It's not mere math: Norway and Swiss have much more hydro than they normally need, last summer they have imported electricity due to drought (rare for both country, especially for Norway) and both who sell to them are mostly Sweden and France from nuclear.
When you need X from renewable you actually need 4X at least to be sure having enough in bad moments, energy is extremely* important and we can't going soft with it. Hydro is largely the best renewable since is almost constant (with their seasons, but still pretty stable) however is not as predictable and constant ad an NPP or an oil/gas/coal one.
So far very few countries have been able to run on mostly hydro only, all small, with little industry and very mountainous. Unfortunately too many dream miracles of free energy everywhere instead of trying...
Hum, I think not, you are talking about math, like "hey, you p.v. produce 130% of your yearly consumption!!!" vs "yes, sure, but self-consumption is only 50% because at night I need energy and I miss it, while in the sunny day I have much more than my average needs".
Or to be less vague: I understand you think a country can run with hydro storage, I think definitely not for most countries: yes we can regulate our network frequency with pumped storage, when energy demand goes down (for instance also because p.v. and eolic produce much) we pump water in altitude and we release it when demand grow. It's nice and it does work very well: ONLY if our storage in altitude suffice for FAR more than our normal needs. Enough more to have water during a drought period + high energy demand, enough to survive days etc.
If you live nearby a waterfall or a quick/big enough river you might get 99% of your needs out of it to power your home. But at a nation scale is much more complicated and 99% would be still not enough...
You said there is not enough water and mountains. This is the point I disagree with.
For pumped storage you don't need a river or to worry about drought. Just coastline with mountains.
1 small lake could store enough to power the US for a peak hour. 20 could store enough for a day.
Yes you would need to charge them, yes it would cost money. But geograpy is not the limiting factor for most countries.
That's fantasy: you can't pump water for long distances and you need to make it fall to get electricity back. Salt water pollute land, corrode turbines and pipes quickly, can't be used anyway, surely can't be used from the sea to the mountains.
Not only: a small lake can store enough for a single home, not more. Pumped storage is far from efficient in energy terms. Consider a thing: we (nearly all nations on the world) have already implemented much of the hydro we can make, simply because it's effective and cheap. We can just do a bit more, but a bit.
BTW the principle is:
- you have a large basin in altitude, with some gates to control the falling flow
- you have a river with a low altitude lake because anyway you do not pump all water back, nor you can't recovery it once used to produce energy and we talk about much water
- you have pipes and turbines and pumps with other pipes
Normally you let a bit of water falling in the pipes making turbines turn producing electricity. When demand low a little bit you just divert part of the falling water out of turbines, eventually pumping back a bit, if the demand fall MUCH you need to consume to keep the network frequency. Normal hydro pump back very little water. With p.v. and eolic who can produce a significant amount of energy just few hours/day you can pump more. So from the low altitude basin/lake you pump back to the higher one. That's is. Depending on the meteo you need to dump more or less water, or you have too little quantity to produce etc.
That simple game means you can't do hydro anywhere on any mountains and grabbing water even far from them.
I'm not, but anyway if you want try do describe visually your pumped-hydro nationwide revolutionary system so we can discuss with something tangible what can be done and what can't.
US peak demand is around 700 GW. That is about 0.25 km3 of water with 3000 m of elevation.
This is a lake 5km x 5 km and 10 m deep