I'm no expert, but I did find this[1] recent (May 2020) information posted by the U.S. National Renewable Energy Lab that indicates that non-inverted power sources (such as solar and wind) may be able to produce synthetic current frequency in order to maintain grid stability. This technology can be included within large-scale storage batteries.

In addition, these inertial techniques ('fast frequency response') are digital and as a result could provide lower-latency and higher-accuracy response compared to mechanical approaches.

If I understand that correctly, then eventually these approaches could phase out the need for rotational inertia (no pun intended).

[1] - https://www.nrel.gov/news/program/2020/inertia-and-the-power...

Edit: adding a useful quote from the linked report, below:

"In the United States, the Texas grid (the Electric Reliability Council of Texas, or ERCOT) is the smallest of three main grids. ERCOT’s relatively small size, combined with its large wind deployment, has required it to compensate for declining inertia by adopting several low-cost solutions, including allowing fast-responding noncritical loads to respond to changes in frequency. This has enabled ERCOT to achieve increasingly high instantaneous wind penetrations—reaching a record of 58% in 2019—while maintaining reliability."

If you're building a grid-scale battery storage system, isn't it a relatively straightforward engineering problem to emulate the inertia of a flywheel?

I would be much more concerned about batteries' ability to respond on the days/weeks/months scale than the milliseconds scale.

What challenges do you foresee in responding over days/weeks/months?

The challenge is just having enough raw capacity to meet demand using intermittent renewable sources. Weather varies on the scale of days/weeks, and winter is cold because of limited sunlight. What energy source will we use to stay warm all winter?

Make hydrogen, store it underground, and have enough combustion turbines available to back up the grid. A simple cycle combustion turbine power plant is about 5% of the cost of a nuclear power plant, per unit of power output.

That seems physically plausible, though it would be a lot easier if we could make methane efficiently, because we already have the infrastructure to transport and burn it.

The problem then is where do you get the carbon to make the methane. Ammonia might be a possibility, if it can be kept from escaping (toxic) or dissolving in underground water.

Yet another possibility is underground storage of high temperature heat, artificial geothermal, if you will. But it would have to be extractable with cheap equipment. Perhaps it could be used to superheat hydrogen for injection into those combustion turbines.

Making hydrogen via electrolysis is very lossy though.. it's only worth it if you have nothing else to burn the power on.

Or if you need a chemical energy store with very low $/kWh of storage capacity, for long term or rarely used storage. There, the efficiency penalty is much less important than it would be for rapidly cycling diurnal storage.