06 determining conductor cross sectional areas

507

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Industrial electrical network design guide T & D 6 883 427/AE

6. Determining conductor cross-

sectional areas

508




6. DETERMINING CONDUCTOR CROSS-SECTIONAL AREAS

Owing to the respective characteristics of LV and MV conductors, they have been dealt with in

separate paragraphs.

6.1. Determining conductor cross-sectional areas and choosing protective

devices in low voltage

n definition of terms relating to low voltage wiring systems

(Insulated) cable

Assembly comprising:

- one or more insulated conductors

- their eventual individual screening

- any eventual assembly protection

- any eventual protective shielding

It may also comprise one or several bare conductors.

Multi-core cable

Cable comprising more than one conductor, which may eventually include bare conductors.

Note: the term three-core cable is used to designate the cable making up the phases of a three-phase

system.

Single-core cable

Cable comprising a single insulated conductor.

Note: the term single-core cable is especially used to designate a cable making up one of the phases of a

three-phase system.

Wiring system

Assembly made up of one or more electric conductors and the devices ensuring their fixation and, if

necessary, their mechanical protection.

Cable channel

Ventilated or enclosed duct located above or in the ground, having dimensions preventing persons from

moving around inside it but allowing access to the cables over their entire length during and after

installation.

Note: a cable channel may or may not form part of the building construction.

Cable tray

Holder made up of a base and sides but no cover.

Note: A cable tray may be perforated or unperforated.

Electrical circuit (of an installation)

All the electrical equipment of the installation fed from the same source and protected against

overcurrents by the same protective device(s).

509




(Insulated) conductor

Assembly comprising the conductor, its insulating envelope and eventual screens.

(Circular) conduit

Enclosed envelope, having a circular cross-section, designed for the installation or the replacement of

insulated conductors or cables by capstan, in electrical installations.

Ducting

Assembly of closed envelopes having a non circular cross-sectional area, designed for the installation or

the replacement of insulated conductors or cables by capstan, in electrical installations.

Brackets

Horizontal cable supports fixed at one of their ends, arranged from point to point and on which the cables

rest.

Design current of a circuit

Current to be carried in a circuit in normal service

(Continuous) current carrying capacity of a conductor

Maximum value of the current that, in given conditions, can continuously flow in a conductor without its

steady-state operating temperature being higher than the specified value.

Cable ladder

Cable support made up of a series of non-touching elements firmly fixed to main vertical rods.

Sleeve (or tube)

Element surrounding wiring and providing it with extra protection in building passages (walls, partitions,

floor, ceiling) or in buried passages.

Sheath

Enclosure located above ground level having dimensions preventing persons from moving around inside

it but allowing access to the cables over their entire length. A sheath may or may not be built into the

masonry.

Trough

Assembly of envelopes closed by a cover and ensuring mechanical protection of insulated conductors or

cables not installed or removed by a capstan and which allow other electrical equipment to be added .

Building void

Space in a structure or building parts which is only accessible at certain places.

Note: - spaces in walls, supported floors, ceilings and certain types of window or door frames and

jamb linings are examples of building voids.

- specially built building voids are also called "ducts".

510




6.1.1. Method principle

In compliance with the recommendations of IEC 364-4-43, the cross-sectional area of wiring

systems and the protective device must be chosen to meet several conditions necessary for

the security of the installation.

The wiring system must:

- carry the maximum design current and its normal transient peaks

- not generate voltage drops above the allowed values.

The protective device must:

- protect the wiring system against any overcurrents up to the short-circuit current

- ensure the protection of persons against indirect contact.

The logigram in figure 6-1 sums up the principle of the method which may be described by the

following stages:

1st stage:

- using the load power, the maximum design current IB is calculated and the rated current

In of the protective device is deduced from this

- the maximum short-circuit current Isc at the origin of the circuit is calculated and the

breaking capacity of the protective device is deduced from this.

2nd stage:

- depending on the installation conditions (installation method, ambient temperature, etc.),

the overall correction factor f is determined

- the suitable conductor cross-sectional area is chosen in relation to In and f .

511




3rd stage:

- the maximum voltage drop is checked

- the thermal withstand of the conductors in the event of a short circuit is checked

- for TN and IT systems, the maximum length relating to the protection of persons against

indirect contact is checked.

The conductor cross-sectional area meeting all these conditions is then chosen.

Note: an economic cross-sectional area larger than the cross-sectional area determined above maybe chosen if necessary (see § 6.3).

maximumwiring

system length chek

apparent power

to be carried

short-circuit

power at the origin

of the circuit

design currentshort-circuit

current

rated current of

protective deviceprotective device

breaking capacity

wiring system conductor

cross-sectional area

check of thermal

withstand in case

of short-circuit

maximumvoltage

drop check

confirmation of the choice of wiring system

cross-sectional area and its electrical protection

economiccross-sectional

area possibly chosen

installation

conditions

IT or TN earthing system

choice of

protective device

TT earthingsystem

upstream or

downstream

network

choice of

protective device

conductor cross-

sectional area

determination

In

IB Isc

Figure 6-1: wiring system cross-sectional area and protective device choice logigram

512




6.1.2. Determining the maximum design current

The maximum design current ( IB ) is defined according to the type of installation fed by the

wiring system.

In the case of individual power supply to a device, the current IB will be equal to the rated

current of the device being fed. On the other hand, if the wiring system feeds several devices,

the current IB will be equal to the sum of currents absorbed, taking into account the

installation utilisation and coincidence factors.

In the case of motor starting or cyclical operating conditions of loads (spot welding station,

see § 3.4.2), current inrushes must be taken into account when their thermal effects are

cumulated.

Some installations are subject to future extensions. The current corresponding to this

extension will be added to the existing value.

In direct current: IP

U

power consumed in W

duty voltage in V=

( )

( )

In alternating current: IS

U= in single-phase and I

S

U=

3 in three-phase.

S : apparent power consumed (VA)

U : . voltage between the two conductors for a single-phase power supply

. phase-to-phase voltage for a three-phase power supply

When high harmonic currents circulate in the conductor, they must be taken into account. In

order to choose the cross-sectional area, the following must therefore be taken:

I Ir m s p

p

. . . =

=

∞

∑ 2

1

1

(see § 8)

I1 : current value at 50 Hz (or 60 Hz)

I p : value of harmonic current of order p

For example, for a speed variatorI

I

r m s. . . .1

1 7≅

When there are compensation capacitors downstream of the wiring system, the design current

is determined as follows:

- assuming that compensation is in operation: in case of failure of the capacitors, the wiring

system is placed out of service

- assuming that compensation is out of service; in case of failure of the capacitors, the

conductor cross-sectional area is sufficient and availability is thus improved.

513




n factor taking into account the power factor and efficiency: a

The apparent power of a load is:

SP

Fp

=×η

in kVA

P : active power in kW

η : efficiency

Fp : power factor

We define the coefficient: aFp

=×1

η

When a current stripped of harmonics flows through the conductor, Fp = cosϕ .

n load utilisation factor: b

In an industrial installation, it is assumed that loads will never be used at their full power level.

A utilisation factor ( b ) is therefore introduced which generally varies from 0.3 to 1.

Without knowing the accurate values, we may take:

- b = 0 75. for motors

- b =1 for lighting and heating

514




n coincidence factor: c

In an industrial installation, the loads (of a workshop, for example) fed by the same wiring

system do not operate simultaneously in all cases. To take this phenomenon, which is linked to

the operating conditions of the installation, into account, the coincidence factor is applied to

the sum of the load powers in conductor sizing.

In the absence of precise indications resulting from experience of standard installations, the

values of tables 6-1 et 6-2 may be applied:

Use Coincidence factor c

Lighting 1

Lighting and air conditioning 1

Power outlets 0.1 to 0.2 (for a number > 20)

Table 6-1: coincidence factor for an administrative building

Number of circuits having

similar nominal currents

Coincidence factor

2 and 3 0.9

4 and 5 0.8

5 to 9 0.7

10 and more 0.6

Table 6-2: coincidence factor for industrial distribution switchboards

n factor taking into account possible future extensions: d

The value of factor d must be estimated according to the foreseeable extensions of the

installation.

In the absence of precise indications, the value 1.2 is often used.

515




n power conversion factor in current: e

The power conversion factor in current is:

- e = 8 in single-phase 127 V - e = 4 35. in single-phase 230 V

- e = 2 5. in three-phase 230 V - e =1.4 in three-phase 400 V

n maximum design current

The maximum design current is thus:

I P a b c d eB = × × × × ×

P : active power in kW

6.1.3. Choosing the protective device

516




n general rule

In compliance with IEC 364, a protective device (circuit-breaker or fuse) correctly fulfils its

function if the conditions outlined below are met.

o nominal or setting current

This must be between the design current and the current carrying capacity Ia of the wiring

system:

I I IB n a≤ ≤ , which corresponds to zone a in figure 6.2.

o conventional tripping current

This must meet the following relation:

I Ia2 1≤ .45 , which corresponds to zone b in figure 6.2.

case of circuit-breakers

- For domestic circuit-breakers, standard IEC 898 specifies:

I In2 1= .45

- For industrial circuit-breakers, standard IEC 947-2 specifies:

I Iset2 130= .

we thus have I In2 1≤ .45 (or Iset )

while I In a≤ (above condition)

The condition I Ia2 1≤ .45 (zone b ) is thus automatically met.

517




case of fuses

Standard IEC 269-1 specifies that I2 is the current which ensures that the fuse fuses in the

conventional time (1 h or 2 h); I2 is referred to as the conventional fusing current (see § 6.3.1

of the Protection guide).

I k In2 2= × where k2 16 1 9= . .to depending on the fuses

Let us define the coefficient k3 such that:

kk

32

1=.45

Thus, the condition I Ia2 1≤ .45 is met if:

II

kn

a≤3

For gG fuses:

- I An ≤10 à k3 = 1.31

- 10 25A I An< ≤ à k3 = 1.21

- I An > 25 à k3 = 1.10

o breaking capacity

This must be higher than the three-phase maximum short-circuit current ( )Isc 3 at its

installation point:

Breaking capacity Isc≥3, which corresponds to zone c in figure 6.2.

518




o associating protective devices

The use of a protective device having a breaking capacity below the short-circuit current at the

point where it is installed is permitted by standard IEC 364 under the following conditions:

- there is another device upstream having at least the necessary breaking capacity

- the energy that the device placed upstream lets through is lower than the energy that the

downstream device and wiring systems protected by these devices can withstand without

being damaged.

This possibility is implemented:

. in circuit-breaker/fuse associations

. in the cascading technique which uses the high current limitation capacity of certain

circuit-breakers (e.g. the Compact).

The possible associations resulting from actual tests performed in a laboratory are given in

manufacturer catalogues.

6.1.4. Current-carrying capacity of wiring systems

This is the maximum current that the wiring system can continuously carry without this being

prejudicial to its lifetime.

To determine this current, it is necessary to carry out the following:

- using tables 6-3 to 6-5, define the installation method, its associated selection number and

letter, and correction factors to be applied

- using the installation conditions, the correction factor values which must be applied are

determined (see tables 6-6 to 6-15)

- calculate the overall correction factor f equal to the product of the correction factors

- using table 6-16 for selection letters B, C, E, F and table 6-17 for selection letter D, the

maximum current I0 that the wiring system can carry under standard conditions

( f f0 10 1to = ) is determined

- calculate the maximum current that the wiring system can carry in relation to its installation

conditions: I f Ia = 0 .

519




n installation methods

Tables 6-3 to 6-5 give the main installation methods used in industrial networks.

For each installation method, the following is given:

- its associated selection number and letter

- the correction factors to be applied.

Factor f0 corresponds to the installation method; factors f f1 10to are explained below

(see tables 6-6 to 6-15).

Example Description N° Selection Correction factors

letter f0 to be applied

Single or multi-core cables with orwithout armour

- fixed on a wall 11 C 1 f1 f4 f5

- fixed to a ceiling 11A C 0.95 f1 f4 f5

- on unperforated trays 12 C 1 f1 f4 f5

cablesmulti-core single-

core

- on perforated trays runhorizontally or vertically 13 E F 1 f1 f4 f5

- on brackets 14 E F 1 f1 f4 f5

- on ladders 16 E F 1 f1 f4 f5

Table 6-3: installation methods for selection letters C, E and F

520






Single or multi-core cables inbuilding voids

21 B 0.95 f1 f4 f5--

Single or multi-core cables inconduits in building voids

22A B 0.865 f1 f4 f5 f6

Single or multi-core cables inducting in building voids

23A B 0.865 f1 f4 f5 f6

Single or multi-core cables inducting built into the masonry

24A B 0.865 f1 f4 f5 f7

Single or multi-core

conductors :

- in false ceilings

- in suspended ceilings

25 B 0.95 f1 f4 f5--

Single or multi-core cables introughs fixed to walls:

- run horizontally

31A B 0.9 f1 f4 f5--

- run vertically 32A B 0.9 f1 f4 f5--

Table 6-4: installation methods for selection letter B

521






Single or multi-core cables introughs built into floors 33A B 0.9 f1 f4 f5

--

Single or multi-core cables insuspended troughs 34A B 0.9 f1 f4 f5

--

Multi-core cables in enclosedchannels run horizontally orvertically

41 B 0.95 f1 f4 f5--

Single or multi-core cables inopen or ventilated channels

43 B 1 f1 f4 f5--

Table 6-4 (cont.): installation methods for selection letter B

522






Single or multi-core cables inconduits or in buried ducting 61 D 0.8 f2 f3 f8 f9

Single or multi-core cablesburied without any extramechanical protection 62 D 1 f2 f3 f10

--

Single or multi-core cablesburied with extra mechanicalprotection 63 D 1 f2 f3 f10

--

Table 6-5: installation methods for selection letter D

523




n correction factors for ambient temperatures other than 30 °C (wiring systems above

ground): f1

When electrical wiring systems are built into walls having heating elements, it is generally

necessary to reduce current-carrying capacities by applying the reduction factors in table 6-6.

This supposes that the distribution of temperatures inside the heated walls in contact with the

electrical wiring system is known.

When the air temperature is other than 30 °C, the correction coefficient to be applied is given

in the formula:

fp

p1

0

30=

−

−

θ θ

θ o

θ p : maximum temperature permitted by the insulating material under steady-state conditions, °C

θ 0 : air temperature, °C

The value of f1 is given in table 6-6 for different values of θ p and θ 0 .

Insulation

Ambient

temperatures (°C)

θ 0

Elastomers

(rubber)

θ p = 60 °C

PVC

θ p = 70 °C

XLPE and EPR

θ p = 90 °C

10 1.29 1.22 1.15

15 1.22 1.17 1.12

20 1.15 1.12 1.08

25 1.07 1.06 1.04

35 0.93 0.94 0.96

40 0.82 0.87 0.91

45 0.71 0.79 0.87

50 0.58 0.71 0.82

55 - 0.61 0.76

60 - 0.50 0.71

65 - - 0.65

70 - - 0.58

75 - - 0.50

80 - - 0.41

85 - - -

90 - - -

95 - - -

Table 6-6: correction factors for ambient temperatures other than 30 °C

(above ground wiring systems)

524




n correction factors for ground temperatures other than 20 °C

(buried wiring systems): f2

When the ground temperature is other than 20°C, the correction coefficient to be applied is

given in the formula:

fp

p2

0

20=

−−

θ θθ

θ p : maximum temperature permitted by the insulating material under steady-state conditions, °C

θ 0 : ground temperature, °C

The value of f2 is given in table 6-7 for different values of θ p and θ 0 .

Ground temperature Insulation

θ 0 (°C) PVC

θ p = 70 °C

XLPE and EPR

θ p = 90 °C

10 1.10 1.07

15 1.05 1.04

25 0.95 0.96

30 0.89 0.93

35 0.84 0.89

40 0.77 0.85

45 0.71 0.80

50 0.63 0.76

55 0.55 0.71

60 0.45 0.65

65 - 0.60

70 - 0.53

75 - 0.46

80 - 0.38

Table 6-7: correction factor for ground temperatures other than 20 °C

(buried wiring systems)

525




n correction factors for buried wiring systems, in relation to the soil thermal

resistivity: f3

The soil thermal resistivity depends on the type and humidity of the ground. The correction

factor to be applied according to the soil resistivity is given in table 6-8.

Soil Correction Observations

thermal resistivity

K.m/W

factor Humidity Type of soil

0.40 1.25 underwater installation marshes

0.50 1.21 very moist soil sand

0.70 1.13 moist soil clay

0.85 1.05 normal soil and

1.00 1.00 dry soil chalk

1.20 0.94

1.50 0.86 very dry soil ash

2.00 0.76 and

2.50 0.70 clinker

3.00 0.65

Table 6-8: correction factors for buried wiring systems

in relation to the soil thermal resistivity

n correction factors for a group of several multi-core cables or groups of single-core

cables

The circuits or cables may be:

- touching; the correction factor f4 must be applied

- arranged in several layers; the correction factor f5 must be applied

- both touching and arranged in several layers (see fig. 6-3); correction factors f4 and f5

must then be applied.

Figure 6-3: 6 multi-core cables - 2 layers of 3 touching cables

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o touching multi-core or groups of single-core cables: f4

The factors in table 6-9 are to be applied to homogenous groups of cables, equally loaded, for

the given installation methods.

When the horizontal distance between neighbouring cables is greater than twice their external

diameter, no reduction factor is necessary.

The same correction factors are applicable:

- to groups of two or three single-core cables

- to multi-core cables.

N° of installation

methods

Number of touching multi-core cables or

groups of single-core cables

1 2 3 4 5 6 7 8 9 12 16 20

21, 22A, 23A, 24A,25, 31, 31A, 32, 32A,33A, 34A, 41, 43

1.00 0.80 0.70 0.65 0.60 0.55 0.55 0.50 0.50 0.45 0.40 0.40

11, 12 1.00 0.85 0.79 0.75 0.73 0.72 0.72 0.71 0.70 No extra

11A 1.00 0.85 0.76 0.72 0.69 0.67 0.66 0.65 0.64 reduction

13 1.00 0.88 0.82 0.77 0.75 0.73 0.73 0.72 0.72 factor for

14, 16 1.00 0.88 0.82 0.80 0.80 0.79 0.79 0.78 0.78 more than 9 cables

Table 6-9: correction factors for touching multi-core cables or

groups of single-core cables

o multi-core cables or groups of single-core cables arranged in several layers: f5

When cables are arranged in several layers, the correction factors in table 6-10 must be

applied.

Number of layers 2 3 4 or 5 6 to 8 9 plus

Correction factors f5 0.80 0.73 0.70 0.68 0.66

table 6-10: correction factors for a group of multi-core cables

or groups of single-core cables arranged in several layers

527




n correction factors in relation to the number of conduits in air and their arrangement

(see table 6-11): f6

Number of Number of conduits arranged horizontally

conduits arranged

vertically1 2 3 4 5 6

1 1 0.94 0.91 0.88 0.87 0.86

2 0.92 0.87 0.84 0.81 0.80 0.79

3 0.85 0.81 0.78 0.76 0.75 0.74

4 0.82 0.78 0.74 0.73 0.72 0.72

5 0.80 0.76 0.72 0.71 0.70 0.70

6 0.79 0.75 0.71 0.70 0.69 0.68

Table 6-11: correction factors in relation to the number of conduits in the air and their arrangement

n correction factors in relation to the number of conduits buried or built into concrete

and their arrangement (see table 6-12): f7

Number of conduits Number of conduits arranged horizontally

arranged vertically1 2 3 4 5 6

1 1 0.87 0.77 0.72 0.68 0.65

2 0.87 0.71 0.62 0.57 0.53 0.50

3 0.77 0.62 0.53 0.48 0.45 0.42

4 0.72 0.57 0.48 0.44 0.40 0.38

5 0.68 0.53 0.45 0.40 0.37 0.35

6 0.65 0.50 0.42 0.38 0.35 0.32

Table 6-12: correction factors in relation to the number of conduits buried or built into concrete and their

arrangement

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n correction factors for non-touching buried conduits run horizontally or vertically on

the basis of one cable or group of 3 single-core cables per conduit

(see table 6-13) : f8

Distance between conduits (a)

Number of conduits 0.25 m 0.5 m 1.0 m

2 0.93 0.95 0.97

3 0.87 0.1 0.95

4 0.84 0.9 0.94

5 0.81 0.7 0.93

6 0.79 0.6 0.93

Table 6-13: correction factors for non-touching buried conduits run horizontally or vertically on the basis

of one cable or group of 3 single-core cables per conduit

The distances between conduits are measured as shown in figure 6-4.

a

multi-core cables

a

single-core cables

Figure 6-4: distance between conduits (a)

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n correction factors in the case of several circuits or cables in the same buried conduit

(see table 6-14): f9

This is applicable to groups of cables with varying cross-sectional areas but having the same

allowable maximum temperature.

Arrangement of

touching circuits

or cables

Correction factors

Number of circuits or multi-core cables

1 2 3 4 5 6 7 8 9 12 16 20

Installed in a buriedconduit

1 0.71 0.58 0.5 0.45 0.41 0.38 0.35 0.33 0.29 0.25 0.22

Table 6-14: correction factors in the case of several circuits or cables

in the same buried conduit

n correction factors for a group of several cables installed directly in the ground - single

or multi-core cables arranged horizontally or vertically (see table 6-15): f10

Distance between cables or groups of 3 single-core cables (a)

Number of cables

or circuits

Zero

(touching

cables)

One cable

diameter

0.25 m 0.5 m 1.0 m

2 0.76 0.79 0.84 0.88 0.92

3 0.64 0.67 0.74 0.79 0.85

4 0.57 0.61 0.69 0.75 0.82

5 0.52 0.56 0.65 0.71 0.80

6 0.49 0.53 0.60 0.69 0.78

Table 6-15: correction factors for a group of several cables installed directly in the ground -

single or multi-core cables arranged horizontally or vertically

The distances between cables are measured as shown in figure 6-5.

a

single-core cablesmulti-core cables

aa

Figure 6-5: distance between cables (a)

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n current-carrying capacities (in amps) of wiring systems in standard installation

conditions for selection letters B, C, E, F

The current carrying capacities given in table 6-16 are valid for simple circuits made up of the

following number of conductors:

Selection letter B:

- two insulated conductors or two single-core cables or one two-core cable

- three insulated conductors or three single-core cables or one three-core cable

Selection letter C:

- two single-core cables or one two-core cable

- three single-core cables or one three-core cable

Selection letters E and F (see fig. 6-6):

- one two-core or three-core cable for letter E

- two or three single-core cables for letter F .

E E F F

Figure 6-6: illustration of installation methods for selection letters E and F

The number of conductors to be considered in a circuit is that of the conductors through which

the current actually flows. When, in a three-phase circuit, the currents are assumed to be

balanced, it is not necessary to take into account the corresponding neutral conductor.

When the current value of the neutral conductor is close to that of the phases, a reduction

factor of 0.84 is to be applied. Such currents may, for example, be due to the presence of third

harmonic currents in the phase conductors (see § 6.2).

531




Selection letter Insulating material and number of loaded conductors

B PVC 3 PVC 2 XLPE 3 XLPE 2

C PVC 3 PVC 2 XLPE 3 XLPE 2

E PVC 3 PVC 2 XLPE 3 XLPE 2

F PVC 3 PVC 2 XLPE3 XLPE2

Copper cross-

section (mm²)

1.5

2.5

4

6

15.5

21

28

36

17.5

24

32

41

18.5

25

34

43

19.5

27

36

48

22

30

40

51

23

31

42

54

24

33

45

58

26

36

49

63

10

16

25

35

50

68

89

110

57

76

96

119

60

80

101

126

63

85

112

138

70

94

119

147

75

100

127

158

80

107

138

169

86

115

149

185

161

200

50

70

95

120

134

171

207

239

144

184

223

259

153

196

238

276

168

213

258

299

179

229

278

322

192

246

298

346

207

268

328

382

225

289

352

410

242

310

377

437

150

185

240

300

299

341

403

464

319

364

430

497

344

392

461

530

371

424

500

576

395

450

538

621

441

506

599

693

473

542

641

741

504

575

679

783

400

500

630

656

749

855

754

868

1005

825

946

1088

940

1083

1254

Aluminium cross-

section (mm²)

2.5

4

6

16.5

22

28

18.5

25

32

19.5

26

33

21

28

36

23

31

39

24

32

42

26

35

45

28

38

49

10

16

25

35

39

53

70

86

44

59

73

90

46

61

78

96

49

66

83

103

54

73

90

112

58

77

97

120

62

84

101

126

67

91

108

135

121

150

50

70

95

120

104

133

161

186

110

140

170

197

117

150

183

212

125

160

195

226

136

174

211

245

146

187

227

263

154

198

241

280

164

211

257

300

184

237

289

337

150

185

240

300

227

259

305

351

245

280

330

381

261

298

352

406

283

323

382

440

304

347

409

471

324

371

439

508

346

397

470

543

389

447

530

613

400

500

630

526

610

711

600

694

808

663

770

899

740

856

996

Table 6-16: current carrying capacities (in amps) of wiring systems in standard installation conditions

( )f to f0 10 1= for selection letters B, C, E, F

532




n current-carrying capacities (in amps) of wiring systems in standard installation conditions

for selection letter D (buried wiring systems) (see table 6-17)

The number of conductors to be considered in a circuit is that of the conductors through which

the current actually flows. When, in a three-phase circuit, the currents are assumed to be

balanced, it is not necessary to take into account the corresponding neutral conductor.

When the current value of the neutral conductor is close to that of the phases, a reduction

factor of 0.84 is to be applied. Such currents may, for example, be due to the presence of third

harmonic currents in the phase conductors (see § 6.2).

Selection letter Insulating material and number of loaded conductors

D PVC 3 PVC 2 XLPE 3 XLPE 2

Copper cross-sectional

area (mm²)

1.5

2.5

4

6

10

16

25

35

50

70

95

120

150

185

240

300

26

34

44

56

74

96

123

147

174

216

256

290

328

367

424

480

32

42

54

67

90

116

148

178

211

261

308

351

397

445

514

581

31

41

53

66

87

113

144

174

206

254

301

343

387

434

501

565

37

48

63

80

104

136

173

208

247

304

360

410

463

518

598

677

Aluminium cross-sectional

area (mm²)

10

16

25

35

50

70

95

120

150

185

240

300

57

74

94

114

134

167

197

224

254

285

328

371

68

88

114

137

161

200

237

270

304

343

396

447

67

87

111

134

160

197

234

266

300

337

388

440

80

104

133

160

188

233

275

314

359

398

458

520

Table 6-17: current carrying capacities (in amps) of wiring systems in standard installation conditions

( )f to f0 10 1= for selection letter D (buried wiring systems)

533




6.1.5. Practical method for determining the minimum cross-sectional area of an LV

wiring system

determination of the protective device rated current or

setting current taken to be just higher than the designcurrent:

determination of the cross-sectional area of the wiring systemconductors able to carry or :

- calculate the equivalent current (1)

- determine the cross-sectional area able to carry in standard

installation conditions, depending on the insulating material, the

number of loaded conductors and the type of conductor (copper or

aluminium) (see tab. 8-16 and 8-17)

check of other required conditions:

- maximum voltage drop

- maximum length for protection against indirect contact

(IT and TN earthing systems)

- check of thermal withstand in case of short circuit

conductor

installation

conditions

determination of theselection letter and

overall correction

factor

(see tab. 8-3 to 8-5)

design current

determination of current of the wiring system to be

protected by the protective device

fuse circuit-breaker

f

IB

In

Iz1 Iz2

I Iz nand

In

Iz

SIz1 Iz2

Iz'

In I Iset B

I I if I A

I I if I A

z n n

z n n

1 31 10

1 21 10

.

.

I An 25or

S

(1) is an equivalent current which, in standard installationconditions, causes the same thermal effect as or

in actual installation conditions

Iz'

Iz1 Iz2

or

Isetor

Iset

I I if I Az n n110 25.

II

f

I

fz

z z' 1 2or

Iset

Figure 6-7: logigram for determining the cross-sectional area of a LV wiring system

534




6.1.6. Cross-sectional area of protective conductors (PE), equipotential bonding

conductors and neutral conductors (IEC 364)

In a low voltage installation, the protective conductors ensure that the exposed conductive

parts of loads are interconnected and insulation fault currents are evacuated to the ground.

The equipotential bonding conductors allow the exposed conductive parts and extraneous

conductive parts to be set at the same potential, or similar potentials.

In this chapter, we will limit ourselves to conductor sizing rules. Refer to paragraph 2 for the

protection and connection rules.

n cross-sectional area of protective conductors between MV/LV transformer and main

LV switchboard (see fig. 6-8)

PE

main LV switchboard

Figure 6-8: PE conductors between transformer and main switchboard

Table 6-18 gives the protective conductor cross-sectional areas (in mm²) in relation:

- to the nominal power of the MV/LV transformer

- to the operating time t (in seconds) of the MV protection. When protection is ensured by a

fuse, the cross-sectional area to be taken into account corresponds to t s= 0 2.

- to the insulating material and type of conductor metal.

In an IT earthing system, if an overvoltage limiter is inserted between the neutral and earth,

the same sizing is applied to its connecting conductors.

In the case where several transformers operate in parallel, the sum of their nominal powers will

be used to determine the cross-sectional area.

535




Transformer power

(kVA)

Type of conductors Bare

conductors

PVC-insulated

conductors

XLPE-insulated

conductors

LV voltage Copper t (s) 0.2 s 0.5 s - 0.2 s 0.5 s - 0.2 s 0.5 s -

127/220 V 230/400 V Aluminium - 0.2 s 0.5 s - 0.2 s 0.5 s - 0.2 s 0.5 s

≤ 63 ≤ 100 25 25 25 25 25 25 25 25 25

100 160 25 25 35 25 25 50 25 25 35

125 200 25 35 50 25 35 50 25 25 50

160 250 25 35 70 35 50 70 25 35 50

200 315 Potective conductor 35 50 70 35 50 95 35 50 70

250 400 cross-sectional area 50 70 95 50 70 95 35 50 95

315 500 SPE (mm²) 50 70 120 70 95 120 50 70 95

400 630 70 95 150 70 95 150 70 95 120

500 800 70 120 150 95 120 185 70 95 150

630 1 000 95 120 185 95 120 185 95 120 150

800 1 250 95 150 185 120 150 240 95 120 185

Table 6-18: cross-sectional area of protective conductors

between MV/LV transformer and main LV switchboard

n cross-sectional areas of low voltage exposed conductive part protective conductors: (PE)

The cross-sectional area of the PE conductor is defined in relation to the cross-sectional area

of the phases (for the same metal conductor) as follows:

- for S mmphase ≤16 ² , S SPE phase= (1)

- for 16 35mm S mmphase² ²< ≤ , S mmPE =16 ²

- for S mmphase > 35 ² , SS

PEphase=2

(1) when the protective conductor is not part of the wiring system, it must have a cross-sectional area of

at least:

- 2.5 mm² if it comprises a mechanical protection

- 4 mm² if it does not comprise a mechanical protection

536




In the TT earthing system, the protective conductor cross-sectional area may be limited to:

- 25 mm² for copper

- 35 mm² for aluminium

on condition that the neutral and exposed conductive part earth electrodes are separate,

otherwise the conditions of the TN earthing system are applicable (in a TT earthing

system, there may be an involuntary connection via the metal structure or other part between

the two earth electrodes; the earth fault current is then high).

n cross-sectional area of equipotential bonding conductors

o main equipotential bonding conductor

Its cross-sectional area must be at least equal to half the cross-sectional area of the

installation's largest protective conductor, with a minimum of 6 mm². However, it may be limited

to 25 mm² for copper or 35 mm² for aluminium.

o supplementary equipotential bonding conductor

If it connects two exposed conductive parts, its cross-sectional area must not be smaller than

the smallest of the protective conductors connected to these parts (see fig. 6-9-a).

If it connects an exposed conductive part to an extraneous conductive part, its cross-sectional

area must not be smaller than half the cross-sectional area of the protective conductor

connected to this exposed conductive part (see fig. 6-9-b).

IfS SPE PE1 2≤

S SLS PE= 1S

SLS

PE=2

(*)

SPE1 SPE2

SLS

P1 P2

SLS

SPE

P

a) between two exposed conductive parts b) between an exposed conductive part and a

structure

Figure 6-9: cross-sectional area of supplementary equipotential bonding conductors

(*) with a minimum of: - 2.5 mm² if the conductors are mechanically protected

- 4 mm² if the conductors are not mechanically protected

Conductors which are not incorporated in a cable are mechanically protected when they are

installed in conduits, troughs or casing or protected in a similar way.

537




n cross-sectional area of PEN conductors

In the case of a TNC earthing system, the protective conductor also plays the role of the

neutral conductor.

In this case, the cross-sectional area of the PEN must be at least equal to the greatest value

resulting from the following requirements:

- SPEN ≥−

−

10

16

2

2

mm

mm

for copper

for aluminium

- meet the conditions relating to the PE conductor

- meet the conditions required for the neutral conductor cross-sectional area.

n cross-sectional area of the neutral conductor

- The neutral conductor must have the same cross-sectional area as the phase conductors in

the following cases:

. single-phase circuit

. three-phase circuit having phase cross-sectional areas smaller than or equal to 16 mm²

for copper or 25 mm² for aluminium.

- For three-phase circuits having a phase cross-sectional area greater than 16 mm² for

copper or 25 mm² for aluminium, the neutral cross-sectional area may be smaller than that

of the phases as long as the following conditions are met:

. the maximum current likely to continuously circulate in the neutral is lower than the

current-carrying capacity of the chosen cross-sectional area. The unbalance of single-

phase loads and third and multiples of third harmonics which may require the use of a

cross-sectional area greater than the phases must be taken into account (see § 8.2 -

neutral conductor heating).

. the neutral conductor is protected against overcurrent by a fuse or a circuit-breaker trip

setting suitable to its cross-sectional area.

. the cross-sectional area of the neutral conductor is at least equal to 16 mm² for copper or

25 mm² for aluminium.

538



Industrial electrical network design guide T & D 6 883 427/A

6.1.7. Checking voltage drops

The voltage drop over a wiring system is calculated using the following formula:

∆V bL

SL IB= +

×ρ ϕ λ ϕ1 cos sin

∆V : voltage drop, in volts

b : coefficient

=

=

1

2

for three - phase circuit

for single - phase circuit

ρ1 : conductor resistivity during normal service, i.e. 1.25 times that at 20 °C

ρ1 = 0.0225 Ω mm²/m for copper; ρ1 = 0.036 Ω mm²/m for aluminium

L : length of wiring system, in metres

S : cross-sectional area of conductors, in mm²

cosϕ : power factor, in the absence of specific indications we can take cosϕ = 0.8 ( sinϕ = 0.6)

IB : maximum design current, in amps

λ : reactance per unit length of the conductors, in Ω/m

The values of λ in LV are:

- 0 08 10 3. /× − Ω m for three-core cables

- 0 09 10 3. /× − Ω m for single-core cables in a flat formation or triangular formation

- 0 15 10 3. /× − Ω m for single-core cables spaced by d r= 8

d : mean distance between conductor

r : radius of conductor cores

The relative voltage drop is defined as:

∆V

Vn

for phase-to-neutral fed three-phase or single-phase circuits

∆V

Un

for phase-to-phase fed single-phase circuits (in this case,

∆V represents a phase-to-phase voltage drop)

Vn : nominal single-phase voltage

Un : nominal phase-to-phase voltage

539




In accordance with IEC 364-5-52, in the absence of other considerations, it is recommended

that in practice the voltage between the origin of consumer's installation and the equipment

should not be greater than 4% of the nominal voltage of the installation.

n circuits feeding motors

The voltage drop is calculated by replacing the design current IB by the motor starting current.

Taking into account all the motors able to start simultaneously, the voltage drop must be lower

than 10% to ensure correct motor starting and not disturb the rest of the installation too much.

540




6.1.8. Maximum lengths of wiring systems for protection against indirect contact (TN

and IT earthing system)

Standard IEC 364 specifies that the fault current for TN and IT earthing systems must be

cleared in a time compatible with the protection of persons.

This time is determined by a curve in relation to the prospective touch voltage; it is based on

the physiological effects of the electrical current on the human body. To simplify matters, using

this curve, it is possible to determine a maximum disconnecting time in relation to the nominal

voltage of the installation (see table 6-20 and 6-21).

Nominal a.c. voltage

Vn / Un

Disconnecting time

(seconds) (*)

(Volts)non-distributed neutral distributed neutral

120/240

230/400

400/690

580/1000

0.8

0.4

0.2

0.1

5

0.8

0.4

0.2

Table 6-20: maximum disconnecting times in the IT earthing system (second fault)

Nominal a.c. voltage Vn

(Volts) (**)

Disconnecting time

(seconds) (*)

120

230

277

400

> 400

0.8

0.4

0.4

0.2

0.1

Table 6-21: maximum disconnecting times in the TN earthing system

(*) these values are not valid in premises containing a bath or shower.

541




Note 1: if the disconnecting time is more than the time t0 , but less than 5 seconds, protection is

allowed by IEC 364 (§ 413.1.3.5) in the following cases:

- in distribution circuits when the protective conductor at the downstream end of the circuit isdirectly connected to the main equipotential bonding.

- in terminal circuits supplying stationary equipment only and having a protective conductorthat is connected to the main equipotential bonding and which is located in the area that isinfluenced by the main equipotential bonding.

Note 2 : in the TT earthing system, protection is in general ensured by residual current devices whichare set to meet the following condition (see IEC 364, § 413.1.4.2):

R I VA A ≤ 50

RA : resistance of the earth electrode of the exposed conductive parts

IA : rated residual current of the circuit-breaker

If selectivity is seen to be necessary, an operating time at the most equal to 1 second isallowed in the distribution circuits without taking into account the touch voltage

Note 3 : in an IT earthing system, when the exposed conductive parts are earthed individually or in

groups, the conditions of the TT earthing system given in Note 2 must be met (see IEC 364,§ 413.1.5.3).

n circuit-breaker protection

IEC 364 specifies that the magnetic tripping threshold of the circuit-breaker in TN and IT

earthing systems must be lower than the minimum short-circuit current. Furthermore, any

eventual circuit-breaker time delay must be shorter than the maximum disconnecting time

defined in tables 6-20 and 6-21.

For a given circuit-breaker and cross-sectional area, there is thus a maximum circuit length not

to be exceeded in order to comply with the requirements concerning the protection of persons

against indirect contact.

In the following part of the chapter, we will apply the conventional method for determining

maximum circuit lengths. This is more restrictive than the impedance method, but can be

applied by carrying out the calculations by hand.

In the conventional method, we neglect the influence of the reactance of the conductors for

cross-sectional areas smaller than 150 mm².

For large cross-sectional areas, we will take into account the influence of the reactance by dividing

Lmax by:

- 1.15 for a cross-sectional area of 150 mm²



- 1.30 for a cross-sectional area of 300 mm².

542




Note: for minimum short-circuit current calculations, refer to the "Industrial network protection guide"§ 4.4.1.

o TN earthing system

The maximum length of a circuit in a TN earthing system is:

( )LV S

m I

n ph

mmax

.=

× ×× + ×0 8

1ρ

Lmax : maximum length in m

Vn : single-phase voltage in volts

S ph : cross-sectional area of the phases in mm²

ρ : resistivity of the conductors taken to be equal to 1.5 times that at 20 °C ( ρ = 0 027 2. /Ω mm m for

copper; ρ = 0 043 2. /Ω mm m for aluminium)

m =Sph

SPE

:

:

cross - sectional area of phases

cross - sectional area of protective conductor

Im : circuit-breaker magnetic trip operating current

o IT earthing system

The maximum length of a circuit in an IT earthing system is:

- if the neutral conductor is not distributed:

( )LV S

m I

n ph

mmax

.=

× × ×× + ×

0 8 3

2 1ρ

- if the neutral conductor is distributed:

( )LV S

m I

n

mmax

.=

× ×× + ×0 8

2 1

1

ρ

S1 :=

=

Sph

Sneutral

if the outgoing feeder considered does not have a neutral

if the outgoing feeder considered has a neutral

o TT earthing system

No condition on the wiring system length is specified since the protection of persons is

ensured by the residual current device.

543




n fuse protection

Using the fuse fusing curve, we can determine the current Ia ensuring fusion of the fuse in

the time t0 specified in tables 6-20 and 6-21 (see fig. 6-10). We can then calculate the

maximum length of the wiring system in the same way as for the circuit-breaker replacing Im

by Ia .

t

t0

IaI

Figure 6-10: fuse fusing curve

n application

In practice, checking the cross-sectional area of the wiring system in relation to the protection

of persons against indirect contact consists in making sure that the length of the wiring system

is less than Lmax for a given arrangement.

If the wiring system length is greater than Lmax , we can take the following measures:

- choose a circuit-breaker (or trip relay) with a lower magnetic threshold if the selectivity

requirements permit this

- install a residual current circuit-breaker for TNS and IT earthing system (in a TNC

earthing system it is not possible to use a RCD)

- take larger phase and protective conductor cross-sectional areas meeting the maximum

length condition.

544




6.1.9. Checking the thermal withstand of conductors

When a short-circuit current flows through the conductors of a wiring system for a very short

time (up to five seconds), the heating of the conductors is considered to be adiabatic; this

means that the energy stored remains in the metal of the core and is not transmitted to the

insulating material. It is therefore necessary to check that the short-circuit thermal stress is

lower than the conductor thermal withstand:

t I k Sdis sc2 2 2≤

tdis : protective device disconnecting time in seconds

S : cross-sectional area of conductors in mm²

Isc : short-circuit current in A

The value of k depends on the core metal and the type of insulating material

(see table 6-22).

Insulating material

Core

PVC XLPE

Copper 115 135

Aluminium 74 87

Table 6-22: value of factor k in accordance with IEC 364-4-43

If the disconnecting time is given, the cross-sectional area must comply with:

SI

ktscdis≥ ×

545




n circuit-breaker protection

The check must be carried out for the maximum short-circuit current at the circuit-breaker

location.

The curves in manufacturers' catalogues give the maximum disconnecting time of the circuit-

breaker. When circuit-breaker tripping is time delayed, the disconnecting time is taken to be

equal to the time delay.

To check the thermal withstand, the short-circuit current value must be calculated with a

resistivity ρ of the conductors taken to be equal to 1.5 times that at 20 °C :

- ρ = 0 027 2. /Ω mm m for copper

- ρ = 0 043 2. /Ω mm m for aluminium

o case of current-limiting circuit-breakers

On occurrence of a short circuit, current-limiting circuit-breakers only let a current below the

prospective fault current through (see fig. 6-11).

t

prospective

limited peak Isc

Isc prospective peak Isc

Isc

Figure 6-11: current limiting curve

The wiring system protected by this type of device is not therefore subjected to the

(prospective) calculated Isc thermal stress, but a much smaller stress defined by

manufacturers' limiting curves for each type of circuit-breaker.

The limiting curves give the thermal stress t Idis sc2 expressed in A2 × second .

546




o example

We want to check the thermal withstand of a PVC-insulated 6 mm² copper conductor protected

by a Compact NS 80H-MA 380/415 V circuit-breaker fitted with an LR2-D33 63 thermal relay.

The themal withstand of the cable is: ( )k S A s2 2 2 2 5 2115 6 4 76 10= × = × ×. .

The limiting curves in figure 6-12 give the maximum thermal stress of the circuit-breaker:

2 105 2× ×A s .

The cable is thus protected up to the circuit-breaker breaking capacity.

The curves are in the table order

Figure 6-12: thermal stress limiting curves

for Compact NS 80H-MA-380/415V circuit-breakers

n fuse protection

The current causing the most stress is the minimum short-circuit current at the end of the

wiring system.

The fusing time t f of the fuse corresponding to Isc min must comply with the relation:

t I k Sf scmin2 2 2≤

The method for calculating Isc min is given in paragraph 4.4.1 of the Protection guide.

547




6.1.10. Application example

n hypotheses

Let us consider the diagram in figure 6-13 the data of which is given below.

Since the installation feeds loads requiring good continuity of service the IT earthing system

without distributed neutral is chosen.

o W2 wiring system

This is made up of a PVC insulated copper three-core cable which is installed touching 3 other

multi-core cables on perforated trays in an ambient temperature of 40°C. It is protected by

fuses. It feeds a load having the following characteristics:

- active power P kW=15

- efficiency η = 0 89.

- cos .ϕ = 0 85

- utilisation factor b = 0 9. .

o W1 wiring system

This is made up of 3 XLPE-insulated copper single-core cables in a triangular formation. The

cables are buried alone, without any extra mechanical protection, in soil which has a thermal

resistivity of 0.85 K.m/W and a temperature of 35 °C. They are protected by a circuit-breaker.

The wiring system feeds load L1 and 3 other outgoing feeders the IB current values of which

are given in figure 6-13.

548




250 kVA

= 4 %

400 V

= 100 m

cos = 0.8

400 V

I B

25 A 50 A 40 A

= 15 m

L1

R1

L2

unearthed neutral

U sc

W1

W2

Figure 6-13: diagram of the installation

n determining the maximum design current

o W2 wiring system

- P kW=15

- the factor a = =1

132η ϕcos

.

- the utilisation factor b = 0 9.

- for a single load the coincidence factor is c =1

- no extension is planned, thus d =1

- for a 400 V three-phase network, the power conversion factor in current is e =1.4 .

We then have: I P a b c d e AB = × × × × × = × × × × =15 132 0 9 1 1 24 9. . .4 .

549




o W1 wiring system

The maximum design current of the W1 wiring system is obtained by calculating the sum of

currents ( )IB of all the outgoing feeders fed by W1 and by applying a coincidence factor

estimated at 0.8 (see table 6-2):

( )I AB = + + + × =25 50 40 24 9 0 8 115 9. . .

n correction factors

o W2 wiring system

Table 6-3 gives the installation method N° 13 and the selection letter E .

The correction factors to be applied are:

- ambient temperature (see table 6-6) : f1 = 0.87

- cable group (see tables 6-9 et 6-10) : f4 = 0.77 and f5 = 1

The overall correction factor is:

f = × × =0 87 0 77 1 0 67. . .

o W1 wiring system

Table 6-3 gives the installation method N° 62 and the selection letter D .


- ground temperature (see table 6-7) : f2 = 0.89

- soil thermal resistivity (see table 6-8) : f3 = 1.05

- cable group (see table 6-15) : f10 = 1

The overall correction factor is:

f = × × =0 89 1 05 1 0 935. . .

550




n determining the cross-sectional area and choosing the protective device

o W2 wiring system

I AB = 24 9.

f = 0 67.

The fuse nominal current must comply with the condition I In B≥ .

The fuse with a rating of I An = 25 is chosen.

For 10 25A In< ≤ A , the current Iz of the wiring system protected by this fuse is:

I k I I Az n n= = =3 1 21 30 3. .

The equivalent current that the wiring system must be able to carry in standard installation

conditions is: II

fAz

z'.= = 451

Table 6-16 (selection letter E , PVC3, copper) gives a minimum cross-sectional area of

S mm= 10 2 which has a current-carrying capacity of I A0 60= .

o W1 wiring system

I AB =115 9.

f = 0 935.

For an adjustable circuit-breaker, the setting current must comply with the condition I Iset B≥ ;

I Aset =120 is chosen.

The current Iz of the wiring system protected by this setting is:

I I Az n= = 120

The equivalent current that the wiring system must be able to carry in standard installation

conditions is: II

fAz

z'.= =128 3

Table 6-17 (selection letter D , XLPE3, copper) gives a minimum cross-sectional area of

S mm= 25 2 which has a current-carrying capacity of I A0 144= .

551




n maximum length of the wiring system

o W2 wiring system

For S mmph = 10 ² , we have S S mmPE ph= = 10 ²

whence mS

S

ph

PE

= =1

Table 6-20 gives a maximum disconnecting time of t s= 0.4 for a network with non-distributed neutral.

The time-current characteristic for a 25 A rated fuse gives us a current of I Aa = 200 for a

disconnecting time of 0.4 s.

The neutral is not distributed and we thus have:

( )LV S

m Im

n ph

amax

. .

..=

× × ×+

=× × ×

× × ×=

0 8 3

2 1

0 8 3 230 10

2 0 027 2 200147 5

ρ

The length of the W2 wiring system (15 m) is far smaller than Lmax and the protection of

persons against indirect contact is thus ensured.

o W1 wiring system

For 16 35mm S mm² ²< ≤ , we have S mmPE =16 ²

whence mS

S

ph

PE

= = =25

16156.

The circuit-breaker chosen is a Compact NS 125E with an STR 22SE trip relay having a

magnetic tripping threshold set at Im = 1 250 A because of the selectivity.

The neutral is not distributed and we thus have:

( )LV S

m Im

n ph

mmax

. .

. ..=

× × ×+

=× × ×

× × ×=

0 8 3

2 1

0 8 3 230 25

2 0 027 2 56 1250461

ρ

The length of the W1 wiring system (100 m) is greater than Lmax .

By taking cross-sectional areas greater, i.e. S mmph = 35 ² and S mm mPE = =35 1² ( ) , we find

L m mmax .= <82 6 100 ; which is not sufficient.

So as not to oversize the conductors, it is decided that the outgoing feeder should be fitted

with a residual current device which ensures the protection of persons against indirect contact.

552




n checking the voltage drop

o W2 wiring system

S = 10 mm² , L = 15 m , IB = 24.9 A

The cable is three-core and we thus have λ = × −0 08 10 3. /Ω m .

The power factor is cos .ϕ = 0 85 , whence sin .ϕ = 0 53 .

For a three-phase circuit b = 1 .

For copper ρ120 0225= . /Ωmm m .

We deduce from this that ∆ V = × × + × × ×

×−

0 022515

100 85 0 08 10 15 0 53 24 9

3. . . . .

∆ V V= 0 73.

whence∆ V

Vn

= =0 73

2300 3

.. %

The total voltage drop is 4.2 % (the voltage drop in the W1 wiring system is 3.9 %, see below).

o W1 wiring system

S = 25 mm² , L = 100 m , IB = 115.9 A

The 3 single-core cables are in a flat formation and we thus have:

λ = × −0 09 10 3. /Ω m

The overall power factor of the installation is cos .ϕ = 0 8 , whence sin .ϕ = 0 6 .

We deduce from this that ∆ V = × × + × × ×

×−

0 0225100

250 8 0 09 10 100 0 6 115 9

3. . . . .

∆ V V= 8 97.

whence∆ V

Vn

= =8 97

2303 9

.. %

553




n checking the thermal stress

o W2 wiring system

For fuse protection, the current to be taken into account is the minimum short-circuit current at

the end of the wiring system. For the IT earthing system, this is the short-circuit current for a

double phase-earth fault.

By applying the conventional method (see § 4.4.1.2 of the Protection guide), we can calculate:

IV

LS S

kAscn

ph PE

min. .

.

.= × ×

+

= × ×

× × +

=3 0 8

21 1

3 230 0 8

2 15 0 0271

10

1

10

197

2 ρ

The time-current characteristic of the 25 A rated fuse gives us a fusing time of t msf = 5 for a

current of 1.97 kA.

The maximum thermal stress is thus:

( )I t A sscmin . .42 3 2 3 3 2

197 10 5 10 19 10× = × × × = × ×−

The permitted cable thermal withstand is: ( )k S A s2 2 2 2 3 2115 10 1322 10= × = × × .

The cross-sectional area of S mm= 10 2 is thus largely able to withstand to the fuse thermal

stress.

o W1 wiring system

The maximum short-circuit current of the circuit-breaker (neglecting the connection linking the

circuit-breaker to the transformer) is:

IS

U UkAsc

n

n sc

= × =××

× =3

1 250 10

3 400

100

49 02

3

.

We assume that the circuit-breaker trip relay is delayed by 0.1 second, the maximum short-

circuit thermal stress is then:

( )I t A ssc2 3 2 6 2

9 02 10 0 1 814 10= × × = × ×. . .

The permitted cable thermal withstand is: k S A s2 2 2 2 6 2143 25 12 78 10× = × = × ×.

The cross-sectional area of S mm= 25 2 is thus largely able to withstand the circuit-breaker

thermal stress.

554




n conclusion

The cross-sectional areas to be chosen are:

- W1 wiring system: 3 35 1 162 2× + ×mm mm copper

- W2 wiring system: 3 10 1 102 2× + ×mm mm copper

555




6.2. Determining conductor cross-sectional areas in medium voltage

6.2.1. Method principle

The method for determining the cross-sectional area of conductors in medium voltage consists

in:

- determining the maximum design current IB of the loads to be supplied

- determining the cross-sectional area S1 complying with the heating of the cable core under

normal operating conditions, which may be continuous or discontinuous. To do this, it is

necessary to know:

. the actual installation conditions of the wiring system and consequently the overall

correction factor f

. the current-carrying capacities of the different types of cable in standard installation

conditions.

- determining the cross-sectional area S2 required for the thermal withstand of the cable in

the event of a three-phase short circuit

- determining the cross-sectional area S3 required for the thermal withstand of the cable

screen in the event of an earth fault

- possibly checking the voltage drop in the wiring system for the chosen cross-sectional

area S. The technical cross-sectional area S to be selected is the maximum value among

cross-sectional areas S1 , S2 and S3 .

- possibly calculating and choosing the economical cross-sectional area.

6.2.2. Determining the maximum design current

The maximum design current IB is determined on the basis of the sum of powers of the loads

fed, applying if necessary utilisation and coincidence coefficients (see § 6.1.2.).

In medium voltage, a wiring system most often feeds a single load (transformer, motor,

furnace, steam generator), in this case IB is taken to be equal to the rated current of the

device.

556




6.2.3. Current-carrying capacities in wiring systems

n general rules

The current-carrying capacity is the maximum current that a wiring system can continuously

carry without this affecting its life span.

The current-carrying capacities of cables are given in standards or by manufacturers for

standard installation conditions.

To determine the current-carrying capacity of a wiring system in actual installation conditions,

the following must be carried out:

- using table 6-23, define the installation method, its associated table column number and

correction factors to be applied

- using the installation conditions, determine the correction factor values which must be

applied (see tables 6-24 to 6-28)

- calculate the overall correction factor f equal to the product of the correction factors

- using table 6-29 for impregnated paper-insulated cables and tables 6-30 to 6-34 for

synthetically-insulated cables, determine the maximum current that the wiring system can

carry in standard conditions ( )f f0 6 1to =

- calculate the maximum current-carrying capacity of the wiring system in relation to its

installation conditions: I f Ia = 0 .

557




n installation methods

Table 6-23 gives, for each installation method, the current-carrying capacity table column to be

used for choosing the cross-sectional area of the conductors (see tables 6-29 to 6-34).

Factor f0 corresponds to the installation method; factors f1 to f6 are explained below

(see tables 6-24 to 6-28).

Installation methods Example Table Correction factors

column f0 to be applied

A Conduits on wall

(3) 0.90 f1 f5

B Flush mountedconduits (3) 0.90 f1 f5

F Installed on cabletrays (3) 1 f1 f5

G Installed on bracketsor cable ladders (3) 1 f1 f6

H Troughs (enclosed) (3) 0.90 f1 f5

J Ducts (open troughs)

(3) 1 f1 f6

L1 Conduits in open orventilated channels (3) 0.80 f1 f5

558




Installation method Example Table Correction factors


L3 Directly installed inopen or ventilatedchannels (3) 0.90 f1 -- f5

L4 Directly installed inenclosed channels

(3) 0.80 f1 -- f5

L5 Directly installed inchannels filled withsand (3) 0.80 f1 -- f5

N Troughs (in masonry)

(3) 0.90 f1 -- f5

P Manufactured blocks

(3) 0.90 f1 -- f5

S1 Directly buried(armoured cables)

P___

(1)

D____ (2)

1 f2 f3 f4

S2 Buried withmechanical protection (1) (2) 1 f2 f3 f4

P : steady-state operating conditions

D : discontinuous operating conditions

559




Installation method Example Table Correction factors


S3 Buried in sleeves

P

____

(1)

D

___

(2)

0.8 f2 f3 f4

S4 Cables installed in

trefoil formation in a

prefabricated channel,

buried directly in the

ground, possibly with

extra backfill

(1) (2) 0.8 f2 f3 f4

S5 Single-core cables

installed in individual

channels, buried

directly in the


extra backfill

(1) (2) 0.8 f2 f3 f4

Single-core cables in a

flat formation spaced

out in a prefabricated

channel, buried

directly in the


extra backfill

(1) (2) 0.8 f2 f3 f4

V Overhead lines (3) 1,1 f1 -- --

P : steady-state operating conditions

D : discontinuous operating conditions

Table 6-23: installation methods

560




n correction factors for ambient temperatures other than 30 °C (cables installed in air): f1

Temperature Type of insulating material

°C PVC

PE

XLPE

EPR

10 1.22 1.15

15 1.17 1.12

20 1.12 1.08

25 1.06 1.04

30 1.00 1.00

35 0.94 0.96

40 0.87 0.91

45 0.79 0.87

50 0.71 0.82

55 0.61 0.76

Table 6-24: correction factors for ambient temperatures other than 30 °C (cables installed in air)

561




n correction factors for ground temperatures other than 20 °C (buried cables): f2

Temperature Type of insulating material

°C PVC

PE

XLPE

EPR

0 1.18 1.13

5 1.14 1.10

10 1.10 1.07

15 1.05 1.04

20 1.00 1.00

25 0.95 0.96

30 0.89 0.93

35 0.84 0.89

40 0.77 0.85

45 0.71 0.80

50 0.63 0.76

60 0.45 0.65

65 - 0.60

70 - 0.53

75 - 0.46

80 - 0.38

Table 6-25: correction factors for ground temperatures other than 20 °C (buried cables)

562




n correction factors for soil thermal resistivities other than 1 K.m/W (buried cables): f3

Soil thermal

resistivity

(K.m/W)

Humidity Type of soil Assembly of

three single-

core cables

Three-core

cables

0.5 Very moist soil 1.25 1.20

0.7 Moist soil 1.14 1.10

0.85 Normal soil Clay 1.06 1.05

1 Dry soil and 1.00 1.00

1.2 Sand Chalk 0.93 0.95

1.5 Very dry soil Ash 0.85 0.88

2 and 0.75 0.79

2.5 Clinker 0.68 0.72

3 0.62 0.68

Tableau 6-26: correction factors for soil thermal resistivities other than 1 K.m/W (buried cables)

n correction factors for a group of several wiring systems (buried cables): f4

Number of

circuits

Distance between cables "a"

Zero (cables

touching)

One cable

diameter

0.125 m 0.25 m 0.5 m

2 0.75 0.80 0.85 0.90 0.90

3 0.65 0.70 0.75 0.80 0.85

4 0.60 0.60 0.70 0.75 0.80

5 0.55 0.55 0.65 0.70 0.80

6 0.50 0.55 0.60 0.70 0.80

Determination of the distance "a" in the case of single-core cables installed in a flat or trefloid

formation and three-core cables.

single-core cables three-core cables

a

a

a

Table 6-27: correction factors for a group of several wiring systems (buried cables )

563




n correction factors for a group of several circuits or several cables

(cables installed in air and away from direct sunlight): f f5 6,

Installation

method

Arrangement Number of circuits or

multi-core cables

2 3 4 6 > 9

f5 On unperforated horizontal trays......................... 0.85 0.80 0.75 0.70 0.70

f6 On perforated horizontal trays

or on brackets .................................................... 0.90 0.80 0.80 0.75 0.75

Table 6-28: correction factors for a group of several circuits or several cables (cables installed in air and

away from direct sunlight)

n current-carrying capacities of cables in standard installation conditions ( )f f0 6 1to =

References (1), (2) and (3) of tables 6-29 to 6-34 correspond to the column number given in

table 6-23.

o impregnated paper-insulated cables

Impregnated paper-insulated cables have stopped being manufactured for several years.

However, for calculation purposes for existing installations, the current-carrying capacities may

be calculated to an approximate value of ± 5% using the following formula:

I SB A= ×10

I : current-carrying capacity, in A

S : nominal cross-sectional area of the cable, in mm²

A and B : are coefficients given for each type of cable (see table 6-29)

564




Wiring systems Columns Copper Aluminium

A B A B

Three-core (1) 0.540 1.446 0.549 1.321

collectively (2) 0.543 1.492 0.544 1.386

screened cable (3) 0.588 1.371 0.598 1.293

3 single-core (1) 0.556 1.269 0.571 1.130

cables (2) 0.567 1.286 0.573 1.179

(3) 0.587 1.196 0.605 1.064

Three-core individually (1) 0.581 1.215 0.594 1.089

screened cables (2) 0.573 1.264 0.578 1.155

(3) 0.600 1.117 0.608 1.004

Table 6-29: values of coefficients A and B for impregnated paper-insulated cables

o synthetically-insulated cables

The detailed calculation method for current-carrying capacities of cables under steady-state

operating conditions is given in IEC publication 287.

The current-carrying capacities are given in tables 6-30 to 6-34, according to the type of

conductor, the type of insulating material and the rated voltage.

The rated voltage for which a cable is designed is expressed by a set of three values, in kV, as

( )U U Um0 / , where:

- U0 : voltage between the conductor core and a reference potential (screen or earth)

- U : voltage between the cores of two phase conductors

- Um : maximum voltage which may occur between the network phases in normal operating

conditions

The expression of the rated voltage differs depending on whether the cable is an individually

screened type or not (see fig. 2.2.a and 2.2.b). For an individually screened cable, U0 is

different from U , both values being generally in the ratio of 3 .

However, due to the way it is made, a collectively screened cable has an equivalent insulation

level between two phases and between one phase and the screen. This results in U0 and U

having identical values.

565




PVC-insulated Nominal

cross-

sectional

area (mm²)*

EPR or XLPE-insulated

(1) (2) (3) Copper (1) (2) (3)

72

94

120

145

185

225

270

310

345

385

445

78

100

130

160

205

250

300

345

390

430

500

62

81

105

130

165

205

250

290

330

370

440

10

16

25

35

50

70

95

120

150

185

240

86

110

145

170

215

260

315

360

405

450

525

94

120

155

190

240

295

355

405

455

505

590

78

100

130

165

205

255

310

360

410

460

550

(1) (2) (3) Aluminium (1) (2) (3)

56

72

94

115

145

175

210

240

270

300

350

61

79

100

125

160

195

235

270

300

335

390

48

62

82

100

130

160

195

225

255

285

345

10

16

25

35

50

70

95

120

150

185

240

67

86

110

135

165

205

245

280

315

350

410

73

94

120

145

185

230

275

315

355

395

460

60

79

105

125

160

195

240

280

320

360

430

(*) Above 50 mm², the values are calculated for sector conductors

Table 6-30: current-carrying capacities in three-core collectively screened cables having a rated voltage

lower than or equal to 6/6 (7.2) kV

566




Nominal

cross-

sectional

area (mm²)

PVC-insulated PE-insulated* EPR or XLPE-insulated

Copper (1) (2) (3) (1) (2) (3) (1) (2) (3)

10162535507095

120150185240300400500630800

1 0001 2001 4001 600

80105135160190235285320360410475540610680770850930980

1 0301 080

89115150180215265320365410470540610700780880980

1 0701 1301 1901 250

7195

125150180230280320370425500580670760870990

1 1101 2101 2901 360

86110140170200245295335375425490550600700790870950

1 0001 0501 100

97125160195230285340385435490570640690810920

1 0101 1001 1601 2201 280

76100130160190240295340385445530600700790920

1 0401 1601 2601 3501 420

99125165195230285340385430485560630720800910

1 0001 1001 1601 2201 280

110145185225265325390445500560650730840940

1 0601 1701 2701 3501 4201 480

93120160200235295360420475550650740860990

1 1401 3001 4501 5701 6801 770

Aluminium (1) (2) (3) (1) (2) (3) (1) (2) (3)

10162535507095

120150185240300400500630800

1 0001 2001 4001 600

6280

105125150180220250280320370420480540620700780840890940

6989

115140170205250285320365425485550630720810900970

1 0301 080

557396

115140175215250285330390455530610710820940

1 0301 1101 180

6786

110130160190230260290330385435495560640720800860910950

7697

125150180220265300335380445500580650750840930

1 0001 0601 110

5978

100125150185230265300345410470550640750860980

1 0801 1601 230

7798

125150180220260300335380440500570640740830920990

1 0501 100

87110145175205250300345385440510580660750860970

1 0701 1501 2301 290

7295

125150185230280325370425510580680790920

1 0701 2201 3401 4501 530

(*) For cables having high density polythene insulation, the values are to be multiplied by:1.05 for columns (1) and (2)1.06 for column (3)

Table 6-31: current-carrying capacities in cables made up of three single-core cables having a rated

voltage lower than or equal to 6/10 (12) kV

567




PE-insulated* Nominal

cross-

sectional

area (mm²)


(1) (2) (3)* Copper (1) (2) (3)

110140170200250295335375425490550630700790870960

1 0101 0701 110

125160195230280335385430490560640720810920

1 0101 1001 1701 2401 290

105135165200250300350395455530610710810930

1 0501 1801 2701 3601 430

162535507095

120150185240300400500630800

1 0001 2001 4001 600

125165195230280335385430490560640720810910

1 0101 1101 1801 2401 290

140185220260320385440495560650730830940

1 0601 1701 2801 3601 4401 500

130170200245305375425485560660750870

1 0001 1501 3001 4701 5901 7001 790

(1) (2) (3) Aluminium (1) (2) (3)

86110130155190230260290330385435495560640720800860920960

96125150180220260300335380445500570650740830930

1 0001 0601 110

81105130155190235270305355420480560650750860990

1 0901 1701 240

162535507095

120150185240300400500630800

1 0001 2001 4001 600

98125150180220260300335380440500570640740830930

1 0001 0601 110

110140170205250300340385435510570660740850960

1 0701 1601 2301 290

99130160190235290330375430510590680790930

1 0601 2301 3501 4501 540


Table 6-32: current-carrying capacities in cables made up of three single-core cables having a rated

voltage greater than 6/6 (7.2) kV and lower than or equal to 18/30 (36) kV

568




Nominal

cross-

sectional

area (mm²)

PVC-insulated PE-insulated* EPR or XLPE-insulated

Copper (1) (2) (3) (1) (2) (3) (1) (2) (3)

10

16

25

35

50

70

95

120

150

185

240

300

80

100

130

160

185

230

275

310

345

390

450

500

87

115

145

175

205

255

305

345

385

435

500

560

71

90

120

145

175

215

260

300

340

385

450

520

85

110

140

165

195

240

285

325

365

410

475

530

94

120

155

190

220

270

320

365

415

465

530

605

75

98

125

155

185

230

275

315

365

410

485

560

97

125

160

190

225

275

330

370

420

470

540

610

110

140

180

215

250

310

370

420

475

535

610

690

92

120

155

190

225

280

340

385

445

510

590

680

Aluminium (1) (2) (3) (1) (2) (3) (1) (2) (3)

10

16

25

35

50

70

95

120

150

185

240

300

62

79

100

120

145

180

210

240

270

305

350

395

68

87

115

135

160

195

235

270

300

340

390

440

55

71

93

115

135

165

205

235

265

300

355

405

66

84

110

130

150

185

220

250

285

320

370

420

73

94

120

145

170

210

250

285

325

360

420

475

58

76

99

120

140

175

215

245

280

320

380

435

75

96

125

150

175

215

255

290

325

365

425

480

84

110

140

165

195

240

285

325

370

415

480

540

71

92

120

145

175

215

260

300

345

395

465

530


Table 6-33: current-carrying capacities in three-core individually screened cables having a rated voltage

lower than or equal to 6/10 (12) kV

569




Nominal cross-

sectional area (mm²)


Copper (1) (2) (3)

16

25

35

50

70

95

120

150

185

240

125

160

190

225

270

330

370

415

465

540

140

175

210

250

305

370

420

465

525

610

125

160

195

230

280

345

395

450

510

600

Aluminium (1) (2) (3)

16

25

35

50

70

95

120

150

185

240

96

125

145

175

210

255

290

320

360

420

105

135

165

195

235

285

325

360

410

475

95

125

150

175

220

265

305

345

395

470

Table 6-34: current-carrying capacities in three-core individually screened cables having a rated voltage

greater than 6/6 (7,2) kV and lower than or equal to 18/30 (36) kV

570




6.2.4. Thermal withstand of conductors in the event of a short circuit and

determination of the cross-sectional area S2

The thermal withstand of live conductors must be checked for the maximum short-circuit

current at the origin of the cable. It is calculated using the impedance method taking into

account the participation of all the network elements (motors, generators, etc., see Protection

guide § 4.2).

In the case of an installation with an internal generator set, the thermal withstand is

established on the basis of the short-circuit current during the transient period, this

approximately corresponding to the short-circuit clearance time (see Protection guide § 4.1.2).

For a short-circuit time less than 5 seconds, cable heating is considered to be adiabatic; this

means that the energy stored stays in the core and is not transmitted to the insulating material.

The thermal calculations are then simplified. They are given below.

Note: to check the thermal withstand of protective and equipotential bonding conductors, the earthfault current must be taken into account (see § 4.2.2 of the Protection guide)

n general method

The heating calculation results are shown by the curves in figure 6-14. They give the current

density withstands δ 0 in different types of cable for a short-circuit time of one second, in

relation to the cable temperature before the short circuit.

The minimum conductor cross-sectional area complying with heating in the case of a short

circuit is determined by the fomula:

SIsc=δ

Isc : maximum short-circuit current, in A

δ : current density withstand, in A mm/ ²

for a short-circuit time other than one second, we have:

δ δ= 0

t

t : short-circuit time

571




Figure 6-14: short circuit in the core

572




n simplified method

This assumes that the cable temperature before the short circuit is equal to the temperature

allowed in steady-state operating conditions.

In this case, the conductor cross-sectional area must meet the following condition:

SI

ktsc≥

Isc : maximum short-circuit current

t : short-circuit time

k : coefficient the value of which is given in table 6-35

For protective conductors, the current to be taken into account is the earth fault current I f .

Insulating material

PVC

PE

XLPE

EPR

Live conductors

- in copper 115 143

- in aluminium 74 94

Protective conductors a b a b

- in copper 143 115 176 143

- in aluminium 95 75 116 94

- in steel 52 _ 64 _

a protective conductors not incorporated in cables

b protective conductors incorporated in cables

Table 6-35: coefficient k values

573




6.2.5. Short-time withstand currents in cable screens with extruded synthetic

insulation (determination of S3 )

In the event of a phase-to-screen short circuit, the thermal withstand resulting from the

passage of the fault current I f for a time t , must not exceed the thermal withstand of the

cable screen. I f is the earth fault current and the method for determining its value is

described in the Protection guide, paragraph 4-2.

The calculation of the overcurrent permitted in the cable screens depends on what the screen

is made of and the type of cable.

In the absence of precise indications, the values of tables 6-37, 6-38 and 6-39 can be used.

These values correspond to a screen made up of a copper band 0.1 mm thick wrapped around

the insulating material with an overlap of 15 %.

Table 6-36 gives, for each type of insulating material, the temperatures during normal service

and at the end of overcurrents used for calculating cable screen heating.

Type of insulating

material

Temperature on the screen during

service (°C)

Final temperature following

overcurrent

(°C)

XLPE

EPR

PE

PVC

70

70

60

60

250

250

150

160

Table 6-36: temperature conditions used for the calculation

574




o overcurrent values permitted in cable screens with extruded synthetic insulation

See tables 6-37, 6-38 and 6-39.

Rated voltage 6/10 (12) kV 8.7/15 (17.5) kV 12/20 (24) kV 18/30 (36) kV

Short-circuit time 0.5 s 1 s 2 s 0.5 s 1 s 2 s 0.5 s 1 s 2 s 0.5 s 1 s 2 s

Conductor cross-sectional

area in mm²

16 1 100 900 650 1 350 1 000 800 1 800 1 400 1 100

25 1 200 950 700 1 400 1 050 800 1 800 1 400 1 100

35 1 400 1 000 900 1 650 1 250 1 000 1 850 1 400 1 100

50 1 600 1 150 1 000 1 750 1 350 1 050 1 950 1 450 1 150 2 500 1 950 1 550

70 1 750 1 250 1 050 1 900 1 450 1 150 2 100 1 600 1 250 2 700 2 050 1 650

95 1 850 1 350 1 100 2 050 1 550 1 200 2 200 1 700 1 300 2 800 2 150 1 700

120 1 900 1 400 1 150 2 150 1 650 1 300 2 500 1 950 1 550 3 100 2 400 1 900

150 2 150 1 650 1 300 2 400 1 850 1 500 2 600 2 000 1 600 3 150 2 450 1 950

185 2 400 1 850 1 450 2 600 2 000 1 600 2 750 2 150 1 700 3 350 2 600 2 100

240 2 700 2 050 1 650 2 800 2 150 1 700 3 100 2 400 1 950 3 600 2 750 2 200

300 2 800 2 150 1 750 3 150 2 450 1 950 3 300 2 550 2 050 3 800 2 950 2 350

400 3 050 2 350 1 800 3 450 2 650 2 150 3 650 2 800 2 250 4 200 3 300 2 650

500 3 400 2 550 1 950 3 800 2 950 2 350 4 100 3 200 2 550 4 550 3 550 2 850

630 3 750 3 000 2 300 4 250 3 300 2 650 4 450 3 450 2 800 4 950 3 850 3 100

800 4 400 3 400 2 600 4 650 3 600 2 900 4 850 3 750 3 000 5 300 4 150 3 300

1 000 5 100 3 900 3 050 5 200 4 050 3 250 5 350 4 200 3 350 5 850 4 550 3 650

1 200 5 350 4 100 3 300 5 450 4 250 3 400 5 650 4 400 3 550 6 150 4 800 3 850

1 400 5 600 4 400 3 550 5 900 4 550 3 650 6 050 4 700 3 800 6 550 5 100 4 100

1 600 6 000 4 700 3 800 6 200 4 850 3 900 6 400 5 000 4 000 6 900 5 350 4 300

Table 6-37: single-core or three-core individually screened cables with XLPE or EPR insulation -

short-circuit current permitted in the screen (A)

575




Rated voltage 6/10 (12) kV 8.7/15 (17.5) kV 12/20 (24) kV 18/30 (36) kV

Short-circuit time 0.5 s 1 s 2 s 0.5 s 1 s 2 s 0.5 s 1 s 2 s 0.5 s 1 s 2 s

Conductor cross-sectional

area in mm²

16 800 650 490 1 000 740 560 1 200 870 660

25 900 700 510 1 000 750 570 1 200 870 660

35 1 000 750 540 1 100 800 600 1 200 880 660

50 1 100 800 580 1 150 840 640 1 250 1 000 770 1 750 1 300 990

70 1 300 920 700 1 350 990 760 1 450 1 100 820 1 750 1 300 1 000

95 1 350 1 000 750 1 450 1 050 820 1 550 1 150 880 2 050 1 550 1 200

120 1 450 1 050 800 1 500 1 150 860 1 650 1 200 930 2 150 1 650 1 230

150 1 550 1 100 840 1 600 1 200 910 1 700 1 300 1 000 2 250 1 700 1 300

185 1 650 1 150 900 1 700 1 250 970 2 000 1 500 1 200 2 350 1 800 1 400

240 1 800 1 450 1 100 2 000 1 550 1 200 2 150 1 650 1 250 2 650 2 050 1 600

300 2 000 1 550 1 200 2 150 1 650 1 300 2 300 1 750 1 350 2 800 2 150 1 700

400 2 300 1 750 1 400 2 600 2 000 1 550 2 650 2 050 1 600 3 000 2 300 1 800

500 2 550 1 900 1 500 2 900 2 200 1 750 3 050 2 350 1 850 3 400 2 600 2 050

630 2 750 2 050 1 550 3 000 2 300 1 800 3 150 2 400 1 900 3 500 2 650 2 050

800 3 000 2 250 1 700 3 300 2 500 2 000 3 450 2 600 2 100 3 700 2 800 2 200

1 000 3 300 2 400 1 800 3 500 2 700 2 100 3 650 2 800 2 200 3 950 3 000 2 400

1 200 3 550 2 550 1 900 3 700 2 850 2 200 3 850 2 950 2 300 4 200 3 200 2 550

1 400 3 650 2 750 2 000 3 900 3 000 2 350 4 050 3 100 2 450 4 350 3 350 2 650

1 600 3 750 2 850 2 100 4 000 3 100 2 400 4 150 3 200 2 500 4 500 3 400 2 700

Table 6-38: single-core or three-core individually screened cables with PE insulation -


576




Conductor cross-

sectional area

Short-cicuit time

mm²0.5 s 1 s 2 s

10 1 550 1 200 980

16 1 700 1 300 1 050

25 1 950 1 450 1 200

35 2 050 1 550 1 250

50 2 150 1 600 1 300

70 2 300 1 700 1 400

95 2 550 1 900 1 550

120 2 750 2 100 1 650

150 2 900 2 200 1 750

185 3 350 2 450 2 050

240 3 500 2 650 2 200

Table 6-39: PVC-insulated three-core collectively screened cables with a rated voltage of 6/6 (7.2 kV) -


o example

Let us consider a PE-insulated single-core cable in a 10 kV network having an earth fault

current I f limited to 1 000 A.

According to table 6-38, the minimum cross-sectional area of the conductor depends on the

short-circuit time:

- for t = 0.5 s , Smin = 35 mm²

- for t = 1 s , Smin = 95 mm²

- for t = 2 s , Smin = 240 mm² .

The cross-sectional area S3 is selected in relation to I f and the short-circuit time, which is

taken to be equal to the longest time needed to clear the fault (e.g., the back-up protection

time delay).

577




6.2.6. Checking voltage drops

Voltage drops in medium voltage cables in industrial networks are in general negligible.

However, it seems useful to give the calculation method able to be applied notably for very

long wiring systems.

For a three-phase circuit, the voltage drop (single-phase voltage) is calculated by the fomula:

∆VL

SL IB= +

ρ ϕ λ ϕ1 cos sin

ρ1 : conductor resistivity during normal service, i.e. 1.25 times that at 20 °C

ρ120 0225= . /Ω mm m for copper; ρ1

20 036= . /Ω mm m for aluminium

L : length of wiring system, in metres

S : conductor cross-sectional areas, in mm²

cosϕ : power factor; in the absence of precise indications, we may take ( )cos . sin .ϕ ϕ= =0 8 0 6

IB : maximum design current in A

λ : reactance per unit length of the wiring system, in Ω /m .

The values of λ in MV are:

- 0 08 10 3. /× − Ω m for three-core cables

- 0 15 10 3. /× − Ω m for single-core cables

We define the relative voltage drop as:

∆V

Vn

Vn : nominal single-phase voltage

578




6.2.7. Practical determination of the minimum cross-sectional area of a medium

voltage cable (see fig. 6-15)

determination of

maximum design

current

equivalent current (1)

thermal withstand

screen thermal

withstand:

voltage drop

check

determination of the cross-sectional area of the cable

able to carry in standard installation conditions in

relation to the type of cable, its insulation and rated

voltage (see tab. 8-29 to 8-34)

determination of the

cable column and

overall correction

factor (see tab. 8-23)

IB

S S S Smax ( , , )1 2 3

cable installation

conditions

Iz

S1

economic cross-sectional

area possibly chosen

(1) is an equivalent current which, in standard installation conditions,

causes the same thermal effect as in actual installation

conditions

IzIB

II

fz

B

Iscmax

(see tab. 8-37 to 8-39)

S I tf3 ,functionIf

SI

ktsc

2max

Figure 6-15: logigram for determining the minimum cross-sectional area of a medium voltage cable

579




6.2.8. Cable screen earthing conditions

n single-core cables

The passage of a current in the cable core produces an induced voltage in the screen. This

voltage depends on the geometrical arrangement of the cables, the length and the current

carried:

Ea

dI0 100145

2= ×

× ×. log l

a : distance between cable axes (mm)

d : mean diameter of the screen (mm)

l : connection length (km)

I : current carried in the core (A).

For very long cables, E0 may reach dangerous values for persons. The standard

recommends screen earthing at both ends when E0 is likely to exceed the limit of 50 V

under steady-state operating conditions.

However, screen earthing at both ends produces currents continuously circulating in the

screen.

For screen earthing at one end only, on occurrence of a short circuit, the potential induced on

the second end may be high and cause a breakdown of the screen insulation where it is

connected. The necessary precautions must therefore be taken.

o calculation of the current circulating in screens earthed at both ends

In balanced steady-state operating conditions (or during a three-phase short circuit), the

induced voltage in screens earthed at both ends causes a three-phase current to circulate.

This current is given by the formula:

IE

R Xs s

00

2 2=

+

where Xa

ds = ×

×0145

210. log l

Rs : screen resistance (Ω)

Xs : screen reactance (Ω)

l : length of cable or line

580




o example

Let us consider a 20 kV aluminium single-core cable with a cross-sectional area of 300 mm² ,

with PE insulation and a length of l = 3 km , buried in soil having a resistivity of ρ = ⋅100Ω m ,

the characteristics of which are as follows:

- I Acapacity = 500- d mm= 33 5.- a mm= 38 5.- R kms = 0.45 /Ω

It is installed in a network such that:

- I AB = 400- I kAsc = 8

The induced voltage under steady-state operating conditions is:

Ea

dI VB0 100145

263= ×

× × =. log l

The 50 V limit is exceeded and the screen must therefore be earthed at both ends.

The circulation current in the screen is in this case:

IE

R Xs s

00

2 2=

+

Rs = 1.35 Ω

Xs = 0 1452

015710. log .×

× =a

dl Ω

whence I A0 46= .4

Note: the circulation current in the screen is independent of the cable length.

581




The induced voltage in the event of a short circuit is:

Ea

dI Vsc sc0 100145

21260= ×

× × =. log l

The circulation current in the screen is then:

I Asc0 927=

This current must be withstood by the screen for the maximum short-circuit time. This is the

case since it can withstand 1 350 A for 2 s (see table 6-38).

Note: if the cable length was 2 km, the screen would be earthed at one end only. The voltage inducedin the screen on occurrence of the short circuit will then be equal to 840 V. In this case it isnecessary to check that the screen insulation at the point where the terminal box is located issufficient.

Evaluation of Ws losses in the screen

W R Is s= 02

for R kms = 0.45 /Ω , l = 3 km and I A0 46= .4

( )W kWs = × × =0 3 46 2 92

.45 .4 .

The losses in the core are:

W R Ic c B= × 2

Rc : core resistance

For an aluminium conductor with a cross-sectional area of S mm= 300 ² , R kmc = 01. /Ω

whence ( )W kWc = × × =0 1 3 400 482

.

We determine the ratioW

W

s

c

= 6%

The screen losses represent 6 % of the core losses. They must therefore be taken into

account when determining the maximum current-carrying capacity of the cable.

582




o thermal effect in the cable screens

As we saw in the previous example, when the screen is earthed at both ends, the continuous

circulation of induced current in the screen causes extra heating in the cable and consequently

reduces its current-carrying capacity.

Generally, this phenomenon is only to be taken into account for cables with a cross-sectional

area greater than 240 mm².

We can apply the following rule:

- thin screen without armour, for S mm>1000 ² the current-carrying capacity is reduced by 5 %

- non-thin screen without armour, the current-carrying capacity is to be reduced by:

. 5 % for 240 800mm S mm² ²≤ ≤

. 10 % for S mm> 800 ²

- cables with screen and armour, the current-carrying capacity is to be reduced by:

. 5 % for 240 400mm S mm² ²≤ ≤

. 10 % for 500 800mm S mm² ²≤ ≤

. 15 % for S mm> 800 ²

n three-core cables

For three-core collectively screened cables, the electromagnetic field is zero in balanced

operating conditions.

In normal operating conditions, there is no circulation current in the screen.

583




6.2.9. Application example

Let us determine the conductor cross-sectional area of the W1 wiring system inserted into the

network illustrated in figure 6-17.

The W1 wiring system is made up of three single-core three-phase 6/10 (12) kV aluminium

cables with XLPE insulation, directly installed in a enclosed channel in a temperature of 35 °C.

The time delay of the protection against phase-to-phase short circuits is: t s= 0 2. .

400 V

wiring system

= 1200 ml

= 630 kVASnT2

T1

= 10 MVASn

= 8 %

20 kV

1000 AUsc

W1

= 4 %Usc

Un = 5.5 kV

Figure 6-17: diagram of the installation

584




n determining the maximum design current IB

The W1 wiring system only feeds the 630 kVA power transformer T2 .

The current IB is thus taken to be equal to the nominal transformer current:

I IS

UAB n

n

n

= = = ×× ×

=3

630 10

3 5 5 1066

3

3.

n correction factors and choice of S1

The direct installation in an enclosed channel corresponds to installation type L4 (see

table 6-23). Column (3) in the current-carrying capacity tables must be used.


- installation method: f0 0 8= .

- ambient temperature (see table 6-24): f1 0 96= .

- group of several cables (see table 6-28): f5 1=

The overall correction factor is: f = × =0 8 0 96 0 77. . .

The equivalent current that the cable must be able to carry in standard installation conditions

is:

II

fAz

B= = 86

Table 6-31 (column (3), XLPE, aluminium) gives a minimum cross-sectional area of

S mm1216= which has a current-carrying capacity of I A0 95= .

585




n checking thermal withstand ( )S2

Neglecting the impedance upstream of the transformer and the impedance of the transformer-

busbar connection, the maximum short-circuit current at the origin of the cable is equal to the

short-circuit current of the transformer.

The impedance of the transformer T1 is:

( )Z

U

S

UT

n

n

sc1

2 3 2

6100

5 5 10

10 10

8

1000 242= × =

×

×× =

.. Ω

The maximum short-circuit current is thus:

IU

ZkAsc

n

T

= = ××

×=11

311

5 5 10

3 0 24214

1

3

. ..

..4 (see Protection guide § 4.2.1)

The cross-sectional area complying with the short-circuit requirement is:

SI

ktsc

2 ≥

k = 94 : value of the coefficient corresponding to a XLPE-insulated aluminium conductor (see table 6-35)

t s= 0 2. : short-circuit time equal to the protection time delay

whence S mm2269≥

The minimum cross-sectional area to be chosen is thus S mm2270=

586




n checking the cable screen thermal withstand ( )S3

The 5.5 kV distribution network has an earthing system with a 1 000 A current limiting resistor.

The fault current is then:

IV

RIf

n

NC= + (see Protection guide § 4.3.2)

Vn : single-phase network voltage

RN : limiting resistance

IC : 5.5 kV network capacitive current ( )I jC VC n= 3 ω

The capacitive current of an industrial network is of the order of several amps to several dozen

amps and it can thus be neglected in relation to the 1 000 A limiting current.

We thus have I f = 1 000 A

We assume that the screen must be able to withstand the fault current for 2 seconds, in order

to take into account the maximum time delay of the protection against phase-earth faults and

eventual reclosing.

The cross-sectional area of the conductor complying with the thermal withstand of the cable

screen is then:

S mm3250= (see table 6-37)

587




n checking voltage drops

The voltage drop is given by the formula:

∆VS

IB= +

ρ ϕ λ ϕ1l

lcos sin

l =1200m ; S mm= 70 ² ; λ = × −015 10 3. /Ω m ; I AB = 66 ; ρ120 036= ⋅. /Ω mm m

We assume that the cable load has a ( )cos . sin .ϕ ϕ= =0 6 0 8

whence ∆V = × + × × ×

×−

0 0361200

500 8 015 10 1200 0 6 66

3. . . .

∆V V= 53

The relative voltage drop is: ∆V

Vn

=

=53

1755003

. %

In spite of a very long cable length for an industrial network, the voltage drop is acceptable.

n choosing the technical cross-sectional area

The calculations carried out give the following cross-sectional areas:

S mm1 16= ²

S mm2 70= ²

S mm3 50= ²

The technical cross-sectional area to be chosen is thus:

S mm= 70 ²

588




6.3. Calculating the economic cross-sectional area

The methods described in chapters 6-1 and 6-2 lead to the choice of technical cross-sectional

areas of wiring systems, complying with the different thermal withstands, voltage drops and

protection of persons.

But it may be useful to take into account the economic criterion, based on the cost of

investment and the operating costs, when looking for the optimum cross-sectional area.

The investment cost is essentially composed of:

- the cable cost, linear function of the cross-sectional area S and length L ,

i.e. K L K L S1 2+

- the cost of civil engineering and installation, depending on the length and regardless of the

cross-sectional area in a limited interval, i.e. K L3 .

The operating costs comprise:

- the Joule losses in the cable

- the maintenance costs.

To calculate the economic cross-sectional area, only the cost of the Joule losses w relative to

the wiring system is taken into account:

w nL

SIH C= × ×ρ 2

1 000 Euros.

n : number of live conductorsρ : resistivity of the live conductor during normal service, i.e. 1.25 times that at 20 °C.

ρ = 0 0225. ²/Ω mm m for copper; ρ = ×0 036, ² /Ω mm m for aluminium

L : cable length

S : cross-sectional area of conductors

I : current carried, assumed to be constant, in A

H : number of cable operating hours (for a year H = 8 760)

C : cost of kWh, Euro/kWh.

The cost of investment and the cost of losses w do not have the same term of payment. It is

necessary to change in order to carry out the sum of their values. This can be done by

converting the operating costs paid at the end of consecutive years to current value, i.e. by

converting them to the period in which the cable is purchased.

589




If N (years) is the amortizement time forecast for the cable, and if the price of energy and

the cable load are assumed to be constant for the entire period, the sum of converted values

of Joule losses is:

( ) ( )( )

( )W w

t t t

wt

t tN

N

N=

++

++ +

+

= ×+ −

+

1

1

1

1

1

1

1 1

12

.......

t being the forecast conversion to current value rate.

We can write Ww

A= , where

( )( )

At t

t

N

N=

+

+ −

1

1 1

The total cost is therefore:

( )P S K L K L K L S nL

SI

H C

A= + + +

×3 1 22

1000ρ

The function ( )P S goes via a minimum∂∂P

S=

0

for a cross-sectional area of S In H C

K A0

2 1000=

×ρ

For an approximate calculation we can use the following formula:

SK I H C

Amm0

100= , ²

where K = 2 56. for copper and 4 61. for aluminium.

The value of the economic cross-sectional area to be chosen is the closest standard

value to S0 .

590




n example

Taking the elements from the application example of § 6.2.9:

- design current I AB = 66

- energy cost: C Euro kWh= 0 061. /

- aluminium conductor, K = 4 61.

- conversion to current value rate of 8 %

- amortizement time N = 20 years

- number of operating hours H = 3 800 hours.

( )( )

A =× +

+ −=

0 08 1 0 08

1 0 08 10102

20

20

. .

..

S mm0

66 4 61

100

3 800 0 061

0102145= × × =. .

.²

The economic cross-sectional area is the closest standard value to S0 , i.e. S mm= 150 2 .

In practice, the economic cross-sectional area is often greater than the technical cross-

sectional area.

n advantages of cable oversizing

- Improved voltage quality under normal operating conditions and reduced amplitude of

voltage surges during motor or other machine starting.

- Presence of reserve power offering the possibility of future extensions.

Documents

06 determining conductor cross sectional areas