Large-scale pumped hydro storage isn't nearly as easy many people seem to think.
Let's assume a small-sized city of 10,000 homes, which would have a power requirement of about 100 megawatts, in a mountainous area like Colorado where we can put the storage reservoir way up a valley somewhere, let's say 500 meters. With an effective head of 500 meters and an overall turbine/generator efficiency of 0.8 you'd need 25 m^3/sec of water to run the plant. A 3 meter diameter concrete pipe that's 500m long would have a head loss of about 200 meters, so you'd have to put the reservoir up that much higher to offset that - now you're at 700 meters above the plant. To power the plant for twelve hours you'd need to store 25m^3/sec * 43,200 sec = 1,100,000 m^3 of water. That's about 890 acre-feet, so you have to find a place where you can put an 89 acre lake that averages ten feet deep. Note: that's enough water to supply the daily needs of about 12,200 households.
As far as I can tell - good math so far - although I'm just reading fast but you're using all the right terms. I don't do these calculations myself but just read the papers that pass peer-review - I'm a
humanities geek myself.
Then, assuming a pumping efficiency of 0.8, you need to build a 125 megawatt pumping station to get the water up there. To supply it you'd need either a sufficiently large river, or else another 890 acre-foot reservoir to store the water at the bottom of the hill for reuse (in which case you'd still need a river to supply makeup water as it evaporates).
Yes - pumped hydro is only 80% efficient.
Now you get to build the 125+ megawatt solar farm that will be used exclusively to pump the storage water uphill during the daytime.
With you so far.
So in order to build one 100MW hydro plant to use pumped-storage water, you need to actually build three plants that each handle 100MW or more of energy. This is a VERY expensive proposition.
Now I'm lost - but I might be misunderstanding you?
You only need 1 lot of solar to push the water up that hill to get 80% of the energy back. That's true. This might just be semantics but it's how my brain sees this picture. (Again, I'm a humanities geek that sees things in stories and metaphors, not equations as much.)
Where I see the extra solar being required is that while your first solar farm is pumping the water up the hill, and 'only' going to get 80% back (which is the figure the Australian National University guys I'm reading give), then what's it not doing. It's
not running your
town.
So you need two "lots" of solar (of whatever required size.) No figures here - just broad concepts to illustrate what almost any geography would be dealing with (south of the Arctic circle at least).
Then we have to deal with the fact that winter has a lot less sunshine, and there are even Dunkelflautes (Dark Lulls) to deal with. So you overbuild your "lot" again (either in a local town grid, or a state or even national sense.)
Now you have roughly 3 lots of VRE (Variable renewable energy) to both run your town and pump all that water uphill. Every time there's a power excess - like peak solar output - your town grid 'breathes in' all that VRE and pumps water uphill. Then at night as there's only a little scattered wind around, your town 'breathes out' as all that water runs downhill, keeping your grid running.
BUT WAIT THERE's MORE! We still haven't talked about replacing OIL!
Converting transport to EV's and e-fuels (hydrogen, synfuels, etc) apparently takes us through to 6 TIMES today's electricity grids. But with solar at 1/4 the cost of nuclear, and wind even cheaper - the accumulative cost is still CHEAPER than today's grid. And that does not even include 'outsourced' expenses of fossil fuels like the health cost of coal and oil and gas particulates,
which basically doubles your electricity bill. But you just pay it over in your healthcare sector! It's a stealth-cost.
So what did the
Australian National University Blakers team model? This study was also accepted and published by our CSIRO. (Like your DARPA).
Blakers
PV and wind allow Australia to reach 100% renewable electricity rapidly at low cost.
Wide dispersion of wind and PV over 10–100 million hectares reduces cost.
Off-river pumped hydro energy storage is the cheapest form of mass storage.
There are effectively unlimited sites available in Australia.
LCOE from a 100% renewable Australian electricity system is US$70/MWh (2017 prices).
100% renewable electricity in Australia - ScienceDirect
That's the cost with 6 times overbuild! Clean skies, energy independence, and a cheaper health bill. Local jobs. Let alone not annoying other trading nations that take climate change seriously. What's not to love?
When counting off-river, Australia has 300 TIMES the POTENTIAL off-river pumped hydro storage required to take Australia 100% renewable.
Other maps show America has 100 times. Pick the best 1% and you're done!
100% Renewable Energy Group