Phasor analysis of six-step 120° conduction permanent magnet motor drives

The simplest drive for a permanent magnet motor is a three-phase bridge inverter switched according to the six-step, "120° conduction" algorithm. For the more complicated, higher frequency, switching algorithms which give (approximately) a sinusoidal current, phasor analysis of the per-phase equivalent circuit provides a simple accurate description of the phase current and voltage, at least for a motor with near-sinusoidal back-emf and near-uniform inductance. But for six-step switching, there are no well-known general formulae, even describing the relationship between applied DC voltage and motor no-load speed. This paper presents exact analytic phasor analysis for six-step, 120° conduction switching of permanent magnet motors with sinusoidal back-emf. Formulae are given for the fundamental components of voltage and current and for the inferred torque. These formulae enable the DC voltage and the switching advance angle to be determined to operate the motor at any desired torque, speed and fundamental current advance angle. In particular, it is frequently desired to operate the motor with minimum copper loss for a given torque. The copper loss will be close to minimum if the current fundamental is aligned with the back-emf. Using the formulae presented in the paper and a two-dimensional root-finding algorithm, the required switching angle and commutation angle can be determined and the DC link voltage inferred. The paper thus allows simple phasor analysis theory to be translated into six-step switching prescriptions.