Modeling and Design of Net ZEBs as Integrated Energy Systems - Modeling, Design, and Optimization of Net-Zero Energy Buildings - page 31

the poles of the wall transfer function. When we limit the computations
to the first N poles, an error is introduced, which will affect the system
response for the following time. Stephenson and Mitalas (1971) applied ZT
to non-steady-state heat transfer and showed how the physical behavior
of walls can be properly described by using few numerical coefficients that
decrease fast in magnitude (with time) after applying the input.
The walls in the TRNSYS software ( Figure 2.5 ) are modeled based on the
transfer function relationships defined from surface to surface. The
evaluation of CTFs can be performed with an approximate mathematical
approach because the exact solution requires an infinite number of
calculations. The CTF method identifies the relationship between the signal
that is input to the system (a multilayered wall) called the “input” and the
response of the system (the temperature of the wall surfaces or a thermal
fluxthroughthewall)calledthe“output.”ThisrelationiscalledtheTransfer
Function of the system (a time domain transfer function).
Following the approach developed by Stephenson and Mitalas (1971), based
ontheuseofthe Z -transform(ZT)(Jury,1964),considerawallinwhich u ( t )
is the input signal and y ( t ) is the correlated output signal.