Load Matching, Grid Interaction, and Advanced Control - Modeling, Design, and Optimization of Net-Zero Energy Buildings - page 320

Oncetheparametersofalinearmodel-suchasthecoefficientsofatransfer
function - are determined, calculations are straightforward and
computationally efficient. For this reason, CTFs are commonly used in
building simulation tools for conduction heat transfer calculations. If fact,
CTFs are still the default method in EnergyPlus and TRNSYS for the
calculation of conduction heat transfer through walls, roofs, and floors.
6.4.2 Thermal Modeling of an Entire Building
Low-order RC circuits have been used since the middle of the twentieth
century to calculate cooling loads in buildings (Rees et al. , 2000). Room
response factors, developed in the late 1960s, also make use of z -transfer
functions to calculate cooling loads (Stephenson and Mitalas, 1967).
Methods for the determination of comprehensive room transfer functions
for load calculation have also been investigated (Seem, 1987).
As computational power became more accessible and affordable, prompting
the emergence of building simulation tools since the 1970s, the use of
low-order linear models for the thermal modeling gradually fell out of favor
for building design and load calculation, even if building simulation tools
rely on large sets of interrelated linear models - effectively forming a
high - order linear model or quasi-linear model . 5) The main difference
between a building simulation thermal model and a simple linear model is
the number of parameters employed.
The number of parameters can grow very rapidly in a building simulation
model,ashasbeennotedbycontrolengineeringresearchers.Forexample,a
recent control engineering paper (Deng etal. , 2010) shows that a four-room
building can quickly generate a model of nearly fortieth order. Models with
hundreds or thousands of capacitors emerge in relatively small buildings.
In spite of the rapidly growing order of the model, a few parameters suffice
to capture most of the relevant dynamics. For example, a third- or
fourth-order model is often enough to model a house satisfactorily
(Athienitis, Stylianou, and Shou, 1990; Kämpf and Robinson, 2007),
especially if we focus on a specific output - such as the average indoor
temperature or the required cooling load. In other words, it is possible to
approximate reasonably well a more complex model with a simpler one.
Linear models might take different mathematical shapes. The following
pages present an overview of these alternative representations.