Efficient, steady state solution of a time variable RC network, for building thermal analysis

Abstract In buildings, variable influences such as time dependent ventilation lead to thermal systems where the time-constant of the building becomes a function of time. This paper introduces an efficient method for obtaining the steady state, periodic thermal response of a building with arbitrary, time dependent ventilation. The method is applicable to a single time-constant thermal model but can be extended to higher order models. A simple, elementary numerical method for integrating the governing differential equation is proposed which does not need Fourier analysis, convolution or even evaluating an exponential, as required by most other methods. The initial value is also obtained explicity. Hence, the usual initial period of integration—to get rid of transients—is not required. By direct comparison of the numerical method with an exact analystical solution in a special case, it is proved that the method is sufficiently accurate, provided the sampling interval is not too large compared to the thermal time-constant of the building. The method is further demonstrated by calculating the interior temperature of a building subjected to forced night cooling.