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

Abstract

This paper 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 controloriented 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 paper. The COP non-linearity 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.

A Methodology for Long-Term Model Predictive Control of Hybrid Geothermal Systems: The Shadow-Cost Formulation

“…The work does not give details about whether a load-aggregation algorithm was used or the length of the considered load history. More recently, Laferrière and Cimmino [33,34] used a GSHP model represented by second-degree polynomial correlations and a borefield model that requires a discretized thermal response factor as input to compute the fluid temperature in a self-assisted water-to-air GSHP configuration, i.e., it uses a heating element on the source side of the GSHP to prevent too low operating fluid temperatures. Both works considered relatively short horizons of 5 days and 6 days respectively, for which the RC diffusion approximation is also suitable.…”

“…More recently, Laferrière and Cimmino [33,34] used a GSHP model represented by second degree polynomial correlations and a borefield model that requires a discretized thermal response factor as input to compute the fluid temperature in a self-assisted water-to-air GSHP configuration, i.e. it uses a heating element on the source side of the GSHP to prevent too low operating fluid temperatures.…”

Fluid temperature predictions of geothermal borefields using load estimations via state observers

“…Model-based optimal control aims to minimize an objective function over a finite period of time, relying on the predictions made by the model. A common strategy for these models is to model the heat diffusion in the ground as a 1D RC network, considering a constant undisturbed ground temperature in the far field [16], incorporating the geothermal gradient [17] or even taking into account the effects of the fluid mass flow rate [18].…”

“…Other authors prefer data-driven modeling approaches using data from more accurate models [20,21]. More recently, Laferriere and Cimmino [22,23] proposed a ground model formulation for optimal control based on the thermal response of the borefield.…”