A control device for an AC rotary machine, comprising: a DC power supply configured to output a DC voltage; an AC rotary machine (1, 1A) having m sets of n-phase windings, where m is a natural number and n is a natural number no smaller than 3; a current detector (11a, 11b, 11c, 11f, 11g) configured to detect respective current values of the m sets of n-phase windings; a power converter (4a, 4b) that includes high potential side switching elements and low potential side switching elements, configured to convert the DC voltage into an AC voltage in response to switching control implemented on the high potential side switching elements and the low potential side switching elements on the basis of ON/OFF signals, and to apply the AC voltage to the windings; and a control unit (5a, 5c, 5d) configured to calculate voltage commands on the basis of respective differences between a current command for the AC rotary machine (1, 1A) and current detection values obtained by the current detector (11a, 11b, 11c, 11f, 11g), and to output the ON/OFF signals to the high potential side switching elements and the low potential side switching elements of the power converter (4a, 4b) by comparing applied voltages calculated on the basis of the voltage commands with a carrier wave signal, wherein the current detector (11a, 11b, 11c, 11f, 11g) is further configured to, when detecting currents flowing through the n-phase windings on the basis of currents flowing through current detection resistance elements that are inserted in series into the low potential side switching elements provided in the power converter (4a, 4b) for at least (n - 1) phases, detect the currents at two or more fixed timings, including a first timing and a second timing, over a single period of the carrier wave signal, characterized in that, in a first condition where the n-phase voltages of the applied voltages in each of the m sets are respectively lower than a first predetermined value or equal to a maximum value of the carrier wave signal, the current detector is further configured to calculate detected currents on the basis of current detection values obtained at the first timing where at least the low potential side switching elements of respective phases other than the phase having a maximum voltage command are all switched ON, and in a condition other than the first condition, the current detector is further configured to calculate the detected currents on the basis of current detection values obtained at the second timing that is different to the first timing, where at least the low potential side switching element of the phase having a minimum voltage command is switched ON. a DC power supply configured to output a DC voltage; an AC rotary machine (1, 1A) having m sets of n-phase windings, where m is a natural number and n is a natural number no smaller than 3; a current detector (11a, 11b, 11c, 11f, 11g) configured to detect respective current values of the m sets of n-phase windings; a power converter (4a, 4b) that includes high potential side switching elements and low potential side switching elements, configured to convert the DC voltage into an AC voltage in response to switching control implemented on the high potential side switching elements and the low potential side switching elements on the basis of ON/OFF signals, and to apply the AC voltage to the windings; and a control unit (5a, 5c, 5d) configured to calculate voltage commands on the basis of respective differences between a current command for the AC rotary machine (1, 1A) and current detection values obtained by the current detector (11a, 11b, 11c, 11f, 11g), and to output the ON/OFF signals to the high potential side switching elements and the low potential side switching elements of the power converter (4a, 4b) by comparing applied voltages calculated on the basis of the voltage commands with a carrier wave signal, wherein the current detector (11a, 11b, 11c, 11f, 11g) is further configured to, when detecting currents flowing through the n-phase windings on the basis of currents flowing through current detection resistance elements that are inserted in series into the low potential side switching elements provided in the power converter (4a, 4b) for at least (n - 1) phases, detect the currents at two or more fixed timings, including a first timing and a second timing, over a single period of the carrier wave signal, characterized in that, in a first condition where the n-phase voltages of the applied voltages in each of the m sets are respectively lower than a first predetermined value or equal to a maximum value of the carrier wave signal, the current detector is further configured to calculate detected currents on the basis of current detection values obtained at the first timing where at least the low potential side switching elements of respective phases other than the phase having a maximum voltage command are all switched ON, and in a condition other than the first condition, the current detector is further configured to calculate the detected currents on the basis of current detection values obtained at the second timing that is different to the first timing, where at least the low potential side switching element of the phase having a minimum voltage command is switched ON.