Schweitzer Engineering Laboratories SEL-587Z - Equation 3.32

3.33
Date Code 20020903 SEL-587Z Instruction Manual
Relay Elements
Demand Ammetering
Equation 3.32
where:
DMTC = time constant
ln = natural logarithm
After five time constants, the results from both equations are equal:
Equation 3.33
Calculate the time when PDEMP will assert for a 15 percent (1.25 A)
overload, starting with zero element register values and a full-load
step-function current flowing:
Equation 3.34
PDEMP I
FL
1e
10()t• ln–
DMTC
----------------------------
–
èø
ç÷
æö
• =
1.09 1 e
10 120• ln–
120
------------------------------
–
èø
ç÷
æö
• =
0.98 A (90 percent of 1.09 A)=
PDEMP
θ=
CHAR
1.2 1 e
600–
120
------------
–
èø
ç÷
æö
• =
1.2 1 e
10 600• ln–
120
------------------------------
–
èø
ç÷
æö
• =
1.2 A=
t
DMTC–
10
()ln
---------------------
1
PDEMP
I
FL
---------------------–
èø
æö
• =
120–
10
()ln
----------------
1
1.2
1.25
----------–
èø
æö
ln• =
168 min (or 1.4 time constants)=