电力系统课程设计：两机五节点潮流计算与牛顿-拉夫逊法

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"两机五节点网络潮流计算是电力系统稳态分析中的一个重要课题，主要涉及电力系统的运行状态分析，包括电压、功率的分布计算。该文档由XX科技大学的学生X润民完成，作为电力工程及其自动化专业课程设计的一部分，由教师X景霞指导。文档详细介绍了潮流计算的基本概念、数学模型、牛顿-拉夫逊法的原理和应用，并提供了实际的手工计算和MATLAB程序实现。潮流计算是电力系统分析的核心部分，旨在确定在特定运行条件下，电力网络中的电压、功率因数、电流等关键参数。对于两机五节点的简单网络，计算过程通常包括以下几个方面： 1. 潮流计算简介：介绍潮流计算在电力系统中的作用，如检查设备的过电压和过载情况，为继电保护设置提供依据，以及为系统规划和经济运行提供数据支持。 2. 数学模型：基于导纳矩阵的原理，构建电力系统的数学模型，该模型由一组非线性方程表示，反映了网络中功率的平衡关系。 3. 牛顿-拉夫逊法：这是一种强大的非线性方程求解方法，通过迭代的方式逐渐接近实际解。在电力系统中，这种方法用于求解电压和功率分布问题，通过修正方程的连续迭代，计算出每个节点的电压和功率。 4. 手工计算与计算机算法：文档中详细阐述了如何手动构建节点导纳矩阵、简化雅可比矩阵，并进行迭代修正的过程。同时，还提供了MATLAB程序，通过编程实现牛顿-拉夫逊法进行潮流计算，并展示了程序的运行结果。 5. MATLAB程序：MATLAB程序的编写和运行结果分析，进一步证明了牛顿-拉夫逊法的有效性，为读者提供了实践操作的示例。 6. 总结与感想：作者对整个设计过程进行了总结，分享了学习和实施牛顿-拉夫逊法计算潮流的心得体会。关键词聚焦于电力系统潮流计算、牛顿-拉夫逊法的应用以及程序设计，这些内容对于理解和掌握电力系统分析至关重要。通过这样的课程设计，学生能够深入理解电力系统的稳态特性，并掌握解决实际问题的工具和技术。"

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0.1136...............................................................................................................................................49
0.1076...............................................................................................................................................49
0.1183...............................................................................................................................................49
各点的电压实部 e(单位:V)为(节点号从小到大排列):................................................................49
1.0600 1.0847 1.1123 1.1136 1.1183...............................................................................................49
各点的电压虚部 f 单位:V)为(节点号从小到大排列):.................................................................50
0 0.0473 0.0863 0.0922 0.1076.......................................................................................................50
节点电压的第 C(k)次近似值:........................................................................................................50
1.0600 1.0847 + 0.0473i 1.1123 + 0.0863i 1.1136 + 0.0922i 1.1183 + 0.1076i.............................50
迭代次数:........................................................................................................................................50
1........................................................................................................................................................50
雅克比矩阵 J:..................................................................................................................................50
35.8747 9.9974 -5.5023 -1.5717 -5.5023 -1.5717 -8.2535 -2.3570................................................50
-10.4317 35.6555 1.5717 -5.5023 1.5717 -5.5023 2.3570 -8.2535................................................50
-5.7052 -1.4227 44.0333 11.4624 -34.2310 -8.5339 0 0.................................................................50
1.4227 -5.7052 -10.5844 44.3968 8.5339 -34.2310 0 0..................................................................50
-5.7215 -1.3952 -34.3289 -8.3688 44.2915 11.2101 -4.2911 -1.0461............................................50
1.3952 -5.7215 8.3688 -34.3289 -10.4101 44.3915 1.0461 -4.2911...............................................50
-8.6564 -1.9888 0 0 -4.3282 -0.9944 12.8846 3.5831.....................................................................50
1.9888 -8.6564 0 0 0.9944 -4.3282 -2.3831 13.0846......................................................................50
C =....................................................................................................................................................51
0.3304...............................................................................................................................................51
0.8291...............................................................................................................................................51
0.0524...............................................................................................................................................51
0.1350...............................................................................................................................................51
-0.0408.............................................................................................................................................51
-0.0426.............................................................................................................................................51
-0.0602.............................................................................................................................................51
-0.0764.............................................................................................................................................51
第 M 次修正方程的解 A:...............................................................................................................51
0.0006...............................................................................................................................................51
0.0426...............................................................................................................................................51
-0.0023.............................................................................................................................................51
0.0355...............................................................................................................................................51
-0.0031.............................................................................................................................................51
0.0350...............................................................................................................................................51
-0.0053.............................................................................................................................................51
0.0331...............................................................................................................................................51
各点的电压实部 e(单位:V)为(节点号从小到大排列):................................................................52
1.0600 1.1273 1.1478 1.1486 1.1514..............................................................................................52
各点的电压虚部 f 单位:V)为(节点号从小到大排列):.................................................................52
0 0.0479 0.0840 0.0891 0.1023.......................................................................................................52
节点电压的第 C(k)次近似值:........................................................................................................52
1.0600 1.1273 + 0.0479i 1.1478 + 0.0840i 1.1486 + 0.0891i 1.1514 + 0.1023i............................52
.                                                                                             .word..

.                                                                                                                                                            .
迭代次数:........................................................................................................................................52
2........................................................................................................................................................52
雅克比矩阵 J:..................................................................................................................................52
36.5102 10.7859 -5.7161 -1.6398 -5.7161 -1.6398 -8.5741 -2.4592..............................................52
-10.5284 37.7985 1.6398 -5.7161 1.6398 -5.7161 2.4592 -8.5741................................................52
-5.8791 -1.4933 45.2683 12.0512 -35.2747 -8.9577 0 0.................................................................52
1.4933 -5.8791 -11.0902 45.8582 8.9577 -35.2747 0 0..................................................................52
-5.8913 -1.4693 -35.3479 -8.8133 45.6420 11.7320 -4.4185 -1.1017............................................52
1.4693 -5.8913 8.8133 -35.3479 -11.0364 45.6733 1.1017 -4.4185...............................................52
-8.8914 -2.1111 0 0 -4.4457 -1.0555 13.2980 3.6887.....................................................................53
2.1111 -8.8914 0 0 1.0555 -4.4457 -2.6446 13.3761......................................................................53
C =....................................................................................................................................................53
0.2161...............................................................................................................................................53
0.0969...............................................................................................................................................53
-0.4743.............................................................................................................................................53
-0.2439.............................................................................................................................................53
-0.4389.............................................................................................................................................53
-0.0915.............................................................................................................................................53
-0.6573.............................................................................................................................................53
-0.1748.............................................................................................................................................53
第 M 次修正方程的解 A:...............................................................................................................53
-0.0475.............................................................................................................................................53
-0.0199.............................................................................................................................................53
-0.0853.............................................................................................................................................53
-0.0428.............................................................................................................................................53
-0.0908.............................................................................................................................................53
-0.0436.............................................................................................................................................53
-0.1052.............................................................................................................................................53
-0.0469.............................................................................................................................................54
各点的电压实部 e(单位:V)为(节点号从小到大排列):................................................................54
1.0600 1.1073 1.1050 1.1049 1.1045..............................................................................................54
各点的电压虚部 f 单位:V)为(节点号从小到大排列):.................................................................54
0 0.0003 -0.0013 -0.0018 -0.0029...................................................................................................54
节点电压的第 C(k)次近似值:........................................................................................................54
1.0600 1.1073 + 0.0003i 1.1050 - 0.0013i 1.1049 - 0.0018i 1.1045 - 0.0029i...............................54
迭代次数:........................................................................................................................................54
3........................................................................................................................................................54
雅克比矩阵 J:..................................................................................................................................54
35.2528 12.2858 -5.5373 -1.8443 -5.5373 -1.8443 -8.3059 -2.7659..............................................54
-11.6866 36.7320 1.8443 -5.5373 1.8443 -5.5373 2.7659 -8.3059.................................................54
-5.5229 -1.8487 42.6422 14.3784 -33.1375 -11.0901 0 0...............................................................54
1.8487 -5.5229 -14.2717 42.9630 11.0901 -33.1375 0 0................................................................54
-5.5217 -1.8507 -33.1299 -11.1022 42.7999 14.3166 -4.1412 -1.3878..........................................54
1.8507 -5.5217 11.1022 -33.1299 -14.3648 42.7857 1.3878 -4.1412.............................................55
.                                                                                             .word..

.                                                                                                                                                            .
-8.2764 -2.7827 0 0 -4.1382 -1.3913 12.4285 4.1382.....................................................................55
2.7827 -8.2764 0 0 1.3913 -4.1382 -4.2098 12.4007......................................................................55
C =....................................................................................................................................................55
-0.1154.............................................................................................................................................55
-0.7223.............................................................................................................................................55
-0.5335.............................................................................................................................................55
-0.4211.............................................................................................................................................55
-0.4122.............................................................................................................................................55
-0.0837.............................................................................................................................................55
-0.6177.............................................................................................................................................55
-0.1596.............................................................................................................................................55
第 M 次修正方程的解 A:...............................................................................................................55
-0.0480.............................................................................................................................................55
-0.0757.............................................................................................................................................55
-0.0836.............................................................................................................................................55
-0.1040.............................................................................................................................................55
-0.0889.............................................................................................................................................56
-0.1059.............................................................................................................................................56
-0.1025.............................................................................................................................................56
-0.1128.............................................................................................................................................56
各点的电压实部 e(单位:V)为(节点号从小到大排列):................................................................56
1.0600 1.0317 1.0010 0.9990 0.9917..............................................................................................56
各点的电压虚部 f 单位:V)为(节点号从小到大排列):.................................................................56
0 -0.0476 -0.0849 -0.0907 -0.1054..................................................................................................56
节点电压的第 C(k)次近似值:........................................................................................................56
1.0600 1.0317 - 0.0476i 1.0010 - 0.0849i 0.9990 - 0.0907i 0.9917 - 0.1054i................................56
迭代次数:........................................................................................................................................56
4........................................................................................................................................................56
雅克比矩阵 J:..................................................................................................................................56
32.8618 12.9089 -5.0789 -1.9580 -5.0789 -1.9580 -7.6183 -2.9364..............................................56
-12.5417 33.1637 1.9580 -5.0789 1.9580 -5.0789 2.9364 -7.6183................................................56
-4.8637 -2.0933 37.8960 15.7849 -29.1823 -12.5579 0 0...............................................................57
2.0933 -4.8637 -16.6571 37.4917 12.5579 -29.1823 0 0................................................................57
-4.8439 -2.1187 -29.0634 -12.7105 37.6263 16.0192 -3.6329 -1.5888..........................................57
2.1187 -4.8439 12.7105 -29.0634 -16.8168 37.4541 1.5888 -3.6329.............................................57
-7.1742 -3.2695 0 0 -3.5871 -1.6347 10.9259 4.3071.....................................................................57
3.2695 -7.1742 0 0 1.6347 -3.5871 -5.5013 10.5968......................................................................57
C =....................................................................................................................................................57
-0.3120.............................................................................................................................................57
-0.8692.............................................................................................................................................57
-0.0798.............................................................................................................................................57
-0.2558.............................................................................................................................................57
-0.0060.............................................................................................................................................57
-0.0339.............................................................................................................................................57
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