Application of high‐order Levenberg–Marquardt method for solving the power flow problem in the ill‐conditioned systems

In an ill‐conditioned power system, the Jacobian matrix is singular or near singular and solving the power flow equations by the traditional methods such as Newton method may lead to divergence. In this paper, we have applied a high‐order Levenberg–Marquardt approach for solving the power flow problems in the ill‐conditioned power systems. High reliability and high speed are the main characteristics of the proposed method. Using the controlling parameters of this method ( σ and μ ) can decrease the number of iterations and the computation time in solving the power flow problem of the ill‐conditioned power systems. The proposed formulations and algorithm are tested on the 11‐bus, 57‐bus, 118‐bus and 2383‐bus ill‐conditioned test systems. The simulation results show that the proposed method can significantly reduce the computation time and the number of iterations.