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

Residential electric water heaters have significant load shifting capabilities due to their thermal heat capacity and large energy consumption. Model predictive control (MPC) has been shown to be an effective control strategy to enable water heater load shifting in home energy management systems. In this work, we analyze how modeling tank stratification in an MPC formulation impacts control performance for stratified electric water heaters under time-of-use (TOU) rates. Specifically, we propose an MPC formulation based on a three-node thermal model that captures tank stratification, and compare it to a one-node formulation that does not capture stratification and a standard thermostatic controller. These strategies are compared through both real-time laboratory testing and simulation-based evaluation for different water 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 the thermostatic controller. The performance of the one-node MPC is limited by significant plant-model mismatch, while the three-node formulation better approximates real-world dynamics and results in much more effective cost reduction and load shifting. A simple analysis of how each strategy performs under water use forecast errors is also provided.