# Cables

### Automatic circuit breaker design

The basis for the design of the AC protective devices is the rated current $I_\text{B}$. This is the current that can be permanently carried by the conductor. Preferred values for the rated current $I_\text{N}$ are assumed to be 6, 10, 13, 16, 20, 25, 32, 40, 50, 63, 80, 100, 125 A. The calculation of the rated current is based on a reference current $I_\text{R}$ and a rated protection factor $f_\text{B}$.

Generally applies:

$$I_\text{N} = I_\text{R} \cdot f_\text{B}$$

Cable type Reference current $I_\text{R}$
AC-Leitung (Alle Wechselrichter) Summe aller maximaler Wechselrichterausgangsströme
AC-Leitung (Wechselrichter)   Nach Wechselrichter   Im Wechselrichter Maximaler Wechselrichterausgangsstrom -
DC-Hauptleitung STC Strom am MPP-Kabel bzw. in der DC-Hauptleitung
Strangleitung STC Strom im Strang

Maximum inverter output current = (Maximum apparent power * Displacement factor) / (Mains voltage * Number of inverter phases)

#### Residual current circuit breaker (FI/RCD)

As standard, type B earth leakage circuit breakers are designed with a rated residual current of 100 mA in PV*SOL®. The rated protection factor $f_\text{B}$ is set to 1.1.

#### Circuit breaker

For the miniature circuit breaker, PV*SOL® initially assumes a type B with a rated protection factor $f_\text{B}$ of 1.3. If a transformer is present in the inverter used, the rated protection factor changes to 1.1 and the type to C.

### 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:

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