You wouldn't multiply the volts, you'd multiply the amps, by using a separate sub-breaker for each shop, which you're doing anyway since you want to meter them separately.

This is already the norm in lots of Europe. It's not some weird new thing. In Sweden, no mall food courts have natural gas hookups, it's all three-phase electrical appliances. It's been like this forever (since Sweden has craploads of hydro and nuclear and zero gas).

We use 400V in Europe (in the most modern infrastructure, probably since the early 2000s) and have roughly 1.7x the power of gas for cooking. Gas measures at around 4.5kW and the modern induction stoves are at 7.5kW (old "ceran" electric cooking fields are 3.5kW)

> The future might wonder why we accepted the danger of 5,000v power lines running through food courts just to avoid using gas burners.

... but this was already the case before induction cooking?

There's no getting around Ohm's Law, so any serious consumer is going to have its own transformer to avoid either having massive last-mile losses or insanely thick cables. A large shopping mall will already have multiple transformer stations (and the associated 10kV cabling) to power all the lighting, advertising displays, air conditioning, and so on. Adding induction cooking to that is almost a rounding error.

I agree there's a huge amount of energy that would need to go into a commercial kitchen to replace gas, and I also agree its probably a bit unfeasible at a lot of locations with current technology to do it at any reasonable scale and have it be economically efficient.

However, you're not really being honest by suggesting things have to either be 110VAC or 5,000V. Even residentially, an electric range isn't often going to be operating at 110VAC aide from some portable single burner things, you'll likely see them operate at 208V or 240V. And when it comes to commerical equipment it'll likely be three-phase, so its not like you need a single massive conductor running thousands of volts to power it. For something like a shopping mall, you're already likely to have some pretty massive electrical infrastructure feeding the facility running at something like 13.8kV. At that step down point, do a few big 480Y three-phase runs over towards the food court, then do 208Y three-phase to the ranges.

To be fair though, I'm mostly speaking from a US-grid mindset here. I don't really know the specifics about what would be done in Japan, but I imagine it would be somewhat similar. I'm also not necessarily arguing they should do it, but its not as impossible or ridiculous as you're making it seem.

haha who is cooking on 5kv?