Optimal Decentralized Microgrid Coordination via the Schur’s Complement and S-Procedure

The evolving landscape of the electricity sector along with increasing environmental concerns necessitate modern power grids to be more efficient, sustainable, and adaptive. Microgrids are typically composed of distributed energy sources which have great potential for enabling energy independence, sustainability, and flexibility. However, practical difficulties that deter the widespread deployment of microgrids include the unpredictability of local generation sources (e.g., renewables) and the lack of inertia that is naturally present in systems containing bulk synchronous plants. In this paper, we propose a near real-time microgrid coordination algorithm that allows actuating components to adapt to changing system conditions. We account for the electrical dependencies and limits in microgrid systems by constructing voltage/current balance relations in the $dq0$ frame and applying strategic decompositions to invoke the Schur’s complement and S-procedure that allow for zero duality gap. We highlight the convergence, feasibility, and scalability features of the proposed decentralized algorithm via theoretical and comparative practical simulation studies.