Abstract
Abstract:
This paper demonstrates that the sum and difference of the upper and lower arm voltages are suitable variables for deriving a generalized state-space model of an MMC which settles at a constant equilibrium in steady-state operation. The presented modelling approach allows for separating the multiple frequency components appearing within the MMC as a first step of the model derivation, to avoid variables containing multiple frequency components in steady-state. On this basis, it is shown that Park transformations at three different frequencies (+ω, -2ω and +3ω) can be applied for deriving a model formulation where all state-variables settle at constant values in steady-state, corresponding to an equilibrium point of the model. The resulting model is accurately capturing the internal current and voltage dynamics and the coupling between the different frequency components appearing in the variables of a three-phase MMC. Independently from the control system implementation, the derived equations are valid for accurate representation of the MMC in the applied dqz reference frames, and it can be linearized for utilization in eigenvalue-based analysis of small-signal dynamics. Furthermore, the model can be utilized for control system design by multi-variable methods requiring any stable equilibrium to be defined by a fixed operating point. Time-domain simulations in comparison to an established average model of the MMC, as well as results from a detailed simulation model of an MMC with 400 sub-modules per arm, are presented as verification of the validity and accuracy of the developed model.
This paper demonstrates that the sum and difference of the upper and lower arm voltages are suitable variables for deriving a generalized state-space model of an MMC which settles at a constant equilibrium in steady-state operation. The presented modelling approach allows for separating the multiple frequency components appearing within the MMC as a first step of the model derivation, to avoid variables containing multiple frequency components in steady-state. On this basis, it is shown that Park transformations at three different frequencies (+ω, -2ω and +3ω) can be applied for deriving a model formulation where all state-variables settle at constant values in steady-state, corresponding to an equilibrium point of the model. The resulting model is accurately capturing the internal current and voltage dynamics and the coupling between the different frequency components appearing in the variables of a three-phase MMC. Independently from the control system implementation, the derived equations are valid for accurate representation of the MMC in the applied dqz reference frames, and it can be linearized for utilization in eigenvalue-based analysis of small-signal dynamics. Furthermore, the model can be utilized for control system design by multi-variable methods requiring any stable equilibrium to be defined by a fixed operating point. Time-domain simulations in comparison to an established average model of the MMC, as well as results from a detailed simulation model of an MMC with 400 sub-modules per arm, are presented as verification of the validity and accuracy of the developed model.