7 equation non linear system converge too slow
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I try to solve this non linear system with voltage points obtained from laboratory measurments.
% voltage value
Eoc=18.09;
v2=13.69;
v3=12.73;
v4= 11.31;
v5=10.22;
v6=9.71;
v7=8.91;
v8=8.41;
% current value
Ifc2=1;
Ifc3=2;
Ifc4=4;
Ifc5=6;
Ifc6=7;
Ifc7=9;
Ifc8=10;
% point 1
E1 = @(x)[Eoc - x(1)*log(Ifc2/x(2))-x(3)*exp(x(4)*Ifc2)-x(5)- x(6)*log(Ifc2/x(2))-x(7)*Ifc2-v2;
%% point 2
Eoc - x(1)*log(Ifc3/x(2))-x(3)*exp(x(4)*Ifc3)-x(5)- x(6)*log(Ifc3/x(2))-x(7)*Ifc3-v3;
%% point 3
Eoc - x(1)*log(Ifc4/x(2))-x(3)*exp(x(4)*Ifc4)-x(5)- x(6)*log(Ifc4/x(2))-x(7)*Ifc4-v4;
%% point 4
Eoc - x(1)*log(Ifc5/x(2))-x(3)*exp(x(4)*Ifc5)-x(5)- x(6)*log(Ifc5/x(2))-x(7)*Ifc5-v5;
%% point 5
Eoc - x(1)*log(Ifc6/x(2))-x(3)*exp(x(4)*Ifc6)-x(5)- x(6)*log(Ifc6/x(2))-x(7)*Ifc6-v6;
%% point 6
Eoc - x(1)*log(Ifc7/x(2))-x(3)*exp(x(4)*Ifc7)-x(5)- x(6)*log(Ifc7/x(2))-x(7)*Ifc7-v7;
%% point 7
Eoc - x(1)*log(Ifc8/x(2))-x(3)*exp(x(4)*Ifc8)-x(5)- x(6)*log(Ifc8/x(2))-x(7)*Ifc8-v8];
% x(1) A
% x(2) Io
% x(3) M
% x(4) N
% x(5) C
% x(6) D
% x(7) Rohm
x0 = [ 0.5 0.5 0.5 0.5 0.5 0.5 0.5];
options = optimoptions('fsolve','Display','iter','StepTolerance',1e-9);
options.MaxFunctionEvaluations = 16000000;
options.MaxIterations = 500000;
[x,fval,exitflag] = fsolve(E1,x0,options)
Norm of First-order Trust-region
Iteration Func-count f(x) step optimality radius
0 8 7536.71 7.41e+04 1
1 16 1031.27 1 1.03e+04 1
2 24 227.732 1 2.96e+03 1
3 32 71.3023 1 760 1
4 33 71.3023 2.5 760 2.5
5 41 21.3747 0.625 118 0.625
6 42 21.3747 1.5625 118 1.56
7 43 21.3747 0.390625 118 0.391
8 44 21.3747 0.0976563 118 0.0977
9 52 14.6733 0.0244141 122 0.0244
10 60 11.96 0.0610352 163 0.061
11 68 10.2985 0.152588 114 0.153
12 76 9.71052 0.152588 67.4 0.153
13 84 8.93493 0.38147 140 0.381
14 92 8.87528 0.953674 82.4 0.954
15 100 6.9487 0.953674 70 0.954
16 108 6.69045 2.38419 51.4 2.38
17 109 6.69045 5.96046 51.4 5.96
18 117 5.27646 1.49012 40.9 1.49
19 118 5.27646 3.72529 40.9 3.73
20 126 3.63694 0.931323 28 0.931
21 127 3.63694 2.32831 28 2.33
22 135 2.15387 0.582077 13.4 0.582
23 143 1.84128 1.45519 34.7 1.46
24 144 1.84128 1.45519 34.7 1.46
25 152 1.33448 0.363798 8.85 0.364
26 153 1.33448 0.909495 8.85 0.909
27 161 1.04473 0.227374 40 0.227
28 169 0.779429 0.227374 6.58 0.227
29 170 0.779429 0.568434 6.58 0.568
30 171 0.779429 0.142109 6.58 0.142
31 179 0.744596 0.0355271 68.1 0.0355
32 187 0.478181 0.0355271 6.32 0.0355
33 195 0.46088 0.0888178 9.22 0.0888
34 196 0.46088 0.222045 9.22 0.222
35 204 0.448007 0.0555112 7.54 0.0555
36 212 0.436195 0.0555112 6.63 0.0555
37 220 0.426734 0.138778 7.97 0.139
38 228 0.411175 0.138778 5.08 0.139
39 236 0.0659658 0.346945 19.1 0.347
40 244 0.0290188 0.867362 1.06 0.867
41 245 0.0290188 2.1684 1.06 2.17
42 246 0.0290188 0.542101 1.06 0.542
43 254 0.0283883 0.135525 1.1 0.136
44 255 0.0283883 0.338813 1.1 0.339
45 263 0.0277058 0.0847033 0.878 0.0847
46 271 0.0249458 0.211758 5.65 0.212
47 272 0.0249458 0.211758 5.65 0.212
48 280 0.0219848 0.0529396 0.757 0.0529
49 288 0.0218098 0.132349 1.18 0.132
50 296 0.0216618 0.132349 1.73 0.132
51 304 0.0216008 0.132349 2.38 0.132
52 312 0.021558 0.132349 2.28 0.132
53 320 0.0212921 0.132349 2.4 0.132
54 328 0.0212058 0.132349 2.91 0.132
55 336 0.0211371 0.132349 3.45 0.132
56 337 0.0211371 0.132349 3.45 0.132
57 345 0.0205764 0.0330872 0.625 0.0331
58 353 0.0201497 0.0827181 0.79 0.0827
59 354 0.0201497 0.206795 0.79 0.207
60 362 0.0201133 0.0516988 1.03 0.0517
61 370 0.0200177 7.23749e-05 0.533 0.0517
62 378 0.0199727 0.0516988 1.42 0.0517
63 386 0.0198181 0.0516988 0.579 0.0517
64 394 0.0195865 0.129247 2.14 0.129
65 395 0.0195865 0.323117 2.14 0.323
66 403 0.0194586 0.0807794 1.39 0.0808
67 411 0.019438 0.0807794 1.39 0.0808
68 419 0.0194004 0.0807794 1.26 0.0808
69 427 0.019352 0.0807794 1.11 0.0808
70 435 0.019286 0.0807794 1.05 0.0808
71 443 0.0192459 0.0807794 1.19 0.0808
72 451 0.0192173 0.0807794 1.4 0.0808
73 459 0.0191947 0.0807794 1.61 0.0808
74 467 0.0191761 0.0807794 1.82 0.0808
75 475 0.0191607 0.0807794 2.05 0.0808
76 483 0.019155 0.0807794 2.02 0.0808
77 491 0.0191264 0.0807794 2.05 0.0808
78 499 0.0191207 0.0807794 2.02 0.0808
79 507 0.0190922 0.0807794 2.05 0.0808
80 515 0.0190867 0.0807794 2.02 0.0808
81 523 0.0190673 0.0807794 1.84 0.0808
82 531 0.0190423 0.0807794 1.66 0.0808
83 539 0.0190036 0.0807794 1.64 0.0808
84 547 0.0189913 0.0807794 1.62 0.0808
85 555 0.0189639 0.0807794 1.47 0.0808
86 563 0.0189286 0.0807794 1.31 0.0808
87 571 0.0188787 0.0807794 1.29 0.0808
88 579 0.0188568 0.0807794 1.28 0.0808
89 587 0.0188182 0.0807794 1.15 0.0808
90 595 0.0187622 0.0807794 1.13 0.0808
91 603 0.0187341 0.0807794 1.12 0.0808
92 611 0.0186827 0.0807794 1.13 0.0808
93 619 0.0186564 0.0807794 1.13 0.0808
94 627 0.018606 0.0807794 1.14 0.0808
95 635 0.0185754 0.0807794 1.3 0.0808
96 643 0.0185526 0.0807794 1.48 0.0808
97 651 0.0185403 0.0807794 1.48 0.0808
98 659 0.0185039 0.0807794 1.5 0.0808
99 667 0.0184848 0.0807794 1.69 0.0808
100 675 0.0184694 0.0807794 1.89 0.0808
101 683 0.0184572 0.0807794 2.11 0.0808
102 684 0.0184572 0.0807794 2.11 0.0808
103 692 0.0183764 0.0201948 0.47 0.0202
104 700 0.0179044 0.0504871 3.27 0.0505
105 701 0.0179044 0.126218 3.27 0.126
106 709 0.0177134 0.0315544 0.523 0.0316
107 710 0.0177134 0.0788861 0.523 0.0789
108 718 0.0176956 0.0197215 0.397 0.0197
109 719 0.0176956 0.0493038 0.397 0.0493
110 727 0.0176743 0.012326 0.96 0.0123
111 735 0.0176478 0.0308149 0.413 0.0308
112 743 0.0173592 0.0770372 0.97 0.077
113 744 0.0173592 0.192593 0.97 0.193
114 752 0.0173545 0.0481482 0.955 0.0481
115 760 0.0173381 0.0481482 0.626 0.0481
116 768 0.017329 0.0481482 0.563 0.0481
117 776 0.0173179 0.0481482 0.511 0.0481
118 784 0.0173084 0.0481482 0.532 0.0481
119 792 0.0173006 0.0481482 0.601 0.0481
120 800 0.0172946 0.0481482 0.696 0.0481
121 808 0.0172901 0.0481482 0.741 0.0481
122 816 0.0172835 0.0481482 0.753 0.0481
123 824 0.0172787 0.0481482 0.76 0.0481
124 832 0.017272 0.0481482 0.76 0.0481
125 840 0.0172668 0.0481482 0.821 0.0481
126 848 0.017263 0.0481482 0.84 0.0481
127 856 0.0172577 0.0481482 0.793 0.0481
128 864 0.0172508 0.0481482 0.773 0.0481
129 872 0.0172461 0.0481482 0.774 0.0481
130 880 0.01724 0.0481482 0.725 0.0481
131 888 0.0172323 0.0481482 0.699 0.0481
132 896 0.0172268 0.0481482 0.701 0.0481
133 904 0.0172198 0.0481482 0.654 0.0481
134 912 0.0172111 0.0481482 0.624 0.0481
135 920 0.0172042 0.0481482 0.667 0.0481
136 928 0.017199 0.0481482 0.692 0.0481
137 936 0.0171923 0.0481482 0.655 0.0481
138 944 0.0171843 0.0481482 0.596 0.0481
139 952 0.0171744 0.0481482 0.555 0.0481
140 960 0.0171663 0.0481482 0.585 0.0481
141 968 0.0171597 0.0481482 0.657 0.0481
142 976 0.0171545 0.0481482 0.746 0.0481
143 984 0.0171505 0.0481482 0.777 0.0481
144 992 0.0171449 0.0481482 0.737 0.0481
145 1000 0.0171377 0.0481482 0.717 0.0481
146 1008 0.0171324 0.0481482 0.707 0.0481
147 1016 0.0171255 0.0481482 0.711 0.0481
148 1024 0.0171202 0.0481482 0.77 0.0481
149 1032 0.0171158 0.0481482 0.847 0.0481
150 1040 0.017112 0.0481482 0.929 0.0481
151 1048 0.0171092 0.0481482 0.941 0.0481
152 1056 0.017105 0.0481482 0.889 0.0481
153 1064 0.0170993 0.0481482 0.873 0.0481
154 1072 0.0170958 0.0481482 0.874 0.0481
155 1080 0.0170904 0.0481482 0.874 0.0481
156 1088 0.017087 0.0481482 0.875 0.0481
157 1096 0.0170822 0.0481482 0.823 0.0481
158 1104 0.0170759 0.0481482 0.798 0.0481
159 1112 0.0170719 0.0481482 0.803 0.0481
160 1120 0.0170665 0.0481482 0.754 0.0481
161 1128 0.0170602 0.0481482 0.693 0.0481
162 1136 0.0170528 0.0481482 0.626 0.0481
163 1144 0.0170444 0.0481482 0.562 0.0481
164 1152 0.0170346 0.0481482 0.493 0.0481
165 1160 0.0170229 0.0481482 0.419 0.0481
166 1161 0.0170229 0.120371 0.419 0.12
167 1169 0.0170063 0.0300927 0.346 0.0301
168 1170 0.0170063 0.0752316 0.346 0.0752
169 1178 0.0168328 0.0188079 2.66 0.0188
170 1186 0.0166736 0.0470198 0.506 0.047
171 1187 0.0166736 0.117549 0.506 0.118
172 1195 0.0166597 0.0293874 0.314 0.0294
173 1203 0.0152434 0.0734684 1.55 0.0735
174 1204 0.0152434 0.183671 1.55 0.184
175 1212 0.0152104 0.0459177 0.714 0.0459
176 1213 0.0152104 0.0459177 0.714 0.0459
177 1221 0.0152026 0.0114794 0.0386 0.0115
178 1222 0.0152026 0.0286986 0.0386 0.0287
179 1230 0.0152022 0.00717465 0.0848 0.00717
180 1231 0.0152022 0.0179366 0.0848 0.0179
181 1239 0.015202 0.00448416 0.0534 0.00448
182 1247 0.0152017 0.0112104 0.0413 0.0112
183 1248 0.0152017 0.028026 0.0413 0.028
184 1256 0.0152014 0.00700649 0.138 0.00701
185 1264 0.015201 0.00700649 0.0399 0.00701
186 1272 0.0152006 0.0175162 0.455 0.0175
187 1280 0.0151977 0.0175162 0.104 0.0175
188 1281 0.0151977 0.0437906 0.104 0.0438
189 1289 0.0151974 0.0109476 0.0386 0.0109
190 1297 0.0151921 0.0273691 0.134 0.0274
191 1298 0.0151921 0.0684228 0.134 0.0684
192 1306 0.015192 0.0171057 0.144 0.0171
193 1314 0.0151917 0.0171057 0.0853 0.0171
194 1322 0.0151915 0.0171057 0.0638 0.0171
195 1330 0.0151912 0.0171057 0.0488 0.0171
196 1331 0.0151912 0.0427642 0.0488 0.0428
197 1339 0.0151909 0.0106911 0.0419 0.0107
198 1340 0.0151909 0.0267276 0.0419 0.0267
199 1348 0.0151907 0.00668191 0.112 0.00668
200 1356 0.0151904 0.00668191 0.0404 0.00668
201 1357 0.0151904 0.0167048 0.0404 0.0167
202 1365 0.0151898 0.00417619 0.212 0.00418
203 1373 0.0151891 0.0104405 0.038 0.0104
204 1381 0.0151884 0.0261012 0.0996 0.0261
205 1382 0.0151884 0.065253 0.0996 0.0653
206 1390 0.0151882 0.0163133 0.0656 0.0163
207 1398 0.015188 0.0163133 0.0461 0.0163
208 1399 0.015188 0.0407832 0.0461 0.0408
209 1407 0.0151876 0.0101958 0.0445 0.0102
210 1408 0.0151876 0.0254895 0.0445 0.0255
211 1416 0.0151874 0.00637237 0.0999 0.00637
212 1424 0.0151872 0.00637237 0.0407 0.00637
213 1425 0.0151872 0.0159309 0.0407 0.0159
214 1433 0.0151867 0.00398273 0.177 0.00398
215 1441 0.0151862 0.00995682 0.0385 0.00996
216 1449 0.0151841 0.0248921 0.0409 0.0249
217 1450 0.0151841 0.0622302 0.0409 0.0622
218 1451 0.0151841 0.0155575 0.0409 0.0156
219 1459 0.0151837 0.00388938 0.158 0.00389
220 1467 0.0151832 0.00972346 0.0388 0.00972
221 1475 0.0151788 0.0243087 0.202 0.0243
222 1476 0.0151788 0.0607716 0.202 0.0608
223 1484 0.0151783 0.0151929 0.118 0.0152
224 1492 0.015178 0.0151929 0.0607 0.0152
225 1500 0.0151778 0.0151929 0.0379 0.0152
226 1501 0.0151778 0.0379823 0.0379 0.038
227 1509 0.0151773 0.00949557 0.107 0.0095
228 1510 0.0151773 0.0237389 0.107 0.0237
229 1518 0.015177 0.00593473 0.0509 0.00593
230 1526 0.0151767 0.0148368 0.039 0.0148
231 1534 0.0151693 0.0370921 0.0378 0.0371
232 1535 0.0151693 0.0927302 0.0378 0.0927
233 1543 0.0151688 0.0231825 0.0757 0.0232
234 1544 0.0151688 0.0579563 0.0757 0.058
235 1552 0.0151686 0.0144891 0.0376 0.0145
236 1553 0.0151686 0.0362227 0.0376 0.0362
237 1561 0.0151682 0.00905568 0.0859 0.00906
238 1562 0.0151682 0.0226392 0.0859 0.0226
239 1570 0.015168 0.0056598 0.0575 0.00566
240 1578 0.0151677 0.0141495 0.0389 0.0141
241 1586 0.0151638 0.0353737 0.107 0.0354
242 1587 0.0151638 0.0884344 0.107 0.0884
243 1588 0.0151638 0.0221086 0.107 0.0221
244 1596 0.0151635 0.00552715 0.041 0.00553
245 1604 0.0151634 0.0138179 0.237 0.0138
246 1612 0.0151626 0.0138179 0.0576 0.0138
247 1613 0.0151626 0.0345447 0.0576 0.0345
248 1621 0.0151623 0.00863617 0.0421 0.00864
249 1622 0.0151623 0.0215904 0.0421 0.0216
250 1630 0.0151621 0.00539761 0.105 0.0054
251 1638 0.0151619 0.00539761 0.041 0.0054
252 1646 0.0151615 6.26998e-06 0.154 0.0135
253 1654 0.015161 0.013494 0.0387 0.0135
254 1662 0.0151595 0.033735 0.171 0.0337
255 1663 0.0151595 0.0843376 0.171 0.0843
256 1671 0.0151593 0.0210844 0.147 0.0211
257 1679 0.0151591 0.0210844 0.143 0.0211
258 1687 0.015159 0.0210844 0.143 0.0211
259 1695 0.0151589 0.0210844 0.138 0.0211
260 1703 0.0151588 0.0210844 0.134 0.0211
261 1711 0.0151586 0.0210844 0.134 0.0211
262 1719 0.0151585 0.0210844 0.133 0.0211
263 1727 0.0151584 0.0210844 0.133 0.0211
264 1735 0.0151583 0.0210844 0.133 0.0211
265 1743 0.0151581 0.0210844 0.133 0.0211
266 1751 0.015158 0.0210844 0.137 0.0211
267 1759 0.0151579 0.0210844 0.138 0.0211
268 1767 0.0151578 0.0210844 0.138 0.0211
269 1775 0.0151576 0.0210844 0.138 0.0211
270 1783 0.0151575 0.0210844 0.138 0.0211
271 1791 0.0151574 0.0210844 0.138 0.0211
272 1799 0.0151573 0.0210844 0.138 0.0211
273 1807 0.0151572 0.0210844 0.138 0.0211
274 1815 0.015157 0.0210844 0.138 0.0211
275 1823 0.0151569 0.0210844 0.142 0.0211
276 1831 0.0151568 0.0210844 0.146 0.0211
277 1839 0.0151567 0.0210844 0.147 0.0211
278 1847 0.0151566 0.0210844 0.147 0.0211
279 1855 0.0151565 0.0210844 0.147 0.0211
280 1863 0.0151564 0.0210844 0.142 0.0211
281 1871 0.0151563 0.0210844 0.139 0.0211
282 1879 0.0151561 0.0210844 0.138 0.0211
283 1887 0.015156 0.0210844 0.142 0.0211
284 1895 0.0151559 0.0210844 0.142 0.0211
285 1903 0.0151558 0.0210844 0.142 0.0211
286 1911 0.0151557 0.0210844 0.146 0.0211
287 1919 0.0151556 0.0210844 0.147 0.0211
288 1927 0.0151555 0.0210844 0.143 0.0211
289 1935 0.0151554 0.0210844 0.139 0.0211
290 1943 0.0151552 0.0210844 0.135 0.0211
291 1951 0.0151551 0.0210844 0.13 0.0211
292 1959 0.0151549 0.0210844 0.129 0.0211
293 1967 0.0151548 0.0210844 0.129 0.0211
294 1975 0.0151547 0.0210844 0.126 0.0211
295 1983 0.0151545 0.0210844 0.125 0.0211
296 1991 0.0151544 0.0210844 0.128 0.0211
297 1999 0.0151543 0.0210844 0.129 0.0211
298 2007 0.0151541 0.0210844 0.129 0.0211
299 2015 0.015154 0.0210844 0.129 0.0211
300 2023 0.0151538 0.0210844 0.126 0.0211
301 2031 0.0151537 0.0210844 0.125 0.0211
302 2039 0.0151536 0.0210844 0.124 0.0211
303 2047 0.0151534 0.0210844 0.121 0.0211
304 2055 0.0151532 0.0210844 0.12 0.0211
305 2063 0.0151531 0.0210844 0.123 0.0211
306 2071 0.015153 0.0210844 0.124 0.0211
307 2079 0.0151528 0.0210844 0.121 0.0211
308 2087 0.0151526 0.0210844 0.117 0.0211
309 2095 0.0151524 0.0210844 0.106 0.0211
310 2103 0.0151523 0.0210844 0.106 0.0211
311 2111 0.0151521 0.0210844 0.106 0.0211
312 2119 0.0151519 0.0210844 0.106 0.0211
313 2127 0.0151517 0.0210844 0.103 0.0211
314 2135 0.0151515 0.0210844 0.102 0.0211
315 2143 0.0151513 0.0210844 0.104 0.0211
316 2151 0.0151511 0.0210844 0.108 0.0211
317 2159 0.0151509 0.0210844 0.109 0.0211
318 2167 0.0151508 0.0210844 0.107 0.0211
319 2175 0.0151506 0.0210844 0.103 0.0211
320 2183 0.0151503 0.0210844 0.0992 0.0211
321 2191 0.0151501 0.0210844 0.0948 0.0211
322 2199 0.0151499 0.0210844 0.0894 0.0211
323 2207 0.0151496 0.0210844 0.0866 0.0211
324 2215 0.0151493 0.0210844 0.0833 0.0211
325 2223 0.015149 0.0210844 0.0826 0.0211
326 2231 0.0151488 0.0210844 0.0838 0.0211
327 2239 0.0151485 0.0210844 0.0809 0.0211
328 2247 0.0151482 0.0210844 0.0784 0.0211
329 2255 0.0151479 0.0210844 0.0785 0.0211
330 2263 0.0151476 0.0210844 0.0759 0.0211
331 2271 0.0151472 0.0210844 0.0715 0.0211
332 2279 0.0151468 0.0210844 0.0654 0.0211
333 2287 0.0151464 0.0210844 0.0564 0.0211
334 2288 0.0151464 0.052711 0.0564 0.0527
335 2296 0.0151458 0.0131777 0.0421 0.0132
336 2297 0.0151458 0.0329444 0.0421 0.0329
337 2305 0.015145 0.00823609 0.162 0.00824
338 2313 0.015144 0.00823609 0.0405 0.00824
339 2321 0.0151409 0.0205902 0.517 0.0206
340 2329 0.0151318 0.0205902 0.0931 0.0206
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700 4460 0.0102839 0.00915342 0.128 0.00915
701 4468 0.010283 0.00915342 0.0134 0.00915
702 4469 0.010283 0.0228836 0.0134 0.0229
703 4477 0.010283 0.00572089 0.00643 0.00572
704 4485 0.0102792 0.0143022 0.197 0.0143
705 4486 0.0102792 0.0357556 0.197 0.0358
706 4494 0.0102772 0.00893889 0.0159 0.00894
707 4495 0.0102772 0.0223472 0.0159 0.0223
708 4503 0.0102772 0.00558681 0.00642 0.00559
709 4511 0.0102771 0.013967 0.135 0.014
710 4519 0.0102762 0.013967 0.0355 0.014
711 4520 0.0102762 0.0349175 0.0355 0.0349
712 4528 0.0102762 0.00872938 0.0119 0.00873
713 4536 0.0102761 0.00872938 0.0075 0.00873
714 4537 0.0102761 0.0218235 0.0075 0.0218
715 4545 0.0102761 0.00545587 0.00711 0.00546
716 4546 0.0102761 0.0136397 0.00711 0.0136
717 4554 0.0102761 0.00340992 0.0133 0.00341
718 4562 0.0102761 0.00852479 0.00722 0.00852
719 4563 0.0102761 0.021312 0.00722 0.0213
720 4571 0.0102761 0.00532799 0.00784 0.00533
721 4572 0.0102761 0.01332 0.00784 0.0133
722 4580 0.010276 0.00333 0.0129 0.00333
723 4588 0.010276 0.00333 0.00688 0.00333
724 4589 0.010276 0.00832499 0.00688 0.00832
725 4597 0.010276 0.00208125 0.0172 0.00208
726 4605 0.010276 0.00520312 0.00626 0.0052
727 4613 0.0102748 0.0130078 0.108 0.013
728 4614 0.0102748 0.0325195 0.108 0.0325
729 4622 0.0102742 0.00812987 0.0187 0.00813
730 4630 0.0102742 0.0203247 0.0152 0.0203
731 4631 0.0102742 0.0203247 0.0152 0.0203
732 4639 0.0102742 0.00508117 0.00642 0.00508
733 4640 0.0102742 0.0127029 0.00642 0.0127
734 4648 0.010274 0.00317573 0.0627 0.00318
735 4656 0.0102738 0.00793933 0.0115 0.00794
736 4657 0.0102738 0.0198483 0.0115 0.0198
737 4665 0.0102738 0.00496208 0.00662 0.00496
738 4666 0.0102738 0.0124052 0.00662 0.0124
739 4674 0.0102738 0.0031013 0.0266 0.0031
740 4682 0.0102737 0.00775325 0.00912 0.00775
741 4683 0.0102737 0.0193831 0.00912 0.0194
742 4691 0.0102737 0.00484578 0.00687 0.00485
743 4692 0.0102737 0.0121145 0.00687 0.0121
744 4700 0.0102737 0.00302861 0.0165 0.00303
745 4708 0.0102737 0.00302861 0.00678 0.00303
746 4709 0.0102737 0.00757153 0.00678 0.00757
747 4717 0.0102737 0.00189288 0.018 0.00189
...
x = 1×7
-0.2307 0.0163 0.3180 -0.0003 -0.5394 1.2682 0.3232
fval = 7×1
0.0278
-0.0545
0.0001
0.0231
0.0500
-0.0570
0.0105
exitflag = -2
I work with 500000 iterations but the f(x) converge to 0 too slow, I try to change xO values but the improvements are negiglible.
I am grateful for any help solving the issue.
Thanks!
1 个评论
Walter Roberson
2022-6-18
If you have the Symbolic Toolbox, you can solve the equations 1, 2, 3, 4, 6,for x(1), x(2), x(3), x(7), x(5) as closed form, leaving two equations in x(4), x(6)
However going further for symbolic solutions is difficult. You could try more, or you could switch to numeric at that point, using matlabFunction to generate a function handle (hint: use the 'vars' option) that you could fsolve. The equations are notably messier than what you started with but there would be only two variables.
采纳的回答
Walter Roberson
2022-6-19
% voltage value
Eoc=18.09;
v2=13.69;
v3=12.73;
v4= 11.31;
v5=10.22;
v6=9.71;
v7=8.91;
v8=8.41;
% current value
Ifc2=1;
Ifc3=2;
Ifc4=4;
Ifc5=6;
Ifc6=7;
Ifc7=9;
Ifc8=10;
% point 1
E1 = @(x)[Eoc - x(1)*log(Ifc2/x(2))-x(3)*exp(x(4)*Ifc2)-x(5)- x(6)*log(Ifc2/x(2))-x(7)*Ifc2-v2;
%% point 2
Eoc - x(1)*log(Ifc3/x(2))-x(3)*exp(x(4)*Ifc3)-x(5)- x(6)*log(Ifc3/x(2))-x(7)*Ifc3-v3;
%% point 3
Eoc - x(1)*log(Ifc4/x(2))-x(3)*exp(x(4)*Ifc4)-x(5)- x(6)*log(Ifc4/x(2))-x(7)*Ifc4-v4;
%% point 4
Eoc - x(1)*log(Ifc5/x(2))-x(3)*exp(x(4)*Ifc5)-x(5)- x(6)*log(Ifc5/x(2))-x(7)*Ifc5-v5;
%% point 5
Eoc - x(1)*log(Ifc6/x(2))-x(3)*exp(x(4)*Ifc6)-x(5)- x(6)*log(Ifc6/x(2))-x(7)*Ifc6-v6;
%% point 6
Eoc - x(1)*log(Ifc7/x(2))-x(3)*exp(x(4)*Ifc7)-x(5)- x(6)*log(Ifc7/x(2))-x(7)*Ifc7-v7;
%% point 7
Eoc - x(1)*log(Ifc8/x(2))-x(3)*exp(x(4)*Ifc8)-x(5)- x(6)*log(Ifc8/x(2))-x(7)*Ifc8-v8];
syms X [1 7]
E = E1(X);
sol1 = solve(E(1:4), X([1 2 3 7]))
Warning: Solutions are only valid under certain conditions. To include parameters and conditions in the solution, specify the 'ReturnConditions' value as 'true'.
sol1 = struct with fields:
X1: -(3*X5 + 4*X6*log(exp((1576*log(2) - 788*log(3) - 400*X5*log(2) + 200*X5*log(3) - 2624*exp(X4)*log(2) + 1082*exp(X4)*log(3) + 1509*exp(3*X4)*log(2) - 344*exp(3*X4)*log(3) - 394*exp(5*X4)*log(2) - 400*X5*exp(3*X4)*log(2) + 100*X5*exp(3*X4)*log(…
X2: exp(-(1576*log(2) - 788*log(3) - 400*X5*log(2) + 200*X5*log(3) - 2624*exp(X4)*log(2) + 1082*exp(X4)*log(3) + 1509*exp(3*X4)*log(2) - 344*exp(3*X4)*log(3) - 394*exp(5*X4)*log(2) - 400*X5*exp(3*X4)*log(2) + 100*X5*exp(3*X4)*log(3) + 100*X5*exp(5…
X3: (X5 + 2*X6*log(exp((1576*log(2) - 788*log(3) - 400*X5*log(2) + 200*X5*log(3) - 2624*exp(X4)*log(2) + 1082*exp(X4)*log(3) + 1509*exp(3*X4)*log(2) - 344*exp(3*X4)*log(3) - 394*exp(5*X4)*log(2) - 400*X5*exp(3*X4)*log(2) + 100*X5*exp(3*X4)*log(3) …
X7: (log(exp((1576*log(2) - 788*log(3) - 400*X5*log(2) + 200*X5*log(3) - 2624*exp(X4)*log(2) + 1082*exp(X4)*log(3) + 1509*exp(3*X4)*log(2) - 344*exp(3*X4)*log(3) - 394*exp(5*X4)*log(2) - 400*X5*exp(3*X4)*log(2) + 100*X5*exp(3*X4)*log(3) + 100*X5*e…
E2 = subs(E(5:end), sol1)
E2 =
sol5 = solve(E2(2), X(5))
E5 = subs(E2([1 3:end]), X(5), sol5)
%at this point E5 should be a system of two equations in X(4) and X(6), and
%you should be able to solve from there
%I do not show it because this demonstration system times out trying to
%compute sol5
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