REDUCTION OF ACTIVE POWER LOSS BY ADAPTIVE CHARGED SYSTEM SEARCH ALGORITHM

This paper presents a new optimization algorithm called Adaptive Charged System Search Algorithm (ACA) for solving optimal power problem. Coulomb law from electrostatics and the Newtonian laws of mechanics are forming the basics of the proposed algorithm. Adaptive Charged System Search Algorithm (ACA) is a multi-agent approach in which each agent is a Charged Particle (CP) & they affect each other based on their fitness values, separation of distances. The quantity of the resultant force is determined by using the electrostatics laws and the quality of the movement is determined using Newtonian mechanics laws. Proposed Adaptive Charged System Search Algorithm (ACA) has been tested in Standard IEEE 57,118 bus systems & real power loss has been comparatively reduced with voltage profiles are within the limits.


Introduction
Optimal reactive power problem plays most important role in the stability of power system operation and control. In this paper the main aspect is to diminish the real power loss and to keep the voltage variables within the limits. Previously many mathematical techniques like gradient method, Newton method, linear programming [4][5][6][7] has been utilized to solve the optimal reactive power dispatch problem and those methods have many difficulties in handling inequality constraints. Voltage stability and voltage collapse play an imperative role in power system planning and operation [8]. Recently Evolutionary algorithms like genetic algorithm have been already utilized to solve the reactive power flow problem [9,10].In [11][12][13][14][15][16][17][18][19][20] Genetic algorithm, Hybrid differential evolution algorithm, Biogeography Based algorithm, fuzzy based methodology, improved evolutionary programming has been used to solve optimal reactive power flow problem and all the algorithm successfully handled the reactive power problem. The Artificial Bee Colony (ABC) algorithm was introduced by Karaboga [21] as a technical report, and then its performance was measured using benchmark optimization functions [22][23][24][25][26][27][28][29][30][31][32][33]. This paper presents a new optimization algorithm called Adaptive Charged System Search Algorithm (ACA) for solving optimal power problem. Coulomb law from electrostatics and the Newtonian laws of mechanics are forming the basics of the proposed algorithm. Adaptive Charged System Search Algorithm (ACA) is a multi-agent approach in which each agent is a Charged Particle (CP) [34][35][36][37] & they affect each other based on their fitness values, separation of distances. The quantity of the resultant force is determined by using the electrostatics laws and the quality of the movement is determined using Newtonian mechanics laws. Proposed Adaptive Charged System Search Algorithm (ACA) has been tested in Standard IEEE 57,118 bus systems & real power loss has been comparatively reduced with voltage profiles are within the limits.

Active Power Loss
The objective of the reactive power dispatch problem is to minimize the active power loss and can be defined in equations as follows: Where g k : is the conductance of branch between nodes i and j, Nbr: is the total number of transmission lines in power systems.

Voltage Profile Improvement
To minimize the voltage deviation in PQ buses, the objective function can be written as: Whereω v : is a weighting factor of voltage deviation.
VD is the voltage deviation given by:

Equality Constraint
The equality constraint of the problem is indicated by the power balance equation as follows: Where the total power generation PG has to cover the total power demand PD and the power losses PL.

Inequality Constraints
The inequality constraint implies the limits on components in the power system in addition to the limits created to make sure system security. Upper and lower bounds on the active power of slack bus, and reactive power of generators are written as follows: P gslack min ≤ P gslack ≤ P gslack max (5)  Q gi min ≤ Q gi ≤ Q gi max , i ∈ N g (6) Upper and lower bounds on the bus voltage magnitudes: Upper and lower bounds on the transformers tap ratios: Upper and lower bounds on the compensators Q c min ≤ Q c ≤ Q C max , i ∈ N C (9) Where N is the total number of buses, NT is the total number of Transformers; Nc is the total number of shunt reactive compensators.

Adaptive Charged System Search Algorithm (ACA)
In this section, a new efficient optimization algorithm is established utilizing the aforementioned physics laws, which is called Adaptive Charged System Search Algorithm (ACA). In the Adaptive Charged System Search Algorithm (ACA), each solution candidate X i containing a number of decision variables i.e ( X i = {x i,j } ) is considered as a charged particle [34][35][36][37]. The charged particle is affected by the electrical fields of the other agents. The quantity of the resultant force is determined by using the electrostatics laws and the quality of the movement is determined using the Newtonian mechanics laws. It seems that an agent with good results must exert a stronger force than the bad ones, so the amount of the charge will be defined considering the objective function value, fit (i). In order to introduce ACA, the following rules are developed: Rule 1 Many of the natural evolution algorithms maintain a population of solutions which are evolved through random alterations and selection. Similarly, ACA considers a number of Charged Particles (CP). Each CP has a magnitude of charge (qi) and as a result creates an electrical field around its space. The magnitude of the charge is defined considering the quality of its solution, as follows: where, fitbest and fitworst are the so far best and the worst fitness of all particles; fit (i) represents the objective function value or the fitness of the agent i; and N is the total number of CPs. The separation distance rij between two charged particles is defined as follows: Where Xi and Xj are the positions of the i th and j th CPs, Xbest is the position of the best current CP, and ε is a small positive number to avoid singularities.
Rule 2 the initial positions of CPs are determined randomly in the search space Http://www.granthaalayah.com ©International Journal of Research -GRANTHAALAYAH [37] where x i,j (0) determines the initial value of the i th variable for the j th CP; x i,min andx i,max are the minimum and the maximum allowable values for the i th variable; rand is a random number in the interval [0,1]; and n is the number of variables. The initial velocities of charged particles are zero v i,j (0) = 0 , i = 1,2, . . , n.
Rule 3 Three conditions could be considered related to the kind of the attractive forces: Any CP can affect another one; i.e., a bad CP can affect a good one and vice versa (p ij = 1). A CP can attract another if its electric charge amount (fitness with revise relation in minimizing problems) is better than other. In other words, a good CP attracts a bad CP: All good CPs can attract bad CPs and only some of bad agents attract good agents, considering following probability function: According to the above conditions, when a good agent attracts a bad one, the exploitation ability for the algorithm is provided, and vice versa if a bad CP attracts a good CP, the exploration is provided. When a CP moves toward a good agent it improves its performance, and so the selfadaptation principle is guaranteed. Moving a good CP toward a bad one may cause losing the previous good solution or at least increasing the computational cost to find a good solution. To resolve this problem, a memory which saves the best-so-far solution can be considered. Therefore, it seems that the third kind of the above conditions is the best rule because of providing strong exploration ability and an efficient exploitation.  Http://www.granthaalayah.com ©International Journal of Research -GRANTHAALAYAH [38] Where Fj is the resultant force acting on the j th CP, as illustrated in Fig. 1.
In this algorithm, each CP is considered as a charged sphere with radius a, which has a uniform volume charge density. In this paper, the magnitude of set to unity; however, for more complex examples, the appropriate value for a must be defined considering the size of the search space. One can utilize the following equation as a general formula: According to this rule, in the first iteration where the agents are far from each other the magnitude of the resultant force acting on a CP is inversely proportional to the square of the separation between the particles. Thus the exploration power in this condition is high because of performing more searches in the early iterations. It is necessary to increase the exploitation of the algorithm and to decrease the exploration gradually. After a number of searches where CPs are collected in a small space and the separation between the CPs becomes small, say 0.1, then the resultant force becomes proportional to the separation distance of the particles instead of being inversely proportional to the square of the separation distance. Therefore, the parameter a separates the global search phase and the local search phase, i.e., when majority of the agents are collected in a space with radius a, the global search is finished and the optimizing process is continued by improving the previous results, and thus the local search starts. Besides, using these principles controls the balance between the exploration and the exploitation. It should be noted that this rule considers the competition step of the algorithm. Since the resultant force is proportional to the magnitude of the charge, a better fitness (great qi) can create a stronger attracting force, so the tendency to move toward a good CP becomes more than toward a bad particle. Rule 5 the new position and velocity of each CP is X j,new = rand j1 • k a • F j m j • ∆t 2 + rand j2 • k v • V j,old • ∆t + X j,old , Where ka is the acceleration coefficient; kv is the velocity coefficient to control the influence of the previous velocity; and rand j1 and rand j2 are two random numbers uniformly distributed in the range of (0,1). Here, m j is the mass of the jth CP which is equal to qj • ∆tis the time step and is set to unity. The effect of the pervious velocity and the resultant force acting on a CP can be decreased or increased based on the values of the kv and ka, respectively. Excessive search in the early iterations may improve the exploration ability; however, it must be decreased gradually, as described before. Since ka is the parameter related to the attracting forces, selecting a large value for this parameter may cause a fast convergence and vice versa a small value can increase the computational time. In fact ka t is a control parameter of the exploitation. Therefore, choosing an incremental function can improve the performance of the algorithm. Also, the direction of the pervious velocity of a CP is not necessarily the same as the resultant force. Thus, it can be concluded that the velocity coefficient kv controls the exploration process and therefore a decreasing function can be selected. Thus, kv and ka are defined as, k v =0.5(1 − iter iter max ⁄ ), k a = 0.5(1 + iter iter max ⁄ ) Http://www.granthaalayah.com ©International Journal of Research -GRANTHAALAYAH [39] Where iter is the actual iteration number and itermax is the maximum number of iterations. With this equation, kv decreases linearly to zero while ka increases to one when the number of iterations rises. In this way, the balance between the exploration and the fast rate of convergence is saved. Considering the values of these parameters, Eqs. (21) and (22) can be rewritten as V j,new = X j,new − X j,old,  Rule 7 There are two major problems in relation to many meta-heuristic algorithms; the first problem is the balance between exploration and exploitation in the beginning, during, and at the end of the search, and the second is how to deal with an agent violating the limits of the variables. The first problem is solved naturally through the application of above-stated rules; however, in order to solve the second problem, one of the simplest approaches is utilizing the nearest limit values for the violated variable. Alternatively, one can force the violating particle to return to its previous position, or one can reduce the maximum value of the velocity to allow fewer particles to violate the variable boundaries. Although these approaches are simple, they are not sufficiently efficient and may lead to reduce the exploration of the search space. This problem has previously been addressed and solved using the harmony search-based handling Http://www.granthaalayah.com ©International Journal of Research -GRANTHAALAYAH [40] approach [38]. According to this mechanism, any component of the solution vector violating the variable boundaries can be regenerated from the CM as Rule 8 the terminating criterion is one of the following: Maximum number of iterations: the optimization process is terminated after a fixed number of iterations, for example, 1,000 iterations. Number of iterations without improvement: the optimization process is terminated after some fixed number of iterations without any improvement. Minimum objective function error: the difference between the values of the best objective function and the global optimum is less than a pre-fixed anticipated threshold. Difference between the best and the worst CPs: the optimization process is stopped if the difference between the objective values of the best and the worst CPs becomes less than a specified accuracy. Maximum distance of CPs: the maximum distance between CPs is less than a pre-fixed value. Now we can establish a new optimization algorithm utilizing the above rules.

Adaptive Charged System Search Algorithm (ACA) For Solving Optimal Power Problem
Level 1: Initialization Step 1: Initialization. Initialize ACA algorithm parameters; Initialize an array of Charged Particles with random positions and their associated velocities (Rules 1 and 2).
Step 2: CP ranking. Evaluate the values of the fitness function for the CPs, compare with each other and sort increasingly.
Step 3: CM creation. Store the CMS number of the first CPs and their related values of the objective function in the CM. Level 2: Search Step 1: Attracting force determination. Determine the probability of moving each CP toward others (Rule 3), and calculate the attracting force vector for each CP (Rule 4).
Step 2: Solution construction. Move each CP to the new position and find the velocities (Rule 5).
Step 3: CP position correction. If each CP exits from the allowable search space, correct its position using Rule 7. Http://www.granthaalayah.com ©International Journal of Research -GRANTHAALAYAH [41] Step 4: CP ranking. Evaluate and compare the values of the objective function for the new CPs, and sort them increasingly.
Step 5: CM updating. If some new CP vectors are better than the worst ones in the CM, include the better vectors in the CM and exclude the worst ones from the CM (Rule 6) Level 3: Terminating criterion controlling Repeat search level steps until a terminating criterion is satisfied (Rule 8).

Simulation Results
At first Adaptive Charged System Search Algorithm (ACA) has been tested in standard IEEE-57 bus power system. The reactive power compensation buses are 18, 25 and 53. Bus 2, 3, 6, 8, 9 and 12 are PV buses and bus 1 is selected as slack-bus. The system variable limits are given in Table 1.
The preliminary conditions for the IEEE-57 bus power system are given as follows: P load = 12.118 p.u. Q load = 3.074 p.u. The total initial generations and power losses are obtained as follows: ∑ = 12.462 p.u. ∑ = 3.3152 p.u. P loss = 0.25848 p.u. Q loss = -1.2062 p.u. Table 2 shows the various system control variables i.e. generator bus voltages, shunt capacitances and transformer tap settings obtained after optimization which are within the acceptable limits. In Table 3, shows the comparison of optimum results obtained from proposed methods with other optimization techniques. These results indicate the robustness of proposed approaches for providing better optimal solution in case of IEEE-57 bus system.   the changes step of 0.025. The limitations of reactive power source are listed in Table 4, with the change in step of 0.01.  The statistical comparison results of 50 trial runs have been list in Table 5 and the results clearly show the better performance of proposed Adaptive Charged System Search Algorithm (ACA) in reducing the real power loss.

Conclusion
In this paper a novel approach Adaptive Charged System Search Algorithm (ACA) used to solve optimal reactive power problem, by considering various generator constraints. To handle the mixed variables a flexible representation scheme was proposed. Adaptive Charged System Search Algorithm (ACA) is a multi-agent approach in which each agent is a Charged Particle (CP) & they affect each other based on their fitness values, separation of distances. The quantity of the resultant force is determined by using the electrostatics laws and the quality of the movement is determined using Newtonian mechanics laws. Proposed Adaptive Charged System Search Algorithm (ACA) has been tested in Standard IEEE 57,118 bus systems & real power loss has been comparatively reduced with voltage profiles are within the limits.