Betriebsoptimierung von elektrischen Energieerzeugungsanlagen und Übertragungssystemen bei unvollständiger Information (English shop)

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The mathematical modelling and analysis of electrical power transmission systems with decentralised generation is motivated by the growing importance of renewable energy sources such as wind and solar power. Using such systems requires controlling not only the generating facilities but also the energy flows, and this while taking uncertainties into account. From a mathematical point of view, this gives rise to combinations of combinatorial and stochastic effects together with the inclusion of networks, which lead to highly nonlinear structures and call for suitable approximation techniques. Different interpretations of risk, from risk-neutral to risk-averse modelling using appropriate statistical parameters, are addressed. Decomposition algorithms for two-stage stochastic mixed-integer models are presented, with which it is possible to take into account both linear and nonlinear approximations of the energy flows while modelling randomness adequately. Numerous sample computations are presented.