Yep. Messed up the TWH. Not used to dealing with TWH. I see now the graph was for a month of production.
The California duck curve is about 10 years old now and they have added about 2 GW of solar (and now include wind in that) per year averaged over those years. The latest addition added 5 GW which needed a home which was in the form of the battery farms. The latest 5 GW was spread across about 6 hours or 30 GWh. So at $400,000,000 per GWh requires a 12 billion investment to make that solar and wind investment usable to California.
Cali wind has been pretty static. Annual output since 2017:
2017: 19TWh
2018: 16.5TWh
2019: 16.5TWh
2020: 16.4TWh
2021: 20.1TWh
2022: 21.6TWh
2023: 20.9TWh
Installed wind capacity is 6.29GW, so I'm not sure where you are getting that they are adding 2GW per year average?
Now, solar is absolutely increasing, though the elimination of the generous NEM 2.0 subsidies put a big damper on that.
Surplus solar that the grid can't use (which I assume is the 5GW you are referencing) being shuffled into batteries at incredible cost pretty much illustrates my point, and you are still burning massive amounts of gas

As it stands, that 30GWh represents 1/16th of Cali daily consumption in the low demand fall.
The recently completed Site C dam cost $11 B USD and can deliver 1.3 x 24 = 31.2 GWhr each 24 hours.
No, Site C will produce at less than 50% capacity factor, something like 48%. So its 1.25GW will actually generate around 600MW on average, so it will produce around 5.26TWh/year. It's also a 100-year asset however, owned by the province with an extremely long-term payback schedule, rolled into the provincial utility's debt, so the rate impact of the project will be negligible.
The value of 30 GWh at say $0.30 per kWh is $0.30 x 1000 x 1000 x 30 = $9 million per day and one years worth is 9 x 365 = $3.3 B per year. The 12 billion investment would be paid off in 12/3.3= 3.6 years.
This is more complicated than that.
One thing we have to consider is how the batteries are charged. You are looking at it like a monolith, but the reality is that these are individual battery projects all with their own CAPEX (and as I said, that $400K/MWh is low) and some may be colocated with solar, while others aren't. So, ones that are colocated, they may be charged by solar that's behind the inverter, so no real cost other than the CAPEX of the whole project (no round-trip charge cost). Others however, are being charged from the grid, so you can't use the discharge price plotted against CAPEX to determine the payback schedule, because the battery has to buy power on the grid, like almost 1GW of it was doing this AM at 1AM, generated by gas. And so then the round trip cost is the cost of the power, plus losses, plus CAPEX, O&M...etc. That can be as high as $0.48/kWh IIRC. When Diablo Canyon is delivering 2,260MW for $0.036/kWh, that's not looking like much of a deal. But then, they've been paying full retail to rooftop solar for years (NEM 1 and 2) so the whole rate situation is already a disaster.
Batteries are also never fully cycled.
As you and I already discussed, the actual discharge right now is ~20GWh, from almost 10GW of installed capacity, or roughly 2 hours at nameplate and this was all procured at considerably more than $400,000/MWh, so there's also the legacy cost of existing projects (which, if I had to guess, is probably around $16 billion).
A $400M say 250MW/1,000MWh (4hr) standalone battery project presumably charged via solar can charge/discharge once a day if being cycled close to capacity (you can cycle it twice if you can charge it overnight using something else, but obviously not solar, so colocated batteries would only be able to do one full discharge unless they are buying power from the grid). If it wants to discharge twice, it can only discharge less than half of capacity during each of the two ramp periods (morning/evening). This is likely the reason we only see battery output in Cali hit about 50% of nameplate, most of them are probably restricting output so that they have capacity to discharge again during the morning ramp (hence only ~1GW charging with gas).
Either way, you have say 800MWh of usable capacity if you aren't trying to max cycle the batteries (which you won't be for longevity). So, that's 292,000MWh/year. If we wanted to pay off the battery in 10 years, we'd need to generate $40 million in revenue every year, above and beyond O&M, so that's a base cost of $137/MWh, which is a lot better than the $300/MWh you used, but still very expensive, more expensive than Vogtle, and Vogtle is generating 2,274MW; 54.6GWh/day for 60+ years while a battery generates nothing, you still have to factor in the cost of generating the electricity to charge the battery into the equation.
Rinse and repeat. Of course the cost of the panels and transmission line upgrades is not included but California has no intention of stopping solar development just for the reason they need battery farms to be able to use the power that is coming on each year. We will see what happens in the next year and decide if they are serious about it.
I sure hope I "carried the knots" correctly. Where is Jethro?
Yep, it's certainly an interesting exercise to watch. And their electricity prices are insane, but it's a potential lesson I guess. What that lesson is, I don't think we'll know for a few more years.