Selecting 3-Phase Cable for 230m Distance with 40-50A Load: Voltage Drop Consideration

Hello
A friend of mine has a problem with the selection of a cable, he has to run a 3-phase cable with a length of 230 m, with approximately 40-50 A going through it, and the problem is that I don`t know which cable to lay, can anyone advise or tell me how to calculate it, with the drop the voltage cannot be large
many thanks in advance for your help

Hello.
What is the way of laying this cable (in the ground, on ladders, on the plaster)?
Regards

Hello!
The calculation can be done in 2 ways:
- according to thermal conditions (so that the cable can withstand...);
- according to permissible losses.

If we want to install a "free-lying" installation, the current density in the copper wires should not exceed 15A/mm2 in a 1-phase, 2-wire installation, or 10A/mm2 in a 3-phase, 4-wire installation. This condition shows that for currents of approximately 40 - 50A, a cable with wire cross-sections larger than 5mm2 each should be used (because thinner wires will melt the insulation...).

Calculation for the second condition: we assume that the allowable losses on this installation are 5%. The load resistance (in the phase-earth system) is 230/50 = 4.6 ohms, so the resistance of a 230 m long transmission line can be at most 5% of it, i.e. 0.23 ohms. The resistance of copper is 17.5 milliohms with a cross-section of 1 mm2 and a length of 1 m. The calculation shows that the condition of losses <5% is met if the cable core has a cross-section of 17.5 mm2. We can choose from two similar standardized cross-sections: 16mm2 and 25mm2. Using the former will result in losses being exceeded and amounting to 5.46% (I guess this can still be accepted...), and in the latter case the losses will be lower (only 3.5%), but the cost of the cable will be higher by over 50%.

Now you have a choice.

HeSz wrote:

Hello.
What is the way of laying this cable (in the ground, on ladders, on the plaster)?
Regards

As far as I know, this will only be a temporary solution and the cable will run on the surface, attached to a fence somewhere

With such a long section and such a load, the cross-section is 50 mm². It is calculated like this:
Voltage drop on 1 phase not more than 4%; ΔU=230V*4%=9.2V.
Let`s calculate the cable selection according to the formula:
- for uneven loading of phases:
S=(wire length * 2 * copper current/conductivity * ΔU) * cosφ
- for uniform loading of phases
S=√3*(wire length*current/copper conductivity*ΔU)*cosφ
In this arrangement, the cross-section will be 35 mm².

copper conductivity = 57 m/Ωmm²

lesrog!
The copper cable you propose with a cross-section of 35 mm2 has a resistance of 0.115 ohm over a length of 230 m. A phase current of 50A in such a cable causes a voltage drop of 5.75V, which is much less than the 9.2V you assumed.
A 230m cable with a cross-section of 25mm2 has a resistance of 0.161 ohms and a current of 50A gives a drop of 8.05V, which is better than the assumed 9.2V.
So maybe it`s not worth giving as much as 35mm2?

With uneven load, I calculated as for phase 1. In such a case, the length should be counted * 2, which gives a resistance of 0.23Ω for a cross-section of 35 mm². For a uniform load, I agree with my colleague Węgloż. ΔU=16V. Sorry for the miscalculation.
In sum:
For an even load on the phases, 25mm² is enough, while for uneven load on the phases it must be 50mm² (I assume that there may be a situation in which only one 50A phase will be loaded).