Induction Motor Torque angle derivation

1
Induction Motor Torque angle derivation
Field rotation is CCW
I1L- I2L
I1total
Vs -
I1L
Vm -
I1m
I1total
Vm
R2/s
?2
I1m
?mr
?sr
I1totaltotal stator current I1m magnetizing
component of stator current I1L load component
of stator current I2L rotor current (equal and
opposite to I1L) ?2 Power factor angle of
rotor Vm phase angle and position of Vm. ?sr
angle by which rotor mmf pole lags adjacent
stator mmf pole of opposite polarity ?mr
angle by which rotor mmf pole lags the
"resultant" (total) mmf. For this
simplified circuit, the resultant mmf is also
the magnetizing mmf associated with I1m
(hence the m for magnetizing in ?mr)
I2L
To build the phasor diagram 1 arbitrarily
assign angle of Vm as 1200 2 I1L lags Vm by ?2
. 3 I1m lags Vm by 90º 4 Itotal I1LIm. 5
I2L - I1L 6 ?sr angle by which I2L lags
I1total 7 90 (Assume 2-pole motor).
2
Excerpt from somewhere. I added the 90 degree
arrows.
90
90