Multistage capacitor switching: an analytical approach

Presented in this paper is a novel mathematical formulation for the multistage capacitor scheduling problem in a radial distribution feeder using a predetermined reactive load duration curve. The objective is to determine the optimal switching times of the predetermined capacitor stages to minimize the energy losses under varying load conditions. The presented methodologies are superior to previous works in generalizing the solution to avoid constraints on the number of capacitors and their switching stages. Three different models for the reactive load duration curve are considered. A closed-form solution for the switching time and energy loss reduction is derived from each case. The presented methodologies are simple and efficient. They provide several capacitor control alternatives of value in distribution automation control. The new methodologies are applied to representative radial systems for validation.