Modeling and Design of Net ZEBs as Integrated Energy Systems - Modeling, Design, and Optimization of Net-Zero Energy Buildings - page 87

Generally, in time domain analysis, time-series coefficients are generated
to relate the current outputs to its current and past inputs. Discrete-time
transfer functions are used in this kind of approaches. Continuous-time
transfer functions can also be used. Since discrete-time sampled values
(e.g., hourly weather data) are commonly used in building simulations,
time-series coefficient approaches are more popular. The transfer function
method is also used in frequency domain analysis as described in Section
2.1.2.
Toderivetransferfunctions,eitherintimeorfrequencydomain,theLaplace
transform method has been traditionally used. In time domain modeling,
after taking a Laplace transform, time-series (discrete) response
coefficients, such as thermal response factors (Stephenson and Mitalas,
1967), CTFs (Stephenson and Mitalas, 1971), and radiant time series (Spitler
and Fisher, 1999; Spitler, Fisher, and Pedersen, 1997) are derived with
different methods. CTF can also be obtained with state space formulation
(Ceylan and Myers, 1979; Seem et al. , 1989).
When using transfer functions of thermal systems, the system under
consideration can be a whole building or a component. In building thermal
modeling software using z -transfer functions (see Section 2.1.3), such as
EnergyPlus and TRNSYS, the outputs from each building component are
calculated with their associated transfer functions (see Section 2.1.4). The
inputs or response of these components for the next time step, such as
the interior radiative heat transfer and room air temperature, are then
calculated based on heat balance equations following the energy
conservation principle (ASHRAE, 2009b). For a solid bounded by two
parallel planes, such as wall and slab assemblies, the Laplace transform
method is used in deriving transfer functions for transient heat conduction
within them (Carslaw and Jaeger, 1959; Kimura, 1977) as described
previously inSection2.1.2.1. Forassemblies withinternal heatsources,such
as the case of active BITES systems, Strand (1995) incorporated “source
transfer functions” into CTF using Laplace transform and state space
formulations. Considerations in substituting two-dimensional models with
one-dimensional ones were further discussed by Strand (1995).
The frequency response (FR) approach facilitates the integration of design
andmodel-basedcontrol.Itcanprovideadditionalinformation,particularly
for design optimization and comparison of design alternatives on relative
bases and, without tedious simulation (Athienitis, Stylianou, and Shou,