Research Article
Contingency-Constrained Optimal Power Flow Using Simplex-Based Chaotic-PSO Algorithm
(a) Optimal settings of control variables in 26-bus system |
| Control variable | SCPSO | CPSO | MPSO | IPSO | HGA | DE |
| PG1 | 446.1746 | 448.1017 | 445.7566 | 453.3504 | 451.8483 | 452.6614 | PG2 | 164.7378 | 166.1304 | 200.0000 | 165.0258 | 166.6793 | 165.7782 | PG3 | 258.4341 | 258.1863 | 262.1278 | 259.9621 | 257.4760 | 256.2267 | PG4 | 149.5769 | 149.9920 | 118.0309 | 136.5176 | 144.1294 | 142.0623 | PG5 | 164.5429 | 164.4053 | 200.0000 | 164.5045 | 166.6446 | 163.0210 | PG26 | 91.1452 | 87.9374 | 50.0000 | 103.2680 | 94.6340 | 102.8937 | V1 | 1.0327 | 1.0279 | 1.0411 | 1.0404 | 1.0403 | 1.0286 | V2 | 0.9920 | 1.0500 | 1.0088 | 1.0174 | 1.0186 | 1.0190 | V3 | 1.0345 | 1.0201 | 1.0211 | 0.9943 | 0.9959 | 0.9907 | V4 | 1.0346 | 0.9823 | 1.0004 | 0.9754 | 1.0308 | 1.0320 | V5 | 1.0233 | 1.0101 | 0.9751 | 1.0090 | 1.0055 | 1.0053 | V26 | 1.0208 | 1.0291 | 1.0248 | 1.0048 | 1.0055 | 1.0082 | | 1.0200 | 1.0200 | 1.1000 | 1.0100 | 1.0600 | 1.0600 | TP2-13 | 1.0200 | 1.0000 | 0.9700 | 1.0000 | 0.9300 | 0.9200 | TP3-13 | 0.9700 | 0.9700 | 0.9500 | 0.9900 | 0.9900 | 0.9700 | TP4-8 | 0.9800 | 0.9800 | 1.0200 | 1.0200 | 1.0200 | 1.0300 | TP4-12 | 0.9800 | 0.9900 | 1.0400 | 1.0300 | 1.0000 | 1.0100 | TP6-19 | 0.9600 | 0.9500 | 1.0100 | 0.9800 | 0.9700 | 0.9300 | TP7-9 | 0.9800 | 0.9800 | 0.9500 | 0.9600 | 0.9600 | 0.9600 | YH1 | 0.0500 | 0.0000 | 0.0050 | 0.0500 | 0.0400 | 0.0500 | YH4 | 0.0300 | 0.0350 | 0.0400 | 0.0300 | 0.0300 | 0.0150 | YH5 | 0.0500 | 0.0500 | 0.0500 | 0.0400 | 0.0500 | 0.0150 | YH6 | 0.0500 | 0.0500 | 0.0150 | 0.0200 | 0.0450 | 0.0500 | YH9 | 0.0150 | 0.0400 | 0.0150 | 0.0400 | 0.0300 | 0.0250 | YH11 | 0.0250 | 0.0450 | 0.0350 | 0.0250 | 0.0350 | 0.0300 | YH12 | 0.0500 | 0.0350 | 0.0250 | 0.0500 | 0.0300 | 0.0200 | YH15 | 0.0500 | 0.0350 | 0.0100 | 0.0500 | 0.0200 | 0.0450 | YH19 | 0.0450 | 0.0500 | 0.0150 | 0.0250 | 0.0200 | 0.0500 |
| Fitness | 15499 | 15503 | 15545 | 15552 | 15568 | 15575 | CI($) | 15487 | 15491 | 15532 | 15539 | 15558 | 15562 | (MW) | 11.6166 | 11.7561 | 12.9153 | 12.5594 | 12.8161 | 12.6880 | | 0.3432 | 0.3411 | 0.5225 | 0.4599 | 0.4402 | 0.3485 |
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(b) Optimal settings of control variables in IEEE 57-bus system |
| Control variable | SCPSO | CPSO | MPSO | IPSO | HGA | DE |
| PG1(W) | 330.6258 | 331.4865 | 331.3076 | 331.8135 | 330.6408 | 331.6042 | PG2(W) | 50.0000 | 56.1645 | 83.7176 | 84.4205 | 83.7784 | 83.9324 | PG3(W) | 117.5876 | 117.7136 | 117.6009 | 117.8681 | 92.7311 | 117.6796 | PG6(W) | 84.8626 | 85.8677 | 84.8836 | 87.4047 | 85.0812 | 60.2967 | PG8(W) | 300.0000 | 256.9933 | 256.9824 | 257.0185 | 257.0101 | 256.9304 | PG9(W) | 84.8851 | 119.8924 | 95.4473 | 91.9031 | 120.0000 | 120.0000 | PG12(W) | 300.0000 | 299.9529 | 300.0000 | 300.0000 | 300.0000 | 300.0000 | VG1 | 1.0500 | 1.0500 | 1.0500 | 1.0500 | 1.0500 | 1.0500 | VG2 | 1.0480 | 1.0495 | 1.0500 | 1.0497 | 1.0497 | 1.0500 | VG3 | 1.0500 | 1.0500 | 1.0500 | 1.0498 | 1.0079 | 1.0478 | VG6 | 1.0496 | 1.0462 | 1.0500 | 1.0500 | 1.0500 | 1.0500 | VG8 | 1.0500 | 1.0498 | 1.0500 | 1.0500 | 1.0500 | 1.0456 | VG9 | 1.0341 | 1.0446 | 1.0438 | 1.0433 | 1.0500 | 1.0500 | VG12 | 1.0252 | 1.0500 | 1.0500 | 1.0500 | 1.0500 | 1.0498 | TP4-18 | 0.9700 | 0.9600 | 0.9600 | 0.9400 | 1.0100 | 0.9600 | TP7-29 | 0.9700 | 1.0300 | 1.0000 | 1.0500 | 0.9400 | 0.9400 | TP9-55 | 0.9700 | 1.0300 | 0.9900 | 1.0500 | 0.9400 | 0.9400 | TP10-51 | 0.9400 | 0.9400 | 0.9400 | 0.9600 | 0.9500 | 1.0100 | TP11-41 | 0.9900 | 1.0300 | 0.9700 | 0.9300 | 0.9600 | 1.1000 | TP11-43 | 0.9300 | 0.9200 | 0.9300 | 1.1000 | 0.9400 | 0.9200 | TP13-49 | 0.9000 | 0.9000 | 0.9000 | 0.9200 | 0.9000 | 1.0100 | TP14-46 | 0.9200 | 0.9200 | 0.9200 | 0.9400 | 0.9300 | 0.9800 | TP15-45 | 0.9300 | 0.9400 | 0.9400 | 0.9400 | 0.9300 | 0.9600 | TP20-21 | 1.0200 | 1.0400 | 1.0100 | 1.0000 | 1.1000 | 0.9400 | TP24-25 | 1.0300 | 0.9500 | 1.0000 | 0.9200 | 0.9600 | 0.9300 | TP24-26 | 1.0400 | 1.0900 | 1.0800 | 1.1000 | 1.0000 | 0.9500 | TP32-34 | 0.9800 | 0.9600 | 0.9500 | 0.9400 | 0.9600 | 0.9000 | TP40-56 | 1.0300 | 1.0100 | 1.0400 | 1.0800 | 1.0300 | 0.9600 | TP39-57 | 0.9900 | 1.0400 | 0.9800 | 1.0400 | 1.0200 | 0.9400 | YH18 | 0.0900 | 0.0500 | 0.0250 | 0.0300 | 0.1000 | 0.0700 | YH25 | 0.1000 | 0.0800 | 0.1000 | 0.0600 | 0.1000 | 0.0650 | YH53 | 0.0800 | 0.1000 | 0.1000 | 0.1000 | 0.0700 | 0.0650 |
| Fitness | 15426 | 15435 | 15436 | 15443 | 15453 | 15470 | CI($) | 15407 | 15415 | 15414 | 15420 | 15429 | 15448 | (MW) | 17.1611 | 17.2709 | 19.1394 | 19.6284 | 18.4116 | 19.6433 | | 2.3280 | 2.6581 | 2.7262 | 2.6219 | 2.8305 | 2.1472 |
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