Probabilistic forecasting for solar energy

: This paper describes the forecasting of 15 minute solar irradiation on a horizontal plane (GHI) for Seattle, USA, as well as 15 minute solar f arm output for Broken Hill, Australia. The goal is to set error bounds on the forecast, specifically estimating 15 quantiles, from essentially minimum to m aximum. In practice, the quantiles calculated are { 0 . 005 , 0 . 025 , 0 . 05 , 0 . 1 , 0 . 2 , . . . , 0 . 8 , 0 . 9 , 0 . 95 , 0 . 975 , 0 . 995 } . The forecast horizons for both variables are one step ahead (for time t + 1 time interval performed at time t ). The procedure entails first calculating point f orecasts, and then using quantile regression techniques to form the quantiles of the resulting noise terms. The modelling process is performed on a year’s data for 2017 for both locations, and then tested on data from 2018. In the standard modelling manner, the models developed for both the point forecasts and quantiles on the 2017 data are applied to the 2018 data, whereupon the quantiles are added to the point forecasts for initial verification of the efficacy of the procedure. The point forecast contains a model for the seasonality using Fourier series for the significant cycles. For GHI, they are once a year, once and twice a day, plus beat frequencies to modulate the daily cycle to suit the time of year. Since the solar farm has an oversized field, thus capping the output, the only necessary cycles are once and twice a day. Once the seasonality model is subtracted from the original series, the residuals are represented by an ARMA ( p, q ) forecast model. The combination of the models forms the point forecast. The noise terms from this process are modelled using quantile regression. For quantile level τ of the response, the goal is to