PoW's hunger for electricity is one of the reasons people try to come up with alternatives - including this one:

Instead of miners solving computationally difficult "puzzles" for every block, what if they only had to demonstrate they have the MEANS to do so?

For example, there might be a 5-10 minute contest once a week, during which all miners demonstrate how much processing capacity they have.
Those with the most capacity would be granted the right to publish a larger share of the blocks over the following week, against much lighter competition and with much lighter processing power per block.

I find it appealing is that it would take cryptocurrency to a new level of absurdity as far as the outside world is concerned:  Not only would miners do lots of (otherwise) pointless calculations to earn money, with this they would own a bunch of expensive hardware that sits idle all week, but which they need to win chances to publish blocks during the brief contest period each week.

I have some ideas about how this might be done, but nothing like 'white paper' level.
I'm just tossing it out as an interesting idea that others might want to mull over.