Trains have batteries. They don't last forever, though, and in modern times, even a simple passenger car comes with a sophisticated software... which may be ill designed and shut down the system in the 'wrong' kind of emergency. (I could tell stories.)

And you may not want to run a train across a section of broken but still possibly live wire. It shouldn't be a problem (trains are pretty good Faraday cages), but with this sort of voltages you prefer safe over sorry.

- Jake

Friends come and go. Enemies accumulate.

Assume ice at -20C - requires 40kJ/kg to reach 0 plus 334kJ/kg to melt - so let's say 400kJ / kg.

A catenary with a 100g of ice / m would be heavily loaded, and we only want to melt a layer 0.5mm thick on a 1cm dia wire (00 gauge), or about 1.5g of water / m - i.e. 3kg/km or about 600kJ / km

To provide this heat we might heat the wire for 20s every 5 minutes (or perhaps per section ahead of the train?), requiring 30kW of power when heating.  The resistance of 00gauge wire is about 0.25ohm and i^2r = 30kW => 350A which is well within the current rating of the OHW.  To provide this current we do not need to provide 350A*25kV, but rather v^2/r => 86V per km.

To get this 90V per km we might treat up and down wires as separate lines, running the current up one side and back down the other.  We would connect the overheat wires together at one and, and insert a 350A, 90V*km*2 transformer between them at the other end, normally shorted together, but turned on to deice.  Such a transformer might consist of four turns of catenary wire on the secondary, and for a 25kV supply, 1000/(km*2) turns on the primary.

If an electric train normally uses 1MW, on a 25kV line, it should in fact produce enough heating to melt the ice (apparently not quickly enough to prevent damage), but this approach would only need 30kW*20s/300s = 2kW average to maintain the ice free wire.

Numbers are all made up; substitute better ones if you know them.

"Catenary" is American English for "overhead wire"; though recently it is increasingly in use in rail literature this side of the pond, too (I prefer to use it, too).

In French: Caténaire. Comes from the same Latin root:

Catenary - Wikipedia, the free encyclopedia

The word catenary is derived from the Latin word catena, which means "chain". Huygens first used the term catenaria in a letter to Leibniz in 1690. However, Thomas Jefferson is usually credited with the English word catenary.