The world’s largest demonstration plant for a new kind of renewable energy storage is up and running in the west of the China. Called liquid-air energy storage (LAES) the plant uses renewable electricity to compress air to extreme densities until it turns to liquid. It can then be rapidly released to power a turbine and discharge that green energy back into the grid.
That is all besides the point though in a process where H2 is both produced and consumed, as long as that process is competitive with other storage solutions. It appears it isn’t, even compared to air compression, as I found out in the meanwhile. However there is no technological reason why one would need some carbon source for producing H2. Electrolysis from water is a well established process.