Abstract

Wind and solar energies have significant potential to mitigate climate change by eliminating society's dependence on fossil fuels. One recognized challenge with their use in the power grid is their meteorologically induced high degree of variability coupled with the grid’s relatively stringent stability conditions. Given this reality, one might think achieving a high degree of predictability would be considered imperative. Unfortunately, this is not the case. Relying on the advice of the renewable energy forecasters, electricity system operators employ metrics of forecast accuracy that significantly understate the forecast errors. Specifically, the accepted metric of the generation forecast error in the renewable energy sector is calculated by dividing the forecast's mean absolute forecast error or RMSE by the capacity of the equipment used to generate the renewable energy. While non-statisticians may approve of this approach, statisticians will note that it can make an inaccurate forecast appear accurate if the technology has a low capacity factor (solar energy has a capacity factor of about 10%, i.e., the average level of generation relative to capacity is about 10%). Indicative of this, the forecasts of solar energy generation in Belgium have a capacity-weighted mean absolute error (CWMAE) of about 1.1%, a value that is not credible given that researchers who are strictly guided by science have conceded that their skill in forecasting solar radiation, a key driver of solar energy generation, is very low.
Using data from Belgium, this paper demonstrates that a capacity-weighted solar energy forecast error of 1.1 % corresponds to a statistically valid error metric of about 9.8% and a forecast skill score that is negative(Figure 1). With these dismal results in mind, this paper presents a statistical methodology to improve the predictability of solar energy generation with the hope that the results will help dispel the illusion of predictability that currently prevails. The paper's analysis indicates that the existing forecasts do not fully reflect expected meteorological conditions. It is further observed that solar energy generation is highly volatile at times but also has a significant diurnal autoregressive pattern. An ARCH/ARMAX time series model is formulated based on those properties. One of the key modeling innovations is the implementation of ARCH-in-mean effects, which boosts predictive accuracy by capturing the information in the conditional variance. The model is estimated using 15-minute data from Jan 1, 2017, through Dec 31, 2022. The model is evaluated using out-of-sample data from Jan 1, 2023, to Dec 31, 2023. The period-ahead out-of-sample predictions have a weighted-mean-absolute-percentage-error (WMAPE) of about 3.0 %, substantially less than the approximately 9.8 % WMAPE associated with the solar energy forecasts used by the system operator over the same period. While this finding may not be fully effective in getting renewable energy forecasters to rethink their approach, it may serve the larger purpose of informing the broader community, including system operators, that the misleading error metrics reported by solar energy forecasters are blocking the use of forecasting methods that can deliver true solar energy predictability.