(537d) Multi-Objective Economic Model Predictive Control for Heat Pump Water Heaters for Cost and Greenhouse Gas Emission Optimization

Water heating is the second-largest energy consumer accounting for 20% of total residential end-use energy consumption in the U.S. [1]. Heat pump water heaters (HPWHs) offer a way to produce hot water using electricity which aligns with efforts towards electrification to leverage renewable energy sources. HPWHs are energy efficient and used in industrial, commercial, and residential water heating [2]. They are typically controlled by rule-based strategies to regulate the heat pump to maintain a water temperature in a region around the setpoint. However, such control strategies do not account for time-varying electric rates and may lead to suboptimal performance. Economic model predictive control (EMPC) addresses both control and economic optimization [3]. Therefore, EMPC is an ideal control strategy, and a few studies have demonstrated the potential benefit when applied to HPWHs (e.g., [4]-[7]). However, this prior work only focuses on minimizing energy consumption or cost and used simplified water tank models.

Time-of-use electricity rate structures include a peak (high-cost) and an off-peak (low-cost) period to incentivize customers to shift electricity consumption from peak to off-peak periods. Residential electric rates are typically constant-in-time or time-of-use in the U.S. (e.g., [8] in California). During the off-peak periods, the energy storage of HPWHs provides additional opportunities for optimizing secondary objectives. For example, during off-peak periods, the HPWH operation may be shifted to periods when the grid greenhouse gas (GHG) emissions are low with little to no cost penalty.

In this work, a multi-objective EMPC is presented for cost and GHG optimization of residential HPWHs with constant speed heat pumps and an auxiliary electric resistance heating element. The EMPC is formulated as a regulatory controller to activate the heat pump and electric resistance heating element. First, the fidelity of the HPWH predictive model used in EMPC is considered. Second, the formulation of a multi-objective EMPC for co-optimizing the cost and the grid GHG emissions is developed and applied. A warm-start strategy is proposed that guarantees an integer-feasible initial guess. As an alternative, EMPC can be implemented as a supervisory controller above the existing rule-based control. This EMPC formulation as a supervisory controller used to manipulate the temperature setpoint is presented. For all EMPC formulations, simulations with a detailed water tank model are performed to compare the performance and computational efficiency.

References

1. U.S. Energy Information Administration, "Residential Energy Consumption Survey," 2015.
2. S. Tangwe, M. Simon, and E. Meyer, “Mathematical modeling and simulation application to visualize the performance of retrofit heat pump water heater under first hour heating rating,” Renew. Energy, vol. 72, pp. 203–211, 2014.
3. M. Ellis, H. Durand, and P. D. Christofides, “A tutorial review of economic model predictive control methods,” J. Process Control, vol. 24, no. 8, pp. 1156–1178, 2014.
4. E. M. Wanjiru, S. M. Sichilalu, and X. Xia, “Model predictive control of heat pump water heater-instantaneous shower powered with integrated renewable-grid energy systems,” Appl. Energy, vol. 204, pp. 1333–1346, 2017.
5. F. Sossan, A. M. Kosek, S. Martinenas, M. Marinelli, and H. Bindner, “Scheduling of domestic water heater power demand for maximizing PV self-consumption using model predictive control,” 2013 4th IEEE/PES Innov. Smart Grid Technol. Eur. ISGT Eur. 2013, pp. 4–8, 2013.
6. S. Kuboth, F. Heberle, A. König-Haagen, and D. Brüggemann, “Economic model predictive control of combined thermal and electric residential building energy systems,” Appl. Energy, vol. 240, no. July 2018, pp. 372–385, 2019.
7. X. Jin, J. Maguire, and D. Christensen, “Model predictive control of heat pump water heaters for energy efficiency,” Proc. from 18th ACEEE Summer Study Energy Effic. Build., pp. 133–145, 2014,
8. https://www.pge.com/en_US/residential/rate-plans/rate-plan-options/under...