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This paper presents a control strategy for fuel cell vehicle (FCV) traction drive systems using the Z-source inverter. The Z-source inverter utilizes an inductor-capacitor (LC) network (impedance-source) to link the main inverter circuit to the fuel cell. One of the Z-source network capacitors can be replaced with a battery. By controlling the shoot-through duty cycle and modulation index, we can control the battery state of charge (SOC), produce any output AC voltage to the traction motor, and control the fuel cell output power, all independently and simultaneously. There is no need for any DC-DC converters to manage and control battery SOC and fuel cell output power. With the impedance network, the Z-source inverter can advantageously use the shoot through state to boost voltage. This one-stage power conversion and control system has higher reliability, higher efficiency, and lower cost. These facts make the Z-source inverter desirable for use in hybrid electric vehicles, as the cost and complexity is reduced when compared to the traditional inverters. This paper explores a control strategy to regulate battery SOC, fuel cell output power, and produce desired AC voltage to the traction motor.