Four modified versions of particle swarm optimizer (PSO) have been applied to the economic power dispatch with valve-point effects. In order to obtain the optimal solution, traditional PSO search a new position around the current position. The proposed strategies which explore the vicinity of particle's best position found so far leads to a better result. In addition, to deal with the equality constraint of the economic dispatch problems, a simple mechanism is also devised that the difference of demanded load and total generating power is evenly shared among units except the one reaching its generating limit. To show their capability, the proposed algorithms are applied to thirteen. Comparison among particle swarm optimization and other modified particle swarm optimization is given. The results show that the proposed algorithms indeed produce more optimal solutions in both cases.
The different PSO techniques are New PSO, Self Adaptive PSO and Chaotic PSO. Among the different PSO techniques, it is found that Self-Adaptive PSO is better than other PSO techniques in terms of better solution, speed of convergence, time of execution and robustness but it has more premature convergence.
Table of Contents
Chapter One
1.1 Introduction
1.2 Literature survey
1.3 Methodology in brief
1.4 Organization of the Report
Chapter Two
2.1 Introduction to Economic Dispatch
2.1.1 Generator operating cost:
2.2 Mathematical Analysis
2.2.1 Analytical method
2.2.2 Gradient method
2.3 Valve Point Loading
2.4 Problem Formulation
Chapter Three
3.1 Evolutionary Algorithm
3.2 Ant Colony Optimization
3.3 Particle Swarm Optimization
3.4 Over view of Particle Swarm Optimization
3.5 Implementation of PSO method in ED
3.5.1 Advantages of PSO
Chapter Four
4.1 Introduction to various PSO techniques
4.2 Adaptive Particle Swarm Optimization
4.2.1 The procedure of Adaptive PSO
4.3 Chaotic Particle Swarm Optimization
4.3.1 CPSO methods for EP
4.4 New Particle Swarm Optimization
Chapter Five
5.1 Introduction
5.1.1 Organization of the result
5.2 The Test Bus System in Detail
5.3 Results obtained by using the PSO
5.3.1 Parameters
5.3.2 Overall Report
5.4 Results obtained by using the APSO
5.4.1 Parameters
5.4.2 Overall Report
5.5 Results obtained by using the CPSO
5.5.1 Parameters
5.5.2 Overall Report
5.6 Results obtained by using the NPSO
5.6.1 Parameters
5.6.2 Overall Report
5.7 Analysis of four PSO techniques
5.8 Comparison of graphs
Chapter Six
6.1 Analysis of different pso techniques
6.2 Conclusion
Project Objective and Themes
The primary goal of this project is to minimize the total generation cost in an electrical power system by applying various modified Particle Swarm Optimization (PSO) techniques, specifically focusing on the valve-point effect in Economic Load Dispatch problems.
- Economic Load Dispatch (ELD) optimization strategies.
- Implementation and comparison of PSO, APSO, CPSO, and NPSO algorithms.
- Mathematical modeling of generation costs with valve-point effects.
- Computational performance analysis regarding convergence speed and execution time.
- Validation using the IEEE 13-generator test system.
Excerpt from the Book
3.3 Particle Swarm Optimization
Kennedy and Eberhart first introduced PSO in year 1995. The features of the method are as follows:
The method is based on researches about swarms such as fish schooling and a flock of birds. It is based on a simple concept. Therefore, the computation time is short and it requires less memory. It was originally developed for nonlinear optimization problems with continuous variables. However, it is easily expanded to treat problems with discrete variables. Therefore, it is applicable to both continuous and discrete variables. The basic assumption behind the PSO algorithm is, birds find food by flocking and not individually. This leads to the assumption that information is owned jointly in flocking.
Particle swarm optimization (PSO) is a form of swarm intelligence. Imagine a swarm of insects or a school of fish. If one sees a desirable path to go (e.g., for food, protection, etc.) the rest of swarm will be able to follow quickly even if they are on the opposite side of the swarm. On the other hand, in order to facilitate felicitous exploration of the search space, typically one wants to have each particle to have a certain level of “craziness” or randomness in their movement.
This is modeled by particles in multidimensional space that have a position and a velocity. These particles are flying through hyperspace (i.e. Rn) and have two essential reasoning capabilities: their memory of their own best position and knowledge of the swarms best. Members of the swarm communicate good positions to each other and adjust their own position and velocity based on these good positions. There are two main ways this communication is done:
Summary of Chapters
Chapter One: Provides an introduction to Economic Load Dispatch, the research methodology, and the organizational structure of the report.
Chapter Two: Discusses the theoretical background of Economic Load Dispatch, generator operating costs, valve-point loading, and the problem formulation.
Chapter Three: Explores evolutionary algorithms, specifically detailing the concepts and mathematical implementation of Particle Swarm Optimization.
Chapter Four: Introduces various modified PSO techniques, including Adaptive PSO, Chaotic PSO, and New PSO.
Chapter Five: Presents the experimental results for the IEEE 13-generator system using the different PSO algorithms and analyzes their performance.
Chapter Six: Analyzes the different PSO techniques based on the study findings and provides a final conclusion.
Keywords
Economic Load Dispatch, Particle Swarm Optimization, Adaptive PSO, Chaotic PSO, Valve-point effect, IEEE 13 generator system, Generation cost, Optimization techniques, Swarm intelligence, Convergence, Power systems, Metaheuristic, Mathematical modeling, Fitness function, Computational efficiency
Frequently Asked Questions
What is the primary focus of this project?
The project focuses on minimizing the total generation cost in power systems, specifically addressing the Economic Load Dispatch problem while accounting for valve-point effects.
Which optimization techniques are utilized in this research?
The project employs four variations of the Particle Swarm Optimization algorithm: standard PSO, Adaptive Particle Swarm Optimization (APSO), Chaotic Particle Swarm Optimization (CPSO), and New Particle Swarm Optimization (NPSO).
What is the core objective or research question?
The main objective is to determine which of the modified PSO techniques provides the most robust and optimal solution for economic load dispatch under generator constraints.
Which scientific methodology is applied?
The research uses metaheuristic swarm intelligence algorithms, implementing them in MATLAB to simulate and compare the performance of different population-based search strategies.
What topics are covered in the main section of the document?
The main section covers the mathematical formulation of generation costs, the detailed step-by-step algorithms for different PSO techniques, and a comparative analysis of their performance on an IEEE 13-generator test system.
How would you describe the project using key terms?
The project is best described by terms such as Economic Load Dispatch, Particle Swarm Optimization, Power Systems, Metaheuristic Optimization, and Computational Intelligence.
What is the significance of the "valve-point effect" mentioned in the study?
The valve-point effect is included in the cost function to increase the accuracy of fuel cost calculations, as it introduces ripples in the heat-rate curve that standard models often neglect.
How do the algorithms handle the search space exploration?
The algorithms use particles with velocity and position vectors that evolve based on individual memory (Pbest) and group knowledge (Gbest), with modifications for adaptivity and chaos to avoid local optima.
- Citar trabajo
- Vikramarajan Jambulingam (Autor), 2008, Economic dispatch with valve point effect using various PSO techniques, Múnich, GRIN Verlag, https://www.grin.com/document/270063
