How to calculate rotor flux of the three phase squirrel cage induction motor?

  • #1
adamaero
109
1
Homework Statement
How to calculate rotor flux of the three phase squirrel cage induction motor?
Relevant Equations
Rotor flux and more
Three phase squirrel cage induction motor with given parameters (stator winding connected in delta)

  • nominal power: Pn=22.4kW
  • nominal stator voltage: Vsn=230V
  • nominal stator current: Isn=39.5A
  • nominal stator frequency: fsn=60Hz
  • nominal speed: nn=1168min−1
  • number of pole pairs: 3
  • stator resistance per phase (T equivalent circuit): Rs=0.294Ω
  • stator leakage inductance per phase (T equivalent circuit): Lsl=0.00139H
  • rotor resistance per phase (T equivalent circuit): Rr=0.156Ω
  • rotor leakage inductance per phase (T equivalent circuit): Lrl=0.0007401H
  • magnetizing inductance per phase (T equivalent circuit): Lm=0.041H

I have been struggling with calculation of the nominal value of the rotor flux. My idea was that I will use the T equivalent circuit for that purpose
8tYEX.jpg


and I will use nominal values of the motor quantities i.e. I set the motor operating point into the nominal operation point (nominal slip, nominal stator voltage etc.). Then I calculate phasor of the stator current (Is) and phasor of the rotor current (Ir) according to the below given set of equations
https://forum.allaboutcircuits.com/attachments/1620849888346-png.238168/

For the motor parameters mentioned above the Scilab command linsolve gave mehttps://forum.allaboutcircuits.com/attachments/1620849901203-png.238169/
Based on the known phasors of the stator and rotor current I used the below given equation for calculation of the phasor of the rotor flux
https://forum.allaboutcircuits.com/attachments/1620849925020-png.238170/
which gives λr=0.5554856−0.0613638j i.e. |λr|=0.5588647V⋅s.

This value seems to me to be too low. So I have doubts regarding the way I have used for its calculation. Unfortunately I don't know any other way for its calculation which I can use for verification. Can anybody tell me whether the applied procedure is correct or not?
 
Physics news on Phys.org
  • #2
@adamaero, please repost the 2nd, 3rd, and 4th images. Use the Attach files button to attach files. A link to an external site won't work.
 
  • #3
adamaero said:
Homework Statement:: How to calculate rotor flux of the three phase squirrel cage induction motor?
Relevant Equations:: Rotor flux and more

Three phase squirrel cage induction motor with given parameters (stator winding connected in delta)

  • nominal power: Pn=22.4kW
  • nominal stator voltage: Vsn=230V
  • nominal stator current: Isn=39.5A
  • nominal stator frequency: fsn=60Hz
  • nominal speed: nn=1168min−1
  • number of pole pairs: 3
  • stator resistance per phase (T equivalent circuit): Rs=0.294Ω
  • stator leakage inductance per phase (T equivalent circuit): Lsl=0.00139H
  • rotor resistance per phase (T equivalent circuit): Rr=0.156Ω
  • rotor leakage inductance per phase (T equivalent circuit): Lrl=0.0007401H
  • magnetizing inductance per phase (T equivalent circuit): Lm=0.041H

I have been struggling with calculation of the nominal value of the rotor flux. My idea was that I will use the T equivalent circuit for that purpose
View attachment 283353

and I will use nominal values of the motor quantities i.e. I set the motor operating point into the nominal operation point (nominal slip, nominal stator voltage etc.). Then I calculate phasor of the stator current (Is) and phasor of the rotor current (Ir) according to the below given set of equations
1.png
For the motor parameters mentioned above the Scilab command linsolve gave me
2.png

Based on the known phasors of the stator and rotor current I used the below given equation for calculation of the phasor of the rotor flux
3.png

which gives λr=0.5554856−0.0613638j i.e. |λr|=0.5588647V⋅s.

This value seems to me to be too low. So I have doubts regarding the way I have used for its calculation. Unfortunately I don't know any other way for its calculation which I can use for verification. Can anybody tell me whether the applied procedure is correct or not?
 
  • #4
I am not sure what do you mean by "rotor magnetic flux”. I don't think the leakage rotor magnetic field it has to be included since the stator and rotor main magnetic field has to be the same.
However, you may calculate-using T equivalent diagram-the current Is . At first calculate the equivalent impedance of parallel Xm with Xlr and Rr/s and then divide Vsn by total impedance Rs+jXs+jXm||(Rr/s+jXlr).The result will be the same. Ir you may calculate by dividing the Is voltage drop on the equivalent impedance of jXm and Rr/s+jXlr by Zr=Rr/s+jXlr.
I think the flux units are average values but Is and Ir are rms.
i=Imax*sin(ωt) Iav=Imax/π Irms=Imax/√2 Iav=√2*Irms/π
 
  • #5
I am sorry. Iav=1/ π ʃ Imax*sin(ωt)dt| ωt=0 up to ωt= π| then
Iav=2*Imax/π ; Irms=Imax/√2; Iav=2*√2*Irms/π
My mistake!
 

Similar threads

Replies
7
Views
2K
Replies
6
Views
2K
Replies
4
Views
2K
Replies
2
Views
2K
Replies
14
Views
7K
Replies
5
Views
2K
Back
Top