Mathieu David

Spatial and temporal variability of solar energy

This article summarizes and analyzes recent research by the authors and others to understand, characterize and model solar resource variability. This research shows that understanding solar energy variability requires a definition of the temporal and spatial context for which variability is assessed; and describes a predictable, quantifiable variability-smoothing space-time continuum from a single point to 1000’s of km and from seconds to days. Implications for solar penetration on the power grid and variability mitigation strategies are discussed.

Solar Resource Variability

In this chapter, we describe a methodology to quantify variability of the solar resource. We describe how the considered temporal scales, from seconds to hours, and geographical scales, from a single point to a subcontinent, are interrelated and lead to a quantifiable smoothing effect. We discuss implications of the temporal/spatial nature of solar-resource variability for the solutions needed to absorb a growing proportion of solar-generated energy on power grids. Variability is a general term that applies to many aspects of solar radiation. For example, it is used to refer to change in the solar resource from one year or one season to the next, as well as change from one site to another ( Gueymard and Wilcox 2011, Vignola 2001).

Bayesian and Sensitivity Analysis Approaches to Modeling the Direct Solar Irradiance

In this paper, emphasis is put on the design of a neural network (NN) to model the direct solar irradiance. Since, unfortunately, a neural network is not a statistician -in-a-box, building a NN for a particular problem is a nontrivial task. As a consequence, we argue that in order to properly model the direct solar irradiance, a systematic methodology must be employed. For this purpose, we propose a two-step approach to building the NN model. The first step deals with a probabilistic interpretation of the NN learning by using Bayesian techniques. The Bayesian approach to modeling offers significant advantages over the classical NN learning process. Among others, one can cite (i) automatic complexity control of the NN using all the available data and (ii) selection of the most important input variables. The second step consists of using a new sensitivity analysis-based pruning method in order to infer the optimal NN structure. We show that the combination of the two approaches makes the practical implementation of the Bayesian techniques more reliable.

Solar Forecasting in a Challenging Insular Context

This paper aims at assessing the accuracy of different solar forecasting methods in the case of an insular context. Two sites of La Reunion Island, Le Tampon and Saint-Pierre, are chosen to do the benchmarking exercise. Reunion Island is a tropical island with a complex orography where cloud processes are mainly governed by local dynamics. As a consequence, Reunion Island exhibits numerous micro-climates. The two aforementioned sites are quite representative of the challenging character of solar forecasting in the case of a tropical island with complex orography. Hence, although distant from only 10 km, these two sites exhibit very different sky conditions. This work focuses on day-ahead and intra-day solar forecasting. Day-ahead solar forecasts are provided by the European Center for Medium-Range Weather Forecast (ECMWF). This organization maintains and runs the Numerical Weather Prediction (NWP) model named Integrated Forecast System (IFS). In this work, post-processing techniques are applied to refine the output of the IFS model for day-ahead forecasting. Statistical models like a recursive linear model or a nonlinear model such as an artificial neural network are used to produce the intra-day solar forecasts. It is shown that a combination of the IFS model and the neural network model further improves the accuracy of the forecasts.

Solar Radiation Probabilistic Forecasting

In contrast to deterministic forecasts, probabilistic forecasts give additional information about the inherent uncertainty embodied in weather predictions. In the realm of solar forecasting, prediction intervals are especially important to assess risks in grid operations and to optimize the energy storages needed to ensure the supply–demand balance. Even if the development of probabilistic solar forecasts is relatively recent, the main available methods come from other fields of meteorology, particularly from the wind domain. This chapter reviews some of the methods used to generate probabilistic solar forecasts. A special emphasis is put on short term (from several hours to several days) and very short term (from several minutes to several hours) forecasts. As the verification of the quality of the probabilistic forecasts is of major interest, graphical tools like reliability diagram and rank histogram are depicted. These diagnostic tools are relevant for assessing the good calibration of the probabilistic forecasts. In addition, a quantitative score, the CRPS, is also proposed. The CRPS takes into account the different sources of uncertainties and as a proper score, the CRPS is useful to rank competing forecasting methods.