Multi-objective thermodynamic optimization of solar parabolic dish stirling heat engine with regenerative losses using NSGA-II and decision making

The proposed work investigates optimal values of various decision variables that simultaneously optimize power output, net-work output and second law efficiency of solar driven Stirling heat engine with regenerative heat losses, conducting thermal bridging losses using evolutionary algorithm based on NSGA-II in Matlab simulink environment. Effects of design parameters as absorber temperature, concentrating ratio, radiative and convective heat transfers are included in the analysis. Pareto frontier is obtained for triple and dual objectives and the best optimal value is selected through four different decision making techniques viz. Fuzzy, Shannon entropy, LINMAP and TOPSIS. Triple objective evolutionary approach applied to the proposed model gives power output, net-work output and second law efficiency as (38.87 kW, 1.24 kJ, 0.3156) which are 18.19, 16.78 and 31.51% lower in comparison with reversible system. With the objective of error investigation, the average and maximum error of the obtained results are figured at last.     

Multi-objective optimization for GPU3 Stirling engine by combining multi-objective algorithms

Stirling engine has become preferable for high attention towards the use of alternate renewable energy resources like biomass and solar energy. Stirling engine is the main component of dish Stirling system in thermal power generation sector. Stirling engine is an externally heating engine, which theoretical efficiency is as high as Carnot cycle's, but actual ones are always far below compared with the Carnot efficiency. A number of studies have been done on multi-objective optimization to improve the design of Stirling engine. In the current study, a multi-objective optimization method, which is a combination of multiple optimization algorithms including differential evolution, genetic algorithm and adaptive simulated annealing, was proposed. This method is an attempt to generalize and improve the robustness and diversity with above three kinds of population based meta-heuristic optimization techniques. The analogous interpreter was linked and interchanged to find the best global optimal solution for Stirling engine performance optimization. It decreases the chance of convergence at a local minimum by powering from the fact that these three algorithms run parallel and members from each population and technique are swapped. The optimization considers five decision variables, including engine frequency, mean effective pressure, temperature of heating source, number of wires in regenerator matrix, and the wire diameter of regenerator, as multiple objectives. The Pareto optimal frontier was obtained and a final optimal solution was also selected by using various multi-criteria decision making methods including techniques for Order of Preference by Similarity to Ideal Solution and Simple Additive Weighting. The multi-objective optimization indicated a way for GPU-3 Stirling engine to obtain an output power of more than 3 kW and an increase by 5% in thermal efficiency with significant decrease in power loss due to flow resistance.     

Energy,exergy, and exergoeconomics (3E) analysis and multi-objective optimization of a multi-generation energy system for day and night time power generation - Case study: Dezful city

The present study aimed to investigate a multi-generation energy system for the production of hydrogen, freshwater, electricity, cooling, heating, and hot water. Steam Rankine cycle (SRC), organic Rankine cycle (ORC), absorption chiller, Parabolic trough collectors (PTCs), geothermal well, proton exchange membrane (PEM) electrolyzer, and reverse osmosis (RO) desalination are the main subsystems of the cycle. The amount of exergy destruction is calculated for each component after modeling and thermodynamic analysis. The PTCs, absorption chiller, and PEM electrolyzer had the highest exergy destruction, respectively. According to meteorological data, the system was annually and hourly tested for Dezful City. For instance, it had a production capacity of 13.25 kg/day of hydrogen and 147.42 m³/day of freshwater on 17th September. Five design parameters are considered for multi-objective optimization after investigating objective functions, including cost rate and exergy efficiency. Using a Group method of data handling (GMDH), a mathematical relation is obtained between the input and output of the system. Next, a multi-objective optimization algorithm, a non-dominated sorting genetic algorithm (NSGA-II), was used to optimize the relations. A Pareto frontier with a set of optimal points is obtained after the optimization. In the Pareto frontier, the best point is selected by the decision criterion of TOPSIS. At the TOPSIS point, the exergy efficiency is 31.66%, and the total unit cost rate is 21.9 $/GJ.     

Design and optimization of a non-TEMA type tubular recuperative heat exchanger used in a regenerative gas turbine cycle

A special non-TEMA type tubular recuperative heat exchanger used as a regenerator of a gas turbine cycle is considered for multi-criteria optimization. It is assumed that the recuperator is designed for an existing gas turbine cycle to be retrofitted. Three scenarios for optimization of the proposed system have been considered. In one scenario, the objective is minimizing the cost of recuperator; while in another scenario maximizing the cycle exergetic efficiency is considered. In third scenario, both objectives are optimized simultaneously in a multi-objective optimization approach. Geometric specification of the recuperator including tubes length, tubes outside/inside diameters, tube pitch in the tube bundle, inside shell diameter, outer and inner tube limits of the tube bundle and the total number of disc and doughnut baffles are considered as decision variables. Combination of these objectives and decision variables with suitable engineering and physical constraints (including NO_x and CO emission limitations) makes a set of MINLP optimization problem. Optimization programming in MATLAB is performed using one of the most powerful and robust multi-objective optimization algorithms namely NSGA-II. This approach which is based on the Genetic Algorithm is applied to find a set of Pareto optimal solutions. Pareto optimal frontier is obtained and a final optimal solution is selected in a decision-making process. It is shown that the multi-objective optimization scenario can be considered as a generalized optimization approach in which balances between economical viewpoints of both heat exchanger manufacturer and end user of recuperator.     

Exergetic sustainability evaluation and optimization of an irreversible Brayton cycle performance

Owing to the energy demands and global warming issue, employing more effective power cycles has become a responsibility. This paper presents a thermodynamical study of an irreversible Brayton cycle with the aim of optimizing the performance of the Brayton cycle. Moreover, four different schemes in the process of multi-objective optimization were suggested, and the outcomes of each scheme are assessed separately. The power output, the concepts of entropy generation, the energy, the exergy output, and the exergy efficiencies for the irreversible Brayton cycle are considered in the analysis. In the first scheme, in order to maximize the exergy output, the ecological function and the ecological coefficient of performance, a multi-objective optimization algorithm (MOEA) is used. In the second scheme, three objective functions including the exergetic performance criteria, the ecological coefficient of performance, and the ecological function are maximized at the same time by employing MOEA. In the third scenario, in order to maximize the exergy output, the exergetic performance criteria and the ecological coefficient of performance, a MOEA is performed. In the last scheme, three objective functions containing the exergetic performance criteria, the ecological coefficient of performance, and the exergy-based ecological function are maximized at the same time by employing multi-objective optimization algorithms. All the strategies are implemented via multi-objective evolutionary algorithms based on the NSGAII method. Finally, to govern the final outcome in each scheme, three well-known decision makers were employed.     

回热式布雷顿-两平行逆布雷顿联合循环第一定律分析与优化

提出了回热式布雷顿-两平行逆布雷顿联合循环模型。对该模型进行了第一定律性能分析与优化,得出了该循环最优效率和最优比功的表达式,分析了回热度及其他参数对联合循环最优热效率和最优比功的影响。分析表明,增加回热器后能提高联合循环的热效率,但此时联合循环的输出比功较小。     

Multiobjective optimization and analytical comparison of single‐ and 2‐stage (series/parallel) thermoelectric heat pumps

The thermodynamic modeling of various thermoelectric devices does not consider the influence of nonlinear Thomson effect. It leads to incomplete solutions of the heat transfer equations and serious analytical errors. On the other hand, appropriate balance among various performance parameters of thermoelectric devices is also required to improve its operating characteristics. In this context, the thermodynamic modeling on the basis of first/second laws for multielement single‐ and 2‐stage (series/parallel) thermoelectric heat pumps, including the influence of Thomson effect in combination with Fourier heat conduction and Joule effects, is done. The optimization of the heat pumps has been carried out to obtain the optimal values of 4 input parameters by using the second version of nondominated sorting genetic algorithm in matrix laboratory. The optimal values from Pareto frontier of dual/triple objectives are obtained through 3 decision makings viz. Shannon's entropy, Fuzzy Bellman‐Zadeh, and TOPSIS. It is observed that triple‐objective optimization gives much lower difference between ideal and obtained solution, termed as deviation index, as compared with the single/dual one. Additionally, sensitivity analysis has been carried out to study the influence of Thomson effect on heating capacity and coefficient of performance of the pumps. To validate the evolutionary algorithm, the optimal values are compared with analytical ones from previous literature.     

有机工质低温余热发电系统多目标优化设计

针对现有有机朗肯循环单目标优化设计的局限性,从热力性、经济性等多方面对有机工质低温余热发电系统进行多目标优化设计.以系统效率最大和总投资费用最小为目标函数,选取透平进口温度、透平进口压力、余热锅炉节点温差、接近点温差和冷凝器端差等5个关键热力参数作为决策变量,利用非支配解排序遗传算法(NSGA-II)分别对采用R123、R245fa和异丁烷的有机工质余热发电系统进行多目标优化,获得不同工质的多目标优化的最优解集(Pareto最优前沿),并采用理想点辅助法从最优解集中选择出最优解及相应的系统最佳热力参数组合.结果表明:在给定余热条件下,从热力性能和经济性两方面考虑,R245fa是最优的有机工质,从多目标优化的最优解集中选择出的最佳效率为10.37%,最小总投资费用为455.84万元.     

S-CO2布雷顿循环太阳能电力淡水系统火用分析

设计一种使用S-CO₂布雷顿循环的太阳能电力淡水系统,对系统的工作原理和结构组成进行介绍,并对系统开展运行性能和火用分析。结果表明,设计工况下系统的输出电功率为233.8 MW,布雷顿循环效率为37.5%,淡水日产量为3981.6 t。增大太阳辐照度有利于提高系统的电力输出和总的能量效率。定工况下的火用分析结果表明,太阳塔集热器中的火用损最大,为303.99 MW,对应的火用效率为64.45%。海水淡化换热器的火用效率最低,且其火用损值也较大。随着太阳辐照度的增加,太阳塔集热器、海水淡化系统换热器和回热器内的火用损均有不同幅度的增加。因此,对于该S-CO₂布雷顿循环太阳能电力淡水系统的后续优化而言,应重点考虑改进这些部件的性能。     

Multi-objective optimization in a finite time thermodynamic method for dish-Stirling by branch and bound method and MOPSO algorithm

There are various analyses for a solar system with the dish-Stirling technology. One of those analyses is the finite time thermodynamic analysis by which the total power of the system can be obtained by calculating the process time. In this study, the convection and radiation heat transfer losses from collector surface, the conduction heat transfer between hot and cold cylinders, and cold side heat exchanger have been considered. During this investigation, four objective functions have been optimized simultaneously, including power, efficiency, entropy, and economic factors. In addition to the four-objective optimization, three-objective, two-objective, and single-objective optimizations have been done on the dish-Stirling model. The algorithm of multi-objective particle swarm optimization (MOPSO) with post-expression of preferences is used for multi-objective optimizations while the branch and bound algorithm with pre-expression of preferences is used for single-objective and multi-objective optimizations. In the case of multi-objective optimizations with post-expression of preferences, Pareto optimal front are obtained, afterward by implementing the fuzzy, LINMAP, and TOPSIS decision making algorithms, the single optimum results can be achieved. The comparison of the results shows the benefits of MOPSO in optimizing dish Stirling finite time thermodynamic equations.     

Performance assessment and optimization of an integrated solid oxide fuel cell-gas turbine cogeneration system

The combined solid oxide fuel cells and gas turbine (SOFC/GT) system is known to be a potential alternative for distributed power generation. In this paper, a novel SOFC/GT based cogeneration system, which integrated a transcritical carbon dioxide cycle (TRCC) with a LNG cold energy utilization system is proposed. A mathematical (zero-dimensional) model is developed to analyze the co-generation system performance from the perspective of thermodynamic (energy and exergy) and economic costs. The main parameters of the system are chosen to analyze their effects on thermodynamic performance. The results show that the current system can achieve 64.40% thermal efficiency and 62.13% exergy efficiency under given conditions, and can further improve efficiency through parameter optimization. Finally, the multi-objective optimization program using NSGA-II (Non-dominated Sorting Genetic Algorithm II) is used to obtain the optimal value of the system design parameters. In the multi-objective analysis, the thermodynamic efficiency and economic cost of the system are considered as objective functions. The optimization results show that the final optimized design selected from the Pareto front can achieve 63.08% thermal efficiency and 61.10% exergy efficiency, respectively.     

Multi-objective optimization of a joule cycle for re-liquefaction of the Liquefied Natural Gas

A LNG re-liquefaction plant is optimized with a multi-objective approach which simultaneously considers exergetic and exergoeconomic objectives. In this regard, optimization is performed in order to maximize the exergetic efficiency of plant and minimize the unit cost of the system product (refrigeration effect), simultaneously. Thermodynamic modeling is performed based on energy and exergy analyses, while an exergoeconomic model based on the total revenue requirement (TRR) are developed. Optimization programming in MATLAB is performed using one of the most powerful and robust multi-objective optimization algorithms namely NSGA-II. This approach which is based on the Genetic Algorithm is applied to find a set of Pareto optimal solutions. Pareto optimal frontier is obtained and a final optimal solution is selected in a decision-making process. An example of decision-making process for selection of the final solution from the available optimal points of the Pareto frontier is presented here. The feature of selected final optimal system is compared with corresponding features of the base case and exergoeconomic single-objective optimized systems and discussed.     

Performance optimisation for two classes of combined regenerative Brayton and inverse Brayton cycles

This paper proposes a new cyclic model of combined regenerative Brayton and inverse Brayton cycles. The new combined regenerative Brayton and inverse Brayton cycles recover heat energy after the working fluid leaves the turbine of the inverse Brayton cycle while the original combined regenerative Brayton and inverse Brayton cycles recover heat energy before the working fluid enters the turbine of the inverse Brayton cycle. Performance analysis and optimisation of the two classes combined cycles are carried out. Furthermore, the effect of the regenerator on the performance of the two combined cycles is analysed. It is found that the new combined cycle can obtain higher thermal efficiency and larger specific work than those of the original combined cycle at low compressor pressure ratio of the top cycle, and the regenerator can improve the performance of both the combined cycles. By theoretical analysis of this paper, it reveals that the new combined cycle will be well applied in the prospect, and the original combined cycle will be suited to low power output equipments. This paper aims at enriching the gas turbine theory and providing a possible way to save energy.     

Ecological performance analysis of an endoreversible modified Brayton cycle

An endoreversible closed modified simple Brayton cycle model with isothermal heat addition coupled to variable-temperature heat reservoirs is established using finite-time thermodynamics. Analytical expressions of dimensionless power output, thermal efficiency, dimensionless entropy generation rate and dimensionless ecological function are derived. Influences of cycle thermodynamic parameters on ecological performance and optimal compressor pressure ratio, optimal power output, optimal cycle thermal efficiency and optimal entropy generation rate corresponding to maximum ecological function are obtained and compared with those corresponding to maximum power output. The results show that cycle thermal efficiency improvement and entropy generation rate reduction are obtained at the expense of higher compressor pressure ratio and a little sacrifice of power output at maximum ecological function. The compromises between power output and entropy generation rate and between power output and cycle thermal efficiency, respectively, are achieved.     

Multi-objective optimization design of condenser in an organic Rankine cycle for low grade waste heat recovery using evolutionary algorithm

The optimum design of a condenser is significant in an organic Rankine cycle to achieve higher waste heat utilization efficiency. Based on the mathematical model of a condenser using plate heat exchanger (PHE), some key geometric parameters on the total heat transfer surface area and pressure drop of the condenser are examined. In order to obtain geometric parameters of a plate heat exchanger, a multi-objective optimization of the condenser in organic Rankine cycle is conducted to achieve the optimal geometry design. The total heat transfer surface area and pressure drop are selected as two objective functions to minimize both total heat transfer surface area and pressure drop under the constant heat transfer rate and LMTD conditions. The plate width, plate length and plant distance are selected as the decision variables. Non-dominated sorting generic algorithm-II (NSGA-II) which is an effective multi-objective optimization method is employed to solve this multi-objective optimization design of PHE. The results show that an increase in channel distance or plate width increases the total heat transfer surface area and decreases pressure drop in the condenser. It is noted that the plate length of PHE has a positive effect on the optimization design of PHE. By multi-objective optimization design of the PHE, a Pareto optimal point curve is obtained, which shows that a decrease in total heat transfer surface area of a condenser can increase the pressure drop through the condenser.     

太阳能驱动闭式简单燃气轮机循环热力学优化

研究太阳能通过换热器的闭式简单燃气轮机循环有限时间热力学性能，导出内可逆循环的最佳功率与效率间的关系，并得到最大功率输出及其相应的效率界限。用压气机和涡轮内效率表征循环内不可逆性，可得实际不可逆循环的最优性能。所得结果对闭式简单燃气轮机装置热力参数的选择有定指导意义。     

Dynamic multi-objective optimization applied to a solar-geothermal multi-generation system for hydrogen production,desalination, and energy storage

The design of optimal energy systems is vital to achieving global environmental and economic targets. In the design of solar-geothermal multi-generation systems, most previous investigations have relied on the static multi-objective optimization approach (SMOA), which may leave considerable room for improvement under certain conditions. In this numerical study, the optimal condition at which to operate a solar-geothermal multi-generation system – which can simultaneously produce hydrogen, fresh water, electricity, and heat, along with storing energy ? is determined via a dynamic multi-objective optimization approach (DMOA). Optimization is performed using a combination of NSGA-II and TOPSIS, and the results are benchmarked against those of SMOA. The decision variables include the solar area, geothermal water extraction mass flow, and hydrogen storage pressure. The objective functions include the production of electricity, heat, hydrogen, and fresh water, along with the exergy and energy efficiencies and the payback period. It is found that when compared with SMOA, DMOA can significantly improve all the objective functions. The annual production of electricity, heat, hydrogen, and fresh water increases by 14.4, 16.1, 13.5, and 14.3%, respectively, while the average annual exergy and energy efficiencies increase by 5.2 and 3.0%, respectively. The use of DMOA also reduces the payback period from 5.56 to 4.43 years, with a 4.4% reduction in hydrogen storage pressure. This shows that compared with a static approach such as SMOA, DMOA can improve the exergy and energy efficiencies, economic viability, and safety of a solar-geothermal multi-generation system.     

Implementing of the multi-objective particle swarm optimizer and fuzzy decision-maker in exergetic, exergoeconomic and environmental optimization of a benchmark cogeneration system

Multi-objective optimization for design of a benchmark cogeneration system namely as the CGAM cogeneration system is performed. In optimization approach, Exergetic, Exergoeconomic and Environmental objectives are considered, simultaneously. In this regard, the set of Pareto optimal solutions known as the Pareto frontier is obtained using the MOPSO (multi-objective particle swarm optimizer). The exergetic efficiency as an exergetic objective is maximized while the unit cost of the system product and the cost of the environmental impact respectively as exergoeconomic and environmental objectives are minimized. Economic model which is utilized in the exergoeconomic analysis is built based on both simple model (used in original researches of the CGAM system) and the comprehensive modeling namely as TTR (total revenue requirement) method (used in sophisticated exergoeconomic analysis). Finally, a final optimal solution from optimal set of the Pareto frontier is selected using a fuzzy decision-making process based on the Bellman-Zadeh approach and results are compared with corresponding results obtained in a traditional decision-making process. Further, results are compared with the corresponding performance of the base case CGAM system and optimal designs of previous works and discussed.     

Exergetic Optimization of Shell-and-Tube Heat Exchangers Using NSGA-II

In this article, a multi-objective exergy-based optimization through a genetic algorithm method is conducted to study and improve the performance of shell-and-tube type heat recovery heat exchangers, by considering two key parameters, such as exergy efficiency and cost. The total cost includes the capital investment for equipment (heat exchanger surface area) and operating cost (energy expenditures related to pumping). The design parameters of this study are chosen as tube arrangement, tube diameters, tube pitch ratio, tube length, tube number, baffle spacing ratio, and baffle cut ratio. In addition, for optimal design of a shell-and-tube heat exchanger, the method and Bell–Delaware procedure are followed to estimate its pressure drop and heat transfer coefficient. A fast and elitist nondominated sorting genetic algorithm (NSGA-II) with continuous and discrete variables is applied to obtain maximum exergy efficiency with minimum exergy destruction and minimum total cost as two objective functions. The results of optimal designs are a set of multiple optimum solutions, called “Pareto optimal solutions.” The results clearly reveal the conflict between two objective functions and also any geometrical changes that increase the exergy efficiency (decrease the exergy destruction) lead to an increase in the total cost and vice versa. In addition, optimization of the heat exchanger based on exergy analysis revealed that irreversibility like pressure drop and high temperature differences between the hot and cold stream play a key role in exergy destruction. Therefore, increasing the component efficiency of a shell-and-tube heat exchanger increases the cost of heat exchanger. Finally, the sensitivity analysis of change in optimum exergy efficiency, exergy destruction, and total cost with change in decision variables of the shell-and-tube heat exchanger is also performed.     

Thermodynamic optimization of Stirling heat engine with methane gas using finite speed thermodynamic model

With the daily rise in environmental issues due to the use of conventional fuels, researchers are motivated to use renewable energy sources. One of such waste heat and low-temperature differential driven energy sources is the Stirling engine. The performance of the Stirling engine can be improved by finding out the optimum operating and geometrical parameters with suitable working gas and thermal model. Based on this motivation, the current work focuses on the multiobjective optimization of the Stirling engine using the finite speed thermodynamic model and methane gas as the working fluid. Considering output power and pressure drop as two objective functions, the system is optimized using 11 geometrical and thermal design parameters. The optimization results are obtained in the form of the Pareto frontier. A sensitivity assessment is carried out to observe the decision variables, which are having a more sensitive effect on the optimization objectives. Optimization results reveal that 99.83% change in power output and 78% change in total pressure drop can take place in the two-dimensional optimization space. The optimal solution closest to the ideal solution has output power and pressure drop values as 12.31 kW and 22.76 kPa, respectively.