A gray-box model for unitary air conditioners developed with symbolic regression

Abstract

In this paper, we present the development of a gray-box model for unitary air conditioning equipment that can be trained with as little as 5 data points with higher accuracy on test data. The model utilizes the same model inputs as is typical in building energy simulation, and is accurate. While black-box models require large data sets to deliver accurate results, white-box models require higher computational and engineering efforts along with detailed knowledge of the system, and are often difficult to obtain. The model presented here addresses a hybrid solution that is a steady-state, component-based, gray-box model that requires inputs from the source and sink fluids and rated performance of the specific piece of equipment, only. The basic physics of a vapor compression cycle are captured in individual component models for the heat exchangers, compressor, and expansion valve. These components are generalized to eliminate refrigerant-side inputs. A key addition is the development of correlations for the overall heat transfer coefficient times surface area (UA) obtained from Symbolic Regression (SR). The model successfully predicts the cooling capacity, coefficient of performance (COP), and sensible heat ratio (SHR) for three state-of-the-art variable speed, split-system, air conditioning systems with capacities of 12.3(3.5), 14(4), and 17.6(5) kW(tons), achieving a mean absolute percentage error (MAPE) of less than 3.4%. These results suggest that the gray-box model can be useful in predicting the performance of similar systems in the future, which could be valuable for energy management and optimization purposes.