Multi-objective optimization of a hybrid distributed energy system using NSGA-II algorithm

In this paper, a multi-objective optimization model is established for the investment plan and operation management of a hybrid distributed energy system. Considering both economic and environmental benefits, the overall annual cost and emissions of CO₂ equivalents are selected as the objective functions to be minimized. In addition, relevant constraints are included to guarantee that the optimized system is reliable to satisfy the energy demands. To solve the optimization model, the nondominated sorting generic algorithm II (NSGA-II) is employed to derive a set of non-dominated Pareto solutions. The diversity of Pareto solutions is conserved by a crowding distance operator, and the best compromised Pareto solution is determined based on the fuzzy set theory. As an illustrative example, a hotel building is selected for study to verify the effectiveness of the optimization model and the solving algorithm. The results obtained from the numerical study indicate that the NSGA-II results in more diversified Pareto solutions and the fuzzy set theory picks out a better combination of device capacities with reasonable operating strategies.     

Thermodynamic multi-objective optimization of a solar-dish Brayton system based on maximum power output,thermal efficiency and ecological performance

Solar-dish Brayton system driven by the hybrid of fossil fuel and solar energy is characterized by continuously stable operation, simplified hybridization, low system costs and high thermal efficiency. In order to enable the system to operate with its highest capabilities, a thermodynamic multi-objective optimization was performed in this study based on maximum power output, thermal efficiency and ecological performance. A thermodynamic model was developed to obtain the dimensionless power output, thermal efficiency and ecological performance, in which the imperfect performance of parabolic dish solar collector, the external irreversibility of Brayton heat engine and the conductive thermal bridging loss were considered. The combination of NSGA-II algorithm and decision makings was used to realize multi-objective optimization, where the temperatures of absorber, cooling water and working fluid, the effectiveness of hot-side heat exchanger, cold-side heat exchanger and regenerator were considered as optimization variables. Using the decision makings of Shannon Entropy, LINMAP and TOPSIS, the final optimal solutions were chosen from the Pareto frontier obtained by NSGA-II. By comparing the deviation index of each final optimal solution from the ideal solution, it is shown that the multi-objective optimization can lead to a more desirable design compared to the single-objective optimizations, and the final optimal solution selected by TOPSIS decision making presents superior performance. Moreover, the fitted curve between the optimal power output, thermal efficiency and ecological performance derived from Pareto frontier is obtained for better insight into the optimal design of the system. The sensitivity analysis shows that the optimal system performance is strongly dependent on the temperatures of absorber, cooling water and working fluid, and the effectiveness of regenerator. The results of this work offer benefits for related theoretic research and basis for solar energy industry.     

Optimal operation management of fuel cell/wind/photovoltaic power sources connected to distribution networks

In this paper a new multiobjective modified honey bee mating optimization (MHBMO) algorithm is presented to investigate the distribution feeder reconfiguration (DFR) problem considering renewable energy sources (RESs) (photovoltaics, fuel cell and wind energy) connected to the distribution network. The objective functions of the problem to be minimized are the electrical active power losses, the voltage deviations, the total electrical energy costs and the total emissions of RESs and substations. During the optimization process, the proposed algorithm finds a set of non-dominated (Pareto) optimal solutions which are stored in an external memory called repository. Since the objective functions investigated are not the same, a fuzzy clustering algorithm is utilized to handle the size of the repository in the specified limits. Moreover, a fuzzy-based decision maker is adopted to select the ‘best’ compromised solution among the non-dominated optimal solutions of multiobjective optimization problem. In order to see the feasibility and effectiveness of the proposed algorithm, two standard distribution test systems are used as case studies.     

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.     

Single and Multi-Objective Optimization of a Cogeneration System Using Hybrid Algorithms

Current design and operation of energy systems must consider the efficient utilization of energy resources, reduced environmental harms, and sustainable development. Many techniques for energy systems analysis and optimization have thus been developed worldwide. To evaluate different methodologies, the benchmark CGAM problem was proposed, which consisted of the optimization of a cogeneration system with explicit physical, thermodynamic, and economic models. The original CGAM problem was formulated as a single objective optimization problem, where the objective function was the sum of the purchased equipment, maintenance and operation, and fuel consumption costs. However, in real-life applications, costs must be analyzed individually: for example, one might increase equipment costs but save in fuel consumption for the entire system life. In this paper, single- and multi-objective hybrid optimizations of the CGAM system are performed. A hybrid optimization algorithm combines the strengths of deterministic and heuristic methods. Usually, it employs a heuristic method to locate a region where the global extreme point lies, and then switches to a deterministic method to get to the exact point faster. The objective functions are the fuel consumption cost rate and the total capital investment. Thus, a Pareto front is obtained for all non-dominated solutions, from which the final decision can be made considering appropriate scenarios.     

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.     

A practical multi-objective PSO algorithm for optimal operation management of distribution network with regard to fuel cell power plants

In this paper a novel Multi-objective fuzzy self adaptive hybrid particle swarm optimization (MFSAHPSO) evolutionary algorithm to solve the Multi-objective optimal operation management (MOOM) is presented. The purposes of the MOOM problem are to decrease the total electrical energy losses, the total electrical energy cost and the total pollutant emission produced by fuel cells and substation bus. Conventional algorithms used to solve the multi-objective optimization problems convert the multiple objectives into a single objective, using a vector of the user-predefined weights. In this conversion several deficiencies can be detected. For instance, the optimal solution of the algorithms depends greatly on the values of the weights and also some of the information may be lost in the conversion process and so this strategy is not expected to provide a robust solution. This paper presents a new MFSAHPSO algorithm for the MOOM problem. The proposed algorithm maintains a finite-sized repository of non-dominated solutions which gets iteratively updated in the presence of new solutions. Since the objective functions are not the same, a fuzzy clustering technique is used to control the size of the repository, within the limits. The proposed algorithm is tested on a distribution test feeder and the results demonstrate the capabilities of the proposed approach, to generate true and well-distributed Pareto-optimal non-dominated solutions of the MOOM problem.     

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.     

Multi-objective optimization of the hybrid wind/solar/fuel cell distributed generation system using Hammersley Sequence Sampling

As the development of China's economy, environmental problems in China become more and more serious. Solar energy and wind energy are considered as ones of the best choices to solve the environmental problems in China and the hybrid wind/solar distributed generation (DG) system has received increasing attention recently. However, the instability and intermittency of the wind and solar energy throw a huge challenge on designing of the hybrid system. In order to ensure the continuous and stable power supply, optimal unit sizing of the hybrid wind/solar DG system should be taken into consideration in the design of the hybrid system. This paper establishes a multi-objective optimization framework based on cost, electricity efficiency and energy supply reliability models of the hybrid DG system, which is composed of wind, solar and fuel cell generation systems. Detailed models of each unit for the hybrid wind/solar/fuel cell system were established. Advanced ε-constraints method based on Hammersley Sequence Sampling was employed in the multi-objective optimization of the hybrid DG system. The approximate Pareto surface of the multi-objective optimization problems with a range of possible design solutions and a logical procedure for searching the global optimum solution for decision makers were presented. In this way, this work provided an efficient method for decision makers in the design of the hybrid wind/solar/fuel cell system.     

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.     

Thermodynamic and thermoeconomic optimization of a cooling tower-assisted ground source heat pump

Thermodynamic and thermoeconomic optimization of a cooling tower-assisted ground source heat pump (GSHP) in a multi-objective optimization process is performed. A thermodynamic model based on energy and exergy analyses is presented, and an economic model of the hybrid GSHP (HGSHP) system is developed according to the total revenue requirement (TRR) method. The proposed hybrid cooling tower-assisted GSHP system, including 12 decision variables, is considered for optimization. Three optimization scenarios, including thermodynamic single objective, thermoeconomic single objective, and multi-objective optimizations, are performed. In multi-objective optimization, both thermodynamic and thermoeconomic objectives are simultaneously considered. An optimization process is performed using the genetic algorithm (GA). In the case of multi-objective optimization, an example of a decision-making process for selection of the final solution from the Pareto optimal frontier is presented. The results obtained using the various optimization approaches are compared and discussed. Further, the sensitivity of optimized systems to the interest rate, the annual number of operating hours in cooling mode, the electricity price, and the water price are studied in detail. It is shown that the thermodynamic optimization is focused on provision for the limited source of energy, whereas the thermoeconomic optimization only focuses on monetary resources. In contrast, the multi-objective optimization considers both energy and monetary. Further, it is found that thermodynamic optimization is economical when the operating time in cooling mode is long and/or the electricity price is high, and water prices variations have no marked impact on the total product cost.     

Design and techno-economical optimization for stand-alone hybrid power systems with multi-objective evolutionary algorithms

The optimal design of the hybrid energy system can significantly improve the economical and technical performance of power supply. However, the problem is formidable because of the uncertain renewable energy supplies, the uncertain load demand, the nonlinear characteristics of some components, and the conflicting techno-economical objectives. In this work, the optimal design of the hybrid energy system has been formulated as a multi-objective optimization problem. We optimize the techno-economical performance of the hybrid energy system and analyse the trade-offs between the multi-objectives using multi-objective genetic algorithms. The proposed method is tested on the widely researched hybrid PV-wind power system design problem. The optimization seeks the compromise system configurations with reference to three incommensurable techno-economical criteria, and uses an hourly time-step simulation procedure to determine the design criteria with the weather resources and the load demand for one reference year. The well-known efficient multi-objective genetic algorithm, called NGAS-II (the fast elitist non-dominated sorting genetic algorithm), is applied on this problem. A hybrid PV-wind power system has been designed with this method and several methods in the literature. The numerical results demonstrate that the proposed method is superior to the other methods. It can handle the optimal design of the hybrid energy system effectively and facilitate the designer with a range of the design solutions and the trade-off information. For this particular application, the hybrid PV-wind power system using more solar panels achieves better technical performance while the one using more wind power is more economical. Copyright © 2006 John Wiley & Sons, Ltd.     

Intelligent optimization of renewable resource mixes incorporating the effect of fuel risk,fuel cost and CO2 emission

Power system planning is a capital intensive investment-decision problem. The majority of the conventional planning conducted since the last half a century has been based on the least cost approach, keeping in view the optimization of cost and reliability of power supply. Recently, renewable energy sources have found a niche in power system planning owing to concerns arising from fast depletion of fossil fuels, fuel price volatility as well as global climatic changes. Thus, power system planning is under-going a paradigm shift to incorporate such recent technologies. This paper assesses the impact of renewable sources using the portfolio theory to incorporate the effects of fuel price volatility as well as CO₂ emissions. An optimization framework using a robust multi-objective evolutionary algorithm, namely NSGA-II, is developed to obtain Pareto optimal solutions. The performance of the proposed approach is assessed and illustrated using the Indian power system considering real-time design practices. The case study for Indian power system validates the efficacy of the proposed methodology as developing countries are also increasing the investment in green energy to increase awareness about clean energy technologies.     

Thermal–economic–environmental analysis and multi-objective optimization of an internal-reforming solid oxide fuel cell–gas turbine hybrid system

In this article, an internal-reforming solid oxide fuel cell–gas turbine (IRSOFC–GT) hybrid system is modeled and analyzed from thermal (energy and exergy), economic, and environmental points of view. The model is validated using available data in the literature. Utilizing the genetic algorithm optimization technique, multi-objective optimization of modeled system is carried out and the optimal values of system design parameters are obtained. In the multi-objective optimization procedure, the exergy efficiency and the total cost rate of the system (including the capital and maintenance costs, operational cost (fuel cost), and social cost of air pollution for CO, NO_x, and CO₂) are considered as objective functions. A sensitivity analysis is also performed in order to study the effect of variations of the fuel unit cost on the Pareto optimal solutions and their corresponding design parameters. The optimization results indicate that the final optimum design chosen from the Pareto front results in exergy efficiency of 65.60% while it leads to total cost of 3.28 million US$ year⁻¹. It is also demonstrated that the payback time of the chosen design is 6.14 years.     

Evolutionary algorithms for multi-objective energetic and economic optimization in thermal system design

Thermoeconomic analyses in thermal system design are always focused on the economic objective. However, knowledge of only the economic minimum may not be sufficient in the decision making process, since solutions with a higher thermodynamic efficiency, in spite of small increases in total costs, may result in much more interesting designs due to changes in energy market prices or in energy policies. This paper suggests how to perform a multi-objective optimization in order to find solutions that simultaneously satisfy exergetic and economic objectives. This corresponds to a search for the set of Pareto optimal solutions with respect to the two competing objectives. The optimization process is carried out by an evolutionary algorithm, that features a new diversity preserving mechanism using as a test case the well-known CGAM problem.     

Genetic fuzzy rule extraction for optimised sizing and control of hybrid renewable energy hydrogen systems

A major challenge related to the design of a hybrid renewable energy hydrogen system is which energy sources to include and at what capacity, for regionally different potentials of renewable energy and hydrogen demand. In addition, once the plant is in operation, control variables need to be optimised. The problem resorts to an area of multiple criteria decision making referred to as multi-objective optimisation. The results obtained from these type of algorithms include not only one optimal solution, but a set of optimal solutions (Pareto front) thereby offering a system designer several options. This set of solutions can be hard to interpret and a method is needed to automatically extract useful design and control strategies from this information. A methodology that is quite successful in deriving human interpretable rules from this type of information is genetic fuzzy systems. In this work a k-means clustering algorithm is used to generate membership functions and a fuzzy rule-base is trained by means of a genetic algorithm. The genetic fuzzy system obtained is reduced by determining the minimum number of rules followed by a membership function reduction process. The reduced genetic fuzzy system is deemed more interpretable. Geographic weather data from three different sites are used to generate data to be used in the genetic fuzzy method. Results show that the technique provides valuable information that can be used for the design of such hybrid renewable energy hydrogen production systems.     

Multi-objective optimization of shell and tube heat exchangers

The effectiveness and cost are two important parameters in heat exchanger design. The total cost includes the capital investment for equipment (heat exchanger surface area) and operating cost (for energy expenditures related to pumping). Tube arrangement, tube diameter, tube pitch ratio, tube length, tube number, baffle spacing ratio as well as baffle cut ratio were considered as seven design parameters. For optimal design of a shell and tube heat exchanger, it was first thermally modeled using ε–NTU method while Bell–Delaware procedure was applied to estimate its shell side heat transfer coefficient and pressure drop. Fast and elitist non-dominated sorting genetic algorithm (NSGA-II) with continuous and discrete variables were applied to obtain the maximum effectiveness (heat recovery) and the minimum total cost as two objective functions. The results of optimal designs were a set of multiple optimum solutions, called ‘Pareto optimal solutions’. The sensitivity analysis of change in optimum effectiveness and total cost with change in design parameters of the shell and tube heat exchanger was also performed and the results are reported.     

Multi-objective design optimization of topology and performance of branching networks of cooling passages

The objective of this study was to develop an automatic, self-sufficient, preliminary design algorithm for optimization of topologies of branching networks of internal cooling passages. Optimization with four levels of fractal branching channel networks was tested. The number of branches per level was optimized in order to minimize coolant mass flow rate, total pressure drop, and maximize total heat removed. The software package includes a random branches generator, a quasi 1-D thermo-fluid analysis code, and a multi-objective hybrid optimizer. The heat transfer/flow-field analysis software has been verified against a similar analysis code used by Pratt & Whitney Company. The hybrid multi-objective optimization code was verified against classical test cases involving multiple objectives. In this work the total number of Pareto-optimal designs was 100. After finding the Pareto optimized configurations, the user has to decide which optimized cooling network configuration is the best for the desired application. It was demonstrated that this can be accomplished by utilizing Pareto-optimal solutions to create a curve representing pumping power vs. total heat removed and by observing which designs provide favorable break-even energy transfer.     

Modeling and multi-objective optimization of a stand-alone photovoltaic-wind turbine-hydrogen-battery hybrid energy system based on hysteresis band

Hybrid renewable energy system (HRES) can provide power without emission for off-grid areas. Due to intermittency of renewable energy, energy storage system (ESS) is essential for reliable power supply, while its cost is still relatively high. Appropriate power management strategy (PMS) can help to delay the degradation of energy storage devices and reduce the system cost. In this study, power management strategy and configuration optimization of the system are focused and the study includes three main contributions. First, mathematical models of the system, including photovoltaics (PVs), wind turbines (WTs), batteries, fuel cells (FCs), electrolyzers (ELZs), and hydrogen tanks are developed. The degradation of fuel cells and electrolyzers is considered in the modeling process. Second, power management strategy considering hysteresis band is employed to control energy flow to delay fuel cell and electrolyzer degradation. Third, a multi-objective optimization function including the system net annual value (NAV), loss of power supply probability (LPSP) and excess energy (E_excess) is established. Non-dominating Sorting Genetic Algorithm II (NSGA-II) is used to solve objective function. The results demonstrate that using hysteresis band help improve the system performance and reduce the cost. In addition, by setting the goal of excess energy, system reliability is well preserved with a LPSP as low as 0.92%. Compared with other optimization algorithms such as MOEA/D, NSGA-II has a smaller SI value of 422.10 and a larger DI value of 830.78, therefore the Pareto solution obtained by NSGA-II has a more uniform distribution and larger coverage.     

基于多目标决策分析的水资源承载力研究

水资源承载力具有自然和社会双重属性,为描述水资源承载力与社会经济及生态环境之间的相互作用,构建了以水资源所能承载的国民生产总值最大、人口最多、污染物排放量最小为目标的水资源承载力多目标决策分析模型。同时,将快速非支配排序遗传算法(NSGA-Ⅱ)应用于水资源承载力多目标决策分析模型的求解,得到多目标最优Pareto前沿。将模型及算法应用于邯郸东部平原区水资源承载力评估,有效分析了该地区丰、平、枯水平年能承载的人口、经济、污染物排放量情况,得出的最优Pareto前沿可以辅助该地区规划水资源可承载的经济社会发展指标,具有重要的现实意义。