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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
LV Distribution
Protection against electric shocks
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)

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 software (a Schneider Electric product).
This is followed by the same calculations carried out by the simplified method described in this guide.


FigG65.jpg

Fig. G65: Example of single-line diagram


Calculation using software Ecodial

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

Fig. G66: Partial results of calculation carried out with Ecodial software (Schneider Electric)


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{22.5 \times 5}{240\times 2}=0.23 m\Omega  (cable resistance: 22.5 mΩ.mm2/m)

X = 0,08 x 5 = 0,4 mΩ (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{22.5\times 20}{95\times 2}=2.37 m\Omega

X = 0.8 \times 20 = 1.6m \Omega

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{22.5\times 5}{95}=1.18m\Omega  (cable resistance: 22.5 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. G67: Example 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 page F25 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 2302 \times 95}{22.5 \times 10^{-3}\times \left ( 1 + 2 \right )\times 630\times 11 }=75m

(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:

c.s.a. C1 C3 C7
2 x 240mm² 2 x 95mm² 1 x 95mm²
∆U per conductor
(V/A/km) see Fig. G28
0.21 0.42 0.42
Load current (A) 866 509 255
Length (m) 5 20 5
Voltage drop (V) 0.45 2.1 0.53
Voltage drop (%) 0.11 0.53 0.13

Fig. G68: Voltage drop introduced by the different cables



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