Currently the highest DC voltage in use is 3kV, which traditionally required pairs of 1,500 volt motors permanently connected in series. I don't know if that still applies to newer 3kV rolling stock, or whether that instead has something called a DC-to-DC converter.
Traditionally, DC systems required the line voltage to be the same as the voltage of the traction motors, except for the 3kV DC systems where it was double, motors permanently connected in series. For now, bear in mind that 3kV DC is both the weighted average (R.M.S) and the peak voltage.
D.C systems take three-phase power from the national grid, convert it to six phase at a lower voltage, and then rectify it, all phases loaded evenly and power delivery is constant.
A.C allows a higher voltage than the traction motors, 25 kV root mean squared in case of standard frequency electrification, with a transformer on-board stepping down the voltage, which is then rectified. But single wire overhead with rail return means it's only single phase, each section of a 25kV A.C network is typically fed with one of the three phases of the national network, with phase breaks between different sections. Additionally, being fed straight off the national grid means that the frequency is the same as the national grid, 50Hz in this country, meaning that transformers on board need to be quite large. And after rectification, being single phase at standard frequency, the ripple filters also need to be quite large.
Let me introduce something called a DC-DC converter. Just as a transformer changes A.C voltage, a DC-DC converter does the same with DC voltage. Like transformers, they can also provide dielectric isolation. Any transformer is designed to change the voltage of A.C at some given frequency, and when used with A.C at a frequency any less than that, it becomes more like an inductor, and most definitely an inductor on D.C.
The first basic principle of a DC-DC converter is that switching a D.C supply off an on repeatedly, a transformer can be made to work without an external A.C source. The faster the switching, the greater the transformer's power rating can be in relation to size and weight. The primary coil of a transformer might be integrated into a tank circuit with the power switched on and off repeatedly, connections to the tank circuit being reversed between pulses of current.
The second principle is reversing the connections from the secondary coil every time the secondary current changes direction, see here.
It is now technically possible to use DC-DC converters instead of classic transformers to step down the voltage, this meaning that new D.C electrification could also have a line voltage higher than what's used internally. This would combine the advantages of high voltage A.C (such as greater distance between substations) with the constant power delivery and even phase loading of D.C electrification.
On-board conversion of D.C would not be limited to one phase, so power delivery can be kept constant, and at a frequency higher than the mains, say 400Hz, so a smaller and lighter transformer could be used, and the higher frequency and phase order also makes the rectified current easier to filter.
In fact, a 30kV DC system could use smaller insulators than are needed with 25kV A.C, the peak voltage of the latter, rounded to the nearest volt is 35,355.