Analysis of a Permanent Magnet Synchronous Machine Supplied from a 180° Inverter with Phase Control

Reference frame theory is used to establish the equations which describe the steady-state and dynamic behavior of an electric drive system consisting of a permanent magnet synchronous machine supplied from an inverter operating in the 180° conduction mode and with provisions to shift the phase of the stator voltages relative to the rotor position. An expression for the phase-shift angle which yields maximum torque is derived. It is shown that a comparison of the stator time constant and the no-load rotor speed without phase shift, can be used to anticipate the increase in average torque achievable by phase shifting. It is also shown that advancing the phase of the stator voltages advances the phase of the fundamental component of the stator phase currents relative to the phase voltages. A method of calculating the steady-state harmonic currents and torque is also given. The information given in this paper should serve as a guide for the operation of brushless dc motors and the design of speed or position controls that employ phase shifting techniques along with or instead of pulse width modulation.