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How to calculate motor capacitance?
2

How to calculate motor capacitance?

How to calculate motor capacitance?

(OP)
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?

 

RE: How to calculate motor capacitance?

Quote:

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.  

=====================================
(2B)+(2B)'  ?

RE: How to calculate motor capacitance?

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.

=====================================
(2B)+(2B)'  ?

RE: How to calculate motor capacitance?

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

RE: How to calculate motor capacitance?

(OP)
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.

RE: How to calculate motor capacitance?

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

RE: How to calculate motor capacitance?

Quote:

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.

=====================================
(2B)+(2B)'  ?

RE: How to calculate motor capacitance?

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

RE: How to calculate motor capacitance?

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?

RE: How to calculate motor capacitance?

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.

=====================================
(2B)+(2B)'  ?

RE: How to calculate motor capacitance?

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

RE: How to calculate motor capacitance?

Gunnar... do you read Shakespeare?
  

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

RE: How to calculate motor capacitance?

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
www.edison.co.in

RE: How to calculate motor capacitance?

(OP)
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.

RE: How to calculate motor capacitance?

(OP)

Quote:

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.

RE: How to calculate motor capacitance?

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

Gunnar Englund
www.gke.org
--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...

RE: How to calculate motor capacitance?

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

=====================================
(2B)+(2B)'  ?

RE: How to calculate motor capacitance?


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
www.hydropower-consult.com  

RE: How to calculate motor capacitance?

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).   

=====================================
(2B)+(2B)'  ?

RE: How to calculate motor capacitance?


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
www.hydropower-consult.com  

RE: How to calculate motor capacitance?

Yes, good clarification.   It is rare that anyone is interested in capacitance by itself, so the only time I have ever seen that measurement is as part of an insulation power factor test (that is the sense that it is "typical").  But if all you want is capacitance, then it can be measured with less expensive and less specialized equipment.

But I have to pause to mention there would be a correction factor applied to any off-line measurement to account for the for the difference in voltage distribution within the windings between test and operation:  Voltage accross the insulation during off-line test is uniform along the entire entire winding, whereas  voltage accross the insulation during operation varies smoothly from VLG at the line terminal down to 0 at the neutral.  This difference in voltage distribution affects the equivalent capacitance as can be shown with the energy approach described above.   **

We can derive a correction factor to account for the difference in voltage distribution in test and during operation:
Let's say we are given Capacitance Per Length of conductor:  CPL.
If we apply uniform voltage, the capacitance is easy C = CPL * L
But if we apply graded voltage V0 on one end and zero on the other (V = V0-V0*x/L) where x is position along the line), we have energy We given as:
We = Int 0.5 * CPL * (V0 – V0*x/L)^2  dx for x=0..L
We = Int 0.5 * CPL * (V0^2 – 2*V0^2*x/L + V0^2*x^2/L^2)  dx for x=0..L
We = 0.5 * CPL * [V0^2*x – V0^2*x^2/L + (1/3)*V0^2*x^3/L^2] evaluated at x=L minus x=0
Since the quantity at x=0 is 0, we have:
We = 0.5 * CPL * [V0^2*L – V0^2*L^2/L + (1/3)*V0^2*L^3/L^2]
We = 0.5 * CPL * [V0^2*L – V0^2*L + (1/3)*V0^2*L]
We = 0.5 * CPL * [(1/3)*V0^2*L]
Ceq = 2*We/V0^2 = 2*0.5 * CPL * [(1/3)*V0^2*L] /V0^2 = (1/3)*CPL*L
Ceq = (1/3)*CPL*L = 1/3 of what we would measure if uniform voltage was applied to the whole winding.

So there is a factor of 3 to account for the voltage distribution going to zero at the neutral.  This is different than the factor of 3 for converting 3-phase test to per-phase basis.  i.e. take your 3-phase-to-ground offline measurement and divide it by 9 to account for both effects.

The approach of the F.E. that I linked was appropriate for the problem I was tackling (finding the relative contribution of local turn insulation changes within overall phase-to-phase impedance measurements), but would definitely be overkill for determining ground capacitance considering all the limitations/inaccuracy of the input data / model to begin with.    Your initial mentioned approach of capacitance per length of conductor might not be too far off, as long as:
1 – account for the conductors along the periphery of the slot (ignore the others in the interior)
2 – use a capacitance of a series of individual conductor adjacent to conducting plane which accounts for that configuration. You might be able to estimate it analytically.  I would be inclined to do a simple F.E. of a single insulated conductor a specified distance above a bottom grounded boundary surface, with left/right boundary potentials matching each other as if we have mirror image of another conductor on left/right, and top boundary either same potential as conductor or symmetric boundary.
3 – Determine equivalent capacitance by "combining" all of the individual capacitances.  i.e. by summing the energies 0.5*Ci*Vi^2 where Vi varies by conductor (probably good enough to assume all conductors of a given phase in a given slot are the same voltage). **

But I do think measurement (with correction factors) is the better approach.  Or else try to find someone that has already taken measurements of similar motors.  

** It may seem non-intuitive:  after all... capacitance shouldn't depend on voltage...  we can model this as a bunch of capacitances in parallel between the conductor and ground, so why can't we just add the parallel capacitances Ceq = C1+C2+C3....?   The answer is that capacitance of each sub-element is a function of geometry and not voltlage, but if we want to combine them into an equivalent capacitance seen at a terminal with a different voltage, that equivalent capacitance does depend upon the internal voltage distribution.   See appendix of my linked paper for further justification of the energy approach to determine equivalent capacitance.

=====================================
(2B)+(2B)'  ?

RE: How to calculate motor capacitance?

Now that I think about it, it is not straightforward to figure out which capacitance is more relevant for system grounding calcs – the capacitance based on on-line voltage distribution or off-line distribution.  Presumably the analysis involves swinging of all three phases together with respect to ground.  Now voltage to ground to ground along a given phase looks like a constant plus that linear gradient from line to neutral.  Don't know where that leads.

=====================================
(2B)+(2B)'  ?

RE: How to calculate motor capacitance?

The reference below gives means for calculating minimum neutral grounding resistance based on analysis of system capacitance.  Section 4.9 is devoted to capacitance of various system elements.  The data for induction motors is excerpted below:

Quote (Industrial Power Systems Textbook):


"Industrial Power Systems" by  Shoaib Khan, Sheeba Khan, Ghariani Ahmed.
ISBN 978‑0‑8247‑2443‑6.....

4 System Neutral Grounding...

4.9 System Capacitance Data...

4.9.9 Induction Motors

Zero-sequence capacitance (C0) in uf/phase is given in table 4.8.

Table 4.8
Zero-Sequence Capacitance Data for Induction Motors (uf/phase)
Rating, kW kV 1800 rpm 1200 rpm 900 rpm 600 rpm
225 4.0 0.009 0.012 0.014 0.016
300 4.0 0.01 0.013 0.015 0.017
350 4.0 0.012 0.014 0.016 0.018
400 4.0 0.014 0.016 0.017 0.021
Source: Westinghouse, "System Neutral Grounding and Ground Fault Protection," publication PRSC- 4B-1979, Westinghouse, 1979.

=====================================
(2B)+(2B)'  ?

RE: How to calculate motor capacitance?

Since the relevant quantity is a "zero-sequence capacitance", I tend to think the factor of 3 correction factor to apply to measured values that I derived above would not be relevant. (because the voltage gradient between line and neutral does not exist if zero sequence voltage is applied ... same voltage at all three phases and neutral).

=====================================
(2B)+(2B)'  ?

RE: How to calculate motor capacitance?

Can you give a complete description of your motor?

=====================================
(2B)+(2B)'  ?

RE: How to calculate motor capacitance?

(OP)
The response overwhelmed me with lots of information. Basically I am required to give a budgetry fora  motor cartridge for subsea compression. The motor which I am supposed to quote, excludes thrust bearing and pump which will be provided by other vendor.

The motor must be sized so that it could fit into a large housing. Therefore, the stator lamination outer diameter should be about 650mm, with its bore 300mm, and pack length of about 400mm. The motor is VF driven, rated at 600kW 3300V 2pole 50Hz. 3Hz starting, and max speed 53Hz.

I am able to provide all other information to the customer, except I am a little bit unsure on how to calculate the windings capacitance per phase, and therefore would like to have some ideas on how to go about it.

There are many ideas here, and most of it looks complicated to calculate. Since the motor is for a RFQ, I would thought an estimate of capacitance would suffice....?

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