Mathematical Problems in Engineering

Volume 2017 (2017), Article ID 1063045, 11 pages

https://doi.org/10.1155/2017/1063045

## An Improved Particle Swarm Optimization Algorithm Using Eagle Strategy for Power Loss Minimization

^{1}The Graduate School of Natural and Applied Science, Selçuk University, Konya, Turkey^{2}Electrical & Electronics Engineering Department, Selçuk University, Konya, Turkey

Correspondence should be addressed to Hamza Yapıcı; rt.ude.aynok@icipayh

Received 12 January 2017; Accepted 15 March 2017; Published 30 March 2017

Academic Editor: Blas Galván

Copyright © 2017 Hamza Yapıcı and Nurettin Çetinkaya. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The power loss in electrical power systems is an important issue. Many techniques are used to reduce active power losses in a power system where the controlling of reactive power is one of the methods for decreasing the losses in any power system. In this paper, an improved particle swarm optimization algorithm using eagle strategy (ESPSO) is proposed for solving reactive power optimization problem to minimize the power losses. All simulations and numerical analysis have been performed on IEEE 30-bus power system, IEEE 118-bus power system, and a real power distribution subsystem. Moreover, the proposed method is tested on some benchmark functions. Results obtained in this study are compared with commonly used algorithms: particle swarm optimization (PSO) algorithm, genetic algorithm (GA), artificial bee colony (ABC) algorithm, firefly algorithm (FA), differential evolution (DE), and hybrid genetic algorithm with particle swarm optimization (hGAPSO). Results obtained in all simulations and analysis show that the proposed method is superior and more effective compared to the other methods.

#### 1. Introduction

The reactive power optimization approach is important for power quality, system stability, and optimal operation of electrical power systems. Reactive power control can be set with adjusting the voltage levels, tap positions of transformers, shunt capacitors, and other control variables. The reactive power optimization approach can minimize the power losses and improve the voltage profiles. Many conventional methods such as dynamic programming, linear and nonlinear programing, interior point method, genetic algorithm, and quadratic programming have been employed for solving reactive power optimization problem [1–5].

Moreover, in the last years, various intelligence computation methods have proposed for the reactive power optimization such as particle swarm optimization, differential evolution, ant colony, and BC [6–9]. The optimization methods along with fuzzy logic [10] have been used to adjust the optimal setting of power system variables, containing flexible AC transmission systems (FACTs) devices, where the power system losses have been reduced by the optimal placement of thyristor-controlled series compensation (TCSC) and static VAR compensator (SVC). A dynamic weights based particle swarm optimization (PSO) algorithm has been used for reducing power loss [11]. This approach has been implemented to IEEE 6-bus system. The PSO based reactive power optimization method has been presented in [12] for minimizing the total support cost from generators and reactive compensators. In [13], modified artificial fish swarm algorithm (MAFSA) has been proposed to optimize the reactive power optimization and this method has been applied to IEEE 57-bus system. A seeker optimization algorithm has been presented for reactive power dispatch method in [14]; the authors applied the algorithm to several benchmark functions, IEEE 57 and IEEE 118 test systems and then compared with different conventional nonlinear programming methods (such as different versions of GA, DE, and PSO). The optimum conditions for operating the electric power systems have been determined by GA [15]. Authors selected the main objective of the study as the definition of the load buses voltage amplitude values. By this way, they get the minimum power losses in the transmission lines. In [16], reactive power optimization has been solved by adjusting generator voltages, transformer taps, and capacitors/reactors and three GA/SA/TS hybrid algorithms have been used. In the other study [17], the reactive power optimization problem has been solved by using evolutionary computation techniques such as genetic and particle swarm optimization algorithms, and voltage bus magnitude, transformer tap setting, and the reactive power injected by capacitor banks were selected as control variables. Authors applied the proposed algorithms to IEEE 30-bus and IEEE 118-bus systems. In [18], distributed generation has been taken into distribution system and a multiobjective model for reactive power optimization has been investigated to reduce the system loss and voltage deviation and minimize the total reactive compensation devices capacity. Simulation and analysis have been carried out on IEEE 33-bus system with a dynamically adaptive multiobjective particle swarm optimization (DAMOPSO) algorithm. In [19], an improved mind evolutionary algorithm (IMEA) has been presented for optimal reactive power dispatch and voltage control. The proposed method has been carried out on IEEE 30-bus system and simulation results have been compared with GA to prove its efficiency and superiority. On the other study, GA has been proposed for optimization of reactive power flow in a power system [20]. The authors used two different objective functions: active power losses and the voltage-stability-oriented index.

In this study, a particle swarm optimization algorithm using eagle strategy (ESPSO) has been developed to implement reactive power optimization for reducing power losses. Eagle strategy (ES) has been originated by the foraging behavior of eagles such as golden eagles. This strategy has two important parameters: random search and intensive chase. At first it explores the search space globally, and then in the second case the strategy makes an intensive local search with using an effective local optimizer method [21–23]. So, SPO has been improved using ES and implemented to reactive power optimization problem.

Moreover, simulations and analysis of reactive power optimization problem have been performed on IEEE 30-bus test system, IEEE 118-bus test system, and a real power subsystem, and the proposed approach has been compared with various algorithms to show performance. It can be seen that, in case studies, the proposed approach has been outperformed compared to other methods mentioned.

#### 2. Problem Formulation

This paper defines the objective function as reducing power losses of power system. The objective function given in [14, 15, 17, 24] for reactive power optimization problem is given in (1). The equality and inequality constraints are denoted in (3). Note that the real distribution subsystem considered in this paper has no generators; therefore, we did not handle the generator constraints for this power system. Moreover, control variables are self-constrained but dependent variables are implemented to the objective function by using penalty terms. So, the objective function can be given as in (2) as follows:where , , and are the penalty factors which are equal to 1000, is the number of load buses, and is the number of generator buses which injected reactive power. If then is equal to and if then is equal to . On the other hand, if then is equal to and if then is equal to . If then is equal to .

Note that superscripts “min” and “max” in (3) express lower and upper limits, respectively. Here, is the vector of control variable where and is the vector of dependent variable where .

#### 3. Method

##### 3.1. Eagle Strategy (ES)

Eagle strategy (ES) is a two-stage process, developed by Yang et al. [22]. ES is inspired by the foraging behavior of eagles that they fly random in analogy to the Lévy flights. It uses different algorithms which make global search and local search for fitting different proposes. ES has some similarities with random restart hill climbing method, but there are two important differences: ES is a two-stage method, and so a global search randomization method and an intensive local search are combined and ES uses Lévy walks so it can explore the global search space more effectively. Essentially, ES makes the global search in the -dimensional space with Lévy flights; if any probable solution is found, an intensive local optimizer is put to use for local search such as differential evolution, particle swarm optimization algorithm, and artificial bee colony that these have local search capability. Then the procedure starts again with new global search in the new area [21–23, 25, 26].

Note that ES is not an algorithm; it is a method. In fact, various algorithms can be used at the different stages. This provides that it combines the advantages of these different algorithms so as to obtain better results.

Lévy distribution [22] is given as follows:where is standard gamma function and* s* is the step length. When , it becomes Brownian motion as a special case. We used ; thus Lévy walks become the Cauchy distribution.

Pseudocode of ES can be given as in Pseudocode 1.