Laplace and State-Space Methods for Calculating the Heat Losses in Case of Heavyweight Building Elements and Short Sampling Times

Mergim Gaši (), Bojan Milovanović (), Marino Grozdek and Marina Bagarić
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Mergim Gaši: Department of Materials, Faculty of Civil Engineering, University of Zagreb, Fra Andrije Kačića Miošića 26, 10000 Zagreb, Croatia
Bojan Milovanović: Department of Materials, Faculty of Civil Engineering, University of Zagreb, Fra Andrije Kačića Miošića 26, 10000 Zagreb, Croatia
Marino Grozdek: Department of Thermodynamics and Thermal and Process Engineering, Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lučića 5, 10000 Zagreb, Croatia
Marina Bagarić: Department of Materials, Faculty of Civil Engineering, University of Zagreb, Fra Andrije Kačića Miošića 26, 10000 Zagreb, Croatia

Energies, 2023, vol. 16, issue 11, 1-18

Abstract: Reducing heat losses through the building envelope is one of the most important aspects to be met if the targets set by the European Union are to be achieved. In order to obtain a more realistic energy demand, dynamic heat transfer simulations are used to calculate the energy consumption of buildings, since steady-state calculations do not take into account the thermal mass in buildings. These dynamic simulations employ methods based on analytical models since numerical models are unsuitable for longer time periods. The analytical models used herein fall into the category of conduction transfer functions (CTFs). Two methods for computing CTFs that are addressed in this research are the Laplace method and the State-Space method. The objective of this paper is to verify the efficiency of the Laplace and State-Space methods for calculating the energy demand of a building in the case of heavyweight building elements and shorter sampling times, and to provide a means for improving the algorithms used by these methods. The Laplace and State-Space method algorithms were implemented in Mathematica, and the results were compared to EnergyPlus and TRNSYS, which use similar algorithms to calculate energy demand. It was shown in this paper that for the heavyweight wall element and a time step of 0.25 h, the difference between the total energy transferred through the inner surface was about 31% for EnergyPlus and 78% for TRNSYS compared to the reference solution. For the lightweight wall element, the results were stable for the time step of 0.25 h, but for the time step of 0.1 h, the differences were 45.64% and 303% between EnergyPlus, TRNSYS and the reference solution, respectively, compared to the State-Space and Laplace methods for which the maximum difference was 12.03% with a time step of 0.1 h. While dynamic heat transfer simulations are better than calculations based on steady-state boundary conditions, they also have their limitations and could lead to unsatisfactory results for short sampling times and if not applied properly.

Keywords: Laplace method; State-Space method; building energy simulation; conduction transfer functions; short sampling times; heavyweight building elements (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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