Stability Analysis of Equilibrium of DC Microgrid Under Distributed Control

Constant power loads (CPLs) often lead to system instability and voltage collapse. This paper analyzes the existence and stability of equilibrium of meshed DC microgrids with multiple CPLs under distributed control, which aims to realize current sharing and voltage regulation. Firstly, the power-flow equation of the system is derived. To analyze the solvability of power-flow equation, we transform the problem of the multidimensional quadratic equation solvability into the existence of a fixed-point for a contraction mapping. Then, the sufficient solvability condition is derived based on Banach's fixed-point theorem. Secondly, we build the small-signal model to determine the system qualitative behavior around equilibrium. By analyzing the eigenvalue of system Jacobian matrix based on inertia theorem, the analytical stability conditions are obtained. Further, under the load uncertainty, a robust stability condition which only depends on the maximum load information instead of the real-time load information is derived. Simulation results verify the feasibility of the proposed theorems.