Thermo-economic Multi-objective Optimization Research Articles

Thermoeconomic multi-objective optimization of a dual loop organic Rankine cycle (ORC) for CNG engine waste heat recovery

Asbtract In this paper, a thermoeconomic model of a dual loop organic Rankine cycle (ORC) system has been developed to analyze both the thermodynamic and economic performance of several working fluid groups for the purpose of compressed natural gas (CNG) engine waste heat recovery. The effects of six key parameters on the thermoeconomic indicators of the dual loop ORC system are investigated. Furthermore, a multi-objective genetic algorithm (GA) is employed to solve the Pareto optimal solutions from the viewpoints of maximizing net power output and minimizing total investment cost over the whole operating range of the CNG engine. The most suitable working fluid group is screened out, then the optimal parameter regions are determined. The results show that a higher evaporation pressure and a lower condensation temperature exhibit a positive effect on the thermoeconomic performances of the dual loop ORC system while the effects of variation in superheat degree and exhaust outlet temperature on the thermoeconomic performances are not obvious. The optimal evaporation pressure of the high temperature loop ORC (HT cycle) is always above 2.5 MPa. The optimal condensation temperature of the HT cycle, optimal evaporation temperature and condensation temperature of the low temperature loop ORC (LT cycle) are all kept almost constants. In addition, the optimal exhaust outlet temperature is mainly influenced by the engine speed. At the rated condition, the dual loop ORC system has the maximum net power output of 23.62 kW and the minimum electricity production cost (EPC) of 0.41 $/kW h. The thermal efficiency of the dual loop ORC system is in the range of 8.97–10.19% over the whole operating range.

Thermo-economic assessment of three-stage combined cycle power system using ammonia-water mixture

Thermo-economic modeling and multi-objective optimization studies are performed for a three-stage combined cycle system using ammonia water mixture as working fluid. This combined cycle plant is composed of three main subsystems, Brayton cycle, Rankine and Kalina cycles. Energy and exergy analyses and multi-objective optimization are included. In order to optimize the system, a multi-objective optimization method based on a fast and elitist non-dominated sorting genetic algorithm is applied to determine the best design parameters of the system. The two objective functions considered for the optimization purpose are the total cost rate of the system including equipment costs, and the second objective function is the system exergy efficiency. The total cost rate of the system is minimized while the cycle exergy efficiency is maximized using an evolutionary algorithm. In order to convey a deeper understanding and identify the necessary trade-offs within the optimized objectives in a multifaceted fashion, multi-objective optimizations are conducted in the study. Moreover, a closed form equation is derived to provide the relationship between the exergy efficiency and total cost rate. Finally, sensitivity analyses are performed to better understand the effects of various key design parameters on the total exergy destruction rate, exergy efficiency and total cost rate of the system.

Performance comparison of low-grade ORCs (organic Rankine cycles) using R245fa, pentane and their mixtures based on the thermoeconomic multi-objective optimization and decision makings

Based on the thermoeconomic multi-objective optimization and decision makings, considering both exergy efficiency and LEC (levelized energy cost), the performance comparison of low-grade ORCs (organic Rankine cycles) using R245fa, pentane and their mixtures has been investigated. The effects of mass fraction of R245fa and four key parameters on the exergy efficiency and LEC are examined. The Pareto-optimal solutions are selected from the Pareto optimal frontier obtained by NSGA-II algorithm using three decision makings, including Shannon Entropy, LINMAP and TOPSIS. The deviation index is introduced to evaluate different decision makings. Research demonstrates that as the mass fraction of R245fa increasing, the exergy efficiency decreases first and then increases, while LEC presents a reverse trend. The optimum values from TOPSIS decision making are selected as the preferred Pareto-optimal solution for its lowest deviation index. The Pareto-optimal solutions for pentane, R245fa, and 0.5pentane/0.5R245fa in pairs of (exergy efficiency, LEC) are (0.5425, 0.104), (0.5502, 0.111), and (0.5212, 0.108), respectively. The mixture working fluids present lower thermodynamic performance and moderate economic performance than the pure working fluids under the Pareto optimization.

Thermoeconomic multi-objective optimization of an organic Rankine cycle for exhaust waste heat recovery of a diesel engine

In this paper, the ORC (Organic Rankine cycle) technology is adopted to recover the exhaust waste heat of diesel engine. The thermodynamic, economic and optimization models of the ORC system are established, respectively. Firstly, the effects of four key parameters, including evaporation pressure, superheat degree, condensation temperature and exhaust temperature at the outlet of the evaporator on the thermodynamic performances and economic indicators of the ORC system are investigated. Subsequently, based on the established optimization model, GA (genetic algorithm) is employed to solve the Pareto solution of the thermodynamic performances and economic indicators for maximizing net power output and minimizing total investment cost under diesel engine various operating conditions using R600, R600a, R601a, R245fa, R1234yf and R1234ze as working fluids. The most suitable working fluid used in the ORC system for diesel engine waste heat recovery is screened out, and then the corresponding optimal parameter regions are analyzed. The results show that thermodynamic performance of the ORC system is improved at the expense of economic performance. Among these working fluids, R245fa is considered as the most suitable working fluid for the ORC waste heat application of the diesel engine with comprehensive consideration of thermoeconomic performances, environmental impacts and safety levels. Under the various operating conditions of the diesel engine, the optimal evaporation pressure is in the range of 1.1 MPa–2.1 MPa. In addition, the optimal superheat degree and the exhaust temperature at the outlet of the evaporator are mainly influenced by the operating conditions of the diesel engine. The optimal condensation temperature keeps a nearly constant value of 298.15 K.

Thermoeconomic comparison between pure and mixture working fluids of organic Rankine cycles (ORCs) for low temperature waste heat recovery

Based on the thermoeconomic multi-objective optimization, simultaneously considering exergy efficiency and levelized energy cost (LEC), the thermoeconomic comparisons between pure and mixture working fluids of organic Rankine cycles (ORCs) have been investigated. Four models are proposed based on the different location of evaporating bubble point temperature or condensing dew point temperature for mixture working fluids. The effects of mass fraction and four key parameters (evaporator temperature, condenser temperature, pinch point temperature difference and degree of superheat) on exergy efficiency and levelized energy cost (LEC) are examined. Pareto-optimal solutions of four models using 0.7R245fa/0.3R227ea are obtained and compared. Taking mass fraction into account, the thermoeconomic comparisons between pure and mixture working fluids have been studied. Research demonstrates that the mixtures don’t always present better thermodynamic performance and economic performance than pure working fluids. Model 2 (T7=TE,T3=TC) is the favorable operation condition for its highest thermodynamic performance and relatively low economic factor. Taking mass fraction as decision variable, Pareto-optimal solutions for models 1, 2, 3 and 4 in pairs of (exergy efficiency (%), LEC ($/kWh)) are (56.71, 0.188), (57.67, 0.192), (57.11, 0.194), and (56.91, 0.192), respectively. Compared with pure working fluids, the mixture working fluids present better exergy efficiency but worse LEC except model 1.

Multi-objective thermo-economic optimization of solar parabolic dish Stirling heat engine with regenerative losses using NSGA-II and decision making

Abstract The proposed work investigates optimal values of various decision variables that simultaneously optimize power output, overall thermal efficiency and thermo-economic function of solar driven Stirling heat engine with regenerative heat losses, conducting thermal bridging losses using evolutionary algorithm based on second version of non-dominated sorting genetic algorithm (NSGA-II) in matrix laboratory (MATLAB) simulink environment. Effects of design parameters as absorber temperature, concentrating ratio, radiative and convective heat transfers are considered for the investigation. Pareto frontier is obtained for triple and dual objectives and the best optimal value is selected through four different decision making techniques viz. Fuzzy Bellman-Zadeh, Shannon’s entropy, LINMAP and TOPSIS. The optimum values of average absorber temperature and concentrating ratio are found to be 1168 K and 1300, respectively. Triple objective evolutionary approach applied to the proposed model gives power output, overall thermal efficiency and thermo-economic function as (38.96 kW, 0.2392, 0.3124) which are 17.09%, 35.09% and 10.74%, respectively lower in comparison with reversible system. With the objective of error investigation, the average and maximum error of the obtained results are reckoned at last.

Parametric investigation and thermo-economic multi-objective optimization of an ammonia–water power/cooling cycle coupled with an HCCI (homogeneous charge compression ignition) engine

A parametric study and multi-objective optimization strategy are performed for a bottoming cycle of a trigeneration system with an HCCI (homogeneous charge compression ignition) engine as prime mover. To assess the influences of decision parameters on the performance and total cost of cycle, a parametric investigation is conducted. Two different multi-objective optimization scenarios are carried out to determine the best design parameters. For the first scenario, the objective functions which are utilized in the optimization study are exergy efficiency and the sum of the unit costs of the system products. The system cost criteria is minimized while the cycle exergy efficiency is maximized using an evolutionary algorithm. Exergy efficiency increases about 16.34% and reduction in the unit costs of the system products is about 10%. However, it is found that cooling capacity of the system is reduced to 83%. For the second scenario, the objective functions are considered to be the sum of the unit costs of the system products, net power generation, and exergy flow rate of refrigeration output. Employing the second scenario improved both power generation and cooling capacity of the system. The increase in exergy efficiency is 5.61%. These are achieved with even a slight reduction in the system cost criteria.

Multi-Objective Thermo-Economic Optimization Strategy for ORCs Applied to Subcritical and Transcritical Cycles for Waste Heat Recovery

Organic Rankine cycles (ORCs) are an established technology to convert waste heat to electricity. Although several commercial implementations exist, there is still considerable potential for thermo-economic optimization. As such, a novel framework for designing optimized ORC systems is proposed based on a multi-objective optimization scheme in combination with financial appraisal in a post-processing step. The suggested methodology provides the flexibility to quickly assess several economic scenarios and this without the need of knowing the complex design procedure. This novel way of optimizing and interpreting results is applied to a waste heat recovery case. Both the transcritical ORC and subcritical ORC are investigated and compared using the suggested optimization strategy.

Comparison between regenerative organic Rankine cycle (RORC) and basic organic Rankine cycle (BORC) based on thermoeconomic multi-objective optimization considering exergy efficiency and levelized energy cost (LEC)

Based on the thermoeconomic multi-objective optimization by using non-dominated sorting genetic algorithm (NSGA-II), considering both thermodynamic performance and economic factors, the thermoeconomic comparison of regenerative organic Rankine cycles (RORC) and basic organic Rankine cycles (BORC) are investigated. The effects of five key parameters including evaporator outlet temperature, condenser temperature, degree of superheat, pinch point temperature difference and degree of supercooling on the exergy efficiency and levelized energy cost (LEC) are examined. Meanwhile, the Pareto frontier solution with bi-objective for maximizing exergy efficiency and minimizing LEC is obtained and compared with the corresponding single-objective solutions. Research demonstrates that there is a significant negative correlation between thermodynamic performance and economic factors. And the optimum exergy efficiency and LEC for the Pareto-optimal solution of the RORC are 55.97% and 0.142$/kWh, respectively, which are 8.1% higher exergy efficiency and 21.1% more LEC than that of the BORC under considered condition. Highest exergy and thermal efficiencies are accompanied with lowest net power output and worst economic performance. Furthermore, taking the net power output into account, detailed investigation on the three-objective optimization for maximizing exergy efficiency, maximizing net power output and minimizing LEC is discussed.

Thermo-economic multi-objective optimization for a solar-dish Brayton system using NSGA-II and decision making

A 100kW regenerative Brayton heat engine driven by the hybrid of fossil fuel and solar energy was considered for optimization based on multiple criteria. A thermodynamic model of such hybrid system was developed so that the power output, thermal efficiency and dimensionless thermo-economic performance with the imperfect performance of parabolic dish solar collector, the external irreversibility of Brayton heat engine and conductive thermal bridging loss could be obtained. Evolutionary algorithm based on NSGA-II (Elitist Non-dominated Sorting Genetic Algorithm) was employed to optimize triple-objective and dual-objective functions, where the temperatures of hot reservoir, cold reservoir and working fluid, the effectiveness of hot-side heat exchanger, cold-side heat exchanger and regenerator were considered as design variables. Using decision makings, including Shannon Entropy, LINMAP and TOPSIS methods, the final optimal solutions were selected from Pareto frontier obtained by NSGA-II. The results show that there exists an appropriate working fluid temperature to cause optimal solution under each given condition. The comparisons of triple-objective and dual-objective optimization with single-objective optimization indicate that multi-objective optimization can yield the more suitable results due to the lower deviation index from the ideal solution. In the analysis of triple-objective optimization, an expected result is obtained that the optimal values of the power out, efficiency and dimensionless thermo-economic performance of solar-dish Brayton system (68.65kW, 0.2331 and 0.3077) are 22.6%, 34.9% and 18.4% respectively less than that of convectional Brayton heat engine. Finally, a range of functional relationship between the optimized objectives in Pareto frontier is fitted to provide more detailed insight into the optimal design of solar-dish Brayton system.

Thermoeconomic multi-objective optimization of a novel biomass-based integrated energy system

Both thermoeconomic modeling and multi-objective optimization studies are undertaken for a novel integrated multigeneration system, containing a biomass combustor, an organic Rankine cycle to produce electricity, a double-effect absorption chiller for cooling, a heat exchanger, a proton exchange membrane electrolyzer to produce hydrogen, a domestic water heater to produce hot water and a reverse osmosis desalination unit to produce fresh water. Energy and exergy analyses and an environmental impact assessment are included. A multi-objective optimization method based on a fast and elitist NSGA-II (non-dominated sorting genetic algorithm) is developed and employed to determine the best design parameters for the system. The two objective functions utilized in the optimization study are the total cost rate of the system, which is the cost associated with fuel, component purchasing and environmental impact, and the system exergy efficiency. The total cost rate of the system is minimized while the cycle exergy efficiency is maximized using an evolutionary algorithm. To provide insight, the Pareto frontier is shown for a multi-objective optimization. In addition, a closed form equation for the relationship between exergy efficiency and total cost rate is derived. A sensitivity analysis is performed to assess the effects of several design parameters on the system total exergy destruction rate, CO2 emission and exergy efficiency.

Thermo-economic multi-objective optimization of solar dish-Stirling engine by implementing evolutionary algorithm

In the recent years, remarkable attention is drawn to Stirling engine due to noticeable advantages, for instance a lot of resources such as biomass, fossil fuels and solar energy can be applied as heat source. Great number of studies are conducted on Stirling engine and finite time thermo-economic is one of them. In the present study, the dimensionless thermo-economic objective function, thermal efficiency and dimensionless power output are optimized for a dish-Stirling system using finite time thermo-economic analysis and NSGA-II algorithm. Optimized answers are chosen from the results using three decision-making methods. Error analysis is done to find out the error through investigation.

A Thermoeconomic Study of Low-Temperature Intercooled-Recuperated Cycles for Pure-Solar Gas-Turbine Applications

A dynamic model of a megawatt-scale low-temperature intercooled-recuperated solar gas-turbine power plant has been developed in order to allow determination of the thermodynamic and economic performance. The model was then used for multi-objective thermoeconomic optimization of both the power plant performance and cost, using a population-based algorithm. In order to examine the trade-offs that must be made and identify ‘optimal’ plant sizes and operating conditions, two conflicting objectives were considered, namely minimum investment costs and maximum annual electricity production. Levelized electricity costs from a 65 MWe power plant operating at 950 °C are predicted to be below 130 USD/MWhe, competitive with other solar thermal power technologies. Optimal plant sizes and configurations have been identified.

Thermoeconomic optimization of a combined-cycle solar tower power plant

A dynamic model of a pure-solar combined-cycle power plant has been developed in order to allow determination of the thermodynamic and economic performance of the plant for a variety of operating conditions and superstructure layouts. The model was then used for multi-objective thermoeconomic optimization of both the power plant performance and cost, using a population-based evolutionary algorithm. In order to examine the trade-offs that must be made, two conflicting objectives will be considered, namely minimal investment costs and minimal levelized electricity costs. It was shown that efficiencies in the region of 18–24% can be achieved, and this for levelized electricity costs in the region of 12–24 UScts/kWhe, depending on the magnitude of the initial investment, making the system competitive with current solar thermal technology.

Multi-objective thermoeconomic optimization of coupling MSF desalination with PWR nuclear power plant through evolutionary algorithms

This paper deals with the application of an evolutionary algorithm to multi-objective thermoeconomic optimization of coupling a multi stage flash desalination (MSF) plant with a pressurized water reactor (PWR) nuclear power plant. The thermodynamic simulation of this initial PWR plant has been performed in a Thermoflex simulator. An Excel add-in called Thermoflex Link has been developed to calculate the exergy of each stream from Thermoflex simulation results. Meanwhile, a computer code has been developed for thermoeconomic and improved combined pinch–exergy analysis in Matlab environment. Both the design configuration (feed water heater structure) and the process variables are optimized simultaneously. The optimization algorithm can choose among several design options included in a superstructure of the feed water heater in dual purpose plant. For the assumptions and simplifications made in this study, a 3000 MW (thermal) PWR power plant such as the Bushehr power plant has been considered. A detailed exergy and exergoeconomic analysis of selected final optimal design identifies the magnitude, location and causes of the thermodynamic inefficiencies. Improved combined pinch and exergy analysis has been applied to display the system information graphically for one to visualize the performance of the system in the initial and final case.

Optimization of the coupling of pressurized water nuclear reactors and multistage flash desalination plant by evolutionary algorithms and thermoeconomic method

Thermodynamic simulation programs are widely used for designing complex thermal systems, but most of them do not incorporate second law optimization techniques. In this study, an efficient optimization strategy is presented, which integrates three optimization techniques with a professional power plant and a cogeneration simulator so as to perform exergoeconomic optimization of complex thermal systems and generate combined pinch and exergy representations. This paper deals with the application of an evolutionary algorithm based on NSGA-II to multi-objective thermoeconomic optimization of coupling desalination plant with pressurized water reactor (PWR). In addition, one-objective thermoeconomic optimization through genetic algorithm and mixed integer non-linear mathematical programming methods has been applied for evaluation of multi-objective optimization. The thermodynamic simulation of this plant has been performed in the THERMOFLEX simulator. An Excel Add-in called THERMOFLEX link has been developed to calculate the exergy of each stream from THERMOFLEX simulation results. In addition, a computer code has been developed for thermoeconomic and improved combined pinch–exergy analysis in the MATLAB environment. Also, multi-objective and one-objective evolutionary algorithm optimization has been performed in MATLAB and one-objective mathematical programming has been performed in LINGO software. Both the design configuration and the process variables are optimized simultaneously. The optimization algorithm can choose among several design options included in a superstructure of the feed water heaters and multistage flash desalination in a dual-purpose plant. For the assumptions and simplifications made in this study, a 3000 MWh PWR power plant similar to Bushehr power plant has been considered. Copyright © 2008 John Wiley & Sons, Ltd.

Thermo-Economic Optimization of a Solid Oxide Fuel Cell, Gas Turbine Hybrid System

Large scale power production benefits from the high efficiency of gas-steam combined cycles. In the lower power range, fuel cells are a good candidate to combine with gas turbines. Such systems can achieve efficiencies exceeding 60%. High-temperature solid oxide fuel cells (SOFC) offer good opportunities for this coupling. In this paper, a systematic method to select a design according to user specifications is presented. The most attractive configurations of this technology coupling are identified using a thermo-economic multi-objective optimization approach. The SOFC model includes detailed computation of losses of the electrodes and thermal management. The system is integrated using pinch based methods. A thermo-economic approach is then used to compute the integrated system performances, size, and cost. This allows to perform the optimization of the system with regard to two objectives: minimize the specific cost and maximize the efficiency. Optimization results prove the existence of designs with costs from 2400$∕kW for a 44% efficiency to 6700$∕kW for a 70% efficiency. Several design options are analyzed regarding, among others, fuel processing, pressure ratio, or turbine inlet temperature. The model of a pressurized SOFC–μGT hybrid cycle combines a state-of-the-art planar SOFC with a high-speed micro-gas turbine sustained by air bearings.