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Residential electric water heaters have significant load shiftingcapabilities due to their thermal heat capacity and large energy consumption.Model predictive control (MPC) has been shown to be an effective controlstrategy to enable water heater load shifting in home energy managementsystems. In this work, we analyze how modeling tank stratification in an MPCformulation impacts control performance for stratified electric water heatersunder time-of-use (TOU) rates. Specifically, we propose an MPC formulationbased on a three-node thermal model that captures tank stratification, andcompare it to a one-node formulation that does not capture stratification and astandard thermostatic controller. These strategies are compared through bothreal-time laboratory testing and simulation-based evaluation for differentwater use patterns. Laboratory experiments show cost reductions of 12.3-23.2%for the one-node MPC and 31.2-42.5% for the three-node MPC relative to thethermostatic controller. The performance of the one-node MPC is limited bysignificant plant-model mismatch, while the three-node formulation betterapproximates real-world dynamics and results in much more effective costreduction and load shifting. A simple analysis of how each strategy performsunder water use forecast errors is also provided.

Improving the Load Flexibility of Stratified Electric Water Heaters: Design and Experimental Validation of MPC Strategies