Economic Emission Load Dispatch Problem Research Articles

Improved Pelican optimization algorithm for solving load dispatch problems

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

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

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

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

The fundamental objective of economic load dispatch is to operate the available generating units such that the needed load demand satisfies the lowest generation cost and also complies with the various constraints. With proper power system operation planning using optimized generation limits, it is possible to reduce the cost of power generation. To fulfill the needs of such objectives, proper planning and economic load dispatch can help to plan the operation of the electrical power system. To optimize the economic load dispatch problems, various classical and new evolutionary optimization approaches have been used in research articles. Classical optimization techniques are outdated due to many limitations and are also unable to provide a global solution to the ELD problem. This work uses a new variant of particle swarm optimization techniques called modified particle swarm optimization, which is effective and efficient at finding optimum solutions for single as well as multi-objective economic load dispatch problems. The proposed MPSO is used to solve single and multi-objective problems. This work considers constraints like power balance and power generation limits. The proposed techniques are tested for three different case studies of ELD and EELD problems. (1) The first case is tested using the data of 13 generating unit systems along with the valve point loading effect; (2) the second case is tested using 15 generating unit systems along with the ramp rate limits; and (3) the third case is tested using the economic emission dispatch (EELD) as a multi-objective problem for 6 generating unit systems. The outcomes of the suggested procedures are contrasted with those of alternative optimization methods. The results show that the suggested strategy is efficient and produces superior optimization outcomes than existing optimization techniques.

Constrained Static/Dynamic Economic Emission Load Dispatch Using Elephant Herd Optimization

The rapid growth in greenhouse gases (GHGs), the lack of electricity production, and an ever-increasing demand for electrical energy requires an optimal reduction in coal-fired thermal generating units (CFTGU) with the aim of minimizing fuel costs and emissions. Previous approaches have been unable to deal with such problems due to the non-convexity of realistic scenarios and confined optimum convergence. Instead, meta-heuristic techniques have gained more attention in order to deal with such constrained static/dynamic economic emission load dispatch (ELD/DEELD) problems, due to their flexibility and derivative-free structures. Hence, in this work, the elephant herd optimization (EHO) technique is proposed in order to solve constrained non-convex static and dynamic ELD problems in the power system. The proposed EHO algorithm is a nature-inspired technique that utilizes a new separation method and elitism strategy in order to retain the diversity of the population and to ensure that the fittest individuals are retained in the next generation. The current approach can be implemented to minimize both the fuel and emission cost functions of the CFTGUs subject to power balance constraints, active power generation limits, and ramp rate limits in the system. Three test systems involving 6, 10, and 40 units were utilized to demonstrate the effectiveness and practical feasibility of the proposed algorithm. Numerical results indicate that the proposed EHO algorithm exhibits better performance in most of the test cases as compared to recent existing algorithms when applied to the static and dynamic ELD issue, demonstrating its superiority and practicability.

A modified artificial bee colony algorithm based on a non-dominated sorting genetic approach for combined economic-emission load dispatch problem

The multi-objective optimization algorithms (MOO) are used to obtain the best compromising solutions when two or more objective functions need to be optimized simultaneously. The convergence and diversity are critical factors to consider while solving the MOO problems because they determine the possibility of obtaining an evenly distributed Pareto front. This paper proposes a hybrid optimization algorithm to solve a multi-objective economic emission dispatch (MOEED) problem of electrical power systems. The electrical power generated by consuming fossil fuels is very costly and also burning of these fuels contributes to global warming. Hence, electrical power is generated at the least cost and emission. The MOEED problems have been solved in the past by using swarm intelligence and evolutionary algorithms. However, the solutions reported in the literature, are either inferior or the constraints are violated. The algorithm proposed in this paper is an integration of an Artificial Bee Colony optimization algorithm and a Non-Dominated Sorting Genetic Algorithm-II. The effectiveness of the proposed algorithm is evaluated by applying it to three test systems having 6, 10, and 40 coal-based generators. Additionally, various multi-criteria decision-making algorithms are used to identify the best non-dominated solutions obtained by the proposed algorithm and compared with previously reported results. The best fuel costs obtained by the proposed approach, for a 6-unit test system with and without transmission losses are found to be 605.9983 and 600.11140 $/h respectively. While the best emission values, for this test system, with and without transmission losses are found to be 0.1941 and 0.1942 tons/h. Moreover, the best fuel costs obtained by the proposed approach, for 10 and 40-unit test systems are found to be 111181.9871 and 121369.0838 $/h respectively. Furthermore, the best emission values for these test systems are found to be 3932.24322 and 176682.264 tons/h respectively. All these results are obtained without constraint violations and within 10–600 iterations.

Solution of the Multi-objective Economic and Emission Load Dispatch Problem Using Adaptive Real Quantum Inspired Evolutionary Algorithm

Economic load dispatch is a complex and significant problem in power generation. The inclusion of emission with economic operation makes it a Multi-objective economic emission load dispatch (MOEELD) problem. So it is a tough task to resolve a constrained MOEELD problem with antagonistic multiple objectives of emission and cost. Evolutionary Algorithms (EA) have been widely used for solving such complex multi-objective problems. However, the performance of EAs on such problems is dependent on the choice of the operators and their parameters, which becomes a complex issue to solve in itself. The present work is carried out to solve a Multi-objective economic emission load dispatch problem using a Multi-objective adaptive real coded quantum-inspired evolutionary algorithm (MO-ARQIEA) with gratifying all the constraints of unit and system. A repair-based constraint handling and adaptive quantum crossover operator (ACO) are used to satisfy the constraints and preserve the diversity of the suggested approach. The suggested approach is evaluated on the IEEE 30-Bus system consisting of six generating units. These results obtained for different test cases are compared with other reputed and well-known techniques.

Chaos-enhanced multi-objective tunicate swarm algorithm for economic-emission load dispatch problem

Climate change and environmental protection have a significant impact on thermal plants. So, the main principles of combined economic-emission dispatch (CEED) problem are indeed to reduce greenhouse gas emissions and fuel costs. Many approaches have demonstrated their efficacy in addressing CEED problem. However, designing a robust algorithm capable of achieving the Pareto optimal solutions under its multimodality and non-convexity natures caused by valve ripple effects is a true challenge. In this paper, chaos-enhanced multi-objective tunicate swarm algorithm (CMOTSA) for CEED problem. To promote the exploration and exploitation abilities of the basic tunicate swarm algorithm (TSA), an exponential strategy based on chaotic logistic map (ESCL) is incorporated. Based on ESCL in CMOTSA, it can improve the possibility of diversification feature to search different areas within the solution space, and then, gradually with the progress of iterative process it converts to emphasize the intensification ability. The efficacy of CMOTSA is approved by applying it to some of multi-objective benchmarking functions which have different Pareto front characteristics including convex, discrete, and non-convex. The inverted generational distance (IGD) and generational distance (GD) are employed to assess the robustness and the good quality of CMOTSA against some successful algorithms. Additionally, the computational time is evaluated, the CMOTSA consumes less time for most functions. The CMOTSA is applied to one of the practical engineering problems such as combined economic and emission dispatch (CEED) with including the valve ripples. By using three different systems (IEEE 30-bus with 6 generators system, 10 units system and IEEE 118-bus with 14 generating units), the methodology validation is made. It can be stated for the large-scale case of 118-bus systems that the results of the CMOTSA are equal to 8741.3 $/h for the minimum cost and 2747.6 ton/h for the minimum emission which are very viable to others. It can be pointed out that the cropped results of the proposed CMOTSA based methodology as an efficient tool for CEED is proven.

A Novel Oppositional Approach for Solving Different Economic Emission Dispatch Problems

An oppositional-based learning approach with a real coded chemical reaction algorithm (ORCCRO) has been considered in this manuscript. The ORCCRO algorithm has been used here to find the near-global optimum solution for multi-objective economic-emission load dispatch problem with having nonlinear constraints. Emission extract from thermal power plants like NO x , inequality constraints like power generation operating limit and equality constraints like power balance consideration are considered here. ORCCRO follows the process to reach a stable state in lower energy with different molecular chemical collision. Oppositional-based learning mechanism has also hybrid here with RCCRO to find out more effective solution. Three different test systems are considered for simulation studies revealed that the ORCCRO method is much superior in comparison with other effective algorithms. The results obtained in these three test systems prove the robustness and the efficiency of ORCCRO.

Economic Emission and Energy Scheduling for Renewable Rich Network Using Bio-Inspired Optimization

This paper deals with the combined economic emission load dispatch (CEELD) problem with and without the integration of renewable energy sources (RESs), in some more rational test scenarios of single CEELD and multi-objective CEELD (MO-CEELD) optimization. Hence, an efficient and coherent approach is presented to minimize the generation and emission cost using one of the bio-inspired metaheuristic algorithms named flower pollination algorithm (FPA). The evolution of a power system along with the integration of RESs demands equal advancement in the operation and control algorithms of the power grid. Therefore, the proposed approach in this paper offers an evolutionary single and multi-objective optimization process based on a bio-inspired FPA. Further, it has been validated by achieving the best compromise solution (BCS) using the Pareto categorizing process and fuzzy membership function. Moreover, different study cases comprising eleven and fifteen thermal units with and without considering RESs are tested with the proposed technique. Finally, the effectiveness of the proposed approach is tested by comparing the simulation results with some already existing techniques in terms of overall fuel and emission cost. Significantly, it has been noticed from the results that it outperforms all the previously presented approaches like PSO, DE, GSA, AEO, BA, and dBA, thus justifying its applicability.

A Modified Artificial Bee Colony Algorithm Based on a Non-Dominated Sorting Genetic Approach for Combined Economic-Emission Load Dispatch Problem

A Modified Artificial Bee Colony Algorithm Based on a Non-Dominated Sorting Genetic Approach for Combined Economic-Emission Load Dispatch Problem

A Modified Artificial Bee Colony Algorithm Based on a Non-Dominated Sorting Genetic Approach for Combined Economic-Emission Load Dispatch Problem

A Modified Artificial Bee Colony Algorithm Based on a Non-Dominated Sorting Genetic Approach for Combined Economic-Emission Load Dispatch Problem

A Hybrid Optimization Technique for Solving Economic Emission Load Dispatch Problem

A Hybrid Optimization Technique for Solving Economic Emission Load Dispatch Problem

Using the Barnacles Mating Optimizer for Economic Emission Load Dispatch Problems

Using the Barnacles Mating Optimizer for Economic Emission Load Dispatch Problems

Bare Bones Teaching Learning-Based Optimization Technique for Economic Emission Load Dispatch Problem Considering Transmission Losses

Economic emission load dispatch plays a great role in power system cost analysis. The purpose of economic emission load dispatch is to minimize the fuel and emission cost satisfying load demand. Various iterative techniques had been used to solve economic emission load dispatch problem in previous years by different authors. In this article, the new teaching learning-based optimization (TLBO) technique using variant bare bones TLBO has been proposed for solving economic emission load dispatch problem with convex and non-convex constraints by considering transmission losses and valve point loading effects. Conventional TLBO has two phases like teacher phase and learner phase. In teacher phase, learners update their knowledge through sharing knowledge with teacher, and finally, learners improve their knowledge by interactions among learners. Bare bones TLBO employs an interactive learning strategy, which is the hybridization of the learning strategy in the conventional TLBO. The proposed algorithm has been applied on six-, ten- and forty-unit systems, and the results obtained are compared with existing techniques; hence, superiority of the proposed algorithm is proved.

Relaxed I-SHOT trust-region algorithm for solving multi-objective economic emission load dispatch problem

ABSTRACTIn this paper, a new algorithm for tackling nonlinear constrained multi-objective optimization problems is introduced. This algorithm, which we call relaxed the interactive sequential hybrid optimization technique (relaxed I-SHOT), is based on a hybrid method between the I-SHOT method and step method (STEM) to transform a multi-objective problem into a single-objective one. An active set strategy is used together with a suggested penalty method to transform a single-objective constrained optimization problem into unconstrained one. A trust-region globalization strategy is added to the algorithm to solve the obtained unconstrained problem to ensure global convergence. The suggested approach is utilized to solve the multi-objective economic emission load dispatch (EELD) problems to assert the effectiveness of the proposed algorithm. The proposed algorithm is tested on the standard IEEE 30-bus 6-generator test system. The results of the proposed approach are compared against those reported in the literature. The comparison asserts the potential of the proposed algorithm to solve the EELD problem.

Combined Economic and Emission Load Dispatch Problem Solving by ITLBO Algorithm

Recent trends in economic and emission dispatch problem which turn has to promote the rise in the number of power generating stations and their capacity of generation. The Sulphur Dioxide (S02), Nitrogen Oxides (N2O) and Carbon Dioxide (CO2) are yields the CEED problem and they are created from generation of electricity from fossil fuel. Combined economic and emission load dispatch problem is a procedure to determine the generation of electrical power isdevoted generating units in a power system so that the both total generation costand total emission of the system is minimized, while fulfilling the load demand in directly. Improved teaching learning based optimization algorithm is used to solve combined economic emission load dispatch problem with constraints in generation of power system. This method was verified by thirteen generating bus and use with different load demand and compared with other existing techniques display the advantage of the proposed algorithm. The simulation has been done in MATLAB/Simulink with required formulation and the result is gotten in graph and numerical.

A novel parallel hurricane optimization algorithm for secure emission/economic load dispatch solution

This paper proposes a parallel hurricane optimization algorithm (PHOA) for solving economic emission load dispatch (EELD) problem in modern power systems. In PHOA, several sub-populations moving independently in the search space with the aim of simultaneously optimizing the problem objectives considering the local behavior between sub-populations. By this way, it is intended to search for the Pareto optimal solutions which are contrasting to the single optimal solution. The inherent characteristics of parallelization strategy can enhance the Pareto solutions and increase the convergence to reach the Pareto optimal solutions. Simulations are conducted on three test systems and comparisons with other optimization techniques that reported in the literature are demonstrated. The obtained results demonstrate the superiority of the proposed PHOA compared to other optimization techniques. Additional economic benefits with secure settings are fulfilled, while preserving all system constraints within their permissible limits. Added to that, two security indices are proposed from generation units and transmission lines. The highest security index from generation units reflects that the operating condition achieves more power reserve. In transmission lines, the highest security index means that the transmission lines operated beyond their congestion limits. For justification of the proposed security indices, the proposed solution methodology is employed to assure their benefits in terms of economical and environmental issues. The proposed algorithm improves the economic issue as well as enhances the power system operation in the technical point of view with acceptable levels of emissions. Moreover, design of experiments using the Taguchi approach is employed to calibrate the parameters of the algorithms. So, it can be considered as a promising alternative algorithm for solving problems in practical large-scale power systems.

Population variant differential evolution-based multiobjective economic emission load dispatch

Summary This paper presents a novel heuristic optimization approach using population variant differential evolution algorithm for solving the multiobjective economic emission load dispatch (EELD) problem. The EELD problem simultaneously takes into consideration the effect of gaseous pollutants like NOx, SOx, etc, including the cost of the fossil fuel used in the thermal power plants. A population refreshment mechanism, based on the concept of interquartile range, has been applied to the classical differential evolution method to compute the EELD problem successfully. The algorithm has been tested on IEEE-30 bus 6-generator test system and a standard 40-generator test system, taking valve point loading effects into consideration for effective solutions. The results have been compared with the standard existing techniques in the literature such as linear programming, multiobjective stochastic search technique, nondominated sorting genetic algorithm, fuzzy clustering particle swarm optimization, and modified bacterial foraging algorithm, which authenticate the capability of the proposed algorithm. A novel concept of applying the proposed methodology to a deregulated power market has also been presented in this paper, where successful results have been obtained. This method appears as an efficient and robust optimization algorithm in terms of minimizing the total cost, emission, and computational time.

Quadratic approximation-based hybrid Artificial Cooperative Search algorithm for economic emission load dispatch problems

Summary In this article, Artificial Cooperative Search (ACS) algorithm is incorporated with the quadratic approximation (QA) operator to solve the multi-objective economic emission load dispatch (EELD) problems with different generation units. ACS is a Swarm Intelligence–based metaheuristic algorithm, based on the interaction between prey and predator organisms in a habitat, which is effective at global search; however, it does not perform so well at exploring promising regions. The QA operator, on the other hand, is a non-derivative–based efficient local search method that finds the minimum of a quadratic hyperspace passing through three points in a D-dimensional space. Solving the EELD problems with the hybridized ACS-QA algorithm, as being proposed in the present article, leads to more accurate results with fewer function evaluations. Also, multi-objectivity of the problem is handled by transforming it into a single-objective problem by using the weighted sum method. The efficiency of the proposed ACS-QA algorithm is tested in comparison to the algorithms existing in literature by implementing it on six different benchmark optimization problems. Afterward, the proposed ACS-QA algorithm and the ACS algorithm are implemented on multi-objective EELD problems with different generation units. The results are compared with the solutions in literature utilizing different metaheuristic optimization algorithms. Both studies firmly showed that the ACS-QA algorithm is able to find more accurate results even though it uses fewer function evaluation calls.

Symbiotic organisms search optimization algorithm for economic/emission dispatch problem in power systems

This paper presents symbiotic organisms search (SOS) algorithm to solve economic emission load dispatch (EELD) problem for thermal generators in power systems. The basic objective of the EELD is to minimize both minimum operating costs and emission levels, while satisfying the load demand and all equality–inequality constraints. In other research direction, this multi-objective problem is converted into single-objective function by using price penalty factor approach in order to solve it with SOS. The proposed algorithm has been implemented on various test cases, with different constraints and various cost curve nature. In order to see the effectiveness of the proposed algorithm, its results are compared to those reported in the recent literature. The results of the algorithms indicate that SOS gives good results in both systems and very competitive with the state of the art for the solution of the EELD problems.