Solar radiation forecasting

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Table of contents

1 Introduction 
1.1 Forecasting photovoltaic power production with meteorological forecasts
1.1.1 Context
1.1.2 Weather forecasting
1.1.3 Solar radiation forecasting
1.1.4 PV power data and statistical modeling
1.1.5 Probabilistic forecasts of PV power with meteorological forecasts
1.2 Sequential aggregation
1.2.1 Context
1.2.2 Algorithm evaluation with regret bounds
1.2.3 Online learning algorithms
1.2.4 Examples of loss functions
1.3 Probabilistic forecasting with non-local strictly proper scoring rules
1.3.1 Binary case
1.3.2 Ranked and continuous case
1.3.3 Examples with the CRPS
2 Ensemble forecast of solar radiation using TIGGE weather forecasts and HelioClim database 
2.1 Introduction
2.2 Analysis of TIGGE solar radiation and HelioClim database
2.2.1 Description of TIGGE data
2.2.2 Analysis of the TIGGE ensembles of forecasts
2.2.3 Reference performance measures
2.2.4 Comparison with HelioClim
2.3 Ensemble forecast strategy: sequential aggregation
2.3.1 Notation
2.3.2 Sequential aggregation: method
2.3.3 Algorithm
2.4 Application
2.4.1 Experiment setup
2.4.2 Results
2.5 Conclusion
2.A.1 Methods
2.A.2 Numerical results
3 Online learning with the CRPS for ensemble forecasting
3.1 Mathematical background
3.1.1 Bibliographical remarks
3.1.2 The Continuous Ranked Probability Score (CRPS)
3.1.3 The ensemble CRPS
3.1.4 Bias of the ensemble CRPS with underlying mixture model
3.1.5 Mixture model described by classes of members
3.2 Online learning methods
3.2.1 Theoretical background
3.2.2 Ridge regression
3.2.3 Exponentiated gradient
3.3 Numerical example
3.3.1 Simple model
3.3.2 Experiments without online learning
3.3.3 Experiments with weight updates
4 Scoring and learning forecasts densities 
4.1 Extension to threshold-weighted and quantile-weighted scoring rules
4.1.1 Effect of threshold-weighting
4.1.2 Effect of quantile-weighting
4.2 Probabilistic forecasting with observational noise
4.2.1 Generalized least square with the CRPS
4.2.2 Discussion and further work
5 Application of online CRPS learning to probabilistic PV power forecasting
5.1 Methods
5.1.1 Production and meteorological data
5.1.2 Conversion of meteorological forecasts to production forecasts
5.1.3 Quantile forecasts
5.1.4 Linear opinion pools
5.2 Evaluation
5.2.1 The CRPS
5.2.2 Other diagnostic tools
5.3 Online learning with the CRPS
5.3.1 Background
5.3.2 Example of general algorithm
5.3.3 ML-Poly
5.4 Application
5.4.1 Experiment setup
5.4.2 Results
6 PV probabilistic forecasts with the AROME high resolution forecasts
6.1 Building an ensembles of forecasts from AROME forecasts
6.1.1 Leveraging the high spatio-temporal resolution
6.1.2 First sequential aggregation results with AROME meteorological experts
6.1.3 Adding rolling quantiles experts
6.2 Sequential aggregation results with AROME statistically calibrated experts
6.2.1 Improvements with rolling quantile experts
6.2.2 Comparison of AROME with other forecasts from Météo France and ECMWF
6.3 Discussion and perspectives
7 PV probabilistic forecasts with intraday updates for insular systems
7.1 Intraday PV updates experimental setup
7.1.1 Operational forecasts
7.1.2 Building new forecasts with intraday updates
7.1.3 Online learning experiment
7.2 Results
7.2.1 Time-series, spread and weights
7.2.2 Probabilistic forecasts performance and calibration
Appendix 7.A Empirical results of quantile-weighted scoring rules with realworld data
8 Thesis conclusions