Error bound of convex approximation for optimal power flow model: A general solving approach based on optimality gap

Regarding the nonconvexity of the optimal power flow (OPF) problem, power industry typically employs convex approximation approaches to satisfy the computational demand. However, the accuracy performances of the convex OPF models are hard to be predicted in actual operating power systems. To control the maximum effect of the approximation error on power dispatch, it is important to solve and compare the worst-case approximation errors of these OPF models (i.e., the error bounds). In this paper, the error bound is represented by the maximum gap of the optimal solutions of the nonconvex and convex OPF models (i.e., the optimality gap) which is further equivalent to be the Hausdorff distance of the feasible regions of the two OPF models. Subsequently, an optimization model is proposed to generally solve the Hausdorff distance as well as the error bound. Case studies show that the proposed error bound is tight and effective when the power system is not seriously congested. The relaxation rate of the error bounds is less than 5% when congestion rate is less than 10%. It provides theoretical guidance for selecting the convex OPF model under the condition without historical operating data.