Comments on Arbitrary Orientation and Tilt

Comments

I use this equation to calculate the incident irradiation however always end up with one of two negative values, I am not sure what went wrong...

Hello,
Getting NaN for Sincident and others. Got a warning on Mathjax.js. The site has migrated to a new version of Mathjax and the old version has been retired.
var newMathJax = 'https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js';
var oldMathJax = 'cdn.mathjax.org/mathjax/latest/MathJax.js';
transition page:
var newMathJax = 'https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js';
var oldMathJax = 'cdn.mathjax.org/mathjax/latest/MathJax.js';
Thanks for the site.
Jim Julian

The problems with MathJax are fixed

I believe the formula given for solar radiation on a panel with arbitrary orientation and tilt is incorrect. I think it should be:
Smodule = Sincident .cos(Ψ-θ).[cos(α)sin(β) + sin(α)Cos(β)]

Reason: On the previous page, for a module directly facing the sun, at tilt β:
Smodule = Sincident. sin(α+ β), where
sin(α+ β) = cos(α)sin(β) + sin(α)Cos(β)
For a module at orientation θ,
Smodule = Sincident .cos(Ψ-θ). sin(α+ β), so
Smodule = Sincident .cos(Ψ-θ).[cos(α)sin(β) + sin(α)Cos(β)], not as given.
Note: this is a repeat of a comment made earlier, which was not appended to the correct page.

I came across this article and also this comment suggesting its correction. However, I believe that both these formulae don't solve the mentioned problem from the real world. problem in them is the cos(Ψ-θ) which makes the result positive only in case the solarAzimuth is +/- 90 degrees from the solarPanelAzimuth.

Anyway, I found a research article [1] where the author defines this formula to compute the incident angle:

cos(incidentAngle) = cos(90 - sunZenithAngle) * cos(sunAzimuth - solarPanelAzimuth) * sin(solarPanelTilt)
+ sin(90 - sunZenithAngle) * cos(solarPanelTilt)

So from my point of view the resulting formula should be like this:

Smodule = Sincident * cos(incidentAngle)

These formulae did the trick for me. I verified it on various charts in our application for PVE production prediction using the weather forecast.

[1] https://www.researchgate.net/publication/252018864_Clear_sky_global_solar_irradiance_on_tilt_angles_of_photovoltaic_module_in_Perlis_Northern_Malaysia/download