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ANNEX 1 THERMAL IMAGE UNIT
11-2
MIF Digital Feeder Protection
GEK-106273L
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
a
):
Being:
R = Ohm Resistance (
Ω
)
I =
Current flowing through the element. (Amps)
m = Mass of the element (kg)
C
e
= Specific Heat (Jul/kg/ºC)
θ
= Element Temperature over ambient temperature (ºC)
a = Heat Transmission Coefficient, (adding conduction and convection effects (w/m
2
/ºC))
S = Element Surface (m
2
)
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:
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:
Where:
θ
0:
Initial temperature.
τ
:
Heating Constant, defined as: m * C
e
/ (a * S), according to the defined parameters. It indicates the heating
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
I
R
[1]
[2]
)
*
*
*
(
)
*
*
(
*
*
2
dt
S
a
d
C
m
dt
R
I
e
θ
θ
+
=
τ
τ
θ
α
θ
/
0
/
2
*
)
1
(
t
t
e
e
I
−
−
+
−
=
Содержание GEK-106273L
Страница 19: ...GETTING STARTED 1 12 MIF Digital Feeder Protection GEK 106273L ...
Страница 95: ...SETTINGS 5 38 MIF Digital Feeder Protection GEK 106273L ...
Страница 101: ...I O CONFIGURATION 6 44 MIF Digital Feeder Protection GEK 106273L ...
Страница 127: ...KEYPAD AND DISPLAY 8 26 MIF Digital Feeder Protection GEK 106273L ...
Страница 147: ...INSTALLATION AND MAINTENANCE 10 2 MIF Digital Feeder Protection GEK 106273L ...
Страница 154: ...ANNEX 1 THERMAL IMAGE UNIT GEK 106273L MIF Digital Feeder Protection 11 7 Figure A 1 1 THERMAL CURVE FOR τ1 3 MINUTES ...
Страница 155: ...ANNEX 1 THERMAL IMAGE UNIT 11 8 MIF Digital Feeder Protection GEK 106273L Figure A 1 2 THERMAL CURVES FOR τ1 3 MIN ...
Страница 199: ...ANNEX 5 HARMONIC FILTERING 15 4 MIF Digital Feeder Protection GEK 106273L ...