Convex Relaxation with ADMM and Second‐Order Cone Programming for Renewable Energy Microgrids

This chapter introduces a new framework of optimization, applying alternating direction method of multipliers (ADMM) to second-order cone programming (SOCP) to optimize renewable energy microgrids. The study resolved the key issues in microgrid function that are not involved in convectivity, using a convex relaxation procedure that converted complicated power flow constraints into second-order cone formulations that are resolvable. The framework demonstrated strong scalability, achieving near-linear speedup on multi-core processors. This makes it well suited for real-world renewable energy microgrid applications, where computational efficiency is critical. The SOCP solver used open-source interior-point strategies with the ADMM framework by adapting it with an original central layer. The suggested ADDM-SOCP framework was evaluated with a comparative study with three other methodologies: direct interior-point method used on a non-convex problem, a distributed gradient descent method and a traditional heuristic-based control method. The tests were focused on the computational speed, solution optimization, the reliability of convergence and scalability features.