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Optimal power flow (OPF) is the fundamental mathematical model in powersystem operations. Improving the solution quality of OPF provide huge economicand engineering benefits. The convex reformulation of the original nonconvexalternating current OPF (ACOPF) model gives an efficient way to find the globaloptimal solution of ACOPF but suffers from the relaxation gaps. The existenceof relaxation gaps hinders the practical application of convex OPF due to theAC-infeasibility problem. We evaluate and improve the tightness of the convexACOPF model in this paper. Various power networks and nodal loads areconsidered in the evaluation. A unified evaluation framework is implemented inJulia programming language. This evaluation shows the sensitivity of therelaxation gap and helps to benchmark the proposed tightness reinforcementapproach (TRA). The proposed TRA is based on the penalty function method whichpenalizes the power loss relaxation in the objective function of the convexACOPF model. A heuristic penalty algorithm is proposed to find the properpenalty parameter of the TRA. Numerical results show relaxation gaps exist intest cases especially for large-scale power networks under low nodal powerloads. TRA is effective to reduce the relaxation gap of the convex ACOPF model.

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