Chaotic ant swarm optimization to economic dispatch

doi:10.1016/j.epsr.2006.10.006

Electric Power Systems Research

Volume 77, Issue 10, August 2007, Pages 1373-1380

https://doi.org/10.1016/j.epsr.2006.10.006 Get rights and content

Abstract

This paper developed a novel algorithm named chaotic ant swarm optimization (CASO) for solving the economic dispatch (ED) problems of thermal generators in power systems. This algorithm combines with the chaotic and self-organization behavior of ants in the foraging process. It includes both effects of chaotic dynamics and swarm-based search. The algorithm was employed to solve the ED problems of thermal generators. The proposed method was applied to three examples of power systems. Simulation results demonstrated that the method can obtain feasible and effective solutions, and it is a promising alternative approach for solving the ED problems in practical power systems.

Introduction

Economic dispatch (ED) problem is one of the mathematical optimization issues in power system operation that attracts researchers’ attention all the way. It aims to seek “the best” generation schedule for the generating plants whereby the required demand together with the transmission losses can be produced with the minimum production cost. Because good solutions from ED problem would result in great economical benefits, numerous investigations on it have been undertaken until now. As matters stand, a lot of researches have been done and various mathematical programming optimization methods have been employed for solving the ED problems. A number of conventional approaches have been developed for solving the ED problems such as gradient method [1], linear programming algorithm [2], lambda iteration method [3], quadratic programming [4], non-linear programming algorithm [5], lagrangian relaxation algorithm [6], etc., and the artificial intelligence technology has been successfully used to solve the ED problems, such as genetic algorithm [7], [8], [9], neural networks [10], [11], simulated annealing and tabu search [12], evolutionary programming [13], [14], particle swarm optimization [15], ant colony optimization [16], and so on. Every conventional methods has the defect of its own: it would generate large errors to use the linear programming algorithm to linearize the ED model; in the lambda iteration method, adjustment of the λ-multiplier is not easy and effective; gradient method is only a quasi-optimal scheme based on the hill climbing method; for the quadratic programming and nonlinear programming algorithms the objective function should be continuous and differentiable; dynamic programming algorithm maybe result in “curse of dimensionality”; for the lagrangian relaxation algorithm, it would lead to the phenomenon of solution oscillation. Therefore, with the development of the computer science and technology, more and more interests have been focused on the application of artificial intelligence technology for the ED problems.

In this paper, we developed CASO approach for solving the ED problem in power system. The proposed CASO method for the ED was demonstrated to be feasible by the application in three different power systems [10], [11].

This paper is organized as follows. In Section 2, the problem formulation is presented. In Section 3, the overview of ant colony optimization is introduced. In Section 4, chaotic ant swarm optimization is described. In Section 5, an algorithm for solving the ED problem based on CASO is developed. In Section 6, the studies of application cases are presented that demonstrate the potential of the presented algorithm. Finally, in Section 7, the conclusions are given.

Section snippets

Mathematical model of ED

The ED problem is to determine the optimal combination of power generations that minimizes the total generation cost and satisfies various constraints. Its mathematical model can be mathematically described as follows:

(1)
The objective function
The objective of ED is to simultaneously minimize the generation cost rate and to meet the load demand of a power system over some appropriate period while satisfying various equality and inequality constraints. Its objective function is $min F_{t} = \sum_{i = 1}^{m} F_{i} (P_{i}) = \sum i = 1$

Overview of ant colony optimization

In 1992, Marco Dorigo first introduced ant colony optimization (ACO) inspired by the behavior of ant colonies. ACO is one of the adaptive meta-heuristic optimization methods. In ACO algorithm, every artificial ant colony cooperates in order to find good solutions for difficult discrete optimization problems. Each of artificial ants constructs one solution according to the heuristic information as well as pheromone information, and good solutions are the emergent property of the agents’

Chaotic ant swarm optimization

CASO is essentially a search algorithm based on the chaotic behavior of individual ant and the intelligent organization actions of ant colony. In CASO, the search behavior of the single ant is “chaotic” at first, and the organization variable r_i is introduced to achieve self-organization process of the ant colony. Initially the influence of the organization variable on the behavior of individual ant is sufficiently small. With the continual change of organization variable evolving in time and

CASO for solving ED problem

In this section, we describe how to use CASO to solve ED problem. CASO is utilized mainly to determine the optimal generation power of each unit that is submitted to operate at the specific period, thus in order to minimize the total generation cost.

Application examples

In order to validate the feasibility of the proposed CASO method for the ED problems, we employed it on different power systems, which have 3, 13, 20 units.

The software was written in Matlab 7.0 and the simulation cases were done on an AMD Athlon (tm) XP 2500+ personal computer with 512 MB RAM.

Conclusions

This paper developed a novel CASO for solving the ED problems of thermal generators in power systems. This algorithm combined with the chaotic and self-organization behavior of ants in the foraging process. The proposed algorithm was successfully employed to solve the ED problem considering some constraints, such as power balance constraints and generation limits constraints. The numerical simulation results show that the CASO is feasible for solving ED problem for practical power systems.

The

Acknowledgements

This work is supported by the Key (Key grant) Project of Chinese Ministry of Education (Grant No. 205033), the National Basic Research Program (also called 973 Program) of China (Grant No. TG1999035804), the National Natural Science Foundation of China (Grant Nos. 90204017, 60372094).

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View full text

Chaotic ant swarm optimization to economic dispatch

Abstract

Introduction

Section snippets

Mathematical model of ED

Overview of ant colony optimization

Chaotic ant swarm optimization

CASO for solving ED problem

Application examples

Conclusions

Acknowledgements

Electr. Power Syst. Res.

Electr. Power Syst. Res.

Electr. Power Syst. Res.

Electr. Power Syst. Res.

Electr. Power Syst. Res.

Electr. Power Syst. Res.

Electr. Power Syst. Res.

Soliton Fractals

An optimal formulation and solution of short-range operating problems for a power system with flow constraints

Proc. IEEE

A homogeneous linear programming algorithm for the security constrained economic dispatch problem

IEEE Trans. Power Syst.

Branch-and bound scheduling for thermal generating units

IEEE Trans. Energy Convers.

Economic emission load dispatch with line flow constraints using a classical technique

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