Economic Load Dispatch Problem Research Articles

Optimize power generation of thermal generating sources in solving the green energies-based economic load dispatch using Electric Eel Foraging Optimization

This research focuses on solving the green energies-based economic load dispatch problem (ELD) with the consideration of both solar and wind power to minimize the total electricity production cost (TEPC) of all thermal generating sources (TGSs) existing in the given power system. Two power systems, including a 6-TGS and a 15-TGS power system, were selected to conduct the research. Besides, the prohibited operating zones (POZs) of the TGSs are also considered while solving the GE-ELD problem. Golf optimization algorithm (GOA) and Electric Eel Foraging Optimization (EEFO) are applied to find the optimal power generation of TGSs to minimize the TEPC value and satisfy all the related constraints featured by the considered problem, especially the POZ constraints. The results obtained by GOA and EEFO in the two power systems are evaluated and compared using different criteria. The comparison indicates that EEFO is superior to GOA at all criteria, especially in the minimum value of TEPC (Min. TEPC) and the standard deviation (Std). In particular, EEFO is better than GOA 0.052($/h) on Min.TEPC and 98.34% on Std while applied in the first power system. The better values of EEFO over GOA in the second power system are 199.474 ($/h) and 78.703%. By considering these results, EEFO is considered a powerful search method and highly suggested for use to solve such GE-ELD problems.

Comparison of the PSO Algorithm and JAYA Algorithm for Economic Load Dispatch

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

Minimization of fuel cost for generator systems with valve point effect using modified PSO

The goal of this research is to lay the groundwork for understanding the particle swarm optimization technique. The applicability of this technique is proven by solving a variety of Constraint and unconstraint optimization problems. During the operation of the power system, economic load dispatch is a vital optimization activity for allocating generation between the committed units to divide the power while meeting various system constraints economically. In this work, the modified PSO method's application to the electrical power system's economic load dispatch problem on 3-generator, 5-generator and 13-generator systems are also investigated. In this research work Exterior penalty method is applied to convert constraint optimization problem into unconstraint optimization problem

Golden jackal optimization for economic load dispatch problems with complex constraints

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.

Optimal renewable-integrated economic load dispatch for a large-scale power system using One-to-One Optimization Algorithm

This study presents the application of a new meta-heuristic algorithm called One-to-One optimization algorithm (OOBO) for solving the renewable-integrated economic load dispatch problem (RI-ELD) with consideration of both wind and solar power plants. The whole study focuses on minimizing the overall expenses of fuel (OEF) for all thermal electric power plants (TEPPs). The considered power system consists of twenty TEPPs with different working limits. OOBO is applied to solve the given problem in three cases of load demand level, including 2500, 2600, and 2700 MW. The results achieved by OOBO in the three cases are compared with other meta-heuristic algorithms called Coati optimization algorithm (COA) in the four aspects, such as Best OEF (Bst.OEF), Average OEF (Aver.OEF), Maximum OEF (Max.OEF). OOBO not only outperforms COA in all comparison aspects but also provides faster convergence speed to the optimal values of OEF at all three cases of load demand. Moreover, OOBO shows its surprising stability over COA regardless of the increase of load demand in Case 2 and Case 3. By observing these results, OOBO deserved the highly effective search tool for solving the large-scale and highly complex RI-ELD problem. 

Efficient economic operation based on load dispatch of power systems using a leader white shark optimization algorithm

AbstractThis article proposes the use of a leader white shark optimizer (LWSO) with the aim of improving the exploitation of the conventional white shark optimizer (WSO) and solving the economic operation-based load dispatch (ELD) problem. The ELD problem is a crucial aspect of power system operation, involving the allocation of power generation resources to meet the demand while minimizing operational costs. The proposed approach aims to enhance the performance and efficiency of the WSO by introducing a leadership mechanism within the optimization process, which aids in more effectively navigating the complex ELD solution space. The LWSO achieves increased exploitation by utilizing a leader-based mutation selection throughout each generation of white sharks. The efficacy of the proposed algorithm is tested on 13 engineer benchmarks non-convex optimization problems from CEC 2020 and compared with recent metaheuristic algorithms such as dung beetle optimizer (DBO), conventional WSO, fox optimizer (FOX), and moth-flame optimization (MFO) algorithms. The LWSO is also used to address the ELD problem in different case studies (6 units, 10 units, 11 units, and 40 units), with 20 separate runs using the proposed LWSO and other competitive algorithms being statistically assessed to demonstrate its effectiveness. The results show that the LWSO outperforms other metaheuristic algorithms, achieving the best solution for the benchmarks and the minimum fuel cost for the ELD problem. Additionally, statistical tests are conducted to validate the competitiveness of the LWSO algorithm.

Ekonomik yük dağıtım problemi için elektrik baliği optimizasyonu

The Economic Load Dispatch (ELD) problem is an essential aspect of power system planning and operational scheduling. Different techniques and algorithms have been recommended to solve it, aiming to minimize the cost of power generation with satisfying the load requirements. In this paper, a new algorithm called Electric Fish Optimization (EFO) is used to solve the ELD problem by considering the line losses, ramp rate limits, maximum and minimum capacities of the generators and prohibited operating zones (POZ). The algorithm has been utilized in test systems consisting of 6 and 15 units and its outcomes have been compared to those from previous research studies. The proposed algorithm has been shown to achieve minimum cost, indicating its superiority and effectiveness in addressing power system planning challenges. It is evident that the presented algorithm offers a valuable solution for optimizing ELD problems.

An application of Gorilla troops optimizer in solving the problem of economic load dispatch considering valve point loading effect

Economic load dispatch (ELD) is one of the fundamental and important optimization problems in an electrical power system. The goal of the ELD problem is to minimize the overall cost of fuel used by generators while satisfying the different constraints like power balance limitations, operational capacity limits, ramp-rate limits, and prohibited operating zones and valve point loading effect (VPLE). The paper introduces a novel optimization technique, termed Gorilla Troop Optimization (GTO), inspired by the mimic’s behavior of gorilla troops, for solving the Economic Load Dispatch (ELD) Problem. The ELD Problem is assessed both with and without the valve-point effect, considering best, average, and worst fuel costs in dollars per hour ($/hr). The proposed GTO is applied to four different case studies to find the best global solution. The effectiveness of the GTO is evaluated using four distinct IEEE unit systems, including the IEEE 3-unit, 6-unit, 10-unit, and 40-unit test systems. From the simulation results, it has been realized that GTO show superior results as compared to other algorithms in terms of the total fuel cost minimization, convergence speed, and computation time to achieve the global optimal solution in all the case studies.

Jellyfish search algorithm for economic load dispatch under the considerations of prohibited operation zones, load demand variations, and renewable energy sources

<span lang="EN-US">This paper suggests a modified version of the former economic load dispatch (MELD) problem with the integration of wind power plant (WPP) and solar power plants (SPP) into thermal units (TUs). The target of the whole study is to cut the total producing electricity cost (TPEC) as much as possible. Three meta-heuristic algorithms, including particle swarm optimization (PSO), jellyfish search (JS) and salp swarm algorithm (SSA), are applied to solve the MELD. The real performance of these optimization tools is tested on the first system with six thermal units considering prohibited zones, and the second system with the combination of the first system and one solar, and two WPPs. In addition, the variation of load demand in 24 hours per day is also taken into account in the second system. JS is proved to be the most effective method for dealing with MELD. Furthermore, JS can also reach lower or the same TPEC as other previous algorithms. Hence, JS is a recommended to be a strong computing method for dealing with the MELD problem. </span>

Economic Load Dispatch using IYSGA

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. 

Performance of the Walrus Optimizer for solving an economic load dispatch problem

<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>

Improved Pelican optimization algorithm for solving load dispatch problems

The Pelican Optimization Algorithm (POA) is a newly developed algorithm inspired by the hunting behavior of pelicans. Despite its fast convergence rate, it suffers from premature convergence, the imbalance between exploration and exploitation, and lack of population diversity. In this work, an improved POA is proposed to attenuate these shortcomings. IPOA benefits from three motion strategies and predefined knowledge-sharing factors that better describe the stochastic hunting behavior of pelicans, as well as a modified dimension-learning-based hunting (DHL) behavior to retain diversity. To test the effectiveness of these improvements, it was used to solve 23 benchmark functions, including unimodal, multimodal, and 6 composite functions (CEC 2017). To evaluate performance, it was applied to solve economic and combined economic emission load dispatch problems that play a critical role in real-world power system planning and operation while considering environmental impacts. This experiment includes 6, 10, 11, 40, 140, 160, and 320 generating units with nonconvex and non-smooth objective functions. The comparison is performed for benchmark functions and the optimal dispatch problems. The results confirm the competitive and almost superior performance of the IPOA in several cases, which proves the applicability and efficiency of the proposed approach in solving real-world problems.

Solving the Green Economic Load Dispatch by Applying the Novel Meta-heuristic Algorithm

This study focuses on solving the green economic load dispatch problem by considering the presence of green energy sources, including wind energy and solar power plants. The main objective function of the whole study is to minimize the total fuel cost (TFC) of all the thermal generating sources (TGSs) in the system. Moreover, the multiple selection of all TGSs is also evaluated. Fire hawk optimization (FHO) and the Zebra optimization algorithm (ZOA) are applied to solve the problem of achieving the best TFC value and satisfying all the constraints involved. The results indicated that ZOA can achieve a better optimal solution compared to FHO. Particularly, the results obtained by ZOA are completely superior to FHO in all comparison criteria at two load demand levels, such as Best TFC value (Best.Cost), Average TFC value (Aver.Cost), and Maximum TFC value (Max.Cost). On top of that, ZOA is the only algorithm of two applied ones providing the fast convergence capability to the optimal value of the main objective functions in two cases of load demand levels. Therefore, ZOA is an efficient search method to deal with such GELD problems.

Snow avalanches algorithm (SAA): A new optimization algorithm for engineering applications

This paper proposes a novel efficient inspired algorithm based on snow avalanches in nature which is named the Snow Avalanches Algorithm (SAA), for solving the benchmark and engineering optimization problems and determining the global solution. The proposed algorithm is modeled using four phases including avalanche due to mountain slope, human factors, weather in the region as well as normal conditions and it has only one control parameter. The advantages of this algorithm are low control parameters, simple structure and also easy implementation. The effectiveness of the SAA algorithm is examined on 23 classic benchmark test functions. Then, the effectiveness of the SAA to achieve accurate results in different aspects is examined and proved on engineering problems including six different cases. The superiority of the SAA to solve the classic benchmark test functions is compared with spotted hyena optimization (SHO), particle swarm optimization (PSO), Aquila optimizer (AO), differential evolution (DE), bat algorithm (BA), dwarf mongoose optimization (DMO), genetic algorithm (GA), artificial bee colony (ABC), and ant colony optimization (ACO). The simulation results provide evidence for the well-organized and efficient performance of the SAA in solving a great diversity of engineering problems. The results demonstrated that the SAA can be more effective than other algorithms to solve the test functions in terms of optimization accuracy and convergence rate. Moreover, the results proved that the SAA obtained more competitive results than the previous methods to solve constrained engineering optimization problems, especially hybrid energy system design as well as economic load dispatch problems.

Solutions of economic load dispatch problems for hybrid power plants using Dandelion optimizer

In this paper, an economic load dispatch problem (ELD) is solved for reaching optimal power output of hybrid systems in addition to cost minimization. The systems consider the forbidden working zones (FWZs), dynamic load demand, wind farms, and solar photovoltaic fields (SPs). The cost minimization solutions for the ELD problem are found by applying the Dandelion optimizer (DO), the salp swarm algorithm (SSA), and the particle swarm optimization (PSO). In the study case, the power system consists of six thermal power plants (TPs), two wind farms, and two SPs. In addition, the variation of load demand over 24 hours of one day is applied. DO and SSA can achieve the best cost of $15443.0753 for the first system, but PSO cannot. However, DO is the most stable method reaching the standard deviation of 0.0184 for fifty runs but that of SSA and PSO is about 1.0439 and 8.9664. For the second system, DO can reach smaller cost than PSO by $11.17, $137.74 and $323.09 for the best, mean and worst solutions among fifty found solutions. As a result, DO is strongly recommended for solving the ELD problem.

Performance of Osprey Optimization Algorithm for Solving Economic Load Dispatch Problem

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.

Equilibrium optimiser for the economic load dispatch problem with multiple fuel option and renewable sources

The integration of thermal units with renewable sources leads to a highly nonlinear and difficult Economic Load Dispatch (ELD) problem. However, dependency of wind speed and solar irradiance, renewable sources like wind-solar plants cannot guarantee their output. It has been possible to anticipate the wind speed and solar irradiation by Weibull and beta probability density functions. Wind and solar energy output powers have been estimated using the 2-m point estimation method. The renewable-based ELD problem has a solution thanks to the equilibrium optimizer (EO) technique. Finding the answer in a relatively short amount of computing time is made possible by the method's exploration and exploitation stages. The suggested technique has been validated in three, five, six, fifteen, and huge 160 thermal units linked to renewable energy sources by meeting restrictions such generator operating restrictions, valve point loading impact, and numerous fuel possibilities.

A New PSO Technique Used for the Optimization of Multiobjective Economic Emission Dispatch

Most power is generated using fossil fuels like coal, natural gas, and diesel. The contribution of coal to power generation is very high compared to other sources. Almost all thermal power plants use coal as a fuel for power generation. Such sources of fossil fuels are limited and thus the cost of power generation increases. At the same time, the induced toxic gases due to these fossil fuels pollute the environment. The objective of this work is to solve the economic emission dispatch problem. Economic emission dispatch helps to find out how to operate power plants at the minimum cost and induce the minimum emissions at a thermal power plant. Economic emission dispatch with constraints is a nonlinear optimization problem. For the solution of such nonlinear economic emission load dispatch problems, this work considers a new particle swarm optimization technique. The proposed new PSO gives the best solution for economic emission load dispatch and handles the constraints. For the testing of the proposed new PSO algorithm, this work considered a case study of a system of six generating units, and it was tested for load demands of 700 MW, 800 MW, and 1000 MW. The results of the new PSO for the three load demands considered give the minimum generation cost, minimum emission, and minimum total cost compared to other optimization algorithms. The proposed techniques are effective, and they can help obtain the minimum generation cost and minimize emissions.

Novel Heuristic Optimization Technique to Solve Economic Load Dispatch and Economic Emission Load Dispatch Problems

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.

Five Phases Algorithm: A Novel Meta-heuristic Algorithm and Its Application on Economic Load Dispatch Problem

<p>A new meta-heuristic algorithm named the five phases algorithm (FPA) is presented in this paper. The proposed method is inspired by the five phases theory in traditional Chinese thought. FPA updates agents based on the generating and overcoming strategy as well as learning strategy from the agent with the same label. FPA has a simple structure but excellent performance. It also does not have any predefined control parameters, only two general parameters including population size and terminal condition are required. This provides flexibility to users to solve different optimization problems. For global optimization, 10 test functions from the CEC2019 test suite are used to evaluate the performance of FPA. The experimental results confirm that FPA is better than the 6 state-of-the-art algorithms including particle swarm optimization (PSO), grey wolf optimizer (GWO), multi-verse optimizer (MVO), differential evolution (DE), backtracking search algorithm (BSA), and slime mould algorithm (SMA). Furthermore, FPA is applied to solve the Economic Load Dispatch (ELD) from the real power system problem. The experiments give that the minimum cost of power system operation obtained by the proposed FPA is more competitive than the 14 counterparts. The source codes of this algorithm can be found in https://ww2.mathworks.cn/matlabcentral/fileexchange/118215-five-phases-algorithm-fpa.</p> <p> </p>