A permanent magnet rotating electrical machine capable of conducting a variable speed operation at high output in a wide range from low speed to high speed and improving efficiency and reliability in a wide operating range. Two kinds of permanent magnets having different shapes or different magnetic characteristics are embedded in a rotor core, to form a magnetic pole. The permanent magnets arranged at the magnetic pole include a permanent magnet whose product of coercive force and thickness along a magnetizing direction is small and the permanent magnet whose product of coercive force and thickness along the magnetizing direction is large. A magnetic field created by passing a current to an armature coil for a short time is used to irreversibly magnetize the permanent magnet whose product of coercive force and thickness along magnetizing direction is small, thereby changing a total linkage flux amount, and a positive d-axis current is passed when torque is large.