The problem with many large industrial processes is that they cannot be run that way. Think a steamcracker for example: Shutdown takes days, starting up as well. It's so (energy) hungry that its cost-efficient to leave all parts in the chain running if one fails and just burn the resulting light oil. (Makes for a spectacular flame on the skyline). Aluminum processing falls in the same category.
There are other processes where this is possible (steel smelting via electric power for example) and where this is already done. Those plants usually run at night and consume large amounts of the base load. The issue with solar/wind-energy is that the availability may fluctuate within very short time frames - sometimes minutes - so that you cannot use this.
In a smaller scale this works the other way round. There are some small-scale fuel-powered plants that can be used to heat/cool a house or a block as well as produce electricity and those power up when electrical power is needed and store the heat for when it's needed (it's somewhat easier to store heat). This can be used to cut off some of the load spikes.
I know very little about heavy industrial processes, but probably in many cases there are alternative processes that are not optimal in the case of continuous power, but with fluctuating power supplies they might become viable.
A possible alternative would be running some process which produces some valuable output, which can be stockpiled. What I'm thinking about is that rather than trying to store energy, one could rather make e.g. PET bottles (probably a stupid idea). Then if there is too many PET bottles, they are burned for energy, but otherwise they are slowly consumed.
What about making a small piece of some ridiculously grand project, slowly, little by little. For instance, building a train tunnel across the Atlantic with robots that only run when power is available? The bad points with that is that it will only be useful when ready, but perhaps a similar kind of mining operation? Dig a little deeper every time energy is cheap enough.
Surely most industrial operation would not work, because the startup costs are large, making the returns convex in the size of investment. But maybe there are concave operations? Many human operated tasks are. It is easy to make a good meal for 4 people, but much more difficult for 40. With robotics at least, one would think that operations with similar properties would be available.
There are other processes where this is possible (steel smelting via electric power for example) and where this is already done. Those plants usually run at night and consume large amounts of the base load. The issue with solar/wind-energy is that the availability may fluctuate within very short time frames - sometimes minutes - so that you cannot use this.
In a smaller scale this works the other way round. There are some small-scale fuel-powered plants that can be used to heat/cool a house or a block as well as produce electricity and those power up when electrical power is needed and store the heat for when it's needed (it's somewhat easier to store heat). This can be used to cut off some of the load spikes.