You're using the instantaneous numbers, which matters for the peak (because if you hit 48 GW for just one hour you still have to meet the demand) but not the trough (because having overcapacity for a negligible number of hours a year is fine). The real base demand number for California is ~24 GW:
That is the average base demand over a year. Meaning for about half the year it will be less and you have to shut down parts of the nuclear fleet.
Either way, solving a 24 GW or 35 GW on top of ~20 GW something base is about as easy. Nuclear simply does not fit modern grids.
> Nobody is going to do this. It doesn't make sense to build entirely nuclear plants. It does make sense to build some more than we have now.
Exactly. Which is why nuclear power does not fit modern grids, because they will be required to shut down. As is seen time and time again in Europe when no one wants their expensive energy.
Then it's not clear where you came up with 13 GW, which is inconsistent with the ~24 GW from the Department of Energy.
> Either way, solving a 24 GW or 35 GW on top of ~20 GW something base is about as easy.
Needing 48GW instead of 24GW would literally double the cost, on top of doubling the cost of renewable generation since you'd need an average of 48GW of that instead of 24 to avoid regular use of a backup system which is presumably fossil fuels. That is not a small difference.
> Which is why nuclear power does not fit modern grids, because they will be required to shut down.
There is no point at which they shut down. They provide baseload. You get 24 GW from nuclear, which is the minimum load on the grid. If you also get something from renewables at this time, that's when you charge your batteries for later. This won't get you a week but allows you to do peak shaving. If the load is 48GW and you get 24GW from nuclear and 24GW from renewables, everything is fine. If the load is 48GW and you get 24GW from nuclear and anything less from renewables, now you discharge the batteries.
And then you only need 24 GW of peaker plants in the event that the batteries are dead and current load exceeds current generation.
https://www.eia.gov/todayinenergy/detail.php?id=42915
Which is a pretty sizable fraction of 48 (not that 16 wasn't).
> The other option would be having more nuclear plants and turning them off for large parts of the year.
Nobody is going to do this. It doesn't make sense to build entirely nuclear plants. It does make sense to build some more than we have now.