A Fourier Transform Approach to Building Simulations With Thermostatic Controls

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Abstract
Analyzing the thermal behavior of a linear system, such as a building (with some commonly made approximations), is greatly simplified in the frequency domain because of the decoupling of different frequencies. Thermostatic controls, an important part of building systems, invalidate this decoupling since they respond only to the temperature at a particular time (i.e., to the sum of all frequencies). Nevertheless, it is shown that by suitably formulating the problem, buildings with thermostatic controls can be simulated in the frequency domain, even when the set-point is a function of time. An hour-by-hour profile of indoor temperature and auxiliary energy requirements are obtained without doing an hour-by-hour simulation. In the solution process, a function—the “temp-aux” function—is introduced which determines both the temperature and auxiliary energy profiles. This function is of general interest in building energy calculations.

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