A Low-Rank Algorithm Based on Riemannian Optimization for Optimal Power Flow Problem - Huang, Shengquan; Bai, Xiaoqing; Shang, Qinghua; Wang, Rui (2023 3rd Power System and Green Energy Conference (PSGEC), 2023)
The optimal power flow (OPF) problem is essentially a mathematical programming that aims to seek an optimal operation condition subject to network and physical constraints. The semidefinite programming (SDP) relaxation has emerged as a popular technique to solve the OPF problem, but it often finds a high-rank solution and encounters difficulties in obtaining an exact solution for mesh network. Therefore, this paper utilizes a Riemannian optimization method to solve the low-rank optimal solution for OPF problem via SDP. Firstly, a Burer-Monteiro factorization-based augmented Lagrangian method is applied to the standard SDP of OPF. Then, the Riemannian gradient and Hessian are derived to solve the subproblem with the Riemannian trust-region method. Finally, the strategy for escaping from saddle points and the technique that adjusts the parameters for solving a low-rank solution are given. The simulation results verify the accuracy of the proposed algorithm can obtain a lower-rank solution compared to other advanced SDP solvers.