Mean Square Stability Criterion for Power Systems Under Stochastic Continuous Disturbances

To determine the stability of a power system integrated with numerous wind power generators, considering the stochastic fluctuation of wind power output, this paper mainly studies the stability criterion of power systems under stochastic continuous disturbances (SCDs). The dynamic performance of a power system under SCDs is described through stochastic differential equations (SDEs) based on nonlinear state equations. Under the framework of SDEs, a criterion for determining the mean square stability of a power system under SCDs is proposed, and it is proved that the proposed stability criterion is a necessary and sufficient condition for determining the mean square stability. In addition, the bi-level nonlinear semidefinite programming (NLSDP) problem in the stability criterion is transformed into a single-level NLSDP problem by using the improved Karush–Kuhn–Tucker condition of the inner-layer problem, and an extended primal-dual interior point algorithm is proposed to solve the single-level NLSDP problem. In addition, the optimal objective value calculated from the proposed stability criterion is used to quantify the stability degree of the system under SCDs. Finally, case studies on the modified IEEE-39 and 118 bus systems, and an actual provincial power grid demonstrate the correctness and effectiveness of the proposed stability criterion and solution algorithm.