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4.6 S5 THERMAL MODEL
Unbalanced phase currents also cause additional rotor heating not accounted for by electromechanical relays
and also not accounted for in some electronic protective relays. When the motor is running, the rotor rotates in
the direction of the positive-sequence current at near synchronous speed. Negative-sequence current, with a
phase rotation opposite to positive-sequence current (and hence, opposite to the rotor rotation), generates a
rotor voltage that produces a substantial rotor current. This induced current has a frequency approximately 2
times the line frequency: 100 Hz for a 50 Hz system or 120 Hz for a 60 Hz system. The skin effect in the rotor
bars at this frequency causes a significant increase in rotor resistance and therefore a significant increase in
rotor heating. This extra heating is not accounted for in the thermal limit curves supplied by the motor manufac-
turer, as these curves assume only positive-sequence currents from a perfectly balanced supply and motor
design.
The 469 measures the ratio of negative to positive-sequence current. The thermal model may be biased to
reflect the additional heating that is caused by negative sequence current when the motor is running. This bias-
ing is accomplished by creating an equivalent motor heating current rather than simply using average current
( I
). This equivalent current is calculated using the equation shown below.
per_unit
4
2
I
=
I
per_unit
eq
where: I
= equivalent motor heating current
eq
I
= per unit current based on FLA
per_unit
I
= negative sequence current
2
I
= positive sequence current
1
k = constant
The figure below shows recommended motor derating as a function of voltage unbalance recommended by
NEMA (the National Electrical Manufacturers Association). Assuming a typical induction motor with an inrush
of 6 x FLA and a negative sequence impedance of 0.167, voltage unbalances of 1, 2, 3, 4, and 5% equal cur-
rent unbalances of 6, 12, 18, 24, and 30% respectively. Based on this assumption, the GE Power Management
curve illustrates the motor derating for different values of k entered for the UNBALANCE BIAS K FACTOR setpoint.
Note that the curve created when k = 8 is almost identical to the NEMA derating curve.
1.05
1.00
0.95
0.90
0.85
0.80
0.75
0.70
0
1
PERCENT VOLTAGE UNBALANCE
Figure 4–16: MEDIUM MOTOR DERATING FACTOR DUE TO UNBALANCED VOLTAGE
If a k value of 0 is entered, the unbalance biasing is defeated and the overload curve will time out against the
measured per unit motor current. k may be calculated conservatively as:
175
k
(typical estimate); k
=
--------- -
2
I
LR
4-42
I
2
⋅
⋅
2
1
+
k
--- -
I
1
2
3
4
NEMA
230
(conservative estimate), where I
=
--------- -
2
I
LR
469 Motor Management Relay
1.05
1.00
0.95
0.90
0.85
0.80
0.75
0.70
0
1
5
PERCENT VOLTAGE UNBALANCE
GE POWER MANAGEMENT
is the per unit locked rotor current
LR
4 SETPOINT PROGRAMMING
4.6.4 UNBALANCE BIAS
2
3
4
GE Power Management
k=2
k=4
k=6
k=8
k=10
5
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