Table 7 Optimum control variables for IEEE 30-bus grid for minifying real power loss.

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

CGSCE50

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

52.3425

51.33418

51.25777

52.16676

59.8116

51.2878

53.889

51.308

51.5010

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

79.7942

80

80

79.7063

78.5750

80

80

80

79.9997

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

49.9318

50

50

49.9449

50

50

48.4452

50

50

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

34.9041

35

34.9999

34.9542

35

35

35

35

34.9999

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

29.6905

30

29.9999

29.9962

23.5632

30

30

30

30

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

39.6394

40

40

39.5551

40

40

39.2044

40

40

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

1.09893

1.1

1.1

1.09122

1.1

1.1

1.1

1.1

1.0621

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

1.09457

1.1

1.09829

1.08720

1.1

1.0985

1.1

1.1

1.0579

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

1.07498

1.08611

1.08119

1.06905

1.1

1.0828

1.08142

1.08575

1.0385

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

1.08221

1.1

1.08827

1.07432

1.1

1.0890

1.1

1.08995

1.0448

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

1.09747

1.1

1.1

1.09716

1.1

1.0996

1.1

1.08898

1.0791

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

1.09909

1.1

1.1

1.09850

1.1

1.1

1.1

1.08088

1.0558

\({T}_{11}\) (6–9)

1.01155

1.01589

1.00979

0.99453

1.08586

0.98000

1.1

1.00356

1.0824

\({T}_{12}\) (6–10)

0.93759

0.99626

0.95378

0.93651

0.9

1.02196

0.91405

1.00289

0.9017

\({T}_{15}\) (4–12)

0.99101

0.98397

0.98387

0.98839

0.94535

1.00061

0.98785

0.99901

0.9956

\({T}_{36}\) (28–27)

0.97091

1.01589

0.98040

0.97522

1.03166

0.97447

1.01656

0.99591

0.9772

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

3.89421

5

4.642197

3.39678

0

4.98964

0.76948

5

2.1245

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

4.77147

5

4.852034

4.87548

2.73792

4.65688

3.43345

5

2.1490

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

3.84970

5

4.773109

3.43138

0

0.33029

2.91064

5

4.2533

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

4.12313

5

4.758789

4.90404

1.53436

4.58416

3.51662

5

4.9964

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

4.46517

5

4.920185

4.66356

0.828348

3.93139

1.90675

5

3.9417

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

4.41188

5

4.999950

4.02067

2.90876

5

1.01628

5

5

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

3.26619

4.97466

4.482629

4.63745

0

4.99994

4.34705

5

2.9168

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

4.33241

5

4.992978

4.64350

0

4.25083

0.21415

5

4.9992

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

2.62251

5

3.373429

3.10008

1.91637

1.39732

4.25971

5

2.3996

Fuel cost ($/h)

964.688

967.266

967.084

965.11

953.377

967.156

958.301

967.205

967.663

Power losses (MW)

2.90269

2.93419

2.85767

2.9237

3.54983

2.88785

3.13870

2.90849

3.10060

Voltage deviations (pu)

1.91941

1.95581

2.04259

1.86249

1.53477

1.86299

1.60215

1.79152

0.89096

Iterations time (s)

47.74

337.6

50.8

58

32.37

33.61

31

34.54

–

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