Ow Electricity (energy) could be saved by producing Hydrogen and the use of an Fuel Cell> Science Project

I need a written report about an idea i had explained with chemical formulas and how and why it works etc. feel free to discuss it, i would pay for extras which benefit for the projects success presentation at the end.

My idea for the science Project.
I had the Idea that when at night the big companys shut down their big energy consuming machines the energy municipals can not easily shut down their energy chain energy gets lost which can not be used ( i am pretty sure it is like that ) so my idea is that you could use this lost energy for an Electrolysis to produce hydrogen which could be storage under earth and at day time used true an fuel cell to get it in for the energy need at day or sth. else cars etc.
I need to express it how this could work in chemical meaning etc. how it possible could work.