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High penetration of renewable energies through fast-response power converters results in a considerable displacement of conventional synchronous generators and losing of system inertia for frequency control. Modular multilevel converters (MMCs) can be employed serving as an interface between the large-scale renewable generation and power grids. In a microgrid with high shares of renewables integrating through MMCs, submodule (SM) capacitors can be used as energy storage to provide a degree of synthetic inertia for system frequency support. This paper quantitatively exploits the MMC synthetic inertia in a microgrid with flexible renewable penetration levels. An MMC inertia coefficient concept is proposed. It is mainly affected by the penetration ratio, the SM capacitance, and the modulation index of an MMC, with the system operation constraints. According to the analysis, a substantial portion of system inertia can be provided by properly designed MMCs. Detailed MMC frequency control loops are presented. The capacitor average voltage is proportionally linked to the frequency deviation, in order to flexibly adjust the capacitor energy during frequency events. The MMC output active power is deliberately and simultaneously regulated according to the capacitor energy change rate. By controlling the MMC capacitor voltage, dc side power, and output active power, an amount of energy can be released or absorbed by SM capacitors to improve the system frequency response during the frequency event transients, while the renewable generation is scarcely influenced. The proposed concept is experimentally verified and the results show that, with proper system parameters and control loops, the line frequency deviation and the rate of change of frequency can be significantly reduced. Good agreements of the system frequency characteristics have been achieved between the theoretical calculation and experimental results. [ABSTRACT FROM AUTHOR]