Multivariate Forecasting of Solar Energy

When methods for forecasting solar radiation time series were first developed, the principal applications were for estimating performance of rooftop photovoltaic or hot water systems. If there were significant errors in the forecast, the consequences were not severe. In recent times there has been increasing development of larger solar installations, both large scale photovoltaic and also concentrated solar thermal. In order to first influence financial backers to participate in their development, and also to potentially compete in the electricity markets, better forecasting models are required than simple Box-Jenkins models, such as those outlined in Boland (2008). In Huang et al (2013), we developed a combination model linking a standard autoregressive approach with a resonating model borrowed from work on dynamical systems, and also an additional component that greatly enhances forecasting ability. This model was developed for a solar radiation series at a single site. In this article I give an introduction to the tools needed for the multivariate forecasting of solar radiation. The modelling was developed for three sites in Guadeloupe, approximately 20 km. jointly from each other. One would expect significant cross correlation between the sites since they are affected by a common climate influence, Les Alizes, the Trade Winds. Thus, cloud bands inevitably pass over the sites at regular intervals. I demonstrate the techniques required to pre whiten the data (as far as possible) for a single site. The next step involved checking the cross correlation of the noise between sites, finding significant correlation between the sites at time t and also between the values at time t and time t - 1. A subsequent one lag multivariate time autoregressive model was estimated. It was hoped that the three noise variables resulting from this modelling would be iid. However, this was not to be the case and all three noise series exhibited conditional heteroscedasticity. In this case, ARCH models sufficed to describe this behaviour.