Engineering Applications of Artificial Intelligence
A hybrid self-adaptive particle swarm optimization and modified shuffled frog leaping algorithm for distribution feeder reconfiguration
Introduction
In the radially distribution system, the configuration may be varied to obtain a new network structure to reduce power loss, increase system security and enhance power quality. In these system there are many switches that they are divided into two types: sectionalizing-switch (normal closed) and tie-switch (normal open). The change (reconfiguration) in distribution system is performed by opening sectionalizing and closing tie switches so that the radiallity of the network is maintained and all of the loads are energized. The discrete nature of the switch values and radiallity constraint prevent the use of classical optimization techniques to solve the distribution feeder reconfiguration (DFR) problem. Therefore, the most of the algorithms in the literature are based on heuristic search techniques.
In recent years, considerable research has been conducted for loss minimization in the DFR. Kim et al. (1993) proposed a neural network-based method to identify network configurations corresponding to different load levels. Taylor and Lubkeman (1990) presented an expert system using heuristic rules to shrink the search space. Kashem et al. (1999) proposed “distance measurement technique algorithm” that finds a loop first, and then, to improve the load balancing, a switching scheme was determined in that loop. Jeon incorporated the simulated annealing algorithm with Tabu search for loss reduction in Jeon and Kim (2000). The Tabu search attempted to determine a better solution in the manner of a greatest-descent algorithm, but it could not give any guarantee for the convergence property. Lin et al. (2000) presented a refined genetic algorithm (RGA) to reduce losses. Morton and Mareels (2000) presented a brute-force solution for determining a minimal-loss radial configuration. The graph theory involving semi-sparse transformations of a current sensitivity matrix was used, which guarantees a globally optimal solution but needs an exhaustive search. Goswami and Basu (1992) proposed a power-flow-minimum heuristic algorithm for DER problem. Lopez and Opaso (2004) proposed a method for online reconfiguration. Das (2006) presented a fuzzy multi-objective approach to solve DFR. Niknam and New, 2009a, Niknam, 2009b presented two approaches based on norm2 for multi-objective distribution feeder reconfiguration. Niknam, 2009b proposed a hybrid approach based on DPSO, ant colony optimization and fuzzy system for reconfiguration of distribution system. Liu and Chen (2000) proposed a fuzzy genetic algorithm for DFR problem. Bi et al. (2002) proposed a refined genetic algorithm for distribution network reconfiguration. Shirmohammadi proposed the reconfiguration in electric distribution networks for resistive line loss reduction (Shirmohammadi and Hong, 1998). Li et al. (2007) proposed a hybrid particle swarm optimization approach for DFR problem. Yu et al. (2009) presented an improved genetic algorithm with infeasible solution disposing for DFR problem. Chiou proposed a method-variable scaling hybrid differential evolution (VSHDE) for solving the network reconfiguration for power loss reduction and voltage profile enhancement of distribution systems (Chiou et al., 2005). Su proposed a method for reducing power loss and enhancing the voltage profile by the improved mixed-integer hybrid differential evolution (MIHDE) method for distribution systems (Su and Lee, 2003). Cheng and Kou (1994) used simulated annealing for network reconfiguration in distribution system. Raju proposed an algorithm based on sensitivity and heuristics for minimum loss reconfiguration of distribution system (Viswanadha Raju and Bijwe, 2008). Ahuja proposed an AIS–ACO hybrid approach for multi-objective DFR problem (Ahuja et al., 2007).
In the distribution system, since there are many candidate switching combinations, the DFR problem is modeled as a complicated combinatorial, non-differentiable, constrained optimization problem. Therefore, it is difficult to solve the problem by conventional approaches and most optimal algorithms cannot effectively solve this kind of problem and they usually achieve local optimal solutions rather than global optimal solutions.
In this paper, a new hybrid algorithm is presented to find the optimal operating condition of the distribution networks. The algorithm is based on the combination of self-adaptive particle swarm optimization (SAPSO) and modified shuffled frog leaping algorithm (MSFLA).
The PSO algorithm has been recently proposed and proved as a powerful competitor to the other well-known algorithms in the field of optimization (Niknam, 2009b, Niknam, 2009c). Although PSO eventually determines the desired solution, its convergence rate is slow. Proper selection of parameters may increase the performance efficiency by itself. However, as in other evolutionary algorithms (EA), appropriate adjustment of its parameters is cumbersome and usually requires a lot of time. Thus, in this paper a self-adaptive framework is proposed for adjusting PSO algorithm’s parameters. In this paper, the algorithm’s parameters are coevolved with the particles. In proposed paper the (SAPSO) composed of two parts:
- 1.
Self-adaptive discrete particle swarm optimization (SADPSO) which determines the status of sectionalizing switch number.
- 2.
Self-adaptive binary particle swarm optimization (SABPSO) used for determining the status of the tie switches (open or close).
The SFLA which is a population-based optimization algorithm can be used for solving many complex optimization problems, which are nonlinear, non-differentiable and multi-modal. In this paper, a new frog leaping rule is proposed to improve the local exploration of the SFLA. The main idea behind the new frog leaping rule is to extend the direction and the length of each frog’s jump by emulating frog’s perception and action uncertainties. The modification widens the local search space, thus helps to improve the performance of the SFLA. The most prominent profit of MSFLA is its fast convergence speed (Elbeltagi et al., 2005). However, some limitations in MSFLA may slow down the convergence speed and even cause premature convergence.
Taking advantage of the compensatory property of SAPSO and MSFLA, we propose a new algorithm that combines the evolutionary natures of both algorithms (denoted as SAPSO–MSFLA). The robustness of proposed algorithm will be tested on two distribution test feeders and the results are compared with those obtained by other methods.
Section snippets
Distribution feeder reconfiguration problem
The DFR problem is a mixed integer nonlinear and multi-objective problem optimization problem. In the multi-objective DFR, there are many different objectives such as loss minimization, balancing load on transformers, balancing load on feeders, maximum load on feeders and deviation of voltages from their nominal values. In this paper, loss minimization has been considered as the main objective while the others are formulated in the constraints. The DFR problem is described as:
The original PSO
The particle swarm optimization (PSO) algorithm was first proposed by Eberhart and Kennedy (Carlisle and Dozier, 2001; Sakthivel et al., 2009; Taylan and Das, 2009) and has been deserved some attention during the recent years in the global optimization field. PSO is based on the population of agents or particles and tries to simulate its social behavior in optimal exploration of problem space.
In this paper the vector of control variables are composed of two parts
- 1.
- 2.
Shuffled frog-leaping algorithm (SFLA)
SFL algorithm, originally developed by Eusuff and Lansey (2003) and Zhang et al. (2008). The SFL algorithm is a memetic meta-heuristic that is designed to seek a global optimal solution by performing an informed heuristic search using a heuristic function. It is based on evolution of memes carried by interactive individuals and a global exchange of information among the population. The SFL algorithm progresses by transforming ‘‘frogs’’ in a memetic evolution. In this algorithm, frogs are seen
Hybrid self-adaptive PSO and modified SFLA (SAPSO–MSFLA)
The goal of integrating self-adaptive particle swarm optimization (SAPSO) and modified shuffled frog-leaping algorithm (MSFLA) is to combine their advantages and avoid disadvantages, For example, MSFLA is a very efficient procedure but in the MSFLA exist limitations that these limitations might not only slow down the convergence speed, but also cause premature convergence. Furthermore SABPSO, SADPSO algorithms belong to the class of global search procedures but require much computational effort
Simulation and results
In this section, the SAPSO–MSFLA algorithm is employed to solve the DFR for problem. Two networks from different distribution systems were used to evaluate the approach proposed. Due to we use the self adaptive rule to determine the PSO’s parameters and the new frog leaping rule, there is not any assumption to apply the algorithm.
Conclusion
This paper proposes a hybrid evolutionary algorithm based on the combination of SAPSO and MSFLA, called SAPSO–SFLA, to optimally reconfigure radial distribution systems. In the SAPSO, learning factors of BPSO and DPSO, are coevolved with the particles during optimization process also a new frog leaping rule is considered for modification of SFL algorithm. In this paper, power loss minimization is considered as the objective function and load balancing on the transformers and feeders, maximum
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