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Implementation of Thermal Model to IEC60255-8
Heating by overload current and cooling by dissipation of an electrical system follow exponential time
constants. The thermal characteristics of the electrical system can be shown by equation (1).
θ =
I
I
e
AOL
t
2
2
1100−
⎛
⎝
⎜
⎞
⎠
⎟
×
−
τ
% (1)
where:
θ = thermal state of the system as a percentage of allowable thermal capacity,
I = applied load current,
I
AOL
= kI
B
= allowable overload current of the system,
τ = thermal time constant of the system.
The thermal stateθis expressed as a percentage of the thermal capacity of the protected system, where 0%
represents the cold state and 100% represents the thermal limit, that is the point at which no further
temperature rise can be safely tolerated and the system should be disconnected. The thermal limit for any
given electrical plant is fixed by the thermal setting I
AOL
. The relay gives a trip output when θ = 100%.
If current I is applied to a cold system, then θ will rise exponentially from 0% to (I
2
/I
AOL
2
× 100%), with time
constant τ, as in Figure N-1. If θ = 100%, then the allowable thermal capacity of the system has been reached.
Figure N-1
A thermal overload protection relay can be designed to model this function, giving tripping times
according to the IEC60255-8 ‘Hot’ and ‘Cold’ curves.
t =τ·
Ln
I
II
AOL
2
22
−
⎡
⎣
⎢
⎤
⎦
⎥
(1) ····· Cold curve
t =τ·
Ln
II
II
P
AOL
2
2
22
−
−
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
(2) ····· Hot curve
θ (%)
t (s)
100%
%1001
2
2
×−
=
⎟
⎠
⎞
⎜
⎝
⎛
−
τ
θ
t
AOL
e
I
I
%100
2
2
×
AOL
I
I