A stable series expansion method for calculating thermal response factors of multi-layer walls

Thermal response factors (TRFs) of walls are fundamental data for calculating air conditioning loads and annual energy consumption of buildings. Among the methods for calculating TRFs, the state space method developed by Ouyang and Haghighat (Build. Environ. 26(2)(1991)173) is based on the s-transfer functions but has the advantage of avoiding conventional root-finding process. However, it is found that the calculation of TRFs may not be convergent with increase of the terms in expansion polynomials. In this paper, detailed analysis shows that the problem originates from the instability of reduced s-transfer functions obtained from the power series expansion. As a substitute, a stable series expansion approach based on the Routh stability theory is proposed. It keeps advantages of the existing method and guarantees the stability in calculation of TRFs.