Considering problems as nuke does have them I wonder about wind backed up by gas but that can't last for ever.
One idea is to generate hydrogen from surplus electricity (very easy).
Recombine it in a fuel cell (or even a turbine) to generate electricity in time of need.
Like market-stabilising intervention stocks, it's self financing, and even profitable (buy it when it's cheap, sell it when it's expensive)
I suppose it might even be possible to create hydrocarbons using extracted CO2, which would be carbon-neutral.
Doubtless there are billions being spent on research. It will be interesting to see some commercial solutions. Imagine if you were Shell or Exxon and got it right.