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 including a reactor and a second switch (S1, D41) connected in series with the reactor at a side close to the second power supply line between the first power supply line and the second power supply line, and boosting a rectified voltage (Vrec) from said converter to charge said capacitor, said control method comprising the steps_ providing power, by control of said first switch (Sc, D42) in said buffer circuit, 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); receiving power, by control of said second switch (S1, D41) in said boost circuit, from said first power supply line and said second power supply line in a second period in which said cosine value is negative, wherein said converter is conductive at a rectifying duty (drec), said rectifying duty taking a value of √2-times an absolute value (|sin(ωt)|) of said sine value in said first period, and characterized in that, a power (Vdc·Idc) input to said inverter is a product of an absolute value (Im / √2) of an input current input to said converter at a boundary between said first period and said second period, an effective value (Vm / √2) of an AC voltage (Vin) of said single-phase AC power supply, and a value ((1-(1 - k)·cos(2ωt)) obtained by subtracting, from one, a value obtained by multiplying said cosine value (cos(2ωt)) by a positive constant (1 - k) less than one. 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 including a reactor and a second switch (S1, D41) connected in series with the reactor at a side close to the second power supply line between the first power supply line and the second power supply line, and boosting a rectified voltage (Vrec) from said converter to charge said capacitor, said control method comprising the steps_ providing power, by control of said first switch (Sc, D42) in said buffer circuit, 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); receiving power, by control of said second switch (S1, D41) in said boost circuit, from said first power supply line and said second power supply line in a second period in which said cosine value is negative, wherein said converter is conductive at a rectifying duty (drec), said rectifying duty taking a value of √2-times an absolute value (|sin(ωt)|) of said sine value in said first period, and characterized in that, a power (Vdc·Idc) input to said inverter is a product of an absolute value (Im / √2) of an input current input to said converter at a boundary between said first period and said second period, an effective value (Vm / √2) of an AC voltage (Vin) of said single-phase AC power supply, and a value ((1-(1 - k)·cos(2ωt)) obtained by subtracting, from one, a value obtained by multiplying said cosine value (cos(2ωt)) by a positive constant (1 - k) less than one.