6–110
350 FEEDER PROTECTION SYSTEM – INSTRUCTION MANUAL
S3 PROTECTION
CHAPTER 6: SETPOINTS
Cable Thermal Model
The thermal overload protection (Thermal Model) can be applied to prevent damage to the
protected cables, dry transformers, capacitor banks, or even overhead lines. Loads
exceeding the load ratings of the protected equipment can, over time, degrade the
insulation, and may, in return, lead to short circuit conditions. As the heating of plant
equipment such as cables or transformers is resistive (I
2
R), the generated heat is directly
proportional to the square of the flowing current (I
2
). The relay uses a thermal time
characteristic based on current squared and integrated over time.
The relay will continuously calculate the thermal capacity as a percentage of the total
thermal capacity. The thermal capacity is calculated as follows:
Where:
θ
(t)
= Cable thermal capacity (%) at time
t
θ
(t-1)
= Cable thermal capacity (%) at time
t-1
Δ
t
/
τ
= Time step
Δ
t
divided by the heating/cooling time constant
τ
I
2
= (
I
phase
/
I
pickup
)
2
= Squared ratio between the actual load current and the pickup setting
τ
= Heating and cooling time constant, usually provided by the manufacturer.
The heating time constant is used when the squared load/pickup ratio is greater than the
thermal capacity
θ
(t-1)
estimated in the previous time step. Otherwise the formula uses the
cooling time constant.
The time to trip is estimated when the load current exceeds the PKP setting, and the 49
element picks up. At the same time the thermal capacity will start to increase at a rate
depending on the current amplitude and the prior loading condition of the cable. When the
thermal capacity exceeds the alarm level, the element will generate an alarm signal. The
thermal model alarm can be used as a warning for the start of dangerous overloading
conditions, and can prevent unnecessary tripping. When the thermal capacity exceeds the
trip level, the element will generate a trip signal. As per the formula below, the operate time
(time to trip) is determined from when the element picks up until it trips, and depends on
both the measured load over time, and the equipment heating and cooling time constants.
Where:
T
TRIP
= Time to trip in seconds
θ
2
= 1 = Trip thermal state set to 100%
τ
= Heating and cooling time constant, usually provided by the manufacturer.
I
2
= Squared ratio of the actual phase current and the pickup setting.
The time to trip will start timing out once the level of the computed thermal capacity (%)
becomes higher than 100 % thermal capacity (
θ
=1
). The trip flag will dropout when the
Thermal capacity falls below 97% of the pickup level.
The following path is available using the keypad. For instructions on how to use the
keypad, please refer to
Chapter 3 - Working with the Keypad
.
PATH
:
SETPOINTS > S3 PROTECTION > SETPOINT GROUP 1(2) > THERMAL MODEL
