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Correnti Corto Circ.

 

The different types of short-circuit fault which occur on a power system are:
- single phase to earth,
- double phase,
- double phase to earth,
- three phase,
- three phase to earth.

For each type of short-circuit fault occurring on an unloaded system:
- the first column states the phase voltage and line current conditions at the fault,
- the second column states the phase 'a' sequence current and voltage conditions at the fault,
- the third column provides formulae for the phase 'a' sequence currents at the fault,
- the fourth column provides formulae for the fault current and the resulting line currents.
By convention, the faulted phases are selected for fault symmetry with respect to reference phase 'a'.

I f = fault current
Ie = earth fault current
Ea = normal phase voltage at the fault location
Z1 = positive phase sequence network impedance to the fault
Z2 = negative phase sequence network impedance to the fault
Z0 = zero phase sequence network impedance to the fault

Single phase to earth - fault from phase 'a' to earth:

Va = 0
Ib = Ic = 0
I f = Ia = Ie

Ia1 = Ia2 = Ia0 = Ia / 3
Va1 + Va2 + Va0 = 0
  

Ia1 = Ea / (Z1 + Z2 + Z0)
Ia2 = Ia1
Ia0 = Ia1

I f = 3Ia0 = 3Ea / (Z1 + Z2 + Z0) = Ie
Ia = I f = 3Ea / (Z1 + Z2 + Z0)
  

Double phase - fault from phase 'b' to phase 'c':

Vb = Vc
Ia = 0
I f = Ib = - Ic

Ia1 + Ia2 = 0
Ia0 = 0
Va1 = Va2

Ia1 = Ea / (Z1 + Z2)
Ia2 = - Ia1
Ia0 = 0

I f = - jÖ3Ia1 = - jÖ3Ea / (Z1 + Z2)
Ib = I f = - jÖ3Ea / (Z1 + Z2)
Ic = - I f = jÖ3Ea / (Z1 + Z2)

Double phase to earth - fault from phase 'b' to phase 'c' to earth:

Vb = Vc = 0
Ia = 0
I f = Ib + Ic = Ie

Ia1 + Ia2 + Ia0 = 0
Va1 = Va2 = Va0
  

Ia1 = Ea / Znet
Ia2 = - Ia1Z0 / (Z2 + Z0)
Ia0 = - Ia1Z2 / (Z2 + Z0)

I f = 3Ia0 = - 3EaZ2 / Szz = Ie
Ib = I f / 2 - jÖ3Ea(Z2 / 2 + Z0) / Szz
Ic = I f / 2 + jÖ3Ea(Z2 / 2 + Z0) / Szz

  Znet = Z1 + Z2Z0 / (Z2 + Z0)   and   Szz = Z1Z2 + Z2Z0 + Z0Z1 = (Z2 + Z0)Znet

Three phase (and three phase to earth) - fault from phase 'a' to phase 'b' to phase 'c' (to earth):

Va = Vb = Vc (= 0)
Ia + Ib + Ic = 0 (= Ie)
I f = Ia = hIb = h2Ic

Va0 = Va (= 0)
Va1 = Va2 = 0
  

Ia1 = Ea / Z1
Ia2 = 0
Ia0 = 0

I f = Ia1 = Ea / Z1 = Ia
Ib = Eb / Z1
Ic = Ec / Z1

The values of Z1, Z2 and Z0 are each determined from the respective positive, negative and zero sequence impedance networks by network reduction to a single impedance.

Note that the single phase fault current is greater than the three phase fault current if Z0 is less than (2Z1 - Z2).

Note also that if the system is earthed through an impedance Zn (carrying current 3I0) then an impedance 3Zn (carrying current I0) must be included in the zero sequence impedance network.


Three Phase Fault Level

The symmetrical three phase short-circuit current Isc of a power system with no-load line and phase voltages Eline and Ephase and source impedance ZS per-phase star is:
Isc = Ephase / ZS = Eline /
Ö3ZS

The three phase fault level Ssc of the power system is:
Ssc = 3Isc2ZS = 3EphaseIsc = 3Ephase2 / ZS = Eline2 / ZS

Note that if the X / R ratio of the source impedance ZS (comprising resistance RS and reactance XS) is sufficiently large, then ZS » XS.

Transformers
If a transformer of rating ST (taken as base) and per-unit impedance ZTpu is fed from a source with unlimited fault level (infinite busbars), then the per-unit secondary short-circuit current I2pu and fault level S2pu are:
I2pu = E2pu / ZTpu = 1.0 / ZTpu
S2pu = I2pu = 1.0 / ZTpu

If the source fault level is limited to SS by per-unit source impedance ZSpu (to the same base as ZTpu), then the secondary short-circuit current I2pu and fault level S2pu are reduced to:
I2pu = E2pu / (ZTpu + ZSpu) = 1.0 / (ZTpu + ZSpu)
S2pu = I2pu = 1.0 / (ZTpu + ZSpu)
where ZSpu = ST / SS