Identification of simplified energy performance models of variable-speed air conditioners using likelihood ratio test method

Variable-speed air conditioners (ACs) are gradually replacing single-speed ACs in residential buildings in densely populated cities like Hong Kong due to better control accuracy and higher energy efficiency at part-load conditions. Simplified energy performance models of variable-speed ACs are needed for different purposes, including building energy analysis, model-based fault detection and diagnosis, and model-based optimal control. However, how to identify the most suitable model from a series of candidate models with various complexities is rarely discussed. This study presents a model selection approach based on the likelihood ratio test (LRT) method to identify the most suitable energy performance model of variable-speed ACs. A full model and a range of reduced models/submodels for variable-speed ACs are first formulated for model selection procedure. The maximum likelihood estimation method is applied to estimate the parameters in each candidate model. Performances of the candidate models in each step of the selection process are compared using LRTs. Test results demonstrate that the model selection approach can effectively select the cooling capacity and coefficient of performance (COP) models for a typical variable-speed AC with reasonable complexity and satisfactory accuracy. The root mean square errors of the selected models of cooling capacity factor and COP factor are 0.0188 and 0.0463, respectively.