Observer-based thermocline tracking and heat transfer coefficient estimation in packed bed thermal energy storage systems

Abstract

Efficient operation and control of packed bed thermal energy storage (PBTES) systems critically depend on precise knowledge of the thermocline position and shape, as it directly determines storage efficiency, usable energy content, and operational flexibility. However, direct measurement of the full temperature distribution is impractical in real applications due to limited sensor availability and harsh operating conditions. This work, therefore, addresses the problem of thermocline tracking through model-based state observation and online parameter identification. A novel observer-based methodology is proposed for the real-time reconstruction of the spatial temperature distribution inside a PBTES and the simultaneous estimation of the heat transfer coefficient (HTC) between the heat transfer fluid and the storage material. A reduced-order temperature model is derived using Snapshot Proper Orthogonal Decomposition, enabling computationally efficient estimation while preserving the dominant thermocline dynamics. The observability properties of the reduced model are analyzed using the observability Gramian, which in turn guides optimal sensor placement and observer design. To account for parameter uncertainties and operational changes, an online HTC estimation scheme based on the Ternary Search Algorithm is integrated into the observer framework. The combined approach allows robust thermocline reconstruction and parameter identification during operation using only a small number of optimally placed sensors. Validation against experimental measurements and high-fidelity simulations demonstrates high estimation accuracy and robustness with respect to initialization errors and parameter mismatches. The proposed framework provides a practical solution for thermocline tracking in PBTES systems and supports efficient, reliable, and sensor-efficient operation of thermal energy storage.