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A mathematical formulation of the optimal reactive power control problem using fuzzy set theory is presented. The objectives are to minimize real power losses and improve the voltage profile of a given system. Transmission losses are expressed in terms of voltage increments by relating the control variables to the voltage increments in a modified Jacobian matrix. This formulation does not require Jacobian matrix inversion, and hence it will save computation time and memory space. The objective function and the constraints are modeled by fuzzy sets. Linear membership functions of the fuzzy sets are defined and the fuzzy linear optimization problem is formulated. The solution space is defined as the intersection of the fuzzy sets describing the constraints and the objective functions. Each solution is characterized by a parameter that determines the degree of satisfaction with the solution. The optimal solution is the one with the maximum value for the satisfaction parameter. Results for test systems reveal the advantages of the approach.>
Abdul-Rahman et al. (Sat,) studied this question.