Existence Conditions and Stability for the Power-Flow of DC Micro-Grids With CPLs

The power flow equation of the DC micro-grid with distributed generations (DGs) under MPPT control (MPPT-DGs) and constant power loads (CPLs) is a strongly coupled nonlinear equation, which is difficult to solve. Moreover, the negative impedance of CPL tends to make the system unstable. This paper analyzes the existence conditions and stability of the power-flow of DC micro-grids, which contain distributed generations (DGs) under droop control (Droop-DGs), MPPT-DGs, and constant power loads (CPLs). To begin with, the power-flow equation of the DC micro-grid is derived. Next, by constructing a contraction mapping, the analytic solvability condition of the nonlinear power-flow equation is obtained based on Banach's fixed-point theorem. Under the proposed solvability condition, an equivalent linearized model around the equilibrium is developed to analyze the stability of the DC micro-grid. By analyzing the eigenvalues of the Jacobian matrix, we have obtained a robust stability condition of the equilibrium. Finally, simulation results verify the presented results.