Non-convex Economic Load Dispatch Problem Research Articles

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.

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.

A social spider algorithm for solving the non-convex economic load dispatch problem

Economic Load Dispatch (ELD) is one of the essential components in power system control and operation. Although conventional ELD formulation can be solved using mathematical programming techniques, modern power system introduces new models of the power units which are non-convex, non-differentiable, and sometimes non-continuous. In order to solve such non-convex ELD problems, in this paper we propose a new approach based on the Social Spider Algorithm (SSA). The classical SSA is modified and enhanced to adapt to the unique characteristics of ELD problems, e.g., valve-point effects, multi-fuel operations, prohibited operating zones, and line losses. To demonstrate the superiority of our proposed approach, five widely adopted test systems are employed and the simulation results are compared with the state-of-the-art algorithms. In addition, the parameter sensitivity is illustrated by a series of simulations. The simulation results show that SSA can solve ELD problems effectively and efficiently.

Solution of non-convex economic load dispatch problem using Grey Wolf Optimizer

Grey Wolf Optimizer (GWO) is a recently developed meta-heuristic search algorithm inspired by grey wolves (Canis lupus), which simulate the social stratum and hunting mechanism of grey wolves in nature and based on three main steps of hunting: searching for prey, encircling prey and attacking prey. This paper presents the application of GWO algorithm for the solution of non-convex and dynamic economic load dispatch problem (ELDP) of electric power system. The performance of GWO is tested for ELDP of small-, medium- and large-scale power systems, and the results are verified by a comparative study with lambda iteration method, Particle Swarm Optimization algorithm, Genetic Algorithm, Biogeography-Based Optimization, Differential Evolution algorithm, pattern search algorithm, NN-EPSO, FEP, CEP, IFEP and MFEP. Comparative results show that the GWO algorithm is able to provide very competitive results compared to other well-known conventional, heuristics and meta-heuristics search algorithms.

Solving nonconvex economic load dispatch problem using particle swarm optimization with time varying acceleration coefficients

This article presents the design and application of an efficient hybrid heuristic search method to solve the practical economic dispatch problem considering many nonlinear characteristics of power generators, and their operational constraints, such as transmission losses, valve‐point effects, multi‐fuel options, prohibited operating zones, ramp rate limits and spinning reserve. These practical operation constraints which can usually be found at the same time in realistic power system operations make the economic load dispatch (ELD) problem a nonsmooth optimization problem having complex and nonconvex features with heavy equality and inequality constraints. A particle swarm optimization with time varying acceleration coefficients is proposed to determine optimal ELD problem in this paper. The proposed methodology easily takes care of solving nonconvex ELD problems along with different constraints like transmission losses, dynamic operation constraints, and prohibited operating zones. The proposed approach has been implemented on the 3‐machines 6‐bus, IEEE 5‐machines 14‐bus, IEEE 6‐machines 30‐bus systems and 13 thermal units power system. The proposed technique is compared with solve the ELD problem with hybrid approach by using the valve‐point effect. The comparison results prove the capability of the proposed method give significant improvements in the generation cost for the ELD problem. © 2015 Wiley Periodicals, Inc. Complexity 21: 299–308, 2016

Comparative analysis of optimal load dispatch through evolutionary algorithms

This paper presents an evolutionary algorithm named as Cuckoo Search algorithm applied to non-convex economic load dispatch problems. Economic load dispatch (ELD) is very essential for allocating optimally generated power to the committed generators in the system by satisfying all of the constraints. Various evolutionary techniques like Genetic Algorithm (GA), Evolutionary programming, Particle Swarm Optimization (PSO) and Cuckoo Search algorithm are considered to solve dispatch problems. To verify the robustness of the proposed Cuckoo Search based algorithm, constraints like valve point loading, ramp rate limits, prohibited operating zones, multiple fuel options, generation limits and losses are also incorporated in the system. In the Cuckoo Search algorithm, the levy flights and the behavior of alien egg discovery is used to search the optimal solution. In comparison with the solution quality and execution time obtained by five test systems, the proposed algorithm seems to be a promising technique to solve realistic dispatch problems.

English

This paper presents a biogeography-based optimization (BBO) algorithm to solve both convex and nonconvex economic load dispatch (ELD) problems of thermal plants. Lack of exploration capability of biogeographybased optimization (BBO) leads to slow convergence. The proposed methodology can take care of economic dispatch problems involving constraints such as transmission losses, valve point loading, multi-fuel options and prohibited operating zones. Biogeography is the study of the geographical distribution of biological organisms. Mathematical equations that govern the distribution of organisms were first discovered and developed during the 1960s. The mindset of the engineer is that we can learn from nature. This motivates the application of biogeography to optimization problems; the BBO is based on two steps mutation and migration. The purpose of this work is to find out the advantages of application of the soft computing technique and BBO in particular to the economic load dispatch problem.

Economic load dispatch using krill herd algorithm

Economic load dispatch (ELD) is an important topic in the operation of power plants which can help to build up effective generating management plans. The practical ELD problem has non-smooth cost function with nonlinear constraints which make it difficult to be effectively solved. This paper presents, a new and efficient krill herd algorithm (KHA) to solve both convex and non-convex ELD problems of thermal power units considering valve point loading, multiple fuel operation, transmission losses and constraints such as ramp rate limits and prohibited operating zones. To enhance the overall performance and effectiveness of the proposed algorithm, the crossover and mutation operation of differential evolution (DE) are integrated with the proposed method. The different versions of KHA are successfully applied to small, medium, and large-scale power systems for solving six different ELD problems. The simulation results obtained by the proposed algorithms are compared with the results obtained using other recently develop methods available in the literature. From numerical results, it is found that the proposed KHA with crossover and mutation operators approach is able to provide better solution than other reported techniques in terms of fuel cost. Furthermore, this algorithm is better in terms of robustness than most of the existing algorithms used in this study.

Particle swarm optimization with smart inertia factor for solving non-convex economic load dispatch problems

SUMMARY This paper proposes a new approach to solve the non-convex economic dispatch problem using particle swarm optimization with smart inertia factor (PSO-SIF) algorithm in which, inertia coefficients are controlled with respect to cost function in each population. Hence, each population has unique inertia coefficient and as a result unique velocity in convergent direction for the best group solution. The new algorithm has been implemented on four test systems in different dimensions (6, 15, 20 and 40 units) with convex and non-convex cost functions. The numerical results have been compared with the results of a few PSO variants and some recently published results. The results prove the robustness and effectiveness of the proposed method and show that it could be used as a reliable tool for solving optimization problems. Copyright © 2013 John Wiley & Sons, Ltd.

An improved harmony search algorithm to solve economic load dispatch problems with generator constraints

This paper presents a new improved harmony search (IHS) algorithm to solve non-convex economic load dispatch problems in the power system. In the proposed IHS algorithm, multiple harmony memory consideration rates and dynamic pitch adjusting rate are used to generate a new harmony/solution vector with enhanced solution quality. The effectiveness of the proposed IHS algorithm has been successfully tested in the test systems which consists of six units with ramp rate limits, prohibited operating zones and transmission loss, thirteen units with valve point effect, and ten units with multiple fuel options and valve point effect. The results obtained using the proposed IHS algorithm are compared with the results of other techniques reported in the literature. The comparative results reveal that the proposed IHS algorithm has good searching capacity to find the global optimal solution, than the other methods reported in the literature and also has good convergence characteristic.

Economic load dispatch with nonsmooth cost functions using evolutionary particle swarm optimization

AbstractThis paper presents an evolutionary particle swarm optimization (EPSO) method for solving the nonconvex economic load dispatch (ELD) problem. In practice, the nonconvex and the discontinuous cost function should be considered when optimizing ELD problem with constraints such as valve point effects, prohibited operating zones, ramp‐rate limits, and transmission loss of the system. In view of these constraints, the ELD problem is difficult to solve by any mathematical method. In EPSO, the evolutionary programming concept (combination, tournament competition, sorting, and selection) is employed in the classical PSO method in order to find the best individual and best group position based on the survival particle. The effectiveness of the EPSO is tested on 3‐, 6‐, 15‐, and 38‐unit systems. The results obtained by EPSO are also compared with classical PSO and other results reported in the literature. It is concluded that the EPSO method can produce lower generation cost compared to the existing methods. © 2013 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

An effective differential harmony search algorithm for the solving non-convex economic load dispatch problems

Solving the non-convex economic load dispatch (ELD) problem with evolutionary algorithms has gained increasing research in recent years. In this paper, a differential harmony search (DHS) algorithm is proposed by combining the mechanisms of both differential evolution and harmony search. In the DHS, the pitch adjustment operation is cooperated with the different mutation operation to enhance the exploitation ability of harmony search, and both the memory consideration and the pitch adjustment are used to enhance the exploration ability of evolution search. In addition, a repair procedure and three simple selection rules are proposed for constraint handling. Numerical simulations are carried out based on different kinds of testing problems with various constraints including valve point effects, multi-fuels, ramp rate limit and prohibited operation zones. Simulation results and comparisons with the some existing algorithms demonstrate the effectiveness, efficiency and robustness of the proposed DHS algorithm. Finally, the effect of parameter setting on the DHS is investigated as well.

Non-convex economic dispatch with heuristic load patterns, valve point loading effect, prohibited operating zones, ramp-rate limits and spinning reserve constraints using harmony search algorithm

This paper attempts to investigate the applicability of harmony search algorithm (HSA) to solve extremely challenging non-convex economic load dispatch problem with valve point loading effect, prohibited operating zones, ramp-rate limits, spinning reserve constrains and transmission losses involving variations of consumer load patterns. The performance of the proposed approach HSA has been tested successfully on the standard 6-bus, IEEE-14 bus and IEEE-30 bus system with several heuristic load patterns. The results of this study reveals that the proposed approach is able to find appreciable economical load dispatch solutions than those of improved fast evolutionary program and particle swarm optimization. Besides this, the transmission line losses are also considerably reduced and the computation time is reasonably even and less when compared to other methods.

Discussion of “Hybrid Differential Evolution With Biogeography-Based Optimization for Solution of Economic Load Dispatch”

We commend the authors of for application of an interesting optimization methodology to solve economic dispatch problem. Their discussion presents a hybrid technique combining differential evolution with the biogeography-based optimization (DE/BBO) algorithm to solve both convex and nonconvex economic load dispatch (ELD) problems of thermal power units considering transmission losses, and constraints such as ramp-rate limits, valve-point loading, and prohibited operating zones (POZ). The proposed DE/BBO algorithm has been applied to solve ELD problems in four different test cases to verify its feasibility. In the test Case 1 of the paper, the authors examined a three-generator test system with ramp rate limit and prohibited operating zone constrains, as explained well in the paper.

Economic load dispatch using population-variance harmony search algorithm

This paper presents a novel stochastic optimization approach to solve the constrained economic load dispatch (ELD) problem using the harmonic search algorithm (HS). HS is a recently developed derivative-free, meta-heuristic optimization algorithm, which draws inspiration from the musical process of searching for a perfect state of harmony. This work analyses the evolution of the population-variance over successive generations in HS and thereby draws some important conclusions regarding the explorative power of HS. The proposed methodology easily takes care of solving non-convex ELD problems along with different constraints like transmission losses, ramp rate limits of the generators and prohibited operating zones. Simulations were performed over various standard test systems with different number of generating units and a comparative study is carried out with other existing relevant approaches. The findings affirmed the robustness and proficiency of the proposed methodology over other existing techniques.

Economic Load Dispatch Using Hybrid Swarm Intelligence Based Harmony Search Algorithm

This article presents a novel stochastic optimization approach to solve the constrained economic load dispatch problem using a hybridization of the harmony search algorithm and particle swarm optimization, named hybrid harmony search based on the swarm intelligence principle. Harmony search is a recently developed derivative-free, meta-heuristic optimization algorithm, which draws inspiration from the musical process of searching for a perfect state of harmony. This work is an attempt to utilize the velocity-based particle updating process from particle swarm optimization in the improvisation process of the harmony search algorithm for a better convergence of the proposed algorithm. The proposed methodology also easily takes care of solving non-convex economic load dispatch problems along with different constraints, such as power balance, ramp rate limits of the generators, and prohibited operating zones. Simulations were performed over four various standard test systems with different numbers of generating units, and a comparative study is carried out with other existing relevant approaches. The findings affirm the robustness and proficiency of the proposed methodology over other existing techniques.

Non-convex Economic Dispatch with Heuristic Load Patterns using Harmony Search Algorithm

paper presents an attempt to explore the applicability of harmony search algorithm (HSA) to solve extremely challenging non-convex economic load dispatch (ELD) problem with transmission losses involving variations of consumer load patterns. The efficiency of the proposed approach HSA has been tested successfully on the standard 6-bus system, IEEE-14 bus system, and the IEEE-30 bus system with several heuristic load patterns. The results of this study reveals that the proposed approach is able to find appreciable economical load dispatch solutions than the improved fast evolutionary program (IFEP) and particle swarm optimization (PSO). Besides this, the transmission line losses also considerably reduced and the computation time is reasonably even in all test cases and less when compared to other methods.

Economic load dispatch solution by improved harmony search with wavelet mutation

This paper presents a new evolutionary optimisation algorithm to solve economic load dispatch (ELD) problem with operational constraints using the improved harmony search algorithm. Harmony search algorithm is a recently developed derivative-free, meta-heuristic optimisation algorithm, which draws inspiration from the musical process of searching for a perfect state of harmony. In this paper we replace the random selection process in the classical harmony search method by wavelet theory based mutation process to improve the performance of the algorithm. The proposed methodology easily takes care of solving non-convex ELD problems along with different constraints like power balance, ramp rate limits of the generators and prohibited operating zones. Simulations were performed over various standard test systems with different number of generating units and a comparative study is carried out with other existing relevant approaches. The results obtained reveal the robustness and ability of the proposed methodology over other existing techniques.

Hybrid Differential Evolution With Biogeography-Based Optimization for Solution of Economic Load Dispatch

This paper presents a hybrid technique combining differential evolution with biogeography-based optimization (DE/BBO) algorithm to solve both convex and nonconvex economic load dispatch (ELD) problems of thermal power units considering transmission losses, and constraints such as ramp rate limits, valve-point loading and prohibited operating zones. Differential evolution (DE) is one of the very fast and robust evolutionary algorithms for global optimization. Biogeography-based optimization (BBO) is a relatively new optimization. Mathematical models of biogeography describe how a species arises, migrates from one habitat (Island) to another, or gets extinct. This algorithm searches for the global optimum mainly through two steps: migration and mutation. This paper presents combination of DE and BBO (DE/BBO) to improve the quality of solution and convergence speed. DE/BBO improves the searching ability of DE utilizing BBO algorithm effectively and can generate the promising candidate solutions. The effectiveness of the proposed algorithm has been verified on four different test systems, both small and large. Considering the quality of the solution and convergence speed obtained, this method seems to be a promising alternative approach for solving the ELD problems in practical power system.

Biogeography-Based Optimization for Different Economic Load Dispatch Problems

This paper presents a biogeography-based optimization (BBO) algorithm to solve both convex and non-convex economic load dispatch (ELD) problems of thermal plants. The proposed methodology can take care of economic dispatch problems involving constraints such as transmission losses, ramp rate limits, valve point loading, multi-fuel options and prohibited operating zones. Biogeography deals with the geographical distribution of biological species. Mathematical models of biogeography describe how a species arises, migrates from one habitat to another and gets wiped out. BBO has some features that are in common with other biology-based optimization methods, like genetic algorithms (GAs) and particle swarm optimization (PSO). This algorithm searches for the global optimum mainly through two steps: migration and mutation. The effectiveness of the proposed algorithm has been verified on four different test systems, both small and large, involving varying degree of complexity. Compared with the other existing techniques, the proposed algorithm has been found to perform better in a number of cases. Considering the quality of the solution obtained, this method seems to be a promising alternative approach for solving the ELD problems in practical power system.