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Medium and long-duration energy storage systems are expected to play a critical role in the transition towards electrical grids powered by renewable energy sources. ACAES is a promising solution, capable of handling power and energy ratings over hundreds of MW and MWh, respectively. One challenge with ACAES is achieving the required highly efficient operation in the compressor over the range of conditions encountered in the system as the pressure in the air store changes. In this paper, an application-oriented axial-flow compressor is designed, aiming towards efficient operation throughout the operation range, whilst also associating the performance prediction to a practical compressor geometry. A two-step design methodology based on inviscid, axisymmetric flow conditions has been implemented, leading to the flowtrack, blade-row geometries and the compressor performance map. The compressor model is integrated into an ACAES model, including two compression spools, two expansion stages with preheat, a constant volume high pressure storage operating between 5.5 and 7.7 MPa and two separate Thermal Energy Storage units. While the existing ACAES literature either ignores the transient off-design operation or uses generic numerical correlations (which are not associated to a particular geometry), the key novelty of this paper is the application of a detailed design method for turbomachinery to ACAES. The results indicate that the designed compressor requires 33 stages over the two spools, and is able to operate efficiently over the storage pressure range, showing that if the application-oriented design procedure is applied to the compressor, it does not stop ACAES reaching 70% round-trip efficiency, outputting 35MW for approximately 15 h. Importantly, the specific ACAES requirement of conserving heat at higher temperatures has been fulfilled by decreasing the number of intercoolers. Finally, it is recommended that a similar level of scrutiny is applied to the other components (i.e. expanders, heat exchangers and TES units), keeping in mind the unique set of operational requirements of ACAES. This work is an important step towards removing the common misconception that off-the-shelf components can be easily be used in typical ACAES designs. • ACAES imposes unique conditions on its components, aiming system reversibility. • The compressors must run efficiently and keep the airflow temperature high. • This paper develops an axial-flow compressor geometry and performance map for ACAES. • The compressor is integrated into an ACAES model, operating within 5.5 and 7.7 MPa. • The ACAES system results indicate the system reaches 70% RTE after stabilisation. [ABSTRACT FROM AUTHOR]