What the relationship among flux linkage / back EMF constant and torque constant ?

Question

JINYU ZHANG 2019-8-23

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评论： Nabilah Farhat 2020-3-17

HI,

the field oriented control algorithms require the setting of motor electrical parameters for its proper functionality.

I want to measure the Electrical parameters of my PMSM，but I am confused about the different interpretations of the same parapeters of MATLAB.

The MATLAB documentation "Parameterize a Permanent Magnet Synchronous Motor" said that the measured torque and back EMF constants have approximately the same value and are related to the permanent magnet flux linkage via the number of pole pairs of the motor:

while , the Webinar"Parameterizing and Verifying a Permanent Magnet Synchronous Motor Model"(21:01) said that the above parameter have the following relationships :

I don't know which fomula is right ,could you give me some advice?

here is my back-EMF experimental test data:

=418.87902 rad/s ; Pole pairs = 4;

= 33.7V;

= 3.73ms ; rotor wiring diagram : triangle

how can I using above data caculate the motor torque consant

?

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Answer 1

Sabin 2019-8-29

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Both definitions of torque constant Kt are correct. The second definition takes into account also the 3/2 factor from the torque equation. In the PMSM block from Simscape Electrical Kt does not contain the 3/2 factor, but this factor is included in the torque equation. If you follow the procedure from the "Parameterize a Permanent Magnet Synchronous Motor" you should obtain the parameter that you can use on the PMSM block from Simscape Electrical. Hope this helps.

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Sanket Garade 2020-2-21

I did not understand the relationship between the bemf constant (Ke) and the rotor PM flux linkage (lambda_m), especially their "units". Cause unit of Ke is [Volt-sec / rad] and unit of lambda_m is [Volt-sec]. If the 3rd variable in the equation (Ke = P x lambda_m) linking these 2 is just the no. of pole pairs (P), which itself is unitless, then how do the units on the LHS and RHS match ? Where does the "1/rad" disappear ?

Nabilah Farhat 2020-3-17