A Comprehensive Study on Existence and Stability of Equilibria of DC Distribution Networks with Constant Power Loads

Constant power loads (CPLs) may cause instability of direct-current (DC) distribution networks. This paper studies the existence and stability of equilibria of DC distribution networks where the sources are buck converters under droop control, the cables are resistances and inductances, and the loads are ZIP (constant impedance, constant current, constant power) loads. Particularly, a sufficient and necessary condition that guarantees the existence of equilibria is determined. Then, the conditions to guarantee that the system has at least one stable equilibrium are determined. Firstly, a sufficient condition for power-flow solvability of the DC distribution networks is obtained based on the monotone convergence theorem. Then, the sufficient and necessary condition is obtained based on successive approximations. When the system has multiple equilibria, it is proved that only the high-voltage equilibrium is stabilizable and all the low-voltage equilibria are inherently unstable and unstabilizable under droop control. Moreover, the robust stability condition for the high-voltage equilibrium is obtained by analyzing the eigenvalues of the linearized system dynamics. Overall, the obtain