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The modular multilevel converter (MMC) is an emerging and highly attractive multilevel converter topology for high-voltage and high-power applications. This paper proposes the control method of parallel-connected modular multilevel converters (parallel-MMCs), which assumes that the multiple MMCs are directly connected at both ac and dc sides to effectively enhance the power rating as expected. Two key problems were first solved for the parallel-MMCs under the normal operation conditions: voltage balancing of submodules and mitigation of circulating currents, where the novel transformed third-order harmonic resonant controller in the synchronous reference frame was employed to mitigate the dominant second-order and fourth-order circulating currents and a sixth-order harmonic resonant controller is used to attenuate the zero-sequence sixth-order circulating current existed in all phase currents per MMC. Considering the high risk of switches fault in the parallel-MMCs, the fault-tolerant operation schemes were then proposed in this paper to address the major concerns of open-circuit and short-circuit switch fault in a submodule, respectively. Carefully controlling the healthy submodules and the corresponding phase arms, the parallel-MMCs can successfully maintain their balanced capacitor voltages and mitigate the circulating currents with the qualified output waveform obtained. In addition, the parallel configuration of MMCs provides the unique solution for the short-circuit switch fault operation which was seldom discussed in the published literature works with respect to the MMC fault-tolerant operation schemes. MATLAB simulations and the constructed experimental prototype have verified the performance of the proposed control strategy. [ABSTRACT FROM AUTHOR]