Table 15 Optimum control variables for modified 30-bus grid to decrease the fuel cost.

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

AHA49

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

149.92

146.41

149.40

149.404

160.5720

149.6841

149.2895

149.9794

157.6299

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

41.508

37.959

41.629

42.36418

29.66025

42.15954

39.68164

41.46893

42.98818

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

19.256

21.429

19.489

18.94601

19.949

19.17919

20.167

19.69758

19.78803

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

10.233

11.480

10.380

10

11.67302

10

10.27059

10

7.860474

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

10.092

12.503

10.058

10

11.07418

10.014

10.46737

10

7.891434

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

12.047

13.133

12.053

12

12

12

13.1577

12

7.627846

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

1.0996

1.1

1.0983

1.1

1.054987

1.1

1.1

1.1

1.098665

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

1.0854

1.0885

1.0859

1.088544

1.029493

1.088596

1.081552

1.08872

1.084298

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

1.0557

1.0664

1.0613

1.063379

0.987231

1.061839

1.06254

1.061481

1.056581

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

1.0705

1.0664

1.0720

1.075225

1.033714

1.072335

1.0672

1.077548

1.065559

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

1.0917

1.1

1.0943

1.1

1.076689

1.070003

1.095583

1.096235

1.048832

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

1.0828

1.0713

1.0862

1.1

1.090592

1.097708

1.1

1.1

1.047008

\({T}_{11}\) (6–9)

0.9593

1.0101

0.9989

1.014891

1.1

1.027803

0.979908

1.003916

0.977883

\({T}_{12}\) (6–10)

0.999

1.0428

0.9337

0.903449

0.9

0.9

0.932093

0.952543

1.030724

\({T}_{15}\) (4–12)

0.998

1.0101

0.9857

0.993016

0.9

0.982716

1.025951

1.052827

0.998454

\({T}_{36}\) (28–27)

1.064

1.039

1.0640

1.057892

1.1

1.061452

1.071894

1.077832

1.077131

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

2.06449

0.05312

0.36457

1.63973

0

4.165117

2.854821

3.316669

2.603767

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

3.03463

0.51095

4.54831

0.74507

2.203478

0.682474

1.274359

2.121810

1.15499

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

4.14295

1.25666

4.10624

1.40521

0

4.471524

3.588500

0.858680

1.84191

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

3.56717

1.45444

3.80277

0.54270

0

4.878320

0.134908

3.030433

2.21311

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

4.34507

0.84688

2.83075

0.05370

4.391702

4.556146

2.405562

1.603250

3.07042

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

3.50887

1.71031

3.73776

2.06235

0

4.491089

0.507956

1.118070

3.40776

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

4.77626

0.22136

3.59316

0.02950

0

0.192129

2.229644

0.106010

2.98057

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

3.92792

0.05312

4.22822

4.08968

0

4.982721

2.621859

1.996898

2.07048

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

1.94678

2.22246

1.30591

0.13392

 

0.360806

2.255161

1.761838

1.299162

Fuel cost ($/h)

636.07

638.55

636.05

636.0871

644.9163

635.9247

636.9435

636.3569

635.8983

Power losses (MW)

7.4721

7.3377

7.4283

7.515853

9.341338

7.449714

7.446704

7.558806

8.850231

Voltage deviations (pu)

1.7053

1.2196

1.7636

1.709431

0.614245

1.788635

1.613575

1.498983

1.11413

Iterations time (s)

57.43

528.7

60

85.16

52.84

47.72

50.8

53.5

–

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