parametres of equivalent circuit for three phases induction motor

[faycalleroi]

hello
I have an 3 phases IM 5.5kv ,2450kw , 291 amps, Id/In=4.5, Td/Tn=0.3 , 50Hz, 2983tr/min
when I calculate the current in full load with equivalent circuit(see attachment file ) i can't found 291 amps
if i do a mistake? I don't know, can anyone give helpregards

 

[waross]

It looks like an efficiency of 96%

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

 

[electricpete]

I don't understand why you have two values for X1 and two values for R1.
For X2, R2, I believe the higher-R, lower X at bottom of table corresponds to starting and lower-R higher X at top of the table corresponds to running (deep bar effect). But there is no deep bar effect for stator....why two values?

Interesting that the French word for torque seems to be"couple".


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(2B)+(2B)' ?

 

[faycalleroi]

yes you are right in french couple means torque.

the document in attachment is an official document from ABB the motor type is : AMDT 500-700 with directive atex ,
if we compare between this document and other induction machine guide books there is a named difference for the resistance and reactance stator and rotor example: in the theorie books there is : R1 , X1 for stator R2 ,X2 rotor for no load test and R2' , X2' for blocked rotor test however in this attachement there is a data about the temperature , and when i have done a current and torque calculation (i take for 50° a blocked rotor and 120° a full load value the outcome is wrong.
what is the solution?
regards

 

[electricpete]

I think the ' designation simply means the rotor parameters are referred to primary (stator).

Two values each for R2,X2 are expected (running and locked rotor).
Two values each for R1, X1 are not.

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[electricpete]

In attached spreadsheet, I have used:
R_1 0.0704000
X_1 1.9801000
R_2 0.0653000
X_2 1.1985000
X_M 98.5000000
R_NL 2950.0000000

RPM = 2981.3 (lower than your 2983, but5 this is the value required to produce rated output by this model).

Using the equivalent circuit with above (i.e. FullLoadSlip = 0.0062333), it generates:
FullLoadAmps 288.9717651
FullLoadEff 0.9829193
FullLoadPF 0.9241550
FullLoadPower 2,500,583.81693
FullLoadTorque 8009.5315818
Full Load Slip 0.0062333

This seems to match the data sheet reasonably well.

Note my equivalent circuit is slightly different in that my R_NL (which plays the role of your Rfe) is on the supply side of the primary impedance, rather than in parallel with magnetizing reactance. The expected difference from this change is small.

To recalculate, the spreadsheet requires the "analysis toolpak" for excel.


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[electricpete]

Sorry, I was using P = 2500 instead of 2450
Another run of the same spreadheet, using the same model
R_1 0.0704000
X_1 1.9801000
R_2 0.0653000
X_2 1.1985000
X_M 98.5000000
R_NL 2950.0000000

But this time set RPM a few tenths higher at RPM = 2981.75 (Full Load Slip 0.0060833)
This results in calculated
FullLoadAmps 282.7061375
FullLoadEff 0.9831461
FullLoadPF 0.9256792
FullLoadPower 2,450,965.01628
FullLoadTorque 7849.4145590

The number of decimal places is not intended to convey the precision... just didn't spend time cleaning it up.


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(2B)+(2B)' ?

 

[faycalleroi]

thanks a lot
but what means by changing speed ,is the machine manufacturer make mistake about speed measured?
regards

 

[electricpete]

The difference between 2981.75 and 2983 is relatively small. The difference between calculated full load currents (282 vs 291) is bigger. I don't really know how to explain those differences.

A few random thoughts:
1 - small errors in speed measurement cause big errors in slip
2 - the resistances are dependent upon temperature. All resistances affect efficiency. Rotor resistance also affects slip for a given power pretty dramatically. We don't really know if all of these numbers represent the same temperature.
3 - per NEMA standards the accuracy requirement for nameplate speed is pretty loose. I don't know about other standards.
4 - small error due to position of that R_NL vs Rfe as discssed above.
5 - I never did figure out the significance of the extra value R1 and X1


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(2B)+(2B)' ?

 

[electricpete]

Also, I have seen some calculations that vary the parameters between locked rotorand no-load linearly with slip. I just used the no-load value. The error is relatively small I think. But if you're looking to dissect the error you may have to sharpen your pencil more than I did. Best way of course is contact the OEM and ask them to explain their calc.

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[faycalleroi]

i think that the best question is: why ABB gives this induction motor data like this?, it's easy to calculate all parametres of motors if the parametres was given like what wehave study in school (paremetres in no load and blocked rotor)not in depend of temperature(my english is not well pardom)
regards

 

[electricpete]

If users are going to do simulations or drive setup, they would probably rather see equivalent circuit parameters rather than having to calculate them.

One problem as we've stumbled onto is that there are various ways to determine performance and equivalent circuit and there may be some assumptions that need to be known about what is being presented. Ideally the definition of each term if not standard, and how was it determined, and what temperature is assumed,

IEEE112 section 5.9.2 presents three standard test / calculation methods to develop equivalent circuit model. It might be a useful reference for NEMA motors. Probably not much used in the IEC world.


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[faycalleroi]

thanks electricpete your response is very helpful
best regards

 

[electricpete]

Attached I reformatted the calculation to be more transparent.

Part 1 recreates the calculation reported above (7 May 13 9:13).
s:=0.006083 is required to make P = 2450 and results in FLA = 282.7

Part 2 adjusts the parameters based on slip. Result is not much different.
s:=s:=0.006125 is required to make P = 2450 and results in FLA = 282.

282 is around 3% away from 291. So a combined error of 3% in pf*eff compared to the value reported (pretty big error).

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[7anoter4]

I simplified the calculation in this way:
1) transforming from [parallel] Rfe||jXm in Ro+jXo [in series].
2)transforming Zeq= Z1+Zo||Z'2 where Zo=Ro+jXo Z1=R1+jX1 Z2=R'2/s+jX'2 I=UN/sqrt(3)/Zeq and for 2981.15 rpm I got 291 A.
As electricpete said: the result is very sensitive to the rpm changes[namely to slip].
For instance if rpm=2980 I=306 A and for 2983 I=265 A.
I get, approximately, same result if I neglect Rfe and Xm [264 A]for 2983 rpm.