Table 13 Achieved solutions of the proposed LSDO and its competitors for case 11.

From: A leader supply-demand-based optimization for large scale optimal power flow problem considering renewable energy generations

Variables

Min

Max

LSDO

SDO

ABC

AEO

DE

PSO

\(P_{g2}\)

0

150

149.9869

149.9979

101.6808

149.9480

149.9373

150.0000

\(P_{g3}\)

40

140

40.0190

41.4222

75.5268

41.9813

65.0723

40.0000

\(P_{g6}\)

0

150

149.9852

149.9998

150.0000

149.9726

143.1387

149.5369

\(P_{g8}\)

100

550

384.0763

370.1775

397.0061

392.0774

371.4336

367.3130

\(P_{g9}\)

0

120

119.9840

119.9928

114.9231

119.9816

114.5233

120.0000

\(P_{g12}\)

100

410

309.2269

323.9497

303.1151

305.3395

285.2056

324.1490

\(V_{g1}\)

0.95

1.1

1.0468

1.0458

1.0844

1.0421

1.0247

1.0294

\(V_{g2}\)

0.95

1.1

1.0480

1.0402

1.0736

1.0441

1.0227

1.0232

\(V_{g3}\)

0.95

1.1

1.0435

1.0381

1.0505

1.0392

1.0048

0.9904

\(P_{g6}\)

0.95

1.1

1.0653

1.0473

1.0397

1.0622

1.0206

0.9918

\(V_{g8}\)

0.95

1.1

1.0651

1.0314

1.0225

1.0731

1.0265

0.9865

\(V_{g9}\)

0.95

1.1

1.0436

1.0121

1.0135

1.0331

0.9951

0.9650

\(V_{g12}\)

0.95

1.1

1.0498

1.0293

1.0382

1.0166

1.0033

0.9821

\(Q_{c18}\)

0

20

15.7069

4.7349

13.6560

16.3110

17.1528

0.0000

\(Q_{c25}\)

0

20

13.8184

14.6576

16.4312

8.7039

16.8865

20.0000

\(Q_{c53}\)

0

20

12.5339

13.4582

12.6849

8.2655

0.9974

0.0000

\(T_{19}\)

0.9

1.1

1.0664

1.0617

1.0539

1.0525

0.9865

0.9155

\(T_{20}\)

0.9

1.1

0.9797

1.0693

1.0982

0.9991

0.9696

0.9029

\(T_{31}\)

0.9

1.1

0.9923

1.0077

1.0287

0.9962

1.0061

0.9438

\(T_{35}\)

0.9

1.1

0.9882

0.9602

0.9987

0.9187

0.9579

1.0336

\(T_{36}\)

0.9

1.1

1.0285

0.9671

1.0419

1.0095

1.0001

0.9000

\(T_{37}\)

0.9

1.1

0.9924

0.9521

1.0031

1.0264

0.9825

0.9908

\(T_{41}\)

0.9

1.1

1.0048

0.9921

0.9903

1.0054

1.0146

1.0186

\(T_{46}\)

0.9

1.1

0.9856

0.9922

0.9632

0.9494

0.9748

0.9906

\(T_{54}\)

0.9

1.1

0.9241

1.0152

1.0358

0.9083

0.9499

0.9292

\(T_{58}\)

0.9

1.1

0.9668

1.0236

0.9655

0.9638

0.9664

0.9000

\(T_{59}\)

0.9

1.1

0.9893

0.9714

0.9479

0.9600

0.9439

0.9529

\(T_{65}\)

0.9

1.1

1.0178

0.9550

1.0245

0.9954

0.9331

1.0066

\(T_{66}\)

0.9

1.1

0.9478

0.9059

0.9299

0.9476

0.9318

0.9000

\(T_{71}\)

0.9

1.1

0.9689

0.9416

0.9453

0.9968

0.9411

0.9100

\(T_{73}\)

0.9

1.1

0.9822

1.0071

0.9218

0.9889

1.0581

1.0111

\(T_{76}\)

0.9

1.1

0.9903

0.9966

0.9575

0.9753

0.9156

0.9003

\(T_{80}\)

0.9

1.1

1.0264

0.9753

0.9487

0.9738

0.9815

0.9000

\(C_T\) ($/h)

–

–

26490.4174

26560.9184

28755.3530

26500.9984

27247.6331

26695.5204

\(C_{W}\) ($/h)

–

–

1231.1081

1231.2280

1009.1192

1230.8696

1198.2998

1229.0353

\(C_{S}\) ($/h)

–

–

461.2707

461.3112

439.2436

461.9111

437.0527

463.1334

E (t/h)

–

–

0.9039

0.8874

0.9483

0.9164

0.8554

0.8870

VD (p.u.)

–

–

1.1424

1.3345

1.2478

1.0188

1.0682

1.4830

\(P_{L}\) (MW)

–

–

17.1879

17.6400

19.6197

17.6620

19.5208

20.5897

P\({}_{g1}\)

0

575.88

114.7097

112.9001

128.1678

109.1615

141.0100

120.3908

  1. The best values obtained are in bold.
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