Linear model predictive control for the reduction of auxiliary electric heating in residential self-assisted ground-source heat pump systems

This article presents a linear model predictive control strategy for the operation of a “self-assisted” ground-source heat pump (GSHP) to reduce auxiliary electric heating in residential applications equipped with undersized boreholes. The self-assisted configuration uses an electric heating element at the heat-pump outlet to inject heat into the bore field when approaching peak power demand. A linear control-oriented model is proposed to account for both the source-side and load-side GSHP dynamics. The ground heat transfer is predicted using the bore field's ground-to-fluid thermal response factor, thus allowing for any bore field configuration while accounting for thermal capacity effects. Real historic ambient temperature forecasts and their corresponding historic recorded ambient temperatures from Montreal are used in this article. The coefficient of performance (COP) nonlinearity is circumvented with an iterative approach. A Kalman filter is used to dynamically adjust the bias on the predicted returning fluid temperature. On a borehole undersized by 15%, the control strategy reduces auxiliary electric heating by 96% over 20 years at the cost of a 5.53% increase in total energy consumption. Due to the occasional simultaneous heat injection and auxiliary heating, the yearly peak power demand is increased.