1. Fault Analysis
As per ANSI standard
NO.ANSI/IEEEStd141-1986
S. A. Soman
S. A. Soman
Department of Electrical Engineering
Department of Electrical Engineering
IIT Bombay Powai Mumbai-400076
IIT Bombay Powai Mumbai-400076
Email: soman@ee.iitb.ac.in
Email: soman@ee.iitb.ac.in
3. Organization
PART-I
• Fundamental consideration
Why?
How?
Sequence Components Review.
Apparatus Modeling.
Fault Analysis Program.
PART –II
• Advanced Topics
Purpose of Fault Analysis Reviewed.
Role of multipliers for Rotating Machines impedances.
E/X and X/R methods.
Example.
PART –III
• FAQ’S
4. Why?
• Electric systems occasionally experience short circuits.
• This results in abnormally high currents.
• Overcurrent protective devices should isolate faults at a
given location safely, with minimal damage.
• The parts of system shall be able to withstand the
resulting mechanical and thermal stresses.
• The magnitudes of fault currents are usually estimated by
calculations.
• The equipment is selected using the calculation results.
6. Sources of Fault Current
– Synchronous Generators
– Synchronous Motors and Condensers
– Induction Machines
– Electrical Utility System
– Distributed Generation ( modeling in fault analysis. resea
problem!)
Representation of Rotating Machines.
This fault current diminishes as the magnetic fiel
the machine decays.
7. What does a fault
Analysis program do?
• Simulates a fault ( steady state analysis)
SLG
LLG
LL
Three phase
• Results
SC – MVA
Fault current (in A)
Contribution of various lines to fault current
analysis.
p.u.
in
(MVA)
I
V
3
phase)
-
MVA(3
-
SC .....
..........
Base
sc
prefault
MVA.
in
.......
..........
KA
In
I
KV
In
V
3
phase)
-
MVA(3
-
SC sc
prefault
(Continued…..)
10. a
b
c
a
b
c
a
b
c
+ve Seq. Component
+ve Seq. Component 0 Sequence
0 Sequence
-ve Sequence
-ve Sequence
Sequence components
• Unbalanced 3-phase system has six degrees of freedom.
• Every balanced set of phasors has two degrees of freedom
(Forteskue,1918).
• Together +ve,-ve and 0 sequence phasors have six degrees of
freedom.
• Hence they can be used to synthesize 3phase unbalanced systems.
13. Advantages of Sequence
Transformation
• Used when the network is balanced.
Provides decoupling in the network. A
3nX3n Linear System Solver is decoupled
into three n X n Linear System Solver.
• Load may be balanced or unbalanced.
• Zero sequence currents provide
sensitive earth fault detection technique.
14. • Sequence Components in Fault Analysis
Program
Step 1-
Three Phase Model .
Formulate Admittance Matrix.
Step 2-
Sequence Model Formulation.
Step 3-
Inject 1.0 p.u. current at bus l i.e. Let,
Compute Vl of desired sequence i.e. solve
Zth
0,1,2
at l bus= Vl
012
1
3
]
[
]
[
]
[
n
abc
V
3n
3n
1
3n abc
abc Y
I
1
]
[
]
[
]
[ 012
012
012
n
V
n
n
1
n Y
I
'
]
0
0
.
.
1
0
0
0
0
[
]
[
l
e
]
[
]
][
Y
[ 012
012
012 e
1 l
n
V
15. Input to Fault Analysis
program
Depends on type of fault
Three phase fault.
Only Positive Sequence Data. Negative, Zero sequence
Network not excited.
SLG fault
Positive, Negative, Zero sequence Data.
Typical fault study
SLG (√ )
Fault current can range in utility systems from a few percent to
possibly 125% of the three phase fault value.
Three phase(√ )
In industrial systems line to ground fault current of more than
three phase value is rare.
LL (X) }fault currents are
approximately 87% of three-
phase fault current
LLG (X)
22. Role of Per Unit calculation
• In the per-unit there are four base quantities: base apparent
power in volt-amperes, base voltage, base current and base
impedance.
• Per – unit quantity = actual quantity/base quantity
• The following formulae apply to three- phase system, where
the base voltage is the line-to-line voltage in volts or
kilovolts and the base apparent power is the three- phase
apparent power in kilovolt – amperes or megavolt-amperes.
VOLTS
BASE
3
000
BASE(KVA)1
amp.)
CURRENT(
BASE
AMPERES
BASE
3
BASE(VOLT)
Ohm.)
IMPEDANCE(
BASE
2
P.U.
(KV)
BASE
(MVA)
BASE
IN(Ohm)
IMPEDANCE
ACTUAL
Z
23. Advantages of PU
Calculations
• Manufactures provide equipment data with name
plate rating as base.
• Range for acceptable % or p.u. values can be
easily fixed.
• Especially useful in networks with multiple voltage
levels interconnected through transformers.
• p.u. impedance of transformer is independent of
the base.
• Standard base conversion (scaling with MVA Base)
formulae are available.
24. Modeling Aspects for Static
Apparatus
• Transmission Lines, feeder cables etc
• Two winding and Three Winding Transformers
• Positive sequence Data = Negative sequence
Data.
• Zero Sequence Data different
Rule of Thumb for Lines---
Zero Sequence Data about Three Times Positive
Sequence Data.
• Zero Sequence Modes of Transformers.
28. Modeling of Rotating Machines
Modeling of Synchronous Generator
• Xd” = Subtransient reactance; determines the current
during the first cycle after fault occurs. In about 0.1 s
reactance increases to
• Xd’= Transient reactance; assumed to determine
current after several cycles at 60Hz. In about 0.5-2 s
reactance increases to
• Xd=Synchronous reactance; this is the value that
determines the current flow after a steady state
condition is reached.
• Synchronous generator data available from
manufacturers includes two values of direct axis
reactance – X``dv and X``di. The X``dv value should be
used for short – circuit calculations.
29. Modeling of Synchronous Motors
and Condensers
• During fault motor acts as a generator to supply
fault current
• The rotor carrying the field winding is driven by the
inertia of the rotor and load. Stator excitation is
reduced due to drop in voltage.
• The fault current diminishes as the rotor decelerates
• The generator equivalent circuit is used for
synchronous motor.
• The constant driving voltage and three reactance X
d”, Xd’ and Xd are used to establish the current
values at three points in time.
• Synchronous condensers can be treated in same
manner as synchronous motors.
30. Modeling of Induction
Machines
• During fault rotor is driven by inertia of load and rotor itself.
• No dc field excitation on rotor. Rotor winding is short circuited.
Hence, whatever rotor excitation is present, it is due to the
induced fields in the rotor from the rotating stator mmf. As stator
excitation is lost and rotor slows down this field is lost quickly.
• The current contribution of an induction motor to a terminal fault
reduces and disappears completely after a few cycles. As a
consequence only the sub transient value of reactance X``d is
assigned. This value is about equal to the locked – rotor reactance.
• For fault calculations an induction generator can be treated as an
Induction motor.
• Wound rotor induction motors normally operating with their rotor
rings short – circuited will contribute fault current in the same
manner as a squirrel cage induction motor.
• Occasionally large wound – rotor motors operated with some
external resistance maintained in their rotor circuits may have
sufficiently low short circuit time constants that their fault
contribution is not significant and may be neglected.
31. Negative Sequence Impedance
for Synchronous Machines
• Positive and negative sequence impedances
cannot be equal.
• In case of synchronous machine, -ve sequence
currents creates a rotating mmf in opposite
direction to the rotor mmf. Double frequency
emf and currents induced in rotor.
• -ve sequence impedance is 70-95 % of
subtransient reactance. It can be approximated
by subtransient reactance. For a salient pole
machine it is taken as a mean of Xd” and Xq”.
32. Zero Sequence Impedance of
Synchronous Machine
• Zero Sequence Currents cannot create rotating mmf
(why ?)
• Hence, Zero Sequence Impedance is only a small %
(0.1-0.7) of the +ve sequence impedances.
• It varies so critically with armature winding pitch that an
average value can hardly be given.
• Since synchronous machines only generate +ve
sequence voltage, the internal voltages used with
negative sequence and zero sequence networks is
zero.
• If Y point is grounded through an impedance Zg, then
3Zg will have to be added to zero sequence impedance
of generator before incorporating in YBUS.
33. Sequence Modeling of
Asynchronous Machines (IM)
• Transient state of the current damped
quickly (1-2 cycles)
• Subsequently machine behaves as a
passive element with impedance of value
Z=kVll^2/Smva where rated LL voltage
and 3phase MVA rating is used.
• Zero Sequence modeling can be treated
in similar lines to as synchronous
machines because rotor plays no
significant role.
34. Modeling of Electric Utility
Systems
• The generator equivalent circuit can be used to represent the
utility system
• The utility generators are usually remote from the industrial
plant.
• The current contributed to a fault in the remote plant appears to
be merely a small increase in load current to the very large
central station generators, and this current contribution tends to
remain constant.
• Usually represented at the plant by a single – valued equivalent
impedance referred to the point of connection.
35. Modeling of Mutually Coupled Lines
• If the lines a1, b1 and c1 carry balanced +ve or –ve sequence currents,
flux linking circuit 2 is zero (as per Ampere’s law).
• For zero sequence currents in circuit 1, flux linking circuit 2 is not zero.
• Hence, mutual coupling is only considered in zero sequence networks.
• Procedure is given in the book.
a1
b1
c1
a2
c2
b2
Circuit 1 Circuit 2
36. Effect of Mutual Coupling on Sequence
Network representation
Let two X mission lines emanating from the same tower (double
circuit) be coupled with each other.
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
c
b
a
d
c
b
a
s
m
m
m
s
m
m
m
s
c
b
a
I
I
I
j
I
I
I
z
z
z
z
z
z
z
z
z
v
v
v
If both lines are transposed ,then average mutual coupling
between any two phases of the 2-lines will be identical.
37. Mutual Coupling contd…
After sequence transformation.
2
2
2
1
1
1
2
1
1
2
1
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
3
I
I
I
j
I
I
I
z
z
z
z
z
z
v
v
v
m
s
m
s
m
s
MUTUAL COUPLING IS SEEN ONLY IN ZERO
SEQUENCE NETWORK
38. Conclusions
1. 3
Fault currents, LL fault currents will not be affected
by Mutual Coupling.
2. For all faults involving ground (SLb,LLb), If will be
affected by mutual coupling.
3. It will affect performance of relays & relay coordination
should account for it.
Editor's Notes
#31:The induced emf in the rotor will set up double frequency currents which create rotating mmf at double frequency w.r.t rotor in opposite direction. Since the rotor rotates at syn speed in +ve direction, as seen by observer on stator, speed of rotation of this mmf is syn, but in opposite direction. This flux has been set up based on Lenz law, hence it reduced overall –ve seq flux. Hence, -ve seq reactance is less than subtranient reactance. In +ve seq case both rotor and stator mmfs rotate in +ve direction with synchronous speed. Hence Lenz law does not come into picture.
#32:For zero sequence currents, field winding will act as short circuit (secondary of tranformer). As per Lenz law, the flux that it will create will try to oppose the cause. Hence, net flux should reduce. Hence, reactance below the sub transient value
![• Sequence Components in Fault Analysis
Program
Step 1-
Three Phase Model .
Formulate Admittance Matrix.
Step 2-
Sequence Model Formulation.
Step 3-
Inject 1.0 p.u. current at bus l i.e. Let,
Compute Vl of desired sequence i.e. solve
Zth
0,1,2
at l bus= Vl
012
1
3
]
[
]
[
]
[
n
abc
V
3n
3n
1
3n abc
abc Y
I
1
]
[
]
[
]
[ 012
012
012
n
V
n
n
1
n Y
I
'
]
0
0
.
.
1
0
0
0
0
[
]
[
l
e
]
[
]
][
Y
[ 012
012
012 e
1 l
n
V
](https://image.slidesharecdn.com/faultlevelcalculation-250515114507-a64add3c/85/fault-level-analysis-fault-level-analysis-14-320.jpg)
