Statistical modelling and estimation of solar radiation.

Abstract

Solar radiation is a primary driving force behind a number of solar energy applications such as photovoltaic systems for electricity generation amongst others. Hence, the accurate modelling and prediction of the solar flux incident at a particular location, is essential for the design and performance prediction of solar energy conversion systems. In this regard, literature shows that time series models such as the Box-Jenkins Seasonal/Non-seasonal Autoregressive Integrated Moving Average (S/ARIMA) stochastic models have considerable efficacy to describe, monitor and forecast solar radiation data series at various sites on the earths surface (see e.g. Reikard, 2009). This success is attributable to their ability to capture the stochastic component of the irradiance series due to the effects of the ever-changing atmospheric conditions. On the other hand at the top of the atmosphere, there are no such conditions and deterministic models which have been used successfully to model extra-terrestrial solar radiation. One such modelling procedure is the use of a sinusoidal predictor at determined harmonic (Fourier) frequencies to capture the inherent periodicities (seasonalities) due to the diurnal cycle. We combine this deterministic model component and SARIMA models to construct harmonically coupled SARIMA (HCSARIMA) models to model the resulting mixture of stochastic and deterministic components of solar radiation recorded at the earths surface. A comparative study of these two classes of models is undertaken for the horizontal global solar irradiance incident on the solar panels at UKZN Howard College (UKZN HC), located at 29.9º South, 30.98º East with elevation, 151.3m. The results indicated that both SARIMA and HCSARIMA models are good in describing the underlying data generating processes for all data series with respect to different diagnostics. In terms of the predictive ability, the HCSARIMA models generally had a competitive edge over the SARIMA models in most cases. Also, a tentative study of long range dependence (long memory) shows this phenomenon to be inherent in high frequency data series. Therefore autoregressive fractionally integrated moving average (ARFIMA) models are recommended for further studies on high frequency irradiance.