Design Considerations for the Liquid Air Energy Storage System Integrated to Nuclear Steam Cycle

: A nuclear power plant is one of the power sources that shares a large portion of base-load. However, as the proportion of renewable energy increases, nuclear power plants will be required to generate power more ﬂexibly due to the intermittency of the renewable energy sources. This paper reviews a layout thermally integrating the liquid air energy storage system with a nuclear power plant. To evaluate the performance realistically while optimizing the layout, operating nuclear power plant conditions are used. After revisiting the analysis, the optimized performance of the proposed system is predicted to achieve 59.96% of the round-trip efﬁciency. However, it is further shown that external environmental conditions could deteriorate the performance. For the design of liquid air energy storage-nuclear power plant integrated systems, both the steam properties of the linked plants and external factors should be considered.


Introduction
The concerns around global warming and environmental issues are growing, and thus the development of eco-friendly renewable energies plays an important role as a solution [1][2][3]. Unfortunately, renewable energy sources such as solar and wind, unlike conventional power generation systems, cannot produce electricity consistently and follow the demand. It means that renewable power sources cannot generate extra energy or reduce output power due to sudden changes in demand [4]. They should, therefore, have an energy storage system that can store a large amount of energy and discharge when needed. To solve this problem of reliability, research has been conducted to integrate renewable sources with the energy storage system (ESS). The integrated ESS supports renewable power systems by playing the function of time shifting or moving electric load from one time to another. ESS can also smooth out the sharp output from renewable power sources that could damage the electricity grid [5][6][7].
Furthermore, to optimize renewable power sources, attention should be focused on electricity generation as well. As renewable power sources such as wind and solar have a high dependency on time and location, they cannot be controlled artificially. To maximize the efficiency of renewable energy and to reduce loss from the use of renewable energy, balancing the existing electricity supply and renewable energy supply is essential. According to research from the National Renewable Energy Lab (NREL), the production of electricity from solar power can affect the supply of electricity from conventional sources. According to the data provided from the California grid [8], the increase of solar power leads to the decrease of remaining net load during the daytime and increase at a rapid rate after the sun sets. Known as the duck curve phenomenon, this effect occurs because the load needs to balance out the overgeneration for the grid stability [9]. As the renewable sources, mainly solar and wind, take a greater portion in the grid, the energy sources that have been generated at a stable base load are required to change their load during the day. gested design poses several technical challenges, as marked in Figure 1. First, the discharge mode involves 100% steam bypass from the nuclear secondary side which poses integrity issues to the nuclear power plant's steam cycle. Second, excessively ideal design conditions were used for the performance prediction, including zero pressure drop and low pinch temperatures across heat exchangers [16]. Such assumptions are not suitable for a technically feasible design, especially when nuclear retrofitting requires more realistic and safety-based considerations.

General Code
The first goal of this research is to reproduce the model proposed in the reference [15] with the KAIST Closed Cycle Design code (KAIST-CCD). This work gives an insight to how the LAES system performs and how each design parameter will influence the round-trip efficiency. After the model is verified to produce similar results to the previous study, the model can be modified to optimize the operating conditions of the LAES system with APR1400 under more realistic conditions.
To test the LAES system under realistic conditions, three design parameters were modified from the reference [15].
(1) Pinch temperature of heat exchanger: The pinch temperature for heat exchangers in the reference [15] is 2K pinch. However, when designing a heat exchanger, typically 5K or larger values are assumed for the pinch due to economic reason and increased pressure drop for excessively low pinch design condition. Therefore, in this paper, the pinch temperature in the heat exchangers is changed to 5K. (2) Pressure drop: Pressure drop in components and piping always occurs. Due to this pressure drop, the pressure of fluid decreases while flowing through the system. This generally influences the overall performance of the system. (3) Ambient temperature: In the realistic system, the ambient temperature is always changing. As an LAES system is an open system that takes in air from the atmosphere, the temperature of ambient air affects the performance of the system.
The KAIST-CCD is a MATLAB based code used to calculate and optimize thermodynamic processes. It can be separated into two main subroutines: the layout section and the design parameter section. The layout section determines the process layout of a thermal system, and it gives the information on how components are connected to each other. In the design parameter section, it provides the design conditions for the layout code: the pressure and temperature for ambient air, the efficiency, and operating conditions for each component. The properties of fluid are obtained from REFPROP developed by NIST [17].
The layout adopted for code modelling is depicted in Figure 1. It is separated into two parts: before the liquid air tank and after the liquid air tank. The layout before the liquid air tank is the storage part of the system (i.e., charging mode) and the layout after the liquid air tank is the system for discharge operation. The code calculates the charging system first, until the result converges in the charging system and then starts to calculate the discharging system with the results from the charging system. The algorithm of the code is shown in Figure 2. The following describes the thermodynamic for constructing the model of the proposed system. The calculation in the components follows the fundamental laws of general thermodynamics. However, certain components follow the calculations below for better accuracy. The specific parameters for calculation are stated in Tables 1 and 2.

Compressor (Isothermal)
In Figure 1, for flow numbers 2 to 3 and 4 to 5, two isothermal compressors were used for the system in the reference [15]. In paper [15], the exact method of calculation for an isothermal compressor was not presented. Therefore, the analysis methodology in this paper follows the reference [18], which presents how to evaluate an isothermal compressor. In the isothermal compressor model, inlet temperature and pressure, target pressure, and the compression process number are required for the performance evaluation. The compression process number determines the numerical discretization of a continuous process to evaluate work and cooling in the isothermal compressor. As shown in Figure 3, in order to describe isothermal compression, compression and cooling are repeated several times numerically. In this paper, the step number (i.e., numerical discretization) of the isothermal compressors is set to 500, a large enough number to reproduce the outcome of reference [15]. The final compression work required, which is shown in Equation (1), is calculated by summing up the discretized work provided through the whole process.

Compressor (Isothermal)
In Figure 1, for flow numbers 2 to 3 and 4 to 5, two isothermal compressors were used for the system in the reference [15]. In paper [15], the exact method of calculation for an isothermal compressor was not presented. Therefore, the analysis methodology in this paper follows the reference [18], which presents how to evaluate an isothermal compressor. In the isothermal compressor model, inlet temperature and pressure, target pressure, and the compression process number are required for the performance evaluation. The compression process number determines the numerical discretization of a continuous process to evaluate work and cooling in the isothermal compressor. As shown in Figure  3, in order to describe isothermal compression, compression and cooling are repeated several times numerically. In this paper, the step number (i.e., numerical discretization) of the isothermal compressors is set to 500, a large enough number to reproduce the outcome of reference [15]. The final compression work required, which is shown in Equation (1), is calculated by summing up the discretized work provided through the whole process.
= step number

Heat Exchanger
The methodology is applied for evaluating all heat exchangers except heat exchanger 4 in Figure 1. The heat exchanger model requires the following information: the inlet temperature and pressure of the hot and cold side, the pinch temperature, and the pressure drop condition.
The inlet temperature and pressure of the hot and cold side, pinch temperature, and pressure drop condition are required for the heat exchanger calculation. As heat exchangers include 3-way heat exchangers, the effectiveness model is used for the calculation: . T-s diagram of the isothermal compression adapted from [18].

Heat Exchanger
The methodology is applied for evaluating all heat exchangers except heat exchanger 4 in Figure 1. The heat exchanger model requires the following information: the inlet temperature and pressure of the hot and cold side, the pinch temperature, and the pressure drop condition.
The inlet temperature and pressure of the hot and cold side, pinch temperature, and pressure drop condition are required for the heat exchanger calculation. As heat exchangers include 3-way heat exchangers, the effectiveness model is used for the calculation: Effectiveness is assumed to obtain h hot,out . If the calculated pinch is lower than the prescribed condition, then the effectiveness value is decreased until the calculated pinch exceeds the prescribed pinch conditions. The process is shown in Figure 4.
Effectiveness is assumed to obtain ℎ , . If the calculated pinch is lower than the prescribed condition, then the effectiveness value is decreased until the calculated pinch exceeds the prescribed pinch conditions. The process is shown in Figure 4.

Heat Exchanger (Air to Steam)
As shown in Figure 1, heat exchanger 4 is designed to exchange heat between air and steam flow channels. This model requires information on the mass flow rate of air, the inlet temperature and pressure of air side and steam side, the outlet temperature of steam side, and pinch and pressure drop conditions. As the temperature of the steam side is fixed to integrate with the steam cycle of the APR1400, the pinch condition should be satisfied by changing the air side temperature. Figure 5 shows that the initial calculation of air temperature profile may result in an overlap with the steam temperature profile. To avoid the overlap, the cold side outlet temperature is corrected in the first iteration until a result satisfying the pinch condition is obtained. Finally, the mass flow rate of steam side is calculated as shown in Equation (4):

Heat Exchanger (Air to Steam)
As shown in Figure 1, heat exchanger 4 is designed to exchange heat between air and steam flow channels. This model requires information on the mass flow rate of air, the inlet temperature and pressure of air side and steam side, the outlet temperature of steam side, and pinch and pressure drop conditions. As the temperature of the steam side is fixed to integrate with the steam cycle of the APR1400, the pinch condition should be satisfied by changing the air side temperature. Figure 5 shows that the initial calculation of air temperature profile may result in an overlap with the steam temperature profile. To avoid the overlap, the cold side outlet temperature is corrected in the first iteration until a result satisfying the pinch condition is obtained. Finally, the mass flow rate of steam side is calculated as shown in Equation (4) Effectiveness is assumed to obtain ℎ , . If the calculated pinch is lower than the prescribed condition, then the effectiveness value is decreased until the calculated pinch exceeds the prescribed pinch conditions. The process is shown in Figure 4.

Heat Exchanger (Air to Steam)
As shown in Figure 1, heat exchanger 4 is designed to exchange heat between air and steam flow channels. This model requires information on the mass flow rate of air, the inlet temperature and pressure of air side and steam side, the outlet temperature of steam side, and pinch and pressure drop conditions. As the temperature of the steam side is fixed to integrate with the steam cycle of the APR1400, the pinch condition should be satisfied by changing the air side temperature. Figure 5 shows that the initial calculation of air temperature profile may result in an overlap with the steam temperature profile. To avoid the overlap, the cold side outlet temperature is corrected in the first iteration until a result satisfying the pinch condition is obtained. Finally, the mass flow rate of steam side is calculated as shown in Equation (4):

Exergy Calculation
From the input code, the temperature and pressure of ambient conditions are used to calculate ambient enthalpy and ambient entropy for exergy calculations. The exergy for each point is calculated as follows [19]: The exergy destruction calculation of the components is performed next:

Round-Trip Efficiency
Round-trip efficiency is the most important parameter to evaluate the performance of energy storage systems. It is the ratio of energy released by the system and energy consumed by the system. In the case of LAES integrated NPP, the power from NPP is reduced during the energy release. This is because the system utilizes power from the NPP through steam bypass while operating in discharge mode. Moreover, the system is designed to have storage mode eight times longer than release mode. This is also considered in the calculation of round-trip efficiency.
The total power from release mode in LAES system is a sum of power from air turbines and power consumption of cryogenic pump. This process is shown in the Figure 1, flow number 15 to 32.
The power loss from NPP is calculated from the efficiency of NPP, steam flow rate, and enthalpy from inlet and outlet of NPP steam side. This is number 33 and 34 in Figure 1.
The specific values of efficiency and boundary conditions for NPP are in Tables 1 and 2, respectively.
The power consumption from storage mode in LAES system is sum of power consumption from compressors and power output from cryogenic turbine. This process is described in the Figure 1, flow number 1 to 14.
The round-trip efficiency of LAES system is calculated by the total power from release mode, power loss from NPP, and power consumption from storage mode following Equation (9). The operation time for each mode is shown in Tables 1 and 2.

Comparison of Result
When all the parameters are assumed to be the same as the reference [15], the results from the reference and the results obtained from this study are compared first to verify KAIST-CCD for investigating this problem. There are differences between steam parameters obtained in this study compared to the values reported in the reference [15].
The most significant difference is the mass flow change from point 9 to 10. This is due to the difference in yield for producing liquid air. The reference [15] shows 84% liquid air yield; therefore, it has less amount of air flowing in stations 9 and 10. However, the current study shows 83% liquid air yield, and this difference increases the amount of gaseous air in the liquid air tank, and the mass flow rate in station 9 is also increased as a result. Moreover, this effect induces the temperature difference in stations 3 to 5 as it is connected with stations 9 and 10 via a heat exchanger. This difference in liquid air yield is due to the difference of temperature in the flow number 7 (the inlet of liquid air tank), which seems to be rooted in two reasons. The first cause is the difference in the thermal properties database. The thermal properties used in this study are from REFROP 10.0 while the reference [15] used the older version, REFROP 8.0. As shown in Table 3, station numbers 7 and 15, the reference shows the temperature of vapor air to be 81K (flow number 7), and the temperature of liquid air as 80K (flow number 15). In the current study, the temperatures of vapor air and liquid air are both 79K due to the difference in the fluid thermal properties database. The second cause is the difference in how isothermal compressor is modeled between the reference [15] and the current study. Since not enough detail is provided in reference [15] for modeling the isothermal compressor, this study adopted the approach presented in reference [18] for the isothermal compressor model. As a result, the outlet temperature of the isothermal compressor obtained in this study is different with the reference [15]. Table 3. The main steam parameter for reference data from [15] (left) and KAIST-CCD (right).

Pinch Effect
As the increasing pinch is assumed to utilize a less effective heat exchanger, it is natural to expect that the liquid air yield and the round-trip efficiency of the system will be reduced compared to the previous 2K pinch assumption in the reference. The temperature of the coolant follows Table 5. The outlet temperature of methanol from the heat exchanger 6 changes with the assumed pinch temperatures. For instance, the outlet temperature of methanol (i.e., cold side) from the heat exchanger 6 is set to 283K since the hot side (i.e., air side) inlet is 288K while the pinch temperature is assumed to be 5K. As expected, the round-trip effectiveness was lower for 5K pinch compared to 2K pinch. As shown in Table 6, In the storage mode, the case of 2K pinch consumed less power than the case of 5K pinch. In the release mode, more energy was produced in the 2K pinch case than in the 5K pinch case. It led to a similar trend for the difference in power output. As shown in Table 7, the inlet temperatures for air turbine in 5K pinch case and for 2K pinch case are 555K and 558K, respectively. These differences resulted in a round-trip efficiency difference of about 1%.

Realistic Nuclear Power Plant Model (APR1400)
Considering the realistic integration with NPP and LAES system, the steam from NPP cannot be bypassed 100% to the LAES discharging cycle. Operating between full power and complete shutdown of the secondary side may cause substantial thermal stress to the turbine components, and this operation method requires more time for hot startup [20]. Therefore, this paper suggests a more realistic integration to the reference nuclear plant, APR1400. The portion of steam bypass is modified to 20% of the total mass flow rate in the secondary side to avoid the aforementioned operational issues. Another modification is the steam condition of the flow sent to the steam-air heat exchanger (heat exchanger 4), as this work assumes the superheated steam to be split from the inlet of the low-pressure turbine, which the temperature and pressure are shown in Table 2. Under these conditions, the temperature profile inside the heat exchanger 4 creates a unique design issue due to the condensation of steam occurring at the steam side. The NPP side steam changes phase from a superheated condition to a subcooled condition, as shown in Figure 6. The heat exchange between air and steam in LAES in the discharging cycle leads to a significant difference between the air and steam temperature profiles. Hence, the heat exchanger has the highest exergy destruction in release mode, as shown in Figure 7. However, the temperature profile has the advantage of maximizing latent heat from the steam side. Comparing point 33 in Tables 6 and 8, the APR1400 condition allows the LAES system to operate with a relatively low flow rate. In the condition of APR1400, since the entry temperature of steam is low, the entry temperature of the air turbine is also low. As shown in Table 8, the turbine inlet temperature of the LAES discharging cycle is 471K, which is about 87K lower than the turbine inlet temperature from Table 7. The turbine inlet temperature difference resulted in relatively low power output, as shown in Table 9. However, in actual nuclear power plant conditions, it is no longer possible to link LAES with high temperature, so the practical limit of round-trip efficiency is expected to be about 60% at the maximum.  Rejection  29  723  101  288  Methanol  30  723  101  217  Methanol  31  1337  101  214  Propane  32  1337  101  93  Propane  33  270  1458  500  Water  34  270  1346 412 Water    28  Rejection  29  723  101  288  Methanol  30  723  101  217  Methanol  31  1337  101  214  Propane  32  1337  101  93  Propane  33  270  1458  500  Water  34  270  1346 412 Water

Pressure Drop and Ambient Temperature Effects
In any type of hydrodynamic component and pipe, the pressure of fluid is decreased by frictional pressure drop while traveling in the components and pipelines. In this study, the pressure drop is modeled as a fractional pressure drop of the system pressure while ignoring the shape and flow path of air going through the system. The pressure drop changes the properties of fluid; therefore, the output and consumption power of each component will change. The increase of pressure drop lowers the round-trip efficiency, shown in the top of Figure 8. This is because the liquid air yield is substantially reduced in the separator, which leads to a decrease in overall flow rate of the LAES system during release mode as shown in the bottom of Figure 8. Consequently, the reduced mass flow rate of air in the heat exchanger 4 results in the decreased steam mass flow rate from the steam cycle, and thus, the delivered thermal power is reduced to have an increasing effect on the round-trip efficiency. However, net output power from the air turbines reduces due to lowered expansion ratio, and overall, the round-trip efficiency decreases. It is thus necessary to minimize the number of components that make up the system in order to prevent round-trip efficiency degradation caused by pressure drop in the actual system.
The sensitivity of the overall system to the change in ambient temperature is also studied. As the LAES system is an open system that inhales air from the outside of the system to operate, there is a significant impact on the operation with respect to the ambient condition. The ambient temperature was set to 288K in the above calculations. However, the ambient temperature can increase or decrease due to seasonal change or the weather conditions in the installed location. Since it is trivial that a decrease of the ambient temperature will be helpful to increase the round-trip efficiency, as cold air will consume less energy to be liquefied, only the increase of ambient temperature case is presented in this study.
The rise in ambient temperature decreases the round-trip efficiency of the system because of the increased energy consumption in storage mode. Due to the nature of the LAES using the air as an energy storage medium, the higher the temperature of the ambient air, the more energy is consumed to cool the air, as shown in the top of Figure 9. The increase in ambient air temperature also increases the temperature of the No. 5 hot side inlet of heat exchanger 6. This increases the temperatures of outlet No. 6 and No. 9 from heat exchanger 6, which leads to a decrease in the liquid air yield. Moreover, the reduction of the liquid air yield reduces the mass flow rate in the system during the release mode and consequently reduces the generated power of the release mode. This trend is shown in the bottom of Figure 9. The reduction of power output leads to a decrease in round-trip efficiency. The round-trip efficiency is further deteriorated by the net power consumption increase during the storage mode, which is shown in the top of Figure 9. This consequently reduces the round-trip efficiency as the ambient temperature increases. Appl. Sci. 2021, 11, x FOR PEER REVIEW 14 of 18