Aigner KM (2024)
Publication Language: English
Publication Type: Thesis
Publication year: 2024
URI: https://open.fau.de/handle/openfau/30750
This cumulative doctoral thesis presents a comprehensive exploration of data-driven optimization under uncertainty in the context of power system analysis. Critical mathematical challenges related to the operation of power grids are addressed, accompanied by innovative solution approaches. The primary focus is on several extensions of the optimal power flow problem which is the predominantly used model in the literature to optimize the power distribution in an electricity network. We study nonconvex mixed-integer nonlinear programs arising in power system analysis, which we solve by the construction and successive refinement of piecewise linear relaxations. Our work introduces various problem-specific and generally applicable algorithmic enhancements to obtain an efficient implementation that outperforms state-of-the-art solvers. Another focus are stochastic mixed-integer linear optimal power flow problems with probabilistic constraints. The solution approach is based on the robust safe approximation of the computationally intractable chance constraints. To construct the approximative problems, suitably defined confidence sets from historical data are computed. We derive a tractable reformulation of the resulting problems and prove quality guarantees about the robustness of the calculated solutions. Numerical experiments on benchmark instances with real weather and network data demonstrate the quality of our solutions. Further improvements are achieved by combining stochastic programming with a model-based prediction of uncertainties. Finally, we present a novel algorithmic framework for optimization under uncertainty over time. The approach uses online learning and scenario observations arriving as a data stream to learn more about the uncertain parameters. We provide a dynamic regret bound for our solutions and illustrate the broad applicability of our approach.
APA:
Aigner, K.-M. (2024). Data-driven Optimization under Uncertainty for Power Networks (Dissertation).
MLA:
Aigner, Kevin-Martin. Data-driven Optimization under Uncertainty for Power Networks. Dissertation, 2024.
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