论文标题

气体和能源网络的型号降低

Model Order Reduction for Gas and Energy Networks

论文作者

Himpe, Christian, Grundel, Sara, Benner, Peter

论文摘要

为了应对可再生能源的挥发性,气体网络发挥了至关重要的作用。但是,为了确保在这种情况下履行合同,必须提前模拟许多可能的情况,包括不确定的供求。这项多质量气体网络模拟任务可以通过降低模型来加速,但是,大规模,非线性,参数,双曲线部分差分( - 代理)方程系统,对天然气传输进行建模,是模型订单降低算法的挑战性应用。 对于这种工业应用,我们将科学计算主题汇总在一起:气体传输网络的数学建模,双曲线偏微分方程的数值模拟以及非线性系统的参数模型降低。这项研究导致了“ Morgen”(气体和能源网络的模型订单降低)软件平台,该平台能够对模型,求解器和模型还原方法的各种组合进行模块化测试。在这项工作中,我们介绍了有关系统建模和结构化的,数据驱动的,系统理论模型减少的理论背景,以及实施“ Morgen”和相关的数值实验测试模型降低适合于气体网络模型的模型。

To counter the volatile nature of renewable energy sources, gas networks take a vital role. But, to ensure fulfillment of contracts under these circumstances, a vast number of possible scenarios, incorporating uncertain supply and demand, has to be simulated ahead of time. This many-query gas network simulation task can be accelerated by model reduction, yet, large-scale, nonlinear, parametric, hyperbolic partial differential(-algebraic) equation systems, modeling natural gas transport, are a challenging application for model order reduction algorithms. For 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 parametric model reduction for nonlinear systems. 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. 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.

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