A grey-box modelling methodology to express home heat-energy usage as statistical distributions — case studies in urban Ireland

Abstract

Home energy retrofit has recurred in public policy throughout recent decades. However, the savings in energy usage attributable to home retrofit have remained difficult to accurately predict. Occupants cause prediction inaccuracies by varying different factors, especially heating setpoints temperatures and heating patterns. Acting together, such occupant factors result in distributions — not single values — of heat-energy usage, even among similar homes. Datasets of heat-energy distributions can be found by building performance simulation using modern grey-box models. This study presents a methodology to simulate grey-box models of home heating through ranges of heating setpoints and patterns. An entire process to calibrate, validate and simulate at a large scale is described, and then demonstrated using case studies. Grey-box models, written in Modelica language, can conveniently simulate through large ranges of occupant factors. The case studies exploited this advantage of grey-box models to simulate empirical data on occupant factors. (For instance, empirical data found that home heating setpoints shifted before and after home energy retrofit.) In doing so, the datasets of simulation results enabled the exploration of home heat-energy usage with the normal and Weibull statistical distributions. Additionally, the heat-energy distributions of case-study homes were statistically tested, first for retrofit savings, second for equality to each other and third for equality to an official heat-energy estimate. Results demonstrate that home heat-energy usage, at a large scale, is best expressed as a Weibull distribution not normality. After home energy retrofit, heat-energy usage displays less variation (in general), less skewness, and thus becomes closer to normality. Occupant factors were found to vary home heat-energy usage into distinct distributions, even within similar homes. Therefore, in most case-study homes, heat-energy usage did not equal an official estimate. Finally, shallow retrofit of a modern home in Ireland fails to save heat-energy usage by most occupants.