Structured Model Reduction and its Application to Power Systems

Abstract: Many of today’s engineering systems have a network structure. Consider for instance power systems, where multiple grids of different geographical coverage are interconnected to form larger grids, a set of vehicles moving in formation or distributed control systems, where several controllers act locally with limited information. These systems are all comprised of multiple sub- systems and the full system can easily become very large, which can make it intractable for analysis or controller design.Model reduction is a means to overcome this issue. Most traditional model reduction algorithms do not preserve the network structure, however some algorithms can be used to reduce the subsystems locally, while retaining the network topology and approximating the global behavior of the interconnection. These algorithms will be the focus of this thesis.In the first half of the thesis we will deal with one such structure preserving model reduction algorithm. An important property of model reduction algorithms is their ability to give some performance guarantees prior to their application, for instance in terms of an upper bound of the model error. This can be achieved by formulating the reduction method as a linear matrix inequality, but since they are not always feasible it imposes a limitation on its usefulness. However it is showed in this thesis that certain network structures where the subsystems are either stable or strictly positive real always allow for solutions of their corresponding linear matrix inequalities. We show that common boiler-header systems modeled with grey-box identification belong to this class of systems and we demonstrate how the model order of them can be significantly reduced.In the other half of the thesis the focus lies on power systems and the model reduction of them. We formulate it as a structured model reduction problem and propose an algorithm for the reduction of part of the grid while retaining a high-fidelity model of the study area. This can be of relevance for a subsequent contingency analysis. We also demonstrate how reduced models can be of use for controller design by suppressing certain modes. The algorithm is applied to the Klein-Rogers-Kundur 2-area system which dynamics is well understood and to a much larger real-sized model of the Nordic power grid. We conclude that a significant model reduction can be done without losing critical dynamics of the study area.