A direct AC power converter comprising: a first rectifying circuit (5, 51) having a plurality of input terminals configured to receive an input of an AC voltage (Vin), and a pair of output terminals (51c, 51d) each connected to a DC link; said DC link having a first power supply line, and a second power supply line to which a potential lower than a potential of said first power supply line is applied; a boost chopper having a boost switch and a capacitor in an output stage thereof; said boost switch being configured to be conductive/non-conductive in accordance with activity/non-activity of a control signal (Sb); a switch configured to switch a discharge and non-discharge from said capacitor to said DC link in accordance with activity/non-activity of a control signal (Sc); an inverter configured to convert a voltage applied to said DC link into another multi-phase AC voltage according to a control signal (Sg), and a controller configured to receive signals indicating the waveform of said AC voltage (Vin), a current output from the inverter (Iinv) and a voltage (Vc) between both ends of said capacitor and to output said control signals (Sb, Sc, Sg), wherein either a rectified voltage (Vrec) from a second rectifying circuit is applied to an input side of said boost chopper, or said pair of output terminals of said first rectifying circuit (5, 51) are connected to said input side of said boost chopper, characterized in that in said boost chopper, said capacitor is charged at least during a first period being a part of a period during which a discharge duty (dc) is greater than 0, said discharge duty being a time ratio at which said switch is conductive, a virtual DC link voltage (Vdc) is greater than or equal to a first value and smaller than or equal to a second value, said virtual DC link voltage being expressed as a sum of a product (dc·Vc) of said discharge duty and said voltage (Vc) between both ends of said capacitor and a product (dr· Vrec) of a rectifying duty (dr) and a rectified voltage (Vrec) of said AC voltage, said rectifying duty takes a value obtained by subtracting a sum of said discharge duty and a zero voltage duty (dz) from 1, said zero voltage duty is a time ratio at which said inverter adopts a zero voltage vector irrespective of magnitude of a voltage output from said inverter, said first value is a maximum value (max(|Vuv|, |Vvw|, |Vwu|)) among absolute values of respective line-to-line voltages of said multi-phase AC voltage, and said second value is a maximum value that said absolute values are capable of taking. a first rectifying circuit (5, 51) having a plurality of input terminals configured to receive an input of an AC voltage (Vin), and a pair of output terminals (51c, 51d) each connected to a DC link; a plurality of input terminals configured to receive an input of an AC voltage (Vin), and a pair of output terminals (51c, 51d) each connected to a DC link; said DC link having a first power supply line, and a second power supply line to which a potential lower than a potential of said first power supply line is applied; a first power supply line, and a second power supply line to which a potential lower than a potential of said first power supply line is applied; a boost chopper having a boost switch and a capacitor in an output stage thereof; said boost switch being configured to be conductive/non-conductive in accordance with activity/non-activity of a control signal (Sb); a switch configured to switch a discharge and non-discharge from said capacitor to said DC link in accordance with activity/non-activity of a control signal (Sc); an inverter configured to convert a voltage applied to said DC link into another multi-phase AC voltage according to a control signal (Sg), and a controller configured to receive signals indicating the waveform of said AC voltage (Vin), a current output from the inverter (Iinv) and a voltage (Vc) between both ends of said capacitor and to output said control signals (Sb, Sc, Sg), wherein either a rectified voltage (Vrec) from a second rectifying circuit is applied to an input side of said boost chopper, or said pair of output terminals of said first rectifying circuit (5, 51) are connected to said input side of said boost chopper, in said boost chopper, said capacitor is charged at least during a first period being a part of a period during which a discharge duty (dc) is greater than 0, said discharge duty being a time ratio at which said switch is conductive, a virtual DC link voltage (Vdc) is greater than or equal to a first value and smaller than or equal to a second value, said virtual DC link voltage being expressed as a sum of a product (dc·Vc) of said discharge duty and said voltage (Vc) between both ends of said capacitor and a product (dr· Vrec) of a rectifying duty (dr) and a rectified voltage (Vrec) of said AC voltage, said rectifying duty takes a value obtained by subtracting a sum of said discharge duty and a zero voltage duty (dz) from 1, said zero voltage duty is a time ratio at which said inverter adopts a zero voltage vector irrespective of magnitude of a voltage output from said inverter, said first value is a maximum value (max(|Vuv|, |Vvw|, |Vwu|)) among absolute values of respective line-to-line voltages of said multi-phase AC voltage, and said second value is a maximum value that said absolute values are capable of taking.