(459e) Estimating and Forecasting Hot Water Demand for Economic Model Predictive Control of Heat Pump Water Heaters

Water heating accounts for about 19% of U.S. residential energy consumption [1]. Heat pump water heaters (HPWHs) electrify water heating through a heat pump and are two to three times more energy efficient than electric resistance water heaters [2]. HPWHs are ideal for providing load flexibility as their built-in storage tank serves as thermal energy storage, storing water heated with low-cost, emissions-free renewable electricity for later use in the day [3]. Despite the ability of HPWHs to shift electric loads, they are typically controlled by a rule-based control (RBC) strategy that tracks a temperature setpoint, regardless of the cost of electricity or grid greenhouse gas (GHG) emissions.

Economic model predictive control (EMPC) is an advanced control strategy that uses a dynamic model of the system to predict system behavior over a finite-time horizon and computes the control actions that minimize an economic cost function [4]. EMPC is suitable for providing automated load flexibility for HPWHs as it can account for utility/grid signals and predict tank temperature evolution and hot water use events to determine how to operate the HPWH. In [5], a cloud-based supervisory EMPC was proposed to minimize operating costs and comfort violations associated with HPWH use. The advantage of this implementation is that EMPC can be used to retrofit cloud-connected HPWHs without requiring physical modifications to the HPWH. In [6], a multi-objective EMPC was developed to minimize the operating costs, environmental impacts, and comfort violations associated with HPWH operation by incorporating a marginal grid GHG emissions signal into the EMPC. However, the aforementioned work only analyzed the EMPC performance under the assumption of perfect forecasting of all future hot water use events. Accurately predicting future draw events is necessary to maintain user comfort under EMPC. A hot water draw prediction algorithm was proposed in [7] that computes the predicted draw volume at each time step from the average daily draw volumes of the past ten days. Water use data was collected by installing long-term monitoring equipment. In [8], a hot water use predictor was developed for a cloud-based EMPC that forecasts hot water use events based on flow meter data. However, a flow meter is rarely available on residential HPWHs.

To this end, a method for estimating and forecasting hot water demand for the EMPC is needed to enable EMPC to proactively account for upcoming draw events. In this work, a model-based estimation approach for estimating hot water flow rate based on tank temperature sensor measurements is developed. Specifically, the model-based estimation approach is achieved by designing a state/disturbance estimator that utilizes a first-principles system model augmented with an integrating disturbance model. The unmeasured flow rate is treated as the disturbance. The resulting hot water flow rate estimates are used to train a data-driven model to forecast hot water demand. The data-driven hot water demand model uses time-of-day and day type as predictor variables. The forecast generated by the data-driven hot water demand model is provided as input data to the EMPC. The closed-loop behavior of a simulated HPWH under the EMPC that utilizes the data-driven hot water demand model is compared against a typical RBC strategy for HPWHs and an EMPC that assumes perfect forecasting of hot water use events.

References

[1] C. Berry, “Space heating and water heating account for nearly two thirds of U.S. home energy use”, Technical report, U.S. Energy Information Administration, 2018.

[2] Heat pump water heaters. Energy Saver. [Online]. Available: https://www.energy.gov/energysaver/heat-pump-water-heaters

[3] P. Delforge, “Heat pump water heaters as clean-energy batteries”, Jan 2020. [Online]. Available: www.nrdc.org/experts/pierre-delforge/heat-pump-water-heaters-clean-energ....

[4] M. Ellis, H. Durand, and P. D. Christofides, “A tutorial review of economic model predictive control

methods”, Journal of Process Control, 24:1156–1178, 2014.

[5] L. dela Rosa, C. Mande, and M. Ellis, “Supervisory multi-objective economic model predictive control for heat pump water heaters for cost and carbon optimization”, In Proceedings of the ASHRAE Conference, Atlanta, GA, Feb 2023.

[6] L. dela Rosa, C. Mande, H. Richardson, and M. Ellis, “Integrating greenhouse gas emissions into model predictive control of heat pump water heaters”, In Proceedings of the American Control Conference, San Diego, CA, May 2023, accepted.

[7] X. Jin, J. Maguire, and D. Christensen, “Model predictive control of heat pump water heaters for energy efficiency,” in Proceedings of the 18th ACEEE Summer Study on Energy Efficiency in Buildings, Pacific Grove, CA, Aug. 2014.

[8] M. Starke, J. Munk, H. Zandi, T. Kuruganti, H. Buckberry, J. Hall, and J. Leverette, “Agent-based system for transactive control of smart residential neighborhoods,” in 2019 IEEE Power & Energy Society General Meeting, Aug. 2019, pp. 1–5