Control-Oriented, Data-Driven Models of Thermal Dynamics

Abstract

Energy savings from efficiency methods in individual residential buildings are measured in 10's of dollars, while the energy savings from such measures nationally would amount to 10's of billions of dollars, leading to the "tragedy of the commons" effect. The way out of this situation is via deployment of automated, integrated residential energy systems, that provide the user with a seamless, cost effective service leading to improvement of comfort and residential experience. Models are of critical importance in this context, as intelligent operating systems depend on them strongly. However, most of the currently used models of thermal behavior of buildings have high complexity leading to problems and implementation. The complexity also obscures the utilization of well know physical properties of buildings such as the thermal mass. In view of this, we investigate data-driven, simpleto-implement residential environmental models that can serve as the basis for energy saving algorithms in both retrofits and new designs of residential buildings. Despite the nonlinearity of the underlying dynamics, using Koopman operator theory framework in this study we show that a linear second order model embedding, that captures the physics that occur inside a single or multi-zone space does well when compared with data simulated using EnergyPlus. This class of models has low complexity. We show that their parameters have physical significance for the large-scale dynamics of a building and are correlated to concepts such as the thermal mass. We investigate consequences of changing the thermal mass on the energy behavior of a building system and provide best practice design suggestions.

Koopman Mode Decomposition of Oscillatory Temperature Field inside a Room

“…[11] focus on long-term (24 h period) thermal dynamics for a whole building system, for which a minimal component is a room. The same focus appears in the papers [12,13,15]. In Refs.…”

“…The technique is capable of decomposing multichannel time series into modal oscillations, each of which contains a single frequency, characterized by the eigenvalues. KMD has the solid mathematical foundation on an operator theory of dynamical systems [8], a clear property of timescale separation of complex spatiotemporal dynamics, and has been used widely in modeling and analysis of thermal dynamics in buildings [11][12][13][14][15].…”

“…The current application of KMD is novel in terms of the previous studies [6,7,[11][12][13][14][15]. The authors of Ref.…”