#### MTPA and MTPV

Permanent magnet synchronous motor is the core driving device of the power unit of new energy vehicles. At low speed, the permanent magnet synchronous motor adopts the maximum torque current ratio control, that is, a torque is given and the minimum synthetic current is used to achieve it, so that the copper loss can be minimized.

So at high speed, we cannot use the MTPA curve for control. We have to use MTPV, that is, the maximum torque voltage ratio, for control. That is to say, at a certain speed, the motor outputs the maximum torque. According to our actual control idea, a torque is given and the maximum speed is achieved by adjusting iq and id. Then where is the voltage reflected? Because it is the maximum speed at this time, the voltage limit circle is certain. Only by finding the maximum power point on this limit circle can the maximum torque point be found.

#### Driving conditions

Generally, the field weakening starts at the turning speed (also called the base speed), which is point A1 in the figure below. Therefore, the reverse electromotive force will be relatively large at this point. If you do not weaken the field at this time, assuming that we force the cart to increase the speed, your iq will be forced to be negative, and you will not be able to output positive torque, and you will be forced to enter the power generation state. Therefore, the ellipse is shrinking, and you cannot stay at point A1. We can only reduce iq and increase id along the ellipse, so that we are getting closer and closer to point A2.

#### Power generation conditions

Why does power generation also require weak magnetic field? Shouldn’t strong magnetic field be used to generate a relatively large iq when generating power at high speed? This is not possible, because if the magnetic field is not weakened at high speed, the reverse electromotive force + transformer electromotive force + impedance electromotive force may be very large, far exceeding the power supply voltage, resulting in terrible consequences. This is SPO uncontrollable rectifier power generation!

Therefore, weak magnetic field must also be performed under high-speed power generation, so that the inverter voltage generated is controllable.

Let’s analyze it. Assuming that braking, that is, feedback braking, starts at the high-speed operating point B2, the speed is getting lower and lower, then weak magnetic field is less and less needed, and finally reaches point B1. At this time, iq and id can be constant, but as the speed decreases, the negative iq generated by the reverse electromotive force will become less and less. At this time, power supply compensation is needed to enter energy consumption braking.

#### Summary

We should first draw the two circles of MTPA and MTPV, and realize that the iq and id at this time are absolute, and are obtained by considering the reverse electromotive force.

As for whether iq and id are generated more by power supply or reverse electromotive force, the inverter is needed to adjust them. iq and id are also limited. The adjustment cannot exceed the two circles. If the current limit circle is exceeded, the IGBT will be damaged; if the voltage limit circle is exceeded, the power supply will be damaged.

In the process of adjustment, the target iq and id, the actual iq and id are the key. Therefore, the calibration method is used in engineering to calibrate the appropriate iq and id distribution ratio at different speeds and target torques to achieve the best efficiency.