Table 9 Optimum control variables for the 30-bus grid to minimize fuel cost and power losses.

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)

177.0931

175.5109

176.0591

176.4130

189.5175

176.4369

176.6683

173.564

100.8346

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

48.76131

48.46011

48.71275

48.74285

37.16635

48.07728

48.43647

46.9036

54.8671

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

21.4638

19.38189

21.47426

21.48944

17.45434

21.30445

20.28966

20.47343

38.1537

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

20.51172

16.32334

21.39346

21.41286

21.01935

21.6203

23.41367

26.21112

34.9623

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

12.0561

15.52938

12.32207

11.9425

10.393

12.28089

11.71707

11.55522

30

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

12.17641

17.14297

12.00147

12

17.87807

12.26235

12

13.15282

28.7706

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

1.099296

1.1

1.1

1.1

1.1

1.099784

1.1

1.1

1.1

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

1.085022

1.088287

1.087533

1.088118

1.077111

1.085994

1.071508

1.087778

1.0929

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

1.060608

1.084032

1.060822

1.062336

1.071001

1.059365

1.029004

1.059761

1.0719

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

1.067104

1.072722

1.068763

1.069603

1.059109

1.067244

1.032739

1.0725

1.0835

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

1.087851

1.074855

1.099949

1.099836

1.088153

1.089793

1.1

1.1

1.0997

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

1.099112

1.057605

1.099997

1.099998

1.001946

1.095

1.1

1.1

1.1

\({T}_{11}\) (6–9)

1.045693

1.003073

1.029156

1.0473

0.981436

1.018356

0.9

0.998058

1.1329

\({T}_{12}\) (6–10)

0.907026

1.018954

0.903674

0.900537

0.924547

0.938597

1.1

0.970844

0.9

\({T}_{15}\) (4–12)

1.004052

1.069846

0.988155

0.998731

0.998942

1.002393

1.088772

0.968337

1.0031

\({T}_{36}\) (28–27)

0.974703

1.041105

0.969473

0.970013

0.971083

0.97472

0.985332

0.997868

0.9783

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

4.447787

0.707715

4.52375

3.438364

3.783976

4.331209

3.468405

3.297766

3.4906

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

3.859251

1.196239

3.97058

2.846555

1.32943

4.9296261

1.47400

2.58092

4.079

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

4.900656

2.932422

4.84955

3.787102

0

4.6612761

2.140105

0.925562

5

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

3.816908

1.719433

4.9999

0.948367

0

4.0272437

1.75447

1.913396

0.2021

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

4.183282

2.696676

2.15121

4.972533

2.3980128

4.7595398

2.298828

1.26444

4.7291

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

4.589494

2.431736

4.62922

4.998385

2.7757761

4.8752976

1.98450

3.69092

4.1547

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

4.46654

2.33526

2.854919

1.961131

1.3605141

3.980208

2.26344

0.54035

5

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

4.896263

3.115011

4.9656

5

3.8662456

4.590352

3.144415

3.59317

0.0054

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

2.06742

0.597591

4.27857

1.788983

4.8538048

3.024216

1.622321

3.617967

1.0601

Objective function

801.9555

804.7762

801.8704

801.9097

809.9703

801.9277

803.9152

802.7551

–

Fuel cost ($/h)

799.2024

801.966

799.1388

799.17

806.9349

799.1922

801.0698

800.0492

860.9599

Power losses (MW)

8.662526

8.948682

8.56314

8.600676

10.02863

8.582226

9.125181

8.4602

4.1883

Voltage deviations (pu)

1.622949

0.720765

1.814924

1.658613

0.933144

1.638002

0.818398

1.485045

1.7751

Iterations time (s)

32

280

40.6

54

28.2

33.46

30.308

28.1

–

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