Conductor current

The permissible current rating of a power cable can be derived from the expression for the temperature rise above ambient temperature.

The equation is different for cables in air and buried cables.

The current rating for a four-core low-voltage cable may be taken to be equal to the current rating of a three-core cable for the same voltage and conductor size having the same construction, provided that the cable is to be used in a three-phase system where the fourth conductor is either a neutral conductor or a protective conductor. When it is a neutral conductor, the current rating applies to a balanced load.

Where it is desired that moisture migration be avoided by limiting the temperature rise of the cable surface to not more than $\Delta\theta_x$, the corresponding rating shall be obtained from the equation below.However, depending on the value of $\Delta\theta_x$ this may result in a conductor temperature which exceeds the maximum permissible value. The current rating used shall be the lower of the two values obtained.

For transient calculations, $I_c$ is the constant steady-state current applied to cable prior to application of a step function, a cyclic load or prior to emergency loading.

*** These formulae are valid when the outer temperature $\theta_o$ defines the load of a system.

Symbol
$I_{c}$
Unit
A
Formulae
$\sqrt{\frac{- \Delta \theta_{d} - \Delta \theta_{sun} - \theta_{a} + \theta_{c}}{R_{c} \left(T_{1} + T_{2} n_{c} \left(\lambda_{1} + 1\right) + \lambda_{3} n_{cc} \left(\frac{T_{4ii}}{2} + T_{4iii}\right) + \left(T_{3} n_{c} + n_{cc} \left(T_{4i} + T_{4ii} + T_{4iii}\right)\right) \left(\lambda_{1} + \lambda_{2} + 1\right)\right)}}$cables in air
$\sqrt{\frac{- \Delta \theta_{d} - \Delta \theta_{p} v_{4} + \Delta \theta_{x} \left(v_{4} - 1\right) - \theta_{a} + \theta_{c}}{R_{c} \left(T_{1} + T_{2} n_{c} \left(\lambda_{1} + 1\right) + \lambda_{3} n_{cc} \left(\frac{T_{4ii}}{2} + T_{4\mu} v_{4}\right) + \left(T_{3} n_{c} + n_{cc} \left(T_{4i} + T_{4ii} + T_{4\mu} v_{4}\right)\right) \left(\lambda_{1} + \lambda_{2} + 1\right)\right)}}$cables buried
$\sqrt{\frac{- \Delta \theta_{d} + \theta_{c} - \theta_{de}}{R_{c} \left(T_{1} + T_{2} n_{c} \left(\lambda_{1} + 1\right) + \left(T_{3} n_{c} + n_{cc} \left(T_{4i} + T_{4ii}\right)\right) \left(\lambda_{1} + \lambda_{2} + 1\right)\right)}}$cables in tunnel
$\sqrt{\frac{- \Delta \theta_{0t} - \Delta \theta_{d} - \theta_{a} + \theta_{c}}{R_{c} \left(T_{1} + T_{2} n_{c} \left(\lambda_{1} + 1\right) + n_{c} \left(T_{3} + T_{4t}\right) \left(\lambda_{1} + \lambda_{2} + 1\right)\right)}}$cables in tunnel (IEC 60287-2-3)
$\sqrt{\frac{- \Delta \theta_{d} - \theta_{at} + \theta_{c}}{R_{c} \left(T_{1} + T_{2} n_{c} \left(\lambda_{1} + 1\right) + \left(T_{3} n_{c} + n_{cc} \left(T_{4i} + T_{4ii} + T_{4iii}\right)\right) \left(\lambda_{1} + \lambda_{2} + 1\right)\right)}}$cables in trough or channel
$DF I_{c}$cables crossing external heat sources
$\sqrt{\frac{- \Delta \theta_{p} v_{4} + \Delta \theta_{x} \left(v_{4} - 1\right) - \theta_{a} + \theta_{c}}{R_{c} \left(T_{1} + n_{c} \left(\lambda_{1} + 1\right) \left(T_{4\mu} v_{4} + T_{prot}\right)\right)}}$GIL buried (not used directly)
$\sqrt{\frac{- \Delta \theta_{sun} - T_{4iii} W_{d} n_{cc} - \theta_{a} + \theta_{o}}{R_{c} T_{4iii} n_{cc} \left(\lambda_{1} + \lambda_{2} + \lambda_{3} + 1\right)}}$*** cables in air
$\sqrt{\frac{- \Delta \theta_{p} v_{4} + \Delta \theta_{x} \left(v_{4} - 1\right) - T_{4ss} W_{d} n_{cc} v_{4} - \theta_{a} + \theta_{o}}{R_{c} T_{4\mu} n_{cc} v_{4} \left(\lambda_{1} + \lambda_{2} + \lambda_{3} + 1\right)}}$*** cables buried
$\theta_{de}$*** cables in tunnel
$\sqrt{\frac{- \Delta \theta_{0t} - T_{4t} W_{d} n_{cc} - \theta_{a} + \theta_{o}}{R_{c} T_{4t} n_{c} \left(\lambda_{1} + \lambda_{2} + 1\right)}}$*** cables in tunnel (IEC 60287-2-3)
$\sqrt{\frac{- T_{4iii} W_{d} n_{cc} - \theta_{at} + \theta_{o}}{R_{c} T_{4iii} n_{cc} \left(\lambda_{1} + \lambda_{2} + 1\right)}}$*** cables in trough or channel
$\sqrt{\frac{- \Delta \theta_{d} - \Delta \theta_{p} - \theta_{a} + \theta_{c}}{R_{c} \left(T_{1} + T_{2} n_{c} \left(\lambda_{1} + 1\right) + \left(T_{3} n_{c} + T_{4iii} n_{cc}\right) \left(\lambda_{1} + \lambda_{2} + 1\right)\right)}}$cables subsea
$\sqrt{\frac{D_{ext} U_{OHTC} \pi \left(- \Delta \theta_{d} - \Delta \theta_{p} - \theta_{a} + \theta_{o}\right)}{R_{c} n_{cc} \left(\lambda_{1} + \lambda_{2} + 1\right)}}$*** cables subsea
Related
$D_{ext}$
$\Delta \theta_{0t}$
$\Delta \theta_{sun}$
$\Delta \theta_{x}$
$R_{c}$
$\theta_{a}$
Ambient temperature [$^{\circ}$C]
$\theta_{at}$
$\theta_{c}$
$\theta_{de}$
$\theta_{o}$
Outer temperature [$^{\circ}$C]
$U_{OHTC}$
$W_{d}$
Used in
$\Delta W_{0}$
$L_{crit}$
$W_{c}$
$W_{encl}$