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.
Besides the above non-EA approaches, many EA methods have also been developed to solve various formulations of ELD. Orero and Irving proposed a simple Genetic Algorithm (GA) to solve ELD with POZ @cite_3 . Besides the standard GA, this work also devised a deterministic crowding GA model to solve the problem. Chiang developed an improved GA with the multiplier updating scheme for ELD with VPE and MFO @cite_28 . In this work, the proposed GA is incorporated with an improved evolutionary direction operator. In addition, the tailor-made migration operator efficiently searches the solution space. He proposed a hybrid GA approach to solve ELD with VPE @cite_9 . The algorithm proposed is a hybrid GA with differential evolution (DE) and sequential quadratic programming (SQP). Sinha developed an Evolutionary Programming (EP) method to solve ELP with VPE @cite_18 . Pereira-Neto proposed an Evolutionary Strategy (ES) method to solve ELP with VPE and POZ @cite_24 . DE has also been adapted to solve ELD @cite_43 @cite_0 .
@cite_18 @cite_28 @cite_9 @cite_3 @cite_24 @cite_43 @cite_0
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Evolutionary programming has emerged as a useful optimization tool for handling nonlinear programming problems. Various modifications to the basic method have been proposed with a view to enhance speed and robustness and these have been applied successfully on some benchmark mathematical problems. But few applications have been reported on real-world problems such as economic load dispatch (ELD). The performance of evolutionary programs on ELD problems is examined and presented in this paper in two parts. In Part I, modifications to the basic technique are proposed, where adaptation is based on scaled cost. In Part II, evolutionary programs are developed with adaptation based on an empirical learning rate. Absolute, as well as relative, performance of the algorithms are investigated on ELD problems of different size and complexity having nonconvex cost curves where conventional gradient-based methods are inapplicable. This paper presents an improved genetic algorithm with multiplier updating (IGA spl I.bar MU) to solve power economic dispatch (PED) problems of units with valve-point effects and multiple fuels. The proposed IGA spl I.bar MU integrates the improved genetic algorithm (IGA) and the multiplier updating (MU). The IGA equipped with an improved evolutionary direction operator and a migration operation can efficiently search and actively explore solutions, and the MU is employed to handle the equality and inequality constraints of the PED problem. Few PED problem-related studies have seldom addressed both valve-point loadings and change fuels. To show the advantages of the proposed algorithm, which was applied to test PED problems with one example considering valve-point effects, one example considering multiple fuels, and one example addressing both valve-point effects and multiple fuels. Additionally, the proposed algorithm was compared with previous methods and the conventional genetic algorithm (CGA) with the MU (CGA spl I.bar MU), revealing that the proposed IGA spl I.bar MU is more effective than previous approaches, and applies the realistic PED problem more efficiently than does the CGA spl I.bar MU. Especially, the proposed algorithm is highly promising for the large-scale system of the actual PED operation. Abstract An efficient hybrid genetic algorithm (HGA) approach for solving the economic dispatch problem (EDP) with valve-point effect is presented in this paper. The proposed method combines the GA algorithm with the differential evolution (DE) and sequential quadratic programming (SQP) technique to improve the performance of the algorithm. GA is the main optimizer, while the DE and SQP are used to fine tune in the solution of the GA run. To improve the performance of the SQP, the cost function of EDP is approximated by using a smooth and differentiable function based on the maximum entropy principle. An initial population obtained by using uniform design exerts optimal performance of the proposed hybrid algorithm. The combined algorithm is validated for two test systems consisting of 13 and 40 thermal units whose incremental fuel cost function takes into account the valve-point loading effects. The proposed combined method outperforms other algorithms reported in literatures (EP, EP–SQP, PSO, PSO–SQP) for EDP considering valve-point effects. The work explores the use of a genetic algorithm for the solution of an economic dispatch problem in power systems where some of the units have prohibited operating zones. Genetic algorithms have a capability to provide global optimal solutions in problem domains where a complete traversion of the whole search space is computationally infeasible. Two different implementations of the genetic algorithm for the solution of this dispatch problem are presented: a standard genetic algorithm, and a deterministic crowding genetic algorithm model. The results demonstrate that the genetic algorithm can be applied successfully in the solution of problems represented with nonconvex functions. A simple and efficient algorithm based on evolutionary strategies is proposed for the solution of the economic dispatch (ED) problem with noncontinuous and nonsmooth nonconvex cost functions and with generator constraints being considered. The proposed method solves both, the ED problem with nonconvex nonsmooth cost functions due to valve-point loading and the ED problem that takes into account nonlinear generator characteristics such as ramp-rate limits and prohibited operating zones in the power system operation. The effectiveness of the algorithm is demonstrated using six different test systems and the performance is compared with other relevant methods reported in the literature. In all cases, the proposed algorithm either matches or outperforms the behaviour reported for the existing algorithms. This level of performance is obtained despite the simplicity of the approach. This paper presents a novel stochastic optimisation approach to determining the feasible optimal solution of the economic dispatch (ED) problem considering various generator constraints. Many practical constraints of generators, such as ramp rate limits, prohibited operating zones and the valve point effect, are considered. These constraints make the ED problem a non-smooth non-convex minimisation problem with constraints. The proposed optimisation algorithm is called self-tuning hybrid differential evolution (self-tuning HDE). The self-tuning HDE utilises the concept of the 1 5 success rule of evolution strategies (ESs) in the original HDE to accelerate the search for the global optimum. Three test power systems, including 3-, 13- and 40-unit power systems, are applied to compare the performance of the proposed algorithm with genetic algorithms, the differential evolution algorithm and the HDE algorithm. Numerical results indicate that the entire performance of the proposed self-tuning HDE algorithm outperforms the other three algorithms. In this work, differential evolution (DE) algorithm was studied for solving economic load dispatch (ELD) problems in power systems. DE has proven to be effective in solving many real world constrained optimization problems in different domains. ELD problems are complex and nonlinear in nature with equality and inequality constraints and here special measures were taken to satisfy those. Five ELD problems of different characteristics were used to investigate the effectiveness of the proposal. Comparing with the other existing techniques, the current proposal was found better than, or at least comparable to, them considering the quality of the solution obtained.