Electricity markets under the influence of renewables: Modelling, prediction, and stochastic optimization

The German energy mix, which provides an overview of the sources of electricity available in Germany, is changing as a result of the expansion of renewable energy sources. With this shift towards sustainable energy sources such as wind and solar power, the electricity market situation is also in flux. Whereas in the past there were few uncertainties in electricity generation and only demand was subject to stochastic uncertainties, generation is now subject to stochastic fluctuations as well, especially due to weather dependency. To provide a supportive framework for this different situation, the electricity market has introduced, among other things, the intraday market, products with half-hourly and quarter-hourly time slices, and a modified balancing energy market design. As a result, both electricity price forecasting and optimization issues remain topical. In this thesis, we first address intraday market modeling and intraday index forecasting. To do so, we move to the level of individual bids in the intraday market and use them to model the limit order books of intraday products. Based on statistics of the modeled limit order books, we present a novel estimator for the intraday indices. Especially for less liquid products, the order book statistics contain relevant information that allows for significantly more accurate predictions in comparison to the benchmark estimator. Unlike the intraday market, the day ahead market allows smaller companies without their own trading department to participate since it is operated as a market with daily auctions. We optimize the flexibility offer of such a small company in the day ahead market and model the prices with a stochastic multi-factor model already used in the industry. To make this model accessible for stochastic optimization, we discretize it in time and space using scenario trees. Here we present existing algorithms for scenario tree generation as well as our own extensions and adaptations. These are based on the nested distance, which measures the distance between two distributions of stochastic processes. Based on the resulting scenario trees, we apply the stochastic optimization methods of stochastic programming, dynamic programming, and reinforcement learning to illustrate in which context the methods are appropriate.