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Short Circuit CalculationsIIEE Presentation
SHORT CIRCUIT CALCULATIONSREVISITED
FORTUNATO C. LEYNESFORTUNATO C. LEYNESFORTUNATO C. LEYNESFORTUNATO C. LEYNESChairman
Professional Regulatory
Board of Electrical Engineering
Professional Regulation Commission
Short Circuit CalculationsIIEE Presentation
Short Circuit (Fault) Analysis
FAULT-PROOF SYSTEM not practical neither economical faults or failures occur in any power system
In the various parts of the electrical network under short circuit or unbalanced condition, the determination of the magnitudes and phase angles Currents Voltages Impedances
Short Circuit CalculationsIIEE Presentation
Application of Fault Analysis
1. The determination of the required mechanical strength of electrical equipment to withstand the stresses brought about by the flow of high short circuit currents
2. The selection of circuit breakers and switch ratings
3. The selection of protective relay and fuse ratings
Short Circuit CalculationsIIEE Presentation
4. The setting and coordination of protective devices
5. The selection of surge arresters and insulation ratings of electrical equipment
6. The determination of fault impedances for use in stability studies
7. The calculation of voltage sags caused resulting from short circuits
Application of Fault Analysis
Short Circuit CalculationsIIEE Presentation
8. The sizing of series reactors to limit the short circuit current to a desired value
9. To determine the short circuit capability of series capacitors used in series compensation of long transmission lines
10. To determine the size of grounding transformers, resistances, or reactors
Application of Fault Analysis
Short Circuit CalculationsIIEE Presentation
Per Unit Calculations
Short Circuit CalculationsIIEE Presentation
Three-phase Systems
Φ
−
Φ
−
=
×=
3
2
3
2
),(
1000),(
MVAbase
kVvoltagebaseZ
kVAbase
kVvoltagebaseZ
LLB
LLB
Short Circuit CalculationsIIEE Presentation
Per Unit Quantities
)(
)(
)(
)(
B
pu
B
pu
B
pu
ZimpedanceBase
impedanceactualZ
kVVoltageBase
kVvoltageactualV
ICurrentBase
currentactualI
=
=
=
Short Circuit CalculationsIIEE Presentation
Changing the Base of Per Unit Quantities
( )
( )
( )
][
][
][
2
][
][
][
2
][][
][
2
][
][
)(
1000
1000)(
1000
)(,
newB
newpu
new
new
newB
old
oldoldpu
old
old
oldpu
Z
ZZ
kVAbase
kVbaseZ
kVAbase
kVbaseZZ
kVAbase
kVbase
ZimpedanceactualZ
Ω=
×=
×=Ω
×
Ω=
Short Circuit CalculationsIIEE Presentation
Changing the Base of Per Unit Quantities
( )
( )
( )
][
][
][
2
][
][
][
2
][][
][
2
][
][
)(
1000
1000)(
1000
)(,
newB
newpu
new
new
newB
old
oldoldpu
old
old
oldpu
Z
ZZ
kVAbase
kVbaseZ
kVAbase
kVbaseZZ
kVAbase
kVbase
ZimpedanceactualZ
Ω=
×=
×=Ω
×
Ω=
Short Circuit CalculationsIIEE Presentation
kVA Base for Motors
Induction < 100 hp1.00
Synchronous 1.0 pf0.80
Induction > 1000 hp0.90
Induction 100 < 999 hp0.95
Synchronous 0.8 pf1.00
hp ratingkVA/hp
Short Circuit CalculationsIIEE Presentation
SYMMETRICAL COMPONENTS
Short Circuit CalculationsIIEE Presentation
1cV 1aV
1bV
Positive Sequence
2aV
2cV
2bV
Negative Sequence
Unbalanced PhasorsZero Sequence
000 cbaVVV ==
cV
aV
bV
0cV
1cV
2cV
0bV
2bV
1bV
1aV
2aV
0aV
Short Circuit CalculationsIIEE Presentation
Symmetrical Components of Unbalanced Three-phase Phasor
( )
( )
( )cbaa
cbaa
cbaa
aVVaVV
VaaVVV
VVVV
++=
++=
++=
2
2
2
1
0
3
1
3
1
3
1
2
2
10
21
2
0
210
aaac
aaab
aaaa
VaaVVV
aVVaVV
VVVV
++=
++=
++=
Short Circuit CalculationsIIEE Presentation
In matrix form:
Symmetrical Components of Unbalanced Three-phase Phasor
=
2
1
0
2
2
1
1
111
a
a
a
c
b
a
V
V
V
aa
aa
V
V
V
=
c
b
a
a
a
a
V
V
V
aa
aa
V
V
V
2
2
2
1
0
1
1
111
3
1
Short Circuit CalculationsIIEE Presentation
Sequence Networks
Power System Short Circuit Calculations
Short Circuit CalculationsIIEE Presentation
Fault Point
The fault point of a system is that point to which the unbalanced connection is attached to an otherwise balanced system.
Short Circuit CalculationsIIEE Presentation
Definition of Sequence Networks
Positive-sequence Network
Ea1 = Thevenin’s equivalent voltage as seen at the fault point
Z1 = Thevenin’s equivalent impedance as seen from the fault point
1111 ZIEV aaa −=
Z1
Ea1
Ia1
Va1
+
-
Short Circuit CalculationsIIEE Presentation
Negative-sequence Network
Z2 = Thevenin’s equivalent negative-sequence impedance as seen at the fault point
Definition of Sequence Networks
222 ZIV aa −=Z
2
Ia2
Va2
+
-
Short Circuit CalculationsIIEE Presentation
Zero-sequence Network
Z0 = Thevenin’s equivalent zero-sequence impedance as seen at the fault point
Definition of Sequence Networks
000 ZIV aa −= Z0
Ia0
Va0
+
-
Short Circuit CalculationsIIEE Presentation
Sequence Network Models ofPower System Components
Power System Short Circuit Calculations
Short Circuit CalculationsIIEE Presentation
Synchronous Machines(Positive Sequence Network)
djxZ ''1 =
Short Circuit CalculationsIIEE Presentation
Synchronous Machines(Negative Sequence Network)
2
''''2
qd xxjZ
+=
Where:
Z2
Ia2
Va2
+
-
x”d = direct-axis sub-transient reactance
x”q = quadrature-axis sub-transient reactance
Short Circuit CalculationsIIEE Presentation
Synchronous Machines(Zero Sequence Network)
Solidly-Grounded Neutral
jX0
I0
n
ground
Short Circuit CalculationsIIEE Presentation
Impedance-Grounded Neutral
Synchronous Machines(Zero Sequence Network)
jX0
I0
n
3Zg
ground
Short Circuit CalculationsIIEE Presentation
Ungrounded-Wye or Delta Connected Generators
Synchronous Machines(Zero Sequence Network)
jX0
I0
n
ground
Short Circuit CalculationsIIEE Presentation
Two-Winding Transformers(Positive Sequence Network)
Standard
Symbol
P S
ZPS
Equivalent
Positive-seq. Network
P S
Short Circuit CalculationsIIEE Presentation
Three-Winding Transformers(Positive Sequence Network)
tsst
tppt
spps
ZZZ
ZZZ
ZZZ
+=
+=
+= ( )
( )
( )psstptt
ptstpss
stptpsp
ZZZZ
ZZZZ
ZZZZ
−+=
−+=
−+=
2
1
2
1
2
1
PT
Standard
Symbol
Zp
P
ZS
S
Zt
T
Equivalent Positive-Sequence
Network
S
Short Circuit CalculationsIIEE Presentation
Transformers(Negative Sequence Network)
The negative-sequence network of two-winding and three-winding transformers are modeled in the same way as the positive-sequence network since the positive-sequence and negative-sequence impedances of transformers are equal.
Short Circuit CalculationsIIEE Presentation
Simplified Derivation of Transformer Zero-Sequence Circuit Modeling
P Q
S1 = 1 and S3 = 0or
S2 = 1 or S4 = 0
Grounded wye
S1 = 0 and S3 = 0or
S2 = 0 and S4 = 0
Ungrounded wye
S1 = 0 and S3 = 1or
S2 = 0 and S4 = 1
Delta
(Thanks to Engr. Antonio C. Coronel, Retired VP, Meralco, and former member, Board of Electrical Engineering)
Short Circuit CalculationsIIEE Presentation
Simplified Derivation of Transformer Zero-Sequence Circuit Modeling
S1 = 1S2 = 1S3 = 0S4 = 0
P Q
Z
S1
S3 S4
S2
Grounded wye – Grounded wye
Short Circuit CalculationsIIEE Presentation
Simplified Derivation of Transformer Zero-Sequence Circuit Modeling
S1 = 1S2 = 0S3 = 0S4 = 0
P Q
Grounded wye – Ungrounded wye
Short Circuit CalculationsIIEE Presentation
Simplified Derivation of Transformer Zero-Sequence Circuit Modeling
S1 = 1S2 = 0S3 = 0S4 = 1
P Q
Grounded wye – Delta
Short Circuit CalculationsIIEE Presentation
Simplified Derivation of Transformer Zero-Sequence Circuit Modeling
S1 = 0S2 = 0S3 = 0S4 = 0
P Q
Delta – Delta
Short Circuit CalculationsIIEE Presentation
Transformers(Zero-Sequence Circuit Model)
TransformerConnection
Zero-SequenceCircuit Equivalent
P Q ZPQ
P Q
P Q ZPQ
P Q
Short Circuit CalculationsIIEE Presentation
TransformerConnection
QP ZPQ
P Q
P Q ZPQ
P Q
Transformers(Zero-Sequence Circuit Model)
Transformers(Zero-Sequence Circuit Model)
Zero-SequenceCircuit Equivalent
Short Circuit CalculationsIIEE Presentation
TransformerConnection
Zero-SequenceCircuit Equivalent
P Q
R
ZP
ZQ
ZR
P
R
Q
P Q ZPQ
P Q
Transformers(Zero-Sequence Circuit Model)
Transformers(Zero-Sequence Circuit Model)
Short Circuit CalculationsIIEE Presentation
TransformerConnection
Zero-SequenceCircuit Equivalent
ZP ZQ
ZR
P
R
Q
P Q
R
QP
R
ZP
ZQ
ZR
P
R
Q
Transformers(Zero-Sequence Circuit Model)
Transformers(Zero-Sequence Circuit Model)
Short Circuit CalculationsIIEE Presentation
Transmission Lines(Positive Sequence Network)
ra jXL
Z1
Short Circuit CalculationsIIEE Presentation
Transmission Lines(Negative Sequence Network)
The same model as the positive-sequence network is used for transmission lines inasmuch as the positive-sequence and negative-sequence impedances of transmission lines are the same
Short Circuit CalculationsIIEE Presentation
Transmission Lines(Zero Sequence Network)
The zero-sequence network model for a transmission line is the same as that of the positive- and negative-sequence networks. The sequence impedance of the model is of course the zero-sequence impedance of the line. This is normally higher than the positive- and negative-sequence impedances because of the influence of the earth’s resistivity and the ground wire/s.
Short Circuit CalculationsIIEE Presentation
Power System Short Circuit Calculations
Classification of Power SystemShort Circuits
Short Circuit CalculationsIIEE Presentation
Shunt Faults
Single line-to-ground faults
Double line-to-ground faults
Line-to-line faults
Three-phase faults
Short Circuit CalculationsIIEE Presentation
Series Faults
One-line open faults
Two-line open faults
Short Circuit CalculationsIIEE Presentation
Combination of Shunt andSeries Faults
Single line-to-ground and one-line open
Double line-to-ground and one-line open faults
Line-to-line and one-line open faults
Three-phase and one-line open faults
Short Circuit CalculationsIIEE Presentation
Single line-to-ground and two-line open faults
Double line-to-ground and two-line open faults
Line-to-line and two-line open faults
Three-phase and two-line open faults
Combination of Shunt andSeries Faults
Short Circuit CalculationsIIEE Presentation
Balanced Faults
Symmetrical or
Three-Phase Faults
Short Circuit CalculationsIIEE Presentation
Derivation of Sequence Network Interconnections
Boundary conditions:
fccfbbfaaF
cba
ZIVZIVZIVV
III
−=−=−=
=++ 0 Eq’n (1)
Eq’n (2)
Zf
Zf
Vf
System A System B
A
B
C
Va
Vb
Vc
Ia
Ib
Ic
Zf
Short Circuit CalculationsIIEE Presentation
Z0
Ia0
Va0
+
-
Z1
Ea1
Ia1
Va1
+
-
Zf
Z2
Ia2
Va2
+
-
Zf
1
11
1
11
210
1
11
,0
Z
EII
Z
ZZ
EII
IIII
ZZ
EI
aaf
f
aaf
aaaf
f
aa
f
==
=
+==
++=
+=
Short Circuit CalculationsIIEE Presentation
Unbalanced Faults
Single Line-to-Ground Faults
Short Circuit CalculationsIIEE Presentation
0
0
==
==
faa
cb
ZIV
II
Zf
System A System B
A
B
C
Va
Vb
Vc
Ia
Ib
Ic
Derivation of Sequence Network Interconnections
Boundary conditions:
Short Circuit CalculationsIIEE Presentation
f
aaaa
ZZZZ
EIII
3210
1210 +++===
Z1
Ea1
Ia1
Va1
+
-
Z2
Ia2
Va2
+
-
Z0
Ia0
Va0
+
-
3Zf
10
1
21
01210
10
1210
21
210
1
210
2
3
0
33
2
0
ZZ
EII
ZZandZIf
IIIIIII
ZZ
EIII
ZZ
ZZZ
EIII
ZIf
aaf
f
aaaaaaf
aaaa
a
aaa
f
+==
==
==++==
+===
=
++===
=
Short Circuit CalculationsIIEE Presentation
Unbalanced Faults
Line-to-Line Faults
Short Circuit CalculationsIIEE Presentation
fbcbcfbb
cb
a
ZIVVVZIV
II
I
=−=−
−=
=
or ;
0
Zf
System A System B
A
B
C
Va Vb Vc
Ia
Ib
Ic
Derivation of Sequence Network Interconnections
Boundary conditions:
Short Circuit CalculationsIIEE Presentation
1
11
21
21
11
2
0
Z
EI
ZZandZIf
ZZZ
EI
aa
f
f
aa
=
==
++=
( ) 11
2
21
21
2
0
3
;0
aaf
aaao
aaacbf
IjIaaI
III
aIIaIIII
currentfaultThe
−=−=
−==
++=−==
Z1
Ea1
Ia1
Va1
+
-
Zf
Z2
Ia2
Va2
+
-
Z0
Ia0
Va0
+
-
Short Circuit CalculationsIIEE Presentation
]3[][
1
1]3[
1
1
1
1
1
1
21
2
3
2
3
2
3
0 if
23
with ,thus
φ
φ
fLLf
af
aaf
f
f
af
II
Z
EI
Z
E
Z
EjI
Z
ZZ
EjI
ZZ
=
=
=−=
=
+−=
=
−
Short Circuit CalculationsIIEE Presentation
Unbalanced Faults
Double-to-line Ground Fault
Short Circuit CalculationsIIEE Presentation
( )( ) gcbfcc
gcbfbb
a
ZIIZIV
ZIIZIV
I
++=
++=
= 0 Eq’n BC-1
Eq’n BC-2
Eq’n BC-3
Zf
System A System B
A
B
C
Va
Vb
Vc
Ia
Ib
Ic
Zf
Vf
Zg (I
b+I
c)
Derivation of Sequence Network Interconnections
Boundary conditions:
Short Circuit CalculationsIIEE Presentation
( )( )gf
gff
f
aa
ZZZZ
ZZZZZZZ
EI
32
3
02
02
1
11
+++
+++++
=
Z0
Ia0
Va0
+
-
Z2
Ia2
Va2
+
-
Zf
Zf
Zf+3Z
g
Z1
Ea1
Ia1
Va1
+
-
Short Circuit CalculationsIIEE Presentation
Negative-sequence Component:
+++
++−=
gf
gf
aaZZZZ
ZZZII
32
3
02
0
12
Zero-sequence Component:
The fault current( ) ( )
( ) ( )( ) ( ) ( )
( )0
210210
210210
2
2
1
2
0
2
2
1021
2
0
3 thus,
or ;0but
2112
2
af
aaaaaa
aaaaaaf
aaaf
aaaaaacbf
II
IIIIII
IIIIIII
IaaIaaII
IaaIIaIIaIIII
=
+−==++
+−=−+−+=
++++=
+++++=+=
+++
+−=
gf
f
aaZZZZ
ZZII
3202
2
10
Short Circuit CalculationsIIEE Presentation
( )
01
2
1
10
01
0
01
011
1
01
012
01
2
1
101
01
011
11
21
2
2
0
ZZZ
EZ
ZZ
Z
ZZ
ZZZ
E
ZZ
ZII
ZZZ
EZZ
ZZ
ZZZ
EI
ZZandZZIf
a
aaa
aaa
gf
+−
=
+
++
−=
+−=
++
=
++
=
===
Short Circuit CalculationsIIEE Presentation
01
10
01
1
01
2
1
11
01
1
01
011
1
01
110
2
33
22
ZZ
EII
ZZ
E
ZZZ
EZ
ZZ
Z
ZZ
ZZZ
E
ZZ
ZII
aaf
aa
aaa
+==
+=
+=
+
++
=
+−=
( )
01
2
1
10
01
0
01
011
1
01
012
01
2
1
101
01
011
1
1
21
2
2
0
ZZZ
EZ
ZZ
Z
ZZ
ZZZ
E
ZZ
ZII
ZZZ
EZZ
ZZ
ZZZ
EI
ZZandZZIf
a
aaa
aa
a
gf
+−
=
+
++
−=
+−=
++
=
++
=
===
Short Circuit CalculationsIIEE Presentation
Voltage Rise Phenomenon
Single-to-line Ground Fault
Short Circuit CalculationsIIEE Presentation
Unfaulted Phase B Voltage During Single Line-to-Ground Faults
Unfaulted Phase B Voltage During Single Line-to-Ground Faults
+
−−=
+
−
−=
+
−
−=
+
−−=
+−
+−+
+−=
++=
1
0
1
0
2
1
01
1
0
1
0
2
1
1
0
1
0
1
12
1
01
102
1
1
01
1
1
01
1
1
2
0
01
1
21
2
0
2
1
;R and R s,resistance neglecting
2
1
2
1
2
222
X
X
X
X
aEV
Z
Z
Z
Z
aEV
Z
Z
Z
Z
Z
ZaE
ZZ
ZZaEV
ZZZ
EaZ
ZZ
EEaZ
ZZ
EV
aVVaVV
ab
ab
aab
aa
a
a
b
aaab
Short Circuit CalculationsIIEE Presentation
Unfaulted Phase B Voltage During Single Line-to-Ground Faults
Neglecting resistances R0 & R1
0
5
10
15
20
25
30
35
40
45
50
-10 -6 -3 -2.8 -2.6 -2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 0 1 2 5 9 25 45 65 85
X0/X1
Phase B
Voltage (p.u
.)
Short Circuit CalculationsIIEE Presentation
Fault MVA
10
)(
1
)3(
2
3
1
:p.u.in fault ground-to-line singefor
:p.u.in fault phasefor three
p.u.; 1.01
for where,
ZZI
ZI
MVAIMVA
SLGF
F
baseFF
aE
+=
=
×=
−
=
φ
Short Circuit CalculationsIIEE Presentation
Fault MVA
( ) ( )
( )
( ) ( )
( )
( )10
01
3
1
33
23
..3
2
.).(
:
..1
.).(
:
ZI
Z
upI
ZZ
MVAupIMVA
MVAfaultgroundtolineSingle
upI
Z
MVAupIMVA
MVAfaultphaseThree
SLGF
SLGF
baseSLGFSLGF
F
baseFF
−=
=+
×=
−−
=
×=
−
φ
φφ
Short Circuit CalculationsIIEE Presentation
Assumptions Made to SimplifyFault Calculations
1. Pre-fault load currents are neglected.
2. Pre-fault voltages are assumed equal to 1.0 per unit.
3. Resistances are neglected (only for 115kV & up).
4. Mutual impedances, when not appreciable are neglected.
5. Off-nominal transformer taps are equal to 1.0 per unit.
6. Positive- and negative-sequence impedances are equal.
Short Circuit CalculationsIIEE Presentation
Outline of Procedures for Short Circuit Calculations
1 Setup the network impedances expressed in per unit on a common MVA base in the form of a single-line diagram
2 Determine the single equivalent (Thevenin’s) impedance of each sequence network.
3 Determine the distribution factor giving the current in the individual branches for unit total sequence current.
Short Circuit CalculationsIIEE Presentation
Outline of Procedures for Short Circuit Calculations
4 Interconnect the three sequence networks for the type of fault under considerations and calculate the sequence currents at the fault point.
5 Determine the sequence current distribution by the application of the distribution factors to the sequence currents at the fault point
6 Synthesize the phase currents from the sequence currents.
Short Circuit CalculationsIIEE Presentation
Outline of Procedures for Short Circuit Calculations
7 Determine the sequence voltages throughout the networks from the sequence current distribution and branch impedances
8 Synthesize the phase voltages from the sequence voltage components
9 Convert the pre unit currents and voltages to actual physical units
Short Circuit CalculationsIIEE Presentation
CIRCUIT BREAKING SIZING(Asymmetrical Rating Factors)
Momentary Rating
Multiplying Factor = 1.6
Interrupting Rating
Multiplying Factor8 cycles = 1.0
5 cycles = 1.1
3 cycles = 1.2
1 ½ cycles = 1.5
Short Circuit CalculationsIIEE Presentation
EXAMPLE PROBLEM
In the power system shown, determine the momentary and interrupting ratings for primary and secondary circuit breakers of transformer T2.
Short Circuit CalculationsIIEE Presentation
Solution:
pux
pux
puI
puI
SLGF
F
05.0125.0210
3
125.08
1
10100
1000
8100
800
:100MVA system@ 69kV Equivalent
0
1
)(
)3(
=×−=
==
=
=
=
=φ
pux
pux
pux
pux
pux
3333.35.4
10015.0
4.5MVAor
450050000.9kVA :M2 M1,
80.075
10006.0
:T3 T3, T2,
24.025
10006.0
40.025
10010.0"
:G1
2667.030
10008.0
:T1
B
B
0
=
=
=
=×=
=
=
=
=
=
=
=
=
Short Circuit CalculationsIIEE Presentation
Solution:Positive sequence network:
Short Circuit CalculationsIIEE Presentation
Solution:
Zero sequence network:
Short Circuit CalculationsIIEE Presentation
Improper Sequence Network Models
Short Circuit CalculationsIIEE Presentation
Improper Sequence Network Models
Short Circuit CalculationsIIEE Presentation
Improper Sequence Network Models
Short Circuit CalculationsIIEE Presentation
Incorrect Sequence Network Models
Short Circuit CalculationsIIEE Presentation
QUESTIONS?
Short Circuit CalculationsIIEE Presentation