State-space modelling with Steady-State Time Invariant Representation of Energy based Controllers for Modular Multilevel Converters

The average value model of the Modular Multilevel Converter (MMC) is in general non-linear with time periodic variables. Recent developments demonstrated how the MMC model can be transformed into a a Steady-State Time Invariant (SSTI) representation allowing for linearization of the model. While previous modeling efforts for small-signal eigenvalue analysis considered mainly the classical Circulating Current Suppressing Controller (CCSC), this paper presents an approach for representing a complete energy-based control system in a set of Synchronously Rotating Frames (SRFs). This is obtained by separating the state variables according the their frequency components and applying corresponding Park transformations. The resulting model is based on existing controllers implemented in the stationary abc frame, and enables small-signal stability studies of MMCs with such control systems. Simulations results comparing an EMT type MMC model with the complete SSTI system validate the proposed approach.