Heuristic Methods for Solution of FACTS Optimization ... - IEEE Xplore

2011 IEEE Student Conference on Research and Development

Heuristic Methods for Solution of FACTS Optimization Problem in Power Systems Ahmad Rezaee Jordehi, Jasronita Jasni, University Putra Malaysia

use, it is necessary to consider the following three issues: the type of FACTS devices, their location and their settings. The simultaneous solution of the three issues mentioned above represents a very complex and difficult multi-objective optimization problem, because in one side, the power system itself is a highly complex, nonlinear and non-stationary system and in other side, from the optimization perspective, the inclusion of multiple objectives, discontinuous and discrete variables, the existence of highly non-convex and highly scattered feasible regions, and multiple local minima, all make it formidable to find an appropriate technique with the ability to find global optimum in a reasonable computational effort. For solving this problem, there are four groups of methods, classical, technical, heuristic and mixed methods. Classical methods have been used in some researches [1], [2] for FACTS optimization, despite excellent advancements have been made in these methods, they suffer from following drawbacks that make their usage in power system optimization, especially FACTS optimization problem intractable and problematic.

Abstract –This paper presents a comprehensive review on various heuristic methods for solution of flexible AC transmission systems (FACTS) optimization problem in power systems. First, it classifies FACTS optimization methods into four main groups, then subdivides heuristic methods into different subsets and discusses thoroughly about characteristics, advantages and disadvantages of each heuristic subset. Finally, some hints for future researches on this area will be offered. Keywords--FACTS, Heuristics, Optimization

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INTRODUCTION

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HE continual increase in demand for electricity has created so problems for power systems owners and planners such as transmission lines overloading, voltage deviation, stability margin reduction and so on. For dealing with this problem, the appropriate solution is using Flexible AC Transmission system (FACTS) devices to upgrade existing transmission system. FACTS devices consist of diverse devices such as static var compensator (SVC), static synchronous compensator (STATCOM), thyristor controlled series compensator (TCSC), static synchronous series compensator (SSSC), thyristor controlled phase shifting transformer (TCPST), thyristor controlled voltage regulator (TCVR), and unified power flow controller (UPFC). FACTS devices can conduct various control functions such as power flow control, voltage control, phase angle control, damping power system oscillations and so on. Using so called controlling capabilities of FACTS devices, the thermal limit of transmission lines and voltage limit of buses are not exceeded, losses reduce, and stability margin improves. Nowadays, the numerous advantages of FACTS devices in power system is undeniable, however the current concern of power system planners and owners is to extract the maximum possible benefit of these expensive devices. In order to optimize and obtain maximum potential benefit from their

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They do not guarantee reaching to global optima, especially because they start from a single point, not a population, so it is likely that they converge to local optima. ƒ When the size of the problem increases, solution process becomes so difficult and in many cases, it will have convergence problems. (curse of dimensionality) • These methods usually require problem knowledge which in some cases is not available. ƒ Most often, these methods need some preconditions such as continuity, differentiability of objective function and convexity of problem, whereas in most cases the problem does not meet these preconditions. ƒ Computational time (especially when the dimension of problem is high) is so much. Technical methods are second group of optimization methods used in literature [3], [4], which although has the advantage of simplicity, but their salient drawback is that since optimization method is done in two stages and the variables to be optimized, are not optimized simultaneously, the accuracy level of results is not high.

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The third group of methods that have not most of the drawbacks of two previous methods are heuristic methods that their application in FACTS optimization problem is so promising and encouraging. This review is mainly intended to analyze and discuss about the different heuristic methods have been applied on FACTS optimization problem, explain their strengths and drawbacks and also offer some hints for future researches on this area. The paper is organized as follows; in section II, different types of heuristics are discussed meticulously, in section III, an overall view on heuristic methods for FACTS optimization problem is expressed and finally, conclusion is presented in section IV.

In 1999, Paterni et al. [5] applied genetic algorithms to find optimal location of phase shifter in French network consisting of 200-bus and 400 transmission lines in order to maximize ratio of the gain on the annual cost of production to the total investment cost of the phase shifters (return on investment). The computational time was 1.5 hours which was so high. In 2001, Gerbex et al. [6] applied genetic algorithms to determine optimal type, location and setting of multiple FACTS devices (including SVC, TCSC, TCPST and UPFC) in power system in order to maximize loadability. Their main results were threefold; first, using FACTS devices, the loadability of power system improves significantly, second, using different types of FACTS devices enhances the loadability more (synergy effect), and third, there is always a maximum number of devices beyond which, the loadability does not increase further. Although their research was considered comprehensive in that time, but they did not take into account some important issues such as, power losses, FACTS devices cost and generation cost.

II. HEURISTIC TECHNIQUES Heuristics are techniques which seek optimal or near optimal solutions with a population-based and stochastic-based manner and inspired of biological or human intelligence phenomena. In the following, various heuristic algorithms and their application in FACTS optimization problem will be discussed.

B. Evolution Strategies A. Genetic Algorithms Evolution Strategies (ES) are another subset of heuristics which use mutation and selection as their search operators. In the developed ES strategies, namely (µ+λ) and (µ, λ) strategies , the mutation rate is not directly controlled. It is adapted during the process of evolution. This mechanism to adapt strategy parameters is referred to as self-adaptation, which is one of the most powerful characteristics of ES [14]. In FACTS optimization literature, few researches has used this method [14], [15]. In 2006, Santiago et al. [14] applied evolution strategies to find optimal type, location and setting of FACTS devices. From different variants of ES, they used (µ, λ) variant of ES.

Genetic algorithms (GAs) are a subset of heuristic methods which are inspired of the process of natural evolution. In a genetic algorithm, a population of strings which called chromosomes evolves toward better solution. In each generation, the fitness function for each individual is calculated, some of individuals are selected and two operators (mutation and recombination) are applied to them to create offsprings. If the fitness value of offsprings be more than parents, the offsprings replace parents. In this manner, chromosomes evolve from generation to generation. The advantages of GA are 9 It does not require detailed knowledge about objective function, and also does not need convexity or differentiability of objective function. Because of this property, GA is a general-purpose optimization technique. 9 Optimal solutions are not affected by initial solutions, because after choosing initial solutions randomly, stochastic operators (mutation and recombination) are applied to them. One essential point about GA and also other heuristics is that their control parameters should be selected optimally so that the algorithm has a good computational behavior. For example for GA, if the mutation rate be so high, the computational time increases tremendously and if mutation rate be so low, the algorithm is likely to get trapped in local optima. In literature, [5]-[13] has used GA for FACTS optimization problem.

C. Evolutionary Programming Evolutionary Programming (EP) was coined by Fogel in 1960, and involves four steps; ¾ Initialization: Initial population is selected randomly. ¾ Reproduction: New individuals are reproduced by applying mutation operator to current individuals. ¾ Selection: Each individual is evaluated by its fitness value and individuals with higher fitness value constitute next generation ¾ Termination: The algorithm continues until termination criterion reaches. According to above description of evolutionary programming, it seems so similar to GA and ES. But there are a few differences between EP and those two

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other heuristics. The differences between EP and GA are twofold. First is that, in EP, there is no constraint on representation, the typical GA approach involves encoding the problem solutions as a string of representative tokens. Second difference is that in EP, mutation rate changes in evolution process according to a normal distribution (self-adaptation). The main differences between EP and ES is that EP typically uses stochastic selection, but ES uses deterministic selection. In FACTS optimization literature, there are few researches that have used EP for optimization. In [16], Hao et al. applied self-adaptive evolutionary programming to determine optimal location and setting of UPFC in order to achieve maximum attainable loadability in power system and in [17], Zhang et al. applied multi-objective evolutionary programming to tune TCSC and SVC settings in order to enhance power system transient stability.

search and in some cases particle swarm optimization) which its explanation comes in the following section. F. Tabu Search Tabu Search (TS), is an optimization method which belongs to the class of trajectory-based methods. It uses a local or neighborhood search procedure to move from current solution to new solution repeatedly, until termination criterion meets. To explore regions of search space that would be left unexplored by local search procedure, tabu search modifies the neighborhood structure of each solution as the search progresses. The new neighborhood is determined by memory structures. The simplest forms of these memory structures are tabu lists. Tabu search excludes solutions which are in tabu list from neighborhood [22]. In literature, there are few application of TS on FACTS optimization, only in [23], Mori et al. used parallel tabu search (PTS) to maximize available transfer capacity (ATC) in power system with FACTS devices. They used PTS to enhance the performance of TS in some aspects. One aspect is the decomposition of neighbourhoods which contributes to reducing computational effort significantly, and the other aspect is to introduce the multiple tabu lengths. It results in increasing the diversity of solution candidates and provides better solutions. Usually, TS is used in the form of hybrid with SA to solve FACTS optimization problems.

D. Differential Evolution Differential Evolution (DE), Similar to other population-based heuristics has mutation, crossover and selection as its operators. Its main operator which evolves solution in search space and makes it selfadaptive, is the mutation. For applying mutation, three individuals from current population are selected, then the weighted difference between two of them will be added with the third individual to form new individual. In recent years, DE has gained the attraction of researchers on FACTS optimization. [18]-[20]. In 2008, Baghaee et al. [18] used differential evolution for placement of TCSC and UPFC in order to maximize loadability considering power losses and cost functions of FACTS devices. They tested the method on IEEE 30-bus test system. In 2009, Sookanata [19] applied DE in order to minimize generation cost. Also, he used GA and sensitivity analysis and compared the results of them with DE results. The computational time with DE was less than GA and sensitivity analysis.

G. Fuzzy Logic Fuzzy Logic was introduced by Zadeh in 1964 to address uncertainty and imprecision which widely exist in the engineering problems [24]. The advantages of Fuzzy logic for FACTS optimization are that it can represent power system constraints more accurately and fuzzified constraints are softer than crisp constraints. In [25], Thukaram et al. used fuzzy approach for contingency ranking in power system and then to find optimal location of UPFC in power system. Like some other heuristics such as TS, and SA, fuzzy logic is usually used in hybrid form with other heuristics not alone.

E. Simulated Annealing Simulated Annealing (SA) is inspired from annealing process in metallurgy. Its salient advantage is simplicity and its main disadvantage is getting trapped in local optima. Because of this drawback, SA application in FACTS optimization problem is relatively limited. Only in [21] Gitizadeh applied modified SA to find optimal placement of SVC and TCSC in order to alleviate congestion in power system. He used a new perturbation mechanism for SA, but he validated the method just on IEEE 14-bus test system. Most often, SA is used in form of hybrid with other optimization methods (usually tabu

H. Gravitational Search Algorithm Gravitational Search Algorithm (GSA) is based on law of gravity and mass interactions and uses the theory of newtonian physics and its searcher agents are the collection of masses. In GSA, agents are considered as objects and their performance is evaluated by their masses. All these objects attract each other by gravity force and this force causes a movement of all objects globally towards the objects with higher masses. The heavy masses

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correspond to solutions of problem and the position of agents corresponds to solutions and its mass is determined using fitness function. By lapse of time, masses are attracted by heaviest mass which presents the optimum solution in search space [26]. In [27], Rashedi et al. proposed GSA to place SVC in power systems in order to enhance voltage stability. They showed that GSA not only has the merits of particle swarm optimization (PSO), but also its computational time is less. Nevertheless, they did not apply it to large-scale power systems.

constants, maximum velocity, number of particles in the swarm and maximum number of iterations. Two important advantages of PSO are that it is easy to implement and there are few parameters to adjust, also takes real numbers as particles, so it does not require coding and encoding like GA. In recent years some researchers have focused on applying PSO to FACTS optimization problem and trying to improve its computational behavior [33]-[40]. In 2005, Saravanan et al. [33] applied PSO to find optimal type, location and setting of FACTS devices in order to reach maximum loadability and minimum installation cost of FACTS devices. They used SVC, TCSC and UPFC as FACTS controllers. They tested the method on IEEE 6-bus and 30-bus test systems and proposed TCSC as the best FACTS device for the power systems considering both system loadability and installation cost of devices. In 2009, Benabid et al. [37], proposed a new variant of PSO specialized in multi-objective optimization, called non-dominated sorting particle swarm optimization (NSPSO). They found optimal location, type and setting of SVC and TCSC in order to maximize static voltage stability margin, minimize power losses, and minimize load voltage deviation. Comparing the results of NSPSO with non-dominated sorting GA (NSGA) and traditional PSO, they showed more efficiency of NSPSO in multiobjective FACTS optimization problem.

I. Bee Colony Algorithm Bee Colony Algorithm (BCA), is inspired by natural food foraging behavior of honey bees to find the optimal solution. In a colony, foraging process begins by sending scout bees for seeking flower patches. They move from one patch to another randomly. The scout bees that find a patch, deposit their pollen or nectar when return to hive, and perform waggle dance containing information about a flower patch which helps colony to send its bees to appropriate flower patches. The dancer goes back to flower patch with follower bees waiting inside hives after waggle dance. More follower bees are sent to more suitable patches. These steps result in a fast and efficient food foraging process. Bee colony algorithm (BCA) mimics such mentioned behavior exactly [28]. In 2009, Idris eta al. [29] applied bee algorithm to find optimal setting and location of SVC and TCSC in order to maximize ATC in power systems. They validated their results by comparing them with genetic algorithms. They showed that bee algorithm can converge to global solution in one-fourth time of genetic algorithms, but applicability of proposed algorithm to large-scale reallife power system was not proved.

K. Bacterial Foraging Algorithm Bacterial foraging algorithm (BFA) is based on the movement patterns of E. Coli in the intestines. Each individual (bacterium) represents a potential solution of the problem. The algorithm conducts a four-sequential process; chemotaxis, swarming, reproduction and elimination. [41], [42]. In 2010 Kumar et al. [43], applied bacterial foraging algorithm to find optimal location of TCSC for voltage profile improvement and power loss minimization

J. Particle Swarm Optimization Particle Swarm Optimization (PSO) is a stochastic, population-based algorithm inspired by social behavior of animals such as bird flocking and fish schooling. In PSO, a population (swarm) of potential solutions (particles) is used to probe the search space. Particles probe the search space according to a few simple formulae. The movements of particles are guided by their own best known position in the search space as well as the entire swarm's best known position (each bird utilizes its own experience and others experiences). When improved positions are being discovered, these will then come to guide the movements of the swarm. The process is repeated and by doing so it is hoped but not guaranteed that a satisfactory solution will finally be reached [30]-[32]. In PSO, tuning the parameters is so effective on its computational behavior. Its parameters are, type and value of inertia constant, acceleration

L. Other Heuristics There are some other heuristics such as ant colony search, intelligent water drops algorithms, firefly algorithm, artificial immune systems, harmony search, charged system search, monkey search, and cuckoo search which have not been applied to FACTS optimization problem yet, maybe in following years, they will gain attraction of researchers and will be used in FACTS optimization problem. M. Hybrid Heuristics In some cases, FACTS optimization problems cannot be solved efficiently by a single heuristic method. The approach for dealing this problem is to hybridize

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heuristics. By hybridization, two methods remove or attenuate each other's weaknesses and consolidate each others' strengths, so the overall efficiency of optimizer becomes much better [44]. In literature, [45] has used TS/SA, [46] and [47] have used Fuzzy/GA approach and [48] has used PSO/GA. In 2003, Bhasaputra et al. [45] applied hybrid TS/SA to find optimal placement of multi-type FACTS devices to minimize power system generation cost. Hybrid TS/SA approach is an integrated approach between TS and SA, by using TS as a main algorithm. The trial generated neighborhood solution of SA is used for generating neighborhood solution for TS. Also, the probabilistic acceptance criterion of SA is used instead of aspiration level of TS. In 2006, Baskaran et al. [46] applied a micro-genetic algorithm in conjunction with fuzzy logic to find optimal type, location and setting of FACTS devices in order to minimize power system losses. They conducted optimization process in two stages, in the first stage, fuzzy logic was applied to reduce the search space and in second stage, a micro-genetic algorithm was applied. Using this hybrid method, they reduced search space and execution time.

area have been expressed, then different types of heuristic methods have been discussed thoroughly. Authors strongly believe that this review can be so beneficial for researchers who want to research on FACTS optimization problem. V. REFERENCES [1] G.Y. Yang, G. Hovland, R. Majumder, and Z.Y. Dong, “TCSC allocation based on line flow based equations via mixed-integer programming,” IEEE Trans. Power Syst., vol. 22, no. 4, pp. 22622269, November. 2007. [2] F.G.M. Lima, F.D. Galiana, I. Kockar, and J. Munoz, “Phase shifter placement in large-scale systems via mixed-integer programming,” IEEE Trans. Power Syst., vol. 18, no. 3, pp. 10291034, August. 2003. [3] R. Rajaraman, F. Alvarado, A. Maniaci, R. Camfield, S. Jalali, “Determination of location and amount of series compensation to increase power transfer capability,” IEEE Trans. Power Syst., vol. 13, no. 2, pp. 294-300, May. 1998. [4] N.K. Sharma, A. Ghosh, and R.K. Varma, “A novel placement strategy for FACTS controllers,” IEEE Trans. Power Syst., vol. 18, no. 3, pp. 982-987, July. 2003. [5] P. Paterni, S. Vitet, M. Bena, and A. Yokoyama, “Optimal location of phase shifters in French network by genetic algorithm,” IEEE Trans. Power Syst., vol. 14, no. 1, pp. 37-42, February. 1999. [6] S. Gerbex, R. Cherkaoui, and A.J. Germond, “Optimal location of multi-type FACTS devices in a power system by means of genetic algorithms,” IEEE Trans. Power Syst., vol. 16, no. 3, pp. 537-544, August. 2001.

III. OVERALL VIEW ON HEURISTICS Finally considering all the discussion, it should be noted that, heuristics outperform other optimization methods. They have a better computational behavior, are more flexible, do not require conditions such as convexity, continuity or differentiability of objective function and so on. All of them provide satisfactory results, but there is no heuristic algorithm that could provide a superior performance than others in solving all optimization problems, an algorithm may solve some problems better and some problems worse than others, it depends on objective function, equality and inequality constraints considered in the problem. In one word, it is strongly problem-dependent. One important point which authors emphasize on it is that, there should be more research effort on tuning setting parameters of heuristic methods. Most often, researchers tend to test new and various optimization methods on FACTS optimization, but in most of cases, they use a simple and inefficient method (most often just try and error for few combinations of settings) for tuning parameters of optimization methods. By tuning setting parameters appropriately, significantly better computational behavior can be extracted.

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IV. CONCLUSION In this paper, an attempt has been made to review heuristic optimization methods for placement and coordination of FACTS devices. First, the characteristics of an ideal optimization method on this

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