As part of the change towards a higher deployment of renewable energy sources, which naturally deliver energy intermittently, the need for energy storage systems is increasing. For compensation of disturbance in power production due to inter -day to seasonal weather changes, long-term energy storage is required. In the spectrum of storage systems, one out of a few geographically independent possibilities is the storage of electricity in heat, so -called Carnot - batteries. This paper present s a Pumped Thermal Energy Storage (PTES) system based on a recuperated and recompressed supercritical CO 2 Brayton cycle. It is analysed if this configuration of a Brayton cycle , which is most advantageous for supercritical CO 2 Brayton cycles, can be favourably integrated in to a Carnot -battery and if a similar high efficiency can be achieved , despite the const raints caused by the integration . The modelled PTES operates at a pressure ratio of 3 with low nominal pressure 8 MPa, between the temperatures 16 °C and 513 °C. The modelled system provides a round -trip efficiency of 38.9% and was designed for a maximum of 3.5 MW electric power output . The research shows that an acceptable round - trip efficiency can be achieved with a recuperated and recompressed Brayton Cycle employing supercritical CO 2 as working fluid. However, a higher e fficiency would be expected to justify the complexity of the configuration. Keywords: pumped thermal energy storage ( PTES), Carnot -batter y, power -to-heat-to-power (P2H2P), supercritical CO 2 cycle, Brayton cycle, heat exchange, pinch -point analysis 1 Introduc tion As the demand for renewable energies is increasing, so is the importance of its reliability. Unfortunately, the availability of energy from renewable sources and the electricity demand are usually not corresponding . Most renewable energy is obtained f rom so-called variable renewable energy sources (VRES) like sun and wind , which the electric grid could handle , up to maximum integration of 10% without any further changes [1]. The variation of hourly wind speed, as well as the solar radiation, compared to the feed-in, at the example of Nuremberg in Germany , can be visually compa red in Figure 1 and Figure 2 . This shall give an idea of the fluctuation of “available weather ” and energy demand throughout a day. For this purpose, Figure 1 also shows the variation of the wind by highlighting its minimum and maximum values (at the diffe rent hours of the day throughout the year). The wind speed and sun radiation data is obtained from the MERRA database [2–5]1, and the feed -in values from a local energy supplier called N -ERGIE [6]. 1 The data from the MERRA data base was, with kind permission, retrieved and processed with an Excel -Tool (version 18.03.2016) from Prof. Dr. -Ing. Matthias Popp, Burgstraße 19, D -95632 Wunsiedel, Germany . Figure 1: Intraday load curve network supply and wind speed in Nuremberg, Germany, 2015 [7,6] Figure 2: Intraday load curve network supply and sun radiation in Nuremberg, Germany, 2015 [7,6] These kinds of inequalities of offer and demand can be observed worldwide and the whole year round, also requiring shifting energy between different se asons of the year. To encounter this problem , besides focusing on making the energy production as flexible as possible, energy storages are about to become of great importance in the change to a decarbonised future , as also stated by the International Ener gy Agency (IEA) [8]. Energy storage can also be an enabler for making VAES power plants like a Concentrated Solar Power (CSP) more competitive to traditional, fossil fuel burning power plants [9]. Thermal storage, directly integrated into the power cycle , can replace the sun as a source of thermal energy during shady times and allow the CSP plant to deliver energy more continuously and reliable. With a competitive solution like this, places with high availabil ity of sun radiation , like for example W estern China, could effectively use the sun instead of a fossil fuel power plant, even if the interest would be from more economic nature , rather than sole ly for the protection of the environment. In the spectrum of storage systems, thermal energy storage (TES) is one out of a few possibilities how to store energy environmentally friendly and geographically independent. The in this paper , proposed pumped thermal ener gy storage (PTES) is also called Carnot - battery, Electro -Thermal Energy storage ETES or Pumped Heat Energy Storage PHES2. The principle is described schematically in Figure 3. 2 Not to be confused with PHS (Pumped Hydro Storage). 024681012 0,00,20,40,60,81,01,21,4 123456789101112131415161718192021222324 Wind [km/h]feed-in [GW] Hour of day feed-in average wind wind min wind max 050100150200250300350400450 0,00,20,40,60,81,01,21,41,61,8 123456789101112131415161718192021222324 Radiation energy [W/m²] feed-in [GW] Hour of day feed-in sun Figure 3: Principle of a Carnot -battery (modified from [10]) The potential of different storage principles is visualised in Figure 4. Electro -Thermal Energy Storage (ETES ) is rated as a technology, feasible for longer storage time and higher power . Especially d ue to th e possib le storage time of several hours and days , it is feasible for handl ing the offset between offer and demand caused by volatile renewable energies like wind and sun (as can be seen in Figure 1 and Figure 2 ). However, it is also still in its concept phase [11], with the first demonstrators being tested. Figure 4: Comparison between different storage technologies (modif ied from [11,12]) By 202 0, several Carnot -battery pilot plants have been operat ed successfully . The Argon -based Brayton Cycle with 150 kW (600 kWh electric) of the Newcastle University , built with the help of the company Isentropic Ltd. in the United Kingdom , is deploying reciprocating devices. The system has a round -trip efficiency of 60% to 65% [13] and is based on the theoretical concept by Howes [14]. SIEMENS Gamesa built a PTES pilot in Hamburg, Germany which went into operation in summer 2019 [15–17]. They us e an electric heater to heat air which is blown through a packed bed storage for charging it. For retrieving power from the system, the thermal energy can be used to generate steam for a conventional Rankine cycle. The maximum electrical output power is th en 1.5 MW, while the storage has a capacity of 30 MWh electric , with a round -trip efficiency of about 45% [8–10]. Further, two thermally integrated PTES (TI-PTES) with heat pump /organic Rankine cycle in lab -scale were built in Liege, Belgium [18]. Utilising waste thermal energy at 75 °C as the cold source for the heat pump a round -trip efficiency of 100% is reached [18,19]. A liquid -air energy storage (LAES) with 8% round -trip efficiency from the company Highview Power delivering 350kW (2.5MWh) was tested from 2011 to 2014 in Greater London [20,21]. However, t here are already several other projects of Carnot -battery pilot plants under development, construction or in testin g. 2 CO 2 as working fluid for PTES cycles CO 2 is an interesting candidate as a working fluid for PTES system s, because of its critical point at nearly ambient temperature and high densit ies. The low temperature is good for rejection of thermal energy in a Brayton cycle [22]. The high density results in a comparably low compression work and high power density, which results in small turbomachinery [23]. Additionally, it is widely available, inexpensive and nontoxic [23]. Problems with CO 2 are, that it is highly diffusive, enhancing corrosion of surrounding materials or lead s to rapid depressurisation and that it is very sensitive to small changes in pressure or temperatur e near the critical point [23]. Additionally, the specific heat capacity of carbon dioxide is strongly variable, leading to high changes in the temperature difference be tween the hot and cold fluid in heat exchangers, which can cause the minimal temperature difference to be not at inlet or exit but inside the heat exchanger, which i s called pinch -point -problem [22]. Compared to cycles running with other working fluids, CO 2 cycles are not so widely tested and used yet, which can lead to possible problems, but also offers great potential. Table 1: Physicochemical properties of CO 2 [24] Name Formula Molecular weight Critical temperature Critical pressure Critical density Carbon dioxide CO 2 44.01 kg/mol 31.03 °C 7.383 MPa 466 kg/m3 Most proposed PTES systems which employ CO 2 as the working fluid are based on transcritical Rankine cycles, reaching between 40.9% and 68.6% round -trip efficiency [25–29]. Only McTigue et al. propose a supercritical CO 2 Brayton cycle, reaching 60.4% round -trip efficiency with a low -temperature cycle and 78.4% in a high -temperature cycle [30]. A very different approach is the transcritical isothermal Rankine cycle by Kim et al., using a double -acting liquid piston system with direct heat transfer to the storage media water , reaching 68.6% round -trip efficiency [31]. For the proposed transcritical CO 2 Rankine cycles the pinch -point problem is usually encountered by using multiple hot storage tanks , using indirect heat transfer to (mostly pressurised) water tanks [25,26,32]. For Ayachi et al . [28], who are using ground storage , the heat transfer is directly between the CO 2 and the solid storage material through which it is flowing (direct, passive multi -tube packed bed storage) . Their pinch -point considerations are direct ly connected with the overall storage design. Steinmann et al . [29] point out that it is generally im possible to achieve a mean temperature difference of 5 K to 10 K between a single pressurised water storage and the CO 2, while still having a constant mass flow and significant heat transfer (temperature difference) in the heat exchanger. Unlike the before mentioned research , they choose to assume an ideal s torage system , neglecting the pinch -point problem, rather than specifying a possible solution. McTigue et al. designed a simple, no t recuperated Brayton cycle [30], even though they ’re mentioning, that recuperation would be feasible due to the high -temperature difference between compression and expansion. Due to the high potential of CO 2 in its supercritical state , this paper investigates a new layout of a Brayton sCO 2 PTES . The proposed cycle is recompressed and employs double recuperation because this layout is reaching the high est efficiencies for sCO 2 cycles and generally has a great potential for recuperation , as also stated by McTigue et al. [30], whereas other research focused on transcritical CO 2 Cycles or simple non -recuperated supercritical CO 2 cycles [33,34]. The paper will determine if this layout is favourable for a Carnot Batter y and how the boundary conditions limit the power cycles performance (e. g. the Carnot -batteries storage temperature s as well as the flow rates of the working fluid and the storage material limit the options of cycle configuration and influence one another) . The effect of different operating temperatures and pressure ratios , as well as variou s temperature differences of the heat exchangers and efficiencies of turbines and compressors , was analysed . The key in puts are presented together with the best combination of parameters in the Results and Discussion Section. 3 Concept of a supercritical CO 2 Brayton cycle with liquid hot and cold storage 3.1 Description of the h ot and cold storage The proposed supercritical CO 2 Brayton cycle has a liquid hot , as well as cold, two-tank storage . For the discharging cycle , a turbine and two compres sors (one for recompression) are needed. The s ame principle applies to the charg ing cycle, where two turbine sections and one compressor are necessary. For the charging cycle , a heat exchanger to ambient air is necessary due to irreversibilities within the cycle. Further , each configuration needs two heat exchangers for recuperation . Two heat exchangers for transfe rring thermal energy between the cycle and the storage tanks are used for charging an d discharging . Since the heat pump and the power cycle can employ the same pressure ratio due to the flexibility in mass flows through the recompression stage , it seems possible , that some of the turbomachinery can be used in charging and discharging mode. Possible effects are not considered further. Each storage consists out of two tanks , from which one contains storage material at high - temperature and the other one material at low -temperature. Within a tank , the storage mate rial is kept at a constant temperature. Figure 5 shows the work ing principle of the two -tank storage. During charging , the material from the colder tank of the hot storage is pumped through a heat exchanger , which is transferring thermal ene rgy from the cycle to the storage media . It is then stored in the second tank at a higher temperature. For the cold storage , the fluid is cooling down during the charging cycle, heating the cycle fluid . In the discharging phase , the fluid is pumped the oth er way around . The hot tank of the hot storage is emptying while the colder tank is filling up, and the level of fluid in the cold tank of the cold storage is descending while it is rising in the warmer tank. Through maintaining a constant flow between a charged and discharged tank of a storage, where both tanks maintain a constant temperature but only vary in the amount of stored material, the heat flux in the heat exchanger is constant . The constant heat flux is an advantage to packed beds , where the problem of a non-constant temperature output , is a challenge faced in cycle design. The hot storage material is solar salt with the chemical composition of 60% NaNO 3 + 40% KNO 3. It has a melting temperature of 221.04 °C and thermal stability up to 588.51 °C [35]. The mean heat capacity for the operating temperatures of the hot storage is 1.518 kJ kg-1K-1 [36]. The cold storage can work with thermal oil, like THERMINOL 66, due to the lower temperatures (thermal stability up t o 380 °C) [37]. The mean heat capacity of the thermal oil at cold storage temperatures is 1.782 kJ kg-1K-1. Self-dischar ge of the storage s is neglected. Figure 5: Scheme of the hot and cold two-tank storage 3.2 Double r ecuperated and recompressed Brayton Cycle with CO 2 as working fluid The PTES is designed to deliver 10 MW of thermal power (3.4 MW electric) . Self-discharging of the storages , the pumps on the storage side, as well as mechanical and electrical losses , are neglected , while losses due to heat transfer were considered . A parameter variation , as well as a pinch -point analysis, were carried out to determine the best cycle performance . 3.2.1 Cycle layout for charging the (hot) storage In Figure 6, the layout of the charging cycle is shown. At a pressure ratio of 3, the system is operating between 16 °C and 513 °C. From point 1 to 2 the CO 2 is compressed to a pressure of 24 MPa , and between 2 and 3 , the thermal energy is used for charging the hot storage, cooling down the fluid. The thermal energy at the lower temperature is recuperated between 3 and 4 . At point 4 , the mass flow is split , to continue with recuperation from 4 to 5 and expansion from 4 to 8. After point 5 , irreversibilities are dissipated to the environment in a heat exchanger between 5 and 6. From 6 to 7 , the second portion of the working fluid is expanded back to 8 MPa in the turbine and then heated from 7 to 8 by cooling down the cold storage . At point 8 the flow is merged with the parallel expanded portio n, and from 8 to 9 and 9 to 1 heated with the recuperated thermal energy from 3 to 4 and 4 to 5 . By splitting the flow in point 4 and merging it in point 8, the amount of heat, transferred to the cold storage can be influenced . Figure 6: Double recuperated sCO 2 Brayton Cycle as a heat pump with dual expansion (charging) 3.2.2 Cycle layout for discharging the (hot) storage The layout for the discharging cycle can be seen in Figure 7. The upper and lower temperature are given through the terminal temperature difference of 8K between the working fluid and the hot storage during charging and discharging. The pressure ratio for this cycle is 3 as well (8 MPa /24 MPa) . From state A to B the CO 2 is expanded , following recuperation B to C and C to D. At D the flow is split into a share which is cooled by discharging the cold storage (D to E) compressed (E to F) and recuperated (F to G) and a part being directly recompressed (D to G) before merg ed again in point G. Second heating with recuperation from G to H and with the theral energy from th e hot storage from H to A. Figure 7: Double recuperated and recompressed CO 2 Brayton Cycle (discharging) 3.2.3 Thermodynamic model Both the charging and discharging cycle are illustrated in Figure 8. The nominal value of the low pressure is 8 MPa and therefore, close to the critical value . With the mentioned pressure ratio of 3, the nominal high pressure is 24 MPa . The efficiency of the discharging cycle of the PTES system dcis 34.9% (1), and the coefficient of performance of the heat pump (charging cycle) ccCOP of the PTES system is 1.11 (2). All CO 2 properties were retr ieved from the REFPROP library [38]. exp, , , , ,AB comp EF comp DG net dc dc hotstor dc HAW W W W QQ−−== ( 1 ) ,, 23 , ,12 exp,67 exp,48out hotstor cc cc net cc compQ QCOPW W W W==−− ( 2 ) netW denotes the cycle work (net cycle work) , expW the expansion work and compW the compression work, while hotstorQ and coldstorQ describe the heat flux between cycle and hot and cold storage, respectively. The indices dc and cc are further describing the discharging or charging cycle , while the numbers (for the charging cycle) and letters (for the discharging cycle) describe specifically between which states the change takes place. The round -trip efficien cy rt of the proposed system is 38.9% and calculated with the net work ratio of charging and discharging cycle (3) or expressed differently with (1) and (2), by multiplying the COP of the heat pump and the efficiency of the heat engine (4). exp, , , , , ,12 exp,67 exp,48AB comp EF comp DG net dc rt net cc compW W W W W W W W−−==−− ( 3 ) rt cc dcCOP= ( 4 ) Table 2 lists the isentropic efficiencies of the turbomachinery , the work and the heat transfer rates within and over the boundaries of the cycle . The heat flux from the hot storage to the cycle during discharging is set by the power of the system systemQ =3.4MW and the efficiency of the discharging cycle (5). Further , the total mass flow rate m is calculated with the enthalpy difference h of the storage (6). dcsystem hotstorQQ= ( 5 ) hotstor HA dcQ m h= ( 6 ) Around a mass flow ratio ,, /dc maincomp dc totalmm of 0.8, the pinch -points within and between the charging and discharging cycle are in the desired range . Together with the enthalpy difference from D to E , the heat flux fro m the cycle to the cold storage fluid is calculated (7) , coldstor dc maincomp DEQ m h=  ( 7 ) The mass flow on the storage side, between the two tanks, is calculated in the same manner but is a little bit lower due to the irreversibilities in the heat exchanger . The effectiveness of the heat exchangers is represented by a mi nimum pinch -point between storage side and cycle. The enthalpy difference on the storage side then results fro m the corresponding temperature s and the heat capacity of the storage material . The minimum amount of stored thermal energy (8) and storage material (9) for the hot and cold storage, respectively, can be found by multiplying the mass flow rate with the storage discharging time . arg stor sto e rdisch Q Q t= ( 8 ) , arg stor stor dc disch em m t= ( 9 ) Five hours were chosen for the duration of charging and discharging as this is a typical wind farm production time [39]. Figure 8: T-s diagram of the charging (red) and discharging (blue) of the proposed PTES with recuperated and recompressed sCO 2 Brayton Cycle 3.2.4 Effect of different syste m parameters on the systems round -trip efficiency To get full use of the positive effects of CO 2 close to its critical pressure, a low pressure of 8 MPa was chosen. In Figure 9 can be seen , that the round -trip efficiency (eta_ rt) is higher with a higher pressure ra tio of the discharging cycle and a lower pressure ratio in the charging cycle . However, pressure ratios lower than 3 in the charging cycle and lower than 4, with a discharging cycle pressure ratio of 4, as well as pressure ratios during discharging higher than 4 , are not possi ble in this PTES system , because minimum temperature differences would get violated . The best combination is a pressure ratio of 3 for charging as well as discharging cycle. Figure 9: Effect of the pressure ratio s of charging and discharging cycle on the systems round -trip efficiency A greater difference between the minimum and maximum temperature results in a higher round - trip efficiency , as to be expected. 10 °C are therefore suggested as the minimum temperature of the ideal PTES (t_low) . The resulting minimum temperature of the cycle fluid for the rejection of thermal energy to ambient is 20 °C. Figure 10 shows that a raise in the cycle s low temperature would cause a drastic drop in the systems round -trip efficiency. The PTES is further proposed with a maximum temperature of 500 °C (t_high) , which is the limit for many materials which could be used for the storage containers, turbomachinery, and storage materials. 200300400500600700800 1,0 1,2 1,4 1,6 1,8 2,0 2,2 2,4 2,6 2,8T [K] s [kJ/(kg*K)]DC EFGH BA 12 3 4 6 795 8 15%20%25%30%35%40%45% 2,0 3,0 4,0 5,0 6,0 7,0ηrt PRccPR_dc = 2 PR_dc = 3 PR_dc = 4PRdc PRdcPRdc Figure 10: Effect of the low temperature on the systems round -trip efficiency (with a high temperature of 500°C) It can be seen in Figure 11 that with temperatures greater 600 °C, nearly 50% efficiency can be achieved. At temperatures as high as this, storage materials like the solar salt mixture 40% NaNO 2 + 7% NaNO 3 + 53% KNO 3 with a work ing range between 142.24 °C (melting point) and 630.97 °C and a heat capacity of J/kgK1439 , as proposed for CSP plants by Fernández et al., could be used [35]. Figure 11: Effect of the high temperature on the systems round -trip efficiency (with a low temperature of 10 °C) The effect of the isentropic efficiencies of the compressors and expanders is also clear . In Figure 12, the change of the round -trip efficiency w ith the isentropic compressor efficiency (eta_comp) is show n. Once with a constant isentropic expander efficiency of 0.9 (eta_exp=0.9) and one time with equal efficiency for all turbomachinery (eta_comp=eta_exp) . The latter is a very simplified approach because generally, the turbine efficiency can be expected to be much higher than the compressor ’s efficiency . It is though certain, that the isentropic efficiency of the turbomachinery has a great impact on the systems round -trip efficiency. 34%35%36%37%38%39%40%41%42% 5 10 15 20 25 30ηrt tlow[ C]t_high = 500°Cthigh 25%30%35%40%45%50% 300 350 400 450 500 550 600 650ηrt thigh[ C]t_low=10°Ctlow Figure 12: Effect of the isentropic efficiencies of compressor and expander on the systems round -trip efficiency The last analysed impact are the temperature differences of the various heat exchangers of the system . A special focus was also on the pinch -point problem, as investigated for the best configuration of the cycle in the next chapter ( 3.2.5 ). Generally, a smaller temperature difference , e.g. higher effectiveness of the heat exchangers , means a higher round -trip efficiency of the system , as to be seen in Figure 13. Besides the case , where the terminal temperature difference of the cold storage heat exchanger and the recuperat or is each 5K (tdT_coldst = 5; tdT_recup = 5 , yellow line), the temperature difference of the heat exchanger to the cold storage is shown on the x -axis. In the mentioned case (tdT_coldst = 5; tdT_recup = 5), it is the temperature difference of the hot storage heat exchanger (tdT_hotst) instead. All variations are displ ayed in this one diagram to allow an easy visual choice of the best combination. The temperature difference compared in the diagram is the terminal temperature difference at the two ends of the heat exchanger and is therefore not transferrable to the heat exchanger effectiveness , which is corresponding to the minimum temperature difference . The minimum temperature difference in the cycle -to-storage heat exchangers is sometimes lower than the temperature difference at the ends of the heat exchanger , due to the severe pinch -point problem of sCO 2 (explained in 2 and visualised for th e proposed cycl e in 3.2.5 ). Figure 13: Effect of the temperature differences at the heat exchanger ends on the systems round -trip efficiency 3.2.5 Heat exchanger analysis The heat exchangers were checked on the pinch -point problem with the following analysis. The hot storage heat exchanger is transferring thermal energy between the CO 2 cycle and the solar salt of the storage. Figure 14 shows the c harging and Figure 15 the dischar ging of the hot 0%5%10%15%20%25%30%35%40%45% 0,70 0,75 0,80 0,85 0,90ηrt ηcompeta_comp = eta_exp eta_exp = 0.9ηcomp = ηexp ηexp = 0.9 32%33%34%35%36%37%38%39%40%41%42% 10 15 20ηrt ΔTcoldstor / ΔThotstor K]tdT_coldst = 15; tdT_recup = 5 tdT_hotdst = 5; tdT_recup = 5 tdT_hotst = 8; tdT_recup = 8 tdT_hotst = 20; tdT_recup = 5 tdT_hotst = 15; tdT_recup = 10 tdT_hotst = 15; tdT_recup = 5ΔTcoldstor = 15 K ΔTrecup = 5 K ΔThotstor = 5 K ΔTrecup = 5 K ΔThotstor = 8 K ΔTrecup = 8 K ΔThotstor = 20 K ΔTrecup = 5 K ΔThotstor = 15 K ΔTrecup = 10 K ΔThotstor = 15 K ΔTrecup = 5 K storage. The terminal temperature difference at the hot and cold end of the heat exchanger is 8K with a pinch -point of 7.5K (during charging mode ). The necessary heat flux i s 10 MJ/s. In total, an amount of 180GJ thermal energy is stored in the solar salt , and 777 tons are required as a minimum to transfer the thermal energy between the two-tank storage and the charging cycle. The molten salt ha s a work ing range between 221.04 °C (melting point) and 588.51 °C [35], with a mean heat capacity of 1518 J/kgK for the working temperature range of the storage [36]. Figure 14: Heat transfer from the (charging) cycle to the hot storage Figure 15: Heat transfer from the hot storage to the (discharging) cycle Between the CO 2 cycle and the thermal oil of the cold storage , a heat exchanger with pinch - point of 7.5K is used (Figs. 16, 17 ). The terminal temperature difference during discharge operation is 18K. The necessary heat flux is about 6.5 MJ/s. The heat capacity of the oil (THERMINOL66) is 1779 J/kgK [37] on average between the heat capacity at the minimum and maximum temperature of the heat transfer . The thermal oil is stable up to a maximum temperature of 380 °C. 117GJ of thermal energy is stored in the thermal oil, also assuming no losses through self -discharging. This amount of heat, transferred between the given temperatures , equals 387 tons of thermal oil . 327347367387407427447467487507 600620640660680700720740760780800 0 2 4 6 8 10 T [ C]T [K] [MJ/s]charging hot storage - cycle charging hot storage - storage2 3 327347367387407427447467487507 600620640660680700720740760780800 0 2 4 6 8 10 T [ C]T [K] [MJ/s]discharging hot storage - cycle discharging hot storage - storageA H Figure 16: Heat transfer from the (charging) cycle to the cold storage Figure 17: Heat trans fer from the cold storage to the (discharging) cycle The heat transfer in the recuperators is shown in Figure 18 to Figure 21. The y have a pinch - point of 8K (in the high -temperature recuperator ) or greater , and the terminal temperature difference is always higher than that, up to 4 3K. Figure 18: Heat transfer in the high-temperature recuperator during charging 020406080100120140160 273293313333353373393413433 0 1 2 3 4 5 6 T [ C]T [K] [MJ/s]charging cold storage - cycle charging cold storage - storage8 7 020406080100120140160 273293313333353373393413433 0 1 2 3 4 5 6 T [ C]T [K] [MJ/s]discharging cold storage - cycle discharging cold storage - storageDE 227247267287307327347367387407 500520540560580600620640660 0 1 2 3 4 5 T [ C]T [K] [MJ/s]reg BC reg GHrecupBC recupGH Figure 19: Heat transfer in the high -temperature recuperator during discharging Figure 20: Heat transfer in the low -temperature recuperator during charging Figure 21: Heat transfer in the low -temperature recupera tor during discharging 127147167187207227247267287 400420440460480500520540560580 0 1 2 3 4 5 6 7 8 T [ C]T [K] [MJ/s]reg CD reg GFrecupCD recupGF 77127177227277327377 350400450500550600650 0 2 4 6 8 10 12 14 T [ C]T [K] [MJ/s]reg 34 reg 19recup34 recup19 100110120130140150160170 373383393403413423433443453 0,0 0,2 0,4 0,6 0,8 1,0 T [ C]T [K] [MJ/s]reg 45 reg 89recup45 recup89 4 Results and discussion Table 2 summarises the results of the chosen thermodynamic model. The efficiency of the discharging cycle of the PTES system dc is 34.9%, which is a little bit lower than the maximum efficiency , which can be theoretically reached without integration in a PTES system. Such a standard supercritical CO 2 Brayton cycle (without integration in a PTES system) can reach efficiencies of about 20.5%. If it is recuperated, 42.6% are possible. If it is recompressed, with double recuperation, it can be up to 45.0% [22]. The lower efficiency of the cycle while being integrated into a PTES system as its discharging cycle could be explained with t he boundary conditions applying to the cycle through the attached storages, and due to the unavoidable rejection of thermal energy to the environment , as well as simply through the desired optimum between high COP of the heat pump and high efficiency of th e power cycle . The heat dissipation to the environment is necessary because of the inevitable irreversibilities (entropy generation) during charging and discharging. The coefficient of performance of the heat pump (charging cycle) ccCOP is 1.1 1, reaching a round -trip efficiency rt of 38.9% for the proposed system. Table 2: Thermal model key inputs and results for the proposed PTES Temperatures and pressures Tlow 16 [°C] Thigh 513 [°C] pnom,low 8 [MPa] Pressure ratio 3 [-] Mass flow c harging cycle Mass flow disc harging cycle ṁtotal,cc 56.9 [kg/s] ṁtotal,dc 56.9 [kg/s] Ratio ṁ 0.8 [-] Ratio ṁ 0.4 [-] Efficiency compressor and turbine ηcomp 0.9 [-] ηexp 0.9 [-] Terminal temperature difference Pinch Point Cold storage 18 [K] 7.5 [K] Hot storage 8 [K] 7.4 [K] Recuperation 8 [K] 8 [K] Cycle efficiency COP cc 1.10 [-] ηdc 0.342 [-] ηoverall 0.378 [-] Charging cycle Discharging cycle Wcomp,12 9294 [kW] Wexp,AB -7249 [kW] Wexp,48 -272 [kW] Wcomp,EF 2530 [kW] Wexp,67 -33 [kW] Wexp,DG 1225 [kW] Qin,coldstor,78 6506 [kW] Qout_coldstor,DE -6506 [kW] Qout,hotstor,23 -10000 [kW] Qin,hotstor,HA 10000 [kW] Qamb,56 -5495 [kW] Qrecup,BC -5664 [kW] Qrecup,34 -14987 [kW] Qrecup,GH 5664 [kW] Qrecup,91 14987 [kW] Qrecup,CD -8876 [kW] Qrecup,45 -1139 [kW] Qrecup,FG 8876 [kW] Qrecup,89 1139 [kW] Wnet,cc 8989 [kW] Wnet,dc -3494 [kW] Pressure losses due to heat exchange were calculated for each heat exchanger , assuming the use of shell and tube heat exchangers. The power consu mption of the pumps transporting the liquid through the storages, as well as the power drain of the motor and generator , are neglected. However, if we assume 98%generator= and 98%motor= , while the hot storage pump reduces the net work by 10.6hotstorPumpW kW = and the cold storage pump by 15.9coldstorPumpW kW = , the round -trip efficiency reduces to about 3 7.6% as by formula ( 10). ( ) ( ), , ,net dc storPump gen rt reduced net cc storPump motWW WW  − = − ( 10 ) Formula (10) can also be written as in (11), with , , ,net dc reduced net dc hotstorPumpW W W =− and , , ,net cc reduced net cc coldstorPumpW W W =− . ,, ,, , ,, ,,net dc reduced gen net dc reduced rt reduced gen mot net cc reduced net cc reduced motW W W W   = =   ( 11 ) This allows us to express the reduced round -trip efficiency with the reduced COP of the charging cycle and the reduced efficiency of the discharging cycle (12). , , ,rt reduced cc reduced dc reduced gen mot COP    =    ( 12 ). The parameters of the above -proposed cycle were chosen according to the parameter variation presented in Fehler! Verweisquelle konnte nicht gefunden werden. . It is apparent that maximising the pressure ratio and the difference betwe en the minimum and maximum temperature is improving not only the efficiency of the stand -alone cycle but also of the overall system and that although the COP of the heat pump is decreasing through these measur es. If materials and cost wouldn ’t limit the upper temperature, th is configuration could reach more than 50% round -trip efficiency at already 800 °C without any further changes to the ori ginal system. The lower temperature of the cycle is limited by the minimum temperature for heat exchange with the environment. Higher turbine efficiency is , of course , resulting in a higher round -trip efficiency as well, but limited by available technology. For today ’s available gas sCO 2 turbines , 90% efficiency might be possible, while for the compressor this theoretical value is most likely too high . If the compressor didn’t reach such high efficiency, the round -trip efficiency would reduce drastically , and a realisat ion would most likely not be feasible , especially considering the complexity of the cycle. The heat exchanger effectiveness is in a more realistic rang e, and it is also clear that a higher efficiency (lower temperature difference) leads to better overall results. Because the same pressure ratio was chosen for the charging and the discharging cycle , which is only possible through the recompression, the temperatures for storing and r ecuperating thermal energy are relatively fixed and the possibilities for improving the cycle efficiency limited. This cycle configuration was , howe ver, still chosen and analysed because it could allow the use of reciprocating devices and all heat exchange rs for both, the heat pump and the power cycle. For a similar cycle, with slightly different pressure ratios , recompression would not be necessary , and a similar or higher round -trip efficiency could be reached. 5 Conclusion This paper investigated the feasibility of a Carnot -battery with a recuperated and recompressed supercritical CO2 Brayton cycle . The pressure ratio is 3 with a low nominal pressure of 8 MPa . The system operates between the temperatures 16 °C and 513 °C and provides a round -trip efficiency of 38.9% with a maximum electric power output of 3.5 MW. The Carnot -battery could be attached to a small wind park (two to four wind turbines) or, for example , in a domestic area with a high rate of installed solar power generation. Both could charge the storage with a power of 9 MW. CO 2 in its supercritical state can be used in a Brayton cycle as part of an energy storage system with hot and cold storage . The usual measures to enhance the CO 2 cycle performance are much harder to realise for a Carnot -battery , due to its complexity . The upside of a recuperated s CO 2 Brayton cycle, the small turbomachinery , are being reduced by the space needed for the heat exchangers (heat exchanger areas around 70 to 100 m²) . Therefore other cycle layouts , as well as other working mediums , should definitely be further investigated. Some thermal energy needs to be released to ambient for energy balance within the system . This thermal energy could be used in district heating or for an attached ORC as it is still at a temperature of about 130 °C. The modelled system provides a round -trip efficiency of 38.9%. For such a comple x system, with recompression and double recuperation, th is round -trip efficiency is comparably low . Simple r configurations of sCO 2 Brayton cycles might reach same or higher efficiencies, as also the analysis of McTigue et al. in 2019 suggests. They proposed a simple sCO 2 Brayton cycle, which could reach up to 60.4% with a low-temperature cycle (200 °C) and 78.4% with a high - temperature cycle (560 °C). They ’re mentioning that recuperation would be feasible due to the high-temperature difference between compression and expansion but didn’t analyse it . This paper , however, shows that recuperation is difficult to implement and might actually not improve the round -trip efficiency of a s CO 2 Brayton PTES as expec ted, due to the limitations of the integration in the storage system . Nomenclature Abbreviations CHEST Compressed Heat Energy Storage CO 2 Carbon Dioxide COP Coefficient Of Performance ES Energy storages ETES Electro -Thermal Energy Storage ORC Organic Rankine Cycle P2H2P Power -to-Heat -to-Power PCM Phase Change Material PHES Pumped Heat Energy Storage PTES Pumped Thermal Energy Storage TES Thermal Energy Storages Symbols ℎ Specific enthalpy in kJ/kg 𝑚̇ Mass flow in kg/s PR Pressure ratio 𝑄 Heat in J 𝑄̇ Heat flow rate in J/s=W s Specific Entropy in J/(kg*K) 𝑡 Time ( e. g. discharging time 𝑡𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒) in s 𝑇 Temperature in °C 𝑊 Work rate (power) in W 𝜂 Isentropic efficiency Subscripts amb Ambient cc Charging cycle coldstor Cold storage comp Compression dc Discharging cycle exp Expansion gen generator hotst or Hot storage in “in”, as added to the cycle mot motor out “out” , as extracted from the cycle recup Recuperation / recuperated rt Round -trip stor Storage 1,2,3,… Cycle state points during charging A,B,C ,… Cycle state points during discharging Acknowledg ements This work was supported by the Grant Agency of the Czech Technical University in Prague, grant No. SGS20/116/OHK2/2T/12.