Schweitzer Engineering SEL-387-0 - Figure 3.16 Top-Oil and Hot-Spot Temperatures

3.34
SEL-387-0, -5, -6 Relay Instruction Manual Date Code 20170601
Differential, Restricted Earth Fault, Thermal, and Overcurrent Elements
Thermal Element (SEL-387-6 Relay)
Figure 3.16 Top-Oil and Hot-Spot Temperatures
Thermal Element With Ambient and Top-Oil Temperature Inputs
In this case the relay receives measured ambient and top-oil temperature
inputs and uses the top-oil temperature to calculate the hot-spot temperature.
The ambient temperature is reported in the thermal event reports.
For a single tank, three-phase transformer, you will have as many as two
thermal inputs: the ambient temperature input and the top-oil input. For
independent, single-phase transformers, normally you will have as many as
four thermal inputs: an ambient temperature input and a top-oil input for each
of the three tanks. During a fixed time interval, t = 1 minute, the relay
calculates the winding hot-spot temperature at the end of the interval,
according to the following expression:
Equation 3.14
The relay calculates winding hot-spot rise over top-oil temperature, 
H
,
according to the following:
Equation 3.15
(A)
(C)
ΔΘ
H
ΔΘ
H
ΔΘ
TO
˚C
Θ
H
Θ
H
Θ
H
Θ
H
= Calculated hot-spot
temperature using ΔΘ
H
Θ
TO
= Measured top-oil
temperature
Θ
H
= Calculated hot-spot
temperature using ΔΘ
H
and ΔΘ
TO
Θ
TO
= Calculated top-oil
temperature using ΔΘ
TO
Θ
A
= Measured ambient
temperature
Θ
H
= Calculated hot-spot
temperature using ΔΘ
H
and ΔΘ
TO
Θ
TO
= Calculated top-oil
temperature using ΔΘ
TO
Θ
A
= From DTMP setting
Θ
TO
Θ
TO
Θ
TO
(B)
˚C
ΔΘ
H
˚C
ΔΘ
TO
Θ
A
Θ
A
where:

H
= winding hot-spot temperature, C

TO
= top-oil temperature, °C

H
= winding hot-spot rise over top-oil temperature, °C
where:

H,U
= the ultimate hot-spot rise over top-oil temperature for any
load, °C

H,i
= initial hot-spot rise over top-oil temperature at the start
time of the interval, °C
T
hs
= thermal time constant of hot spot, in hours (set from
Table 3.3)
t = one-minute temperature data acquisition interval

H

TO

H
+=

H

HU

Hi
–1e
t–
60 T
hs
•
--------------------
–





Hi
+• =