## 2 Carnot Battery Technology  
A Carnot battery is an innovative approach to electrical energy storage (EES) which consists, at least, of electrical input and output [5]. The operating principle of the Carnot battery is simple. The electric energy is first converted to thermal energy, then stored in TES (during TES charging), and can later be recovered (during TES discharging). The charging and discharging can proceed due to several energy conversion technologies. Based on literature studies [5; 7], patents related to Carnot battery technology date back to 1979, and the original concept was suggested in 1922 by [PERSON]. According to various studies, Carnot batteries may include technology such as pumped thermal electricity storage (PTES) [18], which can be traced back to [PERSON]'s work in 1883 [5; 19]. A Carnot battery consists of a heat pump, a heat engine, and a high/low-temperature control region during operation, and is illustrated in the literature [5]. In one case, electric energy is used to pump the heat from a low temperature to a high-temperature reservoir, which can be performed with the help of a heat pump. Once the thermal energy is collected in the high-temperature reservoir and TES is charged, thermal energy can be stored for a certain time period. Then, the energy of this high-temperature reservoir can be utilized to generate electricity with the help of heat engines. In another case, the electric input is used to pump the cooled or liquefied working fluid to a low-temperature reservoir (the temperature of which is below the ambient temperature) with the help of a heat pump. This kind of cold energy can then be utilized to generate electricity with the help of a heat engine whose lower operating temperature (i.e., a condenser temperature) is designed around this point. This can even be performed by a cryogenic cycle that works significantly below room temperatures. There are many possible configurations of Carnot batteries. One example is PTES (which can also be called pumped heat energy storage (PHES) or compressed heat energy storage (CHEST)) [20]. This type of battery may be configured using Rankine-based or Brayton-based cycles with further sub-classes [5]. The Lamm-Honigmann process is a form of thermochemical energy storage invented to be charged with the input of heat or mechanical work, and discharged with the release of heat or mechanical work [21]. The discharging of the Lamm-Honigmann process can be achieved by heating a solution of water in another liquid (e.g., LiBr or NaOH) [5]. In liquefied air energy storage (LAES), electric energy is used to liquefy air with the help of air compression and an air-cooling system (the so-called liquefaction process). Both Brayton-based and Rankine-based systems show promise for application in Carnot batteries. Brayton-based cycles mainly operate under gas conditions, whereas Rankine-based cycles may involve the two-phase condition. Typical configurations for Brayton- and Rankine-based systems consist of a separated system (heat pump and heat engine), a reversible system (heat pump and heat engine in one compact system), and a combined system with an electrical heater. The significant difference between Brayton- and Rankine-based cycles is in the energy consumption: the Rankine-based cycle consumes relatively lower power to pump the working fluid than the Brayton cycle [22]. The Rankine cycle features a closed-loop cycle, and the Brayton cycle operates in an open loop. It has been found that the Brayton cycle may work in a closed-loop configuration if it employs a compressor in the process, in which the operating conditions and efficiency may be sensitive to the polytropic performance of the machine [5]. For this reason, in this study, we selected the Rankine-based cycle because it offers good performance and low power consumption of the pump. There are various potential means to design a reversible heat pump/ORC system; two possibilities are shown in literature.