An accelerated primal-dual method for semi-definite programming relaxation of optimal power flow

The application of a semi-definite programming (SDP) approach to the Alternating Current Optimal Power Flow problem has attracted significant attention in recent years. However, the SDP relaxation of optimal power flow (OPF) can be computationally intensive and lead to memory issues when dealing with large-scale power systems. To overcome these challenges, we have developed APD–SDP, an optimisation solver based on a first-order primal–dual algorithm. This framework incorporates various acceleration techniques, such as rescaling, step size decay and reset, adaptive line search, and restart, to improve efficiency. To further speed up computations, we have developed a customised eigenvalue decomposition component by exploiting the 3 × 3 block structure in the dual SDP formulation. Experimental results demonstrate that APD–SDP outperforms other commercial and open-source SDP solvers on large-scale and high-dimensional PGLib-OPF datasets.