An adaptive multi-step Levenberg-Marquardt continuation power flow method for voltage stability assessment in the Ill-conditioned power systems

Continuation power flow (CPF) is a well-known way for determining voltage instability point in electrical power systems. In an ill-conditioned power system, solving traditional CPF using the Newton's method encounters divergence or very slow convergence, because the Jacobian matrix is singular or near singular. This paper presents the application of the adaptive multi-step Levenberg-Marquardt (AMSLM) method to solve the power flow problem in an ill-conditioned power system. In the next step and based on the new proposed AMSLM power flow (AMSLM-PF) method, an AMSLM continuation power flow (AMSLM-CPF) method for voltage stability assessment of the ill-conditioned power systems is presented. Moreover, a fuzzy inference system (FIS) is proposed to optimize the parameters of the new AMSLM-PF method. To demonstrate the effectiveness of the proposed AMSLM-PF and AMSLM-CPF methods, detailed simulation results are presented and analyzed for IEEE 14bus, IEEE 43-bus, IEEE 118-bus and 2383-bus power systems.