[课程设计z.doc

一．任务描述 要求根据给定的参数或工程具体要求收集和查阅资料学习相关软件（） data for test case 各节点参数：节点编号,注入有功,注入无功,(Sn=100MVA)电压幅值,电压相位,类型 类型：1=PQ节点,2=PV节点,3=平衡节点 (bus#)(volt)(ang)(p)(q)(bus type) bus=[ 1,1.06,0.0,0.4,-0.4,2; 2,1.045,0.0,0,0,3; 3,1.01,0.0,1.3188,0.266,3; 4,1.0,0.0,0.6692,0.1,1; 5,1.0,0.0,0.1064,0.0224,1; 6,1.07,0.0,0.1568,0.105,3; 7,1.0,0.0,0.0,0.0,1; 8,1.09,0.0,0.0,0.0,3; 9,1.0,0.0,0.413,0.2324,1; 10,1.045,0.0,0.126,0.0812,1; 11,1.010,0.0,0.049,0.0252,1; 12,1.70,0.0,0.0854,0.0224,1; 13,1.90,0.0,0.189,0.0812,1; 14,1.060,0.0,0.2068,0.07,1]; %各支路参数：起点编号,终点编号,电阻,电抗,电导,电纳 line = [ 1,2,0.01938,0.05917,0.0,0.0528,0; 2,3,0.04699,0.19797,0.0,0.0438,0; 2,4,0.05811,0.17632,0.0,0.0374,0; 1,5,0.05403,0.22304,0.0,0.0492,0; 2,5,0.05695,0.17388,0.0,0.034,0; 3,4,0.06701,0.17103,0.0,0.0346,0; 4,5,0.01335,0.04211,0.0,0.0128,0; 5,6,0.0,0.25202,0.0,0.0,0; 4,7,0.0,0.20912,0.0,0.0,0; 7,8,0.0,0.17615,0.0,0.0,0; 4,9,0.0,0.55618,0.0,0.0,0; 7,9,0.0,0.11001,0.0,0.0,0; 9,10,0.03181,0.0845,0.0,0.0,0; 6,11,0.09498,0.19890,0.0,0.0,0; 6,12,0.12291,0.25581,0.0,0.0,0; 6,13,0.06615,0.13027,0.0,0.0,0; 9,14,0.12711,0.27038,0.0,0.0,0; 10,11,0.08205,0.19207,0.0,0.0,0; 12,13,0.22092,0.19988,0.0,0.0,0; 13,14,0.17093,0.34802,0.0,0.0,0]; 三．算法原理 1. 牛顿-拉夫逊原理 牛顿迭代法（Newtons method）又称为牛顿-拉夫逊方法（Newton-Raphson method），它是牛顿在17世纪提出的一种在实数域和复数域上近似求解方程的方法。多数方程不存在求根公式，因此求精确根非常困难，甚至不可能，从而寻找方程的近似根就显得特别重要。方法使用函数f(x)的泰勒级数的前面几项来寻找方程f(x) = 0的根。牛顿迭代法是求方程根的重要方法之一，其最大优点是在方程f(x) = 0的单根附近具有平方收敛，而且该法还可以用来求方程的重根、复根。设r是f(x) = 0的根，选取x0作为r初始近似值，过点（x0,f(x0)）做曲线y = f(x)的切线L，L的方程为y = f(x0) f(x0)(x-x0)，求出L与x轴交点的横坐标?x1 = x0-f(x0)/f(x0)，称x1为r的一次近似值。过点（x1,f(x1)）做曲线y = f(x)的切线，并求该切线与x轴的横坐标 x2 = x1-f(x1)/f(x1)，称x2为r的二次近似值。重复以上过程，得r的近似值序列，其中x(n+1)=x(n)－f(x(n))/f(x(n))，称为r的n+1次近似值，上式称为牛顿迭代公式。解非线性方程f(x)=0的牛顿法是把非线性方程线性化的一种近似方法。把f(x)在x0点附近展开成泰勒级数 f(x) = f(x0)+(x－x0)f(x0)+(x－x0)^2*f(x0)/2! +… 取其线性部分，作为非线性方程f(x) = 0的近似方程，即泰勒展开的前两项，则有f(x0)+f(x0)(x－x0)=f(x)=0 设f(x0)≠0则其解为x1=x0－f(x0)/f(x0) 这样，得到牛顿法的一个迭代序列：x(n+1)=x(n)－f(x(n))/f(x(n))。 1）形成各节点导纳矩阵Y。 （