Modular multilevel converters (MMCs) have shown great potential in the area of multimegawatt wind energy conversion system (WECS) based on permanent magnet synchronous generators (PMSGs). However, the studies in this area are few, and most of them refer to the MMC used in high-voltage direct current (HVDC) systems, and hence the characteristics of the PMSG are not considered. This paper proposes a steady-state analysis method for MMCs connected to a PMSG-based WECS. In the proposed method, only the wind speed (operating condition) is required as input, and all the electrical quantities in the MMC, including the amplitudes, phase angles and their harmonics, can be calculated step by step. The analysis method is built on the proposed d-q frame mathematical model. Interactions of electrical quantities between the MMC and PMSG are comprehensively considered. Moreover, a new way to calculate the average switching functions are adopted in order to improve the accuracy of the analysis method. Applications of the proposed method are also presented, which includes the characteristic analysis of capacitor voltage ripples and the capacitor sizing. Finally, the accuracy of the method and the correctness of the analysis are verified by simulations and experiments.Energies 2018, 11, 461 2 of 31 require a large amount of series or parallel connected power devices in order to achieve the required power, which reduces the reliability of WECS. Moreover, the traditional converters are not suitable for medium-voltage (3-33 kV) WECS, which is becoming popular for turbine power ratings greater than 3.0 MW [6,7]. These drawbacks lead to the studies of new full-scale power converters.The modular multilevel converter (MMC), which became the most common type of voltage-source converter used in the high-voltage direct current (HVDC) applications, is also a suitable converter for PMSG-based WECS. In [8,9], MMC was used for medium-voltage motor drives, which opened up the study of MMC applied to variable-speed machines. The application of MMCs in PMSG-based WECS was first studied in [10]. That paper concluded that MMC should be considered a suitable option for transformerless 10 MW PMSG-based WECS, and performs well in the full system. In [11], the authors proposed an improved online fault identification scheme for the MMC applied to WECS, which avoided the use of extra sensors by only using the already available variables in detection, and therefore the maintenance cost of the distant offshore wind farms can be reduced. In [12], the complete control scheme of MMC applied to the PMSG-based WECS was proposed. Low voltage ride-through problems and capacitor voltage ripple problems were also studied in that paper. In addition, the increasing interest in all-dc wind farms, in recent years, will also enlarge the application of MMC in WECS [13][14][15].Steady-state analysis can be used for component sizing and assessment of the impact of different parameters on the MMC performance. However, there is no reference available for the steady-state anal...