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 $\theta_{omax}$ defines the load of a system.

Symbol
$I_c$
Unit
A
Formulae
$\sqrt{\frac{\theta_c-\theta_a-\Delta \theta_d-\Delta \theta_{sun}}{R_c \left(T_1+n_c \left(1+\lambda_1\right) T_2+\left(1+\lambda_1+\lambda_2+\lambda_3\right) \left(n_c T_3+n_{cc} \left(T_{4i}+T_{4ii}+T_{4iii}\right)\right)+n_{cc} \lambda_4 \left(\frac{T_{4ii}}{2}+T_{4iii}\right)\right)}}$Cables in air
$\sqrt{\frac{\theta_c-\theta_a+\left(v_4-1\right) \Delta \theta_x-v_4 \Delta \theta_p-\Delta \theta_d}{R_c \left(T_1+n_c \left(1+\lambda_1\right) T_2+\left(1+\lambda_1+\lambda_2+\lambda_3\right) \left(n_c T_3+n_{cc} \left(T_{4i}+T_{4ii}+T_{4\mu} v_4\right)\right)+n_{cc} \lambda_4 \left(\frac{T_{4ii}}{2}+T_{4\mu} v_4\right)\right)}}$Cables buried
$\sqrt{\frac{\theta_c-\theta_{de}-\Delta \theta_d}{R_c \left(T_1+n_c \left(1+\lambda_1\right) T_2+\left(1+\lambda_1+\lambda_2+\lambda_3\right) \left(n_c T_3+n_{cc} \left(T_{4i}+T_{4ii}\right)\right)\right)}}$cables in tunnel
$\sqrt{\frac{\theta_c-\theta_a-\Delta \theta_d-\Delta \theta_{0t}}{R_c \left(T_1+n_c \left(1+\lambda_1\right) T_2+n_c \left(1+\lambda_1+\lambda_2+\lambda_3\right) \left(T_3+T_{4t}\right)\right)}}$Cables in tunnel (IEC 60287-2-3)
$\sqrt{\frac{\theta_c-\theta_{at}-\Delta \theta_d}{R_c \left(T_1+n_c \left(1+\lambda_1\right) T_2+\left(1+\lambda_1+\lambda_2+\lambda_3\right) \left(n_c T_3+n_{cc} \left(T_{4i}+T_{4ii}+T_{4iii}\right)\right)\right)}}$Cables in trough
$\sqrt{\frac{\theta_c-\theta_a-\Delta \theta_d-\Delta \theta_p}{R_c \left(T_1+n_c \left(1+\lambda_1\right) T_2+\left(1+\lambda_1+\lambda_2+\lambda_3\right) \left(n_c T_3+n_{cc} T_{4iii}\right)\right)}}$Cables subsea
$\sqrt{\frac{\theta_c-\theta_e}{R_c \left(T_1+n_c \left(1+\lambda_1\right) T_2+\left(1+\lambda_1+\lambda_2+\lambda_3\right) n_c T_3\right)}}$Cables in riser
$I_c F_{red}$With reduction (derating) factor
$\sqrt{\frac{\theta_{omax}-\theta_a-W_d n_{cc} T_{4iii}-\Delta \theta_{sun}}{R_c n_{cc} T_{4iii} \left(1+\lambda_1+\lambda_2+\lambda_3+\lambda_4\right)}}$*** Cables in air
$\sqrt{\frac{\theta_{omax}-\theta_a+\left(v_4-1\right) \Delta \theta_x-v_4 \Delta \theta_p-W_d n_{cc} T_{4ss} v_4}{R_c n_{cc} T_{4\mu} v_4 \left(1+\lambda_1+\lambda_2+\lambda_3+\lambda_4\right)}}$*** Cables buried
$\sqrt{\frac{\theta_{omax}-\theta_a-W_d n_{cc} T_{4t}-\Delta \theta_{0t}}{R_c n_c \left(1+\lambda_1+\lambda_2+\lambda_3\right) T_{4t}}}$*** Cables in tunnel (IEC 60287-2-3)
$\sqrt{\frac{\theta_{omax}-\theta_{at}-W_d n_{cc} T_{4iii}}{R_c \left(1+\lambda_1+\lambda_2+\lambda_3\right) n_{cc} T_{4iii}}}$*** Cables in trough
$\sqrt{\frac{\theta_{omax}-\theta_a-\Delta \theta_d-\Delta \theta_p}{R_c n_{cc} \frac{1}{U_{OHTC} \pi D_{ext}} \left(1+\lambda_1+\lambda_2\right)}}$*** Cables subsea
$\sqrt{\frac{\theta_{omax}-\Delta \theta_d-\theta_{air}}{R_c \left(T_1+n_c \left(1+\lambda_1\right) T_2+\left(1+\lambda_1+\lambda_2\right) n_c T_3\right)}}$*** Cables in riser
$\sqrt{\frac{\theta_c-\theta_a+\left(v_4-1\right) \Delta \theta_x-v_4 \Delta \theta_p-\Delta \theta_d}{R_c \left(T_1+n_c \left(1+\lambda_1\right) T_2+\left(1+\lambda_1+\lambda_2+\lambda_3\right) \left(n_c T_3+n_{cc} T_{4\mu} v_4\right)+n_{cc} \lambda_4 \left(\frac{T_{4ii}}{2}+T_{4\mu} v_4\right)\right)}}$Cables buried in ducts with bentonite filling and transient loading
Related
$\Delta \theta_{0t}$
$\Delta \theta_{sun}$
$\Delta \theta_x$
$\theta_a$
$\theta_{air}$
$\theta_{at}$
$\theta_c$
$\theta_{omax}$
$U_{OHTC}$