Comparing Solar Power In Summer And Winter ..........

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.........A Theoretical Approach.

Everyone in the UK who has solar panels finds that significantly more solar energy is harvested in the summer than in the winter.
And those who live at more northerly latitudes expect to harvest less solar energy than those living in the south.

To put this another way, it's generally accepted that we can harvest more solar energy in the summer and more solar energy at more southerly latitudes.
As a rule of thumb the guidance often given for the UK is something like 'In the winter expect to get about 10% of the solar energy you get in the summer' and 'If you're lucky enough to get to Spain in the winter you'll do better than in the UK'.

Previously I've had a wander around the internet searching for a theoretical approach that confirms these anecdotal comments, but haven't managed to find the sort of thing I was looking for. At the time I decided that if I couldn't find what I wanted, then I would have a go at theoretically quantifying the effect of season and latitude on solar harvesting. The Autumn Equinox is fast approaching and I have some time available while Moho-ing in the West Country - so the time is nigh!
Please bear in mind when judging the following that I'm in the Moho and only have a phone (occasionally) connected to the internet, paper, pencil, pens and the sort of basic calculator that an 'A' level maths student might have had as of about 10 years ago.

I've deliberately kept this post a maths-free zone but I should add right here and now that some people will find some of the technical content that follows somewhat tedious and/or of little interest.
If that's the case for you, then please feel free to scroll down to the graph in the last photo, which summarises the outcome of this earlier stuff.

As always with these things, one has to make a few assumptions. Here are mine:

1. The solar panel is used horizontally.
2. The weather in the winter is generally the same as in summer. That is to say, there is roughly the same proportion of cloud and clear sky in summer and winter.
3. The sun crosses the sky following all or part of something called a sine curve (the sort of pattern that non-breaking waves follow on the surface of the sea or that ripples follow on a pond).
4. Light falling on the solar panel isn't obstructed by trees, hills etc. at any time of the day. That is, light from the sun reaches the solar panel as the sun rises above the true horizon at sunrise and similarly leaves the solar panel as the sun sinks below the true horizon at sunset.
5. The amount of solar energy arriving at a solar panel is proportional to the angle of the sun above the horizon and how long it's at that position.
6. A solar panel and controller starts charging a battery at sunrise and stops at sunset. This assumption agrees extremely well with what my own solar panel and controller does throughout the year.

There are other assumptions such as what happens to light falling on a solar surface at low angles, but I feel that the six assumptions above are those that can be recognised intuitively and are those probably having the greatest impact on the approach I'm taking on solar harvesting.

If you've been lucky enough to be on or above the Artic Circle at midsummer, you may have seen the midnight sun. It's a wonderful sight.
This is a time lapse photo (not produced by me) of the passage of the sun as it crosses the sky in a 24 hour period (fig. 1):

cc396f70ae041f5294a8206d7aac36bd.jpg

It can clearly be seen that the path of the sun follows a sine curve as described in assumption 3.
Considering fig.1 and assumption 5 together leads us to the conclusion that under these conditions the solar energy arriving at a solar panel in a two hour period (there are 12 strips representing 24 hours) will be proportional to the area between the sun and the horizon of one of the strips on the photo. And the total energy arriving at the solar panel in a 24 hour period would be proportional to the total area of all 12 strips.

That's all very interesting, but what happens at lower latitudes south of the Artic Circle where most of us use our mohos?
(From now on the images are hand drawn so please bear with me!).
If we were to travel further south to the latitude of the Artic Circle (about latitude 67°) and take similar photos on midsummer day, we'd find that the path of the sun just clips the horizon and the path of the sun would look thus (fig.2):

IMG_20200918_083139~2.jpg

Again, the total energy arriving at the solar panel will be proportional to the area under the curve (the red hatched area is a precise area under the sine curve, whereas the 12 strips described above are an approximation).

If we now travel south of the Artic Circle at midsummer, the horizon blocks the sunlight for part of the day and the red hatched area becomes smaller; the solar energy arriving at the solar panel is diminished (fig.3):

IMG_20200918_083139~3.jpg

Finally, if we were to revisit this latitude at midwinter the horizon would be blocking even more of our view of the sun's path and the red hatched area would be smaller still (fig.4):

IMG_20200918_083139~4.jpg

Fortunately there's a mathematical method that allows us to calculate the area below curves (such as the sine curve) extremely precisely. It's one of those things where the outcome is far more interesting than the method so I'll miss the method out here. Having said that, should anyone want to discuss the maths, I'm happy to do so at a meet.

So how can we use this information?
I've selected a latitude (48°) and established the times of sunrise and sunset at midsummer for that latitude.
Using the mathematical method hinted at above, I've then calculated the red hatched area (it looks similar to that shown in fig.3) for midsummer.
For the same latitude (48°), I've then repeated the above for the times of sunrise and sunset at midwinter (this time the hatched area looks similar to that shown in fig 4) to establish the area under the sine curve at midwinter.

In order to compare the solar power available at midwinter with that at midsummer, we can divide the red hatched area for midwinter by the red hatched area for midsummer. In this case we get the ratio 0.21. In other words, the output at midwinter at latitude 48° is 0.21 (or 21%) of the output at midsummer.

I've then repeated the calculations described above at midsummer and midwinter for latitudes 30°, 58° and the Artic Circle at approximately latitude 67°.
At latitude 30° the proportion is 0.46 or 46%.
At latitude 58° the proportion is 0.081 or 8.1%.
At the Artic Circle (about latitude 67°) the proportion is 0.0 or 0% - which is to be expected since the sun doesn't rise at the Artic Circle at midwinter.

And finally, to hopefully make at least some of this information useful, I've plotted proportion of solar output (midwinter divided by midsummer) versus latitude for the 4 latitudes I've mentioned above (fig.5):

IMG_20200918_082547~2.jpg

For information I've marked the latitude of a few cities on this graph. If the location of interest to you isn't included, then simply establish your latitude and from the graph read off the theoretical solar proportion figure for that location.

I'm somewhat pleased to find that the mean figure for the UK (at a mean latitude of about 55°) is 0.11 or 11%, which agrees very well with the anecdotal comments one hears and is mentioned in the third paragraph at the beginning of this post.

Other observations I thought interesting:
1. The north of Scotland has a winter/summer proportion half that of southern England.
2. Faro has a winter/summer proportion over twice that of southern England.
3. Marrakech has a winter/summer proportion we should all be jealous of!

Do bear in mind that a solar panel rarely delivers it's rated output, simply because the rated output is measured under a particular set of test conditions that are rarely experienced outdoors in the UK.
If you have a 300 watt panel and the information presented here gives you a winter/summer proportion of 0.15 (15%) then in winter you can assume that your solar panel should be considered the equivalent of a 300 X 0.15 = 45 watt panel under the conditions that you generally use it.

If you've found this post interesting and/or useful I'd appreciate a happy smiley or similar. If the opposite is true then please post a sad smiley or other obviously negative emoji. Your feedback will help me decide whether it's worth expanding on this work to help members estimate, for instance, their winter solar output in a more southerly location compared with their summer solar output in the UK etc, etc.

© Please note that this post is copyrighted and may only be reproduced or distributed in total or part by any means including electronic by permission of the copyright holder who may be contacted via the owner of Motorhomer Ltd.

Colin🙂🙂🙂
 
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Allen

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Sorry, it means nothing to me....(didn't read all of it)
This techy stuff goes over my head.
All I know is that since my solar panel was installed I haven't needed to find a campsite with electric hook up.
The leisure battery indicates fully charged and everything works..
 

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Less Daylight
Sun Lower
More clouds
View attachment 56560
No fancy analysis needed just observation and common sense. My readings from solar on a house roof !

Thanks for your feedback, jagmanx.
Do you have any data available from the solar system installed on your house when you take your house to southern Europe?
It would be very useful to be able to compare your data with the information posted at #1.

Colin 🙂🙂🙂
 
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jagmanx

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Hi Colin,
No not planning to move house !

House near Reading. I suspect (bearing in mind angles and sine waves) that thinks will be more extreme in Say Scotland.

In a motorhome you need enough solar to keep batteries in order.
Solar on a house just provides income ( after a significant investment !)
 

Izwozral

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Far too technical for me to fully understand but appreciate the time and effort put into the calculations and writing the post.
As usual, I am in awe of some members knowledge around technology and the ability explain it, unfortunately I am a lost cause.
 

jagmanx

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Intended to augment post no 1
Asumming ahorizontal solar panel.
There are 2 angles to consider
1 The alngle of Altitude at midday (Altitude
I have chosen Reading @ 50 degrees north on June 21st and other dates

The sun at midday is at an angle of 63.5 degrees inevitable at the sun is over the tropic at 23.5 deg
50 - 23 .5 = 26.5 so 90 deg (vertical) - 26.5 = 63.5
This elevation angle has been verified via websites and is obviously as good as it gets.
On June 1st The elevation at noon is 60 degrees
On May 1st 54 degrees
April 1st 43 degres
March 31st 40 degrees
Thus the main factor reducing solar power is determined by the sine of the angle (of elevation)
Sine of 90 degres = 1 so directly overhead sun is 100%
June 21st (sine of 63.5) 0.89 so 89%
June 1st 87%
May 1st 81%
April 1st 68%
March 31st 64 %
and for interest
Dec 21st @14 degrees so 24%


A second angle comes into play which I will call the skew angle
This only comes into play if you can tilt your panels when the panels may not be at the best angle compass-wise
Just to say a bit like sunshine on a pryramind with a square base at midday the sun may be directly on one of the sloping faces but 6 hors later will be broadside on to a differnt face (@90 deg)
This is a tilted panel is at the correct angle it will receive 100 % but ONLY if the sun is broadside on to yout panels ir at 90 degrees so panels facing east west at noon but lets say South west or west late afternoon
The reduction effect is similar to the above figures for elevation but of course the tilting benefit outweighs this secondaray angle. especially if you increase the tilt as needed

In winter other factors simply exacerbate the situation eg
June 21st has almost 16 hours daylight whereas Dec 21st only 8 hours
I gets much worse as you go north.
Also the sun is not as bright in general although a cold frosty sunny day will be a bonus
So although the elevation of the sun in December is about 1/4 to 1/5th of the june figues the "half daylight time" reduces the daily input to about 1/8th
Others have observed that tilting works and I fully support that.
I repeat my "house Solar graph". The panels are slightly tilted and westerly orientated.
Yo can see the best figure is 340 and the lowest 50 so about 1/7th of peak performance
1600606575297.png
 
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xsilvergs

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Here at Bradford on Avon (mid September) the peak I have seen from a single 100W with a Victron MPPT controller is 64W over the last 9 days. This 100W panel is horizontally mounted, thankfully the 3 others are tiltable.

As one that has tried a number of ways of getting the most from solar panels, I found Colin's post interesting and worth his effort.

Solar tracking panels have proved great in theory in my experience but making it portable is more difficult.
 

Exwindsurfer

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Far too technical for me to fully understand but appreciate the time and effort put into the calculations and writing the post.
As usual, I am in awe of some members knowledge around technology and the ability explain it, unfortunately I am a lost cause.
I am the same as you Izwazral right over my head but nicely written.
 

Exwindsurfer

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I find now that I can tilt my panels up to 90 degrees I can get nearly as much solar in the winter as I can in the summer when my panels are flat on my roof as there is know need to tilt them .I have 400 watts of solar and 2 100amp lithium battery’s never had a problem up to now.
 

Exwindsurfer

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I found this solar angle calculator helpful when I had solar panels.
In winter the panel should work better on the side of the van (sunny side :)) than on the roof.
To get the right angle for my panels I just keep adjusting it with my remote till I get the best on my phone app for my mppt charger and it works fine.
 

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This is my solar harvest for the last month mostly on my drive View attachment 56582

I guess that even when your Moho is sat on your drive, you're still using a fair amount of energy, Jeff? A high drain alarm system and compressor fridge are taking power? Or perhaps the headlights are left on (😅😂🤣) ?
Your solar charger has been putting about 300Wh of power per day into your batteries during bulk charging for September, plus a very small absorption charge followed on average by about 65Wh per day during float charging.
Or am I reading your data incorrectly?

Colin 🙂🙂🙂
 

Exwindsurfer

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I guess that even when your Moho is sat on your drive, you're still using a fair amount of energy, Jeff? A high drain alarm system and compressor fridge are taking power? Or perhaps the headlights are left on (😅😂🤣) ?
Your solar charger has been putting about 300Wh of power per day into your batteries during bulk charging for September, plus a very small absorption charge followed on average by about 65Wh per day during float charging.
Or am I reading your data incorrectly?

Colin 🙂🙂🙂
The fridge is on all the time Colin I must learn to turn it off lolol
 
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