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For the same generated and transmitted RMS value of power from an electrical power plant station, which transmission line used, assuming having the same wire specification (i.e. wire material conductivity, length, diameter etc) will exhibit the most power losses in the form of heat a DC or an AC line and why?

We assume besides both lines having the same wire specifications also being of the same length and that in the AC power line (50 or 60Hz) there are no intermediate voltage step-up transformers.

What is analytically the contribution of the skin effect on such an AC power (i.e. 50 or 60Hz) line to its power loss? Will this skin effect on the AC line make its losses more than the normal ohmic power loss of the DC line?

I'm asking because I have read assuming that both lines are identical, the power loss to heat per unit length is higher in an AC power line than in a DC power line and try to understand what is the physical reason. Keep in mind that the major reason why AC line was preferred over DC historically and until today is that the voltage can be step-up with transformers allowing longer transmission of electrical power (i.e. voltage drop in the line is a small fraction of the total transmitted).

However, the question remains, does a DC power transmission line have less power loss per unit of length?

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  • $\begingroup$ In my question I assume the same RMS power transmitted in both lines so ohmic power loss $P=I^{2} R$ to heat will be the same in both lines. However, the AC line will have an additional power loss to heat because the skin effect. I am asking which specific equation given calculates this power loss due to the skin effect in the AC line? $\endgroup$
    – Markoul11
    Commented Jan 11, 2022 at 18:57
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    $\begingroup$ See related discussion: physics.stackexchange.com/q/682020/149541 $\endgroup$ Commented Jan 11, 2022 at 19:03
  • $\begingroup$ As mentioned in the link in one of the answers, strands can reduce the impact of skin effect. For very long transmission lines (more than 1/4 wavelength at the frequency used) the impact of radiative losses become important. So conversion to DC becomes attractive for the long haul, then back to AC for local distribution. $\endgroup$
    – Dan
    Commented Jan 12, 2022 at 4:29

2 Answers 2

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Power lines have slightly higher resistance for AC than for DC due to the skin effect.

The wiki article has extensive information on your question, including the AC vs. DC resistance of round wires. In practice, as power wires are stranded, the skin effect losses can be kept very small.

Why is AC still used? You also have to factor in power generation methods, safety, voltage transformation, ... That's where AC wins.

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    $\begingroup$ At the normal frequencies used for long-distance power transmission, the skin depth is of the order of 10mm for aluminium. However the biggest consideration in such systems is the efficiency with which the high voltages used for transmission can be scaled down to those suitable for domestic use. For that purpose you really can't beat a transformer - which requires AC. $\endgroup$
    – Martin CR
    Commented Jan 11, 2022 at 19:36
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    $\begingroup$ @Markoul11 yes, 60 Hz will suffer a bit more from the skin effect, but 60Hz also requires smaller transformers. It is a compromise. I genuinely wonder if there will be a return to DC at the utility level, given how efficient DC-DC converters now are and how high voltages they can switch (think SiC). DC also has the advantage of lossless transmission using superconducting cables. There are actual SC cables in use in some pilot projects, by e.g. Nexans. $\endgroup$
    – tobalt
    Commented Jan 11, 2022 at 19:38
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    $\begingroup$ @tobalt whilst DC-DC converters are very efficient, they not suitable for transforming power at the multi-megawatt scale as required in a national grid $\endgroup$
    – Martin CR
    Commented Jan 11, 2022 at 19:40
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    $\begingroup$ At the risk of flogging a dead horse, another key advantage of AC is that you can control it with very compact switches, so long as you synchronise the moment of switching with the regular zero crossings. With DC, when you open the switch you tend to just draw an arc between the two contacts (some designs blow this out using high pressure gas jets - it's quite a dramatic process) $\endgroup$
    – Martin CR
    Commented Jan 11, 2022 at 19:45
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    $\begingroup$ @MartinCR Why not ? This is of course assuming SC distribution becomes commonplace. The grid scale voltage could be much lower. Perhaps 10s of kV and instead currents much higher. You don't need insane voltage if your cable is superconducting. And at those voltage a step-down converter could be probably much cheaper than a 50 Hz transformer of the same power rating. Again let's assume some more advances in wide bandgap semiconductors and not use today's tech for judgement. $\endgroup$
    – tobalt
    Commented Jan 11, 2022 at 19:45
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. . . . . does a DC power transmission line have less power loss per unit of length?

An important factor is that for ac the voltage swings between two voltages, $\pm V_{\rm peak} = \pm\sqrt 2 V_{\rm rms}$, which are larger than the equivalent (in terms of power transmission) dc voltage, $V_{\rm dc}=V_{\rm rms} = V{\rm peak}/\sqrt 2$.
At very high transmission voltages this means that insulation becomes a significant challenge particularly in terms of the breakdown of air resulting in corona discharge which represents a loss of electrical power.

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