I have a very specific question,
I have hourly total (i.e. global) solar irradiance on horizontal plane (measured by a building rooftop pyranometer) next to an array of PV modules mounted at a tilt angle of 20 deg and an azimuth angle of 10deg east of due south (i.e. -10°). All I wish to do is to correct the global horizontal irradiance output from the pyranometer (in W/m2) to become the incident irradiance (in W/m2) on the PV module.
A similar question was asked (https://www.researchgate.net/post/Calculating_Solar_radiation_on_a_tilted_solar_panel2) where Frank Veroustraetehad offered the following relationship between total solar irradiance on a tilted PV module (S(m)) and total global irradiance on horizontal (S(h)):
S(m) = [1/sin α] S(h) sin[α+ β]
β being the panel tilt angle from the horizontal (in my case 90°-20°=70°) and α being the solar elevation angle which needs to be calculated for every hour of the year (i.e. 8760 instances).
My questions are:
1- Is it at all possible to convert horizontal irradiance to module irradiance independently from solar elevation angles?
2- What is the formulae for solar elevation angle that produces hourly outputs as a function of latitude, longitude, time of the day, Julian day and tilt angle? (did I miss any other variables?)
Thanks
Dear Mohammad,
To answer the first question since the incident solar radiation depends on orientation to the sun such that for maximum incident solar radiation one has to make the indecent solar radiation perpendicular to the surface receiving the radiation. So, it is impossible to calculate the incident solar radiation on any inclined in terms of horizontal insolation without considering the elevation angle.
For the other part of the question you can refer to the calculation of the solar insolation given in the link: https://pveducation.org/pvcdrom/properties-of-sunlight/calculation-of-solar-insolation
Best wishes
Hi Abdel / all
If latitude, tilt angle and total solar irradiation were my starting points, I think I only need the formulae for solar hour angle to correct total irradiance to module irradiance. Can anybody suggest solar hour angle formulae that can generate the results at hourly intervals over the entire year? It is missing from PVEducation website (see below):
1. For the declination angle (δ):
δ=−23.45°×cos(360/365)×(d+10))
d is the Julian day and declination angle is to be computed at daily intervals as the changes over hourly time steps are too small to consider.
2. For Solar elevation
α =sin−1 [sinδ sinφ + cosδ cosφ cos(HRA)]
φ is the latitude. HRA is the hour angle (also denoted as ω). However this is not reported in PV education.
In the following paper, you will find a detailed mathematical model for performing your required transformation.
https://www.researchgate.net/publication/239792384_Sizing_optimisation_of_stand-alone_photovoltaic_generators_for_irrigation_water_pumping_systems
You are also welcome to refer to
https://www.researchgate.net/publication/326175847_Optimized_fixed_tilt_for_incident_solar_energy_maximization_on_flat_surfaces_located_in_the_Algerian_Big_South?_sg=g3DD2qSk90hqL3BNyRWtLB4gZ0_1XE5hDIejXJ9W78ouYrbAfJY5pYJSEx9o3IDlZ4SsNJolMXl6UgIXqUJNnQZ93EXGWwg_dl0gnf8R.PgETlu6ALs33qxhysbv2cg1Oc1oUqplg2cbiH27aFMDv-UxMuR05bDXzHdNgngOAEEWLNO7xG6gwVW9N-oBqZA
If you need a software tool for conducting the required calculations and/or perform this transformation, you are welcome to contact me.
The formula you quote is not appropriate.
The _transposition_ (the proper term used in the solar literature) from horizontal to tilt involves 3 steps:
- transposition of the direct component with a formula that involves the angle of incidence of the sun of the collector (which varies continuously during the day).
- transposition of the sky diffuse component; many anisotropic models have been proposed for that, e.g. Article Direct and indirect uncertainties in the prediction of tilte...
Article Solar radiation on inclined surfaces: Corrections and benchmarks
- addition of the reflected component from the reflecting surface (roof in your case); this is typically small, unless the roof has a very bright color.
The whole process is explained in countless references, including this landmark:
Article Solar Engineering of Thermal Process
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