Here in Brazil we have voltages in different regions but we also have different voltages inside the home. My washer has its separate 220v circuit while the rest of the home is 110v.
In a three-phase system (like the ones used in most of Europe), that effect isn’t as pronounced since you usually have at most 120 degrees phase difference instead of 180 and the voltage between two phases is less than double, so less appliances make use of that (I think some stoves do).
We Brazilians tend to call it "110V", but it's often a three-phase system with 127V between phase and neutral and 220V between phases.
Or sometimes it's 115V from phase to neutral and 230V from phase to phase (probably a split-phase system like you said). And in that case, us Brazilians would still call the lower voltage "110V", and the higher voltage "220V".
You can't trust a Brazilian when they say the voltage is "110V" or "220V". These numbers are only an approximation, which might have been correct for some places a century or two ago.
And yes, it's a mess. Check the official list at https://www2.aneel.gov.br/aplicacoes/srd/frmConcessionaria.c... (link found at https://www.gov.br/aneel/pt-br/centrais-de-conteudos/relator...), which shows which voltages can be found in each city for the whole country. For instance, take a look at the city of São Paulo in the state of São Paulo (yes, it's the same name for the state and its capital city, this is also the case for Rio de Janeiro):
- 115V / 230V
- 120V / 208V
- 127V / 220V
- 220V / 380V
- 220V / 440V
At least the frequency is always 60Hz (unlike the rest of South America, which uses 50Hz; we have to use HVDC links when importing or exporting electricity to the neighboring countries).
Using HVDC to interconnect async grids is very common.
This presentation is a nice deep dive on the situation in Europe: we are even building HVDC “corridors” embedded inside some of the sync grids. Pricey gear but valuable too!
http://catedraendesa.us.es/documentos/jornadas_uimp_2015/201...
This isn't really true, new overhead lines are being built all over the place. It definitely depends where they're being built and there is definitely strong opposition from councils in e.g. some parts of Germany, but see for example in the Netherlands there are definitely new overhead lines being built: https://www.tennet.eu/nl/projecten/provincies/groningen/eems...
That being said it's true that it's much more challenging than it used to be to get planning permission.
We also have that here in Brazil; the Xingu-Estreito and Xingu-Terminal Rio HVDC links run in parallel with the high-voltage AC links. On the other hand, the Madeira HVDC link (https://en.wikipedia.org/wiki/Rio_Madeira_HVDC_system) is AFAIK normally disconnected from the AC grid on the generation end (it has a direct connection, probably used to start up the power plants, but normally uses a back-to-back HVDC converter instead of it).
Currently it's at 121.8V - either they have finally adjusted the tap on the neighborhood transformer or there's a heavy load at the moment (hot water heaters running from people showering this morning?)
I could imagine that utilities calculate some average base load and adjust transformers accordingly to accommodate the expected voltage drop, given that 110/120V is relatively low and drops can be significant?
Households these days often do have a 3-phase hookup, but it's quite rare to have 3-phase equipment. Maybe a stove, and with the energy transition larger solar setups, electric car chargers, and large heat pumps. But most of the time that 3-phase hookup is just treated as three separate 1-phase sections.