Earlier quoted context omitted.
"A 1-phase transmission line needs 2 conductors" Right, but for many single phase installations a ground/earth return is often employed. This often simplifies things and saves a lot of infrastructure costs. Whether it's single or 3-phase, calculating the coupling efficiency will, at best, only be a rough guesstimate unless great care is taken to accurately collect and collate all physical and electrical parameters. N…
> Right, but for many single phase installations a ground/earth return is often employed Often? Not what I as a complete laymen in power transmission have observed. The mentioned power grid of the German railways uses 2 conductors. Why they would pay nearly 100% more in infrastructure cost than just using ground as conductor for return current I have no idea. There must be a reason. The Finnish railways don't have th…
First, it depends on the country and its rules (some permit it others don't); second, it depends on the application.
The balanced system in your Wiki link is common too and it has advantages over the single system. For starters, it's a balanced power feed from a center-tapped transformer, and thus they are often used in sound studios and laboratories to reduce hum. noise and ground currents. Sometimes in the US you'll see the three-wire 110/220V systems. As they use three-wire feeds, they're more expensive than single-wire ones such as here: https://en.m.wikipedia.org/wiki/Single-wire_earth_return
Earth return is mostly used in rural areas to feed small communities and such. This is to save cost. It is usually only employed on medium voltage feeds (6,600, 11,000 Volt lines). Rather than terminating in a substation, lines generally terminate in a single stepdown transformer. I would imagine it wouldn't be very common in Europe as it's pretty built up/has a large population (when I was living there I never saw any - but then, I was mostly in large cities, so I wouldn't have expected to see them).
I've not been to Iceland but with its smallish population I wouldn't be surprised if single lines with earth return are used there - it would make sense to use them there.
You are also unlikely to see single line feeds if the current is high or the line voltage is very high (intercity transmission lines, etc.) as ground eddies are potentially dangerous. Nor will you see it used where high current without sufficient voltage would lead to excessive I^2R losses.
That said, many railways effectively use ground return. As you mentioned, many electricified lines use the rail tracks as a return and they're effectively earthed. In lines where the rails aren't welded together but only joined by fishplates you'll see multi-strand copper wire connecting each rail to ensure that the return also doesn't suffer excessive I^2R losses.
I've lived in Europe but it's not my usual home so I'm not overly conversant with railway power systems there. However, I do know there are three common European electrification standards for normal railway services (i.e.: standard and Iberian guages - not specialized ones, narrow guage etc.). And roughly by country they are 25kV (Fr & Eastern EU), 15kV (De), and 3kV (Es & It). France, I think, still has some of the older 1.5kV standard. Not sure what Scandinavian countries use but I think it's 15kV and or possibly 25kV (so Finnish railways are likely to be 15kV or 25kV but I'm guessing here).
Therefore, the max/min ratio of voltages in use is 25/1.5 or 16.67 : 1. This is very significant, for what engineering calls for at 1.5kV DC is very different to that at 25kV. AC Both 1.5 and 3kV will nearly always use a single overhead line with earth/rail return. The higher voltages will more likely use two lines (this is likely both an enginering matter and a safety requirement). So this would mostly account for the differences you mention. Note: 1.5 and 3kV are DC and the 15 & 25kV are AC.
(Note: trams and small/light rail often use 750VDC.)
The mixture of different voltages in use across Europe and the fact that they have this high ratio of 16.6 : 1 has called for some innovative solutions. For instance, there are classes of locomotives that now use all three common voltages (3kV, 15kV & 25kV) and they automatically switch between them when moving from one county to another.