Table 13 Optimum control variables for the 30-bus grid for minifying multi-objective function with emission.

From: Application of modified artificial hummingbird algorithm in optimal power flow and generation capacity in power networks considering renewable energy sources

Control variables

AHA

HHO

mAHA

RUN

SCA

SMA

TSA

WOA

FKH40

\({P}_{G1}\) (MW)

165.400

166.8056

166.4721

166.5516

166.724

164.969

156.645

168.9629

123.6836

\({P}_{G2}\) (MW)

47.79336

46.25959

48.60795

51.88644

45.45169

48.78904

50.36477

49.08558

51.5998

\({P}_{G5}\) (MW)

23.99595

18.1686

22.54116

22.11936

15.25348

23.20754

24.91179

19.7571

31.4264

\({P}_{G8}\) (MW)

26.37857

27.31501

30.67165

20.14404

26.94864

26.89674

30.9148

20.74778

34.9189

\({P}_{G11}\) (MW)

15.4945

21.15653

11.53718

15.24274

20.02407

15.25062

10.21388

17.12666

27.1416

\({P}_{G13}\) (MW)

13.17305

12.81335

12.60599

16.63903

18.62736

13.05962

19.2427

16.99289

20.0125

\({V}_{1}\) (pu)

1.039098

1.040652

1.039056

1.047613

1.035358

1.043882

1.036548

1.04753

1.1

\({V}_{2}\) (pu)

1.020842

1.024997

1.022437

1.03056

1.007994

1.027929

1.019686

1.023413

1.0883

\({V}_{5}\) (pu)

1.007009

1.014929

1.007678

1.010245

0.95

1.004604

0.95

1.004138

1.0626

\({V}_{8}\) (pu)

1.002955

1.002843

1.007759

1.005067

0.984175

1.001507

0.981303

1.003892

1.0723

\({V}_{11}\) (pu)

1.027677

1.029506

1.005235

1.049557

1.073876

1.027916

1.1

1.072832

1.0661

\({V}_{13}\) (pu)

1.01166

1.059816

1.001543

0.990098

1.075011

1.00591

1.018861

1.018827

1.0220

\({T}_{11}\) (6–9)

1.025236

0.973647

1.012411

1.048338

1.003556

1.023669

1.1

1.022662

1.0909

\({T}_{12}\) (6–10)

0.909392

0.960301

0.914416

0.90002

0.982152

0.923891

0.9

0.94292

1.0210

\({T}_{15}\) (4–12)

0.982708

0.992372

0.950994

0.934678

0.991057

0.974637

0.995898

0.987179

1.0619

\({T}_{36}\) (28–27)

0.959825

0.985456

0.967399

0.968509

0.928281

0.962299

0.9

0.954627

1.0283

\({Q}_{10}\) (MVAR)

2.75864

0.893957

4.50358

3.88395

1.9883

4.72861

3.7866

2.54853

0.3568

\({Q}_{12}\) (MVAR)

0.848113

1.099

0.07098

0.965388

0

3.9491

0.0750

3.74059

4.6954

\({Q}_{15}\) (MVAR)

4.97757

2.832

2.4058

2.3171

2.43085

3.45173

2.6479

1.18119

3.6401

\({Q}_{17}\) (MVAR)

1.13727

3.328

2.348087

2.8309

0

0.23348

5

2.301628

3.1174

\({Q}_{20}\) (MVAR)

4.99764

0.975976

5

4.9971

0.83895

4.92498

4.83476

0.974147

0.8760

\({Q}_{21}\) (MVAR)

4.36739

0.831048

4.995866

0.78898

3.43964

4.86885

1.5173

1.48059

4.9595

\({Q}_{23}\) (MVAR)

4.7651

3.02398

4.9535

4.29237

0

4.93974

4.6711

4.1572

3.9324

\({Q}_{24}\) (MVAR)

4.84673

0.84786

5

3.29885

0.56658

4.91916

2.6284

1.3137

5

\({Q}_{29}\) (MVAR)

1.626306

3.607

2.39323

3.41025

2.51957

1.95153

0.41082

4.1195

1.9857

Objective function

865.0322

879.4284

864.735

867.2717

888.6845

864.9008

885.6557

873.5397

–

Fuel cost ($/h)

804.8632

807.3554

804.8359

804.9669

811.4686

804.3571

810.2148

805.1315

828.3271

Power losses (MW)

8.835931

9.118731

9.036036

9.183196

9.629671

8.772594

8.893501

9.272956

5.3828

Voltage deviations (pu)

0.113104

0.226543

0.106119

0.125655

0.267482

0.118206

0.236763

0.184763

0.4925

Iterations time (s)

46.6

290

56

72.23

45.4

48.6

47.62

57.6

–

Back to article page