This protection scheme uses a simple first order thermal model of the motor to determine the tripping
characteristic. It is fundamentally different to the Over Current protection outlined above in that it all
current levels contribute to the model heating, and the effects of that heating persist in the model, where
as in the Over Currents functions, the trip accumulator resets relatively quickly if the current falls below
the selected full load current level.
The three measured phase currents are squared and added together to provide the heating input into the
thermal model. The cooling is assumed to be proportional to the model’s ‘temperature’ at any given time.
The Thermal Accumulator (TAC) is the model’s ‘temperature’ where 0% represents the motor being cold,
and 100% means the motor has reached its maximum temperature (and is therefore tripped).
The trip time is dependant not only on the present current level, but also the prior current history. Since
motor currents typically vary widely during starting and running, the actual trip time is also variable. To
facilitate co-ordination of the protection with motor capabilities (and upstream protection), the trip time in
seconds for a simple (theoretical) scenario of a fixed overload current of I is given by:
Where:
t(I) = the idealised trip time,
I = the input current ratio relative to the full load current set point – ie per unit current,
TMS = the Over Current Time Multiplier Setting,
Ip = the load current that was flowing (long enough to reach thermal stability) prior to the
overload occurrence.
ln = the natural logarithm.
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