Grey-box model of a short-term-operated pit thermal energy storage system

As the heat and power sectors become increasingly coupled, storing excess heat for later use is key to improvingenergy system efficiency. Pit thermal energy storage (PTES) systems, when integrated with district heating (DH)networks, offer a large storage capacity at a low investment cost. PTES systems can leverage stored heat for short-term operation to shave heat demand peaks. However, optimizing this dispatch requires accurate long-term forecastsof the available heat, which depend on reliable models of the pit’s thermal dynamics.To this end, we develop a grey-box model based on the heat transfer equation in fluids. By spatially discretizingthis equation, we describe the time evolution of water temperature at different depths within the pit. A stochasticnoise term is added to account for model uncertainties. This approach combines physically consistent dynamics withstatistical parameter estimation. On real-world operational data, the model achieves a root mean squared error of0.1◦C for one-hour ahead and 1.5◦C for one-week ahead forecasts. This performance stems from careful attention tonumerical stability of parameter estimation tools. Implicit differential equation solvers ensure robust state propagationover long time horizons, while automatic differentiation provides accurate gradients for optimization. The resultinghigh-fidelity model is well-suited for integration into economic dispatch tools, supporting more efficient DH operation.