I think the solution will come from storage but also from a massive grid-wide ability to shed non-critical loads on-demand. The current grid is built on early 20th century principles, before we had real-time digital communications.

As a though experiment - imagine a 19th century world suddenly getting all of our current digital tech and wind farms and solar power - there would be no point in trying to create a "static" grid where producers and consumers weren't communicating with each other. Every consumer would negotiate power availabity based on momentary price.