Second Conic Approximation
摘要
This chapter presents the application of second-order cone programming (SOCP) to solve the optimal power flow (OPF) problem in direct current (DC) distribution networks. The proposed approach reformulates nonlinear constraints, particularly those involving products of positive variables, into convex second-order conic constraints, ensuring computational efficiency and maintaining solution accuracy. The mathematical formulation begins with a generic nonlinear constraint and introduces auxiliary variables to approximate quadratic terms, leveraging conic relaxations to handle non-convexities effectively. The methodology is validated using the 33-bus DC test system, which includes distributed generation (DG) units at nodes 12, 15, and 31. Numerical results demonstrate the reliability and effectiveness of the proposed SOCP approach. Daily energy losses were reduced by \(43.98\%\) when DG units were operational, highlighting the significant impact of integrating renewable energy sources. The maximum line loadability and thermal constraints across all branches were also respected, ensuring safe and efficient network operation. Furthermore, detailed power generation analyses reveal that DG units operate below their maximum capacities due to thermal limitations and optimal coordination with the slack generator. This strategic operation minimizes energy losses while maintaining voltage and current constraints within permissible limits. The chapter concludes with a discussion on the computational advantages and practical implications of the SOCP-based OPF solution for future energy systems, underscoring its potential for scalability and real-world applications.