REDUCTION OF ACTIVE POWER LOSS BY CHAOTIC SEARCH BASED ARTIFICIAL BEE COLONY ALGORITHM

This paper presents Chaotic Search Based Artificial Bee Colony Optimization Algorithm (CSABC) for solving the optimal reactive power problem. Basic Artificial Bee Colony algorithm (ABC) has the advantages of strong robustness, fast convergence and high flexibility, fewer setting parameters, but it has the disadvantages premature convergence in the later search period and the accuracy of the optimal value which cannot meet the requirements sometimes. In this paper the Chaotic Local Search method is applied to solve the reactive power problem of global optimal value. The premature convergence issue of the Artificial Bee Colony algorithm has been improved by increasing the number of scout and rational using of the global optimal value and Chaotic Search. The proposed Chaotic Search Based Artificial Bee Colony Optimization (CSABC) algorithm has been tested in stand IEEE 30, 118bus & practical 191 Indian utility test systems. The results show that the proposed algorithm performs well in reducing the real power loss and prevent premature convergence to high degree with rapid convergence.


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 techniques such as, gradient based optimization algorithm [1,2] quadratic programming, nonlinear programming [3] and interior point method [4][5][6][7]. In recent years standard genetic algorithm (SGA) [8] and the adaptive genetic algorithm (AGA) [9], Partial swarm optimization PSO [10][11] have been applied for solving optimal reactive power problem. This paper presents Chaotic Search Based Artificial Bee Colony Optimization Algorithm (CSABC) for solving the optimal reactive power problem. Artificial Bee Colony algorithm is a global optimization algorithm which is motivated by the Http://www.granthaalayah.com ©International Journal of Research -GRANTHAALAYAH [378] foraging behaviour of honey bee swarms. Basic Artificial Bee Colony algorithm (ABC) [12][13][14] has the advantages of strong robustness, fast convergence and high flexibility, fewer setting parameters, but it has the disadvantages premature convergence in the later search period and the accuracy of the optimal value which cannot meet the requirements sometimes. In this paper the Chaotic Local Search method [15] is applied to solve the reactive power problem of global optimal value. The premature convergence issue of the Artificial Bee Colony algorithm has been improved by increasing the number of scout and rational using of the global optimal value and Chaotic Search. The proposed Chaotic Search Based Artificial Bee Colony Optimization (CSABC) algorithm has been tested in stand IEEE 30, 118-bus & practical 191 Indian utility test systems. The results show that the proposed algorithm performs well in reducing the real power loss and prevent premature convergence to high degree with rapid convergence.

Problem Formulation
The OPF problem is considered as a common minimization problem with constraints, and can be written in the following form: And Where f(x,u) is the objective function. g(x.u) and h(x,u) are respectively the set of equality and inequality constraints. x is the vector of state variables, and u is the vector of control variables.
The state variables are the load buses (PQ buses) voltages, angles, the generator reactive powers and the slack active generator power: x = (P g1 , θ 2 , . . , θ N , V L1 , . , V LNL , Q g1 , . . , Q gng ) T The control variables are the generator bus voltages, the shunt capacitors and the transformers tap-settings: Where Ng, Nt and Nc are the number of generators, number of tap transformers and the number of shunt compensators respectively.

Active Power Loss
The objective of the reactive power dispatch is to minimize the active power loss in the transmission network, which can be mathematically described as follows: Or Where g k : is the conductance of branch between nodes i and j, Nbr: is the total number of transmission lines in power systems. P d : is the total active power demand, P gi : is the generator active power of unit i, and P gsalck : is the generator active power of slack bus.

Voltage Profile Improvement
For minimizing the voltage deviation in PQ buses, the objective function becomes: Where ω v : is a weighting factor of voltage deviation.
VD is the voltage deviation given by:

Equality Constraint
The equality constraint g(x,u) of the reactive power problem is represented by the power balance equation, where the total power generation must cover the total power demand and the power losses:

Inequality Constraints
The inequality constraints h(x,u) imitate the limits on components in the power system as well as the limits created to ensure system security. Upper and lower bounds on the active power of slack bus, and reactive power of generators: 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 reactive powers: Where N is the total number of buses, N T is the total number of Transformers; N c is the total number of shunt reactive compensators.

Artificial Bee Colony (Abc) Algorithm
The Artificial Bee Colony (ABC) algorithm contains three groups: employed bee, onlooker bee and scout. The bee going to the food source which is visited by itself previously is employed bee. The bee waiting on the dance area for making decision to choose a food source is onlooker bee. The bee carrying out random search is scout bee. The onlooker bee with scout also called unemployed bee . In the ABC algorithm, the collective intelligence searching model of artificial bee colony consists of three essential components: employed, unemployed foraging bees, and food sources. The employed and unemployed bees search for the rich food sources, which close to the bee's hive. The employed bees store the food source information and share the information with onlooker bees. The number of employed bees is equal to the number of food sources and also equal to the amount of onlooker bees. Employed bees whose solutions cannot be improved through a predetermined number of trials, specified by the user of the ABC algorithm and called "limit", become scouts and their solutions are abandoned . The model also defines two leading modes of behaviour which are necessary for self-organizing and collective intelligence: recruitment of foragers to rich food sources resulting in positive feedback and abandonment of poorsources by scout causing negative feedback.

The Procedure of ABC
The classical ABC includes four main phases. Initialization Phase: The food sources, whose population size is SN, are randomly generated by scout bees. The number of Artificial Bee is NP. Each food source x m is a vector to the optimization problem, x m has D variables and D is the dimension of searching space of the objective function to be optimized. The initiation food sources are randomly produced via the expression (17). Employed Bee Phase: A employed bee flies to a food source and finds a new food source within the neighborhood of the food source. The higher quantity food source will be selected. The food source information stored by employed bee will be shared with onlooker bees. A neighbor food source vmi is determined and calculated by the following equation (18).
where x k is a randomly selected food source, i is a randomly chosen parameter index, Φ mi is a random number within the range [-1,1]. The range of this parameter can make an appropriate adjustment on specific issues. The fitness of food source is essential in order to find the global optimal. The fitness is calculated by thefollowing formula (19). After that a greedy selection is applied between x m and v m .
where f m (x m ) is the objective function value of x m .
Onlooker Bee Phase: Onlooker bees observe the waggle dance in the dance area and calculate the profitability of food sources, then randomly select a higher food source. After that onlooker bees carry out randomly search in the neighborhood of food source. The quantity of a food source is evaluated by its profitability and the profitability of all food sources. Pm is determined by the formula where fit m (x m ) is the fitness of x m .
Onlooker bees search the neighborhood of food source according to the expression (21) Scout Phase: If the profitability of food source cannot be improved and the times of unchanged greater than the predetermined number of trials, which called "limit" and specified by the user of the ABC algorithm, the solutions will be abandoned by scout bees. Then, the scouts start to randomly search the new solutions. If solution xi has been abandoned, the new solution x m will be discovered by the scout. The x m is defined by expression (22) = + (0.1) * ( − ) Where is the new generated food source, rand (0, 1) is a random number within the range

The Main Concepts of ABC Algorithm
Food sources: According to different problems, the initial food sources are randomly generated in the search space.
Local optimization strategy: In the employed bee phase, employed bees look for the local optimization value in the neighborhood of food source. Generally, different local search strategies will are used for different problems.
Random selection strategy in accordance with probability: In the onlooker bee phase, the random selection strategy will be used to looking for local optimization value in the neighborhood of food source and the higher probability solution will be chosen by onlooker bees.
Feedback strategy: In scout bee phase, food sources which are initially poor or have been made poor by exploitation will be abandoned, this means that if a solution cannot be improved and the unchanged times greater than the predetermined "limit" parameter, the new solution will be discovered by the scout using the negative feedback strategy.
Global optimization strategy: After local optimization and random selection carried out, the global optimization strategy will be used to obtain global optimal value.

Chaotic Search Based Artificial Bee Colony (CSABC) Algorithm
In the basic Artificial Bee Colony algorithm, the best solution founded by onlooker bee which adopted the local search strategy is unable to reach the ideal level of accuracy . In order to improve the accuracy of optimal solution and obtain the fine convergence ability, we use the chaotic search method to solve this problem. In the Chaotic Search based ABC algorithm, onlooker bees apply chaotic sequence to enhance the local searching behavior and avoid being trapped into local optimum. In onlooker bee phase, chaotic sequence is mapped into the food source. Onlooker bees make a decision between the old food source and the new food source according to a greedy selection strategy. In this paper, the well-known logistic map which exhibits the sensitive dependence on initial conditions is employed to generate the chaotic sequence . The chaos system used in this paper is defined by Wherex is the new food source and xi is the chaotic variable, R is the radius of new food source being generated. The food source x mi is in the central of searching region. After the food source has been generated, onlooker bee will exploit the new food source and select the higher profitable one using a greedy selection. Chaotic search method includes the following steps: Step1. Setting the iterations (cycle parameter) of chaotic search and produce a vector 0 =[ 0,1 0,2 0,3 ], which is the initial value of chaotic search; Step2. The chaotic sequence is generated according to expression (23) and a new food source, which combining the chaotic sequence with the original food source, is obtained following the equation (24).
Step3. Calculating the profitability of the new food source and using the greedy selection select the higher profitability food source; Step4. If the number of chaotic search iterations greater than maximum, the artificial bee algorithm will enter the scout bee phase, or else enter the next chaotic search iteration.

Global Search Strategy
In the basic Artificial Bee Colony algorithm only one scout, but we added another one into the modified Artificial Bee Colony algorithm in order to improve the global convergence ability. When a scout bee find the food source unchanged times greater than the limit parameter, it will produce a new food source and replace the original one .Scout bee discover the new food source using the best optimal value strategy which accelerate the global convergence rate. Assume that the solution x i has been abandoned and the scout bee will generate the new solution x m using the following equation Where x m is new food source produced by scout bee using the global optimal value x best and is a random number within the range [-1, 1].

The Procedure of Chaotic Search based Artificial Bee Colony (CSABC) algorithm
The procedure of CABC is as following: Initial Phase According to equation (17)  Step2. Onlooker bee in the guide of equation (21) exploiting the local optimal solution; Step3. Calculating the function value of new food source; Step4. Evaluate the new food source fitness according to equation (20). Scout Bee Phase if (trial>limit) Step1. The first scout randomly discovering the new food source; Step2 The second scout bee updating the food source, which hit the limit parameter, according to formula (25) and (26). Search the global optimal value Global Min End while

Simulation Results
Validity of proposed Chaotic Search Based Artificial Bee Colony Optimization Algorithm (CSABC) has been verified by testing in IEEE 30-bus, 41 branch system and it has 6 generatorbus voltage magnitudes, 4 transformer-tap settings, and 2 bus shunt reactive compensators. Bus 1 is taken as slack bus and 2, 5, 8, 11 and 13 are considered as PV generator buses and others are PQ load buses. Control variables limits are given in Table 1.  Table 2 the power limits of generators buses are listed.  Table 3 shows the proposed CSABC approach successfully kept the control variables within limits. Table 4 narrates about the performance of the proposed CSABC algorithm and Table 5 list out the overall comparison of the results of optimal solution obtained by various methods.  Secondly, Chaotic Search Based Artificial Bee Colony Optimization Algorithm (CSABC), has been tested in standard IEEE 118-bus test system [22].The system has 54 generator buses, 64 load buses, 186 branches and 9 of them are with the tap setting transformers. The limits of voltage on generator buses are 0.95 -1.1 per-unit., and on load buses are 0.95 -1.05 per-unit. The limit of transformer rate is 0.9 -1.1, with the changes step of 0.025. The limitations of reactive power source are listed in Table 6, with the change in step of 0.01.    Table 8 shows the optimal control values of practical 191 test system obtained by CSABC method. And Table 9 shows the results about the value of the real power loss by obtained by Chaotic Search Based Artificial Bee Colony Optimization Algorithm (CSABC).

Conclusion
In this paper proposed Chaotic Search Based Artificial Bee Colony Optimization Algorithm (CSABC) successfully solved optimal reactive power optimization problem. The premature convergence issue of the Artificial Bee Colony algorithm has been improved by increasing the number of scout and rational using of the global optimal value and Chaotic Search. The proposed Chaotic Search Based Artificial Bee Colony Optimization (CSABC) algorithm has been tested in stand IEEE 30, 118-bus & practical 191 Indian utility test systems. The results show that the proposed algorithm performs well in reducing the real power loss and prevent premature convergence to high degree with rapid convergence.