In this article, we consider a dc microgrid composed of distributed generation units (DGUs) trading energy among each other, where the energy price depends on the total current generated by all the DGUs. We then use a Cournot aggregative game to describe the self-interested interaction among the DGUs, where each DGU aims at minimizing the deviation with respect to the given reference signals and maximizing the revenue from the sale of the generated power. Thus, we design a fully distributed continuous-time equilibrium-seeking algorithm to compute the generalized Nash equilibrium (GNE) of the game. We interconnect the designed decision-making algorithm with the dynamics of the microgrid in a passive way, and, by leveraging passivity theory, we prove the convergence of the closed-loop system trajectory to a feasible operating point that is also a Nash equilibrium of the collective aggregative game. Finally, we present extensive simulation results that validate the proposed distributed optimal control scheme, showing excellent performance.

In this letter, our objective is to explore how two well-known projection dynamics can be used as dynamic controllers for stabilization of nonlinear systems. Combining the properties of projection operators, Lyapunov stability theory and LaSalle's theorem, we confirm that the projection dynamics on the feasible set and tangent cone are Krasovskii passive. To show the effectiveness of the proposed approach, we use the projection dynamics on the tangent cone for stabilizing boost converters in a DC microgrid while satisfying predefined input constraints.

In this paper we propose an original distributed control framework for DC microgrids. We first formulate the (optimal) control objectives as an aggregative game suitable for the energy trading market. Then, based on duality, we analyze the equivalent distributed optimal condition for the proposed aggregative game and design a distributed control scheme to solve it. By interconnecting the DC microgrid and the designed distributed control system in a power preserving way, we steer the DC microgrid's state to the desired optimal equilibrium, satisfying a predefined set of local and coupling constraints. Finally, based on singular perturbation system theory, we analyze the convergence of the closed-loop system. The simulation results show excellent performance of the proposed control framework.