How to calculate motor capacitance? 2

[lyen12]

I have done a quick search on this forum, but unable to find a thread on this.

Is this the right way to calculate "motor capacitance"?
Take C = Epsilon * A/d

with C = capacitance
Epsilon = Epsilon0 * relative_permitivity_of_air
A = Area of stator lamination bore
d = airgap

Why is it useful to know the motor capacitance?

 

[electricpete]

Why is it useful to know the motor capacitance?

A - For grounding system calcs
B - When you are doing an ac test
C - Possibly for detailed evaluation of the reflection/amplification of surge upon transitioning from cable to motor... although that is more a characteristic impedance.

I think it has been discussed but I don't have the threads handy.

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(2B)+(2B)' ?

 

[electricpete]

I guess you might also be interested in capacitance if you were looking at how vfd pulses can couple from the winding onto the rotor. This is the only one I can imagine airgap would have any role. And the equation still doesn't look right to me.

Can you will have to clarify which aspect you're interested in.

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(2B)+(2B)' ?

 

[lyen12]

Thanks for the quick response, electricpete.
I would like to know more about point B. Could you please elaborate, with some examples if possible?

 

[lyen12]

I was asked to calculate the "motor capacitance" of a VFD motor. The term motor capacitance sounds too general, and I do not know why it is needed. I would have thought capacitance is between two or more plates separated by a medium (eg airgap), that's how I assumed the capacitance equation.

 

[Skogsgurra]

The rotor-to-frame capacitance is very important when it comes to evaluation of bearing current damages. A discharge through the bearing is more violent and causes more damage when the discharged capacitance is high (W=0.5*C*U^2), so it is sometimes necessary to know the rotor-frame capacitance.

A great thesis on bearing currents is this:

http://www.ew.e-technik.tu-darmstadt.de/cms/fileadmin/pdf/Dissannette.pdf

There, on page 9, you can find a first presentation of different capacitances in the motor.

Page 115 and 116 give formulae and calculated/measured results for capacitances.

Search Crf within the document for all occurances.

Gunnar Englund

http://www.gke.org

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100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...

 

[electricpete]

Thanks for the quick response, electricpete.I would like to know more about point B. Could you please elaborate, with some examples if possible?

Point B – AC testing. If you perform an ac hi-pot test or a Doble power factor (tan delta) test of the groundwall insulation, then capacitance to ground will determine the magnitude of the current drawn during the test. Your test set needs to be able to handle this much current so that it won’t trip. Also there are sometimes obscure inferences you might draw when interpretting capacitance to ground measured with a Doble set (the Doble manual slices it a lot of different ways), these would be directly related to the capacitance to ground.

The capacitance measured during any of the above standard ac ground insulation tests would be primarily based on capacitance between the conductor and the slot wall... the area of interest would be the slot wall area (not the airgap area). Only a teensy weensy contribution of that measurement would be from top of stator coil accross the slot to grounded rotor. But that is the path of interest if you are looking at how vfd pulses are coupled onto the rotor. If you wanted to attempt to measure that capacitance from stator to rotor winding you could do it with a Doble set IF your motor bearings are insulated by guarding out the large contribution from the the stator core. But I'm not recommending anyone do that test because I don't know exactly what you'd do with it. I’ll have to read Gunnar’s link when I get a chance.

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(2B)+(2B)' ?

 

[lyen12]

Thank you all. That's a lot of new things here for me to absorb.

 

[rockman7892]

Electricpete

Can you share your thoughts on how this effects A. (grounding system calcs) in your first post.

Are you referring to the charging current of the motor to ground in order to determine the minimum pickup and trip level for the ground falut relay?

 

[electricpete]

For selecting neutral grounding resistor in a high-resistance grounding scheme:

http://www.crcnetbase.com/doi/abs/10.1201/9781420015393.ch4

"The resistor current must exceed the total system charging current...."

In other words the neutral resistor is selected to have less resistance that the system capacitive reactance to ground. The components of the power system contribute in parallel so each component of the power system (including motors) decreases that system capacitive reactance.

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(2B)+(2B)' ?

 

[Skogsgurra]

The OP heading says 'motor capacitance' - and that is a very general term that could mean just about any capacitance found in a motor. Not necessarily an induction motor.

The formula given in the OP is the formula used to calculate capacitance between rotor and stator, so I assumed that was the capacitance asked for and also that lyen12 was interested in how rotor-stator capacitance influences bearing destruction, so called EDM.

Now, I am not so sure that was what lyen12 asked about.

Please, lyen12, could you tell more about the background and what you actually was asking about?

BTW, Pete: What about 2C+/2C?

Gunnar Englund

http://www.gke.org

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100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...

 

[ScottyUK]

Gunnar... do you read Shakespeare?


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If we learn from our mistakes I'm getting a great education!

 

[edison123]

If you mean by capacitance, the dielectric, then I know of no method to calculate it. You use a schering ac bridge to measure it.

Muthu

http://www.edison.co.in

 

[lyen12]

Hi all,

It is actually the capacitance of motor windings per phase to ground. Since the stator is a wet-wound type of induction motor, I can actually assume that the capacitance is between conductor and the winding insulation outer diameter(including conductor).

Therefore,
Capacitance [uF/mile] = 0.038 x Epsilon / lg (D/d)
with
D = diameter of winding cable (insulation + conductor)
d = diameter of winding conductor

I got the above equation from one of a textbook, can't remember what the title was.

 

[lyen12]

could you tell more about the background and what you actually was asking about?

It was asked from a customer to furnish the motor capacitance of stator windings to ground. I would assume, as electricpete mentioned above, it will be used for system grounding calcs and ac flash test. Being a novice in this area, the term motor capacitance as it was initially requested for, is the C between the stator-rotor airgap, without knowing why the C was needed.

 

[Skogsgurra]

The Annette Mütze thesis that I referred to earlier contains some actually measured data that could help.


Gunnar Englund

http://www.gke.org

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100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...

 

[electricpete]

Scotty - Ay, there's the rub.
Gunnar - 2C+/2C? I don't understand the question.

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(2B)+(2B)' ?

 

[wolf39]

lyen12:

It's the same old story: You can't expect to get a meaningful answer if you don't provide us with sufficient information.

What's the motor rating you have in mind? For large motors with rectangular copper strands your formula

C = E * A/d

would work. However, you have to apply the following technical data to the above formula:

E = dielectric constant of insulation (not air)
A = total copper surface area of stator winding (not stator bare data)
d = main insulation thickness (not air gap data)

For small motors with round copper strands the above formula wouldn't work as you don't have a defined main insulation thickness.

Wolf

http://www.hydropower-consult.com

 

[electricpete]

Good point. It can be estimated analytically.

There was a lot of discussion of calculation of motor capacitance in this thread on a predictive maintenance bulletin board:

http://maintenanceforums.com/eve/forums/a/tpc/f/7161085912/m/5531041793/p/4

Regarding phase to ground, the last post on that thread describes actual measurements by JanK made before/after VPI of a form-wound motor. The measurement agrees with the analyitcal calculation that JanK posted on the previous page of that thread (click on the 3 to go from page 4 to 3) on 08 December 2008 10:13 PM. In case you can't see the attachment which gives coil description (requires forum registration), I have posted it as attachment to this message.

When you get into random wound motors it gets somewhat more complicated. I have used a numerical method focusing on phase-to-phase impedance (including the miniscule contribution from turn to turn capacitance) here

http://home.comcast.net/~electricpete/maintenanceforums/motorcap/motorcapacitanceR4.pdf

Adapting that approach to phase to ground capacitance is easier. If we want to mimic a test with one phase energized and the other two grounded:
1 - Assume voltage distirbution in the conductor coils varies linearly between VLG at the line terminal and 0 at the neutral terminal. Assume slot is grounded.
2 - Do F.E. solution of the electric field in the area between conductors and slot (including insulation).
3 - Compute stored electrostatic energy
We = Integral 0.5*Epsilon*E^2 dVolume
4 - Compute equivalent capacitance to ground per phase:
Ceq = 2*We/VLG^2 (this is We = 0.5*C*V^2 solved for C)

It's not a difficult calculation to do with the free program "FEMM" as I did, but there are some errors. The biggest would be in the assumptions we must inevitably make about positioning of those random wound conductors. Next biggest would be unknowns about actual dimensions and relative permittivity. Also we neglected phase-to-phase effects (They are relatively small since most of the interaction is between conductor and slot wall, not as much between phases. )

Or as Muthu said you can measure the same thing (with a Doble tester typically).

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(2B)+(2B)' ?

 

[wolf39]

lyen12:

You don't have to use a Schering bridge to measure the motor winding capacitance.

Use an isolating transformer and connect one of the secondary terminals to the motor stator core (stator core to be grounded). Then connect the other secondary to one of the motor winding terminals. Measure the secondary voltage and secondary current flow. To calculate the motor winding capacitance apply the following formula:

C = current / 6.28 * frequency * voltage

Assuming that all three motor winding phases are connected with each other, divide the result by 3 to arrive at the motor winding phase capacitance.

Wolf

http://www.hydropower-consult.com