Why don't we think about battery storage for all sources of electricity on a utility scale instead of just renewables?
Taking, at random, Overland Park, Kansas, as an example:


Population 191,278 (2017).
Area 195 km2.
Annual energy demand (per capita) 13,500 kWh = 37 kWh/day. World Bank.
City demand = 191278 x 37 = 7 x 106 kWh/day = 7 x 109 Wh/day = 3600 x 7 x 109 = 25.5 TJ/day.


For pumped storage the formula for energy stored is \$ E = mg\Delta h \$. Assuming we could create a pair of lakes with a &Delta;h of 100 m somewhere nearby then we would need to move \$ m = \frac{E}{m \Delta h} = \frac {25.5T}{9.81 \times 100} = 25.5 \$ million tonnes of water to the upper lake to store one day's worth of energy. That's 25.5 Mm3 in volume.

Making a lake the size of Overland Park we would fill it to a depth of \$ \frac {25.5M}{195 \times 1000 \times 1000} = 130 \ \text m \$ which is deeper than the 100 m we suggested raising the lake to.

The point is that the energy requirements are huge and any storage system would have to be equally huge. You can find battery energy densities on Wikipedia. 

Last time I looked online battery storage was a little below US$200/kWh. That requires an investment of 37 x $200 $7400 just for you and $1,415,457,200 for your city for a one-day battery backup.