## 2 Methodology  
For increased flexibility and cost efficiency of A-CAES systems, modifications are investigated through the integration of the P2H element. For this purpose, a promising configuration is based on an original two-stage compression and expansion process, in which sensible thermal energy storage systems are integrated in each pressure stage to conserve the heat during compression (Figure 1a). Therefore, a regenerator-based solid-media heat storage is used in the first stage in the presence of low to moderate pressure levels, and a two-tank heat storage system based on a liquid medium integrated via a heat exchanger is used in the second high-pressure stage. Additionally, two safety coolers are required to ensure the specified temperature inlet conditions of the high-pressure compressor and the cavern. On the basis of this original A-CAES configuration (reference concept), system extensions consisting in the integration of P2H elements (extended concept) and system modifications (alternative concept) are investigated. Figure 1 schematically illustrates the investigated concepts. The modified system (Figure 1b) is based on the original A-CAES system with P2H elements in the low- and high-pressure range before the thermal energy storage systems. This concept allows the investigation of electrical heating in the low- or in the high-pressure ranges individually, as well as in both pressure ranges. The basic idea behind these modifications includes an additional electrical heating stage during charging to elevate the temperature after compression, thus allowing increased thermal storage densities during thermal cyclic operation. In contrast, the alternative concept is based on only one thermal energy storage system (Figure 1c). Here, heat during compression in the low-pressure stage--additionally elevated by the  
Figure 1: Reference concept (**a**); extended concept (**b**) with power-to-heat element (P2H) elements in the low- and/or in the high-pressure stage; alternative concept (**c**) with P2H element in the low-pressure (LP) stage and without high-pressure thermal energy storage systems (HP-TES). P2H element--is stored in the regenerator-based heat storage and cooled down during compression in the second stage. Differing from the previous concepts, the temperature of the pressurized air leaving the cavern during discharging is elevated by the stored heat via a heat exchanger and expanded over the whole pressure range to ambient conditions. Additional potentials are offered by the P2H elements to both concepts by simultaneous adaptations of the pressure ratios to utilize the exergetic effects due to the elevated temperatures. In order to identify efficient configurations on the base of central specifications with increased storage densities compared to the reference concept, variation studies are conducted considering TES efficiencies (\(\eta_{\text{TES}}\)), electrical heating power (\(\text{P}_{\text{P2H}}\)), and pressure in the first stage (\(\text{P}_{\text{LP}}\)). For clarification, this simulation methodology is illustrated in Figure 2.  
In the variation study of the reference concept without additional electric heating, a constant pressure in the first stage is set to achieve equal pressure ratios in all stages. With respect to TES efficiency, simulation runs are conducted to identify suitable solutions with high round trip efficiencies and moderate dimension sizes of the TES components. On the basis of appropriate TES efficiencies, variations studies of the extended and alternative concepts are performed in order to investigate the effects of the first-stage pressure level and of the additional electric heating on total round trip efficiency and component-specific results. Because of the same set of specifications for all concepts under investigation, the output parameters allow comparative statements regarding system efficiencies and component sizes.