But how is this ever possible? How can we produce more power than we consume? As far as I know, it is impossible to store electricity directly. You can of course use some processes like electrolysis to decompose, for example, water into oxygen and hydrogen and then store hydrogen but it is more of a sci-fi movie than reality yet. If you actually mean that we can produce more than we now consume, I don't think it justifies mining because it would still be a waste of resources.
Imagine that you have a hydroelectric power plant that produces 1000 MW (has 4 250 MW) turbines and the whole thing is supposed to supply neighboring cities and small towns. The combined use of power during the day is 800 MW, which is the load the power plant constantly working under. Since turning off one turbine would make it drop to 750 it's forced to run all of them constantly, which means that it is producing 1000 MW anyway, even if nobody is using it. It's a common thing worldwide there's always some margin of power that is being supplied but not used. If somebody starts to it will only mean more money for the power company.
Load balancing comes into play at that time.
In my country we have them all, nuclear, hydro,gas, sun and wind.
When there is simply too much power generated from free sources gas and coal are turned off.
Then pump storage starts.
Besides, there is nothing "local", and certainly not at that scale. You don't build a 4000 MW hydroelectric plant for the neighborhood, that thing is connected to the grid and might deliver power to god knows what town a thousands miles ways.