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

[adamaero]

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

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?

 

[Mark44]

@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.

 

[adamaero]

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

For the motor parameters mentioned above the Scilab command linsolve gave me

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

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?

 

[Babadag]

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

 

[Babadag]

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!