Electronic – the purpose of the thin wire at the top of power transmission lines

Placing two or more transmission lines (transformers, cables, ...) in parallel is a common way to obtain increased capacity and redundancy against single failures. It also lets you take one line out of service for maintenance, while the second line carries the load.

Mathematically, you would obtain the same results by combining the parallel transmission lines, but you would lose the ability to simulate a scenario where only one of the two transmission lines is in use. Simulating contingency scenarios ("what happens if one line has a fault?") is one of the main reasons we do power systems analysis, so I would tend to model the two transmission lines as two separate elements.

After nearly 2 years, I found the answer to my question.

I recently walked past an electric utility's storage yard and noticed this reel of twisted pair cable.

The manufacturer is Southwire Company of Carrollton, Georgia and the cable is called VR2, Vibration Resistant Cable.

Their web page says VR2 uses a twist to provide resistance to Aeolian vibration and ice galloping.

Since I had never heard of Aeolian vibration, here is a quote from this article titled: "Aeolian Vibration Basics" en-ml-1007-4aeolianvibook-1.pdf

When a smooth stream of air passes across a cylindrical shape, such as a conductor or OHSW, vortices (eddies) are formed on the leeward side (back side). These vortices alternate from the top and bottom surfaces, and create alternating pressures that tend to produce movement at right angles to the direction of the air flow. This is the mechanism that causes aeolian vibration.

Here is an example of an Aeolian Vibration Failure.

Here is a YouTube clip showing these vibrations.