Short-circuits in ES
Short-circuit: cross fault, quick emergency change in ES the most often fault in ES transient events occur during short-circuits
Short-circuit formation: fault connection between phases or between phase(s) and the ground
in the system with the grounded neutral point
Main causes: insulation defect caused by overvoltage direct lightning strike insulation aging direct damage of overhead lines or cables
Short-circuit impacts: total impedance of the network affected part decreases currents are increasing => so called short-circuit currents Ik the voltage decreases near the short-circuit Ik impacts causes device heating and power strain problems with Ik disconnecting, electrical arc and overvoltage
occurred during the short-circuit synchronism disruption of ES working in parallel communication line disturbing => induced voltages
Note: In short-circuit places transient resistances arise.
transient resistance is a sum of electrical arc resistance and resistance of other Ik way parts (determination of exact resistances is difficult)
current and electrical arc length is changing during short-circuit => resistance of electrical arc is also changing
transient resistances are neglected for Ik calculation (dimensioning of electrical devices) → perfect short-circuits
Short-circuits types
Symmetrical short-circuits: Three-phase short-circuit => all 3 phases are affected by short-circuit
little occurrence in the case of overhead lines the most occurrences in the case of cable lines => other kinds of
faults change to 3ph short-circuit due to electrical-arc impact
Unbalanced (asymmetrical) short-circuits: phase-to-phase short-circuit double-phase-to-ground short-circuit single-phase-to-ground short-circuit:
in MV a different kind of fault => so called ground fault in case of ground fault in MV (insulated or indirectly grounded
neutral point) => no change in LV (grounded neutral point)
Occurrence probability (%) Short-
circuit type
Diagram MV 110
kV 220 kV
3ph 5 0,6 0,9
2ph 10 4,8 0,6
2ph to ground 20 3,8 5,4
1ph * 91 93,1
Short-circuit current time behaviour
2L Li
21W
dt
dWP L → transient event
Time behaviour: open-circuit, resistances neglected → reactance, current of inductive character, higher Ik values
Impact of R on Ik attributes:
finite R values decrease short-circuit impacts R neglecting results in time constants prolongation = L/R
U = Umax in the short-circuit moment → Ik starts from zero (min. value)
Short-circuit components (f = 50 Hz): sub-transient – exponential envelope, kT transient – exponential envelope, kT steady-state – constant magnitude
It is caused by synchronous machine behaviour during short-circuit → more significant during short-circuits near the machine.
Values symmetrical short-circuit current ksI - steady-state, transient and
sub-transient component sum, RMS value sub-transient short-circuit current kI - ksI RMS value in the period
of sub-transient component kT30t initial sub-transient short-circuit current 0kI - kI value in the
moment of short-circuit origin t = 0 transient short-circuit current kI - ksI RMS value in the period from
the sub-transient component end to the transient component end kk T3T3t
initial transient short-circuit current 0kI - RMS value of the steady-state and transient component for t = 0
steady-state short-circuit current kuI - ksI after transient components end kT3t
U = 0 in the short-circuit moment → Ik starts from max. value
Values DC component kaI - disappears exponentially, kaT initial DC component 0kaI - kaI in the moment t = 0, forced by the
current continuous behaviour unbalanced short-circuit current knsI - steady-state, transient, sub-
transient and DC component sum, RMS value peak short-circuit current kmI - the first half-period magnitude
during the maximal DC component
Short-circuit current power factor
tot
totk R
Xarctg
lines overhead cable
U (kV) 22 110 220 400 750 1150 10 35 110
X : R 1/1 2/1 5/1 12/1 15/1 27/1 1/4 1/2 1/0,7
|Z| : X 1,41 1,12 1,02 1,01 1,005 1,00 4,1 2,24 1,22
k (°) 45 64 78,7 85,2 86,2 87,9 13 26 54
Short-circuits in 3ph system
Conversion between phase values and symmetrical components
120
0
2
1
2
2
C
B
A
ABC UTUUU
1aa1aa111
UUU
U
ABC1
C
B
A2
2
0
2
1
120 UTUUU
111aa1aa1
31
UUU
U
Impedance matrix in symmetrical components (for series sym. segment)
Z2Z00
0ZZ000ZZ
Z000Z000Z
Z
0
2
1
120
3ph system during short-circuit – internal generator voltage E (or Ui)
ABCABCABCABC UIZE
Symmetrical system (independent systems 1, 2, 0)
120120120120 UIZE 0000
2222
1111
UIZE
UIZE
UIZE
Generator symmetrical voltage → only positive sequence component Reference phase A:
00E
00
E
EaEa
E
111aa1aa1
31ETE
A
A
A2
A2
2
ABC1
120
0
2
1
0
2
1
0
2
1
0
2
1
UUU
III
Z000Z000Z
00E
EEE
Negative and zero sequence are caused by voltage unbalance in the faulted place.
In the fault point 6 quantities (U120, I120) → 3 equations necessary to be added by other 3 equations according to the short-circuit type (local unbalance description).
Three-phase (to-ground) short-circuit
3 char. equations
0UUU CBA
Hence 6 equations for 6 unknowns
000
222
111
UIZ0
UIZ0
UIZE
02
21
0212
021
UUaUa0
UUaUa0
UUU0
Components
000
000
111aa1aa1
31UTU 2
2
ABC1
120
0UUU 021
0I;0I;ZEI 02
11
Phases 120ABC ITI
1C
1
2B
1A Z
EaI;ZEaI;
ZEI
Only the positive-sequence component included.
Single-phase-to-ground short-circuit
3 char. equations
0II;0U CBA
Hence 6 equations for 6 unknowns
000
222
111
UIZ0
UIZ0
UIZE
02
21
0212
021
IIaIa0
IIaIa0
UUU0
Components
A
A
AA2
2
ABC1
120
III
31
00I
111aa1aa1
31ITI
021
021 ZZZEIII
100
122
1201
IZU
IZU
IZZU
All three components are in series.
Phases
00I3
III
1aa1aa111
ITI1
1
1
1
2
2120ABC
0I;0I;ZZZ
E3I CB021
A
1
022
02
22
10
12
120
2
2120ABC I
Z1aZaaZ1aZaa
0
IZIZ
IZZ
1aa1aa111
UTU
Current phasor diagram
Voltage phasor diagram
Phase-to-phase short-circuit
3 char. equations
0I;II;UU ACBCB
Hence 6 equations for 6 unknowns
000
222
111
UIZ0
UIZ0
UIZE
0III
IIaIaIIaIa
UUaUaUUaUa
021
022
10212
022
10212
Components
0
I3jI3j
31
II0
111aa1aa1
31I B
B
B
B2
2
120
0I;II;ZZ
EI 01221
1
0U
IZZZEZUU
0
1221
221
Positive and negative components in parallel.
Phases
1
11
1
2
2120ABC
I3jI3j
0
0I
I
1aa1aa111
ITI
21C
21BA ZZ
E3jI;ZZE3jI;0I
12
12
12
1
1
1
1
1
2
2120ABC
IZIZIZ2
UUU2
0UU
1aa1aa111
UTU
Current phasor diagram
Voltage phasor diagram
Double-phase-to-ground short-circuit
3 char. equations
0I;0UU ACB
Hence 6 equations for 6 unknowns
000
222
111
UIZ0
UIZ0
UIZE
0III
0UUaUa
0UUaUa
021
022
1
0212
Components
A
A
AA2
2
120
UUU
31
00
U
111aa1aa1
31U
120
201
20
02
20
201
1
IZZ
ZI;IZZ
ZI
ZZZZZ
EI
20
201
20
20
021
ZZZZZ
ZZZZE
UUU
All three components are in parallel.
Phases 120ABC ITI
201021
22
20
B ZZZZZZ)1a(Z)aa(ZEI
201021
22
0C ZZZZZZ
)1a(Z)aa(ZEI
00U3
UUU
1aa1aa111
UTU1
1
1
1
2
2120ABC
Phasor diagrams
Components during short-circuit: 3ph positive 2ph positive, negative 2ph ground positive, negative, zero
1ph positive, negative, zero
Short-circuits calculation by means of relative values
Relative values – related to a defined base.
base power (3ph) Sv (VA) base voltage (phase-to-phase) Uv (V) base current Iv (A) base impedance Zv (Ω)
vvv IU3S
v
vfv I
UZ
Relative impedance
2v
v2vf
v
vf
vf
vf
v
v
vfv USZ
U3SZ
U3U3
UIZ
IUZ
ZZz
Initial sub-transient short-circuit current (3ph short-circuit)
1
fA0k
Z
UII
v
2v
11 SUzZ
v
1v
v
1
v
2v
1
v
0k Iz1
U3S
z1
SUz
3U
I
Initial sub-transient short-circuit power
v11
vv0kv0k S
z1
zIU3IU3S
Similarly for 1ph short-circuit
v021
)1(0k I
zzz3I
2ph short-circuit
v21
)2(0k I
zz3I
Note: Sometimes it is respected generator loading, more precisely higher internal generator voltage than nominal one.
v1
0k Iz1kI
k > 1
