Economic Load Dispatch Problem Research Articles

SOLVING COMBINED ECONOMIC AND EMISSION DISPATCH PROBLEM USING THE SLIME MOULD ALGORITHM

In this paper, a novel optimization method called Slime Mould Algorithm (SMA) for solving the ELD and CEED problem is presented. To investigate the effectiveness of the proposed algorithm, the 10 and 40 units considering the valve point loading effect test has been executed. The solving the Economic Load Dispatch (ELD) and Combined Economic and Emission Dispatch (CEED) are crucial task in modern power systems. The aim of ELD is assigning the best generation scheduling for minimum cost generation with satisfying the load demands while the CEED means assigning the best generation scheduling for cost and emission reduction simultaneously. The effectiveness of the proposed algorithm is compared with other algorithms. In this paper, a novel optimization method called Slime Mould Algorithm (SMA) for solving the ELD and CEED problem is presented. To investigate the effectiveness of the proposed algorithm, the 10 and 40 units considering the valve point loading effect test has been executed. The solving the Economic Load Dispatch (ELD) and Combined Economic and Emission Dispatch (CEED) are crucial task in modern power systems. The aim of ELD is assigning the best generation scheduling for minimum cost generation with satisfying the load demands while the CEED means assigning the best generation scheduling for cost and emission reduction simultaneously. The effectiveness of the proposed algorithm is compared with other algorithms.

Modified Krill Herd Algorithm for constrained economic load dispatch problem

ABSTRACT Meta-heuristic techniques are gaining attractiveness to solve constrained economic load dispatch problems due to higher global solution capacity, flexibility and derivative-free structure. In this paper, Modified Krill Herd Algorithm (MKHA) is used to solve economic load dispatch problem having non-linear characteristics of generators and considering transmission losses. The proposed MKHA is a nature-inspired technique that incorporates crossover and mutation process designed in differential evolution which causes the krill to execute local search within definite section. Constraints manipulation trial is also made functional in the direction of approaching equality constraints to change total power generation depending upon the requirement of power by consumers. The proposed algorithm is testified on three systems and assessment is prepared on the basis of minimisation of fuel cost and arithmetic procedures. Relative examination of obtained outcome illustrates the efficacy of the proposed algorithm, with regard to the quality of solutions and higher efficiency.

Design of moth flame optimization heuristics for integrated power plant system containing stochastic wind

In this investigation, nature-inspired heuristic strategy exploiting moth flame optimization (MFO) algorithm combined with active-set algorithm (ASA), interior point algorithm (IPA) and sequential quadratic programming (SQP) are presented to take care of the enhancement issues of economic load dispatch (ELD) problem involving valve point loading effect (VPLE) and stochastic wind (SW). The strength of MFO algorithm is used as a global search mechanism that explore and exploit the entire search space while ASA, IPA and SQP are responsible for refinement of local optimum. The performance of the design system is based on 40 generating units including 37 thermal and 3 wind power units and is evaluated to verify the effectiveness of the scheme. The worth of the design integrated heuristic of MFO algorithm is endorsed through outcomes of the state of the art counterpart solvers in case of ELD problems integrated with wind power units in terms of cost minimization and computational complexity parameters.

Efficient Energy Load Distribution Model using Modified Particle Swarm Optimization Algorithm

Reduction of emission and energy conservation plays a major role in the current power system for realizing sustainable socio-economic development. The application prospects and practical significance of economic load dispatch issue in the electric power market is remarkable. The various generating sets must be assigned with load capacity in a reasonable manner for reducing the cost of electric power generation. This problem may be overcome by the proposed modified particle swarm optimization (PSO) algorithm. The practical issue is converted and modelled into its corresponding mathematical counterpart by establishing certain constraints. Further, a novel interdependence strategy along with a modified PSO algorithm is implemented for balancing the local search capability and global optimization. Multiple swarms are introduced in the modified PSO algorithm. Certain standard test functions are executed for specific analysis. Finally, the proposed modified PSO algorithm can optimize the economic load dispatch problem while saving the energy resources to a larger extent. The algorithm evaluation can be performed using real-time examples for verifying the efficiency. When compared to existing schemes like artificial bee colony (ABC), genetic algorithms (GAs), and conventional PSO algorithms, the proposed scheme offers lowest electric power generation cost and overcomes the load dispatch issue according to the simulation results.

A Review Paper on Economic Load Dispatch Problem

Efficient methods for solving economic load dispatch (ELD) problems have been provided to build effective multi-objective evolutionary algorithms (MOEAs). ELD is a dynamic bi-objective optimization problem that is strictly limited. The MOEA applications to solve the ELD problems have been published in various publications since the 1990s. This paper explores the state of the art of this direction-related research. It addresses subjects such as standard MOEAs, traditional ELD problems, dynamic ELD problems, wind power integration ELD problems, electric car integration ELD problems and micro-grid ELD problems. Furthermore, several potential directions are also provided for future study.

Optimal Economic Load Dispatch with Prohibited Operating Zones Using Large to Small Area Technique

In practical power plant operation, the economic load dispatch problem is not straightforward. The objective function is generally differentiable (in a quadratic form). It can change to non-differentiable (non-smoothing) or discontinuous fuel cost curve (prohibited operating zones) in the actual power plant operation. The economic load dispatch problem (non-differentiable) solved by calculus methods based on differential (LaGrange method) will not be relevant again. The method currently being developed is based on artificially (for example, Genetic Algorithm), which does not depend on the form of the objective function. It is very relevant to be implemented. There are prohibited operating zones that will make the economic load dispatch problem more complicated to solve. This complicated problem will be solved more easily by area to smaller area technique, which is the simplest artificial method. In addition, this method can give good accuracy because all subareas are traceable and can work for a large scale based on a big candidate size. The simulation results for 15-unit generators with prohibited zones show that the proposed method is working well. The method has shown a small reduction in total cost compared to particle swarm optimization method, and the total cost has closed to the Lambda Iteration and Dynamic Programming methods.

Dragonfly algorithm: a comprehensive survey of its results, variants, and applications

This paper thoroughly introduces a comprehensive review of the so-called Dragonfly algorithm (DA) and highlights its main characteristics. DA is considered one of the promising swarm optimization algorithms because it successfully applied in a wide range of optimization problems in several fields, such as engineering design, medical applications, image processing, power and energy systems, and economic load dispatch problems. The review describes the available literature on DA, including its variants like binary, discrete, modify, and hybridization of DA. Conclusions focus on the current work on DA, highlighting its disadvantages with suggests possible future research directions. Researchers and practitioners of DA belonging to a wide range of audiences from the domains of optimization, engineering, medical, data mining, and clustering, among others will benefit from this study.

An Improved Symbiosis Particle Swarm Optimization for Solving Economic Load Dispatch Problem

To realize the sustainable development of social economy, energy conservation and emission reduction has become one of the problems that must be considered in the current power system. Under the electric power market system, the economic load dispatch problem not only is important but also has practical significance and broad application prospects. In order to minimize the costs of electric-power generation, the load capacity should be reasonably assigned among many different generating sets. In this paper, an improved symbiosis particle swarm optimization algorithm was proposed, aiming at providing a better solution to this problem. First of all, a mathematical model was established with certain constraints, which successfully converted the practical problem into a mathematical one. Then, to balance the global optimization and local search capability, an improved symbiosis particle swarm optimization algorithm with mutualistic symbiosis strategy in nature was presented. The improved symbiosis particle swarm optimization algorithm consisted of three swarms inspired by the proverb “two heads are better than one,” and its specific analysis was through the standard test functions. At last, the economic load dispatch problem could be optimized by the proposed improved symbiosis particle swarm optimization algorithm. In addition, two different kinds of practical examples were also adopted for algorithm evaluation. From the simulation results, it can be seen clearly that the costs of electric-power generation gained were the lowest compared with the results of particle swarm optimization algorithm, improved chaos particle swarm optimization algorithm, and symbiotic organisms search algorithm, well demonstrating the effectiveness of the improved symbiosis particle swarm optimization algorithm in solving the economic load dispatch problem.

Performance of Turbulent Flow of Water Optimization on Economic Load Dispatch Problem

The economic load dispatch (ELD) problems considering nonlinear characteristics where an optimal combination of power generating units is selected in order to minimize the total cost by economic allocation of power produced and the emission cost. As a consequence, optimal allocation is performed by considering both fuel cost and emission leading to Combined Economic and Emission Dispatch (CEED). This study presents a new Meta-heuristic algorithms (MHs) called the Turbulent Flow of Water Optimization (TFWO), which is based on the behaviour of whirlpools created in turbulent water flow, for solving different variants of ELD and CEED. To verify the robustness of the TFWO, various test network of CEED with effect of valve, and ELD with losses of transmission are incorporated. In comparison with seven well-known MHs such as Cuckoo Search Algorithm (CSA), Grey Wolf Algorithm (GW), Sine Cosine Algorithm (SCA), Earth Worm Optimization Algorithm (EWA), Tunicate Swarm Algorithm (TSA), Moth Search Algorithm (MSA) and Teaching Learning Based Optimization (TLBO), the TFWO provides the minimum fuel cost and significantly robust solutions of ELD problem over all tested networks. The results confirm the potential and effectiveness of the GWO to be a promising technique to solve various ELD problems.

A Multi-Restart Dynamic Harris Hawk Optimization Algorithm for the Economic Load Dispatch Problem

In this study, we propose an algorithm based on a recently proposed metaheuristic called the Harris Hawk Optimization (HHO). We utilized a dynamic control strategy to enhance the exploration capability. To further avoid trapping in local optima, we incorporate opposition-based learning (OLB) and a multi-restart strategy. The proposed algorithm is used to solve economic load dispatch (ELD) problems with non-smooth cost functions. The ELD problems have a very large search space and therefore it is difficult to find global optimum using analytical methods. The results of the proposed approach are very competitive compared with notable results from previous research.

Recent Methodology-Based Gradient-Based Optimizer for Economic Load Dispatch Problem

Economic load dispatch (ELD) in power system problems involves scheduling the power generating units to minimize cost and satisfy system constraints. Although previous works propose solutions to reduce CO2 emission and production cost, an optimal allocation needs to be considered on both cost and emission-leading to combined economic and emission dispatch (CEED). Metaheuristic optimization algorithms perform relatively well on ELD problems. The gradient-based optimizer (GBO) is a new metaheuristic algorithm inspired by Newton's method that integrates both the gradient search rule and local escaping operator. The GBO maintains a good balance between exploration and exploitation. Also, the possibility of the GBO getting stuck in local optima and premature convergence is rare. This paper tests the performance of GBO in solving ELD and CEED problems. We test the performance of GBO on ELD for various scenarios such as ELD with transmission losses, CEED and CEED with valve point effect. The experimental results revealed that GBO has been obtained better results compared to eight other metaheuristic algorithms such as Slime mould algorithm (SMA), Elephant herding optimization (EHO), Monarch butterfly optimization (MBO), Moth search algorithm (MSA), Earthworm optimization algorithm (EWA), Artificial Bee Colony (ABC) Algorithm, Tunicate Swarm Algorithm (TSA) and Chimp Optimization Algorithm (ChOA). Therefore, the simulation results showed the competitive performance of GBO as compared to other benchmark algorithms.

Quasi Oppositional Population Based Global Particle Swarm Optimizer With Inertial Weights (QPGPSO-W) for Solving Economic Load Dispatch Problem

In recent years, power companies have shown increasing interest in making strategic decisions to maintain profitable energy systems. Economic Load Dispatch (ELD) is a complex decision-making process where the output power of the entire power generating units must be set in a way that results in the overall economic operation of the power system. Moreover, it is a constrained multi-objective optimization problem. Now a days, there is a tendency to use metaheuristic methods to deal with the complexity of the ELD problem. Particle swarm optimization (PSO) is a subclass of metaheuristic methods inspired by fish schooling and bird flocking behaviors. However, the optimization performance of the PSO is highly dependent on fitness landscapes and can lead to local optima stagnation and premature convergence. Therefore, in the proposed study, two new variants of the PSO called global particle swarm optimizer with inertial weights (GPSO-w) and quasi-oppositional population based global particle swarm optimizer with inertial weights (QPGPSO-w) are proposed to address the complexity of the ELD problem. The ELD problem is formulated as an optimization problem and validation of the proposed methods is performed on IEEE standards (3, 6, 13, 15, 40 & 140) unit Korean grid ELD test systems under numerous constraints and the obtained results are compared with the several recent techniques presented in the literature. The results obtained with convex systems showed excellent cost-effectiveness, while for non-convex systems sequential quadratic programming (SQP) optimizer was added to discover global minima even more efficiently. The proposed techniques were successful in solving the ELD problem and yielded better results compared to the reported results in the selected cases. It is further inferred that the proposed techniques with less algorithmic parameters reflected improved exploration and convergence characteristics.

Dynamic economic dispatch problem in hybrid wind based power systems using oppositional based chaotic grasshopper optimization algorithm

This article introduces a relatively current method named grasshopper optimization algorithm (GOA) for explaining power system based dynamic economic load dispatch (DELD) problem. However, like other optimization approaches, GOA suffers from premature convergence and a slow convergence rate. Thus, to boost the convergence mobility of GOA, oppositional based learning (OBL) is merged with the GOA approach. Moreover, another improvization, namely, chaotic concept, is also integrated with the GOA to improve its solution quality. The suggested oppositional based chaotic grasshopper optimization algorithm (OCGOA) method is applied to handle the DELD problem in the most efficient manner. Among the renewable energies, intermittent wind energy (WE) is the most sustainable one and remains technically and economically advantageous for electrical energy generation. The thermal and wind based power systems are hybridized, so that power generation is distributed among the operating units in an equivalent manner such that overall cost and loss part are optimized until all practical constraints are fulfilled. The production cost of the unpredictable wind generation power is further incorporated in the operational cost by employing a probability density function (PDF) formula. The precision and performance of the suggested GOA and OCGOA approaches are validated on 6-unit and 10-unit DELD systems for conventional and wind based energy systems. The efficacy and performance of the suggested OCGOA is judged by comparing it with conventional GOA and other presently developed meta-heuristic optimization techniques found in the literature.

Solution to economic load dispatch using quasi-oppositional based CoDE by considering transmission line losses

The main objective of economic dispatch problem is to optimally allocate the load demand among the generating stations such that there is decrease in production cost of the power generation. In the present paper, a quasi-oppositional based composite differential evolution (QOCoDE) technique is proposed to economic load dispatch (ELD) problem. The suggested method provides optimal solutions by combining various strategies in generating trial vector with suitable control parameter settings. The proposed technique is applied on various generating units by considering fixed boundary conditions and transmission losses. The obtained results are compared with various evolutionary algorithms. The results demonstrate the capability of QOCoDE to provide optimal solutions when compared to other evolutionary techniques.

Solving Renewables-Integrated Economic Load Dispatch Problem by Variant of Metaheuristic Bat-Inspired Algorithm

One of the most important concerns in the planning and operation of an electric power generation system is the effective scheduling of all power generation facilities to meet growing power demand. Economic load dispatch (ELD) is a phenomenon where an optimal combination of power generating units is selected in such a way as to minimize the total fuel cost while satisfying the load demand, subject to operational constraints. Different numerical and metaheuristic optimization techniques have gained prominent importance and are widely used to solve the nonlinear problem. Although metaheuristic techniques have a good convergence rate than numerical techniques, however, their implementation seems difficult in the presence of nonlinear and dynamic parameters. This work is devoted to solving the ELD problem with the integration of variable energy resources using a modified directional bat algorithm (dBA). Then the proposed technique is validated via different realistic test cases consisting of thermal and renewable energy sources (RESs). From simulation results, it is observed that dBA reduces the operational cost with less computational time and has better convergence characteristics than that of standard BA and other popular techniques like particle swarm optimization (PSO) and genetic algorithm (GA).

A New Aggrandized Class Topper Optimization Algorithm to Solve Economic Load Dispatch Problem in a Power System.

Optimization techniques are widely being used to solve large and complex economical load dispatch (ELD) and combined emission economical dispatch (CEED) problems in power systems. These techniques can solve these problems in a short computational time. In this article, a new human intelligence-based metaheuristic optimization technique, that is, aggrandized class topper optimization (CTO), is proposed to solve ELD and CEED problems. This proposed algorithm is an upgraded form of classical CTO in which the concept of remedial classes is incorporated to enhance the learning ability of weak students of a class. To validate the exploration, exploitation, convergence, and local minima avoidance capabilities of the proposed algorithm, 29 benchmark functions are considered. Furthermore, seven different test cases for the ELD problem and four test cases for a CEED problem are considered to test the effectiveness of the proposed algorithm to solve these complex problems. The result analysis proves that the proposed algorithm provides better and effective results in almost each test case.

A Cauchy-Gaussian Quantum-Behaved Bat Algorithm Applied to Solve the Economic Load Dispatch Problem

In this paper, a novel Cauchy-Gaussian quantum-behaved bat algorithm (CGQBA) is applied to solve the economic load dispatch (ELD) problem. The bat algorithm (BA) is an acknowledged metaheuristic optimization algorithm owing to its performance. However, the classical BA presents some weaknesses, such as premature convergence. To withstand the drawbacks of the BA, quantum mechanics theories and Gaussian and Cauchy operators are integrated into the standard BA to enhance its effectiveness. Since the economic load dispatch is a nonlinear, complex and constrained optimization problem, its main objective is to reduce the total generation cost while matching the equality and inequality constraints of the system. The validity of the CGQBA is tested on six standard benchmark functions with different characteristics. The numerical results indicate that the CGQBA is effective and superior to many other algorithms. Moreover, the CGQBA is applied to solve the ELD problems on various test systems including 3,6,20, 40,110 and 160 implemented generating units. The simulation results illustrate the strength of the CGQBA compared with other algorithms recently reported in the literature.

Economic power dispatch for an interconnected power system based on reliability indices

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.

The Use of Spreadsheets in Teaching the Economic Load Dispatch Problem

Economic Load Dispatch problems in electrical power networks have been investigated over the years and several calculation methods were introduced. In order to determine the work state of power network, it is often necessary to solve a large system of non-linear transcendent equations. Therefore, the program routines are complex to develop, while specialized commercial software packages are expensive and not easily available. On the other hand, Microsoft Excel as a part of Microsoft office software package is widely spread in the world and relatively easily available. This paper presents the design and development of Microsoft Excel based economic load dispatch analysis tool and its application for system planning and operation. Three different economic load dispatch methods, namely, Merit Order, Lambda-Iteration and Dynamic Programming methods have been implemented to provide wider choice for the users. The emphasis of this paper is on the educational value of spreadsheets in the analysis of power system.

SOLVING ECONOMIC LOAD DISPATCH WITH RELIABILITY INDICATORS

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.