Optimization of economic load dispatch of higher order general cost polynomials and its sensitivity using modified particle swarm optimization

This paper presents a modified particle swarm optimization (MPSO) for economic load dispatch (ELD) problem. Considering multifuel operations, valve-point effects, accurate curve fitting, etc., real cost function is more complex than a conventional second order cost function in the deregulated changing market. Modified PSO consists of problem dependent variable number of promising values (in velocity vector), unit vector, error-iteration dependent step length, etc. It reliably and accurately tracks a continuously changing solution of the complex cost function and no extra concentration/effort is needed for more complex higher order cost polynomial in ELD. Constraint management is incorporated in the modified PSO. The modified PSO has balance between local and global searching abilities, and an appropriate fitness function helps to converge it quickly. To avoid the method to be frozen, stagnated/idle particles are reset. In this paper, sensitivity of higher order cost polynomial is also analyzed visually to realize the importance of higher order cost polynomial in ELD. Finally, benchmark data and methods are used to show the effectiveness of the proposed method.

Economic Load Dispatch (ELD) optimization is an important and difficult task in power system planning. Previously, most of the research mainly focused on proposing various evolutionary algorithms (EAs) to pursue better results of ELD problems. However, few comprehensive analysis of the effects of various constraint handling techniques (CHTs) on the performance of EA-based techniques are available so far. In this paper, we try to fill this gap by experimentally testing the algorithmic variants of combining four effective and widely used EAs with three CHTs. From the experimental results on the ELD problems with valve-point and those problems with both valve-point and multiple-fuel effect, several important conclusions can be achieved, including 1) for the low scale ELD problem with valve-point only, the selection of EAs is more important than CHTs; 2) for the large scale problems, CHTs play crucial roles; 3) the appropriate combination of EA and CHT is helpful to achieve better performance. This study is also expected to provide solid basis for further strengthening the robustness of EAs for ELD optimization. It is also interesting to observe that the experimental results obtained in this paper are much better than those of the previous effective ELD optimization algorithms.

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.

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.

This paper is an extension made in biogeography based optimization (BBO) by modifying its migration models to make it more realistic. This BBO technique is then applied on simple economic load dispatch (ELD) problem and ELD with valve point effect to analyze the effect of different migration models. Our analysis concludes that the quadratic and sinusoidal models provide the best result for the ELD and ELD valve point effect problem respectively.

Using suitable solution techniques to the unit commitment (UC) and economic load dispatch (ELD) problems play major role on finding an optimal power scheduling in electrical power system. The UC and ELD problems are to decide when and which generating units to commit and decommit, in order to minimize the total fuel cost over specified period subject to a large number of difficult constraints. Lagrangian relaxation (LR) has been widely used to solve UC and ELD. Recently bundling method (BM) has appeared to be one of the best multipliers updated techniques for LR. This method has promising and the fastest convergence characteristics for UC and ELD problems. For that reason, this paper is to solve the UC and ELD problems via LR, BM and interior point method. This paper explores also the best possible way of updating Lagrangian multipliers with minimum computation time using fast programming techniques.

Solving non-convex economic load dispatch problem via artificial cooperative search algorithm

A multi-objective particle swarm optimization (MOPSO) approach for multi-objective economic load dispatch problem in power system is presented in this paper. The economic load dispatch problem is a non-linear constrained multi-objective optimization problem. The proposed MOPSO approach handles the problem as a multi-objective problem with competing and non-commensurable fuel cost, emission and system loss objectives and has a diversity-preserving mechanism using an external memory (call “repository”) and a geographically-based approach to find widely different Pareto-optimal solutions. In addition, fuzzy set theory is employed to extract the best compromise solution. Several optimization runs of the proposed MOPSO approach were carried out on the standard IEEE 30-bus test system. The results revealed the capabilities of the proposed MOPSO approach to generate well-distributed Pareto-optimal non-dominated solutions of multi-objective economic load dispatch. Comparison with Multi-objective Evolutionary Algorithm (MOEA) showed the superiority of the proposed MOPSO approach and confirmed its potential for solving multi-objective economic load dispatch.

This research paper uses the golden jackal optimization (GJO), a novel meta-heuristic algorithm, to address power system economic load dispatch (ELD) problems. The GJO emulates the hunting behavior of golden jackals. GJO algorithm uses the cooperative attacking behavior of golden jackals to tackle complicated optimization problems efficaciously. The objective of ELD problem is to distribute power system load requirement to the different generators with a minimum total fuel cost of generation. ELD problems are highly complex, non-linear, and non-convex optimization problems while considering constraints namely valve point loading effect (VPL) and prohibited operating zones (POZs). The proposed GJO algorithm is applied to solve complex, non-linear, and non-convex ELD problems. Six different test systems having 6, 10, 13, 40, and 140 generators with various constraints are used to validate the usefulness of the suggested GJO method. Simulation outcomes of the test system are compared with various algorithms reported in the algorithms such as particle swarm optimization (PSO), ant colony optimization (ACO), and backtracking search algorithm (BSA). Results show that the proposed GJO algorithm produces minimal fuel cost and has good convergence in solving ELD problems of power system engineering.

Economic Load Dispatch (ELD) is one of the important optimization problem in advanced power system and control. In this paper, six and fifteen generating units in ELD problem has been considered. Prohibited zone and ramp rate limit constraints has been also considered. ELD problem has been solved using three types of optimization techniques. These optimization techniques are Particle Swarm Optimization (PSO), Particle Swarm Optimization with Constriction Factor and Inertia Weight factor Approach (PSOCFIWA) and Time Varying Acceleration Based Particle Swarm Optimization with Constriction Factor and Inertia Weight factor Approach (TVAC-PSOCFIWA) algorithms. Optimum result of each optimization techniques have been compared.

Nature Inspired algorithms have been so far proved as some of the best problem solvers. The Artificial Fish Schooling Algorithm (AFSA) which falls under this category has been deployed to solve the classic Economic Load Dispatch problem. A modified implementation has been illustrated in this paper to enhance the precision and speed of the algorithm.KeywordsArtificial fishOptimizationEconomic load dispatchCostSwarmIAFSA (Improvised Artificial Fish Swarm Algorithm)

Economical dispatch of power is a significant real time optimization problem in the operation of power system, which allocates the loads on the committed generating units to reduce the generation cost, while meeting all the inequality and equality constraints. Traditionally, economic load dispatch problems have been formulated as convex optimization problem and various classical methods such as gradient methods, base-point participation factor method, etc. have been used for solving them. The traditional formulation is a quadratic input-output curve or piece wise linear cost curve, which are continuous and convex, however, real generating units have valve loading effects, which make the cost curve discontinuous and non-convex and hence the economic dispatch problem is no longer simple to handle. Thus, the classical methods cannot be employed for non-convex problems. The non-convex, non-linear and discontinuous economic dispatch (ED) problem can be better solved by metaheuristic approaches. Such approaches often require tuning of their respective evolutionary parameters. Although, solution to such type of problem have already been solved by different metaheuristic optimization techniques in previous studies as well, however, the algorithm employed in this paper to solve Power Economic Load Dispatch (PELD) problem is adaptive real coded quantum-inspired evolutionary algorithm, which does not require tuning of evolutionary parameters and performs better than some of the existing techniques on standard 6-bus 3 machine system and IEEE 14 bus 5 unit system.

Economic load dispatch can be defined as a technique of generation allocation among the units committed with an objective of fuel cost minimization by meeting the set constraints. This paper presents a novel DNLP approach using general algebraic modeling system (GAMS) software for scheduling generators for obtaining electrical power more economically. In power systems for optimal planning and efficient operation, economic load dispatch (ELD) problem is considered essential and vital. It is a highly nonlinear type of constrained optimization problem. The suggested approach is tested on three distinct well-known test systems to demonstrate its applicability in the ELD problem. In comparison with other methods for robustness, quality, and time of computation, the proposed method outperforms in all aspects. In this paper, both the losses of transmission and valve-point effects are considered for various test systems with 13, 40, and 10 generators.KeywordsEconomic load dispatchValve-point effectsTransmission line lossGeneral algebraic modeling system

An optimal solution to the unit commitment (UC) and economic load dispatch (ELD) problems lead to remarkable saving in the power system operational cost. UC and ELD main problems are to find the maximum profit and fast computation simulation time for the scheduling program. Lagrangian relaxation (LR) has become one of the best solution methods in solving the UC and ELD problems. The approach is claimed to be more efficient and easier than other methods in solving large-scale problems. When applying LR, the dual function needed to be updated at the higher level. Lately, bundling method (BM) is one of the best solution methods to Lagrangian dual problem. This paper presents LR technique, BM and interior point method for solving the UC and ELD problems. It will also explore the best possible way of updating Lagrangian multipliers with minimum computation time using fast programming techniques.

In this paper, an effective and reliable variant of particle swarm optimization with time-varying acceleration coefficients (PSO-TVAC) technique is proposed for the economic load dispatch problem considering valve-point loading effect. Main objective of the economic load dispatch (ELD) problem is to minimize the fuel cost by allocating the generation of the committed units subjected to the equality and inequality constraints. Equation of the economic dispatch objective function gets modified with the addition of a new parameter which represents the effect of valve-point loading. While exploring the use of PSO and its other variants to the economic dispatch problem, a number of research works have not considered the transmission losses properly. This paper represents the usefulness of the proposed PSO-TVAC algorithm to significantly reduce the fuel cost while taking into account the effect of transmission losses along with the non-convex characteristic due to valve loading. The results have been demonstrated for three-generator and ten-generator test systems.