A Substitutive Coefficients Network for the Modelling of Thermal Systems: A Mono-Zone Building Case Study

Abstract

A modelling approach based on the Substitutive Coefficients Network (SCN) is developed to predict the thermal behavior of a system in the dynamic state-space, without requiring knowledge of the thermal mass. The method can apply either to large- (building, combined solar systems, geothermal energy, and thermodynamic installations) or to small-scale systems (heat exchangers, electronic devices cooling systems, and Li-ion batteries). This current method is based on a dimensionless formulation of the simplified dynamic thermal balance model, using relaxation time as a key parameter to establish the model. The introduction of relaxation time reduces the parameters set as guidance coefficients. The parameters are finally expressed by a combination of global heat transfer coefficients related to each layer and/or sub-layer of the system. Advantages of the method are reliability, “non-destructibility”, i.e., it allows a reliable prediction of the thermal behavior which experimentally is inaccessible, and reducibility of the parameters size estimate. Additionally, the method is inexpensive in terms of computation memory. It is also easy to implement in practical numerical schemes. In this paper, the method leads to a simplified mathematical model that predicts the thermal behavior of a mono-zone eco-cottage building installed at Lorraine University (in Longwy, France) as a case study. Thermal performance of the building is estimated under the hourly weather conditions onsite, as obtained from the Meteonorm software. The thermal dynamics within hourly Typical Meteorological Year 2 (TMY2) Meteonorm data disturbances and the internal heating input state in the winter period were simulated with a simplified numerical discretization method. Results provide a general dynamic state of the different sub-components of the system, with limited design of the model parameters.

Keywords

• substitutive coefficients network (SCN)
• reduced-order model
• relaxation time
• dynamic state-space model
• thermal behavior modeling
• thermal building simulation