B Why can't Solar panels be hemispherical, or a curved strip type?

[Aashna4M]

TL;DR Summary

wont a curved surface have more area exposed to sunlight while simultaneously occupying less land space

comparing a flat solar panel of area 2π r² and a hemisphere of the same area, the hemispherical solar panel would only occupy the area π r² of while the flat panel would occupy an entire 2π r² of land. wouldn't the hemispherical version have the same area of panel exposed to the sun, occupy less land space and can therefore increase the number of panels one land can have fitted? this would increase the power output proportionally as well.
when I searched it up I wasn't satisfied with the answer that came up- that the entire panel would not be lit. In my argument, the entire hemisphere can be lit and it can also generate electricity from the sunlight for a longer duration of the day too? if the lateral sides of the hemisphere are an issue, why not a curved strip?

 

[phinds]

Have you given any consideration to the effectiveness of highly angled sunlight on a panel?

 

[DaveE]

Solyndra tried something like that. It didn't work out very well for them. Solar panels need to be cheap. Flat is cheap to make and easy to install.

 

[Aashna4M]

Have you given any consideration to the effectiveness of highly angled sunlight on a panel?

wouldn't the same issue persist with the flat panels too?

 

[Aashna4M]

Solyndra tried something like that. It didn't work out very well for them. Solar panels need to be cheap. Flat is cheap to make and easy to install.

financial aspect yes i guess

 

[jbriggs444]

comparing a flat solar panel of area 2π r² and a hemisphere of the same area, the hemispherical solar panel would only occupy the area π r² of while the flat panel would occupy an entire 2π r² of land. wouldn't the hemispherical version have the same area of panel exposed to the sun,

Let me make sure I understand the comparison.

On the one hand we have a disc shaped flat solar panel with area $2\pi r^2$. So the radius of the disc must be about $1.4 r$. It is sitting flat on the ground.

On the other hand we have a hemispherical solar panel sitting flat on the ground with the domed side up. It has a surface area of $2\pi r^2$ as well. So the radius of the hemisphere must be $r$.

You ask whether the amount of sun intercepted by both would be the same.

If the sun is directly overhead then the disc will intercept twice as much sun as the hemisphere.

If the sun is angled (and if the collectors are not angled to match) then the ratio would not be two to one. The hemisphere would intercept sunlight from the side. And consequently shade adjacent areas.

There is no advantage to be gained in this manner. It is not surface area that counts. It is cross-sectional area on a plane facing the sun that is relevant.

 

[phinds]

wouldn't the same issue persist with the flat panels too?

No, it would not, not at all to the same degree **. and this is just an extra issue on top of the ridiculous added cost of manufacturing hemispherical "panels"

In short, your idea is a non-starter.

** Also, some flat panels are on motor driven gimbals and stay pointing at the sun at lot of the day.

 

[Baluncore]

Cells in series produce a current proportional to illumination. If one cell underperforms others in series, its current is wasted, while its voltage is reversed. The total voltage of the series cells is then less. A shadow across one cell will limit the entire panel output.

Cells in parallel produce a voltage proportional to the log of illumination current. A poorly performing cell will conduct the current generated by other cells in parallel.

A panel is made from many cells in series and in parallel. If the illumination of all cells is not the same, the output is limited to the least cell performance. That requires a panel be flat, to match the illumination, and output all the cells.

The same things effect panels within an array, as effect the cells within a panel.

A solar array is made from many panels connected as series strings. Strings in parallel are rarely used, as they must be arranged to have close to the same illumination. The grid-tie inverters used, are optimised to accept high-voltage at low-current inputs, from one string to each inverter module.

Keep all solar cells facing the same way in one panel, and all panels facing the same way in one string of panels.

 

[sophiecentaur]

Keep all solar cells facing the same way in one panel, and all panels facing the same way in one string of panels.

That's certainly the most trouble free system. We should be talking in terms of massive panel arrays so that factor should dominate any choices.

With a complicated circuit, you could combine very different panel outputs and optimise the net output power.

Steerable panels would do a better job than hemispherical panels but maintenance of moving parts would be a huge problem at remote sites.

 

[Aashna4M]

Let me make sure I understand the comparison.

On the one hand we have a disc shaped flat solar panel with area $2\pi r^2$. So the radius of the disc must be about $1.4 r$. It is sitting flat on the ground.

On the other hand we have a hemispherical solar panel sitting flat on the ground with the domed side up. It has a surface area of $2\pi r^2$ as well. So the radius of the hemisphere must be $r$.

You ask whether the amount of sun intercepted by both would be the same.

If the sun is directly overhead then the disc will intercept twice as much sun as the hemisphere.

If the sun is angled (and if the collectors are not angled to match) then the ratio would not be two to one. The hemisphere would intercept sunlight from the side. And consequently shade adjacent areas.

There is no advantage to be gained in this manner. It is not surface area that counts. It is cross-sectional area on a plane facing the sun that is relevant.

i understood it now, thanks!

 

[snorkack]

Steerable panels would do a better job than hemispherical panels but maintenance of moving parts would be a huge problem at remote sites.

So, where you cannot move the panel but still want to capture light as the light source moves, would you be better off with a curved panel, or just with a few panels at angle to each other?

 

[jbriggs444]

So, where you cannot move the panel but still want to capture light as the light source moves, would you be better off with a curved panel, or just with a few panels at angle to each other?

What is your metric for goodness?

Total energy gathered per day for a fixed cell surface area?
Total energy gathered per day for a fixed footprint?
Total hours at a specified minimum power for a fixed cell surface area?

Does system reliability, cost and servicibility figure in?

Rows of cell arrays in a fixed orientation sounds like a good start to me. Adding banks at different angles would add complexity without adding to energy gathered per day per square meter of cell surface area.

 

[phinds]

So, where you cannot move the panel but still want to capture light as the light source moves, would you be better off with a curved panel, or just with a few panels at angle to each other?

I know you REALLY want this to be a good idea, but I think you're beating a dead horse. It's not a terrible idea, it's just that you seem to have no feel for the engineering complexity that you are adding at little, if any, benefit.

 

[sophiecentaur]

just with a few panels at angle to each other

If you control the power from a panel appropriately, to get the most out of it then, if it is not pointing right at the Sun, you could still get a suitable voltage with a maximum power factor controller such that all similar panels would be producing the same output volts as the other panels with their controllers.

But again, it's a matter of which is the best engineering solution in terms of watts per £ over its lifetime and optimal pointing angles of all the individual panel arrays.It's possible that there is no point in that because the panels are so cheap and you just cover the land with them.

 

[sophiecentaur]

So, where you cannot move the panel but still want to capture light as the light source moves, would you be better off with a curved panel, or just with a few panels at angle to each other?

If you turn the panels to face the light, you will get the maximum output (as long as they don't shade each other. IF they don't move then each panel will suffer from the Cos θ effect for the panels that don't face away. Also if you don;t use somr form of control, you can have one panel wasting its power through another panel.

 

[DaveC426913]

Doing a sort of peri-mortem meta-analysis of this thread, I'd like to draw attention to the types of answers:

- it's not a good plan because of extra cost
- it's not a good plan because of the nuances and losses of the electrical voltage/current depending on how they're hooked up

Both of these answers are certainly valid but they are "you've got your work cut out for you" type answers. They would not necessarily give pause to a determined budding engineer, looking to improve a system. One can always look for cheaper materials or reconfigure electronics to try to get an edge. Cost and configuration can be equivocated.

But this answer cuts to the core of the issue:

- it is not surface area that counts. It is cross-sectional area on a plane facing the sun that is relevant.

That is not merely a practical issue - not one that might lend itself to a resourceful engineer's tinkering - this is show-stopper. It says the idea (as proposed in the OP) won't work in principle. It can't be equivocated.

That's a good thing, because it releases the budding engineer from spinning their wheels on a flawed idea, allowing them to redirect their resources to a better idea, sooner rather than later.

So, with due respect to others, bonus point goes to @jbriggs444 .

 

[sophiecentaur]

I'd like to draw attention to the types of answers:

That's a bit negative. A suitable electronic way to add the optimum VA from each set of panels (avoiding the losses of a simple paralleling system) would get more energy than you'd get from a static setup. I'm looking at a solution with no moving parts.
The answer to the 'curved panel' suggestion is clearly no, for a good reason.

 

[DaveC426913]

That's a bit negative. A suitable electronic way to add the optimum VA from each set of panels (avoiding the losses of a simple paralleling system) would get more energy than you'd get from a static setup.

Maybe I didn't express myself well. Optimizing the electronics and materials costs are certainly good ways to improve a given setup. I wasn't saying otherwise.

The point I was trying to make is that - as long as a budding engineer thinks a hemispherical panel is viable (i.e. a better collector overall) - he may get lost tinkering with improving the electronics or materials - while missing the bigger picture that the hemispherical setup is leading him down a flawed design path.

Another way of saying this is penny-wise, pound-foolish.

A more vulgar way of phrasing this is (forgive me, it is not meant as an insult): polishing a turd. The budding engineer may polish it (optimize it), oblivious that it's a turd (a non-starter).

The answer to the 'curved panel' suggestion is clearly no, for a good reason.

Right.

 

[russ_watters]

So, where you cannot move the panel but still want to capture light as the light source moves, would you be better off with a curved panel, or just with a few panels at angle to each other?

The issue with the OP was that he was using the wrong "r"(or, rather, mixing and matching). The radius of curvature of the panels for a curved solar array that catches rays perpendicular is the distance from the sun, not the radius/width of the panels. At the Earth's distance from the sun the benefit of curvature is many decimal places too small to matter.

 

[Baluncore]

A more vulgar way of phrasing this is (forgive me, it is not meant as an insult): ...

Perfection is the enemy of progress. I would describe an electrical engineer's obsessive attention to optimisation, as "polishing the electrons".

 

[DaveC426913]

Perfection is the enemy of progress. I would describe an electrical engineer's obsessive attention to optimisation, as "polishing the electrons".

Right, but are you seeing my point? No point in trying to optimize an inherently flawed design. He should move on.

 

[DaveC426913]

The issue with the OP was that he was using the wrong "r"(or, rather, mixing and matching). The radius of curvature of the panels for a curved solar array that catches rays perpendicular is the distance from the sun, not the radius/width of the panels. At the Earth's distance from the sun the benefit of curvature is many decimal places too small to matter.

: blinks audibly:

I thought the OP was talking about domes - I.e. convex

Are you saying the design is concave??

Like a radio dish?

Oh dear. I have erred badly. I have made a mess of this and I feel like fool.

 

[russ_watters]

: blinks audibly:

I thought the OP was talking about domes - I.e. convex

Are you saying the design is concave??

Like a radio dish?

Ehh, rereading, you may be right, but it isn't clear from the OP. The flaw is the same either way, and OP says some things that are wrong for both of those cases. The only case where "technically" there is an advantage is for a curvature matching the sun's.

 

[Baluncore]

Right, but are you seeing my point? No point in trying to optimize an inherently flawed design. He should move on.

Yes, I agree. "Polishing the electrons", is a more polite term.
Curved panels or arrays, there madness lies.

 

[sophiecentaur]

Perfection is the enemy of progress.

. . . particularly when politics is introduced. If the 'help' from the government is proportional to the total area of the farm then there is no incentive to improve the kW/$m^2$

 

[mongotuslan]

This gets to the heart of the trade off between tracking panel arrays and fixed panel arrays. Fixed panels are subject to the Cosine effect or Cosine error which reduces the effective power incident by the Cosine of the angle from normal.

In space, where the day/night cycle is irrelevant, some spacecraft have flat panel array with some mechanism to keep them pointed at the sun, so they trade having panel sizes optimized for the power they need versus the weight and complexity of the tracking system. Other spacecraft have fixed panels pointed in all directions, the ultimate being a sphere.

So, I would compare a hemisphere to a circular flat panel of the same radius. The total area of the hemisphere is twice the area of the circular flat panel of the same radius, but one hemisphere of a sphere is always presented to the Sun without a tracking mechanism. However, not all of the area of the hemisphere is normal to the Sun so its output will not be twice the flat panel. Cosine error will accumulate over the surface of the sphere, and calculating this would require integrating the cosine effect over the hemisphere.

Since my calculus is rusty, I drafted a numerical integration in a spreadsheet over half a hemisphere, and came up with a factor of 0.635. That is, the effective illuminated area of a hemisphere is 0.635 the geometric surface area. Since the hemisphere has twice the surface area of a flat disc with the same radius, the equivalent illuminated area will be 2 * 0.635 = 1.27. Thus, a spherical solar array in space will always produce 1.27 time the power output of a disc flat panel with the same radius without any tracking mechanism, but of course the sphere contains 4 times as many solar cells.

 

[Herman Trivilino]

I think engineers have figured this out, and the results are obvious if you just look at the way solar panels are designed and installed; and also what's available for purchase.

It's based on cost versus effectiveness.

For example, for smaller residential applications with limited available space I've seen smaller flat panels mounted on a moving stand so that the panel turns to face the sun as it crosses the sky. Thus it's optimized for the time of day, the time of year, and the latitude. And it's more affordable than other options that produce the same amount of energy.

 

[mongotuslan]

I agree that cost effectiveness for a terrestrial PV solar energy installation favors favors fixed flat panels. I have such an array on the roof over my head.

When I drive across town, I see many utility scale solar installations with a single axis tracking system. This improves power output earlier in the morning and later in the afternoon at the expense of lower power in the middle of the day. However, the power grid sees greater power demand earlier and later, so this is cost effective for the utility.

I didn't see that the OP question specified a terrestrial installation, so I felt free to comment on spacecraft solar power. Larger spacecraft like the International Space Station find it more cost effective to have flat panels with a tracking mechanism, while smaller spacecraft like cube sats place PV cells on every face just so they don't need a tracking mechanism and are willing to deal with the extra weight and expense of roughly 4 times the number of solar cells just so they don't have to deal with the complexity of Sun tracking.

The big difference in my answer is that I have been emphasizing better power output, while you are prioritizing energy collected.

The main thing I was hoping to see comments on was my math on how the cosine effect applies to a hemisphere.

 

[Herman Trivilino]

When I drive across town, I see many utility scale solar installations with a single axis tracking system. This improves power output earlier in the morning and later in the afternoon at the expense of lower power in the middle of the day.

Why is there lower power in the middle of the day? I thought they oriented at the optimal angle at all times. How can you do better than that given a lack of space or desire for a larger panel?

The main thing I was hoping to see comments on was my math on how the cosine effect applies to a hemisphere.

You lost me when you said half a hemisphere. Did you mean half a sphere? Because half a hemisphere has the same area as a circle of the same radius.

 

[DaveC426913]

You lost me when you said half a hemisphere. Did you mean half a sphere? Because half a hemisphere has the same area as a circle of the same radius.

Half a hemisphere is a semihemisphere.

 

[russ_watters]

Why is there lower power in the middle of the day? I thought they oriented at the optimal angle at all times. How can you do better than that given a lack of space or desire for a larger panel?

You lost me when you said half a hemisphere. Did you mean half a sphere? Because half a hemisphere has the same area as a circle of the same radius.

Single axis means they trace one arc across the sky. The sun traces a different arc every day. I'd presume that the optimal arc for maximizing annual energy production is somewhere between maximum summer and maximum winter peak power.

 

[mongotuslan]

Why is there lower power in the middle of the day? I thought they oriented at the optimal angle at all times. How can you do better than that given a lack of space or desire for a larger panel?



You lost me when you said half a hemisphere. Did you mean half a sphere? Because half a hemisphere has the same area as a circle of the same radius.

The lower power in the middle of the day is due to the single axis oriented horizontally, North to South, so there is Cosine effect due to the Sun angle at Noon from the Latitude. At some time during the morning and afternoon, the single axis tracking will align the panel normal to the Sun.

I integrated form 0 to 90 degrees, half a hemisphere, instead of -90 to +90 degrees, a full hemisphere, and assumed symmetry from this arc to a hemisphere. I am not sure I did this correctly, which is why I am asking for someone to check my math.

 

[renormalize]

I integrated form 0 to 90 degrees, half a hemisphere, instead of -90 to +90 degrees, a full hemisphere, and assumed symmetry from this arc to a hemisphere. I am not sure I did this correctly, which is why I am asking for someone to check my math.

I don't see enough equations in any of your 3 posts in this thread for readers to check. Don't make us guess! Learn enough LaTeX to post your work here, including basic assumptions, equations, and the form of the integral you evaluated numerically by spreadsheet. A diagram of the geometry you're considering would also be helpful.

 

[Herman Trivilino]

The lower power in the middle of the day is due to the single axis oriented horizontally, North to South, so there is Cosine effect due to the Sun angle at Noon from the Latitude. At some time during the morning and afternoon, the single axis tracking will align the panel normal to the Sun.

Okay, I didn't pay attention to what "single axis" means. Got it now. I was under the mistaken impression that the tracking system compensated for the seasons.

I integrated form 0 to 90 degrees, half a hemisphere, instead of -90 to +90 degrees, a full hemisphere, and assumed symmetry from this arc to a hemisphere. I am not sure I did this correctly, which is why I am asking for someone to check my math.

Well, I did as close to that as I could. If you were thinking that half a hemisphere has twice the area of a circle of the same radius, that would have been an error.

As @renormalize points out, we can't check your math because you didn't show us your math. You described the math you did, but describing what you did is not the same thing as showing what you did.

 

[256bits]

I drafted a numerical integration in a spreadsheet over half a hemisphere, and came up with a factor of 0.635. That is, the effective illuminated area of a hemisphere is 0.635 the geometric surface area

The 0.635 seems awfully close to the average value of a half cycle of a sign wave, from 0 to pi, which should be the same for a quarter cycle from 0 to pi/2.

also, please define 'effective illuminated area'. I am not sure what is meant.

 

[sophiecentaur]

I’m assuming that the driving force in choice of panel shape has been large areas of panels.
It may have been mentioned above but I’ll say it anyway. At low incidence, the mutual shading would reduce output of many 3D panels. Offsetting could reduce this but when the Sun is low, the performance would be compromised at different times of year.

Cylindrical arrays are great for some rotating satellites but, otherwise they don’t get my vote.