Second-order cone AC optimal power flow: convex relaxations and feasible solutions

Optimal power flow (OPF) is the fundamental mathematical model to optimize power system operations. Based on conic relaxation, Taylor series expansion and McCormick envelope, we propose three convex OPF models to improve the performance of the second-order cone alternating current OPF (SOC-ACOPF) model. The underlying idea of the proposed SOC-ACOPF models is to drop assumptions of the original SOC-ACOPF model by convex relaxation and approximation methods. A heuristic algorithm to recover feasible ACOPF solution from the relaxed solution of the proposed SOC-ACOPF models is developed. The proposed SOC-ACOPF models are examined through IEEE case studies under various load scenarios and power network congestions. The quality of solutions from the proposed SOC-ACOPF models is evaluated using MATPOWER (local optimality) and LINDO-GLOBAL (global optimality). We also compare numerically the proposed SOC-ACOPF models with other two convex ACOPF models in the literature. The numerical results show robust performance of the proposed SOC-ACOPF models and the feasible solution recovery algorithm.