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From my understanding there are two causes for power losses in transmission lines:

  1. Losses due to resistance:

    \$ R = \frac{\rho l}{A} \$, where \$\rho\$ is the resistivity, \$A=\pi r^2\$ and \$ l \$ is the length of the cable.

  2. Losses caused by the transformer, which again can be calculated or the transformer can be assumed to be ideal and to simply ignore the losses.

I assume that skin effect can be ignored in this case, as the frequency is relatively low (50Hz) and the diameter of the cables is not large.

Are there any other causes for power loss in transmission lines or are those the only two (or three as the transformer has core and copper losses)? If there are any other causes, how can they be calculated?

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  • \$\begingroup\$ I've heard that in undersea cables, there are losses from the capacitance between the lines constantly charging and discharging which is why HVDC is preferred. \$\endgroup\$ – DKNguyen May 27 '19 at 21:45
  • \$\begingroup\$ Do some web searching yet? electrical-engineering-portal.com/… If not enough , why not? \$\endgroup\$ – Tony Stewart Sunnyskyguy EE75 May 27 '19 at 22:13
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    \$\begingroup\$ I see what you mean @Transistor. The capacitance gives rise to current which does not flow into the load. That current incurs power loss due to real resistance in the cable. Very good point. I will delete my comment after a while, because I think I am just being overly literal in this case. \$\endgroup\$ – mkeith May 27 '19 at 22:43
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    \$\begingroup\$ @mkeith: I'd leave it. It might provoke some thought in others. I think you're describing ESR in a type of capacitor we seldom think of. \$\endgroup\$ – Transistor May 27 '19 at 22:54
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    \$\begingroup\$ At 60Hz in Copper, skin depth is 8cm, thus is a problem. Those largest power cables you see aloft are groups of "wires" separated by air, for that reason. \$\endgroup\$ – analogsystemsrf May 27 '19 at 23:24
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I assume that skin effect can be ignored in this case, as the frequency is relatively low (50Hz) and the diameter of the cables is not large.

Actually, the skin effect on aluminium conductors in 50Hz transmission lines cannot be neglected. It's effective for a layer of more than about 10mm. This is easily reached as conductor ropes are typically up to 40mm in diameter.


You have already found the immediate reason for losses, but I doubt that was asked for.

A general view has to take account of losses related to the structure of the power transmission system as a whole.

  • Your notion of transformers accounts to this.
  • Then there's dielectric losses on isolation material, which is much worse in cables than overhead lines, and worse at higher voltages and frequencies than lower. DC brings them to nearly zero.
  • And finally there is losses because of imperfect phase-shift compensation. As such devices are costly, they aren't used in the medium and low voltage range. Here some power is pumped from the substation to the consumers back and forth without doing any work.
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Are there any other causes for power loss in transmission lines or are those the only two (or three as the transformer has core and copper losses)? If there are any other causes, how can they be calculated?

A bulk circuit model of a transmission like could look like the one below. The losses include:

  • resistive losses in the line
  • leakage inductance/ mutual inductance between the transmission lines and each other and the ground
  • mutual capacitance between the lines (there should be more capacitors one between each line, I only modeled three for simplicity's sake) and the ground also.

There are ways that this model could be improved, each of these can be modled from physical parameters and the losses calculated. For example, the capacitance could be calculated from a the wire to the ground (it should be really small, but over hundreds of km would be significant)

schematic

simulate this circuit – Schematic created using CircuitLab

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