ABB DCS 500B Description page 78

Functional Software description
70
Q act
Motor's thermal capacity
100%
A
Q k
B
Accel. Constant speed
Figure 49 Q act as a function of different loads
Previous figure shows how Q ACT (motor's thermal capacity) is for-
med of rising and falling sections of the time constant function. On
curve 0-A-C-D an overload trip occurs at point D owing to a too
short time constant even though the heating up clearly does not
reach the limit Q ACT = 100% which corresponds to the motor's
thermal capacity.
In point A acceleration does not yet cause a trip because a cold
start was made
On curve 0-B-C-E-F-H the desired loading cycle can be repeated as
many times as necessary because its time constant is sufficiently
long.
The temperature rise of the motor behaves as a time constant
which is proportional to the motor current in power of two.
I act 2
Q act =  * ( 1 - e -t/τ ) * 100
I ref 2
where:
Q act
thermal value
I act motor current actual
I ref reference current, normally rated current of motor
τ
temperature time constant.
100 scaling factor
t time
D
E
C
F
Decel. Standstill Accel.
DCS 500 Software Description
H
time
(1)