The strings survive and propagate into later generations.

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.

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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.