Extended DQ transformation for vectorial control applications of non-sinusoidal permanent magnet synchronous machines

This paper presents air extended dq trans-formation model of non-sinusoidal Permanent Magnet Synchronous Machines (SM-PMSM). This transformation permits to obtain a simpler electromagnetic torque equation for this type of machine. The resultant electromagnetic torque equation obtained from this model is directly proportional to the machine quadracture stator current. Initially, the three-phase equations of the motor are presented. These equations are widely used for sinusoidal permanent magnetic machines, as well as for non-sinusoidal ones. The well known vectorial model for sinusoidal PM machines is shown. Then, a vectorial model for a non-sinusoidal PM machine is presented and the proposed vectorial model with variable dq axis magnitude is developed. Simulation results of the electromagnetic torque, produced by a brushless DC drive system using conventional six step open loop control are presented. These results are compared with those produced by the same system rising the proposed model into an open loop system and into a closed loop system.