Abstract
Abstract The Levenberg-Marquardt (L-M) method and the path following interior point (PFIP) method are two most popular methods to solve the optimal power flow (OPF) problem. The performance comparison between the L-M method and the PFIP method applied to solve the OPF problem has not been made so far. The main objective of this paper provides a more comprehensive reference for researcher by analysing, comparing and evaluating the performances of the two methods. The L-M method is employed to solve the OPF problem formulated by the nonlinear complementarity problem (NCP). After the Karush-Kuhn-Tucker (KKT) conditions of OPF model are represented in term of a set of semismooth equations by introducing the NCP function, the semismooth equations are solved by the L-M method. The PFIP method, combined logarithmic barrier function with Newton-Raphson method, has been then applied to solve the OPF problem. Finally, the two methods are tested on the 5-bus, the IEEE 30-bus and the IEEE 118-bus system, respectively. Simulation results show that the two methods get the same optimal value of the objective function under the convergent criterion, while the L-M method has higher computation precision and faster convergence speed than the PFIP method.
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