Schweitzer Engineering Laboratories SEL-701 - Figure E.3 Typical Induction Motor Current, Torque, and Rotor Resistance Versus Slip

701 Motor Protection Relay Date Code 20010719
Motor Thermal Element
The Basic Thermal Element
E.6
Figure E.3 Typical Induction Motor
Current, Torque, and Rotor Resistance versus Slip.
Figure E.3 shows a plot of a typical induction motor current, torque, and rotor
resistance versus slip. When motor slip is 1 per unit, rotor speed is zero. As the motor
approaches rated speed, slip decreases to near zero.
Calculate the positive-sequence rotor resistance plotted in Figure E.3 using
Equation E.2.
Equation E.2
Where:
S = Motor slip
Q
m
= Motor torque at slip S
I = Motor positive-sequence current at slip S
The positive-sequence rotor resistance is represented as a linear function of slip S
by Equation E.3.
Equation E.3
Where:
R
1
= Positive-sequence rotor resistance at slip S = 1
R
0
= Positive-sequence rotor resistance at slip S = 0
To properly account for the heating effects of the negative-sequence current,
calculate the negative-sequence rotor resistance. The rotor has slip with respect to the
stator negative-sequence current. To determine the value of the negative-sequence slip
as a function of positive-sequence slip, S, observe that negative-sequence stator
currents cause counter-rotating magnetic poles on the inside face of the stator. When
rotor speed is zero, the counter-rotating poles induce fundamental frequency currents
in the rotor: negative-sequence slip equals positive-sequence slip, S. When the rotor is
1 0.8 0.6 0.4 0.2
0
2
4
6
Slip, s
0
Current
Torque, Q
M
R
1
R
0
Per Unit
R
r
Q
M
I
2
--------
èø
ç÷
æö
S•=
R
r+
R
1
R
0
–()SR
0
+•=