## 2 System Description  
The sketch of the proposed system, which comprises an LAES unit, an NG power plant, and a CO\({}_{2}\) capture unit, is depicted in Figure 1. A Linde-Hampson liquefaction cycle is adopted for the air liquefaction. The present study does not discuss the purification and pre-treatment of the feed gas, LNG transmission, and storage processes [20]. In the proposed arrangement, methanol and propane are exploited to recycle the cryogenic energy of the LA in the discharging period, to pre-cool the compressed air in the charging process. To explore the overall performance of the proposed complex system, assume that the compressors and turbines are operating at a steady state. A brief schematic is provided in Figure 1A to indicate the temperature, pressure, heat, and power of all the inlets and exits. Figure 1: _Cont_. During the charging period, the 1-2 air compressor (AC) in the first stage, the 3-4 AC in the second stage, and the 5-6 AC in the third stage, are operated to pressurize the purified air with surplus power from the grid. The air compression process is associated with a huge amount of waste heat release at a high outlet temperature. Therefore, the 2-3 inter-cooler (IC) in the first stage, the 4-5 IC in the second stage, and the 6-7 IC in the third stage, use O1-O2 thermal oil to recover the compression heat [25]. In the air liquefaction unit, compressed air is cooled down by circulating refrigerants (i.e., M1-M2 methanol and P1-P1 propane) and the 11-13 reflux air in the 7-9 air condensers (ACONs). Meanwhile, the refrigerants are stored in thermal insulated containers, i.e., liquid methanol tanks (LMTs) and liquid propane tanks (LPIs), and thermal oil is stored in liquid thermal oil tanks (LOTs). Afterwards, a two-phase mixture of air is produced through an expansion in the 9-10 throttle valve (ATV). As a result, LA is separated in the 10-14 air separator (AS) and stored in the 14-15 liquid air tank (LAT), while gas-phase air (state 11) flows back into the ACONs. During the discharging period, LA and LNG are pumped into the 16-18 evaporators (EVAs) by the 15-16 liquid air pump (LAP) and the 27-28 LNG pump (LNGP), respectively, and then the LA and LNG are gasified. The required evaporating heat is supplied by the heated M3-M4 methanol and P3-P4 propane. Then, the air splits into two streams, one entering the 30-31 CRV being mixed with NG (state 29) for combustion, and the other entering the 19-20 re-heater (RH), the 20-21 AT in the first stage, the 21-22 AT in the second stage, the 23-24 AT in the third stage, and the 25-26 AT in the fourth stage. The exhaust air from the AT (stages 22 and 24) is heated up by the thermal oil in the Q3-O4 superheater (SH). Flue gas from the combustion (state 31) is mainly composed of CO\({}_{2}\), water (H\({}_{2}\)O), and nitrogen (N\({}_{2}\)), etc. The flue gas is at a high temperature and pressure (approximately 1600-1750 \({}^{\circ}\)C, 7 MPa) and is used to drive the 31-32 GT to generate power. The RH is responsible for condensing the moisture of the flue gas (state 32) and heating the inlet air in the AT in the first stage, and the 33-43 vapor separator 1 (VS1) is employed to remove the condensed H\({}_{2}\)O. For deep moisture removal, the flue gas (state 34) is further cooled in the 34-35 vapor  
Figure 1: (**A**) Control volume schematic of the proposed system. (**B**) A sketch of the proposed system. condenser (VCON), and all of the condensed H\({}_{2}\)O is separated in the 35-44 vapor separator 2 (VS2). Then, the dry flue gas (state 36) passes through the 36-37 carbon dioxide condenser (CCON) and the 37-38 carbon dioxide separator (CS) serially, where partial CO\({}_{2}\) can be condensed and removed, while the residual CO\({}_{2}\) is separated in the 38-46 gas separator (GS). Since the decarbonized flue gas (state 39) is still at a high pressure (approximately 0.546 MPa), it expands in the 39-40 cryo-turbine (CT) to generate electricity and cold energy.