Schweitzer Engineering SEL-387-0 - Page 85

3.35
Date Code 20170601 Instruction Manual SEL-387-0, -5, -6 Relay
Differential, Restricted Earth Fault, Thermal, and Overcurrent Elements
Thermal Element (SEL-387-6 Relay)
Equation 3.16
Thermal Element With Ambient Temperature Input
In this case the relay receives a measured ambient temperature input and uses
this input to calculate top-oil and hot-spot temperatures.
Where the relay has a measured ambient temperature input without a top-oil
temperature input, you have one thermal input (for ambient temperature)
regardless of whether you have a single three-phase transformer or
independent single-phase transformers. The relay calculates winding hot-spot
temperature, 
H
, according to the equation in the earlier case:
Equation 3.17
and calculates top-oil temperature, 
TO
, according to the following:
Equation 3.18
The relay calculates top-oil rise over ambient temperature according to the
following:
Equation 3.19
The relay calculates the ultimate top-oil rise over ambient temperature,

TO,U
, according to the following expression:
where:
K = load expressed in per unit of transformer nameplate rating
according to the cooling system in service (phase current
divided by the nominal current)
EXPm = winding exponent (set from Ta ble 3 .3)
TH
gr
= rated winding hot-spot rise over top-oil at rated load, °C
(set from Table 3.3)

HU
K
2EXPm•
TH
gr
• =
where:

A
= ambient temperature, °C

TO
= top-oil rise over ambient temperature, °C
where:

TO,U
= the ultimate top-oil rise over ambient temperature for any
load, °C, and is a function of load and the values in
Table 3.3

TO,i
= initial top-oil rise over ambient temperature at the start
time of the interval, °C (
TO,i
)
T
o
= thermal top-oil time constant of transformer, in hours

H

TO

H
+=

TO

A

TO
+=

TO

TO U

TO i
–1e
t–
60T
o
------------
–




T
Oi
+• =