A Distributed Optimal Control Strategy for DC Microgrids with MPPT-DGs Based on Exact Convex Relaxation and Distributed Observers

With the high penetration of distributed energy resources (DERs), which are characterized by stochasticity and intermittency, traditional centralized optimization methods face challenges such as communication packet loss, low reliability, and poor scalability in large-scale DC microgrids. Therefore, distributed optimization methods have attracted attention due to their robustness and scalability. This paper extends our previous conference work by proposing a convex-relaxation-based distributed control strategy for DC microgrids with constant power loads (CPLs) and maximum power point tracking (MPPT)-controlled distributed generations (MPPT-DGs). Furthermore, a control strategy based on distributed observers is designed to achieve global optimal control under sparse communication networks. First, an exact convex relaxation method is applied to transform the original non-convex optimal power flow (OPF) problem into a convex problem, with theoretical guarantees of exactness. Then, the Karush–Kuhn–Tucker (KKT) conditions are equivalently transformed into a consensus-based optimality condition and integrated into the distributed control framework. Next, small-signal stability analysis is performed to verify the system’s robustness. To reduce communication costs, a distributed observer-based control strategy is proposed, which can achieve optimal control under sparse communication networks. The impact of communication delays on system stability is also investigated. Finally, the simulation results verify the accuracy of convex relaxation, the effectiveness of the proposed control strategy, and its performance under communication delay.