## 1 Introduction
The model was used in a slave problem within an optimization strategy for district energy systems. A different approach was proposed for design optimization of a hybrid steam storage consisting of a Ruths steam storage combined with phase change materials (PCM) [11]. The problem was simplified by neglecting actual load requirements, but auxiliary parameters were introduced that account for different charging and discharging requirements. Optimization models have also been used for operation optimization of TES. For the optimization of a CHP-based district heating system including TES with fixed size, upper and lower bounds for the SOC and also maximum charging/discharging rates were applied in order to maintain reliable operation [12]. The objective for this optimization model was to minimize energy acquisition costs. Dynamic programming was applied to find the optimal scheduling of power selling at the day-ahead market for solar thermal power plants with integrated TES [13]. In another work, the complex relations of design, operation and economics of solar thermal energy plants including the use of TES were studied [14]. In contrast to the works highlighted previously, dimensionless analysis was used in order to quantify TES efficiency. Most of these approaches rely on predefined cost parameters, even though the actual TES requirements can have a significant impact on TES costs. Comparison of different TES technologies based on general KPIs is not possible, since performance of the individual storage depends significantly on various requirements (required temperature range, case specific restrictions, required heat loads, required capacities, etc.). For example, for Ruths steam storage, the applicable temperature range and especially the maximum allowable storage temperature and pressure both influence the volume and mass specific storage capacity in terms of energy content, but also the capacity-specific storage costs. The capacity-specific storage costs are the total storage costs per unit of energy content (e.g., \(\epsilon\)/kWh). Higher storage pressures not only result in thicker pressure vessels to contain increased internal pressures, but also reduce steel strength due to increased temperatures. Furthermore, load-dependent costs, which are especially important for TES systems that depend on heat transfer as a storage phenomenon, are often neglected. But it is obvious that many storage technologies require components whose costs are driven by load, such as heat exchangers and pumps. The present study proposes an optimization-based method for identifying the most cost-efficient TES system for load shifting and exploitation of fluctuating renewable energy sources in industrial steam production. The method considers case-specific TES requirements and accounts for heat load specific storage costs. P2H technologies and TES are combined to enable the interaction between thermal and electric energy systems, which allows the industry to actively participate in energy markets. The proposed methodology is demonstrated by different case studies representing different scenarios for electricity prices and process requirements such as temperature levels and dynamic heat demand.