# How to calculate power loss & voltage drop in three-phase power cables

What is the correct formula/method to calculate cable power losses in a three-phase system? I'm unable to find any IEC standard outlining the same.

If you consider 3C/4C cables, the manufacturer datasheet specifies the resistance in Ω/km (R). Does this imply the resistance per conductor core, or is it for all the three cores added together?

The standard three phase power formula is:

$$\sqrt{3}V_LI_Lcos(\phi)$$

where $$\V_L\$$ is the Line-Line voltage (e.g. 415 V) and $$\I_L\$$ is the Line current.

Would my cable power loss be calculated as $$\3I_L^2RL\$$ or $$\\sqrt{3}I_L^2RL\$$, with voltage drop as $$\\sqrt{3}I_LR\$$ or just $$\I_LR\$$ respectively for the above? $$\L\$$ is the total cable length.

As I understand it, R values are measured/specified on the basis of IEC 60502/IEC 60228. How is the resistance measured in the case of 3C/4C cables (in terms of setup and process)?

My question in general relates to cable sizing and selection for three phase power applications.

I have seen Annex G of IEC 60364-5-52 (which seems quite complicated) as far as voltage drop is concerned. Is there a prescribed way to calculate power loss and voltage drop from the cable manufacturer datasheet alone?

This maybe quite simple, but has been bugging me for some time. Thanks in advance for your valued responses.

• There is also a reactance. You do it per phase. Apr 28, 2021 at 16:36

Power loss is simply $$\ I^2R \$$ for each cable. It doesn't matter what the voltage of the circuit is or what the load is - resistive or reactive.
Ignoring inductance, voltage drop in each conductor will be simply $$\IR\$$ where $$\R\$$ is the cable resistance.
If you wish to take inductance into account then you must calculate the cable impedance. This will depend on conductor size spacing and spacial arrangement. I this case the voltage drop on each line is given by $$\ V = IZ \$$ where $$\Z\$$ is the line impedance.