A Survey of Particle Swarm Optimization Applications in Electric Power Systems

M. R. AlRashidi, Student Member, IEEE, and M. E. El-Hawary, Fellow, IEEE

Abstract—Particle swarm optimization (PSO) has received increased attention in many research fields recently. This paper presents a comprehensive coverage of different PSO applications in solving optimization problems in the area of electric power systems. It highlights the PSO key features and advantages over other various optimization algorithms. Furthermore, recent trends with regard to PSO development in this area are explored.
This paper also discusses PSO possible future applications in the area of electric power systems and its potential theoretical studies. Index Terms—Particle swarm optimization (PSO), power system control, power system operations



 I. INTRODUCTION

OPTIMIZATION problems are widely encountered in various fields of science and technology. Sometimes such problems can be very complex due to the actual and practical nature of the objective function or the model constraints. Traditionally, optimization methods involved derivative-based techniques such as those summarized in [1]–[3]. These techniques are robust and have proven their effectiveness in handling many classes of optimization problems. However, such techniques can encounter difficulties such as getting trapped in local minima, increasing computational complexity, and not being applicable to certain classes of objective functions. This led to the need of developing a new class of solution methods that can overcome these shortcomings. Heuristic optimization techniques are fast growing tools that can overcome most of the limitations foundin derivative-based techniques.Kennedy and Eberhart first introduced particle swarm optimization(PSO) in 1995 as a new heuristic method [4], [5]. Theoriginal objective of their research was to mathematically simulatethe social behavior of bird flocks and fish schools. As theirresearch progressed, they discovered that with some modifications,their social behavior model can also serve as a powerfuloptimizer. The first version of PSO was intended to handle onlynonlinear continuous optimization problems. However, manyadvances in PSO development elevated its capabilities to handlea wide class of complex engineering and science optimizationproblems. Summaries of recent advances in these areas are presentedin [6] and [7] and will not be addressed in this paper dueto space limitations.

II. AREAS OF PSO APPLICATIONS IN ELECTRIC POWER SYSTEMS
Research in power systems has its share in applying PSO to various optimization problems. Fig. 2 shows the number of published papers in which PSO was applied to different areas of electric power systems (based on IEEE/IEE/Elsevier databases). It clearly indicates its applicability and the fast growing interest in PSO utilization in this research area.Electric power system optimization problems are fairly diverse and they can be categorized in terms of the objective function characteristics and/or type of constraints. They are commonly referred to as linear, nonlinear, integer, and/or mixed integer constrained optimization problems. Traditionally,
a derivative-based optimization technique is utilized to tackle a specific problem based on its formulation which requires differentiability among many other things. However, the PSO technique can be easily adapted to suit various categories of optimization problems with minor modifications. This key attribute makes the PSO a general purpose optimizer that solves a wide range of optimization problems. PSO applications in electric power systems are similar to those in different research fields once a common formulation is established. However, PSO parameter tuning might be different from one application to another. Reference [19] appears to be the first published paper that applied PSO in the area of electric power systems to minimize the real power losses of an electric power grid. The problem is classified as one of mixed-integer nonlinear optimization because some control variables are continuous while others are discrete. This introductory application was followed by a series of PSO related papers to solve similar problems [20]–[22]. The initial motivation to apply PSO in this research field is mainly due to the complexity of this problem, since power flow calculations that involve solving a system of nonlinear equations, are required to evaluate each solution candidate. The PSO technique demonstrated its effectiveness in solving this difficult optimizationproblem by improving the solution’s accuracy and computation time. The following are the major areas in which PSO was applied.

A. Economic Dispatch

El-Gallad et al. [23] and Park et al. [12] adapted PSO to solve the traditional economic dispatch problem. In both papers the objective function was formulated as a combination of piecewise quadratic cost functions with nondifferential regions, instead of adopting a single convex function for each generating unit. This innovation in problem formulation is due to the incorporation of practical operating conditions, like valvepoint effects and fuel types. The system constraints included in [23] were system demand and the balance of power, withnetwork losses incorporated and the generating capacity limits. Park et al. did not account for transmission line losses in [12] forsimplicity. El-Gallad et al. added newconstraints to the problem formulation in [24] by introducing system spinning reserve andgenerator prohibited operating zones. In this formulation, theyincluded the same constraints as those used in [23] and considereda single convex cost function.In [9], a different formulation was proposed by including thegenerator ramp rate limits in the same problem treated in [24].In Gaing’s work [9], a comparison between PSO and geneticalgorithm performance in solving the same economic dispatch problem is made. Gaing introduced a dynamic aspect to thesame problem by adding a time-varying system load in additionto accounting for some of the generator operation relatedrestrictions, such as ramping rate limits and prohibited operatingzones, while imposing system spinning reserve requirementand line flow as inequality constraints [25]. Victoire and Jeyakumar extended Gaing’s research by forming a hybrid optimizer to tackle the same problem [26]. They used sequential quadratic programming to fine-tune the PSO search in finding the optimal solution.Kumar et al. included emission aspects of power dispatching

problem [27]. They utilized PSO in solving a multiobjective optimization problem that includes both cost and emission functions.They combined the two objective functions by assigning  a single price penalty factor to the emission function to form a  single objective function. B. Reactive Power Control and Power Losses Reduction In this area, PSO was used to optimize the reactive power flow in the power system network in order to minimize real power system losses. Yoshida et al. [19], [20], [22] and Fukuyama et al. [21] took the initiative of introducing PSO to reactive power optimization. In their problem formulation, the objective was to find the optimal settings of some control variables that would minimize the total real power losses in a network. The control variables are automatic voltage regulator operating values, transformer tap positions, and a number ofreactive power compensation equipment subject to equality and inequality constraints. Based on the nature of the control variables, the problem is classified as a mixed-integer nonlinear optimization problem since some variables are continuous while others are discrete. Mantawy and Al-Ghamdi investigated

the same problem using a different test system [28]. Miranda and Fonseco appear to be the first to introduce a hybrid  PSO approach in this area [29], [30]. They combined evolutionary  strategies with PSO to improve the robustness of the  classical PSO. In [31], Zhao et al. combined multiagent systems  with PSO to solve the same problem. Esmin et al. considered  shunt capacitor banks as the only type of control variables in  their problem formulation [32]. They incorporated the tangent  vector technique to identify the critical area of power system network where voltage stability might be in danger. Then, they applied PSO to find the “needed” reactive power compensation. A new hybrid method was introduced by Chuanwen and Bompard as they combined PSO with a linear interior point technique to solve a reactive power optimization problem [33]. In their work, PSO was used as a global optimizer to search  the entire solution space, while the linear interior point method acted as a local optimizer to search the space around the optimal  solution.To show the effectiveness of PSO in reactive power control  and power losses reduction, it was successfully applied to a

practical power system in the province of Heilongjiang in China  [13]. This system consists of 151 buses and 220 transmission  lines with 71 control variables. A different problem formulation  was proposed by Coath et al. where they considered reactive  power losses minimization as an objective function [34]. They  also introduced generator real power outputs as additional control  variables. The difference in their problem formulation was  mainly due to the inclusion of wind farms as modern integral  parts of the power system networks.

C. Optimal Power Flow (OPF)
Abido is credited with introducing PSO to solve the OPF problem [35]. In OPF, the goal is to find the optimal settings of the control variables such that the sum of all generator’s cost functions is minimized. The generator real power outputs  are considered control variables in addition to the other control  variables considered previously in the reactive power optimization  problem. PSO was effective in dealing with this complex optimization problem that has various equality and inequality  constraints and both continuous and discrete variables. In a different  approach to the problem, Zhao et al. solved the highly  constrained OPF optimization problem by minimizing a nonstationary  multiagent assignment penalty function [10]. In this

formulation, PSO was used to solve the highly constrained OPF  optimization problem in which the penalty values were dynamically modified in accordance with system constraints. In [36],the passive congregation concept was incorporated in PSO tosolve the OPF problem. This hybrid technique improved the convergence characteristics over the traditional PSO in solving the same OPF problem.D. Power System Controller DesignIn [37] and [38], PSO was employed to find the optimal settingsof power system stabilizer parameters. The problem was formulated as one of min–max optimization of two eigenvaluebased objective functions. Okada et al. went along the samelines when they used PSO to optimally design a fixed-structure

controller to enhance the stability of power systems [39]. In this work, the authors’ goal was to find the global optimal solution of a multimodal optimization problem. PSO was also used  in optimizing the feedback controller gains. Al-Musabi et al.made use of PSO in finding optimal controller gain values for  a load frequency problem of a single area power system [40].Abdel-Magid and Abido extended PSO usage in this area when they enlarged the control system to two areas [41]. In their work, they considered two types of controllers, namely an integral  controller and a proportional plus integral controller. Juang and  Lu combined the genetic algorithm with PSO in [42] to perform  the same optimization process as in [41] on a fuzzy proportional- integral-controller. Ghoshal augmented the problem by  trying to find the optimal proportional-integral-derivative controller gains of a three area power system [43]. He tackled the problem using PSO in addition to other heuristic techniques. Lu and Juang applied PSO to design a fuzzy controller for a thyristor-controlled series capacitor to enhance the transient stability of flexible AC transmission systems [44].
E. Neural Network Training  Neural networks emerged as a valuable artificial intelligence tool in many areas in electric power systems. El-Gallad et al.used PSO to train a neural network for power transformer protection  [45]. The objective was to develop a model that would  be able to intelligently distinguish between magnetizing inrush  current and internal fault current in power transformers. PSO  was employed to improve the accuracy and the execution time of the identification process. Hirata et al. used PSO to determine the optimal connection weights of a neural network model used  to improve stability control of power systems [46]. They formulated  the optimization problem as a min–max problem with  an objective function that has nondifferential and discontinuous  nature. Kassabalidis et al. integrated PSO with a neural network
to identify the dynamic security border of power systems under a deregulated power system environment [47]. F. Other Electric Power System Areas  In [48] and [49], the performance of PSO was explored in the
area of electric power quality by improving the process of feeder reconfiguration. The problem is formulated as a nonlinear optimizationproblemwithnondifferentiablecharacteristics.Victoire and Jeyakumar combined PSO, sequential-quadratic-programming, and tabu search to form a hybrid technique to tackle the
unit commitment combinatorial optimization problem [50]. In the area of short-term load forecasting, Huang et al. were  able to identify the autoregressive moving with exogenous  variable (ARMAX) model using PSO [11]. Slochanal et al. and Kannan et al. introduced PSO in the area of generation  expansion planning in [51] and [52] to solve discrete nonlinear  optimization problems. They used it in [51] to maximize the profit of a generating utility subject to certain market conditions  and various system constraints. In [52], PSO was employed to  minimize the capital and operation cost of the generation expansion  planning problem. Also in this area, PSO was utilized  in solving the expansion planning problem of a transmission  line network [53].

Koay and Srinivasan solved the multiobjective generator maintenance scheduling problem by creating a hybrid technique by means of combining PSO with evolutionary strategies  in [54]. In power system reliability studies, PSO was applied  to a feeder-switch relocation problem in a radial distributionsystem [55]. The authors in [55] used PSO to allocate the mostappropriate positions to place sectionalized devices in distribution lines. The objective function of this problem is categorized as nonlinear with nondifferentiable characteristics. In [56],applications of PSO in finding optimal operation settings of a system composed of distributed generators and energy storagesystems were illustrated. Naka et al. and Fukuyama formed hybrid techniques by combining PSO with other heuristic techniques to improve the performance of a distribution of state estimator in [57] and [58], respectively. PSO was later applied to solve a short-term hydroelectric system scheduling problem in [59]. The problems in references [57]–[59] are formulated as continuous nonlinear optimization problems. Yu et al. applied PSO to tackle the discrete optimal capacitor placement problem in a noisy environment [60].

III. CONCLUSION

This paper presents a summary of PSO applications in power  systems. It highlights many applications in which PSO was  successfully applied, yet it reveals some additional unexplored  areas where it can be further employed like protection, restoration,  etc. Also, deregulating all major parts of the electric power  industry led to the emergence of a new operation philosophy  that will reformulate many optimization problems. Another  promising research area with regard to PSO is hybridization.  Recently, many researchers in power systems attempted to   combine the PSO algorithm with other techniques to form  hybrid tools. PSO adaptability to be integrated with other deterministic and evolutionary optimization algorithms isexpanding. This hybridization extended PSO capabilities and improved its accuracy and computation time. This paper lso emphasizes the need for future mathematical investigations of PSO characteristics and behavior in its search for optimal solution. PSO is still in its infancy and further development and research are needed to enhance its overall performance characteristics.

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