Modeling the Thermal Dynamics of Buildings

Abstract

Minimizing the energy consumed by heating, ventilation, and air conditioning (HVAC) systems of residential buildings without impacting occupants’ comfort has been highlighted as an important artificial intelligence (AI) challenge. Typically, approaches that seek to address this challenge use a model that captures the thermal dynamics within a building, also referred to as a thermal model. Among thermal models, gray-box models are a popular choice for modeling the thermal dynamics of buildings. They combine knowledge of the physical structure of a building with various data-driven inputs and are accurate estimators of the state (internal temperature). However, existing gray-box models require a detailed specification of all the physical elements that can affect the thermal dynamics of a building a priori. This limits their applicability, particularly in residential buildings, where additional dynamics can be induced by human activities such as cooking, which contributes additional heat, or opening of windows, which leads to additional leakage of heat. Since the incidence of these additional dynamics is rarely known, their combined effects cannot readily be accommodated within existing models. To overcome this limitation and improve the general applicability of gray-box models, we introduce a novel model, which we refer to as a latent force thermal model of the thermal dynamics of a building, or LFM-TM. Our model is derived from an existing gray-box thermal model, which is augmented with an extra term referred to as the learned residual. This term is capable of modeling the effect of any a priori unknown additional dynamic, which, if not captured, appears as a structure in a thermal model’s residual (the error induced by the model). More importantly, the learned residual can also capture the effects of physical elements such as a building’s envelope or the lags in a heating system, leading to a significant reduction in complexity compared to existing models. To evaluate the performance of LFM-TM, we apply it to two independent data sources. The first is an established dataset, referred to as the FlexHouse data, which was previously used for evaluating the efficacy of existing gray-box models [Bacher and Madsen 2011]. The second dataset consists of heating data logged within homes located on the University of Southampton campus, which were specifically instrumented to collect data for our thermal modeling experiments. On both datasets, we show that LFM-TM outperforms existing models in its ability to accurately fit the observed data, generate accurate day-ahead internal temperature predictions, and explain a large amount of the variability in the future observations. This, along with the fact that we also use a corresponding efficient sequential inference scheme for LFM-TM, makes it an ideal candidate for model-based predictive control, where having accurate online predictions of internal temperatures is essential for high-quality solutions.