An operating method of a synchronous machine is provided, the operating method including: generating an MTPA (Maximum Torque Per Ampere) curve, based on a current limiting circle depending on a rated current of an inverter or a motor and a torque curve depending on a torque command; generating a voltage limiting ellipse, based on a DC-link voltage; displaying, on an X-Y plane, the current limiting circle, the torque curve, the MTPA curve, and the voltage limiting ellipse; and computing a d-axis current and a q-axis current, based on an intersection point between at least two of the current limiting circle, the torque curve, the MTPA curve, and the voltage limiting ellipse, displayed on the X-Y plane.