Results for selected gas and power networks are presented, including a first version of the partDE-Hy demonstrator for analysis of power-togas scenarios.Adams, T., Vu, H.D.
BENNER LAB PROJECT PISCES SOFTWARE
Several new theoretical results as well as related software prototypes are introduced. This chapter gives an overview of MathEnergy by discussing selected new developments related to model order reduction for gas networks, state estimation for gas and power networks, as well as cross-sectoral modeling, simulation and ensemble analysis. The German MathEnergy project aims to overcome these shortcomings by developing selected mathematical key technologies for energy networks and respective software. Despite rapid progress, the energy industry is insufficiently equipped for the super-ordinate planning, monitoring and control tasks, based on increasingly large and coupled network simulation models. Both methods are well suited for high performance environments and only rely on basic numerical linear algebra building blocks.įor a sustainable and CO 2 neutral power supply, the entire energy cycles for power, gas and heating grids have to be taken into account simultaneously. The other one improves the expected accuracy, compared to methods currently in use, with a comparable performance. One requires less computational effort while providing the same degree of accuracy. This new viewpoint is used to develop two new methods for solving the eigenvalue problem. These results enable us to develop a new perspective on the state-of-the-art solution approach for crystalline systems. In this work, we present new theoretical results characterizing the structure of the two forms in the language of non-standard scalar products. One form can be acquired for crystalline systems, another one is more general and can for example be used to study molecules. Additionally, certain definiteness properties typically hold. The matrix always shows a $2\times 2$ block structure. The eigenpairs of the resulting large, dense, structured matrix can be used to compute dielectric properties of the considered crystalline or molecular system. To harness the predictive power of the equation, it is mapped to an eigenvalue problem via an appropriate discretization scheme. without the need for empirical data in the model. The Bethe-Salpeter equation is the state-of-the-art approach to describe these processes from first principles (ab initio), i.e. Optical properties of materials related to light absorption and scattering are explained by the excitation of electrons. In this work we present the theoretical background on systemic modeling and structured, data-driven, system-theoretic model reduction for gas networks, as well as the implementation of "morgen" and associated numerical experiments testing model reduction adapted to gas network models. This research resulted in the "morgen" (Model Order Reduction for Gas and Energy Networks) software platform, which enables modular testing of various combinations of models, solvers, and model reduction methods. This many-query gas network simulation task can be accelerated by model order reduction, yet, large-scale, nonlinear, parametric, hyperbolic partial differential(-algebraic) equation systems, modeling natural gas transport, are a challenging application for model reduction algorithms.įor this industrial application, we bring together the scientific computing topics of: mathematical modeling of gas transport networks, numerical simulation of hyperbolic partial differential equation, and model reduction for nonlinear parametric systems. But, to ensure fulfillment of contracts under these new circumstances, a vast number of possible scenarios, incorporating uncertain supply and demand, has to be simulated ahead of time. To counter the volatile nature of renewable energy sources, gas networks take a vital role.
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