Josselin Le Gal La Salle

In recent years, the prominence of probabilistic forecasting has risen among numerous research fields (finance, meteorology, banking, etc.). Best practices on using such forecasts are, however, neither well explained nor well understood. The question of the benefits derived from these forecasts is of primary interest, especially for the industrial sector. A sound methodology already exists to evaluate the value of probabilistic forecasts of binary events. In this paper, we introduce a comprehensive methodology for assessing the value of probabilistic forecasts of continuous variables, which is valid for a specific class of problems where the cost functions are piecewise linear. The proposed methodology is based on a set of visual diagnostic tools. In particular, we propose a new diagram called EVC (“Effective economic Value of a forecast of Continuous variable”) which provides the effective value of a forecast. Using simple case studies, we show that the value of probabilistic forecasts of continuous variables is strongly dependent on a key variable that we call the risk ratio. It leads to a quantitative metric of a value called the OEV (“Overall Effective Value”). The preliminary results suggest that typical OEVs demonstrate the benefits of probabilistic forecasting over a deterministic approach.

With the fast increase of solar energy plants, a high-quality short-term forecast is required to smoothly integrate their production in the electricity grids. Usually, forecasting systems predict the future solar energy as a continuous variable. But for particular applications, such as concentrated solar plants with tracking devices, the operator needs to anticipate the achievement of a solar irradiance threshold to start or stop their system. In this case, binary forecasts are more relevant. Moreover, while most forecasting systems are deterministic, the probabilistic approach provides additional information about their inherent uncertainty that is essential for decision-making. The objective of this work is to propose a methodology to generate probabilistic solar forecasts as a binary event for very short-term horizons between 1 and 30 min. Among the various techniques developed to predict the solar potential for the next few minutes, sky imagery is one of the most promising. Therefore, we propose in this work to combine a state-of-the-art model based on a sky camera and a discrete choice model to predict the probability of an irradiance threshold suitable for plant operators. Two well-known parametric discrete choice models, logit and probit models, and a machine learning technique, random forest, were tested to post-process the deterministic forecast derived from sky images. All three models significantly improve the quality of the original deterministic forecast. However, random forest gives the best results and especially provides reliable probability predictions.

In the realm of solar forecasting, it is common to use a clear sky model output to deseasonalise the solar irradiance time series needed to build the forecasting models. However, most of these clear sky models require the setting of atmospheric parameters for which accurate values may not be available for the site under study. This can hamper the accuracy of the prediction models. Normalisation of the irradiance data with a clear sky model leads to the construction of forecasting models with the so-called clear sky index. Another way to normalize the irradiance data is to rely on the extraterrestrial irradiance, which is the irradiance at the top of the atmosphere. Extraterrestrial irradiance is defined by a simple equation that is related to the geometric course of the sun. Normalisation with the extraterrestrial irradiance leads to the building of models with the clearness index. In the solar forecasting domain, most models are built using time series based on the clear sky index. However, there is no empirical evidence thus far that the clear sky index approach outperforms the clearness index approach. Therefore the goal of this preliminary study is to evaluate and compare the two approaches. The numerical experimental setup for evaluating the two approaches is based on three forecasting methods, namely, a simple persistence model, a linear AutoRegressive (AR) model, and a non-linear neural network (NN) model, all of which are applied at six sites with different sky conditions. It is shown that normalization of the solar irradiance with the help of a clear sky model produces better forecasts irrespective of the type of model used. However, it is demonstrated that a nonlinear forecasting technique such as a neural network built with clearness time series can beat simple linear models constructed with the clear sky index.