Worked example of cable calculation
From Electrical Installation Guide
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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.
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 (mm^{2}) | 2 x 95 | ||
Rating (kVA) | 630 | Neutral conductor selected csa (mm^{2}) | 2 x 95 | |
Short-circuit impedance voltage (%) | 4 | PE conductor selected csa (mm^{2}) | 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 Ik_{3} (kA) | 21.54 | 3-phase short-circuit current Ik_{3} (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 (mm^{2}) | 2 x 240 | Number of poles and protected poles | 3P3d | |
Neutral conductor selected csa (mm^{2}) | 2 x 240 | Tripping unit | Micrologic 2.3 | |
PE conductor selected csa (mm^{2}) | 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 Ik_{3} (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 (mm^{2}) | 1 x 95 | |
Overload trip Ir (A) | 900 | Neutral conductor selected csa (mm^{2}) | - | |
Short-delay trip Im / Isd (A) | 9000 | PE conductor selected csa (mm^{2}) | 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 Ik_{3} (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. G66: Partial 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:
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 240mm^{2}.
The resistance and the inductive reactance, for the two conductors in parallel, and for a length of 5 metres, are:
(cable resistance: 23.7 mΩ.mm^{2}/m)
(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:
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 95mm^{2}.
The resistance and the inductive reactance, for the two conductors in parallel, and for a length of 20 metres, are:
(cable resistance: 23.7 mΩ.mm^{2}/m)
(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:
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 95mm^{2}.
The resistance and the inductive reactance for a length of 20 metres is:
(cable resistance: 23.7 mΩ.mm^{2}/m)
(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:
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:
A single 120 mm^{2} 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 mm^{2}, the PE conductor minimum c.s.a. will be Sph / 2. Then, for circuit C3, the PE conductor will be 95mm^{2}, and for circuit C7, the PE conductor will be 50mm^{2}.
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:
(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 240mm^{2} | 2 x 95mm^{2} | 1 x 95mm^{2} |
∆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. G68: Voltage drop introduced by the different cables