Global Asymptotic Stability of Submodule Capacitor Voltage Self-converging Modular Multilevel Converters Based on Characteristic Root Method

Abstract

This study presents global asymptotic stability verification of submodule capacitor voltage self-converging modular multilevel converters (SC-MMCs) according to the characteristic root method, which constructs a submodule switching state matrix for voltage balancing control. The mathematical model of MMC is established in form of the state-space equation. It is proved that SC-MMCs have the characteristic of global asymptotic stability at a certain time from the perspective of switching state matrix characteristic roots, according to the theories of Lyapunov stability and continuous-time piecewise linear system stability. Then, the submodule capacitor voltage self-convergence over a period of time is deduced based on the capacitor voltage deviation vector. Under the constraints of linearly independent switching state matrix row vectors, submodule capacitor voltage self-convergence without real-time voltage calculation and feedback can be achieved. The global asymptotic stability of SC-MMCs and the efficacy of submodule capacitor voltage self-convergence based on switching state matrix are testified by simulations.