Load Matching, Grid Interaction, and Advanced Control - Modeling, Design, and Optimization of Net-Zero Energy Buildings - page 324

(6.25)
(6.26)
Translation , a property of the z -transform, can be exploited at this point.
The translation theorem implies that
(6.27)
This means that multiplying a z -transform by the expression z −n results in a
backward displacement of n time steps. Equation (6.26) can be written as
(6.28)
Finally, applying the inverse z -transform (i.e., returning to the sequence in
the time domain), one obtains
(6.29)
The current value of the output, y ( t ), can then be expressed in terms of the
current and previous values of the input and previous values of the output.
(6.30)
Using Eq. (6.30) , it is quite easy to model the output y ( t ) having data for
the expected values of the input u ( t ) at regular intervals. When more than
one input comes into play, the effect of each of the inputs can be considered
separately; the superposition principle can then be applied in a similar way
to that shown in Figure 6.10 .
6.4.3.3 Time Series Models
The difference equation shown in Eq. (6.30) describes a set of rules for
a sequence of values over time. Essentially, this is a time series model.
Time series analysis is a branch of mathematics concerned with the study
of patterns in ordered trails of measurements or observations collected