Calculation of optimal load margin based on improved continuation power flow model

•An improved self-adjustment step-size controlling scheme is proposed for CPF.•A rapid approach is proposed to detect the limit induced bifurcation by calculate the VQ sensitivity while the reactive power generation of specific bus reaches the limit.•A hybrid optimal approach that combines the PSO with the improved CPF is established to search the optimal distribution of imbalanced power.•Parallel processing is deployed in the PSO programming to enhance the performance of the proposed method.

This study proposed an improved continuation power flow (CPF) model to calculate the load margin for voltage stability. A self-adjusting step-size controlling scheme of CPF, which is based on the iterations in the corrector and the reactive power reserve of generator buses, is presented. The load margin here is defined either by encountering the saddle node bifurcation (SNB) or the limit-induced bifurcation (LIB). To confirm the LIB, a rapid approach is proposed to calculate the sensitivity of voltage magnitude to reactive power injection change for load buses. Because CPF with distributed slack bus (DSB) could generate different load margin results corresponding to various allocations of imbalanced power, optimization techniques should be adopted in the search for maximizing the load margin. Therefore, the improved CPF is integrated with an evolutionary mechanism-based particle swarm optimization (PSO) method via coordinate transformation. Furthermore, parallel processing is deployed in the programming for high-performance computing. The case studies for the IEEE 5-bus and IEEE 14-bus test systems demonstrate the efficiency of the proposed approaches.