In that situation over half the power supplied from the feeder is wasted as heat in the rail, plus the train won't be able to regenerate. This is a worst case but averaging along the length of the route the power required is still probably 30% more than for an AC system.
Indeed, however with such a lightly used scheme as a branch line with a handful of relatively low speed multiple units running on it - the energy costs are likely to pale into insignificance compared to the installation costs. Which are drastically lower than they would be for an AC installation that had substation feeders.
Also during off peak hours you could always design the substation to reduce its output voltage to more standard levels closer to the nominal value to allow a modicum of regeneration. But I do not believe regeneration in rural settings would outweigh the savings from fewer substations further apart.
You also have to consider what happens if the one feeder station is out of use or loses its supply, which I think means the each one would need twice the rating you give.
The emergency response would be likely to instruct the signaller to instruct the drivers to limit power use to notch 1-2 to clear the affected section.
Some modicum of infeeding from Ormskirk and Southport can be provided, so hopefully the surviving station would be able to clear the line.
If the substation is out for maintenance than an obvious option would be to short form trains to only 3 carriages. (As I believe Merseyrail insist on maintaining two seperate units with the replacement fleet - otherwise you would likely have to terminate trains short).
And have you allowed for the resistance of the return path through the running rails?
Ooops, however this is not necessarily massively problematic as resistance of the return rails can be reduced not only by fitting aluminium cables in parallel with the rails but also by the positioning of multiple earth bonding stakes along the route.
Even with earth/return resistance it seems likely that two substations at Burscough and Southport would be able to easily handle the supply. I make Burscough-Southport only 11km.
The Delta Rail report suffered from considering branch lines in (literal) isolation, whereas in reality they would almost always be connected to an electrified main line. That's not a criticism of the expert former colleagues of mine who wrote it, but of the remit they no doubt had from DfT.
Indeed, but there are several situations where branch lines will not be connected to the 25kV system in the near future, and may even be connected directly to the 750V system. With the debacle seizing up the 25kV electrification programme at the moment we have no clear idea what will happen.
However if the route is electrified at 25kV to Preston or Wigan it effectively becomes part of the larger WCML/NW electrified network and shares its power accordingly. I think we would all want that to happen and if Ormskirk-Southport is electrified it is highly likely that at least one connection to the WCML would be electrified either at the same time or within the lifetime of the new 750V equipment
While I am one of the most vocal supporters of electrification on this forum (indeed I wish we would pursue total electrification as a matter of urgency) I am not so sure that we will do so soon.
The problems in the existing schemes are building up rapidly and will threaten the future of the programme.
The low capital cost of a 750V scheme is a big selling point in my opinion in this climate.
Its not technically the best, but it is considerably better than a diesel railway.
If this network did need to be on a separate phase, then feeder stations can now be fitted with inverters, similar to a traction package, to provide single phase current with a balanced load on the three incoming phases. If one of these is provided then single train could be supplied from a 33kV grid at 25kV just as easily as at 750V - in fact more easily as the lower losses mean less power demand in total.
While that is technically possible I am not sure that is the best solution.
It might work out cheaper in maintenance and procurement terms to simply erect a ~12km pole line fitted with a single phase 25kV (or 25kV-0-25kV split phase) circuit between Burscough and the WCML at Coppul.
It would be no less reliable than a single substation (and I doubt you would be able to justify 2 25kV substations) - probably better as the WCML is far less likely to suffer a total power outage and a simple transmission line at a relatively low voltage and power is likely highly reliable.
The same might hold for other detached sections of railway in rural areas.