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The Genetic Algorithm Searches

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The genetic algorithm searches for an optimal solution using the principles of evolution based on a certain string which is judged and propagated to form the next generation. The algorithm is designed such that the “fitter” strings survive and propagate into later generations. Genetic Algorithm has been reported to produce superior results because it has the capability to search a near global optimum solution.

The theoretical foundations for genetic algorithms (GA) were first described by John Holland [52] and then presented by David Goldberg [53]. G. Boone and H. Chiang [54] devised a method based on GA’s to determine optimal capacitor sizes and locations. The sizes and locations of capacitors are encoded into binary strings and a crossover is performed to generate a new population. This problem formulation only considered the costs of the capacitors and the reduction of peak power losses. S. Sundhararajan and A. Pahwa [55] proposed an optimization method using the genetic algorithm to determine the optimal selection of capacitors. However, their work differs from [54] in that they use an elitist strategy; whereby the coded strings chosen for the next generation do not go through mutation or crossover procedures. In addition, this formulation includes the reduction of energy losses which was omitted. K. Miu, H. Chiang and G. Darling [56] revisited the GA formulation in [54] and included additional features of capacitor replacement and control for unbalanced distribution systems.

H. Kim and S. You [57] have used the genetic algorithm for obtaining the optimum values of shunt capacitor bank. They have treated the capacitors as constant reactive power loads. M. Delfanti et al. [58] present a procedure for solving the capacitor placement problem. The objective is to determine the minimum investment required to satisfy suitable reactive constraints. D. Das [59] presents the optimal places for capacitors under varying load levels using GA to minimize the energy loss while keeping the voltage at load buses within the specified limit by taking the cost of the capacitors into account. S. Karaki et al. [60] have presented an efficient method for determining the optimal number, location, and sizing of fixed and switched shunt capacitors in radial distribution systems using GA.

K. Kim et al. in [61] proposed a simplex GA hybrid approach combined with multi population GA to determine the location, size, and the number of capacitors in unbalanced distribution systems, although the harmonic distorted systems were not considered in this study. Z. Hu et al. [62] have used GA for off-line VVO to minimizing energy losses. Here switching operation of OLTC was limited by the time interval based approach, therefore search space for GA was reduced. M. Masoum et al. [63] have reported a GA based method that incorporates nonlinear load models for the problem of finding optimal shunt capacitors on distribution systems. R. Santos et al.[64] proposed a nested procedure to solve the optimal capacitor placement problem for distribution networks. At the outer level, a reduced-size genetic algorithm is adopted aimed at maximizing the net profit associated with the investment on capacitor banks.

B. Milosevic and M. Begovic [65] have proposed a strategy based on Non-Sorting Genetic Algorithm for optimal allocation of capacitors in the distribution system to minimize system losses, savings are obtained through reduced demand and energy charges. Besides a positive economic response, load reduction associated with improved power factor at the substation has a beneficial effect on voltage stability by increasing the system stability limit margin. M. Haghifam and O. Malik [66] proposed a GA based method for capacitor allocation in a balanced system which could evaluate the uncertainty of loads. K. Reddy and M. Sydulu [67] have developed the GA-based method for solving the discrete optimization problem of fixed shunt capacitor placement and sizing in the presence of voltage and current harmonics.

S. Jalilzadeh et al. [68] proposed genetic algorithm as search method to determine the optimum value of injected reactive power while considering the effects of the loads harmonic component on the network. D. Zhang, Z. Fu and L. Zhang [69] have developed an improved adaptive genetic algorithm to optimize capacitor switching, and a simplified branch exchange algorithm is developed to find the optimal network structure for each genetic instance at each iteration of capacitor optimization algorithm. G. Carpinelli et al. [70] proposed methods based on the reduction of the search space of GAs or based on micro-genetic algorithms. These methods generally guarantee good solutions with acceptable levels of computational effort. In this study, some fast, GA-based methods are compared and applied for solving the problem of optimal sizing and siting of capacitors in unbalanced multi-converter distribution systems. The algorithms have been implemented and tested on the unbalanced IEEE 34-bus test distribution system, and their performances have been compared with the performance of the simple genetic algorithm technique.

A. Poushafie et al. [71] presented a GA based capacitor placement procedure in ten steps. A. Swarnkar, N. Gupta and N. Niazi [72] have reported a method using index and GA algorithm to determine suitable candidate nodes in distribution systems for capacitor installation. M. Davoodi et al. [73] presented optimal capacitor placement and capacitance computation in the power distribution networks using a method based on GA considering the majority of the influencing factors in its multi-objective target function. S. Moradian, S. Jadid and O. Homaee [74] have applied GA for optimal location and sizing of capacitors in the radial distribution system to minimize power losses and cost of VAr generated by capacitors. The applied method is implemented for a 15-bus, an 85-bus, and a 28-bus distribution network. The results are compared with those the prevalent method. It is shown that for all study cases, the net savings for the proposed method is higher than that of the prevalent method.

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