## 1 Introduction  
The energy requirement has been marked with a sharp increase worldwide in the last several decades by referring to the statistical data on the consumption of energy resources amongst 69 countries [1]. In particular, the scarcity of energy is directly intensified due to the significant augment of energy consumption in developing economies like China, India, South Africa, and Brazil, which are accelerating the urbanization process. For example, the energy use in China is inferred to be 15 times larger by 2050 in comparison with that in 1970 [2]. It is also reported that the oil demand will increase by 30% all around the world from 2007 to 2035 [2]. The increasing consumption of fossil fuels has brought serious energy shortages, environmental pollution, and global warming [3; 4; 5]. On one hand, measures can be made to promote the conversion efficiency of the existing energy systems. On the other hand, more efforts should be made to increase the utilization of renewable energies like wind, solar, and biomass energy to improve the currently unreasonable energy structure. However, the remarkable randomness and intermittency make renewable energies the inordinate and discordant sources when integrated to an electricity grid, bringing the discard of some redundant energy during the dispatching stage [6]. The technology of compressed air energy storage (CAES)has been proven to be a promising option to integrate the power obtained from renewable resources into the grid system by many researchers [7; 8]. The main demerit of this conventional CAES system is the compressed heat loss, which causes the low efficiency of the system (e.g., the efficiencies of the Huntorf plant is 42%). The advanced adiabatic CAES (AA-CAES) was therefore proposed with high operation efficiency by configuring with thermal energy storage to recover and reutilize the heat of compression [9; 10; 11; 12]. Moreover, in the CAES system, storing a huge amount of pressurized air must use large-scale caverns like salt mines, hard rocks, and porous rocks [13]. The liquid air energy storage [14; 15] is therefore put forward as the solution with the advantages of increasing energy storage density dramatically when storing liquid air. However, the extremely low-temperature requirement for air liquefaction decreases the economic feasibility of liquid and supercritical CAES and its security and reliability. To use the energy of CAES in step, the combined cooling, heating, and power (CCHP) technology has been developed, which has higher thermal efficiency and lowers operating cost per energy output. A CAES-based CCHP system was proposed and examined thermodynamically in a 300 MW wind farm [16]. The energy efficiency values of this system were 30.6%, 32.3%, and 92.4% for electrical power, cooling, and heating productions, respectively. [PERSON] et al. [17] demonstrated that the CCHP performance was highly dependent upon the gas turbine parameters when coupled with gas turbine and CAES. [PERSON] and [PERSON] [18] evaluated the thermodynamic performance of a CAES-based CCHP under four different operation strategies of charging-discharging by means of both energy and exergy analyses. Research demonstrated that the sliding-sliding scenario retained the largest cycle, thermal and exergy efficiencies compared to the constant-constant, sliding-constant and constant-sliding operation strategies. A hybrid CCHP was developed by [PERSON] et al. [19] by integrating the wind turbine, biogas, and photovoltaic cells resources, in which the CAES compression heat was provided for heating users and the cooling load was satisfied through taking advantage of absorption chiller combining with the cryogenic air from CAES. Unlike air, CO\({}_{2}\) is more susceptible to liquefaction by using current measures [20]. The working fluid CO\({}_{2}\) has high density and favorable heat transfer properties, making the thermal systems extremely compact [21].