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Z-source converter configurations make it possible to overcome intrinsic limits present in conventional ac-dc and dc-ac converters. A typical three-phase inverter cannot supply output voltages greater than the voltages at its input; in the same manner, a typical three-phase boost rectifier cannot supply output voltages lower than input voltages. Using Z-source topology permits overcoming both these limits. In fact, a Z-source boost rectifier can theoretically either step-up or step-down the output voltage to any desired value starting from the conventional three-phase diode bridge rectifier output voltage level. In addition, it presents intrinsic immunity to shoot-through states, resulting in improved reliability of the entire system. In this study, attention is focused on the mathematical modelling of a three-phase Z-source boost rectifier for power factor correction power supply applications; using such a topology as first-stage converter allows designing the second-stage converters with the same voltage constraints of single-phase units.