Fuzzy modeling of capacitor switching for radial distribution systems

In this paper, a new approach with fuzzy variables is proposed for solving the capacitor-switching problem in radial distribution systems. This method incorporates the load uncertainty in optimizing capacitor on/off status to minimize real power losses and improving bus voltages. Capacitor switching is an important measure for loss minimization of distribution systems. It aims at determining the optimal banks of adjustable capacitor banks to compensate the reactive load demand. Uncertainties in system data, especially those in load demands, may often affect the final decision. Therefore, it is necessary to take uncertain factors into consideration. In this paper, fuzzy distribution power flow is calculated and is treated as the base of capacitor switching calculation. Uncertain load values are represented as trapezoidal fuzzy numbers via fuzzy sets. All variables during the computation are presented as trapezoidal fuzzy complex numbers. The principles of fuzzy set theory are applied to form a methodology suitable for calculations of fuzzy complex numbers while maintaining the fast speed of calculations. A computer program has been developed according to this approach, and numerical studies on a radial distribution system are verified in details