Available transfer capability model and calculation considering static security constraints and the saddle node bifurcation

In power market environment, available transfer capability (ATC) is an important index concerned by market participants and system operators. Conventional ATC model includes a set of equality and inequality constraints. In this paper, using a pointwise maximum function, inequalities constraints of static security are transformed into one semismooth equation which can be smoothed by the introduction of a smoothing function. By integrating the saddle node bifurcation limit with smoothing static security constraints, a smoothing ATC model is constructed, which considers security and stability simultaneously. The Levenberg-Marquardt algorithm is applied to solve the smoothing ATC model. Numerical simulation results of the 30-bus system show the proposed model and calculation method are feasible and effective.