Thermal dynamic models using z-transform coefficients: an algorithm to improve the reability of simulations

The Transfer Function Method (TFM) is a tool able to solve heat transfer problems in building envelopes and environments and it is recommended by the American Society of Heating, Refrigerating and Air- Conditioning Engineers (ASHRAE). Authors have investigated TFM mathematical features, especially concerning the reliability and the quality of the thermal dynamic simulations. Using some basilar control systems tools like Bode plots, step response, model validation, results show clearly that, for a very massive building, a simply application of TFM very often fails. We have developed a software, THELDA 2000, founded upon a new TFM algorithm, to determine the Z-transform coefficients able to perform a thermal building simulation. Target of our work is to identify an automatic procedure able to optimise the reliability of the simulation by selecting and using in a more correct way poles and the residuals of the transfer functions. Paper explains as applying to TFM some concepts coming from system theory, like choosing the only significant poles in the transfer function, it is possible to obtain a drastic improvement of the quality of the simulation. Some cases studies show that using a limited number of coefficients can give a faster and more reliable simulation and sometimes it is the only method to obtain some results. Furthermore, the analysis shows as the choice of the sampling period is crucial to carry out a reliable simulation.