# Active power at load receptor

The maximum transmitted power in an underground radial link is dependent on the frequency, length and voltage across the insulation. However a large conductor can transfer higher loads than a smaller conductor can. Therefore the charging current becomes of less importance when the conductor area becomes larger, if the generated power is unchanged. Assuming purely resistive loads and no compensation, the power transfer of a long cable system can be found.

For lower voltages the critical length is longer when the conductor area is larger (due to $I_{Z}$, higher ratings). At higher voltages as the conductor area increases the capacitance increases and counters the increase of critical length due to higher current ratings seen at lower voltages.

For actual systems as discussed above it is mandatory to do a system planning study which determines the actual current taking into account required load currents, charging current in the cable, and other reactive currents in the wider power system.

It should be noted that the charging current will vary along the length of the cable route. The thermal bottleneck of the cable system may not be at the end of the circuit and the required current carrying capacity (taking into account both load and charging current) should be verified at the position that the thermal bottleneck occurs.

As DC cable systems have no charging currents the length of a DC cable system does not have the same considerations and this is an advantage of such systems.

Symbol
$P_{L}$
Unit
kW
Formulae
$\sqrt{- 1.0 \cdot 10^{-10} C_{b}^{2} L_{sys}^{2} U_{o}^{2} \omega^{2} + S_{G}}$
Related
$C_{b}$
$L_{sys}$
$\omega$
$S_{G}$
$U_{o}$