Modeling, control, and reduced-order representation of modular multilevel converters

This paper presents a reduced-order model of the modular multilevel converter (MMC) for electromechanical transient simulations and small-signal analysis. The MMC model is firstly developed in detail; then, simplifications are introduced to reduce it to eleventh- and fourth-order models. The dynamic behaviors of the traditional voltage-source converter and the MMC are also compared. A thorough description of the MMC control system is presented including the inner current control loops, the outer voltage control loops, and the strategy to balance the floating capacitor voltages. Control systems in continuous- and discrete-time domains are given to enable their use in power system simulations and in practical implementations, respectively. Several tests are performed to compare the steady-state and transient response of the detailed and the reduced models. The results show that the fourth-order reduced model can properly capture the input-output dynamics of a complete MMC and significantly reduce the computational cost of large-scale power system simulations with multiple ac/dc converter stations.