Currents of short-circuit

a : three-phase short-circuit
b : two-phase short-circuit
c : two-phase short-circuit with the ground
d : short-circuit single-phase current with the terrer
a : three-phase defect
b : two-phase defect
c : defect single-phase current
d : defect ground
Symbol short-circuit, breaking capacity
PdC Capacity breaking Scc Power of short-circuit
S Section of the drivers Sn Power connects transformer
α Angle of interlocking C Factor of tension
cos φ Power-factor e Instantaneous electromotive force
E Electromotive force (effective value) φ Angle of dephasing
I Current instantaneous I Intensity (effective value)
iCC Component continues current instantaneous
iCA component sinusoidal alternative of the current instantaneous
iρ Value maximum of the current Ib Current of cut short-circuit
icc Steady short-circuit current Ik Steady short-circuit current
I"K SymmetrICAl current of short-circuit Ir Running assigned alternator
IS Current of service k Constant of correction
K Factor of correction of the impedances Ra Resistance are equivalent of the network upstream
RL Linear electrICAl resistance of the lines U Instantaneous tension
λ Factor depend on the inductance of saturation of the alternator
ucc Tension of a short-circuit U Tension made up of the network except load
Un Nominal voltage in load of the network X reactance in % of the revolving machines
Xa Equivalent reactance of the network upstream XL Linear reactance of the lines
Xt Subtransitory reactance of the alternator Za Equivalent impedance of the network upstream
Zcc Impedance upstream of the network known three-phase defect Zd or Z1 Direct Imédance
Zi or Z2 Opposite impedance Zo or Z0 Homopolar impedance
ZL Impedance of connection G Generator
K or k3 Three-phase short-circuit k1 Short-circuit single-phase current
k2 Two-phase short-circuit k2E ⁄ kE2E Two-phase short-circuit with the ground
S Group with on-load tap changer SO Group sanc changer on-load tap

The current of short-circuit of a dipole is the current one which would cross it if its terminals were connected to a perfect conductor of null resistance. The current of short-circuit of a perfect generator of tension is infinite. In practice, the generators of tension are not perfect and the value of the current of short-circuit is finished, limited by the internal impedances of the source, the various sections of line and the components placed on the way of this current.
Interest to know the currents of shortcircuit
calculations into electrokinetic
The current of short-circuit of a linear dipole makes it possible to determine the useful current of Norton to establish the model are equivalent of Norton of a linear active dipole.
Dimensioning of protections of an installation
The knowledge of the current of short-circuit is very important for the dimensioning of the concerned with safety units. The knowledge of the value of the current of short-circuit Icc at all the places of an installation, where one wants to place a safety device charged to stop it, makes it possible to make sure that the breaking capacity of the fuse or the circuit breaker is quite higher than the current of short-circuit at this place. Incapacity of a fuse or a circuit breaker to stop a current of short-circuit which can produce catastrophic results.
For the installations, the value of the current of short-circuit of a feeding must be given in two places:
a point for which the value is known as minimal Iccmin, when the short-circuit occurs at the end of the protected connection, that is to say at the entry of the next body of protection, and in the most favorable case (two-phase defect)
a point for which the value known as maximum and is calculated after one duration of 1 or 3 second Iccmax, when the short-circuit occurs at the boundaries even body of protection and in the most unfavourable case (three-phase defect).
The values of this current are generally expressed in kA.
The maximum value defines
breaking capacity necessary of the fuse or the circuit breaker in charge of protection to this place
capacity of closing necessary of this same circuit breaker
electrodynamic behavior of the lines and the switchgear.
The minimal value defines the choice of the curve of release of the circuit breaker or the fuse, ensuring the selectivity of releases.
Types of short-circuit
On a three-phase network, the short-circuits can be several types
three-phase defect: the three phases are joined together
two-phase defect: two phases are connected together
One distinguishes between defect two-phase ⁄ ground and two-phase isolated. The isolated two-phase defects are frequently caused by a strong wind which makes touch the conductors of 2 phases on a line with high voltage
defect single-phase current: a phase is connected to the neutral or the ground. On a line with high voltage, this type of defect is frequently caused by the lightning which initiates a short-circuit between a phase and the ground.
Current of initial symmetrical short-circuit
It is the effective value of the alternate component of the current of short-circuit during the appearance of the fault current. When the defect is close to the generators, being current in the subtransitory field temporal, it is also called simply current of subtransitory or initial shortcircuit. When the defect is far from the generators, this current is the same one as the steady short-circuit current because the subtransitory phenomena are negligible.
Peak of the current of short-circuit
From the current of initial symmetrical short-circuit, the maximum peak value is deduced (in kA peak) from : Ip = k√2I"k between 1 and 2, and can be calculated by a formula of standard CEI 60909-0 following the resistive components and inductive (R/X) of the network.
Current of cut short-circuit
The current of cut short-circuit is the current one which the circuit breaker will have to cut. It is the value of the current of short-circuit at the time of the cut. Its value is linear with the current of short-circuit initial (or subtransitory): Ib = µ * I"k. The coefficient µ depends on the characteristics of the generator as of minimal time so that the circuit breaker acts. Its value can be found thanks to abacuses and with the formulas of standard CEI 60909. For a defect far from the generator, µ = 1 because it does not have there a symmetrical transitory effect.
Steady short-circuit current
It is the effective value of the current of short-circuit in permanent mode when the subtransitory and transitory phenomena are negligible. As one is located in the permanent mode, its value is by applying the law of ohm with the usual values of the permanent mode for resistances and the reactances of the system and with a null impedance for the defect if the short-circuit is frankly or not null for a impédant short-circuit. Time in order to arrive at the permanent mode after a short-circuit depends on the characteristics of the generator for a short-circuit close to the generator or instantaneous value to the tension for a short-circuit far from a generator.
Methods of calculating employed
The principle of the calculation of Icc is simple, since it is enough to apply the law of Ohm : Icc = U ⁄ Zi + ΣZl + ΣZa where: U is the tension of the network (of phase with neutral)

Short-circuit close to a generator
Zi is the internal impedance of the source
Zl is the impedance of the crossed sections of line
Za is the impedance of equipment met.
In practice, this calculation proves to be delicate for several reasons
it utilizes elements of low value, neglected the remainder of the times and little or badly specified by the manufacturers
the energy source is complex, when it is about a distribution network, because it is then made up of many inter-connected generators and lines. The provider of energy characterizes simply his network at the point of delivery by a power of short-circuit, specified in Mva
for these extreme values of the intensity, it not linearity of certain impedances is not easily negligible
the establishment of the current of short-circuit is complex, and its form and the amplitudes reached strongly depend on the moment when the short-circuit occurred. The transitory mode is even more complex, when a generator is close to the place of the defect
the appearance of the short-circuit generally causes an imbalance of the three-phase mode
other elements can introduce additional parameters difficult to take into account: capacitor batteries, appearance of arcs of defect, machines revolving in the installation, filters antiharmonic, transformer of current
For these reasons, all the methods of calculating of the currents of short-circuit use approximations, neglect certain phenomena, defining of this fact their fields of validity, where the results obtained offer an acceptable precision and by excess.
Method of the impedances
This method makes it possible to obtain a good precision in BT (1000 V). It consists in counting all the impedances being on the path of the current of short-circuit. Tables facilitate the determination of the impedances of the distribution network starting from its power of short-circuit, and those of the transformers starting from their apparent power. Other tables give for each type of line and their mode of pose the relative share of resistance and the reactance in their impedances.
The finished census, the module of the total impedance is calculated, which allows, by application of the law of Ohm, to deduce the value from the current of short-circuit
Method of composition
This method is usable when the characteristics of the feeding are not known. The impedance upstream of the circuit considered is calculated starting from an estimate of the current of short-circuit at its origin. This approximate method has a sufficient precision to add a circuit to an existing installation, since its power does not exceed 800 kVA.
Synchronous machine
After the appearance of a short-circuit at the boundaries of a synchronous generator, the fault current decreases according to three scales of time corresponding to three currents:
a subtransitory current I’’cc, the first to be appeared, it is also most extremely
a transitory current I’cc, appearing between the subtransitory mode and the permanent mode
a closed-circuit current Icc
These three currents correspond to three internal impedances known as direct X’’d,X’d,Xd.Thus, with the values of the impedances in reduced unit and In the nominal intensity of the generator:
I"cc = In ⁄ X"d,    I’cc = In ⁄ X’d,    Icc = In ⁄ Xd,
Asynchronous motor
At the boundaries of the asynchronous motor, the current of short-circuit is equal to the inrush current thus Icc ≈ 5 à 8 In. In the case of a defect on the network (not on its terminals), its contribution to the fault current will depend on the distance of the defect.
Calculations by computer
Many softwares were developed to calculate the currents of short-circuit in accordance with the standards. Most advanced can take into account the dynamic aspect of the short-circuit and can also make simulations.
Formulas of computation of the current of short-circuit
On a three-phase network, for a defect far away from the revolving machines, the steady short-circuit currents can be calculated by:
three-phase defect : Icc3 = C * Un ⁄ √3 * Zcc
isolated two-phase defect : Icc2 = C * Un ⁄ √2 * Zcc
two-phase defect ground : Icc2 = C * Un * √3 ⁄ (Zcc + 2 * Z0)
defect single-phase current : Icc1 = C * Un * √3 ⁄ (2 * Zcc + Z0)
Note : Zcc is the total impedance direct by phase crossed by the current of short-circuit, and Z0 is the homopolar impedance, which is in particular related to the impedance of the line of the neutral or the ground according to the case. C is a factor of tension according to the tolerances accepted on the value of the tension. This factor can vary between 0.95 and 1.1.
At the time of a shortcircuit at the boundaries of the secondary of a transformer, the current is limited by the impedance of the transformer. When it occurs on a conductor of the distribution, the resistance of the conductors and the transformer determine the capacity of short-circuit together.
The computer makes it possible to determine an approximation of the capacity of short-circuit at several points of a distribution system. The points are represented with the following diagram.

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