Relation between flux linkage and voltage constant | power_PMSy​nchronousM​achinePara​ms

Hello to everyone,

I am currently working on mathematical modeling of permanent magnet synchronous motor and stuck in computing some variables from standart manufacturer specifications.

Actually, I want to understand how can I compute flux linkage from Back EMF (Ke) constant.

In Simulink, the Permanent Magnet Synchronous Machine block (Simulink Library -> Simscape/Power Systems/Specialized Technology/Fundamental Blocks/Machines), under the Advanced tab, there is a GUI which name is "Compute from standard manufacturer specifications". In this GUI, I am able to understand the math beyond the Voltage constant (ke) transformations between Vpeak/kRPM and Vrms/(rad/s). But I can't understand how the "flux linkage established by magnets (V*s)" is calculating from this voltage constant value.

Unfortunately, there is no information in Help section of this block about this topic.

Can someone please explain this relation by mathematical derivations.

Thanks in advance.

Best Regards,

Yasin

Answer 1

[Yasin Cetin]

solved, thanks.

[Jacob]

seems correct.

Using the above equation and data, where omega M = 1 and 4 pole pairs

flux linkage = sqrt(2)/sqrt(3)*0.03133/(4*1) = 0.0063952

[Mohammad Nair]

Could you please specify the source for this?

[Radek]

Why divide by sqrt(3) if voltage is already stated as rms? And then why multiply by sqrt(2)?

[Radek]

Ah, I get it,

1/√3 converts Line-Line RMS measurment to Line-Neutral RMS.

And then for that single phase, √2 converts RMS to peak.

Similar:

https://electronics.stackexchange.com/questions/611683/connecting-peak-voltage-rms-line-to-line-and-line-to-neutral

https://www.how2power.com/pdf_view.php?url=/newsletters/1604/articles/H2PToday1604_design_TeledyneLeCroy_part3.pdf page5

Answer 2

[armorfid]

The exact relationships between voltage constant Ke [V/krpm], torque constant Kt [N·m/A], and flux linkage λpm [V·s] are described on this page: https://www.mathworks.com/help/mcb/ref/surfacemountpmsm.html

These are valid for both surface and interior PMSM.

[Radek]

Why mathworks divides Ke based on peak voltage by sqrt(3) ? That implies RMS regime. But RMS is meanigless in FOC theory.

At least I can exaplin the 2/3 term seems they can be exaplained by from adding https://e2e.ti.com/support/microcontrollers/c2000-microcontrollers-group/c2000/f/c2000-microcontrollers-forum/298101/torque-calculation-and-definition-of-flux-unit-v-hz/1043212#1043212

[Radek]

Also, here mathworks doesn't use sqrt(3) https://www.mathworks.com/help/sps/ug/parameterize-a-permanent-magnet-synchronous-motor.html. But they talk about Voltage peak to ground.

And the voltage between line conductors is √3 times the phase conductor to neutral voltage, so I guess that is what is happening. V_L-L is converted to V_L-N.

Answer 3

[Yasin Cetin]

Hello again,

I found at the bottom of the following link

"As expected, the measured torque and back EMF constants have approximately the same value (0.18) and are related to the permanent magnet flux linkage via the number of pole pairs N of the motor:

flux linkage = (back EMF constant)/(number of pole pairs)"

https://www.mathworks.com/help/physmod/sps/examples/parameterize-a-permanent-magnet-synchronous-motor.html

But, in the GUI which I mentioned above post, results are not satisfying this equation. (0.03133/0.00639521 = 4.899)

Answer 4

[Kadir Akgül]

I have same problem. Did you solve the problem?