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Transient temperature rise of conductor by ohmic losses

This is the transient temperature rise of conductor above outer surface caused by ohmic losses. The transient response of a cable circuit to a step function of load current, considered in isolation, that is with the right-hand pair of terminals of the thermal circuit short-cuircuited, is found with the following formula calculating the transient temperature rise of conductor above outer surface. The parameter $W_c$ is the power loss per unit length in a conductor or an equivalent conductor based on the maximum conductor temperature attained. The power loss is assumed to be constant during the transient.

Symbol
$\Delta \theta_{c,t,o}$
Unit
K
Formulae
$n_{ph} W_c \left(T_{a0} \left(1-e^{-a_0 \tau}\right)+T_{b0} \left(1-e^{-b_0 \tau}\right)\right)$
Related
$a_0$
Coefficient a for partial transient temperature rise [1/s]
$b_0$
Coefficient b for partial transient temperature rise [1/s]
$n_{ph}$
Number of phases in a cable
$T_{a0}$
Apparent thermal resistance a [K.m/W]
$T_{b0}$
Apparent thermal resistance b [K.m/W]
$\tau$
Transient load period [s]
$W_c$
Conductor losses [W/m]
Used in
$\Delta \theta_{c,t}$
Transient temperature rise of conductor [K]
Image
IEC standard 60853-2 Ed. 1.0 (1989) Figure 2