Worked example of cable calculation
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. 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 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: [math]\displaystyle{ I_B=\frac{630 \times 10^3}{\sqrt 3 \times 420}=866 A }[/math] 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:
[math]\displaystyle{ R=\frac{23.7 \times 5}{240\times 2}=0.25 m\Omega }[/math] (cable resistance: 23.7 mΩ.mm2/m)
[math]\displaystyle{ X = 0,08 \times 5 = 0.4 m\Omega }[/math] (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: [math]\displaystyle{ I_B=\frac{300 \times 10^3}{\sqrt 3 \times 400 \times 0.85}=509 A }[/math]
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:
[math]\displaystyle{ R=\frac{23.7\times 20}{95\times 2}=2.5 m\Omega }[/math] (cable resistance: 23.7 mΩ.mm2/m)
[math]\displaystyle{ X = 0.08 \times 20 = 1.6m \Omega }[/math] (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: [math]\displaystyle{ I_B=\frac{150 \times 10^3}{\sqrt 3 \times 400 \times 0.85}=255 A }[/math]
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:
[math]\displaystyle{ R=\frac{23.7\times 5}{95}=1.25m\Omega }[/math] (cable resistance: 23.7 mΩ.mm2/m)
[math]\displaystyle{ X = 0.8 \times 5 = 0.4m\Omega }[/math] (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:
[math]\displaystyle{ S_{PE}=\frac{\sqrt {I^2 . t} }{k} }[/math]
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:
[math]\displaystyle{ S_{PE}=\frac{\sqrt {I^2 . t} }{k}=\frac {20200 \times \sqrt {0.5} }{143}=100 mm^2 }[/math]
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:
[math]\displaystyle{ L_{max}=\frac{0.8 \times U_0 \times S_{ph} }{\rho \times \left ( 1 + m \right )\times I_a } }[/math]
[math]\displaystyle{ 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 }[/math]
(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:
| 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. G68: Voltage drop introduced by the different cables
The total voltage drop at the end of cable C7 is then: 0.77%.
