Antlion optimization algorithm for optimal non-smooth economic load dispatch

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.

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.

This paper presents an application of a marine predator algorithm to solve the economic load dispatch problem. By using the fuel cost function with the valve-point loading effects or non-smooth cost function. The objective function is needed to find the minimum fuel cost based on the power balance and power limit of the generator constrain. The Brownian and Lévy randomization in the marine predator are used for finding the best answer. The three and six unit generator systems are case studies. The simulation results were compared by other methods of the optimization techniques. This study is found that the proposed method can be able to determine the power of the generator resulting in lower fuel costs.

The Economic Dispatch (ED) is one of the most important optimization problems in power systems the ultimate goal of the ED is to minimize the cost of operations in a power generation. In this paper, the Woodpecker Mating Algorithm (WMA) is used to solve the ED problem considering the nonlinear properties of generators such as valve point effects (VPE), prohibited operating zones (POZ), ramp rate limits, multiple fuel options, and transmission loss. The WMA algorithm is a novel metaheuristic algorithm inspired by the mating behavior of woodpeckers and sound intensity (a physical quantity). The WMA is implemented on six test systems of different operational dimensions and characteristics to show its capacity for solving the ED problem. The results are compared with the latest and most efficient methods introduced in the literature. Proving the efficiency of the WMA to solve the ED problem, simulation results are promising and offer the optimal fuel cost of production.

The economic load dispatch problem is a very important practical problem in electric power systems operation, where an efficient solution can lead to cost and emissions reductions. The use of metaheuristics, as the Firefly Algorithm, for the solution of economic load dispatch problems has been shown to be a more appropriate alternative than classical optimisation methods. In this work, we have proposed a new variant for the Firefly Algorithm, considering a non-homogeneous population. This new variant was validated using ten benchmark functions, and then applied to solve a 15-units economic load dispatch problem, considering transmission line losses, power limits, ramp limits and prohibited zones for each generator, and a 13-units non-convex system with valve-point loading effect in the cost function and power generation limits. The results show that the proposed non-homogeneous variant is able to reach better solutions than the original Firefly Algorithm, using both penalty and non-penalty power balance constraint handling methods. In general, the non-penalty approach reached better results than the penalty method. Moreover, the new variant presented relatively competitive results for the economic load dispatch problems considered, when compared to the best results found in the literature.

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.

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

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

Economic dispatch (ED) problem exhibits highly nonlinear characteristics, such as prohibited operating zone, ramp rate limits, and non-smooth property. Due to its nonlinear characteristics, it is hard to achieve the expected solution by the classical methods. To overcome the challenging difficulty, this paper proposes an improved firefly algorithm (FA) to solve economic dispatch (ED) problem. The improved FA employs two strategies to enhance the search ability and avoid the premature usually suffered from in standard FA. The first one is based on the distance information among the fireflies, and it adjusts the light absorption coefficient adaptively. The other one is a decreasing strategy for the randomization parameter. Additionally, a crossover operation is employed to create potential solution with high diversity. The designs are able to enhance the search ability and performance of FA, which have been demonstrated on six benchmark functions. To validate the proposed algorithm, we also use three different systems to demonstrate its efficiency and feasibility in solving ED problem. The experimental results show that the proposed FA method was capable of achieving higher quality solutions in ED problems.

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.

This paper presents a novel and efficient method for solving the economic dispatch (ED) problem with non-smooth cost function by modifying the particle swarm optimization algorithm employing time varying acceleration and time varying penalty (PSO-TVAC&P) coefficients. The proposed approach is suggested to deal with equality and inequality constraints with high degree of non linearity in the ED problems. To show the efficiency and effectiveness of proposed PSO-TVAC&P algorithm, it is tested on two test systems considering ramp rate limits, prohibited zones and valve point loading effects.

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.

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)

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

Firefly Algorithm for solving non-convex economic dispatch problems with valve loading effect