The grid currently has almost zero storage. Saying we should build several times as much storage seems to suggest we need a lot of storage. But, it’s relative to a very small baseline. 1 hour of storage would be a vast increase, but it’s 1/10th the cost of 10 hours of storage. So, you need an accurate estimate to work from.
Further, the ideal amount of storage is heavily influenced by price and cost of production. The grid is a huge complex system and simple models don’t provide good answers.
Power generation must match demand very closely and in real time.
Demand is very predictable. As for supply, the generation capacity of fossil or nuclear power plants is known ahead of time and can be managed to provide power in a predictable fashion. These plants don't randomly begin generating more power when the wind blows or when the clouds part or the sun rises and they don't randomly generate less power when the winds die or the clouds arrive or the sun sets.
You don't need storage mechanisms with this type of generating capacity. But if you try to shift significantly towards solar/wind to provide power you now have an unpredictable generating system. That can be mitigated to some extent by adjusting the output of the traditional plants but the more your generating capacity is moved towards the unpredictable renewables the harder it becomes to keep the balance.
Even if you manage to keep things balanced, you can't decommission the old plants because sometimes (dark windless nights), your renewables aren't going to generate any power and most or all of the power has to come from those plants you were trying to replace with the renewables.
The only way around this is to come up with some sort of storage mechanism that can react quickly to the varying supply of renewables to maintain a smooth/constant power supply. Which wouldn't necessarily be a problem except for the fact that we actually know how to build high-capacity cost-effective storage mechanisms.
These number should are off the top of my head but should be reasonable.
Suppose, you want to supply an island with nuclear power. Lowest recorded useage at was 1GW of power and the peak recorded daytime use is 3.5KW of power. Average annual power useage was 2GW and peak daily useage was 2.4 GW.
You can buy nuclear power in 0.25 GW increments with 95% of the cost being there of the power is used or not.
Nuclear costs 149x per GW, Wind 45x, solar 40x average daily output. Nuclear needs to be offline 4 days out of the year for maintenance, wind and solar provide a minimum daily output of 40% their maximum.
Now, without lot of storage nuclear needs 3.5GW even if one plant is offline at a minimum but preferably some cushion if future needs are over 3.5GW. Thus we need 4GW of Nuclear for 596x to be safe. (Larger grids need less cushion, but still need to plan for multiple GW or Nuclear to be offline.)
Wind and solar need some storage, but even using the lowest values of 40% average output that’s 45 /.4 x 3.5GW = 400x.
Though if we had some storage we could also drop Nuclear to 2.4GW + safty factor to get closer to 400x. But remember we now produce 2.5x as much solar/wind on the average day for the numbers to get close, and we still need to use storage for nuclear. Further, those assumptions are unfair as in practice solar and wind minimums don’t occur on the same days as maximum power usage.
