Regime-Based Forecast Corrections Using Support Vector Machines

Numerical weather prediction (NWP) is widely accepted as the most accurate method to produce day-ahead energy forecasts. However, numerous studies have shown day-ahead solar and wind energy forecasts contain systematic errors. Typically, forecast bias error is removed using bulk-statistic corrections such as model-output-statistics (MOS). However, when applied universally, MOS will indiscriminately adjust all forecasts. In conditions in which distinct error regimes exist, a universal MOS correction can result in larger mean-absolute-error (MAE) even as bias is removed.

This can be demonstrated for solar forecasts. Solar forecasts contain two distinct error regimes: observed clear and observed cloudy. In general, forecast accuracy is very high for observed clear days as NWP accurately predict irradiance in the absence of clouds. However, since forecast predictions are imperfect, some days forecast as clear inevitably will be observed as cloudy. As such, the error distribution is inherently skewed towards large, but infrequent over-predictions on forecast-clear days. A simple MOS model applied to eliminate mean-bias-error (MBE) will subsequently adjust every forecast downward, including those that were initially correct. In this example, error on a typical day will slightly increase even though overall MBE is being reduced to zero.

Therefore, when independent error regimes exist, MOS methods are insufficient to accurately adjust forecast data. Instead, a regime-based method may be implemented to discriminately apply MOS corrections to each regime. This results in a two-step forecast correction process. First, using independent forecast variables, the likely regime is identified. Second, the MOS correction is chosen based on the likely regime. In the example of solar forecasting, independent MOS corrections are created for likely-clear and likely-cloudy regimes.

In this study, support vector machines (SVMs) are used to classify forecast data into distinct regimes. SVMs are a method of supervised classification which mathematically describe the boundary between defined classes as a function of multiple input variables. For example, given forecast relative humidity, forecast temperature, and observed regime, an SVM would define the optimal division of regime as a function of forecast relative humidity and temperature. Here, 40 independent forecast variables from the North American Mesoscale (NAM) and Global Forecast System (GFS) model were used to determine the optimum classification function to define observed clear and cloudy regimes. Next, MOS correction functions were generated for each regime independently. Finally, the method was applied to operational solar forecasts. Out of sample results showed overall forecast improvements of 2% MAE. Cloudy conditions were especially improved, with MAE reduced by greater than 15%. Additionally, this method is applied to wind power forecasts with similar results.