Thermal Energy Storage in Multi-Energy System Optimization: How to Consider Temperatures?

The transition from fossil-based to renewable energy sources requires the adoption of intermittent, decentralized energy generation technologies. Therefore, the integration of energy storage technologies is becoming increasingly important. The impact of optimal design and operation of thermal energy storage (TES) systems can be assessed through simulation and optimization studies. However, models that accurately describe TES systems while considering storage temperatures are inherently nonlinear, presenting challenges such as prolonged computation times during optimization studies. As a result, most studies on district-size multi-energy systems (MES) employ a simplified capacity model for TES, which does not account for storage temperature levels. In this study, we present first results of a linearized stratified TES model for a residential building, implemented using the Python-based modeling package Pyomo. The study aims to assess the performance of this linearized TES model for potential future implementation in a district-size MES model. As a benchmark, the optimization of the residential energy system was carried out for both the simple capacity TES model and the linearized multi-node TES model for two weeks of operation with hourly timesteps. As an objective, operation cost was minimized. The results indicate that the capacity model underestimates the operation costs by 6.7% and 2.4% compared to the multi-node model for initial conditions of TES discharged and TES fully charged, respectively. Further, it was shown that the computation time for the multi-node model depends strongly on the solver type and the initial conditions, ranging from a few seconds to several minutes.