Process design, integration, and optimization of a novel compressed air energy storage for the coproduction of electricity, cooling, and water

The use of fluctuating renewable energy over a certain threshold may lead to an unmanageable mismatch be-tween the electricity generation and demand profiles threatening the grid ’ s stability. In this study, an innovative complex energy storage/conversion system is proposed for the cogeneration of electricity, cooling, and water by integrating the liquefied natural gas (LNG) regasification process, an organic Rankine cycle, a compressed air energy storage (CAES) system


Introduction
Renewable energy has been the fastest-growing energy source in many countries around the world since the cost of renewable energy has plummeted in the last decade [1,2].Even though the renewable energy share has been increasing sharply, natural gas is still an irreplaceable energy source due to its lower CO 2 emissions, well-developed infrastructure, and being widely used in both the energy and chemical industries [3].Currently and in the foreseeable future, renewable energy and natural gas are the most significant energy resources for power generation.
Although renewable energy generates electricity in an environmentally-friendly manner, the variable and uncertain characteristics lead to new challenges, such as grid instability and the mismatch between demand and supply [4,5].To overcome these problems, energy storage technologies, which can be categorized as short-term (several minutes), mid-term (several hours), and long-term (several days or months) energy storage systems, are considered as promising solutions [6].However, for the grid-scale application, only long-term energy systems are effective.Therefore, long-term energy storage systems are indispensable to increase the penetration of renewable energy to an unprecedented high level and guarantee grid stability.
Among long-term storage systems, compressed air energy storage (CAES) plants are advantageous due to their high efficiency and flexibility with low cost and emissions [7].The energy efficiency of CAES plants ranges from 40 % to 70 %.The present CAES plants achieve energy efficiencies of 54 % (McIntosh) and 42 % (Huntorf) [8].In contrast, more advanced CAES units like adiabatic ones yield energy efficiencies of about 60 % (Goodrich installations in Canada) and 67 % (Feicheng installations in China) [9].Besides, many researchers have investigated the CAES performance from different aspects.Chen et al. [10] studied the feasibility of a CAES system integrated with solar and wind energy and enumerated 13 suitable sites in China.Razmi et al. [11] proposed a CAES system for power generation and peak modification.They added an absorption-compression refrigeration cycle to the CAES system and enhanced the round-trip efficiency (RTE) by 13.15 %.Alirahmi et al. [12] integrated a CAES system with a desalination unit, which can cogenerate 226,782 m 3 of freshwater and 27,551 MWh of electricity per year in consumption periods.Yao et al. [13] investigated a small-scale CAES and concluded that turbine temperature and pressure had the most significant effect on system performance based on sensitivity analysis.
However, the compression heat and heat in the exhaust gas from the combustion chamber (CC) are usually wasted in CAES systems.Thus, waste heat recovery (WHR) can improve the systems' efficiency significantly.Bashiri Mousavi et al. [14] investigated a CAES system with thermal energy storage.They concluded that RTE and exergy round-trip efficiency (ERTE) can reach 61.5 % and 68.2 % respectively with waste heat recovery.Other than thermal energy storage, organic Rankine cycle (ORC) is another effective technology to utilize compression heat.ORC is a mature technology for WHR due to its mild operational conditions, simple arrangement, low repair, and maintenance cost, etc. [15].To further increase the ORC efficiency, a low-temperature heat sink such as the regasification of liquified natural gas (LNG) was proposed to be integrated with the ORC [16].In addition, LNG is regasified simultaneously into natural gas, which can be used as fuel for the CAES system [17].The LNG cold energy can be utilized for air separation [18], CO 2 absorption [19], power generation [20], energy storage [21], and desalination [22], where power generation provides a high economic profit.Hence, power generation has become a more popular way to utilize LNG cold energy.Zhang et al. [23] analyzed a hybrid system integrating three ORCs and the LNG regasification process.Their results revealed that the integrated LNG-ORC system outperforms the separate LNG and ORC systems in terms of both power output and system investment.Yu et al. [24] investigated ORCs that operated below the ambient temperature with 22 working fluids to utilize the cold energy of LNG.In this study, R125, R143a, R290, and R1270 were identified as the most energy-efficient working fluids.Broniszewski et al. [25] performed a techno-economic assessment of an ORC system and concluded that the standalone ORC system is not profitable and integration with the waste heat to form the cogeneration system is necessary to justify a configuration with an ORC system.Therefore, ORC is usually coupled with other processes in real applications.
Other than energy, water is another critical resource for our society.Since seawater is abundant on our planet, seawater desalination is the most common approach to deal with water crises and scarcity.Desalination technologies can be categorized into thermal, chemical, and membrane-based technologies.The chemical method is not suitable for seawater desalination due to the significant solid substances dissolved in seawater.Among the most popular membrane types, reverse osmosis (RO) is highly efficient and 60 % of all commercial desalination units fall into this category [12].However, the investment cost and energy consumption escalate at higher temperatures and saltiness.Due to these challenges, many Persian Gulf states exploit thermal desalination methods [26].
The thermal method includes multistage flash distillation (MSF), multi-effect distillation (MED), and MED with thermal vapor compression (MED-TVC).Among these methods, the MED-TVC unit is competitive, especially when waste heat is available.MED-TVC has the merits of lower maintenance and investment costs, simpler configuration, less corrosion, and lower energy consumption.
Energy consumption is the primary performance indicator for thermal desalination units.Heat recovery steam generators (HRSGs) are often integrated with gas or steam turbines of power plants to harvest the waste heat.Under this context, the extracted vapor from steam turbines or the exhaust of GTs is fed to the HRSG to recover the waste heat.In recent years numerous researchers have studied the performance of the MED-TVC unit and its integration with renewable energy.
A steady-state mathematical model of a MED-TVC system with a parallel-intersecting configuration was presented by Al-Mutaz and Wazee [27].This model was developed according to energy and mass balance and heat transfer.Likewise, to evaluate MED-TVC systems from a techno-economic perspective, Elsayed et al. [28] applied three different approaches to estimate the mean total cost of water under four different feed conditions.They also examined how the number of effects influenced the system's performance.Energy and water are intricately connected, and the interdependency of energy and water is going to intensify in the coming years with population growth and climate change.This interdependency is reflected in the sustainable development goals (SDGs), which include the goal of ensuring access to affordable, reliable, and sustainable energy and water for all.In addition, from a process systems engineering perspective, industrial systems considering energy and water simultaneously will improve the efficiency and profitability of the system and minimize the environmental impacts at the same time.Based on the literature on CAES, ORC, LNG cold energy utilization, and multi-effect distillation, these processes can be tightly integrated into one system.The integrated energy system (IES) consists of a network of energy generation, distribution, and storage that utilizes both traditional and renewable energy resources.The integration of CAES with an ORC for a 5 MW unit was proposed by Rahbari et al. [29].In another study, the CAES integrated with ORC was designed by Mousavi et al. [30] which utilizes solar and geothermal energy as green thermal sources.
This study proposes a novel IES termed LNG-ORC-CAES-MED for the simultaneous production of energy and water, which is driven by both renewable energy sources and natural gas.The proposed IES has significant potential for implementation at LNG receiving terminals, where there is an abundant supply of LNG, seawater, and readily available renewable energy sources like offshore wind farms and solar farms.Additionally, some countries with ports located in high-temperature regions face the need for substantial freshwater and cooling resources; for instance, countries like Japan [31], Spain [32], and those situated along the Persian Gulf, such as Iran [33] and Kuwait [34].
The proposed system's originality lies in its four subsystems being tightly coupled, enabling more efficient resource usage.In addition, the proposed system can not only produce energy and water simultaneously at much lower cost, it can also overcome the intermittency of wind and solar energy.Further, the proposed system contributes to a more sustainable environment by reducing the need for fossil fuels.It is also more efficient than traditional energy systems that produce only one product.However, the evaluation, integration, and optimization of this system is challenging since several subsystems are involved and interconnected and they do not operate at the same time.The evaluation of IESs is not trivial since multiple products (e.g.electricity, cooling, fresh water, and regasified natural gas) are produced in this system and different objectives usually contradict each other.To address these challenges, the present study presents energy, exergy, exergoeconomic, and environmental impacts (4E) analysis of this IES.Based on the model developed in Engineering Equation Solver (EES), a neural network model is developed for the optimization of this tightly coupled IES.On the basis of the developed neural network model, a multi-objective optimization (MOO) method called the Grasshopper algorithm, which has not yet been applied to any IES, is adopted to identify the optimal operating conditions of the IES.Following is a summary of the main contributions of this study: • Introducing a novel environmentally friendly design based on LNG-ORC-CAES-MED with the aim of cooling and potable water production, and peak shaving.• Using 4E analyses to provide a comprehensive evaluation of the performance of the IES in order to improve its efficiency and sustainability.• Analysis of the sensitivity of decision variables to gain a deeper understanding of the optimization process.• Analyzing and comparing two optimization algorithms to provide a trade-off between the objective functions.• Proposing the Grassmann and Chord diagrams for optimal conditions, to show the exergy flow in the system and the contribution of every sub-system to the total cost rate.

System description
Fig. 1 illustrates the process flow diagram of the proposed IES, which comprises four subsystems, namely an LNG gasification process, an ORC power generation unit, a CAES system, and a MED-TVC desalination unit.Since one of the functions of the IES is to store, balance, and stabilize renewable energy at grid scale, the four subsystems operate at different times of a day.Based on the operating time, the IES are divided into three sections, namely full time, off-peak hour and peak hour processes, as shown in Fig. 1.

Off-peak hour process
During off-peak hours, the surplus renewable energy could be stored by charging the CAES system.During the charging process, the air is compressed to higher pressure through multi-stage compression.The compression heat can be recovered and stored as the heat source of the ORC.Therefore, the charging process includes compressors, intercoolers, heat storage, and high-pressure compressed-air storage.A three-stage compression trains with an equal pressure ratio (PR) is used to estimate the optimal design aiming to reduce electricity consumption and enhance compression efficiency.Specifically, ambient air (Stream 1) enters the compressor and is compressed to high pressure through three stages (Streams 1-6).The compression heat is recovered by a heat transfer medium of the heat storage system (Streams 8-12).Water is used as the intermedium for compression heat recovery, and hightemperature water could be stored in a heat storage tank.

Peak-hour process
During peak hours, the energy stored in the compressed air should be discharged.The high-pressure compressed air is regulated to a certain pressure level and then heated up to a high temperature in the combustor to drive the gas turbine.The exhaust gas contains huge amounts of thermal energy, which can be utilized in a recuperator and a desalination unit.Therefore, the discharging process constitutes a pressure regulator, a combustion chamber (CC), a recuperator, a gas turbine (GT), and a desalination unit.Specifically, the compressed air is preheated by the recuperator after passing through the pressure regulator (Streams 33-35).Then, it enters the CC and is mixed with natural gas (NG) to produce a high temperature and pressure stream (Stream 36) to drive the GT.The exhaust gas from the GT is used to preheat Stream 34 and generate steam for the MED-TVC unit to further enhance the utilization of heat in the exhaust gas.
Flash tanks, evaporators, a steam ejector, and a condenser are the main components of the MED-TVC unit.The generated motive steam enters the TVC system as the primary flow with high temperature and pressure and is mixed with the vapor of the last effect.Then secondary flow, with intermediate pressure as a thermal source enters the first effect.For the proposed MED-TVC unit, the parallel-crossflow configuration is chosen due to its high efficiency.
Meanwhile, some portion of the condenser's output preheated seawater is shared equally among the effects, and the rest is rejected back to the sea.The motive steam vaporizes the feedwater that has been sprayed on the shell side in the first effect.Then, the generated steam is used as the thermal source for the evaporation on the tube side of the second effect.Finally, the condensed vapor at low pressure enters the flash tank.Hence, the vapor generated from the shell side of the last effect is mixed with a small fraction of the evaporated portion.To improve system efficiency and produce more vapor, the remaining brine is fed into the next effect with relatively high pressure and temperature.
In a similar way for the other effects, the rejected brine and freshwater are produced from the system ultimately.

Full time process
The LNG regasification process should run around-the-clock to reduce the costs of the LNG gasification and maintain a stable supply of natural gas.To effectively recover the LNG cold energy, ORC as a power generation technology is adopted in the novel system.The lowtemperature LNG acts as the heat sink of the ORC system.The hot water produced during the off-peak hours is used as the heat source in ORC.Therefore, the efficiency of the ORC is boosted significantly because both the compression heat and LNG cold energy are utilized simultaneously.Specifically, LNG is pumped into the ORC condenser and re-gasified (evaporated) (Streams 26-28).The ORC operates between the LNG and the hot water (Streams 18-25 and 27-28 are involved in the ORC system).The LNG temperature is still low after the regasification in the condenser.Thus, it is directed to a cooling unit for the production of cold water or other cooling fluids that could be used for air conditioning systems in buildings.The gasification process terminates in this phase, and LNG is converted into NG.Due to the high pressure of NG, it can be expanded through a turbine to generate electricity (Streams 29-30).Finally, a large portion of NG is injected into the natural gas grid for other end users, and the remaining small portion of natural gas is combusted in the CAES power plant (Streams 31-32).

Process modeling
Energy systems can be evaluated from thermodynamic and economic perspectives.We should not pursue the best thermodynamic performance of an energy system ignoring the economic performance.Generally speaking, the thermodynamic and economic metrics often contradict each other in the near-optimal region.The thermodynamic model of the proposed IES is developed in accordance with the following assumptions: • The chemical reactions are at equilibrium and the proposed IES operates at steady-state conditions during charging, discharging, and full-time processes.• Kinetic and potential energies are negligible.
• The air is composed of 79 % nitrogen and 21 % oxygen by volume.
• Pressure drop inside the pipes and heat loss in the heat exchangers are neglected.• The maximum allowable salinity is assumed to be 70,000 ppm.
In this study, some other design parameters are taken from open literature as shown in Table 1.

CAES subsystem
The key equations of the thermodynamic model of the CAES system are provided in Table 2.The volume of the storage of the CAES system can be calculated by Eq.( 1), where ρ and ṁ denote the density and mass flowrate of air respectively.Eq.( 2) is the energy balance equation of the combustion chamber, where LHV is the lower heating value of the fuel, and it is assumed to be 46.5 MJ/kg in this study.Eqs. ( 3)-( 5) are the equations for the compressors, while Eqs.( 7)-( 10) are the equations for the heat exchangers.Eq.( 11) is the governing equation for the regulator valve.

LNG regasification and ORC subsystem
In this study, LNG re-gasification is considered as the heat sink of the ORC.A low-temperature ORC is a good choice for generating electricity from low temperatures heat.An ORC uses an organic fluid with lower boiling temperature as working fluid and this is the main difference between an ORC and a traditional steam Rankine cycle.In this study, R143a is chosen as the ORC working fluid because of the good performance in this low-temperature range compared with other working fluids [24].Table 3 shows the energy balance equations for each LNG and ORCs component (see Table 4).

MED-TVC subsystem
Each component and effect of the MED-TVC unit is simulated mathematically using a set of heat transfer equations and mass and energy balances.As shown in Table 4, Eqs. ( 21)-( 23) are the temperature difference in each effect, the temperature of the produced vapor in each effect, and the temperature of the produced vapor in the flash tank, while Eqs.(24) and (25) give the boiling point elevation and nonequilibrium allowance.The parameters of these equations and more details about the MED-TVC can be found in Ref. [27].

Assessment of the IES
After the mathematical models have been developed, comprehensive energetic, exergetic, exergoeconomic, and environmental evaluations (4E) are performed to assess the novel IES.

Energy analysis
The aim of energy analysis is to determine the thermodynamic properties of each stream of the proposed IES.The first law of thermodynamics is applied to each component of the system in order to accomplish this aim.In this regard, the following equations show mass and energy balances for steady-state conditions [38].

Table 4
Temperature profile equations for modeling of the MED-TVC unit.

Description Equation
Temperature difference in each effect Temperature of the produced vapor in each effect Temperature of the produced vapor in the flash tank Boiling point elevation Here ṁ and h are mass flow rate and specific enthalpy, while u, g, and z are velocity, acceleration of gravity, and height of the flow.The change in kinetic and potential energies is ignored in this work.

Exergy analysis
During the energy conversion prosses a part of the energy input is lost.Due to the shortcomings of energy analysis in these energy losses, exergy analysis was proposed based on the concept of exergy.The exergy rate of a stream, which contains physical and chemical exergies is defined as [39]: where in physical part h and s and specific enthalpy and specific entropy and in chemical part Y and ex ch are molar fraction and standard chemical exergy of each chemical component i.The exergy destruction in system component k is defined as follows: However, it is important to note that exergy analysis has some limitations.Exergy analysis often involves assumptions, which can introduce uncertainty into the analysis.For instance, the results of an exergy analysis are influenced by the choice of reference environment, which can impact the interpretation of the results.
Table 5 summarizes the simplified forms of the exergy destruction rate based on Eq. ( 29) for all components in the IES.
According to Fig. 1, the conventional exergy efficiency cannot be determined since various units operate at different periods.Therefore, Eq. ( 49) defines ERTE as a key metric for evaluating system performance.

Economic analysis
A reliable economic study is required to determine the feasibility of a project.Estimating various fixed and operating costs is essential in economic analysis.Capital investment ( ŻPEC ) and operating & maintenance costs ( ŻO&M ) can be obtained from the following equations [40].
where PEC and CRC are purchasing equipment cost and cost recovery coefficient, respectively.Further, τ and γ are the operating hours of the system and the operating and maintenance coefficient.The CRC parameter is defined by the following equation [41]: where i eff and N are effective interest rate and system life span.In this study, maintenance costs and interest rate account for 5 % and 6 % of the total capital investment cost, respectively.As shown in Table 6, the PEC of the components is determined by precise correlations based on their operating conditions.

Exergoeconomic analysis
To assess and improve the performance of the IES, exergoeconomic analysis has been proposed, which combines thermodynamic analysis and economic analysis by applying the cost concept to exergy accounting for the quality of energy [45].
In exergoeconomic analysis, inefficiencies associated with the 1st and 2nd laws of thermodynamics are assessed, i.e., exergy losses, exergy destruction, and costs related to these inefficiencies.Exergoeconomic analysis can be carried out after energy, exergy, and economic analysis as shown below.An exergy cost associated with the exergy stream is part of the exergoeconomic analysis.The mass, energy, and exergy balances should be conducted for each component of the proposed IES to determine the amount of exergy flow in different streams.Then in the second step, economic analysis should be performed.In this regard, the cost balance for the components is given as follows [46]: Here, for each component k, the subscripts in, q, out and w represent inlet, heat load, outlet, and work, respectively.Further, Ċ and Ż are the cost rate and capital cost rate and expressed as follows: where c and Ėx are the specific cost and exergy rate of the stream.Finally, Table 6 provides a summary of the cost rate balance (Based on Eq. ( 53)) for all components of the proposed IES.The system's economic performance largely depends on the availability and cost of LNG in the future, and thus the uncertainty of LNG cost could have significant impacts on the results of this study.

Environmental impact analysis
Pollutant emissions resulting from the production of electricity in fossil fuel based power plants is unavoidable.So, analyzing the energy systems from just energy and economic viewpoints is not sufficient, and it would be valuable to include environmental implications in the analysis of energy systems.Accordingly, investigating the environmental impact of energy systems is a crucial priority for addressing ocean acidification and global warming issues.In this regard, Eq. (78) defines the CO 2 emission index in ton/MWh, as the ratio of CO 2 discharged to the atmosphere to the net produced exergy.

Multi-objective optimization framework
MOO must be performed to find optimal solutions while considering the exergetic, economic, and environmental objectives simultaneously.Throughout the history of this planet, nature has continuously solved challenging problems through evolution.Nature provides many creative solutions to various problems, so it is rational to get inspired by nature to solve various problems [47].Concerning optimization, Holland and Reitman [48] introduced a revolutionary idea where the evolutionary concepts of nature were simulated in computers for the solution of optimization problems in 1997.When one of the most popular heuristic algorithms, called the genetic algorithm (GA), was proposed, a new horizon was opened for addressing and solving complex and challenging problems in different areas [49,50].One of the primary intricacies of a heuristic algorithm is its inability to compare solutions with more than a single objective.To solve this problem, researchers compared solutions using the Pareto dominance [51].MOO via heuristic algorithms has recently received enormous attention, and MOO is adopted to determine )( Gas turbine PECGT = ( 479.3 ṁ36 Recuperator PECRec = 12000 ( ARec 100 the optimal design in this study [52].The literature contains several algorithms for solving multi-objective problems, e.g., MOPSO 1 and NSGA. 2 All these algorithms are effective in solving multi-objective problems and have been applied to optimize many IESs.However, the question is, do we still need more algorithms?The answer to this question lies in the no free lunch (NFL) theorem [53], which has logically proved that there is no single optimization technique for solving all optimization problems.In other words, the algorithms of this domain manifest similar performance when all optimization problems are considered.
A recently-introduced algorithm is the grasshopper optimization algorithm (GOA), which benefits from high heurism and displays fast convergence [54].High exploration and local optimal avoidance are advantages of GOA due to the high repulsive force between grasshoppers.These features enable the GOA algorithm to outperform other algorithms like the PSO, 3 BA, 4 and FA 5 in its ability to adapt to difficult multi-objective problems [55,56].
These properties enable the GOA to manage problems in the multiobjective search space and overtake other techniques.These robust properties also motivated the use of the MOO algorithm in this study.The grasshopper optimization algorithm simulates the swarming behavior of grasshoppers in nature.
Eq. ( 79) is a representation of the mathematical model used to simulate the swarming behavior of grasshoppers: Here X i is the position of the ith grasshoppers and S i , G i, and A i are social interaction, the gravity force on the solution, and wind advection (since nymph grasshoppers lack wings, the direction of the wind greatly influences their movements), respectively.
A i = uê w (82) Substituting Eqs. ( 80)-(82) in Eq. ( 79), this equation can be expanded as follows: In order to find an accurate approximation of the global optimum, a stochastic algorithm must successfully execute exploitation and exploration.Eq. ( 83) should include unique parameters to show exploitation and exploration in different stages of optimization.To solve optimization problems, a modified version of Eq. ( 83) is proposed as follows: where LB d and UB d are the lower and upped bounds in dth dimension.
The mathematical equations and further information about the GOA are available in Ref. [54].Simulation of the proposed IES is developed in the EES, which has a comprehensive library for thermodynamic properties.Since EES is lacking the ability of MOO, this software should be coupled with MATLAB.However, a significant issue in connecting EES to MATLAB directly is the lengthy run time required.Therefore, artificial neural network (ANN) is used as a bridge between EES and MATLAB in this study.ANN has been proved as a reliable tool to predict outputs with the highest degree of accuracy, the least amount of complexity, and the least amount of computational expense in many applications.
ANNs are computational approaches that incorporate several processing elements derived from biological neurons.An ANN consists of input, hidden, and output layers that connect a group of neurons that transmit data to each other.The data set number, network structure, and training algorithm are critical for the ANN accuracy.The quantity of data is a key parameter, and under-fitted networks occur when the number of data is small, while overfitting occurs when the number of neurons is excessive.According to the literature, cascade-forward neural networks (CFNN) structure, and the Levenberg-Marquardt training algorithm are reliable options for energy systems [57].
The framework of the modeling and the MOO is depicted in Fig. 2. Based on this figure, first the mathematical model is developed in EES, and then a 1000 random data set is introduced to the ANN.After the training process, three mathematical correlations for objective function are extracted and provided to the MOO algorithms as a function.Finally, the best point in the Pareto frontier is selected through the TOPSIS 6  method according to all three objective functions.TOPSIS is used for multi-criteria decision-making and ranks alternatives in terms of distance from ideal and negative-ideal solutions.In the context of the Pareto frontier, TOPSIS can be applied to select the best solution among the nondominated solutions generated by a MOO and it can helpful in reducing the computational complexity and improving the quality of decisions [58].

Model validation
The IES will be simulated and optimized based on the proposed framework as shown in Fig. 2. Since the proposed IES is a novel system that has not been reported in the literature, the subsystems need to be validated before the assessment and optimization of the proposed IES.In this regard, the CAES model is validated with study [59], and the results are shown in Table 7, indicating that the model is acceptable.In addition, Table 8 provides the performance of the MED-TVC unit, and the results match well with the results from the study [27].
The optimization process of complex energy systems often requires a significant computational cost and artificial neural networks (ANNs) can reduce the computational time and facilitate the optimization.In this regard, ANNs are designed separately for the system's three objective functions.ANNs are evaluated by comparing the predicted outputs and the simulation results using the coefficient of determination (R 2 ).The ideal conditions occur when R 2 is equal to one.
Overfitting is a concern for ANN validation, where the model gives accurate predictions for training data but not for new data.This undesirable behavior occurs due to various reasons, but the most critical parameters are the size of the training data and the noise level in the data.To prevent this problem, a large dataset containing 1000 samples is used in this study [57,60].Furthermore, the simulation results indicated negligible noise, and the validation depicted in Fig. 3 reveals no cause for concern regarding overfitting.As shown in Fig. 3, R 2 for the ERTE, cost rate, and CO 2 emission are 0.99996, 0.99997, and 0.99987, respectively, indicating a very accurate prediction of the trained ANN model. 1 Multi-Objective Particle Swarm Optimization. 2 Non-dominated Sorting Genetic Algorithm. 3Particle swarm optimization. 4Bat optimization algorithm. 5Firefly algorithm. 6Technique for Order Preference by Similarity to Ideal Solution.

Optimization results
As mentioned before, MOO should be performed if thermodynamic, exergoeconomic, and environmental objectives have to be considered simultaneously to determine the optimal operating conditions.Storage pressure, charging to discharging PR, the inlet temperature of the GT, and the number of MED effects are selected as the decision variables in this study.Reasonable ranges for these decision variables, some of which are derived from previous reports, are listed in Table 9.
The relatively new algorithm MOGOA is used for optimization.Fig. 4 indicates the Pareto frontiera group of optimal points obtained during the optimization process.To better evaluate the performance of the MOGOA algorithm, the results obtained from this algorithm have been compared with the multi-objective genetic algorithm (NSGA).As shown in Fig. 4, The two optimization algorithms can get similar Pareto fronts.However, the MOGOA performs slightly better than the NSGA since the Pareto front from MOGOA is closer to the assumed ideal point.
To better view the difference between the two algorithms, a 2D diagram is presented in Fig. 5.It is clear that when the exergy round-trip efficiency is higher than 54 %, the MOGOA algorithm has a much better Pareto front compared with the NSGA algorithm.
Figs. 4 and 5 show that the maximum ERTE (55.4 %) and the highest total cost rate (549.7 h/$) are located at design point C. On the other hand, the lowest total cost rate (237.2h/$) occurs at design point A, which is the optimum when the total cost rate is the only objective function.Similarly, design point C is the optimum when the ERTE is the only objective function.In MOO, a decision-making process is necessary for selecting the final optimum point, because in MOO usually, all objectives have their optimum values independent of other objectives and it is impossible to have all the objectives at the optimum point simultaneously.As shown in Fig. 4, the ideal point is not in the Pareto frontier.Finally, the best point (B) is selected through the TOPSIS method.Table 10 represents detailed information of three representative points on the Pareto front including the optimal design point based on TOPSIS.The design parameters of the optimal point B in TOPSIS analysis demonstrate practicality, indicating that they are set at achievable levels.Moreover, the key metrics of the system exhibit promising results in terms of exergy efficiency, cost rate, and CO2 emission index.
To better understand the changes in all design parameters, the scatter matrix of the design parameters is shown in Fig. 6.Scatter plot matrix is used for visualizing relationships between bivariate combinations of variables.In the matrix, each scatter plot illustrates the relationship between two variables, allowing many relationships to be explored in one chart.Also, the diagonal of the graph contains a histogram of each parameter, which is a powerful tool for visualizing the distribution of data.The results show that on the Pareto front, the storage pressure tends to be as low as possible, whereas the inlet temperature of the GT tends to be as high as possible.Therefore, these results indicate that it is not necessary to design the CAES system at a high storage pressure level, while high turbine inlet temperature will boost the system performance.It is obvious that the MOGOA algorithm converges to the upper bound for the inlet temperature of the GT.However, the turbine inlet temperature is limited by materials.If new materials can be developed, that can withstand temperatures higher than 1500 K, the performance of the system can be improved further.The charging to discharging PR tends to be as low as possible, which indicates that the exergy destruction of the regulating valve should be avoided as much as possible.The regulating valve could be a key component for the system performance improvement.The number of MED effects is scattered even more compared with other parameters.Interestingly, the MOGOA algorithm favors the maximum number of MED effects (8), while the NSGA algorithm favors 7 effects for the MED system.

Sensitivity analysis
The sensitivity analysis is performed for a better understanding of the optimization results.The impacts of each design parameter are evaluated for points A-C in terms of all three objective functions.Figs.7 and 8 show the results from the sensitivity analysis when design parameters change according to Table 9. Fig. 7a shows the impact of the storage pressure on the system ERTE, the total cost rate, and the CO 2 emission index.An increase in this parameter negatively affects the total cost and increases the system's exergy efficiency.An increase in the storage pressure increases power production during discharging hours and the efficiency of the system.However, higher storage pressure results in higher energy input, and costs of compressors, storage, and gas turbines.It should be noticed that at design point C, the exergy round-trip efficiency is not susceptible to the storage pressure, while the cost rate is very sensitive to this parameter.This justifies the multi-objective optimization and the storage pressure must be determined carefully.Fig. 7b shows the impact of the charging to discharging PR on the three objective functions.An increase in this parameter reduces the system's efficiency and increases the CO 2 emission index because the higher the pressure ratio, the lower the gas turbine power output.However, with an increase in the charging to discharging PR, the storage capacity and consequently the system's total cost is reduced, while the exergy round-trip efficiency is decreased since the higher pressure ratio results in more exergy destruction in the regulation valve.Fig. 8a shows the impact of the inlet temperature of the GT on all      three objective functions.This parameter is directly related to the turbine power output and the CO 2 emission index.The higher the inlet temperature of the GT is, the better the overall performance of the system.However, this parameter cannot be unrealistically high due to limitations in the turbine material.Fig. 8b indicates that the number of effects in the desalination unit has no significant effect on any of the objective functions because this unit is separated from the others, and therefore changes in this unit do not affect other units.A comparison of Figs. 7 and 8 shows that the storage pressure has the highest impact on the cost rate and CO 2 emission index, while the charging to discharging PR has the highest impact on the exergy roundtrip efficiency.The number of MED effects is not a critical parameter regarding the three objective functions.

Exergoeconomic analysis of the TOPSIS point
The share of exergy destruction and irreversibility are crucial in an energy system and this information can guide us in how to improve the system.Therefore, exergy can be used instead of energy for describing the thermodynamic processes.In this regard, the Grassman diagram for the exergy rate is depicted in Fig. 9 for a better understanding of exergy flow in the proposed LNG-ORC-CAES-MED system and the exergy destruction in each equipment.In this diagram, the thickness of each flow represents the exergy rate.Since the system charging and discharging time is at different times, the figure is plotted in megawatthour (MWh), providing a more detailed comparison of the exergy flows.
In off-peak hours, the ambient air with zero exergy enters the first compressor and its exergy increases by 4.08 MWh.To store the renewable energy, 14.13 MWh of green electricity is consumed to drive the three compressors and increase the exergy in the air.Since the compressors are irreversible, 1.25 MWh of the inlet exergy is destroyed, and 12.88 MWh is transferred to the air.The high-pressure air with large exergy content enters the coolers and exergy is transferred to the cooling medium, which is used as the heat source of the ORC system with an exergy rate of 1.26 MWh; 1.38 MWh exergy is wasted in the coolers, which account for the most exergy destruction during the charging process.
In the full-time section, LNG is pumped to the ORC condenser with an exergy of 23.21 MWh; 4.21 MWh of LNG cold exergy is transferred to the ORC working fluid, and the corresponding exergy destruction is 4.04 MWh.The LNG can also provide 0.49 MWh exergy for the district cooling unit.Finally, the regasified LNG enters the natural gas turbine that produces 1.66 MWh of electrical power.The expanded natural gas can be sent to the natural gas pipeline network and part of it can be used as fuel during CAES discharging time.The highest exergy destruction occurs in the ORC condenser in the full-time section due to the large temperature difference in this heat exchanger.Since the LNG chemical exergy is only involved in the combustion chamber, the chemical exergy is not shown for other units.
During peak hours, the pressurized air with an exergy rate of 10.21 MWh enters the regulator valve, 39 % of which is destroyed during the isenthalpic throttling process.Then the air with 6.22 MWh exergy rate  reaches the recuperator that recovers 10.31 MWh of the exhaust gas exergy from the gas turbine.The preheated air and the natural gas with exergy rates of 16.53 MWh and 33.16 MWh, respectively, are mixed and combusted in the combustion chamber.The high pressure and temperature exhaust gas with high exergy drives the gas turbine to produce 25.82 MWh of electricity.After recovering part of the exergy in the recuperator, the exhaust gas from the gas turbine is used as the heat source for the desalination unit to produce fresh water.
The ambient temperature is an important external factor that affects the system's performance, especially for the exergy calculations and according to Eq. ( 28), physical exergy depends on the ambient temperature.As shown in Fig. 10 an increase in the ambient temperature can increase the work consumption in the compressors and decrease the efficiency of the system.In addition, for cooling the compressors, more cold energy is required, and more LNG enters the system, which increases the full-time section work consumption.An increase in the ambient temperature also increases the amount of energy that flows the desalination unit.
Fig. 11 presents the cost rate chord diagram to illustrate the distribution of the total cost rate.The total cost rate at the TOPSIS point equals 322.8 $/h, of which 55 % pertains to the peak-time unit.The figure also reveals that the gas turbine has the highest cost rate among all the peak-time components since gas turbines are usually costly compared with other components.Another reason is that the cost of the gas turbine is a function of mass flowrate, and the discharging time is less than the charging time, which results in a higher mass flowrate during the discharging period.
As shown in Fig. 12, the proposed IES can produce 72,223 L of freshwater per day at the TOPSIS design point with the desalination device.In a comparison of the produced freshwater and the daily water demand of 144 L/day per capita of European families, the proposed system can meet the daily water needs of 501 persons.The MED-TVC is an effective way to utilize the waste heat from the CAES system, and thus the 4E performance of the IES can be improved.

Conclusions
In this study, the obstacles concerning liquefied natural gas (LNG) regasification and the unpredictable nature of renewable energy are tackled.To address these challenges, a novel integrated multigeneration energy system is proposed.The proposed system integrates a CAES system, an ORC system, an LNG regasification process, and a MED thermal desalination unit.The CAES system stores energy from renewable sources and provides heat to the ORC system during its charging period.The ORC system then generates electricity and connects the CAES and LNG units.In the discharge period, natural gas is supplied to the CAES system through LNG regasification, which generates electricity and provides heat to the MED unit.
Through the utilization of a 4E analysis approach implemented in EES programming, the system has been effectively modeled and evaluated.The proposed energy system demonstrates great potential as a promising solution for LNG receiving terminals, where both renewable energy and LNG cold energy resources are available.By integrating various components, it offers an efficient and sustainable approach to energy generation and desalination, which could have significant implications for energy policy and regulations.
To optimize the system design and achieve multiple objectives, a framework incorporating the EES model, an ANN training model, and two multi-objective optimization algorithms (GOA and NSGA) has been applied.Notably, the results indicate GOA performs better than NSGA.A sensitivity analysis has been conducted to evaluate the influence of design parameters on the objective functions, providing valuable

Fig. 3 .
Fig. 3. Validation of the ANN for three objective functions.

Fig. 4 .
Fig. 4. The 3D Pareto frontier for the proposed IES using the MOGOA and NSGA.

Fig. 5 .
Fig. 5.The 2D optimization diagram for the proposed IES using the MOGOA and NSGA.

Fig. 6 .
Fig. 6.Scatter matrix of the design parameters in the MOGOA and NSGA.

Fig. 7 .Fig. 8 .
Fig. 7. Impact of the design parameters on the objective functions for a) storage pressure and b) charging to discharging PR.

Fig. 9 .
Fig. 9. Grassmann diagram of the proposed IES for the point B.

Fig. 10 .
Fig. 10.Impact of ambient temperature on the system's performance.

Fig. 11 .
Fig. 11.The chord diagram of the cost rate of the IES.

Table 1
Input values and design conditions for the proposed IES.

Table 2
Thermodynamic modeling equations for the CAES.

Table 6
Purchasing equipment cost, cost balance and auxiliary equation for different components.

Table 7
Verification of the results for the CAES unit.

Table 8
Validation of the MED-TVC unit.

Table 9
Constraints of optimization design parameters.

Table 10
The optimum values for design parameters and objective functions for points A, B, and C.