State-space modelling of modular multilevel converters for constant variables in steady-state

This paper presents an approach for obtaining a dynamic model of a Modular Multilevel Converter (MMC) where all state variables settle at a constant point of equilibrium during steady-state operation. The resulting model can be expressed as a steady-state time-invariant (SSTI) state-space model, which can be linearized for assessment of small-signal stability by eigenvalue analysis or can be utilized for applying advanced control methods. The proposed modelling approach relies on an aggregated voltage-based representation of the internal capacitor dynamics of the MMC, and the derivation is based on the application of three Park transformations at different frequencies (+ω, -2ω and +3ω). The presented voltage-based modelling is suitable when the MMC insertion indexes for the modulation of the individual arms are calculated directly from the controller output references, without compensating for the dynamic variations and continuous oscillations in the internal capacitor voltages of the individual arms. Time-domain simulations with comparison to established MMC models are presented to verify that the proposed state-space model is accurately representing the dynamics of an MMC.