Economic Emission Load Dispatch Problem Research Articles

Bat Algorithm for Economic Emission Load Dispatch Problem

This paper presents a Bat Algorithm (BA) for solving economic emission dispatch (EELD) problem with quadratic fuel function. The BA is a new meta-heuristic algorithm which is a powerful optimal solution search algorithm owing easily selected control parameters and high successful rate as well as high ability for dealing with complex constraints. In addition to minimizing electricity generation fuel cost, emission released into the air from thermal plants is also another main objective needs to be minimized. In order to test the performance of the proposed BA one system with two load cases is employed. The obtained result by the BA compared to that from other methods has revealed that the proposed BA is a very promising meta-heuristic algorithm for solving economic emission load dispatch problem.

I-SHOT line-search algorithm for solving multi-objective economic emission load dispatch problem

I-SHOT line-search algorithm for solving multi-objective economic emission load dispatch problem

Augmented Lagrange Hopfield Network for Economic Emission Load Dispatch Problem with Quadratic Fuel Cost Function

This paper proposes an augmented Lagrange Hopfield Network (ALHN) based method for solving economic emission dispatch (EELD) problem with quadratic fuel function. The ALHN is the combination of augmented Lagrange function and Hopfield neural network in aim to improve performance in terms of convergence speed and getting global optimization. In addition to minimizing electricity generation fuel cost, emission released into the air from thermal plants is also another main objective needs to be minimized. In order to test the performance of the proposed ALHN two systems including a three unit system with one load case and a six unit system with three load cases are employed. The obtained result by the ALHN compared to that from other methods has revealed that the proposed ALHN is a very promising artificial intelligent algorithm for solving economic emission load dispatch problem.

Modified particle swarm optimization for economic-emission load dispatch of power system operation

This paper proposes a modified particle swarm optimization considering time-varying acceleration coefficients for the economic-emission load dispatch (EELD) problem. The new adaptive parameter is introduced to update the particle movements through the modification of the velocity equation of the classical particle swarm optimization (PSO) algorithm. The idea is to enhance the performance and robustness of classical PSO. The price penalty factor method is used to transform the multiobjective EELD problem into a single-objective problem. Then the weighted sum method is applied for finding the Pareto front solution. The best compromise solution for this problem is determined based on the fuzzy ranking approach. The IEEE 30-bus system has been used to validate the effectiveness of the proposed algorithm. It was found that the proposed algorithm can provide better results in terms of best fuel cost, best emissions, convergence characteristics, and robustness compared to the reported results using other optimization algorithms.

Best Compromise Alternative to EELD Problem using Hybrid Multiobjective Quantum Genetic Algorithm

A novel hybrid multiobjective quantum genetic algorithm (HM-QGA) for economic emission load dispatch (EELD) optimization problem is presented. The EELD problem is formulated as a nonlinear constrained multiobjective optimization problem with both equality and inequality constraints. HM-QGA are population based evolutionary algorithms that imitate quantum physics by introducing quantum bits for a basic probabilistic genotypic representation a nd hence better population diversity, and quantum gates for evolving the population of solutions. We use quantum genetic algorithm to exploits the power of quantum computing to speed up genetic algorithm procedure. We present methodology that allows the decision maker (DM) to be a partner in problem solving, where DM specifies input values (namely the weight values) according his need s. Simulation results on the standard IEEE 30-bus 6-generator test system show that the proposed algorithm outperforms other heuristic algorithms and is characterized by robustness, high success, fast convergence and excellent capability on global searching.

Economic Emission Load Dispatch with Multiple Fuel Options Using Cuckoo Search Algorithm with Gaussian and Cauchy Distributions

Cuckoo Search Algorithm (CSA), a new meta-heuristic algorithm based on natural phenomenon of Cuckoo species and Levy flights random walk, has been successfully applied to several optimization problems so far. In the paper two modified versions of CSA, where new solutions are generated using two distributions including Gaussian and Cauchy distributions are proposed for economic emission load dispatch (EELD) problem with multiple fuel options. The advantages of CSA with Gaussian distribution (CSA-Gauss) and CSA with Cauchy distribution (CSA-Cauchy) over CSA with Levy distribution are fewer parameters and fewer equations and shorter computational process. The proposed method is tested on one test system consisting of ten generating units with various load demands and compared to other methods. In addition, the best compromise from the set of obtained solutions is found and compared to this from lamda-iteration (LI) method and Hopfield Lagrange Network (HLN). The result comparisons have indicated that the proposed method is a highly effective method.

Multi-Objective Economic Emission Load Dispatch Solution Using Evolutionary Algorithm with and without Considering Wind Power Penetration and Valve Point Effect

The electrical power system is considered as the most complex man-made systems mainly due to their wide geographical coverage. Electrical energy industries contributes environmental pollution which rise questions concern environmental protection and methods of eliminating or reducing pollution from power plants either by design or by operational strategies. Electric power plants are mainly aimed to operate al low fuel cost strategies .In this paper a Multi –Objective Economic Emission Load Dispatch problem is solved to minimize the emission of nitrogen oxides (NOx) , oxides of other fuels that release during generation of electricity and fuel cost considering both Thermal generators and Wind turbines. A large number of iterations and oscillation are those of the major concern in solving the economic load dispatch problem by using the BFO(bacterial foraging optimization) method. By applying BFO method the economic dispatch problem is optimized to minimize the total generation cost of a power system while satisfying various equality and inequality constraints. The effect of Wind power on overall emission is also investigated here using Quadratic programming by wolf’s method. This method has better convergence characteristic. Wolf’s method is an extended simplex procedure which can be applied to Quadratic programming problems in which all the problem variables are non-negative.

Hybrid ant optimization system for multiobjective economic emission load dispatch problem under fuzziness

In this paper, a new hybrid optimization system is presented. Our approach integrates the merits of both ant colony optimization and steady state genetic algorithm and it has two characteristic features. Firstly, since there is instabilities in the global market and the rapid fluctuations of prices, a fuzzy representation of the economic emission load dispatch (EELD) problem has been defined, where the input data involve many parameters whose possible values may be assigned by the expert. Secondly, by enhancing ant colony optimization through steady state genetic algorithm, a strong robustness and more effectively algorithm was created. Also, stable Pareto set of solutions has been detected, where in a practical sense only Pareto optimal solutions that are stable are of interest since there are always uncertainties associated with efficiency data. Moreover to help the decision maker DM to extract the best compromise solution from a finite set of alternatives a Technique for Order Performance by Similarity to Ideal Solution (TOPSIS) method is adopted. It is based upon simultaneous minimization of distance from an ideal point (IP) and maximization of distance from a nadir point (NP). The results on the standard IEEE systems demonstrate the capabilities of the proposed approach to generate true and well-distributed Pareto optimal nondominated solutions of the multiobjective EELD.

Solution of Economic Emission Load Dispatch problems of power systems by Real Coded Chemical Reaction algorithm

This paper presents a Real Coded Chemical Reaction algorithm (RCCRO) approach to solve the Economic Emission Load Dispatch (EELD) problem of thermal generators of power systems. Emission substance like NOX, power demand equality constraint and operating limit constraint are considered here. EELD problem has been originated as a multi-objective problem by considering both economy and emission simultaneously. Chemical Reaction Optimization (CRO) mimics the interactions of molecules in a chemical reaction to reach a low energy stable state. Basically, the CRO is designed to work in the discrete domain optimization problems. A real coded version of it, known as Real-Coded Chemical Reaction Optimization (RCCRO) is applied here to solve multi-objective EELD problems, in order to show the advantages of proposed algorithm to solve complex continuous optimization problems. Different test systems having 10, 13 and 40 generators, addressing valve-point loading and NOX emission have been considered. The solutions obtained are quite encouraging and superior to different existing optimization techniques.

Multi-Objective Economic Emission Load Dispatch using Teacher-Learning-Based Optimization Technique

Abstract In this paper, a new parameter-less diversity preservation approach to solve the non-linear multi-objective economic emission load dispatch (EED) problem is envisaged using Teacher-Learning Based Optimization (TLBO) method. The TLBO technique is totally parameter less and takes less computation time as compared to other optimization techniques for the determination of solutions in the Pareto-optimal front. The TLBO method is tested for EED problem on 6-generator test system (IEEE 30- bus) and the results obtained are compared with those obtained from Non-dominated Sorting Genetic Algorithm (NSGA). The simulation results confirm the computational advantage of the TLBO method.

Multi-objective economic emission load dispatch problem with trust-region strategy

In this paper, we present a trust region algorithm for solving multi-objective economic emission load dispatch problem (EELD). The trust region algorithm has proven to be a very successful globalization technique for solving a single objective constrained optimization problems. The proposed approach is suitable for multi-objective problem (EELD) such that its objective functions may be ill- defined or having a non convex pareto-optimal front. Also, we identify the weight values which reflect the degree of satisfaction of each objective. The proposed approach is carried out on the standard IEEE 30-bus 6-generator test systems to confirm the effectiveness of the algorithm used to solve the multi-objective problem (EELD). Our results with the proposed approach have been compared to those reported in the literature. The comparison demonstrates the superiority of the proposed approach and confirm its potential to solve the multi-objective problem (EELD).A Matlab implementation of our algorithm was used in solving one case study and the results are reported.

A novel hybrid particle swarm optimization and gravitational search algorithm for solving economic emission load dispatch problems with various practical constraints

Particle swarm optimization (PSO) is inspired by social behaviors of bird flocking, gravitational search algorithm (GSA) is based on the law of gravity and interaction between masses, and both of them are pertain to meta-heuristic algorithms. A novel hybrid particle swarm optimization and gravitational search algorithm (HPSO–GSA), having attributes of PSO and GSA, is proposed in this paper to solve economic emission load dispatch (EELD) problems considering various practical constraints. These constraints consist of the generator ramp rate limits, non-convex and discontinuous nature of prohibited operating zones, non-smooth characteristic of valve-point effects, multiple fuels type of generation units, and transmission losses in realistic power systems. The proposed approach embodies interesting concepts and fully incorporates the social essence of PSO with the motion mechanism of GSA. The proposed HPSO–GSA adopts co-evolutionary technique to simultaneously update particle positions with PSO velocity and GSA acceleration. HPSO–GSA, therefore, is expected to obtain an efficient balance between exploration and exploitation. From results of canonical benchmark test functions, HPSO–GSA does significantly improve PSO and GSA with better performance. As a real application, the EELD problems on five test systems including different constraints are solved by the HPSO–GSA to assess the optimizing performance of the proposed hybrid approach. The results obtained confirm the potential and effectiveness of the proposed approach compared to PSO, GSA and other algorithms published in the recent state-of-the art literatures for the solution of the EELD problems.

Multi-objective quasi-oppositional teaching learning based optimization for economic emission load dispatch problem

This paper proposes an efficient optimization approach, namely quasi-oppositional teaching learning based optimization (QOTLBO) for solving non-linear multi-objective economic emission dispatch (EED) problem of electric power generation with valve point loading. In this article, a non-dominated sorting QOTLBO is employed to approximate the set of Pareto solution through the evolutionary optimization process. The proposed approach is carried out to obtain EED solution for 6-unit, 10-unit and 40-unit systems. For showing the superiority of this optimization technique, numerical results of the four test systems are compared with several other EED based recent optimization methods. The simulation results show that the proposed algorithm gives comparatively better operational fuel cost and emission in less computational time compared to other optimization techniques.

Multi-objective economic emission load dispatch solution using gravitational search algorithm and considering wind power penetration

In this paper an economic emission load dispatch (EELD) problem is solved to minimize the emission of nitrogen oxides (NOX) and fuel cost, considering both thermal generators and wind turbines. The effects of wind power on overall NOX emission are also investigated here. To find the optimum emission dispatch, optimum fuel cost, best compromising emission and fuel cost, a newly developed optimization technique, called Gravitational Search Algorithm (GSA) has been applied. GSA is based on the Newton’s law of gravity and mass interactions. In GSA, the searcher agents are collection of masses which interact with each other using laws of gravity and motion of Newton. IEEE 30-bus system having six conventional thermal generators has been considered as test system. Two extra wind turbines are also placed at two weak load bus of the system. Two Weak load buses have been selected based on their L-index value. After placing the wind power sources, those buses have been considered as generator bus. Minimum fuel cost, minimum emission and best compromising solution obtained by GSA are compared with those of biogeography-based optimization (BBO). The results show that the GSA surpasses the other available techniques in terms of solution quality and computational efficiency.

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 (EELD) optimization problem. 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 -dominance. The use of -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 literature. The comparison demonstrates the superiority of the proposed approach and confirms its potential to solve the multiobjective EELD problem. Key words: Economic emission load dispatch, evolutionary algorithms, multiobjective optimization, local search.

Optimal Solution of Combined Economic Emission Load Dispatch using Genetic Algorithm

paper, a genetic algorithm (GA) approach is presented for optimal solution of combined economic emission load dispatch (CEELD) problem. Fuel cost and emission are considered to formulate the multi-objective optimization problem. An optimal trade-off between fuel cost and emission is obtained using genetic algorithm. Two test systems are considered to show the effectiveness of the GA approach. An extensive analysis is done by presenting a short term thermal generation scheduling for the Test system-1.

Emission constrained economic dispatch with valve-point effect using Maclaurin series-based Lagrangian method

This paper presents Lagrangian-based technique to solve economic emission load dispatch (EELD) of valve-point loaded generating units considering emission constraint. The EELD problem has gained recent attention due to the deregulation of power industry and environmental regulations. In this paper, two conflicting functions (fuel cost and emission) are considered and formulated as a single objective optimisation problem by the weighted sum method. Based on the literature survey, it is found that cost function is taken as a quadratic function and solved for emission economic dispatch. Here, in cost function, a sine term is added to model the valve-point effect and an exponential term is used to model the emission function. Using Maclaurin series, the sine and exponential terms are expanded and solved with Lagrangian multiplier method. The objective function is highly non-linear and the feasibility of the proposed method is validated with IEEE 30-bus system and ten-unit system. Results obtained with the proposed approach are compared with genetic algorithm.

Hybrid differential evolution with biogeography-based optimization algorithm for solution of economic emission load dispatch problems

This paper presents 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 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.

A Hybrid Optimization Technique Coupling an Evolutionary and a Local Search Algorithm for Economic Emission Load Dispatch Problem

This paper presents an optimization technique coupling 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 maintains a finite-sized archive of non-dominated solutions which gets iteratively updated in the presence of new solutions based on the concept of ε-dominance. To improve the solution quality, local search technique was applied as neighborhood search engine, where it intends to explore the less-crowded area in the current archive to possibly obtain more non-dominated solutions. TOPSIS technique can incorporate relative weights of criterion importance, which has been implemented to identify best compromise solution, which will satisfy the different goals to some extent. Several optimization runs of the proposed approach are carried out on the standard IEEE 30-bus 6-genrator test system. The comparison demonstrates the superiority of the proposed approach and confirms its potential to solve the multiobjective EELD problem.

Interval-based differential evolution approach for combined economic emission load dispatch

In this paper we propose an Interval based Differential Evolution (IDE) algorithm, an improved version of Differential Evolution (DE) algorithm using interval arithmetic. After estimating the global minimum roughly, the IDE algorithm constructs a mechanism which updates the upper bound of global minimum at each generation and defines an efficient termination criterion. Also at each generation it modifies the new population using the subset of current population and thus reduces the computational effort. We apply the proposed algorithm to the Combined Economic Emission Load Dispatch (CEELD) problem which obtains the optimal amount of generated power for the thermal generating units in the system by simultaneously minimising the fuel and emission costs. We find the proposed algorithm to be more efficient than the conventional DE when applied to IEEE 6 generators system. We also find that these results using the IDE algorithm are better than some recently reported evolutionary algorithms.