基于高斯赛德尔法潮流计算

电力系统稳态分析

姓名: 学号：

学院(系):自动化学院

专业: 电气工程

题目: 基于Matlab的高斯和高斯—赛德尔法的潮流计算指导老师：

2014年12月

摘要

电力系统潮流计算是电力系统稳态运行分析中最基本和最重要的计算之一，是电力系统其他分析计算的基础，也是电力网规划、运行研究分析的一种方法，在电力系统中具有举足轻重的作用。经典算法有高斯法，高斯－赛德尔迭代法及牛顿法等，近年来学者们开始应用非线性规划法及智能算法等优化方法求解潮流问题，提高了收敛的可靠性。

高斯－赛德尔迭代法开始于上世纪50年代，是一种直接迭代求解方程的算法，既可以解线性方程组，可以解非线性方程组。高斯法求解节点电压的特点是: 在计算节点 i第k+1次的迭代电压时，前后所用的电压都是第k次迭代的结果，整个一轮潮流迭代完成后，把所有计算出的电压新值用于下一轮电压新值的计算过程中。该计算方法简单，占用计算机内存小，能直接利用迭代求解节点电压方程，对电压初值的选取要求不是很严格。但它的收敛性能较差，系统规模增大时，迭代次数急剧上升。

本文首先对高斯—赛德尔算法进行了综述，然后推导了该算法的计算过程，通过MATLAB软件计算了该算法的实例。

关键字：潮流计算高斯法高斯－赛德尔法迭代

Abstract

Power flow calculation is the one of the most basic and the most important calculation in the steady state analysis of power system .It is the foundation of other analytical calculation of power system, a method of analysis and planning, operation of power network.So it plays a decisive role in the power system. The classical algorithm is the Gauss method, Gauss - Seidel iterative method and Newton's method, in recent years.Scholars began to applicate nonlinear programming method and intelligent algorithm optimization method for solving power flow problem, enhances the reliability of convergence.

Gauss - Seidel iterative method began in the 50's of last century, is a direct iteration equation algorithm, which can solve the linear equation and nonlinear equations. Characteristics of Gauss's method to calculate the node voltage is: in the iterative calculation of node i’s K + 1-times voltage, the voltage is used the results of K-times iterative.After completing the whole round of power flow iteration, all voltage value is used to calculate the next round of new voltage value of . The method is simple and captures small memory.It also can directly use the iterative solution of the node voltage equation .the selection of initial values are not very strict. But it has poor convergence performance. The system scale increases,when the number of iterations rise.

This paper gives an overview of the Gauss Seidel algorithm at the first.Then it show the calculation process of this algorithm through the MATLAB software.

Keywords: Gauss Gauss - Seidel iterative method the method of power flow calculation

目录

1 高斯迭代法和高斯—赛德尔迭代法概述 (5)

2 节点导纳矩阵 (6)

2.1不定导纳矩阵 (6)

2.2导纳矩阵 (6)

3 高斯迭代法 (7)

4 高斯-赛德尔迭代法 (8)

4.1高斯-赛德尔法的原理 (8)

4.2 关于高斯法和高斯-赛德尔法的讨论 (8)

5实例验证 (9)

5.1 案例描述 (9)

5.2 模型的建立 (10)

5.3 案例程序流程图 (11)

5.4 案例程序 (13)

5.5 程序运行步骤和结果 (17)

6结果分析 (20)

7总结 (21)

7参考文献 (22)