they don't even have individual meters for the the individual apartments.
Are you in the USA?
If so, check with your state Utility Regulatory Board - that sort of arrangement is illegal in at least one state, though it is also specifically legal in at least one other state.
In any event, unless your rental contract specifies some sort of specific applicable limits or conditions (I had an apartment once that stated I would pay $25/month more if I had an A/C unit), the landlord has ZERO legal standing for trying to charge you if you use the maximal electric available to your appartment.
The odd thing is that I've NEVER seen a large apartment building anywhere in the USA that didn't have individual meters somewhere, just small "house converted to apartment" type places.
There has to be a way to make it legal. I lived in student housing and they had a max electricity charge for me and 3 roommates. It was 25 each. Even if we used more then max it could not go over this amount.
But we only got like a few bucks a month during heavy ac usage or heat usage. But I signed an agreement to it and i was a big corporation that owned student housing buildings so there has to be some way they can come up with these numbers and still is legal.