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Constant power loads (CPLs) are often the cause of instability and no equilibrium of dc microgrids. In this study, we analyze the existence and stability of equilibrium of dc microgirds with CPLs and the sufficient conditions for them are provided. To derive the existence of system equilibrium, we transform the problem of quadratic equation solvability into the existence of a fixed point for an increasing fractional mapping. Then, the sufficient condition based on the Tarski fixed-point theorem is derived. It is less conservative compared with the existing results. Moreover, we adopt the small-signal model to predict the system qualitative behavior around equilibrium. The analytic conditions of robust stability are determined by analyzing quadratic eigenvalue. Overall, the obtained conditions provide the references for building reliable dc microgrids. The simulation results verify the correctness of the proposed conditions.

Existence and Stability of Equilibrium of DC Microgrid With Constant Power Loads