Types of Traction Current

This part really makes very little sense. There have been several new systems using low-voltage third rail power supply built since 1905, mainly in Metro applications.

That some systems used AC of low or high voltage in DC traction motors is an artifact of early power generation technology. What then was "industrial standard" was often low-frequency AC, which you could use in the DC engines of the day. This is one of the reasons why Sweden, Norway, Germany and other countries use the 15.75 Hz AC in their mainline electrification systems.

Low-voltage AC and DC systems were employed partly because they did not need a transformer on board the vehicle to be powered -thus saving on a big, heavy, fragile and expensive piece of equipment. Of course, transmission losses are high with low-voltage systems, so a lot of countries or networks with longer lines went for the more expensive, but also more energy-effective solution of high-voltage catenary and transformers on vehicles.

The construction of catenary is indeed partly dependant on what voltages and amperes you expect it to see in use -the crossectional area of the catenary is critical in the transfer of power to the pantograph collector strip without overloading the catenary wire, for example- but also the expected weather conditions and a myriad other factors.

And while low-voltage lines does not need as large clearances and as much insulation as a high-voltage one, they also tend to carry vastly higher ampere ratings (because as the volts go down , the amperes go up, since you have to transmit an equivalent amount of energy), and thus the wire can be much thicker that a high-voltage one.

Static rectifiers are, indeed, a type of rectifier commonly used today, in both mobile and static applications. The electric current, however, does not care how it is generated, transformed or rectified. You can use static rectifirers, rotary generators, mercury arc rectifiers -whatever. Italy built a three-phase AC system in the early 1900's and used it for quite a while. Technically, it worked very well, but the complicated equipment necessary was hideously expensive to operate and maintain, which is why the system was eventally scrapped.

What modern solid-state power control electronics has done, however, is to make the equipment needed for a three-phase AC traction motor very compact, very low on maintenance and relatively cheap. And this is why they are used in virtually all rail vehicles being built today -they can be used to give an excellent "creep control" for a locomotive starting a fully loaded iron ore train , as well as a small, compact, wheel-mounted traction package for a low-floor tram with split axles.

And do note that 50 hz as the standard for industrial/national grid electrical current is a relatively new standard, an one not employed all over the world either. For long times, other frequencies and voltages were used -sometimes, such as in the USA, competiting power companies deliberately used their own frequencies, to keep their customers captive. Thus, a lot of systems use other voltages and frequencies, because that is what the standard was when they were built.