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
I_{e} = earth fault current
E_{a} = normal phase voltage at the fault location
Z_{1} = positive phase sequence network impedance to the fault
Z_{2} = negative phase sequence network impedance to the fault
Z_{0} = zero phase sequence network impedance to the fault
Single
phase to earth
- fault from phase 'a' to earth:
V_{a}
= 0 |
I_{a1}
= I_{a2} = I_{a0} = I_{a} / 3 |
I_{a1}
= E_{a} / (Z_{1} + Z_{2} + Z_{0}) |
I_{
f} = 3I_{a0} = 3E_{a} / (Z_{1} + Z_{2}
+ Z_{0}) = I_{e} |
Double
phase
- fault from phase 'b' to phase 'c':
V_{b}
= V_{c} |
I_{a1}
+ I_{a2} = 0 |
I_{a1}
= E_{a} / (Z_{1} + Z_{2}) |
I_{
f} = - jÖ3I_{a1} = - jÖ3E_{a}
/ (Z_{1} + Z_{2}) |
Double
phase to earth
- fault from phase 'b' to phase 'c' to earth:
V_{b}
= V_{c} = 0 |
I_{a1}
+ I_{a2} + I_{a0} = 0 |
I_{a1}
= E_{a} / Z_{net} |
I_{
f} = 3I_{a0} = - 3E_{a}Z_{2} / S_{zz}
= I_{e} |
Z_{net} = Z_{1} + Z_{2}Z_{0} / (Z_{2}
+ Z_{0}) and
S_{zz}
= Z_{1}Z_{2} + Z_{2}Z_{0} + Z_{0}Z_{1}
= (Z_{2} + Z_{0})Z_{net}
Three
phase (and three phase to earth)
- fault from phase 'a' to phase 'b' to phase 'c' (to earth):
V_{a}
= V_{b} = V_{c} (= 0) |
V_{a0}
= V_{a} (= 0) |
I_{a1}
= E_{a} / Z_{1} |
I_{
f} = I_{a1} = E_{a} / Z_{1} = I_{a} |
The
values of Z_{1}, Z_{2} and Z_{0} 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 Z_{0} is less than (2Z_{1} - Z_{2}).
Note
also that if the system is earthed through an impedance Z_{n} (carrying
current 3I_{0}) then an impedance 3Z_{n} (carrying current I_{0})
must be included in the zero sequence impedance network.
Three
Phase Fault Level
The
symmetrical three phase short-circuit current I_{sc} of a power
system with no-load line and phase voltages E_{line} and E_{phase}
and source impedance Z_{S} per-phase star is:
I_{sc} = E_{phase} / Z_{S} = E_{line} /
Ö3Z_{S}
The
three phase fault level S_{sc} of the power system is:
S_{sc} = 3I_{sc}^{2}Z_{S} = 3E_{phase}I_{sc}
= 3E_{phase}^{2} / Z_{S} = E_{line}^{2}
/ Z_{S}
Note
that if the X / R ratio of the source impedance Z_{S} (comprising
resistance R_{S} and reactance X_{S}) is sufficiently large,
then Z_{S}
»
X_{S}.
Transformers
If a transformer of rating S_{T} (taken as base) and per-unit
impedance Z_{Tpu} is fed from a source with unlimited fault level
(infinite busbars), then the per-unit secondary short-circuit current I_{2pu}
and fault level S_{2pu} are:
I_{2pu} = E_{2pu} / Z_{Tpu} = 1.0 / Z_{Tpu}
S_{2pu} = I_{2pu} = 1.0 / Z_{Tpu}
If
the source fault level is limited to S_{S} by per-unit source
impedance Z_{Spu} (to the same base as Z_{Tpu}), then the
secondary short-circuit current I_{2pu} and fault level S_{2pu}
are reduced to:
I_{2pu} = E_{2pu} / (Z_{Tpu} + Z_{Spu}) =
1.0 / (Z_{Tpu} + Z_{Spu})
S_{2pu} = I_{2pu} = 1.0 / (Z_{Tpu} + Z_{Spu})
where Z_{Spu} = S_{T} / S_{S}