TN system - Earth-fault current calculation
Methods of determining levels of fault current
In TN-earthed systems, a fault to earth will, in principle, provide sufficient current to operate an overcurrent device.
The source and supply mains impedances are much lower than those of the installation circuits, so that any restriction in the magnitude of earth-fault currents will be mainly caused by the installation conductors (long flexible leads to appliances greatly increase the “fault-loop” impedance, with a corresponding reduction of the fault current).
The most recent IEC recommendations for fault protection on TN earthing systems only relates maximum allowable tripping times to the nominal system voltage (see Figure F13).
The reasoning behind these recommendations is that, for TN systems, the current which must flow in order to raise the potential of an exposed conductive part to 50 V or more is so high that one of two possibilities will occur:
- Either the fault path will blow itself clear, practically instantaneously, or
- The conductor will weld itself into a solid fault and provide adequate current to operate overcurrent devices.
To ensure correct operation of overcurrent devices in the latter case, a reasonably accurate assessment of earth-fault current levels must be determined at the design stage of a project.
A rigorous analysis requires the use of phase-sequence-component techniques applied to every circuit in turn. The principle is straightforward, but the amount of computation is not considered justifiable, especially since the zero-phase sequence impedances are extremely difficult to determine with any reasonable degree of accuracy in an average LV installation.
Other simpler methods of adequate accuracy are preferred.
Three practical methods are:
- The “method of impedances”, based on the summation of all the impedances (positive-phase-sequence only) around the fault loop, for each circuit
- The “method of composition”, which is an estimation of short-circuit current at the remote end of a loop, when the short-circuit current level at the near end of the loop is known
- The “conventional method” of calculating the minimum levels of earth-fault currents, together with the use of tables of values for obtaining rapid results.
These methods are only reliable for the case in which the cables that make up the earth-fault-current loop are in close proximity (to each other) and not separated by ferromagnetic materials.
Note: Schneider Electric’s Ecodial software is based on the “method of impedances”.
Method of impedances
This method summates the positive-sequence impedances of each item (cable, PE conductor, transformer, etc.) included in the earth-fault loop circuit from which the earth-fault current is calculated, using the formula:
[math]\displaystyle{ I=\frac{U_0}{\sqrt{\left ( \sum R \right )^2 + \left ( \sum X \right )^2 } } }[/math]
where
U_{0} = nominal system phase-to-neutral voltage.
(ΣR)^{2} = (the sum of all resistances in the loop)^{2} at the design stage of a project.
(ΣX)^{2} = (the sum of all inductive reactances in the loop)^{2}
The application of the method is not always easy, because it supposes a knowledge of all parameter values and characteristics of the elements in the loop.
In many cases, a national guide can supply typical values for estimation purposes.
Method of composition
This method permits the determination of the short-circuit current at the end of a loop from the known value of short-circuit at the sending end, by means of the approximate formula:
[math]\displaystyle{ I_{sc}=\frac {I.U_0}{U_0 + Z_s.I} }[/math]
where
I_{sc} = upstream short-circuit current
I = end-of-loop short-circuit current
U_{0} = nominal system phase voltage
Z_{s} = impedance of loop
Note: In this method the individual impedances are added arithmetically^{[1]} as opposed to the previous “method of impedances” procedure.
Conventional method
This method is generally considered to be sufficiently accurate to fix the upper limit of cable lengths.
Principle
The short-circuit current calculation is based on the assumption that the voltage at the origin of the circuit concerned (i.e. at the point at which the circuit protective device is located) remains at 80% or more of the nominal phase to neutral voltage.
The 80% value is used, together with the circuit loop impedance, to compute the short-circuit current.
This coefficient takes all voltage drops upstream of the point considered. In LV cables, when all conductors of a 3-phase 4-wire circuit are in close proximity (which is the normal case), the inductive reactance internal to and between conductors is negligibly small compared to the cable resistance.
This approximation is considered to be valid for cable sizes up to 120 mm².
Above that size, the resistance value R is increased as follows:
Core size (mm^{2}) | Value of resistance |
---|---|
S = 150 mm^{2} | R+15% |
S = 185 mm^{2} | R+20% |
S = 240 mm^{2} | R+25% |
The maximum length of a circuit in a TN-earthed installation is given by the formula:
[math]\displaystyle{ Lmax=\frac{0.8\ U_0\ S_{ph}}{\rho \left ( 1+m \right )I_a} }[/math]
where:
Lmax = maximum length in metres
U_{0} = phase volts = 230 V for a 230/400 V system
ρ = resistivity of conductors at the maximum permissible steady-state operating temperature, in Ω⋅mm² / m (see Fig. G38 for values of ρ)
I_{a} = trip current setting for the instantaneous operation of a circuit-breaker,
or:
I_{a} = the current which assures operation of the protective fuse concerned, in the specified time.
S_{ph} = cross-sectional area of the phase conductors of the circuit concerned in mm²
S_{PE} = cross-sectional area of the protective conductor concerned in mm².
[math]\displaystyle{ m=\frac{S_{ph}}{S_{PE}} }[/math]
(see Fig. F23)
Tables
The following tables, applicable to TN systems, have been established according to the “conventional method” described above.
The tables give maximum circuit lengths, beyond which the ohmic resistance of the conductors will limit the magnitude of the short-circuit current to a level below that required to trip the circuit breaker (or to blow the fuse) protecting the circuit, with sufficient rapidity to ensure fault protection.
Note: for industrial circuit breakers (IEC 60947-2), a 20% tolerance is taken concerning the magnetic trip current, i.e. the real trip level Ia may be 20% higher (or lower) than the magnetic trip setting Im of the circuit breaker. Table Fig. F25 includes this 20% tolerance and calculates the maximum length of the circuit for the worst-case, which is for Ia = Im x 1.2. For domestic circuit breakers (IEC 60898), the tripping value is stated without tolerance (for example, Ia = Im = 10 In for C curve), so Tables Fig. F26 to Fig. F28 are calculated with short-circuit value exactly equal to Im, without tolerance.
Correction factor m
Fig. F24 indicates the correction factor to apply to the values given in Fig. F25 to Fig. F28, according to the ratio Sph/SPE, the type of circuit, and the conductor materials.
The tables take into account:
- The type of protection: circuit breakers or fuses
- Operating-current settings
- Cross-sectional area of phase conductors and protective conductors
- Type of earthing system (see Fig. F16)
- Type of circuit breaker (i.e. B, C or D)^{[2]}
The tables may be used for 230/400 V systems.
Similar tables for protection by Schneider Electric Compact and Acti 9 circuit breakers are included in the relevant catalogues.
Circuit | Conductor material | m = Sph/SPE (or PEN) | |||
---|---|---|---|---|---|
m = 1 | m = 2 | m = 3 | m = 4 | ||
3P + N or P + N | Copper^{[a]} | 1 | 0.67 | 0.50 | 0.40 |
Aluminium | 0.63 | 0.42 | 0.31 | 0.25 |
- ^ Tables F25 to F28 have been calculated with ρ = ρ1 = 0.023 Ω⋅mm² / m, as defined by UTE C 15-105 (table GA) for calculation of minimum short-circuit current and for circuits protected by a circuit breaker
Nominal cross- sectional area of conductors | Instantaneous or short-time-delayed CB tripping current setting Im (amperes) | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
mm^{2} | 50 | 63 | 80 | 100 | 125 | 160 | 200 | 250 | 320 | 400 | 500 | 560 | 630 | 700 | 800 | 875 |
1.5 | 100 | 79 | 63 | 50 | 40 | 31 | 25 | 20 | 16 | 13 | 10 | 9 | 8 | 7 | 6 | 6 |
2.5 | 167 | 133 | 104 | 83 | 67 | 52 | 42 | 33 | 26 | 21 | 17 | 15 | 13 | 12 | 10 | 10 |
4 | 267 | 212 | 167 | 133 | 107 | 83 | 67 | 53 | 42 | 33 | 27 | 24 | 21 | 19 | 17 | 15 |
6 | 400 | 317 | 250 | 200 | 160 | 125 | 100 | 80 | 63 | 50 | 40 | 36 | 32 | 29 | 25 | 23 |
10 | 417 | 333 | 267 | 208 | 167 | 133 | 104 | 83 | 67 | 60 | 53 | 48 | 42 | 38 | ||
16 | 427 | 333 | 267 | 213 | 167 | 133 | 107 | 95 | 85 | 76 | 67 | 61 | ||||
25 | 417 | 333 | 260 | 208 | 167 | 149 | 132 | 119 | 104 | 95 | ||||||
35 | 467 | 365 | 292 | 233 | 208 | 185 | 167 | 146 | 133 | |||||||
50^{[a]} | 495 | 396 | 317 | 283 | 251 | 226 | 198 | 181 | ||||||||
70 | 417 | 370 | 333 | 292 | 267 | |||||||||||
95 | 452 | 396 | 362 | |||||||||||||
120 | 457 |
- Note: this table is calculated according to IEC60947-2, thus includes a 20% tolerance on the actual tripping current compared to the circuit breaker tripping setting (see upper note)
- ^ For 50 mm^{2} cables, the actual cross-section used for calculation is 47.5 mm²^{[3]}
Nominal cross- sectional area of conductors | Instantaneous or short-time-delayed CB tripping current setting Im (amperes) | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
mm^{2} | 1000 | 1120 | 1250 | 1600 | 2000 | 2500 | 3200 | 4000 | 5000 | 6300 | 8000 | 10000 | 12500 |
1.5 | 5 | 4 | 4 | ||||||||||
2.5 | 8 | 7 | 7 | 5 | 4 | ||||||||
4 | 13 | 12 | 11 | 8 | 7 | 5 | 4 | ||||||
6 | 20 | 18 | 16 | 13 | 10 | 8 | 6 | 5 | 4 | ||||
10 | 33 | 30 | 27 | 21 | 17 | 13 | 10 | 8 | 7 | 5 | 4 | ||
16 | 53 | 48 | 43 | 33 | 27 | 21 | 17 | 13 | 11 | 8 | 7 | 5 | 4 |
25 | 83 | 74 | 67 | 52 | 42 | 33 | 26 | 21 | 17 | 13 | 10 | 8 | 7 |
35 | 117 | 104 | 93 | 73 | 58 | 47 | 36 | 29 | 23 | 19 | 15 | 12 | 9 |
50^{[a]} | 158 | 141 | 127 | 99 | 79 | 63 | 49 | 40 | 32 | 25 | 20 | 16 | 13 |
70 | 233 | 208 | 187 | 146 | 117 | 93 | 73 | 58 | 47 | 37 | 29 | 23 | 19 |
95 | 317 | 283 | 263 | 198 | 158 | 127 | 99 | 79 | 63 | 50 | 40 | 32 | 25 |
120 | 400 | 357 | 320 | 250 | 200 | 160 | 125 | 100 | 80 | 63 | 50 | 40 | 32 |
150 | 435 | 388 | 348 | 272 | 217 | 174 | 136 | 109 | 87 | 69 | 54 | 43 | 35 |
185 | 459 | 411 | 321 | 257 | 206 | 161 | 128 | 103 | 82 | 64 | 51 | 41 | |
240 | 400 | 320 | 256 | 200 | 160 | 128 | 102 | 80 | 64 | 51 |
- Note: this table is calculated according to IEC60947-2, thus includes a 20% tolerance on the actual tripping current compared to the circuit breaker tripping setting (see upper note)
- ^ For 50 mm^{2} cables, the actual cross-section used for calculation is 47.5 mm²^{[3]}
Sph | Rated current (A) | ||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
mm^{2} | 1 | 2 | 3 | 4 | 6 | 10 | 16 | 20 | 25 | 32 | 40 | 50 | 63 | 80 | 100 | 125 | |||||||||||||
1.5 | 1200 | 600 | 400 | 300 | 200 | 120 | 75 | 60 | 48 | 37 | 30 | 24 | 19 | 15 | 12 | 10 | |||||||||||||
2.5 | 1000 | 666 | 500 | 333 | 200 | 125 | 100 | 80 | 62 | 50 | 40 | 32 | 25 | 20 | 16 | ||||||||||||||
4 | 1066 | 800 | 533 | 320 | 200 | 160 | 128 | 100 | 80 | 64 | 51 | 40 | 32 | 26 | |||||||||||||||
6 | 1200 | 800 | 480 | 300 | 240 | 192 | 150 | 120 | 96 | 76 | 60 | 48 | 38 | ||||||||||||||||
10 | 800 | 500 | 400 | 320 | 250 | 200 | 160 | 127 | 100 | 80 | 64 | ||||||||||||||||||
16 | 800 | 640 | 512 | 400 | 320 | 256 | 203 | 160 | 128 | 102 | |||||||||||||||||||
25 | 800 | 625 | 500 | 400 | 317 | 250 | 200 | 160 | |||||||||||||||||||||
35 | 875 | 700 | 560 | 444 | 350 | 280 | 224 | ||||||||||||||||||||||
50^{[a]} | 760 | 603 | 475 | 380 | 304 |
- ^ For 50 mm^{2} cables, the actual cross-section used for calculation is 47.5 mm²^{[3]}
Sph | Rated current (A) | ||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
mm^{2} | 1 | 2 | 3 | 4 | 6 | 10 | 16 | 20 | 25 | 32 | 40 | 50 | 63 | 80 | 100 | 125 | |||||||||||||
1.5 | 600 | 300 | 200 | 150 | 100 | 60 | 37 | 30 | 24 | 18 | 15 | 12 | 9 | 7 | 6 | 5 | |||||||||||||
2.5 | 500 | 333 | 250 | 167 | 100 | 62 | 50 | 40 | 31 | 25 | 20 | 16 | 12 | 10 | 8 | ||||||||||||||
4 | 533 | 400 | 267 | 160 | 100 | 80 | 64 | 50 | 40 | 32 | 25 | 20 | 16 | 13 | |||||||||||||||
6 | 600 | 400 | 240 | 150 | 120 | 96 | 75 | 60 | 48 | 38 | 30 | 24 | 19 | ||||||||||||||||
10 | 677 | 400 | 250 | 200 | 160 | 125 | 100 | 80 | 63 | 50 | 40 | 32 | |||||||||||||||||
16 | 640 | 400 | 320 | 256 | 200 | 160 | 128 | 101 | 80 | 64 | 51 | ||||||||||||||||||
25 | 625 | 500 | 400 | 312 | 250 | 200 | 159 | 125 | 100 | 80 | |||||||||||||||||||
35 | 875 | 700 | 560 | 437 | 350 | 280 | 222 | 175 | 140 | 112 | |||||||||||||||||||
50^{[a]} | 760 | 594 | 475 | 380 | 301 | 237 | 190 | 152 |
- ^ For 50 mm^{2} cables, the actual cross-section used for calculation is 47.5 mm²^{[3]}
Sph | Rated current (A) | ||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
mm^{2} | 1 | 2 | 3 | 4 | 6 | 10 | 16 | 20 | 25 | 32 | 40 | 50 | 63 | 80 | 100 | 125 | |||||||||||||
1.5 | 429 | 214 | 143 | 107 | 71 | 43 | 27 | 21 | 17 | 13 | 11 | 9 | 7 | 5 | 4 | 3 | |||||||||||||
2.5 | 714 | 357 | 238 | 179 | 119 | 71 | 45 | 36 | 29 | 22 | 18 | 14 | 11 | 9 | 7 | 6 | |||||||||||||
4 | 571 | 381 | 286 | 190 | 114 | 71 | 57 | 46 | 36 | 29 | 23 | 18 | 14 | 11 | 9 | ||||||||||||||
6 | 857 | 571 | 429 | 286 | 171 | 107 | 86 | 69 | 54 | 43 | 34 | 27 | 21 | 17 | 14 | ||||||||||||||
10 | 952 | 714 | 476 | 286 | 179 | 143 | 114 | 89 | 71 | 57 | 45 | 36 | 29 | 23 | |||||||||||||||
16 | 762 | 457 | 286 | 229 | 183 | 143 | 114 | 91 | 73 | 57 | 46 | 37 | |||||||||||||||||
25 | 714 | 446 | 357 | 286 | 223 | 179 | 143 | 113 | 89 | 71 | 57 | ||||||||||||||||||
35 | 625 | 500 | 400 | 313 | 250 | 200 | 159 | 125 | 100 | 80 | |||||||||||||||||||
50^{[a]} | 679 | 543 | 424 | 339 | 271 | 215 | 170 | 136 | 109 |
- ^ For 50 mm^{2} cables, the actual cross-section used for calculation is 47.5 mm²^{[3]}
Example
A 3-phase 4-wire (230/400 V) installation is TN-C earthed. A circuit is protected by a type B circuit breaker rated at 63 A, and consists of an aluminium core cable with 50 mm² phase conductors and a neutral conductor (PEN) of 25 mm².
What is the maximum length of circuit, below which fault protection is assured by the instantaneous magnetic tripping relay of the circuit breaker?
Figure F26 gives, for 50 mm^{2} and a 63 A type B circuit-breaker, 603 metres, to which must be applied a factor of 0.42 (Figure F24 for [math]\displaystyle{ m=\frac{Sph}{SPE}=2 }[/math]).
The maximum length of circuit is therefore:
603 x 0.42 = 253 meters.
Particular case where one (or more) exposed conductive part(s) is (are) earthed to a separate earth electrode
Fault Protection must be provided by a RCD at the origin of any circuit supplying an appliance or group of appliances, the exposed conductive parts of which are connected to an independent earth electrode.
The sensitivity of the RCD must be adapted to the earth electrode resistance (R_{A2} in Figure F16). See specifications applicable to TT system.
Notes
- ^ This results in a calculated current value which is less than what would actually flow. If the overcurrent settings are based on this calculated value, then operation of the relay, or fuse, is assured.
- ^ ^{1} ^{2} ^{3} ^{4} For the definition of type B, C, D circuit breakers, refer to Fundamental characteristics of a circuit-breaker
- ^ ^{1} ^{2} ^{3} ^{4} ^{5} In fact, the cable (maximum) resistance values that should be used for precise calculation are the ones given by the IEC 60228 "conductors of insulated cables" standard. Calculation of cable resistance with the formula R = ρ L / S, as used for this table, provides values that are sufficiently close to these values (in the order of 1%), except for 50 mm² cables for which a "theoretical" cross-section of 47.5 mm² should be used.