Even if you are the monopoly, you can still price-discriminate in order to maximize your profit. For example, if Malboro is the monopoly for cigarettes, it can still sell $50 to the chain smoker and $20 to the non-smoker and get to maximize its profits. Of course there are problems such as non-smoker buying the cigarettes and selling them to the smokers (black market problem) and other things but this example just illustrates how monopoly doesn't mean there should not be any price discrimination.
I think some of the things you can do (realistic and non-realistic) are :
1. Survey the areas with highest electricity consumption and charge them the most, while the lower electricity consumption are charged less.
The problem with that strategy is that people can move from the expensive area to the cheap area. So that is not very efficient. However, you have remember that moving is not something that people can do in a day or two time. So because of the inelasticity of housing, this strategy will still work in the short run but I do not think it is sustainable in the long run.
2. Since elasticity is very important to determine where you want to price discrminate, another strategy is to charge all non-residential buildings to be charged more than residential building.
This strategy will definitely force the non-residential buildings such as offices, shops, schools, factories, to pay more and since they HAVE TO turn on those lights, computers, and whatnot, you get the most profit out of this. This strategy seems to work in the short run and probably the long run too if everything else stays constant (including technology, amount of buildings, etc).
I'm kind of tired so I am not thinking about more.
But you know, there are definitely many strategies to make this work.
Think in terms of elasticities. Always go for something that is inelastic. This problem seems like a microeconomics problem to me.