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1

Lamba, Prof Kanika. "Economic Load Dispatch." International Journal for Research in Applied Science and Engineering Technology 9, no. VI (2021): 1646–51. http://dx.doi.org/10.22214/ijraset.2021.35330.

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ELD or Economic load dispatch is an online process of allocating generating among the available generating units to minimize the total generating cost and satisfy the equality and inequality constraint. ELD means the real and reactive power of the generator vary within the certain limits and fulfils theload demand with less fuel cost. There are some traditional methods for = 1; 2; :::;N) isgiven as Vi=[Vi;1; Vi;2; :::; Vi;D]. The index ivaries from solving ELD include lambda irritation method, Newton-Raphson method, Gradient method, etc. All these traditional algorithms need the incremental fuel cost curves of the generators to be increasing monotonically or piece-wise linear. But in practice the input-output characteristics of a generator are highly non-linear leading to a challenging non-convex optimization problem. Methods like artificial intelligence, DP (dynamic programming), GA (genetic algorithms), and PSO (particle swarm optimization), ALO ( ant-lion optimization), solve non convex optimization problems in an efficient manner and obtain a fast and near global and optimum solution. In this project ELD problem has been solved using Lambda-Iterative technique, ALO (ant-lion Optimization) and PSO (Particle Swarm Optimization) and the results have been compared. All the analyses have been made in MATLAB environment
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2

Brar, Mandhir Singh, and Gursewak Singh Brar. "Economic Load Dispatch using IYSGA." European Journal of Theoretical and Applied Sciences 2, no. 1 (2024): 595–606. http://dx.doi.org/10.59324/ejtas.2024.2(1).52.

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The Economic Load Dispatch (ELD) problem is a pivotal aspect of power system management, focusing on the efficient allocation of power generation among various units to meet the demand while minimizing costs. This research paper presents an Improved Yellow Saddle Goat Fish Algorithm (IYSGA) based method for resolving ELD issues. The key objective of proposed IYSGA method is to reduce error between demanded and generated load along with its unit cost. This objective is accomplished by using YSGA whose exploration ability is improved by exploring ability of Grasshopper Optimization Algorithm (GOA). By implementing IYSGA in given ELD problem, the convergence rate, exploring ability and solution quality is enhanced. The fitness function is determined by IYSGA in terms of error and cost reduction, which should be as minimum as possible. The simulations are performed on standardized IEEE bus system with 3-unit and 6-units to meet load demand of 850MW to 1263MW respectively. The experimental simulations conducted provide evidence that the proposed approach met the load demand with zero error. Furthermore, proposed method attained best cost of $8197.633 and $15,285.7055 for the 3-unit and 6-unit generation unit. These outcomes underscore the robustness and superiority of the proposed method in addressing the Economic Load Dispatch (ELD) problem, emphasizing its capacity to optimize power generation with unparalleled precision and cost-effectiveness.
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3

Mandhir, Singh Brar, and Singh Brar Gursewak. "Economic Load Dispatch using IYSGA." European Journal of Theoretical and Applied Sciences 2, no. 1 (2024): 595–606. https://doi.org/10.59324/ejtas.2024.2(1).52.

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The Economic Load Dispatch (ELD) problem is a pivotal aspect of power system management, focusing on the efficient allocation of power generation among various units to meet the demand while minimizing costs. This research paper presents an Improved Yellow Saddle Goat Fish Algorithm (IYSGA) based method for resolving ELD issues. The key objective of proposed IYSGA method is to reduce error between demanded and generated load along with its unit cost. This objective is accomplished by using YSGA whose exploration ability is improved by exploring ability of Grasshopper Optimization Algorithm (GOA). By implementing IYSGA in given ELD problem, the convergence rate, exploring ability and solution quality is enhanced. The fitness function is determined by IYSGA in terms of error and cost reduction, which should be as minimum as possible. The simulations are performed on standardized IEEE bus system with 3-unit and 6-units to meet load demand of 850MW to 1263MW respectively. The experimental simulations conducted provide evidence that the proposed approach met the load demand with zero error. Furthermore, proposed method attained best cost of $8197.633 and $15,285.7055 for the 3-unit and 6-unit generation unit. These outcomes underscore the robustness and superiority of the proposed method in addressing the Economic Load Dispatch (ELD) problem, emphasizing its capacity to optimize power generation with unparalleled precision and cost-effectiveness. 
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4

Singh, Nagendra, Tulika Chakrabarti, Prasun Chakrabarti, et al. "Novel Heuristic Optimization Technique to Solve Economic Load Dispatch and Economic Emission Load Dispatch Problems." Electronics 12, no. 13 (2023): 2921. http://dx.doi.org/10.3390/electronics12132921.

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The fundamental objective of economic load dispatch is to operate the available generating units such that the needed load demand satisfies the lowest generation cost and also complies with the various constraints. With proper power system operation planning using optimized generation limits, it is possible to reduce the cost of power generation. To fulfill the needs of such objectives, proper planning and economic load dispatch can help to plan the operation of the electrical power system. To optimize the economic load dispatch problems, various classical and new evolutionary optimization approaches have been used in research articles. Classical optimization techniques are outdated due to many limitations and are also unable to provide a global solution to the ELD problem. This work uses a new variant of particle swarm optimization techniques called modified particle swarm optimization, which is effective and efficient at finding optimum solutions for single as well as multi-objective economic load dispatch problems. The proposed MPSO is used to solve single and multi-objective problems. This work considers constraints like power balance and power generation limits. The proposed techniques are tested for three different case studies of ELD and EELD problems. (1) The first case is tested using the data of 13 generating unit systems along with the valve point loading effect; (2) the second case is tested using 15 generating unit systems along with the ramp rate limits; and (3) the third case is tested using the economic emission dispatch (EELD) as a multi-objective problem for 6 generating unit systems. The outcomes of the suggested procedures are contrasted with those of alternative optimization methods. The results show that the suggested strategy is efficient and produces superior optimization outcomes than existing optimization techniques.
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5

Et.al, Aditya Tiwari. "Solving Economic Load Dispatch Problem UsingParticle Swarm Optimization Technique." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 3 (2021): 3203–9. http://dx.doi.org/10.17762/turcomat.v12i3.1565.

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Economic load dispatch (ELD)is one of the important problems ofpower system operation. Conventional methods like Lambda iteration methodare not efficientfor complex ELD problems. Particle swarm optimization is preferred in ELD problem due to its high performance.The Inertia Weight PSO and Constriction Factor PSO algorithms are performed on threeunit and sixunit systems. The analysis of ELD problem is performed by Conventional method and PSO method. In this paper,losses are neglected in the ELD problem. PSO algorithm obtains the best solution forELD problem.
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6

Athab, Falah Abodahir, and Wafaa Saeed Majeed. "Economic power dispatch for an interconnected power system based on reliability indices." Indonesian Journal of Electrical Engineering and Computer Science 20, no. 2 (2020): 777. http://dx.doi.org/10.11591/ijeecs.v20.i2.pp777-787.

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Reliability indices are always one of the most important factors in the power systems. In this paper, the problem of the economic load dispatch (ELD) and the problem of economic emission load dispatch (CEELD) have been improved taking into account reliability indices. That is, the problem and reliability of ELD are proposed as combined economic load dispatch reliability (CELDR) and the problem CEELD is suggested as (CEELDR). In solving CELDR and CEELDR problems, tried to use power generators in a very reliable way to save system load, as well as minimum fuel and emission costs. In this effort, the ELD of power plants is successfully implemented in a single system containing 6 generating units, taking into account the reliability and emissions of the system with and without system power loss, inequality and inequality constraints, and valve point effects using the exchange market algorithm(EMA). The results suggest that reliability indicators in ELD can be used to create greater reliability in providing consumers with uninterrupted power.
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7

Singh, Pragya, and Aayushi Priya. "A Comprehensive Review on Economic Load Dispatch using Evolutionary Approach." SMART MOVES JOURNAL IJOSCIENCE 3, no. 2 (2017): 7. http://dx.doi.org/10.24113/ijoscience.v3i2.172.

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Economic Load Dispatch, ELD can be defined as the way of allocating the load level to the generators of the power plant in such a way that the total demand would be supplied in a most economic manner and completely. In a practical power system, the power plants are not located at the same distance from the centre of loads and their fuel costs are different. Also, under normal operating conditions, the generation capacity is more than the total load demand and losses. Thus, there are many options for scheduling generation. In an interconnected power system, the objective is to find the real and reactive power scheduling of each power plant in such a way as to minimize the operating cost. This means that the generator‟s real and reactive powers are allowed to vary within certain limits so as to meet a particular load demand with minimum fuel cost. This is called optimal power flow problem. In this paper, Economic Load Dispatch (ELD) of real power generation is considered. Economic Load Dispatch (ELD) is the scheduling of generators to minimize total operating cost of generator units subjected to equality constraint of power balance within the minimum and maximum operating limits of the generating units. This paper gives a survey of research work covering the concept of economic load dispatch. Economic load dispatch gives the best saving in cost for any power generation plant operation in which the methodology can be applied by various means from conventional to the advanced. In the past years up to 90s, the conventional techniques were used to make this happen but in the past decades AI techniques have fulfilled the requirements with satisfactory results that are being reviewed.
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8

A. Athab, Falah, and Wafaa S. Majeed. "SOLVING ECONOMIC LOAD DISPATCH WITH RELIABILITY INDICATORS." Journal of Engineering and Sustainable Development 24, no. 06 (2020): 103–14. http://dx.doi.org/10.31272/jeasd.24.6.9.

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Due to the great importance of reliable indicators in electrical operating systems in all its different parts, it has been considered the most important factors in the design and maintenance of the electrical system, especially during its operation. The main reason for attention to reliability indicators relates to interruptions in the power system that are provided to consumers. The introduction of reliable indicators to solving an economic load dispatch (ELD) issue increases the possibility of providing customers with a required load with the highest degree of reliability. The ELD issue has been solved with reliability indicators. This means that the ELD problem with reliability is combined into one problem called combined the economic load dispatch with reliability (CELDR). Solving the above problem lowers the fuel cost while increasing the reliability of the generators while preparing the required load. The exchange market algorithm (EMA), in this work, has been implemented in a system of 26 generating units to solve the CELDR issue.considering system reliability, inequality, and equality constraints. The results obtained show the direct effect of using reliability indicators in solving the above problem, where the best results were obtained using the EMA algorithm to solve the mentioned problem, compared to other algorithms.
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9

V.P., Sakthivel, Suman M., and Sathya P.D. "Large-scale economic load dispatch using squirrel search algorithm." International Journal of Energy Sector Management 14, no. 6 (2020): 1351–80. http://dx.doi.org/10.1108/ijesm-02-2020-0012.

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Purpose Economic load dispatch (ELD) is one of the crucial optimization problems in power system planning and operation. The ELD problem with valve point loading (VPL) and multi-fuel options (MFO) is defined as a non-smooth and non-convex optimization problem with equality and inequality constraints, which obliges an efficient heuristic strategy to be addressed. The purpose of this study is to present a new and powerful heuristic optimization technique (HOT) named as squirrel search algorithm (SSA) to solve non-convex ELD problems of large-scale power plants. Design/methodology/approach The suggested SSA approach is aimed to minimize the total fuel cost consumption of power plant considering their generation values as decision variables while satisfying the problem constraints. It confers a solution to the ELD issue by anchoring with foraging behavior of squirrels based on the dynamic jumping and gliding strategies. Furthermore, a heuristic approach and selection rules are used in SSA to handle the constraints appropriately. Findings Empirical results authenticate the superior performance of SSA technique by validating on four different large-scale systems. Comparing SSA with other HOTs, numerical results depict its proficiencies with high-qualitative solution and by its excellent computational efficiency to solve the ELD problems with non-smooth fuel cost function addressing the VPL and MFO. Moreover, the non-parametric tests prove the robustness and efficacy of the suggested SSA and demonstrate that it can be used as a competent optimizer for solving the real-world large-scale non-convex ELD problems. Practical implications This study has compared various HOTs to determine optimal generation scheduling for large-scale ELD problems. Consequently, its comparative analysis will be beneficial to power engineers for accurate generation planning. Originality/value To the best of the authors’ knowledge, this manuscript is the first research work of using SSA approach for solving ELD problems. Consequently, the solution to this problem configures the key contribution of this paper.
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10

Athab, Falah Abodahir, and Wafaa Saeed Majeed. "Economic power dispatch for an interconnected power system based on reliability indices." Indonesian Journal of Electrical Engineering and Computer Science 20, no. 2 (2020): 777–87. https://doi.org/10.11591/ijeecs.v20.i2.pp 777 - 787.

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Reliability indices are always one of the most important factors in the power systems. In this paper, the problem of the economic load dispatch(ELD) and the problem of combined economic emission load dispatch(CEELD) have been improved taking into account reliability indices. That is, the problem of reliability and ELD are proposed as combined economic load dispatch reliability(CELDR) and the problem of CEELD and reliability are suggested as (CEELDR). In solving CELDR and CEELDR problems, tried to use power generators in a very reliable way to save system load, as well as minimum fuel and emission costs. In this effort, the ELD of power plants is successfully implemented in a single system containing 6 generating units, taking into account the reliability and emissions of the system with and without system power loss, equality & inequality constraints,and valve point effects, by using the exchange market algorithm (EMA). The results suggest that the reliability indicators in ELD can be used to create greater reliability in providing consumers with uninterrupted power.
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11

Said, Mokhtar, Essam H. Houssein, Eman Abdullah Aldakheel, Doaa Sami Khafaga, and Alaa A. K. Ismaeel. "Performance of the Walrus Optimizer for solving an economic load dispatch problem." AIMS Mathematics 9, no. 4 (2024): 10095–120. http://dx.doi.org/10.3934/math.2024494.

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<abstract> <p>A new metaheuristic called the Walrus Optimizer (WO) is inspired by the ways in which walruses move, roost, feed, spawn, gather, and flee in response to important cues (safety and danger signals). In this work, the WO was used to address the economic load dispatch (ELD) issue, which is one of the essential parts of a power system. One type of ELD was designed to reduce fuel consumption expenses. A variety of methodologies were used to compare the WO's performance in order to determine its reliability. These methods included rime-ice algorithm (RIME), moth search algorithm (MSA), the snow ablation algorithm (SAO), and chimp optimization algorithm (ChOA) for the identical case study. We employed six scenarios: Six generators operating at two loads of 700 and 1000 MW each were employed in the first two cases for the ELD problem. For the ELD problem, the second two scenarios involved ten generators operating at two loads of 2000 MW and 1000 MW. Twenty generators operating at a 3000 MW load were the five cases for the ELD issue. Thirty generators operating at a 5000 MW load were the six cases for the ELD issue. The power mismatch factor was the main cause of ELD problems. The ideal value of this component should be close to zero. Using the WO approach, the ideal power mismatch values of 4.1922E−13 and 4.5119E−13 were found for six generator units at demand loads of 700 MW and 1000 MW, respectively. Using metrics for the minimum, mean, maximum, and standard deviation of fitness function, the procedures were evaluated over thirty separate runs. The WO outperformed all other algorithms, as seen by the results generated for the six ELD case studies.</p> </abstract>
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12

S, Nagaraju. "Comparison of the PSO Algorithm and JAYA Algorithm for Economic Load Dispatch." INTERANTIONAL JOURNAL OF SCIENTIFIC RESEARCH IN ENGINEERING AND MANAGEMENT 08, no. 04 (2024): 1–5. http://dx.doi.org/10.55041/ijsrem30314.

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The electrical power industry has undergone the significant changes, leading to a competitive market and the need for optimal economic dispatch solutions. As energy resources becoming scarce, prices rise, environmental concerns intensify, and electricity consumption increases, classical optimization techniques struggle to handle these complex issues. This project compares particle swarm optimization (PSO) and JAYA optimization method for economic load dispatch (ELD) problems in the electrical power industry. PSO has gained recognition as an effective solution for ELD problems in the last decade. The aim of this study is to show that Jaya optimization is the best optimization methodology for ELD problems. By comparing the performance, convergence speed, and accuracy of PSO and JAYA optimization, this paper aims to provide insights into the superiority of JAYA optimization. Key Words: Economic Load dispatch, Optimization method, PSO algorithm, JAYA algorithm, Incremental fuel cost
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13

Maharana, Himanshu Shekhar, and Saroj Kumar Dash. "Dual objective multiconstraint swarm optimization based advanced economic load dispatch." International Journal of Electrical and Computer Engineering (IJECE) 11, no. 3 (2021): 1924. http://dx.doi.org/10.11591/ijece.v11i3.pp1924-1932.

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In electric power system, the vital topic to be mooted is economic load dispatch (ELD). It is a non-linear problem with some unavoidable constraints such as valve point loading and ramp rate constraint. For solving ELD problem distint methods were devised and tried for different electric supply systems yielding slow convergence rates. To achieve fast convergence, dual objective multi constraint swarm optimization based advanced economic load dispatch (DOMSOBAELD) algorithm is proposed making use of simulated values of real power outages of a thermal power plant as initial estimates for PSO technique embedded in it and used for optimizing economic dispatch problem in this article. DOMSOBAELD method was developed in the form of amalgamating fluids. Presence of power line losses, multiple valves in steam turbines, droop constraints and inhibited zones were utilized to optimize the ELD problem as genuinely approximate as possible. The results obtained from DOSOBAELD are compared with particle swarm optimization (PSO), PSOIW and differential particle swarm optimization (DPSO) techniques. It is quite conspicuous that DOMSOBAELD yielded minimum cost values with most favourable values of real unit outputs. Thus the proposed method proves to be advantageous over other heuristic methods and yields best solution for ELD by selecting incremental fuel cost as the decision variable and cost function as fitness function.
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Himanshu, Shekhar Maharana, and Kumar Dash Saroj. "Dual objective multiconstraint swarm optimization based advanced economic load dispatch." International Journal of Electrical and Computer Engineering (IJECE) 11, no. 3 (2021): 1924–32. https://doi.org/10.11591/ijece.v11i3.pp1924-1932.

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In electric power system, the vital topic to be mooted is economic load dispatch (ELD). It is a non-linear problem with some unavoidable constraints such as valve point loading and ramp rate constraint. For solving ELD problem distint methods were devised and tried for different electric supply systems yielding slow convergence rates. To achieve fast convergence, dual objective multi constraint swarm optimization based advanced economic load dispatch (DOMSOBAELD) algorithm is proposed making use of simulated values of real power outages of a thermal power plant as initial estimates for PSO technique embedded in it and used for optimizing economic dispatch problem in this article. DOMSOBAELD method was developed in the form of amalgamating fluids. Presence of power line losses, multiple valves in steam turbines, droop constraints and inhibited zones were utilized to optimize the ELD problem as genuinely approximate as possible. The results obtained from DOSOBAELD are compared with particle swarm optimization (PSO), PSOIW and differential particle swarm optimization (DPSO) techniques. It is quite conspicuous that DOMSOBAELD yielded minimum cost values with most favourable values of real unit outputs. Thus the proposed method proves to be advantageous over other heuristic methods and yields best solution for ELD by selecting incremental fuel cost as the decision variable and cost function as fitness function.
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15

Said, Mokhtar, Ali M. El-Rifaie, Mohamed A. Tolba, Essam H. Houssein, and Sanchari Deb. "An Efficient Chameleon Swarm Algorithm for Economic Load Dispatch Problem." Mathematics 9, no. 21 (2021): 2770. http://dx.doi.org/10.3390/math9212770.

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Economic Load Dispatch (ELD) is a complicated and demanding problem for power engineers. ELD relates to the minimization of the economic cost of production, thereby allocating the produced power by each unit in the most possible economic manner. In recent years, emphasis has been laid on minimization of emissions, in addition to cost, resulting in the Combined Economic and Emission Dispatch (CEED) problem. The solutions of the ELD and CEED problems are mostly dominated by metaheuristics. The performance of the Chameleon Swarm Algorithm (CSA) for solving the ELD problem was tested in this work. CSA mimics the hunting and food searching mechanism of chameleons. This algorithm takes into account the dynamics of food hunting of the chameleon on trees, deserts, and near swamps. The performance of the aforementioned algorithm was compared with a number of advanced algorithms in solving the ELD and CEED problems, such as Sine Cosine Algorithm (SCA), Grey Wolf Optimization (GWO), and Earth Worm Algorithm (EWA). The simulated results established the efficacy of the proposed CSA algorithm. The power mismatch factor is the main item in ELD problems. The best value of this factor must tend to nearly zero. The CSA algorithm achieves the best power mismatch values of 3.16×10−13, 4.16×10−12 and 1.28×10−12 for demand loads of 700, 1000, and 1200 MW, respectively, of the ELD problem. The CSA algorithm achieves the best power mismatch values of 6.41×10−13 , 8.92×10−13 and 1.68×10−12 for demand loads of 700, 1000, and 1200 MW, respectively, of the CEED problem. Thus, the CSA algorithm was found to be superior to the algorithms compared in this work.
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Manohar Kalgunde. "Economic Load Dispatch for Thermal Power Plants using Excel Solver." Panamerican Mathematical Journal 34, no. 2 (2024): 254–61. http://dx.doi.org/10.52783/pmj.v34.i2.1104.

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Economic load dispatch (ELD) is a technique used in power system operation to determine the optimal allocation of power generation among available generators to meet the system demand while minimizing the total operating cost. The goal of ELD is to achieve a balance between the demand for electricity and the supply of electricity in the most cost-effective manner. Excel Solver is one of the powerful add-in tools in Microsoft Excel which can be utilized to find global optimum solution for a given optimization problem. It allows users to find the optimal solution to a variety of problems by adjusting specific input variables within certain constraints. In this article, an optimization problem is developed for ELD and Excel Solver is proposed to find the solution. Two case studies viz. 3-unit and 10-unit system are considered and results are obtained using proposed tool. The results show that the proposed tool is effective and user-friendly for solving ELD problem. Overall, this article provides a valuable overview of Excel Solver to solve the ELD problem.
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Khobaragade, Tejaswita, and K. T. Chaturvedi. "Enhanced Economic Load Dispatch by Teaching–Learning-Based Optimization (TLBO) on Thermal Units: A Comparative Study with Different Plug-in Electric Vehicle (PEV) Charging Strategies." Energies 16, no. 19 (2023): 6933. http://dx.doi.org/10.3390/en16196933.

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This research paper presents an enhanced economic load dispatch (ELD) approach using the Teaching–Learning-Based Optimization (TLBO) algorithm for 10 thermal units, examining the impact of Plug-in Electric Vehicles (PEVs) in different charging scenarios. The TLBO algorithm was utilized to optimize the ELD problem, considering the complexities associated with thermal units. The integration of PEVs in the load dispatch optimization was investigated, and different charging profiles and probability distributions were defined for PEVs in various scenarios, including overall charging profile, off-peak charging, peak charging, and stochastic charging. These tables allow for the modeling and analysis of PEV charging behavior and power requirements within the power system. By incorporating PEVs, additional controllable resources were introduced, enabling more effective load management and grid stability. The comparative analysis showcases the advantages of the TLBO-based ELD model with PEVs, demonstrating the potential of coordinated dispatch strategies leveraging PEV storage and controllability. This paper emphasizes the importance of integrating PEVs into the load dispatch optimization process, utilizing the TLBO algorithm, to achieve economic and reliable power system operation while considering different PEV charging scenarios.
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Abba-Gana, Modu, Zainab Musa Gwoma, and Isa Muhammad Sani. "Whale Optimization Technique Based Economic Load Dispatch." ABUAD Journal of Engineering Research and Development (AJERD) 7, no. 2 (2024): 207–15. http://dx.doi.org/10.53982/ajerd.2024.0702.20-j.

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This study concentrates on optimizing the Economic Load Dispatch (ELD) for three major Nigerian power systems: Sapele, Jebba, and Egbin. These systems, each comprising varying numbers of generating units and facing fluctuating load demands ranging from 300 MW to 1000 MW, necessitate efficient resource allocation to minimize operational expenses. Employing the innovative Whale Optimization Algorithm (WOA), inspired by the cooperative behaviour of humpback whales, this research tackles the intricate non-linear characteristics of the ELD problem. The primary goal is to determine the ideal power generation timetable that reduces total generation costs while fulfilling power demand constraints. Through mathematical modelling, the power systems and their economic aspects are represented. The proposed WOA-based approach is implemented and juxtaposed against optimization methods to gauge its efficacy in achieving cost-effective load dispatch. In addition to the fast convergence characteristics of the optimization technique, the study reveals minimum optimal generation costs of 150,567 Naira/Hr, 189,352 Naira/Hr, and 244,075 Naira/Hr for the Sapele, Jebba, and Egbin power systems, respectively, under various load conditions. Conversely, maximum optimal generation costs reach 480,431 Naira/Hr, 590,871 Naira/Hr, and 750,453 Naira/Hr for the same systems, demonstrating the algorithm's adaptability to diverse load scenarios.
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Singh, O. V., and M. Singh. "A Comparative Analysis on Economic Load Dispatch Problem Using Soft Computing Techniques." International Journal of Software Science and Computational Intelligence 12, no. 2 (2020): 50–73. http://dx.doi.org/10.4018/ijssci.2020040104.

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This article aims at solving economic load dispatch (ELD) problem using two algorithms. Here in this article, an implementation of Flower Pollination (FP) and the BAT Algorithm (BA) based optimization search algorithm method is applied. More than one objective is hoped to be achieve in this article. The combined economic emission dispatch (CEED) problem which considers environmental impacts as well as the cost is also solved using the two algorithms. Practical problems in economic dispatch (ED) include both nonsmooth cost functions having equality and inequality constraints which make it difficult to find the global optimal solution using any mathematical optimization. In this article, the ELD problem is expressed as a nonlinear constrained optimization problem which includes equality and inequality constraints. The attainability of the discussed methods is shown for four different systems with emission and without emission and the results achieved with FP and BAT algorithms are matched with other optimization techniques. The experimental results show that conferred Flower Pollination Algorithm (FPA) outlasts other techniques in finding better solutions proficiently in ELD problems.
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Ragunathan, Ramamoorthi, and Balamurugan Ramadoss. "Golden jackal optimization for economic load dispatch problems with complex constraints." Bulletin of Electrical Engineering and Informatics 13, no. 2 (2024): 781–93. http://dx.doi.org/10.11591/eei.v13i2.6572.

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This research paper uses the golden jackal optimization (GJO), a novel meta-heuristic algorithm, to address power system economic load dispatch (ELD) problems. The GJO emulates the hunting behavior of golden jackals. GJO algorithm uses the cooperative attacking behavior of golden jackals to tackle complicated optimization problems efficaciously. The objective of ELD problem is to distribute power system load requirement to the different generators with a minimum total fuel cost of generation. ELD problems are highly complex, non-linear, and non-convex optimization problems while considering constraints namely valve point loading effect (VPL) and prohibited operating zones (POZs). The proposed GJO algorithm is applied to solve complex, non-linear, and non-convex ELD problems. Six different test systems having 6, 10, 13, 40, and 140 generators with various constraints are used to validate the usefulness of the suggested GJO method. Simulation outcomes of the test system are compared with various algorithms reported in the algorithms such as particle swarm optimization (PSO), ant colony optimization (ACO), and backtracking search algorithm (BSA). Results show that the proposed GJO algorithm produces minimal fuel cost and has good convergence in solving ELD problems of power system engineering.
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Pradhan, Moumita, Provas Kumar Roy, and Tandra Pal. "Economic Load Dispatch Using Oppositional Backtracking Search Algorithm." International Journal of Energy Optimization and Engineering 6, no. 2 (2017): 79–97. http://dx.doi.org/10.4018/ijeoe.2017040105.

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In this paper, an oppositional backtracking search algorithm (OBSA) is proposed to solve the large scale economic load dispatch (ELD) problem. The main drawback of the conventional backtracking search algorithm (BSA) is that it produces a local optimal solution rather than the global optimal solution. The proposed OBSA methodology is a highly-constrained optimization problem has to minimize the total generation cost by satisfying several constraints involving load demand, generation limits, prohibited operating zone, ramp rate limits and valve point loading effect. The proposed method is applied for three test systems and provides the unique and fast solutions. The new heuristic OBSA approach is successfully applied in three test systems consisting of 13 and 140 thermal generators. The test results are judged against various methods. The simulation results show the effectiveness and accuracy of the proposed OBSA algorithm over other methods like conventional BSA, oppositional invasive weed optimization (OIWO), Shuffled differential evolution (SDE) and oppositional real coded chemical reaction optimization (ORCCRO). This clearly suggests that the new OBSA method can achieve effective and feasible solutions of nonlinear ELD problems.
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R, Ramamoorthi, and Balamurugan R. "Solving Economic Load Dispatch Problem Using Grey Wolf Optimization Algorithm." International Journal for Research in Applied Science and Engineering Technology 11, no. 5 (2023): 2556–62. http://dx.doi.org/10.22214/ijraset.2023.52161.

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Abstract: This article presents a new evolutionary optimization approach named grey wolf optimization (GWO), which is based on the behavior of grey wolves, for the optimal operating strategy of economic load dispatch (ELD). Nonlinear characteristics of generators like ramp rate limits, valve point discontinuities and prohibited operating zones are considered in the problem. GWO method does not require any information about the gradient of the objective function, while searching for an optimum solution. The GWO algorithm concept appears to be a robust and reliable optimization algorithm is applied to the nonlinear ELD problems. The proposed algorithm is implemented and tested on two test systems having 40 Thermal generators. The results confirm the potential and effectiveness of the proposed algorithm compared to various other methods available in the literature. The outcome is very encouraging and proves that the GWO is a very effective optimization technique for solving various ELD problems.
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Shaban, Ahmed Ewis, Alaa A. K. Ismaeel, Ahmed Farhan, Mokhtar Said, and Ali M. El-Rifaie. "Growth Optimizer Algorithm for Economic Load Dispatch Problem: Analysis and Evaluation." Processes 12, no. 11 (2024): 2593. http://dx.doi.org/10.3390/pr12112593.

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The Growth Optimizer algorithm (GO) is a novel metaheuristic that draws inspiration from people’s learning and introspection processes as they progress through society. Economic Load Dispatch (ELD), one of the primary problems in the power system, is resolved by the GO. To assess GO’s dependability, its performance is contrasted with a number of methods. These techniques include the Rime-ice algorithm (RIME), Grey Wolf Optimizer (GWO), Elephant Herding Optimization (EHO), and Tunicate Swarm Algorithm (TSA). Also, the GO algorithm has the competition of other literature techniques such as Monarch butterfly optimization (MBO), the Sine Cosine algorithm (SCA), the chimp optimization algorithm (ChOA), the moth search algorithm (MSA), and the snow ablation algorithm (SAO). Six units for the ELD problem at a 1000 MW load, ten units for the ELD problem at a 2000 MW load, and twenty units for the ELD problem at a 3000 MW load are the cases employed in this work. The standard deviation, minimum fitness function, and maximum mean values are measured for 30 different runs in order to evaluate all methods. Using the GO approach, the ideal power mismatch values of 3.82627263206814 × 10−12, 0.0000622209480241054, and 5.5893360695336 × 10−7 were found for six, ten, and twenty generator units, respectively. The GO’s dominance over all other algorithms is demonstrated by the results produced for the ELD scenarios.
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Çetinkaya, Nurettin, Abdullah Ürkmez, İsmet Erkmen, and Tankut Yalçinöz. "A New Algorithm and Computation Approach for Economic Dispatch with Prohibited Operating Zones in Power Systems." Energy Exploration & Exploitation 23, no. 4 (2005): 267–75. http://dx.doi.org/10.1260/014459805775219148.

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This paper presents a new algorithm and computation approach to solve the economic load dispatch (ELD) in electrical power systems. We applied a new power formula to solve the ELD problem. If production units cost curves are represented properly then ELD becomes more correct. In this respect we assumed that production units have prohibited operating zones. Cost curves of the production units are generally accepted as piece-wise quadratic function. The power production is cheaper since we do not use the production units in the prohibited operating zones. The proposed method and algorithm are compared to other ELD methods on the standard test systems. The proposed method solve the dispatch problem faster than the other ELD methods.
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Ismaeel, Alaa A. K., Essam H. Houssein, Doaa Sami Khafaga, Eman Abdullah Aldakheel, Ahmed S. AbdElrazek, and Mokhtar Said. "Performance of Osprey Optimization Algorithm for Solving Economic Load Dispatch Problem." Mathematics 11, no. 19 (2023): 4107. http://dx.doi.org/10.3390/math11194107.

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The osprey optimization algorithm (OOA) is a new metaheuristic motivated by the strategy of hunting fish in seas. In this study, the OOA is applied to solve one of the main items in a power system called economic load dispatch (ELD). The ELD has two types. The first type takes into consideration the minimization of the cost of fuel consumption, this type is called ELD. The second type takes into consideration the cost of fuel consumption and the cost of emission, this type is called combined emission and economic dispatch (CEED). The performance of the OOA is compared against several techniques to evaluate its reliability. These methods include elephant herding optimization (EHO), the rime-ice algorithm (RIME), the tunicate swarm algorithm (TSA), and the slime mould algorithm (SMA) for the same case study. Also, the OOA is compared with other techniques in the literature, such as an artificial bee colony (ABO), the sine cosine algorithm (SCA), the moth search algorithm (MSA), the chimp optimization algorithm (ChOA), and monarch butterfly optimization (MBO). Power mismatch is the main item used in the evaluation of the OOA with all of these methods. There are six cases used in this work: 6 units for the ELD problem at three different loads, and 6 units for the CEED problem at three different loads. Evaluation of the techniques was performed for 30 various runs based on measuring the standard deviation, minimum fitness function, and maximum mean values. The superiority of the OOA is achieved according to the obtained results for the ELD and CEED compared to all competitor algorithms.
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Ly, Huu Pham, Trung Nguyen Thang, Duc Pham Lam, and Hoang Nguyen Nam. "Stochastic fractal search based method for economic load dispatch." TELKOMNIKA Telecommunication, Computing, Electronics and Control 17, no. 5 (2019): 2535–46. https://doi.org/10.12928/TELKOMNIKA.v17i5.12539.

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This paper presents a nature-inspired meta-heuristic, called a stochastic fractal search based method (SFS) for coping with complex economic load dispatch (ELD) problem. Two SFS methods are introduced in the paper by employing two different random walk generators for diffusion process in which SFS with Gaussian random walk is called SFS-Gauss and SFS with Levy Flight random walk is called SFS-Levy. The performance of the two applied methods is investigated comparing results obtained from three test system. These systems with 6, 10, and 20 units with different objective function forms and different constraints are inspected. Numerical result comparison can confirm that the applied approach has better solution quality and fast convergence time when compared with some recently published standard, modified, and hybrid methods. This elucidates that the two SFS methods are very favorable for solving the ELD problem.
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Roy, Subhajit, Kuntal Bhattacharjee, and Aniruddha Bhattacharya. "A Modern Approach to Solve of Economic Load Dispatch using Group Leader Optimization Technique." International Journal of Energy Optimization and Engineering 6, no. 1 (2017): 66–85. http://dx.doi.org/10.4018/ijeoe.2017010104.

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Economic load dispatch plays an important role of power system operation & control by using different soft techniques that have been used to solve convex and non-convex economic load dispatch (ELD) problems. This paper presents a new global optimization algorithm to the economic load dispatch problems for minimization of fuel cost of generations with different constraints such as ramp rate limits, valve-point loading and prohibited operating zones of large-scale thermal plants. Power transmission loss has also been considered in few cases. Group leader optimization algorithm (GLOA) is a relatively new optimization technique. Mathematical models of this algorithm demonstrate the efficiency, quality of solution and convergence speed of the method and successful application of the algorithm on ELD problems. Simulation results found that the proposed approach outperforms several other existing optimization techniques in terms quality of solution obtained and computational efficiency. Results also be confirmed the robustness of the proposed methodology.
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Nguyen, Trung Thang, Duy Phuong Nguyen, Van Thanh Pham, and Trong Hien Chiem. "An Effectively Modified Firefly Algorithm for Economic Load Dispatch Problem." TELKOMNIKA Telecommunication, Computing, Electronics and Control 16, no. 5 (2018): 2436–43. https://doi.org/10.12928/TELKOMNIKA.v16i5.10545.

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This paper proposes an effectively modified firefly algorithm (EMFA) for searching optimal solution of economic load dispatch (ELD) problem. The proposed method is developed by improving the procedure of new solution generation of conventional firefly algorithm (FA). The performance of EMFA is compared to FA variants and other existing methods by testing on four different systems with different types of objective function and constraints. The comparison indicates that the proposed method can reach better optimal solutions than other FA variants and most other existing methods with lower population and lower maximum iteration. As a result, it can lead to a conclusion that the proposed method is potential for ELD problem.
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Yasin, Z. M., N. F. A. Aziz, N. A. Salim, N. A. Wahab, and N. A. Rahmat. "Optimal Economic Load Dispatch using Multiobjective Cuckoo Search Algorithm." Indonesian Journal of Electrical Engineering and Computer Science 12, no. 1 (2018): 168. http://dx.doi.org/10.11591/ijeecs.v12.i1.pp168-174.

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In this paper, Multiobjective Cuckoo Search Algorithm (MOCSA) is developed to solve Economic Load Dispatch (ELD) problem. The main goal of the ELD is to meet the load demand at minimum operating cost by determining the output of the committed generating unit while satisfying system equality and inequality constraints. The problem formulation is based on a multiobjective model in which the multiobjective are defined as fuel cost minimization and carbon emission minimization. MOCSA is based on the inspiration from the brooding parasitism of cuckoo species in nature. Three cases are considered to test the effectiveness of the proposed technique which are fuel cost minimization, carbon emission minimization and multiobjective function with fixed weighted sum. The effectiveness of the MOCSA’s performances are illustrated through comparative study with other techniques such as Multiobjective Genetic Algorithm (MOGA) and Multiobjective Particle Swarm Optimization (MOPSO) in terms of fitness functions. The proposed study was conducted on three generating unit system at various loading condition. The result proved that MOCSA provide better solution in minimizing fuel cost and carbon emission usage as compared to other techniques.
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Z., M. Yasin, F. A. Aziz N., A. Salim N., A. Wahab N., and A. Rahmat N. "Optimal Economic Load Dispatch using Multiobjective Cuckoo Search Algorithm." Indonesian Journal of Electrical Engineering and Computer Science 12, no. 1 (2018): 168–74. https://doi.org/10.11591/ijeecs.v12.i1.pp168-174.

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In this paper, Multiobjective Cuckoo Search Algorithm (MOCSA) is developed to solve Economic Load Dispatch (ELD) problem. The main goal of the ELD is to meet the load demand at minimum operating cost by determining the output of the committed generating unit while satisfying system equality and inequality constraints. The problem formulation is based on a multiobjective model in which the multiobjective are defined as fuel cost minimization and carbon emission minimization. MOCSA is based on the inspiration from the brooding parasitism of cuckoo species in nature. Three cases are considered to test the effectiveness of the proposed technique which are fuel cost minimization, carbon emission minimization and multiobjective function with fixed weighted sum. The effectiveness of the MOCSA’s performances are illustrated through comparative study with other techniques such as Multiobjective Genetic Algorithm (MOGA) and Multiobjective Particle Swarm Optimization (MOPSO) in terms of fitness functions. The proposed study was conducted on three generating unit system at various loading condition. The result proved that MOCSA provide better solution in minimizing fuel cost and carbon emission usage as compared to other techniques.
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Sanjay, Yadav, and Patidar Lavkesh. "Optimize Scheduling of Generating Unit for Economic Load Dispatch using ANN: A Review." Journal of Power Electronics and Devices 5, no. 1 (2019): 1–7. https://doi.org/10.5281/zenodo.2537444.

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<em>Electrical power frameworks are structured and worked to meet the nonstop variety of intensity request. In power framework limiting, the task cost is critical. Monetary Load Dispatch (ELD) is a strategy to plan the power generator yields regarding the heap requests, and to work the power framework most financially, or at the end of the day, we can say that primary target of financial load dispatch is to distribute the ideal power age from various units at the least cost conceivable while meeting all framework imperatives Over the years, numerous endeavors have been made to tackle the ELD issue, consolidating various types of requirements or different goals through different numerical programming and advancement systems. In any case, these traditional dispatch calculations require the steady cost bends to be monotonically expanding or piece-wise straight. The information/yield qualities of present day units are inalienably profoundly nonlinear (with valve-point impact, rate limits and so forth) and having numerous nearby least focuses in the cost work. Their qualities are approximated to meet the prerequisites of traditional dispatch calculations prompting imperfect arrangements and thusly, bringing about gigantic income misfortune over the time. Thought of profoundly nonlinear qualities of the units requires exceptionally vigorous calculations to abstain from stalling out at neighborhood optima.</em>
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32

Safari, Amin, and Davoud Sheibai. "Artificial bee colony algorithm for economic load dispatch with wind power energy." Serbian Journal of Electrical Engineering 13, no. 3 (2016): 347–60. http://dx.doi.org/10.2298/sjee1603347s.

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This paper presents an efficient Artificial Bee Colony (ABC) algorithm for solving large scale economic load dispatch (ELD) problems in power networks. To realize the ELD, the valve-point loading effect, system load demand, power losses, ramp rate limits and prohibited operation zones are considered here. Simulations were performed on four different power systems with 3, 6, 15 and 40 generating units and the results are compared with two forms of power systems, one power system is with a wind power generator and other power system is without a wind power generator. The results of this study reveal that the proposed approach is able to find appreciable ELD solutions than those of previous algorithms.
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33

Bulbul, Sk Md Ali, and Provas Kumar Roy. "Adaptive Teaching Learning Based Optimization Applied to Nonlinear Economic Load Dispatch Problem." International Journal of Swarm Intelligence Research 5, no. 4 (2014): 1–16. http://dx.doi.org/10.4018/ijsir.2014100101.

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Economic load dispatch (ELD) is a process of calculating real power dispatch by satisfying a set of constraints such a way as fuel cost can be minimized. Inclusion of the effect of valve-points and prohibited operation zones (POZs) in the cost functions make ELD problem a non-linear and non-convex one. For solving ELD in power system a newly proposed evolutionary technique namely adaptive teaching learning based optimization (ATLBO) is presented in this article. TLBO mimics the influence of a teacher on students in a classroom environment by social interaction. ATLBO is an improved version of TLBO which makes TLBO faster and more robust. An adaptive dynamic parameter control mechanism is adopted by the proposed ATLBO algorithm to determine the suitable parameter settings for teaching and learning phases of TLBO algorithm. The proposed ATLBO algorithm is tested in three different cases like 10-unit, 40-unit, and 80-unit systems. A comparison of numerical results with other well established techniques reveals optimization superiority of the proposed scheme both in quality of solution and computational efficiency.
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S, Logadeep, Hariraam N N, and Sujatha Balaraman. "Optimizing ELD in power systems applying GWO: A Practical Approach." June 2024 6, no. 2 (2024): 128–39. http://dx.doi.org/10.36548/jscp.2024.2.002.

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Addressing the Economic load Dispatch (ELD) Problem in power systems is crucial for minimizing generation cost and transmission losses while meeting the load demand. This research explores the application of Grey Wolf Optimization (GWO) to solve the ELD problem, leveraging ‘GWO’s inspiration from grey wolf social behavior. Through simulation, ‘GWO’s superior convergence speed and solution quality compared to traditional techniques is demonstrated. The finding highlights ‘GWO’s effectiveness in enhancing the economic and operational efficiency of power systems, offering promising avenues for sustainable energy management strategies.
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35

Kashyap, Manish, Dr Achala Jain, and Vinita Swarnakar. "Economic Load Dispatch by Improved Drone Optimization Technique." International Journal of Recent Technology and Engineering (IJRTE) 11, no. 2 (2022): 149–52. http://dx.doi.org/10.35940/ijrte.b7180.0711222.

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In this paper, the ELD problem is resolved via ABC (Artificial BEE Colony) technique. The major goal of this study is to use the IDO method to present very efficient &amp; reliable approach for solving ED problem in Power system. The suggested approach is used to solve a variety of non-convex ED issues, including banned operating zones with ramp rate constraints. This problem is described as an optimization of the objective function and minimization of the overall operating cost while gratifying all allied constraints, accompanied by the lowest down &amp; up time limitations, startup cost, and spinning reserve. A six generators scheduling problem is discussed, along with its formulation, representation, and simulation result.
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Manish, Kashyap, Achala Jain Dr., and Swarnakar Vinita. "Economic Load Dispatch by Improved Drone Optimization Technique." International Journal of Recent Technology and Engineering (IJRTE) 11, no. 2 (2022): 149–52. https://doi.org/10.35940/ijrte.B7180.0711222.

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<strong>Abstract: </strong>In this paper, the ELD problem is resolved via ABC (Artificial BEE Colony) technique. The major goal of this study is to use the IDO method to present very efficient &amp; reliable approach for solving ED problem in Power system. The suggested approach is used to solve a variety of non-convex ED issues, including banned operating zones with ramp rate constraints. This problem is described as an optimization of the objective function and minimization of the overall operating cost while gratifying all allied constraints, accompanied by the lowest down &amp; up time limitations, startup cost, and spinning reserve. A six generators scheduling problem is discussed, along with its formulation, representation, and simulation result.
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37

Aristidis, Vlachos. "Particle Swarm Optimization (PSO) techniques solving Economic Load Dispatch (ELD) Problem." Journal of Statistics and Management Systems 11, no. 4 (2008): 761–69. http://dx.doi.org/10.1080/09720510.2008.10701341.

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Vlachos, A., I. Petikas, and S. Kyriakides. "Economic Load Dispatch (ELD) problem based on a Memetic Algorithm (MA)." Journal of Statistics and Management Systems 14, no. 5 (2011): 975–93. http://dx.doi.org/10.1080/09720510.2011.10701596.

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39

Ritu, Sharma, Sharma Raginee, and Achala Jain Dr. "A Comparative Analysis of a Hybrid System with Hybrid Methodologies." International Journal of Innovative Technology and Exploring Engineering (IJITEE) 11, no. 7 (2022): 17–20. https://doi.org/10.35940/ijitee.G9969.0611722.

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<strong>Abstract</strong>: Economic Load Dispatch (ELD) is an important optimization problem in the energy system. Economic Dispatch (ED) is a short-term determination of the optimal performance of a set of power generation assets to meet the system load at the lowest possible cost, taking into account transmission and operational constraints. Economic dispatch problems are solved by dedicated computer software that needs to take into account the operational and system limitations of available resources and corresponding transmission functions. Economic load balancing provides optimal cost savings for power plant operations where methodologies can be applied in a variety of ways, from traditional to advanced. To achieve this, traditional methods have been used from the last few years to the 90&#39;s, but in the last few decades AI methods have met their needs and validated satisfactory results. Some advanced hybrid techniques used are the Modified Salp Swarm Optimization Algorithm (MSSA) with Artificial Intelligent (AI) technique aided with Particle Swarm Optimization (PSO) technique, Improved Moth-Fly Optimization Algorithm (IMFOA) with the Recurrent Neural Network (RNN), the Improved Fruit Fly Optimization Algorithm (IFOA) with Artificial Neural Network (ANN) system and Lightning Search Algorithm (LSA) with Genetic Algorithm (GA) which will encourage the researches for providing better solution for economic load dispatch problem is presented in this paper.
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Banerjee, Sumit, Chandan Chanda, and Deblina Maity. "A Comparative Study of Improved Teaching Learning Based Optimization Technique on Economic Load Dispatch Problem with Generator Constraints." International Journal of Energy Optimization and Engineering 5, no. 4 (2016): 1–25. http://dx.doi.org/10.4018/ijeoe.2016100101.

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This article presents a novel improved teaching learning based optimization (I-TLBO) technique to solve economic load dispatch (ELD) problem of the thermal plant without considering transmission losses. The proposed methodology can take care of ELD problems considering practical nonlinearities such as ramp rate limit, prohibited operating zone and valve point loading. The objective of economic load dispatch is to determine the optimal power generation of the units to meet the load demand, such that the overall cost of generation is minimized, while satisfying different operational constraints. I-TLBO is a recently developed evolutionary algorithm based on two basic concepts of education namely teaching phase and learning phase. The effectiveness of the proposed algorithm has been verified on test system with equality and inequality constraints. Compared with the other existing techniques demonstrates the superiority of the proposed algorithm.
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41

reddy, Y. V. Krishna, Naga Venkata Ramakrishna G, Prof (Dr ). Mohammad Israr, Buddaraju Revathi, Dr Pavithra G, and Dr Nageswara Rao Lakkimsetty. "Economic Load Dispatch of Thermal-Solar-Wind System using Modified Grey Wolf Optimization Technique." International Journal of Electrical and Electronics Research 12, no. 3 (2024): 926–33. http://dx.doi.org/10.37391/ijeer.120324.

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The growing demand for electrical energy, coupled with the uneven distribution of natural resources, necessitates the integration of power plants. Coordinating the operation of interconnected generating units is crucial to meet the fluctuating load demand efficiently. This research focuses on the Economic Load Dispatch (ELD) problem in hybrid power systems that incorporate solar thermal and wind energy. Renewable energy resources, such as wind and solar thermal energy, depend on atmospheric conditions like wind speed, solar radiation, and temperature. This study addresses the ELD problem using a Modified Grey Wolf Optimization (MGWO) approach to obtain the most optimal solution for generator fuel costs. The Grey Wolf Optimization (GWO) approach, inspired by natural processes, is utilized but may exhibit both exploratory and exploitative behavior. To enhance its performance, we propose a novel version called MGWO, integrating memory, evolutionary operators, and a stochastic local search approach. The suggested MGWO approach is applied to two distinct test systems comprising 13 and 26 units, respectively, to solve the ELD with variable load requirements. Comparative analyses with other strategies demonstrate the effectiveness of MGWO in addressing the ELD problem. This modification enhances the GWO method, making it more robust and efficient for optimizing ELD in hybrid power systems.
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Gihare, Sonam, and Prof Arun Pachori. "A Deep Neural Network Approach for Optimizing Economic Load Dispatch in Power Systems." International Journal of Advances in Engineering and Management 6, no. 10 (2024): 568–75. https://doi.org/10.35629/5252-0610568575.

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To ensure minimization of power losses as well as economic feasibility of electrical power generation, economic load dispatch happens to be one of the most challenging optimization problems which is faced in electrical engineering. With the advent of distributed power systems, an interconnection of power systems generating from different sources have come into consideration. However, all sources do not operate in the same manner and hence the generation cost for different sources varies significantly. Economic Load Dispatch (ELD) can be defined as a technique to schedule the power generator outputs with respect to the load demands, and to operate the power system in the most economical way. This paper presents a neural network model for implementing economic load dispatch for a three as well as six generation system. The load is also varied for both the 3 and 6 generations systems. The results clearly indicate that the cost of generation increases with the increase in load, which is also intuitive and hence gets tested. Thus the proposed model can be used to implement an optimized economic load dispatch mechanism for multi-unit power systems which is a typical characteristic of distributed power systems.
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Saha, Bikram, Provas Kumar Roy, and Barun Mandal. "Economic Load Dispatch Incorporating Wind Power Using Hybrid Biogeography-Based Optimization." International Journal of Applied Metaheuristic Computing 12, no. 3 (2021): 54–80. http://dx.doi.org/10.4018/ijamc.2021070103.

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This article represents salp swarm algorithm (SSA) for the most favourable operating solution of economic load dispatch (ELD). For making the convergence first along with SSA, another optimization algorithm (i.e., BBO [biogeography;based optimization]) is also used. For lowering the operational cost, wind power is employed with thermal units. SSA is inspired by swarming behaviour of salp, which belongs to salpiside family. Salp possess a special kind of swarm while hunting for food and navigating. The recommended algorithm is executed on two systems of SIX units and 40 units. In both of the cases, load dispatch problem is carried out with renewable sources and also without renewable sources. Individually, BBO, SSA, and hybrid BBO-SSA are applied to all the test systems to justify effectiveness of hybrid BBO-SSA. Obtained results assure the prospective and advantages of recommended algorithm in contrast to algorithms mentioned in the article. Results come out to be very satisfying and reveal that hybrid BBO-SSA is a powerful algorithm to solve ELD problems.
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Anil Kumar Jain, Lata Gidwani. "Sustainable Economic Load Dispatch Integrating Renewable Energy for Multi-Load Systems." Power System Technology 49, no. 1 (2025): 736–47. https://doi.org/10.52783/pst.1605.

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The growing adoption of renewable energy in power networks calls for effective strategies to manage economic load dispatch (ELD) sustainably. This study introduces an innovative approach to Sustainable Economic Load Dispatch (SELD) by integrating multiple renewable sources, such as solar and wind energy, into a system serving diverse loads. The proposed method utilizes the Botox Optimization Algorithm (BOA), a nature-inspired metaheuristic, to enhance power distribution while reducing operational expenses and environmental impact. BOA efficiently tackles challenges related to fluctuations and unpredictability in renewable energy by improving solution accuracy and dynamically balancing load demand. The model incorporates key system constraints, including power equilibrium and generation limits, ensuring steady and optimized performance. A comparative assessment against conventional and advanced optimization methods highlights BOA’s effectiveness in cutting costs and maximizing renewable energy penetration. Findings demonstrate that the proposed SELD framework offers a resilient and adaptable approach for managing energy in smart grids and microgrid systems. This research supports the shift toward a cost-efficient, environmentally friendly, and reliable power infrastructure.
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Peesapati, Rajagopal, Yogesh Kumar Nayak, Swati K. Warungase, and Surender Reddy Salkuti. "Constrained Static/Dynamic Economic Emission Load Dispatch Using Elephant Herd Optimization." Information 14, no. 6 (2023): 339. http://dx.doi.org/10.3390/info14060339.

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The rapid growth in greenhouse gases (GHGs), the lack of electricity production, and an ever-increasing demand for electrical energy requires an optimal reduction in coal-fired thermal generating units (CFTGU) with the aim of minimizing fuel costs and emissions. Previous approaches have been unable to deal with such problems due to the non-convexity of realistic scenarios and confined optimum convergence. Instead, meta-heuristic techniques have gained more attention in order to deal with such constrained static/dynamic economic emission load dispatch (ELD/DEELD) problems, due to their flexibility and derivative-free structures. Hence, in this work, the elephant herd optimization (EHO) technique is proposed in order to solve constrained non-convex static and dynamic ELD problems in the power system. The proposed EHO algorithm is a nature-inspired technique that utilizes a new separation method and elitism strategy in order to retain the diversity of the population and to ensure that the fittest individuals are retained in the next generation. The current approach can be implemented to minimize both the fuel and emission cost functions of the CFTGUs subject to power balance constraints, active power generation limits, and ramp rate limits in the system. Three test systems involving 6, 10, and 40 units were utilized to demonstrate the effectiveness and practical feasibility of the proposed algorithm. Numerical results indicate that the proposed EHO algorithm exhibits better performance in most of the test cases as compared to recent existing algorithms when applied to the static and dynamic ELD issue, demonstrating its superiority and practicability.
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Karthik, N., A. K. Parvathy, and R. Arul. "Non-convex Economic Load Dispatch using Cuckoo Search Algorithm." Indonesian Journal of Electrical Engineering and Computer Science 5, no. 1 (2017): 48. http://dx.doi.org/10.11591/ijeecs.v5.i1.pp48-57.

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&lt;p&gt;This paper presents cuckoo search algorithm (CSA) for solving non-convex economic load dispatch (ELD) problems of fossil fuel fired generators considering transmission losses and valve point loading effect. CSA is a new meta-heuristic optimisation technique inspired from the obligate brood parasitism of some cuckoo species by laying their eggs in the nests of other host birds of other species. The strength of the proposed meta-heuristic optimization technique CSA has been tested and validated on the standard IEEE 14-bus, 26-bus and 30-bus system with several heuristic load patterns. The results have indicated that the proposed approach is able to obtain significant economic load dispatch solutions than those of Firefly Algorithm (FFA) and other soft computing techniques reported in the literature.&lt;/p&gt;
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Feng, Xiao Hua, Yu Yao He, and Juan Yu. "Economic Load Dispatch Using Bacterial Foraging Optimization Algorithm Based on Evolution Strategies." Advanced Materials Research 860-863 (December 2013): 2040–45. http://dx.doi.org/10.4028/www.scientific.net/amr.860-863.2040.

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This paper presents a novel modified bacterial foraging optimization(BFO) to solve economic loaddispatch (ELD) problems. BFO isalready successfully employed to solve variousoptimization problems. However original BFOfor small problems with moderate dimensionand searching space is satisfactory. As searchspace and complexity growexponentially in scalable ELD problems, it shows poorconvergence properties. To tackle this complex problem considering itshigh-dimensioned search space, the Evolution Strategies is introduced to thebasic BFO. The chemotactic step is adjusted to have a dynamic non-linearbehavior in order to improve balancing the global and local search. Theproposed algorithm is validated using several thermal generation test systems.The results are compared with those obtained by other algorithms previouslyapplied to solve the problem considering valve-point effects and power losses.
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48

Khobaragade, Tejaswita, and Dr K. T. Chaturvedi. "A Review on Evolutionary Methodology more appropriate for implementation in Economic Load Dispatch." YMER Digital 21, no. 03 (2022): 422–45. http://dx.doi.org/10.37896/ymer21.03/45.

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Economic Load Dispatch (ELD) is approach to reduced the cost of electricity generation without any compromisation on its quality and its reliability. As per the economic point of view the production cost must be minimized. For the different load demands at different time period vary as well as requirement of power also vary. For this it is very important to monitorized the demand and its production. The principle factor in Thermal and Nuclear power plant is Fuel cost. In this paper we have studied different evolutionary method and obtain the best method among them perhaps, in order to bring the best solution to ELD problems an evolution of soft computing methods and many other methods have been successfully conducted such as Simulated Annealing (SA), Genetic Algorithm (GA), Honey Bee Mating Optimization (HBMO), Particle Swarm Optimization (PSO), Gravitational Search Algorithm (GSA) and PSO-GSA hybrid method. To bring more appropriate optimized solution for ELD problems.
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Nguyen, Hung Duc, and Ly Huu Pham. "Determining solutions to new economic load dispatch problems by war strategy optimization algorithm." International Journal of Renewable Energy Development 14, no. 1 (2024): 124–35. https://doi.org/10.61435/ijred.2025.60618.

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Abstract:
The paper applies three cutting-edge algorithms - War Strategy Optimization Algorithm (WSO), Egret Swarm Optimization Algorithm (ESOA), and Black Widow Optimization Algorithm (BWOA) - as potential tools to determining the optimal generation power of power plants in both the Economic Load Dispatch problem (ELD) and the New ELD problem (NELD), which incorporates renewable energy resources into the traditional power system. These algorithms underwent rigorous evaluation using various test systems with complex constraints, a multi-fuel objective function, and 24-hour load demands. In System 1, at various load levels, WSO method achieves a lower total minimum cost compared to BWOA and ESOA. Specifically, WSO outperforms BWOA and ESOA by $0.68 and $2.79 for a load of 2400 MW, by $0.49 and $4.41 for a load of 2500 MW, by $0.79 and $4.83 for a load of 2600 MW, and by $0.54 and $4.53 for a load of 2700 MW. In System 2, WSO method is less cost in a day than ESOA by $ 80.92 and BWOA by $ 46.73, corresponding to 0.39% and 0.23%, respectively. Additionally, WSO excels in response capability, providing a quicker reaction time than BWOA and ESOA across all four subcases while maintaining the same control parameters. Moreover, WSO demonstrated comparable or superior results and improved search capabilities compared to previous methods. The comparison of these results underscored WSO's effectiveness in addressing these challenges and its potential for resolving broader engineering issues beyond ELD. Ultimately, the study aimed to offer valuable insights into the role of renewable energy resources in the traditional power system, particularly in cost savings.
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50

C., Durga Prasad, and Siva Krishna Rao G.V. "Solution to Economic Load Dispatch Problem of a Distributed Generating System using Pattern Search Algorithm." International Journal of Innovative Technology and Exploring Engineering (IJITEE) 9, no. 11 (2020): 1–4. https://doi.org/10.35940/ijitee.B7755.0991120.

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Abstract:
The solution of Economic Load Dispatch (ELD) problem is to allocate the total load demand to committed generating units with an objective to minimize the operating cost without violating the unit and system constraints. The growing power demand, atmospheric pollution and increased population makes it essential to invent a new power system with low pollution and transmission losses. The growing price and limited availability of fossil fuels makes installation of conventional power plants uneconomical. Installation of non-conventional power plants like roof top solar plants is essential to meet the increased load demand and environmental pollution standards. The output of roof top solar systems is intermittent because it depend on atmospheric conditions. To find a solution to economic load dispatch of distributed generation system (ELDDGS) with roof top solar plants is a difficult problem because of its intermittent and scattered nature. This paper will explain a solution to economic load dispatch of a distributed generation system using pattern search algorithm.
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