A Log-Logistic Predictor for Power Generation in Photovoltaic Systems

Photovoltaic (PV) systems are dependent on solar irradiation and environmental temperature to achieve their best performance. One of the challenges in the photovoltaic industry is performing maintenance as soon as a system is not working at its full generation capacity. The lack of a proper maintenance schedule affects power generation performance and can also decrease the lifetime of photovoltaic modules. Regarding the impact of environmental variables on the performance of PV systems, research has shown that soiling is the third most common reason for power loss in photovoltaic power plants, after solar irradiance and environmental temperature. This paper proposes a new statistical predictor for forecasting PV power generation by measuring environmental variables and the estimated mass particles (soiling) on the PV system. Our proposal was based on the fit of a nonlinear mixed-effects model, according to a log-logistic function. Two advantages of this approach are that it assumes a nonlinear relationship between the generated power and the environmental conditions (solar irradiance and the presence of suspended particulates) and that random errors may be correlated since the power generation measurements are recorded longitudinally. We evaluated the model using a dataset comprising environmental variables and power samples that were collected from October 2019 to April 2020 in a PV power plant in mid-west Brazil. The fitted model presented a maximum mean squared error (MSE) of 0.0032 and a linear coefficient correlation between the predicted and observed values of 0.9997. The estimated average daily loss due to soiling was 1.4%.