ELECTROMECHANICAL MOTION DEVICES
Rotating Magnetic Field Based Analysis
3^rd Edition

We simulate the free acceleration from stall of the BLDC machine under each of the three control strategies described on the BLDC Control tab. In free acceleration, the machine is unloaded (load torque $T_L = 0$) and accelerates freely until it reaches the steady state speed where its back emf matches the supply voltage. For this simulation, the total rotational inertia of the machine and load is $J = 5\times10^4~\text{kg}\cdot\text{m}^2$.

There are three animations below, one for each control method. Normal Mode ($\phi_v=0$) is on the left, Maximum-Torque per Volt ($\phi_{vMT/V}$) is in the middle, and Maximum-Torque per Ampere ($\phi_{vMT/A}$) is on the right. Each animation is the dynamic (instantaneous) phasor diagram described earlier, illustrating the stator and rotor north and south magnetic poles, respectively, as viewed from the synchronous frame. In other words, we are riding along on the rotor and viewing the stator and rotor magnetic fields and voltage and current instantaneous phasors. Recall that the stator poles are aligned with the rotating magnetic field and are created by the stator currents controlled with the inverter. The rotor poles are created by the permanent magnet; thus, because we are riding on the rotor, its field appears stationary. Additionally, the magnitude and orientation of the net stator voltage is shown by the blue arrow (recall that $\phi_v$ controls its angle) and the resulting net stator current is shown by the purple arrow. Clicking on one of the three pole diagrams will activate it, greying out the other two diagrams and highlighting that control method in the torque and speed plots below; the torque and speed for the other two methods are shown greyed out for comparison.

Directly below the three magnetic pole animations is another way of looking at the same phenomenon. In this animation we are viewing the stator and rotor rotating magnetic fields while running at $\omega = \omega_r = \omega_e$ counterclockwise with “360$^\circ$ vision.” The full spatial sinusoidal mmf fields are shown, as well as the stator current vector. Notice that the rotor north pole is aligned at $\phi_e=-\pi/2$; this is the d axis, by design. By toggling between the “Net Stator mmf” or “Stator Phase mmfs” settings, the three-phase stator mmfs corresponding to the phase currents in the top animation on the Introduction tab can be turned off or on, respectively.

The “Play/Pause” button will animate/stop the animated figures. Clicking the button to the right of this will cycle through fast (10x), nominal (1x) and slow (0.1x) playback speeds, and the slider bar will move the simulation to a specific time. The torque and speed are plotted below this.

While interacting with the simulation, notice the differences between the three methods. Namely, focus on the location of the stator voltage with respect to the q axis, the resultant stator current and its $q$- and $d$-axis components, and the relative positions of the rotor and stator poles and how they relate to torque. You should notice that in Normal mode, the stator voltage always lies along the q axis, in Maximum Torque per Volt mode there is significant d axis voltage and current and $i^r_{qs}$ and $T_e$ are greater than or equal to their values in the other two methods throughout the simulation, and in Maximum Torque per Ampere mode stator current always lies along the $q$-axis. Finally, notice that Maximum Torque per Volt mode achieves a much higher speed than the other two methods due to its large d axis current, which serves to reduce the back emf.