Measuring rotor inductance
Measuring rotor inductance
(OP)
I've been doing some tests on a rotor from a GE generator, 12MW, vintage around 1960. In doing a stationary AC impedance test, I have some inexplicable results. I am applying an AC voltage to the rotor rings, the rotor is in the machine but the brush rigging has been removed. The rotor is stationary. I am starting with 10VAC and bringing this up to 120VAC at 10 volts per step. At each step I measure voltage and current, and then calculate impedance. The impedance is not constant. It acts as though it is a function of voltage. It increases with voltage, but not linearly. Can someone explain why this is happening?
EE
EE






RE: Measuring rotor inductance
The effective permeability increases as you increase excitation roughly up to beginning of saturation, at which point it begins decreasing.
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(2B)+(2B)' ?
RE: Measuring rotor inductance
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If we learn from our mistakes I'm getting a great education!
RE: Measuring rotor inductance
1 - B vs H (blue)
2 - Mu vs H (magenta)
for M-22 steel used in motor cores.
This is the "normal" or effective permeability calculated as slope from the origin to the point (B,H).... different than differential permeability.
You can see the slope is constant nowhere. Anywhere to the left of the "knee" of the curve, we expect permeability (and magnetizing inductance) to increase with increasing voltage.
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(2B)+(2B)' ?
RE: Measuring rotor inductance
The normal excitation current is 70 - 100A. I believe there are 480 turns. My tests ranged from 0.15 A to a little over 1A. The inductance varied from about 210mH to 290mH. The inductance can be closely approximated as L = 70*i + 214.
Thanks for your insight.
RE: Measuring rotor inductance
We can determine the exponent a by comparing two points (H,B) = (22, 0.1) and (44, 0.4), where H doubles, B quadruples. So the exponent is a=2 (B~H^2 in this low range). That would suggest L~H in this low range.
Since H~I, this curve alone would predict inductance varying with current (neglecting hysteresis effects). i.e. L~I
You may ask why your experiments show LESS variation than L~I.
You may also ask why the current doesn't look distorted at low excitation levels if there is such non-linearity there.
I would say the answer to both of above self-inflicted questions is that the reluctance of the airgap tends to dominate at low excitation levels, and the iron only begins to dominate above saturation. That may be one of the reasons why we erroneously tend to associate iron non-linearity only with levels above saturation. The iron non-linearity is still there at low levels but it doesn't show up as much when it's masked by the air.
What about a transformer? I would think transformer excitation current at low levels would be somewhat distorted, with the peaks cut off and the slope high near zero crossings... somewhere between a sinusoid and a square wave. Of course if there is remnant magnetism, that skews things asymmetrically.
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(2B)+(2B)' ?
RE: Measuring rotor inductance
RE: Measuring rotor inductance
There is insight gained in making the system simpler thru approximation.
Carrying a more detailed model requires more complicated calculation and often brute force numerical. It may or may not lend insight depending on your perspective.
That's a good segue...
I was a little bored today, so I did numerical simulation of a simple gapped iron core toroid with the following paramters:
Vsmax= Applied sin voltage (peak value). Varied through several simulations.
Freq = 60 hz
Diron = 1m = distance flux travels thru iron
Dair = 0.002m
Area = 0.04 m^2
Mu0 = 1.25664E-06
N_ = 400 = # turns
LenTurn = 0.8m
Dturn = 0.01 meter
Sigma = 59000000
Resistance of winding = 0.217 ohms
Magnetic characteristics - M22 steel as per previous attachment.
Attached is the spreadsheet which was used to do the calculation. If you go to the tab labeld "ppt" and double-click on the ppt icon you can open my summary.
The numerical results:
[truetype]
Vmax Imax
1 0.0033
2 0.0066
20 0.066
200 0.66
400 1.0488 (flat top distortion becomes evident)
1000 1.4628
2000 2.146
4000 3.548 (pointy-top saturation becoming evident )
8000 8.97
10000 36.4
12500 487 [/truetype]
For Vmax = 1 to – 200, the results are perfectly linear because they are dominated by airgap (effect of changing magnetics not yet evident). Also the waveform is very sinusoidal.
At Vmax – 400, we start to see less than linear increase. The reluctance of magnetics is now starting to enter the picture and also we see the flat-top type of waveform.
At Vmax = 4000, we begin to recognize obvious saturation and beyond that the peak current starts skyrocketing more than linear.
The calculation is pretty simple but perhaps not well documented. Guts of magnetic model is in tab MagChar (magnetic characteristics). The rest of the spreadsheet just manages the simulation. I'd be glad to answer any questions if it's of interest to anyone out there.
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(2B)+(2B)' ?
RE: Measuring rotor inductance
The correct attachment is attached to THIS message.
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(2B)+(2B)' ?
RE: Measuring rotor inductance
It's not a real linearity. It's an error that results from my copying a constant value for dPhidi from B= -0.15 to B=0.15. Let me correct that and re-post the results.
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(2B)+(2B)' ?
RE: Measuring rotor inductance
A sumary is included in powerpoint embedded in tab PPT_SUMMARY
slide 1:System Studied
slide 2:Iron characteristics. Two kinds of permeability:
1 - Differential permeability is used for simulation (reflects instantaneous slope of B vs H).
2 - Normal or average permeability used for test case hand-calculation at end.
slide 3:This curve shows how air and iron are combined. Exciting current associated with air is added to exciting current associated with iron to give total.
slide 4: dPhi/di curve derived from previous curve. This parameter is used for simulation (Leffective = N*d(Phi)/di)
slide 5:Summary results Imax vs Vmax show slight dip below linear followed by increase as saturation is entered.
slides 6 thru 13 show waveforms as Vs is swept from 1 volt to 10,000 volt.
(Interestingly, in this corrected simulation, there is now no flat-topped waveform in this series. However we can still create the flattop waveform if we get rid of the airgap - see slide 17)
slide 14: - Test Case Hand Calculation with AIR ONLY validates the simulation.
slide 15: Test Case Hand Calculation with IRON ONLY validates the simulation. Used MuNormal since it represents an average slope.
slide 16: Somewhat flat-topped curent waveform still possible if select all iron (airgap=0, Diron=1) and select Vsmax=2000 which is near the peak of the differential permeability curve.
As before we have completely neglected hystesis. And it's a simple single-phase model, some thought would be required to apply results to 3-phase model. Offhand, I'd think we could filter the timewaveforms filter to remove out the 3rd and 9th harmonics and qualitatively get a pretty good approximation of a 3-phase wye-connected machine behavior. Would require lots of thought to get the right numbers. Also representing an entire machine with one lump of iron is limited because different areas of the machine go into saturation at different excitation levels and conditions.
I didn't know it for a long time either. As you can see from simulations, there is not significant distortion of the waveform at low excitation, so the non-linearity is not as obvious as when the core is saturated.
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(2B)+(2B)' ?
RE: Measuring rotor inductance
I'm done now.
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(2B)+(2B)' ?
RE: Measuring rotor inductance
Inductance is the ratio of flux linkages per ampere: L = (Nø)/I
ø = flux
N = coil turns
I = current
L = inductance
so unless the magnetic circuit is linear, L is a function of I.
Like electricpete says, Laplace transforms work with linear parameters. Typically, other techniques are used to determine the 'large signal' operating point of a circuit. Then, a value for L is looked up or calculated and that is used to approximate a circuit's small signal behavior around this point.
For power systems, small signal analysis doesn't make sense (everything is pretty large) so simulation and analysis software uses other numerical techniques to model nonlinear components.
RE: Measuring rotor inductance
Thank you very much for this information. I'm sure that took some time to put together.
EE