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.