if x<ximax, 0if ximin ≤xi≤ximax. (11) where: h(xi)is the penalty function of variable xi, here the xirepresents dependent variables, ximin and ximax are the upper and lower limits of xivariable, respectively. The value of the penalty function grows with a quadratic form when the constraints are violated, and equals to zero if the constraints are not violated, while the extended objective function Eq. (6) can be rewritten as: f(Pgi) = NG P i=1 fi+ηP(Pg1−Plim g1)2+ηQ(Qg1−Qlim g1)2 +ηVPNL i=1(VLi −Plim Li )2+ηS NB P i=1 (Sit −Plim it )2, (12) where: ηp,ηq,ηvand ηsare penalty factors or weights of active power generation of slack bus, reactive power output of generator buses, PQ bus magnitudes and transmission line loadings respectively. Their values are generally taken to be 100 for the same reason in Eq. (9) [14], [15], [16] and [17]. 2.2. OPF Problem Formulation with Wind Power The fuel cost objective in Eq. (6) is augmented with the cost associated with stochastic wind power, as in Eq. (13) [28] FT= NG P i=1 aiP2 gi +biPgi +ci+ +F(Pwj) + Cwj ($/h), (13) where; F(Pwj)is the cost for generation of wind power which is directly proportional to the wind power output and is given by: F(Pwj) = dj×Pwj ($/h),(14) dj: is the direct cost coefficient of non-utility service, which equals to zero for the utility services. Cwj: represents the imbalance cost of investment in jth wind power source due to two components as in Eq. (15) [29]: Cw= Nw P j=1 (Kp,j ×Wj,ue)+ + Nw P j=1 (KR,j ×Wj,oe) ($/h), (15) where: Wj,ue and Wj,oe, are given by the following expressions: Wj,ue =                       (Pwr,j −Pwj )exp −vkj r,j ckj i −exp −vkj o,j ckj i+Pwr,j vin,j vr,j −vin,j +Pwjexp −vkj r,j ckj i −exp −vkj 1,j ckj i+Pwr,j vin,j vr,j −vin,j ·(Γ"1 + 1 ki,vkj 1,j ckj ikj# −Γ"1 + 1 ki,vkj r,j ckj ikj#)                       ,(16) c 2018 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 473 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 16 |NUMBER: 4 |2018 |DECEMBER Wj,oe =                       (Pwr,j)1−exp −vkj in,j ckj i −exp −vkj o,j ckj i+Pwr,j vin,j vr,j −vin,j +Pwjexp −vkj r,j ckj i −exp −vkj 1,j ckj i+Pwr,j vin,j vr,j −vin,j ·(Γ"1 + 1 ki,vkj 1,j ckj ikj# −Γ"1 + 1 ki,vkj r,j ckj ikj#)                       ,(17) where: v1=vin,j + (vr,j −vin,j)PW,j /PW r,j;k > 0, c > 0are the shape factor and scale factor, respectively. PW r; is the available active power for the jth wind turbine. PW r,j , is the rated wind power output, PW,j is the actual wind power output of jth wind turbine. Vin,V0and Vrare the cut-in, cut-off and rated wind speed, respectively. Equation (15) represents the stochastic nature of wind power output for which the following parameters are associated: •Kp,j: penalty cost coefficient for not using all available power from jth wind turbine due to under-generation estimated from jth wind turbine, •KR,j: reserve cost coefficient due to the reserve capacity used to compensate the over-estimated wind power of jth wind turbine. •Wj,ue and Wj,oe, are the expected value of jth wind turbine for over-estimated and under-estimated energy output which was calculated using Eq. (16) and Eq. (17) [2]. To deal with wind speed variations of wind turbine, the generated power from wind can be approximated with respect to particular wind speed V, as follows [2]: Pw(V) =          0V≤Vin, aV 3+bV 2+cV +d Vr> V > Vin, Pwe Voff > V ≥Vr, 0V≥Voff. (18) Pw(V)is the available wind power output, a,b,c, and d; are constants, in this study the generated wind power output is used as negative real power load connected at special bus in the test system. 1) System Equality Constraints with Wind Energy The equality constraints for the case of wind power are expressed by [26]: NG X i=1 PGi + Nw X j=1 PW j =Pd+P−l. (19) The active power losses are given by the formula: Ploss = Nl P n=1 Gnij |Vi|2+|Vj|2−2|Vi|| Vj| cos(δi−δj)] , (20) where: iand jare the sending and receiving ends of particular line n.Nl; is the number of lines. The equality constraints from Eq. (8) and Eq. (9) are rewritten for the wind node jas: PW j −Pdj −Pj,cal(V, δ) = 0,(21) QW j −Qdj −Qj,cal(V, δ) = 0.(22) The control variables vector is modified as: ~uT= [VG1, ..VNG, .PG2..PGN , Pw1, ..PNw, Tp1, ..TpNT , QC1, ..QCNC ],(23) where: NWrepresents the number of wind generators in the power system network. 2) Wind Generators Constraints In addition to the precedent inequality constraints, we can write; 0≤PW i ≤PW r,i, i = 1, ..Nw,(24) where: PW r, is the rated active power output of the ith wind turbine unit. 3) Spinning Reserve Constraints Model for OPF with Wind Energy The spinning reserve is the reserve capacity used for sudden load increase, unpredictable fall in wind power output or forced outage of thermal generators units. The spinning reserve has two limits which are the upper and lower limits that represent system up and system down spinning reserves USR and DSR; given by the following expressions: [2] and [30]: PUS ≥RUSR +r%× Nw X j=1 PW,j,(25) PDS ≥RDSR ×s% + r%× Nw X j=1 PW,j,(26) c 2018 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 474 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 16 |NUMBER: 4 |2018 |DECEMBER where; ris the influence coefficient that gives the percentage of wind power contributing to USR and DSR. The USR can be represented with respect to the total load and total wind power by: N X i=1 PUSi≥Pd×s% + r%×PW T ,(27) where: USirepresents the maximum up spinning reserve limit of ith thermal unit, and sis the percentage of load contributing to USR, these constraints will be considered during the implementation of GWO algorithm. As the rate of wind power penetration increases, it becomes more difficult to predict the exact amount of power injected by all generators into the power grid. This added more uncertainty when accounting the spinning reserve requirements. 3. Used Algorithm 3.1. GWO Algorithm Grey Wolf Optimizer (GWO) is a new algorithm proposed by Mirjalili et al. in 2014 [31]. This algorithm mimics the leadership hierarchy and hunting technique used by grey wolves to catch their prey until stopping its movement. GWO is similar to other populationbased meta-heuristic algorithms, by simulating the natural behavior of grey wolves in their social life when searching for food; they follow hierarchy structure in the group (Fig. 1). The first level representing the leaders of the group is called (alpha), the second level in the hierarchy of grey wolves is (beta) which helps alpha to make decisions. The next levels are delta and omega; they are the lowest ranks in the group; they have to eat after all levels. In fact, these wolves are group-hunting that take three main steps; chasing, encircling and attacking. The algorithm starts with a given number of wolves whose positions are randomly generated. 3.2. Steps of GWO Algorithm Four types of wolves groups can be used to simulate the leadership hierarchy of grey wolves. This hierarchy is represented in Fig. 1, respecting the social dominant degree, the high class is named alpha (α), mostly responsible for making decisions about hunting and order the other wolves in the pack. (α) (β) (δ) (ω) Kappa (κ) and lambda (λ) Fig. 1: Hierarchy levels of grey wolves. Fig. 2 a) attacking prey b) hunting prey by wolves (a) (b) Fig. 2: (a) attacking prey (b) hunting prey by wolves. They can be considered as the fittest solution. The next level in the chain is called beta (β), the wolves of this level help the alpha ones in supervising other groups’ actions. They can replace the alpha wolves when they die or become aged and begin to be the best candidate solution. The lowest ranking grey wolves are delta (δ) wolves and omega (ω) wolves [27] and [32]. Therefore types α,β, and δleading the optimization (hunting) process, while ωgroup is to track them. Kappa (κ) and lambda (λ) wolves are directed by omega in the hierarchy. The main steps involved in the original GWO algorithm are as follows: c 2018 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 475 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 16 |NUMBER: 4 |2018 |DECEMBER •Initialize the search agents. •Assign Alpha, Beta and Gamma by fitness. •Encircling the prey: represent the circular area around the best solution (prey). This step can be represented by the following equations: D=|C·~ Xp(t)−X(t)|,(28) X(t+ 1) =|~ Xp(t)−A·D|,(29) where: ~ Xpis the prey’s position vector. ( ~ A) and (~ C), are vectors given by the following equations: a= 2(1 −t/Tmax),(30) ~ A= 2 ·ar1−a, (31) ~ C= 2r2,(32) where: tis the current iteration and Tmax, total iterations. The parameter a decreases linearly in the range of [2,0] for successive iterations using Eq. (30); that model wolfs behaviour approaching the prey; r1and r2 are random vectors in the range [0,1]. •Hunting step: the encircling process comes to the second step involving hunting guided by the alpha wolf group. The following equations represent this step: Dα=|C1·Xα(t)−X(t)|,(33) Dβ=|C2·Xβ(t)−X(t)|,(34) Dδ=|C3·Xδ(t)−X(t)|,(35) X1=Xα−A1·DαX2,(36) X2=Xβ−A2·DβX3,(37) X3=Xδ−A3·Dδ,(38) X(t+ 1) = (x1+X2+X3)/3.(39) •Attacking the prey: Firstly, r1and r2are randomly selected for mutation (Aand C), then the base vector (X) is randomly selected within the range [r1, r2], that is to drive the algorithm to global solution and avoid local optima. The fact that “a” decreases from 2 to 0 makes the exploration more efficient, but slows down the GWO convergence characteristics. So, the final step of attacking the prey is done by decreasing linearly the value of “a” from 2 to 0 [33]. •Steps 2 to 5 are then repeated until the maximum number of iterations is reached. 3.3. Pseudo Code for GWO Algorithm Initialize the grey wolf population; Xi; i=1. . . n Initialize parameters; a, A, and C Calculate the fitness of each Search_Agent; Xa=the best search agent; Xβ=the second best search agent; Xδthe third best search agent; While Iter≤Max_Iter For j∈{search space} Sort the population of grey wolves according to their fitness Update the Update the position of the current Search Ahent using Eq. (39); endfor % search space Update a, A and C Calculate the fitness of the new search agents; Update Xa,Xβand Xδ Iter=Iter+1; End; Return, Best solution found so far Xa; 4. Case Study and Simulation Results In this section, the optimal power flow problem is implemented using GWO algorithm and two case studies are considered. For the first case study, the simulation is carried out on IEEE30bus system as used in [34], by solving conventional OPF and considering quadratic model of thermal generators cost using Eq. (6). Then, the OPF problem is implemented considering wind power for a given wind speed and cost profiles. Later, the OPF problem is implemented considering different wind speed profiles. In the second case study, the simulation is carried out on IEEE57-bus system. The purpose of these studies is to validate the results obtained using GWO algorithm by comparing them with the results available in the literature. 4.1. Case Study N◦1: IEEE30 Bus Test System 1) Case 1.1: OPF with Quadratic Fuel Cost The objective function for this case study is given by Eq. (6), for all thermal generators units, the numerical data and parameters are taken from [35], the PQ bus voltages are between 0.95 and 1.05 p.u, the shunt Var Compensator are not considered in this case study, except for the two shunt capacitors banks, at nodes 10 c 2018 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 476 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 16 |NUMBER: 4 |2018 |DECEMBER and 24 of 19 and 4.3 Mvars respectively. The optimum control settings obtained by using GWO algorithm are presented in Tab. 1. Tab. 1: Optimal power flow without considering dependent variables. Control variables Lower/up per limits Case 1.1 Case 1.2 Case 1.3 P1(MW) 50 200 176.1721 176.472 199.988 P2 20 80 48.0926 48.795 20.0000 P5 15 35 21.1376 21.506 15.0152 P8 10 30 23.3591 21.799 10.0000 P11 10 30 11.3591 11.993 10.0000 P13 12 40 12.0000 12.000 12.0000 V1 0.95 - 1.05 1.0600 1.0600 1.06000 V2 0.95 - 1.10 1.0512 1.0512 1.0512 V5 0.95 - 1.10 1.0224 1.0224 1.0224 V8 0.95 - 1.10 1.0333 1.0333 1.0333 V11 0.95 - 1.10 1.0820 1.0820 1.0820 V13 0.95 - 1.10 1.0910 1.0910 1.0910 T11 0.90 - 1.10 1.0150 1.0150 1.0170 T12 0.90 - 1.10 0.9070 0.9070 0.9070 T13 0.90 - 1.10 0.9680 0.9680 0.9680 T14 0.90 - 1.10 0.9550 0.9550 0.9550 Fuel cost $/h -801 .1769 804 .4726 910 .6575 Power loss - 9.1528 9.202 12.709 Voltage deviations -0.10 0.1082 - In order to assess the potential of the proposed approach, a comparison between the obtained results of fuel cost and those reported in the literature has been carried out. The results of this comparison are given in Tab. 2. It is worth mentioning that the comparison has been carried out with the same test system data. Different OPF results of active generation powers and losses for different case studies are given in Tab. 1. 50 100 150 200 250 300 350 400 Iteration 798.5 799 799.5 800 800.5 801 801.5 Best fuel cost ($/h) GWO Fig. 3: Convergence characteristic of IEEE30 bus system case 1.1. The best fuel cost calculated by the proposed algorithm for this case is 801.1769 $/h, which is better than Tab. 2: Comparison of quadratic fuel cost case 1.1. Methods Fuel cost ($/h) MDE [35] 802.376 ABC [3] 802.305 EGA [4] 802.060 GAMS [5] 801.519 GWO 801.176 that obtained by many other algorithms as depicted in Tab. 2. The corresponding convergence graph is shown in Fig. 3. Tab. 3: Optimal power flow considering dependent variables. Control variables Lower/up per limits Case 1.1 Case 1.2 Case 1.3 P1 (MW) 50 200 176.9340 176.953 199.636 P2 20 80 48.7328 48.8151 20.0000 P5 15 35 21.2692 21.2488 22.2126 P8 10 30 21.0177 21.0724 25.1402 P11 10 30 11.8525 11.7632 13.2466 P13 12 40 12.0000 12.0000 12.2392 V1(p.u) 0.95 - 1.05 1.0999 1.0999 1.0999 V2 0.95 - 1.10 1.0885 1.0885 1.0885 V5 0.95 - 1.10 1.0631 1.0631 1.0631 V8 0.95 - 1.10 1.0712 1.0712 1.0712 V11 0.95 - 1.10 1.0998 1.0998 1.0998 V13 0.95 - 1.10 1.0733 1.0733 1.0733 C10 (Mvars) 0.00 - 5.00 4.1669 4.1669 4.1669 C15 0.00 - 5.00 0.2398 0.2398 0.2398 C17 0.00 - 5.00 4.2017 4.2017 4.2017 C20 0.00 - 5.00 0.1489 0.1489 0.1489 C21 0.00 - 5.00 0.6478 0.6478 0.6478 C22 0.00 - 5.00 4.2499 4.2499 4.2499 C23 0.00 - 5.00 1.3886 1.3886 1.3886 C24 0.00 - 5.00 2.1815 2.1815 2.1815 C29 0.00 - 5.00 2.0780 2.0780 2.0780 T11 0.90 - 1.10 1.0461 1.0150 1.0170 T12 0.90 - 1.10 0.9000 0.9070 0.9070 T13 0.90 - 1.10 0.9997 0.9680 0.9680 T14 0.90 - 1.10 0.9642 0.9550 0.9550 Fuel cost ($/h) -798.3107 806.1530 916.6968 Power loss (MW) -8.4061 8.4526 9.0762 Voltage deviations - 0.422 0.077 0.078 For the methods EADDE in [6], GABC in [7], EEA in [5], CSA in [8], KHA in [9], SA in [10], and ISA in [11], the PQ bus voltages are between 0.95 and 1.1 p.u, the transformers tap setting and shunt Var compensators are considered in the same case study, and the generator voltages are taken close to their high permissible limit. Table 3 shows the corresponding optimal power flow results when using the optimal settings of dependent variables. It can be observed from Tab. 4 that GWO algorithm gives better results. The system reactive generation powers for this case study are within their specified limits as in Tab. 5. Table 6 presents a comparison of optimal power flow results of the proposed algorithm with other methods found in c 2018 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 477 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 16 |NUMBER: 4 |2018 |DECEMBER Tab. 4: Comparison when optimizing dependent variables. Methods Fuel cost ($/h) EADDE [6] 800.204 DSA [7] 800.388 EEA [5] 800.083 CSA [8] 799.707 EGA [12] 799.5600 BBO [13] 799.1116 KHA [9] 799.0310 MFPA [40] 799.1592 GSA [15] 798.675 GWO 798.3107 Tab. 5: Comparison when optimizing dependent variables. React. Power Gen. Limits Qg Q1 -20 200 -18.7646 G2 -40 50 23.1157 Q5 -40 40 27.3300 Q8 -15 40 33.7790 Q11 -6 24 17.9905 Q13 -6 24 2.55070 Tab. 6: GWO-OPF results comparison for case 1.1. Pgi (MW) SA ISA KHA GSO GWO P1 173.15 177.124 177.04 174.920 176.9046 P2 48.54 48.933 48.690 44.150 48.7226 P5 19.23 21.3175 21.300 21.760 21.2697 P8 12.81 21.0006 21.080 25.730 21.0509 P11 11.64 11.8605 11.880 11.120 11.8556 P13 12.00 11.860 12.020 13.810 12.0000 Tot. Gn (MW) 277.37 292.095 292.01 291.49 291.8034 Cost ($/h) 799.45 799.277 799.03 799.06 798.3106 Losses (MW) 9.200 8.695 8.610 8.48 8.4034 the literature as in [3] and [19]. Figure 6(a) shows the voltage profile of case 1.1, without improvement. 2) Case 1.2: OPF with Voltage Profile Improvement Minimizing only the total fuel cost using OPF problem as in case 1.1; can result in a feasible solution, but voltage profile may not be acceptable. Thus, in this second case, the objective here is to minimize the fuel cost and improving the voltage profile at the same time by minimizing the voltage deviation of PQ buses from the unity 1.0. [36]. The results obtained using the proposed approach are compared with other methods in the literature as shown in Tab. 7 where the total cost found by GWO, in this case, is better than that obtained before. Figure 4 shows the convergence graph. Figure 5 presents the transmission load flow of the system, from this figure, we can see that the obtained transmission Tab. 7: Comparison when optimizing dependent variables. Methods Fuel cost ($/h) BBO [13] 804.998 PSO [14] 806.380 DE [1] 805.262 GWO 806.1530 loading amounts are within acceptable limits. As we can see from Fig. 6(a), the voltage magnitude is enhanced after the improvement by GWO, and all the load bus voltages are within the permissible range. 100 200 300 400 500 600 700 Iteration 803 803.5 804 804.5 805 805.5 806 Best fuel cost ($/h) GWO Fig. 4: Convergence characteristic of IEEE30 bus system case 1.2. 0 10 20 30 40 50 line number 0 20 40 60 80 100 120 140 load flow (MW) Normal case Load flow limits Fig. 5: Transmission Load flows obtained by GWO. 3) Case 1.3: OPF for Fuel Cost Including Valve Point Effect Considering the same system data as in [23], the valve point effect is incorporated and the fuel cost is evaluated using the Eq. (7). Simulation of power flow results c 2018 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 478 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 16 |NUMBER: 4 |2018 |DECEMBER 0,95 1 1,05 1,1 1234567 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27282930 Voltage improvement (a) 0,950 1,000 1,050 1,100 12345 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 282930 Vbefore Vafter (b) Fig. 6: a) Bus voltage magnitude case 1.2, b) Comparison of voltage profile of IEEE30 bus case 1.1 & case 1.2. of this case study is compared with other available results as in Tab. 8. Tab. 8: Obtained results comparison case 1.3. Methods Fuel cost ($/h) PSO [14] 932.7642 ABC [3] 945.4495 GSA [15] 929.7240 GABC [19] 931.7450 BBO [13] 919.7647 MFPA [40] 917.8298 GWO 916.6968 4) Case 1.4: System Analysis Under (N-1) Contingency To investigate the efficiency of GWO under contingency, a line outage conditions are created on the test system as in [23], in which four contingency conditions are considered (lines: 12–15, 10–20, 15–23 and 6–28). For these four conditions, the voltage profile for normal and contingency conditions is shown in Fig. 7, and corresponding load flow profile is in Fig. 8. 0,80 0,90 1,00 1,10 12345 6 7 8 9 10 11 12 13 14 1516 17 18 19 20 21 22 23 24 25 2627 28 29 normal_case Fig. 7: Voltage profile for normal and contingency conditions. 0 10 20 30 40 50 line number 0 20 40 60 80 100 120 active load flow (MW) load flow for normal conditions LF for contengency conditions Fig. 8: Load flow profile for normal and contingency conditions. The load-bus voltages of contingency case are below their normal limit (deviated from their normal limits).To alleviate this problem we apply Eq. (11) and Eq. (12), to bring the voltage at these load buses within 0.95 and 1.05 p.u. Figure 9 shows the corrected voltage profile. 4.2. Case 2: OPF with Wind Energy Case Study 1) Case 2.1: OPF with Stochastic Wind Power Modelling In this section, GWO algorithm is used to solve OPF problem for system including stochastic wind power in addition to conventional thermal generators. In this case, the system has been modified by replacing conventional generators by wind farms located at buses 5, 11 and 13; each with a total capacity of 60 MW. Two case studies are considered here: in the first case, the wind power is modelled using Weibull distribution c 2018 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 479 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 16 |NUMBER: 4 |2018 |DECEMBER [13] BHATTACHARYA, A. and P. K. CHATTOPADHYAY. Application of biogeography-based optimisation to solve different optimal power flow problems. IET Generation, Transmission &Distribution. 2011, vol. 5, iss. 1, pp. 70–80. ISSN 17518687. DOI: 10.1049/iet-gtd.2010.0237. [14] ABIDO, M. A. Optimal power flow using particle swarm optimization. International Journal of Electrical Power &Energy Systems. 2002, vol. 24, iss. 7, pp. 563–571. ISSN 0142-0615. DOI: 10.1016/S0142-0615(01)00067-9. [15] DUMAN, S., U. GUVENC, Y. SONMEZ and N. YORUKEREN. Optimal power flow using gravitational search algorithm. Energy Conversion and Management. 2012, vol. 59, iss. 1, pp. 86–95. ISSN 0196-8904. DOI: 10.1016/j.enconman.2012.02.024. [16] VAISAKH, K., L. R. SRINIVAS and K. MEAH. Genetic evolving ant direction PSODV hybrid algorithm for OPF with non-smooth cost functions. Electrical Engineering. 2013, vol. 95, iss. 3, pp. 185–199. ISSN 0948-7921. DOI: 10.1007/s00202-012-0251-9. [17] KUMAR, R. A. and L. PREMALATHA. Optimal power flow for a deregulated power system using adaptive real coded biogeographybased optimization. International Journal of Electrical Power &Energy Systems. 2015, vol. 73, iss. 1, pp. 393–399. ISSN 0142-0615. DOI: 10.1016/j.ijepes.2015.05.011. [18] KHAMEES, K. A., A. E. RAFEI, N. M. BADRA and A. Y. ABDELAZIZ. Solution of optimal power flow using evolutionary-based algorithms. International Journal of Engineering, Science and Technology. 2017, vol. 9, no. 1, pp. 55–68. ISSN 2141-2839. [19] ROY, R. and H. T. JADHAV. Optimal power flow solution of power system incorporating stochastic wind power using Gbest guided artificial bee colony algorithm. International Journal of Electrical Power &Energy Systems. 2015, vol. 64, no. 1, pp. 562–578. ISSN 0142-0615. DOI: 10.1016/j.ijepes.2014.07.010. [20] MASKAR, M. B., A. R. THORAT, P. D. BAMANE and I. KORACHGAON. Optimal power flow incorporating thermal and wind power plant. In: International Conference on Circuit, Power and Computing Technologies. Kollam: IEEE, 2017, pp. 1–6. ISBN 978-1-5090-4967-7. DOI: 10.1109/ICCPCT.2017.8074265. [21] JIANG, S., Z. JI and Y. WANG. A novel gravitational acceleration enhanced particle swarm optimization algorithm for wind–thermal economic emission dispatch problem considering wind power availability. International Journal of Electrical Power &Energy Systems. 2015, vol. 73, iss. 1, pp. 1035–1050. ISSN 0142-0615. DOI: 10.1016/j.ijepes.2015.06.014. [22] PANDA, A. and M. TRIPATHY. Security constrained optimal power flow solution of wind-thermal generation system using modified bacteria foraging algorithm. Energy. 2015, vol. 93, iss. 1, pp. 816–827. ISSN 0360-5442. DOI: 10.1016/j.energy.2015.09.083. [23] MISHRA, S., Y. MISHRA and S. VIGNESH. Security constrained economic dispatch considering wind energy conversion systems. In: IEEE Power and Energy Society General Meeting. Detroit: IEEE, 2011, pp. 1–8. ISBN 978-1-4577-10001. DOI: 10.1109/PES.2011.6039544. [24] SULAIMAN, M. H., Z. MUSTAFFA, M. R. MOHAMED and O. ALIMAN. Using the gray wolf optimizer for solving optimal reactive power dispatch problem. Applied Soft Computing. 2015, vol. 32, iss. 1, pp. 286–292. ISSN 1568-4946. DOI: 10.1016/j.asoc.2015.03.041. [25] EL-FERGANY, A. A. and H. M. HASANIEN. Single and Multi-objective Optimal Power Flow Using Grey Wolf Optimizer and Differential Evolution Algorithms. Electric Power Components and Systems. 2015, vol. 43, iss. 13, pp. 1548–1559. ISSN 1532-5008. DOI: 10.1080/15325008.2015.1041625. [26] IAHKALI, H. and M. VAKILIAN. Stochastic unit commitment of wind farms integrated in power system. Electric Power Systems Research. 2010, vol. 80, iss. 9, pp. 1006–1017. ISSN 0378-7796. DOI: 10.1016/j.epsr.2010.01.003. [27] MIRJALILI, S., S. M. MIRJALILI and A. LEWIS. Grey Wolf Optimizer. Advances in Engineering Software. 2014, vol. 69, iss. 9, pp. 46–61. ISSN 0965-9978. DOI: 10.1016/j.advengsoft.2013.12.007. [28] MIRJALILI, S. and S. Z. M. HASHIM. A new hybrid PSOGSA algorithm for function optimization. In: International Conference on Computer and Information Application. Tianjin: IEEE, 2010, pp. 374–377. ISBN 978-1-4244-8598-7. DOI: 10.1109/ICCIA.2010.6141614. [29] BAI, W., D. LEE and K. LEE. Stochastic Dynamic Optimal Power Flow Integrated with Wind Energy Using Generalized Dynamic Factor Model. IFAC-Papers OnLine. 2016, vol. 49, iss. 27, pp. 129–134. ISSN 2405-8963. DOI: 10.1016/j.ifacol.2016.10.731. c 2018 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 486 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 16 |NUMBER: 4 |2018 |DECEMBER [30] XIE, L., H. D. CHIANG and S. H. LI. Optimal power flow calculation of power system with wind farms. In: IEEE Power and Energy Society General Meeting. Detroit: IEEE, 2011, pp. 1–6. ISBN 978-1-4577-1000-1. DOI: 10.1109/PES.2011.6039105. [31] MONDAL, S., A. BHATTACHARYA and S. H. NEE-DEY. Multi-objective economic emission load dispatch solution using gravitational search algorithm and considering wind power penetration. International Journal of Electrical Power &Energy Systems. 2013, vol. 44, iss. 1, pp. 282–292. ISSN 0142-0615. DOI: 10.1016/j.ijepes.2012.06.049. [32] MOHAMED, A. A., A. M. EL-GAAFARY, Y. S. MOHAMED and A. M. HEMEIDA. Multiobjective Modified Grey Wolf Optimizer for Optimal Power Flow. In: Eighteenth International Middle East Power Systems Conference (MEPCON). Cairo: IEEE, 2016, pp. 982–990. ISBN 978-1-4673-9063-7. DOI: 10.1109/MEPCON.2016.7837016. [33] KAPOOR, S., I. ZEYA, C. SINGHAL and S. J. NANDA. A Grey Wolf Optimizer Based Automatic Clustering Algorithm for Satellite Image Segmentation. Procedia Computer Science. 2017, vol. 115, iss. 1, pp. 415–422. ISSN 1877-0509. DOI: 10.1016/j.procs.2017.09.100. [34] ANANTASATE, S. and P. BHASAPUTRA. A multi-objective bees algorithm for multiobjective optimal power flow problem. In: The 8th Electrical Engineering/ Electronics, Computer, Telecommunications and Information Technology (ECTI) Association of Thailand. Khon Kaen: IEEE, 2011, pp. 852–856. ISBN 978-1-4577-04253. DOI: 10.1109/ECTICON.2011.5947974. [35] SAYAH, S. and K. ZEHAR. Modified differential evolution algorithm for optimal power flow with non-smooth cost functions. Energy Conversion and Management. 2008, vol. 49, iss. 11, pp. 3036–3042. ISSN 0196-8904. DOI: 10.1016/j.enconman.2008.06.014. [36] BOUCHEKARA, H. R. E. H. Optimal power flow using black-hole-based optimization approach. Applied Soft Computing. 2014, vol. 24, iss. 1, pp. 879–888. ISSN 1568-4946. DOI: 10.1016/j.asoc.2014.08.056. [37] ZIMMERMAN, R., C. MURILLO-SANCHEZ and D. GAN. Matlab power System Simulation Package. New York: School of Electrical Engineering, Cornell University, 2007. [38] SINSUPAN, N., U. LEETON and T. KULWORAWANICHPONG. Application of harmony search to optimal power flow problems. In: International Conference on Advances in Energy Engineering. Beijing: IEEE, 2010, pp. 219–222. ISBN 978-1-4244-7831-6. DOI: 10.1109/ICAEE.2010.5557575. [39] REDDY, S. S., and C. SRINIVASA RATHNAM. Optimal Power Flow using Glowworm Swarm Optimization. International Journal of Electrical Power &Energy Systems. 2016, vol. 80, iss. 1, pp. 128–139. ISSN 0142-0615. DOI: 10.1016/j.ijepes.2016.01.036. [40] REGALADO, J. A., B. E. EMILIO and E. CUEVAS. Optimal power flow solution using Modified Flower Pollination Algorithm. In: IEEE International Autumn Meeting on Power, Electronics and Computing. Ixtapa: IEEE, 2015, pp. 1–6. ISBN 978-1-4673-7121-6. DOI: 10.1109/ROPEC.2015.7395073. [41] EL-FERGANY, A. A. and H. M. HASANIEN. Tree-seed algorithm for solving optimal power flow problem in large-scale power systems incorporating validations and comparisons. Applied Soft Computing. 2018, vol. 64, iss. 1, pp. 307–316. ISSN 1568-4946. DOI: 10.1016/j.asoc.2017.12.026. About Authors Sebaa HADDI was born in Setif, Algeria. He received his M.Sc. from University of Setif in 1997. follows his study in the University of Ferhat Abbes Setif 1, has got his B.Sc. degree in Electrical Engineering Power system from Setif University (Algeria) in 1997, and his M.Sc. degree in 2009 in the field of electrical network, now he prepares for the Doctorate degree in the Department of Electrical Engineering, of the university of Setif, His research interests include the optimization in power system, optimal integration of renewable sources, Facts device. Omrane BOUKETIR was born in Setif, Algeria. He received his M Eng. in Electrical Automation from Setif University (Algeria) in 1995. In 1999 he obtained his M.Sc. degree from University Putra Malaysia in the field of Automation and Robotics and Ph.D. degree in power electronics systems from the same university in 2005. His research areas include power electronics and drive systems, SiC switching devices, CAD tools in electrical engineering and trends and methods in tertiary education. Tarek BOUTKIR was born in Setif, Algeria. He received his M.Sc. in Electrical Engineering Power system from Setif University (Algeria) in 1994, his c 2018 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 487 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 16 |NUMBER: 4 |2018 |DECEMBER M.Sc. degree from Annaba University in 1998, his Ph.D. degree in power system from Batna University (Algeria) in 2003. His areas of interest are the application of the meta-heuristic methods in optimal power flow, FACTS control and improvement in electric power systems, Multi-Objective Optimization for power systems, and Voltage Stability and Security Analysis. He is the Editor-In-Chief of Journal of Electrical Systems (Algeria), the Co-Editor of Journal of Automation & Systems Engineering (Algeria). c 2018 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 488