How to model power transmission along a power transmission line?

Question

I am a bit confused on this matter.

Suppose we have an alternating current power source. One can transmit electric power two ways

1. Through radiation, e.g., via an antenna.
2. Through a transmission (power) line.

I suppose mechanism 2, if the line is just one single solid line, as opposed to a waveguide or coaxial cable which I understand the Poynting vector is nonzero and points longitudinally within the hollow space, concentrates the power across near surface of the conductor which is essentially of constant area whereas mechanism 1 the power falls off like $1/r^2$. One possibility I thought of is to model mechanism 2 as a wave guide where the electromagnetic wave travels confined within the hollow tube. That answers the question of power concentration. However, that requires the transmission line to be hollow or coaxial.

My questions: Is the power transmission line one isolated solid line or hollow/coaxial? If it is one isolated solid line, how does the power transmit (We know the AC travels along the surface of a conductor within skin depth) ?

Answer 1

2. Through a transmission (power) line.

I suppose mechanism 2 concentrates the power across near surface of the conductor ... (We know the AC travels along the surface of a conductor within skin depth)

No. Only current and charges are concentrated near the surface of the conductors. But the electromagnetic energy is located outside of the conductors, because that is where the electric and magnetic fields are.

Consider an open transmission line with two conductors.

_{(image from electriciantraining.tpub.com - Electromagnetic Fields About A Transmission Line)}

The electric field ($\mathbf{E}$) goes from one conductor to the other. And the magnetic field ($\mathbf{H}$) curls around the two conductors. So the electromagnetic energy is in the space between and around the the conductors. The electromagnetic power flow (called the Poynting vector, measured in W/m$^2$) for every point in space can be calculated from $$\mathbf{S}=\mathbf{E}\times\mathbf{H}$$ and its direction turns out to be parallel to the conductors, as expected.

Answer 2

I suppose mechanism 2, if the line is just one single solid line,

Two conductors are required to form a transmission line. (Three, for three-phase power, AFAIK).

If there is only one line, then it means the earth (the actual dirt and rock) below the line is being used as the second conductor. This is not very efficient but it is done in some rural systems.

... concentrates the power across near surface of the conductor

As pointed out in another answer, the E and H fields associated with the electrical wave are found in the space between the conductors, not within the wires themselves.

We can gain some understanding by modeling the transmission as voltage and current waves on the wires, but if it comes to the question of "where is the power?", it is more physical to say that it is in the fields surrounding the wires. (On the other hand, Feynmann tells us there isn't actually a unique answer to this question)

One possibility I thought of is to model mechanism 2 as a wave guide where the electromagnetic wave travels confined within the hollow tube.

Yes, this is absolutely how transmission lines are treated in electromagnetics. They are a form of waveguide.

However, that requires the transmission line to be hollow or coaxial.

Not true. Just as twisted pair lines can be used to transmit data signals in data communication systems, two and three wire structures without any enclosing conductor can be used to guide power transmissions.

My questions: Is the power transmission line one isolated solid line or hollow/coaxial?

Neither.

(image source: User Kent Murrell on Wikimedia)

The multiple wires connected to the tower form two or more multi-wire transmission lines (likely two 3-phase lines of three conductors each), comparable, as I mentioned above, to the twisted pair lines used in computer networking.

You can see that on each arm of the transmission tower there are two or three wires attached. These are "bundled conductors" whose geometry reduces the incidence of corona discharge around the line.