Nonlinear Optimal Control of DC Microgrids with Safety and Stability Guarantees

TL;DR

This paper introduces a control framework for DC microgrids that guarantees safety and stability using Control Lyapunov and Barrier Functions, implemented via quadratic programming for real-time application.

Contribution

It develops a systematic method to design safety-critical controllers for DC microgrids with provable guarantees, integrating stability and safety objectives.

Findings

SCC outperforms droop control in safety and stability.

Control Lyapunov and Barrier Functions enable rigorous guarantees.

Quadratic programming facilitates real-time control deployment.

Abstract

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.