This document discusses symmetrical three-phase faults in electrical power systems. It defines a symmetrical fault as one where equal fault currents are produced in each line with 120 degree phase displacement. This is the most severe type of fault. The document covers transient currents on transmission lines during a fault, selection of circuit breakers based on maximum fault currents, fault currents and induced emfs for synchronous machines under no-load and loaded conditions, and provides an algorithm for short circuit studies.

1. ELECTRICAL POWER SYSTEM – II
[2160908]
ACTIVE LEARNING ASSIGNMENT:
TOPIC : SYMMETRICAL THREE PHASE FAULTS.
UNIVERSITY :GUJARAT TECHNOLOGICAL UNIVERSITY.
COLLEGE : VADODARA INSTITUTE OF ENGINEERING.
DEPARTMENT : ELECTRICAL ENGINEERING [E.E.– I].
SEMESTER : VI.
PREPERED BY :
130800109026 [ BHARGAV M. JAYSWAL ]
130800109027 [ JESTY JOSE ]
130800109028 [ JOBIN ABRAHAM ]
GUIDED BY : ASST. PROF. PUSHPA BHATIA.
[ELECTRICAL DEPARTMENT]
ACTIVE LEARNING ASSIGNMENT
1

2.  Contents:
 Introduction
 Transients on a transmission line
 Selection of circuit breakers
 Short circuit of a synchronous machine (on no load)
 Short circuit of a loaded synchronous machine
 Algorithm for short circuit studies
 References
ACTIVE LEARNING ASSIGNMENT 2

3.  Introduction:
 Technical definition:
 The fault on the power system which gives rise to the
symmetrical fault currents i.e. equal fault currents in the line
with 1200 phase displacement is called a symmetrical fault.
 Due to balance nature of fault, for the analysis of the fault only one
phase is to be considered as faults in other two cases will be
identical.
 The following points should be particularly noted:
 This type of fault occurs rarely in practice.
 This type of fault is the most severe type of all faults and it
imposes more heavy duty on the circuit breakers.
ACTIVE LEARNING ASSIGNMENT 3
4

4.  Transients on a transmission line:
 let us consider a transmission line of resistance R and inductance L
supplied by an ac source of voltage V, such that V= Vm sin (𝝎𝒕 + 𝜶) as
shown in figure.
 Consider the short circuit transient on this transmission line.
 In order to analyze this symmetrical 3-phase fault, the following
assumptions are made:
 The supply is a constant voltage source,
 The short circuit occurs when the line is unloaded and
 The line capacitance is negligible.
ACTIVE LEARNING ASSIGNMENT 4

5.  Thus the line can be modeled by a lumped R-L series circuit.
 Let the short circuit take place at t=0. The parameter, 𝜶 controls the
instant of short circuit on the voltage wave.
 From basic circuit theory, it is observed that the current after short
circuit is composed of the two parts as under:
 i =is +it,
 Where, isis the sinusoidal steady state current (i.e. symmetrical short
circuit current) and it is the transient current (i.e. DC off-set
current).
 These component currents are determined as follows:
 is=
𝟐𝑽
!𝒁!
𝒔𝒊𝒏(𝝎𝒕 + 𝜶 − 𝜽)
 𝒁 = (𝑹 𝟐 + 𝝎 𝟐 𝑳 𝟐)∠ 𝜽 = 𝒕𝒂𝒏
𝝎𝑳
𝑹
 it=−is(0)𝒆−(
𝑹
𝑳
)𝒕
 it=
𝟐𝑽
!𝒁!
𝒔𝒊𝒏(𝜽 − 𝜶)𝒆−(
𝑹
𝑳
)𝒕
 i=
𝟐𝑽
!𝒁!
𝒔𝒊𝒏(𝝎𝒕 + 𝜶 − 𝜽)+
𝟐𝑽
!𝒁!
𝒔𝒊𝒏(𝜽 − 𝜶)𝒆−(
𝑹
𝑳
)𝒕
ACTIVE LEARNING ASSIGNMENT 5
 Transients on a transmission line {cont.}:

6.  The maximum momentary short circuit current
(imm) corresponds to the first peak. If the decay of
transient current in this short time is neglected,
then
 imm=
𝟐𝑽
!𝒁!
𝒔𝒊𝒏(𝜽 − 𝜶)+
𝟐𝑽
!𝒁!
 Since transmission line resistance is small, 𝜽=900
 imm=
𝟐𝑽
!𝒁!
𝒄𝒐𝒔(𝜶)+
𝟐𝑽
!𝒁!
 For maximization let 𝜶 = 0.
 imm=
𝟐 𝟐𝑽
!𝒁!
= which is the maximum of symmetrical
short circuit current (doubling effect)
ACTIVE LEARNING ASSIGNMENT
6
 Transients on a
transmission line {cont.}:

7.  Circuit Breaker Selection:
 A typical circuit breaker operating time is given in Figure.
 Once the fault occurs, the protective devices get activated.
 A certain amount of time elapses before the protective relays
determine that there is overcurrent in the circuit and initiate trip
command. This time is called the detection time.
 The contacts of the circuit breakers are held together by spring
mechanism and, with the trip command, the spring mechanism
releases the contacts.
ACTIVE LEARNING ASSIGNMENT 7

8.  When two current carrying contacts part, a voltage instantly appears
at the contacts and a large voltage gradient appears in the medium
between the two contacts.
 This voltage gradient ionizes the medium thereby maintaining the
flow of current. This current generates extreme heat and light that is
called electric arc.
 Different mechanisms are used for elongating the arc such that it can
be cooled and extinguished. Therefore the circuit breaker has to
withstand fault current from the instant of initiation of the fault to
the time the arc is extinguished.
 Two factors are of utmost importance for the selection of circuit
breakers. These are:
1. The maximum instantaneous current that a breaker must
withstand and
2. The total current when the breaker contacts part.
ACTIVE LEARNING ASSIGNMENT 8
 Circuit Breaker Selection {cont.}:

9.  However the instantaneous current following a fault will also contain the
dc component.
 In a high power circuit breaker selection, the sub transient current is
multiplied by a factor of 1.6 to determine the rms value of the current
the circuit breaker must withstand.
 This current is called the momentary current . The interrupting
current of a circuit breaker is lower than the momentary current and
will depend upon the speed of the circuit breaker.
 The interrupting current may be asymmetrical since some dc component
may still continue to decay.
 Breakers are usually classified by their nominal voltage, continuous
current rating, rated maximum voltage, K -factor which is the voltage
range factor, rated short circuit current at maximum voltage and
operating time.
 The K -factor is the ratio of rated maximum voltage to the lower limit of
the range of the operating voltage.
 The maximum symmetrical interrupting current of a circuit breaker is
given by K times the rated short circuit current.
ACTIVE LEARNING ASSIGNMENT 9
 Circuit Breaker Selection {cont.}:

10. Short circuit of a Synchronous machine (On
no load)
 Fig. shows a typical response of the armature current
when a three-phase symmetrical short circuit occurs at
the terminals of an unloaded synchronous generator.
 It is assumed that there is no dc offset in the armature
current. The magnitude of the current decreases
exponentially from a high initial value. The
instantaneous expression for the fault current is given
by:
ACTIVE LEARNING ASSIGNMENT 10

11.  where Vt is the magnitude of the terminal voltage, α is
its phase angle and
 Xd” is the direct axis subtransient reactance
 Xd’ is the direct axis transient reactance
 Xd is the direct axis synchronous reactance
 Td” is the direct axis subtransient time constant
 Td’ is the direct axis transient time constant
 In the expression we have neglected the effect of the
armature resistance hence α = π/2. Let us assume that
the fault occurs at time t = 0.From eqn we get he rms
value of the current as :
 which is called the subtransient fault current. The
duration of the subtransient current is dictated by the
time constant Td . As the time progresses and Td < t <
Td , the first exponential term of eqn. will start
decaying and will eventually vanish. However since t is
still nearly equal to zero, we have the following rms
value of the current
ACTIVE LEARNING ASSIGNMENT 11

12.  This is called the transient fault current. Now as the time
progress further and the second exponential term also
decays, we get the following rms value of the current for
the sinusoidal steady state
 In addition to the ac, the fault currents will also contain
the dc offset. Note that a symmetrical fault occurs when
three different phases are in three different locations in
the ac cycle. Therefore the dc offsets in the three
phases are different. The maximum value of the dc
offset is given by
 where TA is the armature time constant.
ACTIVE LEARNING ASSIGNMENT 12

13.  Short circuit of a loaded synchronous
machine:
 The synchronous machine is loaded when short circuit occurs .
 Fig. shows a synchronous machine operating under steady state
condition supplying a load current Io at terminal voltage Vo.
 Eg is the induced emf under loaded condition. Xd is direct axis
synchronous reactance of the machine.
 When a short circuit occurs at the terminals of machine a short
circuit current starts flowing through it. As it is time dependent it
changes from sub-transient to transient magnitude.
 The induced emfs during sub-transient and transient period are given
as:
Eg”=Vo+jIoXd”
Eg’=Vo+jIoXd’
 For Synchronous motor induced emf is given by:
Em”=Vo-jIoXd”
Em’=Vo-jIoXd’
ACTIVE LEARNING ASSIGNMENT 13

14. ACTIVE LEARNING ASSIGNMENT 14
 Short circuit of a loaded synchronous
machine {cont.}:

15.  Algorithm for short circuit studies:
Algorithm adopted for this type of analysis consists of
following steps:
 STEP 1: Obtain pre-fault voltages at all buses and
currents in all lines through a load flow study.
 STEP 2: Find Bus impedance matrix by inverting the
bus admittance matrix.
 STEP 3: Choose MVA base, KV base & calculate I base.
 STEP 4: Specify the faulty bus and obtain current at the
faulty bus and bus voltages during fault at all buses.
 STEP 5: Find current flows in each line of the system .
 STEP 6: Calculate SCMVA rating of circuit
breaker(choose acc. to the fault current magnitude )
for each line & at each bus.
ACTIVE LEARNING ASSIGNMENT 15

16.  References:
1. D.P. Kothari, I.J. Nagrath “Modern Power System Analysis”, McGraw
Hill Education (INDIA) Pvt. Ltd., Fourth Edition, Eighth Reprint,
2013, ISBN : 978-0-07-107775-0.
2. C.L. WADHWA “ELECTRICAL POWER SYSTEMS”, NEW AGE
INTERNATIONAL (P) LIMITED, PUBLISHERS, SIXTH EDITION, Reprint,
2014, ISBN : 978-81-224-2839-1.
3. J.B. Gupta “A Course in POWER SYSTEMS”, S.K. KATARIA & SONS
PUBLISHERS, Eleventh Edition, Reprint, 2015, ISBN : 978-93-5014-
373-5.
4. V.K. METHA, ROHIT METHA “PRINCIPLES OF POWER SYSTEMS”,
S.CHAND & Co. PVT. LTD., First Multicolour Edition, Reprint, 2014,
ISBN : 978-81-219-2496-0.
5. http://elearning.vtu.ac.in/P6/enotes/EE61/Unit1-8.pdf
6. http://nptel.ac.in/courses/Webcourse-contents/IIT-KANPUR/power-
system/ui/Course_home-6.htm
7. http://www.iosrjournals.org/iosr-jeee/Papers/Vol9-issue2/Version-
3/M092389100.pdf
ACTIVE LEARNING ASSIGNMENT 16

17. ACTIVE LEARNING ASSIGNMENT 17
ANY QUESTIONS?