Control under uncertainty for a physics-informed model of a thermal energy distribution system: Qualitative analysis

Integrated energy systems (IES)s combine various energy sources, such as nuclear power, with thermal energy storage (TES) and hydrogen electrolyzers in order to optimize energy use, peak-load regulation, and demand-side responses. However, their integration introduces operational challenges that can be mitigated with an efficient controller that orchestrates their cooperation. In a recent study, we calibrated a probabilistic linear Sparse Identification of Nonlinear Dynamics with Control (SINDyC) model termed Multivariate Gaussian Fit SINDyC (MvG-SINDyC) on several components of an IES, namely a glycol heat exchanger (GHX) and a thermal energy storage (TES). In this work, we qualitatively demonstrate its performance within control. Specifically, we developed a robust MPC formulation and attempted to replicate known experimental trajectories. While reasonable results were achieved for the GHX, significant model inadequacies persisted, and the base linear formulation of SINDyC failed to track any trajectories for the TES. Consequently, we adopted a Gaussian process (GP)-based error correction model, which was applied to both the GHX and TES and integrated into the control system, demonstrating notable benefits, including lower mean absolute and mean squared errors, U-pooling, and reduced constraint violations. However, large uncertainties persisted for unseen trajectories, prompting us to collect more data to refine the model in the future. Additionally, higher-order SINDyC libraries could be used to construct the base MvG-SINDyC model, thereby lowering model form error uncertainties and helping capture a broader range of real-world operational scenarios prior to deployment.