Accuracy enhancement of second-order cone relaxation for AC optimal power flow via linear mapping

Abstract

• Mapping second-order cone AC OPF equations via semi-Lorentz transformation. • Transforming both variables and network parameters in Model-A. • Applying the proposed linear transformation on the network parameters in Model-B. • Developing an empirical analysis to obtain a good value for the semi-Lorentz factor. • Improving both optimality gap and relaxation error compared to other methods. Optimal power flow (OPF) has always been one of the most crucial tools for power system operations. OPF problem formulation involves non-linear alternative current (AC) power flow equations, and a wide range of challenges occur as a result. This is because the resulting non-convex optimization problems are not only complex and time-consuming, but also difficult to find a global optimum as many local optimums are present. So far, different relaxations have been provided to address these issues. One of the most effective strategies for convexifying such formulations is second-order cone programming (SOCP). Although SOCP is an efficient instrument for convexifying AC OPF equations, it is unable to reach the global optimal solution compared to other methods. The aim of this paper is therefore to provide a new method to approach the global optimum of AC OPF relaxed by SOCP. This method is obtained with the aid of a new linrear tranfsormation called semi-Lorentz transformation as it similar to the Lorentz transformation in the special relativity theory. In this method second-order cone AC OPF equations are mapped to a new model via semi-Lorentz transformation. In addition, an approximation approach is also presented to reach the best semi-Lorentz factor, the main driver in semi-Lorentz transformation, for each particular problem based on the network parameters. From the comparative analysis in case studies, the proposed OPF solution method has robust precision and higher efficiency while consuming less computing time.