Compensate for non-point source irradiance losses on surface

[SunThief]

Hi. To frame things generally, I have a variable indoor light source that shines on an inclined plane. More specifically, I have a 3-D LED matrix that shines light onto a miniature pv array. Essentially, I am using an indoor “sun” to shine on the array. I measure the energy produced, and compare it with the energy predicted for the real sun with the same sunpath.

Because I am using LEDs instead of the sun, the comparison is not direct. For the indoor situation, there are two unique issues of which I’m aware:

1. Significant variation in inverse-squared losses over the surface of the plane.
2. Additional losses that result because the light (LEDs + lenses) is not a point source—the source intensity diminishes as one moves away from the center of the LED beam.

My goal is to calculate a degraded irradiance value that includes the atypical losses the irradiance suffers over the plane. So, for each sun position, I want to replace the given* value of irradiance--with an approximate value that includes the penalty that the use of a "close" LED inflicts. This would allow me to alter the programmed irradiance in the corresponding outdoor prediction, to roughly match the non-ideal effects associated with the LED light.

I previously came up with a messy integral that actually seemed to handle the inverse-squared stuff [#1], but I haven’t been able to figure out a way to also incorporate the losses from #2. I speculated that I would need to integrate the point-by-point product of [the square of] the radial sun distance and the LED’s angular intensity hit (i.e. #2) over the plane. But the approaches I tried seemed to result in formulas in the form of un-integrable ratios of inverse trigonometric functions and square roots. Agh...

Any thoughts on a straight-forward way to approach this, or is it unrealistic? Most of the stuff I’ve read applies to real sunlight, where that light is assumed to consist of parallel rays, etc. Attached is a rough picture of the structure.

Thanks.

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* The values for baseline Direct Normal Irradiance are defined for each sun position. I have software that expects the irradiance as DNI, so I’m not breaking down the DNI into its components. (This issue also applies to diffuse irradiance, but I'm limiting the scope here to focus on the overall issue.)

 

[Andy Resnick]

<snip>
Additional losses that result because the light (LEDs + lenses) is not a point source—the source intensity diminishes as one moves away from the center of the LED beam.
<snip>
I previously came up with a messy integral that actually seemed to handle the inverse-squared stuff [#1], but I haven’t been able to figure out a way to also incorporate the losses from #2. I speculated that I would need to integrate the point-by-point product of [the square of] the radial sun distance and the LED’s angular intensity hit (i.e. #2) over the plane. But the approaches I tried seemed to result in formulas in the form of un-integrable ratios of inverse trigonometric functions and square roots.

I think you mean "the LEDs + lenses are not isotropic sources". I agree, you should account for the angular dependence of LED radiance, but I can't think of a simple way to do so short of numerical integration. It seems to be a straightforward radiative transfer problem- my go-to reference for these problems is Wolfe's "Introduction to radiometry".

Also, just because you didn't expressly state this, don't forget to account for the spectral difference between sunlight and LED output, as it relates to the quantum efficiency of the PV device.

 

[mfb]

The problem is quite challenging even with numerical integration. You'll certainly need the emission characteristics of the LEDs, the datasheet should have that. But that alone is not sufficient: Each LED will lead to some distribution of irradiance and irradiation angle. The effect of the irradiation angle is what you want to investigate, so you cannot just plug that into account for it. A simultaneous fit to all data points could work, with some discrete values for different angle ranges or with some test functions. Alternatively, find some approximation for the behavior at small angle differences first, use that to correct each data point, and then fit for the full range.

To make things worse, a non-uniform irradiation of the solar panel will probably lead to non-linear effects in the measured power.

 

[SunThief]

I think you mean "the LEDs + lenses are not isotropic sources".

Yes; I didn't state that correctly.

- my go-to reference for these problems is Wolfe's "Introduction to radiometry".

Great; thank you for the reference.

...don't forget to account for the spectral difference between sunlight and LED output, as it relates to the quantum efficiency of the PV device.

There is provision for spectral correction adjustments in the simulation software I'm using [PVSyst], but its application is limited to certain module types.

Thank you for the responses; I appreciate it!

 

[SunThief]

Each LED will lead to some distribution of irradiance and irradiation angle. The effect of the irradiation angle is what you want to investigate, so you cannot just plug that into account for it. A simultaneous fit to all data points could work, with some discrete values for different angle ranges or with some test functions. Alternatively, find some approximation for the behavior at small angle differences first, use that to correct each data point, and then fit for the full range.

I'm not following whether you mean issues arising because the angles differ for each sun position, or because of angle errors. I was thinking the former would be okay, because, aside from limitations associated with my mechanical skills, the LEDs are roughly spaced at azimuth/elevation angles that mimic the sun's position in the sky. Regarding the latter, I was hoping that would be handled by addressing the inverse-squared loss issue [#1 above. That is, by integrating the variable distance² over the plane, and dividing by the footprint area to get an average value. The ratio of the two distance values would then be divided into the original dIrect irradiance value, to come up with a degraded value for each sun position.]

Agh, I just realized that I referred to the distance above as a radial distance--that is incorrect. Radial distance would refer only to the expected distance from each LED to the array. I meant to refer to integrating the changing distance from each LED over the array.

To make things worse, a non-uniform irradiation of the solar panel will probably lead to non-linear effects in the measured power.

This, I'm afraid, is a big deal, and it may be something that can't be resolved. I don't think the variations in voltage for the array can be realistically modeled with a simple specification of mismatch loss... as would normally be the case with a uniform light source.

Thank you for your thoughts.

 

[Khashishi]

Why don't you just solve it numerically?

 

[SunThief]

I will need to research that. I would probably quibble with the word just, though.

 

[SunThief]

The effect of the irradiation angle is what you want to investigate, so you cannot just plug that into account for it...

Ok, thought about it some more and I think I see what I missed here. Looks like I have a lot of reading to do. Thanks to you and everyone who weighed in.

 

[mfb]

I'm not following whether you mean issues arising because the angles differ for each sun position, or because of angle errors.

I don't know what you call "errors". The angle won't be constant over the whole panel. This is not just the inverse square law, it is also a cos(angle) term.

You can test this effect by using LEDs at different distances. You can also mimic a more sun-like illumination by using multiple LEDs each focused on some region of the panel.

 

[SunThief]

I don't know what you call "errors". The angle won't be constant over the whole panel. This is not just the inverse square law, it is also a cos(angle) term.

You can test this effect by using LEDs at different distances. You can also mimic a more sun-like illumination by using multiple LEDs each focused on some region of the panel.

(Got it; thanks again.)

 

[SunThief]

It’s been awhile since I posted*. Thanks to everyone who replied with suggestions. They helped nudge me to think about this project in different ways. The numerical integration idea worked out very well. I have run plots comparing energy from the photovoltaic module to the energy predicted by software simulations. I seem to be getting reasonable results, but I'm not confident enough that my methodology is sound. What I’ve tried to do is come up with average hourly irradiance values that incorporate the losses associated with the LED light—preserving the original angle associated with the incoming light. That is I "integrate" the irradiance values over the module surface and divide by the area to get an average.

My uncertainty concerns the proper way to handle the Direct Normal Irradiance, which arrives from a variety of angles. When calculating irradiance from light that is off-angle (not perpendicular) to a surface, the sources I’ve read multiply the LED's radiant intensity by the cosine of the angle between the surface normal and the path back to the source. This approach to “foreshortening” naturally seems to give me values and angles that are dependent on the orientation of the surface. However, the software I’m using for comparison defines irradiance as an input quantity, independent of the deployed surface (e.g. Direct Normal Irradiance, Beam Horizontal irradiance, etc.) Transposition of light relative to the actual surface occurs later on in the software. So my aim is not to transpose the irradiance, it is simply to glean the irregular impact that the particular geometry has on the irradiance. Two attachments--for flat and tilted modules respectively--each provide profile views that compare the real sun to the indoor model. My question boils down to this: "Is it legitimate to replace the surface normal with the normal that would apply to an imaginary patch that the DNI would face, when determining the angle to be used in the cosine multiplier?"

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* [To recap, I built an indoor “sun” that shines hourly LED light on a small photovoltaic module. My goal is to try to reconcile the energy produced by the module, with that predicted by a software package that models the real sun. My approach is to calculate the irradiance losses associated with the LED light, and then reduce the corresponding irradiance input to the software simulation. ]

 

[SunThief]

[Please disregard my recent post. I will post a more pointed question as a new post.]