## 5 Conclusions  
This study represents the first comprehensive systematic structural analysis of Brayton batteries. A universal simulation tool was developed in Epsilon Professional(r) for this purpose. For a specific set of boundary conditions, a concept study was conducted for various purposes, including pure electricity generation as well as various coupled generation of electricity, heat, and cooling with and without waste heat integration, resulting in the calculation of over 200,000 concepts.  
Less than 1% of the calculated concepts lead to physically realizable results. For pure electricity generation, round trip efficiencies range from 20 to 50%. Concepts operating at CDT = 450 \({}^{\circ}\)C show lower round trip efficiencies than those operating at CDT = 625 \({}^{\circ}\)C. There is no discernible trend for the working fluids, and the same applies to the inclusion or exclusion of recuperators. The inclusion of additional waste heat does not lead to significantly higher values.  
Coupled generation of electricity and heat or cooling improves overall efficiency, reflected in increased values for RTU. However, this comes at the expense of RTE. The integration of waste heat leads to increased values for round trip utilization in concepts for heat provision but not in concepts for cooling provision. Concepts operating at CDT = 450 \({}^{\circ}\)C show lower RTE values than those with CDT = 625 \({}^{\circ}\)C; this does not mean that their RTU values must also be lower. For open concepts, very few solutions were achieved, but these have lower efficiency. No clear trend is observed for the working fluids. The inclusion of a recuperator in the charging line enables the development of concepts for coupled generation of electricity and heat at CDT = 450 \({}^{\circ}\)C. There are no physically possible solutions for simultaneous coupled generation of electricity, heat, and cooling. The maximum achievable efficiencies are summarized in Figure 28 for the different applications.  
If solutions were available, two to three lead concepts per application purpose were defined. The identified lead concepts are consistently air-operated systems at relatively low pressure (<13 bar), with or without a recuperator in the charging line, and with heat supply or removal at various points in the process, considering CDT values of 450 \({}^{\circ}\)C or 625 \({}^{\circ}\)C. These lead concepts will be further investigated through dynamic system simulations, including component design, with a focus on thermal energy storage. In addition to dynamic analysis, another focus will be on developing configurations that can generate not only electricity but also heat and cooling, either simultaneously or with a time delay.  
As discussed earlier, the lack of comparable simulation results in the literature underscores the unique advantages of the systematic structural analysis presented here. The most efficient concepts can be found for a specific set of parameters, which show significantly better performance values than concepts from the literature that may not represent the best solution for that particular parameter set. This is particularly the case for concepts with coupled generation of electricity and heat or coupled generation of electricity and cooling, as the published research in this area is limited.  
This research was funded by the German Federal Ministry for Economic Affairs and Climate Action, grant number 03 EI3045.  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The author declares no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of