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CLOSE THIS BOOKCircuits, Formulas and Tables Electrical Engineering - Basic vocational knowledge (Institut fr Berufliche Entwicklung, 201 p.)
VIEW THE DOCUMENT(introduction...)
VIEW THE DOCUMENTPreface
1. Selected Graphical Symbols of Electrotechnology
2. Bell Circuits
3. Basic Circuits of Illumination Engineering
4. Electrical Machines
5. Contactor Circuits
6. Rectifier Circuits
7. Measurement Circuits
VIEW THE DOCUMENT8. Protective Circuits
9. Circuits in Motor Vehicles
VIEW THE DOCUMENT10. Tables
11. Basic symbols and formulas of electrical engineering

10. Tables

Table 1 Natural values of the trigonometric functions sine and cosine

sin 0°...sin 15°

minute

0

6

12

18

24

30

36

42

48

54

60


degree

,0

,1

,2

,3

,4

,5

,6

,7

,8

,9

(1,0)


0

0,00000

00175

00349

00524

00698

00873

01047

01222

01396

01571

01745

89

1

01745

01920

02094

02269

02443

02618

02792

02967

03141

03316

03490

88

2

03490

03664

03839

04013

04188

04362

04536

04711

04885

05059

05234

87

3

05234

05408

05582

05756

05931

06105

06279

06453

06627

06802

06976

86

4

06976

07150

07324

07498

07672

07846

08020

08194

08368

08542

08716

85

5

08716

08889

09063

09237

09411

09585

09758

09932

10106

10279

10453

84

6

10453

10626

10800

10973

11147

11320

11494

11667

11840

12014

12187

83

7

12187

12360

12533

12706

12880

13053

13226

13399

13572

13744

13917

82

8

13917

14090

14263

14436

14608

14781

14954

15126

15299

15471

15643

81

9

15643

15816

15988

16160

16333

16505

16677

16849

17021

17193

17365

80

10

0,17365

17537

17708

17880

18052

18224

18395

18567

18738

18910

19081

79

11

19081

19252

19423

19595

19766

19937

20108

20279

20450

20620

20791

78

12

20791

20962

21132

21303

21474

21644

21814

21985

22155

22325

22495

77

13

22495

22665

22835

23005

23175

23345

23514

23684

23853

24023

24192

76

14

24192

24362

24531

24700

24869

25038

25207

25376

25545

25713

25882

75


(1,0)

,9

,8

,7

,6

,5

,4

,3

,2

,1

,0

degree


60

54

48

42

36

30

24

18

12

6

0

minute

cos 75°...cos 90°

Natural values of the trigonometric functions sine and cosine

sin 15°...30°

minute

0

6

12

18

24

30

36

42

48

54

60


degree

,0

,1

,2

,3

,4

,5

,6

,7

,8

,9

(1,0)


15

25882

26050

26219

26387

26556

26724

26892

27060

27228

27396

27564

74

16

27564

27731

27899

28067

28234

28402

28569

28736

28903

29070

29237

73

17

29237

29404

29571

29737

29904

30071

30237

30403

30570

30736

30902

72

18

30902

31068

31233

31399

31565

31730

31896

32061

32227

32392

32557

71

19

32557

32722

32887

33051

33216

33381

33545

33710

33874

34038

34202

70

20

0,34202

34366

34530

34694

34857

35021

35184

35347

35511

35674

35837

69

21

35837

36000

36162

36325

36488

36650

36812

36975

37137

37299

37461

68

22

37461

37622

37784

37946

38107

38268

38430

38591

38752

38912

39073

67

23

39073

39234

39394

39555

39715

39875

40035

40195

40355

40514

40674

66

24

40674

40833

40992

41151

41310

41469

41628

41787

41945

42104

42262

65

25

42262

42420

42578

42736

42894

43051

43209

43366

43523

43680

43837

64

26

43837

43994

44151

44307

44464

44620

44776

44932

45088

45243

45399

63

27

45399

45554

45710

45865

46020

46175

46330

46484

46639

46793

46947

62

28

46947

47101

47255

47409

47562

47716

47860

48022

48175

48328

48481

61

29

48481

48634

48786

48938

49090

49242

49394

49546

49697

49849

50000

60


(1,0)

,9

,8

,7

,6

,5

,4

,3

,2

,1

,0

degree


60

54

48

42

36

30

24

18

12

6

0

minute

cos 75°...60°

Natural values of the trigonometric functions sine and cosine

sin 30°...45°

minute

0

6

12

18

24

30

36

42

48

54

60


degree

,0

,1

,2

,3

,4

,5

,6

,7

,8

,9

(1,0)


30

0,50000

50151

50303

50453

50603

50754

50904

51054

51204

51354

51504

59

31

51504

51653

51803

51952

52101

52250

52399

52547

52696

52844

52992

58

32

52992

53140

53288

53435

53583

53730

53877

54024

54171

54317

54464

57

33

54464

54610

54756

54902

55048

55194

55339

55484

55630

55775

55919

56

34

55919

56064

56208

56353

56497

56641

56784

56928

57071

57215

57358

55

35

57358

57501

57643

57786

57928

58070

58212

58354

58496

58637

58779

54

36

58779

58920

59061

59201

59342

59482

59622

59763

59902

60042

60182

53

37

60182

60321

60460

60599

60738

60876

61015

61153

61291

61429

61566

52

38

61566

61704

61841

61978

62115

62251

62388

62524

62660

62796

62932

51

39

62932

63068

63203

63338

63473

63608

63742

63877

64011

64145

64279

50

40

0,64279

64412

64546

64679

64812

64945

65077

65210

65342

65474

65606

49

41

65606

65738

65869

66000

66131

66262

66393

66523

66653

66783

66913

48

42

66913

67043

67172

67301

67430

67559

67688

67816

67944

68072

68200

47

43

68200

68327

68455

68582

68709

68835

68962

69088

69214

69340

69466

46

44

69466

69591

69717

69842

69966

70091

70215

70339

70463

70587

70711

45


(1,0)

,9

,8

,7

,6

,5

,4

,3

,2

,1

,0

degree


60

54

48

42

36

30

24

18

12

6

0

minute

cos 60°...45°

Natural values of the trigonometric functions sine and cosine

sin 45°...60°

minute

0

6

12

18

24

30

36

42

48

54

60


degree

,0

,1

,2

,3

,4

,5

,6

,7

,8

,9

(1,0)


45

0,70711

70834

70957

71080

71203

71325

71447

71569

71691

71813

71934

44

46

71934

72055

72176

72297

72417

72537

72657

72777

72897

73016

73135

43

47

73135

73254

73373

73491

73610

73728

73846

73963

74080

74198

74314

42

48

74314

74431

74548

74664

74780

74896

75011

75126

75241

75356

75471

41

49

75471

75585

75700

75813

75927

76041

76154

76267

76380

76492

76604

40

50

0,76604

76717

76828

76940

77051

77162

77273

77384

77494

77605

77715

39

51

77715

77824

77934

78043

78152

78261

78369

78478

78586

78694

78801

38

52

78801

78908

79016

79122

79229

79335

79441

79547

79653

79758

79864

37

53

79864

79968

80073

80178

80282

80386

80489

80593

80696

80799

80902

36

54

80902

81004

81106

81208

81310

81412

81513

81614

81714

81815

81915

35

55

81915

82015

82115

82214

82314

82413

82511

82610

82708

82806

82904

34

56

82904

83001

83098

83195

83292

83389

83485

83581

83676

83772

83867

33

57

83867

83962

84057

84151

84245

84339

84433

84526

84619

84712

84805

32

58

84805

84897

84989

85081

85173

85264

85355

85446

85536

85627

85717

31

59

85717

85806

85896

85985

86074

86163

86251

86340

86427

86515

86603

30


(1,0)

,9

,8

,7

,6

,5

,4

,3

,2

,1

,0

degree


60

54

48

42

36

30

24

18

12

6

0

minute

cos 30°...45°

Natural values of the trigonometric functions sine and cosine sin

sin 60°...75°

minute

0

6

12

18

24

30

36

42

48

54

60


degree

,0

,1

,2

,3

,4

,5

,6

,7

,8

,9

(1,0)


60

0,86603

86690

86777

86863

86949

87036

87121

87207

87292

87377

87462

29

61

87462

87546

87631

87715

87798

87882

87965

88048

88130

88213

88295

28

62

88295

88377

88458

88539

88620

88701

88782

88862

88942

89021

89101

27

63

89101

89180

89259

89337

89415

89493

89571

89649

89726

89803

89879

26

64

89879

89956

90032

90108

90183

90250

90334

90408

90483

90557

90631

25

65

90631

90704

90778

90851

90924

90996

91068

91140

91212

91283

91355

24

66

91355

91425

91496

91566

91636

91706

91775

91845

91914

91982

92050

23

67

92050

92119

92186

92254

92321

92388

92455

92521

92587

92653

92718

22

68

92718

92784

92849

92913

92978

93042

93106

93169

93232

93295

93358

21

69

93358

93420

93483

93544

93606

93667

93728

93789

93849

93909

93969

20

70

0,93969

94029

94088

94147

94206

94264

94322

94380

94438

94495

94552

19

71

94552

94609

94665

94721

94777

94832

94888

94943

94997

95052

95106

18

72

95106

95159

95213

95266

95319

95372

95424

95476

95528

95579

95630

17

73

95630

95681

95732

95782

95832

95882

95931

95981

96029

96078

96126

16

74

96126

96174

96222

96269

96316

96363

96410

96456

96502

96547

96593

15


(1,0)

,9

,8

,7

,6

,5

,4

,3

,2

,1

,0

degree


60

54

48

42

36

30

24

18

12

6

0

minute

cos 15°...30°

Natural values of the trigonometric functions sine and cosine

sin 75°...90°

minute

0

6

12

18

24

30

36

42

48

54

60


degree

,0

,1

,2

,3

,4

,5

,6

,7

,8

,9

(1,0)


75

96593

96638

96682

96727

96771

96815

96858

96902

96945

96987

97030

14

76

97030

97072

97113

97155

97196

97237

97278

97318

97358

97398

97437

13

77

97437

97476

97515

97553

97592

97630

97667

97705

97742

97778

97815

12

78

97815

97851

97887

97922

97958

97992

98027

98061

98096

98129

98163

11

79

98163

98196

98229

98261

98294

98325

98357

98389

98420

98450

98481

10

80

0,98481

98511

98541

98570

98600

98629

98657

98686

98714

98741

98769

9

81

98769

98796

98823

98849

98876

98902

98927

98953

98978

99002

99027

8

82

99027

99051

99075

99098

99122

99144

99167

99189

99211

99233

99255

7

83

99255

99276

99297

99317

99337

99357

99377

99396

99415

99434

99452

6

84

99452

99470

99488

99506

99523

99540

99556

99572

99588

99604

99619

5

85

99619

99635

99649

99664

99678

99692

99705

99731

99731

99744

99756

4

86

99756

99768

99780

99792

99803

99813

99824

99834

99844

99854

99863

3

87

99863

99872

99881

99889

99897

99905

99912

99919

99926

99933

99939

2

88

99939

99945

99951

99956

99961

99966

99979

99974

99978

99982

99985

1

89

99985

99988

99990

99993

99995

99996

99998

99999

99999

1.00000

1.00000

0


(1,0)

,9

,8

,7

,6

,5

,4

,3

,2

,1

,0

degree


60

54

48

42

36

30

24

18

12

6

0

minute

cos 15°...0°

Table 2 Resistances and weights of copper wires

Diameter

Cross section

Resistance per km with 15°(288 k)

Length of a wire of 1 W

Weight per km

Length of a wire of 1 kg

mm

mm2

W

m

kg

m

0,1

0,0079

2215

0,4514

0,070

14306

0,2

0,0314

553,9

1,856

0,280

3577

0,3

0,0707

246,2

4,062

0,629

1590

0,4

0,1257

138,5

7,222

1,118

894,1

0,5

0,1964

88,62

11,28

1,748

572,2

0,6

0,2827

61,54

16,25

2,516

397,4

0,7

0,3848

45,21

22,12

3,425

292,0

0,8

0,5026

34,62

28,89

4,474

223,5

0,9

0,6362

27,35

36,56

5,662

176,6

1,0

0,7854

22,15

45,14

6,990

143,1

1,1

0,9503

18,31

54,62

8,458

118,2

1,2

1,1310

15,38

65,00

10,07

99,35

1,3

1,3273

13,11

76,28

11,81

84,65

1,4

1,5394

11,30

88,47

13,70

72,99

1,5

1,7671

9,846

101,6

15,73

63,58

1,6

2,0106

8,654

115,6

17,89

55,88

1,7

2,2698

7,666

130,5

20,20

49,50

1,8

2,5447

6,838

146,2

22,65

44,15

1,9

2,8353

6,137

162,9

25,23

39,63

2,0

3,1416

5,539

180,6

27,96

35,77

2,1

3,4636

5,024

199,1

30,83

32,44

2,2

3,8013

4,577

218,5

33,83

29,56

2,3

4,1548

4,188

238,8

36,98

27,04

2,4

4,5239

3,846

260,0

40,26

24,84

2,5

4,9087

3,545

282,1

43,69

22,89

2,6

5,3093

3,277

305,1

47,25

21,16

2,7

5,7256

3,039

329,1

50,96

19,62

2,8

6,1575

2,826

353,9

54,80

18,25

2,9

6,6052

2,634

379,6

58,79

17,01

3,0

7,0686

2,462

406,2

62,91

15,90

3,1

7,5477

2,305

433,8

67,17

14,89

3,2

8,0425

2,164

462,2

71,58

13 79

3,3

8,5530

2,034

491,6

76,12

13,14

3,4

9,0792

1,916

521,8

80,80

12,38

3,5

9,6211

1,809

552,9

85,63

11,68

3,6

10,1790

1,709

585,0

90,59

11,04

3,7

10,752

1,618

617,9

95,69

10,45

3,8

11,341

1,534

651,8

100,9

9,907

3,9

11,946

1,457

686,5

106,3

9,406

4,0

12,566

1,385

722,2

111,8

8,941

4,1

13,203

1,318

758,8

117,5

8,510

4,2

13,854

1,256

796,2

123,3

8,110

4,3

14,522

1,198

834,6

129,2

7,737

4,4

15,205

1,144

873,9

135,3

7,389

4,5

15,904

1,094

914,0

141,5

7,065

4,6

16,619

1,047

955,1

147,9

6,761

4,7

17,349

1,003

997,1

154,4

6,476

4,8

18,096

0,9616

1040

161,1

6,209

4,9

18,857

0,9227

1084

167,8

5,958

5,0

19,635

0,8862

1128

174,7

5,722

5,1

20,428

0,8518

1174

181,8

5,500

5,2

21,237

0,8193

1221

189,0

5,291

5,3

22,062

0,7887

1268

196,4

5,093

5,4

22,902

0,7598

1316

203,8

4,906

5,5

23,758

0,7324

1365

211,5

4,729

5,6

24,630

0,7065

1416

219,2

4,562

5,7

25,518

0,6819

1467

227,1

4,403

5,8

26,421

0,6586

1518

235,1

4,253

5,9

27,340

0,6463

1571

243,3

4,110

6,0

28,274

0,6154

1625

251,6

3,974

6,1

29,225

0,5974

1680

260,1

3,845

6,2

30,191

0,5763

1735

268,7

3,722

6,3

31,172

0,5582

1792

277,4

3,604

6,4

32,170

0,5409

1849

286,3

3,493

6,5

33,183

0,5244

1907

295,3

3,386

6,6

34,212

0,5086

1966

304,5

3,284

6,7

35,257

0,4935

2026

313,8

3,187

6,8

36,317

0,4791

2087

323,2

3,094

6,9

37,393

0,4653

2149

332,8

3,005

Table 3 Specific resistance and conductivity of essential materials at 20° C (193 K)

Material

Spec. Resistance

Conductivity


Aluminium, soft

0,028

36

Lead

0,2

5

Gold

0,022

45

Copper E-Cu, soft

0,01754

57

Brass Ms 58

0,059

17

Brass Ms 63

0,071

14

Nickel silver NiMs

0,5...0,15

2,0...6,7

Platinum

0,098

10,2

Mercury

0,960

1,042

Silver

0,01629

61,4

Steel, ingot iron

0,12

8

Grey iron

1

1

Tungsten

0,059

17

Zinc

0,062

16


Resistance alloy:


Chrome nickel

1...1,2

1...0,83

Constantan (WM 50)

0,5

2

Manganin

0,4

2,5

Niccolite

0,5

2

Al-Cr-Steel

1,4

0,7

Arc lamp carbon

13...100

0,08...0,01

Table 4 Temperature coefficient

Material

Temperature coefficient of an electrical resistance between 0° and 100° C (173 and 273 K)

Aluminium

+0,0037

Aluminium bronze

+0,001

Lead

+0,00417

Iron

+0,0045

Electron


Constantan

0,00005

Copper

+0,0043

Manganin

+0,00001

Brass

+0,0015

Molybdenum

+0,0043

Nickel silver

+0,00007

Nickel

+0,0041

Niccolite

+0,00022

Platinum

+0,0039

Platinum-Rhodium (10 % Rh.)

+0,0017

Mercury

+0,00090

Silver

+0,0036

Steel

+0,0045... 0,005

Tantalum

+0,0034

Bismuth

+0,0037

Tungsten

+0,004-1

Zinc

+0,0039

Tin

+0,0042

Table 5 Values of current-carrying capacity and maximum permissible rated current of the overcurrent protection device for lines with copper conductor and plastic, silicone-rubber or glass-silk insulation

Conductor cross-sectional area

Current-carrying capacity

Rated current of overcurrent protection device


A

A

mm2

1

2

3

4

1

2

3

4

0,5

12

10

9

8

10

10

6

6

0,75

16

13

12

11

16

10

10

10

1,0

20

17

15

14

20

16

10

10

1,5

26

22

20

18

25

20

20

16

2,5

36

31

27

24

36

25

25

20

4

50

43

38

34

50

36

36

25

6

63

54

50

46

63

50

50

36

10

86

74

64

59

80

63

63

50

16

117

101

87

80

100

100

80

80

25

155

133

116

105

125

125

100

100

35

192

165

144

130

160

160

125

125

50

240

206

180

163

224

200

160

160

70

300

259

225

204

300

250

224

200

95

365

314

274

248

355

300

250

224

120

425

366

319

289

425

355

300

250

150

480

413

360

326

425

355

355

300

185

542

466

406

368

500

425

355

355

240

640

551

480

435

600

500

425

425

300

735

633

551

500

600

600

500

500

These values also apply to three-phase four-wire systems with neutral conductor and separate protective conductor (five-wire systems).

Pay attention to the current-carrying capacity factors according to the Tables 9 to 12.

Table 6 Values of current-carrying capacity and maximum permissible rated current of the overcurrent protection device for lines with aluminium conductor and plastic, silicone-rubber and glass-silk insulation

Conductor cross- sectional area

Current-carrying capacity

Rated current of overcurrent protection device


A

A


for number of cores carrying current in operation

mm2

1

2

3

4

1

2

3

4

2,5

27

23

30

18

25

20

20

16

4

37

32

28

24

36

25

25

20

6

50

43

37

34

50

36

36

25

10

67

57

50

46

63

50

50

36

16

90

77

67

61

80

63

63

50

25

120

103

90

81

100

100

80

80

35

148

127

111

100

125

125

100

100

50

187

161

140

127

160

160

125

125

70

231

200

173

154

200

200

160

125

95

282

243

212

191

250

224

200

160

120

328

283

246

223



224

200

150

376

325

283

249

355

300

250

224

185

480

370

322

292

425

355

300

250

240

502

492

376

342

500

425

355

300

300

578

497

433

395

500

425

425

355

Use:

With more than one conductor (core), the current-carrying capacity and the rated current of the overcurrent protection device are reduced as stated above.

The values also apply to three-phase four-wire systems with neutral conductor and separate protective conductor (five-wire systems).

Pay attention to the current-carrying capacity factors according to the tables 9 to 12.

Table 7 Values of current-carrying capacity and maximum permissible rated current of the overcurrent protection device for rubber-insulated lines with copper conductor

Conductor cross-sectional area

Current-carrying capacity

Rated current of overcurrent protection device


A

A


for number of cores carrying current in operation

mm2

1

2

3

4

1

2

3

4

0,5

11

9

9

8

10

6

6

6

0,75

15

12

11

10

10

10

10

10

1

19

16

14

13

16

16

10

10

1,5

24

21

19

17

20

20

16

16

2,5

34

29

25

23

25

25

25

20

4

47

41

36

32

36

36

36

25

6

60

51

47

43

50

50

36

36

10

82

70

61

56

80

63

50

50

16

111

96

83

76

100

80

80

63

25

147

126

110

100

125

125

100

100

35

182

157

137

124

160

125

125

100

50

229

196

171

155

224

160

160

125

70

285

246

214

194

250

224

200

160

95

347

300

260

236

300

300

250

224

120

404

348

303

274

355

300

300

250

150

456

393

342

310

425

355

300

300

185

515

442

385

350

500

425

355

300

240

608

523

456

413

600

500

425

355

300

700

602

523

475

600

600

500

425

Use:

With more then one conductor (core), the current-carrying capacity and the rated current of the overcurrent protection device are reduced as stated above.

The values also apply to three-phase four-wire systems with neutral conductor and separate protective conductor (five-wire systems).

Pay attention to the current-carrying capacity factors according to the Tables 9 to 12.

Table 8

Values of current-carrying capacity and maximum permissible rated current of the overcurrent protection device for rubber-insulated lines with aluminium conductor

Conductor cross-sectional area

Current-carrying capacity

Rated current of overcurrent protection device


A

A


for number of cores carrying current in operation

mm2

1

2

3

4

1

2

3

4

2,5

26

22

19

17

25

20

16

16

4

35

30

27

23

25

25

25

20

6

47

41

35

32

36

36

25

25

10

63

54

47

44

63

50

36

36

16

85

73

64

58

80

63

63

50

25

144

98

85

77

100

80

80

63

35

141

121

105

95

125

100

100

80

50

178

153

133

121

160

125

125

100

70

220

190

164

146

200

160

160

125

95

268

231

202

182

250

224

200

160

120

312

269

234

212

300

250

224

200

150

358

309

269

236

355

300

250

224

185

408

351

306

278

355

300

300

250

240

477

410

358

325

425

355

355

300

300

550

472

412

374

500

425

355

355

Use:

With more than one conductor (core), the current-carrying capacity and the rated current of the overcurrent protection device is reduced as sated above.

The values also apply to three-phase four-wire systems with neutral conductor and separate protective conductor (five-wire systems).

Pay attention to the current-carrying capacity factors according to the Tables 9 to 12.

Current-carrying capacity factors

These are factors by which the values of current-carrying capacity given in the Tables 6 to 8 have to be multiplied when special conditions are given.

These conditions may be:

- bundled lines installed freely in air
- bundled lines installed in pipes or conduit subways
- multicore lines with more than 4 conductors (cores)
- multicore lines installed in a piled-up arrangement which are loaded at the same time
- ambient temperatures which deviate from 25° C (298 K) and are higher

If multicore lines are fastened individually by means of spacing clips side by side, the current-carrying capacity factor of 0,9 is applicable irrespective of the number of lines placed side by side.

In the case of ambient temperatures higher than 25° C (298 K), the limiting temperature for the conductor of the line used must be taken into consideration.

There are limiting temperatures of conductors

· of 60°C (333 K),
· of 70°C (343 K) and
· of 180°C (453 K).

If several current-carrying capacity factors are applicable, then the values of current-carrying capacity given in the Tables 6 to 8 must be multiplied by all of the applicable factors.

The rated current of the overcurrent protection device must be specified according to the newly calculated current-carrying capacity when factors of the current-carrying capacity are used.

In this event, the rated current of the overcurrent protection device must be below the value of the newly calculated current-carrying capacity of the line.

Table 9 Current-carrying capacity factors for single-core lines bunched and laid out as open-wire line, in pipe trench or service duct or for multi-core lines with more than 4 cores

Number of lines or cores

Current-carrying capacity factor

2

0,85

3

0,75

4

0,68

5

0,62

6

0,58

7

0,55

8

0,53

9

0,50

10

0,48

15

0,42

20

0,38

25

0,35

30

0,33

35

0,31

40

0,30

45

0,29

50

0,28

Table 10 Current-carrying capacity factors for bunched multi-core lines

Number of multi-core lines

Current-carrying capacity factors in case of


open-air bunching

direct side-by side arrangement on walls or ceilings

bunching in pipe trench or service duct

2

0,89

0,83

0,81

3

0,80

0,76

0,75

4

0,73

0,73

0,69

5

0,69

0,71

0,65

6

0,66

0,70

0,62

7

0,63

0,69

0,60

8

0,61

0,69

0,58

9

0,59

0,68

0,56

10

0,57

0,68

0,55

15

0,50

0,66

0,49

20

0,47

0,64

0,46

25

0,44

0,62

0,43

30

0,42

0,60

0,41

35

0,40

0,59

0,40

40

0,39

0,58

0,39

Table 11 Factors of current-carrying capacity in dependence of constant ambient temperatures for lines with a conductor limiting temperature in continuous operation of 60° C (333 K) and 70° C (343 K)

Ambient temperature

Current-carrying with a conductor capacity factors for lines limiting temperature of

°C

(K)

60°C (333 K)


70°C (343 K)

5

(278)


1,25


10

(283)


1,19


15

(288)


1,13


20

(293)


1,07


25

(298)


1,00


30

(303)

0,92


0,94

35

(308)

0,83


0,87

40

(313)

0,74


0,80

45

(318)

0,63


0,72

50

(323)

0,51


0,64

55

(328)

0,36


0,55

60

(333)

-


0,46

65

(338)

-


0,37

Table 12 Factors of current-carrying capacity in dependence of constant ambient temperatures for lines with a conductor limiting temperature of 180°C

Ambient temperature

Current-carrying capacity factor

Ambient temperature

Current-carrying capacity factor

°C

(K)


°C

(K)


55

(328)

1,00

120

(393)

0,69

60

(333)

0,98

130

(403)

0,63

70

(343)

0,94

140

(413)

0,56

80

(353)

0,90

150

(423)

0,49

90

(363)

0,85

160

(433)

0,40

100

(373)

0,80

170

(443)

0,28

110

(383)

0,75

175

(448)

0,20

Example:

A seven-core plastic-insulated line with copper conductor o and a conductor rated cross-sectional area of 1,5 mm is to be installed at a constant ambient temperature of 35°C (308 K). What is the current-carrying capacity of the line with a conductor limiting temperature of 70°C (343 K)?

Solution:

According to Table 5, the current-carrying capacity of one core is 26 A.

For 7 cores, the factor of current-carrying capacity is 0,55; at a constant ambient temperature of 35°G (308 K) the factor of current-carrying capacity is 0,87 (conductor limiting temperature 70°C or 343 K) according to Table 10.

Actual current-carrying capacity

26 A · 0,55 · 0,87 = 12 A.

Rated current for the overcurrent protection device is 10 A.

Table 13 Limiting temperature for conductors

Type of cable

Conductor limiting temperature


°C

(K)




continuously

at short-circuit

1-kV plastic cable

70

(343)

180

(453)

10-,20-,30-kV plastic cable

70

(343)

200

(473)

1-kV solid-type cable

80

(353)

200

(473)

10-kV solid-type cable

55

(328)

165

(438)

20-kV solid-type cable

55

(328)

145

(418)

30-kV solid-type cable

45

(318)

130

(408)

When selecting cables with respect to their current-carrying capacity, the following factors must be taken into consideration:

- The thermal resistance of the soil; it is dependent on the type of soil and the moisture content of the soil.

- Loaded cables, heating lines and the like installed in close vicinity.

- Heat retention due to air cushions, protective covers, in ducts, pipes or nests of tubes.

Table 14 Current-carrying capacity of 1-kV solid-type cables for individual installation, with reduced solid sheath and fully saturated impregnation

Rated cross-sectional area of conductor

Single -core cables

Two-core cables

Three-core and four-core cables

mm2

Cu

Al

Cu

Al

Cu

Al

1,5

-

-

30

-

25

-

2,5

-

-

35

30

30

25

4

-

-

45

35

40

30

6

-

-

60

45

55

40

10

-

-

85

65

75

60

25

-

-

145

115

125

100

50

285

230

215

175

185

150

70

350

280

260

210

225

180

120

495

395

350

280

315

250

185

630

510

450

360

410

330

240

740

590

525

420

475

380

300

840

675

590

470

545

435

400

1000

800

700

565

645

515

500

1140

910

-

-

-

-

1000

1740

1390

-

-

-

-

Table 15 Current-carrying capacity of three unarmoured single-core solid-type cables with lead sheath, fully impregnated, in three-phase systems, separately lying side by side

Nominal cross-section of the conductor

1 kV


Current - carrying capacity in A

mm2

Cu

Al

50

250

200

70

300

240

120

410

330

185

510

405

240

575

460

300

640

510

400

725

580

500

790

630

1000

950

805

The values of Table 15 are applicable to cables lying side by side in a clearance of about 7 cm, in consideration of the metallic sheath losses in case of cable sheaths short-circuited at both cable ends.

The current-carrying capacity of three unarmoured single-core cables with A1-sheath separately lying side by side amounts to 90 % of the values according to Table 15.

Table 16 Current-carrying capacity of three unarmoured single-core solid-type cables with lead sheath, non-draining, in three-phase systems, separately lying side by side

Nominal cross-section of the conductor

1 kV

mm2

Current-carrying capacity in A


Cu

Al

50

250

200

70

300

240

120

410

330

185

510

405

240

575

460

300

640

510

400

725

580

500

790

630

1000

950

805

The values of Table 16 are applicable to cables lying side by side in a clearance of about 7 cm, in consideration of the metallic sheath losses in case of cable sheaths short-circuited at both cable ends.

The current-carrying capacity of three unarmoured single-core non-draining cables with Al-sheath separately lying side by side amounts to 90 % of the values according to Table 16.

The current-carrying capacity of three touching single-core non-draining cables with Al-sheath arranged in a triangle amounts to 105 % of the values according to Table 16.

Table 17 Current-carrying capacity of 1-kV-plastic cables

Nominal cross-section of the conductor

Single-core cables

Two-core cables

Three- and four-core cables


Current-carrying capacity

in A


mm2

Cu

Al

Cu

Al

Cu

Al

1,5

-

-

25

-

20

-

2,5

-

-

30

25

25

20

4

-

-

40

50

35

25

6

-

-

55

40

45

35

10

-

-

75

55

65

50

25

-

-

120

95

110

90

50

260

210

-

-

165

125

70

315

250

-

-

200

155

120

445

360

-

-

285

220

185

570

455

-

-

370

285

240

665

530

-

-

430

335

300

755

605

-

-

-

-

400

880

720

-

-

-

-

500

990

800

-

-

-

-

The carrying capacity specified in the Tables 14...17 is to be reduced to the following specified percentages in case of deviations from the mentioned conditions of installation.

Table 18 Reduction in case of bunched multi-core cables in three-phase systems and cables in direct current systems

Number of cables in the trench


2

3

4

5

6

8

10

Carrying capacity in

%

90

80

75

70

65

62

60

The carrying capacity of cables under protective hoods diminishes to 90 % of the values found out in application of other reductions (see Tables 18...25).

The reductions are applicable to cables lying side by side in a clearance of about 7 cm.

Table 19 Reduction in case of bunched single-core cables in three-phase systems

Number of systems in the trench

2

3

4

Carrying capacity in %

80

75

70

The reductions are applicable to single-core cables lying side by side in a clearance of about 7 cm.

The values of the Tables 20 and 21 are applicable to cables in unarmoured cement pipes in the earth with a clear interior diameter of about 150 mm and 20 mm wall thickness in an horizontal arrangement with reciprocal touch and an outer diameter of 50 mm.

Table 20 Reduction in case of multi-core cables and single-wire cables in single pipes bunched in a triangle

Number of pipes

1

2

3

4

5

6

7

8

9

10

Carrying capacity of the cables in %

80

72

68

65

63

61

60

59

58

57

Table 21 Reduction, in case of single-core cables in single pipes in three-phase systems

Number of pipes

3

6

9

Number of systems

1

2

3

Carrying capacity of the cables in %

85

76

72

Table 22 Reduction in case of bunched cables in the open air

Cable distance

Carrying capacity in %


3 cables or 3 cable systems

6 cables or 6 cables systems

Space between the cables is equal to the cable diameter

93

87

No space between the cables (reciprocal touch)

81

74

Table 23 Reduction in case of an ambient temperature for plastic cables deviating from 20°C

Rated voltage

Carrying capacity in % in case of an ambient temperature of °C

kV

5

10

15

20

25

30

35

40

1

115

110

105

100

95

89

84

77

Example of calculation:

For the transmission of 1,25 MVA with an operating voltage of 6 kV three-phase current a cable is required. This cable is to be hung by means of an auxiliary cable side by side with two cables hanging already in a shaft. The space between the cables is equal to the cable diameter. The ambient temperature is 30°C.

Solution:

A three-core cable with screened cores and with non-draining, intensified insulation is to be chosen.

Table 24 Reduction in case of an ambient temperature for solid-type cables deviating; from 20 %

Rated voltage kV

Carrying capacity in % in case of an ambient temperature of °C


5

10

15

20

25

30

35

40

1

112

108

104

100

96

91

87

82

10,20

120

113

107

100

93

85

76

65

30

126

118

110

100

90

78

63

45

Occuring factors of reduction:

- 93 % for laying three cables side by side (space between the cables = cable diameter, see Table 22).

- 85 % for raised ambient temperature of 30 % (see Table 23).

Total reduction factor = 0,93 · 0,85 » 0,79

Table 25 Continuous carrying capacity of the most important overhead-line materials for an over temperature of 40°C

Cable cross section

Copper

Pure aluminium

Aldrey

Steel-aluminium





1:6

1:4

mm2

A

A

A

A

A

16

115

92

88

-

-

25

151

121

115

-

-

35

174

149

142

145

225

501)

234

187

178

170

300

502)

231

185

176

-

-

70

282

226

215

235

355

95

357

283

269

290

440

120

411

329

313

345

505

150

477

382

363

400

560

185

544

435

414

455

650

2403)

630

502

479

-

-

2404)

641

513

488

530

770

300

747

598

568

615

-

1) 7-wire (1 layer)
2) 19-wire (2 layers)
3) 37-wire (3 layers)
4) 61-wire (4 layers)

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