Mathematical and Statistical Models and Methods for Describing the Thermal Characteristics of Buildings

This paper describes a number of statistical methods and models for describing the thermal characteristics of buildings using frequent readings of heat consumption, ambient air temperature, and other available climate variables. For some of the methods frequent readings of the indoor air temperature are needed or beneficial. The suite of models described consists of nonlinear stochastic models, linear stochas- tic models, transfer function models, frequency response function models, impulse response models and regression models. The final choice of model depends on the purpose of the modelling, existence of prior physical knowledge, the data and the available statistical soft- ware tools. The importance of statistical model validation is discussed, and some simple tools for that purpose are demonstrated. This paper also briefly describes some of the most frequently used software tools for modelling the thermal characteristics of buildings. Many of the stochastic models are developed and tested using data from outdoor test- ing during a number of EU projects (PASSYS, PASLINK, DAME-BC, ..). These projects have provided the background for new methods for using frequent readings of the energy consumption to an assessment of the energy performance of buildings. Smart meters are now used more and more often. A smart meter facilitates frequent read- ing of the energy consumption, and together with some local meteorological measurements, which almost always are available, the scene is now set for using the developed methods for time series modelling or system identification. Applying these methods the following can be achieved: Characterization of the energy performance of buildings (including energy labelling), identification of how to improve the thermal performance of the building, and improved control of the energy supply.