## 4 Results
### Extended Concept
Here, the benefits regarding higher exergetic utilization with adapted pressures in the first stage are  
Figure 4: Total round trip efficiency without electrical heating (\(\eta_{0}\)) and P2H-specific changes of total round trip efficiency (\(\frac{\Delta\eta}{\Delta P_{P2H}}\)) related to the first-stage pressure (p\({}_{\rm LP}\)). equalized through electrical heating power distribution, leading to a nearly constant loss of specific round trip efficiency of \(-0.38\%/\mathrm{MW_{P2H}}\). With respect to the lowest specific losses in round trip efficiency with additional electrical heating, the results indicate, as integration location, only the low- or high-pressure range with adapted pressure levels in the first stage. To investigate the potential of cost reduction, specific results related to the cyclic stored air mass--as a relevant parameter for cavern and compressor size--as well as the thermal storage density for both options are illustrated. Figure 5 shows the resulting cyclic stored air mass as well as its specific reduction with varying pressure in the first stage for the investigated three integration options. Comparable with the mentioned results regarding the total round trip efficiency, a comparatively constant required air mass of 3450 t is needed for the reference case. Similar to Figure 4, the highest specific reductions in cyclic stored air mass of \(-15.3\) t/MW will be achieved with integration locations only in the low- (\(\mathrm{x_{LP,P2H}}=100\%\)) and in the high-pressure range (\(\mathrm{x_{LP,P2H}}=0\%\)), respectively, with simultaneous pressure adaptions in the first stage. According to the defined boundary conditions and specifications, the specific reductions in cyclic storage mass correspond to smaller cavern and compressors sizes of up to \(-0.5\)\(\mathrm{MW_{Compressor}}/\mathrm{MW_{P2H}}\). In addition, further potentials in cost reduction are linked to electrical heating. These are shown in Figure 6 with varying low pressures related to both thermal energy storage options: left for the TES option in the first stage, and right for the TES option in the second stage. Figure 5: Stored air mass without electrical heating (\(\mathrm{m_{F,0}}\)) and P2H-specific changes of stored air mass (\(\frac{\Delta m_{F}}{\Delta P_{P2H}}\)) related to the first-stage pressure (\(\mathrm{p_{LP}}\)). Concerning the reference case without additional electrical heating, indicated by the thick lines, higher thermal storage densities are visible with increasing low pressure levels for the LP-TES (Figure 6 left) and with decreasing low pressure levels for the HP-TES (Figure 6 right). Both result from higher compression outlet temperatures leading to a higher temperature spread inside the sensible storage media. With a further temperature elevation due to electrical heating, different effects on specific thermal storage density for both TES options are visible, mainly influenced by the P2H integration locations. For electrical heating location only in the low-pressure stage (x\({}_{\text{LP,P2H}}\) = 100%), an additional increased specific thermal storage density of 2.3 kWh/m\({}^{3}\)/MW\({}_{\text{P2H}}\) is reached inside the LP-TES (Figure 6 left), whereas no effects occur inside the HP-TES (Figure 6 right) due to the integrated safety cooler. In contrast, with increasing share of electrical heating inside the high-pressure stage, higher specific thermal storage densities of up to 1.65 kWh/m\({}^{3}\)/MW\({}_{\text{P2H}}\) are achieved in the HP-TES, but with simultaneous lower increasing specific thermal storage densities in the LP-TES. Actually, regarding the limit case of pure electrical heating in the high-pressure stage (x\({}_{\text{LP,P2H}}\) = 0%), negative specific thermal storage densities of -1.3 kWh/m\({}^{3}\)/MW\({}_{\text{P2H}}\) are visible inside the LP-TES (Figure 6 left).