Nonlinear Optimal Control of DC Microgrids with Safety and Stability Guarantees

A DC microgrid is a promising alternative to the traditional AC power grid, since it can efficiently integrate distributed and renewable energy resources. However, as an emerging framework, it lacks the rigorous theoretical guarantees of its AC counterpart. In particular, safe stabilization of the DC microgrid has been a non-trivial task in power electronics. To address that, we take a control theoretic perspective in designing the feedback controller with provable guarantees. We present a systematic way to construct Control Lyapunov Functions (CLF) to stabilize the microgrid, and, independently, Control Barrier Functions (CBF) to enforce its safe operation at all times. The safety-critical controller (SCC) proposed in this work integrates the two control objectives, with safety prioritized, into a quadratic program (QP) as linear constraints, which allows for its online deployment using off-the-shelf convex optimization solvers. The SCC is compared against a robust version of the conventional droop control through numerical experiments whose results indicate the SCC outperforms the droop controller in guaranteeing safety and retaining stability at the same time.