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Okay any engineers up for a hypothetical? As others have pointed out, things like wind, nuclear, and other things are sensible answers. BUT WHAT ABOUT AN INSANE ANSWER?
It obviously would be prohibitive to have a colossal "city battery" that stored excess from the day to be used at night, and environmentally would present issues making a city sized battery. But what about a non-traditional kinetic battery (think F1's KERS). What if there was say a building in the middle of the city, and inside is a metal disk made of solid steel that's a foot thick, and 500 feet across, on an electromagnetic cushion, housed in a room with negative pressure or a vacuum. During the day, the excess solar energy from the city powers this to gradually spin faster and faster, and during the night this process is reversed with the enormous amount of kinetic energy feeding a powerstation generator that would provide power at night. Okay, I told you it was an insane hypothetical, but as thought experiment humour me. It would by definition be a battery, but one that wouldn't deteroriate in the same was as a chemical battery, without the same environmental impact of involving all the cobalt, lithium, etc., although it admittedly would be pretty wildly expensive just from a space, and material cost of the disk perspective. How big would this need to be? Is this remotely possible? I mean WAY less power is used at night after all. Thoughts?
In case you don't already know, that concept has a name: Fly Wheels (wiki link: https://en.wikipedia.org/wiki/Flywheel ).
One of their main problems is that, as you pump enough energy into them to justify their cost compared to other storage mechanisms, the spinning mass becomes more and more of a danger if it ever breaks loose. Not to mention the gyroscopic effect making a "fully charged" fly wheel very hard to safely move.
The statistic you're looking for is energy density. It's usually expressed as Watthour per kilo(Wh/kg). Li-ion batteries are somewhere around 300Wh/kg, or about 1 megajoule though less if you're making it into a building.
Lifting a big weight provides you with Mass x 9.81 x Height amount of joules. So lifting 1 kg for 100m gives you 1x10x100~ 1 kilojoule.
So, to charge my 300kg, 32.000 Wh Nissan leaf battery (130Wh/kg, what you get when you actually build batteries in the real world), you would need to lift a mass of 115tons to 100 meters. So to charge a single car, at 100% efficiency, you need to lift 72 entire cars. Just so I can drive to work and back. And real-world efficiency is far below 100%, just think of the friction.
I think you've spotted the reason why we don't actually build gravity batteries. Imagine lifting 115 tons to 100m, that requires a massive crane, itself weighting nearly half that. That's why all gravity storage in existence basically consists of pumping water uphill, onto pre-existing mountains and lakes that nobody had to fabricate out of concrete and steel.
There's a company in the UK that proposes building gravity batteries using existing shafts that were excavated for mining.
I like insane hypotheticals that are discussed as hypocriticals. Not an engineer on paper, but these are my thoughts.
I think a very heavy weight that fits neatly inside of a protective structure with room to raise and lower it would be the way to get a kinetic battery. I'm talking about a platform stacked with concrete and rocks and sand and building demolition debris until it has stacked up to 2 or 3 stories tall. Then build a basic shell around it to blend into the town and have that 6 to 8 stories tall. The weight would tug at cables or press down on a hydraulic cylinder at a constant rate. A motor would then spin a large set of extreme reduction gears to raise the weight when there's extra power coming in. Then, the tremendous weight could drive the reduction gears to spin the motor as a generator at a constant rate and make reliable power.
The less crazy version of this has been proposed, a set of cranes stacking up and lowering down more reasonably size blocks to store power inside of a tall structure.
None of this is practical. You can't build a tower like this for any real storage, it's just not efficient. The only effective method is running a train up a mountain, or pumping water uphill. If you have to actually build a mountain a first, it's not going to work.