A multiple choice relaxation model to solve the AC optimal power flow

• Presenting an AC OPF model with only bilinear and quadratic functions. • Representing the AC OPF as a multiple choice relaxation model. • Proposing an iterative solution method to improve the relaxation tightness. Mathematically speaking, AC optimal power flow (OPF), seeking an optimal state of a power system, is an NP-hard nonconvex optimization problem. In the past two decades, many researchers have attempted to accurately solve the AC OPF problem, that is, derive its globally optimal solution, primarily using relaxation methods. This paper presents a mixed-integer relaxation of AC OPF relying on polyhedral envelopes and a multiple choice model. To this end, first, we recast all nonlinear terms in the AC OPF as bilinear and quadratic terms having known linear approximation errors. Then, all these terms are replaced with their polyhedral envelopes. Last, the polyhedral envelopes are represented as a mixed-integer linear relaxation model using the multiple choice modeling technique. We also design an iterative solution method with a bound-tightening technique where one can improve the approximate functions and derive tighter relaxations progressively. The conducted computational experiment shows that the presented method can tightly relax the AC OPF and accurately solve the adopted case studies. The presented comparisons with 43 previous studies show that the proposed method can outperform earlier AC OPF solution techniques in solution optimality in the adopted case studies.