1.1 Direct Axis Current Reference

In IPM motors, the quadrature (q-axis) current components in phase with corresponding BEMF voltages, produce only magnetic torque but do not contribute in producing reluctance torque. The direct axis (d-axis) current components 90 degrees out of phase with BEMF voltages, produce reluctance torque in conjunction with quadrature axis currents. Therefore, there exists an infinite number of current vectors providing the same amount of torque. For the most efficient operation, the current vector with the lowest possible magnitude should be chosen to reduce winding losses.

By imposing a negative i_d, the produced torque can be increased which will be the maximum for the same total current drawn. This is called the Maximum Torque per Ampere (MTPA) control and the i_dref is calculated by:

$i_d=\frac{{\mathrm{\Lambda }}_m}{2(L_q-L_d)}-\sqrt{\frac{{\mathrm{\Lambda }}_m^2}{4(L_q-L_d)}+i_q^2}$

In case of SPM motors, the quadrature axis current components, in phase with the corresponding BEMF voltages, produce the magnetic torque and the d-axis current reference (i_dref) is set to zero, (i.e., i_dref = 0. )

The motor characteristics enable some simplification of the mathematical model used in the speed and position estimator, while at the same time enabling the efficient use of the FOC. The mathematical model used in the estimator is explained in the later section.