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This paper describes two distinctive functions of the arm inductor in the modular multilevel converters (MMC): suppressing the circulating current and limiting the fault current rise rate. Based on the equality of the instantaneous power, the characteristics of the circulating current are analyzed and demonstrated that it flows through the three phase of the converter in negative sequence at double-fundamental frequency. The relationship between the amplitude of the circulating current and the value of the arm inductor is discussed, and the first principle to design the parameters is proposed. The second principle to design the parameters is based on the calculation of the fault current rise rates, with different values of the arm inductors. A detailed PSCAD/EMTDC model of MMC is developed. Steady state simulation proves the existence of the circulating current at double fundamental frequency. Simulation results show a close agreement with the calculation of the circulating current, with different arm inductor parameters. The fault between the DC terminals of the converter is investigated; the results verify the above parameter design principles of the arm inductor.