Batteries paired with the right inverters solve this fully. Buys you enough time for powering up backup power in the form of a good old steam turbine (gas or coal powered). No need to keep spinning if they aren't needed.

The good news is that batteries are deployed at almost the same scale as solar now on grids world wide. They can respond in more or less real-time to huge fluctuations in supply and demand and smooth out peaks and dips in those.