Application of Koopman Mode Analysis in Residential Environments
As a step towards our goals of energy efficiency, we investigate data-driven, simple-to-implement residential environmental models that can serve as the basis for energy saving algorithms in both retrofits and new designs of residential buildings. We find that currently used models of thermal behavior of buildings are lacking in a fundamental way associated with the thermal mass of buildings. Despite the nonlinearity of the underlying dynamics, in this study we show that a linear second order model embedding, that captures the physics that occur inside a single or multi-zone of a space does well in comparison with data. In order to validate our model, we used EnergyPlus to simulate indoor air temperature. The error ranges from 3:3% to 7:2% according to different thermal mass properties of the residential building. Using data-driven methods such as Koopman mode decomposition we analyze thermal data from a single zone space. With this analysis we are able to identify stability or instability of the modes present in the dynamics. Using data we were able to find the mode that corresponds to heating and cooling control, as well as identify the location this control originated from and it's period of occurrence to be every 1.5 hours.