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首页两机五节点牛顿法潮流程序设计与实现
两机五节点牛顿法潮流程序设计与实现
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更新于2024-07-18
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该文档是一份内蒙古科技大学电力系统稳态分析课程设计,由学生朱润民完成,主题为"两机五节点网络潮流计算—牛顿法"。课程设计旨在让学生深入了解电力系统潮流计算的基本概念和技术,特别是牛顿-拉夫逊法的应用。 牛顿-拉夫逊法是潮流计算中的核心算法,它是一种迭代求解非线性方程组的有效方法。这种方法通过将非线性方程组转化为一系列线性方程的序列,每次迭代都用当前的近似解去逼近原方程的精确解。在电力系统中,牛顿-拉夫逊法用于求解节点电压和功率分布,确保系统的稳定运行,包括确定合理的运行方式,检查设备过载和电压问题,以及为继电保护整定提供数据基础。 在设计中,作者首先介绍了电力系统潮流计算的基本概念,包括导纳矩阵的原理、潮流计算的基本方程、节点分类和约束条件等。接着详细讲解了牛顿-拉夫逊法的原理和求解过程,还提供了算法的程序框图,展示了其在实际问题中的应用。 该文档还包含了手算部分,通过节点导纳矩阵和简化雅可比矩阵的构建,以及修正和迭代过程,展示了如何用传统方法和计算机算法相结合来进行潮流计算。在Matlab中,作者编写了一个牛顿-拉夫逊法的潮流计算程序,并附有运行结果,以实例演示了算法的具体实现。 最后,总结部分强调了牛顿-拉夫逊法在电力系统潮流计算中的重要性和实用性,同时提到了Matlab作为工具在处理矩阵运算和迭代求解中的关键作用。整个设计不仅涵盖了理论知识,还包含实际操作环节,有助于提升学生的实践能力。 关键词:电力系统潮流计算、牛顿-拉夫逊法、潮流计算程序、迭代方法、Matlab应用。通过这份课程设计,读者可以深入理解潮流计算的数学模型,掌握牛顿-拉夫逊法的实施步骤,并了解如何在实际电力系统中运用这些技术进行问题求解。
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内蒙古科技大学
0.0473..............................................................................................................................................50
0.0847..............................................................................................................................................50
0.0863..............................................................................................................................................50
0.1123..............................................................................................................................................50
0.0922..............................................................................................................................................50
0.1136..............................................................................................................................................50
0.1076..............................................................................................................................................50
0.1183..............................................................................................................................................50
各点的电压实部 e(单位:V)为(节点号从小到大排列):................................................................50
1.0600 1.0847 1.1123 1.1136 1.1183..............................................................................................50
各点的电压虚部 f 单位:V)为(节点号从小到大排列):.................................................................51
0 0.0473 0.0863 0.0922 0.1076......................................................................................................51
节点电压的第 C(k)次近似值:........................................................................................................51
1.0600 1.0847 + 0.0473i 1.1123 + 0.0863i 1.1136 + 0.0922i 1.1183 + 0.1076i............................51
迭代次数:........................................................................................................................................51
1.......................................................................................................................................................51
雅克比矩阵 J:..................................................................................................................................51
35.8747 9.9974 -5.5023 -1.5717 -5.5023 -1.5717 -8.2535 -2.3570...............................................51
-10.4317 35.6555 1.5717 -5.5023 1.5717 -5.5023 2.3570 -8.2535...............................................51
-5.7052 -1.4227 44.0333 11.4624 -34.2310 -8.5339 0 0................................................................51
1.4227 -5.7052 -10.5844 44.3968 8.5339 -34.2310 0 0.................................................................51
-5.7215 -1.3952 -34.3289 -8.3688 44.2915 11.2101 -4.2911 -1.0461...........................................51
1.3952 -5.7215 8.3688 -34.3289 -10.4101 44.3915 1.0461 -4.2911..............................................51
-8.6564 -1.9888 0 0 -4.3282 -0.9944 12.8846 3.5831....................................................................51
1.9888 -8.6564 0 0 0.9944 -4.3282 -2.3831 13.0846.....................................................................51
C =....................................................................................................................................................52
0.3304..............................................................................................................................................52
0.8291..............................................................................................................................................52
0.0524..............................................................................................................................................52
0.1350..............................................................................................................................................52
-0.0408............................................................................................................................................52
-0.0426............................................................................................................................................52
-0.0602............................................................................................................................................52
-0.0764............................................................................................................................................52
第 M 次修正方程的解 A:...............................................................................................................52
0.0006..............................................................................................................................................52
0.0426..............................................................................................................................................52
-0.0023............................................................................................................................................52
0.0355..............................................................................................................................................52
-0.0031............................................................................................................................................52
0.0350..............................................................................................................................................52
-0.0053............................................................................................................................................52
0.0331..............................................................................................................................................52
各点的电压实部 e(单位:V)为(节点号从小到大排列):................................................................53
10
![](https://csdnimg.cn/release/download_crawler_static/10885025/bgc.jpg)
内蒙古科技大学
1.0600 1.1273 1.1478 1.1486 1.1514.............................................................................................53
各点的电压虚部 f 单位:V)为(节点号从小到大排列):.................................................................53
0 0.0479 0.0840 0.0891 0.1023......................................................................................................53
节点电压的第 C(k)次近似值:........................................................................................................53
1.0600 1.1273 + 0.0479i 1.1478 + 0.0840i 1.1486 + 0.0891i 1.1514 + 0.1023i...........................53
迭代次数:........................................................................................................................................53
2.......................................................................................................................................................53
雅克比矩阵 J:..................................................................................................................................53
36.5102 10.7859 -5.7161 -1.6398 -5.7161 -1.6398 -8.5741 -2.4592.............................................53
-10.5284 37.7985 1.6398 -5.7161 1.6398 -5.7161 2.4592 -8.5741...............................................53
-5.8791 -1.4933 45.2683 12.0512 -35.2747 -8.9577 0 0................................................................53
1.4933 -5.8791 -11.0902 45.8582 8.9577 -35.2747 0 0.................................................................53
-5.8913 -1.4693 -35.3479 -8.8133 45.6420 11.7320 -4.4185 -1.1017...........................................53
1.4693 -5.8913 8.8133 -35.3479 -11.0364 45.6733 1.1017 -4.4185..............................................53
-8.8914 -2.1111 0 0 -4.4457 -1.0555 13.2980 3.6887....................................................................54
2.1111 -8.8914 0 0 1.0555 -4.4457 -2.6446 13.3761.....................................................................54
C =....................................................................................................................................................54
0.2161..............................................................................................................................................54
0.0969..............................................................................................................................................54
-0.4743............................................................................................................................................54
-0.2439............................................................................................................................................54
-0.4389............................................................................................................................................54
-0.0915............................................................................................................................................54
-0.6573............................................................................................................................................54
-0.1748............................................................................................................................................54
第 M 次修正方程的解 A:...............................................................................................................54
-0.0475............................................................................................................................................54
-0.0199............................................................................................................................................54
-0.0853............................................................................................................................................54
-0.0428............................................................................................................................................54
-0.0908............................................................................................................................................54
-0.0436............................................................................................................................................54
-0.1052............................................................................................................................................54
-0.0469............................................................................................................................................55
各点的电压实部 e(单位:V)为(节点号从小到大排列):................................................................55
1.0600 1.1073 1.1050 1.1049 1.1045.............................................................................................55
各点的电压虚部 f 单位:V)为(节点号从小到大排列):.................................................................55
0 0.0003 -0.0013 -0.0018 -0.0029..................................................................................................55
节点电压的第 C(k)次近似值:........................................................................................................55
1.0600 1.1073 + 0.0003i 1.1050 - 0.0013i 1.1049 - 0.0018i 1.1045 - 0.0029i..............................55
迭代次数:........................................................................................................................................55
3.......................................................................................................................................................55
雅克比矩阵 J:..................................................................................................................................55
35.2528 12.2858 -5.5373 -1.8443 -5.5373 -1.8443 -8.3059 -2.7659.............................................55
11
![](https://csdnimg.cn/release/download_crawler_static/10885025/bgd.jpg)
内蒙古科技大学
-11.6866 36.7320 1.8443 -5.5373 1.8443 -5.5373 2.7659 -8.3059................................................55
-5.5229 -1.8487 42.6422 14.3784 -33.1375 -11.0901 0 0..............................................................55
1.8487 -5.5229 -14.2717 42.9630 11.0901 -33.1375 0 0...............................................................55
-5.5217 -1.8507 -33.1299 -11.1022 42.7999 14.3166 -4.1412 -1.3878.........................................55
1.8507 -5.5217 11.1022 -33.1299 -14.3648 42.7857 1.3878 -4.1412............................................56
-8.2764 -2.7827 0 0 -4.1382 -1.3913 12.4285 4.1382....................................................................56
2.7827 -8.2764 0 0 1.3913 -4.1382 -4.2098 12.4007.....................................................................56
C =....................................................................................................................................................56
-0.1154............................................................................................................................................56
-0.7223............................................................................................................................................56
-0.5335............................................................................................................................................56
-0.4211............................................................................................................................................56
-0.4122............................................................................................................................................56
-0.0837............................................................................................................................................56
-0.6177............................................................................................................................................56
-0.1596............................................................................................................................................56
第 M 次修正方程的解 A:...............................................................................................................56
-0.0480............................................................................................................................................56
-0.0757............................................................................................................................................56
-0.0836............................................................................................................................................56
-0.1040............................................................................................................................................56
-0.0889............................................................................................................................................57
-0.1059............................................................................................................................................57
-0.1025............................................................................................................................................57
-0.1128............................................................................................................................................57
各点的电压实部 e(单位:V)为(节点号从小到大排列):................................................................57
1.0600 1.0317 1.0010 0.9990 0.9917.............................................................................................57
各点的电压虚部 f 单位:V)为(节点号从小到大排列):.................................................................57
0 -0.0476 -0.0849 -0.0907 -0.1054.................................................................................................57
节点电压的第 C(k)次近似值:........................................................................................................57
1.0600 1.0317 - 0.0476i 1.0010 - 0.0849i 0.9990 - 0.0907i 0.9917 - 0.1054i...............................57
迭代次数:........................................................................................................................................57
4.......................................................................................................................................................57
雅克比矩阵 J:..................................................................................................................................57
32.8618 12.9089 -5.0789 -1.9580 -5.0789 -1.9580 -7.6183 -2.9364.............................................57
-12.5417 33.1637 1.9580 -5.0789 1.9580 -5.0789 2.9364 -7.6183...............................................57
-4.8637 -2.0933 37.8960 15.7849 -29.1823 -12.5579 0 0..............................................................58
2.0933 -4.8637 -16.6571 37.4917 12.5579 -29.1823 0 0...............................................................58
-4.8439 -2.1187 -29.0634 -12.7105 37.6263 16.0192 -3.6329 -1.5888.........................................58
2.1187 -4.8439 12.7105 -29.0634 -16.8168 37.4541 1.5888 -3.6329............................................58
-7.1742 -3.2695 0 0 -3.5871 -1.6347 10.9259 4.3071....................................................................58
3.2695 -7.1742 0 0 1.6347 -3.5871 -5.5013 10.5968.....................................................................58
C =....................................................................................................................................................58
-0.3120............................................................................................................................................58
12
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