• International Journal of Control, Automation, and Systems
• /
• v.6 no.4
• /
• pp.468-476
• /
• 2008

This paper presents a novel approach to economic dispatch (ED) with nonconvex fuel cost function as combinatorial optimization problems (COP) while most of the conventional researches have been developed as function optimization problems (FOP). One nonconvex fuel cost function can be divided into several convex fuel cost functions, and each convex function can be regarded as a generation type (G-type). In that case, ED with nonconvex fuel cost function can be considered as COP finding the best case among all feasible combinations of G-types. In this paper, a genetic algorithm is applied to solve the COP, and the $\lambda$-P table method is used to calculate ED for the fitness function of GA. The $\lambda$-P table method is reviewed briefly and the GA procedure for COP is explained in detail. This paper deals with three kinds of ED problems, namely ED considering valve-point effects (EDVP), ED with multiple fuel units (EDMF), and ED with prohibited operating zones (EDPOZ). The proposed method is tested for all three ED problems, and the test results show an improvement in solution cost compared to the results obtained from conventional algorithms.

• Journal of Electrical Engineering and Technology
• /
• v.3 no.4
• /
• pp.476-483
• /
• 2008

This paper is aimed at presenting techniques of hybrid differential evolution for solving various kinds of Economic Dispatch(ED) problems such as those including prohibited zones, emission dispatch, multiple fuels, and multiple areas. The results obtained for typical problems are compared with those obtained by other techniques such as Particle Swarm Optimization(PSO) and Classical Evolutionary Programming(CEP) techniques. The comparison of the results proves that hybrid differential evolution is quite favorable for solving ED problems with no restrictions on the shapes of the input-output functions of the generator.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.58 no.8
• /
• pp.1485-1495
• /
• 2009

This paper presents a novel approach to economic dispatch (ED) with nonconvex fuel cost function as combinatorial optimization problems (COP) while most of the conventional researches have been developed as function optimization problems (FOP). One nonconvex fuel cost function can be divided into several convex fuel cost functions, and each convex function can be regarded as a generation type (G-type). In that case, ED with nonconvex fuel cost function can be considered as COP finding the best case among all feasible combinations of G-types. In this paper, a genetic algorithm is applied to solve the COP, and the ${\lambda}-P$ function method is used to calculate ED for the fitness function of GA. The ${\lambda}-P$ function method is reviewed briefly and the GA procedure for COP is explained in detail. This paper deals with two kinds of ED problems, namely ED with multiple fuel units (EDMF) and ED with prohibited operating zones (EDPOZ). The proposed method is tested for all the ED problems, and the test results show an improvement in solution cost compared to the results obtained from conventional algorithms.

• Journal of Electrical Engineering and Technology
• /
• v.13 no.3
• /
• pp.1099-1109
• /
• 2018

For practical consideration, economic dispatch (ED) problems in power system have non-smooth cost functions with equality and inequality constraints that makes the problems complex constrained nonlinear optimization problems. This paper proposes a new constraint handling method for equality and inequality constraints which is employed to solve ED problems, where the incremental rate is employed to enhance the modification process. In order to prove the applicability of the proposed method, the study cases are tested based on the classical particle swarm optimization (PSO) and differential evolution (DE) algorithm. The proposed method is evaluated for ED problems using six different test systems: 6-, 15-, 20-, 38-, 110- and 140-generators system. Simulation results show that it can always find the satisfactory solutions while satisfying the constraints.

• Journal of Electrical Engineering and Technology
• /
• v.3 no.1
• /
• pp.52-59
• /
• 2008

This paper describes the secant method for solving the economic dispatch (ED) problem with generator constraints and transmission losses. The ED problem is an important optimization problem in the economic operation of a power system. The proposed algorithm involves selection of minimum and maximum incremental costs (lambda values) and then the evaluation of optimal lambda at required power demand is done by secant method. The proposed algorithm has been tested on a power system having 6, 15, and 40 generating units. Studies have been made on the proposed method to solve the ED problem by taking 120 and 200 units with generator constraints. Simulation results of the proposed approach were compared in terms of solution quality, convergence characteristics, and computation efficiency with conventional methods such as lambda iterative method, heuristic methods such as genetic algorithm, and meta-heuristic methods like particle swarm optimization. It is observed from different case studies that the proposed method provides qualitative solutions with less computational time compared to various methods available in the literature.

• Proceedings of the KIEE Conference
• /
• 2007.11b
• /
• pp.115-117
• /
• 2007

This paper presents a new systematic approach to find a global solution to economic dispatch (ED) with multiple fuel units using a function merger (FM). Currently, no systematic approach has been developed to find a global solution to economic dispatch with multiple fuel units. Various heuristic methods have been proposed, however it is almost impossible to guarantee a global solution by those methods yet. The proposed method uses the FM and $\lambda$-P functions. A FM merges several fuel cost functions into one that satisfies the optimal conditions of an ED. The FM procedures are described in detail with illustrative examples.

• The Transactions of the Korean Institute of Electrical Engineers A
• /
• v.54 no.12
• /
• pp.586-591
• /
• 2005

This paper presents a method of minimizing of generation cost on individual electrical power utility. The method is based on the Economic Dispatch (ED) and linear Available Transfer Capability (ATC). The economic dispatch redistributes the total load to individual units to minimize the generation cost without transmission network constraints. The proposed method is implemented using ATC calculated from Power Transfer Distribution Factor (PTDF) for the transmission network constraints. The performance of the proposed method has been tested for the IEEE-30 bus system. It has also been observed that the results of the proposed method is compared with that of optimal power flow.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.56 no.6
• /
• pp.1023-1030
• /
• 2007

This paper presents a new and efficient approach for solving the economic dispatch (ED) problems with nonconvex cost functions using particle swarm optimization (PSO). Although the PSO is easy to implement and has been empirically shown to perform well on many optimization problems, it may easily get trapped in a local optimum when solving problems with multiple local optima and heavily constrained. This paper proposes an improved PSO, which combines the conventional PSO with chaotic sequences (CPSO). The chaotic sequences combined with the linearly decreasing inertia weights in PSO are devised to improve the global searching capability and escaping from local minimum. To verify the feasibility of the proposed method, numerical studies have been performed for two different nonconvex ED test systems and its results are compared with those of previous works. The proposed CPSO algorithm outperforms other state-of-the-art algorithms in solving ED problems, which consider valve-point and multi-fuels with valve-point effects.

• Journal of Electrical Engineering and Technology
• /
• v.8 no.1
• /
• pp.80-89
• /
• 2013

This paper presents an efficient approach for solving economic dispatch (ED) problems with nonconvex cost functions using a 'Mean-Variance Optimization (MVO)' algorithm with Kuhn-Tucker condition and swap process. The aim of the ED problem, one of the most important activities in power system operation and planning, is to determine the optimal combination of power outputs of all generating units so as to meet the required load demand at minimum operating cost while satisfying system equality and inequality constraints. This paper applies Kuhn-Tucker condition and swap process to a MVO algorithm to improve a global minimum searching capability. The proposed MVO is applied to three different nonconvex ED problems with valve-point effects, prohibited operating zones, transmission network losses, and multi-fuels with valve-point effects. Additionally, it is applied to the large-scale power system of Korea. The results are compared with those of the state-of-the-art methods as well.

• Journal of Electrical Engineering and Technology
• /
• v.4 no.3
• /
• pp.301-309
• /
• 2009

A simple and efficient Lambda logic (${\lambda}-logic$) based algorithm is proposed for the solution of the generator constrained economic dispatch problem when the generating units having prohibited zones. The proposed method solves the economic dispatch (ED) problem that takes into account ramprate limits, transmission losses and prohibited operating zones in the power system operation. The proposed method uses a simple heuristic rule based on average power of prohibited operating zones which produces the feasibility of solution for the restricted operating units. The effectiveness of the algorithm is tested on five different test systems and the performance compared with other relevant methods reported in the literature. In all the cases, the proposed algorithm performs better than the previous existing algorithms with a less computational burden.