Table 11 The obtained results of the proposed LSDO as well as the original SDO techniques for IEEE 57-bus.

P\({}_{g2}\)

30

100

90.6263

90.1633

77.1444

76.0949

55.3909

30.0065

P\({}_{g3}\)

40

140

45.4041

44.7779

54.7384

63.8062

123.6990

112.3814

P\({}_{g6}\)

30

100

70.3122

74.0789

63.0807

54.1637

91.3919

91.6064

P\({}_{g8}\)

100

550

460.9184

460.5164

315.6719

405.2965

331.1286

326.6915

P\({}_{g9}\)

30

100

93.5818

93.4810

48.4015

68.8195

99.1253

99.7742

P\({}_{g12}\)

100

410

361.7702

360.5197

263.3974

261.0801

409.6722

409.3781

V\({}_{g1}\)

0.95

1.1

1.0629

1.0616

1.0234

1.0316

1.0598

1.0656

V\({}_{g2}\)

0.95

1.1

1.0609

1.0600

1.0169

1.0211

1.0584

1.0611

V\({}_{g3}\)

0.95

1.1

1.0540

1.0544

1.0104

1.0082

1.0621

1.0612

V\({}_{g5}\)

0.95

1.1

1.0620

1.0604

1.0061

1.0022

1.0627

1.0600

V\({}_{g8}\)

0.95

1.1

1.0724

1.0741

1.0241

1.0155

1.0693

1.0630

V\({}_{g9}\)

0.95

1.1

1.0460

1.0465

1.0048

1.0010

1.0462

1.0451

V\({}_{g12}\)

0.95

1.1

1.0466

1.0458

1.0268

1.0302

1.0491

1.0544

Q\({}_{c18}\)

0

20

10.2617

12.8767

10.2150

5.6659

5.1816

10.8859

Q\({}_{c25}\)

0

20

13.3938

13.3632

12.9599

18.4242

8.6958

13.9401

Q\({}_{c53}\)

0

20

11.7915

10.7761

19.5538

17.5290

8.9473

15.8698

T\({}_{19}\)

0.9

1.1

1.0126

1.0880

1.0387

0.9875

1.0004

1.0319

T\({}_{20}\)

0.9

1.1

0.9896

0.9384

0.9795

1.0001

0.9736

0.9777

T\({}_{31}\)

0.9

1.1

1.0193

1.0140

0.9709

0.9686

1.0101

0.9823

T\({}_{35}\)

0.9

1.1

1.0502

1.0151

1.0337

1.0352

0.9789

1.0055

T\({}_{36}\)

0.9

1.1

0.9683

1.0128

1.0041

1.0575

1.0327

0.9792

T\({}_{37}\)

0.9

1.1

1.0208

1.0284

1.0281

1.0049

1.0469

0.9943

T\({}_{41}\)

0.9

1.1

0.9965

0.9961

0.9811

0.9869

1.0084

0.9969

T\({}_{46}\)

0.9

1.1

0.9607

0.9572

0.9179

0.9242

0.9937

0.9780

T\({}_{54}\)

0.9

1.1

0.9526

0.9179

0.9010

0.9027

0.9548

0.9255

T\({}_{58}\)

0.9

1.1

0.9780

0.9785

0.9291

0.9343

0.9799

0.9822

T\({}_{59}\)

0.9

1.1

0.9633

0.9591

0.9740

0.9702

0.9671

0.9845

T\({}_{65}\)

0.9

1.1

0.9721

0.9713

1.0055

1.0061

0.9730

0.9979

T\({}_{66}\)

0.9

1.1

0.9339

0.9341

0.9030

0.9011

0.9480

0.9550

T\({}_{71}\)

0.9

1.1

0.9630

0.9687

0.9636

0.9537

1.0103

0.9729

T\({}_{73}\)

0.9

1.1

1.0165

0.9973

0.9622

0.9987

1.0563

0.9501

T\({}_{76}\)

0.9

1.1

0.9867

0.9685

0.9269

0.9020

1.0049

0.9802

T\({}_{80}\)

0.9

1.1

0.9881

0.9863

0.9994

0.9793

1.0059

0.9879

Fuel Cost ($/h)

–

–

41668.7587

41667.7190

50990.2155

45681.7670

43796.8998

43612.0992

Emission (ton/h)

–

–

1.35777

1.35367

1.78130

1.49988

1.10023

1.15161

Voltage Deviation (p.u.)

–

–

1.61981

1.69704

0.63354

0.62165

1.44485

1.53517

Power Loss (MW)

–

–

14.8667

14.9243

29.7593

23.1825

10.4552

10.2332

P\({}_{g1}\)

0

576

143.05363

142.18709

458.12503

344.72168

150.84732

191.19500