The Tesla BatteryI was reading up on that a bit more last night as it's due to go online in a few days, Dec1. the realists are analyzing the thing and pretty much laughing at it. What it will apparently do is help a lot with smoothing the grid from the fluctuations of the RE that state now relys on and keeping the voltage and frequency stable as the now blown up power stations did before. If the wind stops at night, that battery will literally last about 30 sec to a min before it's done and the lights go out. The experts are saying that's basically inevitable and pondering the ramifications for the state, the greenwashed gubbermint and Musk and Tesla whom have hyped this up so much.
Leaving aside, for the moment, the politics, greenwashing etc., I don't believe the battery is there to hold the grid up if the wind stops... It's there, as your 2nd sentence says, to smooth the inevitable fluctuations from wind power.
There are innumerable problems with wind power: It's unreliable, unpredictably intermittent and fluctuates by the moment. It also changes voltage and frequency every time the wind changes speed, unless the windmills are governed to a specific speed (which wastes energy & causes wear increasing maintenance costs, blah). Wind power, in short, is about as useful as a fart in a space suit. It has to be converted to DC to get rid of the variable frequency, then put back through "true sine wave" inverters (which are $$$ at domestic sizes, let alone industrial) which are aligned with the grid, and only then can the power be injected. By which time you've binned a load of it. The purpose of the battery is to store a bunch of that DC power, then you take the feed from the battery at a nice constant voltage & current; yes, it still needs the expensive inverter etc. but now you can size it to somewhere close to the battery bank's output capabilities; and unlike cars, as we know electronics prefer to be run pretty close to flat out, so long as you keep them cool.
So, what happens if the wind stops? Same as happens now; the wind farm stops putting energy onto the grid, and something else (usually a CCGT) takes over. Or a BFO diesel engine. Or a coal plant, if any of them are left... but most likely a gas turbine, because they're dead quick to spool up, and pretty efficient. The thing is, the power companies (the organised ones, at least) use some pretty heavy duty weather forecasting to make sure they've got a damn good idea when the wind is going to stop & start, so they've got their spare capacity ready. They won't run the battery flat when the wind stops, because they'll already be replacing its power with something else.
Full disclosure: My dad used to work in the power distribution industry here in the UK, and only retired a couple of years ago, so I do have some clue as to what I speak of.
Wind power, in my & the power industry's opinion, is a crock of shit - but it's been forced on them by the green weenies. Therefore, we (and they) have to live with it. There are better alternatives. For Australia, solar power is the obvious one.... an industrial sized solar farm - either solar-pv, or more likely a molten salt system ala the solar power plant in southern Spain, would provide a pretty reliable output - and provided they account for any likely clouding, a pretty
predictable output (which is one of the most important factors to the power companies). At night, when it's obviously not producing anything, the electrical load is generally lower anyway, so no great loss. And unlike wind, the sun shines every day (even if it's shining on the tops of rain clouds while they're pissing on us....). Here in the UK, where we sometimes don't see the sun for weeks at a time, tidal power makes more sense. We're a small island, and the tides are rising or falling somewhere around the UK 24x7. Tidal systems are also fraught with difficulties - most difficult of all is the corrosive nature of seawater, and the requirement not to mince to many fish - but these can be overcome with suitable materials, and investment. Unfortunately, the lion's share of investment has gone to...... yep, you guessed it. Wind power. Fecking idiots. But that's getting political again, and is an argument for another place, another time.