I recently played around with the data from Germany 2020. I scaled up the existing renewables (only the ones that are scalable - wind and solar, hydro is pretty much maxed out) so that the yearly consumption can be served from 100% renewables. Then I added a battery to carry the overproduction over to the gaps. A 3 TWh battery would still lead to 50 days of empty battery and thus gaps in the power supply.
This is electricity, not Transport and heating. And obviously my approach is simple, no sector coupling effects, no smart grid just scaling up want we have.
3 TWh is 30 million Model S batteries. Even with sodium ion batteries I think this is not really realistic.
I always wondered why the are talking about hydrogen so much, despite the much higher losses you get in that process. Now I get it. I think batteries will be a good solution for single family homes / buildings with solar panel. But the grunt of the grid storage I think will be hydrogen. Especially because during winter, it can produce heat and electricity and the same gas turbines that are already common in German cities.
Either way, it's a big, hard project, but doable if we really want to.