The Accuracy of Solar Energy Forecasts and Prospects for Improvement

This paper begins by assessing the accuracy of solar energy forecasts relative to load forecasts for various locations in Germany, including the 50Hertz control area in eastern Germany. Two metrics are employed: the Energy Weighted Root-Mean-Squared Error (EWRMSE) and the Mean-Squared-Error Skill Score (MSESS), a metric which evaluates the skill of a forecast relative to a persistence forecast, i.e., a period-ahead forecast that naively assumes the outcome in period t equals the outcome in period t-1. Using either metric, we find that solar energy forecasts are substantially less accurate than load forecasts. Econometric evidence is presented that shows this forecast inaccuracy has adverse implications for power system operations in 50Hertz.

A first step in improving the forecast accuracy of solar energy is to examine the errors in existing forecasts. If the forecasts are optimal in the sense that they reflect all known information, then the forecast errors will be purely random, i.e. “white noise.” Based on Portmanteau (Q) tests for lags 1 through 300, none of the solar energy forecast errors we have evaluated exhibit the white noise property. For example, the null hypothesis of white noise is strongly rejected for 50Hertz’s solar energy forecast errors with p-values of 0.0000.  Specifically, the autocorrelation in these forecast errors exhibits a significant diurnal pattern. Forbes and Zampelli (2014) presented evidence that time–series econometric modeling of this pattern can lead to significant improvements in the accuracy of load forecasts.

Our analysis also indicates that the errors in the solar energy forecasts are statistically related to forecasted weather conditions. Specifically, an OLS regression of 50Hertz’s solar forecast errors on the day-ahead forecasted weather conditions for Berlin yields highly statistically significant coefficients on the forecasted values of temperature, dewpoint, visibility, and the probability of precipitation. A number of the coefficients corresponding to forecasted cloud cover are also highly statistically significant and nontrivial in magnitude. In short, the solar energy forecasts do not fully reflect the information contained in the day-ahead weather forecasts. Additionally, the OLS regression indicates that the magnitude of the solar energy forecast error is not independent of the forecasted level of solar energy. An OLS analysis of 50Hertz’s wind forecast errors indicates that these shortcomings in the forecasts are not limited to solar energy. Nor is the finding is limited to 50Hertz.

Based on the attributes of the forecast errors, an autoregressive–moving-average model with exogenous inputs (ARMAX) was formulated to predict solar energy generation. The model makes use of 50Hertz’s existing solar energy forecasts and day-ahead weather forecasts for Berlin provided to us from CustomWeather, a specialized provider of weather forecasts based in San Francisco (http://customweather.com/).  In the model, the following forecasted weather variables are statistically significant: day-ahead forecasted temperature, day-ahead forecasted probability of precipitation, day-ahead forecasted wind speed, and day-ahead forecasted cloud cover.  The model yields out-of-sample period ahead predictions with an energy weighted RMSE of about 4.8 percent and a MSESS of 0.768 (Figure 2). Variants of this methodology have also yielded significant out-of-sample improvements in the California ISO’s solar energy forecasts.