On the Tightness of Convex Optimal Power Flow Model Based on Power Loss Relaxation

Optimal power flow (OPF) is the important decision-making model in operating the power system. The improvement of the OPF solution quality can provide huge technical and economic benefits. The convex reformulation of the original nonconvex alternating current OPF (ACOPF) model is an efficient way to find the global optimal solution of the ACOPF model but disadvantages with the relaxation gaps. The existence of relaxation gaps hinders the practical application of convex OPF due to the AC-infeasibility problem. We evaluate and improve the tightness of the convex ACOPF model in this paper. Various power networks and nodal loads are considered in the evaluation. A unified evaluation framework is implemented in Julia programming language. This evaluation shows the sensitivity of the relaxation gaps and helps to benchmark the proposed tightness reinforcement approach (TRA). The proposed TRA is based on the penalty function method which penalizes the power loss relaxation in the objective function of the convex ACOPF model. A heuristic penalty algorithm is proposed to find the proper penalty parameter of the TRA. Numerical results show relaxation gaps exist in test cases especially for large-scale power networks under low nodal power loads. TRA is effective to reduce the relaxation gaps of the convex ACOPF model.