Convergence analysis for the primal-dual gradient dynamics associated with optimal power flow problems

In this paper we propose a modified primal-dual gradient dynamical system to solve non-convex optimal power flow problems. The modified gradient dynamics maintains the naturally distributed structure and it has isolated equilibrium points as the primal and dual optima. Under mild conditions we show the locally asymptotic stability of the modified gradient dynamics. Simulations on the IEEE 14-bus benchmark system are provided to demonstrate the effectiveness of the proposed approach.