Solution Of Economic Load Dispatch Research Articles

Economic load dispatch solution of large-scale power systems using an enhanced beluga whale optimizer

The aim of the optimization economic load dispatch (ELD) problem is to assign the optimal generated power of the thermal units for cost reduction with satisfying the loading of the operational constraints. The ELD is a high-dimensional and non-convex problem that became a more complex problem in the case of optimizing the output generated power of large-scale systems. In this regard, an enhanced version of the Beluga whale optimization (EBWO) is proposed to deal with the ELD of the large-scale systems. Beluga whale optimization (BWO) is an efficient new optimization technique that mimics the behavior of the Beluga whales (BWs) in preying, swimming, and whale fall. However, the BWO may suffer from stagnation in local optima and scarcity of population diversity like other metaheuristics. The proposed EBWO algorithm is presented to render the standard BWO more robust and powerful search by using two strategies including the cyclone foraging motion for boosting the exploitation phase of the optimization algorithm and the quasi-oppositional based learning (QOBL) for improving population diversity. Firstly, Simulations are carried out on seven benchmark functions to prove the validation of the proposed EBWO algorihm compared with five recent algorithms. Then, The performance of the EBWO is checked on 11-units, 40-units, and also 110-unit test systems, and the obtained results of EBWO are compared with other well-known techniques such as the classical BWO, FOX Optimization Algorithm (FOX), Skill Optimization Algorithm (SOA), and Sand Cat swarm optimization (SCSO) as well as the with existing algorithms from the literature including DE, TLBO, MPSO, NGWO, IGA, NPSO, CJAYA, SMA, PSO, PPSO, SSA, MPA, MGMPA, and HSSA. The Numerical results show that the proposed algorithm is very competitive compared with the other reported optimization algorithms in obtaining low fuel costs.

A Method for Completing Economic Load Dispatch Using the Technique of Narrowing Down Area

Economic load dispatch solutions based on published methods, both conventional and artificial, have been very well-formulated through point-to-point movement methodologies to reach a convergence point. Iteration always starts from the starting point to obtain the following solution point, leading to the convergence point. This paper presents a new method to solve economic load dispatch problems by narrowing the minimum and maximum power limits between generator units. This idea approximates the solution point with a tiny space formed by the very narrow power limits of each generator. The methodology used is the distance between the minimum and maximum power limits of each generator divided into several segments. Then, the best segment is determined by the minimum total cost calculated based on the center point of the segment. Continue to the following iteration process until the best segment is the smallest. This iteration process is another artificial method that works without calculus calculations, so it does not depend on the objective function. This method has been validated using two generator units with differentiable objective functions, with calculation accuracy less than 0.00001 MW of the power distance of the generator limit, and the iteration stops at the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$23^{\mathrm {rd}}$ </tex-math></inline-formula> step. Furthermore, this method has been successfully applied to the nondifferentiable objective function, piecewise and valve point effects.

Economic load dispatch solutions considering multiple fuels for thermal units and generation cost of wind turbines

In this paper, economic load dispatch (ELD) problem is solved by applying a suggested improved particle swarm optimization (IPSO) for reaching the lowest total power generation cost from wind farms (WFs) and thermal units (TUs). The suggested IPSO is the modified version of Particle swarm optimization (PSO) by changing velocity and position updates. The five best solutions are employed to replace the so-far best position of each particle in velocity update mechanism and the five best solutions are used to replace previous position of each particle in position update. In addition, constriction factor is also used in the suggested IPSO. PSO, constriction factor-based PSO (CFPSO) and bat optimization algorithm (BOA) are also run for comparisons. Two systems are used to run the four methods. The first system is comprised of nine TUs with multiple fuels and one wind farm. The second system is comprised of eight TUs with multiple fuels and two WFs. From the comparisons of results, IPSO is much more powerful than three others and it can find optimal power generation with the lowest total power generation cost.

A new flexibility based probabilistic economic load dispatch solution incorporating wind power

Nowadays, by the growing in renewable energies in the power system, the uncertainty of power output related to these resources increases. This needs to improve power system flexibility to reduce the risk of load shedding or renewable curtailment due to the mentioned challenge. So, nowadays power system flexibility is an important characteristic especially in power system operation which should be evaluated continuously and maintained in the desired value. In operation horizon time such as operational planning or real time operation the system generation flexibility should be monitored, and sufficient system flexibility should be provided to avoid unacceptable generation/load unbalance cause unwanted renewable curtailment or load shedding.This paper presents a new flexibility based risk limiting dynamic economic load dispatch solution incorporating wind power. In the proposed method the generation system flexibility index, introduced by the authors is converted to economic value and included in the total operation cost function. Then by the suitable economic trade-off between system flexibility level and risk of load shedding and wind power curtailment, the best reduction in these two unwanted risks are obtained. Increasing the system generation flexibility comes from the generation rearrangement of thermal generation units imposes more cost to the generation cost but is balanced by reduction in unwanted renewable curtailment or load shedding.

Lambda Iteration and Genetic Algorithms Application to solve the Economic Load Dispatch Problem of Seven Nigerian Thermal Power Plants

Economic load dispatch (ELD) is a method of earmarking the required load demand between the existing generations in power system and principally determining allocation of generators to each generation for various systems load levels. ELD is an essential component in power system planning and operation. ELD solutions are found by solving the conventional load flow equations, while at the same time ensuring that fuel costs are minimized. There are many methods developed for solving ELD problems, but this work is restricted to two, which are the Lambda Iteration Method (LIM) and the Genetic Algorithm (GA) modified with sorting algorithm. The main objective is to apply the two methods to solve ELD problems in power system networks by comparing the performance of GA method with that of LIM in terms of fuel cost efficiency. The usefulness of LIM and GA to solving economic dispatch problem is emphasized. Simulation results obtained on this network using GA and LIM verify their effectiveness in solving ELD problems. Lastly, GA and LIM approaches have been effectively applied to the harmonization of the Nigerian 32-bus system powered by seven thermal and three hydro generating units. The study shows that GA exhibits better results than LIM from both best possible generation allocations. The results obtained demonstrate that GA based method gave better solution in terms of fuel cost reduction, when compared with those obtained using LIM. By blending the probabilities of crossover and mutation, and the application of sorting techniques, computer usage time can be significantly reduced in the system with better fuel cost reduction. Keywords: Economic load dispatch (ELD), genetic algorithm (GA), lambda iteration method (LIM), optimization, sorting algorithm . DOI: 10.7176/JETP/11-4-04 Publication date: August 31 st 2021

Economic Load Dispatch Incorporating Wind Power Using Hybrid Biogeography-Based Optimization

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.

Solution to Economic Load Dispatch Problem of a Distributed Generating System using Pattern Search Algorithm

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.

An Effectively Modified Firefly Algorithm for Economic Load Dispatch Problem

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.

Bio-inspired heuristics hybrid with sequential quadratic programming and interior-point methods for reliable treatment of economic load dispatch problem

In the present study, bio-inspired computational heuristics are exploited for finding the solution of economic load dispatch (ELD) problem with valve point loading effect using variants of genetic algorithm (GA) hybrid with sequential quadratic programming (SQP) and interior-point algorithms (IPAs). Variants of GAs are constructed using different sets of routines for its fundamental operators in order to explore the entire search space for global optimum solutions while SQP and IPA are integrated with GAs for rapid local convergence. Nine variants of each design scheme based on GAs, GA-SQP and GA-IPAs are applied on three different ELD problems of thermal power plant systems. Comparative studies of the proposed schemes are performed through the results of statistical performance indices in order to establish the worth and effectiveness in terms of accuracy, convergence and complexity measures.

Non-convex Economic Load Dispatch using Cuckoo Search Algorithm

&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;

An economic load dispatch and multiple environmental dispatch problem solution with microgrids using interior search algorithm

Microgrid is a novel small-scale system of the centralized electricity for a small-scale community such as villages and commercial area. Microgrid consists of micro-sources like distribution generator, solar and wind units. A microgrid is consummate specific purposes like reliability, cost reduction, emission reduction, efficiency improvement, use of renewable sources and continuous energy source. In the microgrid, the Energy Management System is having a problem of Economic Load Dispatch (ELD) and Combined Economic Emission Dispatch (CEED) and it is optimized by meta-heuristic techniques. The key objective of this paper is to solve the Combined Economic Emission Dispatch (CEED) problem to obtain optimal system cost. The CEED is the procedure to scheduling the generating units within their bounds together with minimizing the fuel cost and emission values. The newly introduced Interior Search Algorithm (ISA) is applied for the solution of ELD and CEED problem. The minimization of total cost and total emission is obtained for four different scenarios like all sources included all sources without solar energy, all sources without wind energy and all sources without solar and wind energy. In both scenarios, the result shows the comparison of ISA with the Reduced Gradient Method (RGM), Ant Colony Optimization (ACO) technique and Cuckoo Search Algorithm (CSA) for the two different cases which are ELD without emission and CEED with emission. The results are calculated for different Power Demand of 24 h. The results obtained to ISA give comparatively better cost reduction as compared with RGM, ACO and CSA which shows the effectiveness of the given algorithm.

Solution of Economic Load Dispatch (ELD) Problem by Path Relinking (PR) Algorithm

Solution of Economic Load Dispatch (ELD) Problem by Path Relinking (PR) Algorithm

Solution of Economic Load Dispatch problem in Power System using Lambda Iteration and Back Propagation Neural Network Methods

Economic load dispatch is the process of allocating the required load demand between the available generators in power system while satisfying all units and system equality and inequality constraints. Economic Load Dispatch solutions are found by solving the conventional methods such as lambda iteration, Gradient search method, Linear Programming and Dynamic Programming while at the same minimizing fuel costs, but convergence is too slow, so in order to get fast convergence and accurate results we are using artificial neural network. Artificial neural network is well-known in the area of power systems. It is a very powerful solution algorithm because of its rapid convergence near the solution. This property is especially useful for power system applications because an initial guess near the solution is easily attained. In this paper a three generator system is considered and by using lambda iteration method Economic Load Dispatch is determined and 150 patterns for different loads will be derived from same method to train neural network. As it is too slow method, we proposed a soft computing based approach i.e. Back Propagation Neural Network (BPNN) for determining the optimal flow. This method provides fast and accurate results when compared with the conventional method.

Artificial bee colony algorithm for economic load dispatch with wind power energy

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.

Multiobjective Economic Load Dispatch Problem Solved by New PSO

Proposed in this paper is a new particle swarm optimization technique for the solution of economic load dispatch as well as environmental emission of the thermal power plant with power balance and generation limit constraints. Economic load dispatch is an online problem to minimize the total generating cost of the thermal power plant and satisfy the equality and inequality constraints. Thermal power plants use fossil fuels for the generation of power; fossil fuel emits many toxic gases which pollute the environment. This paper not only considers the economic load dispatch problem to reduce the total generation cost of the thermal power plant but also deals with environmental emission minimization. In this paper, fuel cost and the environmental emission functions are considered and formulated as a multiobjective economic load dispatch problem. For obtaining the solution of multiobjective economic load dispatch problem a new PSO called moderate random search PSO was used. MRPSO enhances the ability of particles to explore in the search spaces more effectively and increases their convergence rates. The proposed algorithm is tested for the IEEE 30 bus test systems. The results obtained by MRPSO algorithm show that it is effective and efficient.

Solution of economic load dispatch using hybrid chemical reaction optimization approach

In this paper, a new and efficient optimization technique based on hybridization of chemical reaction optimization (CRO) with differential evolution (DE) is developed and demonstrated to solve the ELD problem with thermal cost function having valve point loading effect together with and without multiple fuel options and with and without considering prohibited operating zone and ramp rate constraint. When valve-point effects, multi-fuel operations and the constraints of prohibited operating zone and ramp rate are taken into account, ELD problem become more complex than conventional ELD problem. To show the priority of the proposed algorithm, it is implemented on six different test systems for solving ELD problems. Comparative studies are carried out to examine the effectiveness of the proposed HCRO-DE approach with conventional DE, CRO and the other algorithms reported in the literature. The simulation results show that the proposed HCRO-DE method is capable of obtaining better quality solutions than DE, CRO and the other well popular optimization techniques.

Computational Algorithms for the Solution of Economic Load Dispatch in an Interconnected Power System

The availability of a reliable and low cost electric power is a primary requirement for the rapid development of any nation. The cost of production of electric power is a very important index in national development. Pricing of electricity is a function of the cost of operation of the power system itself. On the generation sector, production costs are mostly in the form of fuel costs which comprise about eighty to ninety percent of the total operation cost. Minimization of costs is necessary so as to keep prices as low as possible. Minimization of costs or optimization of operation can be done through economic load dispatch alongside unit commitment. Use of these concepts should be done in order to obtain a desirable condition. Lagrange Relaxation has become one of the best solution methods in solving the economic load dispatch problems.

Versioning-based service-oriented model for multi-area power system online economic load dispatch

The main objective of this paper is to construct a distributed environment through which the economic load dispatch solutions of multi-area power systems can be monitored and controlled. A single-server/multi-client architecture which enables the neighboring power systems to access the remote economic load dispatch (ELD) server at any time with their respective data and to get the economic load dispatch solutions from the remote server has been proposed. A .NET remoting architectural model has been implemented in such a way that for every specific period of time, the remote server obtains the system data simultaneously from the neighboring power systems which are the clients registered with the remote ELD server and the optimized economic load dispatch solutions from the server have been sent back to the respective clients. The ELD server creates a new thread of control for every client’s request and hence complete distributed environment is exploited.

Closure to Discussion of “Hybrid Differential Evolution With Biogeography-Based Optimization for Solution of Economic Load Dispatch”

The authors think that the results obtained by DE/BBO and BBO, for ten-generator system, are correct and better than the results.

Discussion of “Hybrid Differential Evolution With Biogeography-Based Optimization for Solution of Economic Load Dispatch”

Discussion of “Hybrid Differential Evolution With Biogeography-Based Optimization for Solution of Economic Load Dispatch”