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This paper provides theoretical and experimental discussions on an optimal carrier frequency for a phase-shifted pulsewidth modulation modular multilevel cascade converter for grid connections. The theoretical discussion concludes that a ratio of the optimal carrier frequency with respect to the supply (ac) frequency is 5/2. A three-phase downscaled front-to-front system is designed, constructed, and tested to confirm validity of the theoretical discussion. It consists of a pair of three-phase modular multilevel cascade converters rated at 400 Vdc and 10 kW, where the carrier frequency is set to 450 Hz and the ac frequency to 180 Hz, that is, their ratio is equal to 5/2. Moreover, simulated waveforms are compared to experimental ones under the same operating conditions. Both experimental and simulated waveforms agree well with each other not only in steady states but also in transient states.

This paper presents an intensive discussion on a transformerless back-to-back (BTB) system using modular multilevel cascade converters based on double-star chopper cells (MMCC-DSCC). It is expected to be applied to a power distribution system with many distributed power generators. This paper designs, constructs, and tests a three-phase 200-V, 10-kW DSCC-based BTB system installed on a 200-V, 40-kW power distribution simulator consisting of two radial feeders. Experimental results show that the BTB system can mitigate power-flow imbalance between the two feeders. Moreover, the zero-sequence current circulating between the two feeders can be suppressed to be as small as 10 mA ( $0.02\%$ ) in rms by connecting a common-mode choke to the common dc link of the BTB system.

This paper provides an intensive discussion on analysis, simulation, and experiment of a back-to-back (BTB) system unifying two modular multilevel cascade converters based on double-star chopper cells (MMCCs-DSCCs). Each of the two DSCCs connected back-to-back consists of multiple cascaded chopper cells and a center-tapped inductor per leg. Low voltage steps bring significant reductions in harmonic voltage and current to the BTB system. Neither dc-link capacitor nor voltage sensor is required for regulating the dc-link voltage and controlling the dc-link current. A three-phase 200-V, 10-kW, 50-Hz downscaled BTB system with phase-shifted PWM is designed, constructed, and tested to verify its operating principles and performance. Analytical, simulated, and experimental results agree well with each other in steady and transient states. Experimental waveforms confirm the effectiveness of a self-starting/restarting procedure.