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

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Fig. G65:Example of single-line diagram

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Calculation using software Ecodial 3.3

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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
Single-core or multi-core cable	Single		Switchboard B6
Installation method	F		Reference Linergy 800
Number of layers	1		Rated current (A) 750
Phase conductor selected csa (mm2)	2 x 240		Circuit-breaker Q7
Neutral conductor selected csa (mm2)	2 x 240		Load current (A) 255
240PE conductor selected csa (mm2) 1 x 120			Type Compact
Voltage drop ΔU (%) 0.122			Reference NSX400F
3-phase short-circuit current Ik3 (kA) 21.5			Rated current (A) 400
Courant de défaut phase-terre Id (kA) 15.9			Number of poles and protected poles 3P3d
Circuit-breaker Q1			Tripping unit Micrologic 2.3
Load current (A) 860			Overload trip Ir (A) 258
Type Compact			Short-delay trip Im / Isd (A) 2576
Reference NS1000N			Cable C7
Rated current (A) 1000			Length 5
Number of poles and protected poles 4P4d			Maximum load current (A) 255
Tripping unit Micrologic 5.0			Type of insulation PVC
Overload trip Ir (A) 900			Ambient temperature (°C) 30
Short-delay trip Im / Isd (A) 9000			Conductor material Copper
Tripping time tm (ms) 50			Single-core or multi-core cable Single
Switchboard B2			Installation method F
Reference Linergy 1250			Phase conductor selected csa (mm2) 1 x 95
Rated current (A) 1050			Neutral conductor selected csa (mm2) -
Circuit breaker Q3			PE conductor selected csa (mm2) 1 x 50
Load current (A) 509			Cable voltage drop ΔU (%) 0.14
Type Compact			Total voltage drop ΔU (%) 0.79
Reference NSX630F			3-phase short-circuit current Ik3 (kA) 18.0
Rated current (A) 630			1-phase-to-earth fault current Id (kA) 10.0

   

 

Fig. G66:Partial results of calculation carried out with Ecodial 3.4 software (Schneider Electric)

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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:

 

 

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:

 

                                         (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:

 

 

 

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:

 

 

• 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 95mm².
The resistance and the inductive reactance for a length of 20 metres is:

 

                                           (cable resistance: 22.5 mΩ.mm2/m)

                                           (cable reactance: 0.08 mΩ/m)

 

 

• Calculation of short-circuit currents for the selection of circuit-breakers Q1, Q3, Q7 (seeFig. G67)

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Fig. G67:Example of short-circuit current evaluation

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• 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 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 andF40, 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:

(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 inFigure G28, for balanced three-phase circuits, motor power normal service (cos φ = 0.8).
The results are summarized on figure G68:

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Fig. G68:Voltage drop introduced by the different cables

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

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