Table 9 Achieved solutions of the proposed LSDO and its competitors for case 5.

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

\(P_{g2}\)

20

80

27.4952

28.1190

29.2181

27.8672

29.3493

27.4586

\(P_{ws1}\)

0

75

42.5964

42.4655

43.6871

43.3611

44.0153

44.4882

\(P_{g8}\)

10

35

10.0003

10.0168

10.0000

10.0000

10.0070

10.0000

\(P_{ws2}\)

0

60

36.3138

35.8283

37.2811

37.2411

36.9425

36.9460

\(P_{ss}\)

0

50

37.6781

37.6680

33.8187

35.5632

33.7036

35.1731

\(V_{g1}\)

0.95

1.1

1.0712

1.0736

1.0705

1.0715

1.0720

1.0764

\(V_{g2}\)

0.95

1.1

1.0567

1.0566

1.0547

1.0569

1.0570

1.0610

\(V_{g5}\)

0.95

1.1

1.0350

1.0318

1.0266

1.0350

1.0347

1.0356

\(V_{g8}\)

0.95

1.1

1.0339

1.0372

1.0386

1.0381

1.0383

1.0399

\(V_{g11}\)

0.95

1.1

1.0576

1.0861

1.0377

1.0969

1.0679

1.1000

\(V_{g13}\)

0.95

1.1

1.0640

1.0466

1.0582

1.0532

1.0476

1.0301

\(Q_{c10}\)

0

5

0.9424

4.1096

5.0000

1.6484

3.6814

2.6581

\(Q_{c12}\)

0

5

2.7784

4.6240

4.0577

0.9597

0.9146

5.0000

\(Q_{c15}\)

0

5

4.5231

4.2841

4.0942

2.6031

4.7725

1.8142

\(Q_{c17}\)

0

5

4.7475

2.1458

5.0000

2.5202

4.2278

5.0000

\(Q_{c20}\)

0

5

2.5055

2.5539

4.7588

3.6337

3.7487

1.9695

\(Q_{c21}\)

0

5

4.3127

4.5084

5.0000

3.8520

4.5469

3.5004

\(Q_{c23}\)

0

5

1.6562

2.2216

2.1084

3.3026

4.3059

4.4025

\(Q_{c24}\)

0

5

4.9079

4.1379

4.9920

4.6778

3.6728

4.1748

\(Q_{c29}\)

0

5

2.3821

1.9546

3.1337

1.8963

2.0644

3.2827

\(T_{11}\)

0.9

1.1

1.0224

1.0453

1.0571

1.0272

1.0595

1.0093

\(T_{12}\)

0.9

1.1

0.9262

0.9400

0.9000

0.9470

0.9245

1.0445

\(T_{15}\)

0.9

1.1

1.0018

0.9784

0.9976

0.9811

0.9814

0.9397

\(T_{36}\)

0.9

1.1

0.9718

0.9751

0.9903

0.9720

0.9767

0.9846

\(T_C\) ($/h)

–

–

781.0465

781.0633

781.5679

781.5613

781.8429

781.8984

\(W_C\) ($/h)

–

–

240.1276

238.0496

247.1789

245.9129

247.1596

248.8258

\(S_C\) ($/h)

–

–

103.6752

103.6431

91.2099

97.1776

91.1570

95.9508

E (t/h)

–

–

1.7623

1.7622

1.7683

1.7622

1.7648

1.7623

VD (p.u.)

–

–

0.8136

0.8011

0.7702

0.8816

0.7889

0.7628

\(P_{L}\) (MW)

–

–

5.5916

5.6057

5.5719

5.5407

5.5521

5.5739

P\({}_{g1}\)

50

140

134.9079

134.9080

134.9668

134.9079

134.9343

134.9079

  1. The best values obtained are in bold.
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