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After an overload condition, the protection simulates the cooling process of the machine using a separate time
constant.
11.3
ALGORITHMS
Thermal Image algorithms are based on the heating/cooling process of a resistive element due to the current flowing
through it. Let us assume a temperature reference (θ
Being:
R =
Ohm Resistance (Ω)
I =
Current flowing through the element. (Amps)
m =
Mass of the element (kg)
C
= Specific Heat (Jul/kg/ºC)
e
θ
= Element Temperature over ambient temperature (ºC)
a =
Heat Transmission Coefficient, (adding conduction and convection effects (w/m
S =
Element Surface (m
Disregarding the radiation transmission (that at temperatures under 400 ºC is much lower that the considered effects,
being this assumption a conservative one from the protection point of view), the differential equation describing the
heating process of the element can be written as:
=
2
I
*
R
*
dt
(
m
*
C
We can read this equation as: the heat generated on the resistance during a differential period of time (dt), is
used to rise the element temperature and to rise the ambient temperature.
This separated variables differential equation can be easily integrated, getting the following expression:
−
τ
−
2
t
/
I
1 (
e
)
θ
=
α
θ
τ
+
−
t
/
*
e
0
Where:
θ
Initial temperature.
0:
τ :
Heating Constant, defined as: m * C
speed of the element (it is the amount of time it takes to reach the 63% of the final temperature.)
α :
Parameter which a value equal to: a * S / R
11-2
ANNEX 1 THERMAL IMAGE UNIT
I
R
2
)
θ
θ
+
*
d
)
(
a
*
S
*
*
dt
e
/ (a * S), according to the defined parameters. It indicates the heating
e
MIF Digital Feeder Protection
):
a
)
2
/ºC))
[1]
[2]
GEK-106273L
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