Decentralized Circulant LQR Control for Voltage and Current Synchronization in DC Microgrids

This paper presents the adaptation and validation of an LQR-based circulant network control strategy for voltage and current synchronization in a DC microgrid comprising distributed generation units (DGUs). The proposed method, grounded in the optimal synchronization framework for circulant networked multi-agent systems, partitions the microgrid communication graph into circulant subgraphs and computes local state-feedback gains by independently solving algebraic Riccati equations. A detailed state-space model incorporating converter dynamics and continuous peer-to-peer communication is developed. Time-domain simulations demonstrate that the point-of-common-coupling (PCC) voltages return to the \(380\,\) V reference within \(50\,\) ms and maintain a maximum overshoot below \(0.5\%\) , while current synchronization errors remain on the order of a few tenths of an ampere. These results confirm the efficacy of the circulant LQR-based design in enhancing transient performance and fault tolerance, and indicate its scalability for plug-and-play control in larger DC microgrid networks.