Parametric analysis and optimization of 660 MW supercritical power plant
660 兆瓦超临界发电厂的参数分析与优化

Particle swarm optimization
粒子群优化

Fossil fuel-fired supercritical plant
化石燃料超临界发电厂

Exergy efficiency 能效

Plant efficiency 工厂效率

Cost of electricity 电费

The thermal power plant involves various complex simultaneous competing objectives. Multi-objective optimization follows an effective method for optimizing these objectives. The analysis of thermal power plants is not only limited to thermodynamic analysis. It involves analysis based on economic, combined economic, and thermodynamic analysis, environmental analysis, and combined environmental and thermodynamic analysis. More than one objective is parallel studied to find optimum values of the variables. Researchers worldwide are using different optimization techniques inspired by the behavior of animals, naturally occurring phenomena, to find the alternate tradeoff solution. Ameri et al. [1] performed multi-objective optimization on the natural gas-fired combined cycle power plant. The genetic algorithm technique maximizes exergy efficiency and minimizes electricity costs. The choice
火力发电厂同时涉及各种复杂的竞争目标。多目标优化是优化这些目标的有效方法。火力发电厂的分析不仅限于热力学分析。它包括基于经济、综合经济和热力学分析、环境分析以及综合环境和热力学分析的分析。为了找到变量的最佳值，需要同时研究多个目标。世界各地的研究人员从动物行为和自然现象中汲取灵感，使用不同的优化技术来寻找替代的折衷解决方案。Ameri 等人[1]对天然气联合循环发电厂进行了多目标优化。遗传算法技术最大限度地提高了放能效率，并最小化了电力成本。选择

of objective function plays a key role in comparing a Pareto curve obtained using natural gas and liquid fuel. Roque et al. [2] carried out multi-objective optimization by minimizing economic and environmental objectives. The biased random key-based GA technique was proposed and proven to be better than other approaches from the diversity performance point of view. The tradeoff curves and CPU time were compared. Rahat et al. [3] proposed a new multi-objective optimization technique based on the Gaussian process and minimized nitrogen and oxide, maximizing the efficiency of a coal-fired power plant. Ahmadi et al. [4] optimized an integrated plant by minimizing pollutants, maximizing exergy efficiency, and minimizing the total cost rate. The Genetic algorithm was utilized, and it found decrement in environmental impacts can be achieved by selecting proper components and a low fuel flow rate.
目标函数在比较使用天然气和液体燃料得到的帕累托曲线中起着关键作用。Roque 等人[2]通过最小化经济和环境目标进行了多目标优化。他们提出了基于偏置随机密钥的 GA 技术，并证明从多样性性能的角度来看，该技术优于其他方法。他们还比较了权衡曲线和 CPU 时间。Rahat 等人[3]提出了一种基于高斯过程的新的多目标优化技术，并最小化了氮氧化物，最大化了 燃煤电厂的效率。Ahmadi 等人[4]通过最小化 污染物、最大化能效和最小化总成本率来优化综合电厂。他们利用遗传算法，发现通过选择适当的组件和较低的燃料流量，可以减少对环境的影响。

Naserabad et al. [5] implemented GA for multi-objective optimization where overall exergy efficiency and power output maximize objectives, and electricity cost minimizes the objective function. As per the study's outcomes, the heat recovery steam generator was recommended to install in the existing power plant. Zhou et al. [6] applied a combined artificial neural network and genetic algorithm to optimize multi-objective boiler efficiency and minimize NOx emission concentration as objective functions. The ability of combined ANN and GA techniques is proven better based on lower computation time and online integration with the existing system. Shamoushaki et al. [7] complicated a genetic algorithm for optimizing gas-fueled power plants by lowering the cost of electricity and maximizing energy efficiency. The study also covers a variation of the increase of fuel cell stack temperature on the exergy efficiency of the cycle, showing a increment in gas turbines and a decrement in fuel cell power. Ahmadi and Dincer [8] performed multi-objective optimization of a gas turbine power plant using a nondominated sorting genetic algorithm. Maximizing exergy efficiency, minimizing the cost rate of the product, and environmental impact are objective functions to optimize. Baghsheikhi and Sayyaadi [9] performed optimization using a fuzzy interface system to study the effect of variation of power load on profit for an exergoeconomic analysis of a 250 MW subcritical power plant. Miar Naeimi et al. [10] performed optimization with objective functions such as the total cost rate of the overall system, exergetic efficiency, and an environmental impact rate. Di Somma et al. [11] aimed to reduce yearly electricity costs and improve exergy efficiency. The study result gave a reduction in the configuration compared with the existing thermal power section. Opris et al. [12] resulted in the effect of the presence of bled steam by applying multi-objective optimization of overall energetic efficiency and investment. The inclusion of pre-heaters resulted in an improvement in overall efficiency and decrement in overall investment. Harkin et al.
Naserabad 等人[5] 利用 GA 实现了多目标优化，其中总体能效和功率输出最大化了目标，而电力成本最小化了目标函数。根据研究结果，建议在现有发电厂安装热回收蒸汽发生器。Zhou 等人[6]采用人工神经网络和遗传算法相结合的方法优化多目标锅炉效率，并将氮氧化物排放浓度最小化作为目标函数。基于较低的计算时间和与现有系统的在线集成，证明人工神经网络和遗传算法相结合的技术能力更强。Shamoushaki 等人[7] 将遗传算法复杂化，通过降低电力成本和最大化能源效率来优化燃气发电厂。该研究还涉及燃料电池堆温度的升高对循环能效的影响，结果表明燃气轮机的能效提高 ，而燃料电池的能效降低 。Ahmadi 和 Dincer [8] 使用非支配排序遗传算法对燃气轮机发电厂进行了多目标优化。最大化能效、最小化产品成本率和环境影响是优化的目标函数。Baghsheikhi 和 Sayyaadi [9] 使用模糊界面系统进行了优化，研究了电力负荷变化对 250 兆瓦亚临界发电厂利润的影响，并对其进行了经济效益分析。Miar Naeimi 等人[10]利用整个系统的总成本率、发电效率和环境影响率等目标函数进行了优化。Di Somma 等人[11]的目标是降低每年的电力成本并提高放能效率。研究结果表明，与现有的火电部分相比，配置减少了 。Opris 等人[12]通过对整体能效和投资进行多目标优化，得出了排出蒸汽的效果。预热器的加入提高了整体效率，降低了整体投资。Harkin 等人
[13] utilized the multi-objective genetic algorithm technique to optimize the power output, capture rate, and cost of electricity. The major outcome of the reduction in the cost of electricity of is achieved from optimization. The variation of flue gas temperature on the differential cost of electricity was studied in the research. Urech et al. [14] The Pareto frontier curve of capture rate and overall efficiency was studied by performing multi-objective optimization using a potassium carbonate capture process integrated with the coal-fired power plant. Dong et al. [15] minimized the economic cost rate per unit exergy of fuel consumed by using the GA. Ameri et al. [16] optimized values of excess air concentration by performing multi-objective optimization with cost function from economic analysis, exergy efficiency, and emissions. Wang et al. [17] modeled the evolution algorithm with the deterministic approach to synthesize the thermal power plant with maximizing thermal efficiency as the main objective. Kler et al. [18] developed an optimization approach to maximize the overall efficiency and minimize the initial investment of a supercritical power plant. The validation was performed by comparing the previous literature result with a new approach. H. Barzegar [19] performed multi-objective optimization of a gas-fueled power plant using GA with exergy efficiency, emission concentration, and cost rate as multiple objectives. The relations were developed between three objective functions from the Pareto frontier to find an optimal solution. Wang et al. [20] developed differential evolution multi objectives optimization techniques to maximize first-law efficiency and minimize the total cost rate of electricity of a coal-fired 1100 MW capacity thermal power plant. The realistic view was considered to compare the results from multi-objective optimization. The results show a increase in first-law efficiency and a decrement in the cost of electricity compared with actual available practical data. Using three approaches, Kowalczyk et al. [21] optimize a single objective function of supercritical power plant energetic efficiency. The Rosenbrock method was proven to be a better approach for optimizing a single objective function with multiple independent variables.
[13] 利用多目标遗传算法技术优化了输出功率、 捕获率和电力成本。优化的主要结果是降低了 的电力成本。研究中研究了烟气温度对差别电费的影响。Urech 等人[14]利用与燃煤电厂集成的碳酸钾捕集工艺，通过多目标优化研究了 捕集率和总体效率的帕累托前沿曲线。Dong等人[15]利用GA最大限度地降低了单位燃料能耗的经济成本率。Ameri 等人[16]通过对经济分析成本函数、放能效率和 排放量进行多目标优化，优化了过量空气浓度值。Wang 等人[17]用确定性方法建立了进化算法模型，以热效率最大化为主要目标合成火力发电厂。Kler 等人[18] 开发了一种优化方法，以实现 超临界发电厂总体效率最大化和初始投资最小化。通过将以前的文献结果与新方法进行比较，进行了验证。H. Barzegar [19]使用 GA 对气体燃料发电厂进行了多目标优化，将放能效、 排放浓度和成本率作为多目标。在帕累托前沿的三个目标函数之间建立了关系，从而找到了最优解。Wang 等人[20]开发了微分进化多目标优化技术，以实现燃煤 1100 MW 容量火力发电厂的嫡系效率最大化和总电费率最小化。他们从现实角度出发，比较了多目标优化的结果。结果显示，与现有实际数据相比，一律效率提高了 ，电力成本降低了 。Kowalczyk 等人 [21] 使用三种方法优化了超临界发电厂能效的单一目标函数。事实证明，Rosenbrock 方法是优化具有多个独立变量的单一目标函数的更好方法。

Lopez et al. [22] implemented PSO to optimize nonlinear function concerning improving biomass power plant profitability index. Alrashidi et al. [23] reviewed the application of PSO optimization with fuel cost and emission produced from the power plant as multiple objective functions. Sayyaadi et al. [24] Performed multi-objective optimization with particle swarm optimization of a cogeneration system in which objective functions are taken to maximize second law efficiency and minimize cost and environmental impact rates. Baghernejad and Yaghoubi [25] used particle swarm optimization techniques to minimize the hydro and solar power plants' electricity and exergy destruction costs. The SPECO approach was implemented for exerting economic
Lopez 等人[22]采用 PSO 对有关提高生物质发电厂盈利指数的非线性函数进行了优化。Alrashidi 等人[23] 综述了以燃料成本和发电厂产生的排放为多目标函数的 PSO 优化应用。Sayyaadi 等人[24] 利用粒子群优化技术对热电联产系统进行了多目标优化，其目标函数为第二定律效率最大化、成本和环境影响率最小化。Baghernejad 和 Yaghoubi [25] 使用粒子群优化技术使水力和太阳能发电厂的电力和放能破坏成本最小化。他们采用了 SPECO 方法，以发挥经济效益。

Fig. 1. The layout of a 660 MW power plant.
图 1.660 兆瓦发电厂的布局。

analysis. Groniewsky [26] implemented the PSO optimization technique and successfully reduced the complete system's capital cost at the expense of overall second-law efficiency. Biao et al. and Anetor et al. [27,28] built and tested a mutation-based PSO algorithm to optimize the operation cost involved in the thermal power plant. Zhang et al. [29] review particle swarm optimization's application in the interdisciplinary engineering field and proven better optimization techniques with multiple objectives. Mahmoodabadi et al. [30] revealed that the exergy efficiency increase with the increment in the total cost rate by performing multi-objective optimization with the PSO and GA technique. Kheshti and Ding [31] revealed optimizing the value of the fuel cost and power output by fulfilling the condition of variation in load demand. Elahifar et al. [32] Utilized firefly optimization to find the second law efficiency of the thermal power plant and the result compared with results obtained from other metaheuristic approaches. The researchers from India optimized the availability field for generators, feed-water systems, and coal handling systems of subcritical power generation using PSO and Simulated Annealing to schedule advance maintenance of the mentioned systems [33-35]. Panahizadeh et al. [36] optimized the exergy coefficient of performance and annual operational costing using particle swarm optimization of a chiller plant. They claimed a reduction in yearly operation and maintenance costs.
分析。Groniewsky [26] 采用 PSO 优化技术，以牺牲整体秒速快三精准人工下注计划效率为代价，成功降低了整个系统的资本成本。Biao 等人和 Anetor 等人[27,28] 建立并测试了一种基于突变的 PSO 算法，用于优化火力发电厂的运营成本。Zhang 等人[29] 综述了粒子群优化在跨学科工程领域的应用，并证明了具有多个目标的更好优化技术。Mahmoodabadi 等人[30] 发现，通过使用 PSO 和 GA 技术进行多目标优化，放能效率随着总成本率的增加而提高。Kheshti 和 Ding [31] 发现，通过满足负载需求变化的条件，可以优化燃料成本值和功率输出。Elahifar 等人[32] 利用萤火虫优化找到了火力发电厂的第二定律效率，并将结果与其他元启发式方法得出的结果进行了比较。印度的研究人员利用 PSO 和模拟退火优化了亚临界发电的发电机、给水系统和煤处理系统的可用性领域，以提前安排上述系统的维护[33-35]。Panahizadeh 等人[36] 利用粒子群优化技术优化了冷水机组的能效系数和年度运营成本。他们声称每年的运行和维护成本降低了 。

The previous literature concluded limited work was done on the multi-objective optimization of a coal-fired power plant working above a critical point using PSO. The common objectives, exergy efficiency, and electricity cost were taken for optimization in previously published work using Genetic Algorithm. The article's primary contribution is its emphasis on optimizing multiple parameters that impact the effectiveness and efficiency of a supercritical power plant, which distinguishes it in terms of novelty and originality. Numerous investigations have been conducted on supercritical power plants; however, this manuscript presents an exhaustive examination of the influence of diverse operational parameters on the comprehensive efficacy of the facility. The article thoroughly examines a supercritical power plant through a comprehensive parametric analysis, highlighting its novelty as a relatively recent technological development. This research offers valuable insights into a plant's most favorable operational parameters.
以往的文献认为，使用 PSO 对临界点以上的燃煤发电厂进行多目标优化的工作十分有限。在之前发表的工作中，利用遗传算法对共同目标、放能效率和电力成本进行了优化。文章的主要贡献在于强调优化影响超临界发电厂效益和效率的多个参数，这使其在新颖性和原创性方面脱颖而出。关于超临界发电厂的研究不胜枚举，但这篇手稿对各种运行参数对设备综合效率的影响进行了详尽的研究。文章通过全面的参数分析，对 超临界发电厂进行了深入研究，突出了其作为相对较新的技术发展的新颖性。这项研究为了解电厂最有利的运行参数提供了宝贵的见解。

Table 1 表 1

Operating parameters of power plant.
发电厂的运行参数。

Additionally, it underscores the essential parameters that require close monitoring and optimization to attain optimal efficiency. In addition, the research employs sophisticated optimization methodologies, including the genetic algorithm and particle swarm optimization, to ascertain the most favorable operational parameters for the power generation facility. The methodology employed in this study facilitates the identification of the optimal parameter combination that can yield the highest level of efficacy, which represents a distinctive feature of this research. The present research deals with multi-objectives optimization of the coal-fired 660 MW capacity with energy efficiency, exergy efficiency, and coal cost as objectives function. The power output, the calorific value of coal, and the amount of coal consumed can be independent variables [37-39]. The semi-empirical thermodynamic and economic analysis module was integrated with PSO MATLAB code to find the optimal solution. The outcome of the present study will give an optimal solution for varying load conditions and varying calorific values of coal. An attempt is made to optimize three objective functions with varying load conditions and calorific values of coal. The uniqueness of the current work consists of integrating a semi-empirical energy, exergy, and economic model with the PSO algorithm to determine the optimum plant, exergy efficiency, and cost of electricity.
此外，它还强调了需要密切监测和优化的基本参数，以达到最佳效率。此外，研究还采用了复杂的优化方法，包括遗传算法和粒子群优化，以确定发电设施最有利的运行参数。本研究采用的方法有助于确定能产生最高功效的最佳参数组合，这是本研究的一个显著特点。本研究涉及以能源效率、放能效率和煤炭成本为目标函数的 660 兆瓦燃煤发电能力的多目标优化。输出功率、煤的热值和耗煤量可作为自变量 [37-39]。半经验热力学和经济分析模块与 PSO MATLAB 代码相结合，以找到最优解。本研究的结果将给出不同负荷条件和不同煤炭热值下的最优解。本研究尝试在不同负荷条件和煤炭热值下优化三个目标函数。当前工作的独特之处在于将半经验能源、放能和经济模型与 PSO 算法相结合，以确定最佳发电厂、放能效率和发电成本。

The eastern region's coal-fired supercritical thermal power plant has been selected for the present study. The layout of the 660 MW plant is represented in Fig. 1. Power system is distributed in two main sections: high-pressure and low-pressure. The high-pressure side had equipment: Once through the boiler, high-pressure turbine set, intermediate pressure turbine set, high-pressure water feed heaters set, and boiler feed pump. The remaining equipment belongs to the low-pressure side. The steam cycle starts from steam generation into the once-through boiler (SG) with a forced boiling phenomenon. The superheated steam is then introduced in a series of turbine sets of High-pressure turbine (HPTu), Intermediate pressure turbine (IPTu), and Low-pressure turbine (LPTu). Steam quality is maintained by introducing a heater amongst intermediate and high-pressure turbines. The mass losses at different sections are collected and channeled in the condenser. The steam extracted from the turbine set at points , and 9 has been used to preheat the feed water. Optimizing the overall system will indirectly result in the optimization of all independent variables. The pressures and temperatures at the inlet of high, intermediate, and low-pressure turbines are indirect variables that will be optimized. The designed parameters are represented in Table 1.
本研究选择了东部地区的燃煤超临界火力发电厂。660 兆瓦发电厂的布局如图 1 所示。电力系统分布在两个主要部分：高压和低压。高压侧有设备：一次通过锅炉、高压汽轮机组、中压汽轮机组、高压给水加热器组和锅炉给水泵。其余设备属于低压侧。蒸汽循环从蒸汽产生开始，进入带有强制沸腾现象的直流锅炉（SG）。然后，过热蒸汽被引入一系列汽轮机组，包括高压汽轮机 (HPTu)、中压汽轮机 (IPTu) 和低压汽轮机 (LPTu)。通过在中压汽轮机和高压汽轮机之间引入加热器来保持蒸汽质量。不同部分的质量损失被收集并导入冷凝器。从汽轮机组 点和 9 点抽取的蒸汽被用来预热给水。整体系统的优化将间接导致所有独立变量的优化。高压、中压和低压涡轮机入口处的压力和温度是需要优化的间接变量。设计参数见表 1。

Researchers worldwide have performed energy and exergy analyses by mass balance and energy balance equation of all equipment in the fossil-fueled plant [40,41]. The outcome of these analyses is identifying the equipment with low energy and exergetic efficiency. The first thermodynamic law of efficiency always indicates the quantity of energy involved, while the second thermodynamic law indicates the quality of energy involved. The present study dealt with multi-objective optimization by taking energy and exergetic efficiency as separate objectives. In this study, a method for measuring indirect losses was employed to formulate the thermodynamic model of the steam generator [42]. The utilization of the indirect method is favored due to its ability to minimize the impact of measurement errors on the operational efficiency of the steam generator. The steam generator's efficiency is estimated by considering and minimizing the impact of other losses. The primary objective of the operational data was to identify and quantify the different types of losses. In instances of a Separated Underexpanded Two-Phase (SUPP) flow, no distinct region exists between the two phases of the fluid in operation. In a SUPP, the tube structures are utilized to replace the drum structures of the boiler. The mass and energy balance equations for all components are considered from the available literature [42].
世界各地的研究人员已通过化石燃料发电厂所有设备的质量平衡和能量平衡方程进行了能量和放能分析 [40,41]。这些分析的结果是找出能量和放能效率较低的设备。效率的第一热力学定律总是表示能量的数量，而第二热力学定律则表示能量的质量。本研究将能源效率和能效作为单独的目标，处理多目标优化问题。本研究采用了一种测量间接损失的方法来建立蒸汽发生器的热力学模型[42]。由于间接测量法能够最大限度地减少测量误差对蒸汽发生器运行效率的影响，因此受到青睐。蒸汽发生器的效率是通过考虑并尽量减少其他损失的影响来估算的。运行数据的主要目的是识别和量化不同类型的损失。在分离式低膨胀两相流（SUPP）的情况下，运行中的两相流体之间不存在明显的区域。在低膨胀两相流中，管道结构被用来取代锅炉的汽包结构。所有组件的质量和能量平衡方程均根据现有文献[42]进行考虑。

The current study focuses on the exergy forms of distinct components. Physical exergy and chemical exergy are the two types of exergy. Specific physical exergy is expressed in enthalpy, entropy at present temperature characteristics, and pressure in relation to the surrounding environment's standard temperature and pressure. It is said as follows in equation (1):
目前的研究侧重于不同成分的放能形式。物理放能和化学放能是两种类型的放能。具体的物理放能用焓和熵来表示，在当前的温度特性和压力下，焓和熵与周围环境的标准温度和压力有关。其计算公式为 (1)：

and are the normal reference conditions for exergy analysis [38]. The chemical exergy connected with coal having a fraction of hydrogen(h), carbon(c), nitrogen(n) and oxygen(o) is calculated from Refs. [38,43] relation. Coal's moisture and sulfur contents were considered while calculating the chemical exergy. Following is an expression of the relationship:
和 是放能分析的常规参考条件[38]。煤炭中氢（h）、碳（c）、氮（n）和氧（o）的化学能是根据参考文献[38,43]的关系计算得出的。计算化学能时考虑了煤的水分和硫含量。以下是该关系的表达式：

The specific enthalpy and specific entropy at a diverse stream for estimating physical exergy is deliberate as per [44] with the coefficient to ):
用于估算物理放热量的不同流体的比焓和比熵是按照 [44] 的方法计算的，系数为 至 )：

Table 2 表 2

Economical parameters of points in 660 MW power cycle-
660 兆瓦电力循环中各点的经济参数-- 660 兆瓦电力循环中各点的经济参数

The application of exergy analysis is utilized for ascertaining various components exergetic efficiency. The exergy flow expressions for fuel and products are adopted from available literature [37]. The expression for exergetic efficiency is as follows:
在确定各部件的能效时，采用了放能分析法。燃料和产品的能流表达式来自现有文献[37]。能效表达式如下

The cost of electricity is one of the objectives of the economic study of the thermal power plant in previous literature [41,45-48]. The present study dealt with the price of coal concerning different grades of coal. The various grades of coal come with different calorific values. The premium grade with a high calorific value and high cost is G2 with 7000 value, and /Ton has been considered the upper limit of calorific value. The fuel cost indirectly affects the cost of electricity.
在以往的文献 [41,45-48]中，电力成本是火力发电厂经济研究的目标之一。本研究涉及不同等级煤炭的价格。不同等级的煤具有不同的热值。热值高、成本高的优质煤种是 G2，热值为 7000 ， /吨被认为是热值的上限。燃料成本间接影响电力成本。

The expenses associated with the steam generator island, turbine generator island, BOP electrical packing, BOP mechanical, coal handling unit, civil works, pipe costing and ash handling unit have been assessed through the application of curve fitting techniques to empirical data obtained from a power plant with a capacity of and a variable number of units (n). The range of capacity units varies from one to four. In this context, the currency denomination utilized for economic analysis is the Indian Rupee (Rs). The exchange rate between the American Dollar and the Indian Rupee (INR) is 1 USD equals to 82.20 INR. The tabulated values of the constants and are presented in Table 2. The electrical packing of the steam generator BOP, coal handling unit and ash handling unit exhibit a linear correlation with changes in plant load ranging from to . The turbine generator and the
通过将曲线拟合技术应用于从容量为 、机组数量（n）可变的发电厂获得的经验数据，评估了与蒸汽发生器岛、汽轮发电机岛、BOP 电气填料、BOP 机械、煤处理装置、土建工程、管道成本计算和灰处理装置相关的费用。容量单位的范围从 1 到 4 不等。在这种情况下，用于经济分析的货币面值为印度卢比（Rs）。美元和印度卢比之间的汇率为 1 美元等于 82.20 卢比。表 2 列出了常数 和 的表列值。在 至 的范围内，蒸汽发生器 BOP、煤处理装置和灰处理装置的电气填料与电厂负荷的变化呈线性相关。汽轮发电机和

Fig. 2. Variation of Coal cost with respect to coal grade [50].
图 2.煤炭成本随煤炭等级的变化[50]。

mechanical island of the Balance of the Plant (BOP) exhibit power functionality subject to fluctuations in the plant's load. Civil engineering structures exhibit an exponential increase in response to fluctuations in the power plant's operational load. The value for curve fitting is kept greater than 0.991 . The variation cost of coal concerning coal grade is seen in Fig. 2.
电厂平衡机械岛（BOP）的动力功能受电厂负荷波动的影响。土木工程结构对发电厂运行负荷波动的响应呈指数增长。曲线拟合的 值保持大于 0.991。煤炭成本随煤炭等级的变化见图 2。

The present study involves three objective functions, Energetic Efficiency (%), Exergetic efficiency (%), and Cost of electricity (Rs/Unit). The first law of efficiency for a thermal power plant is formulated as follows:
本研究涉及三个目标函数，即能效（%）、热效率（%）和电力成本（卢比/单位）。火力发电厂效率第一定律的公式如下

where mwe is the power generated (MW), CVcoal is the calorific value of coal, is the plant efficiency (%), and mcoal is the amount of coal consumed .
其中，mwe 是发电量（兆瓦），CVcoal 是煤的热值， 是发电厂效率（%），mcoal 是消耗的煤 。

The present study involved certain assumptions as the constant entropy efficiency of the turbine at , the constant entropy mechanical efficiency of the turbine at , and the Generator and transformation efficiency at [51]. The exergetic efficiency (%) is formulated as follows:
本研究涉及一些假设，如涡轮机的恒定熵效率为 ，涡轮机的恒定熵机械效率为 ，发电机和转换效率为 [51]。能效（%）的计算公式如下：

The expression for the cost of electricity (COE) in terms of the operating cost for a lifetime, power output (mwe), annual time of operation per year in Hrs (No), and annual capacity factor ( ) is estimated as follow:
电能成本（COE）的计算公式为：终生运行成本、输出功率（兆瓦）、每年运行时间（小时，单位：No）和年发电量系数（ ）：

Table 3 表 3

Variables for bounds. 界限变量

Fig. 3. Flowchart for multi-objective PSO (Adapted and redrawn from [54] with permission LIC No.:5571970847791)
图 3.多目标 PSO 流程图（改编自 [54]，经许可，LIC 编号：5571970847791）

The power demand continuously varies with the requirement of the customer for electricity. So it becomes complicated for plant engineers to make the power generation plan per customer demand. Because of this, power output (mwe), the calorific value of coal (CVcoal), and the amount of coal consumed (mcoal) are taken as direct decision variables. The indirect decision variables are pressure and temperature conditions at the inlet of high-pressure turbine, intermediate-pressure turbine, and low-pressure turbine. The inlet pressure and temperature conditions of
电力需求随着客户对电力的要求而不断变化。因此，发电厂工程师要根据客户需求制定发电计划就变得复杂起来。因此，输出功率（mwe）、煤的热值（CVcoal）和耗煤量（mcoal）被作为直接决策变量。间接决策变量是高压汽轮机、中压汽轮机和低压汽轮机入口的压力和温度条件。高压水轮机、中压水轮机和低压水轮机的入口压力和温度条件
HPTu, IPTu, and LPTu play a vital role in the exergy analysis of supercritical coal-fired power plants [37]. The upper and lower bounds of decision variables have been taken from the supercritical power plant design manual and are shown in Table 3.
HPTu、IPTu 和 LPTu 在超临界燃煤电厂的放能分析中起着至关重要的作用 [37]。决策变量的上下限取自超临界发电厂设计手册 ，如表 3 所示。

The present study employs the particle swarm optimization technique for multi-objective optimization. The Particle Swarm Optimization (PSO) technique presents several benefits compared to the
本研究采用粒子群优化技术进行多目标优化。粒子群优化（PSO）技术与传统的多目标优化技术相比，具有多种优势。

Fig. 4. Variation of coal consumption ( ) v/s Objective functions.
图 4.煤炭消耗量 ( ) 与目标函数的关系。

conventional Genetic Algorithm (GA) methodology. Initially, Particle Swarm Optimization (PSO) exhibits a lower susceptibility to becoming trapped in local optima, a prevalent challenge in genetic algorithms. In addition, Particle Swarm Optimization (PSO) exhibits a lower computational cost than genetic algorithms due to its reduced parameter tuning requirements. Thirdly, Particle Swarm Optimization (PSO) is a straightforward and intuitive optimization methodology that is comprehensible and straightforward to execute. Also, PSO converges to a solution faster than GA. PSO does not have a crossover operator, giving a feasible search space solution. PSO best suits the high-dimensional and real-valued optimization problem [8,23]. The particle swarm optimization technique is inspired by flying birds' changing positions. The murmuration phenomenon of flying birds changes position by changing the velocity based upon neighbor birds and experience searching for food. So, this search process has been utilized for optimization problems [54]. Each bird is considered a particle with a fitness value. The individual particle fitness value is PBest, and the group particle fitness values are GBest. The outcome of PSO is to determine fitness value. The initial velocity and position for a jth particle with a population size of are expressed by and , 1) , respectively. The flowchart for multi-objective PSO is shown in Fig. 3. The following relation updates the position and velocity of particles:
传统的遗传算法（GA）方法。最初，粒子群优化（PSO）表现出较低的陷入局部最优的易感性，而这正是遗传算法普遍面临的挑战。此外，由于减少了参数调整要求，粒子群优化（PSO）的计算成本低于遗传算法。第三，粒子群优化（PSO）是一种简单直观的优化方法，易于理解和执行。此外，PSO 比 GA 更快地找到解决方案。PSO 没有交叉算子，可以给出可行的搜索空间解决方案。PSO 最适合高维和实值优化问题 [8,23]。粒子群优化技术的灵感来源于飞鸟的位置变化。飞鸟的杂音现象会根据邻近鸟类的速度和寻找食物的经验改变位置。因此，这种搜索过程被用于优化问题 [54]。每只鸟都被视为一个具有适应度值的粒子。个体粒子的适应度值为 PBest，群体粒子的适应度值为 GBest。PSO 的结果就是确定适应度值。种群数量为 的第 j 个粒子的初始速度和位置分别用 和 , 1) 表示。多目标 PSO 流程图如图 3 所示。粒子位置和速度的更新关系如下：

where , and are the inertia factor in imposing the effect of old velocity on the latest velocity, random numbers with an interval of , positive constants, and coefficient, respectively.
其中， 和 分别是旧速度对最新速度影响的惯性系数、间隔为 的随机数、正常数和系数。

The present study uses multi-objective PSO to optimize the thermodynamic and economic parameters of coal-fired supercritical coalfired power plants. The objective of the optimization study is to maximize energy efficiency, maximize exergy efficiency, and minimize the cost of electricity. The equal weights are assigned to all input variables of 0.33 , and their sum approximates 1 . The common objective value (Xmax) is formed with the following relation:
本研究采用多目标 PSO 优化燃煤超临界火力发电厂的热力学和经济参数。优化研究的目标是能源效率最大化、放能效率最大化和电力成本最小化。所有输入变量的权重均为 0.33，其总和近似为 1。共同目标值（Xmax）由以下关系式形成：

where X1max is the maximum value of energy efficiency, X2max is the maximum value of exergy efficiency, and is the minimum value of the cost of electricity and the terms ' ', ' ', ' ' are the weights assigned to the responses.
其中，X1max 是能源效率的最大值，X2max 是能效的最大值， 是电力成本的最小值，" "、" "、" "是分配给响应的权重。

The effect of variation in the amount of coal consumption with objective functions is presented in Fig. 4. Previously, the inlet temperatures of different turbine stages were taken as parameters for studying
图 4 显示了目标函数对耗煤量变化的影响。之前，不同涡轮机级的入口温度被作为参数来研究

Fig. 5. Variation of low-pressure turbine inlet temperature Objective functions.
图 5.低压涡轮机 入口温度 目标函数的变化。

Fig. 6. 3D plot of inlet pressure of high, intermediate, and low-pressure turbine (bar).
图 6.高、中、低压涡轮机入口压力的三维图（巴）。

Fig. 7. Propagation of GBest value with Particle size and Iteration.
图 7.GBest 值随粒子大小和迭代的传播。

the thermodynamic modeling of 210 MW and 660 MW power plants [42, 55]. The variation is studied by maintaining the calorific value of coal as constant. The increasing trends of plant efficiency, exergetic efficiency, and decreasing cost of electricity are seen with the amount of coal consumption. The increment of and is seen in plant and exergetic efficiency, with an increment of in coal consumption. The decrement of 1.33 INR/Unit is seen in the cost of electricity for the full load capacity of .
210 兆瓦和 660 兆瓦发电厂的热力学模型[42, 55]。在保持煤的热值 不变的情况下，对其变化进行了研究。随着煤炭消耗量的增加，电厂效率、能效和电力成本呈下降趋势。随着耗煤量 的增加，发电厂效率和能效 和 也在增加。当满负荷发电量为 时，电力成本下降了 1.33 印度卢比/度。

The inlet temperature of the low-pressure turbine decreased with increasing variation in plant load from 198 MW to a Full Load of 660 MW. It is seen from Fig. 5 That by keeping a lower temperature at the inlet of a low-pressure turbine up to , a 1.33 INR/Unit reduction in the cost of electricity is achieved with maximum plant efficiency of and exergetic efficiency of .
从 198 兆瓦到满负荷 660 兆瓦，低压涡轮机的入口温度随着电厂负荷的变化而降低。从图 5 中可以看出，通过将低压涡轮机的入口温度保持在 以下，可以在最大发电厂效率 和能效 的情况下降低 1.33 印度卢比/单位的电力成本。

Fig. 6 represents that pressure at the inlet of high, intermediate, and low-pressure turbines shows an increasing trend with a variety of plant loads from to and increasing in a variation of the amount of coal consumption from to .
图 6 显示，高压、中压和低压汽轮机入口处的压力随着从 到 的各种电厂负荷的变化而呈上升趋势，并随着从 到 的煤耗量的变化而上升。

The MATLAB code was executed for different numbers of particle sizes ranging from 10 to 180. It is observed from Fig. 6 That the group fitness value of 0.1402096 remains the same after 150 particle sizes.
MATLAB 代码在 10 到 180 粒径的不同粒数范围内执行。从图 6 中可以看出，在 150 个粒度之后，组适宜度值 0.1402096 保持不变。

Fig. 8. Propagation of plant efficiency and exergy efficiency with iteration.
图 8.工厂效率和放能效率的迭代传播。

Fig. 9. Propagation of cost of electricity with iteration.
图 9.电费的迭代传播。

Hence, the 150 particle size was selected for finding an optimum solution. In continuation with the above context, the group's best fitness value remains constant at 0.1402096 after 131 iterations, as shown in Fig. 7 .
因此，我们选择了 150 粒径的粒子来寻找最优解。根据上述情况，如图 7 所示，经过 131 次迭代后，该组的最佳适应度值仍保持在 0.1402096。

Fig. 8 gives an idea about the propagation of the overall plant and exergy efficiency with iteration. Moreover, it is seen that plant efficiency propagation and exergy efficiency are similar. The maximum overall plant efficiency of and exergy efficiency of have been observed after 21iteration. At 291 iterations, overall plant efficiency and second law efficiency were determined as and , respectively. The propagation of the cost of electricity with iteration is expressed in Fig. 9. It is seen that electricity costs decrease to 3.1309 INR/Unit at 61iteration and further increase to the optimum value of 3.1456 Rs/Unit at 131iteration.
图 8 显示了随着迭代进行的整体工厂效率和放能效率的传播情况。此外，我们还可以看到植物效率的传播和放能效率的传播是相似的。迭代 21 次后，植物总效率 和放能效率 达到最大值。在迭代 291 次后，确定的工厂总效率和第二定律效率分别为 和 。电费随迭代次数增加的情况如图 9 所示。可以看出，电费在 61 次迭代时降至 3.1309 印度卢比/单位，在 131 次迭代时进一步增至最佳值 3.1456 卢比/单位。

The global optimized function best value is determined at each iteration using PSO. The input response of plant efficiency, exergetic
利用 PSO 在每次迭代时确定全局优化函数的最佳值。设备效率、能效和发电量的输入响应

Fig. 10. Pareto curve based on Plant Efficiency and Exergy Efficiency.
图 10.基于工厂效率和能效的帕累托曲线。

efficiency, and cost of electricity has been calculated for each of the iterations, and the variation is plotted in Figs. 10 and 11., respectively. Fig. 10 expresses the Pareto curve between plant and exergy efficiency. The trend of the Pareto curve is linear between plant and exergetic efficiency. The increase in plant efficiency increased exergetic efficiency. The optimized coal calorific value and power output evaluated to maximize objective function are and , respectively. The remaining optimized values are represented in Table 4.
图 10 和图 11 分别显示了每次迭代计算的发电厂效率和发电成本的变化情况。图 10 表示发电厂效率和能效之间的帕累托曲线。工厂效率和能效之间的帕累托曲线呈线性趋势。电厂效率提高，能效也随之提高。为使目标函数最大化而评估的优化煤炭热值和功率输出分别为 和 。其余优化值见表 4。

Also, the optimization has been done based on the plant efficiency and cost of electricity. Fig. 10 shows the best Pareto curve between energy efficiency and the cost of electricity. The increase in plant efficiency reduces the electricity cost and the dependency on high-grade coal. The maximum value of plant efficiency of and exergetic efficiency of with a minimum cost of electricity of 3.1309 INR/ Unit is evaluated at 131 iterations. A similar trend of the Pareto curve is
此外，还根据发电厂的效率和电力成本进行了优化。图 10 显示了能源效率和电力成本之间的最佳帕累托曲线。发电厂效率的提高降低了电费，也减少了对高品位煤炭的依赖。在 131 次迭代中，电厂效率的最大值为 ，能效为 ，最低电费为 3.1309 印度卢比/度。帕累托曲线的类似趋势是

Fig. 11. Pareto curve based on Plant Efficiency, Exergy Efficiency and Cost of Electricity.
图 11.基于发电厂效率、放能效率和电力成本的帕累托曲线。

Table 4 表 4

Multi-objective optimization using PSO in thermal power plant.
在火力发电厂中使用 PSO 进行多目标优化。

observed between exegetic efficiency and cost of electricity, as shown in Fig. 10. The 3D Pareto curve of cost of electricity plant efficiency exergy efficiency is represented in Fig. 12. The present study also compares the previous studies of PSO for multi-objective optimization, as indicated in Table 4. The comparison of the optimized values of the decision variables with operating data is done from the previous literature survey to validate the proposed optimized model (see Table 5).
如图 10 所示，可以观察到发电效率和发电成本之间的关系。电费 工厂效率 放能效率的三维帕累托曲线如图 12 所示。如表 4 所示，本研究还比较了以往针对多目标优化的 PSO 研究。将决策变量的优化值与以往文献调查中的运行数据进行比较，以验证所提出的优化模型（见表 5）。

This study used a particle swarm to perform parametric analysis and multi-objective optimization of a 660 MW coal-fired power plant. The increment in plant efficiency and exergetic efficiency of and with an electricity cost reduction of 1.33 INR/Unit is achieved by lowing inlet temperature at a low-pressure turbine up to . The plant operating parameters are optimized to fulfill the demand for variation in power generation. The increase in plant efficiency and exergetic efficiency reduces the cost of electricity. Hence, the optimization reveals that the overall efficiency and exergy efficiency improvement minimizes the dependency on high-grade coal. The optimized power output and coal calorific value are evaluated as 659 MW and with 150 particle sizes. The maximum value of plant efficiency, , and exergy efficiency, , with a minimum cost of electricity of 3.1456 INR/Unit, are evaluated in the present study. The optimized values of the decision variables are consistent with the operating data, with a minimum and maximum relative error of , validating the precision of our models. It is also concluded that Particle Swarm Optimization has proven suitable techniques for integrating energy, exergy, and economic analysis to perform multiobjective optimization of the supercritical power plant.
本研究使用粒子群对 660 兆瓦燃煤发电厂进行参数分析和多目标优化。通过将低压涡轮机的入口温度降低到 ，实现了 和 的电厂效率和能效的提高，同时降低了 1.33 印度卢比/单位的电力成本。对电厂运行参数进行了优化，以满足发电量变化的需求。发电厂效率和能效的提高降低了电力成本。因此，优化结果表明，整体效率和能效的提高最大限度地减少了对高品位煤炭的依赖。优化后的发电量和煤炭热值分别为 659 兆瓦和 ，粒度为 150。本研究评估了电厂效率 和放能效率 的最大值，最低电力成本为 3.1456 印度卢比/单位。决策变量的优化值与运行数据一致，最小和最大相对误差为 ，验证了我们模型的精确性。此外，研究还得出结论，粒子群优化技术已被证明适用于整合能量、放能和经济分析，对超临界发电厂进行多目标优化。

Fig. 12. Pareto curve based on Cost of Electricity v/s Plant Efficiency v/sExergy Efficiency.
图 12.基于电力成本 v/发电厂效率 v/能源效率的帕累托曲线。

Table 5 表 5

Optimized values of the decision variables.
决策变量的优化值。

Keval Chandrakant Nikam, Laxmikant Jathar, Sagar Dnyaneshwar Shelare and Nabisab Mujawar Mubarak: Conceptualization, Data curation, Methodology, Writing - original draft, Writing - review & editing, Resources, . Kiran Shahapurkar, Sunil Dambhare, Manzoore Elahi M. Soudagar, Nabisab Mujawar Mubarak, Tansir Ahamad, and MA Kalam: Research Support, Review and Editing, Software, Funding acquisition, Visualization, Project administration. All authors have read and agreed to the published version of the manuscript.
Keval Chandrakant Nikam、Laxmikant Jathar、Sagar Dnyaneshwar Shelare 和 Nabisab Mujawar Mubarak：构思、数据整理、方法论、写作 - 原稿、写作 - 审阅和编辑、资源、......。基兰-沙哈普尔卡尔、苏尼尔-丹巴雷尔、曼佐雷-埃拉希-M-苏达加尔、纳比萨布-穆贾瓦尔-穆巴拉克、坦瑟尔-阿哈马德和马-卡拉姆：研究支持、审阅和编辑、写作、资源：研究支持、审阅和编辑、软件、资金获取、可视化、项目管理。所有作者均已阅读并同意手稿的出版版本。

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
作者声明，他们没有任何可能会影响本文所报告工作的已知经济利益或个人关系。

No data was used for the research described in the article.
文章所述研究未使用任何数据。

The authors thank the Researchers Supporting Project number
作者感谢编号为
(RSP2023R6), King Saud University, Riyadh, Saudi Arabia.
(RSP2023R6），沙特阿拉伯利雅得沙特国王大学。

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[1] Ameri M, Mokhtari H, Mostafavi Sani M. 4E analyses and multi-objective optimization of different fuels application for a large combined cycle power plant, vol. 156.Elsevier Ltd; 2018. https://doi.org/10.1016/j.energy.2018.05.039.

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