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The hybrid cascaded multilevel converter is a newly introduced voltage-source converter with dc blocking capability. It has two key parts, that is, the director switch (DS) made of insulated-gate bipolar transistors in series and the wave-shaping circuit (WSC) containing stacks of full-bridge submodules (FSMs). This paper focuses on the modulation schemes of the DSs and the WSCs. First, to reduce switching losses of the DSs, a novel asymmetrical square-wave modulation at a very low frequency is proposed, and the energy flow of the WSC under this modulation is analyzed. Second, modified phase-shifted carrier-based pulsewidth modulation (PSC-PWM) is presented to determine the number of FSMs to be inserted or bypassed; and the specified FSMs to be fired are selected according to the capacitor voltage-balancing strategy. Third, the capability to limit the short-circuit current during the dc fault is investigated, and fast ac overcurrent protection is designed. The effectiveness of the modulation and control strategies is verified by PSCAD/EMTDC simulations.