Adaptive nonlinear optimization of district heating networks based onmodel and discretization catalogs
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Hannes Dänschel [2] ; Volker Mehrmann [2]
;
Marius Roland
[1]
;
Martin Schmidt
[1]
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[1] University of Trier
University of Trier
Kreisfreie Stadt Trier, Alemania
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[2] Inst. f. Mathematik, TU Berlin, Germany
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- Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 81, Nº. Extra 1, 2024, págs. 81-112
- Idioma: inglés
- DOI: 10.1007/s40324-023-00332-6
- Texto completo no disponible (Saber más ...)
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Resumen
We propose an adaptive optimization algorithm for operating district heating networks in a stationary regime. The behavior of hot water flow in the pipe network is modeled using the incompressible Euler equations and a suitably chosen energy equation. By applying different simplifications to these equations, we derive a catalog of models. Our algorithm is based on this catalog and adaptively controls where in the network which model is used. Moreover, the granularity of the applied discretization is controlled in a similar adaptive manner. By doing so, we are able to obtain optimal solutions at low computational costs that satisfy a prescribed tolerancew.r.t. the most accurate modeling level. To adaptively control the switching between different levels and the adaptation of the discretization grids,we derive errormeasure formulas and a posteriori error measure estimators. Under reasonable assumptions we prove that the adaptive algorithm terminates after finitely many iterations. Our numerical results show that the algorithm is able to produce solutions for problem instances that have not been solvable before.
