Complete Large-Signal Stability Analysis of DC Distribution Network via Brayton-Moser's Mixed Potential Theory

For a nonlinear RLC network, Brayton and Moser have proposed the so-called general mixed potential function (GMPF) whose time-derivative is negative semi-definite. Then, the equilibrium of the RLC network is stable if it is a local minimum of the GMPF. Therefore, Brayton-Moser's mixed potential theory is a powerful methodology, which has been widely used in the stability analysis of DC microgrid. However, most of the results in existing references are flawed and incomplete. This paper carries out the complete stability analysis of the DC distribution network with constant power loads via Brayton-Moser's mixed potential theory. Firstly, several critical points in this theory that are often mistaken are emphasized. Secondly, based on Brayton-Moser's mixed potential theory, the condition that the equilibrium is a local minimum is proposed. All the low-voltage equilibria are proved to be unstable, and only the high-voltage equilibrium can be stabilizable and the complete stability conditions are provided. Thirdly, some unsolved problems about the stability issue of DC microgrid via Brayton-Moser's mixed potential theory are presented. Finally, hardware-in-the-loop (HIL) experimental results verify the proposed stability conditions.