Stability Analysis of Vector-Controlled Modular Multilevel Converters in Linear Time-Periodic Framework

Stability analysis of average value models (AVMs) of vector-controlled modular multilevel converters (MMCs) is the subject matter of this paper. Stability analysis of fundamental frequency phasor-based AVMs of MMCs can be conducted in a traditional linear time-invariant framework through eigenvalue computation. This class of models does not consider circulating current control loop and hence fails to capture system instability that occurs in a certain range of gains of the circulating current controller. We propose stability analysis in a linear time-periodic (LTP) framework to solve this issue. To that end, a nonlinear AVM is presented that considers the submodule capacitor insertion dynamics and takes into account the output and the circulating current control schemes in the vector control approach. Upon linearization, an LTP model is derived from this averaged model. It is shown that the Poincare multipliers are indicative of system instability corresponding to a certain range of gains of the circulating current controller.