The article unfortunately equivocates about the meaning of "long-duration", which could mean "a few hours", "a few days", or "a few months". It mentions "four hours", "an eight-hour buffer", "up to 100 hours," and "seasonal energy storage". The first three of these are indeed required; the last is not, which is fortunate, because it is inherently orders of magnitude more expensive.
Conflating them in this way is profoundly unhelpful: it's like writing an article about a requirement for "high-speed vehicles" including both a Kia Forte (top speed 200 kph) and an SR-71 (top speed 3500 kph). But the ≈40 hours we need is further from being the 4000 hours provided by seasonal thermal storage than the Kia is from being an SR-71, which can, after all, only outrun the Kia by a factor of less than 20, not 100. The reporter can only be hoping to get away with this because of the unfamiliarity of grid-scale energy storage.
Absent cost-competitive geothermal, nuclear, or kite energy (or reliance on intercontinental power transmission), decarbonization of grids definitely requires grid-scale energy storage for a few hours, and it probably requires storage lasting a few days, because even over large geographical areas there are large lulls in wind and solar. The sun doesn't shine all day and the wind doesn't blow all night.
But it almost certainly doesn't require seasonal energy storage, because you can overprovision generation capacity sufficiently to provide enough essential power every week of the year. A consequence of such overprovisioning will be that in the high season (either sunny or windy, depending on your power mix, but probably ultimately sunny) you can generate several times as much energy as the essential minimum, so power-hungry applications will benefit from cheap or free energy in the high season.
This is supported by the article's summary of van Gendt et al.'s report: their "most cost-effective path to a world with net-zero emissions by 2040" has 85–140 TWh of storage at a power of 1.5–2.5 TW. Dividing the numbers, that's 34–94 hours. That's energy storage for a few days, not a few months.
Still, it's interesting to consider the ways we could build a seasonal energy store, even if it isn't essential to decarbonizing the grid.
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Unfortunately, the Economist's "All charged up" table of energy storage methods doesn't mention thermochemical energy storage (TCES), compressed gas, or even lithium-ion batteries.
Compressed gas, which they do mention at length in the article, is ridiculously inefficient without some kind of thermal energy storage, and the two thermal energy storage technologies they do list are not useful for seasonal storage — latent heat, i.e., phase change materials, and sensible heat, the kind of heat that makes things hot.
So TCES is a crucial enabling technology for possible seasonal compressed-gas storage. As with electrical storage in flow batteries, TCES can provide thermal energy storage for as long as you like if your tanks are big enough, so in theory it's vastly superior for seasonal thermal stores, and you'd need seasonal thermal stores for efficient seasonal energy stores with compressed gas.
TCES has an enormous advantage over currently-available flow batteries in the cost of the necessary materials. We'll see if the Form Energy gadget, which I hadn't heard of, pans out; that would change the equation radically, because only sand is cheaper than iron and salt. But TCES mineral feedstocks like carnallite, muriate of lime, quicklime, and bischofite are nearly so.