Genetically Optimized Fuzzy Placement and Sizing of Capacitor Banks in Distorted Distribution Networks

A genetic algorithm (GA), in conjunction with fuzzy logic (FL) (approximate reasoning), is proposed for simultaneous improvement of power quality (PQ) and optimal placement and sizing of fixed capacitor banks in distribution networks with nonlinear loads imposing voltage and current harmonics. Economic cost is defined as the objective function and includes the cost of power losses, energy losses, and that of the capacitor banks while the voltage limits, number/size of installed capacitors at each bus, and the PQ limits of harmonic standard IEEE-519 are considered constraints. Fuzzy approximate reasoning is used to calculate the fitness function in order to consider the uncertainty of decision making based on the suitability of constraints ( ${\rm S}_{\rm THD}$, ${\rm S}_{\rm V}$) and the objective function (cost index) for each chromosome. Simulation results for the 18-bus and 123-bus IEEE distorted networks using the proposed GA–FL approach are presented and compared with those of previous methods. The main contribution is an improved fitness function for GA, capable of improving the objective function while directing the PQ constraints toward the permissible region using fuzzy approximate reasoning. This method leads to computing the (near) global solution with a lower probability of getting stuck at a local optimum and weak dependency on initial conditions while avoiding numerical problems in large systems.