COALESCED ALGORITHM FOR SOLVING REACTIVE POWER PROBLEM

This paper combines Parallel Chaos Optimization Algorithm with Outlook Algorithm (PO) to solve optimal reactive power problem. The algorithm is organized in dual phases. The first phase uses parallel chaos optimization grounded on tent map for global exploration, while outlook algorithm is involved in the second phase for local exploration. The projected PO algorithm has been tested in standard IEEE 57,118 bus test systems and simulation results show clearly the improved performance of the proposed PO algorithm in declining the real power loss when compared to other reported standard algorithms.


Introduction
Reactive power optimization places an important role in optimal operation of power systems. Various numerical methods like the gradient method [1,2], Newton method [3] and linear programming [4][5][6][7] have been implemented to solve the optimal reactive power dispatch problem. Both the gradient and Newton methods have the intricacy in managing inequality constraints. The problem of voltage stability and collapse play a key role in power system planning and operation [8] Evolutionary algorithms such as genetic algorithm have been already projected to solve the reactive power flow problem [9][10][11]. Evolutionary algorithm is a heuristic methodology used for minimization problems by utilizing nonlinear and non-differentiable continuous space functions. In [12], Hybrid differential evolution algorithm is projected to increase the voltage stability index. In [13] Biogeography Based algorithm is projected to solve the reactive power dispatch problem. In [14], a fuzzy based method is used to solve the optimal reactive power scheduling method. In [15], an improved evolutionary programming is used to Http://www.granthaalayah.com ©International Journal of Research -GRANTHAALAYAH [2] elucidate the optimal reactive power dispatch problem. In [16], the optimal reactive power flow problem is solved by integrating a genetic algorithm with a nonlinear interior point method. In [17], a pattern algorithm is used to solve ac-dc optimal reactive power flow model with the generator capability limits. In [18][19][20] proposes a two-step approach to calculate Reactive power reserves with respect to operating constraints and voltage stability. This paper proposes Hybridization of chaos optimization algorithm with outlook algorithm (PO) to solve optimal reactive power problem. Chaos is a worldwide occurrence remaining in many systems in all areas of science [21]. It has three key vibrant properties: the inherent stochastic property, ergodicity and regularity [22]. A chaotic movement can go through every state in a certain area bestowing to its own regularity, and every state is attained only one. Taking benefit of chaos, a new penetrating algorithm called chaos optimization algorithm (COA) is presented [23]. The COA has the lack of the sensitive dependence on preliminary condition; minute difference in preliminary value, there may be carrying totally searching process. Some states may be reached costing longer time. Parallel chaos optimization algorithm was projected to solve this problem by searching synchronously from several preliminary points [24].While, further research show that this method has the inferior searching efficiency near the optimum point due to stochastic property of chaotic movement [25]. Outlook algorithm is proposed according to common knowledge that one chooses the highest point of mountains by outlook. It can solve global optimization problem by engaging supervision mechanism of outlook, policies of generating outlook points and mechanisms of building and solving local problems [26]. Outlook algorithm has great rate of convergence, fast exploration velocity and strong heftiness. The proposed Hybridized Parallel Chaos Optimization algorithm with Outlook Algorithm (PO) algorithm has been evaluated in standard IEEE 57,118 bus test systems. The simulation results show that proposed PO approach outperforms all the entitled reported algorithms in minimization of real power loss.

Problem Formulation
Main objective of the reactive power problem is to minimize the real power loss.

2.1.Active Power Loss
The objective of the reactive power dispatch problem is to minimize the active power loss and can be written in equations as follows: Where F-objective function, P Lpower loss, g k -conductance of branch,V i and V j are voltages at buses i,j, Nbr-total number of transmission lines in power systems.

2.2.Voltage Profile Improvement
To minimize the voltage deviation in PQ buses, the objective function (F) can be written as: Http://www.granthaalayah.com ©International Journal of Research -GRANTHAALAYAH [3] Where VD -voltage deviation, ω v -is a weighting factor of voltage deviation. And the Voltage deviation given by: Where Npq-number of load buses

2.3.Equality Constraint
The equality constraint of the problem is indicated by the power balance equation as follows: Where P G -total power generation, P D -total power demand.

2.4.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 (P g ), and reactive power of generators (Q g ) are written as follows: Upper and lower bounds on the bus voltage magnitudes (V i ) is given by: Upper and lower bounds on the transformers tap ratios (T i ) is given by: Upper and lower bounds on the compensators (Q c ) is given by: Where N is the total number of buses, N g is the total number of generators, N T is the total number of Transformers, N c is the total number of shunt reactive compensators.

Parallel Chaos Optimization Algorithm
Parallel Chaos Optimization Algorithm will probe the solution space by different numerous group chaos sequences. Firstly, use the carrier wave technique to make optimization variables vary to chaos variables. Secondly, intensify the ergodic area of chaotic motion to the variation Http://www.granthaalayah.com ©International Journal of Research -GRANTHAALAYAH [4] ranges of every manageable variable. Finally, use the chaos search method to optimization problem.
The process is concise as follows, Initialization Where i= 1,..,p, represents the different preliminary starting points of i classes, j = 1,.., N , articulates the variable number included in the optimized problem, n is the iteration times.

Carrying out the main carrier wave
The chaos variables are trade in into the optimized variables, furthermore, the change range of the chaos variables are distinctly augmented the corresponding value range of optimized variables.
is variable used for optimized problem.

Carrying out iteration exploration
In each generation, set the optimal solution of all classes as the existing solution. If no improved solution is found after N searches, the second carrier wave will be implemented according to the following equation: Where x j * is the present solution, α is regulation constant, x (j,n+1) is chaos variable.

Execution of iteration search
If no improved solution is found after M searches, stopping search and output existing optimal solution.

Chaos Variables
Tent map has improved ergodicity consistency than logistic map, so the Parallel Chaos Optimization Algorithm based on tent map has improved optimization efficiency. In addition, tent map has simple structure and iteration process is appropriate for computing [27,28]. In this paper chaos variables are produced by tent map. The tent map is defined by: Http://www.granthaalayah.com ©International Journal of Research -GRANTHAALAYAH [5] γ(k + 1) = { 2γ(k) 0 ≤ γ(k) ≤ 1 2 ⁄ 2(1 − γ(k)) 1 2 ⁄ < γ(k) ≤ 1 After change transforming, it can be articulated as the following equation:

Outlook Algorithm
Outlook algorithm self-possessed by three parts: direction mechanism of outlook, policies of generating outlook points and mechanisms of constructing and solving local problems. It can resolve global optimization problem bestowing to the following itinerary: 1) Compatible basic point by direction mechanism of outlook; 2) Producing outlook point of base point by policies of generating outlook points; 3) Selecting outlook point bestowing to given standard by direction mechanism of outlook; 4) Building the local problem of outlook point and resolving it by local optimization algorithm; 5) After receiving all the solutions of local problems chosen, conforming next base point and initiate a new iteration until satisfying end condition and set out solution.

Hybridization of parallel Chaos Optimization Algorithm with Outlook Algorithm
Initially, using Parallel Chaos Optimization Algorithm established on tent map for global exploration. It is easy to touch the region near global optimization solution owing to the ergodicity. Yet, Local searching speed become very slowly and it is difficult to get the high accuracy optimization solution due to the stochastic stuff of algorithm. Thus the outlook optimization algorithm is engaged in the second stage for local search. Extraordinary searching efficiency is obtained after bonding Parallel Chaos Optimization Algorithm with outlook algorithm. The technique is presented as follows: Step i) Initialize chaos variable γ j i (0), 0 ≤ γ j i (0) ≤ 1, (i = 1,2, . . , n j = 1,2, . . , P),by means of stochastic way, which have minor differences. There will produce p×n chaos variables having different track. The positive integers N1, N2 are quantified. Let flag = 1, C = 0, k = 0; where flag is outlook symbol, C is base point counter, k is iteration times.
Step iv) Set X B = X * , where X B is outlook base point.
Step v) If flag = 1 and C < N2, Then carry out Step (vi) or Else go to step (vii).
Step vi) Generating outlook point of base point X o i (i = 1,2, . . , m) according to strategies of generating outlook points.
Step vii) While f(X i o ) ≤ f(X B ) Carry out local search and get local optimum solution X i l from the point X i o . If min f(X i l ) < f(X B ) then X B = X i l , flag = 1, return to step (vii). Or Else carry out step (viii).
Step viii) Halt the exploration process and put out X* = XB as the best solution, f * = f (XB ) as the finest value.

Simulation Results
Proposed Hybridized Parallel Chaos Optimization Algorithm with Outlook Algorithm (PO) algorithm 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 = 12.016 p.u. Q load = 3.013 p.u.
The total initial generations and power losses are obtained as follows: Http://www.granthaalayah.com ©International Journal of Research -GRANTHAALAYAH [7] ∑ = 12.5521 p.u. ∑ = 3.3208 p.u. P loss = 0.25708 p.u. Q loss = -1.2027 p.u. Table 2 shows the various system control variables i.e. generator bus voltages, shunt capacitances and transformer tap settings obtained after PO based optimization which are within the acceptable limits. In Table 3, shows the comparison of optimum results obtained from proposed PO with other optimization techniques. These results indicate the robustness of proposed PO approach for providing better optimal solution in case of IEEE-57 bus system.    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 PO algorithm. Http://www.granthaalayah.com ©International Journal of Research -GRANTHAALAYAH [9]

Conclusion
In this paper proposed Hybridized Parallel Chaos Optimization Algorithm with Outlook Algorithm (PO) algorithm has been successfully solved Optimal Reactive Power problem. The proposed Parallel Chaos Optimization Algorithm with Outlook Algorithm (PO) algorithm has been tested on the standard IEEE 57,118 test bus systems. Simulation results indicate the toughness of projected PO approach for providing better optimal solution in reducing the real power loss when compared to other standard reported algorithms.