KONGU ENGINEERING COLLEGE,PERUNDURAI,ERODE – 638 052
(An Autonomous Institution affiliated to Anna University)
Department of Electrical and Electronics Engineering
POWER SYSTEM ANALYSIS AND STABILITY
One Mark questions
UNIT - 1
INTRODUCTION TO MODELING OF POWER SYSTEM COMPONENTS
Q.N
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17.
Question
DOD
Types of
Question
s
General power system studies includes 1).
__________________ 2). ___________ 3).
____________________
The purpose of power flow analysis is to
________________________ of the power system network.
The objective of fault analysis is to ______________.
In power flow analysis, the generator is modeled as a
___________ source.
In fault analysis, the generator is modeled as
_______________ source.
The network equation describing the power flow analysis is
___________.
The network equation describing the fault analysis is
___________.
Elemental impedance/admittance values are known as
______________.
Singular matrix is a matrix in which ________________.
Using singular transformation, the equation for Ybus=
__________.
Addition of branch to the partial ZBus __________ the
number of node.
30 MVA,11kV synchronous generator has its sub-transient
reactance of 11%. Its p.u value on a base of 100 MVA is
_________
The order of the incidence matrix is ____________.
Incidence matrix links _________ quantities and
_________ quantities.
Per unit value is given by the ratio of ____________ to
______________.
In a 5 bus, 10 element system network, the order of the
primitive admittance /impedance matrix is _____________.
The two different type of frame of references are
___________, ________
The different types of modeling includes _________,
1
Concept
1
Concept
1
1
Concept
Concept
1
Concept
1
Concept
1
Concept
1
Concept
2
2
Concept
Concept
1
Concept
2
Formula
2
2
Concept
Concept
1
Concept
1
Formula
1
Concept
2
Concept
19
20.
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35
36
37.
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39.
______________, ____________
Modeling is basically required to
___________________________
2
Concept
If the base kVA is 25,000 then a 5000kVA alternator with 8%
reactance will have
(a) A 4% reactance
(b) A 40% reactance
(c) A 16% reactance
(d) A 20% reactance
Single line diagram is ____________________________ of
power system network
In the Single line diagram, the generator is represented by
______________________( draw the symbol)
In the Single line diagram, the two winding transformer is
represented by ______________________(draw the symbol)
In general power system, bus represents
_______________________
Why static load is not considered for short circuit analysis?
What is the difference between percentage representation & p.u.
representation?
Base impedance is the ratio between _______________ to
_____________
Write an expression to change the p.u. from given base value to
new base value
2
Application
1
Concept
1
Concept
1
Concept
1
Concept
2
2
Concept
Concept
1
Concept
1
Formula
Write an expression to determine the new values of YBus
using kron reduction method
Oriented graph is a graph with ______________________
Addition of branch _____________ the order of the bus
impedance matrix
Addition of the link_______________ the elemental values
of the impedance matrix
What are incidence matrices?
1
Formula
1
1
Concept
Concept
1
Concept
2
Concept
The per unit impedance of a circuit element is 0.15. If the base
KV and base MVA are halved, then the new value of the
per unit impedance of the circuit element will be
(a) 0.075
(b) 0.15
(c) 0.30
(d) 0.60
3
Application
A 230kV, 100 MVA synchronous generator has sub
transient reactance of 20%. Find its value in ohms
Write the equation of the bus admittance matrix using
singular transformation
Partial ZBus matrix is available for the system network. An
element is connected from the reference bus. Write the
modified ZBus matrix
Partial ZBus matrix is available for the system network. An
element is connected from the existing bus so that a new
node is created Write the modified ZBus matrix
Partial ZBus matrix is available for the system network. An
element is connected from the existing bus to the reference
bus. Write the modified ZBus matrix
2
Application
1
Formula
2
Formula
2
Formula
2
Formula
40.
Partial ZBus matrix is available for the system network. An
element is connected between the two existing buses.
Write the modified ZBus matrix
2
Formula
UNIT – 2
POWER FLOW ANALYSIS
DOD
Types
of
Questio
ns
1
Concept
2.
Network equation describing the power flow analysis is
____________________
The purpose of slack bus is ____________
1
Concept
3.
Write the expression for Pi
2
Formula
4.
The expression for Qi is
2
Formula
5.
Scheduled power injected into the network is the difference between
_____________
Mismatch is the difference between
_____________________________.
What are the basic data’s required to carry out the load flow analysis?
2
Concept
2
Concept
2
Concept
3
Concept
1
Concept
1
Concept
1
Concept
1
Concept
13.
Power flow equation is characterized by
(1)_________________________
(2) ____________________________
The buses in the power flow analysis is classified as
_________,________,_________
In load flow analysis, the generator is modeled as a constant
__________ source
In load flow analysis, the transformer is modeled as
__________________
In load flow analysis, the line is represented as __________________
equivalent.
The variables specified for the load bus are ________ and _______
1
Concept
14.
The variables to be calculated for the load bus are ______ and _____
1
Concept
15.
1
Concept
1
Concept
17.
The variables specified for the generator bus are ________ and
_______
The variables to be calculated for the generator bus are ______ and
_____
Write the power flow equation
1
Formula
18.
The purpose of the slack bus is __________
2
Concept
19.
The variables specified for the slack bus are ______ and ______
2
Concept
20.
In a N bus system, bus 1 is the slack bus and all (N-1) buses are load
buses. The number of equations to be solved are ________
The solution for the power flow equation can be obtained by
__________, __________, ______________
2
Formula
1
Concept
Q.N
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6.
7.
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21.
Question
22.
Power flow solution must satisfy the _____ and ____ constraints
1
Concept
23.
The drawback in G-S method is __________
1
Concept
24
The purpose of acceleration factor is
1
Concept
25
The acceleration factor assumes the value between _____ to _____
1
Concept
26
The state variables for the voltage controlled bus is ______, _______
1
Concept
27
In power flow analysis “Bus switching” meant that
_________________________
1
Concept
Q.N
o
UNIT – 3
SYMMETRICAL SHORT CIRCUIT ANALYSIS
Question
DO
D
Types of
Question
s
1.
The purpose of fault analysis is _______________________
1
Concept
2.
Which of the following results in symmetrical fault?
(a) single phase to earth fault
(b) phase to phase
(c) all the three phases to earth
(d) two phases to earth
Which portion of the power system is more prone to faults?
(a) alternator
(b) Transformer
(c) Overhead lines
(d) Underground
cables
The magnitude of fault current depends upon
(a) total impedance upto fault
(b) voltage at the fault point
(c) load current being supplied before occurrence of
fault
(d) both (a) and (b)
In a 3 – phase, 10 MVA, 11KV generator having 12% subtransient
reactance, a 3 –
phase short circuit occurs at its terminals, the fault current will be
(a) 9090 A
(b) 5250 A
(c) 3030 A
(d) 2650 A
A power system network with a capacity of 100 MVA has source
impedance of 10%
at a point. The fault level at that point is
(a) 10 MVA
(b) 30 MVA
(c) 300 MVA
(d) 1000 MVA
Why fault computation is easier in symmetrical analysis?
2
objective
1
Concept
8.
For fault analysis, the generator is represented as a series connection of
Eg″ with __________
1
Concept
9.
Why three phase fault is considered as a severe fault ?
1
Concept
10.
Give the expression for symmetrical fault current
1
Concept
11.
When an alternator is short circuited on the three phases, it settles down
to the steady
short circuit value and limited by
(a) sub-transient reactance
(b) transient
reactance
(c) synchronous reactance
(d) either (a)
or (c)
2
12.
A fault is defined as an ____________________ condition observed in
the power
system
Fault in the power system is classified as ____________ and
______________
1
Concept
1
Concept
3.
4.
5.
6.
7.
13.
1
objective
2
objective
2
Application
3
Application
objective
14.
Bolted fault is ___________________
1
15.
Fault level means
(a) voltage at the fault point
(b) fault
current
(c) fault power factor
(d) fault MVA
The electrical equivalent of representing the fault is _____________
(draw the symbol)
A balance 3-phase system consists of
(a) zero sequence currents only
(b) positive sequence currents only
(c) negative and zero sequence currents
(d) zero, negative, positive sequence currents
2
objective
2
Concept
2
objective
2
Concept
19.
During the period of short circuit at the terminals of the generator, the
generator shows three different reactance namely _____________,
_________________, _________________
Sub-transient period exists up to __________ cycles
1
Application
20.
Transient period exists for a period of __________________ cycles
1
Application
21.
The symmetrical short circuit current is multiplied by a factor
________ to account for the DC offset component.
Momentary current of the circuit breaker =
________________________________
Interrupting current of the 8 cycle circuit breaker =
________________________
Interrupting current of the 5 cycle circuit breaker =
________________________
A typical power system network has thevenins impedance upto fault
point as j0.56. The symmetrical short circuit rms current is
________________
1
Application
2
Application
2
Application
2
Application
2
Application
When the fault is suddenly applied on the transmission line, the
fault current will have ________________ and
___________________ component
The bus impedance matrix of a typical power system is given by
 0.785 0.5817 0.427 


j 0.5817 0.794 0.367 
 0.427 0.367 0.8325 

 . The fault occurs on bus 2. What
1
Concept
2
Application
1
Concept
1
Concept
1
Concept
16.
17.
18.
22.
23.
24.
25.
26.
27.
28.
29.
30
is the value of fault current in p u
Mention the various sources of fault.
Pre-fault condition is the condition of the system network
______________________
Post -fault condition is the condition of the system network
______________________
Concept
Q.N
o
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2.
3.
4.
5.
UNIT – 4
UNSYMMETRICAL SHORT CIRCUIT ANALYSIS
Question
DO
D
Types of
Questions
Who introduce the theory of symmetrical components?
How to solve unbalanced faults?
Write the symmetrical components of the 3 phase system
‘a’ is an operator used symmetrical component analysis
(a) which rotates the vector, it operates upon, through
an angle 90°, in the clockwise direction
(b) which rotates the vector, it operates upon, through
an angle 120°, in the counter-clockwise direction
© which rotates the vector, it operates upon, through
an angle 120°, in the clockwise direction
(d) which rotates the vector, it operates upon, through
an angle 240°, in the clockwise direction
1
1
1
1
Concept
Concept
Concept
Which of the following statement is true?
(a) a =0.5-j 0.866
0.866
(c) a4 = -a
a)
The value of 1+a+a2= _______
1
objective
1
objective
(b) a = 0.5 +j
(d) a2 = -1(1 +
7.
The zero sequence component of currents IA=10∠ 0°, IB=10∠ 120°, IC=10∠ -240° is ____________
1
8.
An unbalanced voltage vector Va =____________________
2
9.
The ________ currents of symmetrical ________ connected circuit
will not have zero sequence component
The ________ voltage of symmetrical ________ connected circuit will
not have zero sequence component
Equivalent circuits of each elements to sequence component of currents
is known as _____________
Organising the individual equivalent circuits according to single line
diagram is known as _____________________
The zero sequence impedance of the star connected network with
grounded impedance Zn is given by
Zero sequence component per phase voltage of delta is
(a) line voltage
(b) zero
2
applicatio
n
applicatio
n
applicatio
n
Concept
2
Concept
2
Concept
2
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2
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2
objective
1
objective
1
Concept
1
Concept
6.
10.
11.
12.
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14.
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16.
17.
(c) 3 line voltage
(d) line voltage/3
In a star-connected system without neutral grounding, zero sequence
currents are
(a) zero
(b) vector sum of phase currents
(c) same as rms value of phase currents
(d) same as the peak value of phase currents
The faults that require zero sequence data of equipments for
analysis are _________
Which unsymmetrical fault is a frequent fault?
1
Concept
1
Concept
1
Concept
1
Concept
2
Concept
1
applicatio
n
24.
25.
The zero sequence circuit is required for the fault involving
____________
For SLG fault on generator, the three sequence circuits are
connected in _________
For L-L fault, the sequence circuits required are
________________
For LLG fault, the equivalent impedance is given by
____________
For a single line to ground fault the zero sequence current is
given by j3 p.u. The current in the neutral is
When a fault occurs on the system, the zero sequence component
of current becomes zero. The type of fault is
(a) 3 phase fault
(b) DLG fault
(c) LL fault
(d) SLG fault
Draw the positive sequence circuit of generator
Draw the negative sequence circuit of generator
1
1
Concept
Concept
26.
27.
28.
29.
Draw the zero sequence circuit of generator
Draw the positive sequence circuit of transmission line
Draw the negative sequence circuit of transmission line
Draw the zero sequence circuit of transmission line
1
1
1
1
Concept
Concept
Concept
30.
Draw the zero sequence circuit of transformer with Υ/Δ
connection. The neutral of the Υ connection is connected to the
grounding reactor
Draw the zero sequence circuit of transformer with Υ/Δ
connection. The neutral of the Υ connection is floating
Draw the zero sequence circuit of transformer with Δ/Δ
connection
Draw the zero sequence circuit of transformer with Υ/Υ
connection. The neutral of the Υ connection is solidly grounded.
1
Concept
1
Concept
1
Concept
1
Concept
18.
19.
20.
21.
22.
23.
31.
32.
33.
Concept
UNIT – 5
STABILITY ANALYSIS
1.
The purpose of stability analysis ________________________
1
Types of
Question
s
Concept
2.
The main factors considered for the stable operation are
__________ and _________
In general, stability is classified as ______________ and
_____________ stability
Stability of the system depends on ___________________
1
Concept
1
Concept
1
Concept
Steady State Condition refers to the state of the power system
which is characterized by ____________________
Transient state is the operating state of the power system which is
characterized ______________
The generator is modeled as ___________________________for
stability studies.
SMIB is the stability analysis of _________________________
1
Concept
1
Concept
1
Concept
1
Concept
1
Concept
10.
Multi-machine stability is the stability analysis of
___________________
Write the swing equation.
1
Concept
11.
Swing equation represents the _______________________
1
Concept
12.
The equal area criterion of stability is applicable to
(a) two machine system and infinite busbars
(b) one machine system and infinite busbars
(c) multi-machine system
(d) none of the above
The maximum value of load angle for stability is _________
1
objecttive
1
Concept
Q.N
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18.
Question
DO
D
The maximum power that can be transferred during normal steady state
1
condition is known as _____________________
The maximum power that can be transferred during transient condition
1 is
known as ___________
If the torque angle δ increases infinitely, the system will show
1
(a) stability
(b) instability
(c) steady state stability
(d) none of
the above
Transient disturbances are caused by
1
(a) sudden load changes
(b) switching operations
(c) inadvertent tripping of lines and generators
(d) faults in the power system
(e) all of the above
The steady state stability of the power system can be improved by 1
(a) increasing the number of parallel lines between the
transmission points.
(b) connecting capacitors in series with the line
(c) reducing excitation of machines
Concept
Concept
objecttive
objecttive
objecttive
24.
(d) either (a) or (b)
(e) both (a) and (b)
The inertia constant of a 100MVA, 11kV water wheel generator
is 4.
the energy stored in the rotor at the synchronous speed is
(a) 400 MJ
(b) 400 KJ
(c) 25 MJ
(d) 25 KJ
Stability is maintained in the power system when the restoring
force
___________ to the disturbing force
Two generators are having the inertia constant H1 and H2 and are
swinging coherently. The equivalent inertia is
The solution for the swing equation is obtained by the numerical
integration methods namely ____________,_____________
According to equal area, the system retains its stability when
__________ area equal to __________ area
Critical clearing angle is ______________________________
25.
Critical clearing time is the time __________________________
1
Concept
26.
Coherent swinging is the swinging of all generators in ________
1
Concept
27.
Draw the power- angle diagram of synchronous machine
1
Concept
28.
At what value of load angle, the power transferred will be
maximum?
Oscillatory instability is caused because of insufficient ________
torque
Non oscillatory instability is caused by insufficient _________
torque.
1
Concept
1
Concept
1
Concept
19.
20.
21.
22.
23.
29
30
1
objecttive
1
Concept
1
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1
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1
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1
Concept
Two Mark questions
UNIT – 1
INTRODUCTION TO MODELING OF POWER SYSTEM COMPONENTS
QUESTION
NO
QUESTIONS
What is the purpose of modeling?
1
1
Types of
Questions
Concept
Concept
3
What are the various methods of modeling?
1
Concept
4
What is primitive model?
2
Concept
5
Write the performance equations of an n-bus
system in the nodal admittance form and
explain the quantities occurring in the
equation.
What is meant by singular transformation?
3
Concept
1
Concept
Give the expression for Y bus matrix in terms
of primitive network elements.
How the transformers are modeled for
analysis?
A branch of impedance Zb is connected to the
existing bus $ to create new bus k.What is the
new ZBus
1
Expression
2
Concept
2
Concept
10
Mention the type of frame of references?
2
Concept
11
3
Concept
1
Expression
13
Mention any two mathematical methods that
help in calculating the bus voltages of industry
based power system
Write an expression to determine the new
values of YBus is known reduction method.
Define a oriented graph.
1
Definition
14
What are incidence matrices?
1
Concept
15
Mention different types of incident matrices?
1
Concept
16
Write the basic equation to model the
armature of a 3φ generator?
How the transmission lines are modeled to
evaluate the performance?
Based in different analysis, mention the
different types of modeling
2
Concept
2
Concept
1
Concept
Define Single Line Diagram
1
Definition
20
Define per unit value.
1
Definition
21
Define Base Current.
1
Definition
22
Define base impedance.
1
Definition
23
Write an expression to change the p.u. from given
base value to new base value?
2
Concept
1
What is meant by modeling?
2
6
7
8
9
12
17
18
19
DOD
24
What is an impedance diagram?
1
Concept
25
List the advantages of the p.u. representation.
1
Concept
26
If the resistance in ohms is 5, find the p.u. value
on a given base KVA=106 & base KV=11.
A generator (which may be represented by an emf
in series with an inductance reactance) is rated
500MVA, 22KV. Its Y-connected windings have a
reactance of 1.1p.u. Find the ohmic value of the
reactance of the winding.
A generator is rated 500MVA, 22KV. Its
reactance in p.u. is 1.1. Calculate p.u. reactance on
a base of 100MVA, 20KV.
What are the assumptions made to derive the
reactance diagram from single line diagram? Static
loads are neglected for fault calculations
What is the difference between percentage
representation & p.u. representation?
How per unit representation is advantages over the
percentage method?
Define base impedance.
3
Problem
3
Problem
2
Problem
3
Concept
1
Concept
1
Concept
1
Definition
27
28
29
30
31
32
UNIT – II
POWER FLOW ANALYSIS
QUESTIO NO
QUESTIONS
DOD
1
2
3
4
5
Define voltage controlled bus.
What is PQ-bus?
What is swing bus (or slack bus)?
What is the need for slack bus?
What are the operating constraints imposed in the
load flow studies?
What is power flow study or load flow study?
What are the informations that are obtained from a
load flow study?
What is the need for load-flow study?
What are the works involved in a load flow study? or
How a load flow study is performed?
What are the quantities that are associated with each
bus in a system?
What are the different types of buses in a power
system? or How the buses are classified and what
are its types?
What are the iterative methods mainly used for the
solution of load flow problems?
Discuss the effect of acceleration factor in the load
flow solution algorithm. How will you account for
voltage controlled buses in this algorithm?
1
1
1
1
1
Types of
Question
s
Definition
Concept
Concept
Concept
Concept
1
2
Concept
Concept
1
2
Concept
Concept
2
Concept
1
Concept
2
Concept
2
Concept
6
7
8
9
10
11
12
13
14
Why do we go for iterative methods to solve load
flow problems?
What do you mean by a flat voltage start?
When the generator bus is treated as load bus?
What will be the reactive power and bus voltage
when the generator bus is treated as load bus?
What are the advantages of Gauss-Seidel method?
. What are the disadvantages of Gauss-Seidel
method? The disadvantages of Gauss- Seidel
methods
How approximation is performed in NewtonRaphson method?
What is Jacobian matrix? How the elements of
Jacobian matirx are computed?
What are the advantages of Newton-Raphson
method?
What are the disadvantages of Newton-Raphson
method?
Mention (any) three advantages of N-R method over
G-S method.
Compare the G-S and N-R methods of load flow
solutions.
How the convergence of N-R method is speeded up?
How the disadvantages of N-R method are
overcome?
What is the need for voltage control in a power
system?
What is the reason for changes in bus voltage?
1
Concept
1
1
2
Concept
Concept
Concept
1
1
Concept
Concept
1
Concept
2
Concept
1
Concept
2
Concept
1
Concept
1
Concept
1
2
Concept
Concept
1
Concept
2
Concept
1
Concept
31
Mention the various methods of voltage control
employed in power system.
What is infinite bus?
2
Concept
32
How the reactive power of a generator is controlled?
1
Concept
33
What are the drawbacks in voltage control using
generator excitation?
What is off-nominal transformer ratio?
2
Concept
2
Concept
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
34
UNIT-III
SYMMETRICAL SHORT CIRCUIT ANALYSIS
QUESTION
NO
1
2
QUESTIONS
Define a Fault
What are the causes of fault?
DOD
1
1
Types of
Question
s
Definition
Concept
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
1
How the faults are classified?
1
What are the various sources of fault current?
1
List the various types of shunt and series faults
2
Define short circuit capacity.
2
Which fault is the worst fault?
1
Why 3 phase fault is considered as severe fault.
1
What is symmetrical fault?
1
Why fault occurs in a power system?
1
What is meant by fault level?
2
For what type of fault, the fault current is maximum
when there is fault at the generator terminals?
1
Name any 2 methods of reducing short circuit current
2
Name the main differences in representation of
power system for load flow and short circuit studies.
1
Name the main differences in representation of
power system for load flow and short circuit studies
1
What is meant by fault calculations?
1
What is the need for short circuit studies or fault
analysis?
2
What is the reason for transients during short
circuits?
1
Draw the waveform of a short circuit current on a
transmission line
2
What is meant by doubling effect?
3
Define DC off-set current
4
Draw the oscillogram of short circuit current when an
unloaded generator is subjected to symmetrical fault,
clearly marking subtransient, transient and steady
state regions.
2
What is synchronous reactance?
2
Define subtransient reactance
1
Define transient reactance\
2
How will you determine the synchronous, transient
and subtransient reactances from the oscillogram of
the short circuit current?
2
What is the significance of subtransient reactance in
short circuit studies?
2
What is the significance of transient reactance in
short circuit studies?
1
Distinguish between the transient and subtransient
reactances of a synchronous machine
1
Why the armature current decreases when the flux
diminishes?
2
Write down the equation determining fault current in
a generator when its reactance are known?
2
Write the equation to find the subtransient current
2
Give one application to find subtransient reactances
2
Write the equation to find the subtransient reactances
and internal voltage of the generator
Concept
Concept
Concept
Definition
Concept
Concept
Concept
Concept
Concept
Concept
Concept
Concept
Concept
Concept
Concept
Concept
Concept
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Definition
Concept
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Definition
Definition
Concept
Concept
Concept
Concept
Concept
Concept
Concept
Concept
Concept
35
36
37
38
39
40
41
42
Write the equation for subtransient and transient
voltages of the motor
A motor is drawing 10,000 KW at 0.85 pf leading
and a terminal voltage of 12 KV. Determine the load
current
2
Concept
2
Problem
The generator emf is 1pu. and the subtransient
reactance is 20%. Find the subtransient current.
The generator emf is 1pu. and the transient reactance
is 25%. Find the transient current
If Eg=1pu. and Xd=40%. Find the short circuit
current.
When a synchronous machine is suddenly short
circuit, what is the maximum possible instantaneous
current in terms of symmetrical short circuit current?
How symmetrical faults are analyzed ?
Define short circuit interrupting MVA of a circuit
breaker
2
Problem
1
Problem
1
Problem
1
Concept
2
2
Concept
Definition
UNIT-IV
UNSYMMETRICAL SHORT CIRCUIT ANALYSIS
QUESTION No
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
QUESTIONS
Define a Fault.
What are the causes of fault?
How the faults are classified?
What are the various sources of fault current?
What are the types of unsymmetrical faults?
What is unsymmetrical fault?
Name the fault in which positive, negative and zero
sequence component current are equal.
Name the fault in which positive, negative sequence
component currents are equal zero sequence component
current in magnitude.
Name the various unsymmetrical faults in a power
system
What is negative sequence impedance?
Name the faults which do not have zero sequence
currents flowing.
Name the faults involving ground.
Name the faults which do not have zero sequence
current flow.
The neutral grounding impedance Zn appears as 3Zn in
the zero sequence circuit.Why?
What is meant by positive sequence impedance.
What is sequence circuit?
DOD
1
1
1
1
1
1
2
Types of
Question
s
Definition
Concept
Concept
Concept
Concept
Concept
Concept
2
Concept
2
Concept
2
2
Concept
Concept
2
1
Concept
Concept
1
Concept
1
1
Concept
Concept
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
What are sequence networks?
What is meant by zero sequence impedance
What is meant by positive sequence reactance.
What are positive sequence components?
Define positive sequence impedance.
What are zero sequence components?
What are sequence impedance and sequence networks?
What is meant by negative sequence reactance
What is meant zero sequence reactance.
Write the boundary condition in line to line fault
Write the boundary condition in line to ground fault
Write the boundary condition in LLG fault
Write the boundary condition in LLLG fault
Draw the connection of sequence networks for a single
line to a ground fault at the terminals of a unloaded
generator.
Draw the connection of sequence networks for a line to
line fault at the terminals of a unloaded generator.
Draw the connection of sequence networks for a double
line to a ground fault at the terminals of a unloaded
generator.
Draw the connection of sequence networks for a line to
line fault without fault impedance
Draw the connection of sequence networks for a single
line to a ground fault without fault impedance
Draw the connection of sequence networks for a double
line to a ground fault without fault impedance
Draw the connection of sequence networks for a single
line to a ground fault through an impedance Zf.
Draw the connection of sequence networks for a line to
line fault through an impedance Zf.
Draw the connection of sequence networks for a double
line to a ground fault through an impedance Zf.
1
1
1
1
1
1
1
1
1
2
2
2
2
2
Concept
Concept
Concept
Concept
Definition
Concept
Concept
Concept
Concept
Concept
Concept
Concept
Concept
Concept
1
Concept
2
Concept
3
Concept
3
Concept
2
Concept
2
Concept
2
Concept
2
Concept
UNIT – V
STABILITY ANALYSIS
QUESTION No
1
2
3
4
5
6
7
8
QUESTIONS
Define stability
Define steady state stability
What do you mean by steady state condition?
How the steady stability is classified?
What do you mean by transient state?
Define transiently stable condition.
Define steady state stability limit.
Define transient stability limit.
DO
D
1
1
1
1
1
1
1
1
Types of
Question
s
Definition
Definition
Concept
Concept
Concept
Definition
Definition
Definition
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Define transient stability
How stability studies are classified, what are they?
Write down the units of inertia constants M and H and
their interrelationship.
Give typical values of inertia constant, H for turbo
generators, synchronous condensers and water
wheel generators
Define swing curve. What is the use of swing curve?
Define power angle
Name the two ways by which transient stability study
can be made in a system where one machine is
swinging with respect to an infinite bus.
Define critical clearing time and critical clearing
angle and give equations for both.
List the methods of improving the transient stability
limit of a power system.
State equal area criterion
If two machines are swinging coherently with inertia
M1 and M2, what will be the inertia of the equivalent
machine?
In a 3 machines system having ratings S1,S2 and S3
and ineria constants M1,M2 an M3. What is the
inertia constant M and H of the equivalent system?
Define synchronizing coefficient. For what value of
synchronizing coefficient the system remains stable.
Give an expression for swing equation. Explaining
each term along with their units.
Give the simplified power angle equation and the
expression for Pmax.
A system has two stability limits, 100 MW and 150
MW. Which is the steady state stability limit and
which is transient stability limit.
The sending end and the receiving end voltages of a
transmission line at 150 MW load are equal at 132
KV. The per phase line impedance is (3+4j)Ω.
Calculate the maximum steady state power that can be
transmitted over the line.
If the maximum power Pmax=50 MW. Find the
electrical power output for a torque angle of 60 deg.
A 50 Hz, 4 pole turbo generator of rating 20
MVA,13.2 KV has an inertia constant of H=9 KWsec/KVA. Find the kinetic energy stored in the rotor
at synchronous speed.
Find the frequency of oscillation for a synchronizing
coefficient of 0.6, inertia constant, H= 4 and system
frequency of 50 Hz
What are called coherent machines?
State the causes of voltage instability.
Write the swing equation for a single synchronizing
1
2
2
Definition
Concept
Concept
2
Concept
2
1
2
Definition
Definition
Concept
2
Definition
2
Concept
1
2
Concept
Concept
2
Problem
2
Definition
2
Concept
2
Concept
2
Problem
2
Problem
2
Problem
2
Problem
2
Problem
1
1
1
Concept
Concept
Concept
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
machine connected to an infinite bus bars.
Write the concept of critical clearing angle.
What is power system stability?
On what basis do you conclude that a given
synchronous machine has lost stability.
Define infinite bus in a power system.
What is the use of Swing equation? What are the
methods used to solve it?
State the applications of Equal area criterion.
How can we classify the stability studies?
Define rotor angle stability.
Distinguish between steady state and transient
stability.
1
1
1
Concept
Concept
Concept
1
1
Definition
Concept
1
1
1
1
Concept
Concept
Concept
Concept
State two consequences of instability of power
system.
State the methods used for the solution of Swing
equation.
Write the power angle equation of an alternator
connected to a synchronous motor through pure
reactance network.
1
Concept
1
Concept
1
Concept
Write the expression for the kinetic energy of the
rotor at synchronous speed in MJ.
A system has two stability limits, 80 MW and 120
MW. Which is the steady state stability limit? Which
is the transient stability limit?
2
Concept
3
Problem
Explain the use of equal area criterion to investigate
sudden loss of one of the parallel lines.
In a double circuit line, one line is suddenly switched
off. Draw the corresponding power angle curves and
illustrate the application of equal area criterian.
Define load angle of a generator
1
Concept
2
Concept
2
Definition
Between steady state and transient stability limits,
which limit will be higher
State whether stability limit is increased or decreased
by (a) Adding one or more transmission circuit in
parallel (b) Having fast acting circuit breakers.
1
Concept
3
Concept
BIG QUESTION
Q.N
o
1
2
3
Question
UNIT - 1
INTRODUCTION TO MODELING OF POWER SYSTEM
COMPONENTS
Draw the 1φ equivalent circuit for the 3φ, 440V,15HP, with Z= 0.3+j1.0 ohms,
90% efficiency and 80% power factor motor. Also obtain the p.u value of
impedance and the voltage at the motor terminals on a base of 220KVA and
440V.
A 3φ transformer is rated 400MVA, 220 Y/22Δ. The Y- equivalent short circuit
impedance measured on the L.V.side of the transformer is 0.121 Ω. Determine
the p.u reactance of the transformer and p.u value to be used to represent this
transformer in a system whose base on H.T.side of the transformer is 100MVA,
230KV.
Three single phase transformers each rated 25 MVA, 38.1 / 3.81 KV are
connected in Y-Δ with a balanced load of three, 0.6 Y-connected resistors.
Choose a base of 75 MVA, 66KV on the H.T side of the transformer and specify
the base for L.T.side. Also determine the p.u.value of RL on L.T and H.T. side.
DO
D
Types of
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s
Problem
2
Problem
2
Problem
2
Problem
4
For the network shown in figure, identify the nodes to be eliminated and hence
find the modified Ybus by (i) Matrix portioning method (ii)Kron reduction method
2
50 MVA
22/220k
V 10%
90 MVA
22kV,
18%
40 MVA
220/11k
V 6%
48.4
5
65.43
40 MVA
22/110k
V 6.4%
40 MVA
110/11k
V 8%
Problem
66.5 MVA
10.45kV
18.5%
57 MVA
10.45kV
0.6 pf lag
2
The Single line diagram of a 3 phase power system network is shown in the
above figure. Select a common base of 100 MVA, 22kV on the generator side.
Draw an impedance diagram with all impedances including the load impedance
marked in p.u
Obtain the pu reactance diagram of the system shown in figure. The positive
sequence reactance for the various accessories and components are given below
G1:
G2:
G3:
T1:
T2:
TL
30 MVA, 10.5kV,X″ = 1.6Ω
15 MVA, 6.6kV,X″ = 1.2Ω
25 MVA, 6.6.5kV,X″ = 0.56Ω
3 Phase, 15 MVA, 33 / 11 kV X =15.2 Ω / phase measured on HT side
3 Phase, 15 MVA, 33 / 6.2 kV X =16 Ω / phase measured on HT side
20.5 ohm / phase
Problem
2
6
7
The reactance data in pu for a sample system is given in the table.
(a) Draw the single line diagram representing the data
(b) Obtain Ybus matrix by two rule method. What modification is to be done if
Problem
2
8
9
10
a line 1-3 is removed.
(c) Eliminate the node 4 by kron reduction and hence obtain the new Ybus
Line
X in pu
1-2
0.04
2-5
0.05
5-4
0.04
4-3
0.03
3-6
0.02
6-1
0.07
3-1
0.10
Discuss in detail how power system analysis helps in power system planning and
operation
The reactance data in pu for a sample system is given in the table. Obtain Ybus
matrix by two rule method. What modification is to be done if a line 1-3 is
removed
Line
X in pu
1-2
0.04
2-5
0.05
5-4
0.04
4-3
0.03
3-6
0.02
6-1
0.07
3-1
0.10
The one line diagram of an unloaded power system is shown in figure.
The ratings of the various components are listed below.
Generator 1: 20MVA, 13.8 KV, X″ = 0.2 
Generator 2: 30MVA, 18 KV, X″ = 0.2 
Generator 3: 30MVA, 20 KV, X″ = 0.2 
Transformer T1: 25MVA, 220  /13.8  , X=10%
Transformer T2: Single phase units, each rated 10 MVA, 127/18 KV, X=10%
Transformer T3: 35MVA, 220  /22  , X=10%
Draw the reactance diagram will all impedances marked in p.u. choose a
base of 50MVA, 13.8 KV in the circuit of generator 1.
Concept
Problem
2
Problem
2
Consider the four bus system shown in figure. Buses 1 and 2 are generator buses.
The generators are rated 11kV, 100 MVA with sub-transient reactance of 10%
each. Both the transformers are rated 100 MVA, 11/110 kV with the leakage
reactance of 5%. The reactance of the lines to a base of 100MVA, 110kV is
indicated in the figure. Obtain the bus impedance matrix by building algorithm
Problem
2
11
Eliminate bus 3 and 4 in bus admittance matrix and find new bus admittance
matrix
12
Ybus =
-j9.8 0
0
8.3j
4j
2.5j
5j
5j
j4
2.5j
14j
8j
Element no
Bus code
Impedance
Y
1
1-2
0.1j
-10j
2
2-3
0.3j
-3.33j
3
2-3
1.2j
-0.833j
4
1-4
0.15j
-6.67j
5
5-4
0.15j
-6.67j
6
5-3
0.35j
-2.85j
A parameter of 3 bus system is shown below. Draw the network, find the bus
admittance matrix.
14
Bus code
Problem
3
Problem
1
Problem
j5
5j
8j
-18j
For the network, take node 4 as reference
Draw
a) oriented graph
b) bus incidence matrix
c) calculate bus admittance matrix using singular transformation method
13
2
Line impedance
Line charging
admittance
15
16
1-2
0.06+0.18j
0.025j
1-3
0.02+0.06j
0.03j
2-3
0.04+0.12j
0.025j
A parameter of 3 bus system is shown below. Draw the network. Find the bus
admittance matrix.
Bus code
Impedance
Admittance
Bus code
Line
charging
admittance
1-2
0.06+0.018j
1.667-5j
1
0.05j
1-3
0.02+0.06j
5-15j
2
0.06j
2-3
0.04+0.12j
2.5-7.5j
3
0.05j
A 300MVA, 20kV, 3 phase generator has a sub transient reactance of 20%. The
generator supplies two synchronous motor through a 64 km transmission line
having transformers at both ends. In this Transformer 1(Generator side) is a 3
phase transformer of rating 350MVA, 20/230kV, 10% of reactance and
transformer 2 is made of 3 single phase units each rated 100MVA, 127/13.2kV
with 10% reactance. Series reactance of transmission line is 0.5Ω/Km. Draw the
reactance diagram with all the reactance are marked in P.U. Select a generator
rating as base value
Formulate Y bus matrix for the sample system shown in fig.
(i)
Eliminate node (1) and (2) by KRON reduction and draw the
(ii)
modified circuit.
(iii)
Find the bus voltage at node (3) and (4)
All Values are in P.U impedance
2
Problem
Problem
3
Problem
2
Problem
17
18
A 100 MVA, 33kV, 3 phase generator has a sub transient reactance of
15%. The generator is connected to 3 motors through a transmission line and 2
transformers. The motor have rated inputs of 30MVA, 20MVA and 50 MVA at
30kV with 20% sub transient reactance. The 3 Ф transformer are rated at
110MVA, 32kV/110kV, Y- with reactance of 8%. The line has a reactance 0f
50Ω. Select the generator rating as the base quantity. determine the base
quantities in other parts of the system and evaluate the corresponding PU values
also draw the impedance diagram.
19
20
21
22
23
24
25
26
Explain the methods adopted in utilities for planning the operation of power
system.
Explain the modeling of generator, load, shunt capacitor and transmission line for
short circuit studies.
Explain in detail about the general aspects relating to short circuit and stability
analysis.
What is the need for system analysis in planning and operation of power system?
Explain.
Derive the equations to find the π –equivalent circuit of transformer with offnominal tap ratio.
Explain the modeling of generator, load shunt capacitor and transmission line for
short circuit studies
Explain briefly about bus incidence matrix with an illustration.
1
Concept
1
Concept
1
Concept
1
Concept
2
Concept
1
Concept
1
Concept
What are the step by step procedure to be followed to find the per-unit impedance
diagram of a power system.
Find the impedance matrix for the system whose reactance diagram is shown in
fig. All the impedances are in p.u
1
Concept
2
Problem
27
The parameters of a 4-bus system are as under:
Bus code
Line impedance
(pu)
28
29
30
1-2
2-3
2-4
3-4
1-3
0.2+j0.8
0.3+j0.9
0.25+j1.0
0.2+j0.8
0.1+j0.4
Problem
charging admittance
(pu)
j0.02
j0.03
j0.04
j0.02
j0.01
Draw the network and find bus admittance matrix
Draw the structure of an electrical power system and describe the components of
the system with typical values.
Write short notes on:
Single line diagram, Change of base and Reactance of synchronous machines.
2
Concept
1
Concept
Q.N
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s
UNIT – 2
POWER FLOW ANALYSIS
Consider a 3 bus system shown in figure.1. The p.u line reactance are indicated in
the figure. The magnitudes of all bus voltages are 1.0 p.u. The bus powers are
specified in table
Bus No
1
2
3
PD
1
0
1
QD
0.6
0
1
PG
?
1.4
0
Problem
QG
Unspecified
Unspecified
unspecified
Carryout the approximate load flow analysis. Mark generation, load demands and
line flows on the single line diagram.
1
2
2
1
j0.2
j0.4
j0.5
3
2
3
4
Discuss the importance of load flow problem. Formulate the power flow problem
and describe the procedure of solving it using Newton – Raphson method.
Assume the sample power system consists of N buses. Bus 1 is the slack bus. The
remaining (N-1) non slack buses are PQ buses. With the neat flow chart, discuss
about the algorithm and procedure for the Newton – Raphson method to obtain the
solution for the load flow equation.
Why the solution converges faster than the
Gauss – Seidel method?
The system load data for load flow solution are given in table 1 and table 2.
Determine the voltage at the end of first iteration by Gauss-Seidel method. Take
α=1.6
Table 1
Table 2 Bus specification
Bus p - q Line
Bus
P
Q
V
admittance ypq
code
1-2
2-j8
1
1.06∠
Slack
0
1-3
1-j4
2
0.5 0.2 PQ
2-3
0.66-j2.664
3
0.4 0.3 PQ
2-4
1-j4
4
0.3 0.1 PQ
3-4
2-j8
Concept
1
Concept
1
Problem
2
The sample system has 3 buses. The pu line reactance of the lines are given in Table
1. Tha magnitudes of all bus voltages are 1.0 pu. The bus power are specified in
Table 2. Carry out one iteration of power flow analysis using Gauss – Seidel method
Table:1
Line
1-2
2-3
3-1
X in p.u
0.2
0.4
0.5
Table:2
Bus No
1
2
3
Problem
1
PD
1
0
1
QD
0.6
0
1
PG
1.4
0
QG
0
Concept
5
Discuss the importance of load flow problem. Formulate the power flow problem
and describe the procedure of solving it using Gauss - Seidel method.
1
6
Obtain the π- equivalent circuit of off nominal transformer with the tap ration of 1:t
and admittance of Y
1
7
Discuss the importance of load flow problem. Formulate the load flow problem and
discuss on the parameter terms scheduled power, calculated power and mismatch
1
Give the advantages and disadvantages of GS, NR methods
1
Concept
With the help of neat flow chart, explain the Newton-Rapson method of load flow
solution when the system contains voltage controlled buses in addition to swing bus
and load bus.
Explain computation of slack bus power, transmission loss and line flow.
1
Concept
1
Concept
2
Problem
11
Determine the bus voltages at the end of first Gauss-seidel iteration.
Bus
P
Q
V
Bus
No.
1
1.05
Slack
0
2
0.5 -0.2
PQ
3
-1.0 0.5
PQ
4
0.3 -0.1
PQ
With the help of neat flow chart, explain the GS method of load
flow solution.
1
Concept
12
Derive the static load flow equation of power flow analysis.
1
Concept
Concept
Concept
8
9
10
13
Compare Gauss-Siedal method and Newton Raphson method of load flow studies.
1
Concept
1
Concept
15
Explain the step by step computational procedure for the Newton-Raphson method of
load flow studies
Explain bus classification in power flow analysis with their known and unknown
quantities.
2
Concept
16
For the sample system shown in fig., the generators are connected at all the four
buses, while the loads are at buses 2 and 3.Values of real and reactive powers are
listed in table, bus 2 be a PV bus with V2=1.04 p.u and bus 3 and 4 are PQ bus.
Assuming a flat voltage start, find bus voltages and bus angles the end of first
Gauss Siedal iterations and consider the reactive power limit 0.2≤Q2≤1.
Bus
Pp p.u
Qp p.u
Vp p.u
Remarks
3
Problem
14
17
1
2
3
4
0.5
-1.0
0.3
0.5
-0.1
1.04∟00
1.04 p.u
-
Slack Bus
PV bus
PQ bus
PQ bus
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Question
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Types of
Question
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UNIT – 3
SYMMETRICAL SHORT CIRCUIT ANALYSIS
1
2
3
4
5
6
Plot the oscillogram of the stator currents of synchronous generator when it is
subjected to 3 phase short circuit and explain the salient features of the waveform
Consider a transmission line feed from constant voltage source, obtain the
expression for calculating the short circuit current when the short circuit occurs on
the line when it is unloaded.
A generator connected through a transformer to a synchronous motor. Reduced to
the same base, the pu sub transient reactances of the generator and motor are 0.15
and 0.35 respectively and the leakage reactance of the transformer is 0.120 pu. A 3
phase fault occurs at the terminals of the motor when the terminal voltage of the
generator is 0.9 pu and the output current is 1 pu at 0.8pf lagging. Find the sub
transient current in the fault, in the generator and in the motor.
Concept
1
Concept
1
Problem
1
A 60 MVA, Y connected 11KV synchronous generator is connected to a 60
MVA, 11/132 KV ∆/Y transformer. The sub transient reactance Xd” of the
generator is 0.12 p.u. on a 60 MVA base, while the transformer reactance is
0.1 p.u on the same base. The generator is unloaded when a symmetrical fault is
suddenly placed at point P as shown in fig. Find the sub transient
symmetrical fault current in p.u. amperes and actual amperes on both sides of the
transformer. Phase to neutral voltage of the generator at no load is 1.0 p.u.
3
Problem
A 15MVA, 6.6KV three phase alternator connected through a 5 cycle oil
circuit breaker has sub transient, transient and synchronous reactance 0f 10%, 15%
and 80% respectively. It is running on no load with rated voltage
developed across the terminals when a 3 phase short circuit occurs just beyond the
circuit breaker. Determine.
(i) The steady short circuit current
(ii) The initial symmetrical current that can be broken on all poles
(iii) The maximum possible DC component of the short circuit current
(iv) The making capacity of the breaker in KA
(v) The RMS value of the symmetrical breaking current
(vi) The asymmetrical breaking current
(vii) The interrupting capacity in MVA
A 3 phase 5MVA, 6.6KV alternator with a reactance of 8% is connected to a feeder
of series impedance (0.12+j0.48) ohm/phase/km through a step up transformer. The
transformer is rated at 3 MVA, 6.6KV/33KV and has a reactance of 5%. Determine
the fault current supplied by the generator operating under no load with a voltage of
6.9KV, when a 3 phase symmetrical fault occurs at a point 15km along the feeder.
3
Problem
2
Problem
7
8
9
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12
13
Derive the symmetrical short circuit analysis fault calculation using bus
impedance matrix
1
Concept
A three phase transmission line operating at 33KV and having a resistance
and reactance of 5 Ω and 15 Ω respectively is connected to the generating
station bus bar through a 5000KVA step up transformer which has a reactance of
0.05 p.u. connected to the bus bars are two alternators, are 10,000KVA having
0.08p.u. reactance and another 5000KVA having 0.06p.u. reactance. Calculate the
KVA at a short circuit fault between phases occurring at the high voltage terminals
of the transformers
A generator connected through a 5-cycle circuit breaker, through a transformer is rated
at 100mva, 18kv with reactance Xd’’=20%, Xd’=25%, Xd=10%. It is operated on no
load and rated voltage, when a 3-phase fault occurs between the breaker and
transformer.
Find 1) short circuit current in a circuit breaker.
2) The initial Symmetrical RMS current in the circuit breaker.
3) The maximum possible D.C component of the S.C
current in the breaker
4) The current to be interrupted by the breaker
5) The interrupting MVA.
A 3-phase 5MVA, 6.6kv alternator with a ‘x’ of 8% is connected to a feeder
of series impedance (0.12+j0.48)ohm/phase/kv through a step up transformer.
The transformer is rated at 3MVA, 6.6kv/33kv and has reactance of 5%.
Determine the fault current supplied by the generator operating under no load
with a voltage of 6.9kv, when 3-phase Symmetrical fault occurs at a point
50km along the feeder.
2
Problem
3
Problem
2
Problem
Explain the procedure for making short-circuit studies of a large power system
networks using digital computers
1
Concept
A generator is connected through a transformer to a synchronous motor. The
subtransient reactances of generator and motor are 0.15 p.u. and 0.35 p.u.
respectively. The leakage reactance of the transformer is 0.1 p.u. All the reactances
are calculated on a common base. A three phase fault occurs at the terminals of the
motor when the terminal voltage of the generator is 0.9 p.f. leading. Find the
subtransient current in p.u. in the fault, generator and motor. Use the terminal
voltage of generator as reference vector.
With a help of a detailed flow chart, explain how a symmetrical fault can be
analysed using Z bus ?
2
Problem
1
Concept
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UNIT – 4
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Problem
UNSYMMETRICAL SHORT CIRCUIT ANALYSIS
1
2
Derive the relationships to determine the fault current for a DLG fault. Draw an 1
equivalent network showing the interconnection of sequence network to simulate
DLG fault
For the network shown in figure, obtain the zero sequence network
2
Concept
Problem
G1 and G2 : 20 MVA, 11KV, X’’= 0.2 pu
Motor M : 30 MVA , 6.6 KV, X’’= 0.25 pu
Transformer :
3
4
Y/Y, 20 MVA, 11/110 KV, 0.1 pu each
Y/  , 15 MVA, 6.6/110 KV 0.1 pu each
Choose a base of 50 MVA, 110 KV in the j60  line. Zero sequence reactance of
each machine is 10% on its own rating for the lines X0 = 3 X1
A synchronous generator has its neutral grounded through reactance Xn. The 1
generator has balance EMF’s and sequence reactances as X1, X2 and X0. Such that
X1 = X2 and X0 << X1
i)
Draw the sequence network of the generator as seen from
the generator terminals.
ii)
Derive an expression for the fault current for a solid L-G fault on
phase ‘a’
For the system shown in figure, draw the reduced sequence network and show their 2
inter connection for a LLG fault at P and calculate the fault impedance
Problem
Concept
Generator A
Generator B
Transformer T1
Transformer T2
Each line
X1
0.3
0.25
0.12
0.10
0.3
X2
0.2
0.15
0.12
0.10
0.3
X0 (all in p.u)
0.05
0.03
0.12
0.10
0.70
5
2
Problem
1
Concept
1
Concept
1
Concept
Each of the machines connected to the two high voltage buses shown in the above
single line diagram is rated 100 MVA, 20 KV with reactance Xd’’ = X1 = X2 = 20%
and X0 = 4%. Each 3 phase transformer is rated 100 MVA, 345 Y/20  kV with
leakage reactance of 8% on a base of 100 MVA, 345 kV, the reactance’s of the
transmission line are X1 = X2 15% and X0 = 50%. Find the 2x2 bus impedance
matrix for each of the three sequence networks.
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11
12
13
Prove that the unbalanced system of voltages may be converted into a balanced
system of voltages by means of symmetrical component methodology.
A single line to ground fault occurs at the terminals of the synchronous generator at
no load condition. The generator has X1=X2=Xd″ and Xd is the sub transient
reactance. Xo is the zero sequence reactance. The fault involves the fault
impedance Zf. Obtain an expression for the fault current in phase A.
Derive the relationships to determine the fault current for a LL fault. Draw an
equivalent network showing the interconnection of sequence network to simulate
DLG fault
Determine the positive, negative and zero sequence networks for the system
shown in fig, Assume zero sequence reactances for the generator and
synchronous motors as 0.06 p.u current limiting reactors of 2.5Ω are
connected in the neutral of the generator and motor: 2. The zero sequence
reactance of the transmission line is j300 Ω.
Derive an expression for the positive sequence current Ia1 of an unloaded
generator when it is subjected to a double line to ground fault.
Derive the expression for fault current in double line to- ground fault on an unloaded
generator in terms of symmetrical components.
Derive the expression for fault current in Line-to-Line fault on an unloaded
generator in terms of symmetrical components.
Develop the connection of sequence network when a line to line fault occurs in a
2
Problem
1
Concept
1
Concept
1
Concept
1
Concept
power network.
14
15
16
Explain how an unbalanced set of three phase voltages can be represented by system
of balanced voltages
Draw the zero sequence network for :
1.∆ ∆ connected transformer.
2.Star connected generator earthed through R.
Draw the sequence network connection for DLG fault at any point in a power
system. From that obtain an expression for the fault current
1
Concept
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Concept
2
Concept
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UNIT – 5
STABILITY ANALYSIS
1
With the detailed flow chart and procedural steps, explain the algorithm for transient
stability analysis using Modified Euler’s method.
3
Write short notes on the following
1. Equal area criterion
2. Classical Machine modeling for stability analysis
Derive the swing equation for the system stability study Also discuss about the
factors that affect the transient stability
4
Explain the procedural steps and algorithm of Runge-kutta method in solving the
suring equation.
2
5
6
7
A three phase 150 MVA, 15kV synchronous generator has its rated speed of 1500
rpm. The moment of inertial of the rotating mass is 75 x 103 kg – m2 and the
machine delivers its rated output at 0.85 pf lagging. Calculate
a) Kinetic Energy b) H constant.
A generator operating at 50 Hz delivers rated power to an infinite bus. Power to an
infinite bys when a fault occurs reduces and it is 0.4 p.u. The maximum power
transferred during prefault is 1.75. the maximum power transferred during post fault
is 1.25. Compute critical clearing angle.
Deduce from the concept of equal are criterion, derive the expression for critical
angle and critical clearing time
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1
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1
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1
Problem
2
Problem
2
Concept
1
Describe the equal area criterion for transient stability analysis of a system
8
9
How can the transient stability of the system be improved? Discuss the
traditional as well as new approaches to the problem
10
Mentioning the assumptions clearly and developing necessary equations
describe the step by step solution of swing bus.
11
12
13
Concept
2
A 30 MVA, 11KV, 3 phase synchronous generator has a direct sub transient
reactance of 0.25 p.u. The negative and zero sequence reactances are 0.35 and 0.1
p.u. respectively. The neutral of the generator is solidly grounded. Find the sub
transient currents and the line to line fault occurs at the terminals of the generator.
Assume that the generator in unloaded and operating at rated terminal voltage when
the fault occurs
Derive the swing equation of a synchronous machine swinging against an infinite
bus. Clearly state the assumption in deducing the swing equation.
A 50 Hz generator is delivering 50% of the power that it is capable of delivering
through a transmission line to an infinite bus. A fault occurs that increases the
reactances between the generator and the infinite bus to 500% of the value before the
Concept
2
Concept
2
Problem
3
Concept
2
Problem
3
fault. When the fault is isolated, the maximum power that can be delivered is 75% of
the orginal maximum value. Determine the critical clearing angle for the condition
described.
What are the steps to be followed for multimachine stability?
14
Concept
2
15
Describe the Runge-Kutta method of solution of swing equation for multi-machine
systems
3
Concept
16
How can the transient stability of the system be improved? Discuss the traditional as
well as new approaches to the problem.
3
Concept