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Worked example of cable calculation

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General rules of electrical installation design
Connection to the MV utility distribution network
Connection to the LV utility distribution network
MV and LV architecture selection guide for buildings
LV Distribution
Protection against electric shocks and electric fires
Sizing and protection of conductors
LV switchgear: functions and selection
Overvoltage protection
Energy Efficiency in electrical distribution
Power Factor Correction
Power harmonics management
Characteristics of particular sources and loads
PhotoVoltaic (PV) installation
Residential and other special locations
ElectroMagnetic Compatibility (EMC)
Measurement

Contents


Worked example of cable calculation

(see Fig. G65)

The installation is supplied through a 630 kVA transformer. The process requires a high degree of supply continuity and part of the installation can be supplied by a 250 kVA standby generator. The global earthing system is TN-S, except for the most critical loads supplied by an isolation transformer with a downstream IT configuration.

The single-line diagram is shown in Figure G65 below. The results of a computer study for the circuit from transformer T1 down to the cable C7 is reproduced on Figure G66. This study was carried out with Ecodial (a Schneider Electric software).

This is followed by the same calculations carried out by the simplified method described in this guide.

Fig. G65Example of single-line diagram

Calculation using software Ecodial

General network characteristics Cable C3
Earthing system TN-S Length 20
Neutral distributed No Maximum load current (A) 509
Voltage (V) 400 Type of insulation PVC
Frequency (Hz) 50 Ambient temperature (°C) 30
Upstream fault level (MVA) 500 Conductor material Copper
Resistance of MV network (mΩ) 0.0351 Single-core or multi-core cable Single
Reactance of MV network (mΩ) 0.351 Installation method F
Transformer T1 Phase conductor selected csa (mm2) 2 x 95
Rating (kVA) 630 Neutral conductor selected csa (mm2) 2 x 95
Short-circuit impedance voltage (%) 4 PE conductor selected csa (mm2) 1 x 95
Transformer resistance RT (mΩ) 3.472 Cable voltage drop ΔU (%) 0.53
Transformer reactance XT (mΩ) 10.64 Total voltage drop ΔU (%) 0.65
3-phase short-circuit current Ik3 (kA) 21.54 3-phase short-circuit current Ik3 (kA) 19.1
Cable C1 1-phase-to-earth fault current Id (kA) 11.5
Length (m) 5 Switchboard B6
Maximum load current (A) 860 Reference Linergy 800
Type of insulation PVC Rated current (A) 750
Ambient temperature (°C) 30 Circuit-breaker Q7
Conductor material Copper Load current (A) 255
Single-core or multi-core cable Single Type Compact
Installation method F Reference NSX400F
Number of layers 1 Rated current (A) 400
Phase conductor selected csa (mm2) 2 x 240 Number of poles and protected poles 3P3d
Neutral conductor selected csa (mm2) 2 x 240 Tripping unit Micrologic 2.3
PE conductor selected csa (mm2) 1 x 120 Overload trip Ir (A) 258
Voltage drop ΔU (%) 0.122 Short-delay trip Im / Isd (A) 2576
3-phase short-circuit current Ik3 (kA) 21.5 Cable C7
Courant de défaut phase-terre Id (kA) 15.9 Length 5
Circuit-breaker Q1 Maximum load current (A) 255
Load current (A) 860 Type of insulation PVC
Type Compact Ambient temperature (°C) 30
Reference NS1000N Conductor material Copper
Rated current (A) 1000 Single-core or multi-core cable Single
Number of poles and protected poles 4P4d Installation method F
Tripping unit Micrologic 5.0 Phase conductor selected csa (mm2) 1 x 95
Overload trip Ir (A) 900 Neutral conductor selected csa (mm2) -
Short-delay trip Im / Isd (A) 9000 PE conductor selected csa (mm2) 1 x 50
Tripping time tm (ms) 50 Cable voltage drop ΔU (%) 0.14
Switchboard B2 Total voltage drop ΔU (%) 0.79
Reference Linergy 1250 3-phase short-circuit current Ik3 (kA) 18.0
Rated current (A) 1050 1-phase-to-earth fault current Id (kA) 10.0
Circuit breaker Q3
Load current (A) 509
Type Compact
Reference NSX630F
Rated current (A) 630
Number of poles and protected poles 4P4d
Tripping unit Micrologic 2.3
Overload trip Ir (A) 510
Short-delay trip Im / Isd (A) 5100

Fig. G66Partial results of calculation carried out with Ecodial software (Schneider Electric). The calculation is performed according to Cenelec TR50480

The same calculation using the simplified method recommended in this guide

Dimensioning circuit C1

The MV/LV 630 kVA transformer has a rated no-load voltage of 420 V. Circuit C1 must be suitable for a current of:

I_B=\frac{630 \times 10^3}{\sqrt 3 \times 420}=866 A per phase

Two single-core PVC-insulated copper cables in parallel will be used for each phase.These cables will be laid on cable trays according to method F.

Each conductor will therefore carry 433A. Figure G21a indicates that for 3 loaded conductors with PVC isolation, the required c.s.a. is 240mm2.

The resistance and the inductive reactance, for the two conductors in parallel, and for a length of 5 metres, are:

R=\frac{23.7 \times 5}{240\times 2}=0.25 m\Omega (cable resistance: 23.7 mΩ.mm2/m)

X = 0,08 \times 5 = 0.4 m\Omega (cable reactance: 0.08 mΩ/m)

Dimensioning circuit C3

Circuit C3 supplies two 150kW loads with cos φ = 0.85, so the total load current is:

I_B=\frac{300 \times 10^3}{\sqrt 3 \times 400 \times 0.85}=509 A

Two single-core PVC-insulated copper cables in parallel will be used for each phase. These cables will be laid on cable trays according to method F.

Each conductor will therefore carry 255A. Figure G21a indicates that for 3 loaded conductors with PVC isolation, the required c.s.a. is 95mm2.

The resistance and the inductive reactance, for the two conductors in parallel, and for a length of 20 metres, are:

R=\frac{23.7\times 20}{95\times 2}=2.5 m\Omega (cable resistance: 23.7 mΩ.mm2/m)

X = 0.08 \times 20 = 1.6m \Omega (cable reactance: 0.08 mΩ/m)

Dimensioning circuit C7

Circuit C7 supplies one 150kW load with cos φ = 0.85, so the total load current is:

I_B=\frac{150 \times 10^3}{\sqrt 3 \times 400 \times 0.85}=255 A

One single-core PVC-insulated copper cable will be used for each phase. The cables will be laid on cable trays according to method F.

Each conductor will therefore carry 255A. Figure G21a indicates that for 3 loaded conductors with PVC isolation, the required c.s.a. is 95mm2.

The resistance and the inductive reactance for a length of 20 metres is:

R=\frac{23.7\times 5}{95}=1.25m\Omega (cable resistance: 23.7 mΩ.mm2/m)

X = 0.8 \times 5 = 0.4m\Omega (cable reactance: 0.08 mΩ/m)

Calculation of short-circuit currents for the selection of circuit-breakers Q1, Q3, Q7

(see Fig. G67)

Circuit components R (mΩ) X (mΩ) Z (mΩ) Ikmax (kA)
Upstream MV network, 500MVA fault level (see Fig. G34) 0,035 0,351
Transformer 630kVA, 4% (see Fig. G35) 2.9 10.8
Cable C1 0.23 0.4
Sub-total 3.16 11.55 11.97 20.2
Cable C3 2.37 1.6
Sub-total 5.53 13.15 14.26 17
Cable C7 1.18 0.4
Sub-total 6.71 13.55 15.12 16

Fig. G67Example of short-circuit current evaluation

The protective conductor

When using the adiabatic method, the minimum c.s.a. for the protective earth conductor (PE) can be calculated by the formula given in Figure G58:

S_{PE}=\frac{\sqrt {I^2 . t} }{k}

For circuit C1, I = 20.2kA and k = 143.

t is the maximum operating time of the MV protection, e.g. 0.5s

This gives:

S_{PE}=\frac{\sqrt {I^2 . t} }{k}=\frac {20200 \times \sqrt {0.5} }{143}=100 mm^2

A single 120 mm2 conductor is therefore largely sufficient, provided that it also satisfies the requirements for indirect contact protection (i.e. that its impedance is sufficiently low).

Generally, for circuits with phase conductor c.s.a. Sph ≥ 50 mm2, the PE conductor minimum c.s.a. will be Sph / 2. Then, for circuit C3, the PE conductor will be 95mm2, and for circuit C7, the PE conductor will be 50mm2.

Protection against indirect-contact hazards

For circuit C3 of Figure G65, Figures F41 and F40, or the formula given in Conventional_method may be used for a 3-phase 4-wire circuit.

The maximum permitted length of the circuit is given by:

L_{max}=\frac{0.8 \times U_0 \times S_{ph} }{\rho \times \left ( 1 + m \right )\times I_a }

L_{max}=\frac{0.8 \times 230 \times 2 \times 95}{23.7 \times 10^{-3}\times \left ( 1 + 2 \right )\times 630\times 11 } = 71 m

(The value in the denominator 630 x 11 is the maximum current level at which the instantaneous short-circuit magnetic trip of the 630 A circuit-breaker operates).

The length of 20 metres is therefore fully protected by “instantaneous” over-current devices.

Voltage drop

The voltage drop is calculated using the data given in Figure G28, for balanced three-phase circuits, motor power normal service (cos φ = 0.8).

The results are summarized on Figure G68

The total voltage drop at the end of cable C7 is then: 0.77%.

C1 C3 C7
c.s.a. 2 x 240mm2 2 x 95mm2 1 x 95mm2
∆U per conductor(V/A/km)

see Fig. G28

0.22 0.43 0.43
Load current (A) 866 509 255
Length (m) 5 20 5
Voltage drop (V) 0.48 2.19 0.55
Voltage drop (%) 0.12 0.55 0.14

Fig. G68Voltage drop introduced by the different cables