Matrixrobustheit Algorithmen, Komplexität Und Anwendung Zur Netzwerküberwachung Zur Erlangung Des Akademischen Grades Diplom-informatiker

For the management of a power network it is essential to know or be able to calculate the current values, e. g. active and reactive powers, voltages etc. such that, in the event of an unexpected behavior emergency actions can be initiated. But in large distribution network some values change over the time. Thus, measurements are installed to determine the required values. This diploma thesis analyzes the question whether a network remains observable, i. e. whether the required values are still calculable, even if any k measurements fail. Using a work of Jochen Alber and Markus Pöller this question leads to the problem Matrix Robustness: Does a given, so-called sensitivity matrix have full rank after dropping an arbitrary set of k rows? In this thesis divers equivalences to other problems are presented, e. g. to the well-known Minimum Distance from coding theory. Using this equivalence the NP -completeness is proven when restricting the sensitivity matrix to finite fields. The complexity for infinite fields remains open. Furthermore, algorithms solving Matrix Robustness are developed. This includes an exact polynomial-time algorithm for a special case, an exact algorithm based on mixed integer programming (MIP) and a non-exact polynomial-time heuristic. Both the MIP based algorithm and the heuristic are tested on realistic data generated from power network models and synthetic data sets. Finally, some interesting relationships to further problems are presented that may provide starting points for future research. In addition, this part of the diploma thesis presents a flaw in a proof in the literature for the case of infinite fields that could have settled the question for the complexity of Matrix Robustness in the case of infinite fields.