Cable Power Loss: Complex Power and I²R Methods

Cable power loss is the electrical power converted into heat as load current flows through the cable impedance. It affects operating temperature, current rating, energy efficiency and life-cycle cost.

For cable sizing, power loss is usually considered as conductor loss, with additional losses such as sheath, armour and dielectric loss included where the voltage level and cable construction make them significant.

Power loss using complex power

Power loss within a cable can be calculated using complex power:

The real part of the result gives the power loss in watts. The imaginary part gives the reactive power requirement in var. For the underlying convention, see Complex Power in AC Circuits.

The complex-power calculation above gives the loss per core. For d.c. and a.c. single-phase circuits, the total cable loss is twice the single-core value. For a balanced three-phase circuit, multiply the single-core value by three.

Power loss using resistance

Power loss can also be estimated directly from cable current and resistance:

For a.c. single-phase and d.c. circuits, n = 2. For balanced a.c. three-phase circuits, n = 3.

For unbalanced circuits, calculate the loss in each conductor and sum the conductor losses:

Why power loss matters

Power loss is a heat source in cable thermal calculations. It influences conductor temperature, insulation ageing and the final current-carrying capacity of the cable. It also has an operating cost, which is why loss calculations are important in economic optimisation of cable size.

For related heat-source calculations, see Cable Thermal Analysis, Cable Sheath and Armour Losses and Dielectric Loss in Cables.

For resistance inputs used in I²R loss calculations, see Conductor Resistance.