Dissipativity-Based Synthesis of Distributed Control and Communication Topology Co-Design for AC Microgrids

This paper introduces a dissipativity-based framework for the joint design of distributed controllers and communication topologies in AC microgrids (MGs), providing robust performance guarantees for voltage regulation, frequency synchronization, and proportional power sharing across distributed generators (DGs). The closed-loop AC MG is represented as a networked system in which DGs, distribution lines, and loads function as interconnected subsystems linked through cyber-physical networks. Each DG utilizes a three-layer hierarchical control structure: a steady-state controller for operating point configuration, a local feedback controller for voltage tracking, and a distributed droop-free controller implementing normalized power consensus for frequency coordination and proportional power distribution. The operating point design is formulated as an optimization problem. Leveraging dissipativity theory, we derive necessary and sufficient subsystem dissipativity conditions. The global co-design is then cast as a convex linear matrix inequality (LMI) optimization that jointly determines distributed controller parameters and sparse communication architecture while managing the highly nonlinear, coupled dq-frame dynamics characteristic of AC systems. Simulation results from an islanded AC MG in a MATLAB/Simulink environment verify that the proposed framework achieves robust voltage regulation, frequency synchronization, and proportional power sharing through the optimized communication topology.