> That means it would take Europe 3700 years to produce enough batteries to build the batteries we need in the next 50ish years.
It would probably help to show the working here:
600 GWh/year times 3700 years is 2220 TWh, but if you really do need them to last a week, 1000 cycles at one per week means they last about 20 years. As 1000 is an underestimate, this seems broadly correct to me given current battery construction.
However:
First, we will occasionally want them to last a week; most of the time you’d only want a day. This gives us longer to build out whatever solutions, more battery factories or reactors or whatever.
Second, it is very plausible the non-linearity of scaling will reduce costs rather than increase them. After all, that is what has happened so far, and as for workforce there will be a lot of coal miners available to switch to copper etc.
I’m not saying this is certain to happen, just that it’s at least plausible.
Third, my personal favourite combo with batteries is intercontinental HVDC — shift time zones or hemispheres and you don’t need to care about night or winter, but even much shorter links will connect you with a desert with a completely different climate and weather. Every 1 GW of capacity is 1 GW * (your desired storage duration in hours) of storage you no longer need (same for every 1 GW of nuclear, obviously). If we need a week of storage as you suggest, a single 1 GW line would save on 168 GWh of batteries.
I’m only expecting us to do HVDC in the order of length of e.g. EU to Sahara and therefore only limiting our storage requirement to about a day of storage, perhaps even as good as just overnight storage, but the longer the storage period we need the better relative value a planetary scale grid looks like.
(Downside: an antipodal ring big enough for world power use about a decade of worldwide aluminium production, or alternatively five decades of copper[0]. Again, this is why I prefer mixed approaches).
[0] One of my older comments did the maths for just Europe and just to the Sahara, so multiply the “3 months” and “about a year” in the linked comment by 10 for antipodal and another 5 for global electrical demand: https://news.ycombinator.com/item?id=28474201