Table 10 Optimum control variables for the 30-bus system for minifying fuel cost and voltage deviation.

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

GWO37

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

175.5229

165.2596

174.9996

180.2959

152.897

176.000

152.3759

175.6838

63.4100

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

48.78027

54.90978

47.908

43.11046

46.21225

49.3706

51.20082

42.94417

77.7900

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

21.95667

19.35698

21.18578

24.74529

23.88146

21.9316

21.44287

21.97456

39.8500

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

21.46253

23.8677

23.89826

19.11117

35

19.29766

32.45254

23.89286

45.4400

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

13.18521

13.86115

13.32854

13.73714

15.75959

13.41639

10.82703

15.50411

30.3100

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

12.32151

15.39698

12.00118

12.49682

18.01988

13.34685

23.45908

12.97393

30.4100

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

1.039515

1.063826

1.031421

1.034383

1.056401

1.0364

1.071509

1.03843

1.0720

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

1.02771

1.043007

1.014417

1.02032

1.02664

1.015553

1.047492

1.024674

1.0710

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

1.014143

0.993806

1.013213

1.017806

1.011091

1.01422

0.984239

0.996189

1.0310

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

1.004954

0.996013

1.009208

1.010292

0.981409

0.99934

0.996136

1.010137

1.0041

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

1.007247

1.047857

1.014779

1.001898

1.059162

1.04089

1.1

1.020358

1.0400

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

0.996524

1.011814

0.998543

1.007497

1.073992

1.018594

1.032821

1.027376

1.0820

\({T}_{11}\) (6–9)

1.012959

1.000785

1.030949

1.006006

0.950253

1.054622

1.060472

0.954086

1.043

\({T}_{12}\) (6–10)

0.913714

0.94624

0.9

0.9000

1.1

0.903902

0.914689

0.93967

0.99

\({T}_{15}\) (4–12)

0.952708

0.947149

0.967012

0.955314

1.048264

0.989138

1.02256

0.973295

0.99

\({T}_{36}\) (28–27)

0.95967

0.959914

0.970758

0.958486

0.96805

0.96049

0.978803

0.963043

0.965

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

4.648409

2.36515

2.173401

1.51318

4.10456

4.259120

3.0328

2.0042

18.93

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

0.609357

3.4281

3.8315

1.82596

3.8632

0.579030

4.5746

3.06927

0

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

4.843797

0.239426

4.93276

1.8356

0.02045

4.11300

1.63617

0.89053

0

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

1.4157006

1.35966

4.0660

3.97469

0.01532

1.103097

1.9630

0.29389

0

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

4.869775

3.910071

4.99048

2.26118

0.4833

4.928113

1.7889

2.41299

0

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

4.4165256

1.666834

5

3.9316

4.6215

4.341355

3.74594

2.2095

0

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

4.918944

3.8529345

4.9518

4.08318

1.70689

4.951307

2.47034

2.07403

0

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

4.610539

3.4359845

4.9373

4.99936

3.86399

4.858122

4.77817

1.028523

15.52

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

1.73194

2.169675

2.73016

1.31833

0.002345

1.930208

3.3332

2.539075

0

Objective function

824.9193

839.7303

824.0697

829.941

882.0512

825.729

856.5994

839.5122

916.1964

Fuel cost ($/h)

803.9283

805.3913

804.5488

805.9561

810.8618

804.2747

811.2805

804.7557

916.1764

Power losses (MW)

9.829075

9.252214

9.921366

10.09684

8.370063

9.963252

8.358272

9.573489

–

Voltage deviations (pu)

0.104955

0.171695

0.097605

0.119924

0.355947

0.107271

0.226594

0.173782

0.4935

Iterations time (s)

28.144

289.74

34

48

27.6

25.2

29.4

38.5

–

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