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I try to calibrate my PV panel's efficiency by means of reference GHI, dHI values measured by our national weather service, which is 12 km away from my local PV site. At the reference site, I calibrate the Ineichen model by trimming its linke-turbidity parameter (LT) such that the measured and computed irradiances match equally. I assume that LT factor is valid within a radius 12km on a clear-sky day with a low aerosol optical depth. So I can port the calibrated LT to my location and height. At the same time, I measure my local PV's DC power (under MPPT condition) as a delta of (being exposed to global normal irradiance) minus (being exposed only to global diffused irradiance). My panel is small, so its shadowing from direct beams is pretty easy. Having computed DNI=(GHI-dHI)/cos(pi-zenith) by Ineichen at my site, I get the PV efficiency from the measured DC power at the given surface temperature (measured as well). So far, everything looks fine. But, I am getting different optimum LT parameters for the two reference matches GHI, dHI!

Is Ineichen model not enough exact for calibration purposes? No, the reason is elsewhere: When using a single, compromised LT value, the both GHI, dHI values can be computed relatively equally greater (+3%) than their measured counterparts. This fact naturally raises a question, which extra-terrestrial irradiance value (GXI) is used by the numeric model? The reason of error stems in the Earth orbit's excentricity 0.017, which causes about 0.034 variance in GXI, well correlating with my observed "compromised" error. The authors' comment in pvlib confirms, that pvlib applies the circular solar geometry. According to my own experience, this one is far enough precise, when calculating the solar azimuth and zenith by the timestamp and position. A typical error of the computed solar angle is about 0.5%. On the other hand, the high 3% error of extra-terrestrial irradiance could be easily fixed, if an accurate Sun-to-Earth distance was calculated by means of the ecliptic orbit model. This is even easier, then the calculation of solar angle by the circular model!

Currently, I use a following workaround: Trim LT so, that equal relative error is reached by the both model outputs GHI, dHI. Then port LT to the local site, and correct the computed DNI here by its (known) relative error.

Milan Hronsky
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1 Answers1

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which extra-terrestrial irradiance value (GXI) is used by the numeric model? ... The authors' comment in pvlib confirms, that pvlib applies the circular solar geometry.

I'm not sure what you mean by this. Can you provide a link to this comment? In any case, several models are available for extraterrestrial irradiance via pvlib.irradiance.get_extra_radiation (docs, v0.9.1 source code). Here's what the default model looks like across a year:

import pandas as pd
import pvlib

times = pd.date_range('2022-01-01', '2022-12-31', freq='d')
dni_et = pvlib.irradiance.get_extra_radiation(times)
dni_et.plot()

enter image description here

There are also functions for calculating earth-sun distance, e.g. pvlib.solarposition.nrel_earthsun_distance.

kevinsa5
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  • The comment is in solarposition.py, line 1427. It explicitly refers to "calculation of solar sunrise, sunset, and transit". Sorry, I haven't found any detailed comment about the calculation of Sun-Earth distance by date, and GXI(date), respectively. The correlation of the model's output error with the variance of GXI has navigated me to this assumption. But if extra_radiation reflects the ecliptic orbit and this is the real input to Ineichen, then my assumption is false, the value error 3% is somewhere else. I just hope, that my meteo-service's data dHI, GHI are better than 3%. – Milan Hronsky Aug 10 '22 at 16:12