# What's wrong with these numbers:

sonhouse
Science 04 Apr '17 12:17
1. sonhouse
Fast and Curious
04 Apr '17 12:17

they claim 100 mw from 4000 square meters they claim, 43,000 odd square feet which is about one acre. Now the sun produces about 125 watts per square foot times 43K is about 5 mw. Off by a factor of 20 or so.

I wonder if they mean 4000 meters by 4000 meters? But even at 20% efficiency, that would be about 4 GIGAwatts. That doesn't work.

Going with 100 Mw generated, times 5 says that area produces 500 Mw hitting the ground, divide by 1350 (watts per meter squared) and that says 0.6 km squared, 600^2 or about 370,000 meters squared.

Do my numbers work out? 600 meters by 600 meters is my guess as to the area covered by photocells.
2. DeepThought
04 Apr '17 13:59
Originally posted by sonhouse

they claim 100 mw from 4000 square meters they claim, 43,000 odd square feet which is about one acre. Now the sun produces about 125 watts per square foot times 43K is about 5 mw. Off by a factor of 20 or so.

I wonder if they mean 4000 meters by 4000 ...[text shortened]... my numbers work out? 600 meters by 600 meters is my guess as to the area covered by photocells.
Your numbers are ok I think, but this is genuinely easier if you stick to SI units. Insolation is of the order 1kW/m^2, so 4000 m^2 gives about 4 megawatts - ignoring matters of efficiency. It says it can provide 330 MWatts for 18 minutes or 100 MWatts for an hour. Assuming 12 hours of insolation it can get 48 megawatt hours, delivered over an hour leaves us with a factor of 2 to account for.

What you are missing is that the system is a solar powered battery. It's like those garden LED lights that have a small solar panel on them an then come on when it gets dark all on the solar power they absorbed during the day. It stores energy and then releases it all at once to satisfy peak demand. So apart from a factor of 2 or so it's plausible. I don't think they are expecting to use it for more than 5 minutes at a time to cope while other power stations spin up their turbines. The 100 MW for an hour is probably just the capacity of the battery. If they use it daily then it will probably only be able to provide 50 MW for an hour or 330 MW for 8 or 9 minutes, depending on the time of year.
3. 04 Apr '17 14:23
Its interesting that for many years, anti-renewable campaigners would tout lack of storage as a major hurdle for renewables. Yet it turns out that storage solutions are coming online long before renewables have reached the point where storage becomes such a big issue. It turns out that fossil fuel sources benefit enormously from storage solutions too.
4. sonhouse
Fast and Curious
04 Apr '17 14:372 edits
Originally posted by DeepThought
Your numbers are ok I think, but this is genuinely easier if you stick to SI units. Insolation is of the order 1kW/m^2, so 4000 m^2 gives about 4 megawatts - ignoring matters of efficiency. It says it can provide 330 MWatts for 18 minutes or 100 MWatts for an hour. Assuming 12 hours of insolation it can get 48 megawatt hours, delivered over an hour le ...[text shortened]... e able to provide 50 MW for an hour or 330 MW for 8 or 9 minutes, depending on the time of year.
The last part of my post WAS in SI, and what hits the ground at best is 1350 watts per square meter so your numbers are off by 30 odd percent. But we are both in the same ballpark.

Oh, I see your point about it having to provide that level of power for only a few minutes at a time, that really lowers the amount of power coming out of the cells, only building up energy put into the batteries, that is the real source of high power.

4000 square meters times 1350 times 0.2 would give about 1 megawatt which after 8 hours would be 8 megawatt hours. Ten days of that = 80 megawatt hours, and a month of that would be 320 megawatt hours. So working backwards if it only wants 320 megawatts for 18 minutes, ~1/3 hour, then ten days would give that. Still, it seems to be way overpriced at one billion US. Most of that would be the price of the batteries seems to me.

So I guess they hope they get ten free days without power problems, eh.
5. DeepThought
04 Apr '17 15:16
Originally posted by sonhouse
The last part of my post WAS in SI, and what hits the ground at best is 1350 watts per square meter so your numbers are off by 30 odd percent. But we are both in the same ballpark.

Oh, I see your point about it having to provide that level of power for only a few minutes at a time, that really lowers the amount of power coming out of the cells, only buil ...[text shortened]... atteries seems to me.

So I guess they hope they get ten free days without power problems, eh.
That 1,350 W/m^2 figure is insolation at the top of the atmosphere, according to Wikipedia [1] it's more like 1.1 kW/m^2 at the earth's surface.

6. 04 Apr '17 15:34
The article says there will be 3.4 million solar panels. If my calculations are right, then spread out over 4000 sq metres, each panel has to be slightly less than four centimetres on a side.
The clue comes from the source article:
Which says the battery will be 4000 square metres. That's the battery only, not the solar panels.
7. sonhouse
Fast and Curious
04 Apr '17 15:521 edit
The article says there will be 3.4 million solar panels. If my calculations are right, then spread out over 4000 sq metres, each panel has to be slightly less than four centimetres on a side.
The clue comes from the source article:
http://www.adelaidenow.com.au/news/south-australia/huge-solar-and-battery-project-to-be-built-by-lyon-group-near-roxby-down ...[text shortened]... hich says the battery will be 4000 square metres. That's the battery only, not the solar panels.
It sounded kookoo from the numbers given. That's funny, each panel 1600 mm^2. Not likely🙂

So suppose each one was half meter by 1 meter. 3.4E6^.5 says about 1800 by 1800.

So that would be 1.8 kilometer by 0.9 kilometer. That makes much more sense.

And they are talking 100 megawatts 24/7 if the sun shone that long. or about 700 megawatthours per day sounds like.

I imagine it would be more like 2 km X 1 km maybe bigger than that. Allowing for spacing between panels. So 100 megawatts would be roughly 30 watts per panel. Sounds a bit low for a panel, I thought they put out 100 watts per panel or so.
8. DeepThought
04 Apr '17 16:29
Originally posted by sonhouse
It sounded kookoo from the numbers given. That's funny, each panel 1600 mm^2. Not likely🙂

So suppose each one was half meter by 1 meter. 3.4E6^.5 says about 1800 by 1800.

So that would be 1.8 kilometer by 0.9 kilometer. That makes much more sense.

And they are talking 100 megawatts 24/7 if the sun shone that long. or about 700 megawatthours per d ...[text shortened]... watts per panel. Sounds a bit low for a panel, I thought they put out 100 watts per panel or so.
The power generation capacity is 330 MW, the batteries can supply 100 MW. So that accounts for your factor of 3. Each "panel" (I think they mean module needs to be able to supply about 100 Watts. If each panel is 1 square metre then they have 3.4E6 square metres which comes to 1.84 km per side. The 1 square metre figure is a little high for 100 watts, but they'll need some space between the panels for access and so that the rows aren't in each other's shadows if they are tilted to always face the sun. At 2km by 2 km it makes sense. I wonder if a dopey hack took 4 square kilometres and "converted" into square metres by multiplying by 1,000?
9. 04 Apr '17 16:461 edit
https://en.wikipedia.org/wiki/List_of_photovoltaic_power_stations

They range from 5 to 64 sq km per MW

Its partly a matter of spacing, many large solar farms are less than half covered with panels, assuming the measurements are an approximately fitting rectangle.
10. sonhouse
Fast and Curious
04 Apr '17 17:34
Originally posted by DeepThought
The power generation capacity is 330 MW, the batteries can supply 100 MW. So that accounts for your factor of 3. Each "panel" (I think they mean module needs to be able to supply about 100 Watts. If each panel is 1 square metre then they have 3.4E6 square metres which comes to 1.84 km per side. The 1 square metre figure is a little high for 100 watts ...[text shortened]... dopey hack took 4 square kilometres and "converted" into square metres by multiplying by 1,000?
It said 330 Mw for only 18 minutes. But that sounds like a battery number. You have to use the number of hours you get sunlight to be able to compute a watt hour number for a cell panel. So 330 Mw for 18 minutes is about 100 Mw stored in the batteries. I think. They really screwed up the reporting.