Table 14 The obtained results of the proposed LSDO as well as the original SDO techniques for IEEE 118-bus.

P\({}_{g1}\)

40.1063

64.4748

V\({}_{g31}\)

1.0368

1.0116

P\({}_{g4}\)

43.8024

34.3105

V\({}_{g32}\)

1.0306

1.0359

P\({}_{g6}\)

55.3404

30.5358

V\({}_{g34}\)

1.0329

1.0020

P\({}_{g8}\)

55.5974

30.1350

V\({}_{g36}\)

1.0317

0.9965

P\({}_{g10}\)

192.3171

307.7051

V\({}_{g40}\)

0.9938

1.0065

P\({}_{g12}\)

73.4690

63.1787

V\({}_{g42}\)

0.9769

1.0477

P\({}_{g15}\)

30.4367

69.2999

V\({}_{g46}\)

1.0100

1.0017

P\({}_{g18}\)

30.9970

37.4440

V\({}_{g49}\)

1.0069

1.0181

P\({}_{g19}\)

44.1664

30.1235

V\({}_{g54}\)

1.0370

0.9989

P\({}_{g24}\)

57.6019

31.1649

V\({}_{g55}\)

1.0311

0.9947

P\({}_{g25}\)

119.2457

136.1038

V\({}_{g56}\)

1.0320

0.9967

P\({}_{g26}\)

151.3569

152.9985

V\({}_{g59}\)

1.0295

1.0074

P\({}_{g27}\)

56.0971

32.4025

V\({}_{g61}\)

1.0340

1.0008

P\({}_{g31}\)

32.1709

32.1071

V\({}_{g62}\)

1.0277

0.9988

P\({}_{g32}\)

51.6170

30.0514

V\({}_{g65}\)

1.0306

1.0398

P\({}_{g34}\)

32.0154

33.4394

V\({}_{g66}\)

1.0117

1.0184

P\({}_{g36}\)

31.4379

30.0830

V\({}_{g69}\)

1.0401

1.0372

P\({}_{g44}\)

32.3694

31.9403

V\({}_{g70}\)

1.0231

1.0133

P\({}_{g42}\)

30.6368

32.5210

V\({}_{g72}\)

1.0276

1.0123

P\({}_{g46}\)

36.1461

35.9978

V\({}_{g73}\)

1.0163

0.9956

P\({}_{g49}\)

112.0778

160.9314

V\({}_{g74}\)

1.0059

1.0019

P\({}_{g54}\)

62.1124

47.7883

V\({}_{g76}\)

0.9781

0.9941

P\({}_{g55}\)

54.0745

30.3659

V\({}_{g77}\)

1.0033

1.0202

P\({}_{g56}\)

44.3759

44.7771

V\({}_{g80}\)

1.0172

1.0369

P\({}_{g59}\)

145.3439

88.6009

V\({}_{g85}\)

1.0039

0.9969

P\({}_{g61}\)

117.0340

126.8220

V\({}_{g87}\)

1.0626

0.9837

P\({}_{g62}\)

45.7334

39.6513

V\({}_{g89}\)

1.0135

0.9986

P\({}_{g65}\)

284.0753

263.3131

V\({}_{g90}\)

1.0207

1.0236

P\({}_{g66}\)

172.3229

278.0789

V\({}_{g91}\)

1.0041

1.0544

P\({}_{g70}\)

50.4983

30.0481

V\({}_{g92}\)

1.0037

1.0095

P\({}_{g72}\)

32.3044

63.0797

V\({}_{g99}\)

1.0198

1.0579

P\({}_{g73}\)

49.1009

53.9478

V\({}_{g100}\)

1.0120

1.0290

P\({}_{g74}\)

55.6390

35.4073

V\({}_{g103}\)

1.0194

1.0151

P\({}_{g76}\)

59.7134

52.1510

V\({}_{g104}\)

1.0150

1.0015

P\({}_{g77}\)

30.0000

32.1093

V\({}_{g105}\)

1.0214

1.0018

P\({}_{g80}\)

282.5561

289.0136

V\({}_{g107}\)

1.0604

1.0147

P\({}_{g85}\)

30.3429

30.3009

V\({}_{g110}\)

1.0154

1.0027

P\({}_{g87}\)

31.2028

31.2072

V\({}_{g111}\)

1.0450

1.0281

P\({}_{g89}\)

370.5745

390.9766

V\({}_{g112}\)

0.9919

0.9919

P\({}_{g90}\)

63.0840

30.7519

V\({}_{g113}\)

1.0317

1.0461

P\({}_{g91}\)

40.2548

31.5360

V\({}_{g113}\)

1.0268

1.0272

P\({}_{g92}\)

50.2085

41.3658

Q\({}_{c5}\)

8.4799

9.6180

P\({}_{g99}\)

31.6909

32.3164

Q\({}_{c34}\)

12.7735

1.8728

P\({}_{g100}\)

200.5469

159.9352

Q\({}_{c37}\)

6.3689

15.4410

P\({}_{g103}\)

48.9003

47.5207

Q\({}_{c44}\)

8.4943

16.1184

P\({}_{g104}\)

30.0499

30.8410

Q\({}_{c45}\)

21.2064

17.7603

P\({}_{g105}\)

30.1693

31.3924

Q\({}_{c46}\)

11.1423

12.8668

P\({}_{g107}\)

30.1765

30.2941

Q\({}_{c48}\)

13.3364

16.5950

P\({}_{g110}\)

37.8482

30.8276

Q\({}_{c74}\)

14.0006

15.7325

P\({}_{g111}\)

76.6624

41.3898

Q\({}_{c79}\)

15.0967

12.5671

P\({}_{g112}\)

30.3786

31.8328

Q\({}_{c82}\)

8.1848

11.6904

P\({}_{g113}\)

56.1582

30.0014

Q\({}_{c83}\)

13.9846

12.7562

P\({}_{g116}\)

32.8097

30.4287

Q\({}_{c105}\)

16.3278

17.0788

V\({}_{g1}\)

1.0028

0.9925

Q\({}_{c107}\)

6.1172

1.8649

V\({}_{g4}\)

1.0138

1.0211

Q\({}_{c110}\)

15.8669

1.2406

V\({}_{g6}\)

1.0173

1.0052

T\({}_{8}\)

0.9652

0.9416

V\({}_{g8}\)

1.0256

0.9878

T\({}_{32}\)

1.0156

0.9997

V\({}_{g10}\)

1.0286

1.0168

T\({}_{36}\)

0.9894

0.9783

V\({}_{g12}\)

1.0199

0.9958

T\({}_{51}\)

0.9879

1.0174

V\({}_{g\ 15}\)

1.0041

1.0070

T\({}_{93}\)

0.9765

1.0166

V\({}_{g18}\)

1.0023

0.9997

T\({}_{95}\)

0.9761

1.0029

V\({}_{g19}\)

0.9993

0.9982

T\({}_{102}\)

1.0115

1.0237

V\({}_{g24}\)

1.0020

1.0165

T\({}_{107}\)

1.0039

1.0447

V\({}_{g25}\)

1.0438

1.0252

T\({}_{127}\)

0.9828

1.0427

V\({}_{g26}\)

1.0701

1.0078

Fuel Cost ($/h)

139923.69

137105.99

V\({}_{g27}\)

1.0407

1.0540

P\({}_{g69}\)

319.5107

374.0803