A novel fuzzy logic Levenberg-Marquardt method to solve the ill-conditioned power flow problem

This paper presents a new three-step Levenberg-Marquardt (TSLM) algorithm by using fuzzy logic theory (FLT) for solving power flow equations in ill-conditioned power systems. Using the proposed fuzzy TSLM (FTSLM) method reduces computation times and the number of iterations. In most cases, the FTSLM method converges in the first iteration due to its biquadratic convergence. The reactive and real power mismatches at each bus of the electrical power system are chosen as the input values for fuzzification. The output values of the FTSLM (after defuzzification) are voltage magnitudes and angles of the buses. The proposed method is tested on standard ill-conditioned 11-bus, 13-bus, 43-bus, 118-bus and 2383-bus test systems and the results are compared with the benchmark methods.