Everyone seems to be assuming that we retain the status quo ie generation capacity =~ supply.
The more likely outcome is generation capacity >> supply, especially if renewables are used. This is because renewables can have poor yield, so if you want a nearly pure renewable grid you will need many times more capacity. For the UK, think something like 150GW wind and 20-30GW solar. (Current capacity is about 25GW wind and 14GW solar - though much of the solar capacity is domestic/workplace installs which aren't strictly suppliers.)
The *side effect* is at many times during the day there will be gigawatts of extra capacity available that is otherwise going to be thrown away, so the cost per kWh will plummet. This will create many times in the day when it is very cheap in the day to use energy and times in the day when it is much more expensive as supply is constrained and we begin to use storage (batteries, hydrogen, pumped) or go to backup fossil fuels (probably with carbon capture)
This is what the National Grid and other country's network distributors are planning on, it is not a matter of if but when we have this. At the current rate wind power is being installed we are adding ca 3-5GW per year and the rate has historically been exponential, so this is likely to be the situation in a decade or two.
Hence the push for smart metering because without smart meters you cannot dynamically price energy, and there is no way to shift load around, the Grid would love to be able to tell your dishwasher to run at the best time, and your car charger. There is a Dutch company that will pay you a small amount every month if you let them control when your car charges, as they can use this to reduce demand charges that the grid would otherwise face.