3phase shortcircuit current (Isc) at any point within a LV installation
In a 3phase installation Isc at any point is given by:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle Isc = \frac{U_{20} }{\sqrt 3 Z_T}} where
U_{20} = phasetophase voltage of the open circuited secondary windings of the power supply transformer(s).
Z_{T} = total impedance per phase of the installation upstream of the fault location (in Ω)
Method of calculating Z_{T}
Each component of an installation (MV network, transformer, cable, busbar, and so on...) is characterized by its impedance Z, comprising an element of resistance (R) and an inductive reactance (X). It may be noted that capacitive reactances are not important in shortcircuit current calculations.
The parameters R, X and Z are expressed in ohms, and are related by the sides of a right angled triangle, as shown in the impedance diagram of Figure G35.
The method consists in dividing the network into convenient sections, and to calculate the R and X values for each.
Where sections are connected in series in the network, all the resistive elements in the section are added arithmetically; likewise for the reactances, to give R_{T} and X_{T}.
The impedance (Z_{T}) for the combined sections concerned is then calculated from Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle Z_T= \sqrt {R_T\ ^2 + X_T\ ^2}}
Any two sections of the network which are connected in parallel, can, if predominantly both resistive (or both inductive) be combined to give a single equivalent resistance (or reactance) as follows:
Let R1 and R2 be the two resistances connected in parallel, then the equivalent resistance R3 will be given by:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle R_3 =\frac {R_1 \times R_2}{R_1 + R_2}} or for reactances Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle X_3 = \frac{X_1 \times X_2}{X_1 + X_2} }
It should be noted that the calculation of X3 concerns only separated circuit without mutual inductance. If the circuits in parallel are close togother the value of X3 will be notably higher.
Determination of the impedance of each component
Network upstream of the MV/LV transformer
(see Fig. G36)
The 3phase shortcircuit fault level P_{SC}, in kA or in MVA^{[1]} is given by the power supply authority concerned, from which an equivalent impedance can be deduced.
Psc  U_{20} (V)  Ra (mΩ)  Xa (mΩ) 

250 MVA  420  0.07  0.7 
500 MVA  420  0.035  0.351 
A formula which makes this deduction and at the same time converts the impedance to an equivalent value at LV is given, as follows:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle Za = \frac{U_{20}\ ^2}{Psc}}
where
Za = impedance of the MV voltage network, expressed in milliohms
U_{20} = phasetophase noload LV voltage, expressed in volts
Psc = MV 3phase shortcircuit fault level, expressed in kVA
The upstream (MV) resistance Ra is generally found to be negligible compared with the corresponding Xa, the latter then being taken as the ohmic value for Za. If more accurate calculations are necessary, Xa may be taken to be equal to 0.995 Za and Ra equal to 0.1 Xa.
Figure G36 gives values for Ra and Xa corresponding to the most common MV^{[2]} shortcircuit levels in utility powersupply networks, namely, 250 MVA and 500 MVA.
Transformers
(see Fig. G37)
The impedance Ztr of a transformer, viewed from the LV terminals, is given by the formula:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle Ztr = \frac {U_{20}\, ^2}{Sn} \times \frac{Usc}{100}} in milliohms
where:
U_{20} = opencircuit secondary phasetophase voltage expressed in volts
Sn = rating of the transformer (in kVA)
Usc = the shortcircuit impedance voltage of the transformer expressed in %
The transformer windings resistance Rtr can be derived from the total loadlosses as follows:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle Pcu=3In^2} so that Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle Rtr=\frac{Pcu \times 10^3}{3In^2}} in milliohms
where
Pcu = total loadlosses in watts
In = nominal fullload current in amps
Rtr = resistance of one phase of the transformer in milliohms (the LV and corresponding MV winding for one LV phase are included in this resistance value).
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle Xtr = \sqrt {Ztr^2  Rtr^2}}
Note: for an approximate calculation, in the absence of more precise information on transformer characteristics, Cenelec 50480 suggests to use the following guidelines:
 if U_{20} is not known, it may be assumed to be 1.05 Un
 in the absence of more precise information, the following values may be used: Rtr = 0.31 Ztr and Xtr = 0.95 Ztr
Example: for a transformer of 630kVA with Usc=4% / Un = 400V, approximate calculation gives:
 U_{20} = 400 x 1.05 = 420V
 Ztr = 420^{2} / 630 x 4% = 11 mΩ
 Rtr = 0.31 x Ztr = 3.5 mΩ and Xtr = 0.95 x Ztr = 10.6 mΩ
Rated Power kVA)  Oilimmersed  Castresin  

Usc (%)  Rtr (mΩ)  Xtr (mΩ)  Ztr (mΩ)  Usc (%)  Rtr (mΩ)  Xtr (mΩ)  Ztr (mΩ)  
100  4  37.9  59.5  70.6  6  37.0  99.1  105.8 
160  4  16.2  41.0  44.1  6  18.6  63.5  66.2 
200  4  11.9  33.2  35.3  6  14.1  51.0  52.9 
250  4  9.2  26.7  28.2  6  10.7  41.0  42.3 
315  4  6.2  21.5  22.4  6  8.0  32.6  33.6 
400  4  5.1  16.9  17.6  6  6.1  25.8  26.5 
500  4  3.8  13.6  14.1  6  4.6  20.7  21.2 
630  4  2.9  10.8  11.2  6  3.5  16.4  16.8 
800  6  2.9  12.9  13.2  6  2.6  13.0  13.2 
1,000  6  2.3  10.3  10.6  6  1.9  10.4  10.6 
1,250  6  1.8  8.3  8.5  6  1.5  8.3  8.5 
1,600  6  1.4  6.5  6.6  6  1.1  6.5  6.6 
2,000  6  1.1  5.2  5.3  6  0.9  5.2  5.3 
Busbars
The resistance of busbars is generally negligible, so that the impedance is practically all reactive, and amounts to approximately 0.15 mΩ/metre^{[3]} length for LV busbars (doubling the spacing between the bars increases the reactance by about 10% only).
In practice, it's almost never possible to estimate the busbar length concerned by a shortcircuit downstream a switchboard.
Circuit conductors
The resistance of a conductor is given by the formula:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle Rc=\rho \frac{L}{S}}
where
ρ = the resistivity of the conductor material at the normal operating temperature
ρ has to be considered:
 at cold state (20°C) to determine maximum shortcircuit current,
 at steady state (normal operating temperature) to determine minimum shortcircuit current.
L = length of the conductor in m
S = c.s.a. of conductor in mm^{2}
20 °C  PR/XLPE 90 °C  PVC 70 °C  

Copper  18.51  23.69  22.21 
Alu  29.41  37.65  35.29 
Cable reactance values can be obtained from the manufacturers. For c.s.a. of less than 50 mm^{2} reactance may be ignored. In the absence of other information, a value of 0.08 mΩ/metre may be used (for 50 Hz systems) or 0.096 mΩ/metre (for 60 Hz systems). For busways (busbar trunking systems) and similar prewired ducting systems, the manufacturer should be consulted.
Motors
At the instant of shortcircuit, a running motor will act (for a brief period) as a generator, and feed current into the fault.
In general, this faultcurrent contribution may be ignored. However, if the total power of motors running simultaneously is higher than 25% of the total power of transformers, the influence of motors must be taken into account. Their total contribution can be estimated from the formula:
Iscm = 3.5 In from each motor i.e. 3.5m In for m similar motors operating concurrently.
The motors concerned will be the 3phase motors only; singlephasemotor contribution being insignificant.
Faultarc resistance
Shortcircuit faults generally form an arc which has the properties of a resistance. The resistance is not stable and its average value is low, but at low voltage this resistance is sufficient to reduce the faultcurrent to some extent. Experience has shown that a reduction of the order of 20% may be expected. This phenomenon will effectively ease the currentbreaking duty of a CB, but affords no relief for its faultcurrent making duty.
Recapitulation table
(see Fig. G39)
Parts of powersupply system  R (mΩ)  X (mΩ)  

Supply network Figure G34 
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \frac {Ra}{Xa} = 0.1}  Xa = 0.995 Za
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle Za = \frac{ U_{20}\, ^2}{Psc}}  
Transformer Figure G35 
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle Rtr = \frac {Pcu \times 10^3 }{3In\, ^2}}
where
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle In = \frac {Sn \times 10^3}{U_{20} \sqrt 3}}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle Xtr = \sqrt {Ztr^2  Rtr^2}}
with Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle Ztr = \frac {U_{20}\, ^2}{Sn}\times \frac{Usc}{100}}  
Circuitbreaker  Not considered in practice  
Busbars  Negligible for S > 200 mm^{2}, below use the formula: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle R = \rho \frac{L}{S}} ^{[a]} 
Xb = 0.15 mΩ/m  
Circuit conductors^{[b]}  Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle R = \rho\frac{L}{S}} ^{[a]}  Cables: Xc = 0.08 mΩ/m  
Motors  See Motors (often negligible at LV)  
Threephase maximum circuit current in kA 
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle Isc= \frac{U_{20} }{\sqrt 3 \sqrt{ R_T\, ^2 + X_T}\, ^2}} 
 U_{20}: Phasetophase noload secondary voltage of MV/LV transformer (in volts).
 Psc: 3phase shortcircuit power at MV terminals of the MV/LV transformers (in kVA).
 Pcu: 3phase total losses of the MV/LV transformer (in watts).
 Sn: Rating of the MV/LV transformer (in kVA).
Usc: Shortcircuit impedance voltage of the MV/LV transfomer (in %).  R_{T} : Total resistance. X_{T}: Total reactance
Example of shortcircuit calculations
(see Fig. G40)
 RT : Total resistance. XT: Total reactance. Isc : 3phase maximum shortcircuit current
Calculations made as described in figure G36
Notes
 ^ Shortcircuit MVA: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \sqrt 3}
E_{L}
Isc where:
 E_{L} = phasetophase nominal system voltage expressed in kV (r.m.s.)
 Isc = 3phase shortcircuit current expressed in kA (r.m.s.)
 ^ up to 36 kV
 ^ For 50 Hz systems, but 0.18 mΩ/m length at 60 Hz