A distributed approach for solving AC–DC multi-objective OPF problem

Abstract

This paper first proposes an optimization model for Multi-Objective Optimal Power Flow (MO-OPF) problem in AC–DC networks. The considered objective functions are the fuel cost, active power losses, and environmental emission. The AC and DC power flow equations, the converter operating limits, the voltage magnitude limits, and line capacity limits are considered in the proposed AC–DC MO-OPF model. Then an equivalent Gradient Dynamical System (GDS) for the AC–DC MO-OPF model is derived. Each equilibrium point of this GDS is a Karush–Kuhn–Tucker (KKT) point of the original AC–DC MO-OPF model. In Theorem 1, we derive condition under which this KKT point is a saddle point of the original AC–DC MO-OPF problem. The equivalent GDS has the property that it can be solved using a distributed solution algorithm. Every bus in the AC–DC power grid is considered as a local agent in the proposed distributed GDS algorithm, which only obtains information only from its neighbors. In Theorem 2, we prove that proposed distributed approach is locally convergent to the saddle point of the original AC–DC MO-OPF problem. To show the performance of our distributed approach to solve our developed AC–DC MO-OPF model, the simulation results based on several test systems are provided.