# Calculation of transmission loss of a power plant

What is the transmission loss due to heat if my power station produces electricity at a power of $$\5 kW\$$ and the electricity consumer is $$\1 km\$$ away?

It is a copper line with a material constant of $$\0.017\Omega \frac{mm^2}{m}\$$, a voltage of $$\1kV\$$ and a cross-section of $$\10mm^2\$$.

My approach, which I don't know if it's true or not, is as follows: $$I_{cable} = \frac{P_{generated}}{U_{grid}} = \frac{5kW}{1kV} = 5A$$ $$R_{cable} = \rho * \frac{l}{A} = 0.017\Omega \frac{mm^2}{m} * \frac{1000m}{10mm^2} = 1.7\Omega$$ $$P_{loss} = (I_{cable}^2R_{cable})* 2 = 85W$$ So that of the $$\5000W\$$ produced about $$\5000W - 85W = 4915W\$$ can be consumed.

Is the calculation so possible? If not, then how?

• for a first contribution, using equation markup like a pro, excellent. Commented Sep 28, 2018 at 7:08

Yes, your engineering is correct, the power loss in the cable is $$\I^2R\$$.
• Thank you very much for the detailed and informative answer. In my calculation I have calculated the loss for the outward and return route of the current ($(I_{cable}^2R_{cable})* 2$), so that the loss of the cable is doubled. Does the return path also have to be considered? Commented Sep 28, 2018 at 7:22