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Obviously, the derived equation describes the temperature evolution for both, a heating process and a cooling
process.
The final temperature value θ
= I
θ
∞
α
∞
In equation [2], solving for time, you get:
⎡
α
θ
⎤
−
2
I
*
τ
=
0
⎢
⎥
t
*
ln
α
θ
−
2
⎣
⎦
I
*
Introducing the following variable change:
θ
= '
θ
θ
/
∞
that implies to refer temperatures to the steady state value, equations [2] and [4] can be written as :
(
)
θ
= '
'
τ
−
−
+
2
t
/
I
*
1
e
⎡
θ
⎤
−
2
I
'
'
τ
=
0
⎢
⎥
t
*
ln
θ
−
2
⎣
⎦
I
'
where I' represents the current value in per unit, based on the permanent current, this is:
=
I
'
I
/
I
∞
To compute the tripping time, substitute in [7], with θ' = 1, and you get:
⎡
θ
⎤
−
2
I
'
'
τ
=
0
⎢
⎥
t
*
ln
−
2
⎣
⎦
I
1
It is necessary that I > 1.
Equation [9], can also be written as a function of current, in p.u., if it has been maintained permanently (in other case,
it is necessary to compute the equivalent current), that is represented by the letter "v":
⎡
⎤
−
2
2
I
'
v
τ
=
⎢
⎥
t
*
ln
−
2
⎣
⎦
I
'
1
Equation [10], represents the basic tripping algorithm for a thermal image relay, that for a given τ and I
drawn, in general using a logarithm plane, using "v" as the parameter, as shown in figures A-1.1 and A-1.2.
GEK-106273L
ANNEX 1 THERMAL IMAGE UNIT
, for a permanent current I
∞
θ
τ
−
'
t
/
*
e
0
MIF Digital Feeder Protection
, will be (according to [2]):
∞
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
, can be
∞
11-3
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