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All three primary transmission wires in the picture below have smaller wires coiled around them. These smaller wires (secondaries?) connect to a transformer and onto a nearby house. The coils follow the primaries for about 1.5m and seem to be insulated. What is the purpose of the coiling? Does it induce a current in the smaller wires?

Transmission pole with secondary wires coiling around primaries for about 1.5m

I think the small wires are also connected to the primaries with hot clamps. And I can also identify the fuses along the wires between the clamps and transformer. But the coiling remains a mystery.

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They are spiral vibration dampers, most likely made from plastic material to prevent damage to the cable.

The Spiral Vibration Damper is a motion control product used to dissipate aeolian vibration that may occur on cable spans. Using the recommended number of Spiral Vibration Dampers minimizes bending strain, protecting the cable from long-term fatigue due to aeolian vibration.

Aeolian : relating to wind

enter image description here

source: https://plp.com/energy/distribution/motion-control/spiral-vibration-damper

disclaimer:
I have no affiliation with PLP, the information was found by searching the internet for power line dampers

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    \$\begingroup\$ If you want to improve your answer, have a look at en.wikipedia.org/wiki/Vortex_shedding , there is even a fotography of a chimeny having a similar helicoidal vibration damper to dissipate aeolian vibrations. the citation points to the work of Scruton et al., 1957 (unpublished, so I cannot refer to it directly). \$\endgroup\$
    – EarlGrey
    Commented Apr 18 at 9:02
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    \$\begingroup\$ Damping would be different than vortex shedding. Vortex shedding alters the geometry of the structure to change its behavior in wind - preventing the formation of vortices. These dampers, per the answer link, "...makes impact with the cable to disrupt the aeolian vibration standing wave" and "...can be installed anywhere on the cable...". \$\endgroup\$
    – CrazyArm
    Commented Apr 18 at 20:38

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