Small-signal state-space modeling of modular multilevel converters for system stability analysis

Small-signal state-space analysis of power system stability relies on linearized models where steady state operation corresponds to constant values of all state variables. Such models are available and commonly used for analysis of configurations with three-phase 2- or 3-level Voltage Source Converters (VSC). However, the Modular Multilevel Converter (MMC), which is emerging as a preferred topology for VSC-based HVDC transmission, is based on single-phase modules with internal capacitors experiencing double frequency voltage oscillations in steady state. Thus, well-established VSC models applied for small-signal stability studies of MMC-based HVDC systems will ignore the internal energy dynamics of the MMC. This paper presents a simplified model of an MMC HVDC terminal, suitable for small-signal linearization while including the aggregated effect of the internal energy dynamics, the internal circulating currents and the corresponding control loops. This model can be combined with models of ac and dc systems and is intended for including the average energy dynamics of MMC-based HVDC terminals in power system stability studies.