Permanent Magnet Synchronous Motor—Maximum Torque-Current Ratio Control

1

Preface

In the torque decoupling stage, the vector control of permanent magnet synchronous motors often adopts the id=0 method. At this time, the torque is decoupled from the dq axis current, which has the characteristic of simple calculation.

However, in this control mode, since the d-axis current is constant and does not participate in the control, the effect of the magnetic resistance torque is ignored, so the capacity of the inverter is not fully utilized. Therefore, this method is not suitable for the salient pole permanent magnet synchronous motor control system. And because the permanent magnet flux is basically unchanged, it can only meet the speed regulation strategy below the base speed.

Therefore, this paper introduces a new maximum torque per ampere (MTPA) control method in which the d-axis current is also involved in the control. This method only requires the minimum stator current, can reduce line losses, and improve the overall system efficiency.

2

Torque decoupling

Both MTPA and id=0 control modes are reflected in torque decoupling, so its control system structure is basically the same as id=0, the only difference is the different torque-to-current decoupling method.

2.1 Maximum torque current ratio

The maximum torque-to-current ratio, as the name implies, is a control method in which the ratio of torque to current vector is the largest, that is, the current is the smallest under the same output torque condition.

Combined with the torque formula mentioned above, the goal is:

According to the above objectives, through a series of derivations, the relationship between torque and q-axis current, and the relationship between q-axis current and d-axis current can be obtained as shown below:

Through the first formula, the q-axis current can be obtained through the torque,

Through the second formula, the d-axis current can be obtained from the q-axis current.

Two points to note here:

1) Although the above formula shows the relationship between the motor torque and the stator current, it is necessary to inversely find the expressions of id and iq with Te as the variable. This solution process is relatively complicated. The relationship between the torque and the dq axis current can be tabulated and the problem can be solved by looking up the table and performing curve fitting.

2) In addition, since the isotropic magnetic circuits of the surface permanent magnet synchronous motor are symmetrical, there is no magnetic resistance torque, and the inductances of the AC and DC axes are equal (Ld=Lq), the maximum torque-to-current ratio control of the surface permanent magnet synchronous motor is exactly the same as the control strategy of id=0.

Draw a picture in MATLAB so that you can intuitively feel the difference between MTPA and id=0 control of salient-pole PMSM.

The horizontal and vertical axes in the figure are the dq axis currents respectively, and the red dotted line is the constant torque curve.

It can be seen that if the motor is to output the same torque, the current vector is OA when the control mode of id=0 is used, and the current vector is OB when the MTPA control is used. It is obvious that the length of OB is smaller than OA, that is, the required stator current is the smallest under MTPA control.

2.2 Derivation of the Conscience Formula

The following is the derivation process of the maximum torque current ratio. If you like it, you can study it. If you don’t like it, you can just ignore it. Let’s take a look at the vector diagram first:

In the figure, γ is the phase angle of the stator current. According to the current vector relationship, we have:

1) Substituting the above formula into the motor torque formula, we can get:

2) The formula for the ratio of torque to current with respect to the current phase angle is:

3) Derivative of the above formula with respect to the current phase angle yields:

4) By setting the above equation to zero, we can find the current phase angle when the ratio of motor torque to stator current is maximum:

It can be solved as:

And then:

Substituting into the above formula, we can get the expressions of id and iq given above. Done!!!

Finally, a structural diagram of the maximum torque current ratio control system is attached: