An Exact Second Order Conic Programming Formulation with McCormick based Relaxation for OPF Solution

Efficient, reliable and economic operation of an electric network is one of the major challenges to the power system operators. Optimal Power Flow (OPF) is a frequently solved fundamental tool, to achieve this goal. OPF is also used as a sub-problem for other complex operational problems like Unit Commitment (UC). Hence, improving the solution quality of OPF with reduced computational burden is a prime motive. In order to attain the computational efficiency, usually the ACOPF models are approximated to linearized DCOPF models. However, these approximations sometimes do not even assure feasibility when implemented on AC network. Hence, computationally efficient strong relaxations of the ACOPF model are required, while achieving near global solution. In this paper, a novel Second Order Conic Programming (SOCP) formulation with McCormick relaxations (MCE-SOCP), has been developed with an aim to get an equivalent linear and convex model similar to the actual nonlinear, non-convex ACOPF. Further, tightening of the variables bound is implemented to improve the fidelity of the proposed model. The quality of the solutions corresponding to global optimum is evaluated on GAMS platform, using IEEE PES PGLib-OPF v19.05 benchmark library. The results thus achieved from MCE-SOCP, have been compared with those achieved from DCOPF, ACOPF, conventional SOCP models for radial networks (SOCP-I) and mesh networks (SOCP-II).