Large-Signal Stability Guarantees for a Scalable DC Microgrid with Nonlinear Distributed Control: The Slow Communication Scenario
Cornelia Skaga, Mahdieh S. Sadabadi, Gilbert Bergna-Diaz
TL;DR
The paper addresses large-signal stability and scalable operation for a DC microgrid with nonlinear distributed control in a slow-communication scenario. It casts the closed-loop dynamics as a singularly perturbed system with fast inner-loop and slow outer-loop dynamics, using Lyapunov functions for the reduced and boundary-layer subsystems to prove Global Exponential Stability ($GES$) under a sufficient time-scale separation. Key contributions include modifying the controller with a saturation mechanism, a leakage function, and an industrial PI component, plus a rigorous stability proof and small-signal analysis, supported by time-domain simulations on a 4-terminal microgrid. The results provide practical guidelines for tuning, showing that diagonal dominance of the mapping $M(oldsymbol{ u})$ and appropriate time-scale separation enable scalable, provably stable proportional current sharing with voltage containment in DC microgrids.
Abstract
The increasing integration of renewable energy sources into electrical grids necessitates a paradigm shift toward advanced control schemes that guarantee safe and stable operations with scalable properties. Hence, this study explores large-signal stability guarantees of a promising distributed control framework for cyber-physical DC microgrids, ensuring proportional current sharing and voltage containment within pre-specified limits. The proposed control framework adopts nonlinear nested control loops--inner (decentralized) and outer (distributed)--specifically designed to simultaneously achieve the control objectives. Our scalable stability result relies on singular perturbation theory to prove global exponential stability by imposing a sufficient time-scale separation at the border between the nested control loops. In particular, by saturating the influence of the outer loop controller in the inner loop, the proposed controller preserves a more convenient mathematical structure, facilitating the scalability of the stability proof using Lyapunov arguments. The effectiveness of our proposed control strategy is supported through time-domain simulations of a case-specific low-voltage DC microgrid following a careful tuning strategy, and a small-signal stability analysis is conducted to derive practical guidelines that enhance the applicability of the method.