Cable losses

The cable power loss $P_\text{ver}$ results from the lead resistance $R_\text{L}$ and the current flowing through the conductor $I_\text{L}$

$$ P_\text{ver} = R_\text{L} \cdot I_\text{L}^2 $$

The line resistance $R_\text{L}$ depends on the line cross section $A$, the line length $l$ and the material-dependent specific electrical resistance $1/\kappa$.

$$ R_\text{L} = \frac{l}{A} \cdot \frac{1}{\kappa} $$

Table 1: Overview of the specific electrical resistances of different materials

Material specific electrical resistance $1/\kappa$ in $\Omega \cdot \text{mm}^2 \cdot \text{m}^{-1}$
Aluminium $2,94 \cdot 10^{−2}$
Copper $1,75 \cdot 10^{−2}$

Relative losses $K$ result from power dissipation $P_\text{ver}$ and reference power $P_\text{ref}$.

$$ K = \frac{P_\text{ver}}{P_\text{ref}} $$

The relative loss can be used to calculate the dependent line cross section $A$. It is:

$$ A = \frac{l \cdot I_\text{L}^2}{\kappa \cdot P_\text{ref} \cdot K } $$

See also