Stochastic Soiling Loss Models for Heliostats in Concentrating Solar Power Plants

Reflectance losses on solar mirrors due to soiling pose a formidable challenge for Concentrating Solar Power (CSP) plants. Soiling can vary significantly from site to site -- from fractions of a percent to several percentage points per day (pp/day), a fact that has motivated several studies in soiling predictive modelling. Yet, existing studies have so far neglected the characterization of statistical uncertainty in their parameters and predictions. In this paper, two reflectance loss models are proposed that model uncertainty: an extension of a previously developed physical model and a simplified model. A novel uncertainty characterization enables Maximum Likelihood Estimation techniques for parameter estimation for both models, and permits the estimation of parameter (and prediction) confidence intervals. The models are applied to data from ten soiling campaigns conducted at three Australian sites (Brisbane, Mount Isa, Wodonga). The simplified model produces high-quality predictions of soiling losses on novel data, while the semi-physical model performance is mixed. The statistical distributions of daily losses were estimated for different dust loadings. Under median conditions, the daily soiling losses for Brisbane, Mount Isa, and Wodonga are estimated as $0.53 \pm 0.62$, $0.1 \pm 0.1$, and $0.57 \pm 0.14$ pp/day, respectively. Yet, higher observed dust loadings can drive average losses as high as $2.50$ pp/day. Overall, the results suggest a relatively simple approach characterizing the statistical distributions of soiling losses using airborne dust measurements and short reflectance monitoring campaigns.