Motor winding temperature vs Ambient and Current formula 2

[roderick]

I have a few stator winding temperatures recorded at a few different current readings and ambient temperatures. What is the formula/relationship of stator temperature as a function of ambient temperature and current? This happens to be a large 2500 hp 3ph 4160 induction motor.
I would like to be able to predict stator temperatures at other operating points using my recorded data to calibrate the formula.
Roderick

 

[electricpete]

Temperature rise (above ambient) is roughly proportional to losses.
I would say the losses can be roughly grouped into the sum of two components.
One component is constant.
One component varies with current^2.

This leads to:
(Twinding-Tambient) = K1 + K2*I^2

If you have measurements of (Tambient, Twinding, I) at two different loads (preferably no-load and full load) , you have all you need to solve for K1 and K2.

From nameplate data you can estimate the motor would run at rated temperature rise at rated current, although actual rise is often less than rated rise.


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[aolalde]

In an attempt to get a formula, we have to consider some approximations.

Into the allowed cooling air ambient temperature (Ta), the total operating temperature is the addition of Ta plus the machine temperature rise (Tr). See NEMA MG1 – 20.40.
T = Ta + Tr

To calculate Tr based on your statistical data, (at least two sets of readings) we will assume:

Tr1 = K1*Ii^2 + K2
Tr2 = K1*Ij^2 + K2
-------------------------
Were K1*I^2 = Temp rise due to Stator I^2R+RotorI^2R+Stray Load Losses
K2 = Temp rise due to Core loss + Friction and windage loss (constant if voltage and frequency are held constant)
Tr1, Tr2 = recorded temperature rises.

From two sets of winding temperature records, subtract ambient (Ta) and get Tr.
Resolving two simultaneous equations we find K1 and K2.

K1= (Tr1-Tr2)/(Í^2-Ij^2)

K2= Tr1 – I1^2(Tr1-Tr2)/(Í^2-Ij^2)

For a new load current I, calculate Tr using the values calculated for K1 and K2

Tr = k1*I^2 + K2

Adding the air ambient temperature T = Ta + Tr

You could check how close this approach is by comparing against the recorded results of a third set of readings.


I see that this is almost an identical proposition to that by Electicpete.

 

[jbartos]

Comment: The motor operating duty will influence the stator winding temperature prediction.
1. If the motor is started, then the motor stator winding temperature will be increasing exponentially and converging to a horizontal line that may be viewed as the maximum temperature either absolute or above ambient.
2. If the motor has a cycling duty, then the winding temperature will increase to a Tmax per cycle. Temperature exponential rises and exponential decays will materialize.

 

[edison123]

If you alerady have the stator temp vs load (or current) data, then it is just a matter of plotting them and finding the equation. I think ms-excel has some sort of function to do this. In the case of ambient temp variation, you just add or subtract the variation to the temp rise (just as standards specify it).

 

[blacksea]

The checking of motor SOA, except measuring of winding temperature, need re-calculation of few motor constants and taking into account environment condition. I was in touch with R.H.Welch Jr., well known motor designed and expert on this complex motor thermal issue. You may contact him directly: (rhwelch@stthomas.edu).
Also must be noted that stator core losses also contribute to stator winding heating. While main flux induced core losses mechanisms - eddy current and hysteresis – are known, PWM core loss theory can be found at

http://www.drbrushless.com

 

[electricpete]

http://www.selinc.com

There are three relevant articles included among the info available for free there. Titles something like the following:

#1 - motor thermal models.
#2 - motor analysis/protection part 1
#3 - motor analysis/protection part 2

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[roderick]

Thanks for the information. The formula worked. I plotted Stator temp - Ambient = Constant1 * Amps square plus Constant2. Then used Excel to do a bestfit trendline.

The results were fairly linear. Rsquared = .87 for one motor and .94 for the second.