Exercise EE1-04.R3

Prof. Dr. Thorsten Jungmann (last updated 2025-12-07)

Relates to EE1-04 Resistance

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Task

At full load, a photovoltaic system on a flat roof produces a direct current of $I=32\mathrm{A}$ at a voltage of $U_{\mathrm{DC}}=400\mathrm{V}$. The copper electric line from the PV generator to the inverter in the basement has a one-way length of $l=35\mathrm{m}$.

The installer plans to use a cable with a cross-section of $A=6\mathrm{m}{\mathrm{m}}^2$.

Boundary conditions:

• The resistivity of the copper electric line at $20°\mathrm{C}$ is ${\rho }_{20}=0.0178\Omega \mathrm{m}{\mathrm{m}}^2/m$
• The temperature coefficient of copper is ${\alpha }_{20}=3.93\cdot 10^{-3}{\mathrm{K}}^{-1}$
• In summer, the cable temperature on the roof can reach $T=70°\mathrm{C}$
• The maximum permissible voltage drop on the DC side is $2\%$ of the system voltage

a) Calculate the conductor resistance at $20°\mathrm{C}$ (take the outgoing and return conductors into account).

b) Calculate the conductor resistance at the maximum operating temperature of $70°\mathrm{C}$.

c) Determine the voltage drop and the power loss in the electric line at $70°\mathrm{C}$.

d) Check whether the planned cable cross-section complies with the $2\%$ limit. If it does not, calculate the minimum required cross-section.

e) What efficiency results for the transmission of electricity over the electric line?

Solution

a) $R_{20}=0.208\Omega$
b) $R_{70}=0.249\Omega$
c) $\Delta U=8.0\mathrm{V}$ ($2.0\%$), $P_{\mathrm{loss}}=255\mathrm{W}$
d) Limit just met; with a margin: $A_{\min }=10\mathrm{m}{\mathrm{m}}^2$
e) $\eta =98.0\%$

Full solution