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In the flyers they send out they urge customers to try cutting their bill by shifting energy intensive activities like running the dishwasher or dryer to off-peak times. They definitely seem to be trying to get customers to reduce the peak load.
The reason is that electricity generally can not be stored, so where there is a huge difference in peak versus off peak load, they want to shift usage, even when the grid can handle the peak (which it can't, per the other posts).
Things that modify whether a utility goes to time of day pricing, (in addition to the ability / authority to do so)...
1) how they can scale back electrical production-- even coal fired plants have to generate a fair amount at "low" setting overnight, this goes to waste if not consumed
2) can they sell the evening electricity to someone? Maybe a neighboring state?
3) can they store it -- batteries (new, expensive, rare), or hydro electric dams are the primary storage mechanisms. Our utility buys coal fired electricity at rock bottom overnight prices from our neighboring province, to
pump water back into the dam...! . Their hydro dams are pretty flexible in scaling how much power they generate, but at times you waste the water held in them to maintain the fish habitats... pumping back in allows the dam to function as if it were a larger resevori...
Utilities generally don't want to have everyone max out their power bill because the cost of new capacity (grid and production) is so much more than the cost of the existing, partly due to higher standards and more difficult sources. Not many regions can build new nuclear or coal plants, for example. Also, most regions require state money to help fund capital projects, and the government refuses to provide this until the utility demonstrates that they have done all that they can. Finally, the governments want a lot of power available for industry, and attracting new industries to their region, which demand affordable and plenty of electricity.