On the usefulness of solar energy forecasting in the presence of asymmetric costs of errors

Because of the weather-associated variability of renewable energy generation, forecasting is an inherent component of an overall solution to reduce the grid integration cost of renewable energy. Accuracy of a forecast is characterized typically by metrics such as root mean square error (RMSE) or mean absolute error (MAE). Such metrics, however, may not comprehensively capture the usefulness of a forecast. Use cases of forecasts are usually complex and are connected to how energy producers, balancers, or traders may apply the forecast to minimize some cost functions in order to improve performance. Often a cost function is asymmetric, unlike RMSE or MAE. Here, we treat complex cost functions as asymmetric perturbations to the symmetric RMSE metric and ask how a forecast can be statistically corrected to minimize the cost function. The analysis leads to an analytical expression for one aspect of a forecast's usefulness, which characterizes the capability of a user to benefit from the knowledge of the asymmetry of the cost function. As a case study, we present a comparison of solar forecasts derived from a number of numerical weather predictions at a test site in Rutland, Vermont.