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Signed-off-by: dmy@lab <dmy@lab.lab>
This commit is contained in:
dmy@lab 2015-01-29 21:32:27 +08:00
commit 3938778d78
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60
NCP函数法/Constant.m Normal file
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function [const,Lz,Lw,L1,U1]=Constant(nodeNum,opfGoal,lineNum,transNum,transI,transJ,transG,transB,...
T,transKmin,transKmax,lineI,lineJ,balNode,mu,G,B,GIJ,BIJ,e,f,Pmin,Pmax,a,b,PG,QR,pvQmin,pvQmax,...
pgNum,pgvNum,xNum,capNum,capK,capKmin,capKmax,pgNode,pvNode,dhx,dgx,L1,U1,LZ,UW,l,u,y,r,capBi,Vmin,Vmax,hx)
%程序功能：预计算过程，形成扰动KKT方程不平衡量矩阵
%编写时间：2010年11月
%% 形成目标函数的一阶偏导矩阵▽f(.)
if(opfGoal==2)
dPG=ones(pgNum,1);
dfx=sparse(transNum+1:transNum+pgNum,ones(pgNum,1),dPG,xNum,1);
else if(opfGoal==1)
dPG=2*a(pgNode).*PG(pgNode)+b(pgNode);
dfx=sparse(transNum+1:transNum+pgNum,ones(pgNum,1),dPG,xNum,1);
else if(opfGoal==3)
dfT=-1*transG.*((f(transI)-f(transJ)).^2+(e(transI)-e(transJ)).^2);
dfPQ=zeros(pgvNum,1);
dfcapK=zeros(capNum,1);
EE=e*ones(1,nodeNum);
FF=f*ones(1,nodeNum);
dfe=2*sum(G.*(EE-EE'));
dff=2*sum(G.*(FF-FF'));
dfx=[dfT;dfPQ;dfcapK;dfe';dff'];
else if(opfGoal==4)
dfT=1*transB.*((f(transI)-f(transJ)).^2+(e(transI)-e(transJ)).^2);
dfPQ=zeros(pgvNum,1);
dfcapK=zeros(capNum,1);
EE=e*ones(1,nodeNum);
FF=f*ones(1,nodeNum);
dfe=-2*sum(B.*(EE-EE'));
dff=-2*sum(B.*(FF-FF'));
dfx=[dfT;dfPQ;dfcapK;dfe';dff'];
end
end
end
end
%% 不等式约束项
gxv=[PG(pgNode);QR(pvNode);capK;e.^2+f.^2]; %约束条件当前值
gxvx=[Pmin(pgNode);pvQmin(pvNode);capKmin.*capBi;Vmin.*Vmin]; %约束下限
gxvs=[Pmax(pgNode);pvQmax(pvNode);capKmax.*capBi;Vmax.*Vmax]; %约束上限
gxl=(e(lineI).*e(lineI)+f(lineI).*f(lineI)-e(lineI).*e(lineJ)-f(lineI).*f(lineJ)).*GIJ+(e(lineI).*f(lineJ)-e(lineJ).*f(lineI)).*BIJ;%线路功率当前值
gxlx=-ones(lineNum,1)*1000; %线路约束下限
gxls=ones(lineNum,1)*1000; %线路约束上限
gxT=T;
gxTx=transKmin; %变比下限
gxTs=transKmax; %变比上限
gx=[gxT;gxv;gxl]; %组合所有约束条件
gxx=[gxTx;gxvx;gxlx];
gsx=[gxTs;gxvs;gxls];
Lz=gx-l-gxx;
Lw=gx+u-gsx;
%% 形成修正方程常数项向量
muUL=mu*(U1-L1);
BB1=UW*Lw-LZ*Lz-muUL*ones(r,1);
BB=dhx*y-dfx+dgx*BB1; %修正方程常数项ψ(.,μ)
balN=transNum+pgvNum+capNum+nodeNum+balNode;
balN1=transNum+pgvNum+capNum+balNode;
BB(balN,1)=0; %保持平衡节点电压虚部不变，始终为0，则常数项平衡节点处置0
BB(balN1,1)=0; %保持平衡节点电压实部不变
const=[BB;hx]; %修正方程常数项向量

425
NCP函数法/IEEE118.dat Normal file
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118 179 100 100 0.1
1.e-5 2
1 69
0
1 1 2 0.0303 0.0999 0.0127
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4 3 5 0.0241 0.1080 0.0142
5 5 6 0.0119 0.0540 0.00713
6 6 7 0.00459 0.0208 0.00275
7 8 9 0.00244 0.0305 0.5810
9 9 10 0.00258 0.0322 0.6150
10 4 11 0.0209 0.0688 0.00874
11 5 11 0.0203 0.0682 0.00869
12 11 12 0.00595 0.0196 0.00251
13 2 12 0.0187 0.0616 0.00786
14 3 12 0.0484 0.1600 0.0203
15 7 12 0.00862 0.0340 0.00437
16 11 13 0.02225 0.0731 0.00938
17 12 14 0.0215 0.0707 0.00908
18 13 15 0.0744 0.2444 0.03134
19 14 15 0.0595 0.1950 0.0251
20 12 16 0.0212 0.0834 0.0107
21 15 17 0.0132 0.0437 0.0222
22 16 17 0.0454 0.1801 0.0233
23 17 18 0.0123 0.0505 0.00649
24 18 19 0.01119 0.0493 0.00571
25 19 20 0.0252 0.1170 0.0149
26 15 19 0.0120 0.0394 0.00505
27 20 21 0.0183 0.0849 0.0108
28 21 22 0.0209 0.0970 0.0123
29 22 23 0.0342 0.1590 0.0202
30 23 24 0.0135 0.0492 0.0249
31 23 25 0.0156 0.0800 0.0432
33 25 27 0.0318 0.1630 0.0882
34 27 28 0.01913 0.0855 0.0108
35 28 29 0.0237 0.0943 0.0119
37 8 30 0.00431 0.0504 0.2570
38 26 30 0.00799 0.0860 0.4540
39 17 31 0.0474 0.1563 0.01995
40 29 31 0.0108 0.0331 0.00415
41 23 32 0.0317 0.1153 0.05865
42 31 32 0.0298 0.0985 0.01255
43 27 32 0.0229 0.0755 0.00963
44 15 33 0.0380 0.1244 0.01597
45 19 34 0.0752 0.2470 0.0316
46 35 36 0.00224 0.0102 0.00124
47 35 37 0.0110 0.0497 0.00659
48 33 37 0.0415 0.1420 0.0183
49 34 36 0.00871 0.0268 0.00284
50 34 37 0.00256 0.0094 0.00429
52 37 39 0.0321 0.1060 0.0135
53 37 40 0.0593 0.1680 0.0210
54 30 38 0.00464 0.0540 0.2110
55 39 40 0.0184 0.0605 0.00776
56 40 41 0.0145 0.0487 0.00611
57 40 42 0.0555 0.1830 0.0233
58 41 42 0.0410 0.1350 0.0172
59 43 44 0.0608 0.2454 0.03034
60 34 43 0.0413 0.1681 0.02113
61 44 45 0.0224 0.0901 0.0112
62 45 46 0.0400 0.1356 0.0166
63 46 47 0.0380 0.1270 0.0158
64 46 48 0.0601 0.1890 0.0236
65 47 49 0.0191 0.0625 0.00802
66 42 49 0.03575 0.1615 0.0860
67 45 49 0.0684 0.1860 0.0222
68 48 49 0.0179 0.0505 0.00629
69 49 50 0.0267 0.0752 0.00937
70 49 51 0.0486 0.1370 0.0171
71 51 52 0.0203 0.0588 0.00698
72 52 53 0.0405 0.1635 0.02029
73 53 54 0.0263 0.1220 0.0155
74 49 54 0.03976 0.1450 0.0734
75 54 55 0.0169 0.0707 0.0101
76 54 56 0.00275 0.00955 0.00366
77 55 56 0.00488 0.0151 0.00187
78 56 57 0.0343 0.0966 0.0121
79 50 57 0.0474 0.1340 0.0166
80 56 58 0.0343 0.0966 0.0121
81 51 58 0.0255 0.0719 0.00894
82 54 59 0.0503 0.2293 0.0299
83 56 59 0.04069 0.12243 0.05525
84 55 59 0.04739 0.2158 0.02823
85 59 60 0.0317 0.1450 0.0188
86 59 61 0.0328 0.1500 0.0194
87 60 61 0.00264 0.0135 0.00728
88 60 62 0.0123 0.0561 0.00734
89 61 62 0.00824 0.0376 0.0049
91 63 64 0.00172 0.0200 0.1080
93 38 65 0.00901 0.0986 0.5230
94 64 65 0.00269 0.0302 0.1900
95 49 66 0.0090 0.04595 0.0248
96 62 66 0.0482 0.2180 0.0289
97 62 67 0.0258 0.1170 0.0155
99 66 67 0.0224 0.1015 0.01341
100 65 68 0.00138 0.0160 0.3190
101 47 69 0.0844 0.2778 0.03546
102 49 69 0.0985 0.3240 0.0414
104 69 70 0.0300 0.1270 0.0610
105 24 70 0.10221 0.4115 0.05099
106 70 71 0.00882 0.0355 0.00439
107 24 72 0.0488 0.1960 0.0244
108 71 72 0.0446 0.1800 0.02222
109 71 73 0.00866 0.0454 0.00589
110 70 74 0.0401 0.1323 0.01684
111 70 75 0.0428 0.1410 0.0180
112 69 75 0.0405 0.1220 0.0620
113 74 75 0.0123 0.0406 0.00517
114 76 77 0.0444 0.1480 0.0184
115 69 77 0.0309 0.1010 0.0519
116 75 77 0.0601 0.1999 0.02489
117 77 78 0.00376 0.0124 0.00632
118 78 79 0.00546 0.0244 0.00324
119 77 80 0.01077 0.03318 0.0350
120 79 80 0.0156 0.0704 0.00945
121 68 81 0.00175 0.0202 0.4040
123 77 82 0.0298 0.0853 0.04087
124 82 83 0.0112 0.03665 0.01898
125 83 84 0.0625 0.1320 0.0129
126 83 85 0.0430 0.1480 0.0174
127 84 85 0.0302 0.0641 0.00617
128 85 86 0.0350 0.1230 0.0138
129 86 87 0.02828 0.2074 0.02225
130 85 88 0.0200 0.1020 0.0138
131 85 89 0.0239 0.1730 0.0235
132 88 89 0.0139 0.0712 0.00969
133 89 90 0.01631 0.06515 0.0794
134 90 91 0.0254 0.0836 0.0107
135 89 92 0.00791 0.03827 0.0481
136 91 92 0.0387 0.1272 0.01634
137 92 93 0.0258 0.0848 0.0109
138 92 94 0.0481 0.1580 0.0203
139 93 94 0.0223 0.0732 0.00938
140 94 95 0.0132 0.0434 0.00555
141 80 96 0.0356 0.1820 0.0247
142 82 96 0.0162 0.0530 0.0272
143 94 96 0.0269 0.0869 0.0115
144 80 97 0.0183 0.0934 0.0127
145 80 98 0.0238 0.1080 0.0143
146 80 99 0.0454 0.2060 0.0273
148 94 100 0.0178 0.0580 0.0302
149 95 96 0.0171 0.0547 0.00737
150 96 97 0.0173 0.0885 0.0120
151 98 100 0.0397 0.1790 0.0238
152 99 100 0.0180 0.0813 0.0108
153 100 101 0.0277 0.1262 0.0164
154 92 102 0.0123 0.0559 0.00732
155 101 102 0.0246 0.1120 0.0147
156 100 103 0.0160 0.0525 0.0268
157 100 104 0.0451 0.2040 0.02705
158 103 104 0.0466 0.1584 0.02035
159 103 105 0.0535 0.1625 0.0204
160 100 106 0.0605 0.2290 0.0310
161 104 105 0.00994 0.0378 0.00493
162 105 106 0.0140 0.0547 0.00717
163 105 107 0.0530 0.1830 0.0236
164 105 108 0.0261 0.0703 0.09222
166 108 109 0.0105 0.0288 0.0038
167 103 110 0.03906 0.1813 0.02305
168 109 110 0.0278 0.0762 0.0101
169 110 111 0.0220 0.0755 0.0100
170 110 112 0.0247 0.0640 0.0310
171 17 113 0.00913 0.0301 0.00384
172 32 113 0.0615 0.2030 0.0259
173 32 114 0.0135 0.0612 0.00814
174 27 115 0.0164 0.0741 0.00986
175 114 115 0.0023 0.0104 0.00138
176 68 116 0.00034 0.00405 0.0820
177 12 117 0.0329 0.1400 0.0179
178 75 118 0.01450 0.04810 0.00599
179 76 118 0.0164 0.0544 0.00678
0
5 -0.4
37 -0.25
45 .1
46 .1
79 .2
83 .1
110 .06
0
1 8 5 0.0 0.0267 0.9850 0.9 1.1 1
2 25 26 0.0 0.0382 0.9600 0.9 1.1 1
3 17 30 0.0 0.0388 0.9600 0.9 1.1 1
4 37 38 0.0 0.0375 0.9350 0.9 1.1 1
5 59 63 0.0 0.0386 0.9600 0.9 1.1 1
6 61 64 0.0 0.0268 0.9850 0.9 1.1 1
7 65 66 0.0 0.0370 0.9350 0.9 1.1 1
8 68 69 0.0 0.0370 0.9350 0.9 1.1 1
9 80 81 0.0 0.0370 0.9350 0.9 1.1 1
10 92 100 0.0648 0.2950 1. 0.9 1.1 0
11 106 107 0.0530 0.1830 1. 0.9 1.1 0
0
1 0. 0. 51. 27.
2 0. 0. 20. 9.
3 0. 0. 39. 10.
4 -9. 0. 30. 12.
5 0. 0. 0. 0.
6 0. 0. 52. 22.
7 0. 0. 19. 2.
8 -28. 0. 0. 0.
9 0. 0. 0. 0.
10 450. 0. 0. 0.
11 0. 0. 70. 23.
12 85. 0. 47. 10.
13 0. 0. 34. 16.
14 0. 0. 14. 1.
15 0. 0. 90. 30.
16 0. 0. 25. 10.
17 0. 0. 11. 3.
18 0. 0. 60. 34.
19 0. 0. 45. 25.
20 0. 0. 18. 3.
21 0. 0. 14. 8.
22 0. 0. 10. 5.
23 0. 0. 7. 3.
24 -13. 0. 0. 0.
25 220. 0. 0. 0.
26 314. 0. 0. 0.
27 -9. 0. 62. 13.
28 0. 0. 17. 7.
29 0. 0. 24. 4.
30 0. 0. 0. 0.
31 7. 0. 43. 27.
32 0. 0. 59. 23.
33 0. 0. 23. 9.
34 0. 0. 59. 26.
35 0. 0. 33. 9.
36 0. 0. 31. 17.
37 0. 0. 0. 0.
38 0. 0. 0. 0.
39 0. 0. 27. 11.
40 -46. 0. 20. 23.
41 0. 0. 37. 10.
42 -59. 0. 37. 23.
43 0. 0. 18. 7.
44 0. 0. 16. 8.
45 0. 0. 53. 22.
46 19. 0. 28. 10.
47 0. 0. 34. 0.
48 0. 0. 20. 11.
49 204. 0. 87. 30.
50 0. 0. 17. 4.
51 0. 0. 17. 8.
52 0. 0. 18. 5.
53 0. 0. 23. 11.
54 48. 0. 113. 32.
55 0. 0. 63. 22.
56 0. 0. 84. 18.
57 0. 0. 12. 3.
58 0. 0. 12. 3.
59 155. 0. 277. 113.
60 0. 0. 78. 3.
61 160. 0. 0. 0.
62 0. 0. 77. 14.
63 0. 0. 0. 0.
64 0. 0. 0. 0.
65 391. 0. 0. 0.
66 392. 0. 39. 18.
67 0. 0. 28. 7.
68 0. 0. 0. 0.
69 516.4 0. 0. 0.
70 0. 0. 66. 20.
71 0. 0. 0. 0.
72 -12. 0. 0. 0.
73 -6. 0. 0. 0.
74 0. 0. 68. 27.
75 0. 0. 47. 11.
76 0. 0. 68. 36.
77 0. 0. 61. 28.
78 0. 0. 71. 26.
79 0. 0. 39. 32.
80 477. 0. 130. 26.
81 0. 0. 0. 0.
82 0. 0. 54. 27.
83 0. 0. 20. 10.
84 0. 0. 11. 7.
85 0. 0. 24. 15.
86 0. 0. 21. 10.
87 4. 0. 0. 0.
88 0. 0. 48. 10.
89 607. 0. 0. 0.
90 -85. 0. 78. 42.
91 -10. 0. 0. 0.
92 0. 0. 65. 10.
93 0. 0. 12. 7.
94 0. 0. 30. 16.
95 0. 0. 42. 31.
96 0. 0. 38. 15.
97 0. 0. 15. 9.
98 0. 0. 34. 8.
99 -42. 0. 0. 0.
100 252. 0. 37. 18.
101 0. 0. 22. 15.
102 0. 0. 5. 3.
103 40. 0. 23. 16.
104 0. 0. 38. 25.
105 0. 0. 31. 26.
106 0. 0. 43. 16.
107 -22. 0. 28. 12.
108 0. 0. 2. 1.
109 0. 0. 8. 3.
110 0. 0. 39. 30.
111 36. 0. 0. 0.
112 -43. 0. 25. 13.
113 -6. 0. 0. 0.
114 0. 0. 8. 3.
115 0. 0. 22. 7.
116 -184. 0. 0. 0.
117 0. 0. 20. 8.
118 0. 0. 33. 15.
0
1 .955 -5. 15.
4 .998 -300. 300.
6 .99 -13. 50.
8 1.015 -300. 300.
10 1.05 -147. 200.
12 .99 -35. 120.
15 .97 -10. 30.
18 .973 -16. 50.
19 .963 -8. 24.
24 .992 -300. 300.
25 1.05 -47. 140.
26 1.015 -1000. 1000.
27 .968 -300. 300.
31 .967 -300. 300.
32 .964 -14. 42.
34 .984 -8. 24.
36 .98 -8. 24.
40 .97 -300. 300.
42 .985 -300. 300.
46 1.005 -100. 100.
49 1.025 -85. 210.
54 .955 -300. 300.
55 .952 -8. 23.
56 .954 -8. 15.
59 .985 -60. 180.
61 .995 -100. 300.
62 .998 -20. 20.
65 1.005 -67. 200.
66 1.05 -67. 200.
69 1.01 -300. 300.
70 .984 -10. 32.
72 .98 -100. 100.
73 .991 -100. 100.
74 .958 -6. 9.
76 .943 -8. 23.
77 1.006 -20. 70.
80 1.04 -165. 280.
85 .985 -8. 23.
87 1.015 -100. 1000.
89 1.005 -210. 300.
90 .985 -300. 300.
91 .98 -100. 100.
92 .993 -3. 9.
99 1.01 -100. 100.
100 1.017 -50. 155.
103 1.001 -15. 40.
104 .971 -8. 23.
105 .965 -8. 23.
107 .952 -200. 200.
110 .973 -8. 23.
111 .98 -100. 1000.
112 .975 -100. 1000.
113 .993 -100. 200.
116 1.005 -1000. 1000.
0
10 0. 1.25 1. 100. 600. 1
12 0. 2.6 1.2 60. 200. 1
25 0. 1.5 1. 50. 300. 1
26 0. 1.5 1. 100. 400. 1
49 0. 2.1 1. 100. 400. 1
54 0. 2.0 1.4 20. 300. 1
59 0. 1.6 1. 50. 350. 1
61 0. 1.5 1. 50. 400. 1
65 0. 1.5 1. 100. 500. 1
66 0. 1.5 1. 100. 500. 1
69 0. 1.0 1. 100. 800. 1
80 0. 1.23 1. 100. 600. 1
89 0. 1.2 1. 100. 800. 1
100 0. 1.6 1. 100. 400. 1
103 0. 2.5 1.2 20. 200. 1
111 0. 2.4 1.1 10. 200. 1
0
1 17 0 0.1 0 0 10
2 34 0 0.1 0.14 0 10
3 44 0 0.1 0.1 0 10
4 107 0 0.1 0.06 0 10
5 82 0 0.1 0.2 0 10
6 48 0 0.1 0.15 0 10
7 74 0 0.1 0.12 0 10
8 105 0 0.1 0.2 0 10
0
0
0
1 100 92 -25. 25.
2 106 107 -18. 18.
0
0
1 17 0 0.05 0 0 6
2 34 0 0.05 0.14 0 6
3 44 0 0.05 0.1 0 6
4 107 0 0.05 0.06 0 6
5 82 0 0.05 0.2 0 6
6 48 0 0.05 0.15 0 6
7 74 0 0.05 0.12 0 6
8 105 0 0.05 0.2 0 6
0
1 17 0 0.1 0 0 6
2 34 0 0.1 0.14 0 6
3 44 0 0.1 0.1 0 6
4 107 0 0.1 0.06 0 6
5 82 0 0.1 0.2 0 6
6 48 0 0.1 0.15 0 6
7 74 0 0.1 0.12 0 6
8 105 0 0.1 0.2 0 6
0
1 17 0 0.2 0 0 6
2 34 0 0.2 0.14 0 6
3 44 0 0.2 0.1 0 6
4 107 0 0.2 0.06 0 6
5 82 0 0.2 0.2 0 6
6 48 0 0.2 0.15 0 6
7 74 0 0.2 0.12 0 6
8 105 0 0.2 0.2 0 6

98
NCP函数法/IEEE30.dat Normal file
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@ -0,0 +1,98 @@
30 41 100.0 100 0.1
1.e-5 2
1 1
0
1 1 2 0.0192 0.0575 0.0264
2 1 3 0.0452 0.1652 0.0204
3 2 4 0.0570 0.1737 0.0184
4 3 4 0.0132 0.0379 0.0042
5 2 5 0.0472 0.1983 0.0209
6 2 6 0.0581 0.1763 0.0187
7 4 6 0.0119 0.0414 0.0045
8 5 7 0.0460 0.1160 0.0102
9 6 7 0.0267 0.0820 0.0085
10 6 8 0.0120 0.0420 0.0045
13 9 11 0.0 0.2080 0.0
15 12 13 0.0 0.1400 0.0
16 12 14 0.1231 0.2559 0.0
17 12 15 0.0662 0.1304 0.0
18 12 16 0.0945 0.1987 0.0
19 14 15 0.2210 0.1997 0.0
20 16 17 0.0524 0.1923 0.0
21 15 18 0.1073 0.2185 0.0
22 18 19 0.0639 0.1292 0.0
23 19 20 0.0340 0.0680 0.0
24 10 20 0.0936 0.2090 0.0
25 10 17 0.0324 0.0845 0.0
26 10 21 0.0348 0.0749 0.0
27 10 22 0.0727 0.1499 0.0
28 21 22 0.0116 0.0236 0.0
29 15 23 0.1000 0.2020 0.0
30 22 24 0.1150 0.1790 0.0
31 23 24 0.1320 0.2700 0.0
32 24 25 0.1885 0.3292 0.0
33 25 26 0.2544 0.3800 0.0
34 25 27 0.1093 0.2087 0.0
36 27 29 0.2198 0.4153 0.0
37 27 30 0.3202 0.6027 0.0
38 29 30 0.2399 0.4533 0.0
39 8 28 0.0636 0.2000 0.0214
40 6 28 0.0169 0.0599 0.0065
41 9 10 0.0 0.1100 0.0
0
0
1 6 9 0.0 0.2080 0.978 0.9 1.1 1
2 6 10 0.0 0.5560 0.969 0.9 1.1 1
3 4 12 0.0 0.2560 0.932 0.9 1.1 1
4 28 27 0.0 0.3960 0.968 0.9 1.1 1
0
1 138.77 -6.49 0. 0.
2 20 41.71 21.7 12.7
3 0. 0. 2.4 1.2
4 0. 0. 7.6 1.6
5 15 16.66 94.2 19.
6 0. 0. 0. 0.
7 0. 0. 22.8 10.9
8 60 29.31 30. 30.
9 0. 0. 0. 0.
10 0. 0. 5.8 2.
11 80 6.71 0. 0.
12 0. 0. 11.2 7.5
13 90 3.37 0. 0.
14 0. 0. 6.2 1.6
15 0. 0. 8.2 2.5
16 0. 0. 3.5 1.8
17 0. 0. 9. 5.8
18 0. 0. 3.2 .9
19 0. 0. 9.5 3.4
20 0. 0. 2.2 .7
21 0. 0. 17.5 11.2
22 0. 0. 0. 0.
23 0. 0. 3.2 1.6
24 0. 0. 8.7 6.7
25 0. 0. 0. 0.
26 0. 0. 3.5 2.3
27 0. 0. 0. 0.
28 0. 0. 0. 0.
29 0. 0. 2.4 .9
30 0. 0. 10.6 1.9
0
1 1.060 -50 50.
2 1.043 -40. 60.
5 1.010 -40. 40.
8 1.010 -10. 40.
11 1.082 -6. 24.
13 1.071 -6. 24.
0
1 10. 2.0 2.0 10. 200. 1
2 10. 1.5 2.4 10. 60. 1
5 20. 1.8 0.8 10. 51. 1
8 10. 1.0 1.2 10. 35. 1
11 20. 1.8 0.8 10. 51. 1
13 10. 1.5 2.0 10. 50. 1
0
1 10 0 0.1 0.19 0 6
2 24 0 0.1 0.043 0 6
0
0

1153
NCP函数法/IEEE300.dat Normal file
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%*******************************************************
% 程序名称：电力系统无功优化程序
% 程序功能：主程序
% 程序算法：现代内点法，采用NCP函数处理离散变量
% 目标函数：发电费用最小（1）、有功出力最小（2）、有功网损最小（3）、无功网损最小（4）
% 编者： 韦园清
% 编写时间：2010年11月
%*******************************************************
function []=OPF(filename)
clc;
%% 读取数据
data=dlmread(filename);
if data(1,1)<1780
%读取1780节点系统格式类型的数据
[nodeNum,lineNum,capacity,kmax,centrPara,accuracy,opfGoal,balNum,balNode,mtrLine,mtrGround,mtrTrans,runPara,Pg,Qg,Pd,Qd,pvNum,pvNode,pvV,...
pvQmin,pvQmax,pgNumall,pgNodeall,pgNum,pgNode,a,b,c,Pmin,Pmax,capNum,capI,capGi,capBi,capK,capKmin,capKmax,Vmin,Vmax]=readData(data);
tic;
%形成节点导纳矩阵
[G,B,transY,transG,transB,transG1,transB1,transNum,lineNum,lineI,lineJ,lineB,transI,transJ,transK0,transKmin,transKmax]=formY(nodeNum,...
mtrLine,mtrGround,mtrTrans,capI,capK);
else
%读取IEEE标准格式数据
[nodeNum,lineNum,capacity,kmax,accuracy,balNum,balNode,mtrLine,mtrGround,mtrTrans,runPara,Pg,Qg,Pd,Qd,pvNum,pvNode,pvV,pvQmin,pvQmax,...
mtrCapacitor,pgNum,pgNode,a,b,c,Pmin,Pmax,Vmin,Vmax,centrPara]=readData_RPP(data) ;
tic;
%形成节点导纳矩阵
[G,B,lineI,lineJ,lineB,transI,transJ,transK0,transNum,transKmin,transKmax,capI,capGi,capBi,capK,capKmin,capKmax,capNum,transG,transB,...
transG1,transB1,lineNum]=formY_RPP(nodeNum,lineNum,mtrLine,mtrGround,mtrTrans,mtrCapacitor) ;
end
%% 初始化
[e,f,PG,QR,Pg,Qg,T,pgvNum,xNum,m,r,l,u,z,w,x,y,mu,dmaxOut1,dmaxOut2,xz1,xz2,dmaxOut3,dmaxOut4,xz3,xz4,xz5,colmut1,hx,k2,opfGoal,times,...
secondBegin,Tn,Tn1,capKn,capKn1,kt0,q0,mut,mub,oneTrans,oneCap,para1,para2,para3,mismatch,ifconverge]=seting(nodeNum,lineNum,transNum,transK0,...
capNum,capK,pvQmin,pvQmax,pvNum,pvNode,pvV,pgNum,pgNode,Pmin,Pmax,Pg,Qg,centrPara);
disp (['迭代次数 互补间隙 最大不平衡量 最优潮流目标'])
%% 进入循环体求解
for k=0:kmax
[mut,mub,dNCPT,dNCPT_dt,d2NCPT_dt2,dT_Zt,transGmut,transBmut,dNCPcap,dNCP_dcap,d2NCP_dcap2,capBi_dBci,H1,N1,diagE,diagF,hx,Gap,max_hx,fx,...
Pg,Qg,xz1,dmaxOut1,xz2,dmaxOut2,xz3,dmaxOut3,xz4,dmaxOut4,PGR,Tn,kt0,capKn,q0,Tn1,capKn1,T,G]=midResult(nodeNum,pgNode,opfGoal,z,l,u,w,Pg,...
Qg,e,f,G,B,a,b,c,PG,Pd,Qd,k,xz1,dmaxOut1,xz2,dmaxOut2,xz3,dmaxOut3,xz4,dmaxOut4,times,mut,mub,oneTrans,oneCap,para3,accuracy,T,capK,transKmin,...
transKmax,capKmin,capBi,mu,transNum,transG,transB,Tn,Tn1,capKn,capKn1,kt0,q0,mismatch);
if Gap<accuracy&&max_hx<mismatch %判断互补间隙和最大不平衡量是否达到精度
if times==1
times=2;
end
if times==2
if secondBegin==1
[secondBegin,m,r,l,u,z,w,y,Gama,Arlfa,meritF,firstT,firstcapK,firstfx,Gap,mu,Vfirst,Pgfirst,Qgfirst]=snd_setting(secondBegin,...
transNum,T,m,r,capNum,capK,para1,para2,fx,centrPara,e,f,Pg,Qg);
end
dicVar=[(T-Tn);(capK-capKn)]>accuracy; %判断靠近下界的离散量是否达到精度
dicVar1=[(Tn1-T);(capKn1-capK)]>accuracy; %判断靠近上界的离散量是否达到精度
ymut=dicVar.*dicVar1;
if (sum(ymut)==0) %判断离散变量是否达到精度
ifconverge=1;
break
end
end
end
mu=(centrPara*Gap)/(2*r); %计算扰动因子
if times==1 %预计算过程
%形成修正方程系数矩阵
[HSB,dhx,dgx,dgxT,N1,H1,diagE,diagF,GIJ,BIJ,L1,U1,LZ,UW]=formHSB(nodeNum,balNode,balNum,opfGoal,lineNum,transNum,lineI,lineJ,transI,...
transJ,T,transG,transB,pgNode,pvNode,G,B,e,f,pgNum,pvNum,pgvNum,xNum,capNum,capI,a,m,r,l,u,z,w,y,H1,N1,diagE,diagF);
%形成扰动KKT方程不平衡量矩阵
[const,Lz,Lw,L1,U1]=Constant(nodeNum,opfGoal,lineNum,transNum,transI,transJ,transG,transB,T,transKmin,transKmax,lineI,lineJ,balNode,...
mu,G,B,GIJ,BIJ,e,f,Pmin,Pmax,a,b,PG,QR,pvQmin,pvQmax,pgNum,pgvNum,xNum,capNum,capK,capKmin,capKmax,pgNode,pvNode,dhx,dgx,L1,U1,LZ,...
UW,l,u,y,r,capBi,Vmin,Vmax,hx);
%求解方程并更新变量
[z,l,u,w,x,y,PG,QR,Pg,Qg,e,f,T,capK,G,B]=solve(HSB,const,mu,r,nodeNum,balNode,pgNum,pvNum,xNum,transNum,capNum,capI,capBi,capK,pgNode,...
pvNode,m,x,y,z,l,u,w,Lz,Lw,LZ,UW,dgxT,L1,U1,G,B,transI,transJ,T,transG,transB,transG1,transB1,PG,QR,Pg,Qg);
else %光滑处理过程
k2=k2+1;
xz5=[xz5,k2]; %保留每次迭代光滑参数的值，用于作图
colmut1=[colmut1,mut(1)];
%形成修正方程系数矩阵
[HSB,dhx,dgx,dgxT,N1,H1,diagE,diagF,GIJ,BIJ,L1,U1,LZ,UW,transG,transB,mut,mub]=snd_formHSB(nodeNum,balNode,balNum,opfGoal,lineNum,...
transNum,lineI,lineJ,transI,transJ,T,transG,transB,pgNode,pvNode,G,B,e,f,pgNum,pvNum,pgvNum,xNum,a,m,r,l,u,z,w,y,capNum,capI,...
mut,mub,dNCPT_dt,d2NCPT_dt2,dT_Zt,transGmut,transBmut,dNCP_dcap,d2NCP_dcap2,H1,N1,diagE,diagF);
%形成扰动KKT方程不平衡量矩阵
[const,Lz,Lw,L1,U1,hx,origConst,gxx,gsx]=snd_Constant(nodeNum,opfGoal,lineNum,transNum,transI,transJ,transG,transB,lineI,lineJ,...
balNode,mu,G,B,GIJ,BIJ,e,f,Pmin,Pmax,a,b,PG,QR,pvQmin,pvQmax,pgNum,pgvNum,xNum,pgNode,pvNode,dhx,dgx,L1,U1,LZ,UW,l,u,y,r,...
dT_Zt,capNum,z,w,Vmin,Vmax,hx);
%求解方程并更新变量
[z,l,u,w,x,y,PG,QR,Pg,Qg,e,f,T,G,B,capK,meritF]=snd_solve(HSB,const,mu,r,nodeNum,balNode,pgNum,pvNum,pgvNum,xNum,transNum,pgNode,...
pvNode,m,Lz,Lw,LZ,UW,dgxT,L1,U1,transI,transJ,transG,transB,transG1,transB1,Tn,capKn,capNum,capI,Tn1,capKn1,x,y,z,l,u,w,...
G,B,PG,QR,Pg,Qg,opfGoal,Gama,Arlfa,meritF,k2,T,capK,lineNum,lineI,lineJ,Pd,Qd,gxx,gsx,mut,mub);
end
end
if k>=kmax
disp '最优潮流计算不收敛！'
disp(k)
else
disp '最优潮流计算收敛！'
disp(['迭代',num2str(k),'次！'])
end
toc;
%% 输出计算结果
OutResult(G,B,balNode,e,f,T,k,Gap,fx,transI,transJ,filename,nodeNum,PGR,pgNode,QR,pvNode,capI,capK,firstT,firstcapK,Tn,Tn1,capKn,capKn1,...
firstfx,toc,max_hx,ifconverge,Vfirst,Pgfirst,Qgfirst);
%% 作互补间隙和最大不平衡量收敛曲线图
% xz=0:1:k;
% plot(xz1,dmaxOut1,'-ks','LineWidth',2,'MarkerEdgeColor','k','MarkerFaceColor','k','MarkerSize',3)
% hold on;
% plot(xz2,dmaxOut2,'-ks','LineWidth',2,'MarkerEdgeColor','k','MarkerFaceColor','k','MarkerSize',3)
% hold on;
% xlabel('迭代次数')
% ylabel('互补间隙')
% plot(xz3,dmaxOut3,'-ks','LineWidth',2,'MarkerEdgeColor','k','MarkerFaceColor','k','MarkerSize',3)
% hold on;
% plot(xz4,dmaxOut4,'-ks','LineWidth',2,'MarkerEdgeColor','k','MarkerFaceColor','k','MarkerSize',3)
% xlabel('迭代次数')
% ylabel('最大不平衡量')
%% 作mut在迭代过程中的变化图
% plot(xz5,colmut1,'-ks','LineWidth',2,'MarkerEdgeColor','k','MarkerFaceColor','k','MarkerSize',3)
% xlabel('第二阶段优化迭代次数')
% ylabel('μ')
% hold on;
%% 作二次优化互补间隙收敛曲线
% plot(xz5,dmaxOut2,'-ks','LineWidth',2,'MarkerEdgeColor','k','MarkerFaceColor','k','MarkerSize',3)
% hold on;
% xlabel('迭代次数')
% ylabel('互补间隙')

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function [e]=OutResult(G,B,balNode,e,f,T,k,Gap,fx,transI,transJ,filename,nodeNum,...
PGR,pgNode,QR,pvNode,capI,capK,firstT,firstcapK,Tn,Tn1,capKn,capKn1,firstfx,toc,max_hx,ifconverge,Vfirst,Pgfirst,Qgfirst)
%程序功能：输出计算结果
%编写时间：2010年11月
mytime=toc;
Y1=G+1j*B;
V1=e+1j*f;
NodeS=zeros(nodeNum,1);
NodeS(pvNode)=V1(pvNode,:).*conj(Y1(pvNode,:)*V1); %计算平衡节点和PV节点的节点复功率，Y1(pvNode,:)*V1为节点的注入电流
balanceP=real(NodeS(balNode,1)); %获取平衡节点的有功功率
PGR(balNode,1)=balanceP;
balanceQ=imag(NodeS(balNode,1));
QR(balNode,1)=balanceQ;
V=sqrt(e.^2+f.^2);
resultFile=['result_' filename];
fid=fopen(resultFile,'w');
result=[k;Gap;fx;firstfx;mytime;max_hx;ifconverge]; %收敛信息
fprintf(fid,'%2.0f %4.4e %6.6f %6.6f %4.4f %4.4e %2.0f\r\n',result);
fprintf(fid,'%1.0f\r\n',0);
trans=[transI';transJ';(1./T)';(1./firstT)';(1./Tn)';(1./Tn1)']; %变压器变比结果
fprintf(fid,'%2.0f %2.0f %5.4f %5.4f %5.4f %5.4f\r\n',full(trans));
fprintf(fid,'%1.0f\r\n',0);
nn=1:nodeNum;
Vresult=[nn;e';f';V';Vfirst']; %节点电压结果
fprintf(fid,'%3.0f %5.4f %5.4f %5.4f %5.4f\r\n',full(Vresult));
fprintf(fid,'%1.0f\r\n',0);
PGresult=[pgNode';PGR(pgNode)';Pgfirst(pgNode)']; %有功出力结果
PGresult=full(PGresult);
fprintf(fid,'%2.0f %4.4f %4.4f\r\n',PGresult);
fprintf(fid,'%1.0f\r\n',0);
QRresult=[pvNode';QR(pvNode)';Qgfirst(pvNode)']; %无功出力结果
QRresult=full(QRresult);
fprintf(fid,'%2.0f %4.4f %4.4f\r\n',QRresult);
fprintf(fid,'%1.0f\r\n',0);
Capresult=[capI';capK';firstcapK';capKn';capKn1']; %电容电抗器投入组数结果
fprintf(fid,'%2.0f %3.2f %5.4f %3.2f %3.2f\r\n',full(Capresult));
fprintf(fid,'%1.0f\r\n',0);
fclose(fid);

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NCP函数法/XB1780.dat Normal file
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function [HSB,dhx,dgx,dgxT,N1,H1,diagE,diagF,GIJ,BIJ,L1,U1,LZ,UW]=formHSB(nodeNum,balNode,balNum,opfGoal,lineNum,transNum,lineI,lineJ,...
transI,transJ,T,transG,transB,pgNode,pvNode,G,B,e,f,pgNum,pvNum,pgvNum,xNum,capNum,capI,a,m,r,l,u,z,w,y,H1,N1,diagE,diagF)
%程序功能：预计算过程，形成修正方程系数矩阵
%编写时间：2010年11月
%% 形成等式约束雅可比矩阵
ef1=e(transI).*e(transJ)+f(transI).*f(transJ);
ef2=e(transI).*f(transJ)-e(transJ).*f(transI);
ef3=e(transI).*e(transI)+f(transI).*f(transI);
ef1G=ef1.*transG;
ef1B=ef1.*transB;
ef2G=ef2.*transG;
ef2B=ef2.*transB;
dhPTi=-ef1G+ef2B+2*ef3.*transG.*T;
dhPTj=-ef1G-ef2B;
dhPT=sparse(1:transNum,transI,dhPTi,transNum,nodeNum)+sparse(1:transNum,transJ,dhPTj,transNum,nodeNum);%有功平衡方程P对变压器变比求偏导
dhQTi=ef1B+ef2G-2*ef3.*transB.*T;
dhQTj=ef1B-ef2G;
dhQT=sparse(1:transNum,transI,dhQTi,transNum,nodeNum)+sparse(1:transNum,transJ,dhQTj,transNum,nodeNum);%无功平衡方程Q对变压器变比求偏导
dhP=sparse(1:pgNum,pgNode,ones(pgNum,1),pgNum,m);
dhQ1=sparse(1:pvNum,pvNode,ones(pvNum,1),pvNum,nodeNum);
dhQ=[sparse(pvNum,nodeNum) dhQ1];
dhcapK1=sparse(1:capNum,capI,(e(capI).^2+f(capI).^2),capNum,nodeNum); %功率平衡方程对电容电抗器组数求偏导
dhcapK=[sparse(capNum,nodeNum) dhcapK1];
%功率方程雅可比矩阵
deG=diagE*G;
dfB=diagF*B;
deB=diagE*B;
dfG=diagF*G;
dH1=sparse(1:nodeNum,1:nodeNum,H1,nodeNum,nodeNum);
dN1=sparse(1:nodeNum,1:nodeNum,N1,nodeNum,nodeNum);
Hij=-dH1-deG-dfB;
Nij=-dN1+deB-dfG;
Jij=dN1-dfG+deB;
Lij=-dH1+dfB+deG;
%合并形成功率方程雅可比矩阵
dhJacb=[Hij Nij;Jij Lij]';
%合并形成等式约束雅可比矩阵h(x)
dhx=[dhPT dhQT;dhP;dhQ;dhcapK;dhJacb];
%% 形成不等式约束雅可比矩阵▽g(x)
dgT1=sparse(1:transNum,1:transNum,ones(transNum,1),transNum,r-lineNum);
dglT=(e(transI).^2+f(transI).^2-e(transI).*e(transJ)-f(transI).*f(transJ)).*transG+(e(transI).*f(transJ)-e(transJ).*f(transI)).*transB;
dgT2=sparse(1:transNum,lineNum-transNum+1:lineNum,dglT,transNum,lineNum);
dgT=[dgT1 dgT2]; %所有不等式对变比求导的模块
dgP=sparse(1:pgNum,transNum+1:transNum+pgNum,ones(pgNum,1),pgNum,r); %所有不等式约束对PG求导的模块
dgQ=sparse(1:pvNum,transNum+pgNum+1:transNum+pgvNum,ones(pvNum,1),pvNum,r); %所有不等式约束对QR求导的模块
dgcapK=sparse(1:capNum,transNum+pgvNum+1:transNum+pgvNum+capNum,ones(capNum,1),capNum,r);%所有不等式约束对capK求导的模块
dgve=2*diagE;
dgvf=2*diagF;
sizeG=size(G);
GIJ=G(sub2ind(sizeG,lineI,lineJ));
BIJ=B(sub2ind(sizeG,lineI,lineJ));
dgleI=(2*e(lineI)-e(lineJ)).*GIJ+f(lineJ).*BIJ;
dgleJ=-e(lineI).*GIJ-f(lineI).*BIJ;
dglfI=(2*f(lineI)-f(lineJ)).*GIJ-e(lineJ).*BIJ;
dglfJ=-f(lineI).*GIJ+e(lineI).*BIJ;
dgle=sparse(lineI,(1:lineNum),dgleI,nodeNum,lineNum)+sparse(lineJ,(1:lineNum),dgleJ,nodeNum,lineNum);
dglf=sparse(lineI,(1:lineNum),dglfI,nodeNum,lineNum)+sparse(lineJ,(1:lineNum),dglfJ,nodeNum,lineNum);
dg0=sparse(m,transNum+pgvNum+capNum);
dgvl=[dgve dgle;dgvf dglf];
dgef=[dg0 dgvl]; %所有不等式约束对电压实部、虚部求偏导的模块
dgx=[dgT;dgP;dgQ;dgcapK;dgef]; %不等式约束雅克比矩阵
%% 形成对角阵
Z=sparse(1:r,1:r,z,r,r);
W=sparse(1:r,1:r,w,r,r);
L1=sparse(1:r,1:r,1./l,r,r);
U1=sparse(1:r,1:r,1./u,r,r);
LZ=L1*Z;
UW=U1*W;
%% 形成海森伯矩阵
%目标函数的海森伯矩阵▽2f(x)
if(opfGoal==2)
HSdfx=sparse(xNum,xNum);
else if(opfGoal==1)
HSdfx=sparse(transNum+1:transNum+pgNum,transNum+1:transNum+pgNum,2*a(pgNode),xNum,xNum);%仅目标函数对PG求偏导处的对角元为非零元素，其他都为0
else if(opfGoal==3)
d2ftei=-2*transG.*(e(transI)-e(transJ));
d2ftej=-d2ftei;
d2ftfi=-2*transG.*(f(transI)-f(transJ));
d2ftfj=-d2ftfi;
d2fte=sparse(1:transNum,transI,d2ftei,transNum,nodeNum)+sparse(1:transNum,transJ,d2ftej,transNum,nodeNum);
d2ftf=sparse(1:transNum,transI,d2ftfi,transNum,nodeNum)+sparse(1:transNum,transJ,d2ftfj,transNum,nodeNum);
d2fT0=sparse(transNum,transNum+pgvNum+capNum);
d2fT=[d2fT0 d2fte d2ftf];
d2fPGQR=sparse(pgvNum,xNum);
d2fcapK=sparse(capNum,xNum);
d2fee=2*(G-sparse(1:nodeNum,1:nodeNum,sum(G,2),nodeNum,nodeNum));
d2fff=d2fee;
zero_nodeNum=sparse(nodeNum,nodeNum);
d2f_ef_ef=[d2fee zero_nodeNum;zero_nodeNum d2fff];
d2efT=[d2fte d2ftf]';
d2f_ef=[d2efT sparse(2*nodeNum,pgvNum+capNum) d2f_ef_ef];
HSdfx=[d2fT;d2fPGQR;d2fcapK;d2f_ef];
else if(opfGoal==4)
d2ftei=2*transB.*(e(transI)-e(transJ));
d2ftej=-d2ftei;
d2ftfi=2*transB.*(f(transI)-f(transJ));
d2ftfj=-d2ftfi;
d2fte=sparse(1:transNum,transI,d2ftei,transNum,nodeNum)+sparse(1:transNum,transJ,d2ftej,transNum,nodeNum);
d2ftf=sparse(1:transNum,transI,d2ftfi,transNum,nodeNum)+sparse(1:transNum,transJ,d2ftfj,transNum,nodeNum);
d2fT0=sparse(transNum,transNum+pgvNum+capNum);
d2fT=[d2fT0 d2fte d2ftf];
d2fPGQR=sparse(pgvNum,xNum);
d2fcapK=sparse(capNum,xNum);
d2fee=-2*(B-sparse(1:nodeNum,1:nodeNum,sum(B,2),nodeNum,nodeNum));
d2fff=d2fee;
zero_nodeNum=sparse(nodeNum,nodeNum);
d2f_ef_ef=[d2fee zero_nodeNum;zero_nodeNum d2fff];
d2efT=[d2fte d2ftf]';
d2f_ef=[d2efT sparse(2*nodeNum,pgvNum+capNum) d2f_ef_ef];
HSdfx=[d2fT;d2fPGQR;d2fcapK;d2f_ef];
end
end
end
end
%等式约束海森伯矩阵与拉格朗日乘子y的乘积▽2h(x)*y
y1=y(1:nodeNum,1);
y2=y(nodeNum+1:2*nodeNum,1);
dhT2=2*ef3.*(transG.*y1(transI)-transB.*y2(transI)); %功率方程对变压器变比求二次偏导所得的列向量
HSdhT=sparse(1:transNum,1:transNum,dhT2,transNum+pgvNum+capNum,transNum+pgvNum+capNum);
eiG=e(transI).*transG;
ejG=e(transJ).*transG;
eiB=e(transI).*transB;
ejB=e(transJ).*transB;
fiG=f(transI).*transG;
fjG=f(transJ).*transG;
fiB=f(transI).*transB;
fjB=f(transJ).*transB;
ejG_fjB=ejG-fjB;
ejGfjB=ejG+fjB;
fjGejB=fjG+ejB;
ejB_fjG=ejB-fjG;
eiGfiB=eiG+fiB;
eiG_fiB=eiG-fiB;
eiB_fiG=eiB-fiG;
fiGeiB=fiG+eiB;
dP2_ei_t=(4*eiG.*T-ejG_fjB).*y1(transI)-ejGfjB.*y1(transJ);
dP2_ej_t=-eiGfiB.*y1(transI)-eiG_fiB.*y1(transJ);
dQ2_ei_t=(-4*eiB.*T+fjGejB).*y2(transI)+ejB_fjG.*y2(transJ);
dQ2_ej_t=eiB_fiG.*y2(transI)+fiGeiB.*y2(transJ);
HSdh_et=sparse(1:transNum,transI,dP2_ei_t+dQ2_ei_t,transNum,nodeNum)+sparse(1:transNum,transJ,dP2_ej_t+dQ2_ej_t,transNum,nodeNum);%功率方程先对变比求偏导，再对电压实部求偏导模块
dP2_fi_t=(4*fiG.*T-fjGejB).*y1(transI)+ejB_fjG.*y1(transJ);
dP2_fj_t=eiB_fiG.*y1(transI)-fiGeiB.*y1(transJ);
dQ2_fi_t=(-4*fiB.*T-ejG_fjB).*y2(transI)+ejGfjB.*y2(transJ);
dQ2_fj_t=eiGfiB.*y2(transI)-eiG_fiB.*y2(transJ);
HSdh_ft=sparse(1:transNum,transI,dP2_fi_t+dQ2_fi_t,transNum,nodeNum)+sparse(1:transNum,transJ,dP2_fj_t+dQ2_fj_t,transNum,nodeNum);%功率方程先对变比求偏导，再对电压虚部求偏导模块
HSdh_eft=[HSdh_et HSdh_ft];
HSdh_tef=HSdh_eft';
HSdhPQ=sparse(pgvNum,2*nodeNum); %功率方程先对PG、QR求偏导，再对其他变量求偏导的部分
d2hcap_e=sparse(1:capNum,capI,2*e(capI).*y2(capI),capNum,nodeNum); %功率方程先对capK求偏导，再对e求偏导的部分
d2hcap_f=sparse(1:capNum,capI,2*f(capI).*y2(capI),capNum,nodeNum); %功率方程先对capK求偏导，再对f求偏导的部分
HSdhcap_ef=[d2hcap_e d2hcap_f];
d2htPQ_ef=[HSdh_eft;HSdhPQ;HSdhcap_ef];
HSdhtPQ=[HSdhT d2htPQ_ef];
HSdhx1=sparse(m,pgvNum);
%潮流方程海森矩阵
diagy1=sparse(1:nodeNum,1:nodeNum,y1,nodeNum,nodeNum);
diagy2=sparse(1:nodeNum,1:nodeNum,y2,nodeNum,nodeNum);
HSdhey=-diagy1*G+diagy2*B+(-G*diagy1+B*diagy2);
HSdhefy=diagy1*B+diagy2*G-(B*diagy1+G*diagy2);
HSdhx2=[HSdhey HSdhefy;HSdhefy' HSdhey];
HSdhx=[HSdhtPQ;HSdh_tef HSdhx1 HSdhcap_ef' HSdhx2];
%形成不等式约束二阶偏导的矩阵▽2g(x)*(z+w)
ZWcl=z(transNum+pgvNum+capNum+nodeNum+1:end)+w(transNum+pgvNum+capNum+nodeNum+1:end);
ZWv=z(transNum+pgvNum+capNum+1:transNum+pgvNum+capNum+nodeNum)+w(transNum+pgvNum+capNum+1:transNum+pgvNum+capNum+nodeNum);
dgeiT=((2*e(transI)-e(transJ)).*transG+f(transJ).*transB).*ZWcl(lineNum-transNum+1:end);
dgejT=(-e(transI).*transG-f(transI).*transB).*ZWcl(lineNum-transNum+1:end);
dgeT=sparse(1:transNum,transI,dgeiT,transNum,nodeNum)+sparse(1:transNum,transJ,dgejT,transNum,nodeNum);%不等式约束先对变比求偏导，再对e求偏导的模块
dgfiT=((2*f(transI)-f(transJ)).*transG-e(transJ).*transB).*ZWcl(lineNum-transNum+1:end);
dgfjT=(-f(transI).*transG+e(transI).*transB).*ZWcl(lineNum-transNum+1:end);
dgfT=sparse(1:transNum,transI,dgfiT,transNum,nodeNum)+sparse(1:transNum,transJ,dgfjT,transNum,nodeNum);%不等式约束先对变比求偏导，再对f求偏导的模块
HSdgefT=[dgeT dgfT];
HSdgT=[sparse(transNum,transNum+pgvNum+capNum) HSdgefT];
HSdgee=sparse(lineI,lineI,2*GIJ.*ZWcl,nodeNum,nodeNum)-sparse(lineI,lineJ,GIJ.*ZWcl,nodeNum,nodeNum)...
-sparse(lineJ,lineI,GIJ.*ZWcl,nodeNum,nodeNum)+sparse(1:nodeNum,1:nodeNum,2*ZWv,nodeNum,nodeNum);
HSdgff=HSdgee;
HSdgef=sparse(lineI,lineJ,BIJ.*ZWcl,nodeNum,nodeNum)-sparse(lineJ,lineI,BIJ.*ZWcl,nodeNum,nodeNum);
HSdgfe=HSdgef';
HSdgx1=[HSdgee HSdgef;HSdgfe HSdgff]; %所有不等式约束对e、f求二次偏导模块
HSdgxtPQ_0=sparse(pgvNum+capNum,xNum);
HSdgef_0=[HSdgefT' sparse(2*nodeNum,pgvNum+capNum)];
HSdgx=[HSdgT;HSdgxtPQ_0;HSdgef_0 HSdgx1]; %合成不等式约束海森矩阵
%求和形成H(.)矩阵.
dgxT=dgx'; %求dgx的转置
MULdgx=dgx*(UW-LZ)*dgxT;
H=HSdhx+HSdgx-HSdfx+MULdgx; %求和形成H(.)矩阵.
%% 根据以上所求的各个矩阵合成海森伯矩阵
HSB0=sparse(m,m);
HSB=[H dhx;dhx' HSB0];
balN=transNum+pgvNum+capNum+nodeNum+balNode;
HSB(balN,:)=0; %保持平衡节点电压虚部不变，始终为0，即将海森矩阵中平衡节点虚部所对应的行列元素置0，对角元素置1
HSB(:,balN)=0;
HSB_balN=sub2ind(size(HSB),balN,balN);
HSB(HSB_balN)=ones(balNum,1);
balN1=transNum+pgvNum+capNum+balNode;
HSB(balN1,:)=0; %保持平衡节点电压实部不变，始终为0，即将海森矩阵中平衡节点实部所对应的行列元素置0，对角元素置1
HSB(:,balN1)=0;
HSB_balN1=sub2ind(size(HSB),balN1,balN1);
HSB(HSB_balN1)=ones(balNum,1);
HSB=sparse(HSB);

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function [G,B,transY,transG,transB,transG1,transB1,transNum,lineNum,lineI,lineJ,lineB,transI,transJ,transK0,transKmin,transKmax]=...
formY(nodeNum,mtrLine,mtrGround,mtrTrans,capI,capK)
%程序功能：形成节点导纳矩阵
%编写时间：2010年11月
%变量定义：
%G--电导矩阵,B--电纳矩阵，lineI,lineJ--节点序号，lineR--线路电阻
%lineX--线路电抗，groundI--接地支路节点序号
%groundR--接地支路电阻，groundX--接地支路电抗
%transI，transJ--变压器支路节点序号
%transR--变压器支路电阻，transX--变压器支路电抗
%transK--变压器变比
%transG--变压器支路等效电导，transB--变压器支路等效电纳
%% 利用线路和接地支路参数形成导纳矩阵
lineI=mtrLine(:,2);
lineJ=mtrLine(:,3);
lineR=mtrLine(:,4);
lineX=mtrLine(:,5);
lineB=mtrLine(:,6);
groundI=mtrGround(:,1);
groundX=mtrGround(:,2);
Yij=1./(lineR+j*lineX);
Y1=-sparse(lineI,lineJ,Yij,nodeNum,nodeNum)-sparse(lineJ,lineI,Yij,nodeNum,nodeNum)...
+sparse(lineI,lineI,Yij+j*lineB,nodeNum,nodeNum)+sparse(lineJ,lineJ,Yij+j*lineB,nodeNum,nodeNum)...
+sparse(groundI,groundI,j*groundX,nodeNum,nodeNum)+sparse(capI,capI,j*capK,nodeNum,nodeNum);
%% 加入变压器支路修改导纳矩阵
transIall=mtrTrans(:,2);
transJall=mtrTrans(:,3);
transR=mtrTrans(:,4);
transX=mtrTrans(:,5);
transK0all=mtrTrans(:,6);
lineNum=length(lineI)+length(transIall);
transY=1./(transR+j*transX);
Y1=Y1-sparse(transIall,transJall,transY./transK0all,nodeNum,nodeNum)-sparse(transJall,transIall,transY./transK0all,nodeNum,nodeNum)...
+sparse(transIall,transIall,transY./transK0all./transK0all,nodeNum,nodeNum)+sparse(transJall,transJall,transY,nodeNum,nodeNum);
Yt=sparse(transIall,transJall,-transY,nodeNum,nodeNum); %这样处理是因为有两台变压器两端的节点号相同，避免在更新节点导纳矩阵时只识别一台变压器
transIJ=sub2ind(size(Yt),transIall,transJall);
transYt=Yt(transIJ);
transCtrl=mtrTrans(:,9);
ctrTransNum=find(transCtrl);
transI=transIall(ctrTransNum);
transJ=transJall(ctrTransNum);
transKmax=1/0.9*ones(size(transI));
transKmin=1/1.1*ones(size(transI));
transK0=transK0all(ctrTransNum);
transG=real(transYt(ctrTransNum));
transB=imag(transYt(ctrTransNum));
transG1=-real(transY(ctrTransNum)); %之所以要取负号是因为transG、transB是作为导纳矩阵中的互导纳来用，在计算自导纳的时候注意要用-transG、-transB!!!!
transB1=-imag(transY(ctrTransNum));
transNum=length(transI);
lineI=[lineI;transI]; %将线路和变压器支路的编号合并，在后面线路约束的时候同时处理
lineJ=[lineJ;transJ];
lineNum=lineNum-length(transIall)+transNum;
%% 求节点导纳的幅值和相角
[Yrows,Ycols,Y1] = find(Y1);
G=real(Y1);
B=imag(Y1);
G=sparse(Yrows,Ycols,G,nodeNum,nodeNum);
B=sparse(Yrows,Ycols,B,nodeNum,nodeNum);

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function [G,B,lineI,lineJ,lineB,transI,transJ,transK0,transNum,transKmin,transKmax,capI,capGi,capBi,capK,capKmin,capKmax,capNum,transG,transB,transG1,transB1,lineNum]=...
formY_RPP(nodeNum,lineNum,mtrLine,mtrGround,mtrTrans,mtrCapacitor)
%程序功能：形成节点导纳矩阵
%编写时间：2010年11月
%变量定义：
%% 利用线路和接地支路参数形成导纳矩阵
%线路参数
lineI=mtrLine(:,2);
lineJ=mtrLine(:,3);
lineR=mtrLine(:,4);
lineX=mtrLine(:,5);
lineB=mtrLine(:,6);
%接地支路数据
groundI=mtrGround(:,2);
groundG=mtrGround(:,3);
groundB=mtrGround(:,4);
%电容器参数
capCtrl=mtrCapacitor(:,2);
capCtrl=ones(length(capCtrl),1);
capIall=mtrCapacitor(:,3);
capGiall=mtrCapacitor(:,4);
capBiall=mtrCapacitor(:,5);
capKall=mtrCapacitor(:,6);
capKminall=mtrCapacitor(:,7);
capKmaxall=mtrCapacitor(:,8);
Yij=1./(lineR+j*lineX);
Y1=-sparse(lineI,lineJ,Yij,nodeNum,nodeNum)-sparse(lineJ,lineI,Yij,nodeNum,nodeNum)...
+sparse(lineI,lineI,Yij+j*lineB,nodeNum,nodeNum)+sparse(lineJ,lineJ,Yij+j*lineB,nodeNum,nodeNum)...
+sparse(groundI,groundI,groundG+j*groundB,nodeNum,nodeNum)...
+sparse(capIall,capIall,j*capKall,nodeNum,nodeNum);
%保留可调电容电抗器参数
capCtrlNode=find(capCtrl);
capI=capIall(capCtrlNode);
capGi=capGiall(capCtrlNode);
capBi=capBiall(capCtrlNode);
capK=capKall(capCtrlNode);
capKmin=capKminall(capCtrlNode);
capKmax=capKmaxall(capCtrlNode);
capNum=length(capI);
%% 加入变压器支路修改导纳矩阵
transCtrl=mtrTrans(:,2);
transIall=mtrTrans(:,3);
transJall=mtrTrans(:,4);
transR=mtrTrans(:,5);
transX=mtrTrans(:,6);
transK0all=mtrTrans(:,7);
transY=1./(transR+j*transX);
Y1=Y1-sparse(transIall,transJall,transY./transK0all,nodeNum,nodeNum)-sparse(transJall,transIall,transY./transK0all,nodeNum,nodeNum)...
+sparse(transIall,transIall,transY./transK0all./transK0all,nodeNum,nodeNum)+sparse(transJall,transJall,transY,nodeNum,nodeNum);
Yt=sparse(transIall,transJall,-transY,nodeNum,nodeNum); %这样处理是因为有两台变压器两端的节点号相同，避免在更新节点导纳矩阵时只识别一台变压器
transIJ=sub2ind(size(Yt),transIall,transJall);
transYt=Yt(transIJ);
%保留可调变压器参数
ctrTransNum=find(transCtrl);
transI=transIall(ctrTransNum);
transJ=transJall(ctrTransNum);
transKmax=1/0.9*ones(size(transI));
transKmin=1/1.1*ones(size(transI));
transK0=transK0all(ctrTransNum);
transG=real(transYt(ctrTransNum));
transB=imag(transYt(ctrTransNum));
transG1=-real(transY(ctrTransNum)); %之所以要取负号是因为transG、transB是作为导纳矩阵中的互导纳来用，在计算自导纳的时候注意要用-transG、-transB!!!!
transB1=-imag(transY(ctrTransNum));
transNum=length(transI);
lineI=[lineI;transI]; %将线路和变压器支路的编号合并，在后面线路约束的时候同时处理
lineJ=[lineJ;transJ];
lineNum=lineNum+transNum;
%% 求节点导纳的幅值和相角
[Yrows,Ycols,Y1] = find(Y1);
G=real(Y1);
B=imag(Y1);
G=sparse(Yrows,Ycols,G,nodeNum,nodeNum);
B=sparse(Yrows,Ycols,B,nodeNum,nodeNum);

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function [mk,meritF,stepp,stepd]=linesearch(r,nodeNum,balNode,pgNum,pvNum,pgvNum,xNum,transNum,pgNode,pvNode,m,x,y,z,l,u,w,G,B,transI,transJ,transG,...
transB,transG1,transB1,Tn,capKn,capNum,capI,Tn1,capKn1,PG,QR,Pg,Qg,dx,dl,du,dy,dz,dw,opfGoal,Gama,Arlfa,meritF,k2,mu,T,capK,lineNum,lineI,...
lineJ,Pd,Qd,gxx,gsx,mut,mub,stepp,stepd)
%程序功能：光滑处理过程，求步长
%编写时间：2010年11月
mk=0;
kk=k2;
isOK=0;
while isOK==0&&mk<10
%更新临时变量
xk=x+Arlfa.^mk*dx;
lk=l+Arlfa.^mk*dl;
uk=u+Arlfa.^mk*du;
yk=y+Arlfa.^mk*dy;
zk=z+Arlfa.^mk*dz;
wk=w+Arlfa.^mk*dw;
%更新临时控制变量和状态变量的值
Tlastk=T;
capKlastk=capK;
T=xk(1:transNum,1);
capK=xk(transNum+pgvNum+1:transNum+pgvNum+capNum);
PG(pgNode,1)=xk(transNum+1:transNum+pgNum,1);
QR(pvNode,1)=xk(transNum+pgNum+1:transNum+pgNum+pvNum,1);
e=xk(transNum+pgNum+pvNum+capNum+1:transNum+pgNum+pvNum+capNum+nodeNum,1);
f=xk(transNum+pgNum+pvNum+capNum+nodeNum+1:xNum,1);
%变比变化后需修正节点导纳矩阵
G=G-sparse(transI,transI,(T.*T-Tlastk.*Tlastk).*transG1,nodeNum,nodeNum)...
+sparse(transI,transJ,transG1.*(T-Tlastk),nodeNum,nodeNum)...
+sparse(transJ,transI,transG1.*(T-Tlastk),nodeNum,nodeNum);
B=B-sparse(transI,transI,(T.*T-Tlastk.*Tlastk).*transB1,nodeNum,nodeNum)...
+sparse(transI,transJ,transB1.*(T-Tlastk),nodeNum,nodeNum)...
+sparse(transJ,transI,transB1.*(T-Tlastk),nodeNum,nodeNum)...
+sparse(capI,capI,capK-capKlastk,nodeNum,nodeNum);
%% 形成等式约束雅可比矩阵
Ezu=exp(-(T-Tn)./mut);
Ezu_1=exp(-(Tn1-T)./mut);
dT_Zt=1;
dNCPT=-mut.*log(Ezu+Ezu_1); %变比对应的凝聚函数常数项
dNCPT_dt=(Ezu-Ezu_1)./(Ezu+Ezu_1); %凝聚函数对T求一次偏导
transGmut=transG.*dT_Zt;
transBmut=transB.*dT_Zt;
Ezbu=exp((capKn-capK)./mub);
Ezbu_1=exp((capK-capKn1)./mub);
dNCPcap=-mub.*log(Ezbu+Ezbu_1); %电容电抗器对应的凝聚函数常数项
dNCP_dcap=(Ezbu-Ezbu_1)./(Ezbu+Ezbu_1); %凝聚函数对capK求一次偏导
ef1=e(transI).*e(transJ)+f(transI).*f(transJ);
ef2=e(transI).*f(transJ)-e(transJ).*f(transI);
ef3=e(transI).*e(transI)+f(transI).*f(transI);
ef1G=ef1.*transGmut;
ef1B=ef1.*transBmut;
ef2G=ef2.*transGmut;
ef2B=ef2.*transBmut;
dhPTi=-ef1G+ef2B+2*ef3.*transGmut.*T;
dhPTj=-ef1G-ef2B;
dhPT=sparse(1:transNum,transI,dhPTi,transNum,nodeNum)+sparse(1:transNum,transJ,dhPTj,transNum,nodeNum);%有功平衡方程P对变压器变比求偏导
dhQTi=ef1B+ef2G-2*ef3.*transBmut.*T;
dhQTj=ef1B-ef2G;
dhQT=sparse(1:transNum,transI,dhQTi,transNum,nodeNum)+sparse(1:transNum,transJ,dhQTj,transNum,nodeNum);%无功平衡方程Q对变压器变比求偏导
dhNCP_T=sparse(1:transNum,1:transNum,dNCPT_dt,transNum,transNum+capNum);
dhP=sparse(1:pgNum,pgNode,ones(pgNum,1),pgNum,m);
dhQ1=sparse(1:pvNum,pvNode,ones(pvNum,1),pvNum,m-nodeNum);
dhQ=[sparse(pvNum,nodeNum) dhQ1];
dhcapK1=sparse(1:capNum,capI,(e(capI).^2+f(capI).^2),capNum,nodeNum); %2011年10月5日修改，去掉.*capBi_dBci
dhNCP_capK=sparse(1:capNum,transNum+1:transNum+capNum,dNCP_dcap,capNum,transNum+capNum);
dhcapK=[sparse(capNum,nodeNum) dhcapK1 dhNCP_capK];
%形成功率方程雅可比矩阵
H1=G*e-B*f;
N1=G*f+B*e;
diagE=sparse(1:nodeNum,1:nodeNum,e,nodeNum,nodeNum);
diagF=sparse(1:nodeNum,1:nodeNum,f,nodeNum,nodeNum);
deG=diagE*G;
dfB=diagF*B;
deB=diagE*B;
dfG=diagF*G;
dH1=sparse(1:nodeNum,1:nodeNum,H1,nodeNum,nodeNum);
dN1=sparse(1:nodeNum,1:nodeNum,N1,nodeNum,nodeNum);
Hij=-dH1-deG-dfB;
Nij=-dN1+deB-dfG;
Jij=dN1-dfG+deB;
Lij=-dH1+dfB+deG;
dhJacb=[Hij Nij;Jij Lij]'; %合并形成功率方程的雅可比矩阵
dhT=[dhPT dhQT dhNCP_T]; %合并形成等式约束雅可比矩阵h(x)
dhx=[dhT;dhP;dhQ;dhcapK;dhJacb sparse(2*nodeNum,transNum+capNum)];
%% 形成不等式约束雅可比矩阵▽g(x)
gtransNum=0; %变比上下限约束维数，用NCP函数后，则不需要再约束其上下限
gcapNum=0;
dgT1=sparse(transNum,r-lineNum);
dglT=(e(transI).^2+f(transI).^2-e(transI).*e(transJ)-f(transI).*f(transJ)).*transGmut+(e(transI).*f(transJ)-e(transJ).*f(transI)).*transBmut;
dgT2=sparse(1:transNum,lineNum-transNum+1:lineNum,dglT,transNum,lineNum);
dgT=[dgT1 dgT2]; %所有不等式约束对T求导的模块
dgP=sparse(1:pgNum,gtransNum+1:gtransNum+pgNum,ones(pgNum,1),pgNum,r); %所有不等式约束对P求导的模块
dgQ=sparse(1:pvNum,gtransNum+pgNum+1:gtransNum+pgvNum,ones(pvNum,1),pvNum,r);%所有不等式约束对Q求导的模块
dgcapK=sparse(capNum,r); %所有不等式约束对capK求导的模块
dgve=2*diagE;
dgvf=2*diagF;
sizeG=size(G);
GIJ=G(sub2ind(sizeG,lineI,lineJ));
BIJ=B(sub2ind(sizeG,lineI,lineJ));
dgleI=(2*e(lineI)-e(lineJ)).*GIJ+f(lineJ).*BIJ;
dgleJ=-e(lineI).*GIJ-f(lineI).*BIJ;
dglfI=(2*f(lineI)-f(lineJ)).*GIJ-e(lineJ).*BIJ;
dglfJ=-f(lineI).*GIJ+e(lineI).*BIJ;
dgle=sparse(lineI,(1:lineNum),dgleI,nodeNum,lineNum)+sparse(lineJ,(1:lineNum),dgleJ,nodeNum,lineNum);
dglf=sparse(lineI,(1:lineNum),dglfI,nodeNum,lineNum)+sparse(lineJ,(1:lineNum),dglfJ,nodeNum,lineNum);
dg0=sparse(2*nodeNum,gtransNum+pgvNum+gcapNum);
dgvl=[dgve dgle;dgvf dglf];
dgef=[dg0 dgvl]; %所有不等式约束对电压实部、虚部求偏导的模块
dgx=[dgT;dgP;dgQ;dgcapK;dgef]; %不等式约束雅克比矩阵
%% 形成对角阵
Z=sparse(1:r,1:r,zk,r,r);
W=sparse(1:r,1:r,wk,r,r);
L1=sparse(1:r,1:r,1./lk,r,r);
U1=sparse(1:r,1:r,1./uk,r,r);
LZ=L1*Z;
UW=U1*W;
Ll=(lk.*zk-mu*ones(r,1));
Lu=(uk.*wk+mu*ones(r,1));
%% 形成目标函数一阶偏导矩阵▽f(.)
if(opfGoal==2)
dPG=ones(pgNum,1);
dfx=sparse(transNum+1:transNum+pgNum,ones(pgNum,1),dPG,xNum,1);
else if(opfGoal==1)
dPG=2*a(pgNode).*PG(pgNode)+b(pgNode);
dfx=sparse(transNum+1:transNum+pgNum,ones(pgNum,1),dPG,xNum,1);
else if(opfGoal==3)
dfT=-1*transG.*dT_Zt.*((f(transI)-f(transJ)).^2+(e(transI)-e(transJ)).^2);
dfPQ=zeros(pgvNum,1);
dfcapK=zeros(capNum,1);
EE=e*ones(1,nodeNum);
FF=f*ones(1,nodeNum);
dfe=2*sum(G.*(EE-EE'));
dff=2*sum(G.*(FF-FF'));
dfx=[dfT;dfPQ;dfcapK;dfe';dff'];
else if(opfGoal==4)
dfT=1*transB.*dT_Zt.*((f(transI)-f(transJ)).^2+(e(transI)-e(transJ)).^2);
dfPQ=zeros(pgvNum,1);
dfcapK=zeros(capNum,1);
EE=e*ones(1,nodeNum);
FF=f*ones(1,nodeNum);
dfe=-2*sum(B.*(EE-EE'));
dff=-2*sum(B.*(FF-FF'));
dfx=[dfT;dfPQ;dfcapK;dfe';dff'];
end
end
end
end
%% 不等式约束项
gxv=[PG(pgNode);QR(pvNode);e.^2+f.^2];
gxl=(e(lineI).*e(lineI)+f(lineI).*f(lineI)-e(lineI).*e(lineJ)-f(lineI).*f(lineJ)).*GIJ+(e(lineI).*f(lineJ)-e(lineJ).*f(lineI)).*BIJ;%线路功率当前值
gx=[gxv;gxl]; %约束条件当前值
Lz=gx-lk-gxx;
Lw=gx+uk-gsx;
muUL=mu*(U1-L1);
BB1=UW*Lw-LZ*Lz-muUL*ones(r,1);
BB=dhx*yk-dfx+dgx*BB1;
BB(transNum+pgvNum+capNum+nodeNum+balNode,1)=0; %保持平衡节点电压虚部不变，始终为0，则常数项平衡节点处置0
BB(transNum+pgvNum+capNum+balNode,1)=0;
%% 等式约束不平衡量
Pg(pgNode)=PG(pgNode);
Qg(pvNode)=QR(pvNode);
P=Pg-Pd;
Q=Qg-Qd;
dP=P-diagE*H1-diagF*N1;
dQ=Q-diagF*H1+diagE*N1;
hx=[dP;dQ;dNCPT;dNCPcap]; %修正方程常数项h(x)
const=[BB;hx]; %修正方程常数项向量
L3=-L1*(Z*Lz+Ll);
L4=U1*(W*Lw-Lu);
L5=Lz;
L6=Lw;
f_NCP=[const;L3;L4;L5;L6];
f_NCPsum=(f_NCP'*f_NCP)/2;
maxfk=max(meritF(kk-min(10,kk)+1:end));
f3=maxfk-Gama*(Arlfa.^mk)*meritF(kk);
if f_NCPsum<=f3
isOK=1; %满足条件，跳出
else
mk=mk+1; %不满足条件，继续搜索
end
end
stepp=stepp*Arlfa.^mk;
stepd=stepd*Arlfa.^mk;

125
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function [mut,mub,dNCPT,dNCPT_dt,d2NCPT_dt2,dT_Zt,transGmut,transBmut,dNCPcap,dNCP_dcap,d2NCP_dcap2,capBi_dBci,H1,N1,diagE,diagF,hx,Gap,max_hx,fx,...
Pg,Qg,xz1,dmaxOut1,xz2,dmaxOut2,xz3,dmaxOut3,xz4,dmaxOut4,PGR,Tn,kt0,capKn,q0,Tn1,capKn1,T,G]=midResult(nodeNum,pgNode,opfGoal,z,l,u,w,Pg,Qg,...
e,f,G,B,a,b,c,PG,Pd,Qd,k,xz1,dmaxOut1,xz2,dmaxOut2,xz3,dmaxOut3,xz4,dmaxOut4,times,mut,mub,oneTrans,oneCap,para3,accuracy,T,capK,transKmin,transKmax,...
capKmin,capBi,mu,transNum,transG,transB,Tn,Tn1,capKn,capKn1,kt0,q0,mismatch)
%程序功能：计算每次迭代后的目标函数值和等式约束的最大不平衡量，并根据每步迭代结果修正光滑参数
%编写时间：2010年11月
Gap=l'*z-u'*w; %计算互补间隙
PGR=PG;
if(opfGoal==2)
sumP=sum(Pg);
sumPd=sum(Pd);
fx=sumP-sumPd;
else if(opfGoal==1)
fx=sum(a(pgNode).*PGR(pgNode).*PGR(pgNode)+b(pgNode).*PGR(pgNode)+c(pgNode));
else if(opfGoal==3)
EE=e*ones(1,nodeNum);
FF=f*ones(1,nodeNum);
fx=-0.5*sum(sum(G.*((EE-EE').^2+(FF-FF').^2),2));
else if(opfGoal==4)
EE=e*ones(1,nodeNum);
FF=f*ones(1,nodeNum);
fx=0.5*sum(sum(B.*((EE-EE').^2+(FF-FF').^2),2));
end
end
end
end
H1=G*e-B*f;
N1=G*f+B*e;
diagE=sparse(1:nodeNum,1:nodeNum,e,nodeNum,nodeNum);
diagF=sparse(1:nodeNum,1:nodeNum,f,nodeNum,nodeNum);
P=Pg-Pd;
Q=Qg-Qd;
dP=P-diagE*H1-diagF*N1;
dQ=Q-diagF*H1+diagE*N1;
firstOK=0;
hx=[dP;dQ];
tmpmax_hx=max(abs(hx));
if Gap<accuracy&&tmpmax_hx<mismatch&& times==1 %判断互补间隙和最大不平衡量是否达到精度
firstOK=1;
times=2;
maxTap=5; %变压器最大调节档位
K=1./T;
Kmax=1./transKmin;
Kmin=1./transKmax;
kt0=(Kmax-Kmin)/(maxTap-1); %变压器单位调节幅度
Kn=fix((K-Kmin)./kt0).*kt0+Kmin; %获取变压器变比连续最优解左右两侧的档位所对应的变比
Kn1=Kn+kt0;
Tn=1./Kn1;
Tn1=1./Kn;
q0=1; %电容器档位的单位调节幅度
capQmin=capKmin.*capBi;
capKn=fix((capK-capQmin)./capBi).*capBi+capQmin; %获取电容电抗器投入组数连续最优解左右两侧的离散值
capKn1=capKn+capBi;
end
if times==2
%% 修正陡度参数μt
tmpmu=para3;
tmpmut=mut;
tmpmub=mub;
Ezu=exp(-(T-Tn)./tmpmut);
Ezu_1=exp(-(Tn1-T)./tmpmut);
dNCPT=-tmpmut.*log(Ezu+Ezu_1); %变压器变比对应的凝聚函数常数项
Ezbu=exp((capKn-capK)./tmpmub);
Ezbu_1=exp((capK-capKn1)./tmpmub);
dNCPcap=-tmpmub.*log(Ezbu+Ezbu_1); %电容电抗器投入组数对应的凝聚函数常数项
dNCP=[dNCPT;dNCPcap];%只有一个光滑参数
oneTC=[oneTrans;oneCap];
mutb=[mut;mub];
mutb=min(max(mu,max(abs(dNCP)))*oneTC,tmpmu*mutb.*oneTC); %修正光滑参数
mut=mutb(1:transNum);
mub=mutb(transNum+1:end);
%% 计算凝聚函数相关参数
Ezu=exp(-(T-Tn)./mut);
Ezu_1=exp(-(Tn1-T)./mut);
dNCPT=-mut.*log(Ezu+Ezu_1); %变压器变比对应的凝聚函数常数项
dT_Zt=1;
dNCPT_dt=(Ezu-Ezu_1)./(Ezu+Ezu_1); %凝聚函数对tij求一次偏导
d2NCPT_dt2=-(oneTrans-dNCPT_dt.^2)./mut; %凝聚函数对tij求二次偏导,原来的公式推导错误d2NCPT_dt2=-(oneTrans+dNCPT_dt.^2)./mut;3月7日修改
transGmut=transG;
transBmut=transB;
Ezbu=exp((capKn-capK)./mub);
Ezbu_1=exp((capK-capKn1)./mub);
dNCPcap=-mub.*log(Ezbu+Ezbu_1); %电容电抗器投入组数对应的凝聚函数常数项
dcapK_Zb=1;
dNCP_dcap=(Ezbu-Ezbu_1)./(Ezbu+Ezbu_1); %凝聚函数对capK求一次偏导
d2NCP_dcap2=-(oneCap-dNCP_dcap.^2)./mub; %凝聚函数对capK求二次偏导
capBi_dBci=capBi.*dcapK_Zb;
end
if times==1
dNCPT=[];dNCPT_dt=[];d2NCPT_dt2=[];dT_Zt=[];transGmut=[];transBmut=[];dNCPcap=[];dNCP_dcap=[];d2NCP_dcap2=[];capBi_dBci=[];
end
hx=[dP;dQ;dNCPT;dNCPcap];
fx=full(fx);
max_hx=full(max(abs(hx)));
if firstOK==1
max_hx=full(tmpmax_hx);
end
fprintf('%4.0f %4.4e %4.4e %7.6f\n',k,Gap,max_hx,fx); %输出每次迭代结果
%% 保留每次迭代的互补间隙和最大不平衡量
if times==1
xz1=[xz1 k];
dmaxOut1=[dmaxOut1 Gap];
xz3=[xz3 k];
dmaxOut3=[dmaxOut3 max_hx];
end
if times==2
if firstOK==1
xz1=[xz1 k];
dmaxOut1=[dmaxOut1 Gap];
xz3=[xz3 k];
dmaxOut3=[dmaxOut3 max_hx];
firstOK=0;
else
xz2=[xz2 k];
dmaxOut2=[dmaxOut2 Gap];
xz4=[xz4 k];
dmaxOut4=[dmaxOut4 max_hx];
end
end

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function [nodeNum,lineNum,capacity,kmax,centrPara,accuracy,opfGoal,balNum,balNode,mtrLine,mtrGround,mtrTrans,runPara,Pg,Qg,Pd,Qd,pvNum,pvNode,pvV,...
pvQmin,pvQmax,pgNumall,pgNodeall,pgNum,pgNode,a,b,c,Pmin,Pmax,capNum,capI,capGi,capBi,capK,capKmin,capKmax,Vmin,Vmax]=readData(data)
%程序功能：读取数据
%编写时间：2010年11月
%% 读取系统参数
nodeNum=data(1,1); %系统节点数
lineNum=data(1,2); %线路变压器数
capacity=data(1,3); %基准容量
kmax=data(1,4); %最大迭代次数
centrPara=data(1,5); %中心参数
accuracy=data(2,1); %计算精度
opfGoal=data(2,2); %目标函数类型
balNum=data(3,1); %平衡节点数
balNode=data(3,2); %平衡节点编号
%% 获取首列元素为0的行号
zeroIndex=find(data(:,1)==0);
%% 读取线路参数
mtrLine=data(zeroIndex(1)+1:zeroIndex(2)-1,:);
%% 读取接地支路参数
mtrGround=data(zeroIndex(2)+1:zeroIndex(3)-1,:);
%% 读取变压器支路参数
mtrTrans=data(zeroIndex(3)+1:zeroIndex(4)-1,:);
%% 读取运行参数
runPara=data(zeroIndex(4)+1:zeroIndex(5)-1,:);
pqNode=runPara(:,1);
Pg=sparse(nodeNum,1);
Qg=Pg;Pd=Pg;Qd=Pg;
Pg(pqNode)=runPara(:,2)/capacity; %节点有功出力
Qg(pqNode)=runPara(:,3)/capacity; %节点无功出力
Pd(pqNode)=runPara(:,4)/capacity; %节点有功负荷
Qd(pqNode)=runPara(:,5)/capacity; %节点无功负荷
%% 读取PV节点和平衡节点参数
mtrPV=data(zeroIndex(5)+1:zeroIndex(6)-1,:);
pvNum=zeroIndex(6)-zeroIndex(5)-1;
pvNode=sparse(mtrPV(:,1),ones(pvNum,1),mtrPV(:,1),nodeNum,1);
pvNode=find(pvNode); %PV节点和平衡节点编号
pvV=sparse(mtrPV(:,1),ones(pvNum,1),mtrPV(:,2),nodeNum,1); %PV节点和平衡节点给定电压
pvQmin=sparse(mtrPV(:,1),ones(pvNum,1),mtrPV(:,3),nodeNum,1)/capacity; %无功出力下限
pvQmax=sparse(mtrPV(:,1),ones(pvNum,1),mtrPV(:,4),nodeNum,1)/capacity; %无功出力上限
%% 读取经济参数
economyPara=data(zeroIndex(6)+1:zeroIndex(7)-1,:);
[ecoRow,ecoCol]=size(economyPara);
if ecoCol==7
pgctrl=find(economyPara(:,7)); %可调发电机的下标
else
pgctrl=1:ecoRow;
end
pgNumall=zeroIndex(7)-zeroIndex(6)-1; %发电机台数
pgNodeall=economyPara(:,1); %发电机节点号
pgNum=length(pgctrl); %可调发电机台数
pgNode=pgNodeall(pgctrl); %可调发电机节点号
c=sparse(economyPara(:,1),ones(pgNum,1),economyPara(:,2),nodeNum,1);
b=sparse(economyPara(:,1),ones(pgNum,1),economyPara(:,3),nodeNum,1);
a=sparse(economyPara(:,1),ones(pgNum,1),economyPara(:,4),nodeNum,1);
Pmin=sparse(economyPara(:,1),ones(pgNum,1),economyPara(:,5),nodeNum,1)/capacity;%发电机有功出力下限
Pmax=sparse(economyPara(:,1),ones(pgNum,1),economyPara(:,6),nodeNum,1)/capacity;%发电机有功出力上限
%% 读可调电容器组参数
capPara=data(zeroIndex(7)+1:zeroIndex(8)-1,:);
capNum=zeroIndex(8)-zeroIndex(7)-1;
capI=capPara(:,2); %电容器投入节点编号
capGi=capPara(:,3); %可调电容器单位电导
capBi=capPara(:,4); %可调电容器单位电纳
capK=capPara(:,5); %初始电纳值
capKmin=capPara(:,6); %电容器最小档位
capKmax=capPara(:,7); %电容器最大档位
Vmin=0.9*ones(nodeNum,1); %节点电压下限
Vmax=1.07*ones(nodeNum,1); %节点电压上限

72
NCP函数法/readData_RPP.m Normal file
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function [nodeNum,lineNum,capacity,kmax,accuracy,balNum,balNode,mtrLine,mtrGround,mtrTrans,runPara,Pg,Qg,Pd,Qd,pvNum,pvNode,pvV,pvQmin,pvQmax,...
mtrCapacitor,pgNum,pgNode,a,b,c,Pmin,Pmax,Vmin,Vmax,centrPara]=readData_RPP(data)
%程序功能：读取数据
%编写时间：2010年11月
%% 获取首列元素为0的行号
zeroIndex=find(data(:,1)==0);
%% 读取系统参数
nodeNum=data(1,1); %系统节点数
capacity=data(1,3); %基准容量
accuracy=data(1,4); %计算精度
balNum=zeroIndex(2)-zeroIndex(1)-1; %平衡节点数
balNode=data(zeroIndex(1)+1:zeroIndex(2)-1,2); %平衡节点编号
kmax=100; %最大迭代次数
centrPara=0.1; %中心参数
%% 读取线路参数
mtrLine=data(zeroIndex(2)+1:zeroIndex(3)-1,:);
lineNum=length(mtrLine);
%% 读取变压器支路参数
mtrTrans=data(zeroIndex(3)+1:zeroIndex(4)-1,:);
%% 读取接地支路参数
mtrGround=data(zeroIndex(5)+1:zeroIndex(6)-1,:);
%% 读可调电容器参数
mtrCapacitor=data(zeroIndex(6)+1:zeroIndex(7)-1,:);
%% 读取运行参数
runPara=data(zeroIndex(8)+1:zeroIndex(9)-1,:);
pqNode=runPara(:,2);
Pg=sparse(nodeNum,1);
Qg=Pg;Pd=Pg;Qd=Pg;
Pg(pqNode)=runPara(:,3); %节点有功出力
Qg(pqNode)=runPara(:,4); %节点无功出力
Pd(pqNode)=runPara(:,5); %节点有功负荷
Qd(pqNode)=runPara(:,6); %节点无功负荷
%% 有功出力限制
mtrPGLimit=data(zeroIndex(9)+1:zeroIndex(10)-1,:);
pgNum=zeroIndex(10)-zeroIndex(9)-1; %发电机台数
pgNode=mtrPGLimit(:,3); %发电机节点号
c=sparse(mtrPGLimit(:,3),ones(pgNum,1),mtrPGLimit(:,8),nodeNum,1);
b=sparse(mtrPGLimit(:,3),ones(pgNum,1),mtrPGLimit(:,9),nodeNum,1);
a=sparse(mtrPGLimit(:,3),ones(pgNum,1),mtrPGLimit(:,10),nodeNum,1);
Pmin=sparse(mtrPGLimit(:,3),ones(pgNum,1),mtrPGLimit(:,4),nodeNum,1); %发电机有功出力下限
Pmax=sparse(mtrPGLimit(:,3),ones(pgNum,1),mtrPGLimit(:,5),nodeNum,1); %发电机有功出力上限
%% 无功出力限制
mtrQGLimit=data(zeroIndex(11)+1:zeroIndex(12)-1,:);
pvNum=zeroIndex(12)-zeroIndex(11)-1;
pvNode=sparse(mtrQGLimit(:,3),ones(pvNum,1),mtrQGLimit(:,3),nodeNum,1);
pvNode=find(pvNode); %PV节点和平衡节点编号
pvV=sparse(mtrQGLimit(:,3),ones(pvNum,1),mtrQGLimit(:,4),nodeNum,1); %PV节点和平衡节点给定电压
pvQmin=sparse(mtrQGLimit(:,3),ones(pvNum,1),mtrQGLimit(:,5),nodeNum,1); %无功出力下限
pvQmax=sparse(mtrQGLimit(:,3),ones(pvNum,1),mtrQGLimit(:,6),nodeNum,1); %无功出力上限
%% 电压限制
mtrVLimit=data(zeroIndex(13)+1:zeroIndex(14)-1,:);
VLimitNum=zeroIndex(14)-zeroIndex(13)-1; %电压限制的节点数
Vmin=sparse(mtrVLimit(:,2),ones(VLimitNum,1),mtrVLimit(:,3),nodeNum,1);
Vmax=sparse(mtrVLimit(:,2),ones(VLimitNum,1),mtrVLimit(:,4),nodeNum,1);
Vmin=0.9*ones(nodeNum,1); %非电压监测点电压限制
Vmax=1.15*ones(nodeNum,1);
node_Z=data(zeroIndex(14)+1:zeroIndex(15)-1,1); %变压器中性点，这些点的电压不考核，设置为0.8-1.2
Vmin(node_Z)=0.85;
Vmax(node_Z)=1.15;
node_220=data(zeroIndex(15)+1:zeroIndex(16)-1,1); %220kV及以上节点
Vmin(node_220)=0.95;
Vmax(node_220)=1.1;
node_750=data(zeroIndex(16)+1:zeroIndex(17)-1,1); %750kV节点
Vmin(node_750)=1;
Vmax(node_750)=1.1;
node_Monitor=data(zeroIndex(17)+1:zeroIndex(18)-1,1); %发电厂升压变以及800kV变电站220、363kV母线节点，电压监测点
Vmin(node_Monitor)=1;
Vmax(node_Monitor)=1.1;

212
NCP函数法/result_IEEE118.dat Normal file
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@ -0,0 +1,212 @@
33 8.7205e-006 0.780222 0.778376 0.5881 2.9858e-006 1
0
8 5 0.9500 0.9739 1.0000 0.9500
25 26 1.0000 1.0133 1.0500 1.0000
17 30 1.0000 1.0052 1.0500 1.0000
37 38 1.0000 1.0102 1.0500 1.0000
59 63 1.0000 1.0046 1.0500 1.0000
61 64 1.0000 1.0085 1.0500 1.0000
65 66 1.0000 0.9816 1.0000 0.9500
68 69 1.0000 1.0263 1.0500 1.0000
80 81 1.0000 1.0017 1.0500 1.0000
0
1 1.0216 -0.1935 1.0397 1.0428
2 1.0326 -0.1797 1.0481 1.0521
3 1.0308 -0.1821 1.0467 1.0493
4 1.0561 -0.1349 1.0647 1.0694
5 1.0621 -0.1302 1.0700 1.0700
6 1.0477 -0.1610 1.0600 1.0647
7 1.0470 -0.1636 1.0597 1.0644
8 1.0445 -0.0651 1.0466 1.0534
9 1.0693 0.0387 1.0700 1.0700
10 1.0542 0.1501 1.0648 1.0578
11 1.0434 -0.1626 1.0560 1.0599
12 1.0486 -0.1621 1.0610 1.0657
13 1.0249 -0.1895 1.0423 1.0468
14 1.0408 -0.1841 1.0570 1.0621
15 1.0268 -0.2184 1.0498 1.0560
16 1.0386 -0.1802 1.0541 1.0593
17 1.0451 -0.1834 1.0611 1.0672
18 1.0287 -0.2187 1.0517 1.0577
19 1.0231 -0.2261 1.0478 1.0540
20 1.0133 -0.2210 1.0371 1.0422
21 1.0126 -0.2037 1.0329 1.0371
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55
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135 1.0006 -0.2267 1.0260 1.0279
136 0.9850 -0.2521 1.0167 1.0223
137 0.9277 -0.2018 0.9494 0.9567
138 0.9861 -0.1949 1.0052 1.0111
139 0.9699 -0.2494 1.0015 1.0224
140 0.9505 -0.2621 0.9860 1.0073
141 0.9052 -0.3399 0.9669 0.9885
142 0.8374 -0.5214 0.9865 0.9791
143 1.0075 -0.3602 1.0700 1.0700
144 0.9269 -0.4046 1.0114 1.0599
145 0.9908 -0.3800 1.0611 1.0700
146 1.0380 -0.2210 1.0613 1.0615
147 1.0321 -0.2361 1.0588 1.0595
148 1.0190 -0.2473 1.0486 1.0568
149 1.0011 -0.2249 1.0260 1.0443
150 1.0172 -0.2578 1.0494 1.0500
151 0.9865 -0.3442 1.0449 1.0418
152 0.9944 -0.3036 1.0397 1.0446
153 1.0311 -0.2698 1.0658 1.0700
154 0.9652 -0.4180 1.0518 1.0559
155 0.9695 -0.3694 1.0375 1.0409
156 1.0189 -0.2026 1.0388 1.0412
157 0.9938 -0.3583 1.0564 1.0566
158 1.0214 -0.2988 1.0642 1.0610
159 0.9343 -0.4963 1.0579 1.0700
160 0.9498 -0.3713 1.0198 1.0308
161 0.9693 -0.3807 1.0413 1.0425
162 0.9918 -0.3402 1.0486 1.0480
163 1.0092 -0.3485 1.0677 1.0700
164 1.0065 -0.3226 1.0569 1.0600
165 0.9925 -0.3228 1.0437 1.0556
166 1.0009 -0.3004 1.0450 1.0503
167 1.0119 -0.3086 1.0579 1.0700
168 1.0453 -0.2284 1.0700 1.0700
169 0.9628 -0.3499 1.0244 1.0507
170 0.9662 -0.3937 1.0433 1.0498
171 1.0045 -0.3347 1.0588 1.0622
172 0.9490 -0.4347 1.0438 1.0486
173 0.9738 -0.3825 1.0462 1.0493
174 0.9286 -0.4584 1.0356 1.0387
175 0.9085 -0.5243 1.0490 1.0619
176 0.8730 -0.4844 0.9983 0.9914
177 0.7906 -0.5393 0.9570 0.9657
178 0.8366 -0.4762 0.9626 0.9732
179 0.7802 -0.5452 0.9518 0.9575
180 0.9041 -0.3323 0.9632 0.9672
181 0.9056 -0.3249 0.9621 0.9662
182 0.9619 -0.2126 0.9851 0.9945
183 0.9183 -0.4083 1.0050 1.0083
184 1.0255 -0.2701 1.0605 1.0611
185 1.0032 -0.2556 1.0352 1.0525
186 0.9818 -0.2151 1.0051 0.9969
187 0.9644 -0.2750 1.0029 1.0236
188 1.0457 -0.2268 1.0700 1.0700
189 0.9960 -0.1445 1.0064 1.0049
190 0.9178 -0.2204 0.9439 0.9447
191 0.8569 -0.4586 0.9719 0.9747
192 0.8721 -0.4551 0.9837 0.9849
193 0.8758 -0.4266 0.9742 0.9751
194 1.0264 -0.1923 1.0443 1.0446
195 0.9039 -0.3326 0.9632 0.9672
196 0.8756 -0.3569 0.9456 0.9495
197 0.9986 -0.3217 1.0491 1.0621
198 1.0242 -0.2717 1.0596 1.0700
199 1.0601 -0.1453 1.0700 1.0700
200 0.9713 -0.3817 1.0436 1.0470
201 0.9368 -0.2562 0.9712 0.9701
202 0.9676 -0.3723 1.0367 1.0684
203 1.0139 -0.2096 1.0354 1.0416
204 0.9588 -0.3970 1.0377 1.0700
205 1.0312 -0.2419 1.0592 1.0700
206 0.9946 -0.2642 1.0291 1.0458
207 0.9864 -0.3182 1.0364 1.0573
208 0.9468 -0.3556 1.0114 1.0353
209 0.9331 -0.4223 1.0242 1.0487
210 0.9457 -0.4143 1.0325 1.0606
211 0.9266 -0.4623 1.0356 1.0580
212 0.9583 -0.3937 1.0360 1.0669
213 0.9792 -0.2985 1.0237 1.0427
214 0.9721 -0.2240 0.9976 1.0181
215 0.9568 -0.2545 0.9900 1.0087
216 0.9503 -0.2273 0.9771 0.9841
217 0.9900 -0.2253 1.0153 1.0156
218 0.9787 -0.0548 0.9802 0.9803
219 0.9587 -0.2095 0.9814 0.9850
220 0.9624 -0.1883 0.9807 0.9838
221 0.9287 -0.2003 0.9500 0.9573
222 0.9760 -0.2249 1.0016 1.0223
223 0.9206 -0.2818 0.9627 0.9845
224 0.9085 -0.3334 0.9677 0.9892
225 0.9607 -0.3895 1.0367 1.0629
226 0.9536 -0.3717 1.0235 1.0700
227 0.9812 -0.3703 1.0488 1.0700
228 0.9543 -0.3907 1.0312 1.0576
229 0.9405 -0.3902 1.0182 1.0450
230 1.0375 -0.1997 1.0565 1.0648
231 1.0349 -0.1959 1.0533 1.0511
232 1.0134 -0.3304 1.0659 1.0528
233 1.0040 -0.2538 1.0356 1.0369
234 1.0366 -0.2610 1.0690 1.0700
235 1.0361 -0.2004 1.0553 1.0553
236 0.9985 -0.2894 1.0396 1.0450
237 0.9903 -0.3749 1.0589 1.0582
238 0.9942 -0.2964 1.0374 1.0425
239 0.9825 -0.3611 1.0468 1.0487
240 0.9819 -0.3066 1.0286 1.0506
241 1.0500 -0.0708 1.0524 1.0533
242 1.0010 -0.3121 1.0485 1.0472
243 1.0157 -0.3213 1.0653 1.0608
244 1.0082 -0.3344 1.0622 1.0638
245 0.9795 -0.3737 1.0483 1.0484
246 0.9775 -0.3468 1.0372 1.0388
247 0.9828 -0.3598 1.0466 1.0504
248 1.0046 -0.2798 1.0428 1.0563
249 0.9746 -0.4039 1.0550 1.0664
250 0.9981 -0.3410 1.0548 1.0573
251 0.9110 -0.5105 1.0443 1.0506
252 0.9063 -0.5024 1.0363 1.0419
253 0.9023 -0.3402 0.9643 0.9696
254 1.0471 -0.2200 1.0700 1.0700
255 0.8763 -0.4127 0.9686 0.9688
256 0.8286 -0.4924 0.9639 0.9723
257 0.8714 -0.4337 0.9733 0.9774
258 1.0206 -0.1511 1.0318 1.0379
259 0.9340 -0.4237 1.0256 1.0330
260 1.0011 -0.3575 1.0631 1.0612
261 0.9578 -0.3255 1.0116 1.0160
262 0.9382 -0.2441 0.9694 0.9683
263 0.9635 -0.3358 1.0204 1.0413
264 0.9707 -0.2405 1.0000 1.0092
265 0.9249 -0.2139 0.9493 0.9575
266 0.9443 -0.2081 0.9670 0.9711
267 0.9332 -0.2714 0.9718 0.9933
268 0.9278 -0.2827 0.9699 0.9915
269 0.9997 -0.2742 1.0366 1.0700
270 0.9248 -0.4044 1.0093 1.0579
271 0.9402 -0.3898 1.0178 1.0653
272 1.0410 -0.1913 1.0584 1.0534
273 1.0324 -0.2443 1.0610 1.0604
274 1.0227 -0.2223 1.0466 1.0550
275 1.0060 -0.3645 1.0700 1.0700
276 1.0257 -0.2440 1.0543 1.0455
277 0.9825 -0.3884 1.0565 1.0667
278 0.9808 -0.3731 1.0494 1.0574
279 0.9291 -0.4591 1.0363 1.0393
280 0.9614 -0.4097 1.0450 1.0506
281 1.0153 -0.1553 1.0271 1.0522
282 0.9573 -0.2248 0.9833 0.9972
283 0.9710 -0.3268 1.0245 1.0480
284 1.0148 -0.2278 1.0401 1.0478
285 1.0110 -0.2177 1.0342 1.0407
286 0.9997 -0.2987 1.0434 1.0613
287 1.0067 -0.2606 1.0399 1.0454
288 0.8907 -0.3360 0.9520 0.9546
289 1.0050 -0.2679 1.0401 1.0700
290 1.0097 -0.2202 1.0334 1.0397
291 0.9998 -0.2757 1.0371 1.0700
292 1.0490 -0.1868 1.0655 1.0617
293 0.9878 -0.3538 1.0492 1.0492
294 0.8456 -0.4676 0.9663 0.9707
295 0.9398 -0.2611 0.9754 0.9745
296 0.9453 -0.2799 0.9859 0.9833
297 0.9998 -0.2738 1.0367 1.0411
298 1.0050 -0.3222 1.0554 1.0700
299 0.9835 -0.1717 0.9984 1.0073
300 0.9313 -0.4048 1.0155 1.0638
0
5 5.7293 5.6918
4 2.0000 2.0000
9 5.3379 5.2651
11 7.0733 7.0885
28 3.0000 3.0000
29 3.0000 3.0000
30 6.0000 6.0000
31 3.2664 3.2460
32 5.0000 5.0000
33 5.0000 5.0000
34 1.0000 1.0000
35 4.0176 4.0537
36 6.0412 6.2637
38 6.0000 6.0000
40 1.4726 1.4494
41 3.4064 3.2301
42 2.7135 2.9160
43 3.0000 3.0000
44 14.3184 14.1409
45 9.0000 9.0000
46 4.0000 4.0000
0
1 -0.1640 -0.4426
2 1.5000 1.5000
3 -0.5000 -0.5000
4 0.1984 0.2756
5 -0.3612 -0.4807
6 0.2364 0.0580
7 -1.7162 -1.8225
8 0.2135 0.1040
9 -0.0943 -0.3148
10 0.4323 0.4246
11 -6.0000 -6.0000
28 0.5568 0.5439
29 0.2355 0.2315
30 0.6231 1.0162
31 0.5937 0.6242
32 0.9209 0.9966
33 2.0060 2.3938
34 0.0576 0.0100
35 -0.0926 0.0438
36 -2.0000 -2.0000
37 0.0000 0.0000
38 0.0617 -0.0225
39 0.0165 0.0000
40 0.2421 0.1834
41 0.3821 0.5126
42 1.5000 1.0503
43 0.5676 0.4873
44 5.8529 5.2962
45 2.1261 1.7263
46 -1.8991 -1.9034
62 0.1108 0.0256
64 0.3800 0.3800
65 0.0600 0.0600
73 0.2000 0.2000
92 -0.3000 -0.3000
100 1.0041 0.9480
102 -0.4530 -0.4574
103 -0.0499 -0.0768
106 -0.5000 -0.5000
108 -0.1000 -0.1000
116 0.8835 0.9000
117 0.3500 0.3500
122 -0.9486 -0.9958
123 -0.5728 -0.6169
124 6.4888 6.4857
133 -0.7492 -0.8976
139 0.4000 0.4000
145 0.0965 0.0294
148 0.0782 0.1000
159 0.2500 0.2500
161 0.1200 0.1200
167 -0.1100 -0.1100
168 0.0346 -0.0509
174 -0.2400 -0.2400
178 0.0242 -0.0253
179 0.3643 0.3858
186 0.1386 0.0120
189 -0.5000 -0.5000
199 -0.3050 -0.3417
203 -3.0000 -3.0000
221 1.0806 1.0139
222 0.9843 1.0000
225 -0.0034 0.0200
232 0.2000 0.2000
254 11.0963 11.0051
258 -0.0874 -0.1160
265 -0.6000 -0.6000
281 0.7548 1.0438
289 -0.2090 0.2658
0
259 0.40 0.4111 0.40 0.50
107 0.00 0.0000 0.00 0.10
200 0.40 0.4150 0.40 0.50
224 0.50 0.4755 0.40 0.50
54 0.00 0.0047 0.00 0.10
300 0.10 0.0928 0.00 0.10
0

1396
NCP函数法/result_S1047.dat Normal file
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2443
NCP函数法/result_XB1780.dat Normal file
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74
NCP函数法/seting.m Normal file
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function [e,f,PG,QR,Pg,Qg,T,pgvNum,xNum,m,r,l,u,z,w,x,y,mu,dmaxOut1,dmaxOut2,xz1,xz2,dmaxOut3,dmaxOut4,xz3,xz4,xz5,colmut1,hx,k2,opfGoal,times,secondBegin,Tn,Tn1,capKn,capKn1,kt0,q0,...
mut,mub,oneTrans,oneCap,para1,para2,para3,mismatch,ifconverge]=seting(nodeNum,lineNum,transNum,transK0,capNum,capK,pvQmin,pvQmax,pvNum,pvNode,pvV,pgNum,pgNode,Pmin,Pmax,Pg,Qg,centrPara)
%程序功能：预计算过程，初始化
%编写时间：2010年11月
%% 设置计算参数
para1=0.6; %Arlfa，计算最优步长所需参数
para2=0.05; %Gama
para3=0.76; %光滑参数修正量
para4=1.5; %光滑参数初始值
if nodeNum==30 %各测试系统要得到最好的优化结果，需要取不同的光滑参数修正值
para3=0.23;
para4=2.7;
else if nodeNum==118
para3=0.3;
para4=1.5;
else if nodeNum==300
para3=0.65;
para4=1;
else if nodeNum==1047
para3=0.59;
para4=0.6;
else if nodeNum==1780
para3=0.76;
para4=1.5;
end
end
end
end
end
%% 设PQ节点电压幅值为1，相角为0
e=ones(nodeNum,1);
f=sparse(nodeNum,1);
e(pvNode)=pvV(pvNode); %初始值对计算结果有一点点影响
%% 发电机有功无功出力以及无功源无功出力初值（分别取上下界的平均值）
PG=(Pmin+Pmax)/2; %发电机有功功率初值,取发电机有功上下限的平均值
QR=(pvQmin+pvQmax)/2; %发电机无功功率初值，取平衡节点、PV节点无功上下限的平均值
Pg(pgNode)=PG(pgNode);
Qg(pvNode)=QR(pvNode);
T=1./transK0;
x=[T;PG(pgNode);QR(pvNode);capK;e;f]; %系统的控制变量和状态变量
%% 设定松弛变量l,u,拉格朗日乘子z,w,y的初值
pgvNum=pgNum+pvNum;
xNum=pgvNum+2*nodeNum+transNum+capNum; %变量个数
m=2*nodeNum; %等式约束条件个数
r=pgvNum+nodeNum+lineNum+transNum+capNum; %不等式约束条件个数，
s=1;
l=s*ones(r,1); %初始化l,u,z为1，w为-1，y为0
u=l;
z=l;
w=-l;
y=sparse(m,1);
Gap=l'*z-u'*w; %计算互补间隙
mu=(centrPara*Gap)/(2*r); %计算扰动因子
Tn=sparse(0,0);Tn1=Tn;capKn=Tn;capKn1=Tn; kt0=Tn;q0=Tn;
oneTrans=ones(transNum,1);
oneCap=ones(capNum,1);
mut=oneTrans*para4; %光滑参数赋初值
mub=oneCap*para4;
dmaxOut1=[];dmaxOut2=dmaxOut1;xz1=dmaxOut1;xz2=dmaxOut1;dmaxOut3=dmaxOut1; %用于保存中间计算结果，以提供作图数据
dmaxOut4=dmaxOut1;xz3=dmaxOut1;xz4=dmaxOut1;xz5=dmaxOut1;colmut1=dmaxOut1;
hx=ones(m,1);
k2=0;
opfGoal=2; %目标函数为有功出力最小
times=1; %计算阶段标志
secondBegin=1; %光滑处理阶段开始标志
ifconverge=0; %收敛标志
mismatch=0.00001; %最大不平衡量计算精度
if nodeNum==1780 %由于1780系统在预计算时最大不平衡量要收敛到0.00001的精度迭代次数会比较多，为了提高整体收敛速度
mismatch=0.01; %在预计算时最大不平衡量精度达到0.01则视为收敛，在连续化处理收敛时最大不平衡量精度可达0.00001
end

58
NCP函数法/snd_Constant.m Normal file
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function [const,Lz,Lw,L1,U1,hx,origConst,gxx,gsx]=snd_Constant(nodeNum,opfGoal,lineNum,transNum,transI,...
transJ,transG,transB,lineI,lineJ,balNode,mu,G,B,GIJ,BIJ,e,f,Pmin,Pmax,a,b,PG,QR,pvQmin,pvQmax,...
pgNum,pgvNum,xNum,pgNode,pvNode,dhx,dgx,L1,U1,LZ,UW,l,u,y,r,dT_Zt,capNum,z,w,Vmin,Vmax,hx)
%程序功能：光滑处理过程，形成扰动KKT方程不平衡量矩阵
%编写时间：2010年11月
%% 形成目标函数的一阶偏导矩阵▽f(.)
if(opfGoal==2)
dPG=ones(pgNum,1);
dfx=sparse(transNum+1:transNum+pgNum,ones(pgNum,1),dPG,xNum,1);
else if(opfGoal==1)
dPG=2*a(pgNode).*PG(pgNode)+b(pgNode);
dfx=sparse(transNum+1:transNum+pgNum,ones(pgNum,1),dPG,xNum,1);
else if(opfGoal==3)
dfT=-1*transG.*dT_Zt.*((f(transI)-f(transJ)).^2+(e(transI)-e(transJ)).^2);
dfPQ=zeros(pgvNum,1);
dfcapK=zeros(capNum,1);
EE=e*ones(1,nodeNum);
FF=f*ones(1,nodeNum);
dfe=2*sum(G.*(EE-EE'));
dff=2*sum(G.*(FF-FF'));
dfx=[dfT;dfPQ;dfcapK;dfe';dff'];
else if(opfGoal==4)
dfT=1*transB.*dT_Zt.*((f(transI)-f(transJ)).^2+(e(transI)-e(transJ)).^2);
dfPQ=zeros(pgvNum,1);
dfcapK=zeros(capNum,1);
EE=e*ones(1,nodeNum);
FF=f*ones(1,nodeNum);
dfe=2*sum(B.*(EE-EE'));
dff=2*sum(B.*(FF-FF'));
dfx=[dfT;dfPQ;dfcapK;dfe';dff'];
end
end
end
end
%% 不等式约束项
gxv=[PG(pgNode);QR(pvNode);e.^2+f.^2]; %约束条件当前值
gxvx=[Pmin(pgNode);pvQmin(pvNode);Vmin.*Vmin]; %约束下限
gxvs=[Pmax(pgNode);pvQmax(pvNode);Vmax.*Vmax]; %约束上限
gxl=(e(lineI).*e(lineI)+f(lineI).*f(lineI)-e(lineI).*e(lineJ)-f(lineI).*f(lineJ)).*GIJ+(e(lineI).*f(lineJ)-e(lineJ).*f(lineI)).*BIJ;%线路功率当前值
gxlx=-ones(lineNum,1)*1000; %线路约束下限
gxls=ones(lineNum,1)*1000; %线路约束上限
gx=[gxv;gxl]; %组合所有约束条件
gxx=[gxvx;gxlx];
gsx=[gxvs;gxls];
Lz=gx-l-gxx;
Lw=gx+u-gsx;
%% 形成修正方程常数项向量
muUL=mu*(U1-L1);
BB1=UW*Lw-LZ*Lz-muUL*ones(r,1);
BB=dhx*y-dfx+dgx*BB1; %修正方程常数项ψ(.,μ)
BB(transNum+pgvNum+capNum+nodeNum+balNode,1)=0; %保持平衡节点电压虚部不变，始终为0，则常数项平衡节点处置0
BB(transNum+pgvNum+capNum+balNode,1)=0; %保持平衡节点电压实部不变
const=[BB;hx]; %修正方程常数项向量
BB0=dhx*y-dfx+dgx*(z+w); %此部分在求步长时使用
BB0(transNum+pgvNum+capNum+nodeNum+balNode,1)=0;
BB0(transNum+pgvNum+capNum+balNode,1)=0;
origConst=[BB0;hx];

209
NCP函数法/snd_formHSB.m Normal file
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function [HSB,dhx,dgx,dgxT,N1,H1,diagE,diagF,GIJ,BIJ,L1,U1,LZ,UW,transG,transB,mut,mub]=snd_formHSB(nodeNum,balNode,balNum,...
opfGoal,lineNum,transNum,lineI,lineJ,transI,transJ,T,transG,transB,pgNode,pvNode,G,B,e,f,pgNum,pvNum,pgvNum,xNum,a,m,r,l,u,z,w,y,...
capNum,capI,mut,mub,dNCPT_dt,d2NCPT_dt2,dT_Zt,transGmut,transBmut,dNCP_dcap,d2NCP_dcap2,H1,N1,diagE,diagF)
%程序功能：光滑处理过程，形成修正方程系数矩阵
%编写时间：2010年11月
%% 形成等式约束雅可比矩阵
ef1=e(transI).*e(transJ)+f(transI).*f(transJ);
ef2=e(transI).*f(transJ)-e(transJ).*f(transI);
ef3=e(transI).*e(transI)+f(transI).*f(transI);
ef1G=ef1.*transGmut;
ef1B=ef1.*transBmut;
ef2G=ef2.*transGmut;
ef2B=ef2.*transBmut;
dhPTi=-ef1G+ef2B+2*ef3.*transGmut.*T;
dhPTj=-ef1G-ef2B;
dhPT=sparse(1:transNum,transI,dhPTi,transNum,nodeNum)+sparse(1:transNum,transJ,dhPTj,transNum,nodeNum);%有功平衡方程P对变压器变比求偏导
dhQTi=ef1B+ef2G-2*ef3.*transBmut.*T;
dhQTj=ef1B-ef2G;
dhQT=sparse(1:transNum,transI,dhQTi,transNum,nodeNum)+sparse(1:transNum,transJ,dhQTj,transNum,nodeNum);%无功平衡方程Q对变压器变比求偏导
dhNCP_T=sparse(1:transNum,1:transNum,dNCPT_dt,transNum,transNum+capNum);
dhP=sparse(1:pgNum,pgNode,ones(pgNum,1),pgNum,m);
dhQ1=sparse(1:pvNum,pvNode,ones(pvNum,1),pvNum,m-nodeNum);
dhQ=[sparse(pvNum,nodeNum) dhQ1];
dhcapK1=sparse(1:capNum,capI,(e(capI).^2+f(capI).^2),capNum,nodeNum);
dhNCP_capK=sparse(1:capNum,transNum+1:transNum+capNum,dNCP_dcap,capNum,transNum+capNum);%功率平衡方程对电容电抗器组数求偏导
dhcapK=[sparse(capNum,nodeNum) dhcapK1 dhNCP_capK];
%功率方程雅可比矩阵
deG=diagE*G;
dfB=diagF*B;
deB=diagE*B;
dfG=diagF*G;
dH1=sparse(1:nodeNum,1:nodeNum,H1,nodeNum,nodeNum);
dN1=sparse(1:nodeNum,1:nodeNum,N1,nodeNum,nodeNum);
Hij=-dH1-deG-dfB;
Nij=-dN1+deB-dfG;
Jij=dN1-dfG+deB;
Lij=-dH1+dfB+deG;
dhJacb=[Hij Nij;Jij Lij]'; %合并形成功率方程雅可比矩阵
dhT=[dhPT dhQT dhNCP_T];
dhx=[dhT;dhP;dhQ;dhcapK;dhJacb sparse(2*nodeNum,transNum+capNum)]; %合并形成等式约束雅可比矩阵h(x)
%% 形成不等式约束雅可比矩阵▽g(x)
gtransNum=0; %变比上下限约束维数，用NCP函数后，则不需要再约束其上下限
gcapNum=0;
dgT1=sparse(transNum,r-lineNum);
dglT=(e(transI).^2+f(transI).^2-e(transI).*e(transJ)-f(transI).*f(transJ)).*transGmut+(e(transI).*f(transJ)-e(transJ).*f(transI)).*transBmut;
dgT2=sparse(1:transNum,lineNum-transNum+1:lineNum,dglT,transNum,lineNum);
dgT=[dgT1 dgT2]; %所有不等式对变比求导的模块
dgP=sparse(1:pgNum,gtransNum+1:gtransNum+pgNum,ones(pgNum,1),pgNum,r); %所有不等式约束对P求导的模块
dgQ=sparse(1:pvNum,gtransNum+pgNum+1:gtransNum+pgvNum,ones(pvNum,1),pvNum,r);%所有不等式约束对Q求导的模块
dgcapK=sparse(capNum,r); %所有不等式约束对capK求导的模块
dgve=2*diagE;
dgvf=2*diagF;
sizeG=size(G);
GIJ=G(sub2ind(sizeG,lineI,lineJ));
BIJ=B(sub2ind(sizeG,lineI,lineJ));
dgleI=(2*e(lineI)-e(lineJ)).*GIJ+f(lineJ).*BIJ;
dgleJ=-e(lineI).*GIJ-f(lineI).*BIJ;
dglfI=(2*f(lineI)-f(lineJ)).*GIJ-e(lineJ).*BIJ;
dglfJ=-f(lineI).*GIJ+e(lineI).*BIJ;
dgle=sparse(lineI,(1:lineNum),dgleI,nodeNum,lineNum)+sparse(lineJ,(1:lineNum),dgleJ,nodeNum,lineNum);
dglf=sparse(lineI,(1:lineNum),dglfI,nodeNum,lineNum)+sparse(lineJ,(1:lineNum),dglfJ,nodeNum,lineNum);
dg0=sparse(2*nodeNum,gtransNum+pgvNum+gcapNum);
dgvl=[dgve dgle;dgvf dglf];
dgef=[dg0 dgvl]; %所有不等式约束对电压实部、虚部求偏导的模块
dgx=[dgT;dgP;dgQ;dgcapK;dgef]; %不等式约束雅克比矩阵
%% 形成对角阵
Z=sparse(1:r,1:r,z,r,r);
W=sparse(1:r,1:r,w,r,r);
L1=sparse(1:r,1:r,1./l,r,r);
U1=sparse(1:r,1:r,1./u,r,r);
LZ=L1*Z;
UW=U1*W;
%% 形成海森伯矩阵
%目标函数的海森伯矩阵▽2f(x)
if(opfGoal==2)
HSdfx=sparse(xNum,xNum);
else if(opfGoal==1)
HSdfx=sparse(transNum+1:transNum+pgNum,transNum+1:transNum+pgNum,2*a(pgNode),xNum,xNum);%仅目标函数对PG求偏导处的对角元为非零元素，其他都为0(目标为发电耗量最小)
else if(opfGoal==3)
d2ftei=-2*transGmut.*(e(transI)-e(transJ));
d2ftej=-d2ftei;
d2ftfi=-2*transGmut.*(f(transI)-f(transJ));
d2ftfj=-d2ftfi;
d2fte=sparse(1:transNum,transI,d2ftei,transNum,nodeNum)+sparse(1:transNum,transJ,d2ftej,transNum,nodeNum);
d2ftf=sparse(1:transNum,transI,d2ftfi,transNum,nodeNum)+sparse(1:transNum,transJ,d2ftfj,transNum,nodeNum);
d2fT0=sparse(transNum,transNum+pgvNum+capNum);
d2fT=[d2fT0 d2fte d2ftf];
d2fPGQR=sparse(pgvNum,xNum);
d2fcapK=sparse(capNum,xNum);
d2fee=2*(G-sparse(1:nodeNum,1:nodeNum,sum(G,2),nodeNum,nodeNum));
d2fff=d2fee;
zero_nodeNum=sparse(nodeNum,nodeNum);
d2f_ef_ef=[d2fee zero_nodeNum;zero_nodeNum d2fff];
d2efT=[d2fte d2ftf]';
d2f_ef=[d2efT sparse(2*nodeNum,pgvNum+capNum) d2f_ef_ef];
HSdfx=[d2fT;d2fPGQR;d2fcapK;d2f_ef];
else if(opfGoal==4)
d2ftei=2*transBmut.*(e(transI)-e(transJ));
d2ftej=-d2ftei;
d2ftfi=2*transBmut.*(f(transI)-f(transJ));
d2ftfj=-d2ftfi;
d2fte=sparse(1:transNum,transI,d2ftei,transNum,nodeNum)+sparse(1:transNum,transJ,d2ftej,transNum,nodeNum);
d2ftf=sparse(1:transNum,transI,d2ftfi,transNum,nodeNum)+sparse(1:transNum,transJ,d2ftfj,transNum,nodeNum);
d2fT0=sparse(transNum,transNum+pgvNum+capNum);
d2fT=[d2fT0 d2fte d2ftf];
d2fPGQR=sparse(pgvNum,xNum);
d2fcapK=sparse(capNum,xNum);
d2fee=-2*(B-sparse(1:nodeNum,1:nodeNum,sum(B,2),nodeNum,nodeNum));
d2fff=d2fee;
zero_nodeNum=sparse(nodeNum,nodeNum);
d2f_ef_ef=[d2fee zero_nodeNum;zero_nodeNum d2fff];
d2efT=[d2fte d2ftf]';
d2f_ef=[d2efT sparse(2*nodeNum,pgvNum+capNum) d2f_ef_ef];
HSdfx=[d2fT;d2fPGQR;d2fcapK;d2f_ef];
end
end
end
end
%等式约束海森伯矩阵与拉格朗日乘子y的乘积▽2h(x)*y
y1=y(1:nodeNum,1);
y2=y(nodeNum+1:2*nodeNum,1);
y3=y(2*nodeNum+1:2*nodeNum+transNum,1);
y4=y(2*nodeNum+transNum+1:end,1);
d2P_T2=(2*ef3.*transG.*dT_Zt).*y1(transI);
d2Q_T2=(-2*ef3.*transB.*dT_Zt).*y2(transI);
dh2NCP_T2=d2NCPT_dt2.*y3;
dhT2=d2P_T2+d2Q_T2+dh2NCP_T2; %功率方程对变压器变比求二次偏导所得的列向量
HSdhT=sparse(1:transNum,1:transNum,dhT2,transNum+pgvNum+capNum,transNum+pgvNum+capNum)+...
sparse(transNum+pgvNum+1:transNum+pgvNum+capNum,transNum+pgvNum+1:transNum+pgvNum+capNum,d2NCP_dcap2.*y4,transNum+pgvNum+capNum,transNum+pgvNum+capNum);
eiG=e(transI).*transGmut;
ejG=e(transJ).*transGmut;
eiB=e(transI).*transBmut;
ejB=e(transJ).*transBmut;
fiG=f(transI).*transGmut;
fjG=f(transJ).*transGmut;
fiB=f(transI).*transBmut;
fjB=f(transJ).*transBmut;
ejG_fjB=ejG-fjB;
ejGfjB=ejG+fjB;
fjGejB=fjG+ejB;
ejB_fjG=ejB-fjG;
eiGfiB=eiG+fiB;
eiG_fiB=eiG-fiB;
eiB_fiG=eiB-fiG;
fiGeiB=fiG+eiB;
dP2_ei_t=(4*eiG.*T-ejG_fjB).*y1(transI)-ejGfjB.*y1(transJ);
dP2_ej_t=-eiGfiB.*y1(transI)-eiG_fiB.*y1(transJ);
dQ2_ei_t=(-4*eiB.*T+fjGejB).*y2(transI)+ejB_fjG.*y2(transJ);
dQ2_ej_t=eiB_fiG.*y2(transI)+fiGeiB.*y2(transJ);
HSdh_et=sparse(1:transNum,transI,dP2_ei_t+dQ2_ei_t,transNum,nodeNum)+sparse(1:transNum,transJ,dP2_ej_t+dQ2_ej_t,transNum,nodeNum);%功率方程先对变比求偏导，再对电压实部求偏导模块
dP2_fi_t=(4*fiG.*T-fjGejB).*y1(transI)+ejB_fjG.*y1(transJ);
dP2_fj_t=eiB_fiG.*y1(transI)-fiGeiB.*y1(transJ);
dQ2_fi_t=(-4*fiB.*T-ejG_fjB).*y2(transI)+ejGfjB.*y2(transJ);
dQ2_fj_t=eiGfiB.*y2(transI)-eiG_fiB.*y2(transJ);
HSdh_ft=sparse(1:transNum,transI,dP2_fi_t+dQ2_fi_t,transNum,nodeNum)+sparse(1:transNum,transJ,dP2_fj_t+dQ2_fj_t,transNum,nodeNum);%功率方程先对变比求偏导，再对电压虚部求偏导模块
HSdh_eft=[HSdh_et HSdh_ft];
HSdh_tef=HSdh_eft';
HSdhPQ=sparse(pgvNum,2*nodeNum); %功率方程先对PG、QR求偏导，再对其他变量求偏导的部分
d2hcap_e=sparse(1:capNum,capI,2*e(capI).*y2(capI),capNum,nodeNum); %功率方程先对capK求偏导，再对e求偏导的部分
d2hcap_f=sparse(1:capNum,capI,2*f(capI).*y2(capI),capNum,nodeNum); %功率方程先对capK求偏导，再对f求偏导的部分
HSdhcap_ef=[d2hcap_e d2hcap_f];
d2htPQ_ef=[HSdh_eft;HSdhPQ;HSdhcap_ef];
HSdhtPQ=[HSdhT d2htPQ_ef];
HSdhx1=sparse(2*nodeNum,pgvNum);
%潮流方程海森矩阵
diagy1=sparse(1:nodeNum,1:nodeNum,y1,nodeNum,nodeNum);
diagy2=sparse(1:nodeNum,1:nodeNum,y2,nodeNum,nodeNum);
HSdhey=-diagy1*G+diagy2*B+(-G*diagy1+B*diagy2);
HSdhefy=diagy1*B+diagy2*G-(B*diagy1+G*diagy2);
HSdhx2=[HSdhey HSdhefy;HSdhefy' HSdhey];
HSdhx=[HSdhtPQ;HSdh_tef HSdhx1 HSdhcap_ef' HSdhx2];
%形成不等式约束二阶偏导的矩阵▽2g(x)*(z+w)
ZWcl=z(gtransNum+pgvNum+gcapNum+nodeNum+1:end)+w(gtransNum+pgvNum+gcapNum+nodeNum+1:end);
ZWv=z(gtransNum+pgvNum+gcapNum+1:gtransNum+pgvNum+gcapNum+nodeNum)+w(gtransNum+pgvNum+gcapNum+1:gtransNum+pgvNum+gcapNum+nodeNum);
dgeiT=((2*e(transI)-e(transJ)).*transGmut+f(transJ).*transBmut).*ZWcl(lineNum-transNum+1:end);
dgejT=(-e(transI).*transGmut-f(transI).*transBmut).*ZWcl(lineNum-transNum+1:end);
dgeT=sparse(1:transNum,transI,dgeiT,transNum,nodeNum)+sparse(1:transNum,transJ,dgejT,transNum,nodeNum);%不等式约束先对变比求偏导，再对e求偏导的模块
dgfiT=((2*f(transI)-f(transJ)).*transGmut-e(transJ).*transBmut).*ZWcl(lineNum-transNum+1:end);
dgfjT=(-f(transI).*transGmut+e(transI).*transBmut).*ZWcl(lineNum-transNum+1:end);
dgfT=sparse(1:transNum,transI,dgfiT,transNum,nodeNum)+sparse(1:transNum,transJ,dgfjT,transNum,nodeNum);%不等式约束先对变比求偏导，再对f求偏导的模块
HSdgefT=[dgeT dgfT];
HSdgT=[sparse(transNum,transNum+pgvNum+capNum) HSdgefT];
HSdgee=sparse(lineI,lineI,2*GIJ.*ZWcl,nodeNum,nodeNum)-sparse(lineI,lineJ,GIJ.*ZWcl,nodeNum,nodeNum)...
-sparse(lineJ,lineI,GIJ.*ZWcl,nodeNum,nodeNum)+sparse(1:nodeNum,1:nodeNum,2*ZWv,nodeNum,nodeNum);
HSdgff=HSdgee;
HSdgef=sparse(lineI,lineJ,BIJ.*ZWcl,nodeNum,nodeNum)-sparse(lineJ,lineI,BIJ.*ZWcl,nodeNum,nodeNum);
HSdgfe=HSdgef'; %所有不等式约束对e、f求二次偏导模块
HSdgx1=[HSdgee HSdgef;HSdgfe HSdgff];
HSdgxtPQ_0=sparse(pgvNum+capNum,xNum);
HSdgef_0=[HSdgefT' sparse(2*nodeNum,pgvNum+capNum)];
HSdgx=[HSdgT;HSdgxtPQ_0;HSdgef_0 HSdgx1]; %合成不等式约束海森矩阵
dgxT=dgx'; %求dgx的转置
MULdgx=dgx*(UW-LZ)*dgxT;
H=HSdhx+HSdgx-HSdfx+MULdgx; %求和形成H(.)矩阵.
%% 根据以上所求的各个矩阵合成海森伯矩阵
HSB0=sparse(m,m);
HSB=[H dhx;dhx' HSB0];
balN=transNum+pgvNum+capNum+nodeNum+balNode;
HSB(balN,:)=0; %保持平衡节点电压虚部不变，始终为0，即将海森矩阵中平衡节点虚部所对应的行列元素置0，对角元素置1
HSB(:,balN)=0;
HSB_balN=sub2ind(size(HSB),balN,balN);
HSB(HSB_balN)=ones(balNum,1);
balN1=transNum+pgvNum+capNum+balNode;
HSB(balN1,:)=0; %保持平衡节点电压实部不变，始终为0，即将海森矩阵中平衡节点实部所对应的行列元素置0，对角元素置1
HSB(:,balN1)=0;
HSB_balN1=sub2ind(size(HSB),balN1,balN1);
HSB(HSB_balN1)=ones(balNum,1);

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function [secondBegin,m,r,l,u,z,w,y,Gama,Arlfa,meritF,firstT,firstcapK,firstfx,Gap,mu,Vfirst,Pgfirst,Qgfirst]=...
snd_setting(secondBegin,transNum,T,m,r,capNum,capK,para1,para2,fx,centrPara,e,f,Pg,Qg)
%程序功能：光滑处理过程重新初始化
%编写时间：2010年11月
%% 光滑处理阶段，各变量重新赋值
secondBegin=secondBegin-1;
Gama=para2;
Arlfa=para1;
meritF=[]; %初始化求最优步长时的效益函数
m=m+transNum+capNum; %等式约束个数增加变压器变比、电容器可调档位对应的凝聚函数
r=r-transNum-capNum; %不等式约束条件个数，考虑有功无功约束、节点电压约束、线路功率约束,变压器变比、电容器可调档位上下限约束不再需要
clear l u z w y;
s=1; %松弛因子和拉格朗日乘子重新赋值
l=s*ones(r,1);
u=l;
z=l;
w=-l;
y=sparse(m,1);
Gap=l'*z-u'*w; %计算互补间隙
mu=(centrPara*Gap)/(2*r); %计算扰动因子
%% 保留预计算结果
firstT=T;
firstcapK=capK;
firstfx=fx;
Vfirst=sqrt(e.*e+f.*f);
Pgfirst=Pg;
Qgfirst=Qg;

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function [z,l,u,w,x,y,PG,QR,Pg,Qg,e,f,T,G,B,capK,meritF]=snd_solve(HSB,const,mu,r,nodeNum,balNode,pgNum,pvNum,pgvNum,xNum,...
transNum,pgNode,pvNode,m,Lz,Lw,LZ,UW,dgxT,L1,U1,transI,transJ,transG,transB,transG1,transB1,Tn,capKn,capNum,...
capI,Tn1,capKn1,x,y,z,l,u,w,G,B,PG,QR,Pg,Qg,opfGoal,Gama,Arlfa,meritF,k2,T,capK,lineNum,lineI,lineJ,Pd,Qd,gxx,gsx,mut,mub)
%程序功能：光滑处理过程，求解修正方程
%编写时间：2010年11月
%% 求解方程，求出各变量的修正量
dX=-HSB\const;
dx=dX(1:xNum,1);
dy=dX(xNum+1:xNum+m,1);
dl=dgxT*dx+Lz;
du=-dgxT*dx-Lw;
Ll=(l.*z-mu*ones(r,1));
Lu=(u.*w+mu*ones(r,1));
diagZ=sparse(1:r,1:r,z,r,r);
diagW=sparse(1:r,1:r,w,r,r);
dz=-LZ*dgxT*dx-L1*(diagZ*Lz+Ll);
dw=UW*dgxT*dx+U1*(diagW*Lw-Lu);
L3=-L1*(diagZ*Lz+Ll);
L4=U1*(diagW*Lw-Lu);
L5=Lz;
L6=Lw;
f_NCP1=[const;L3;L4;L5;L6];
f_NCPsum1=(f_NCP1'*f_NCP1)/2;
meritF=[meritF;f_NCPsum1];
minusdz=find(dz<0);
dzmin=min(-z(minusdz)./dz(minusdz));
minusdl=find(dl<0);
dlmin=min(-l(minusdl)./dl(minusdl));
minusdw=find(dw>0);
dwmin=min(-w(minusdw)./dw(minusdw));
minusdu=find(du<0);
dumin=min(-u(minusdu)./du(minusdu));
ap=min(dlmin,dumin);
ad=min(dzmin,dwmin);
stepp=0.9995*min(ap,1);
stepd=0.9995*min(ad,1);
%% 一维线性搜索，求步长
[mk,meritF,stepp,stepd]=linesearch(r,nodeNum,balNode,pgNum,pvNum,pgvNum,...
xNum,transNum,pgNode,pvNode,m,x,y,z,l,u,w,G,B,transI,transJ,transG,transB,transG,transB,...
Tn,capKn,capNum,capI,Tn1,capKn1,PG,QR,Pg,Qg,dx,dl,du,dy,dz,dw,...
opfGoal,Gama,Arlfa,meritF,k2,mu,T,capK,lineNum,lineI,lineJ,Pd,Qd,gxx,gsx,mut,mub,stepp,stepd);
%% 更新变量
x=x+stepp*dx;
l=l+stepp*dl;
u=u+stepp*du;
y=y+stepd*dy;
z=z+stepd*dz;
w=w+stepd*dw;
%保留上一次计算的变比，用于修正节点导纳矩阵
Tlast=T;
capKlast=capK;
%给控制变量、状态变量重新赋值
T=x(1:transNum,1);
capK=x(transNum+pgvNum+1:transNum+pgvNum+capNum);
PG(pgNode,1)=x(transNum+1:transNum+pgNum,1);
QR(pvNode,1)=x(transNum+pgNum+1:transNum+pgNum+pvNum,1);
e=x(transNum+pgNum+pvNum+capNum+1:transNum+pgNum+pvNum+capNum+nodeNum,1);
f=x(transNum+pgNum+pvNum+capNum+nodeNum+1:xNum,1);
Pg(pgNode)=PG(pgNode);
Qg(pvNode)=QR(pvNode);
%% 变比变化后需修正节点导纳矩阵
transG=transG1;
transB=transB1;
G=G-sparse(transI,transI,(T.*T-Tlast.*Tlast).*transG,nodeNum,nodeNum)...
+sparse(transI,transJ,transG.*(T-Tlast),nodeNum,nodeNum)...
+sparse(transJ,transI,transG.*(T-Tlast),nodeNum,nodeNum);
B=B-sparse(transI,transI,(T.*T-Tlast.*Tlast).*transB,nodeNum,nodeNum)...
+sparse(transI,transJ,transB.*(T-Tlast),nodeNum,nodeNum)...
+sparse(transJ,transI,transB.*(T-Tlast),nodeNum,nodeNum)...
+sparse(capI,capI,capK-capKlast,nodeNum,nodeNum);

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function [z,l,u,w,x,y,PG,QR,Pg,Qg,e,f,T,capK,G,B]=solve(HSB,const,mu,r,nodeNum,balNode,pgNum,pvNum,xNum,transNum,capNum,capI,capBi,capK,...
pgNode,pvNode,m,x,y,z,l,u,w,Lz,Lw,LZ,UW,dgxT,L1,U1,G,B,transI,transJ,T,transG,transB,transG1,transB1,PG,QR,Pg,Qg)
%程序功能：预计算过程，求解修正方程
%编写时间：2010年11月
%% 求解方程，求出各变量的修正量
dX=-HSB\const;
dx=dX(1:xNum,1);
dy=dX(xNum+1:xNum+m,1);
dl=dgxT*dx+Lz;
du=-dgxT*dx-Lw;
Ll=(l.*z-mu*ones(r,1));
Lu=(u.*w+mu*ones(r,1));
diagZ=sparse(1:r,1:r,z,r,r);
diagW=sparse(1:r,1:r,w,r,r);
dz=-LZ*dgxT*dx-L1*(diagZ*Lz+Ll);
dw=UW*dgxT*dx+U1*(diagW*Lw-Lu);
%% 求最大步长
minusdz=find(dz<0);
dzmin=min(-z(minusdz)./dz(minusdz));
minusdl=find(dl<0);
dlmin=min(-l(minusdl)./dl(minusdl));
minusdw=find(dw>0);
dwmin=min(-w(minusdw)./dw(minusdw));
minusdu=find(du<0);
dumin=min(-u(minusdu)./du(minusdu));
ap=min(dlmin,dumin);
ad=min(dzmin,dwmin);
stepp=0.9995*min(ap,1);
stepd=0.9995*min(ad,1);
%% 更新变量
x=x+stepp*dx;
l=l+stepp*dl;
u=u+stepp*du;
y=y+stepd*dy;
z=z+stepd*dz;
w=w+stepd*dw;
%% 给控制变量、状态变量重新赋值
Tlast=T; %保留上一次计算的变比，用于修正节点导纳矩阵
capKlast=capK;
T=x(1:transNum,1);
PG(pgNode,1)=x(transNum+1:transNum+pgNum,1);
QR(pvNode,1)=x(transNum+pgNum+1:transNum+pgNum+pvNum,1);
capK=x(transNum+pgNum+pvNum+1:transNum+pgNum+pvNum+capNum,1);
e=x(transNum+pgNum+pvNum+capNum+1:transNum+pgNum+pvNum+capNum+nodeNum,1);
f=x(transNum+pgNum+pvNum+capNum+nodeNum+1:xNum,1);
Pg(pgNode)=PG(pgNode);
Qg(pvNode)=QR(pvNode);
%% 变比变化后需修正节点导纳矩阵
transG=transG1;
transB=transB1;
G=G-sparse(transI,transI,(T.*T-Tlast.*Tlast).*transG,nodeNum,nodeNum)...
+sparse(transI,transJ,transG.*(T-Tlast),nodeNum,nodeNum)...
+sparse(transJ,transI,transG.*(T-Tlast),nodeNum,nodeNum);
B=B-sparse(transI,transI,(T.*T-Tlast.*Tlast).*transB,nodeNum,nodeNum)...
+sparse(transI,transJ,transB.*(T-Tlast),nodeNum,nodeNum)...
+sparse(transJ,transI,transB.*(T-Tlast),nodeNum,nodeNum)...
+sparse(capI,capI,capK-capKlast,nodeNum,nodeNum);
% GTii=sub2ind(size(G),transI,transI); %GTij为G的第i行第j列在G中所对应的位置
% GTij=sub2ind(size(G),transI,transJ);
% GTji=sub2ind(size(G),transJ,transI);
% BTii=sub2ind(size(B),transI,transI);
% BTij=sub2ind(size(B),transI,transJ);
% BTji=sub2ind(size(B),transJ,transI);
% for i=1:length(GTii)
% G(GTii(i))=G(GTii(i))-(T(i).*T(i)-Tlast(i).*Tlast(i)).*transG(i);
% end
% for i=1:length(GTij)
% G(GTij(i))=G(GTij(i))+transG(i).*(T(i)-Tlast(i));
% end
% for i=1:length(GTji)
% G(GTji(i))=G(GTji(i))+transG(i).*(T(i)-Tlast(i));
% end
% % G(GTij)=G(GTij)+transG.*(T-Tlast);
% % G(GTji)=G(GTij);
% for i=1:length(BTii)
% B(BTii(i))=B(BTii(i))-(T(i).*T(i)-Tlast(i).*Tlast(i)).*transB(i);
% end
% for i=1:length(BTij)
% B(BTij(i))=B(BTij(i))+transB(i).*(T(i)-Tlast(i));
% end
% for i=1:length(BTji)
% B(BTji(i))=B(BTji(i))+transB(i).*(T(i)-Tlast(i));
% end
% % B(BTij)=B(BTij)+transB.*(T-Tlast);
% % B(BTji)=B(BTij);
% deG=G-newG;
% deB=B-newB;
% G(708,708)
% newG(708,708)
% [Grows,Gcols,G1] = find(deG);
% [Brows,Bcols,B1] = find(deB);
% Bcapii=sub2ind(size(B),capI,capI);
% B(Bcapii)=B(Bcapii)+(capK-capKlast);%2011年10月5日修改，去掉*capBi.
% aa=0;
% for i=1:100000
% aa=aa+1/1.1;
% end
% bb=0;
% bb=bb+sparse(ones(100000,1),ones(100000,1),1/1.1*ones(100000,1),1,1);

59
Sigmoid函数法/Constant.m Normal file
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@ -0,0 +1,59 @@
function [const,Lz,Lw,L1,U1]=Constant(nodeNum,opfGoal,lineNum,transNum,transI,transJ,transG,transB,T,transKmin,transKmax,lineI,lineJ,balNode,...
mu,G,B,GIJ,BIJ,e,f,Pmin,Pmax,a,b,PG,QR,pvQmin,pvQmax,pgNum,pgvNum,xNum,capNum,capK,capKmin,capKmax,pgNode,pvNode,dhx,dgx,L1,U1,LZ,UW,l,u,...
y,r,hx,Vmax,Vmin,capBi)
%程序功能：预计算过程，形成扰动KKT方程不平衡量矩阵
%编写时间：2010年10月
%% 形成目标函数的一阶偏导矩阵▽f(.)
if(opfGoal==2)
dPG=ones(pgNum,1);
dfx=sparse(transNum+1:transNum+pgNum,ones(pgNum,1),dPG,xNum,1);
else if(opfGoal==1)
dPG=2*a(pgNode).*PG(pgNode)+b(pgNode);
dfx=sparse(transNum+1:transNum+pgNum,ones(pgNum,1),dPG,xNum,1);
else if(opfGoal==3)
dfT=-transG.*((f(transI)-f(transJ)).^2+(e(transI)-e(transJ)).^2);
dfPQ=zeros(pgvNum,1);
dfcapK=zeros(capNum,1);
EE=e*ones(1,nodeNum);
FF=f*ones(1,nodeNum);
dfe=2*sum(G.*(EE-EE'));
dff=2*sum(G.*(FF-FF'));
dfx=[dfT;dfPQ;dfcapK;dfe';dff'];
else if(opfGoal==4)
dfT=transB.*((f(transI)-f(transJ)).^2+(e(transI)-e(transJ)).^2);
dfPQ=zeros(pgvNum,1);
dfcapK=zeros(capNum,1);
EE=e*ones(1,nodeNum);
FF=f*ones(1,nodeNum);
dfe=-2*sum(B.*(EE-EE'));
dff=-2*sum(B.*(FF-FF'));
dfx=[dfT;dfPQ;dfcapK;dfe';dff'];
end
end
end
end
%% 不等式约束项
gxv=[PG(pgNode);QR(pvNode);capK;e.^2+f.^2]; %约束条件当前值
gxvx=[Pmin(pgNode);pvQmin(pvNode);capKmin.*capBi;Vmin.*Vmin]; %约束下限
gxvs=[Pmax(pgNode);pvQmax(pvNode);capKmax.*capBi;Vmax.*Vmax]; %约束上限
gxl=(e(lineI).*e(lineI)+f(lineI).*f(lineI)-e(lineI).*e(lineJ)-f(lineI).*f(lineJ)).*GIJ+(e(lineI).*f(lineJ)-e(lineJ).*f(lineI)).*BIJ;%线路功率当前值
gxlx=-ones(lineNum,1)*1000; %线路约束下限
gxls=ones(lineNum,1)*1000; %线路约束上限
gxT=T;
gxTx=transKmin; %变比下限
gxTs=transKmax; %变比上限
gx=[gxT;gxv;gxl]; %组合所有约束条件
gxx=[gxTx;gxvx;gxlx];
gsx=[gxTs;gxvs;gxls];
Lz=gx-l-gxx;
Lw=gx+u-gsx;
%% 形成修正方程常数项向量
muUL=mu*(U1-L1);
BB1=UW*Lw-LZ*Lz-muUL*ones(r,1);
BB=dhx*y-dfx+dgx*BB1; %修正方程常数项ψ(.,μ)
BB(transNum+pgvNum+capNum+nodeNum+balNode,1)=0; %保持平衡节点电压虚部不变，始终为0，则常数项平衡节点处置0
BB(transNum+pgvNum+capNum+balNode,1)=0; %保持平衡节点电压实部不变
const=[BB;hx]; %修正方程常数项向量

425
Sigmoid函数法/IEEE118.dat Normal file
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@ -0,0 +1,425 @@
118 179 100 100 0.1
1.e-5 2
1 69
0
1 1 2 0.0303 0.0999 0.0127
2 1 3 0.0129 0.0424 0.00541
3 4 5 0.00176 0.00798 0.00105
4 3 5 0.0241 0.1080 0.0142
5 5 6 0.0119 0.0540 0.00713
6 6 7 0.00459 0.0208 0.00275
7 8 9 0.00244 0.0305 0.5810
9 9 10 0.00258 0.0322 0.6150
10 4 11 0.0209 0.0688 0.00874
11 5 11 0.0203 0.0682 0.00869
12 11 12 0.00595 0.0196 0.00251
13 2 12 0.0187 0.0616 0.00786
14 3 12 0.0484 0.1600 0.0203
15 7 12 0.00862 0.0340 0.00437
16 11 13 0.02225 0.0731 0.00938
17 12 14 0.0215 0.0707 0.00908
18 13 15 0.0744 0.2444 0.03134
19 14 15 0.0595 0.1950 0.0251
20 12 16 0.0212 0.0834 0.0107
21 15 17 0.0132 0.0437 0.0222
22 16 17 0.0454 0.1801 0.0233
23 17 18 0.0123 0.0505 0.00649
24 18 19 0.01119 0.0493 0.00571
25 19 20 0.0252 0.1170 0.0149
26 15 19 0.0120 0.0394 0.00505
27 20 21 0.0183 0.0849 0.0108
28 21 22 0.0209 0.0970 0.0123
29 22 23 0.0342 0.1590 0.0202
30 23 24 0.0135 0.0492 0.0249
31 23 25 0.0156 0.0800 0.0432
33 25 27 0.0318 0.1630 0.0882
34 27 28 0.01913 0.0855 0.0108
35 28 29 0.0237 0.0943 0.0119
37 8 30 0.00431 0.0504 0.2570
38 26 30 0.00799 0.0860 0.4540
39 17 31 0.0474 0.1563 0.01995
40 29 31 0.0108 0.0331 0.00415
41 23 32 0.0317 0.1153 0.05865
42 31 32 0.0298 0.0985 0.01255
43 27 32 0.0229 0.0755 0.00963
44 15 33 0.0380 0.1244 0.01597
45 19 34 0.0752 0.2470 0.0316
46 35 36 0.00224 0.0102 0.00124
47 35 37 0.0110 0.0497 0.00659
48 33 37 0.0415 0.1420 0.0183
49 34 36 0.00871 0.0268 0.00284
50 34 37 0.00256 0.0094 0.00429
52 37 39 0.0321 0.1060 0.0135
53 37 40 0.0593 0.1680 0.0210
54 30 38 0.00464 0.0540 0.2110
55 39 40 0.0184 0.0605 0.00776
56 40 41 0.0145 0.0487 0.00611
57 40 42 0.0555 0.1830 0.0233
58 41 42 0.0410 0.1350 0.0172
59 43 44 0.0608 0.2454 0.03034
60 34 43 0.0413 0.1681 0.02113
61 44 45 0.0224 0.0901 0.0112
62 45 46 0.0400 0.1356 0.0166
63 46 47 0.0380 0.1270 0.0158
64 46 48 0.0601 0.1890 0.0236
65 47 49 0.0191 0.0625 0.00802
66 42 49 0.03575 0.1615 0.0860
67 45 49 0.0684 0.1860 0.0222
68 48 49 0.0179 0.0505 0.00629
69 49 50 0.0267 0.0752 0.00937
70 49 51 0.0486 0.1370 0.0171
71 51 52 0.0203 0.0588 0.00698
72 52 53 0.0405 0.1635 0.02029
73 53 54 0.0263 0.1220 0.0155
74 49 54 0.03976 0.1450 0.0734
75 54 55 0.0169 0.0707 0.0101
76 54 56 0.00275 0.00955 0.00366
77 55 56 0.00488 0.0151 0.00187
78 56 57 0.0343 0.0966 0.0121
79 50 57 0.0474 0.1340 0.0166
80 56 58 0.0343 0.0966 0.0121
81 51 58 0.0255 0.0719 0.00894
82 54 59 0.0503 0.2293 0.0299
83 56 59 0.04069 0.12243 0.05525
84 55 59 0.04739 0.2158 0.02823
85 59 60 0.0317 0.1450 0.0188
86 59 61 0.0328 0.1500 0.0194
87 60 61 0.00264 0.0135 0.00728
88 60 62 0.0123 0.0561 0.00734
89 61 62 0.00824 0.0376 0.0049
91 63 64 0.00172 0.0200 0.1080
93 38 65 0.00901 0.0986 0.5230
94 64 65 0.00269 0.0302 0.1900
95 49 66 0.0090 0.04595 0.0248
96 62 66 0.0482 0.2180 0.0289
97 62 67 0.0258 0.1170 0.0155
99 66 67 0.0224 0.1015 0.01341
100 65 68 0.00138 0.0160 0.3190
101 47 69 0.0844 0.2778 0.03546
102 49 69 0.0985 0.3240 0.0414
104 69 70 0.0300 0.1270 0.0610
105 24 70 0.10221 0.4115 0.05099
106 70 71 0.00882 0.0355 0.00439
107 24 72 0.0488 0.1960 0.0244
108 71 72 0.0446 0.1800 0.02222
109 71 73 0.00866 0.0454 0.00589
110 70 74 0.0401 0.1323 0.01684
111 70 75 0.0428 0.1410 0.0180
112 69 75 0.0405 0.1220 0.0620
113 74 75 0.0123 0.0406 0.00517
114 76 77 0.0444 0.1480 0.0184
115 69 77 0.0309 0.1010 0.0519
116 75 77 0.0601 0.1999 0.02489
117 77 78 0.00376 0.0124 0.00632
118 78 79 0.00546 0.0244 0.00324
119 77 80 0.01077 0.03318 0.0350
120 79 80 0.0156 0.0704 0.00945
121 68 81 0.00175 0.0202 0.4040
123 77 82 0.0298 0.0853 0.04087
124 82 83 0.0112 0.03665 0.01898
125 83 84 0.0625 0.1320 0.0129
126 83 85 0.0430 0.1480 0.0174
127 84 85 0.0302 0.0641 0.00617
128 85 86 0.0350 0.1230 0.0138
129 86 87 0.02828 0.2074 0.02225
130 85 88 0.0200 0.1020 0.0138
131 85 89 0.0239 0.1730 0.0235
132 88 89 0.0139 0.0712 0.00969
133 89 90 0.01631 0.06515 0.0794
134 90 91 0.0254 0.0836 0.0107
135 89 92 0.00791 0.03827 0.0481
136 91 92 0.0387 0.1272 0.01634
137 92 93 0.0258 0.0848 0.0109
138 92 94 0.0481 0.1580 0.0203
139 93 94 0.0223 0.0732 0.00938
140 94 95 0.0132 0.0434 0.00555
141 80 96 0.0356 0.1820 0.0247
142 82 96 0.0162 0.0530 0.0272
143 94 96 0.0269 0.0869 0.0115
144 80 97 0.0183 0.0934 0.0127
145 80 98 0.0238 0.1080 0.0143
146 80 99 0.0454 0.2060 0.0273
148 94 100 0.0178 0.0580 0.0302
149 95 96 0.0171 0.0547 0.00737
150 96 97 0.0173 0.0885 0.0120
151 98 100 0.0397 0.1790 0.0238
152 99 100 0.0180 0.0813 0.0108
153 100 101 0.0277 0.1262 0.0164
154 92 102 0.0123 0.0559 0.00732
155 101 102 0.0246 0.1120 0.0147
156 100 103 0.0160 0.0525 0.0268
157 100 104 0.0451 0.2040 0.02705
158 103 104 0.0466 0.1584 0.02035
159 103 105 0.0535 0.1625 0.0204
160 100 106 0.0605 0.2290 0.0310
161 104 105 0.00994 0.0378 0.00493
162 105 106 0.0140 0.0547 0.00717
163 105 107 0.0530 0.1830 0.0236
164 105 108 0.0261 0.0703 0.09222
166 108 109 0.0105 0.0288 0.0038
167 103 110 0.03906 0.1813 0.02305
168 109 110 0.0278 0.0762 0.0101
169 110 111 0.0220 0.0755 0.0100
170 110 112 0.0247 0.0640 0.0310
171 17 113 0.00913 0.0301 0.00384
172 32 113 0.0615 0.2030 0.0259
173 32 114 0.0135 0.0612 0.00814
174 27 115 0.0164 0.0741 0.00986
175 114 115 0.0023 0.0104 0.00138
176 68 116 0.00034 0.00405 0.0820
177 12 117 0.0329 0.1400 0.0179
178 75 118 0.01450 0.04810 0.00599
179 76 118 0.0164 0.0544 0.00678
0
5 -0.4
37 -0.25
45 .1
46 .1
79 .2
83 .1
110 .06
0
1 8 5 0.0 0.0267 0.9850 0.9 1.1 1
2 25 26 0.0 0.0382 0.9600 0.9 1.1 1
3 17 30 0.0 0.0388 0.9600 0.9 1.1 1
4 37 38 0.0 0.0375 0.9350 0.9 1.1 1
5 59 63 0.0 0.0386 0.9600 0.9 1.1 1
6 61 64 0.0 0.0268 0.9850 0.9 1.1 1
7 65 66 0.0 0.0370 0.9350 0.9 1.1 1
8 68 69 0.0 0.0370 0.9350 0.9 1.1 1
9 80 81 0.0 0.0370 0.9350 0.9 1.1 1
10 92 100 0.0648 0.2950 1. 0.9 1.1 0
11 106 107 0.0530 0.1830 1. 0.9 1.1 0
0
1 0. 0. 51. 27.
2 0. 0. 20. 9.
3 0. 0. 39. 10.
4 -9. 0. 30. 12.
5 0. 0. 0. 0.
6 0. 0. 52. 22.
7 0. 0. 19. 2.
8 -28. 0. 0. 0.
9 0. 0. 0. 0.
10 450. 0. 0. 0.
11 0. 0. 70. 23.
12 85. 0. 47. 10.
13 0. 0. 34. 16.
14 0. 0. 14. 1.
15 0. 0. 90. 30.
16 0. 0. 25. 10.
17 0. 0. 11. 3.
18 0. 0. 60. 34.
19 0. 0. 45. 25.
20 0. 0. 18. 3.
21 0. 0. 14. 8.
22 0. 0. 10. 5.
23 0. 0. 7. 3.
24 -13. 0. 0. 0.
25 220. 0. 0. 0.
26 314. 0. 0. 0.
27 -9. 0. 62. 13.
28 0. 0. 17. 7.
29 0. 0. 24. 4.
30 0. 0. 0. 0.
31 7. 0. 43. 27.
32 0. 0. 59. 23.
33 0. 0. 23. 9.
34 0. 0. 59. 26.
35 0. 0. 33. 9.
36 0. 0. 31. 17.
37 0. 0. 0. 0.
38 0. 0. 0. 0.
39 0. 0. 27. 11.
40 -46. 0. 20. 23.
41 0. 0. 37. 10.
42 -59. 0. 37. 23.
43 0. 0. 18. 7.
44 0. 0. 16. 8.
45 0. 0. 53. 22.
46 19. 0. 28. 10.
47 0. 0. 34. 0.
48 0. 0. 20. 11.
49 204. 0. 87. 30.
50 0. 0. 17. 4.
51 0. 0. 17. 8.
52 0. 0. 18. 5.
53 0. 0. 23. 11.
54 48. 0. 113. 32.
55 0. 0. 63. 22.
56 0. 0. 84. 18.
57 0. 0. 12. 3.
58 0. 0. 12. 3.
59 155. 0. 277. 113.
60 0. 0. 78. 3.
61 160. 0. 0. 0.
62 0. 0. 77. 14.
63 0. 0. 0. 0.
64 0. 0. 0. 0.
65 391. 0. 0. 0.
66 392. 0. 39. 18.
67 0. 0. 28. 7.
68 0. 0. 0. 0.
69 516.4 0. 0. 0.
70 0. 0. 66. 20.
71 0. 0. 0. 0.
72 -12. 0. 0. 0.
73 -6. 0. 0. 0.
74 0. 0. 68. 27.
75 0. 0. 47. 11.
76 0. 0. 68. 36.
77 0. 0. 61. 28.
78 0. 0. 71. 26.
79 0. 0. 39. 32.
80 477. 0. 130. 26.
81 0. 0. 0. 0.
82 0. 0. 54. 27.
83 0. 0. 20. 10.
84 0. 0. 11. 7.
85 0. 0. 24. 15.
86 0. 0. 21. 10.
87 4. 0. 0. 0.
88 0. 0. 48. 10.
89 607. 0. 0. 0.
90 -85. 0. 78. 42.
91 -10. 0. 0. 0.
92 0. 0. 65. 10.
93 0. 0. 12. 7.
94 0. 0. 30. 16.
95 0. 0. 42. 31.
96 0. 0. 38. 15.
97 0. 0. 15. 9.
98 0. 0. 34. 8.
99 -42. 0. 0. 0.
100 252. 0. 37. 18.
101 0. 0. 22. 15.
102 0. 0. 5. 3.
103 40. 0. 23. 16.
104 0. 0. 38. 25.
105 0. 0. 31. 26.
106 0. 0. 43. 16.
107 -22. 0. 28. 12.
108 0. 0. 2. 1.
109 0. 0. 8. 3.
110 0. 0. 39. 30.
111 36. 0. 0. 0.
112 -43. 0. 25. 13.
113 -6. 0. 0. 0.
114 0. 0. 8. 3.
115 0. 0. 22. 7.
116 -184. 0. 0. 0.
117 0. 0. 20. 8.
118 0. 0. 33. 15.
0
1 .955 -5. 15.
4 .998 -300. 300.
6 .99 -13. 50.
8 1.015 -300. 300.
10 1.05 -147. 200.
12 .99 -35. 120.
15 .97 -10. 30.
18 .973 -16. 50.
19 .963 -8. 24.
24 .992 -300. 300.
25 1.05 -47. 140.
26 1.015 -1000. 1000.
27 .968 -300. 300.
31 .967 -300. 300.
32 .964 -14. 42.
34 .984 -8. 24.
36 .98 -8. 24.
40 .97 -300. 300.
42 .985 -300. 300.
46 1.005 -100. 100.
49 1.025 -85. 210.
54 .955 -300. 300.
55 .952 -8. 23.
56 .954 -8. 15.
59 .985 -60. 180.
61 .995 -100. 300.
62 .998 -20. 20.
65 1.005 -67. 200.
66 1.05 -67. 200.
69 1.01 -300. 300.
70 .984 -10. 32.
72 .98 -100. 100.
73 .991 -100. 100.
74 .958 -6. 9.
76 .943 -8. 23.
77 1.006 -20. 70.
80 1.04 -165. 280.
85 .985 -8. 23.
87 1.015 -100. 1000.
89 1.005 -210. 300.
90 .985 -300. 300.
91 .98 -100. 100.
92 .993 -3. 9.
99 1.01 -100. 100.
100 1.017 -50. 155.
103 1.001 -15. 40.
104 .971 -8. 23.
105 .965 -8. 23.
107 .952 -200. 200.
110 .973 -8. 23.
111 .98 -100. 1000.
112 .975 -100. 1000.
113 .993 -100. 200.
116 1.005 -1000. 1000.
0
10 0. 1.25 1. 100. 600. 1
12 0. 2.6 1.2 60. 200. 1
25 0. 1.5 1. 50. 300. 1
26 0. 1.5 1. 100. 400. 1
49 0. 2.1 1. 100. 400. 1
54 0. 2.0 1.4 20. 300. 1
59 0. 1.6 1. 50. 350. 1
61 0. 1.5 1. 50. 400. 1
65 0. 1.5 1. 100. 500. 1
66 0. 1.5 1. 100. 500. 1
69 0. 1.0 1. 100. 800. 1
80 0. 1.23 1. 100. 600. 1
89 0. 1.2 1. 100. 800. 1
100 0. 1.6 1. 100. 400. 1
103 0. 2.5 1.2 20. 200. 1
111 0. 2.4 1.1 10. 200. 1
0
1 17 0 0.1 0 0 10
2 34 0 0.1 0.14 0 10
3 44 0 0.1 0.1 0 10
4 107 0 0.1 0.06 0 10
5 82 0 0.1 0.2 0 10
6 48 0 0.1 0.15 0 10
7 74 0 0.1 0.12 0 10
8 105 0 0.1 0.2 0 10
0
0
0
1 100 92 -25. 25.
2 106 107 -18. 18.
0
0
1 17 0 0.05 0 0 6
2 34 0 0.05 0.14 0 6
3 44 0 0.05 0.1 0 6
4 107 0 0.05 0.06 0 6
5 82 0 0.05 0.2 0 6
6 48 0 0.05 0.15 0 6
7 74 0 0.05 0.12 0 6
8 105 0 0.05 0.2 0 6
0
1 17 0 0.1 0 0 6
2 34 0 0.1 0.14 0 6
3 44 0 0.1 0.1 0 6
4 107 0 0.1 0.06 0 6
5 82 0 0.1 0.2 0 6
6 48 0 0.1 0.15 0 6
7 74 0 0.1 0.12 0 6
8 105 0 0.1 0.2 0 6
0
1 17 0 0.2 0 0 6
2 34 0 0.2 0.14 0 6
3 44 0 0.2 0.1 0 6
4 107 0 0.2 0.06 0 6
5 82 0 0.2 0.2 0 6
6 48 0 0.2 0.15 0 6
7 74 0 0.2 0.12 0 6
8 105 0 0.2 0.2 0 6

98
Sigmoid函数法/IEEE30.dat Normal file
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@ -0,0 +1,98 @@
30 41 100.0 100 0.1
1.e-5 2
1 1
0
1 1 2 0.0192 0.0575 0.0264
2 1 3 0.0452 0.1652 0.0204
3 2 4 0.0570 0.1737 0.0184
4 3 4 0.0132 0.0379 0.0042
5 2 5 0.0472 0.1983 0.0209
6 2 6 0.0581 0.1763 0.0187
7 4 6 0.0119 0.0414 0.0045
8 5 7 0.0460 0.1160 0.0102
9 6 7 0.0267 0.0820 0.0085
10 6 8 0.0120 0.0420 0.0045
13 9 11 0.0 0.2080 0.0
15 12 13 0.0 0.1400 0.0
16 12 14 0.1231 0.2559 0.0
17 12 15 0.0662 0.1304 0.0
18 12 16 0.0945 0.1987 0.0
19 14 15 0.2210 0.1997 0.0
20 16 17 0.0524 0.1923 0.0
21 15 18 0.1073 0.2185 0.0
22 18 19 0.0639 0.1292 0.0
23 19 20 0.0340 0.0680 0.0
24 10 20 0.0936 0.2090 0.0
25 10 17 0.0324 0.0845 0.0
26 10 21 0.0348 0.0749 0.0
27 10 22 0.0727 0.1499 0.0
28 21 22 0.0116 0.0236 0.0
29 15 23 0.1000 0.2020 0.0
30 22 24 0.1150 0.1790 0.0
31 23 24 0.1320 0.2700 0.0
32 24 25 0.1885 0.3292 0.0
33 25 26 0.2544 0.3800 0.0
34 25 27 0.1093 0.2087 0.0
36 27 29 0.2198 0.4153 0.0
37 27 30 0.3202 0.6027 0.0
38 29 30 0.2399 0.4533 0.0
39 8 28 0.0636 0.2000 0.0214
40 6 28 0.0169 0.0599 0.0065
41 9 10 0.0 0.1100 0.0
0
0
1 6 9 0.0 0.2080 0.978 0.9 1.1 1
2 6 10 0.0 0.5560 0.969 0.9 1.1 1
3 4 12 0.0 0.2560 0.932 0.9 1.1 1
4 28 27 0.0 0.3960 0.968 0.9 1.1 1
0
1 138.77 -6.49 0. 0.
2 20 41.71 21.7 12.7
3 0. 0. 2.4 1.2
4 0. 0. 7.6 1.6
5 15 16.66 94.2 19.
6 0. 0. 0. 0.
7 0. 0. 22.8 10.9
8 60 29.31 30. 30.
9 0. 0. 0. 0.
10 0. 0. 5.8 2.
11 80 6.71 0. 0.
12 0. 0. 11.2 7.5
13 90 3.37 0. 0.
14 0. 0. 6.2 1.6
15 0. 0. 8.2 2.5
16 0. 0. 3.5 1.8
17 0. 0. 9. 5.8
18 0. 0. 3.2 .9
19 0. 0. 9.5 3.4
20 0. 0. 2.2 .7
21 0. 0. 17.5 11.2
22 0. 0. 0. 0.
23 0. 0. 3.2 1.6
24 0. 0. 8.7 6.7
25 0. 0. 0. 0.
26 0. 0. 3.5 2.3
27 0. 0. 0. 0.
28 0. 0. 0. 0.
29 0. 0. 2.4 .9
30 0. 0. 10.6 1.9
0
1 1.060 -50 50.
2 1.043 -40. 60.
5 1.010 -40. 40.
8 1.010 -10. 40.
11 1.082 -6. 24.
13 1.071 -6. 24.
0
1 10. 2.0 2.0 10. 200. 1
2 10. 1.5 2.4 10. 60. 1
5 20. 1.8 0.8 10. 51. 1
8 10. 1.0 1.2 10. 35. 1
11 20. 1.8 0.8 10. 51. 1
13 10. 1.5 2.0 10. 50. 1
0
1 10 0 0.1 0.19 0 6
2 24 0 0.1 0.043 0 6
0
0

1153
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%*******************************************************
% 程序名称：电力系统无功优化程序
% 程序功能：主程序
% 程序算法：现代内点法，采用Sigmoid函数处理离散变量
% 目标函数：发电费用最小（1）、有功出力最小（2）、有功网损最小（3）、无功网损最小（4）
% 编者： 韦园清
% 编写时间：2010年10月
%*******************************************************
function []=OPF(filename)
clc;
%% 读取数据
data=dlmread(filename);
if data(1,1)<1780
%读取1780节点系统格式类型的数据
[nodeNum,lineNum,capacity,kmax,centrPara,accuracy,opfGoal,balNum,balNode,mtrLine,mtrGround,mtrTrans,runPara,Pg,Qg,Pd,Qd,pvNum,pvNode,pvV,...
pvQmin,pvQmax,pgNumall,pgNodeall,pgNum,pgNode,a,b,c,Pmin,Pmax,capNum,capI,capGi,capBi,capK,capKmin,capKmax,Vmax,Vmin]=readData(filename);
tic;
%形成节点导纳矩阵
[G,B,transY,transG,transB,transG1,transB1,transNum,lineNum,lineI,lineJ,lineB,transI,transJ,transK0,transKmin,transKmax]=formY(nodeNum,...
lineNum,mtrLine,mtrGround,mtrTrans,capI,capBi,capK);
else
%读取IEEE标准格式数据
[nodeNum,lineNum,capacity,kmax,accuracy,balNum,balNode,mtrLine,mtrGround,mtrTrans,runPara,Pg,Qg,Pd,Qd,pvNum,pvNode,pvV,pvQmin,pvQmax,...
mtrCapacitor,pgNum,pgNode,a,b,c,Pmin,Pmax,Vmin,Vmax,centrPara]=readData_RPP(data) ;
tic;
%形成节点导纳矩阵
[G,B,lineI,lineJ,lineB,transI,transJ,transK0,transNum,transKmin,transKmax,capI,capGi,capBi,capK,capKmin,capKmax,capNum,transG,transB,...
transG1,transB1,lineNum]=formY_RPP(nodeNum,lineNum,mtrLine,mtrGround,mtrTrans,mtrCapacitor);
end
%% 初始化
[e,f,PG,QR,Pg,Qg,T,pgvNum,xNum,m,r,l,u,z,w,x,y,para3,mu0,b0,bei,dmaxOut1,dmaxOut2,xz1,xz2,dmaxOut3,dmaxOut4,xz3,xz4,xz5,muOut,...
opfGoal,times,secondBegin,ifconverge,k2,mismatch]=seting(nodeNum,lineNum,transNum,transK0,capNum,capK,pvQmin,pvQmax,pvNum,pvNode,pvV,...
pgNum,pgNode,Pmin,Pmax,Pg,Qg);
disp (['迭代次数 互补间隙 最优潮流目标'])
%% 进入循环体求解
for k=0:kmax
[H1,N1,diagE,diagF,hx,Gap,max_hx,fx,Pg,Qg,xz1,dmaxOut1,xz2,dmaxOut2,xz3,dmaxOut3,xz4,dmaxOut4,PGR]=midResult(nodeNum,pgNode,opfGoal,...
z,l,u,w,Pg,Qg,e,f,G,B,a,b,c,PG,Pd,Qd,k,xz1,dmaxOut1,xz2,dmaxOut2,xz3,dmaxOut3,xz4,dmaxOut4,times,accuracy,mismatch);
if Gap<accuracy&&max(abs(hx))<mismatch %判断互补间隙和最大不平衡量是否达到精度
if times==1
times=2;
end
if times==2
if secondBegin==1
[x,secondBegin,mut,oneTrans,Zt,tij,Tn,kt0,r,l,u,z,w,y,oneCap,capKn,Bci,Zb,mub,q0,Tn1,capKn1,Kn,capK,firstT,firstcapK,...
firstfx,firstV,Gap]=snd_setting(x,secondBegin,transNum,T,transKmin,transKmax,r,m,capNum,capK,pgvNum,mu0,capBi,fx,e,f);
end
if times==2
tij_Bci=[tij;Bci];
index_0= tij_Bci<0.5; %获取靠近0的值下标
index_1=find(tij_Bci>=0.5); %获取靠近1的值下标
tij_0=max(tij_Bci(index_0));%获取靠近0的值中最大的量
tij_1=max(ones(size(index_1))-tij_Bci(index_1));%获取靠近1的值中最小的量
if isempty(tij_0)
tmax=tij_1;
else if isempty(tij_1)
tmax=tij_0;
else
tmax=max(tij_0,tij_1);%获取所有离散变量远离0或1最大的量
end
end
if (tmax<accuracy) %判断离散变量是否达到精度
ifconverge=1;
break
end
end
end
end
mu=(centrPara*Gap)/(2*r); %计算扰动因子
if times==1 %预计算过程
%形成修正方程系数矩阵
[HSB,dhx,dgx,dgxT,GIJ,BIJ,L1,U1,LZ,UW,transG,transB]=formHSB(nodeNum,balNode,opfGoal,lineNum,transNum,lineI,lineJ,transI,transJ,T,...
transG,transB,pgNode,pvNode,G,B,e,f,pgNum,pvNum,pgvNum,xNum,capNum,capI,a,m,r,l,u,z,w,y,N1,H1,diagE,diagF,balNum);
%形成扰动KKT方程不平衡量矩阵
[const,Lz,Lw,L1,U1]=Constant(nodeNum,opfGoal,lineNum,transNum,transI,transJ,transG,transB,T,transKmin,transKmax,lineI,lineJ,balNode,...
mu,G,B,GIJ,BIJ,e,f,Pmin,Pmax,a,b,PG,QR,pvQmin,pvQmax,pgNum,pgvNum,xNum,capNum,capK,capKmin,capKmax,pgNode,pvNode,dhx,dgx,L1,U1,LZ,...
UW,l,u,y,r,hx,Vmax,Vmin,capBi);
%求解方程并更新变量
[z,l,u,w,x,y,PG,QR,Pg,Qg,e,f,T,capK,G,B]=solve(HSB,const,mu,r,nodeNum,pgNum,pvNum,xNum,transNum,capNum,capI,capK,pgNode,pvNode,Pg,...
Qg,m,x,y,z,l,u,w,Lz,Lw,LZ,UW,dgxT,L1,U1,G,B,transI,transJ,T,transG1,transB1);
else %连续化处理过程
k2=k2+1;
xz5=[xz5 k2]; %保留每次迭代光滑参数的值，用于作图
muOut=[muOut mub(2)];
%形成修正方程系数矩阵
[HSB,dhx,dgx,dgxT,GIJ,BIJ,L1,U1,LZ,UW,transG,transB,dT_Zt,mut,mub]=snd_formHSB(nodeNum,balNode,opfGoal,lineNum,transNum,lineI,...
lineJ,transI,transJ,T,transG,transB,pgNode,pvNode,G,B,e,f,pgNum,pvNum,pgvNum,xNum,a,m,r,l,u,z,w,y,kt0,mut,Zt,oneTrans,oneCap,Zb,...
mub,q0,capBi,capNum,capI,tij,Bci,N1,H1,diagE,diagF,b0,balNum);
%形成扰动KKT方程不平衡量矩阵
[const,Lz,Lw,L1,U1]=snd_Constant(nodeNum,opfGoal,lineNum,transNum,transI,transJ,transG,transB,lineI,lineJ,balNode,mu,G,B,GIJ,BIJ,e,f,...
Pmin,Pmax,a,b,PG,QR,pvQmin,pvQmax,pgNum,pgvNum,xNum,pgNode,pvNode,dhx,dgx,L1,U1,LZ,UW,l,u,y,r,dT_Zt,capNum,hx,Vmax,Vmin,Zt,Zb,bei,...
mu0,oneTrans,oneCap);
%求解方程并更新变量
[z,l,u,w,x,y,PG,QR,Pg,Qg,e,f,T,G,B,Zt,tij,Zb,Bci,capK,mut,mub]=snd_solve(HSB,const,mu,r,nodeNum,pgNum,pvNum,pgvNum,xNum,transNum,pgNode,...
pvNode,Pg,Qg,m,x,y,z,l,u,w,Lz,Lw,LZ,UW,dgxT,L1,U1,G,B,transI,transJ,T,transG1,transB1,kt0,Tn,mut,oneTrans,q0,capKn,mub,oneCap,capK,...
capNum,capI,capBi);
end
end
if k>=kmax
disp '最优潮流计算不收敛！'
disp(k)
else
disp '最优潮流计算收敛！'
disp(['迭代',num2str(k),'次！'])
end
toc;
%% 输出计算结果
OutResult(e,f,T,k,Gap,fx,transI,transJ,filename,nodeNum,PGR,pgNode,QR,pvNode,capI,capK,firstfx,firstT,firstcapK,Tn,Tn1,capKn,capKn1,ifconverge,...
max_hx,G,B,balNode,toc,firstV,capBi);
%% 作互补间隙和最大不平衡量收敛曲线图
% plot(xz1,dmaxOut1,'-ks','LineWidth',2,'MarkerEdgeColor','k','MarkerFaceColor','k','MarkerSize',3)
% hold on;
% plot(xz2,dmaxOut2,'-ks','LineWidth',2,'MarkerEdgeColor','k','MarkerFaceColor','k','MarkerSize',3)
% hold on;
% xlabel('迭代次数')
% ylabel('互补间隙')
% plot(xz3,dmaxOut3,'-ks','LineWidth',2,'MarkerEdgeColor','k','MarkerFaceColor','k','MarkerSize',3)
% hold on;
% plot(xz4,dmaxOut4,'-ks','LineWidth',2,'MarkerEdgeColor','k','MarkerFaceColor','k','MarkerSize',3)
% xlabel('迭代次数')
% ylabel('最大不平衡量')
%% 作mut在迭代过程中的变化图
% plot(xz5,muOut,'-ks','LineWidth',2,'MarkerEdgeColor','k','MarkerFaceColor','k','MarkerSize',3)
% xlabel('迭代次数')
% ylabel('μ')
% hold on;
%% 做二次优化的互补间隙图
% plot(xz5,dmaxOut2,'-ks','LineWidth',2,'MarkerEdgeColor','k','MarkerFaceColor','k','MarkerSize',3)
% hold on;
% xlabel('迭代次数')
% ylabel('互补间隙')

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function OutResult(e,f,T,k,Gap,fx,transI,transJ,filename,nodeNum,PGR,pgNode,QR,pvNode,capI,capK,firstfx,firstT,firstcapK,Tn,Tn1,...
capKn,capKn1,ifconverge,max_hx,G,B,balNode,toc,firstV,capBi)
%程序功能：输出计算结果
%编写时间：2010年10月
Y1=G+1j*B;
V1=e+1j*f;
NodeS=zeros(nodeNum,1);
NodeS(pvNode)=V1(pvNode,:).*conj(Y1(pvNode,:)*V1); %计算平衡节点和PV节点的节点复功率，Y1(pvNode,:)*V1为节点的注入电流
balanceP=real(NodeS(balNode,1)); %获取平衡节点的有功功率
PGR(balNode,1)=balanceP;
balanceQ=imag(NodeS(balNode,1));
QR(balNode,1)=balanceQ;
resultFile=['result_' filename];
fid=fopen(resultFile,'w');
result=[k;Gap;fx;firstfx;toc;max_hx;ifconverge]; %收敛信息
fprintf(fid,'%2.0f %4.4e %6.6f %6.6f %4.4f %4.4e %2.0f\r\n',result);
fprintf(fid,'%1.0f\r\n',0);
trans=[transI';transJ';(1./T)';(1./firstT)';(1./Tn)';(1./Tn1)']; %变压器变比结果
fprintf(fid,'%2.0f %2.0f %5.4f %5.4f %5.4f %5.4f\r\n',trans);
fprintf(fid,'%1.0f\r\n',0);
nn=1:nodeNum;
e=full(e);
f=full(f);
V=sqrt(e.^2+f.^2);
Vresult=[nn;e';f';V';firstV']; %节点电压结果
fprintf(fid,'%3.0f %5.4f %5.4f %5.4f %5.4f\r\n',Vresult);
fprintf(fid,'%1.0f\r\n',0);
PGresult=[pgNode';PGR(pgNode)']; %有功出力结果
PGresult=full(PGresult);
fprintf(fid,'%2.0f %4.4f\r\n',PGresult);
fprintf(fid,'%1.0f\r\n',0);
QRresult=[pvNode';QR(pvNode)']; %无功出力结果
QRresult=full(QRresult);
fprintf(fid,'%2.0f %4.4f\r\n',QRresult);
fprintf(fid,'%1.0f\r\n',0);
capK=capK.*capBi;
capKn=capKn.*capBi;
capKn1=capKn1.*capBi;
Capresult=[capI';capK';firstcapK';capKn';capKn1']; %电容电抗器投入组数结果
Capresult=full(Capresult);
fprintf(fid,'%2.0f %3.2f %5.4f %3.2f %3.2f\r\n',full(Capresult));
fprintf(fid,'%1.0f\r\n',0);
fclose(fid);

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function [HSB,dhx,dgx,dgxT,GIJ,BIJ,L1,U1,LZ,UW,transG,transB]=...
formHSB(nodeNum,balNode,opfGoal,lineNum,transNum,lineI,lineJ,transI,transJ,T,transG,transB,pgNode,pvNode,...
G,B,e,f,pgNum,pvNum,pgvNum,xNum,capNum,capI,a,m,r,l,u,z,w,y,N1,H1,diagE,diagF,balNum)
%程序功能：预计算过程，形成修正方程系数矩阵
%编写时间：2010年10月
%% 形成等式约束雅可比矩阵
ef1=e(transI).*e(transJ)+f(transI).*f(transJ);
ef2=e(transI).*f(transJ)-e(transJ).*f(transI);
ef3=e(transI).*e(transI)+f(transI).*f(transI);
ef1G=ef1.*transG;
ef1B=ef1.*transB;
ef2G=ef2.*transG;
ef2B=ef2.*transB;
dhPTi=-ef1G+ef2B+2*ef3.*transG.*T;
dhPTj=-ef1G-ef2B;
dhPT=sparse(1:transNum,transI,dhPTi,transNum,nodeNum)+sparse(1:transNum,transJ,dhPTj,transNum,nodeNum);%有功平衡方程P对变压器变比求偏导
dhQTi=ef1B+ef2G-2*ef3.*transB.*T;
dhQTj=ef1B-ef2G;
dhQT=sparse(1:transNum,transI,dhQTi,transNum,nodeNum)+sparse(1:transNum,transJ,dhQTj,transNum,nodeNum);%无功平衡方程Q对变压器变比求偏导
dhP=sparse(1:pgNum,pgNode,ones(pgNum,1),pgNum,m);
dhQ1=sparse(1:pvNum,pvNode,ones(pvNum,1),pvNum,nodeNum);
dhQ=[sparse(pvNum,nodeNum) dhQ1];
dhcapK1=sparse(1:capNum,capI,(e(capI).^2+f(capI).^2),capNum,nodeNum); %功率平衡方程对电容电抗器组数求偏导
dhcapK=[sparse(capNum,nodeNum) dhcapK1];
%功率方程雅可比矩阵
deG=diagE*G;
dfB=diagF*B;
deB=diagE*B;
dfG=diagF*G;
dH1=sparse(1:nodeNum,1:nodeNum,H1,nodeNum,nodeNum);
dN1=sparse(1:nodeNum,1:nodeNum,N1,nodeNum,nodeNum);
Hij=-dH1-deG-dfB;
Nij=-dN1+deB-dfG;
Jij=dN1-dfG+deB;
Lij=-dH1+dfB+deG;
%合并形成功率方程雅可比矩阵
dhJacb=[Hij Nij;Jij Lij]';
%合并形成等式约束雅可比矩阵h(x)
dhx=[dhPT dhQT;dhP;dhQ;dhcapK;dhJacb];
%% 形成不等式约束雅可比矩阵▽g(x)
dgT1=sparse(1:transNum,1:transNum,ones(transNum,1),transNum,r-lineNum);
dglT=(e(transI).^2+f(transI).^2-e(transI).*e(transJ)-f(transI).*f(transJ)).*transG+(e(transI).*f(transJ)-e(transJ).*f(transI)).*transB;
dgT2=sparse(1:transNum,lineNum-transNum+1:lineNum,dglT,transNum,lineNum);
dgT=[dgT1 dgT2]; %所有不等式对变比求导的模块
dgP=sparse(1:pgNum,transNum+1:transNum+pgNum,ones(pgNum,1),pgNum,r); %所有不等式约束对PG求导的模块
dgQ=sparse(1:pvNum,transNum+pgNum+1:transNum+pgvNum,ones(pvNum,1),pvNum,r); %所有不等式约束对QR求导的模块
dgcapK=sparse(1:capNum,transNum+pgvNum+1:transNum+pgvNum+capNum,ones(capNum,1),capNum,r);%所有不等式约束对capK求导的模块
dgve=2*diagE;
dgvf=2*diagF;
sizeG=size(G);
GIJ=G(sub2ind(sizeG,lineI,lineJ));
BIJ=B(sub2ind(sizeG,lineI,lineJ));
dgleI=(2*e(lineI)-e(lineJ)).*GIJ+f(lineJ).*BIJ;
dgleJ=-e(lineI).*GIJ-f(lineI).*BIJ;
dglfI=(2*f(lineI)-f(lineJ)).*GIJ-e(lineJ).*BIJ;
dglfJ=-f(lineI).*GIJ+e(lineI).*BIJ;
dgle=sparse(lineI,(1:lineNum),dgleI,nodeNum,lineNum)+sparse(lineJ,(1:lineNum),dgleJ,nodeNum,lineNum);
dglf=sparse(lineI,(1:lineNum),dglfI,nodeNum,lineNum)+sparse(lineJ,(1:lineNum),dglfJ,nodeNum,lineNum);
dg0=sparse(m,transNum+pgvNum+capNum);
dgvl=[dgve dgle;dgvf dglf];
dgef=[dg0 dgvl]; %所有不等式约束对电压实部、虚部求偏导的模块
dgx=[dgT;dgP;dgQ;dgcapK;dgef]; %不等式约束雅克比矩阵
%% 形成对角阵
Z=sparse(1:r,1:r,z,r,r);
W=sparse(1:r,1:r,w,r,r);
L1=sparse(1:r,1:r,1./l,r,r);
U1=sparse(1:r,1:r,1./u,r,r);
LZ=L1*Z;
UW=U1*W;
%% 形成海森伯矩阵
%目标函数的海森伯矩阵▽2f(x)
if(opfGoal==2)%目标为有功出力最小
HSdfx=sparse(xNum,xNum);
else if(opfGoal==1)
HSdfx=sparse(transNum+1:transNum+pgNum,transNum+1:transNum+pgNum,2*a(pgNode),xNum,xNum);%仅目标函数对PG求偏导处的对角元为非零元素，其他都为0(目标为发电耗量最小)
else if(opfGoal==3)
d2ftei=-2*transG.*(e(transI)-e(transJ));
d2ftej=-d2ftei;
d2ftfi=-2*transG.*(f(transI)-f(transJ));
d2ftfj=-d2ftfi;
d2fte=sparse(1:transNum,transI,d2ftei,transNum,nodeNum)+sparse(1:transNum,transJ,d2ftej,transNum,nodeNum);
d2ftf=sparse(1:transNum,transI,d2ftfi,transNum,nodeNum)+sparse(1:transNum,transJ,d2ftfj,transNum,nodeNum);
d2fT0=sparse(transNum,transNum+pgvNum+capNum);
d2fT=[d2fT0 d2fte d2ftf];
d2fPGQR=sparse(pgvNum,xNum);
d2fcapK=sparse(capNum,xNum);
d2fee=2*(G-sparse(1:nodeNum,1:nodeNum,sum(G,2),nodeNum,nodeNum));
d2fff=d2fee;
zero_nodeNum=sparse(nodeNum,nodeNum);
d2f_ef_ef=[d2fee zero_nodeNum;zero_nodeNum d2fff];
d2efT=[d2fte d2ftf]';
d2f_ef=[d2efT sparse(2*nodeNum,pgvNum+capNum) d2f_ef_ef];
HSdfx=[d2fT;d2fPGQR;d2fcapK;d2f_ef];
else if(opfGoal==4)
d2ftei=2*transB.*(e(transI)-e(transJ));
d2ftej=-d2ftei;
d2ftfi=2*transB.*(f(transI)-f(transJ));
d2ftfj=-d2ftfi;
d2fte=sparse(1:transNum,transI,d2ftei,transNum,nodeNum)+sparse(1:transNum,transJ,d2ftej,transNum,nodeNum);
d2ftf=sparse(1:transNum,transI,d2ftfi,transNum,nodeNum)+sparse(1:transNum,transJ,d2ftfj,transNum,nodeNum);
d2fT0=sparse(transNum,transNum+pgvNum+capNum);
d2fT=[d2fT0 d2fte d2ftf];
d2fPGQR=sparse(pgvNum,xNum);
d2fcapK=sparse(capNum,xNum);
d2fee=-2*(B-sparse(1:nodeNum,1:nodeNum,sum(B,2),nodeNum,nodeNum));
d2fff=d2fee;
zero_nodeNum=sparse(nodeNum,nodeNum);
d2f_ef_ef=[d2fee zero_nodeNum;zero_nodeNum d2fff];
d2efT=[d2fte d2ftf]';
d2f_ef=[d2efT sparse(2*nodeNum,pgvNum+capNum) d2f_ef_ef];
HSdfx=[d2fT;d2fPGQR;d2fcapK;d2f_ef];
end
end
end
end
%等式约束海森伯矩阵与拉格朗日乘子y的乘积▽2h(x)*y
y1=y(1:nodeNum,1);
y2=y(nodeNum+1:2*nodeNum,1);
dhT2=2*ef3.*(transG.*y1(transI)-transB.*y2(transI)); %功率方程对变压器变比求二次偏导所得的列向量
HSdhT=sparse(1:transNum,1:transNum,dhT2,transNum+pgvNum+capNum,transNum+pgvNum+capNum);
eiG=e(transI).*transG;
ejG=e(transJ).*transG;
eiB=e(transI).*transB;
ejB=e(transJ).*transB;
fiG=f(transI).*transG;
fjG=f(transJ).*transG;
fiB=f(transI).*transB;
fjB=f(transJ).*transB;
ejG_fjB=ejG-fjB;
ejGfjB=ejG+fjB;
fjGejB=fjG+ejB;
ejB_fjG=ejB-fjG;
eiGfiB=eiG+fiB;
eiG_fiB=eiG-fiB;
eiB_fiG=eiB-fiG;
fiGeiB=fiG+eiB;
dP2_ei_t=(4*eiG.*T-ejG_fjB).*y1(transI)-ejGfjB.*y1(transJ);
dP2_ej_t=-eiGfiB.*y1(transI)-eiG_fiB.*y1(transJ);
dQ2_ei_t=(-4*eiB.*T+fjGejB).*y2(transI)+ejB_fjG.*y2(transJ);
dQ2_ej_t=eiB_fiG.*y2(transI)+fiGeiB.*y2(transJ);
HSdh_et=sparse(1:transNum,transI,dP2_ei_t+dQ2_ei_t,transNum,nodeNum)+sparse(1:transNum,transJ,dP2_ej_t+dQ2_ej_t,transNum,nodeNum);%功率方程先对变比求偏导，再对电压实部求偏导模块
dP2_fi_t=(4*fiG.*T-fjGejB).*y1(transI)+ejB_fjG.*y1(transJ);
dP2_fj_t=eiB_fiG.*y1(transI)-fiGeiB.*y1(transJ);
dQ2_fi_t=(-4*fiB.*T-ejG_fjB).*y2(transI)+ejGfjB.*y2(transJ);
dQ2_fj_t=eiGfiB.*y2(transI)-eiG_fiB.*y2(transJ);
HSdh_ft=sparse(1:transNum,transI,dP2_fi_t+dQ2_fi_t,transNum,nodeNum)+sparse(1:transNum,transJ,dP2_fj_t+dQ2_fj_t,transNum,nodeNum);%功率方程先对变比求偏导，再对电压虚部求偏导模块
HSdh_eft=[HSdh_et HSdh_ft];
HSdh_tef=HSdh_eft';
HSdhPQ=sparse(pgvNum,2*nodeNum); %功率方程先对PG、QR求偏导，再对其他变量求偏导的部分
d2hcap_e=sparse(1:capNum,capI,2*e(capI).*y2(capI),capNum,nodeNum); %功率方程先对capK求偏导，再对e，f求偏导的部分
d2hcap_f=sparse(1:capNum,capI,2*f(capI).*y2(capI),capNum,nodeNum);
HSdhcap_ef=[d2hcap_e d2hcap_f];
d2htPQ_ef=[HSdh_eft;HSdhPQ;HSdhcap_ef];
HSdhtPQ=[HSdhT d2htPQ_ef];
HSdhx1=sparse(m,pgvNum);
%潮流方程海森矩阵
diagy1=sparse(1:nodeNum,1:nodeNum,y1,nodeNum,nodeNum);
diagy2=sparse(1:nodeNum,1:nodeNum,y2,nodeNum,nodeNum);
HSdhey=-diagy1*G+diagy2*B+(-G*diagy1+B*diagy2);
HSdhefy=diagy1*B+diagy2*G-(B*diagy1+G*diagy2);
HSdhx2=[HSdhey HSdhefy;HSdhefy' HSdhey];
HSdhx=[HSdhtPQ;HSdh_tef HSdhx1 HSdhcap_ef' HSdhx2];
%形成不等式约束二阶偏导的矩阵▽2g(x)*(z+w)
ZWcl=z(transNum+pgvNum+capNum+nodeNum+1:end)+w(transNum+pgvNum+capNum+nodeNum+1:end);
ZWv=z(transNum+pgvNum+capNum+1:transNum+pgvNum+capNum+nodeNum)+w(transNum+pgvNum+capNum+1:transNum+pgvNum+capNum+nodeNum);
dgeiT=((2*e(transI)-e(transJ)).*transG+f(transJ).*transB).*ZWcl(lineNum-transNum+1:end);
dgejT=(-e(transI).*transG-f(transI).*transB).*ZWcl(lineNum-transNum+1:end);
dgeT=sparse(1:transNum,transI,dgeiT,transNum,nodeNum)+sparse(1:transNum,transJ,dgejT,transNum,nodeNum);%不等式约束先对变比求偏导，再对e求偏导的模块
dgfiT=((2*f(transI)-f(transJ)).*transG-e(transJ).*transB).*ZWcl(lineNum-transNum+1:end);
dgfjT=(-f(transI).*transG+e(transI).*transB).*ZWcl(lineNum-transNum+1:end);
dgfT=sparse(1:transNum,transI,dgfiT,transNum,nodeNum)+sparse(1:transNum,transJ,dgfjT,transNum,nodeNum);%不等式约束先对变比求偏导，再对f求偏导的模块
HSdgefT=[dgeT dgfT];
HSdgT=[sparse(transNum,transNum+pgvNum+capNum) HSdgefT];
HSdgee=sparse(lineI,lineI,2*GIJ.*ZWcl,nodeNum,nodeNum)-sparse(lineI,lineJ,GIJ.*ZWcl,nodeNum,nodeNum)-...
sparse(lineJ,lineI,GIJ.*ZWcl,nodeNum,nodeNum)+sparse(1:nodeNum,1:nodeNum,2*ZWv,nodeNum,nodeNum);
HSdgff=HSdgee;
HSdgef=sparse(lineI,lineJ,BIJ.*ZWcl,nodeNum,nodeNum)-sparse(lineJ,lineI,BIJ.*ZWcl,nodeNum,nodeNum);
HSdgfe=HSdgef';
HSdgx1=[HSdgee HSdgef;HSdgfe HSdgff]; %所有不等式约束对e、f求二次偏导模块
HSdgxtPQ_0=sparse(pgvNum+capNum,xNum);
HSdgef_0=[HSdgefT' sparse(2*nodeNum,pgvNum+capNum)];
HSdgx=[HSdgT;HSdgxtPQ_0;HSdgef_0 HSdgx1]; %合成不等式约束海森矩阵
%求和形成H(.)矩阵.
dgxT=dgx'; %求dgx的转置
MULdgx=dgx*(UW-LZ)*dgxT;
H=HSdhx+HSdgx-HSdfx+MULdgx; %求和形成H(.)矩阵.
%% 根据以上所求的各个矩阵合成海森伯矩阵
HSB0=sparse(m,m);
HSB=[H dhx;dhx' HSB0];
balN=transNum+pgvNum+capNum+nodeNum+balNode;
HSB(balN,:)=0; %保持平衡节点电压虚部不变，始终为0，即将海森矩阵中平衡节点虚部所对应的行列元素置0，对角元素置1
HSB(:,balN)=0;
HSB_balN=sub2ind(size(HSB),balN,balN);
HSB(HSB_balN)=ones(balNum,1);
balN1=transNum+pgvNum+capNum+balNode;
HSB(balN1,:)=0; %保持平衡节点电压实部不变，始终为0，即将海森矩阵中平衡节点实部所对应的行列元素置0，对角元素置1
HSB(:,balN1)=0;
HSB_balN1=sub2ind(size(HSB),balN1,balN1);
HSB(HSB_balN1)=ones(balNum,1);
HSB=sparse(HSB);

59
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function [G,B,transY,transG,transB,transG1,transB1,transNum,lineNum,lineI,lineJ,lineB,transI,transJ,transK0,transKmin,transKmax]=...
formY(nodeNum,lineNum,mtrLine,mtrGround,mtrTrans,capI,capBi,capK)
%程序功能：形成节点导纳矩阵
%编写时间：2010年10月
%变量定义：
%G--电导矩阵,B--电纳矩阵，lineI,lineJ--节点序号，lineR--线路电阻
%lineX--线路电抗，groundI--接地支路节点序号
%groundR--接地支路电阻，groundX--接地支路电抗
%transI，transJ--变压器支路节点序号
%transR--变压器支路电阻，transX--变压器支路电抗
%transK--变压器变比
%transG--变压器支路等效电导，transB--变压器支路等效电纳
%% 利用线路和接地支路参数形成导纳矩阵
lineI=mtrLine(:,2);
lineJ=mtrLine(:,3);
lineR=mtrLine(:,4);
lineX=mtrLine(:,5);
lineB=mtrLine(:,6);
groundI=mtrGround(:,1);
groundX=mtrGround(:,2);
Yij=1./(lineR+j*lineX);
Y1=-sparse(lineI,lineJ,Yij,nodeNum,nodeNum)-sparse(lineJ,lineI,Yij,nodeNum,nodeNum)...
+sparse(lineI,lineI,Yij+j*lineB,nodeNum,nodeNum)+sparse(lineJ,lineJ,Yij+j*lineB,nodeNum,nodeNum)...
+sparse(groundI,groundI,j*groundX,nodeNum,nodeNum)+sparse(capI,capI,j*capK,nodeNum,nodeNum);
%% 加入变压器支路修改导纳矩阵
transIall=mtrTrans(:,2);
transJall=mtrTrans(:,3);
transR=mtrTrans(:,4);
transX=mtrTrans(:,5);
transK0all=mtrTrans(:,6);
transY=1./(transR+j*transX);
Y1=Y1-sparse(transIall,transJall,transY./transK0all,nodeNum,nodeNum)-sparse(transJall,transIall,transY./transK0all,nodeNum,nodeNum)...
+sparse(transIall,transIall,transY./transK0all./transK0all,nodeNum,nodeNum)+sparse(transJall,transJall,transY,nodeNum,nodeNum);
Yt=sparse(transIall,transJall,-transY,nodeNum,nodeNum); %这样处理是因为有两台变压器两端的节点号相同，避免在更新节点导纳矩阵时只识别一台变压器
transIJ=sub2ind(size(Yt),transIall,transJall);
transYt=Yt(transIJ);
transCtrl=mtrTrans(:,9);
ctrTransNum=find(transCtrl);
transI=transIall(ctrTransNum);
transJ=transJall(ctrTransNum);
transKmax=1/0.9*ones(size(transI));
transKmin=1/1.1*ones(size(transI));
transK0=transK0all(ctrTransNum);
transG=real(transYt(ctrTransNum));
transB=imag(transYt(ctrTransNum));
transG1=-real(transY(ctrTransNum)); %之所以要取负号是因为transG、transB是作为导纳矩阵中的互导纳来用，在计算自导纳的时候注意要用-transG、-transB!!!!
transB1=-imag(transY(ctrTransNum));
transNum=length(transI);
lineI=[lineI;transI]; %将线路和变压器支路的编号合并，在后面线路约束的时候同时处理
lineJ=[lineJ;transJ];
lineNum=lineNum-length(transIall)+length(transI);
%% 求节点导纳的幅值和相角
[Yrows,Ycols,Y1] = find(Y1);
G=real(Y1);
B=imag(Y1);
G=sparse(Yrows,Ycols,G,nodeNum,nodeNum);
B=sparse(Yrows,Ycols,B,nodeNum,nodeNum);

82
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function [G,B,lineI,lineJ,lineB,transI,transJ,transK0,transNum,transKmin,transKmax,capI,capGi,capBi,capK,capKmin,capKmax,capNum,transG,transB,...
transG1,transB1,lineNum]=formY_RPP(nodeNum,lineNum,mtrLine,mtrGround,mtrTrans,mtrCapacitor)
%程序功能：形成节点导纳矩阵
%编写时间：2010年10月
%变量定义：
%G--电导矩阵,B--电纳矩阵，lineI,lineJ--节点序号，lineR--线路电阻
%lineX--线路电抗，groundI--接地支路节点序号
%groundR--接地支路电阻，groundX--接地支路电抗
%transI，transJ--变压器支路节点序号
%transR--变压器支路电阻，transX--变压器支路电抗
%transK--变压器变比
%transG--变压器支路等效电导，transB--变压器支路等效电纳
%% 利用线路和接地支路参数形成导纳矩阵
lineI=mtrLine(:,2);
lineJ=mtrLine(:,3);
lineR=mtrLine(:,4);
lineX=mtrLine(:,5);
lineB=mtrLine(:,6);
%接地支路数据
groundI=mtrGround(:,2);
groundG=mtrGround(:,3);
groundB=mtrGround(:,4);
%电容器参数
capCtrl=mtrCapacitor(:,2);
capCtrl=ones(length(capCtrl),1);
capIall=mtrCapacitor(:,3);
capGiall=mtrCapacitor(:,4);
capBiall=mtrCapacitor(:,5);
capKall=mtrCapacitor(:,6);
capKminall=mtrCapacitor(:,7);
capKmaxall=mtrCapacitor(:,8);
Yij=1./(lineR+j*lineX);
Y1=-sparse(lineI,lineJ,Yij,nodeNum,nodeNum)-sparse(lineJ,lineI,Yij,nodeNum,nodeNum)...
+sparse(lineI,lineI,Yij+j*lineB,nodeNum,nodeNum)+sparse(lineJ,lineJ,Yij+j*lineB,nodeNum,nodeNum)...
+sparse(groundI,groundI,groundG+j*groundB,nodeNum,nodeNum)...
+sparse(capIall,capIall,j*capKall,nodeNum,nodeNum);
%保留可调电容电抗器参数
capCtrlNode=find(capCtrl);
capI=capIall(capCtrlNode);
capGi=capGiall(capCtrlNode);
capBi=capBiall(capCtrlNode);
capK=capKall(capCtrlNode);
capKmin=capKminall(capCtrlNode);
capKmax=capKmaxall(capCtrlNode);
capNum=length(capI);
%% 加入变压器支路修改导纳矩阵
transCtrl=mtrTrans(:,2);
transIall=mtrTrans(:,3);
transJall=mtrTrans(:,4);
transR=mtrTrans(:,5);
transX=mtrTrans(:,6);
transK0all=mtrTrans(:,7);
transY=1./(transR+j*transX);
Y1=Y1-sparse(transIall,transJall,transY./transK0all,nodeNum,nodeNum)-sparse(transJall,transIall,transY./transK0all,nodeNum,nodeNum)...
+sparse(transIall,transIall,transY./transK0all./transK0all,nodeNum,nodeNum)+sparse(transJall,transJall,transY,nodeNum,nodeNum);
Yt=sparse(transIall,transJall,-transY,nodeNum,nodeNum); %这样处理是因为有两台变压器两端的节点号相同，避免在更新节点导纳矩阵时只识别一台变压器
transIJ=sub2ind(size(Yt),transIall,transJall);
%保留可调变压器参数
transYt=Yt(transIJ);
ctrTransNum=find(transCtrl);
transI=transIall(ctrTransNum);
transJ=transJall(ctrTransNum);
transKmax=1/0.9*ones(size(transI));
transKmin=1/1.1*ones(size(transI));
transK0=transK0all(ctrTransNum);
transG=real(transYt(ctrTransNum));
transB=imag(transYt(ctrTransNum));
transG1=-real(transY(ctrTransNum)); %之所以要取负号是因为transG、transB是作为导纳矩阵中的互导纳来用，在计算自导纳的时候注意要用-transG、-transB!!!!
transB1=-imag(transY(ctrTransNum));
transNum=length(transI);
lineI=[lineI;transI]; %将线路和变压器支路的编号合并，在后面线路约束的时候同时处理
lineJ=[lineJ;transJ];
lineNum=lineNum+transNum;
%% 求节点导纳的幅值和相角
[Yrows,Ycols,Y1] = find(Y1);
G=real(Y1);
B=imag(Y1);
G=sparse(Yrows,Ycols,G,nodeNum,nodeNum);
B=sparse(Yrows,Ycols,B,nodeNum,nodeNum);

62
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function [H1,N1,diagE,diagF,hx,Gap,max_hx,fx,Pg,Qg,xz1,dmaxOut1,xz2,dmaxOut2,xz3,dmaxOut3,xz4,dmaxOut4,PGR]=midResult(nodeNum,pgNode,opfGoal,z,l,u,w,...
Pg,Qg,e,f,G,B,a,b,c,PG,Pd,Qd,k,xz1,dmaxOut1,xz2,dmaxOut2,xz3,dmaxOut3,xz4,dmaxOut4,times,accuracy,mismatch)
%程序功能：计算每次迭代后的目标函数值和等式约束的最大不平衡量，并根据每步迭代结果修正光滑参数
%编写时间：2010年10月
Gap=l'*z-u'*w; %计算互补间隙
PGR=PG;
if(opfGoal==2)
sumP=sum(Pg);
sumPd=sum(Pd);
fx=sumP-sumPd;
else if(opfGoal==1)
fx=sum(a(pgNode).*PGR(pgNode).*PGR(pgNode)+b(pgNode).*PGR(pgNode)+c(pgNode));
else if(opfGoal==3)
EE=e*ones(1,nodeNum);
FF=f*ones(1,nodeNum);
fx=-0.5*sum(sum(G.*((EE-EE').^2+(FF-FF').^2),2));
else if(opfGoal==4)
EE=e*ones(1,nodeNum);
FF=f*ones(1,nodeNum);
fx=0.5*sum(sum(B.*((EE-EE').^2+(FF-FF').^2),2));
end
end
end
end
H1=G*e-B*f;
N1=G*f+B*e;
diagE=sparse(1:nodeNum,1:nodeNum,e,nodeNum,nodeNum);
diagF=sparse(1:nodeNum,1:nodeNum,f,nodeNum,nodeNum);
P=Pg-Pd;
Q=Qg-Qd;
dP=P-diagE*H1-diagF*N1;
dQ=Q-diagF*H1+diagE*N1;
hx=[dP;dQ];
fx=full(fx);
max_hx=full(max(abs(hx)));
fprintf('%4.0f %4.4e %4.4e %7.6f\n',k,Gap,max_hx,fx); %输出每次迭代结果
firstOK=0;
if Gap<accuracy&&max_hx<mismatch&& times==1 %判断互补间隙和最大不平衡量是否达到精度
firstOK=1;
end
%% 保留每次迭代的互补间隙和最大不平衡量
if times==1
xz1=[xz1 k];
dmaxOut1=[dmaxOut1 Gap];
xz3=[xz3 k];
dmaxOut3=[dmaxOut3 max_hx];
end
if times==2
if firstOK==1
xz1=[xz1 k];
dmaxOut1=[dmaxOut1 Gap];
xz3=[xz3 k];
dmaxOut3=[dmaxOut3 max_hx];
else
xz2=[xz2 k];
dmaxOut2=[dmaxOut2 Gap];
xz4=[xz4 k];
dmaxOut4=[dmaxOut4 max_hx];
end
end

73
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function [nodeNum,lineNum,capacity,kmax,centrPara,accuracy,opfGoal,balNum,balNode,mtrLine,mtrGround,mtrTrans,runPara,Pg,Qg,Pd,Qd,pvNum,pvNode,pvV,...
pvQmin,pvQmax,pgNumall,pgNodeall,pgNum,pgNode,a,b,c,Pmin,Pmax,capNum,capI,capGi,capBi,capK,capKmin,capKmax,Vmax,Vmin]=readData(filename)
%程序功能：读取数据
%编写时间：2010年10月
%% 将数据整块读入
data=dlmread(filename);
%% 读取系统参数
nodeNum=data(1,1); %系统节点数
lineNum=data(1,2); %线路变压器数
capacity=data(1,3); %基准容量
kmax=data(1,4); %最大迭代次数
centrPara=data(1,5); %中心参数
accuracy=data(2,1); %计算精度
opfGoal=data(2,2); %目标函数类型
balNum=data(3,1); %平衡节点数
balNode=data(3,2); %平衡节点编号
%% 获取首列元素为0的行号
zeroIndex=find(data(:,1)==0);
%% 读取线路参数
mtrLine=data(zeroIndex(1)+1:zeroIndex(2)-1,:);
%% 读取接地支路参数
mtrGround=data(zeroIndex(2)+1:zeroIndex(3)-1,:);
%% 读取变压器支路参数
mtrTrans=data(zeroIndex(3)+1:zeroIndex(4)-1,:);
%% 读取运行参数
runPara=data(zeroIndex(4)+1:zeroIndex(5)-1,:);
pqNode=runPara(:,1);
Pg=sparse(nodeNum,1);
Qg=Pg;Pd=Pg;Qd=Pg;
Pg(pqNode)=runPara(:,2)/capacity; %节点有功出力
Qg(pqNode)=runPara(:,3)/capacity; %节点无功出力
Pd(pqNode)=runPara(:,4)/capacity; %节点有功负荷
Qd(pqNode)=runPara(:,5)/capacity; %节点无功负荷
%% 读取PV节点和平衡节点参数
mtrPV=data(zeroIndex(5)+1:zeroIndex(6)-1,:);
pvNum=zeroIndex(6)-zeroIndex(5)-1;
pvNode=sparse(mtrPV(:,1),ones(pvNum,1),mtrPV(:,1),nodeNum,1);
pvNode=find(pvNode); %PV节点和平衡节点编号
pvV=sparse(mtrPV(:,1),ones(pvNum,1),mtrPV(:,2),nodeNum,1); %PV节点和平衡节点给定电压
pvQmin=sparse(mtrPV(:,1),ones(pvNum,1),mtrPV(:,3),nodeNum,1)/capacity; %无功出力下限
pvQmax=sparse(mtrPV(:,1),ones(pvNum,1),mtrPV(:,4),nodeNum,1)/capacity; %无功出力上限
%% 读取经济参数
economyPara=data(zeroIndex(6)+1:zeroIndex(7)-1,:);
[ecoRow,ecoCol]=size(economyPara);
if ecoCol>=7
pgctrl=find(economyPara(:,7)); %可调发电机的下标
if isempty(pgctrl)
pgctrl=1:ecoRow;
end
else
pgctrl=1:ecoRow;
end
pgNumall=zeroIndex(7)-zeroIndex(6)-1; %发电机台数
pgNodeall=economyPara(:,1); %发电机节点号
pgNum=length(pgctrl); %可调发电机台数
pgNode=pgNodeall(pgctrl); %可调发电机节点号
c=sparse(economyPara(:,1),ones(pgNumall,1),economyPara(:,2),nodeNum,1);
b=sparse(economyPara(:,1),ones(pgNumall,1),economyPara(:,3),nodeNum,1);
a=sparse(economyPara(:,1),ones(pgNumall,1),economyPara(:,4),nodeNum,1);
Pmin=sparse(economyPara(:,1),ones(pgNumall,1),economyPara(:,5),nodeNum,1)/capacity;%发电机有功出力下限
Pmax=sparse(economyPara(:,1),ones(pgNumall,1),economyPara(:,6),nodeNum,1)/capacity;%发电机有功出力上限
%% 读可调电容器组参数
capPara=data(zeroIndex(7)+1:zeroIndex(8)-1,:);
capNum=zeroIndex(8)-zeroIndex(7)-1;
capI=capPara(:,2); %电容器投入节点编号
capGi=capPara(:,3); %可调电容器单位电导
capBi=capPara(:,4); %可调电容器单位电纳
capK=capPara(:,5); %初始档位值
capKmin=capPara(:,6); %电容器最小档位
capKmax=capPara(:,7); %电容器最大档位
Vmax=1.07*ones(nodeNum,1); %节点电压下限
Vmin=0.9*ones(nodeNum,1); %节点电压上限

69
Sigmoid函数法/readData_RPP.m Normal file
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function [nodeNum,lineNum,capacity,kmax,accuracy,balNum,balNode,mtrLine,mtrGround,mtrTrans,runPara,Pg,Qg,Pd,Qd,pvNum,pvNode,pvV,pvQmin,pvQmax,...
mtrCapacitor,pgNum,pgNode,a,b,c,Pmin,Pmax,Vmin,Vmax,centrPara]=readData_RPP(data)
%程序功能：读取数据
%编写时间：2010年10月
%% 获取首列元素为0的行号
zeroIndex=find(data(:,1)==0);
%% 读取系统参数
nodeNum=data(1,1); %系统节点数
capacity=data(1,3); %基准容量
accuracy=data(1,4); %计算精度
balNum=zeroIndex(2)-zeroIndex(1)-1; %平衡节点数
balNode=data(zeroIndex(1)+1:zeroIndex(2)-1,2); %平衡节点编号
kmax=100; %最大迭代次数
centrPara=0.1; %中心参数
%% 读取线路参数
mtrLine=data(zeroIndex(2)+1:zeroIndex(3)-1,:);
lineNum=length(mtrLine);
%% 读取变压器支路参数
mtrTrans=data(zeroIndex(3)+1:zeroIndex(4)-1,:);
%% 读取接地支路参数
mtrGround=data(zeroIndex(5)+1:zeroIndex(6)-1,:);
%% 读可调电容器参数
mtrCapacitor=data(zeroIndex(6)+1:zeroIndex(7)-1,:);
%% 读取运行参数
runPara=data(zeroIndex(8)+1:zeroIndex(9)-1,:);
pqNode=runPara(:,2);
Pg=sparse(nodeNum,1);
Qg=Pg;Pd=Pg;Qd=Pg;
Pg(pqNode)=runPara(:,3); %节点有功出力
Qg(pqNode)=runPara(:,4); %节点无功出力
Pd(pqNode)=runPara(:,5); %节点有功负荷
Qd(pqNode)=runPara(:,6); %节点无功负荷
%% 有功出力限制
mtrPGLimit=data(zeroIndex(9)+1:zeroIndex(10)-1,:);
pgNum=zeroIndex(10)-zeroIndex(9)-1; %发电机台数
pgNode=mtrPGLimit(:,3); %发电机节点号
c=sparse(mtrPGLimit(:,3),ones(pgNum,1),mtrPGLimit(:,8),nodeNum,1);
b=sparse(mtrPGLimit(:,3),ones(pgNum,1),mtrPGLimit(:,9),nodeNum,1);
a=sparse(mtrPGLimit(:,3),ones(pgNum,1),mtrPGLimit(:,10),nodeNum,1);
Pmin=sparse(mtrPGLimit(:,3),ones(pgNum,1),mtrPGLimit(:,4),nodeNum,1); %发电机有功出力下限
Pmax=sparse(mtrPGLimit(:,3),ones(pgNum,1),mtrPGLimit(:,5),nodeNum,1); %发电机有功出力上限
%% 无功出力限制
mtrQGLimit=data(zeroIndex(11)+1:zeroIndex(12)-1,:);
pvNum=zeroIndex(12)-zeroIndex(11)-1;
pvNode=sparse(mtrQGLimit(:,3),ones(pvNum,1),mtrQGLimit(:,3),nodeNum,1);
pvNode=find(pvNode); %PV节点和平衡节点编号
pvV=sparse(mtrQGLimit(:,3),ones(pvNum,1),mtrQGLimit(:,4),nodeNum,1); %PV节点和平衡节点给定电压
pvQmin=sparse(mtrQGLimit(:,3),ones(pvNum,1),mtrQGLimit(:,5),nodeNum,1); %无功出力下限
pvQmax=sparse(mtrQGLimit(:,3),ones(pvNum,1),mtrQGLimit(:,6),nodeNum,1); %无功出力上限
%% 电压限制
mtrVLimit=data(zeroIndex(13)+1:zeroIndex(14)-1,:);
VLimitNum=zeroIndex(14)-zeroIndex(13)-1; %电压限制的节点数
Vmin=sparse(mtrVLimit(:,2),ones(VLimitNum,1),mtrVLimit(:,3),nodeNum,1);
Vmax=sparse(mtrVLimit(:,2),ones(VLimitNum,1),mtrVLimit(:,4),nodeNum,1);
Vmin=0.9*ones(nodeNum,1); %非电压监测点电压限制
Vmax=1.15*ones(nodeNum,1);
node_Z=data(zeroIndex(14)+1:zeroIndex(15)-1,1); %变压器中性点，这些点的电压不考核，设置为0.8-1.2
Vmin(node_Z)=0.85;
Vmax(node_Z)=1.15;
node_220=data(zeroIndex(15)+1:zeroIndex(16)-1,1); %220kV及以上节点
Vmin(node_220)=0.95;
Vmax(node_220)=1.1;
node_750=data(zeroIndex(16)+1:zeroIndex(17)-1,1); %750kV节点
Vmin(node_750)=1;
Vmax(node_750)=1.1;
node_Monitor=data(zeroIndex(17)+1:zeroIndex(18)-1,1); %发电厂升压变以及800kV变电站220、363kV母线节点，电压监测点
Vmin(node_Monitor)=1;
Vmax(node_Monitor)=1.1;

212
Sigmoid函数法/result_IEEE118.dat Normal file
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@ -0,0 +1,212 @@
31 7.9793e-006 0.780222 0.778376 0.2320 2.3864e-006 1
0
8 5 0.9500 0.9739 1.0000 0.9500
25 26 1.0000 1.0133 1.0500 1.0000
17 30 1.0000 1.0052 1.0500 1.0000
37 38 1.0000 1.0102 1.0500 1.0000
59 63 1.0000 1.0046 1.0500 1.0000
61 64 1.0000 1.0085 1.0500 1.0000
65 66 1.0000 0.9816 1.0000 0.9500
68 69 1.0000 1.0263 1.0500 1.0000
80 81 1.0000 1.0017 1.0500 1.0000
0
1 1.0216 -0.1935 1.0397 1.0428
2 1.0326 -0.1797 1.0481 1.0521
3 1.0308 -0.1821 1.0467 1.0493
4 1.0561 -0.1349 1.0647 1.0694
5 1.0621 -0.1302 1.0700 1.0700
6 1.0477 -0.1610 1.0600 1.0647
7 1.0470 -0.1636 1.0597 1.0644
8 1.0445 -0.0651 1.0466 1.0534
9 1.0693 0.0387 1.0700 1.0700
10 1.0542 0.1501 1.0648 1.0578
11 1.0434 -0.1626 1.0560 1.0599
12 1.0486 -0.1621 1.0610 1.0657
13 1.0249 -0.1895 1.0423 1.0468
14 1.0408 -0.1841 1.0570 1.0621
15 1.0268 -0.2184 1.0498 1.0560
16 1.0386 -0.1802 1.0541 1.0593
17 1.0451 -0.1834 1.0611 1.0672
18 1.0287 -0.2187 1.0517 1.0577
19 1.0231 -0.2261 1.0478 1.0540
20 1.0133 -0.2210 1.0371 1.0422
21 1.0126 -0.2037 1.0329 1.0371
22 1.0220 -0.1737 1.0367 1.0399
23 1.0455 -0.1109 1.0513 1.0528
24 1.0365 -0.1213 1.0436 1.0448
25 1.0700 0.0068 1.0700 1.0700
26 1.0676 0.0720 1.0700 1.0700
27 1.0297 -0.1921 1.0475 1.0500
28 1.0184 -0.2123 1.0403 1.0433
29 1.0160 -0.2219 1.0399 1.0435
30 1.0627 -0.1032 1.0677 1.0697
31 1.0196 -0.2188 1.0428 1.0466
32 1.0262 -0.1976 1.0451 1.0481
33 1.0204 -0.2266 1.0453 1.0531
34 1.0321 -0.2187 1.0551 1.0644
35 1.0278 -0.2255 1.0522 1.0616
36 1.0283 -0.2258 1.0528 1.0622
37 1.0355 -0.2111 1.0568 1.0662
38 1.0615 -0.1347 1.0700 1.0700
39 1.0057 -0.2531 1.0370 1.0462
40 1.0017 -0.2657 1.0363 1.0452
41 0.9957 -0.2677 1.0311 1.0398
42 1.0147 -0.2357 1.0417 1.0496
43 1.0201 -0.2059 1.0407 1.0495
44 1.0244 -0.1492 1.0352 1.0429
45 1.0255 -0.1126 1.0317 1.0384
46 1.0432 -0.0678 1.0454 1.0510
47 1.0486 -0.0379 1.0493 1.0543
48 1.0571 -0.0304 1.0575 1.0624
49 1.0631 -0.0104 1.0632 1.0689
50 1.0576 -0.0231 1.0579 1.0637
51 1.0475 -0.0366 1.0481 1.0540
52 1.0440 -0.0431 1.0449 1.0507
53 1.0473 -0.0345 1.0479 1.0537
54 1.0645 -0.0036 1.0645 1.0700
55 1.0597 -0.0194 1.0599 1.0656
56 1.0610 -0.0153 1.0611 1.0667
57 1.0573 -0.0249 1.0575 1.0633
58 1.0512 -0.0320 1.0516 1.0574
59 1.0632 0.0010 1.0632 1.0700
60 1.0596 -0.0064 1.0596 1.0679
61 1.0616 0.0047 1.0616 1.0700
62 1.0577 -0.0139 1.0578 1.0660
63 1.0685 0.0066 1.0686 1.0693
64 1.0693 0.0095 1.0693 1.0694
65 1.0698 0.0193 1.0700 1.0700
66 1.0625 0.0107 1.0625 1.0700
67 1.0549 -0.0146 1.0550 1.0629
68 1.0633 -0.0037 1.0633 1.0688
69 1.0100 -0.0000 1.0100 1.0100
70 0.9987 -0.1218 1.0061 1.0065
71 1.0011 -0.1258 1.0089 1.0094
72 1.0138 -0.1342 1.0227 1.0235
73 0.9996 -0.1282 1.0077 1.0082
74 0.9851 -0.1432 0.9955 0.9958
75 0.9857 -0.1200 0.9930 0.9932
76 0.9718 -0.1357 0.9813 0.9816
77 1.0311 -0.0500 1.0323 1.0327
78 1.0274 -0.0529 1.0288 1.0292
79 1.0313 -0.0441 1.0323 1.0327
80 1.0558 0.0061 1.0558 1.0563
81 1.0665 -0.0004 1.0665 1.0696
82 1.0349 -0.0706 1.0373 1.0380
83 1.0381 -0.0727 1.0407 1.0412
84 1.0418 -0.0659 1.0439 1.0442
85 1.0501 -0.0577 1.0517 1.0518
86 1.0400 -0.0762 1.0428 1.0430
87 1.0487 -0.0698 1.0510 1.0512
88 1.0545 -0.0333 1.0551 1.0551
89 1.0699 0.0148 1.0700 1.0700
90 1.0476 -0.0753 1.0503 1.0503
91 1.0517 -0.0607 1.0535 1.0535
92 1.0588 -0.0252 1.0591 1.0592
93 1.0475 -0.0349 1.0481 1.0483
94 1.0439 -0.0362 1.0445 1.0448
95 1.0302 -0.0497 1.0314 1.0317
96 1.0361 -0.0503 1.0374 1.0378
97 1.0415 -0.0288 1.0419 1.0423
98 1.0532 -0.0168 1.0533 1.0537
99 1.0602 -0.0204 1.0604 1.0606
100 1.0690 0.0013 1.0690 1.0691
101 1.0527 -0.0242 1.0530 1.0531
102 1.0562 -0.0266 1.0565 1.0566
103 1.0700 -0.0016 1.0700 1.0700
104 1.0536 -0.0636 1.0555 1.0556
105 1.0499 -0.0766 1.0527 1.0527
106 1.0405 -0.0869 1.0442 1.0442
107 1.0315 -0.1257 1.0391 1.0392
108 1.0539 -0.0783 1.0568 1.0569
109 1.0533 -0.0774 1.0561 1.0561
110 1.0550 -0.0696 1.0573 1.0574
111 1.0699 -0.0129 1.0700 1.0700
112 1.0362 -0.1103 1.0421 1.0421
113 1.0423 -0.1868 1.0589 1.0643
114 1.0216 -0.2030 1.0416 1.0444
115 1.0213 -0.2033 1.0414 1.0442
116 1.0633 -0.0108 1.0634 1.0683
117 1.0301 -0.1840 1.0464 1.0511
118 0.9720 -0.1339 0.9812 0.9815
0
10 3.6967
12 2.0000
25 1.0556
26 4.0000
49 3.7575
54 2.9977
59 2.9002
61 1.2241
65 3.8134
66 1.0000
69 2.4623
80 5.2137
89 3.8041
100 2.6935
103 1.4836
111 0.7977
0
1 0.1500
4 -0.4047
6 0.1529
8 -0.3565
10 -0.9697
12 0.4891
15 0.2985
18 0.3794
19 0.2394
24 -0.0256
25 -0.0467
26 -0.4585
27 0.3078
31 0.2880
32 0.2330
34 0.0259
36 0.2395
40 0.3458
42 0.4118
46 -0.0159
49 0.3478
54 0.2865
55 0.1839
56 0.1395
59 0.8004
61 -0.3633
62 0.1107
65 -0.6700
66 -0.1902
69 -2.6190
70 0.2231
72 -0.0494
73 -0.0211
74 0.0486
76 0.2300
77 0.7000
80 0.2740
85 0.1728
87 0.0116
89 0.0870
90 0.4446
91 0.0008
92 0.0900
99 -0.0335
100 0.4333
103 0.0524
104 0.2293
105 -0.0031
107 -0.2868
110 0.2255
111 -0.0421
112 0.1253
113 -0.0204
116 0.0947
0
17 0.00 0.0054 0.00 0.10
34 0.30 0.2728 0.20 0.30
44 0.10 0.1038 0.10 0.20
107 0.40 0.4555 0.40 0.50
82 0.30 0.3105 0.30 0.40
48 0.10 0.0803 0.00 0.10
74 0.40 0.4323 0.40 0.50
105 0.20 0.1753 0.10 0.20
0

55
Sigmoid函数法/result_IEEE30.dat Normal file
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@ -0,0 +1,55 @@
28 4.6553e-006 0.024984 0.024929 21.0945 7.2053e-006 1
0
6 9 1.1000 1.1000 1.1000 1.0500
6 10 0.9000 0.9000 0.9500 0.9000
4 12 0.9500 0.9554 1.0000 0.9500
28 27 0.9500 0.9565 1.0000 0.9500
0
1 1.0600 -0.0000 1.0600 1.0600
2 1.0568 -0.0124 1.0569 1.0575
3 1.0508 -0.0252 1.0511 1.0523
4 1.0480 -0.0298 1.0484 1.0500
5 1.0374 -0.0754 1.0401 1.0413
6 1.0494 -0.0383 1.0501 1.0513
7 1.0366 -0.0622 1.0385 1.0397
8 1.0491 -0.0376 1.0497 1.0513
9 1.0366 -0.0125 1.0366 1.0329
10 1.0661 -0.0547 1.0675 1.0695
11 1.0634 0.0895 1.0672 1.0477
12 1.0696 -0.0278 1.0700 1.0700
13 1.0679 0.0377 1.0686 1.0700
14 1.0570 -0.0459 1.0580 1.0582
15 1.0538 -0.0507 1.0550 1.0555
16 1.0600 -0.0441 1.0609 1.0618
17 1.0592 -0.0549 1.0607 1.0623
18 1.0455 -0.0637 1.0475 1.0484
19 1.0438 -0.0682 1.0461 1.0474
20 1.0486 -0.0659 1.0506 1.0521
21 1.0557 -0.0639 1.0576 1.0595
22 1.0569 -0.0644 1.0589 1.0607
23 1.0498 -0.0658 1.0519 1.0526
24 1.0531 -0.0802 1.0561 1.0573
25 1.0550 -0.0923 1.0590 1.0576
26 1.0375 -0.0979 1.0421 1.0406
27 1.0651 -0.0960 1.0694 1.0664
28 1.0446 -0.0435 1.0455 1.0472
29 1.0442 -0.1148 1.0505 1.0474
30 1.0317 -0.1281 1.0396 1.0364
0
1 0.3890
2 0.6000
5 0.5100
8 0.3500
11 0.5100
13 0.5000
0
1 -0.0540
2 0.0763
5 0.2121
8 0.2700
11 0.1811
13 0.0046
0
10 0.30 0.3583 0.30 0.40
24 0.10 0.1051 0.10 0.20
0

489
Sigmoid函数法/result_IEEE300.dat Normal file
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@ -0,0 +1,489 @@
41 1.7917e-006 3.366536 3.336695 0.6797 1.8010e-006 1
0
297 269 1.0000 0.9730 1.0000 0.9500
269 226 1.0000 0.9922 1.0000 0.9500
269 227 0.9500 0.9753 1.0000 0.9500
291 62 1.0000 0.9965 1.0000 0.9500
291 63 0.9000 0.9228 0.9500 0.9000
291 145 1.0000 1.0002 1.0500 1.0000
291 64 1.0500 1.0506 1.1000 1.0500
291 65 1.0000 1.0421 1.0500 1.0000
228 47 1.0000 0.9695 1.0000 0.9500
225 48 1.0000 0.9741 1.0000 0.9500
229 49 1.0000 0.9687 1.0000 0.9500
229 50 1.0000 0.9694 1.0000 0.9500
271 66 0.9500 0.9826 1.0000 0.9500
271 67 0.9500 0.9866 1.0000 0.9500
300 51 0.9500 0.9556 1.0000 0.9500
300 52 0.9500 0.9640 1.0000 0.9500
300 53 0.9500 0.9537 1.0000 0.9500
270 59 0.9500 0.9780 1.0000 0.9500
270 60 0.9500 0.9679 1.0000 0.9500
270 61 0.9500 0.9787 1.0000 0.9500
300 54 0.9500 0.9923 1.0000 0.9500
300 55 0.9500 0.9685 1.0000 0.9500
300 56 0.9500 0.9751 1.0000 0.9500
300 57 0.9500 0.9734 1.0000 0.9500
300 58 0.9500 0.9606 1.0000 0.9500
145 69 1.0000 1.0423 1.0500 1.0000
6 290 1.1000 1.0990 1.1000 1.0500
292 146 1.0000 0.9992 1.0000 0.9500
292 230 0.9500 0.9951 1.0000 0.9500
292 70 1.1000 1.0701 1.1000 1.0500
272 147 0.9500 0.9418 0.9500 0.9000
272 71 1.0000 0.9815 1.0000 0.9500
73 273 0.9000 0.9000 0.9500 0.9000
231 73 1.1000 1.1000 1.1000 1.0500
286 76 1.0000 0.9758 1.0000 0.9500
149 286 0.9500 0.9567 1.0000 0.9500
233 232 0.9500 0.9662 1.0000 0.9500
235 234 1.0000 0.9892 1.0000 0.9500
81 237 0.9500 0.9142 0.9500 0.9000
240 275 1.0000 0.9716 1.0000 0.9500
240 153 1.0000 0.9763 1.0000 0.9500
276 158 0.9000 0.9000 0.9500 0.9000
159 88 1.1000 1.0768 1.1000 1.0500
277 246 1.1000 1.0697 1.1000 1.0500
248 164 1.0000 0.9619 1.0000 0.9500
91 279 1.0000 1.0122 1.0500 1.0000
249 280 1.0000 1.0074 1.0500 1.0000
163 169 1.0500 1.0220 1.0500 1.0000
175 130 1.0000 0.9983 1.0000 0.9500
96 178 1.0000 0.9875 1.0000 0.9500
176 95 1.0000 1.0253 1.0500 1.0000
256 191 1.0000 1.0027 1.0500 1.0000
299 98 0.9500 0.9738 1.0000 0.9500
299 104 0.9500 0.9644 1.0000 0.9500
182 116 0.9000 0.9099 0.9500 0.9000
186 198 0.9500 0.9333 0.9500 0.9000
187 260 0.9500 0.9221 0.9500 0.9000
281 101 0.9500 0.9756 1.0000 0.9500
281 188 1.0000 0.9744 1.0000 0.9500
282 118 0.9000 0.9074 0.9500 0.9000
105 116 0.9000 0.9071 0.9500 0.9000
189 120 0.9500 0.9265 0.9500 0.9000
190 108 0.9500 0.9551 1.0000 0.9500
193 97 1.0000 0.9918 1.0000 0.9500
109 178 1.0000 0.9866 1.0000 0.9500
112 295 0.9000 0.9000 0.9500 0.9000
194 190 1.1000 1.1000 1.1000 1.0500
119 185 0.9500 0.9247 0.9500 0.9000
202 283 1.0000 1.0237 1.0500 1.0000
204 263 1.0000 1.0270 1.0500 1.0000
206 213 0.9500 0.9600 1.0000 0.9500
208 224 1.1000 1.0982 1.1000 1.0500
127 160 1.0500 1.0553 1.1000 1.0500
128 298 1.0000 1.0150 1.0500 1.0000
209 143 1.0500 1.0180 1.0500 1.0000
131 289 1.0500 1.0311 1.0500 1.0000
298 213 1.0500 1.0402 1.0500 1.0000
216 284 0.9500 0.9488 0.9500 0.9000
134 217 0.9500 0.9161 0.9500 0.9000
220 7 0.9000 0.9000 0.9500 0.9000
221 10 0.9000 0.9000 0.9500 0.9000
263 143 1.0000 0.9700 1.0000 0.9500
254 26 1.0000 0.9931 1.0000 0.9500
255 27 1.0500 1.0657 1.1000 1.0500
37 275 0.9500 0.9519 1.0000 0.9500
39 242 0.9500 0.9646 1.0000 0.9500
0
1 1.0137 -0.2238 1.0381 1.0210
2 0.8405 -0.4014 0.9314 0.9342
3 0.9382 -0.3342 0.9959 0.9992
4 1.0010 -0.1506 1.0122 1.0305
5 0.8978 -0.0624 0.9000 0.9000
6 0.8490 -0.2986 0.9000 0.9007
7 1.0213 -0.0864 1.0249 1.0320
8 0.8604 -0.2640 0.9000 0.9118
9 0.8947 -0.0979 0.9000 0.9000
10 1.0606 -0.1402 1.0699 1.0695
11 0.9290 -0.0841 0.9328 0.9392
12 0.9703 -0.3255 1.0234 1.0323
13 0.9889 -0.1898 1.0069 1.0125
14 1.0334 -0.2773 1.0700 1.0700
15 0.9994 -0.3569 1.0612 1.0582
16 0.9524 -0.4416 1.0498 1.0541
17 0.9719 -0.3940 1.0487 1.0599
18 0.8942 -0.4997 1.0243 1.0275
19 0.7993 -0.7066 1.0668 1.0668
20 0.9703 -0.4493 1.0693 1.0677
21 0.9599 -0.3907 1.0364 1.0400
22 1.0158 -0.3363 1.0700 1.0700
23 0.9499 -0.4469 1.0498 1.0690
24 0.9464 -0.4024 1.0284 1.0284
25 1.0404 -0.2013 1.0597 1.0597
26 1.0279 -0.2314 1.0536 1.0700
27 0.8310 -0.3613 0.9062 0.9000
28 1.0568 -0.1678 1.0700 1.0700
29 1.0571 -0.1616 1.0694 1.0700
30 1.0623 -0.1284 1.0700 1.0700
31 1.0535 -0.1873 1.0700 1.0700
32 1.0688 -0.0508 1.0700 1.0700
33 0.9889 -0.2338 1.0162 1.0392
34 1.0429 -0.2393 1.0700 1.0700
35 1.0434 -0.0882 1.0471 1.0506
36 0.9075 0.0184 0.9077 0.9181
37 0.9558 -0.2812 0.9963 1.0168
38 1.0507 -0.0000 1.0507 1.0507
39 0.9711 -0.2200 0.9957 1.0068
40 0.9773 -0.2384 1.0060 1.0141
41 1.0436 -0.2362 1.0700 1.0700
42 0.9776 -0.1323 0.9865 1.0196
43 1.0235 -0.1427 1.0334 1.0306
44 1.0658 0.0945 1.0700 1.0700
45 1.0518 -0.1148 1.0580 1.0700
46 0.8908 0.1284 0.9000 0.9000
47 0.9377 -0.4249 1.0294 1.0700
48 0.9438 -0.4239 1.0346 1.0700
49 0.9449 -0.4084 1.0294 1.0700
50 0.9462 -0.4074 1.0302 1.0700
51 0.9060 -0.4767 1.0238 1.0700
52 0.9231 -0.4667 1.0343 1.0700
53 0.9017 -0.4795 1.0212 1.0700
54 0.9642 -0.4404 1.0600 1.0700
55 0.9324 -0.4606 1.0399 1.0700
56 0.9416 -0.4594 1.0477 1.0700
57 0.9413 -0.4554 1.0457 1.0700
58 0.9156 -0.4720 1.0302 1.0700
59 0.9536 -0.4411 1.0507 1.0700
60 0.9357 -0.4515 1.0390 1.0700
61 0.9533 -0.4439 1.0516 1.0700
62 0.9888 -0.4090 1.0700 1.0700
63 0.9948 -0.3723 1.0622 1.0700
64 1.0208 -0.2017 1.0406 1.0700
65 1.0462 -0.2245 1.0700 1.0699
66 0.9660 -0.4295 1.0572 1.0700
67 0.9735 -0.4237 1.0617 1.0700
68 0.9639 -0.3979 1.0428 1.0492
69 0.9935 -0.3894 1.0671 1.0235
70 0.9676 -0.1807 0.9844 1.0080
71 1.0439 -0.2070 1.0642 1.0629
72 1.0228 -0.2489 1.0526 1.0519
73 0.9199 -0.2415 0.9511 0.9494
74 1.0174 -0.2944 1.0592 1.0514
75 0.9955 -0.2990 1.0394 1.0400
76 0.9945 -0.3137 1.0428 1.0700
77 1.0012 -0.3263 1.0530 1.0429
78 1.0102 -0.2972 1.0530 1.0526
79 0.9654 -0.3787 1.0370 1.0296
80 1.0165 -0.2283 1.0418 1.0530
81 0.9691 -0.3266 1.0226 1.0207
82 1.0117 -0.1799 1.0275 1.0389
83 0.9783 -0.2836 1.0186 1.0250
84 0.9638 -0.3705 1.0326 1.0463
85 0.9920 -0.3231 1.0433 1.0482
86 0.9901 -0.3210 1.0408 1.0452
87 1.0296 -0.2914 1.0700 1.0700
88 0.8945 -0.3990 0.9794 0.9983
89 0.9657 -0.4066 1.0478 1.0462
90 0.9960 -0.3520 1.0564 1.0564
91 0.9503 -0.4357 1.0454 1.0594
92 0.9566 -0.3910 1.0334 1.0387
93 0.9084 -0.5296 1.0515 1.0594
94 0.9311 -0.4625 1.0397 1.0493
95 0.8422 -0.4873 0.9730 0.9712
96 0.8452 -0.4667 0.9655 0.9642
97 0.9001 -0.3466 0.9645 0.9753
98 1.0391 -0.1875 1.0559 1.0484
99 0.9391 -0.3927 1.0179 1.0203
100 0.8928 -0.3453 0.9573 0.9568
101 1.0164 -0.2272 1.0415 1.0488
102 1.0420 -0.0769 1.0449 1.0481
103 1.0440 -0.1326 1.0524 1.0547
104 1.0432 -0.1836 1.0592 1.0560
105 0.9646 -0.1947 0.9841 0.9930
106 1.0599 -0.1469 1.0700 1.0700
107 0.9170 -0.3253 0.9730 0.9848
108 0.9475 -0.2499 0.9799 0.9764
109 0.8586 -0.4675 0.9777 0.9759
110 0.9753 -0.1771 0.9912 0.9905
111 1.0203 -0.0881 1.0241 1.0244
112 0.9812 -0.2343 1.0088 1.0085
113 0.9772 0.0149 0.9773 0.9775
114 0.9327 0.0653 0.9350 0.9351
115 0.8623 -0.3570 0.9333 0.9384
116 1.0356 -0.2693 1.0700 1.0700
117 1.0336 -0.2188 1.0565 1.0560
118 1.0303 -0.2888 1.0700 1.0657
119 0.9435 -0.2716 0.9818 0.9746
120 1.0271 -0.2025 1.0469 1.0700
121 0.9245 -0.3824 1.0005 1.0037
122 0.9500 -0.1836 0.9676 0.9669
123 0.9482 -0.1988 0.9688 0.9682
124 1.0095 0.3548 1.0700 1.0700
125 0.9676 -0.0457 0.9687 0.9728
126 0.9601 -0.3547 1.0235 1.0285
127 0.9679 -0.4302 1.0592 1.0669
128 0.9891 -0.3494 1.0490 1.0638
129 1.0151 -0.3048 1.0599 1.0650
130 0.9328 -0.4850 1.0514 1.0630
131 0.9943 -0.3730 1.0620 1.0700
132 0.9410 -0.2689 0.9787 0.9876
133 0.9088 -0.2181 0.9346 0.9195
134 0.9061 -0.2218 0.9329 0.9173
135 0.9927 -0.2208 1.0169 1.0279
136 0.9850 -0.2477 1.0156 1.0223
137 0.9359 -0.1999 0.9570 0.9567
138 0.9873 -0.1908 1.0055 1.0111
139 0.9783 -0.2485 1.0093 1.0224
140 0.9591 -0.2611 0.9940 1.0073
141 0.9179 -0.3411 0.9792 0.9885
142 0.8285 -0.5152 0.9756 0.9791
143 0.9746 -0.3464 1.0343 1.0700
144 0.9271 -0.4047 1.0116 1.0599
145 0.9992 -0.3827 1.0700 1.0700
146 1.0378 -0.2201 1.0609 1.0615
147 1.0321 -0.2353 1.0585 1.0595
148 1.0299 -0.2491 1.0596 1.0568
149 1.0025 -0.2252 1.0275 1.0443
150 1.0169 -0.2570 1.0489 1.0500
151 0.9869 -0.3432 1.0449 1.0418
152 0.9925 -0.3029 1.0377 1.0446
153 1.0251 -0.2659 1.0590 1.0700
154 0.9588 -0.4160 1.0451 1.0559
155 0.9665 -0.3684 1.0344 1.0409
156 1.0162 -0.2020 1.0361 1.0412
157 0.9808 -0.3542 1.0428 1.0566
158 1.0131 -0.3015 1.0570 1.0610
159 0.9420 -0.5075 1.0700 1.0700
160 0.9601 -0.3740 1.0304 1.0308
161 0.9675 -0.3782 1.0388 1.0425
162 0.9941 -0.3395 1.0505 1.0480
163 1.0096 -0.3481 1.0679 1.0700
164 0.9925 -0.3146 1.0411 1.0600
165 0.9970 -0.3239 1.0483 1.0556
166 1.0032 -0.3010 1.0474 1.0503
167 1.0140 -0.3089 1.0600 1.0700
168 1.0454 -0.2281 1.0700 1.0700
169 0.9635 -0.3495 1.0249 1.0507
170 0.9671 -0.3936 1.0441 1.0498
171 1.0047 -0.3344 1.0589 1.0622
172 0.9495 -0.4346 1.0443 1.0486
173 0.9723 -0.3820 1.0446 1.0493
174 0.9287 -0.4582 1.0356 1.0387
175 0.9134 -0.5252 1.0536 1.0619
176 0.8495 -0.4744 0.9729 0.9914
177 0.7938 -0.5394 0.9597 0.9657
178 0.8383 -0.4754 0.9637 0.9732
179 0.7828 -0.5447 0.9536 0.9575
180 0.9046 -0.3308 0.9632 0.9672
181 0.9062 -0.3234 0.9621 0.9662
182 0.9618 -0.2120 0.9848 0.9945
183 0.9193 -0.4067 1.0053 1.0083
184 1.0262 -0.2678 1.0605 1.0611
185 1.0042 -0.2525 1.0355 1.0525
186 0.9818 -0.2119 1.0044 0.9969
187 0.9971 -0.2776 1.0350 1.0236
188 1.0306 -0.2219 1.0542 1.0700
189 0.9963 -0.1421 1.0064 1.0049
190 0.9183 -0.2181 0.9439 0.9447
191 0.8592 -0.4584 0.9739 0.9747
192 0.8730 -0.4538 0.9839 0.9849
193 0.8760 -0.4249 0.9736 0.9751
194 1.0268 -0.1896 1.0442 1.0446
195 0.9045 -0.3312 0.9632 0.9672
196 0.8762 -0.3555 0.9456 0.9495
197 0.9973 -0.3180 1.0468 1.0621
198 1.0231 -0.2682 1.0576 1.0700
199 1.0604 -0.1429 1.0700 1.0700
200 0.9741 -0.3836 1.0469 1.0470
201 0.9371 -0.2536 0.9708 0.9701
202 0.9852 -0.3777 1.0551 1.0684
203 1.0152 -0.2054 1.0358 1.0416
204 0.9734 -0.4022 1.0533 1.0700
205 1.0424 -0.2413 1.0700 1.0700
206 1.0061 -0.2641 1.0402 1.0458
207 1.0034 -0.3225 1.0539 1.0573
208 0.9651 -0.3591 1.0297 1.0353
209 0.9448 -0.4273 1.0369 1.0487
210 0.9587 -0.4192 1.0463 1.0606
211 0.9365 -0.4646 1.0455 1.0580
212 0.9739 -0.3988 1.0524 1.0669
213 0.9921 -0.2999 1.0365 1.0427
214 0.9794 -0.2229 1.0045 1.0181
215 0.9649 -0.2535 0.9977 1.0087
216 0.9551 -0.2248 0.9812 0.9841
217 0.9787 -0.2180 1.0027 1.0156
218 0.9744 -0.0487 0.9756 0.9803
219 0.9584 -0.2055 0.9802 0.9850
220 0.9611 -0.1839 0.9785 0.9838
221 0.9370 -0.1984 0.9578 0.9573
222 0.9833 -0.2238 1.0085 1.0223
223 0.9295 -0.2808 0.9710 0.9845
224 0.9211 -0.3346 0.9800 0.9892
225 0.9795 -0.3963 1.0566 1.0629
226 0.9537 -0.3717 1.0236 1.0700
227 0.9955 -0.3750 1.0638 1.0700
228 0.9732 -0.3976 1.0513 1.0576
229 0.9597 -0.3971 1.0386 1.0450
230 1.0507 -0.2022 1.0700 1.0648
231 1.0346 -0.1951 1.0528 1.0511
232 1.0137 -0.3295 1.0659 1.0528
233 1.0039 -0.2529 1.0353 1.0369
234 1.0369 -0.2599 1.0690 1.0700
235 1.0363 -0.1992 1.0553 1.0553
236 0.9960 -0.2886 1.0370 1.0450
237 0.9832 -0.3682 1.0499 1.0582
238 0.9915 -0.2955 1.0346 1.0425
239 0.9716 -0.3574 1.0352 1.0487
240 1.0098 -0.3147 1.0577 1.0506
241 1.0496 -0.0708 1.0520 1.0533
242 0.9925 -0.3111 1.0401 1.0472
243 1.0040 -0.3206 1.0540 1.0608
244 1.0115 -0.3345 1.0654 1.0638
245 0.9770 -0.3702 1.0448 1.0484
246 0.9641 -0.3392 1.0220 1.0388
247 0.9888 -0.3612 1.0527 1.0504
248 1.0242 -0.2819 1.0623 1.0563
249 0.9751 -0.4037 1.0554 1.0664
250 0.9978 -0.3407 1.0543 1.0573
251 0.9110 -0.5103 1.0442 1.0506
252 0.9070 -0.5023 1.0368 1.0419
253 0.8981 -0.3356 0.9588 0.9696
254 1.0398 -0.2119 1.0612 1.0700
255 0.8703 -0.4075 0.9609 0.9688
256 0.8353 -0.4955 0.9713 0.9723
257 0.8725 -0.4323 0.9737 0.9774
258 1.0249 -0.1495 1.0357 1.0379
259 0.9272 -0.4190 1.0174 1.0330
260 0.9851 -0.3477 1.0447 1.0612
261 0.9635 -0.3254 1.0170 1.0160
262 0.9384 -0.2414 0.9689 0.9683
263 0.9813 -0.3398 1.0385 1.0413
264 0.9766 -0.2379 1.0051 1.0092
265 0.9351 -0.2129 0.9590 0.9575
266 0.9469 -0.2051 0.9688 0.9711
267 0.9417 -0.2704 0.9797 0.9933
268 0.9371 -0.2820 0.9786 0.9915
269 0.9996 -0.2742 1.0366 1.0700
270 0.9250 -0.4044 1.0095 1.0579
271 0.9404 -0.3899 1.0180 1.0653
272 1.0402 -0.1905 1.0575 1.0534
273 1.0343 -0.2435 1.0626 1.0604
274 1.0197 -0.2209 1.0434 1.0550
275 0.9880 -0.3576 1.0507 1.0700
276 1.0084 -0.2313 1.0345 1.0455
277 0.9945 -0.3948 1.0700 1.0667
278 0.9818 -0.3732 1.0504 1.0574
279 0.9291 -0.4589 1.0363 1.0393
280 0.9622 -0.4096 1.0457 1.0506
281 1.0473 -0.1585 1.0592 1.0522
282 0.9689 -0.2251 0.9947 0.9972
283 0.9895 -0.3317 1.0436 1.0480
284 1.0182 -0.2244 1.0427 1.0478
285 1.0129 -0.2137 1.0352 1.0407
286 1.0132 -0.3026 1.0575 1.0613
287 1.0047 -0.2597 1.0377 1.0454
288 0.8913 -0.3342 0.9519 0.9546
289 1.0247 -0.2748 1.0609 1.0700
290 1.0111 -0.2160 1.0339 1.0397
291 0.9998 -0.2757 1.0371 1.0700
292 1.0471 -0.1859 1.0635 1.0617
293 0.9883 -0.3523 1.0492 1.0492
294 0.8473 -0.4668 0.9674 0.9707
295 0.9404 -0.2585 0.9753 0.9745
296 0.9481 -0.2775 0.9879 0.9833
297 0.9997 -0.2738 1.0365 1.0411
298 1.0195 -0.3248 1.0700 1.0700
299 0.9831 -0.1711 0.9979 1.0073
300 0.9315 -0.4049 1.0157 1.0638
0
5 5.7219
4 2.0000
9 5.2983
11 7.1670
28 3.0000
29 3.0000
30 6.0000
31 3.2707
32 5.0000
33 5.0000
34 1.0000
35 4.0289
36 5.9655
38 6.0000
40 1.4559
41 3.1676
42 3.0381
43 3.0000
44 14.2610
45 9.0000
46 4.0000
0
1 -0.0365
2 1.5000
3 -0.5000
4 0.1493
5 -0.3799
6 0.1412
7 -1.8428
8 0.0357
9 -0.1947
10 0.4173
11 -6.0000
28 0.5767
29 -0.1912
30 0.8331
31 0.5019
32 0.9377
33 2.5379
34 0.0571
35 -0.0839
36 -2.0000
37 0.0000
38 0.0939
39 0.0611
40 0.1496
41 0.6892
42 0.2646
43 0.5071
44 5.8656
45 2.0486
46 -1.8983
62 0.1313
64 0.3800
65 0.0463
73 0.2000
92 -0.2969
100 0.9295
102 -0.5000
103 -0.1820
106 -0.5000
108 -0.1000
116 0.9000
117 0.3500
122 -0.9981
123 -0.6306
124 6.6698
133 -0.8676
139 0.4000
145 0.1219
148 0.1000
159 0.2165
161 0.2495
167 -0.1100
168 0.0245
174 -0.2400
178 0.0889
179 0.3758
186 0.1071
189 -0.5000
199 -0.2692
203 -3.0000
221 0.8947
222 0.9586
225 0.0200
232 0.2000
254 11.2040
258 -0.1500
265 -0.6000
281 1.6383
289 0.0102
0
259 0.40 0.4111 0.40 0.50
107 0.00 0.0000 0.00 0.10
200 0.50 0.4150 0.40 0.50
224 0.50 0.4755 0.40 0.50
54 0.00 0.0047 0.00 0.10
300 0.10 0.0928 0.00 0.10
0

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Sigmoid函数法/result_XB1780.dat Normal file
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Sigmoid函数法/seting.m Normal file
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@ -0,0 +1,66 @@
function [e,f,PG,QR,Pg,Qg,T,pgvNum,xNum,m,r,l,u,z,w,x,y,para3,mu0,b0,bei,dmaxOut1,dmaxOut2,xz1,xz2,dmaxOut3,dmaxOut4,xz3,xz4,xz5,muOut,opfGoal,...
times,secondBegin,ifconverge,k2,mismatch]=seting(nodeNum,lineNum,transNum,transK0,capNum,capK,pvQmin,pvQmax,pvNum,pvNode,pvV,pgNum,pgNode,Pmin,Pmax,Pg,Qg)
%程序功能：预计算过程初始化
%编写时间：2010年10月
%初始化调整参数
para3=0.6; %陡度参数修正量初值β0
para4=5; %陡度参数初值
if nodeNum==30 %各测试系统要得到最好的优化结果，需要取不同的陡度参数修正值
para3=0.51;
para4=3.9;
else if nodeNum==118
para3=0.09;
para4=5;
else if nodeNum==300
para3=0.45;
para4=4.6;
else if nodeNum==1047
para3=0.54;
para4=0.9;
else if nodeNum==1780
para3=0.4;
para4=0.6;
end
end
end
end
end
mu0=para4; %mut,mub的初始值
b0=para3; %β0
bei=20; %对Zt，Zb的上下限限制调整参数
%% 设PQ节点电压幅值为1，相角为0
e=ones(nodeNum,1);
f=sparse(nodeNum,1);
e(pvNode)=pvV(pvNode); %初始值对计算结果有一点点影响
%% 发电机有功无功出力以及无功源无功出力初值（分别取上下界的平均值）
PG=(Pmin+Pmax)/2; %发电机有功功率初值,取发电机有功上下限的平均值
QR=(pvQmin+pvQmax)/2; %发电机无功功率初值，取平衡节点、PV节点无功上下限的平均值
Pg(pgNode)=PG(pgNode);
Qg(pvNode)=QR(pvNode);
T=1./transK0;
x=[T;PG(pgNode);QR(pvNode);capK;e;f]; %系统的控制变量和状态变量
%% 设定松弛变量l,u,拉格朗日乘子z,w,y的初值
pgvNum=pgNum+pvNum;
xNum=pgvNum+2*nodeNum+transNum+capNum; %变量个数
m=2*nodeNum; %等式约束条件个数
r=pgvNum+nodeNum+lineNum+transNum+capNum; %不等式约束条件个数
s=1;
l=s*ones(r,1); %初始化l,u,z为1，w为-1，y为0
u=l;
z=l;
w=-l;
y=sparse(m,1);
xz1=[];xz2=xz1;xz3=xz1;xz4=xz1;dmaxOut1=xz1;dmaxOut2=xz1;dmaxOut3=xz1; %用于保存中间计算结果，以提供作图数据
dmaxOut4=xz1;xz5=xz1;muOut=xz1;
opfGoal=2; %目标函数为有功出力最小
times=1; %计算阶段标志
secondBegin=1; %连续化处理阶段开始标志
ifconverge=0; %收敛标志
k2=0;
mismatch=0.00001; %最大不平衡量计算精度
if nodeNum==1780 %由于1780系统在预计算时最大不平衡量要收敛到0.00001的精度迭代次数会比较多，为了提高整体收敛速度
mismatch=0.01; %在预计算时最大不平衡量精度达到0.01则视为收敛，在连续化处理收敛时最大不平衡量精度可达0.00001
end

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function [const,Lz,Lw,L1,U1]=snd_Constant(nodeNum,opfGoal,lineNum,transNum,transI,transJ,transG,transB,lineI,lineJ,balNode,mu,G,B,GIJ,BIJ,e,f,Pmin,Pmax,...
a,b,PG,QR,pvQmin,pvQmax,pgNum,pgvNum,xNum,pgNode,pvNode,dhx,dgx,L1,U1,LZ,UW,l,u,y,r,dT_Zt,capNum,hx,Vmax,Vmin,Zt,Zb,bei,mu0,oneTrans,oneCap)
%程序功能：连续化处理过程，形成扰动KKT方程不平衡量矩阵
%编写时间：2010年10月
%% 形成目标函数一阶偏导矩阵▽f(.)
if(opfGoal==2)
dPG=ones(pgNum,1);
dfx=sparse(transNum+1:transNum+pgNum,ones(pgNum,1),dPG,xNum,1);
else if(opfGoal==1)
dPG=2*a(pgNode).*PG(pgNode)+b(pgNode);
dfx=sparse(transNum+1:transNum+pgNum,ones(pgNum,1),dPG,xNum,1);
else if(opfGoal==3)
dfT=-transG.*dT_Zt.*((f(transI)-f(transJ)).^2+(e(transI)-e(transJ)).^2);
dfPQ=zeros(pgvNum,1);
dfcapK=zeros(capNum,1);
EE=e*ones(1,nodeNum);
FF=f*ones(1,nodeNum);
dfe=2*sum(G.*(EE-EE'));
dff=2*sum(G.*(FF-FF'));
dfx=[dfT;dfPQ;dfcapK;dfe';dff'];
else if(opfGoal==4)
dfT=transB.*dT_Zt.*((f(transI)-f(transJ)).^2+(e(transI)-e(transJ)).^2);
dfPQ=zeros(pgvNum,1);
dfcapK=zeros(capNum,1);
EE=e*ones(1,nodeNum);
FF=f*ones(1,nodeNum);
dfe=-2*sum(B.*(EE-EE'));
dff=-2*sum(B.*(FF-FF'));
dfx=[dfT;dfPQ;dfcapK;dfe';dff'];
end
end
end
end
%% 不等式约束项
tmp=1;
Zbmin=-tmp*bei*mu0*oneCap; %这里加入了Zt，Zb的取值限制在陡度参数初值的一定倍数（取20倍，Zt，Zb取到这个值已经非常接近0，或1，
Zbmax=tmp*bei*mu0*oneCap; %完全可以保证）范围内，这样处理既能不影响计算精度，还可以避免由于Zt，Zb的绝对值取值过大，
Ztmin=-tmp*bei*mu0*oneTrans; %使得离散变量过早固定在0或1处，而导致收敛困难
Ztmax=tmp*bei*mu0*oneTrans;
gxT=Zt;
gxTx=Ztmin;
gxTs=Ztmax;
gxv=[PG(pgNode);QR(pvNode);Zb;e.^2+f.^2]; %约束条件当前值
gxvx=[Pmin(pgNode);pvQmin(pvNode);Zbmin;Vmin.*Vmin]; %约束下限
gxvs=[Pmax(pgNode);pvQmax(pvNode);Zbmax;Vmax.*Vmax]; %约束上限
gxl=(e(lineI).*e(lineI)+f(lineI).*f(lineI)-e(lineI).*e(lineJ)-f(lineI).*f(lineJ)).*GIJ+(e(lineI).*f(lineJ)-e(lineJ).*f(lineI)).*BIJ;%线路功率当前值
gxlx=-ones(lineNum,1)*1000; %线路约束下限
gxls=ones(lineNum,1)*1000; %线路约束上限
gx=[gxT;gxv;gxl]; %组合所有约束条件
gxx=[gxTx;gxvx;gxlx];
gsx=[gxTs;gxvs;gxls];
Lz=gx-l-gxx;
Lw=gx+u-gsx;
%% 形成修正方程常数项向量
muUL=mu*(U1-L1);
BB1=UW*Lw-LZ*Lz-muUL*ones(r,1);
BB=dhx*y-dfx+dgx*BB1; %修正方程常数项ψ(.,μ)
BB(transNum+pgvNum+capNum+nodeNum+balNode,1)=0; %保持平衡节点电压虚部不变，始终为0，则常数项平衡节点处置0
BB(transNum+pgvNum+capNum+balNode,1)=0; %保持平衡节点电压实部不变
const=[BB;hx]; %修正方程常数项向量

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function [HSB,dhx,dgx,dgxT,GIJ,BIJ,L1,U1,LZ,UW,transG,transB,dT_Zt,mut,mub]=snd_formHSB(nodeNum,balNode,opfGoal,lineNum,transNum,lineI,lineJ,transI,transJ,...
T,transG,transB,pgNode,pvNode,G,B,e,f,pgNum,pvNum,pgvNum,xNum,a,m,r,l,u,z,w,y,kt0,mut,Zt,oneTrans,oneCap,Zb,mub,q0,capBi,capNum,capI,tij,Bci,N1,H1,diagE,...
diagF,b0,balNum)
%程序功能：连续化处理过程，形成修正方程系数矩阵
%编写时间：2010年10月
%% 修正陡度参数μt
dicVar=[tij;Bci];
tmp1=dicVar.*(1-dicVar);
if sum(tmp1)==0
tmp2=0;
else
tmp2=tmp1/sum(tmp1);
end
tmp3=ones(transNum+capNum,1)./(ones(transNum+capNum,1)+tmp2); %计算每一步迭代中陡度参数的修正量
bk=tmp3*b0;
mut_bk=bk(1:transNum);
mub_bk=bk(transNum+1:end);
smallest=0.0000000001; %当陡度参数已经非常接近0时，让其以0.9的速率减小，保证其还能继续下降，
large_mut=find(mut>smallest); %不过只要选择好适当的陡度参数初值和修正参数，陡度参数达到这个精度时基本上都已经收敛
small_mut=find(mut<=smallest);
mut(large_mut)=mut_bk(large_mut).*mut(large_mut);
mut(small_mut)=0.9*mut(small_mut);
large_mub=find(mub>smallest);
small_mub=find(mub<=smallest);
mub(large_mub)=mub_bk(large_mub).*mub(large_mub);
mub(small_mub)=0.9*mub(small_mub);
dT_Zt=oneTrans;
d2T_Zt2=oneTrans;
n_zt= Zt<0; %为了避免指数运算时出现的计算机溢出问题，在计算Sigmoid函数及其一、二阶导数时，
p_zt= Zt>=0; %区分Zt的正负取值情况，采用不同的表达形式（两种形式完全等价），这是算法得以实现的关键。
n_Ezu=exp(Zt(n_zt)./mut(n_zt));
dT_Zt(n_zt)=kt0(n_zt).*(n_Ezu./(mut(n_zt).*(oneTrans(n_zt)+n_Ezu).^2)); %zt为负时，T对zt求一次偏导
d2T_Zt2(n_zt)=(dT_Zt(n_zt)./mut(n_zt)).*(oneTrans(n_zt)-2*n_Ezu./(oneTrans(n_zt)+n_Ezu));%zt为负时，T对zt求二次偏导
p_Ezu=exp(-Zt(p_zt)./mut(p_zt));
dT_Zt(p_zt)=kt0(p_zt).*(p_Ezu./(mut(p_zt).*(oneTrans(p_zt)+p_Ezu).^2)); %zt为正时，T对zt求一次偏导
d2T_Zt2(p_zt)=(dT_Zt(p_zt)./mut(p_zt)).*(oneTrans(p_zt)-2./(oneTrans(p_zt)+p_Ezu)); %zt为正时，T对zt求二次偏导
transGmut=transG.*dT_Zt;
transBmut=transB.*dT_Zt;
dcapK_Zb=oneCap;
d2capK_Zb2=oneCap;
n_zb= Zb<0; %对于Zb，同样要区分其正负取值进行计算
p_zb= Zb>=0;
n_Ezbu=exp(Zb(n_zb)./mub(n_zb));
dcapK_Zb(n_zb)=q0.*(n_Ezbu./(mub(n_zb).*(oneCap(n_zb)+n_Ezbu).^2)); %zb为负时，capK对zb求一次偏导
d2capK_Zb2(n_zb)=(dcapK_Zb(n_zb)./mub(n_zb)).*(oneCap(n_zb)-2*n_Ezbu./(oneCap(n_zb)+n_Ezbu));%zb为负时，capK对zb求二次偏导
p_Ezbu=exp(-Zb(p_zb)./mub(p_zb));
dcapK_Zb(p_zb)=q0.*(p_Ezbu./(mub(p_zb).*(oneCap(p_zb)+p_Ezbu).^2)); %zb为正时，capK对zb求一次偏导
d2capK_Zb2(p_zb)=(dcapK_Zb(p_zb)./mub(p_zb)).*(oneCap(p_zb)-2./(oneCap(p_zb)+p_Ezbu));%zb为正时，capK对zb求二次偏导
capBi_dBci=capBi.*dcapK_Zb;
%% 形成等式约束雅可比矩阵
ef1=e(transI).*e(transJ)+f(transI).*f(transJ);
ef2=e(transI).*f(transJ)-e(transJ).*f(transI);
ef3=e(transI).*e(transI)+f(transI).*f(transI);
ef1G=ef1.*transGmut;
ef1B=ef1.*transBmut;
ef2G=ef2.*transGmut;
ef2B=ef2.*transBmut;
dhPTi=-ef1G+ef2B+2*ef3.*transGmut.*T;
dhPTj=-ef1G-ef2B;
dhPT=sparse(1:transNum,transI,dhPTi,transNum,nodeNum)+sparse(1:transNum,transJ,dhPTj,transNum,nodeNum);%有功平衡方程P对变压器变比求偏导
dhQTi=ef1B+ef2G-2*ef3.*transBmut.*T;
dhQTj=ef1B-ef2G;
dhQT=sparse(1:transNum,transI,dhQTi,transNum,nodeNum)+sparse(1:transNum,transJ,dhQTj,transNum,nodeNum);%无功平衡方程Q对变压器变比求偏导
dhP=sparse(1:pgNum,pgNode,ones(pgNum,1),pgNum,m);
dhQ1=sparse(1:pvNum,pvNode,ones(pvNum,1),pvNum,nodeNum);
dhQ=[sparse(pvNum,nodeNum) dhQ1];
dhcapK1=sparse(1:capNum,capI,(e(capI).^2+f(capI).^2).*capBi_dBci,capNum,nodeNum);%功率平衡方程对电容电抗器组数求偏导
dhcapK=[sparse(capNum,nodeNum) dhcapK1];
%功率方程雅可比矩阵
deG=diagE*G;
dfB=diagF*B;
deB=diagE*B;
dfG=diagF*G;
dH1=sparse(1:nodeNum,1:nodeNum,H1,nodeNum,nodeNum);
dN1=sparse(1:nodeNum,1:nodeNum,N1,nodeNum,nodeNum);
Hij=-dH1-deG-dfB;
Nij=-dN1+deB-dfG;
Jij=dN1-dfG+deB;
Lij=-dH1+dfB+deG;
dhJacb=[Hij Nij;Jij Lij]'; %合并形成功率方程雅可比矩阵
dhx=[dhPT dhQT;dhP;dhQ;dhcapK;dhJacb]; %合并形成等式约束雅可比矩阵h(x)
%% 形成不等式约束雅可比矩阵▽g(x)
gtransNum=transNum; %在原来变比和电容电抗器上下限不等式约束的模块，替换为Zt、Zb的上下限不等式约束
gcapNum=capNum;
dgT1=sparse(1:transNum,1:transNum,ones(transNum,1),transNum,r-lineNum);
dglT=(e(transI).^2+f(transI).^2-e(transI).*e(transJ)-f(transI).*f(transJ))...
.*transGmut+(e(transI).*f(transJ)-e(transJ).*f(transI)).*transBmut;
dgT2=sparse(1:transNum,lineNum-transNum+1:lineNum,dglT,transNum,lineNum);
dgT=[dgT1 dgT2]; %所有不等式对Zt求导的模块
dgP=sparse(1:pgNum,gtransNum+1:gtransNum+pgNum,ones(pgNum,1),pgNum,r); %所有不等式约束对P求导的模块
dgQ=sparse(1:pvNum,gtransNum+pgNum+1:gtransNum+pgvNum,ones(pvNum,1),pvNum,r);%所有不等式约束对Q求导的模块
dgcapK=sparse(1:capNum,transNum+pgvNum+1:transNum+pgvNum+capNum,ones(capNum,1),capNum,r);%所有不等式约束对Zb求导的模块
dgve=2*diagE;
dgvf=2*diagF;
sizeG=size(G);
GIJ=G(sub2ind(sizeG,lineI,lineJ));
BIJ=B(sub2ind(sizeG,lineI,lineJ));
dgleI=(2*e(lineI)-e(lineJ)).*GIJ+f(lineJ).*BIJ;
dgleJ=-e(lineI).*GIJ-f(lineI).*BIJ;
dglfI=(2*f(lineI)-f(lineJ)).*GIJ-e(lineJ).*BIJ;
dglfJ=-f(lineI).*GIJ+e(lineI).*BIJ;
dgle=sparse(lineI,(1:lineNum),dgleI,nodeNum,lineNum)+sparse(lineJ,(1:lineNum),dgleJ,nodeNum,lineNum);
dglf=sparse(lineI,(1:lineNum),dglfI,nodeNum,lineNum)+sparse(lineJ,(1:lineNum),dglfJ,nodeNum,lineNum);
dg0=sparse(m,gtransNum+pgvNum+gcapNum);
dgvl=[dgve dgle;dgvf dglf];
dgef=[dg0 dgvl]; %所有不等式约束对电压实部、虚部求偏导的模块
dgx=[dgT;dgP;dgQ;dgcapK;dgef]; %不等式约束雅克比矩阵
%% 形成对角阵
Z=sparse(1:r,1:r,z,r,r);
W=sparse(1:r,1:r,w,r,r);
L1=sparse(1:r,1:r,1./l,r,r);
U1=sparse(1:r,1:r,1./u,r,r);
LZ=L1*Z;
UW=U1*W;
%% 形成海森伯矩阵
%目标函数的海森伯矩阵▽2f(x)
if(opfGoal==2) %目标为有功出力最小
HSdfx=sparse(xNum,xNum);
else if(opfGoal==1)
HSdfx=sparse(transNum+1:transNum+pgNum,transNum+1:transNum+pgNum,2*a(pgNode),xNum,xNum);%仅目标函数对PG求偏导处的对角元为非零元素，其他都为0(目标为发电耗量最小)
else if(opfGoal==3)
d2ftei=-2*transGmut.*(e(transI)-e(transJ));
d2ftej=-d2ftei;
d2ftfi=-2*transGmut.*(f(transI)-f(transJ));
d2ftfj=-d2ftfi;
d2fte=sparse(1:transNum,transI,d2ftei,transNum,nodeNum)+sparse(1:transNum,transJ,d2ftej,transNum,nodeNum);
d2ftf=sparse(1:transNum,transI,d2ftfi,transNum,nodeNum)+sparse(1:transNum,transJ,d2ftfj,transNum,nodeNum);
d2fT2=-transG.*d2T_Zt2.*((f(transI)-f(transJ)).^2+(e(transI)-e(transJ)).^2);
d2fT0=sparse(1:transNum,1:transNum,d2fT2,transNum,transNum+pgvNum+capNum);
d2fT=[d2fT0 d2fte d2ftf];
d2fPGQR=sparse(pgvNum,xNum);
d2fcapK=sparse(capNum,xNum);
d2fee=2*(G-sparse(1:nodeNum,1:nodeNum,sum(G,2),nodeNum,nodeNum));
d2fff=d2fee;
zero_nodeNum=sparse(nodeNum,nodeNum);
d2f_ef_ef=[d2fee zero_nodeNum;zero_nodeNum d2fff];
d2efT=[d2fte d2ftf]';
d2f_ef=[d2efT sparse(2*nodeNum,pgvNum+capNum) d2f_ef_ef];
HSdfx=[d2fT;d2fPGQR;d2fcapK;d2f_ef];
else if(opfGoal==4)
d2ftei=2*transBmut.*(e(transI)-e(transJ));
d2ftej=-d2ftei;
d2ftfi=2*transBmut.*(f(transI)-f(transJ));
d2ftfj=-d2ftfi;
d2fte=sparse(1:transNum,transI,d2ftei,transNum,nodeNum)+sparse(1:transNum,transJ,d2ftej,transNum,nodeNum);
d2ftf=sparse(1:transNum,transI,d2ftfi,transNum,nodeNum)+sparse(1:transNum,transJ,d2ftfj,transNum,nodeNum);
d2fT2=transB.*d2T_Zt2.*((f(transI)-f(transJ)).^2+(e(transI)-e(transJ)).^2);
d2fT0=sparse(1:transNum,1:transNum,d2fT2,transNum,transNum+pgvNum+capNum);
d2fT=[d2fT0 d2fte d2ftf];
d2fPGQR=sparse(pgvNum,xNum);
d2fcapK=sparse(capNum,xNum);
d2fee=-2*(B-sparse(1:nodeNum,1:nodeNum,sum(G,2),nodeNum,nodeNum));
d2fff=d2fee;
zero_nodeNum=sparse(nodeNum,nodeNum);
d2f_ef_ef=[d2fee zero_nodeNum;zero_nodeNum d2fff];
d2efT=[d2fte d2ftf]';
d2f_ef=[d2efT sparse(2*nodeNum,pgvNum+capNum) d2f_ef_ef];
HSdfx=[d2fT;d2fPGQR;d2fcapK;d2f_ef];
end
end
end
end
%等式约束海森伯矩阵与拉格朗日乘子y的乘积▽2h(x)*y
y1=y(1:nodeNum,1);
y2=y(nodeNum+1:2*nodeNum,1);
ef1Gd2=ef1.*transG.*d2T_Zt2;
ef1Bd2=ef1.*transB.*d2T_Zt2;
ef2Gd2=ef2.*transG.*d2T_Zt2;
ef2Bd2=ef2.*transB.*d2T_Zt2;
d2P_T2=(-ef1Gd2+ef2Bd2+2*ef3.*transG.*(dT_Zt.^2+T.*d2T_Zt2)).*y1(transI)+(-ef1Gd2-ef2Bd2).*y1(transJ);
d2Q_T2=(ef1Bd2+ef2Gd2-2*ef3.*transB.*(dT_Zt.^2+T.*d2T_Zt2)).*y2(transI)+(ef1Bd2-ef2Gd2).*y2(transJ);
dhT2=d2P_T2+d2Q_T2; %功率方程对变压器Zt求二次偏导所得的列向量
HSdhT=sparse(1:transNum,1:transNum,dhT2,transNum+pgvNum+capNum,transNum+pgvNum+capNum)+...
sparse(transNum+pgvNum+1:transNum+pgvNum+capNum,transNum+pgvNum+1:transNum+pgvNum+capNum,...
(e(capI).^2+f(capI).^2).*d2capK_Zb2.*y2(capI),transNum+pgvNum+capNum,transNum+pgvNum+capNum);
eiG=e(transI).*transGmut;
ejG=e(transJ).*transGmut;
eiB=e(transI).*transBmut;
ejB=e(transJ).*transBmut;
fiG=f(transI).*transGmut;
fjG=f(transJ).*transGmut;
fiB=f(transI).*transBmut;
fjB=f(transJ).*transBmut;
ejG_fjB=ejG-fjB;
ejGfjB=ejG+fjB;
fjGejB=fjG+ejB;
ejB_fjG=ejB-fjG;
eiGfiB=eiG+fiB;
eiG_fiB=eiG-fiB;
eiB_fiG=eiB-fiG;
fiGeiB=fiG+eiB;
dP2_ei_t=(4*eiG.*T-ejG_fjB).*y1(transI)-ejGfjB.*y1(transJ);
dP2_ej_t=-eiGfiB.*y1(transI)-eiG_fiB.*y1(transJ);
dQ2_ei_t=(-4*eiB.*T+fjGejB).*y2(transI)+ejB_fjG.*y2(transJ);
dQ2_ej_t=eiB_fiG.*y2(transI)+fiGeiB.*y2(transJ);
HSdh_et=sparse(1:transNum,transI,dP2_ei_t+dQ2_ei_t,transNum,nodeNum)+sparse(1:transNum,transJ,dP2_ej_t+dQ2_ej_t,transNum,nodeNum);%功率方程先对Zt求偏导，再对电压实部求偏导模块
dP2_fi_t=(4*fiG.*T-fjGejB).*y1(transI)+ejB_fjG.*y1(transJ);
dP2_fj_t=eiB_fiG.*y1(transI)-fiGeiB.*y1(transJ);
dQ2_fi_t=(-4*fiB.*T-ejG_fjB).*y2(transI)+ejGfjB.*y2(transJ);
dQ2_fj_t=eiGfiB.*y2(transI)-eiG_fiB.*y2(transJ);
HSdh_ft=sparse(1:transNum,transI,dP2_fi_t+dQ2_fi_t,transNum,nodeNum)+sparse(1:transNum,transJ,dP2_fj_t+dQ2_fj_t,transNum,nodeNum);%功率方程先对Zt求偏导，再对电压虚部求偏导模块
HSdh_eft=[HSdh_et HSdh_ft];
HSdh_tef=HSdh_eft';
HSdhPQ=sparse(pgvNum,2*nodeNum); %功率方程先对PG、QR求偏导，再对其他变量求偏导的部分
d2hcap_e=sparse(1:capNum,capI,2*e(capI).*capBi_dBci.*y2(capI),capNum,nodeNum); %功率方程先对Zb求偏导，再对e求偏导的部分
d2hcap_f=sparse(1:capNum,capI,2*f(capI).*capBi_dBci.*y2(capI),capNum,nodeNum); %功率方程先对Zb求偏导，再对f求偏导的部分
HSdhcap_ef=[d2hcap_e d2hcap_f];
d2htPQ_ef=[HSdh_eft;HSdhPQ;HSdhcap_ef];
HSdhtPQ=[HSdhT d2htPQ_ef];
HSdhx1=sparse(m,pgvNum);
%潮流方程海森矩阵
diagy1=sparse(1:nodeNum,1:nodeNum,y1,nodeNum,nodeNum);
diagy2=sparse(1:nodeNum,1:nodeNum,y2,nodeNum,nodeNum);
HSdhey=-diagy1*G+diagy2*B+(-G*diagy1+B*diagy2);
HSdhefy=diagy1*B+diagy2*G-(B*diagy1+G*diagy2);
HSdhx2=[HSdhey HSdhefy;HSdhefy' HSdhey];
HSdhx=[HSdhtPQ;HSdh_tef HSdhx1 HSdhcap_ef' HSdhx2];
%形成不等式约束二阶偏导的矩阵▽2g(x)*(z+w)
ZWcl=z(gtransNum+pgvNum+gcapNum+nodeNum+1:end)+w(gtransNum+pgvNum+gcapNum+nodeNum+1:end);
ZWv=z(gtransNum+pgvNum+gcapNum+1:gtransNum+pgvNum+gcapNum+nodeNum)+w(gtransNum+pgvNum+gcapNum+1:gtransNum+pgvNum+gcapNum+nodeNum);
dg2T=((e(transI).^2+f(transI).^2-e(transI).*e(transJ)-f(transI).*f(transJ)).*transG.*d2T_Zt2+...
(e(transI).*f(transJ)-e(transJ).*f(transI)).*transB.*d2T_Zt2).*ZWcl(lineNum-transNum+1:end);
HSdg2T=sparse(1:transNum,1:transNum,dg2T,transNum,transNum); %不等式对Zt求二次偏导模块
dgeiT=((2*e(transI)-e(transJ)).*transGmut+f(transJ).*transBmut).*ZWcl(lineNum-transNum+1:end);
dgejT=(-e(transI).*transGmut-f(transI).*transBmut).*ZWcl(lineNum-transNum+1:end);
dgeT=sparse(1:transNum,transI,dgeiT,transNum,nodeNum)+sparse(1:transNum,transJ,dgejT,transNum,nodeNum);%不等式约束先对Zt求偏导，再对e求偏导的模块
dgfiT=((2*f(transI)-f(transJ)).*transGmut-e(transJ).*transBmut).*ZWcl(lineNum-transNum+1:end);
dgfjT=(-f(transI).*transGmut+e(transI).*transBmut).*ZWcl(lineNum-transNum+1:end);
dgfT=sparse(1:transNum,transI,dgfiT,transNum,nodeNum)+sparse(1:transNum,transJ,dgfjT,transNum,nodeNum);%不等式约束先对Zt求偏导，再对f求偏导的模块
HSdgefT=[dgeT dgfT];
HSdgT=[HSdg2T sparse(transNum,pgvNum+capNum) HSdgefT];
HSdgee=sparse(lineI,lineI,2*GIJ.*ZWcl,nodeNum,nodeNum)-sparse(lineI,lineJ,GIJ.*ZWcl,nodeNum,nodeNum)-...
sparse(lineJ,lineI,GIJ.*ZWcl,nodeNum,nodeNum)+sparse(1:nodeNum,1:nodeNum,2*ZWv,nodeNum,nodeNum);
HSdgff=HSdgee; %所有不等式约束对e、f求二次偏导模块
HSdgef=sparse(lineI,lineJ,BIJ.*ZWcl,nodeNum,nodeNum)-sparse(lineJ,lineI,BIJ.*ZWcl,nodeNum,nodeNum);
HSdgfe=HSdgef';
HSdgx1=[HSdgee HSdgef;HSdgfe HSdgff];
HSdgxtPQ_0=sparse(pgvNum+capNum,xNum);
HSdgef_0=[HSdgefT' sparse(2*nodeNum,pgvNum+capNum)];
HSdgx=[HSdgT;HSdgxtPQ_0;HSdgef_0 HSdgx1]; %合成不等式约束海森矩阵
%求和形成H(.)矩阵.
dgxT=dgx'; %求dgx的转置
MULdgx=dgx*(UW-LZ)*dgxT;
H=HSdhx+HSdgx-HSdfx+MULdgx; %求和形成H(.)矩阵.
%% 根据以上所求的各个矩阵合成海森伯矩阵
HSB0=sparse(m,m);
HSB=[H dhx;dhx' HSB0];
balN=transNum+pgvNum+capNum+nodeNum+balNode;
HSB(balN,:)=0; %保持平衡节点电压虚部不变，始终为0，即将海森矩阵中平衡节点虚部所对应的行列元素置0，对角元素置1
HSB(:,balN)=0;
HSB_balN=sub2ind(size(HSB),balN,balN);
HSB(HSB_balN)=ones(balNum,1);
balN1=transNum+pgvNum+capNum+balNode;
HSB(balN1,:)=0; %保持平衡节点电压实部不变，始终为0，即将海森矩阵中平衡节点实部所对应的行列元素置0，对角元素置1
HSB(:,balN1)=0;
HSB_balN1=sub2ind(size(HSB),balN1,balN1);
HSB(HSB_balN1)=ones(balNum,1);

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function [x,secondBegin,mut,oneTrans,Zt,tij,Tn,kt0,r,l,u,z,w,y,oneCap,capKn,Bci,Zb,mub,q0,Tn1,capKn1,Kn,capK,firstT,firstcapK,firstfx,firstV,Gap]=...
snd_setting(x,secondBegin,transNum,T,transKmin,transKmax,r,m,capNum,capK,pgvNum,mu0,capBi,fx,e,f)
%程序功能：连续化处理过程重新初始化
%编写时间：2010年10月
%% 保留预计算结果
firstT=T;
firstcapK=capK;
firstfx=fx;
firstV=sqrt(e.^2+f.^2);
%% 连续化处理阶段赋初值
secondBegin=secondBegin-1;
oneTrans=ones(transNum,1);
oneCap=ones(capNum,1);
mut=oneTrans*mu0; %Zt对应的陡度参数初值
mub=oneCap*mu0; %Zb对应的陡度参数初值
maxTap=5; %变压器最大调节档位
K=1./T; %变压器采用的是k：1模型，但是为了推导公式方便将T=1/k代入公式中，在获取实际变比时要转化回来
Kmax=1./transKmin;
Kmin=1./transKmax;
kt0=(Kmax-Kmin)/(maxTap-1); %变压器单位调节幅度
Kn=fix((K-Kmin)./kt0).*kt0+Kmin; %获取变压器变量连续最优解左右两侧档位对应的变比
Kn1=Kn+kt0;
Tn=1./Kn1;
Tn1=1./Kn;
kt0=Tn1-Tn;
q0=1; %电容器档位的单位调节幅度
capK=capK./capBi; %由于在预计算中capK是表示投入电容器的容量，而这里是要将其转为投入电容器的档位
capKn=floor(capK);
capKn1=capKn+q0;
tij=(T-Tn)./kt0; %经过预计算后，对离散量的求解转变为求解0-1变量
Bci=(capK-capKn)/q0;
Zt=mut.*log(tij./(oneTrans-tij)); %变比对应的新引入连续变量
Zb=mub.*log(Bci./(oneCap-Bci)); %电容电抗器对应的新引入的连续变量
x(1:transNum)=Zt; %在连续化处理阶段，所求的变量不再是原来的离散变量，而是新引入的连续变量
x(transNum+pgvNum+1:transNum+pgvNum+capNum)=Zb;
%% 连续化处理阶段重新给松弛因子和拉格朗日乘子赋初值
l=ones(r,1);
u=l;
z=l;
w=-l;
y=sparse(m,1);
Gap=l'*z-u'*w;

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function [z,l,u,w,x,y,PG,QR,Pg,Qg,e,f,T,G,B,Zt,tij,Zb,Bci,capK,mut,mub]=snd_solve(HSB,const,mu,r,nodeNum,pgNum,pvNum,pgvNum,xNum,transNum,pgNode,pvNode,...
Pg,Qg,m,x,y,z,l,u,w,Lz,Lw,LZ,UW,dgxT,L1,U1,G,B,transI,transJ,T,transG1,transB1,kt0,Tn,mut,oneTrans,q0,capKn,mub,oneCap,capK,capNum,capI,capBi)
%程序功能：连续化处理过程，求解修正方程
%编写时间：2010年10月
%% 求解方程，求出各变量的修正量
dX=-HSB\const;
dx=dX(1:xNum,1);
dy=dX(xNum+1:xNum+m,1);
dl=dgxT*dx+Lz;
du=-dgxT*dx-Lw;
Ll=(l.*z-mu*ones(r,1));
Lu=(u.*w+mu*ones(r,1));
diagZ=sparse(1:r,1:r,z,r,r);
diagW=sparse(1:r,1:r,w,r,r);
dz=-LZ*dgxT*dx-L1*(diagZ*Lz+Ll);
dw=UW*dgxT*dx+U1*(diagW*Lw-Lu);
%求最大步长
minusdz=find(dz<0);
dzmin=min(-z(minusdz)./dz(minusdz));
minusdl=find(dl<0);
dlmin=min(-l(minusdl)./dl(minusdl));
minusdw=find(dw>0);
dwmin=min(-w(minusdw)./dw(minusdw));
minusdu=find(du<0);
dumin=min(-u(minusdu)./du(minusdu));
ap=min(dlmin,dumin);
ad=min(dzmin,dwmin);
stepp=0.9995*min(ap,1);
stepd=0.9995*min(ad,1);
%更新变量
x=x+stepp*dx;
l=l+stepp*dl;
u=u+stepp*du;
y=y+stepd*dy;
z=z+stepd*dz;
w=w+stepd*dw;
%保留上一次计算的变比，用于修正节点导纳矩阵
Tlast=T;
capKlast=capK;
%给控制变量、状态变量重新赋值
Zt=x(1:transNum,1);
Zb=x(transNum+pgvNum+1:transNum+pgvNum+capNum);
tij=oneTrans;
Bci=oneCap;
n_zt= Zt<0;
p_zt= Zt>=0;
tij(n_zt)=exp(Zt(n_zt)./mut(n_zt))./(exp(Zt(n_zt)./mut(n_zt))+oneTrans(n_zt));%为了避免计算机溢出，对Zt为正为负时，分开表达式计算，两种表达式等价
tij(p_zt)=oneTrans(p_zt)./(oneTrans(p_zt)+exp(-Zt(p_zt)./mut(p_zt)));
n_zb= Zb<0;
p_zb= Zb>=0;
Bci(n_zb)=exp(Zb(n_zb)./mub(n_zb))./(exp(Zb(n_zb)./mub(n_zb))+oneCap(n_zb));
Bci(p_zb)=oneCap(p_zb)./(oneCap(p_zb)+exp(-Zb(p_zb)./mub(p_zb)));
T=Tn+tij.*kt0; %根据Sigmoid函数更新T和capK
capK=capKn+Bci.*q0;
PG(pgNode,1)=x(transNum+1:transNum+pgNum,1);
QR(pvNode,1)=x(transNum+pgNum+1:transNum+pgNum+pvNum,1);
e=x(transNum+pgNum+pvNum+capNum+1:transNum+pgNum+pvNum+capNum+nodeNum,1);
f=x(transNum+pgNum+pvNum+capNum+nodeNum+1:xNum,1);
Pg(pgNode)=PG(pgNode);
Qg(pvNode)=QR(pvNode);
%% 变比变化后需修正节点导纳矩阵
transG=transG1;
transB=transB1;
G=G-sparse(transI,transI,(T.*T-Tlast.*Tlast).*transG,nodeNum,nodeNum)...
+sparse(transI,transJ,transG.*(T-Tlast),nodeNum,nodeNum)...
+sparse(transJ,transI,transG.*(T-Tlast),nodeNum,nodeNum);
B=B-sparse(transI,transI,(T.*T-Tlast.*Tlast).*transB,nodeNum,nodeNum)...
+sparse(transI,transJ,transB.*(T-Tlast),nodeNum,nodeNum)...
+sparse(transJ,transI,transB.*(T-Tlast),nodeNum,nodeNum)...
+sparse(capI,capI,(capK-capKlast).*capBi,nodeNum,nodeNum);

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function [z,l,u,w,x,y,PG,QR,Pg,Qg,e,f,T,capK,G,B]=solve(HSB,const,mu,r,nodeNum,pgNum,pvNum,xNum,transNum,capNum,capI,capK,pgNode,pvNode,...
Pg,Qg,m,x,y,z,l,u,w,Lz,Lw,LZ,UW,dgxT,L1,U1,G,B,transI,transJ,T,transG1,transB1)
%程序功能：预计算过程，求解修正方程
%编写时间：2010年10月
%% 求解方程，求出各变量的修正量
dX=-HSB\const;
dx=dX(1:xNum,1);
dy=dX(xNum+1:xNum+m,1);
dl=dgxT*dx+Lz;
du=-dgxT*dx-Lw;
Ll=(l.*z-mu*ones(r,1));
Lu=(u.*w+mu*ones(r,1));
diagZ=sparse(1:r,1:r,z,r,r);
diagW=sparse(1:r,1:r,w,r,r);
dz=-LZ*dgxT*dx-L1*(diagZ*Lz+Ll);
dw=UW*dgxT*dx+U1*(diagW*Lw-Lu);
%% 求最大步长
minusdz=find(dz<0);
dzmin=min(-z(minusdz)./dz(minusdz));
minusdl=find(dl<0);
dlmin=min(-l(minusdl)./dl(minusdl));
minusdw=find(dw>0);
dwmin=min(-w(minusdw)./dw(minusdw));
minusdu=find(du<0);
dumin=min(-u(minusdu)./du(minusdu));
ap=min(dlmin,dumin);
ad=min(dzmin,dwmin);
stepp=0.9995*min(ap,1);
stepd=0.9995*min(ad,1);
%更新变量
x=x+stepp*dx;
l=l+stepp*dl;
u=u+stepp*du;
y=y+stepd*dy;
z=z+stepd*dz;
w=w+stepd*dw;
%保留上一次计算的变比，用于修正节点导纳矩阵
Tlast=T;
capKlast=capK;
%给控制变量、状态变量重新赋值
T=x(1:transNum,1);
PG(pgNode,1)=x(transNum+1:transNum+pgNum,1);
QR(pvNode,1)=x(transNum+pgNum+1:transNum+pgNum+pvNum,1);
capK=x(transNum+pgNum+pvNum+1:transNum+pgNum+pvNum+capNum,1);
e=x(transNum+pgNum+pvNum+capNum+1:transNum+pgNum+pvNum+capNum+nodeNum,1);
f=x(transNum+pgNum+pvNum+capNum+nodeNum+1:xNum,1);
Pg(pgNode)=PG(pgNode);
Qg(pvNode)=QR(pvNode);
%% 变比变化后需修正节点导纳矩阵
transG=transG1;
transB=transB1;
G=G-sparse(transI,transI,(T.*T-Tlast.*Tlast).*transG,nodeNum,nodeNum)...
+sparse(transI,transJ,transG.*(T-Tlast),nodeNum,nodeNum)...
+sparse(transJ,transI,transG.*(T-Tlast),nodeNum,nodeNum);
B=B-sparse(transI,transI,(T.*T-Tlast.*Tlast).*transB,nodeNum,nodeNum)...
+sparse(transI,transJ,transB.*(T-Tlast),nodeNum,nodeNum)...
+sparse(transJ,transI,transB.*(T-Tlast),nodeNum,nodeNum)...
+sparse(capI,capI,(capK-capKlast),nodeNum,nodeNum);