  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.
