Power loss reduction by chaotic based predator-prey brain storm optimization algorithm

Received Jul 19, 2019 Revised Feb 19, 2020 Accepted Mar 3, 2020 In this paper chaotic predator-prey brain storm optimization (CPB) algorithm is proposed to solve optimal reactive power problem. In this work predator-prey brain storm optimization position cluster centers to perform as predators, consequently it will move towards better and better positions, while the remaining ideas perform as preys; hence get away from their adjacent predators. In the projected CPB algorithm chaotic theory has been applied in the modeling of the algorithm. In the proposed algorithm main properties of chaotic such as ergodicity and irregularity used to make the algorithm to jump out of the local optimum as well as to determine optimal parameters CPB algorithm has been tested in standard IEEE 57 bus test system and simulation results show the projected algorithm reduced the real power loss considerably.


INTRODUCTION
The main objective of optimal reactive power problem is to minimize the real power loss and bus voltage deviation. To till date various methodologies has been applied to solve the optimal reactive power problem. The key aspect of solving reactive power problem is to reduce the real power loss. Previously many types of mathematical methodologies [1][2][3][4][5][6] have been utilized to solve the reactive power problem, but they lack in handling the constraints to reach global optimization solution. In the next level various types of evolutionary algorithms [7][8][9][10][11][12][13][14][15] has been applied to solve the reactive power problem. This paper proposes chaotic predator-prey brain storm optimization (CPB) algorithm to solve optimal reactive power problem. Brain storm optimization algorithm commonly uses grouping, replacing, creating, crossing, and selecting operators to generate new-fangled ideas which grounded on the present ideas, in order to perk up the ideas in all generation in order to reach the optimal solution. K-mean clustering method is utilized to group the N ideas into M clusters in the grouping operator. In this work predator-prey brain storm optimization position cluster centers to perform as predators, consequently it will move towards better and better positions, while the remaining ideas perform as preys; hence get away from their adjacent predators.
Finally cluster centers can maintain the most excellent individuals of the swarm and moving in the direction of the global best position, but at the same time the prey operation avert the swarm from getting trapped into local optimum solution. In the projected CPB algorithm chaotic theory has been applied in the modeling of the algorithm. In the proposed algorithm main properties of chaotic such as ergodicity and irregularity used to make the algorithm to jump out of the local optimum as well as to determine optimal parameters. Proposed CPB algorithm has been tested in standard IEEE 57 bus test system and simulation results show the projected algorithm reduced the real power loss effectively.

PROBLEM FORMULATION
Reduction real power loss is the key goal of the work and the objective function has been written as follows: Voltage deviation mathematically written as, Constraint (equality); Constraints (inequality);

CHAOTIC PREDATOR-PREY BRAIN STORM OPTIMIZATION ALGORITHM
Inside the searching space aset of "Nc" ideas are arbitrarily engendered. Brain storm optimization algorithm population (BSO) population is defined as, = { = [ 1 , . . , ]| ∈ , 1 ≤ ≤ } in this symbolize the ith idea of the Brain storm optimization algorithm population, = indicate the idea in solution space, Nc-population size. Preliminary population X (0) and the nth iteration population denoted as X (n). Fitness value ( ) is computed for evaluated idea. Brain storm optimization algorithm [16,17] commonly uses grouping, replacing, creating, crossing, and selecting operators to generate new-fangled ideas which grounded on the present ideas, in order to perk up the ideas in all generation in order to reach the optimal solution. K-mean clustering method is utilized to group the N ideas into M clusters in the grouping operator. In order to engender new-fangled idea = [ 1 , 2 , . . , ], (1 ≤ ≤ ). Brain storm optimization algorithm population first verify whether to generate the new-fangled idea based on one or two chosen clusters. New-fangled idea is generated by: = { , "1" Once the new-fangled idea has been formed, a crossover between new-fangled one and the previous one is conducted [16,17]. Through crossover, ′ , ′ are engendered together both the previous and newly formed one are computed then the previous one is swap by the most excellent one. For "Nc" time's new-fangled idea is created creating for completion of one generation. Once end criterion satisfied then Brain storm optimization algorithm procedure stops, or else it go to the subsequent generations to replicate the grouping, replacing, creating, crossing, and select procedure [17].
In this work predator-prey brain storm optimization position cluster centers to perform as predators, consequently it will move towards better and better positions, while the remaining ideas perform as preys; hence get away from their adjacent predators. Finally cluster centers can maintain the most excellent "P" is a binary variable which determine about the status of the prey; flee or not; -weight factor of the predator operator; a, b-factors used to measure the complexity of fleeing.
In the projected CPB algorithm chaotic theory has been applied in the modeling of the algorithm. In the proposed algorithm main properties of chaotic such as ergodicity and irregularity used to make the algorithm to jump out of the local optimum as well as to determine optimal parameters.
At each generation end, chaotic search will be introduced to the exploration in the neighborhood of the present best solution to prefer superior solution for subsequent generation. Through this when local best is reached then stopping will be avoided and also, reaching the optimal solution time will be reduced.
Step a : Parameters are initialized.
Step b : Assessment of all ideas, then record the most excellent one as the global most excellent idea. In the interim, by k-means clustering algorithm, cluster the Nc ideas into M clusters; subsequently grade the ideas in each cluster and record the most excellent idea as cluster center in every cluster.
Step c : Comparison will be done with Probability to replace the cluster center, when arbitrary value between 0 and 1 is smaller, and then arbitrarily choose a cluster center to be swap by an arbitrarily engendered idea; or else, not anything.
Step d : Comparison will be done with probability to select one cluster, when arbitrary value between 0 and 1 is smaller, subsequently choose one cluster; or else, pick two clusters.
Step e : Comparison will be done with probability to select the center of the one selected when arbitrary value between 0 and 1 is smaller, subsequently choose cluster center and go to step f; or else, choose further ideas and move to step g.
Step f : With reference to , = + × ( , ) + ( , − ) and the most excellent idea, modernize the cluster center (s), and subsequently move to step h.
Step h : Recently engendered idea crossovers with the current idea to engender two more ideas.
Then Compare the four ideas, and the most excellent one will be retained and recorded as the new-fangled individual.
Step i : In the region of the most excellent solution parameters carry out the chaotic exploration with reference to ℎ +1 = 4 ℎ (1 − ℎ ) subsequent to alter the parameters ranges into (0, 1). Amongst the produced series of ideas, choose the most excellent one and employ it to swap the previous finest idea.
Step j : When "Nc" ideas have been modernized, then go to step k. or else move to step d.
Step k : After assessing the Nc ideas, modernize the cluster center.
Step l : When present number of iterations is less than maximum number of iterations, then move to step b or else the algorithm is stopped and the most excellent idea is determined as the most excellent solution.

SIMULATION STUDY
Proposed CPB algorithm has been tested in IEEE 57 bus system [18]. Table 1 shows the constraints of control variables, Table 2 Table 3. Figure 1 shows the comparison of real power loss and Figure 2 indicate about the real power loss reduction in percentage.

CONCLUSION
Chaotic predator-prey brain storm optimization (CPB) algorithm successfully solved the optimal reactive power problem. Predator-prey brain storm optimization position cluster centers to perform as predators, consequently it will move towards better and better positions, while the remaining ideas perform as preys; hence get away from their adjacent predators. In the projected chaotic predator-prey brain storm optimization algorithm chaotic theory has been applied in the modeling of the algorithm. In the proposed algorithm main properties of chaotic such as ergodicity and irregularity used to make the algorithm to jump out of the local optimum as well as to determine optimal parameters. Proposed CPB algorithm has been tested in standard IEEE 57 bus test system and simulation results show the projected algorithm reduced the real power loss efficiently.