A Novel Chaotic Rao-2 Algorithm for Optimal Power Flow Solution
Table 1
Simulation results for the OPF problem obtained from 100 runs for cases 1–5 using the basic Rao-2 and the chaotic Rao-2 algorithms.
Item
Case 1
Case 2
Case 3
Case 4
Case 5
Chaotic Rao-2
Rao-2
Chaotic Rao-2
Rao-2
Chaotic Rao-2
Rao-2
Chaotic Rao-2
Rao-2
Chaotic Rao-2
Rao-2
PG1
177.2183
177.4346
51.5141
51.5233
154.51970
154.37656
104.98274
152.22191
174.49319
178.17728
PG2
48.6385
48.6718
79.999915
80
34.48030
34.68267
48.362810
47.016624
50.085504
49.353585
PG5
21.3935
21.3565
50
49.9986
37.18594
37.16101
50
44.686164
21.022823
21.973359
PG8
21.1472
21.1029
35
34.9873
17.20649
17.28475
35
14.966606
23.319172
21.265377
PG11
12.0366
11.8875
30
29.9999
12.50472
12.49063
30
20.629623
12.271069
10.511163
PG13
12
12
39.994089
40
35.37582
35.26638
19.985984
12
12
12.154924
VG1
1.08586
1.08508
1.06314
1.06257
1.05306
1.05408
1.0225480
1.0165329
1.0425862
1.0380986
VG2
1.06629
1.06594
1.05921
1.05843
1.03867
1.03806
1.0222457
1.0001684
1.0270611
1.0264095
VG5
1.03561
1.0341
1.03942
1.03895
0.99537
0.99604
1.0203167
1.0150936
1.0122406
1.0089113
VG8
1.03935
1.03946
1.04541
1.04488
1.04983
1.05037
1.0118955
1.0089052
1.0076122
1.0057324
VG11
1.09954
1.09748
1.09656
1.0804
1.09968
1.1
0.9933268
1.0815666
1.0397596
1.0744932
VG13
1.04332
1.04541
1.0596
1.06405
1.09954
1.09835
0.9930445
1.0222389
0.9925991
0.9871240
QC10
4.2960820
4.9432025
1.2868321
5
4.96315
5
5
4.5427378
4.8269723
5
QC12
5
4.7369443
0
0
5
5
4.2499666
2.7013885
0
5
QC15
4.3710110
3.6235585
4.3124851
4.93205
4.83057
4.92148
4.4146528
0
4.5883998
5
QC17
4.9946649
4.9686419
5
4.93684
4.93516
4.59684
0
0
0.2796082
0.0260847
QC20
3.5295760
3.6718862
4.4744868
3.81783
4.82535
5
5
4.9694913
5
5
QC21
4.9986735
4.9261690
4.9818134
4.81356
4.85305
4.98047
4.5797353
3.4776893
4.9994249
5
QC23
3.3223836
4.7167140
3.2245977
2.76663
5
4.97265
5
4.9968795
5
5
QC24
4.9656267
4.9611172
5
5
4.96036
5
4.7766748
5
5
4.9822562
QC29
3.0540261
2.4135304
2.5811247
2.69791
5
4.61073
4.5274734
3.0619722
2.6914685
2.1781773
T6,9
1.1
1.0997052
1.1
1.07374
1.08384
1.08306
0.9997491
1.1
1.0577316
1.0999003
T6,10
0.9
0.9
0.9
0.91126
0.90036
0.90047
0.9080701
0.9
0.9020170
0.9000287
T4, 12
0.9720476
0.9753570
0.9964757
1.00559
1.09983
1.09973
0.9567969
0.9800881
0.9449670
0.9508356
T28, 27
0.9756057
0.9733755
0.9753372
0.97506
0.98264
0.98285
0.9744802
0.9673128
0.9680990
0.9655151
Cost ($/h)
800.1537
800.3865
967.66625
967.65998
840.55967
840.27007
889.52282
844.42847
803.7384
803.81043
VD
0.8981
0.9056
0.8938
0.9033
0.9576
0.9509
0.0940385
0.103614
0.09435
0.0970462
Loss (MW)
9.034455
9.0535853
3.0614
3.0975
7.87297
7.862
4.9402625
8.1209366
9.7917672
10.035699
Lmax
0.1263367
0.1264155
0.1275447
0.12694
0.12394
0.1243
0.135523
0.1367273
0.1367101
0.1362592
CT (s)
13.503
16.875
14.807
17.364
14.785
16.803
14.307
15.784
14.914
15.863
No. of iterations
32
43
34
47
38
52
35
48
42
53
The outcomes in intelligible form state optimum solutions obtained from 100 runs using the chaotic Rao-2 algorithm and the basic Rao-2 algorithm; PG (MW); VG (p.u.); QC (Mvar).
