Modeling and optimal strategies in short-term energy markets.

Summary This thesis aims at providing theoretical tools to support the development and management of intermittent renewable energies in short-term electricity markets.In the first part, we develop an exploitable equilibrium model for price formation in intraday electricity markets. To this end, we propose a non-cooperative game between several generators interacting in the market and facing intermittent renewable generation. Using game theory and stochastic control theory, we derive explicit optimal strategies for these generators and a closed-form equilibrium price for different information structures and player characteristics. Our model is able to reproduce and explain the main stylized facts of the intraday market such as the specific time dependence of volatility and the correlation between price and renewable generation forecasts.In the second part, we study dynamic probabilistic forecasts as diffusion processes. We propose several stochastic differential equation models to capture the dynamic evolution of the uncertainty associated with a forecast, derive the associated predictive densities and calibrate the model on real weather data. We then apply it to the problem of a wind producer receiving sequential updates of probabilistic wind speed forecasts, which are used to predict its production, and make buying or selling decisions on the market. We show to what extent this method can be advantageous compared to the use of point forecasts in decision-making processes. Finally, in the last part, we propose to study the properties of aggregated shallow neural networks. We explore the PAC-Bayesian framework as an alternative to the classical empirical risk minimization approach. We focus on Gaussian priors and derive non-asymptotic risk bounds for aggregate neural networks. This analysis also provides a theoretical basis for parameter tuning and offers new perspectives for applications of aggregate neural networks to practical high-dimensional problems, which are increasingly present in energy-related decision processes involving renewable generation or storage.