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Abstract-This paper studies different circulating current references for the modular multilevel converter (MMC). The circulating current references are obtained from the instantaneous values of the output current and modulation signal of the phase-leg. Therefore, determination of the amplitude and phase of the output current is not needed, which is a significant improvement compared to other methods such as those based on injecting specific harmonics in the circulating currents. Among the different methods studied in this paper, a new method is introduced, which is able to reduce the capacitor voltage ripples compared to the other methods. A closed-loop control is also proposed which is able to track the circulating current references. With the discussed methods the average values of the capacitor voltages are maintained at their reference while the voltage ripples are kept low. Experimental results are presented to demonstrate the effectiveness of the proposed and discussed methods.

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This paper proposes a generalized formulation for selective harmonic elimination pulse-width modulation (SHE-PWM) control suitable for high-voltage high-power cascaded multilevel voltage source converters (VSC) with both equal and nonequal dc sources used in constant frequency utility applications. This formulation offers more degrees of freedom for specifying the cost function without any physical changes to the converter circuit, as compared to conventional stepped waveform technique, and hence the performance of the converter is greatly enhanced. The paper utilizes the merits of the hybrid real coded genetic algorithm (HRCGA) in finding the optimal solution to the nonlinear equation system with fast and guaranteed convergence. It is confirmed that multiple independent sets of solutions exist. Different operating points for both five-and seven-level converters including singleand three-phase patterns are documented. Selected experimental results are reported to verify and validate the theoretical and simulation findings.Index Terms-Cascaded multilevel converter, hybrid genetic algorithm, pulse-width modulation (PWM), selective harmonic elimination.