Reduced-Order Dynamic Model of Modular Multilevel Converter in Long Time Scale and Its Application in Power System Low-Frequency Oscillation Analysis

A reduced-order dynamic phasor model of modular multilevel converter (MMC) in long time scale, which is applied for power system low-frequency oscillation analysis, is investigated. A tenth-order dynamic phasor model is derived in consideration of the internal circulation current dynamic of MMC. The model is verified via electromagnetic transient simulation. Then, an application of the singular perturbation method to MMC model reduction is presented. Separation of eigenvalues is used as a characterization of time scales and small time constant states is eliminated in the full-order model of MMC. MMC high-voltage direct current (HVdc) models with various orders are embedded into the four-machine two-area system to compare the low-frequency oscillation analysis results. The frequency domain analysis and time domain simulations show that the second-order model has satisfactory performance in describing the low-frequency characteristics of MMC. Moreover, the influence of MMC-HVdc transmission power and outer loop controller parameters on low-frequency oscillation is investigated using the second-order model. The effectiveness of reduced-order model in supplementary controller parameter design is also validated by comparing the difference in the response of various-order models to supplementary frequency-based control.