During off peak hours, water is pumped up to it.
During peak hours, water from the lake is run h=through turbines to produce electricity.
The system of lakes and dams on the Salt River in Arizona does exactly that.
Makes for some fun rides in the summer, tubing down the Salt.
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“...electricity, all of which is sent to New York City.”
Well, THERE’s your problem right there, lady.
https://en.wikipedia.org/wiki/Blenheim%E2%80%93Gilboa_Hydroelectric_Power_Station
We have one near here, pump storage called Bear swamp. Air compression technology is very inefficient IMHO.
water storage
Yup, about as simple as you can get.
you can use heavy rotating mass as well
Very few people listened when I said Liquid Organic Hydrogen Storage, but finally people are starting to do so.
Soon you will see these plants everywhere taking excess energy splitting it into hydrogen and storing it in a stable at normal temperature liquid form
https://www.hydrogen.energy.gov/pdfs/07-Schmidt-Liquid%20Organic%20Hydrogen%20Carriers.pdf
A large container of compressed air seems much more dangerous than a big tank or resevoir of water at an elevation higher than the pump and turbine.
Same as Raccoon Mt in southeast Tennessee.