Table 12 Achieved solutions of the proposed LSDO and its competitors for case 10.

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

\(P_{ws1}\)

0

150

149.9968

149.9149

150.0000

149.9607

144.5646

150.0000

\(P_{g3}\)

40

140

40.0596

44.6584

132.8028

41.2343

68.4754

40.0000

\(P_{ws2}\)

0

150

149.9959

149.9181

150.0000

149.9662

149.6426

150.0000

\(P_{g8}\)

100

550

378.8350

384.6096

223.1031

387.2554

402.3747

390.3843

\(P_{ss}\)

0

120

119.9969

119.9445

105.4476

119.9906

107.8691

120.0000

\(P_{g12}\)

100

410

315.6892

309.6422

316.7675

306.9151

292.5309

306.6320

\(V_{g1}\)

0.95

1.1

1.0596

1.0336

1.0388

1.0402

1.0431

1.0585

\(V_{g2}\)

0.95

1.1

1.0625

1.0301

1.0336

1.0378

1.0314

1.0534

\(V_{g3}\)

0.95

1.1

1.0572

1.0249

1.0227

1.0344

1.0375

1.0531

\(P_{g6}\)

0.95

1.1

1.0653

1.0399

1.0327

1.0572

1.0369

1.0590

\(V_{g8}\)

0.95

1.1

1.0449

1.0447

1.0465

1.0583

1.0316

1.0409

\(V_{g9}\)

0.95

1.1

1.0297

1.0229

1.0169

1.0380

1.0211

1.0287

\(V_{g12}\)

0.95

1.1

1.0372

1.0271

1.0168

1.0501

1.0421

1.0566

\(Q_{c18}\)

0

20

18.7913

14.6511

3.9084

8.7065

10.3670

16.8329

\(Q_{c25}\)

0

20

16.8467

15.7788

10.4987

13.8436

13.0369

19.9816

\(Q_{c53}\)

0

20

5.5652

7.2514

13.8125

12.7174

19.0196

9.9873

\(T_{19}\)

0.9

1.1

1.0668

0.9850

0.9970

1.0219

0.9398

1.0562

\(T_{20}\)

0.9

1.1

0.9928

1.0229

1.0194

1.0236

1.0274

1.0978

\(T_{31}\)

0.9

1.1

1.0072

1.0090

1.0094

1.0337

0.9462

0.9600

\(T_{35}\)

0.9

1.1

1.0818

1.0780

1.0747

1.0236

0.9998

1.0755

\(T_{36}\)

0.9

1.1

0.9311

0.9868

0.9687

0.9751

1.0441

0.9990

\(T_{37}\)

0.9

1.1

1.0398

1.0483

1.1000

1.0329

1.0677

1.0646

\(T_{41}\)

0.9

1.1

1.0079

0.9762

0.9731

1.0094

0.9680

0.9766

\(T_{46}\)

0.9

1.1

0.9644

0.9895

0.9000

0.9327

0.9500

0.9952

\(T_{54}\)

0.9

1.1

1.0226

0.9595

0.9703

0.9961

0.9332

0.9955

\(T_{58}\)

0.9

1.1

0.9813

0.9512

0.9433

0.9578

0.9568

1.0399

\(T_{59}\)

0.9

1.1

0.9922

0.9491

0.9541

0.9801

1.0382

1.0591

\(T_{65}\)

0.9

1.1

0.9899

1.0342

1.0295

1.0012

0.9597

1.0172

\(T_{66}\)

0.9

1.1

0.9448

0.9519

0.9415

0.9786

0.9355

0.9062

\(T_{71}\)

0.9

1.1

0.9827

0.9549

0.9303

0.9961

0.9840

1.0383

\(T_{73}\)

0.9

1.1

0.9919

1.0501

0.9551

1.0316

0.9147

0.9726

\(T_{76}\)

0.9

1.1

0.9653

1.0026

1.1000

0.9617

1.0116

0.9549

\(T_{80}\)

0.9

1.1

1.0546

1.0213

0.9862

0.9890

1.0895

0.9746

\(C_T\) ($/h)

–

–

26491.8072

26529.4584

30539.0423

26498.1112

27458.7947

26565.5122

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

–

–

1231.2046

1230.4574

1231.2389

1230.8971

1204.5255

1231.2389

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

–

–

461.9679

461.6379

395.9494

463.0663

407.6080

462.7849

E (t/h)

–

–

0.8984

0.9016

0.6918

0.9082

0.9253

0.9177

VD (p.u.)

–

–

1.2561

1.0096

1.1084

1.1498

1.2434

1.5757

\(P_{L}\) (MW)

–

–

17.1841

18.0821

18.6802

17.9220

21.1848

19.9461

P\({}_{g1}\)

0

575.88

113.4107

110.1944

191.3593

113.3998

106.5275

113.7299

  1. The best values obtained are in bold.
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