Prediction of coefficient of performance and simulation design of an air-source heat pump water heater
Authors: Tangwe Stephen Loh , Simon Michael , Meyer Edson Leroy 
Published: April 2017

Purpose
The purpose of this study was to build and develop mathematical models correlating ambient conditions and electrical energy to the coefficient of performance (COP) of an air-source heat pump (ASHP) water heater. This study also aimed to design a simulation application to compute the COP under different heating up scenarios, and to calculate the mean significant difference under the specified scenarios by using a statistical method.

Design/methodology/approach
A data acquisition system was designed with respect to the required sensors and data loggers on the basis of the experimental setup. The two critical scenarios (with hot water draws and without hot water draws) during the heating up cycles were analyzed. Both mathematical models and the simulation application were developed using the analyzed data.

Findings
The predictors showed a direct linear relationship to the COP under the no successive hot water draws scenario, while they exhibited a linear relationship with a negative gradient to the COP under the simultaneous draws scenario. Both scenarios showed the ambient conditions to be the primary factor, and the weight of importance of the contribution to the COP was five times more in the scenario of simultaneous hot water draws than in the other scenario. The average COP of the ASHP water heater was better during a heating cycle with simultaneous hot water draws but demonstrated no mean significant difference from the other scenario.

Research limitations/implications
There was a need to include other prediction parameters such as air speed, difference in condenser temperature and difference in compressor temperature, which could help improve model accuracy. However, these were excluded because of insufficient funding for the purchase of additional temperature sensors and an air speed transducer.

Practical implications
The research was conducted in a normal middle-income family home, and all the results were obtained from the collected data from the data acquisition system. Moreover, the experiment was very feasible because the conduction of the study did not interfere with the activities of the house, as occupants were able to carry out their activities as usual.

Social implications
This paper attempts to justify the system efficiency under different heating up scenarios. Based on the mathematical model, the performance of the system could be determined all year round and the payback period could be easily evaluated. Finally, from the study, homeowners could see the value of the efficiency of the technology, as they could easily compute its performance on the basis of the ambient conditions at their location.

Originality/value
This is the first research on the mathematical modeling of the COP of an ASHP water heater using ambient conditions and electrical energy as the predictors and by using surface fitting multi-linear regression. Further, the novelty is the design of the simulation application for a Simulink environment to compute the performance from real-time data.