First, Texas utility Oncor commissioned a study (pdf link – The Value of Distributed Electricity Storage in Texas) of whether it would be cost-effective to deploy storage throughout the Texas grid (called ERCOT), placing the energy storage at the ‘edge’ of the grid, close to consumers.
The conclusion was an overwhelming yes. The study authors concluded that, at a capital cost of $350 / kwh for lithium-ion batteries (which they expected by 2020, but which Tesla has already beaten), it made sense across the ERCOT region to deploy at least 15,000 MWh of battery storage. (That would be 15 million KWh, or the equivalent battery capacity of nearly 160,000 Tesla model 85Ds.)
The study authors concluded that this additional battery storage would slightly lower consumer electrical bills, reduce outages, reduce the need to build added capacity (by shifting the peak, much as a home battery would), and similarly reduce the need to build additional transmission and distribution lines.
You can also see that at a slightly lower price of storage than the $350 / kwh assumed here, the economic case for 8,000 MW (or 24,000 MWh) of storage becomes clear. And we are very likely about to see such prices.
8,000 MW or 8 GW is a very substantial amount of energy storage. For context, average US electrical draw (over day/night, 365 days a year) is roughly 400 GW. So this study is claiming that in Texas alone, the economic case for energy storage is strong enough to motivate storage capacity equivalent to 2% of the US’s average power draw.
ERCOT consumes roughly 1/11th of the US’s electricity. (ERCOT uses roughly 331,000 GWh / year. The US as a whole roughly 3.7 million GWh / year.) If similar findings hold true in other grids (unknown as of yet), that would imply an economic case fairly soon for energy storage capacity of 22% of US electric draw for 3 hours, meaning roughly 88,000 MW or 264,000 MWh.