Harmonic State Space Modeling of a Three-Phase Modular Multilevel Converter

This paper presents the harmonic state space (HSS) modeling of a three-phase modular multilevel converter (MMC). MMC is a converter system with a typical multi-frequency response due to its significant harmonics in the arm currents, capacitor voltages, and control signals. These internal harmonic dynamics can have a great influence on the operation characteristics of MMC. However, the conventional modeling methods commonly used in two-level voltagesource converters (VSCs), where only the fundamental-frequency dynamic is considered, will lead to an inaccurate model that cannot accurately reflect the real dynamic characteristics of MMC. Therefore, the HSS modeling method, in which harmonics of state variables, inputs, and outputs are posed separately in a state-space form, is introduced in this paper to model the MMC in order to capture all the harmonics and the frequency couplings. The steady-state and small-signal dynamic HSS models of a three-phase MMC are developed, respectively. The validity of the developed HSS model of a three-phase MMC has been verified by the results from both the nonlinear time domain simulation model in MATLAB/Simulink and the laboratory prototype with 12 submodules per arm.