Tim Ritmeester

• The threats posed by climate change require fundamental changes in the nature of the operation of power grids. The increase in fluctuating sources of renewable energy requires flexible and fast-acting control, data processing, and market adjustments. In turn, these lead to complex nonlinear interactions and non-trivial collective fluctuations, which require sophisticated methods of analysis. This dissertation reports on work using a variety of methods from statistical physics to extend the applicability of methods that are already commonly used in control engineering, machine learning, and economic analysis. First, we use the Belief Propagation algorithm (BP), an efficient local algorithm for Bayesian inference, optimization and network analysis, which improves upon Curie-Weiss mean-field theory by taking local correlations into account. We apply the algorithm to statistically analyze conditions under which an accurate estimate of power flows can be obtained from noisy and incomplete measurement sets, and show that it can be used for effective dimensional reduction of power grids. We derive a novel implementation of BP for supply networks, which strongly enhances its convergence and accuracy, explicitly demonstrate its applicability to power grid state estimation and natural gas pipeline network analysis, and discuss further applications to supply networks. Secondly, we map traders' abuse of reserve energy to a minority game and study it using agent-based modeling and the cavity method. The cavity method improves upon Curie-Weiss mean-field theory by including backreactions between traders and market prices, and is formally an approximation on the same level as BP. We show that for this application the cavity method has a natural interpretation in terms of self-consistent linear response. We derive policy recommendations by showing the effectiveness of penalties on large contributors to the abuse of reserve energy, and by demonstrating that external noise is [...]