The solution is to deregulate the market and allow multiple companies to buy and sell electricity. The problem here is not an over supply but poorly regulated demand that causes energy to be priced higher than is justified; mainly to protect expensive sources of energy such as coal and gas plants.
The basic issue is not that there is no demand but that it is unevenly spread. People turn on their ACs when they get home after work. Peak demand is in the evening when the sun is about to go behind the horizon. Peak supply is in the late morning and early afternoon when people are at work.
So, all you need is tuneable demand. Say you had a web service that simply announces the current price of electricity that updates in real time based on your production capacity and a whole bunch of things that can turn themselves on/off based on that price. Whenever there is excess demand it just continues to drop that price until demand picks up. Now say you have an apartment complex with a lot of batteries in the basement and a bit of simple electronics that controls the charging behavior based on the price several energy providers (why limit to one). Now basically you have an energy sink that charges cheaply that automatically picks the cheapest provider.
Now imagine that battery has some overcapacity that can be sold back to the grid when prices are highest (aka. demand is high). Now you have an apartment building that buys energy when it is cheap and sells energy when it is expensive and it has enough capacity to serve its own needs.
Add EVs to the mix and battery to the grid technology and you have a mobile battery capacity that when it is not driving around can be plugged in to act both as an energy source and sink as well.
Now make the rest of the energy available to industrial users that can install their own solar panels and you have even more supply and demand.
The key bottleneck in this system is the current oligarchy that controls prices: the existing energy companies. They make the most profit when prices are high. They don't mind buying in some excess capacity cheaply but they have no incentive to do that when they don't need it. And since they control the market, there's nobody else to sell it to. Worse, since they have fixed cost associated with legacy plants, they have to keep prices high to prevent those becoming loss leaders. The whole system is geared towards protectionism rather than efficiency. Once you create an open market for energy, that's no longer sustainable.