A state-space heating and cooling model for thermal stratification in horizontally configured electric hot water storage cylinders

Domestic water heating significantly impacts global energy demand, with electric hot water storage devices notably contributing to grid load. Efficient management of these widespread devices is contingent on a deep understanding of the internal thermal stratification occurring naturally during heating and cooling phases. While extensive research exists for vertical water heaters, horizontal heaters, more challenging to model, have been comparatively overlooked in scholarly research. This paper introduces a state-space model developed using measured datasets, aimed at accurately describing temperature distributions inside a horizontally-configured electric hot water storage cylinder during heating, thermal diffusion, and cooling stages. The model's effectiveness was validated through various evaluation metrics and separate, unseen evaluation datasets. It achieved an accuracy of 90.6 % for the dimensionless stratification factor, 94.6 % for the dimensionless exergy number, and reported Root Mean Square Errors (RMSEs) of 150 kJ for energy, 11 kJ for exergy, and 0.8 °C for temperature.