A quadratic voltage model with modifications for optimal power flow of meshed networks

A quadratic voltage (QV) model with modifications is proposed to formulate the meshed networks’ optimal power flow (OPF) problem. In the QV model, convex relaxations are imposed without approximated terms. The modifications aim to drive the convex relaxations to be exact so that the obtained solution will be feasible to OPF. In the modifications, the set of nonlinear equality constraints with quadratic and bi-linear terms of voltages’ variables are convexified with the convex–concave procedure (CCP). An iterative algorithm is imposed, of which the convergence and its applicability are proved with the mathematical analysis. The superiority of the QV model with modifications is tested over several systems, which indicates the practicality of the proposed model and algorithm.