Table 20 Optimum control variables for the 118-bus network to optimize voltage deviation.

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

52.82

86.53

58.52

84.95

95.93

40.46

21.95

18.13

\({P}_{G4}\) (MW)

52.822532

86.534929

58.515167

84.9455

95.933873

40.463808

21.948832

18.125984

\({P}_{G6}\) (MW)

46.7889

8.4559332

8.1777681

39.14065

0.5177518

33.998707

65.419773

31.439515

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

72.443451

29.739024

69.4858

60.493318

3.8944833

61.89915

61.622648

81.536623

\({P}_{G10}\) (MW)

44.742481

39.914872

69.647015

51.947028

88.442935

54.08992

29.456074

18.384239

\({P}_{G12}\) (MW)

254.94598

176.40549

121.13453

78.437014

29.266196

309.56541

10.050499

131.17817

\({P}_{G15}\) (MW)

100.87837

7.9782063

45.706402

49.262106

12.116081

71.753132

48.770883

88.116755

\({P}_{G18}\) (MW)

36.108738

83.157416

18.581217

41.530358

58.100739

42.412301

28.273554

39.598782

\({P}_{G19}\) (MW)

66.847449

50.520024

98.726322

73.742826

47.697574

22.493054

7.8748671

65.529929

\({P}_{G24}\) (MW)

65.156197

28.782801

69.168917

47.047217

34.120001

60.344564

32.125257

40.938533

\({P}_{G25}\) (MW)

28.683409

18.118969

1.8470755

83.219766

51.369075

40.390541

33.372819

13.015991

\({P}_{G26}\) (MW)

109.21034

107.13653

122.15009

113.03392

71.074438

185.82211

101.36871

102.30161

\({P}_{G27}\) (MW)

251.14927

372.52551

35.50038

245.47584

45.40322

213.76515

239.72192

335.95466

\({P}_{G31}\) (MW)

76.399316

4.1003473

97.619138

62.996597

75.224936

34.368899

31.640831

31.479638

\({P}_{G32}\) (MW)

64.61721

50.510284

80.022305

35.998888

50.210404

45.10058

105.5269

28.733001

\({P}_{G34}\) (MW)

54.367909

54.481789

73.698048

74.517845

12.648857

18.355511

21.250825

49.913331

\({P}_{G36}\) (MW)

64.739915

33.335546

87.218256

46.58226

64.786678

91.595118

17.974935

59.268433

\({P}_{G40}\) (MW)

65.495945

5.1947102

11.373845

52.247796

67.981499

52.74163

70.318428

6.0074085

\({P}_{G42}\) (MW)

46.524691

52.820251

51.484888

45.519705

51.559365

46.915288

11.719574

41.37987

\({P}_{G46}\) (MW)

28.54616

10.10687

85.625471

53.238145

20.399013

49.712917

14.304283

65.535454

\({P}_{G49}\) (MW)

85.026877

4.5589597

118.91603

33.526012

10.288305

61.268908

70.943099

70.342941

\({P}_{G54}\) (MW)

168.79389

85.08324

229.38704

137.71746

296.80871

189.57607

14.611018

129.14709

\({P}_{G55}\) (MW)

68.372873

67.797872

85.68927

17.482681

144.70944

66.916912

119.95778

22.049981

\({P}_{G56}\) (MW)

21.71997

7.5726755

19.245097

29.391758

11.519586

55.035735

6.6625432

21.330834

\({P}_{G59}\) (MW)

34.864823

80.995542

98.119919

61.282769

82.811177

47.185611

40.407276

47.543443

\({P}_{G61}\) (MW)

151.98909

63.877465

195.13156

139.75611

18.289501

112.37041

255

228.71916

\({P}_{G62}\) (MW)

60.881268

20.146075

153.88487

107.91081

238.30156

104.14495

58.067228

144.74258

\({P}_{G65}\) (MW)

9.4218251

20.131163

39.948874

59.066935

35.328085

13.496392

30.263897

41.463265

\({P}_{G66}\) (MW)

109.04643

322.91442

294.81284

112.05428

251.16337

147.04903

411.54761

359.13276

\({P}_{G69}\) (MW)

70.740547

20.308617

146.2685

260.02602

70.257549

255.82805

21.03211

137.06534

\({P}_{G70}\) (MW)

43.901337

14.30852

56.722197

22.367049

54.48107

61.867748

13.013025

29.649725

\({P}_{G72}\) (MW)

70.289334

24.155251

99.929436

62.17154

35.671253

42.765717

100

31.066932

\({P}_{G73}\) (MW)

19.761606

85.387951

50.354984

33.959724

95.425152

24.475638

100

57.652867

\({P}_{G74}\) (MW)

80.407997

64.387694

98.496524

57.007128

2.2893454

62.03897

18.124487

46.926745

\({P}_{G76}\) (MW)

97.136392

88.843241

96.510912

96.255039

92.000541

96.814903

100

55.777601

\({P}_{G77}\) (MW)

54.464412

22.065468

41.049907

61.237556

39.37593

54.233358

93.404263

53.249031

\({P}_{G80}\) (MW)

338.45338

358.29594

49.764713

283.21856

567.49675

183.60211

422.52689

118.7305

\({P}_{G85}\) (MW)

2.62E+01

9.09E+01

5.22E+01

3.62E+01

3.20E+01

3.57E+01

3.22E+01

2.50E+01

\({P}_{G87}\) (MW)

44.659989

57.054647

15.374826

56.358788

28.223967

16.733744

39.974101

52.714595

\({P}_{G89}\) (MW)

273.42509

196.89184

63.20857

193.36092

295.43476

294.40581

447.25844

306.83683

\({P}_{G90}\) (MW)

25.860891

4.6699173

67.998268

65.232943

17.183073

39.27474

4.0527752

22.828486

\({P}_{G91}\) (MW)

50.393756

41.176445

93.53563

49.838634

90.351806

44.173997

67.990342

24.226635

\({P}_{G92}\) (MW)

46.064114

88.734637

72.349485

42.203932

2.3380964

28.483208

14.626604

23.480601

\({P}_{G99}\) (MW)

76.449496

86.403102

8.7029995

65.671936

61.216134

35.562851

23.802229

18.429791

\({P}_{G100}\) (MW)

196.80331

284.74711

303.31712

159.24444

111.37319

162.19673

153.11885

194.63035

\({P}_{G103}\) (MW)

109.63725

132.79272

108.01333

67.123699

41.852447

69.831514

111.43613

112.04441

\({P}_{G104}\) (MW)

64.407691

48.91815

67.727818

40.808973

20.504444

70.646135

23.428013

74.158657

\({P}_{G105}\) (MW)

46.701177

7.4280396

73.881827

63.157171

81.982191

35.893146

43.60918

42.079564

\({P}_{G107}\) (MW)

59.53491

48.971405

21.425748

54.454785

26.370647

45.431396

16.917964

18.175037

\({P}_{G110}\) (MW)

35.060333

88.039801

83.92072

42.870323

25.222161

50.166939

22.799808

57.450984

\({P}_{G111}\) (MW)

27.822147

4.7383986

79.914024

45.385803

11.901008

55.136908

90.84821

53.407116

\({P}_{G112}\) (MW)

24.049655

30.522041

42.18986

40.976413

38.143633

47.001754

37.008763

24.919959

\({P}_{G113}\) (MW)

12.880797

37.042488

2.1130705

37.209325

27.793511

87.359959

57.751145

22.890486

\({P}_{G116}\) (MW)

48.9738

49.368026

58.801534

90.015056

4.0243278

36.829394

2.0638751

19.614222

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

0.9837169

0.9989332

1.0040714

0.9946496

1.0159518

0.9801384

0.94

0.9943254

\({V}_{4}\) (pu)

1.0171959

0.9987023

1.0052552

1.0147383

0.9949769

1.0170704

0.983829

1.0230408

\({V}_{6}\) (pu)

1.0083777

0.9984379

1.0037718

1.0093424

0.9915861

1.0002216

0.94

1.0214704

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

0.9893358

0.9984178

1.0063478

0.9999738

1.0101761

0.9990695

0.9803742

0.9904311

\({V}_{10}\) (pu)

0.9858529

0.9984143

1.0095494

1.0232675

0.9539494

0.9774348

0.94

1.0032765

\({V}_{12}\) (pu)

1.0025731

0.9984161

1.0047479

1.0056947

1.0192324

1.0011642

0.94

1.0177339

\({V}_{15}\) (pu)

0.9814197

0.9986413

0.9951419

0.9981086

0.9869603

0.9875277

0.94

1.0003939

\({V}_{18}\) (pu)

0.9821415

0.9984084

1.0085976

1.0020251

0.9638907

0.9920888

0.94

1.005803

\({V}_{19}\) (pu)

0.9828388

0.9984333

0.9951357

0.9974385

0.9473387

0.9880534

0.94

0.999233

\({V}_{24}\) (pu)

1.0002703

0.9984191

1.0041248

1.0041834

1.0559348

0.9958298

0.94

0.9965601

\({V}_{25}\) (pu)

0.9693263

0.9984245

1.0137953

1.0001874

0.984345

1.0279515

1.0203475

1.0362323

\({V}_{26}\) (pu)

0.9868014

0.9988742

0.9941351

0.9996746

0.9614965

0.9773494

0.9966932

1.0116661

\({V}_{27}\) (pu)

0.9963548

0.9984343

1.0028144

1.0136335

1.0033783

1.0011873

1.004309

0.999399

\({V}_{31}\) (pu)

1.0089892

0.9984143

1.0063028

1.0117597

1.0515308

1.0040872

0.94

0.9838394

\({V}_{32}\) (pu)

0.9900412

0.9984248

1.0074586

1.004889

1.0221506

1.0025537

0.9799564

0.9970802

\({V}_{34}\) (pu)

0.9992201

0.9984214

1.004583

1.0005623

1.0130548

0.9909856

0.94

1.004611

\({V}_{36}\) (pu)

0.9955713

0.9984108

0.9961919

1.000895

0.9954976

0.9873726

0.94

0.9987836

\({V}_{40}\) (pu)

0.9909765

0.9984272

1.0076372

1.0040013

1.0489144

0.9964579

0.9760751

0.9973915

\({V}_{42}\) (pu)

1.0226928

0.9984107

0.9973069

0.9876911

0.9447065

1.0105486

1.06

0.9985096

\({V}_{46}\) (pu)

1.0033952

0.9984333

0.9915431

1.0023346

1.0219538

0.972747

1.0244405

1.0017381

\({V}_{49}\) (pu)

1.0046369

0.9984325

1.0049397

0.9970443

1.0335898

1.0007238

0.94

1.00432

\({V}_{54}\) (pu)

0.9882552

0.9984143

1.0012355

1.0246685

1.0033544

0.9981182

0.94

1.0188926

\({V}_{55}\) (pu)

0.9796473

0.9984087

1.0004274

1.0174276

1.0141796

0.9921352

0.94

1.0106656

\({V}_{56}\) (pu)

0.982843

0.9984145

0.9999944

1.0182261

1.0148105

0.9933081

0.94

1.0132038

\({V}_{59}\) (pu)

0.9884191

0.9984095

0.998566

1.0130436

0.9450411

0.9962512

0.94

1.0044433

\({V}_{61}\) (pu)

1.003285

0.9989294

1.0094787

1.0004497

0.94

1.0051671

0.94

1.005104

\({V}_{62}\) (pu)

0.99553

0.9988909

0.9972736

0.9971621

0.978322

0.9929546

0.94

1.0037656

\({V}_{65}\) (pu)

1.013367

0.9984248

1.0087647

1.0123909

1.0006405

1.0069515

1.0045633

1.0085153

\({V}_{66}\) (pu)

1.0088278

0.9985688

0.997576

1.0195755

1.0175064

0.9950526

0.94

1.0186962

\({V}_{69}\) (pu)

1.0098445

0.9984135

1.0091532

1.0455458

0.9710221

1.0448585

0.9945533

1.0148784

\({V}_{70}\) (pu)

0.9954592

0.9984138

0.9993955

1.0120441

0.9604082

1.0184288

1.0290654

1.0030583

\({V}_{72}\) (pu)

1.0007014

0.9984236

1.0080069

0.9744352

0.9672843

0.9616424

1.06

0.9905373

\({V}_{73}\) (pu)

0.9943003

0.9984269

0.9978239

1.0203373

0.9536638

1.026781

1.0229002

1.0081383

\({V}_{74}\) (pu)

0.9861425

0.9987103

0.9991108

1.006167

1.0180586

1.0004575

0.94

0.9862239

\({V}_{76}\) (pu)

0.9763866

0.9984097

0.9975045

1.0008878

1.0029675

0.9729707

0.94

0.9769082

\({V}_{77}\) (pu)

0.9854762

0.9984191

1.0039189

1.0131573

0.9536917

0.998818

0.94

1.0014511

\({V}_{80}\) (pu)

0.9847373

0.9984173

1.003484

1.0051557

1.0472714

1.0240386

0.9479476

1.0314414

\({V}_{85}\) (pu)

0.9963885

0.9984133

1.0117173

1.0042518

1.011343

0.9956523

0.9583123

1.0089568

\({V}_{87}\) (pu)

1.0022364

0.9986272

1.0035426

1.0095323

0.9456332

0.984938

0.94

1.0296648

\({V}_{89}\) (pu)

1.0100382

0.9984278

1.0080348

1.0150081

0.9417234

0.9983099

0.9812302

1.0111174

\({V}_{90}\) (pu)

0.9742785

0.9988189

1.0001894

0.9920549

0.947558

0.9483727

1.06

0.9911235

\({V}_{91}\) (pu)

1.0044681

0.9988556

1.0088354

1.0128867

0.9665145

1.0139387

1.0286086

1.0091032

\({V}_{92}\) (pu)

0.990492

0.9984068

1.0064261

0.9933333

1.0371885

0.9960263

0.9711364

0.9994063

\({V}_{99}\) (pu)

0.984746

0.998423

0.9970975

1.019621

1.0279531

1.0338292

0.9622277

0.9940666

\({V}_{100}\) (pu)

1.0024384

0.9984352

1.0103693

0.9998407

1.0161768

1.0123685

0.94

1.0165398

\({V}_{103}\) (pu)

1.0108807

0.9984246

1.0058325

1.0013786

1.0128002

1.0025423

1.0212102

1.0206343

\({V}_{104}\) (pu)

1.010391

0.9984311

1.0046151

1.0045754

1.0129173

0.9916926

1.0088001

1.0032501

\({V}_{105}\) (pu)

1.0082642

0.9989441

0.9992869

1.0050659

0.9944849

0.9914421

0.9719043

1.0027299

\({V}_{107}\) (pu)

0.9961495

0.9988312

0.9977614

1.0073907

0.9960014

0.9784303

0.9866448

1.0120958

\({V}_{110}\) (pu)

0.9969265

0.9989334

1.0020228

1.0075833

1.0315338

0.9914322

1.03678

1.0018077

\({V}_{111}\) (pu)

1.0030909

0.9984206

1.0005508

0.9962088

0.954251

0.9915563

1.0320566

1.0025809

\({V}_{112}\) (pu)

0.9974033

0.9984158

1.006686

1.0278147

1.0472102

1.001725

1.06

0.9917132

\({V}_{113}\) (pu)

0.9874671

0.9984394

1.0050653

0.9916138

0.9926523

0.996391

0.965744

1.0059397

\({V}_{116}\) (pu)

0.9797036

0.9984283

0.9979973

1.0059574

1.0182969

0.9783232

1.0427597

0.9993608

\({T}_{8}\) (8–5)

0.9646251

1.0073863

0.9909622

0.9894006

1.0329934

1.0421873

0.9133254

0.9931396

\({T}_{32}\) (26–25)

1.0507266

1.0083841

0.9944273

1.0357593

1.0281805

0.9842488

0.9742704

0.9737324

\({T}_{36}\) (30–17)

1.0441545

0.9897431

0.9527715

0.96343

0.9759361

0.9614697

0.9

0.9798013

\({T}_{51}\) (38–37)

0.9675287

1.006082

0.9898559

1.0076214

0.9228551

0.9887479

1.0741438

0.9963579

\({T}_{93}\) (63–59)

1.0265237

0.989855

0.9879769

0.9547485

0.9744587

0.9859937

0.9255106

0.9486617

\({T}_{95}\) (64–61)

1.0279707

1.0066901

0.9675022

0.9932502

1.0774062

1.0033831

0.9465455

1.0191361

\({T}_{102}\) (65–66)

0.9868859

0.9878702

0.988658

0.9838461

0.9

0.9933303

1.089632

0.9780493

\({T}_{107}\) (68–69)

0.976303

1.0091634

0.9944131

0.9976022

1.0153946

0.9644926

0.9

0.9688566

\({T}_{127}\) (81–80)

0.9801705

0.9985024

0.9791968

0.9761716

1.05387

0.9827831

0.9426853

0.9507009

\({Q}_{34}\) (MVAR)

13.414654

11.508929

3.8936043

10.133201

20.549395

14.796015

8.4267986

9.7466545

\({Q}_{44}\) (MVAR)

13.226379

10.875672

6.6314131

12.189323

29.907192

17.418497

13.620993

15.765508

\({Q}_{45}\) (MVAR)

8.3579497

15.414236

13.565095

13.702685

20.334043

15.08956

24.974683

4.4859842

\({Q}_{46}\) (MVAR)

13.860582

7.9251187

20.930132

9.0197959

20.2594

15.830149

27.136152

7.9177454

\({Q}_{48}\) (MVAR)

10.464785

25.229334

14.90824

20.695533

9.241588

17.687591

15.737777

9.3538359

\({Q}_{74}\) (MVAR)

14.679007

27.999099

22.236306

13.895714

10.059794

14.299266

18.367341

5.9104357

\({Q}_{79}\) (MVAR)

8.8558048

7.7045075

23.556863

21.378317

14.184079

15.710789

30

20.972436

\({Q}_{82}\) (MVAR)

13.041468

18.992988

24.446815

15.400184

16.977218

16.488823

14.261494

10.13504

\({Q}_{83}\) (MVAR)

25.539978

25.273233

20.906037

19.063106

10.862795

8.1012615

16.847727

10.437319

\({Q}_{105}\) (MVAR)

17.153076

14.202801

26.429986

5.7080354

5.7350681

2.8423988

14.49448

17.289959

\({Q}_{107}\) (MVAR)

14.373873

8.6060195

12.35709

16.736318

15.991045

21.61781

21.622876

12.139966

\({Q}_{110}\) (MVAR)

16.793366

25.18489

26.728857

16.698825

21.185935

8.4194362

15.993423

17.490426

Fuel cost ($/h)

154,450.00

155,710.00

166,130.00

150,250.00

153,300.00

143,650.00

167,490.00

148,630.00

Power losses (MW)

73.731774

104.54867

54.434108

61.367125

113.36205

70.485916

150.1514

66.368218

Voltage deviation (pu)

0.8664091

0.6341614

0.4264959

0.4813462

1.1283125

0.609969

3.2328398

0.4621417

Iterations time (s)

186.96055

4605.978

658.75

388.9675

184.912

264.998

177.3198

244.5468