AOI dependence for soiling losses

[kandersolar]

Is your feature request related to a problem? Please describe.
Soiling losses are known to show a dependence on angle of incidence, but pvlib's soiling loss models don't consider AOI.

Describe the solution you'd like
Implement a model that calculates an adjustment factor, analogous to IAM, that converts soiling loss at AOI=0 to soiling loss at any angle of incidence.

Here is one such model: Guo & Javed 2024, Effect of incidence angle on PV soiling loss. https://doi.org/10.1016/j.solener.2023.112298

Describe alternatives you've considered
N/A

Additional context
One wrinkle: soiling loss models tuned to field measurements probably don't calculate soiling loss at AOI=0, but rather some kind of "average" AOI that depends on both the sun position and the weather conditions (sun AOI matters less in cloudy climates). Conceptually, it seems like soiling loss ought to be considered a combination of direct and diffuse components the same way IAM is. It's not obvious to me how best to apply an AOI correction factor to empirical soiling models.

[echedey-ls]

I've read the paper and I don't dislike the proposed model. The only issues I have with it are:

1. Do we want to provide some kind of fitting functions so the two parameters can be obtained from some kind of curve fit? The paper approach is for some exact soiling values but in the field they change with the weather.
   • In this case, what data can/should I make use of?
   • The $SL_0$ can be left up to the user but I can't think of how to get it from this kind of data.
     I have in mind this data could be two flat reference cells, one that cleans itself (or is cleaned) everyday and another one that gets soiled normally. So at AOI=0º, $SL_0$ is direct. For other cases, I'm not sure.
     Rearranging (7) as $SL_\theta(\theta) = SL_0 · (sec \theta)^P [\frac{1 - F_n/IAM}{1 - F_n}]$ there is another parameter, $SL_0$. Whether this works or not, I'm 0% sure.
2. Data testing - I can do the average functional test of datatypes and some numbers, but they won't guarantee scientific rigour. Maybe from the graphs I can approximate some values...

[mikofski]

ICYMI: @wholmgren , @abhisheksparikh , @mdeceglie

[adriesse]

I don't have access to this paper, but I do recall that Martin & Ruiz discussed representing the dirty modules with a different a_r. That wouldn't accommodate losses at normal incidence.

[adriesse]

Have there been any new developments/publications on this topic? It's pretty relevant since some soiling measurement approaches don't capture this properly.

[williamhobbs]

I'm generally interested in this concept.

Here's an updated paper by Guo with outdoor validation: https://doi.org/10.1016/j.solener.2025.114253

[adriesse]

Thanks @williamhobbs ! A soiling measurement system that gives you one value per day will not be enough to determine which curve you are on. This is a subject of discussion for the revision of IEC 61724-1.

[williamhobbs]

I was revisiting this and think that I've put together something close to what's in Guo 2026. I think the only difference is that I'm using pvlib.iam.physical because it's easy, and Guo used an empirical IAM table.

from pvlib.tools import cosd
import pvlib
import numpy as np
import matplotlib.pyplot as plt

# based on Guo 2026, https://doi.org/10.1016/j.solener.2025.114253
def iam_soil_guo(aoi, SL0, Fn, P):
    costheta = np.maximum(0, cosd(aoi))  # always >= 0
    sec = 1 / costheta
    iam = pvlib.iam.physical(aoi)  # Guo used a table of imperical values, Table 2
    SL_mod = (sec ** P) * ((1 - (Fn / iam)) / (1 - Fn)) * SL0
    return SL_mod

# range of aoi values
aoi = np.arange(0, 80)

# parameters to match Guo 2026 Fig. 7a, left column (soiling loss 0.058)
P = 1
Fn = 0.7
SL0 = 0.058

# calculate modeled soiling loss
SL_mod = iam_soil_gou(aoi, SL0, Fn, P)

# plot it
plt.plot(aoi, SL_mod)
plt.ylabel('Soiling loss')
plt.xlabel('aoi (deg.)')
plt.show()

And the fancy "manually overlay screenshots in powerpoint with transparency and stretching" comparison:

The large negative values surprised me. But then, actually reading some of Guo 2026, I saw

It should be noted that the current model yields negative values at very large AOI (e.g., AOI > 80°). This artifact results from treating Fn as a constant, even though Fn – the ratio of scattered light reaching the PV cell to the normal-incidence transmittance [16] – should decrease at high AOI due to dust particles shading one another. Because solar irradiance is already very low at such large AOI values, the resulting inaccuracy is acceptable for typical applications when the irradiance-weighted soiling loss is of interest. Further work is needed if accurate modeling at high AOI is required.

If I were to continue working with this on my own, I would clip the lower bound of modeled aoi-dependent soiling loss to be no lower than the nominal soiling loss (SL0).

[adriesse]

If further work is needed, is it ready for pvlib? On the other hand, there are a lot of models that could use more work so that may not be the right question. On the other hand if he is actively working on it...

[williamhobbs]

@adriesse, I think it's useful now, with the modification of clipping the loss at a minimum of the nominal soiling. If that sort of modification is ok for pvlib, then I think it could be considered ready.

Without that modification, it could return very bad (large negative) results, which seems like a bad fit for pvlib.

I'll add that modifying the function with a "floor" is somewhat similar to the addition of the cap_adjustment option to pvsystem.pvwatts_dc nonlinear adjustment. That cap was not in the original reference, but Cliff approved that addition (here). A key difference is that what I'm suggesting here would not be optional.

On the other hand if he is actively working on it...

I don't know if anything is still being worked on. I guess we could send an email and ask...

[cwhanse]

@williamhobbs nice work.

I agree with @williamhobbs that the model is useful as is, and that clipping the loss is appropriate (with notes in the docstring).

I would build the empirical IAM table into the pvlib code and give the user an option to substitute a preferred IAM model. The p and F parameter values in the paper are hitched to the empirical IAM model, and I'm inclined to ask that pvlib code include default p and F from the paper. P could be interpolated from the paper's Table 3; open to other ideas here.

[markcampanelli]

This might be relevant in terms of a formulating a consistent implementation of empirical IAM functions across multiple applications in pvlib: #2050

Note: The reason I rail on and on about simpler interfaces in pvlib is that it makes seeing one's contributions across the finish line way easier, especially as the code base grows. Of course, it also reduces the mental load on the consumers, even though many of them don't realize how much of a good thing that is, esp. once they have their particular computational workflow set up in the loosey-goosey world of Python.

[williamhobbs]

@cwhanse thanks.

I agree that the IAM table from the paper should be the default, and it should also default to the paper’s Fn and P.

For P, I think using the values from Table 3 and interpolating probably makes the most sense. Based on the points in fig 5 and the regression used to get the values in Table 3, it seems reasonable to somehow extrapolate to zero soiling (SL0), but to fix the P value at 0.8 for SL0 greater than 15%. But I haven’t tested anything there, so I’m very open to suggestions a.

And clarify it all in the doc string.

And of course allowing custom IAM, Fn, and P should be included.

[williamhobbs]

I'm not sure how much this matters, but I can't seem to confirm where the empirical IAM values in Table 2 of Guo 2026 came from. I don't have a copy of the manuscript for ref 19, but slides are online*, and I don't see anything that matches Table 2. Ref 18 is open access (just the data, the related paper** is not open access), and includes lots of measurements, but I also can't find a match there.

* https://www.kiwa.com/globalassets/us/pvel/resources/kiwa-pvel-pvsc-iam-presentation-2024_06_12.pdf
** https://doi.org/10.1002/pip.3365

[cwhanse]

I am looking at a copy of [19] and I don't see those numbers. I think they may have been derived from the supplementary data for this paper: https://doi.org/10.1002/pip.3365 But the DTU server seems to have lost that file; maybe @AdamRJensen can help?