Physics informed neural network based multi-zone electric water heater modeling for demand response

Devising an effective control strategy to maximize the flexibility potential of electric water heaters (EWHs) requires a highly accurate and computationally inexpensive EWH model. Existing physics-based models are either too simplistic or computationally complex. This paper models EWHs using a physics-informed neural network (PINN) that integrates domain knowledge into the training process to ensure better physical consistency for capturing EWH thermal dynamics at a lower computational cost. Using a physics-based multi-zone (MZ) differential equation model (DEM), the EWH is discretized into multiple zones and modeled using a standard Multiple-Input-Multiple-Output (MIMO) PINN architecture to develop a generic and efficient EWH model. To improve the accuracy and interpretability further, a hybrid model that employs a Multiple-Input-Single-Output (MISO) PINN architecture together with physics derived features from the MZ DEM and a custom designed function for resolving temperature inversion is investigated in detail. Additionally, a customized recursive training strategy is developed to enable longer time-horizon simulations without performance degradation. Performance evaluations in both simulation and optimization frameworks using real-world data demonstrate the computational gains offered by PINN models over traditional MZ DEM.