Optimization Dynamics: A Bus-Level Distributed Approach for Optimal Power Flows

We propose a continuous-time optimization dynamics approach in this paper to solve the nonconvex optimal power flow (OPF) problem. The proposed approach naturally uses the distributed power flow structure for computation. Specifically, each bus in the power network plays as an individual computing agent, which only uses local information to update its own voltage variables as well as Lagrange multipliers. Therefore, the proposed approach is completely distributed at the bus level. Under mild conditions, we first prove the local existence of a unique, continuous solution (with respect to the initial condition) to our optimization dynamics. Next, we show that every trajectory starting from a local neighborhood converges to a pair of primal and dual optima (saddle point) for the associated OPF problem. Simulations based on the IEEE benchmark systems are provided to verify the effectiveness of the proposed approach.