Economic Load Dispatch Problem Research Articles

A Hybrid Big Bang–Big Crunch optimization algorithm for solving the different economic load dispatch problems

In this paper, we applied a Hybrid Big Bang–Big Crunch optimization technique for solving the different types of economic load dispatch (ELD) problems in power systems. Many nonlinear characteristics of the generator, such as ramp rate limits, prohibited operating zone, and non-smooth cost functions are considered using the proposed method in practical generator operation. The proposed method is tested on three different systems (six-unit system considering losses, 15 units: ED considering transmission loss, large system: 40 generating units with valve-point loading effects). Furthermore, results are compared with other optimization approaches proposed in the recent literature, showing the feasibility of this technique to highly nonlinear and different ELD problem.

Optimization of Economic Load Dispatch Problem by Using Particle Swarm Optimization Technique-A Review

Optimization of Economic Load Dispatch Problem by Using Particle Swarm Optimization Technique-A Review

밸브지점 균형과 교환 최적화 방법을 적용한 동적경제급전문제

This paper proposes a balance-swap method for the dynamic economic load dispatch problem. Based on the premise that all generators shall be operated at valve-points, the proposed algorithm initially sets the maximum generation power at . As for generator i with , which is the maximum operating cost $c_i

Synergic predator-prey optimization for economic thermal power dispatch problem

This paper introduces a synergic predator-prey optimization (SPPO) algorithm to solve economic load dispatch (ELD) problem for thermal units with practical aspects. The basic PPO model comprises prey and predator as essential components. SPPO uses collaborative decision for movement and direction of prey and maintains diversity in the swarm due to fear factor of predator, which acts as the baffled state of preys’ mind. In the SPPO, the decision making of prey is bifurcated into corroborative and impeded parts. It comprises four behaviors namely inertial, cognitive, collective swarm intelligence, and prey's individual and neighborhood concern of predator. The prey particle memorizes its best and not-best positions as experiences. In this research work, to improve the quality of prey swarm, which influence convergence rate, opposition based initialization is used. To verify robustness of proposed algorithm general benchmark problems and small, medium, and large power generation test power system are simulated. These test systems have non-linear behavior due to multi-fuel options and practical constraints. The constraints of prohibited operating zone and ramp rate limits of power generators’ are handled using heuristics. Newton–Raphson procedure is exploited to attain the transmission losses using load flow analysis. The outcomes of SPPO are compared with the results described in literature and are found satisfactory.

Combined economic and emission dispatch solution using Flower Pollination Algorithm

Economic Load Dispatch (ELD) is the process of allocating the required load between the available generation units such that the cost of operation is minimized. The ELD problem is formulated as a nonlinear constrained optimization problem with both equality and inequality constraints. The dual-objective Combined Economic Emission Dispatch (CEED) problem is considering the environmental impacts that accumulated from emission of gaseous pollutants of fossil-fueled power plants. In this paper, an implementation of Flower Pollination Algorithm (FPA) to solve ELD and CEED problems in power systems is discussed. A comparison of the simulated results using the proposed FPA is carried out to confirm its effectiveness against other swarm intelligent algorithms for six various power systems. The superiority of the proposed FPA compared with other algorithms is demonstrated even for large scale power system considering valve point loading effect.

Flower pollination algorithm to solve combined economic and emission dispatch problems

Economic Load Dispatch (ELD) is the process of allocating the required load between the available generation units such that the cost of operation is minimized. The ELD problem is formulated as a nonlinear constrained optimization problem with both equality and inequality constraints. The dual-objective Combined Economic Emission Dispatch (CEED) problem is considering the environmental impacts that accumulated from emission of gaseous pollutants of fossil-fuelled power plants. In this paper, an implementation of Flower Pollination Algorithm (FPA) to solve ELD and CEED problems in power systems is discussed. Results obtained by the proposed FPA are compared with other optimization algorithms for various power systems. The results introduced in this paper show that the proposed FPA outlasts other techniques even for large scale power system considering valve point effect in terms of total cost and computational time.

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.

Adaptive Cuckoo Search Algorithm based Method for Economic Load Dispatch with Multiple Fuel Options and Valve Point Effect

This paper presents an Adaptive Cuckoo Search Algorithm (ACSA) for solving economic load dispatch problem where thermal units with multiple fuel options and valve point loading effect are taken into account. ACSA is first developed by improving the optimal solution search ability of conventional Cuckoo search algorithm. In ACSA, the initial eggs are evaluated and classified into two groups including good group and bad group. The updated step size in ACSA at the first new solution generation via Levy is adaptive at each iteration and therefore the selection of the parameter is not an issue in the paper. The proposed ACSA method is tested on a ten-unit system considering multiple fuel options and valve point loading effect with different load cases. The comparisons of obtained results among the proposed method with others reported in the paper have indicated that ACSA is efficient for applying to the problem.

Solution of non-convex economic load dispatch problem for small-scale power systems using ant lion optimizer

Ant lion optimizer (ALO) is a newly developed population-based search algorithm inspired by hunting mechanism of antlions and based on five steps of hunting the ants, i.e., the random walk of ants, building traps, entrapment of ants in traps, catching preys and re-building traps. This paper presents the application of ALO algorithm for the solution of non-convex and dynamic economic load dispatch problem of electric power system. The performance of ALO algorithm is tested for economic load dispatch problem of four IEEE benchmarks of small-scale power systems, and the results are verified by a comparative study with lambda iteration method, particle swarm optimization algorithm, genetic algorithm, artificial bee colony, evolutionary programming and Grey Wolf optimizer (GWO). Comparative results show that the performance of ant lion optimizer algorithm is better than recently developed GWO algorithm and other well-known heuristics and meta-heuristics search algorithms.

Economic load dispatch using memory based differential evolution

Many variants of differential evolution (DE) algorithm and its hybrid versions exist in the literature to solve economic load dispatch (ELD) problem. However, the performance of DE is highly affected by the inappropriate choice of its operators like mutation and crossover. Moreover, in general practice, DE does not employ any strategy of memorising the best results obtained so far in the initial part of the previous cycle. An attempt is made in this paper to propose a 'memory-based DE (MBDE)' where two 'swarm operators' have been introduced. These operators based on the pBEST and gBEST mechanism of particle swarm optimisation (PSO). The proposed MBDE is tested over four different power test systems of ELD problem with varying complexities. Numerical, statistical and graphical analysis reveals the competency of the proposed MBDE.

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

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

This paper presents an efficient Artificial Bee Colony (ABC) algorithm for solving large scale economic load dispatch (ELD) problems in power networks. To realize the ELD, the valve-point loading effect, system load demand, power losses, ramp rate limits and prohibited operation zones are considered here. Simulations were performed on four different power systems with 3, 6, 15 and 40 generating units and the results are compared with two forms of power systems, one power system is with a wind power generator and other power system is without a wind power generator. The results of this study reveal that the proposed approach is able to find appreciable ELD solutions than those of previous algorithms.

A Hybrid Rough Set Theory-PSO Technique for Solving of Non-convex Economic Load Dispatch

This paper applies a novel hybrid rough set theory-particle swarm optimizer technique, namely rough particle swarm optimization (RPSO) algorithm, for solving nonconvex economic load dispatch (NELD) problem. The RPSO algorithm is based on the notion of rough patterns that uses rough values defined with upper and lower intervals in which represent a set of values. This RPSO method is suggested to deal with the practical constraints such as valve point loading effect, generation limitation, ramp rate limits and prohibited operating zones in the NELD problems. Simulations were performed on four different power systems with 3, 6, 15 and 40 generating units and the results are compared with classical PSO and crazy PSO algorithms. The results of this study reveal that the proposed approach is able to find appreciable NELD solutions than those of previous algorithms.

비볼록 발전비용함수 경제급전문제의 개선된 밸브지점 최적화 알고리즘

There is no polynomial-time algorithm that can be obtain the optimal solution for economic load dispatch problem with non-convex fuel cost functions. Therefore, electrical field uses quadratic fuel cost function unavoidably. This paper proposes a valve-point optimization (VPO) algorithm for economic load dispatch problem with non-convex fuel cost functions. This algorithm sets the initial values to maximum powers for each generator. It then reduces the generation power of generator i with an average power cost of to a valve point power . The proposed algorithm has been found to perform better than the extant heuristic methods when applied to 13 and 40-generator benchmark data. This paper consequently proves that the optimal solution to economic load dispatch problem with non-convex fuel cost functions converges to the valve-point power of each generator.

A novel hybrid optimizer for solving Economic Load Dispatch problem

Abstract Economic Load Dispatch (ELD) is one of the major concerns to show the potential and effectiveness of an optimization algorithm. In this context, a novel hybrid algorithm of Differential Evolution (DE) and Particle Swarm Optimization (PSO) proposed. It is based on ‘tri-population’ environment. Initially, the whole population (in increasing order of fitness) is divided into three groups –- Inferior Group, Mid Group and Superior Group. DE is employed in the inferior and superior groups, whereas PSO is used in the mid-group. The proposed method is abbreviated as DPD because it uses DE–PSO–DE on a population. Two strategies namely Elitism (to retain the best obtained values so far) and Non-Redundant Search (to improve the solution quality) have been employed in DPD cycle. Many mutation strategies of DE have emerged in the last couple of years. However, its actual ability has not been well studied yet because every mutation strategy has its own pros and cons. Therefore suitable mutation strategy for both DEs used in DPD is investigated over a set of 8 popular mutation strategies. Combination of 8 mutation strategies is generated 64 different variants of DPD. Top 4 DPDs are investigated through CEC 2006 functions out of 64 different variants of DPDs. Based on the ‘performance’ analysis best DPD is reported using CEC 2006 and 5 Engineering Design Problems. Further best DPD is considered for solving ELD problem. Results reveal that the superiority of the proposed DPD.

Applications of Harmony Search Algorithms in Engineering

In a recent article the authors reviewed the principles of harmony search and journal articles on harmony search algorithm (HSA). This article presents a review of applications of HSA including structural design, hydrologic model design, water distribution network design, water pump switching problem, transmission network expansion planning problem, job shop scheduling problem, university timetable and rosterering problem, training neural networks, clustering, combined heat and power economic dispatch problem, economic load dispatch problem, and economic and emission dispatch problem.

Non-Convex Economic Dispatch with Prohibited Operating Zones through Gravitational Search Algorithm

This paper presents a new approach to the solution of optimal power generation for economic load dispatch (ELD) using gravitational search algorithm (GSA) when all the generators include valve point effects and some/all of the generators have prohibited operating zones. In this paper a gravitational search algorithm is suggested that deals with equality and inequality constraints in ELD problems. A constraint treatment mechanism is also discussed to accelerate the optimization process<strong>. </strong>To verify the robustness and superiority of the proposed GSA based approach, a practical sized 40-generators case with valve point effects and prohibited operating zones is considered. The simulation results reveal that the proposed GSA approach ensures convergence within an acceptable execution time and provides highly optimal solution as compared to the results obtained from well established heuristic optimization approaches.

Colonial competitive differential evolution: An experimental study for optimal economic load dispatch

Differential evolution (DE) algorithm is a population-based algorithm designed for global optimization of the optimization problems. This paper proposes a different DE algorithm based on mathematical modeling of socio-political evolution which is called Colonial Competitive Differential Evolution (CCDE). The two typical CCDE algorithms are benchmarked on three well-known test functions, and the results are verified by a comparative study with two original DE algorithms which include DE/best/1 and DE/rand/2. Also, the effectiveness of CCDE algorithms is tested on Economic Load Dispatch (ELD) problem including 10, 15, 40, and 140-unit test systems. In this study, the constraints and operational limitations, such as valve-point loading, transmission losses, ramp rate limits, and prohibited operating zones are considered. The comparative results show that the CCDE algorithms have good performance and are reliable tools in solving ELD problem.

운전금지영역을 가진 이차 발전비용함수의 경제급전문제 최적화

This paper proposes a deterministic optimization algorithm to solve economic load dispatch problem with quadratic convex fuel cost function. The proposed algorithm primarily partitions a generator with prohibited zones into multiple generators so as to place them afield the prohibited zone. It then sets initial values to and reduces power generation costs of those incurring the maximum unit power cost. It finally employs a swap optimization process of , where > , , . When applied to 3 different 15-generator cases, the proposed algorithm has consistently yielded optimized results compared to those of heuristic algorithms.

Smart Evolutionary Algorithm for Static Economic Load Dispatch Optimization in a Thermal Generating Station

The Economic Load Dispatch (ELD) problem is an optimization task with emphasis on how power generating companies (GENCOs) will be able to meet the power demands of the distribution companies (DISCOs) and electricity consumers, and at the same time minimize both under/over generation of electricity, and also minimize the operational costs of running the units in their various stations. This paper implemented a Smart Evolutionary Algorithm, which combines a standard Evolutionary Algorithm with a smart mutation operator that is applied to the Static ELD problem. It also investigated and analyzed three distinct variants of the smart mutation operator. The operator focused mutation on genes contributing mostly to cost of generation and penalty violations in the fitness function. Rather than using a generic off-the-shelf optimization package, the paper demonstrated a novel approach to solving certain kinds of real-world problems, contributing a method that have advanced the state of the art in solving a specific optimization problem in the area of economic load dispatch.