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This paper investigates the stability of offshore wind farms integration through a modular multilevel converter-based high-voltage dc (MMC-HVdc) transmission system. Resonances or instability phenomena have been reported in between wind farms and MMC-HVdc systems. They are arguably originated due to interactions between the MMC and the wind power inverters. However, the nature of these interactions is neither well understood nor reported in the literature. In this paper, the impedance-based analytical approach is applied to analyze the stability and to predict the phase margin of the interconnected system. For that, analytical impedance models of a three-phase MMC in a compensated modulation case and a direct modulation case are separately derived using the small-signal frequency domain method. Moreover, the impedance models of the MMC take the circulating current control into account. The derived impedance models are then verified by comparing the frequency responses of the analytical model with the impedance measured in a nonlinear time-domain simulation model developed in MATLAB. The results show that the potential resonances or instability of the interconnected system can be readily predicted through the Nyquist diagrams. In addition, the analysis indicates that the circulating current control of the MMC has a significant impact on the stability of the interconnected system. Finally, the time-domain simulations validate the theoretical analysis.
Lyu et al. (Thu,) studied this question.
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