You'd need a very effective booster at Helmsdale for the climb up to Forsinard!
Well it appears there are at most 4 passenger trains moving on the Far North Line at any one time, and it appears another 4 run on the Kyle of Lochalsh line which would also presumably be included in this scheme.
Assuming all services were run by 3 coach Class 377/3s that is roughly 8800hp of power dmenad on the line if they were all to go to Notch 8 at once.
Additionally we will make allowance for one 5000hp range locomotive to cover possible freight operations somewhere on the line. (Although 5000hp is massive overkill for most freight duties).
This means 13800hp or roughly 10.5MW.
If we assume all these loads are in the vicinity of Wick (thus the worst case as it is the farthest point from Inverness and this would put all loads on one "leg" of the line) this would mean our electrical supply system must support 10.5MW roughly 161 miles away.
The minimum voltage allowed on a 25kV system is apparently 19kV, which would mean that 10.5MW would draw roughly 552 Amps.
The maximum voltage allowed on a 25kV system is apparently 27.5kV, so we have roughly 8kV of voltage drop to push 552 Amps through the system.
That translates to a resistant of roughly 14.5 ohms.
For phase balancing purposes there will be three conductors used in this project, supplying power to different parts of the route in an attempt to phase balance the system (although this would be horrendously difficult due to low traffic density), which means that the average resistance of the individual conductor would be approximately 43.5 ohms.
If we assume double track is negligible, and that we will use copper conductors in this example, then we will require a cable with a resistance of roughly 0.16 ohms/km, this translates to roughly 110 square millimetres area, which is less than the size of the cable used on TramPower style catenary (150mm^2), which can supposedly be built to handle 25kV systems. (This would also support the 75mph running on the line so no speed limits would have to be altered)
So it is practical, even with this extremely conservative estimate of the capacity.
The two wires which are not the contact wire at any point on th eline would presumably be carried on the opposite side of the support pole on appropriate insulators.
It may be more practical to fit autotransformers and take advantage of the advances in power transistors and fit two cables that would operate on a single phase, with phase balancing being carried out at the substation in Inverness.
EDIT: 3 x 20m vehicles is probably not enough for KYle of Lochalsh in summer, but I only used 377 as it was the only 3 coach multiple unit I could find power figures for, but due to the fact that rather more conductor is available than I stated there should not be a power supply problem.
Additionally there are normally less than four sets moving on the Kyle of Lochalsh route, since its only 2hr30 each way and the spacings of services are roughly every 2-3hr.
