TINSI Laura

This thesis focuses on providing theoretical tools to help in the development and management of intermittent renewable energy in short term electricity markets.In the first part, we develop a tractable equilibrium model for price formation in intraday electricity markets. For this, we propose a non cooperative game between several producers interacting in the market and facing an intermittent renewable production. Using stochastic control and game theory, we derive explicit optimal strategies for these producers as well as a closed form equilibrium price for different information structures and player characteristics. Our model allows to reproduce and explain the main stylized features of the intraday market such as the specific time dependence of volatility and the correlation between the price and the renewable production forecasts.In the second part, we study dynamic probabilistic forecasts in the diffusion framework. We propose several stochastic differential equation models to capture the dynamic evolution of the uncertainty associated to a forecast, derive the associated predictive densities and calibrate the model on real meteorological data. We then apply it to the problem of a wind energy producer receiving sequential updates of the probabilistic forecasts of the wind speed used to predict her production and make trading decisions in the market. We show to what extent this method can outperform the use of point forecasts in decision-making processes.Finally, in the last part, we propose to study the propertiesof aggregated shallow neural networks. We explore thePAC-Bayesian framework as an alternative to the classicalempirical risk minimization approach. We focus on Gaussianpriors and derive non-asymptotic risk bounds for theaggregated neural networks. These bounds yield minimaxrates of estimation over Sobolev smoothness classes.This analysis also provides a theoretical basis for tuning theparameters and offers new perspectives for applicationsof aggregated neural networks to practical high dimensionalproblems increasingly present in energy decision problemsinvolving renewables or storage.

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.

No summary available.