【配电网】基于MATLAB的Newton-Raphson法电力系统潮流计算

最新推荐文章于 2025-07-08 09:45:32 发布

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最新推荐文章于 2025-07-08 09:45:32 发布

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本文链接：https://blog.youkuaiyun.com/matlab_dingdang/article/details/127260777

针对Newton-Raphson法能快速求解非线性方程组的特点及MATLAB软件在电气工程领域的广泛应用，本文通过理论推导得出适用于MATLAB程序设计的矩阵形式Newton-Raphson法，并以不同规模的IEEE节点系统为案例验证该方法的有效性。

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⛄ 内容介绍

针对Newton-Raphson法能够快速求解非线性方程组和MATLAB软件在电气工程领域的广泛应用,本文经过理论推导,得出符合MATLAB程序设计的矩阵形式Newton-Raphson法,并以IEEE9节点系统为例验证了本方法的可行性和有效性.

⛄ 部分代码

function busdt = busdatas(num)

% |Bus | Type | Vsp | theta | PGi | QGi | PLi | QLi | Qmin | Qmax |

busdat3 = [ 1 1 1.05 0 0 0 0 0 0 0;

2 3 1.0 0 0 0 256.6 110.2 0 0;

3 3 1.0 0 0 0 138.6 45.2 0 0];

% Ref Book: Power System Analysis by Hadi Saadat, Figure 6.9, Example 6.7

% |Bus | Type | Vsp | theta | PGi | QGi | PLi | QLi | Qmin | Qmax |

busdat6 = [ 1 1 1.05 0 0.0 0 0 0 0 0;

2 2 1.05 0 0.5 0 0 0 -0.5 1.0;

3 2 1.07 0 0.6 0 0 0 -0.5 1.5;

4 3 1.0 0 0.0 0 0.7 0.7 0 0;

5 3 1.0 0 0.0 0 0.7 0.7 0 0;

6 3 1.0 0 0.0 0 0.7 0.7 0 0 ];

% |Bus | Type | Vsp | theta | PGi | QGi | PLi | QLi | Qmin | Qmax |

busdat9 = [ 1 1 1.04 0 0.0 0 0 0 0 0;

2 2 1.025 0 163 0 0 0 -99 99;

3 2 1.025 0 85 0 0 0 -99 99;

4 3 1.0 0 0.0 0 0.0 0.0 0 0;

5 3 1.0 0 0.0 0 125 50 0 0;

6 3 1.0 0 0.0 0 90 30 0 0;

7 3 1.0 0 0.0 0 0.0 0.0 0 0;

8 3 1.0 0 0.0 0 100 35 0 0;

9 3 1.0 0 0.0 0 0.0 0.0 0 0 ];

% |Bus | Type | Vsp | theta | PGi | QGi | PLi | QLi | Qmin | Qmax |

busdat14 = [1 1 1.060 0 0 0 0 0 0 0;

2 2 1.045 0 40 42.4 21.7 12.7 -40 50;

3 2 1.010 0 0 23.4 94.2 19.0 0 40;

4 3 1.0 0 0 0 47.8 -3.9 0 0;

5 3 1.0 0 0 0 7.6 1.6 0 0;

6 2 1.070 0 0 12.2 11.2 7.5 -6 24;

7 3 1.0 0 0 0 0.0 0.0 0 0;

8 2 1.090 0 0 17.4 0.0 0.0 -6 24;

9 3 1.0 0 0 0 29.5 16.6 0 0;

10 3 1.0 0 0 0 9.0 5.8 0 0;

11 3 1.0 0 0 0 3.5 1.8 0 0;

12 3 1.0 0 0 0 6.1 1.6 0 0;

13 3 1.0 0 0 0 13.5 5.8 0 0;

14 3 1.0 0 0 0 14.9 5.0 0 0;];

% |Bus | Type | Vsp | theta | PGi | QGi | PLi | QLi | Qmin | Qmax |

busdat30 = [1 1 1.06 0 0 0 0 0 0 0;

2 2 1.043 0 40 50.0 21.7 12.7 -40 50;

3 3 1.0 0 0 0 2.4 1.2 0 0;

4 3 1.06 0 0 0 7.6 1.6 0 0;

5 2 1.01 0 0 37.0 94.2 19.0 -40 40;

6 3 1.0 0 0 0 0.0 0.0 0 0;

7 3 1.0 0 0 0 22.8 10.9 0 0;

8 2 1.01 0 0 37.3 30.0 30.0 -10 40;

9 3 1.0 0 0 0 0.0 0.0 0 0;

10 3 1.0 0 0 19.0 5.8 2.0 0 0;

11 2 1.082 0 0 16.2 0.0 0.0 -6 24;

12 3 1.0 0 0 0 11.2 7.5 0 0;

13 2 1.071 0 0 10.6 0.0 0.0 -6 24;

14 3 1.0 0 0 0 6.2 1.6 0 0;

15 3 1.0 0 0 0 8.2 2.5 0 0;

16 3 1.0 0 0 0 3.5 1.8 0 0;

17 3 1.0 0 0 0 9.0 5.8 0 0;

18 3 1.0 0 0 0 3.2 0.9 0 0;

19 3 1.0 0 0 0 9.5 3.4 0 0;

20 3 1.0 0 0 0 2.2 0.7 0 0;

21 3 1.0 0 0 0 17.5 11.2 0 0;

22 3 1.0 0 0 0 0.0 0.0 0 0;

23 3 1.0 0 0 0 3.2 1.6 0 0;

24 3 1.0 0 0 4.3 8.7 6.7 0 0;

25 3 1.0 0 0 0 0.0 0.0 0 0;

26 3 1.0 0 0 0 3.5 2.3 0 0;

27 3 1.0 0 0 0 0.0 0.0 0 0;

28 3 1.0 0 0 0 0.0 0.0 0 0;

29 3 1.0 0 0 0 2.4 0.9 0 0;

30 3 1.0 0 0 0 10.6 1.9 0 0 ];

% |Bus | Type | Vsp | theta | PGi | QGi | PLi | QLi | Qmin | Qmax |

busdat57 = [1 1 1.040 0 0.0 0.0 0.0 0.0 0.0 0.0;

2 2 1.010 0 3.0 88.0 0.0 -0.8 50.0 -17.0;

3 2 0.985 0 41.0 21.0 40.0 -1.0 60.0 -10.0;

4 3 1.000 0 0.0 0.0 0.0 0.0 0.0 0.0;

5 3 1.000 0 13.0 4.0 0.0 0.0 0.0 0.0;

6 2 0.980 0 75.0 2.0 0.0 0.8 25.0 -8.0;

7 3 1.000 0 0.0 0.0 0.0 0.0 0.0 0.0;

8 2 1.005 0 150.0 22.0 450.0 62.1 200.0 -140.0;

9 2 0.980 0 121.0 26.0 0.0 2.2 9.0 -3.0;

10 3 1.000 0 5.0 2.0 0.0 0.0 0.0 0.0;

11 3 1.000 0 0.0 0.0 0.0 0.0 0.0 0.0;

12 2 1.015 0 377.0 24.0 310.0 128.5 155.0 -150.0;

13 3 1.000 0 18.0 2.3 0.0 0.0 0.0 0.0;

14 3 1.000 0 10.5 5.3 0.0 0.0 0.0 0.0;

15 3 1.000 0 22.0 5.0 0.0 0.0 0.0 0.0;

16 3 1.000 0 43.0 3.0 0.0 0.0 0.0 0.0;

17 3 1.000 0 42.0 8.0 0.0 0.0 0.0 0.0;

18 3 1.000 0 27.2 9.8 0.0 0.0 0.0 0.0;

19 3 1.000 0 3.3 0.6 0.0 0.0 0.0 0.0;

20 3 1.000 0 2.3 1.0 0.0 0.0 0.0 0.0;

21 3 1.000 0 0.0 0.0 0.0 0.0 0.0 0.0;

22 3 1.000 0 0.0 0.0 0.0 0.0 0.0 0.0;

23 3 1.000 0 6.3 2.1 0.0 0.0 0.0 0.0;

24 3 1.000 0 0.0 0.0 0.0 0.0 0.0 0.0;

25 3 1.000 0 6.3 3.2 0.0 0.0 0.0 0.0;

26 3 1.000 0 0.0 0.0 0.0 0.0 0.0 0.0;

27 3 1.000 0 9.3 0.5 0.0 0.0 0.0 0.0;

28 3 1.000 0 4.6 2.3 0.0 0.0 0.0 0.0;

29 3 1.000 0 17.0 2.6 0.0 0.0 0.0 0.0;

30 3 1.000 0 3.6 1.8 0.0 0.0 0.0 0.0;

31 3 1.000 0 5.8 2.9 0.0 0.0 0.0 0.0;

32 3 1.000 0 1.6 0.8 0.0 0.0 0.0 0.0;

33 3 1.000 0 3.8 1.9 0.0 0.0 0.0 0.0;

34 3 1.000 0 0.0 0.0 0.0 0.0 0.0 0.0;

35 3 1.000 0 6.0 3.0 0.0 0.0 0.0 0.0;

36 3 1.000 0 0.0 0.0 0.0 0.0 0.0 0.0;

37 3 1.000 0 0.0 0.0 0.0 0.0 0.0 0.0;

38 3 1.000 0 14.0 7.0 0.0 0.0 0.0 0.0;

39 3 1.000 0 0.0 0.0 0.0 0.0 0.0 0.0;

40 3 1.000 0 0.0 0.0 0.0 0.0 0.0 0.0;

41 3 1.000 0 6.3 3.0 0.0 0.0 0.0 0.0;

42 3 1.000 0 7.1 4.4 0.0 0.0 0.0 0.0;

43 3 1.000 0 2.0 1.0 0.0 0.0 0.0 0.0;

44 3 1.000 0 12.0 1.8 0.0 0.0 0.0 0.0;

45 3 1.000 0 0.0 0.0 0.0 0.0 0.0 0.0;

46 3 1.000 0 0.0 0.0 0.0 0.0 0.0 0.0;

47 3 1.000 0 29.7 11.6 0.0 0.0 0.0 0.0;

48 3 1.000 0 0.0 0.0 0.0 0.0 0.0 0.0;

49 3 1.000 0 18.0 8.5 0.0 0.0 0.0 0.0;

50 3 1.000 0 21.0 10.5 0.0 0.0 0.0 0.0;

51 3 1.000 0 18.0 5.3 0.0 0.0 0.0 0.0;

52 3 1.000 0 4.9 2.2 0.0 0.0 0.0 0.0;

53 3 1.000 0 20.0 10.0 0.0 0.0 0.0 0.0;

54 3 1.000 0 4.1 1.4 0.0 0.0 0.0 0.0;

55 3 1.000 0 6.8 3.4 0.0 0.0 0.0 0.0;

56 3 1.000 0 7.6 2.2 0.0 0.0 0.0 0.0;

57 3 1.000 0 6.7 2.0 0.0 0.0 0.0 0.0];

% | Bus | Type | Vsp | theta | PGi | QGi | PLi | QLi | Qmin | Qmax |

busdat118 = [ 1 1 0.955 10.67 51.0 27.0 0.0 0.0 -5.0 15.0

2 3 1.000 11.22 20.0 9.0 0.0 0.0 0.0 0.0

3 3 1.000 11.56 39.0 10.0 0.0 0.0 0.0 0.0

4 2 0.998 15.28 30.0 12.0 -9.0 0.0 -300.0 300.0

5 3 1.000 15.73 0.0 0.0 0.0 -0.40 0.0 0.0

6 2 0.990 13.00 52.0 22.0 0.0 0.0 -13.0 50.0

7 3 1.000 12.56 19.0 2.0 0.0 0.0 0.0 0.0

8 2 1.015 20.77 0.0 0.0 -28.0 0.0 -300.0 300.0

9 3 1.000 28.02 0.0 0.0 0.0 0.0 0.0 0.0

10 2 1.050 35.61 0.0 0.0 450.0 0.0 -147.0 200.0

11 3 1.000 12.72 70.0 23.0 0.0 0.0 0.0 0.0

12 2 0.990 12.20 47.0 10.0 85.0 0.0 -35.0 120.0

13 3 1.000 11.35 34.0 16.0 0.0 0.0 0.0 0.0

14 3 1.000 11.50 14.0 1.0 0.0 0.0 0.0 0.0

15 2 0.970 11.23 90.0 30.0 0.0 0.0 -10.0 30.0

16 3 1.000 11.91 25.0 10.0 0.0 0.0 0.0 0.0

17 3 1.000 13.74 11.0 3.0 0.0 0.0 0.0 0.0

18 2 0.973 11.53 60.0 34.0 0.0 0.0 -16.0 50.0

19 2 0.963 11.05 45.0 25.0 0.0 0.0 -8.0 24.0

20 3 1.000 11.93 18.0 3.0 0.0 0.0 0.0 0.0

21 3 1.000 13.52 14.0 8.0 0.0 0.0 0.0 0.0

22 3 1.000 16.08 10.0 5.0 0.0 0.0 0.0 0.0

23 3 1.000 21.00 7.0 3.0 0.0 0.0 0.0 0.0

24 2 0.992 20.89 0.0 0.0 -13.0 0.0 -300.0 300.0

25 2 1.050 27.93 0.0 0.0 220.0 0.0 -47.0 140.0

26 2 1.015 29.71 0.0 0.0 314.0 0.0 -1000.0 1000.0

27 2 0.968 15.35 62.0 13.0 -9.0 0.0 -300.0 300.0

28 3 1.000 13.62 17.0 7.0 0.0 0.0 0.0 0.0

29 3 1.000 12.63 24.0 4.0 0.0 0.0 0.0 0.0

30 3 1.000 18.79 0.0 0.0 0.0 0.0 0.0 0.0

31 2 0.967 12.75 43.0 27.0 7.0 0.0 -300.0 300.0

32 2 0.964 14.80 59.0 23.0 0.0 0.0 -14.0 -42.0

33 3 1.000 10.63 23.0 9.0 0.0 0.0 0.0 0.0

34 2 0.986 11.30 59.0 26.0 0.0 -0.14 -8.0 24.0

35 3 1.000 10.87 33.0 9.0 0.0 0.0 0.0 0.0

36 2 0.980 10.87 31.0 17.0 0.0 0.0 -8.0 24.0

37 3 1.000 11.77 0.0 0.0 0.0 0.25 0.0 0.0

38 3 1.000 16.91 0.0 0.0 0.0 0.0 0.0 0.0

39 3 1.000 8.41 27.0 11.0 0.0 0.0 0.0 0.0

40 2 0.970 7.35 20.0 23.0 -46.0 0.0 -300.0 300.0

41 3 1.000 6.92 37.0 10.0 0.0 0.0 0.0 0.0

42 2 0.985 8.53 37.0 23.0 -59.0 0.0 -300.0 300.0

43 3 1.000 11.28 18.0 7.0 0.0 0.0 0.0 0.0

44 3 1.000 13.82 16.0 8.0 0.0 -0.10 0.0 0.0

45 3 1.000 15.67 53.0 22.0 0.0 -0.10 0.0 0.0

46 2 1.005 18.49 28.0 10.0 19.0 -0.10 -100.0 100.0

47 3 1.000 20.73 34.0 0.0 0.0 0.0 0.0 0.0

48 3 1.000 19.93 20.0 11.0 0.0 -0.15 0.0 0.0

49 2 1.025 20.94 87.0 30.0 204.0 0.0 -85.0 210.0

50 3 1.000 18.90 17.0 4.0 0.0 0.0 0.0 0.0

51 3 1.000 16.28 17.0 8.0 0.0 0.0 0.0 0.0

52 3 1.000 15.32 18.0 5.0 0.0 0.0 0.0 0.0

53 3 1.000 14.35 23.0 11.0 0.0 0.0 0.0 0.0

54 2 0.955 15.26 113.0 32.0 48.0 0.0 -300.0 300.0

55 2 0.952 14.97 63.0 22.0 0.0 0.0 -8.0 23.0

56 2 0.954 15.16 84.0 18.0 0.0 0.0 -8.0 15.0

57 3 1.000 16.36 12.0 3.0 0.0 0.0 0.0 0.0

58 3 1.000 15.51 12.0 3.0 0.0 0.0 0.0 0.0

59 2 0.985 19.37 277.0 113.0 155.0 0.0 -60.0 180.0

60 3 1.000 23.15 78.0 3.0 0.0 0.0 0.0 0.0

61 2 0.995 24.04 0.0 0.0 160.0 0.0 -100.0 300.0

62 2 0.998 23.43 77.0 14.0 0.0 0.0 -20.0 20.0

63 3 1.000 22.75 0.0 0.0 0.0 0.0 0.0 0.0

64 3 1.000 24.52 0.0 0.0 0.0 0.0 0.0 0.0

65 2 1.005 27.65 0.0 0.0 391.0 0.0 -67.0 200.0

66 2 1.050 27.48 39.0 18.0 392.0 0.0 -67.0 200.0

67 3 1.000 24.84 28.0 7.0 0.0 0.0 0.0 0.0

68 3 1.000 27.55 0.0 0.0 0.0 0.0 0.0 0.0

69 2 1.035 30.00 0.0 0.0 516.4 0.0 -300.0 300.0

70 2 0.984 22.58 66.0 20.0 0.0 0.0 -10.0 32.0

71 3 1.000 22.15 0.0 0.0 0.0 0.0 0.0 0.0

72 2 0.980 20.98 0.0 0.0 -12.0 0.0 -100.0 100.0

73 2 0.991 21.94 0.0 0.0 -6.0 0.0 -100.0 100.0

74 2 0.958 21.64 68.0 27.0 0.0 -0.12 -6.0 9.0

75 3 1.000 22.91 47.0 11.0 0.0 0.0 0.0 0.0

76 2 0.943 21.77 68.0 36.0 0.0 0.0 -8.0 23.0

77 2 1.006 26.72 61.0 28.0 0.0 0.0 -20.0 70.0

78 3 1.000 26.42 71.0 26.0 0.0 0.0 0.0 0.0

79 3 1.000 26.72 39.0 32.0 0.0 -0.20 0.0 0.0

80 2 1.040 28.96 130.0 26.0 477.0 0.0 -165.0 280.0

81 3 1.000 28.10 0.0 0.0 0.0 0.0 0.0 0.0

82 3 1.000 27.24 54.0 27.0 0.0 -0.20 0.0 0.0

83 3 1.000 28.42 20.0 10.0 0.0 -0.10 0.0 0.0

84 3 1.000 30.95 11.0 7.0 0.0 0.0 0.0 0.0

85 2 0.985 32.51 24.0 15.0 0.0 0.0 -8.0 23.0

86 3 1.000 31.14 21.0 10.0 0.0 0.0 0.0 0.0

87 2 1.015 31.40 0.0 0.0 4.0 0.0 -100.0 1000.0

88 3 1.000 35.64 48.0 10.0 0.0 0.0 0.0 0.0

89 2 1.005 39.69 0.0 0.0 607.0 0.0 -210.0 300.0

90 2 0.985 33.29 78.0 42.0 -85.0 0.0 -300.0 300.0

91 2 0.980 33.31 0.0 0.0 -10.0 0.0 -100.0 100.0

92 2 0.993 33.80 65.0 10.0 0.0 0.0 -3.0 9.0

93 3 1.000 30.79 12.0 7.0 0.0 0.0 0.0 0.0

94 3 1.000 28.64 30.0 16.0 0.0 0.0 0.0 0.0

95 3 1.000 27.67 42.0 31.0 0.0 0.0 0.0 0.0

96 3 1.000 27.51 38.0 15.0 0.0 0.0 0.0 0.0

97 3 1.000 27.88 15.0 9.0 0.0 0.0 0.0 0.0

98 3 1.000 27.40 34.0 8.0 0.0 0.0 0.0 0.0

99 3 1.000 27.04 0.0 0.0 -42.0 0.0 -100.0 100.0

100 2 1.017 28.03 37.0 18.0 252.0 0.0 -50.0 155.0

101 3 1.000 29.61 22.0 15.0 0.0 0.0 0.0 0.0

102 3 1.000 32.30 5.0 3.0 0.0 0.0 0.0 0.0

103 2 1.001 24.44 23.0 16.0 40.0 0.0 -15.0 40.0

104 2 0.971 21.69 38.0 25.0 0.0 0.0 -8.0 23.0

105 2 0.965 20.57 31.0 26.0 0.0 -0.20 -8.0 23.0

106 3 1.000 20.32 43.0 16.0 0.0 0.0 0.0 0.0

107 2 0.952 17.53 28.0 12.0 -22.0 -0.06 -200.0 200.0

108 3 1.000 19.38 2.0 1.0 0.0 0.0 0.0 0.0

109 3 1.000 18.93 8.0 3.0 0.0 0.0 0.0 0.0

110 2 0.973 18.09 39.0 30.0 0.0 -0.06 -8.0 23.0

111 2 0.980 19.74 0.0 0.0 36.0 0.0 -100.0 1000.0

112 2 0.975 14.99 25.0 13.0 -43.0 0.0 -100.0 1000.0

113 2 0.993 13.74 0.0 0.0 -6.0 0.0 -100.0 200.0

114 3 1.000 14.46 8.0 3.0 0.0 0.0 0.0 0.0

115 3 1.000 14.46 22.0 7.0 0.0 0.0 0.0 0.0

116 2 1.005 27.12 0.0 0.0 -184.0 0.0 -1000.0 1000.0

117 3 1.000 10.67 20.0 8.0 0.0 0.0 0.0 0.0

118 3 1.000 21.92 33.0 15.0 0.0 0.0 0.0 0.0 ];

switch num

case 3

busdt = busdat3;

case 6

busdt = busdat6;

case 9

busdt = busdat9;

case 14

busdt = busdat14;

case 30

busdt = busdat30;

case 57

busdt = busdat57;

case 118

busdt = busdat118;

end

⛄ 运行结果

⛄ 参考文献

[1]张随涵, 刘白杨. 基于MATLAB的Newton-Raphson法电力系统潮流计算[J]. 科技传播, 2016(4):2.

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