Heating and cooling time constants of motor and thermal overload protection 2

[RRaghunath]

We input motor time constants in the numerical relay and verify the relay operating times for effective motor protection against overloads. Recently, I came across two types of heating time constants for a motor - winding heating time constant of 5min and machine heating time constant of 30minutes.
Can some one enlighten me the difference between the two please!
Is winding heating time constant measured with winding in open air whereas, the machine heating time constant is measured after winding is put in the stator core slots I.e. after complete assembling of the motor.
If true, I guess I should be considering the machine heating time constant in thermal overload protection calculations and not the winding heating time constant!
Then, what is the significance of winding heating time constant for a protection engineer!
Thanks in advance for sharing!

 

[electricpete]

Thermal time constant is roughly Tau = Rth*Cth where Rthermal is thermal resistance and Cth is thermal capacity. Cth doesn't change, but Rth is dramatically higher while shutdown while running since there is no cooling air flow. The result is that the time constant is much longer while motor is secured than while running. You can see the dramatic differences in time constants by comparing the recorded winding temperature transient following start to the recorded winding temperature transient following shutdown.

I'm not familiar with microprocessor thermal relays and would suggest to read the manufacturer's documentation for definitive info, but that would be my guess (the 5 minutes is a running time constant and 30 minute is a secured time constant).

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(2B)+(2B)' ?

 

[electricpete]

left out a word, corrected in bold

Rth is dramatically higher while shutdown while than running since there is no cooling air flow. The result is that the time constant is much longer while motor is secured than while running

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(2B)+(2B)' ?

 

[electricpete]

I searched and found the old thread where I had posted some related data/conclusions:
thread237-115967

The smallest motor that we have continuous temperature monitoring on is a 300HP TEFC vertical 460vac squirrel cage induction motor.

Based on temperature data recorded by our plant computer, the time constant (tau) for temperature change following a start is 2 - 3 hours (hourly computed time constant remains in this range for 11 hours which leads me to dimiss starting current as an important factor) . Load was constant during the running period. The time constant for temperature change upon stop was 7 - 10 hours.

tau_running / tau_stopped = [C * Rrunning] / [C* Rsecured] = Rrunning/Rsecured ~ (1/3)
where
tau = time constant
C = thermal heat capacity (constant regardless of run or stop)
R = thermal resistance... inversely proportional to cooling effectiveness.....


Below is the data for start and stop in 5 columns, defined as follows:
1 = Date/Time
2 = Winding Temperature
3 =+LN((WindingTemp-183)/(71.5-183)) for start
3 =+LN((WindingTemp-71.5)/(188.3-71.5)) for stop
4 = rate of change of #3 per hour based on this row and previous row.
5 = 1/#4 = estimated time constant in hours

=======START========
2/19/03 7:00 71.54 0.00
2/19/03 8:00 71.63 0.00 0.00 -1286.75
2/19/03 9:00 79.46 -0.07 -0.07 -13.71
2/19/03 10:00 110.39 -0.43 -0.35 -2.82
2/19/03 11:00 130.86 -0.76 -0.33 -3.02
2/19/03 12:00 151.04 -1.25 -0.49 -2.04
2/19/03 13:00 161.57 -1.65 -0.40 -2.50
2/19/03 14:00 169.12 -2.08 -0.43 -2.30
2/19/03 15:00 173.81 -2.50 -0.41 -2.42
2/19/03 16:00 177.96 -3.10 -0.60 -1.66
2/19/03 17:00 179.12 -3.36 -0.26 -3.85
2/19/03 18:00 180.27 -3.71 -0.35 -2.84
2/19/03 19:00 181.42 -4.26 -0.55 -1.82
2/19/03 20:00 182.58 -5.57 -1.31 -0.76
more steady state data deleted here
=======STOP========
2/23/03 10:00 188.32 0.00
2/23/03 11:00 152.03 -0.37 -0.37 -2.69
2/23/03 12:00 141.63 -0.51 -0.14 -7.23
2/23/03 13:00 131.42 -0.67 -0.16 -6.35
2/23/03 14:00 125.05 -0.78 -0.11 -8.90
2/23/03 15:00 118.69 -0.91 -0.13 -7.90
2/23/03 16:00 112.32 -1.05 -0.14 -6.90
2/23/03 17:00 108.39 -1.15 -0.10 -9.89
2/23/03 18:00 104.81 -1.25 -0.10 -9.78
2/23/03 19:00 101.22 -1.37 -0.11 -8.78
2/23/03 20:00 97.63 -1.50 -0.13 -7.77
2/23/03 21:00 95.05 -1.60 -0.10 -9.61
2/23/03 22:00 93.31 -1.68 -0.08 -13.00
2/23/03 23:00 91.56 -1.76 -0.08 -12.00
2/24/03 0:00 89.82 -1.85 -0.09 -10.99
2/24/03 1:00 88.07 -1.95 -0.10 -9.99
2/24/03 2:00 86.33 -2.06 -0.11 -8.99
2/24/03 3:00 84.58 -2.19 -0.13 -7.99
2/24/03 4:00 83.79 -2.25 -0.06 -15.97
2/24/03 5:00 83.13 -2.31 -0.06 -18.07
2/24/03 6:00 82.47 -2.37 -0.06 -17.07
2/24/03 7:00 81.81 -2.43 -0.06 -16.06
2/24/03 8:00 81.14 -2.49 -0.07 -15.06
2/24/03 9:00 80.48 -2.57 -0.07 -14.06
2/24/03 10:00 79.82 -2.64 -0.08 -13.06

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(2B)+(2B)' ?

 

[waross]

Or it could be that the winding heats up and stabilizes much more quickly than the surface of the motor.

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[electricpete]

I'm not sure I get your point. The winding temperature is what was measured in the data above.

Since I don't get your point, let me tell you more about my thought process. Maybe it will address your comment or maybe it will help op (more info to explain my last post).

If we characterize the system by a single time constant, that implies system first order model - single thermal inertia C = Joules / degC and single thermal resistance R = degC / watt.
Relevant temperature would be the rise of winding temperature above ambient temperature (I have assumed constant ambient temprature for analysis of data above since that motor is in a climate controlled environment)

In op we have two time constants mentioned. My suggestion was the it represents the same first order model but under two different conditions (running and stopped). There is zero doubt that motor "thermal resistance" between the winding and the ambient is higher while shut down due to lack of rotor fan-created cooling. Higher thermal resistance R means higher thermal time constant Tau = R*C. Review of above data confirms exactly what we expect (could also plot temperature rise vs time on ln vs lin scale where the absolute magnitude of the slope is the inverse of the time constant. Given this behavior, assuming running thermal time constant during stopped periods would be non-conservative.

On the other hand, multiple time constants might also suggest a more complicated model then simple first order model... for example model with C1--R1--C2--R2 in series and here there is an intermediate temperature of interest between winding and ambient. But to describe such a model effectively would require more info than the two time constants (tau1=R1*C1 and tau2=R2*C2), it would require an additional ratio such as ratio of C1/C2 to be useable to predict motor temperature based on power history. That may be the case, beats me.

Maybe op can tell us what specific relay.
Bill, if you want to explain your comment more, please do. Whatever your point was, I missed it.






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(2B)+(2B)' ?

 

[Skogsgurra]

There are several situations where one has to be careful with what thermal time constant is being used. In this report:

http://www.google.se/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CDAQFjAA&url=http://

http://www.gke.org/pub/files/Solar%...=OIs7asnqmmxPVWP2c8LqbQ&bvm=bv.48572450,d.bGE

, that is very obvious. These guys were measuring the temperature of the main excitation winding in a rather large DC motor and switched on the cooling fan when main winding got hot. That took between one half and one full hour. In the meantime, the armature winding, especially the winding heads, with a much shorter thermal time constant, were literally melted down. See last picture in the report for an example of different thermal time constants and the corresponding temperatures.

That explains the need for different time constants. I do not know what type of electrical machine the OP is discussing, DC machines are somewhat extreme in that respect, but there are certainly parts that get heated a lot faster than others in any electrical machine. No machine is a homogenous lump.

(All person names and company names have been changed in the report in order to keep embarresment level as low as possible).

Gunnar Englund

http://www.gke.org

--------------------------------------
Half full - Half empty? I don't mind. It's what in it that counts.

 

[RRaghunath]

Thanks for sharing.
The motor data sheet I was referring belongs to a 360kW, 3000RPM, 6.6kV motor and the thermal heating time constants at rated speed for winding 5min and for machine 30min.

 

[Skogsgurra]

So, the situation is somewhat similar to the last picture in the report, then? But you have two time constants instead of three.

Gunnar Englund

http://www.gke.org

--------------------------------------
Half full - Half empty? I don't mind. It's what in it that counts.

 

[waross]

Pete:
I assumed that winding temp/constant was hottest spot determined by an embedded sensor and machine temp/constant was the iron temperature measured near the outside of the frame.
Gunnar: Nice explanation and illustrations.
Thanks.

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[rhatcher]

I think that Bill and Gunnar are on the right track. As implied by the names, one constant applies to just the winding while the other applies to the entire machine (motor). However, it is not clear to me what these values represent.

For example, the idea that it is the time for the winding and the machine to reach operating temperature under normal load yields values that are too short (5 minutes for the winding and 30 minutes for the "machine").

Another possibility is that these constants represent minutes/deg C rise under normal load. This yields a time of 400 minutes, or 6.7 hours, for the winding and 2400 minutes, or 40 hours, for the "machine" (assuming 80C rise). These times are a little long but not entirely unreasonable. However, the temperature rise of the motor is not constant (linear) so this would be difficult to reconcile.

Of course, the protection engineer is not really concerned about when or how long until the motor reaches operating temperature, he/she is concerned about preventing damage under overload conditions. This leads to the idea that these constants represent the thermal limit (time until damage occurs) for the motor. However, these times are meaningless unless the corresponding amount of overload is also given.

I am thinking that the OP will have to go back to the source that provided the constants, either the motor or relay manufacturer, to get a definitive answer on what these constants represent.

BTW, nice detective work and report Gunnar.

 

[electricpete]

The op subject said “heating and cooling” time constants, which was the motivation for my suggestion. It has always seemed to me that neglecting the reduced cooling during off periods is a non-conservative assumption for repeated starting. On the other hand, repeated starting is so much more challenging to model than running, there are surely a number of other concerns we could raise for modeling of starting.

I didn't read closely below that, so I missed the words “machine” and “winding” which make it clearer. I agree with waross and rhatcher on that. The model would be
C1==R1==C2==R2 where 1 is winding and 2 is machine.

I arrange them in series vs parallel because the winding transfers the bulk of it’s heat to the core (only small part direclty to air) and core transfers to ambient.

Winding has less mass (lower C) and better thermal transfer to core (lower R) since winding transfers to core by conduction but core transfers to air by convection. This is consistent with your 5 minutes for winding and 30 minutes for core. Also I think ODP tend to have shorter time constants than TEFC (my data was from TEFC).

As I mentioned, based on series model, there needs to be info or assumption about the ratio C1/C2 in order to do anything with that model.


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(2B)+(2B)' ?

 

[electricpete]

I just studied the report by Gunnar. It is a good report.

So, the situation is somewhat similar to the last picture in the report, then? But you have two time constants instead of three.

Yours is a good illustration and I know it’s not intended to be exact representation of a different machine. Maybe this was rhetorical question but I’ll give my take on it... maybe some help for op as well.

I see your model as a parallel thermal model. (You said all three parts reached the same equilibrium temperature... but just took different times to get there... supported by a configuration of interpole in series with armature and presumably-series field which all see same current). In contrast I see the winding/machine as a series thermal model as discussed above. As you know, the series model is tougher because we cannot solve any of the temperatures without knowing all pieces of the series chain. In contrast for parallel model we can solve one branch to find the temperature of that branch without knowing anything about the other branches (but using one branch as representative of other branches presents a subtle problem even though they may have similar steady state temperatures as you highlighted).


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(2B)+(2B)' ?

 

[Skogsgurra]

Yes, Pete. The mistake they did was to forget that some parts of the machine got hot a lot earlier than other parts and the other mistake was to use the slowest (longest thermal time constant) to switch on the cooling fan.

It is hard to believe, but this resulted in me going to southern Germany three times, the last time to attend a meeting with the manufacturer's regional sales manager, the customer's technicians and an attorney. That didn't stop the motors from burning. In all, they burned fourteen of these large DC machines before they believed me and changed the cooling strategy. Each repair cost around EUR 50000.

I still do not understand why they were so reluctant to accept the facts. Perhaps they hoped for a guarantee compensation. One of their technicians said "How can we believe you when you are being paid by the manufacturer?" To which I answered "It is OK if you also pay me, but it won't change the report". I'm not a diplomat.

Gunnar Englund

http://www.gke.org

--------------------------------------
Half full - Half empty? I don't mind. It's what in it that counts.

 

[waross]

What is the return on investment period for the energy saved to pay for the cost of repairs and investigations?

Bill
--------------------
"Why not the best?"
Jimmy Carter