A control apparatus for an AC rotating machine, comprising: - a controller wherein the controller includes a current controller which is adapted to produce a d-axis voltage command vd* and q-axis voltage command vq*, upon receiving current commands id* and iq* from a current command unit, a d-axis current correction value dV calculated by a voltage clamp controller, and a d-axis current detection value id and q-axis current detection value iq from a three-phase/dq-axis coordinate converter, in such a way that the d-axis current detection value id is equal to the sum of the d-axis current command id* and d-axis current correction value dV, and the q-axis current detection value iq is equal to the q-axis current command iq*, and the controller is adapted to produce a switching command based on the voltage commands; - a power converter that is adapted to generate an AC voltage based on the switching command and to apply the AC voltage to the AC rotating machine; - a voltage detector that is adapted to detect an input DC voltage to the power converter; and - a current detector that is adapted to detect an AC current flowing through the AC rotating machine; wherein the controller is adapted - to execute, on the AC rotating machine in a free-running state, a start-up control that starts up the power converter and thereby starts up the AC rotating machine, the start-up control being executed during a start-up period after the power converter has been started up until a predetermined time has passed; wherein, during the start-up control period, in order to cause a sine wave PWM control system of the power converter to switch once in half a period of the carrier wave, the voltage clamp controller of the controller is adapted to calculate the d-axis current correction value dV of the current commands, from an AC voltage amplitude of the voltage commands, so that the AC voltage amplitude of the voltage commands will be a constant value which is not more than a maximum output voltage of the power converter; and to execute a field-weakening control by correcting the current commands; and - to calculate a rotation angular frequency of the AC rotating machine based on the AC current and the voltage commands; and wherein the field-weakening control is adapted to calculate the d-axis current correction value dV of the current commands based on a modulation ratio command so that a modulation ratio PMF becomes not more than 1. - a controller wherein the controller includes a current controller which is adapted to produce a d-axis voltage command vd* and q-axis voltage command vq*, upon receiving current commands id* and iq* from a current command unit, a d-axis current correction value dV calculated by a voltage clamp controller, and a d-axis current detection value id and q-axis current detection value iq from a three-phase/dq-axis coordinate converter, in such a way that the d-axis current detection value id is equal to the sum of the d-axis current command id* and d-axis current correction value dV, and the q-axis current detection value iq is equal to the q-axis current command iq*, and the controller is adapted to produce a switching command based on the voltage commands; - a power converter that is adapted to generate an AC voltage based on the switching command and to apply the AC voltage to the AC rotating machine; - a voltage detector that is adapted to detect an input DC voltage to the power converter; and - a current detector that is adapted to detect an AC current flowing through the AC rotating machine; - to execute, on the AC rotating machine in a free-running state, a start-up control that starts up the power converter and thereby starts up the AC rotating machine, the start-up control being executed during a start-up period after the power converter has been started up until a predetermined time has passed; wherein, during the start-up control period, in order to cause a sine wave PWM control system of the power converter to switch once in half a period of the carrier wave, the voltage clamp controller of the controller is adapted to calculate the d-axis current correction value dV of the current commands, from an AC voltage amplitude of the voltage commands, so that the AC voltage amplitude of the voltage commands will be a constant value which is not more than a maximum output voltage of the power converter; and to execute a field-weakening control by correcting the current commands; and - to calculate a rotation angular frequency of the AC rotating machine based on the AC current and the voltage commands; and wherein the field-weakening control is adapted to calculate the d-axis current correction value dV of the current commands based on a modulation ratio command so that a modulation ratio PMF becomes not more than 1.