Grey-box modeling of a low pressure electric boiler for domestic hot water system

• The physics-based model of the stratified electric boiler is developed.
• Experimental setup is presented to measure the data.
• Measured data is used for parameter estimation and model validation.
• Physics-based model is implemented in Simulink® and its parameters are estimated.
• Model's performance is evaluated analytically and compared to the measured data.

Due to the increasing cost of electricity and its variable price structure throughout the day, it is of interest to shift the loads to off-peak hours. In this work, the grey-box model of a domestic hot water electric boiler is presented. The developed model is useful for the development of new supervisory controller to help offset the boiler heating load to off peak hours in a smart grid environment. The boiler used in this research is an integral part of the domestic hot water system and residential Heating, Ventilating and Air-Conditioning (HVAC) systems in many Swiss homes. The water stored in the boiler is not well mixed and thus the temperature varies along the height of the boiler. The cold water is entering in the boiler from the bottom and the hot water is drawn at the top. This results in a temperature gradient along the height of the boiler which needs to be predicted to accurately simulate the temperature dynamics of the boiler. The boiler was divided into eight stratified virtual layers and physics-based model was developed by writing the heat balance equation for each layer. Experimental setup consisting of boiler, sensors and data logger was prepared at the Institute of Aerosol and Sensor Technology (IAST), University of Applied Sciences and Arts Northwestern Switzerland (FHNW) to measure the training and test data for the model including the temperature of each layer, ambient temperature, boiler's power consumption and flow rate of water entering into the boiler. The parameters of the physics-based model were estimated from the measured data thus converting it into a grey-box model. The model performance was visually compared to the measured data and was also evaluated analytically using several metrics showing the high accuracy of the developed model.