Distributed Optimal Control of AC Microgrids with Coupled Voltage and Frequency Regulation

This paper develops a droop-free distributed optimal control scheme for grid-forming (GFM) inverters operating in islanded AC microgrids (MGs). The proposed scheme jointly addresses voltage and frequency regulation while achieving coordinated and coupled active/reactive power sharing among distributed generators (DGs). The control is described as a distributed optimization problem in which voltage and frequency are selected as decision variables. The resulting formulation explicitly captures both the admissible voltage/frequency ranges and the inherent coupling among active and reactive powers, voltage, and frequency. A distributed primal-dual gradient method is then designed to obtain the optimal solution despite the nonseparable objective function and the lack of globally available average-voltage information. The proposed control strategy is evaluated through simulations on a four-DG islanded microgrid and a modified IEEE 34-bus distribution system. The results verify its effectiveness and demonstrate improved control performance relative to existing approaches.