An Enhanced Semidefinite Relaxation Model Combined with Clique Graph Merging Strategy for Efficient AC Optimal Power Flow Solution

Abstract: Semidefinite programming (SDP) is widely acknowledged as one of the most effective methods for deriving the tightest lower bounds of the optimal power flow (OPF) problems. In this paper, an enhanced semidefinite relaxation model that integrates tighter {\lambda}-based quadratic convex relaxation, valid inequalities, and optimality-based bound tightening algorithms derived in accordance with the branch thermal limit boundary surface into the SDP framework is presented to further tighten the lower bounds of the feasible region of OPF problems, effectively combining the advantages of these recent advancements. Additionally, the utilization of chordal decomposition in the complex matrix formulation of SDP can significantly accelerate the solution time. Notably, for the same SDP problem, different chordal decompositions can result in varying solution time. To address this problem, this paper proposes a clique graph merging strategy within the complex matrix SDP framework, which assesses clique sizes and the computational burden on interior-point solvers, as well as reducing the need for hyperparameter tuning and further enhancing the solution efficiency. Finally, the proposed hybrid relaxation model is evaluated using MATPOWER and PGLib-OPF test cases, demonstrating its effectiveness in reducing the optimality gap and validating its computational performance on test cases with up to 13659-node.