I have measuring data of global radiation on a tilted surface (a solar collector surface). Now I need to do 2 things:

  1. split the tilted global radiation into its diffuse and beam parts
  2. calculate the same terms (diffuse + beam radiation) on a different surface (different tilt and/or azimuth angle)*

I was able to solve problem (1) by inverting a tilted radiation model (HDKR), and combining it with the Erbs model on the horizontal plane. In this way I get quite good results for diffuse and beam parts on the tilted surface. Problems near sunrise / sunset and numeric problems are all under control.

For problem(2) however, I failed. I mention problem (1) because I intended to use its solution as a basis for problem (2): I intended to take the diffuse + beam parts on the horizontal (an intermediate result of problem (1)), feed it into HDKR to calculate diffuse + beam on an arbitrary surface. Now, these steps do not work. From step (1), I do not get diffuse + beam horizontal at times where I need it for step 2. This is because due to the different orientation, sunrise / sunset / sun behind collector happen at different times compared to the original surface. This is why my approach to step (2) fails.

I do not know whether this is a very unusual problem? For us it would be really useful to solve problem (2). It would allow us to use radiation data from one solar energy installation to evaluate a nearby plant with possibly different orientation.

Are there any special models treating with this or a similar problem?

Any help is greatly appreciated! Thank you all!

  • $\begingroup$ Just out of curiosity, how much does diffuse radiation add to solar collector energy output? I always thought that it was very little, but I might have the wrong ideas about it. Thanks! $\endgroup$ – CuriousOne Aug 26 '14 at 1:27
  • $\begingroup$ This is a legitimate remark. The efficiency of solar collectors on harvesting diffuse radiation depends mainly on their construction, anti-reflective or not cover, 1 or 2 covers, concentrating or not, etc. The main part comes from beam radiation, but the motivation behind the question is the following: In general, field measurements are for global radiation as beam and diffuse are both expensive to measure. In order to evaluate solar collectors, you definitely need to know the beam part. But global = beam + diffuse, so once you have global and beam, you've got the diffuse part as well. $\endgroup$ – user986990 Aug 27 '14 at 18:02
  • $\begingroup$ Thanks for the answer! I was aware that concentrating collectors had to lose most of the diffuse radiation, and radiation measurements are always hard, so I can see the motivation why one needs to model this properly. $\endgroup$ – CuriousOne Aug 27 '14 at 18:23

This might be unusual, but I will now give an answer to my own question. Maybe somebody who reads this has the same problem and finds this interesting.

After all, I have been able to successfully solve also problem (2), and both algorithms actually work quite well.

The approach was to calculate both beam and diffuse parts on the horizontal for all timestamps. While the inverse problem can not be solved for all timestamps, I interpolate the clearness factors for timestamps when the inverse problem has no solution. And then I use the clearness factor to get beam and diffuse horizontal.

This makes the solution to problem (2) straightforward.

I also validated the model with high-quality measuring data where both beam and diffuse are available, the model error in beam radiation is around 2-3% most of the day, the error in integrated radiation over 1 day is 0, by design of the algorithm.

I am willing to share the Matlab algorithm, in case somebody is interested.


  • 2
    $\begingroup$ There is nothing unusual about answering your own question. That's why it's permitted! $\endgroup$ – tpg2114 Aug 28 '14 at 3:11

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