Civil Engineering Reference
In-Depth Information
(2002), including a model for a proportional control source in the thermal
network and a technique for modeling time-varying parameters, such as
a conductance representing infiltration based on the substitution network
theorem.
2.1.4.3 Discrete Fourier Series (DFS) Method for Simulation
Steady
-
periodic conditions are usually assumed in this method; for
example, if the simulation is to be performed for a week, it is assumed that
all previous weeks have been identical to the week considered. The steps
needed for a periodic steady-state solution are as follows:
1. Select the number
N
of harmonics to perform the analysis. If
n
represents a harmonic number and
P
is the time length of the
simulation or analysis (e.g., a day or a week), then a harmonic frequency
ω
n
is equal to
2πn/P.
2. Obtain the appropriate discrete Fourier series representations for the
sources. An arbitrary source
M
(
t
) is represented by a complex Fourier
series (inverse discrete Fourier transform) of the form:
(2.20)
where the complex coefficients
m
n
(
jω
n
) are determined numerically by
a discrete Fourier transform as follows:
(2.21)
where is the value of
M
at time
t
k
corresponding to point
k
(for a
total of
K
values over the time period
P
). The number of harmonics
N
cannot exceed
K/2
.
3. Determine the discrete frequency response of the output of
interest to unit input at each node. The periodic response to each source
is obtained by superposition of the output harmonics using complex
(phasor) multiplication. The total response to more than one input is
determined by a double summation for all inputs
Q
i
and all frequencies
of interest
ω
n
. For example, for the room air temperature
T
1
(
t
), we
have:
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