Emission Load Dispatch Research Articles

Application of the Firefly Algorithm for Solving the Economic Emissions Load Dispatch Problem

Efficient and reliable power production is necessary to meet both the profitability of power systems operations and the electricity demand, taking also into account the environmental concerns about the emissions produced by fossil-fuelled power plants. The economic emission load dispatch problem has been defined and applied in order to deal with the optimization of these two conflicting objectives, that is, the minimization of both fuel cost and emission of generating units. This paper introduces and describes a solution to this famous problem using a new metaheuristic nature-inspired algorithm, called firefly algorithm, which was developed by Dr. Xin-She Yang at Cambridge University in 2007. A general formulation of this algorithm is presented together with an analytical mathematical modeling to solve this problem by a single equivalent objective function. The results are compared with those obtained by alternative techniques proposed by the literature in order to show that it is capable of yielding good optimal solutions with proper selection of control parameters.

Solving economic emission load dispatch problems using hybrid differential evolution

This paper presents the combination of differential evolution (DE) and Biogeography-based Optimization (BBO) algorithm to solve complex economic emission load dispatch (EELD) problems of thermal generators of power systems. Emission substances like NO X , SO X , CO X , power demand equality constraint and operating limit constraint are considered here. Differential evolution (DE) is one of the very fast and robust, accurate evolutionary algorithms for global optimization and solution of EELD problems. Biogeography-based Optimization (BBO) is another new biogeography inspired algorithm. Biogeography deals with the geographical distribution of different biological species. This algorithm searches for the global optimum mainly through two steps: migration and mutation. In this paper the combination of DE and BBO (DE/BBO) is proposed to accelerate the convergence speed of both the algorithm and to improve solution quality. To show the advantages of the proposed algorithm, it has been applied for solving multi-objective EELD problems in a 3 generator system with NO X and SO X emission, in a 6 generators system considering NO X emission, in a 6 generator system addressing both valve-point loading and NO X emission. The current proposal is found better in terms of quality of the compromising and individual solution obtained.

Multiobjective bacteria foraging algorithm for electrical load dispatch problem

In this paper the bacteria foraging meta-heuristic is extended into the domain of multiobjective optimization. In this multiobjective bacteria foraging (MOBF) optimization technique, during chemotaxis a set of intermediate bacteria positions are generated. Next, we use pareto non-dominance criterion to determine final set of bacteria positions, which constitute the superior solutions among current and intermediate solutions. To test the efficacy of our proposed algorithm we have chosen a highly constrained optimization problem namely economic/emission dispatch. Economic dispatch is a constrained optimization problem in power system to distribute the load demand among the committed generators economically. Now-a-days environmental concern that arises due to the operation of fossil fuel fired electric generators and global warming, transforms the classical economic load dispatch problem into multiobjective environmental/economic dispatch (EED). In the proposed work, we have considered the standard IEEE 30-bus six-generator test system on which several other multiobjective evolutionary algorithms are tested. We have also made a comparative study of the proposed algorithm with that of reported in the literature. Results show that the proposed algorithm is a capable candidate in solving the multiobjective economic emission load dispatch problem.

Multiobjective fuzzy dominance based bacterial foraging algorithm to solve economic emission dispatch problem

Abstract This paper proposes the bacterial foraging meta-heuristic algorithm for multiobjective optimization. In this multiobjective bacterial foraging optimization technique, the most recent bacterial locations are obtained by chemotaxis process. Next, Fuzzy dominance based sorting procedure is used here to select the Pareto optimal front (POF). To test the suitability of our proposed algorithm we have considered a highly constrained optimization problem namely economic/emission dispatch. Now-a-days environmental concern that arises due to the operation of fossil fuel fired electric generators and global warming, transforms the classical economic load dispatch problem into multiobjective environmental/economic dispatch (EED) problem. In the proposed work, we have considered the standard IEEE 30-bus six-generator test system and the results obtained by proposed algorithm are compared with the other recently reported results. Simulation results demonstrate that the proposed algorithm is a capable candidate in solving the multiobjective economic emission load dispatch problem.

Hybrid Multiobjective evolutionary Algorithm Based Technique for Economic Emission Load Dispatch Optimization Problem

In This paper, we present a hybrid approach combining two optimization techniques for solving Economic Emission Load Dispatch Optimization Problem EELD. The proposed approach integrates the merits of both genetic algorithm (GA) and local search (LS), where it employs the concept of co-evolution and repair algorithm for handling nonlinear constraints, also, it maintains a finite-sized archive of non-dominated solutions which gets iteratively updated in the presence of new solutions based on the concept of e -dominance. The use of e -dominance also makes the algorithms practical by allowing a decision maker to control the resolution of the Pareto set approximation. To improve the solution quality, local search technique was implemented as neighborhood search engine where it intends to explore the less-crowded area in the current archive to possibly obtain more nondominated solutions. Several optimization runs of the proposed approach are carried out on the standard IEEE 30-bus 6- genrator test system. Simulation results with the proposed approach have been compared to those reported in the literature. The comparison demonstrates the superiority of the proposed approach and confirms its potential to solve the multiobjective EELD problem.

Economic emission load dispatch through fuzzy based bacterial foraging algorithm

This paper presents a newly developed optimization approach involving a modified bacterial foraging algorithm (MBFA) applied for the solution of the economic and emission load dispatch (EELD) problem. The approach utilizes the natural selection of global optimum bacterium having successful foraging strategies in the fitness function. The bacterial foraging algorithm (BFA) appears to be a robust and reliable optimization algorithm for the solution of the EELD problems. To obtain the best compromising solution a fuzzy decision making approach using MBFA is applied to the standard IEEE 30-bus six generator test system and a Taiwan power system of 40 generating units with valve point loading effects. The results confirm the potential and effectiveness of the proposed algorithm compared to various methods such as, linear programming (LP), multi-objective stochastic search technique (MOSST), differential evolution (DE), non-dominated sorting genetic algorithm (NSGA), niched pareto genetic algorithm (NPGA), strength pareto evolutionary algorithm (SPEA) and fuzzy clustering based particle swarm optimization (FCPSO) performed in different central load dispatch centers to solve EELD problems. The quality and usefulness of the proposed algorithm is demonstrated through its application to two standard test systems in comparison with the other existing techniques. The current proposal was found to be better than, or at least comparable to them considering the quality of the solutions obtained.

Application of Biogeography-based Optimization for Solving Multi-objective Economic Emission Load Dispatch Problems

This article presents a biogeography-based optimization algorithm to solve complex economic emission load dispatch problems of thermal generators of power systems. Different emission substances, such as NOX, SOX, and COX, are considered for case studies. The methodology considers the power demand equality constraint and the operating limit constraint during the time of solving economic emission load dispatch problems. Biogeography deals with the geographical distribution of biological organisms. Mathematical models of biogeography describe how species migrate from one habitat to another, how species arise, and how species become extinct. Here, it will be discussed how biogeography-based optimization can be used to solve economic emission load dispatch problems. This algorithm searches the global optimum mainly through two steps: migration and mutation. To show the advantages of the proposed algorithm, this algorithm has been applied for solving multi-objective economic emission load dispatch problems in a six-generator system considering NOX emission for different loading condition; in a three-generator system with NOX and SOX emission; in a six-generator system with SOX, NOX, and COX emissions; and in a six-generator system addressing both valve-point loading and NOX emission. Compared with the other existing techniques, the current proposal is found to be better in terms of quality of the compromising and individual solution obtained.

An ɛ-dominance-based multiobjective genetic algorithm for economic emission load dispatch optimization problem

In this paper, a novel multiobjective genetic algorithm approach for economic emission load dispatch (EELD) optimization problem is presented. The EELD problem is formulated as a non-linear constrained multiobjective optimization problem with both equality and inequality constraints. A new optimization algorithm which is based on concept of co-evolution and repair algorithm for handling non-linear constraints is presented. The algorithm maintains a finite-sized archive of non-dominated solutions which gets iteratively updated in the presence of new solutions based on the concept of ɛ-dominance. The use of ɛ-dominance also makes the algorithms practical by allowing a decision maker to control the resolution of the Pareto-set approximation by choosing an appropriate ɛ value. The proposed approach is carried out on the standard IEEE 30-bus 6-genrator test system. The results demonstrate the capabilities of the proposed approach to generate true and well-distributed Pareto-optimal non-dominated solutions of the multiobjective EELD problem in one single run. Simulation results with the proposed approach have been compared to those reported in the literature. The comparison demonstrates the superiority of the proposed approach and confirms its potential to solve the multiobjective EELD problem.

A Novel Multiobjective Genetic Algorithm Based Technique for Economic Emission Load Dispatch Optimization Problem

A Novel Multiobjective Genetic Algorithm Based Technique for Economic Emission Load Dispatch Optimization Problem

Stochastic economic emission load dispatch through a modified particle swarm optimization algorithm

Conventional economic load dispatch problem uses deterministic models, which are however not able to reflect some real situations in practical applications since certain inaccurate and uncertain factors are normally involved in system operations. Stochastic models are more suited to be used for investigating some of the power dispatch problems. In this paper, both deterministic and stochastic models are first formulated, and then an improved particle swarm optimization (PSO) method is developed to deal with the economic load dispatch while simultaneously considering the environmental impact. Comparative studies are carried out to examine the effectiveness of the proposed approach. First, a comparison is made between the proposed PSO approach and other approaches including weighted aggregation and evolutionary optimization. Then, based on the proposed PSO, the impacts of different problem formulations including stochastic and deterministic models on power dispatch results are investigated and analyzed.

05/02204 A simulated annealing-based goal-attainment method for economic emission load dispatch of fixed head hydrothermal power systems

05/02204 A simulated annealing-based goal-attainment method for economic emission load dispatch of fixed head hydrothermal power systems

A simulated annealing-based goal-attainment method for economic emission load dispatch of fixed head hydrothermal power systems

A novel multiobjective optimization method for economic emission load dispatch of fixed head hydro plants and thermal plants with nonsmooth fuel cost and emission level functions is presented. In this paper, the problem treats economic and emission as competing objectives. Assuming that the decision-maker has goals for each of the objective functions, the multiobjective problem is converted into a single-objective optimization by the goal-attainment method, which is then handled by the simulated annealing technique. The solution methodology can offer a global or near-global noninferior solution in a sense close to the decision-maker's requirements. Numerical results for a sample test system have been presented to demonstrate the applicability and validity of the proposed method.

An Interactive Fuzzy Satisfying-Based Simulated Annealing Technique for Economic Emission Load Dispatch with Nonsmooth Fuel Cost and Emission Level Functions

The economic emission load dispatch problem treats economic and emission as competing objectives for optimal dispatch, which requires some form of conflict resolution to arrive at a solution. Assuming that the decision maker (DM) has imprecise or fuzzy goals for each of the objective functions, the multiobjective problem is transformed into a minimax problem, which is then handled by the simulated annealing (SA) technique. The solution methodology can offer noninferior optimal solution for the DM. Numerical results for a sample test system have been presented to demonstrate the performance and applicability of the proposed method.

On-line emission and economic load dispatch using adaptive Hopfield neural network

This paper presents an adaptive Hopfield neural network (AHNN) based methodology, where the slope of the activation function is adjusted, for finding approximate Pareto solutions for the multi-objective optimization problem of emission and economic load dispatch (EELD). We have placed emphasis on finding solutions quickly, rather than the global Pareto solutions, so that our algorithm can be employed in large on-line power systems where variations in load are quite frequent. To enable faster convergence, adaptive learning rates have been developed by using energy function and applied to the slope adjustment method. The proposed algorithm has been tested on selected IEEE bus benchmark systems. The convergence of AHNN is found to be nearly 50% faster than the non-adaptive version.

Fuel constrained economic emission load dispatch using hopfield neural networks

This paper presents a new approach using Hopfield neural networks for solving fuel constrained economic emission load dispatch problems of thermal generating units. This is a multi-objective minimization technique that includes the standard load constraints as well as the fuel constraints. The generation schedule is compared to that which would result if fuel constraints were ignored. The comparison shows that fuel consumed can be adequately controlled by adjusting the power output of various generating units so that the power system operates within its fuel limitations and within contractual constraints. It has been found that one of the two objective functions (fuel cost and emission level) may be increased while other may be decreased to serve the same power demand but this may well compensate for the penalty that might be otherwise imposed for not maintaining the fuel contract. Numerical results for an example system have been presented to illustrate the performance and applicability of the proposed method.

Economic emission load dispatch through an interactive fuzzy satisfying method

Economic emission load dispatch through an interactive fuzzy satisfying method

A Simulated Annealing-Based Goal-Attainment Method for Economic Emission Load Dispatch with Nonsmooth Fuel Cost and Emission Level Functions

A novel multiobjective optimization method for economic emission load dispatch (EELD) with nonsmooth fuel cost and emission level functions in power system operation andscheduling phases is presented. In this paper, the problem treats economy, emission, and transmission line security as competing objectives. The load constraints and operating constraints are taken into account. Assuming that the decision maker (DM) has goals for each of the objective functions, the multiobjective problem is converted into a single-objective optimization by the goal-attainment method, which is then handled by the simulated annealing (SA) technique. The solution methodology can offer a global or near-global noninferior (best compromising) solution in a sense close to the DM's requirements. Results for a sample test system have been presented to demonstrate the applicability and validity of the proposed method.

Economic emission load dispatch through an interactive fuzzy satisfying method

Abstract The economic emission load dispatch (EELD) problem treats economy, emission and security as competing objectives for optimal dispatch, which requires some form of conflict resolution to arrive at a solution. This paper presents an interactive fuzzy satisfying method for solving an EELD problem assuming that the decision maker (DM) has imprecise or fuzzy goals for each of the objective functions. The fuzzy goals are quantified by defining their corresponding membership functions and the DM is then asked to specify the reference (desirable) membership values. Numerical results for an example system have been presented to illustrate the performance and applicability of the proposed method.

Economic emission load dispatch with line flow constraints using a classical technique

An attempt is made to explore the feasibility of developing an approach to solve the power system economic emission load dispatch (EELD) problem with line flow constraints using a classical technique based on co-ordination equations. The inability of the classical technique to handle the line flow constraints so far is circumvented innovatively by expressing the line flows in terms of active power generations through distribution factors. These distribution factors are elegantly developed from existing load flow information using a perturbation technique. The proposed model based on the classical technique for EELD is tested on IEEE 14- and 30-bus test systems and the results are compared with those obtained by quadratic programming, the Hessian method, the Ricochet gradient method and the linear programming method.

Stochastic economic emission load dispatch

The economic emission load dispatch (EELD) problem is a multiple non-commensurable objective problem that minimizes both cost and emission together. In the paper a stochastic EELD problem is formulated with consideration of the uncertainties in the system production cost and nature of the load demand, which is random. In addition, risk is considered as another conflicting objective to be minimized because of the random load and uncertain system production cost. The weighted minimax technique is used to simulate the trade-off relation between the conflicting objectives in the non-inferior domain. Once the trade-off has been obtained, fuzzy set theory helps the power system operator to choose the optimal operating point over the trade-off curve and adjust the generation levels in the most economic manner associated with minimum emission and risk. The validity of the method is demonstrated by analysing a sample system comprising six generators.