A SOCP Relaxation for Cycle Constraints in the Optimal Power Flow Problem

• Published in: IEEE transactions on smart grid Vol. 12; no. 2; pp. 1663 - 1673
• Main Authors: Soofi, Arash Farokhi, Manshadi, Saeed D., Liu, Guangyi, Dai, Renchang
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.03.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: angle recovery; convex relaxation; Convexity; Electric potential; Electronic mail; nonlinear programming; Optimal power flow; Optimization; Power flow; Programming; Reactive power; Relaxation methods; second-order cone programming; Sparse matrices; Three-dimensional displays; Voltage
• ISSN: 1949-3053; 1949-3061
• DOI: 10.1109/TSG.2020.3023890

This article presented a convex relaxation approach for the optimal power flow problem. The proposed approach leveraged the second-order cone programming (SOCP) relaxation to tackle the non-convexity within the feasible region of the power flow problem. Recovering an optimal solution that is feasible for the original non-convex problem is challenging for networks with cycles. The main challenge is the lack of convex constraints to present the voltage angles within a cycle. This article aims to fill this gap by presenting a convex constraint enforcing the sum of voltage angles over a cycle to be zero. To this end, the higher-order moment relaxation matrix associated with each maximal clique of the network is formed. The elements of this matrix are utilized to form a convex constraint enforcing the voltage angle summation over each cycle. To keep the computation burden of leveraging the higher-order moment relaxation low, a set of second-order cone constraints are applied to relate the elements of the higher-order moment relaxation matrix. The case study presented the merit of this work by comparing the solution procured by the introduced approach with other relaxation schemes.