Modeling and Design of Net ZEBs as Integrated Energy Systems - Modeling, Design, and Optimization of Net-Zero Energy Buildings - page 26

and q ′ is assumed positive into the slab (on both sides). As described
previously, the cascade matrix for a multilayered wall is obtained by
multiplying the cascade matrices of consecutive layers. Usually the
temperatures of interest are either the inside or the outside temperatures.
In this way, wall intermediate layer nodes and their temperatures are
eliminated and a simplified but accurate model is obtained. A linear
subnetwork connected to a network at only two terminals (surfaces) can be
represented by its Norton equivalent network, consisting of a heat source
and an admittance connected in parallel between the terminals (Athienitis,
Sullivan, and Hollands, 1986).
The admittance is the subnetwork equivalent admittance as seen from the
virtual connection port (the two terminals) and the heat source is the
short-circuited heatflowattheport.Consider forexample thewallin Figure
2.3 , assumed to be made up of an inner layer of storage mass of uniform
thermal properties and an insulation layer with negligible thermal capacity,
also of uniform thermal properties. The region behind the thermal mass
may be represented by equivalent conductance U in series with the outside
temperature T o (for exterior walls the sol-air temperature T eo ). The
conductance U combines the insulation resistance and a film coefficient.
The determination of Y s (called the wall self-admittance) and the equivalent
heat source Q sc produced by the transformation, is as follows: Firstly, the
total cascade matrix is obtained by multiplying the cascade matrix for the
storage mass layer by the matrix for u (note: u = U / A ):
(2.1f)
After multiplying, wetemporarily set T S =0(i.e., consider ashort-circuit) to
get the Norton equivalent heat source as
(2.1g)
where the transfer admittance Y t is given by