Generalized Dynamic Phasor Modeling of the MMC for Small-Signal Stability Analysis

This paper introduces a dynamic phasor model of a half-bridge modular multilevel converter based on variables in the stationary ABC frame. The application of the dynamic phasor theory makes it possible to use converter eigenvalues to study the effect of steady-state harmonics present in the modular multilevel converter (MMC) on its small-signal stability, since the model is inherently time invariant. Relying on a linear transformation, this paper uses a new set of variables with a modified frequency content, which results in lower order dynamic phasor models. A nonlinear dynamic phasor model is developed and linearized. The linear model is compared with a nonlinear averaged MMC model in time domain. Stability analysis by means of eigenvalues and participation factors is carried out for dynamic phasor models that include different frequency content, and the effect of the circulating current suppression controller is analyzed.