This is how it works in Japan for the newer rate plans for consumers now (replacing the previous method of charging you based on the size of your main breaker), but checked in 30 minute increments rather than 15.

The steps are pretty coarse - on my rate plan there are just 3 steps: 0-10 kW, 11-15 kW, 15 kW+. You're not going to surpass peak 10 kW in an apartment anyway.