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.

中文翻译：

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天然气和能源网络的模型降阶

为了应对可再生能源的波动性，天然气网络发挥着至关重要的作用。但是，为了确保在这些情况下履行合同，必须提前模拟大量可能的情况，包括不确定的供需情况。这种多查询天然气管网模拟任务可以通过模型简化来加速，然而，大规模、非线性、参数化、双曲偏微分（-代数）方程系统，模拟天然气运输，是模型降阶算法的一个具有挑战性的应用。对于这个工业应用，我们汇集了以下科学计算主题：气体输送网络的数学建模、双曲偏微分方程的数值模拟和非线性系统的参数化模型简化。这项研究产生了 morgen（气体和能源网络的模型降阶）软件平台，该平台能够对模型、求解器和模型降阶方法的各种组合进行模块化测试。在这项工作中，我们介绍了天然气网络的系统建模和结构化、数据驱动、系统理论模型简化的理论背景，以及适用于天然气网络模型的 morgen 和相关数值实验测试模型简化的实施。