Solving Economic Load Dispatch Problem Research Articles

Overload Management in Transmission System Using Particle Swarm Optimization

An approach is proposed for transmission system overload management. To achieve this aim, the problem is formulated in an Economic Load Dispatch (ELD) problem to minimize the fuel cost of generation in case of overload. Particle Swarm Optimization (PSO) is used to solve ELD problem. The results have been demonstrated for both normal and overload conditions. The final results show that the PSO algorithm performs well in both conditions.

Chemical reaction optimisation for different economic dispatch problems

This study presents a real coded chemical reaction algorithm to solve economic load dispatch (ELD) problems involving different constraints such as power balance, ramp rate limits and prohibited operating zone constraints. Effects of valve-point loading and multi-fuel options of large-scale thermal plants are also studied. System transmission loss has also been considered in a few cases. Chemical reaction optimisation mimics the interactions of molecules in a chemical reaction to reach from a higher energy unstable state to a low energy stable state. A real coded version, known as real-coded chemical reaction optimisation is implemented here to solve ELD problems. The simulation results establish that the proposed approach outperforms several other existing optimisation techniques in terms of quality of solution obtained and computational efficiency. The results also prove the robustness of the proposed methodology to solve ELD problems.

Differential evolution based on truncated Lévy-type flights and population diversity measure to solve economic load dispatch problems

Economic load dispatch (ELD) is an important constrained optimization task addressing this vital concern for power system operations. ELD problem is the process of allocating generation among available committed generating units such that cost of generation is optimum subject to several equality and inequality constraints. The conventional optimization methods are mainly classical mathematical methods, which include gradient method and Lagrange relaxation method. In recent years, different types of evolutionary algorithms have been used to solve ELD problems. Among the existing evolutionary algorithms, a well-known branch is the differential evolution (DE). The mutation operation of DE applies vector differentials between existing population members for determining both the degree and the direction applied to the individual subject of the mutation operation. With an eye to improve the performance of classical DE, in this paper, a DE algorithm combined with truncated Lévy flight random walks and a population diversity measure (DEL) to improve the crossover and mutation operations is designed to help avoiding premature convergence effectively. A Lévy flight random walks (a sequence of displacements) in which the increments are distributed according to a heavy-tailed probability distribution form the α-stable distribution family. The effectiveness of the proposed DEL is demonstrated for two benchmark ELD problems. In order to evaluate the performance of the proposed DEL, it is applied to benchmark systems consisting of 13 and 140 thermal units. Simulation results reveal that, compared with the classical DE and those other methods reported in literatures recently, the proposed DEL is capable of obtaining better quality solutions with higher efficiency.

Oppositional Real Coded Chemical Reaction Optimization for different economic dispatch problems

This paper proposes an effective oppositional Real Coded Chemical Reaction algorithm (ORCCRO) to solve Economic Load Dispatch (ELD) problems involving different equality and inequality constraints. Effects of valve-point loading, multi-fuel options of large-scale thermal plants are also studied. System transmission loss has also been considered in few cases. Chemical Reaction Optimization (CRO) imitates the interaction of molecules in a chemical reaction to reach from a higher energy unstable state to a low energy stable state. A real coded version of it, known as Real-coded chemical reaction optimization (RCCRO). Oppositional based RCCRO (ORCCRO) have been used here to improve the effectiveness and quality of solutions in minimum time. The proposed opposition-based RCCRO (ORCCRO) of the present work employs opposition-based learning for population initialization and also for generation wise update operation. In the present work, quasi-opposite numbers have been utilized instead of pseudo random numbers to improve the convergence rate of the RCCRO. Simulation results establish that the proposed approach outperforms several other existing optimization techniques in terms quality of solution obtained and computational efficiency. Results also prove the robustness of the proposed methodology to solve ELD problems.

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.

An Intelligent Water Drop Algorithm for Solving Economic Load Dispatch Problem

Economic Load Dispatch (ELD) is a method of determining the most efficient, low-cost and reliable operation of a power system by dispatching available electricity generation resources to supply load on the system. The primary objective of economic dispatch is to minimize total cost of generation while honoring operational constraints of available generation resources. In this paper an intelligent water drop (IWD) algorithm has been proposed to solve ELD problem with an objective of minimizing the total cost of generation. Intelligent water drop algorithm is a swarm-based natureinspired optimization algorithm, which has been inspired from natural rivers. A natural river often finds good paths among lots of possible paths in its ways from source to destination and finally find almost optimal path to their destination. These ideas are embedded into the proposed algorithm for solving economic load dispatch problem. The main advantage of the proposed technique is easy is implement and capable of finding feasible near global optimal solution with less computational effort. In order to illustrate the effectiveness of the proposed method, it has been tested on 6-unit and 20-unit test systems with incremental fuel cost functions taking into account the valve point-point loading effects. Numerical results shows that the proposed method has good convergence property and better in quality of solution than other algorithms reported in recent literature. Keywords—Economic load dispatch, Transmission loss, Optimization, Valve point loading, Intelligent Water Drop Algorithm.

A SelfAdaptive Fuzzy Cmeans based Radial Basis Function Network to Solve Economic Load Dispatch Problems

decades, with a large increase in power demand, fuel cost, and limited fuel supply it has become very essential to run the power systems with minimum cost so that the committed units serve the expected load demand. The basic objective of Economic Load Dispatch (ELD) is to distribute the total generation among the generation units in operation, in order to meet the load demand at minimum operating cost while satisfying the system equality and inequality constraints. Nature inspired computing techniques like Artificial Neural Networks (ANN) are preferred for solving ELD problems because they do not impose any restrictions on the shape of the fuel cost curve and are capable of providing good solution quality, and higher precision solutions very close to the global optimum. In this paper, the application of Fuzzy c*means based Radial Basis Function Network (RBFN) to ELD is proposed in order to minimize the error function through a self adaptive process until the error is less than a given tolerance leading to a best solution. The applicability and viability for practical applications has been tested on two different power systems, viz., a IEEE 30 bus 6 unit test system and a 20 unit test system and the experiments were carried out on MATLAB R2008b software. Comparison of the results with the conventional Lambda Iteration method demonstrates the effectiveness of RBFN in solving ELD problems based on fuel cost, power loss, total generated power, algorithmic efficiency, and computational time.

? constrained differential evolution for economic dispatch with valve-point effect

A novel and effective method for solving economic load dispatch (ELD) problem is presented in this work by integrating the ? constrained method with differential evolution (DE) algorithm. The ? constrained method sets us free from selecting the appropriate value for the penalty coefficient in the objective function, which is difficult and often chosen empirically. Differential evolution with ? constrained method (?DE) has proven to be effective in solving non-linear constrained optimisation problems. Here, the effectiveness of ?DE, in solving ELD problems is investigated by using three different ELD problems that take the valve-point loading effect into consideration. The proposed approach provides very high quality solutions which are very competitive to other existing techniques to ELD considering the valve-point effect.

Modified Shuffled Frog Leaping Algorithm for Solving Economic Load Dispatch Problem

In the recent restructured power system scenario and complex market strategy, operation at absolute minimum cost is no longer the only criterion for dispatching electric power. The economic load dispatch (ELD) problem which accounts for minimization of both generation cost and power loss is itself a multiple conflicting objective function problem. In this paper, a modified shuffled frog-leaping algorithm (MSFLA), which is an improved version of memetic algorithm, is proposed for solving the ELD problem. It is a relatively new evolutionary method where local search is applied during the evolutionary cycle. The idea of memetic algorithm comes from memes, which unlike genes can adapt themselves. The performance of MSFLA has been shown more efficient than traditional evolutionary algorithms for such type of ELD problem. The application and validity of the proposed algorithm are demonstrated for IEEE 30 bus test system as well as a practical power network of 203 bus 264 lines 23 machines system.

Solving economic load dispatch problem with valve-point effects using a hybrid quantum mechanics inspired particle swarm optimisation

Economic load dispatch (ELD) performs an important part in the economic operation of power system. The ELD problem is considered as a non-linear constrained optimisation problem. The problem becomes non-convex and non-smooth when the generators’ prohibited zones and valve-point effect are considered. The purpose of this work is to present a solution strategy to solve ELD problem in an efficient way while considering several aspects of ELD. The strategy employs a hybrid mechanism involving a quantum mechanics inspired particle swarm optimisation (PSO). The conventional PSO is modified by integrating quantum mechanics theory that redefines the particles positions and velocities in more diverse manner and therefore explores more search space. The PSO is further upgraded from a single population-based to a multi-population one. Such feature of the method delivers a fine balance between the local and global searching abilities. The simulations are carried by considering several cases of thermal units by varying different combinations of system configurations such as with/without valve-point effect, with/without network loss and for one or several hours of load demand. The results are quite promising and effective compared with several benchmark methods.

Quantum-Inspired Particle Swarm Optimization for Valve-Point Economic Load Dispatch

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 ELD problem has nonsmooth cost function with equality and inequality constraints which make it difficult to be effectively solved. Different heuristic optimization methods have been proposed to solve this problem in previous study. In this paper, quantum-inspired particle swarm optimization (QPSO) is proposed, which has stronger search ability and quicker convergence speed, not only because of the introduction of quantum computing theory, but also due to two special implementations: self-adaptive probability selection and chaotic sequences mutation. The proposed approach is tested with five standard benchmark functions and three power system cases consisting of 3, 13, and 40 thermal units. Comparisons with similar approaches including the evolutionary programming (EP), genetic algorithm (GA), immune algorithm (IA), and other versions of particle swarm optimization (PSO) are given. The promising results illustrate the efficiency of the proposed method and show that it could be used as a reliable tool for solving ELD problems.

Solving complex economic load dispatch problems using biogeography-based optimization

This paper presents an algorithm, biogeography-based optimization (BBO) to solve both convex and non-convex economic load dispatch (ELD) problems of thermal generators of a power system. The Proposed methodology easily takes care of solving non-convex economic dispatch problems considering different constraints such as transmission losses, ramp rate limits, multi-fuel options and prohibited operating zones. 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. BBO has features in common with other biology-based optimization methods, like genetic algorithms (GAs) and particle swarm optimization (PSO). Here, first it will be discussed how BBO can be used to solve ELD problems. This algorithm searches the global optimum mainly through two steps: migration and mutation. To show the advantages of the proposed algorithm, it has been applied to four different test systems for solving ELD problems. First, a 6-generator system along with ramp rate limits and prohibited operating zone. Second, considers 40 generators with valve-point loading. Third, considers 20-generator systems with simple quadratic cost function considering transmission loss and operating limit constraints. Last one is addressing both valve-point effects and multiple fuels in a 10-generator system. Comparing with the other existing techniques, the current proposal is found better than, or at least comparable to them considering the quality of the solution obtained. This method is considered to be a promising alternative approach for solving the ELD problems in practical power system.

Security constrained economic load dispatch using improved particle swarm optimization suitable for utility system

The objective of this paper is to evolve simple and effective methods for the economic load dispatch (ELD) problem with security constraints in thermal units, which are capable of obtaining economic scheduling for utility system. In the proposed improved particle swarm optimization (IPSO) method, a new velocity strategy equation is formulated suitable for a large scale system and the features of constriction factor approach (CFA) are also incorporated into the proposed approach. The CFA generates higher quality solutions than the conventional PSO approach. The proposed approach takes security constraints such as line flow constraints and bus voltage limits into account. In this paper, two different systems IEEE-14 bus and 66-bus Indian utility system have been considered for investigations and the results clearly show that the proposed IPSO method is very competent in solving ELD problem in comparison with other existing methods.