An Exact SOCP Formulation for AC Optimal Power Flow

Abstract

AC Optimal Power Flow (ACOPF) formulation, in general, is nonlinear and non-convex in nature and hence its application to problems like robust system operation, optimal transmission switching, etc. is a herculean task. Convexification of OPF is desired in order to reduce the complexity of solving such problems. Existing convex formulations such as Semi-Definite Programming (SDP), conventional Second Order Conic Programming (SOCP), and so on and their variants result either in significant optimality gap (OG) or reduced OG, albeit with the presence of non-convexity or approximations which bridge the gap between convexity and non-convexity. Due to these challenges, the current practice in the electricity sector is still to use the DCOPF (approximation of ACOPF). Hence in this paper, an exact and novel SOCP formulation of actual ACOPF has been proposed which aims for getting an equivalent convex formulation similar to the actual nonlinear, non-convex ACOPF. This also ensures attaining zero OG for mesh as well as radial networks and hence, the possibility of easily integrating this formulation in OPFs with data uncertainty. The proposed methodology has been tested on a 3 bus, IEEE 14 bus and IEEE 118 bus test systems on GAMS platform. The results thus obtained, have been compared with those obtained from DCOPF, nonlinear, non-convex ACOPF, conventional SOCP formulation for radial networks (SOCP-I) and conventional SOCP formulation for mesh networks (SOCP-II). The results ensure zero OG of the proposed SOCP formulation.