Hybrid approach to FACTS devices allocation using multi-objective function with NSPSO and NSGA-II algorithms in Fuzzy framework

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Highlights

  • FACTS allocation problem introduced as a multi-objective optimization problem.

  • Introducing two hybrid approaches based on NSPSO and NSGA-II algorithm.

  • Utilizing a hybrid algorithm and Fuzzy logic for solving FACTS allocation problem.

  • Considering technical and economic aspects in optimization.

  • Using active power loss, L index and voltage deviation as objects of optimization.

Abstract

FACTS allocation and assessing its optimal capacity and their undeniable role on improvement of system’s operation is one of most discussed themes in planning and exploitation of the power system. According to the importance of the objects such as power loss reduction, increase of the stability margin, voltage profile improvement and also, less cost imposition need to establish a partial balance between these several goals, FACTS allocation problem introduced as a multi-objective optimization problem. It postulates that the attainment of those registered goals simultaneously, implicates the utilization of the multi-objective optimization methods and finally reaches the Pareto optimal sets. Because of the achievement of this important object, two hybrid approaches based on NSPSO and NSGA-II algorithm and Fuzzy logic is presented in this paper that is able to present the Pareto optimal sets meanwhile to attend the technical and economic aspects. In this work, the problem’s formulation and its analysis is described and finally the efficiency of these approaches in IEEE 14-bus and 30-bus test systems is analyzed.

Introduction

Nowadays the need for more efficient electricity has resulted to innovative technologies in power generation and transmission systems. Flexible AC transmission system (FACTS) is a good example of a new development in transmission systems, FACTS as they are generally known, are new devices that improve transmission systems operations. It is a technology that significantly alters the way transmission systems are developed and controlled together with improvements in asset utilization, system flexibility and system performance. However, to obtain good performance from these controllers, proper placement of these devices in the network is important [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14]. In the past, various optimization techniques have been used for the placement of FACTS devices. In Ref. [1] a sensitivity based method is proposed for finding the optimal placement of FACTS devices in the system. Song et al. [2] have applied an analytical method which is implemented to minimize the security indices. Ref. [3] introduces a PSO based approach to find the optimal location of FACTS devices with minimum cost of installation to improve system loadability. The optimal location of FACTS devices in power system using genetic algorithm is suggested in Ref. [4]. This method optimizes the type and rated value of the FACTS devices simultaneously. In Ref. [5], a genetic algorithm is presented to seek the optimal location of multi-type FACTS devices. In this method the system loadability is applied as measure of power system performance. In [6], the authors proposed an approach for optimal placement of STATCOM which is based on simultaneous application of PSO and CPF to optimize the objective functions. In [7], FACTS devices are optimally allocated to achieve optimal power flow solution. In this approach, the performance of the power system is improved by a Bacterial Swarming Algorithm (BSA). In order to enhance voltage profile and reduce total real power losses, PSO and GA are used for SVC planning in [8]. In Ref. [9], a Micro-Genetic based method which is conjunction with Fuzzy logic, is used to optimize the type and rated value of the FACTS devices. In Ref. [10], the Harmony Search Algorithm (HAS) and GA have been suggested to optimally locate the UPFC, TCPAR and SVC. From a view point to develop a comprehensive solution, in the procedure of transforming the multi-objective function problem to single objective function, it is very difficult to choose appropriate weighting parameters. Considering a range of possible solutions to this problem and that a single best numerical solution may not be applicable in real-life systems due to various not-technical and non-quantifiable constraints, it would be better to identify groups of feasible solutions using multi-objective optimization algorithms. In [11], a multi-objective genetic algorithm is used to characterize the non-dominated solutions. In this method, the optimization process is focused on three parameters: location, type and size of Facts devices. In Ref. [12], the authors have proposed a Multi-Objective Particle Swarm optimization (MOPSO) to find optimal location of SVC. Benabid et al. [13] applied Non-dominated Sorting Particle Swarm Optimization for find the optimal location and rating of SVC and TCSC. But the procedure of the allocation is done in one load level. In Ref. [14], Gitizadeh has presented a multi-objective genetic algorithm (MOGA) to solve FACTS devices problem. A review of these methods reveals that most of these studies are based on technical considerations or economical ones. Both technical and economical criteria are not considered in the selection procedure of the best compromise solution.

In this paper, two hybrid NSPSO + Fuzzy logic and NSGA-II + Fuzzy logic approach are proposed to solve multi-objective FACTS devices allocation problem. Here, active power loss, L index voltage stability and voltage deviation are optimized simultaneously in FACTS devices equipped power systems while maintaining power balance constraints, active and reactive power generation limits, voltage limits, transmission line limits, and physical limits of FACTS devices. Thyristor controlled series capacitor (TCSC) and Static Var Compensator (SVC) are integrated in power flow equations using the reactance model and the injected power model respectively. The optimization procedure is performed for three objective functions: the minimization of active power loss, L voltage stability index and voltage deviation. In this paper, In order to demonstrate the effectiveness of the proposed approaches, the modified IEEE 14-bus and 30-bus systems are taken as test systems. The results extracted by NSPSO + Fuzzy logic algorithm are compared with NSGA-II and hybrid NSGA-II + Fuzzy logic algorithms. The rest of the paper is organized as follows. In Section “Multi-objective optimization overview”, the multi-objective function and problem statement is discussed. Then the proposed hybrid approaches will be introduced, also objective functions are described in Section “Problem formulation”. Steady state model of FACTS devices and decision algorithm are given in Sections “Facts devices modeling” and “Decision algorithm”, respectively. Finally the implementation of the hybrid algorithms is done at the IEEE 14-bus and 30-bus test systems and the results are analyzed in Section “Results and discussion”. The paper closes with the conclusion in Section “Conclusion”.

Section snippets

Multi-objective optimization overview

Many real world problems involve simultaneous optimization of several objective functions. Generally, these functions are non-commensurable and often conflicting objectives. Multi-objective optimization with such conflicting objective functions gives rise to a set of optimal solutions, instead of one optimal solution. The reason for the optimality of many solutions is that no one can be considered to be better than any other with respect to all objective functions. These optimal solutions are

Problem formulation

FACTS devices allocation problem using SVC and TCSC can be formulated as a multi-objective optimization problem. The optimization parameters are FACTS locations and the levels of compensations. In this paper, these objectives include active power loss minimization, L voltage stability index minimization and voltage deviation minimization. They depend strongly on the available control variables. Attaining to the goal of the optimization, could be achieved by placing SVC and TCSC considering the

Facts devices modeling

As the intention is to improve the steady-state operation, the power system as well as the FACTS devices is modeled using static equations. The steady state models of the selected FACTS devices and their models are briefly discussed below [4], [5], [9], [10], [13], [14].

Decision algorithm

The problem of FACTS devices allocation which is described in the past section is a multi-objective optimization problem so it is necessary to use a multi-objective technique for solving it. Thus using a multi-objective technique gives a set of optimal solutions. Selection of the best compromise solution is a crucial step in such algorithms. In this paper, the optimization problem is solved by NSPSO and NSGA-II algorithms and the choice of the optimal solution among the optimal Pareto solutions

Results and discussion

In order to investigate its effectiveness of the proposed algorithm, it is implemented using two standard IEEE 14-bus and 30-bus systems. Data of these systems are taken from [14], [18] respectively and the thermal limits of lines are taken from [19]. The voltage magnitude limits of load buses are set to 0.9 pu and 1.1 pu for lower and upper band respectively. The optimization is made on two parameters: location and size of FACTS devices. Using PV buses and PQ buses for modeling the generators

Conclusion

The present paper makes use of recent advances in multi-objective evolutionary algorithms to develop a method for the combinatorial optimal allocation of FACTS into power systems. Optimizations were performed on two parameters: the locations of FACTS devices, and their rates. The implementation of the proposed hybrid algorithm has performed well when it was used to characterize POF of the FACTS optimal location problem. In order to select the best compromise solution a novel regime which is

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