Non-linear multivariate models for the estimation of global solar radiation received across five cities in South Africa

South Africa continues to lag globally in the adoption of renewable energy systems despite a notable decrease in the cost of applicable renewable energy technologies over the past five years. Most applications of potential solar renewable energy systems are currently in various stages of investigation, leaving this readily accessible resource capacity idle. The present study proposes linear and non-linear analysis of multivariate models for estimating global solar radiation (GSR) received across five cities in South Africa. The significance of this study is to provide effective GSR estimation in the application of solar technologies, while increasing their implementation. The dependency of GSR on meteorological variables such as air temperature, relative humidity and relative sunshine duration was evaluated for January 2007 to June 2018 to realise estimation models for each of the study sites. The Hargreaves-Samani and Angstrom-Prescott empirical models served as the basis for single variable analysis of GSR reliance on each meteorological parameter and their relative variations. The results indicated that the proposed non-linear, multivariate equations perform better than the empirical models as well as linear, single variable regression equations. The suggested models are site-specific and demonstrate a strong correlation to historic GSR values with low, acceptable error indicators. It was also recognised that second- and third-order relationships between the clearness index and multiple meteorological variables provide a more accurate description of GSR for most of the cities under study. These methods are cost-effective, easily accessible and appropriate for the evaluation of the feasibility of solar photovoltaic technologies in South Africa.