Modeling and Design of Net ZEBs as Integrated Energy Systems - Modeling, Design, and Optimization of Net-Zero Energy Buildings - page 83

Two closely related thermal characteristic of BITES systems are their
storage capacity and thermal inertia (i.e., response time). These two
characteristics together with other parameters (e.g., thermal comfort,
location) create challenges in the design and control optimization of BITES
systems. Appropriate numerical models play an important role in these two
aspects. In Section 2.2.3.2, different modeling approaches will be described.
Control methodologies are introduced in Chapter 6 .
2.2.3.2 Modeling Active BITES
Two mainstream modeling methods, finite difference discretization and
transfer functions, are applied in this section to BITES.
Finite Difference Discretization Methods
Among common transient models for active BITES systems, discretization
methods, such as finite difference models (Incropera and DeWitt, 2002;
Kreith and Bohn, 2001), have been widely used. The main advantage of
the finite difference approach is accurate treatment of nonlinearities (e.g.,
convective heat transfer and time-dependent variables). Equation (2.43)
is in explicit finite difference form for the calculation of the temperature
of a control volume node located at coordinate ( x , y , z ) in a
three-dimensional model. By assuming that the current values of the
variables prevail throughout the next time step,
(2.43)
where is the time step and is the capacitance of the node. is
the temperature difference between the current node and the adjacent node
at time in direction (i.e., in negative or positive x , y , or z directions).
is the conductance between the current node and the adjacent node in
direction ( j is between 1 and 6 for the three-dimensional model). The last
term in Eq. (2.43) includes conductive heat transfer from adjacent nodes,
as well as convective and radiative heat transfer in the cases where exterior
nodes are involved.
In the explicit approach, in order to generate physically realistic results and
stabilize forward marching in time, the discretization places a maximum
valueonthetimestep.TheFouriernumber(theratiooftheheatconduction