Saddle-Node Bifurcations of Power Systems in the Context of Variational Theory and Nonsmooth Optimization

This paper presents a new concept for finding saddle-node bifurcation (SNB) points in voltage stability analysis of power systems by applying the extended functional method (EFM). This method enables the finding of the SNB point of power systems by directly calculating the extreme values of a nonsmooth variational functional, which is obtained in its turn by the so-called nonlinear generalized Collatz-Wilandt formula. The main theoretical result establishes the EFM applicability for finding the maximum loading capacity of power systems. The maximum loading capacity of the power system is shown to be located at the maximizing point of the nonsmooth function of bifurcations. The subgradient method for nonsmooth functions was applied. The EFM was performed on various IEEE test systems to find SNB points, and the results were compared with those obtained with the Continuation Power Flow (CPF) and the Point of Collapse (PoC) method. The simulation results show that the proposed method is robust and, unlike the PoC method, finds the SNB point even when good guessing of the turning point is not available. Tasks such as tracking an SNB point displaced by a contingency and infeasible power flow were performed successfully by using the EFM.