Identifying Multiple Local Optima for Optimal Power Flow Based on Nonlinear Dynamics

Abstract

An optimal power flow (OPF) problem of power systems can have multiple local optimal solutions, which is worthwhile studying both in theory and practice. Based on the existing nonlinear dynamic systems, this paper proposes an efficient deterministic algorithm to solve multiple or all local optimal solutions of OPF, which takes some numerical improving measures to enhance the numerical convergence for integration process of dynamics and adapt to OPF problem. The steps of this algorithm are as follows: 1. The reflected gradient system (RGS) is used to calculate the decomposition points to locate different feasible components. 2. The quotient gradient system (QGS) is used to calculate feasible points in different feasible components, and we numerically integrate projected gradient system (PGS) with these feasible points as initial points forward until the trajectories approach the local optima. 3. Slack variable perturbation method (SVPM) is proposed to help escape from the saddle points to the adjacent local optima when the trajectories fall into saddle points. Compared with the interior point method (IPM) with random initialization, multiple IEEE test cases show that the proposed algorithm can identify much more local optimal solutions, and meanwhile, significantly reduce the calculation time.

Keywords

• Global optimization
• nonlinear dynamics
• multiple solutions for OPF
• KKT conditions