On the Input-Output Behavior of a Geothermal Energy Storage: Approximations by Model Order Reduction

Bibliographic Details
Title: On the Input-Output Behavior of a Geothermal Energy Storage: Approximations by Model Order Reduction
Authors: Takam, Paul Honore, Wunderlich, Ralf
Publication Year: 2022
Collection: Computer Science
Mathematics
Subject Terms: Mathematics - Numerical Analysis, 93A15, 93B11, 93C05, 93C15, 37M99
More Details: In this paper we consider a geothermal energy storage in which the spatio-temporal temperature distribution is modeled by a heat equation with a convection term. Such storages often are embedded in residential heating systems and control and management require the knowledge of some aggregated characteristics of that temperature distribution in the storage. They describe the input-output behaviour of the storage and the associated energy flows and their response to charging and discharging processes. We aim to derive an efficient approximative description of these characteristics by a low-dimensional system of ODEs. This leads to a model order reduction problem for a large scale linear system of ODEs arising from the semi-discretization of the heat equation combined with a linear algebraic output equation. In a first step we approximate the non time-invariant system of ODEs by a linear time-invariant system. Then we apply Lyapunov balanced truncation model order reduction to approximate the output by a reduced-order system with only a few state equations but almost the same input-output behavior. The paper presents results of extensive numerical experiments showing the efficiency of the applied model order reduction methods. It turns out that only a few suitable chosen ODEs are sufficient to produce good approximations of the input-output behaviour of the storage.
Comment: arXiv admin note: text overlap with arXiv:2104.05116
Document Type: Working Paper
Access URL: http://arxiv.org/abs/2209.14761
Accession Number: edsarx.2209.14761
Database: arXiv
More Details
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