VAMP 259 - Page 162

3.8 Circuit breaker condition
monitoring
3 Supporting functions
Technical description
162
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Logarithmic interpolation
The permitted number of operations for currents in between
the defined points are logarithmically interpolated using
equation
Equation 3.8-1
n
I
a
C 
, where
C = permitted operations
I = interrupted current
a = constant according Equation 3.8-2
n = constant according Equation 3.8-3
Equation 3.8-2
k
k
k
k
I
I
C
C
n
1
1
ln
ln



Equation 3.8-3
2
kk
ICa 
ln = natural logarithm function
C
k
= permitted operations. k = row 2...7 in Table 3.8-1.
I
k
= corresponding current. k = row 2...7 in Table 3.8-1.
C
k+1
= permitted operations. k = row 2...7 in Table 3.8-1.
I
k+1
= corresponding current. k = row 2...7 in Table 3.8-1.
Example of the logarithmic interpolation
Alarm 2 current is set to 6 kA. What is the maximum number
of operations according Table 3.8-1.
The current 6 kA lies between points 2 and 3 in the table. That
gives value for the index k. Using
k = 2
C
k
= 10000
C
k+1
= 80
I
k+1
= 31 kA
I
k
= 1.25 kA
and the Equation 3.8-2 and Equation 3.8-3, the device
calculates
5038.1
1250
31000
ln
80
10000
ln
n