A study of the nonlinearity of a building thermal behavior based on metamodeling

¹ Laboratoire du Froid, des Systèmes Energétiques et Thermiques (LaFSET), Cnam, HESAM Université, 75003, Paris, France
² LaSIE, University of La Rochelle, 17000, La Rochelle, France

^* Corresponding author: christian.inard@univ-lr.fr

Abstract

In this work, we present a study of the nonlinearity of building thermal behavior based on a metamodel for cooling energy needs. We studied the nonlinearity of the thermal behavior of an office. The building quadratic behavior and interactions between its components were analyzed based on the metamodel coefficients. The metamodel was fitted with a reduced number of dynamic simulations. The nonlinearity was first assessed as function of the mean outdoor air temperature in fifteen typical European climates and then as function of the internal heat gains for the coldest and hottest climates. The metamodel provided highly accurate results with fast calculation time. However, a higher accuracy was generally obtained for hot climates, high internal heat gains and lightweight thermal mass. Conversely, the nonlinearity of thermal behavior was accentuated in cold climates and with low internal heat gains. Moreover, the interactions between the building components were found to be more influential on cooling energy needs than quadratic behavior. We propose a classification of thermal behavior into three regimes: Highly nonlinear when the energy needs are close to zero; intermediate with decreasing nonlinearities that can be expressed by power functions; and finally, a quasi-linear regime with almost-steady nonlinearities.