Optimal Capacitor Placement using Sensitivity Index and Differential Evolution for the Three-Phase Distribution Systems with Harmonic Distortion

Y.-H. Yan, T.-H. Wu, and C.-S. Ho (Taiwan)


Capacitor placement, Sensitivity analysis,Differential Evolution, Harmonic load flow analysis


The purpose of this paper is to derive a systematic procedure which combines with sensitivity indices and differential evolution (DE) to optimize the location and bank sizes of compensation shunt capacitors for distribution feeder with harmonic distortion. The problem is formulated as a nonlinear programming of the minimization of real power loss and capacitor cost under the constraints of voltage limits and total harmonic distortion. Since the problem to be solved is an integer nonlinear programming it will be exhaustive to consider all possible combinations of the capacitor locations and sizes. In this paper, a sensitivity test is executed firstly to determine the initial capacitor locations and sizes to speed up the convergence of DE. A set of indices determined by the sensitivity of voltage variation, real power loss, power factor, and harmonic distortion to the reactive power source are used to decide the initial population of DE. Then, using the DE to find the optimal locations and sizes of shunt capacitors of harmonic distribution system. Finally, the proposed hybrid method has been applied to a test feeder to demonstrate the accuracy.

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