• 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.

• Journal of Electrical Engineering and Technology
• /
• v.10 no.4
• /
• pp.1441-1452
• /
• 2015

This paper proposes a new Hybrid Particle Swarm Optimization (HPSO) method that integrates the Evolutionary Programming (EP) and Particle Swarm Optimization (PSO) techniques. The proposed method is applied to solve Economic Dispatch(ED) problems considering prohibited operating zones, ramp rate limits, capacity limits and power balance constraints. In the proposed HPSO method, the best features of both EP and PSO are exploited, and it is capable of finding the most optimal solution for the non-linear optimization problems. For validating the proposed method, it has been tested on the standard three, six, fifteen and twenty unit test systems. The numerical results show that the proposed HPSO method is well suitable for solving non-linear economic dispatch problems, and it outperforms the EP, PSO and other modern metaheuristic optimization methods reported in the recent literatures.

• The Transactions of the Korean Institute of Electrical Engineers A
• /
• v.50 no.11
• /
• pp.520-527
• /
• 2001

This paper suggests a new methodology of evolutionary computations - an Adaptive Evolutionary Algorithm (AEA) for solving the Economic Load Dispatch (ELD) problem which has piecewise quadratic cost functions and prohibited operating zones with many local minima. AEA uses a genetic algorithm (GA) and an evolution strategy (ES) in an adaptive manner in order to take merits of two different evolutionary computations: global search capability of GA and local search capability of ES. In the reproduction procedure, proportions of the population by GA and the population by ES are adaptively modulated according to the fitness. Case studies illustrate the superiority of the proposed methods to existing conventional methods in power generation cost and computation time. The results demonstrate that the AEA can be applied successfully in the solution of ELD with piecewise quadratic cost functions and prohibited operating zones

• Proceedings of the KIEE Conference
• /
• 2007.07a
• /
• pp.850-851
• /
• 2007

This paper presents an efficient approach for solving the economic dispatch (ED) problems with prohibited operating zones using an improved particle swarm optimization (PSO). Although the PSO-based approaches have several advantages suitable to the heavily constrained nonconvex optimization problems, they still have the drawbacks such as local optimal trapping due to the premature convergence (i.e., exploration problem) and insufficient capability to find nearly-by extreme points (i.e., exploitation problem). This paper proposes an improved PSO framework adopting a crossover operation scheme to increase both exploration and exploitation capability of the PSO. The proposed method is applied to ED problem with prohibited operating zones. Also, the results are compared with those of the state-of-the-art methods.

• Journal of Electrical Engineering and Technology
• /
• v.3 no.3
• /
• pp.320-330
• /
• 2008

This paper presents an improved dynamic programming (IDP) approach to solve the economic power dispatch problem including transmission losses in power systems. A detailed mathematical derivation of recursive dynamic programming approach for the economic power dispatch problem with transmission losses is presented. The transmission losses are augmented with the objective function using price factor. The generalized expression for optimal scheduling of thermal generating units derived in this article can be implemented for the solution of the economic power dispatch problem of a large-scale system. Six-unit, fifteen-unit, and forty-unit sample systems with non-linear characteristics of the generator, such as ramp-rate limits and prohibited operating zones are considered to illustrate the effectiveness of the proposed method. The proposed method results have been compared with the results of genetic algorithm and particle swarm optimization methods reported in the literature. Test results show that the proposed IDP approach can obtain a higher quality solution with better performance.

• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.15 no.5
• /
• pp.155-162
• /
• 2015

This paper proposes a deterministic optimization algorithm to solve economic load dispatch problem with quadratic convex fuel cost function. The proposed algorithm primarily partitions a generator with prohibited zones into multiple generators so as to place them afield the prohibited zone. It then sets initial values to $P_i{\leftarrow}P_i^{max}$ and reduces power generation costs of those incurring the maximum unit power cost. It finally employs a swap optimization process of $P_i{\leftarrow}P_i-{\beta}$, $P_j{\leftarrow}P_j+{\beta}$ where $_{max}\{F(P_i)-F(P_i-{\beta})\}$ > $_{min}\{F(P_j+{\beta})-F(P_j)\}$, $i{\neq}j$, ${\beta}=1.0,0.1,0.01,0.001$. When applied to 3 different 15-generator cases, the proposed algorithm has consistently yielded optimized results compared to those of heuristic algorithms.

• 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.

• 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.9 no.1
• /
• pp.15-26
• /
• 2014

This paper proposes a Modified Particle Swarm Optimization with Time Varying Acceleration Coefficients (MPSO-TVAC) for solving economic load dispatch (ELD) problem. Due to prohibited operating zones (POZ) and ramp rate limits of the practical generators, the ELD problems become nonlinear and nonconvex optimization problem. Furthermore, the ELD problem may be more complicated if transmission losses are considered. Particle swarm optimization (PSO) is one of the famous heuristic methods for solving nonconvex problems. However, this method may suffer to trap at local minima especially for multimodal problem. To improve the solution quality and robustness of PSO algorithm, a new best neighbour particle called 'rbest' is proposed. The rbest provides extra information for each particle that is randomly selected from other best particles in order to diversify the movement of particle and avoid premature convergence. The effectiveness of MPSO-TVAC algorithm is tested on different power systems with POZ, ramp-rate limits and transmission loss constraints. To validate the performances of the proposed algorithm, comparative studies have been carried out in terms of convergence characteristic, solution quality, computation time and robustness. Simulation results found that the proposed MPSO-TVAC algorithm has good solution quality and more robust than other methods reported in previous work.

• 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.