Order reduction for nonlinear dynamic models of district heating networks
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Beschreibung
This thesis focuses on the calculation of reduced order models for a numerically efficient simulation of district heating networks. A control system is derived, describing the transport of energy in incompressible Euler-like equations. The benefits of the suggested surrogate model are demonstrated at existing large-scale networks. One of the presented applications is the numerical computation of an optimal control of the feed-in power.
This thesis focuses on the formulation of reduced order models for a numerically efficient simulation of district heating networks. Their dynamics base upon incompressible Euler equations, forming a system of quasi-linear hyperbolic partial differential equations. The algebraic constraints introduced by the network structure cause dynamical changes of flow direction as a central difficulty. A control system is derived allowing to analyze essential properties of the reduced order model such as Lyapunov stability. By splitting the problem into a differential part describing the transport of thermal energy and an algebraic part defining the flow field, tools from parametric model order reduction can be applied. A strategy is suggested which produces a global Galerkin projection based on moment-matching of local transfer functions. The benefits of the resulting surrogate model are demonstrated at different, existing large-scale networks. In addition, the performance of the suggested model is studied in the numerical computation of an optimal control of the feed-in power employing a discretize-first strategy.
Autor*in
Markus Rein
Themen in »Order reduction for nonlinear dynamic models of district heating networks«
Fraunhofer ITWM numerical analysis heat transfer processes optimization district heating network model order reduction optimal control applications linear time-varying systems Lyapunov stability angewandte Mathematiker Energieingenieur Berechnungsingenieur Angewandte Mathematiker Energieingenieure Berechnungsingenieure