# HSU Soiling Model

Described by Coello and Boyle (2019), the Humboldt State University (HSU) soiling model predicts time series soiling ratio SR based on accumulated particulate mass density $$\omega$$ (g/m2):

$$\DeclareMathOperator\erf{erf} SR = 1 – 34.37 * \erf(0.17 * \omega^{0.8473})$$

where $$\erf$$ refers to the Gauss error function.  Accumulated mass density $$\omega$$ is the cumulative sum of interval accumulation $$m$$, resetting to zero on cleaning events.  $$m$$ is calculated using assumptions of airborne particulate concentrations $$C$$ and settling velocities $$v$$ for PM2.5 and PM10:

$$m = (v_{10} C_{10} + v_{2.5} C_{2.5}) \delta T \cos \theta_T$$

where $$\delta T$$ is the timestep length and $$\theta_T$$ is the array tilt.

Coello and Boyle define three methods for determining the velocities $$v$$, indicating that assuming fixed settling velocities results in the most reasonable predictions of soiling ratio.  Note that, because the input particulate concentrations can be time-varying quantities, the rate of soiling accumulation can vary with time as well.

A peculiarity of the equation predicting $$SR$$ as a function of accumulated mass $$\omega$$ is that the predicted soiling ratio can drop no lower than 0.6563.  Boyle et al. (2015) place an upper limit of $$\omega = 10$$ g/m2 on the valid range for this equation, corresponding to a soiling ratio of roughly 0.6875.

The HSU soiling model is implemented in PVLIB_MATLAB with the pvl_soiling_hsu function and in pvlib-python with pvlib.soiling.hsu.

References

 M. Coello and L. Boyle, “Simple Model for Predicting Time Series Soiling of Photovoltaic Panels,” IEEE Journal of Photovoltaics, vol. 9, no. 5, pp. 1382–1387, Sep. 2019. doi: 10.1109/jphotov.2019.2919628.

 L. Boyle, H. Flinchpaugh, and M. P. Hannigan, “Natural soiling of photovoltaic cover plates and the impact on transmission,” Renewable Energy vol. 77, pp. 166–173, May 2015. doi: 10.1016/j.renene.2014.12.006