ABOUT 90 or so of South Australia's Hornsdale/Tesla batteries.
That's how many it would take to keep Tomago Aluminium smelter running for a night, after a day in which it had been run by a renewables powered grid.
At about $100 million a battery, that's $9 billion.
And as Tomago accounts for just 10 per cent of NSW electricity demand, we would need 900 of them to keep the whole state running for the 12 hours the sun doesn't shine.
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And as you can't use power twice, the power going into storage has to be on top of the power being used, so the grid has to produce 24 hours worth of electricity in 12 hours.
And as just 20 per cent of the state's power comes from renewables, including Snowy Hydro, that means five times present capacity to replace fossil fuels. And then double that, making 10 times all up, to fill the batteries and meet the daytime load.
And then there's Queensland, and Victoria and South Australia and ...
OK. That scenario is a gross simplification, and there are other methods of renewable generation beyond solar.
But the mathematics are inescapable, and no amount of optimism about a green future powered by clean hydrogen and pumped hydro can be allowed to obscure the basics.
I wrote about some of these issues in a piece on Thursday, but with Rio Tinto burnishing its pre-Glasgow environmental credentials by announcing its plans to decarbonise its iron ore and aluminium operations, I thought it was worth a further poke around, given the prominence of Tomago Aluminium to Hunter industry in particular, and the energy debate in general.
This week's investor presentation - available on Rio's website - says the company intends spending $US7.5 billion ($10 billion) in halving its Scope 1 and 2 greenhouse emissions by 2030. That's everything within its direct control: Scope 3 emissions are those created in the use of its products.
Rio's plans go across its portfolio of resources but much of the focus is on aluminium, given its dependence on massive amounts of electricity.
As my colleague Matthew Kelly reported yesterday, Tomago Aluminium chief executive Matt Howell says Rio's announcement is in line with the work Tomago is already doing behind the scenes to ready it for its next power contract, starting in 2029.
Although Howell describes himself as "an eternal optimist" he also says that the world's carbon-intensive industries face "existential threats" if the world cannot find methods to store electricity in far, far greater volumes - and at commercially manageable prices - than is the situation today.
Hence my opening calculations, which continue at the foot of this column.
As I wrote on Thursday, Europe is in the grip of a power shortage, with skyrocketing prices simply the tip of an iceberg.
One of many consequences is a decision by Swiss-owned Nyrstar to cut production at its three European zinc smelters by up to 50 per cent.
"Significant increases in the cost of electricity in recent weeks, and the cost burden of carbon emitted by the electricity sector which is passed on to industrial and domestic customers, mean it is no longer economically feasible to operate the plant at full capacity," Nyrstar said.
The company also owns the Port Pirie lead and silver smelter in South Australia.
Energy markets around the world are gyrating wildly for a range of reasons but Europe's determination to shut down coal-fired and nuclear stations before equivalent replacement renewable capacity can be installed is a major factor.
The NSW power grid looks like calm waters beside such instability but Howell says Tomago has had its supply interrupted for more than 50 hours so far in 2021 under its contract with AGL.
Howell stresses that his concerns are not with AGL: he says the contract interruptions are an unintended consequence of power price spikes, which are "exacerbated by intermittent renewables and a distinct lack of shortage".
Now, to return to the Big Battery calculations, Rio's investor seminar this week said Tomago's demand was 960 megawatts or 8.4 terrawatt-hours (TWh) a year.
Hornsdale says the South Australian operation has a rating of 100 megawatts and 129 megawatt-hours.
In 12 hours of darkness, Tomago would use 960 x 12 = 11.5 TWh.
Dividing that figure by battery capacity gives us 89 - let's call it 90 - batteries to get through the night.
A number in line with the oft-quoted statement that the battery would only run the smelter for eight minutes: 60 minutes divided by eight gives 7.5 multiplied by 12 hours equals 90.
Statewide, the Clean Energy Council says renewables including Snowy Hydro produced 14.3 TWh or 21 per cent of last year' 68.1 TWh of electricity output.
Therefore you'd need five times the renewables to produce the full amount.
But to supply the daytime demand and fill the batteries for night time means twice the capacity, or about 10 times the present output.
Yes, it's a very rough model, but it does reveal the proportion of the task.
And I'd argue it's a failure to appreciate the basic maths that has helped put Europe where it is today, in the grip of an energy crisis.
Something we don't want here.
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