## 1 Introduction  
Cryogenic energy storage, and particularly liquid air energy storage (LAES), is receiving growing interest from the research community as one of the most promising technologies for large-scale energy storage in the power grid. However, real-world LAES applications are still quite limited, mainly because of the complex LAES plant layout, as well as because of the low ratio between the energy recovered from the LAES system during the discharge stage and the total energy input, known as the 'round-trip efficiency' (RTE). A detailed bibliography of numerous publications outlining recent trends in the field of LAES was presented by [PERSON] et al. [1]. A typical LAES plant operates in three stages. In periods of excess power supply, which can come from intermittent renewable sources, electricity is used to liquefy air by means of compression and refrigeration (charge stage). The liquefied air is then stored in a low-pressure insulated tank (storage stage). In periods of high power demand, the liquid air is drawn from the tank, pumped and then heated by utilizing previously stored compression heat. The air is then expanded in a turbine connected to a generator, which supplies power to the grid (discharge stage). Most often, the liquefaction technology for charging needs to be selected amongst the cycles of Linde-Hampson, Claude, Heylandt and Collins, or a cycle with two expanders. [PERSON] and [PERSON] [2] compared different options and concluded that the Claude cycle is optimal for LAES purposes. Thus, the LAES configurations analysed hereafter in Sections 2.2 and 3.2 also resort to the Claude cycle. Many recent studies in the area [3; 4; 5; 6; 7; 8] clearly indicated that the discharging process cannot fully utilise the stored heat of compression in an efficient manner. According to [PERSON] et al. [9], 20-45% of the compression heat is wasted, making this one of the main reasons for the poor RTE of a typical LAES system. Many authors have studied different approaches for the utilization of the aforementioned excess heat. [PERSON] et al. [7], [PERSON] et al. [10] and [PERSON] et al. [11] proposed a hybrid LAES system, involving an organic Rankine cycle (ORC) and a vapour-compression refrigeration cycle. The excess heat of compression is used as a heat source for the ORC, whereas the vapour-compression refrigeration cycle acts as a heat sink. [PERSON] et al. [5] investigated nine options for internal and external use of the excess heat, including standalone electricity production and combined heat, cold and power production (tri-generation) which provides district cooling and heating. The best overall RTE of almost 56% is achieved by a configuration that uses a significant portion of the stored heat from compression to drive an absorption chiller and an ORC. In this configuration, the ORC generates additional electricity, while the absorption chiller and the air turbine with a heat exchanger generate chilled water at 6 \({}^{\circ}\)C to be used for air conditioning. It is worth mentioning that the baseline LAES system in their study had an RTE of 48.22%. [PERSON] et al. [12] integrated a Kalina cycle into the LAES system to utilise surplus heat during discharge in order to generate extra electricity, thus enhancing the RTE by some 5%. Although such hybridizations improve the RTE, they introduce additional complexity to the LAES plant, which already contains a large number of components (i.e., compressors, turbines, heat exchangers, pumps, storage tanks, electrical generators, valves, and pipes). As a result, both the capital and the operation and maintenance costs of the system increase, while the daily cycling and seasonal dependence of such a complex system can be rather challenging. [PERSON] et al. [13] proposed a LAES system with tri-generation capability, which can provide district cooling, district heating and electricity during periods of peak power demand. Their results show an RTE improvement of 8% to 13% in the tri-generation case, as compared with a standalone system. [PERSON] et al.