Solar power calculations, please help!

According to:
http://www.fwi.co.uk/business/hampshire-solar-farm-is-uks-largest.htm
48 MW solar farm is being built.
No info on that page, as expected. Look at:
http://renewables-map.co.uk/details.asp?pageid '54&pagename=Southwick% 20Solar%20Farm
for more details:
Solar Panels: 50000 Capacity: 40 MW Acreage: 200
More info:
200 acres = 80.9 hectares = 809,371.284 square metres.
40 MW from 809,371.284 square metres.
40,000,000 / 809,371.284 = 49.42 watts per square metre.
I am aware that this will be the avaerage over day and night, and over the year. I am aware that solar insolation is very variable. But 49 watts per s quare metre? Can that really be right? Is the 200 acres the site size, or t he combined size of all the panels?
I assume I have calculated something wrong. Can any one help?
Thanks in advance,
David Paste.
Background:
A not-particularly-technologically-minded friend was pondering whether or n ot an electric train covered in PV panels would be viable. I said no, assum ing an easy to calculate figure of 10 MW for a Eurostar (wikipedia has valu es ranging from 3.4 MW to 12.2 MW). I was assuming that the *avaerage* year ly insolation for the UK was 1kW per square metre, garnered from:
https://en.wikipedia.org/wiki/Insolation
so for 10 MW, you'd need (10,000,000/1,000 = 10,000 square metres = 1 h ectare = 2.47 acres of panels for one train.
A rough estimation for BR Class 373 on the Eurostar gives about 1,000 squar e metres of roof on a 20 car set. Or 1 MW at theoretical maximum. But it wo n't be, will it. Curved roof, adverse weather, panel efficiency, all of tha t.
I know that PV panels are not 100% efficient at converting light into leccy , but I was still staggered to see that 49 watts per square metre was the a verage figure used for that solar farm.
And so surely I've done something wrong.
Thanks again.
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On Wed, 15 Jul 2015 06:27:49 -0700 (PDT), David Paste

I'm not sure whether you think your result is too low or too high. The following suggests it's way too high, by up to a factor of 10!
David MacKay has a chapter on solar power, in particular solar farms. http://www.withouthotair.com/c6/page_38.shtml et seq.
Harry will no doubt tell you MacKay talks 'bollix'. But MacKay's credentials are impeccable, unlike Harry's, which are not. http://tinyurl.com/ogwty9z
MacKay estimates (p.38) that the _average_ raw power of sunshine per m^2 of sunshine on flat ground in the UK is 100W. That average takes account of day/night variation, winter/summer day-length variation, geographic variation and sunny/cloudy days. It's a ball-park figure.
In Figure 6.6, page 40, he has a picture of solar panels near Santa Cruz in California. The estimated output is 19W/m^2, a little less than half your figure of 49W/m^2. But California is a sunny place, they tell me. His Figure 6.7, page 41, has a picture of a solar farm in Bavaria, where the average power output is expected to be 5W/m^2, say one tenth of your figure.
In the text on page 41, he notes uses a solar panel efficiency of 10%, typical of the cheaper, mass-produced panels, as it is the cheaper ones that are likely to be most widely used, but that expensive ones may have an efficiency of 20%. His book was first published in 2009. Efficiencies and panel costs may be a little better today, but I suspect not a lot.
--

Chris

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David Paste wrote:

Comparing with one near me
<http://www.larkenergy.co.uk/news/2013/04/09/uk%E2%80%99s-largest-solar-farm-puts-wymeswold-on-the-map/
Panels: 130,000 Capacity: 34 MWp Acreage: c150
Apart from your example clearly using somewhat larger panels, the figures appear compatible.
What the site you quote has done wrong is failing to follow the convention that you quote output power as Wp, ie peak output.
A little closer to home, the panels on my roof total 3.64 kWp. If I divide output to date over total hours, which is not something I have previously looked at, I get an average over a period of 4.6 years of around 400 W, which is about 11% of peak output.
Chris
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Chris J Dixon Nottingham UK
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On Wednesday, 15 July 2015 14:27:53 UTC+1, David Paste wrote:

k%20Solar%20Farm

e year. I am aware that solar insolation is very variable. But 49 watts per square metre? Can that really be right? Is the 200 acres the site size, or the combined size of all the panels?

not an electric train covered in PV panels would be viable. I said no, ass uming an easy to calculate figure of 10 MW for a Eurostar (wikipedia has va lues ranging from 3.4 MW to 12.2 MW). I was assuming that the *avaerage* ye arly insolation for the UK was 1kW per square metre, garnered from:

hectare = 2.47 acres of panels for one train.

are metres of roof on a 20 car set. Or 1 MW at theoretical maximum. But it won't be, will it. Curved roof, adverse weather, panel efficiency, all of t hat.

cy, but I was still staggered to see that 49 watts per square metre was the average figure used for that solar farm.

I have a 4Kw setup. I do an average of 4000Kwh/year. (West Midlands in almost ideal situation.)
I think the figure you mention refers to the whole area of the solar farm n ot the actual panels. The rows have to be spaced to avoid shading. A Kw is usually reckoned to need about 5 square meters of actual panel. This is the peak output usually written as Kwp.
Efficiency is about 11-14% for silicon panels depending if they are mono cr ystaline or poly crystaline. (The crystal junctions cause losses.)
Apparently there are more efficient technologies in the pipeline.
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Not that this will help much. You still can't get more than 100% efficient, and even that is not actually possible anyway.
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On 7/15/2015 5:02 PM, harry wrote:

So 456W average.... How many square metres doe you panels cover?
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Cheers,

John.
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On Thursday, 16 July 2015 13:43:26 UTC+1, John Rumm wrote:

About 20.
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On 7/17/2015 7:39 AM, harry wrote:

So ~23 W/m^2
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Cheers,

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Thanks all for the replies.
The amount oelectricity available seems dismally small.
How would simply harvesting the photons to heat water and running a stirling engine compare?
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On Wednesday, 15 July 2015 22:38:50 UTC+1, David Paste wrote:

Solar steam is much more efficient than PV.
NT
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On 16/07/2015 04:42, snipped-for-privacy@gmail.com wrote:

Probably not by the time you have turned it into electricity.
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On 16/07/2015 14:19, newshound wrote:

Correction, a focussing system generating steam at a few hundred degrees C could be more efficient, but if you are looking to get a few hundred watts off a roof-mounted collector you are going to need significantly more complex technology.
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On Thu, 16 Jul 2015 14:24:41 +0100, newshound

Generally speaking, the higher the temperature difference between input and exhaust in any heat engine, the more efficient it is. That is why most heat engines (gas turbines, steam turbines, etc.) are run with as high an input temperature as possible. Steam turbines in power stations use superheated steam, for example, whether that steam is generated in a conventional boiler of from a solar array. But the sort of heat collected in a domestic roof-top array is essentially low-grade heat, and the efficiency of converting that heat into useful energy is low. It's OK for domestic heating or hot water, but the cost of converting that heat to useful electrical energy usually outweighs the value of the energy. But there's quite a lot of work going on to develop Stirling engines to make use of such heat, but whether any are yet commercially viable, I don't know. See http://tinyurl.com/pjjjnae
--

Chris

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On Wed, 15 Jul 2015 14:38:46 -0700 (PDT), David Paste

Hence the very and depressingly large areas of countryside taken up by solar farms for only modest return.
If you believe Harry's figures, he has a 4kW array, and estimates you need ~5m^2 of actual panels per 1kW, i.e. from which you deduce he has about 20m^2 of panels. He says he gets about 4000kWh/yr, i.e. 4000000/365/24 W =~460 W from 20m^2 of panels, or ~ 23 W/m^2, a lot better than Bavaria, and even better than California!

MacKay briefly considers solar heating of water, using arrays of thermal panels on domestic roofs and using the heat for domestic purposes only (CH+DHW), rather than to produce electricity. See http://www.withouthotair.com/c6/page_38.shtml and the following page.
A more relevant answer to your immediate question will be in one of the articles on this page http://tinyurl.com/nk5v7lm . Various schemes are proposed, some already up and running, using steerable arrays of mirrors focusing sunlight onto a central steam generator, or long lines of pipe at the focus of linear parabolic reflectors. Molten salt systems hold the heat overnight to allow uninterrupted production of steam. They mostly seem to be constructed in desert areas where sunshine is strong, with long hours of daylight. Probably not for the UK.
--

Chris

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Chris Hogg wrote:

Maybe you would prefer my numbers.
I have 14 panels each 260 Wp, and about 1.8 m^2s, giving 25.2 m^2 overall. As I said earlier, averaged over 4.6 years, the output is 400 W, so that gives around 15.9 W/m^2.
Chris
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On Thu, 16 Jul 2015 12:59:12 +0100, Chris J Dixon wrote:

So Harry claims to get almost 45% more output than you.
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On Thursday, 16 July 2015 13:09:29 UTC+1, Adrian wrote:

He might have added diffuse reflection, who knows.
NT
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On Thursday, 16 July 2015 13:09:29 UTC+1, Adrian wrote:

All depends on azimuth, roof angle and shading. My installation is near perfect in all these respects. The house was purchased with this in mind. The installation is almost three and a half years old and will have paid for itself in five years.
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Only because you are indulging in legalised banditry on the rest of us.
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bitch, of course, but that's because bitching is fun, unlike M$ OS's, where
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On 17/07/2015 10:18, Tim Streater wrote:

Well said!
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