A method for controlling a direct power converter, said direct power converter comprising: a first power supply line; a second power supply line which is applied with a potential lower than said first power supply line is applied; a converter including an input side connected with a single-phase AC power supply (1, 2) and an output side connected with said first power supply line and said second power supply line, and performing single-phase full-wave rectification; a charge and discharge circuit located between said first power supply line and said second power supply line; and an inverter that converts a DC voltage between said first power supply line and said second power supply line into an AC voltage, said charge and discharge circuit comprising a buffer circuit including a capacitor and a first switch (Sc, D42) connected in series with said capacitor at a side close to said first power supply line between said first power supply line and said second power supply line, and providing and receiving power between said first power supply line and said second power supply line, and a boost circuit that boosts a rectified voltage (Vrec) from said converter to charge said capacitor, the method comprising the steps: providing, by said buffer circuit, power to said first power supply line and said second power supply line in a first period in which a cosine value (cos(2ωt)) to a value (2ωt) of twice a phase angle (ωt) of an AC waveform output from said single-phase AC power supply (1, 2) is positive when the AC waveform is regarded as a sine value (sin(ωt)) of the phase angle (ωt), and receiving power from said first power supply line and said second power supply line in a second period in which said cosine value is negative, rendering conductive said first switch (Sc, D42) at a discharge duty (dc) to discharge said capacitor in said first period, and is rendering non-conductive said first switch (Sc, D42) (dc=0) in said second period, rendering conductive said converter at a rectifying duty (drec), rendering a sum, in said first period, of a product of said rectified voltage and said rectified duty and a product of a both-end voltage (Vc) of said capacitor and said discharge duty to take a product of a crest value (Vm) of an AC voltage (Vin) of said single-phase AC power supply, a first value ((1 - k·cos(2ωt))/2), and a second value (Im/Idc), rendering a product, in said second period, of said rectified voltage and said rectifying duty to take said product of said crest value (Vm) of an AC voltage (Vin) of said single-phase AC power supply, said first value ((1 - k·cos(2ωt))/2), and said second value (Im/Idc), obtaining said first value as half a value obtained by subtracting, from one, a product of a positive constant (k) less than one and said cosine value (cos(2ωt)), and obtaining said second value as a value obtained by dividing a virtual crest value (Im), which is 2 -times an effective value of a first current (Iin) input to the converter by a second current (Idc) input to said inverter. a first power supply line; a second power supply line which is applied with a potential lower than said first power supply line is applied; a converter including an input side connected with a single-phase AC power supply (1, 2) and an output side connected with said first power supply line and said second power supply line, and performing single-phase full-wave rectification; a charge and discharge circuit located between said first power supply line and said second power supply line; and an inverter that converts a DC voltage between said first power supply line and said second power supply line into an AC voltage, said charge and discharge circuit comprising a buffer circuit including a capacitor and a first switch (Sc, D42) connected in series with said capacitor at a side close to said first power supply line between said first power supply line and said second power supply line, and providing and receiving power between said first power supply line and said second power supply line, and a boost circuit that boosts a rectified voltage (Vrec) from said converter to charge said capacitor, providing, by said buffer circuit, power to said first power supply line and said second power supply line in a first period in which a cosine value (cos(2ωt)) to a value (2ωt) of twice a phase angle (ωt) of an AC waveform output from said single-phase AC power supply (1, 2) is positive when the AC waveform is regarded as a sine value (sin(ωt)) of the phase angle (ωt), and receiving power from said first power supply line and said second power supply line in a second period in which said cosine value is negative, rendering conductive said first switch (Sc, D42) at a discharge duty (dc) to discharge said capacitor in said first period, and is rendering non-conductive said first switch (Sc, D42) (dc=0) in said second period, rendering conductive said converter at a rectifying duty (drec), rendering a sum, in said first period, of a product of said rectified voltage and said rectified duty and a product of a both-end voltage (Vc) of said capacitor and said discharge duty to take a product of a crest value (Vm) of an AC voltage (Vin) of said single-phase AC power supply, a first value ((1 - k·cos(2ωt))/2), and a second value (Im/Idc), obtaining said first value as half a value obtained by subtracting, from one, a product of a positive constant (k) less than one and said cosine value (cos(2ωt)), and obtaining said second value as a value obtained by dividing a virtual crest value (Im), which is 2 -times an effective value of a first current (Iin) input to the converter by a second current (Idc) input to said inverter.