EE6501 - Power System Analysis

Vel Tech High Tech Dr.Rangarajan Dr.Sakunthala Engg. College EE6501 – Power System Analysis (R-2013)
Prepared by Prabaakaran K AP/EEE Page No.1
UNIT – 1 INTRODUCTION
1. What are the advantages of per unit computation? (A/M 2017)
 Manufacturers usually specify the impedance of a device or machine in per unit on the base
of the nameplate rating.
 (ii) The p.u values of widely different rating machines lie within a narrow range, even
though the ohmic values has a very large range.
 (iii) The p.u. impedance of circuit element connected by transformers expressed on a proper
base will be same if it is referred to either side of a transformer.
 The p.u. impedance of a 3-phase transformer is independent of the type of winding
connection (Y or ∆).
2. A Y connected generated rated at 300 MVA, 33kV, has a reactance of 1.24 p.u. Find the
ohmic value of the reactance. (A/M 2017)
Z p.u. =
𝑍𝑎𝑐𝑡
𝑍𝑏𝑎𝑠𝑒
= > 1.24 = Zact / Zbase => Zact = 1.24 x Zbase.
Zbase = KV2
/ MVA => 332
/ 300 = 3.63
Zact = 1.24 x 3.36 = 4.5 Ω
3. How are the loads represented in impedance and reactance diagram. (N/D 2016)
The resistive and reactive loads can be represented by any one of the following representation.
i. Constant power representation.
Load power, S = P + JQ.
ii. Constant current representation.
Load current. , I =
√𝑃2+ 𝑄2
|𝑉|
∠𝛿 − 𝜃
iii. Constant impedance representation.
Load current, Z =
|𝑉|2
𝑃−𝑗𝑄
4. Define per unit value of an electrical quantity and write the equation for the base
impedance for a three phases power system. (A/M 2016)
The per unit value of any quantity is defined as the ratio of the actual value of the quantity to the
base value expressed as a decimal. The base value is an arbitrary chosen value of the quantity.
Per unit Value =
𝐴𝑐𝑡𝑢𝑎𝑙 𝑣𝑎𝑙𝑢𝑒
𝐵𝑎𝑠𝑒 𝑣𝑎𝑙𝑢𝑒
Base Impedance
The equation for base impedance is given as follows
𝐵𝑎𝑠𝑒𝐼𝑚𝑝𝑒𝑑𝑎𝑛𝑐𝑒 =
(𝐵𝑎𝑠𝑒𝐾𝑉)2
𝐵𝑎𝑠𝑒𝑀𝑉𝐴

5. Write the equation for per unit impedance if change of base occurs. (A/M 2016)
The equation for converting per unit impedance form one base to another can be given as
follows.
Zp.u. new = Zpu,oldx
𝑘𝑉 𝑏,𝑜𝑙𝑑
2
𝑘𝑉 𝑏,𝑛𝑒𝑤
2 x
𝑀𝑉𝐴 𝑏,𝑛𝑒𝑤
𝑀𝑉𝐴 𝑏,𝑜𝑙𝑑
6. Draw the simplified model of a generator. (N/D 2015)
7. Distinguished between impedance and reactance diagram. (N/D 2015)
Impedance Diagram :
The power system components are represented by their approximate or simplified equivalent
circuits. It is used in load flow analysis
Reactance Diagram :
The power system components are represented by their reactance. The reactance diagram is
obtained from impedance diagram if all the resistive components are neglected. The reactance
diagram is used for fault analysis.
8. What is single line diagram? (N/D’11,A/M’10,N/D’07)
A Single line diagram is diagrammatic representation of power system in which the
components are represented by their symbols and the interconnections between them are shown by
a single straight line (even though the system is 3- phase system). The ratings and the
impedances of the components are also marked on the single line diagram.
9. What is the need for power system analysis in planning and operation of power
system?(M/J’07)
The system operation engineers at the various points like area, space, regional and national load
dispatch deals with the dispatch of power for maintaining the power balance effective and
efficient manner.
Power balance equation is
PD=∑ PGi
N
i=1 , i=1,2,3……….N
Total demand = Sum of the real power generation.
i.e, the generation should be in such a way that it meet out the required demand. When this
relation is satisfied, it gives good economy and security.

10. Name the diagonal and off diagonal elements of Bus Admittance and Impedance Matrix.
(N/D 2013)
Bus Admittance Matrix.
The diagonal elements of bus admittance matrix are called self admittances of the Buses and off
diagonal elements are called mutual admittances of the buses.
Bus Impedance Matrix.
The diagonal elements of bus impedance matrix are called driving point impedances of the buses
and off diagonal elements of bus impedance matrix are called transfer Impedances of the buses.
11. What are the functions of power system analysis? (N/D 2013)
 To monitor the voltage at various buses, real and reactive power flow between buses.
 To design the circuit breakers.
 To plan future expansion of the existing system
 To analyze the system under different fault conditions
 To study the ability of the system for small and large disturbances (Stability studies)
12. Draw the impedance diagram of the given system. (M/J 2014)
13. List out the application of Y-Bus. (N/D’12)
The application of Y-bus matrix are as follows.
 Y-bus is used in solving load flow problems.
 It has gained applications owing to the simplicity in data preparation.
 It can be easily formed and modified for changes in the network.
 It reduces computer memory and time requirements because of sparse matrix
.
14. Why bus admittance matrix is preferred in load flow?
Bus admittance matrix is preferred in load flow problem because,
 It is easy to formulate.
 No need of taking inverse.
 Computation time is less.
 Matrix is symmetric, so calculation of upper or lower triangular matrix is enough.
 Each bus is connected to ony a few nearby buses.so many diagonal elements are zero.

15. A generator rated at 30MVA, 11KV has a reactance of 20%.Calculate its per unit
reactance for a base of 50 MVA and 10KV.
MVA new = 50 ; KV new = 10 ; MVA old = 30 ; KV old = 11
X p.u = 20% = 20/100 = 0.2 p.u
𝑋 𝑝.𝑢,𝑛𝑒𝑤 = 𝑋 𝑝.𝑢,𝑜𝑙𝑑 × [
𝐵𝑎𝑠𝑒𝐾𝑉 𝑜𝑙𝑑
𝐵𝑎𝑠𝑒𝐾𝑉𝑛𝑒𝑤
]
2
× [
𝐵𝑎𝑠𝑒𝑀𝑉𝐴 𝑛𝑒𝑤
𝐵𝑎𝑠𝑒𝑀𝑉𝐴 𝑜𝑙𝑑
]
𝑋 𝑝.𝑢,𝑛𝑒𝑤 = 𝑗0.2 × [
11
10
]
2
× [
50
30
] = 𝑗0.4033 𝑝. 𝑢
16. What is the need for base values?
The components of various sections of power system may operate at different Voltage and
power levels. It will be convenient for analysis of power system if the voltage, power, current
and impedance ratings of power system components are expressed with reference to a
common value called base value. Then all the voltages, power, current and impedance ratings of
the components are expressed as a percent or per unit of the base value.
17. What is the need for short circuit study.
 To determine the current interrupting capacity of the circuit breakers so that the
faulted equipments can be isolated.
 To establish the requirements and settings to detect the fault and cause the circuit breaker to
operate when the current flowing through it exceeds the max. value.
UNIT – 2 POWER FLOW ANALYSIS
1. Compare Newton Raphson and Gauss Seidal methods of load flow solutions. (A/M 2017)
Gauss Seidal method Newton Raphson method
Variable is expressed in rectangular
coordinates.
Variables are expressed in polar
coordinates.
Computation time per iteration is less Computation time per iteration is more.
It has linear convergence
characteristics.
It has quadratic convergence characteristics.
The number of iterations required for
convergence increases with size of the
system.
The numbers of iterations are independent of
the size of the system.
The choice of slack bus is critical. The choice of slack bus is arbitrary.
2. Write the quantities that are associated with each bus in a system.(A/M 2017)
Each bus in a power system is associated with four quantities and they are
i. real power
ii. reactive power
iii. magnitude of voltage, phase angle of voltage.

3. What is Jacobian Matrix? (N/D 2016)
The matrix formed from the first derivatives of load flow equation is called jacobian
matrix and it is denoted by J.
The elements of jacobian matrix will change in every iteration .the elements of the jacobian
matrix are obtain matrix are obtained by partially differentiating the load flow equation with respect
to a unknown variable and then evaluating the first derivative as using the solution of previous
iteration .
4. Write the need for slack bus in load flow analysis. (N/D 2016)
The slack bus is needed to account for transmission line losses. In a power
system the total power generated will be equal to sum of power consumed by loads and losses. In a
power system only the generated power and load power are specified for buses. The slack bus is
assumed to generate the power required for losses. Since the losses are unknown the real and reactive
power are not specified for slack bus. They are estimated through the solution of load flow equations.
5. What is the need for load flow analysis? (A/M 2016)
The study of various methods of solution to power system network is referred to as load flow
study. The solution provides the voltages at various buses, power flowing in various lines and line-
losses.
The load flow study of a power system is essential to decide the best operation of existing
system and for planning the future expansion of the system. It is also essential for designing a new
power system.
6. Mention the various types of buses in power system with specified quantities for each bus.
(A/M 2016)
The buses of a power system can be classified into three types based on the
quantities being specified for the buses, which are as follows:
 Load bus or PQ bus (P and Q are specified)
 Generator bus or voltage controlled bus or PV bus (P and V are specified)
 Slack bus or swing bus or reference bus (|V| and δ are specified)
7. Write the static load flow equation. (N/D 2015)
Pi = ∑ |𝑉𝑖||𝑌𝑖𝑗||𝑉𝑗|𝑐𝑜𝑠(𝜃𝑖𝑗 + 𝛿𝑗
𝑁
𝑗=1 −𝛿𝑖)
Qi = ∑ |𝑉𝑖||𝑌𝑖𝑗||𝑉𝑗|𝑠𝑖𝑛(𝜃𝑖𝑗 + 𝛿𝑗
𝑁
𝑗=1 −𝛿𝑖)
8. State the role of acceleration factor in GS method. (N/D 2015)
In Gauss Seidal method, the number of iteration required for convergence can be reduced if the
voltage computed at each iteration is multiplied by a factor greater than unity called acceleration factor
to bring the voltage closer to the value to which it is converging. The range of 1.3 to 1.6 is found to be
satisfactory for the typical systems.
𝑉𝑖
𝑛𝑒𝑤
= Vi
old
+ ∝ [𝑉𝑖
𝑛𝑒𝑤
− Vi
old
]
Where Vi
old
= Voltage value obtained in previous iteration

𝑉𝑖
𝑛𝑒𝑤
= New value of Voltage value obtained in current iteration
∝ = Acceleration factor
9. Why the load flow studies are important for planning the existing system as well as its
future expansion?
The load flow studies are very important for planning, economic scheduling, control and
operation of existing systems as well as planning its future expansion depends upon knowing the
effect of interconnections, new loads, new generating stations, or new transmission lines, etc.
before they installed.
10. What is swing bus? (N/D 2013)
A bus is called swing bus when the magnitude and phase for bus voltage are specified for it.
The swing bus is the reference bus for load flow solution and it is required for accounting line
losses. Usually one of the generator bus selected as the swing bus.
Swing bus is also called as Slack bus.
11. When the generator buses are treated as load bus? (N/D’13, M/J’14)
If the reactive power constraints of a generator bus violates the specified limits then the generator
is treated as load bus.
If Qi > Qi(max), substitute Qi = Qi(max)
If Qi
cal
< Qi(min) , substitute Qi= Qi(min)
12. What is meant by flat voltage start?
In iterative methods of load flow solution, the initial voltages of all buses exept slack bus are
assumed as 1+j0 pu. This is referred as flat voltage profile.
V = |𝑉𝑠 𝑝𝑒𝑐| 0 for slack bus
V = |𝑉𝑠𝑝𝑒𝑐| 0 for generator bus
V = 1 0 for load bus
13. What are the works involved in a load flow study? ( Or) How a load flow study is
performed?
The following work has to be performed for a load flow study.
 Representation of the system by single line diagrams.
 Determining the impedance diagram using the information in single line diagram.
 Formulation of network equations.
 Solution of network equations.
14. List the quantities specified and the quantities to be determined from load flow study
for various types of buses.

The following table shows the quantities specified and to be obtained for various types of
buses.
Bus type Quantities specified Quantities to be obtained
Load bus P,Q │V│, δ
Generator bus P, │V│ Q, δ
Slack bus │V│, δ P,Q
15. Why bus admittance matrix is used in load flow instead of bus impedance matrix? (M/J
2014)
Using bus admittance matrix is amenable to digital computer analysis, because it could be
formed and modified for network changes in subsequent cases. Bus admittance matrix is used in Gauss
seidal method because of the following reasons.
 It requires less computation time
 Less memory allocation
16. What are the advantages of Gauss seidal method?
The advantages of Gauss seidal method are as follows
i. Calculations are simple and so the programming task is less.
ii. The memory requirement is less.
iii.Useful for small systems
17. What are the disadvantages of Gauss seidal method?
The disadvantages of Gauss seidal method are listed as follows
i. Requires large no. of iterations to reach converge
ii. Not suitable for large systems.
iii.Convergence time increases with size of the system
18. What are the advantages of Newton-Raphson method?
The advantages of Newton-Raphson method are,
i. This load flow method is faster, more reliable and he results are accurate.
ii. Requires less number of iterations for convergence.
iii.The number of iterations are independent of the size of the system.
iv.Suitable for large size systems.
19. What are the disadvantages of Newton-Raphson method? (N/D’11)
The disadvantages of Newton-Raphson method are,
i. Programming is more complex.
ii. The memory requirement is more.
iii.Computational time per iteration is higher due to larger number of
calculations per iteration.

20. How the disadvantages of N-R method are overcome?
The disadvantage of large memory requirement can be overcome by decoupling the weak
coupling between P-δ and Q-V. (i.e., using decoupled load flow algorithm). The
disadvantage of large computational time per iteration can be reduced by simplifying the
decoupled load flow equations. The simplifications are made based on the practical operating
conditions of a power system.
UNIT 3 – SYMMETRIC FAULT ANALYSIS
1. What is the significance of sub transient reactance and transient reactance in short
circuit studies? (A/M 2017)
The sub-transient reactance can be used to estimate the initial value of fault current
immediately on the occurrence of the fault. The maximum momentary short circuit
current rating of the circuit breaker used for protection or fault clearing should be less
than this initial fault current.
2. For a fault at a given location, rank the various fault in the order of severity.
(A/M 2017)
Types of fault Relative frequency of occurrence of faults
Three phase fault 5%
Double line to ground fault 10%
Line to Line fault 15%
Line to ground fault 70%
3. How shunt and series fault are classified ? (N/D 2016)
 Shunt faults - due to short circuits in conductors
 Series faults - due to open conductors.
 The shunt fault is also called as short circuit faults.
4. What is the need for short circuit study? (N/D 2016)
The short circuit studies are essential in order to design or develop the protective
schemes for various parts of the system. The protective scheme consists of current &
voltage sensing devices, protective relays and circuit breakers. The selection (or proper
choice) of these device mainly depends on various currents that may flow in the fault
conditions.
5. State and explain symmetrical fault. (A/M 2016)
The fault on the power system which gives rise to symmetrical fault currents (i.e. equal
fault current in the lines with 1200
displacement) is called as symmetrical faults. The
symmetrical fault occurs when all the three conductors of phase are brought together
simultaneously in short circuit condition.

6. What is bolted fault or solid fault? (A/M 2016)
A Fault represents a structural network change equivalent with that caused by the
addition of impedance at the place of a fault. If the fault impedance is zero, the fault is
referred as bolted fault or solid fault.
7. Define short circuit capacity. (N/D 2015)
Short circuit capacity or short circuit MVA of fault level at a bus is defined as the
product of the magnitudes of the perfect bus voltage and the post fault current.
SCC = |𝐸 𝑇ℎ||𝐼𝑓| =
|𝐸 𝑇ℎ|2
𝑋 𝑇ℎ
p.u. MVA
8. What is meant by a fault?
A fault in a circuit is any failure which interferes with the normal flow of current. The
faults are associated with abnormal change in current, voltage and frequency of the power
system. The faults may cause damage to the equipments if it is allowed to persist for a long
time. Hence every part of a system has been protected by means of relays and circuit
breakers to sense the faults and to isolate the faulty part from the healthy part in the event
of fault.
9. Why fault occurs in a power system?
In a power system the fault may occur due to the following reasons.
 Insulation failure of equipments.
 Flashover of lines initiated by a lightning stroke.
 Switching surges.
 Sudden releasing of heavy loads at same instant of time.
 Due to accidently faulty operation of power system operators.
10. What are the objectives of short circuit analysis.
 To check the MVA ratings of the existing circuit breaker’s, when new generation are
added into system.
 To select the rating for fuses, circuit breaker’s and switch gear in addition to set up of
protective relays.
 To determine the magnitudes of currents flowing through out the power system at
various time intervals after a fault occurs.
11. State the applications of short circuit analysis.
Short circuit studies are used
 For proper relay setting and co ordination.
 To obtain the rating of the protective switch gears.
 To select the circuit breakers.
 To perform whenever system expansion is planned.

12. What are symmetrical components?
An unbalanced system of N related vectors can be resolved into N systems of balanced vectors
called symmetrical components. The various symmetrical components are as follows.
 Positive sequence components
 Negative sequence components
 Zero sequence components
13. Why delta connected load will not have any zero sequence components
The current in the neutral is three times the zero sequence line current. A delta connected
load provides no path to neutral and hence the line currents flowing to a delta connected load
contain zero component. Hence the delta connected load will not have any zero sequence
components.
14. What is symmetrical components of three phase system.
Symmetrical components of three phase system is given as
For voltage
[
𝑉𝑎
𝑉𝑏
𝑉𝑐
] = [
1 1 1
1 𝑎2
𝑎
1 𝑎 𝑎2
] [
𝑉𝑎0
𝑉𝑎1
𝑉𝑎2
]
For current.
[
𝐼 𝑎
𝐼 𝑏
𝐼𝑐
] = [
1 1 1
1 𝑎2
𝑎
1 𝑎 𝑎2
] [
𝐼 𝑎0
𝐼 𝑎1
𝐼 𝑎2
]
15. What is meant by doubling effect?
If a symmetrical fault occurs when the voltage wave is going through zero then the
maximum momentary short circuit current will be double the value of maximum
symmetrical short circuit current. This effect is called doubling effect.
16. What is synchronous reactance?
The synchronous reactance is the ratio of induced emf and the steady state rms current (i.e.
it is the reactance of a synchronous machine under steady state condition). It is the sum of
leakage reactance and the reactance representing armature reaction.
It is given by,
Xs = Xl + Xa
Where,
Xs = Synchronous reactance
Xl = Leakage reactance
Xa = Armature reaction reactance.
17. What is the reason for transients during short circuits?
The faults or short circuits are associated with sudden change in currents. Most of the
components of the power system have inductive property which opposes any sudden change
in currents and so the faults (short circuit) are associated with transients.

18. What are the advantages of symmetrical components.
 This method is simple.
 This method leads to accurate prediction of system behavior.
 Unsymmetrical faults on the transmission system are studied by the method of
symmetrical components.
 They suitable to determine the currents and voltages in all parts of the power system
after the occurrence of fault.
19. What are the needs of sequence network in power system.
 Sequence network in power system are very much useful in computing unsymmetrical
faults at different points of the power system network.
 Positive sequence network is necessary foe load flow studies.
 Negative and zero sequence networks are for stability studies involving unsymmetrical
fault.
20. What are sequence impedances and sequence networks?
 The sequence impedances are the impedances offered by the devices or
components for the like sequence component of the current.
 The single phase equivalent circuit of a power system consisting of impedances
to current of any one sequence only is called sequence network.
UNIT 4 – UNSYMMETRICAL FAULT
1. Express the unbalance voltage in terms of symmetrical components. (A/M 2017)
0
0
2
2
2
, , .
, , .
1 1 1
1
1
1 120 1 240
a b c
a a a
a a
b a
c a
Let I I I betheunbalanced phasecurrents
Let I I I bethesymmetrical componentsof phase
I I
I a a I
I a a I
wherea and a
 


    
         
         
     
2. Draw the zero sequence network of Y - ∆ transformer with neutral ungrounded. (A/M
2017)

3. Why the neutral grounding impedance Zn appears as 3Zn in zero sequence equivalent
circuit? (N/D 2016)
Voltage drop is ZN*IN=ZN*3*I0
=I0
*3ZN. Therefore, to obtain the correct voltage drop
seen in the neutral conductor with a flow of only, model the zero sequence impedance as 3Zn.
4. What are symmetrical components of a 3ph system? (M/J 2016)
One of the most powerful tools for dealing with unbalanced polyphase circuits is the
method of symmetrical components. An unbalanced system of n related phasors can be resolved
into n systems of balanced phasors called symmetrical components. Symmetrical components
are positive, negative and zero sequence components.
5. Write down the equation to determine symmetrical currents from unbalance current .
(M/J 2016)
 
0
2
2
0
2
2
,
1 1 1
1
1
3
1
1
3
1
3
1
3
a a
a b
a c
a a b c
a a b c
a a b c
Thesymmentrical componetsof currents are
I I
I a a I
I a a I
I I I I
I I aI a I
I I a I aI




     
          
         
  
    
    
6. State Fortescue theorem. (N/D 2015)
Fortescue's Theorem for a Three-Phase Unbalanced System. In 1918, C. L.
Fortescue stated his theorem: unbalanced phasors can be represented by systems of
balanced phasors. Sequence components were created to facilitate calculations in unbalanced
circuits and systems.
7. Which type of fault is very common in power system? (N/D 2015)
Single line to ground fault is most common occurrence fault in power system.
It occurs about nearly 70 % in fault conditions.
8. What are the features of zero sequence current? May/june 2014
It consists of three phasors equal in magnitude and with zero phase displacement from each
other.
Zero sequence phasors a,b,c can be written as
0 0 0
a b cI I I 
Where 0 0 0
, ,a b cI I I are the sequence components of ,a b c
I I and I

9. What are the observation made from the analysis of various fault ? Nov/Dec 2013
 Finding out the value of Fault current under different fault conditions
 Zero sequence is not presence in LL fault conditions
 Positive and negative sequence component of currents are opposite and equal to each
other in LL fault condition
 Positive and negative sequence component of voltage are equal in LLG fault condition
10. Write the boundary condition for the single line to ground fault. Nov/Dec 2013
 If the generator is solidly grounded, Zn = 0 and for bolted fault or solid fault,
Zf = 0.
 If the neutral of the generator is ungrounded, the zero sequence network is open
circuited.
0
0a a a fI I I and I 
   
11. Define negative sequence impedance. May/June 2013
Impedance offered to the flow of negative sequence current is known as negative sequence
impedance and it is denoted by Z-
. The negative sequence impedance is occurred in all the fault
condition and it is important to find the fault current.
12. What is positive, negative and zero sequence impedance?
 Impedance offered to the flow of positive sequence current is known as positive
sequence impedance and it is denoted by Z+
 Impedance offered to the flow of negative sequence current is known as negative
sequence impedance and it is denoted by Z-
 Impedance offered to the flow of zero sequence current is known as Zero sequence
impedance and it is denoted by Z0
13. What is the assumption made in short circuit studies?
 Representing machines by reactance namely X’’
, X’ and X
 Prefault load current are neglected
 Transformer tap are assumed to be nominal
 Shunt capacitance and series resistance are ignored and neglected
14. Find the fault current whose impedance are j0.2 & j015 in series and in parallel with j0.35
if prefault voltage at the fault point is 0.97 p.u.?
Ans:
j0.2 and j0.15 are in series
Its becomes, j0.2 + j0.15 = j0.35
j0.35 is in parallel with j0.15.
0.35 0.15
0.105 . .
0.5 0.15
0.97
9.238 . .
0.105
Th
Th
f
Th
j j
Z j p u
j j
V
Fault current I j p u
Z j

 

  

15. Name the method of reducing short circuit capacity and uses of short circuit capacity.
 By introducing artificial series reactors
 By providing neutral reactance
 By introducing a large value of shunt reactance between buses.
16. What are the reactances used in synchronous machines?
"
'
1. tan
2. tan
3. tan .
d
d
d
Subtransient reac ce X
Transient reac ce X
Synchronous reac ce X
17. Define transient reactance.
It is the ration of induced emf on no-load and the transient symmetrical rms current.
It is given by,
'
| | 1
tan ,
1 1| '|
tan
tan
tan
g
d l
a f
l
f
a
E
Transient reac ce X X
I
X X
where X Leakagereac ce
X Field winding reac ce
X Armaturereactionreac ce
  




18. What is the significant of transient reactance in short circuit studies?
The subtransient reactance can be used to estimate the initial value of fault current immediately
on the occurrence of the fault. The maximum momentary short circuit current rating of the
circuit breaker used for protection or fault clearing should be less than this initial fault current.
19. Difference between Load flow and short circuit studies.
Load flow Studies Short circuit studies
The resistance and reactance are considered The resistance are neglected
To solve load flow analysis, the bus
admittance matrix is used
To solve short circuit analysis, the bus
impedance matrix is used
It is used to determine the exact voltage and
currents
Prefault voltage are assumed to be1 p.u. and
the prefault current can be neglected.
20. Why synchronous impedance more than transient reactance?
The short circuit is of larger magnitude than the current measured half a second later. This mean
that magnitude of Z will have a minimum value immediately following the fault and then grow.
This change of the short circuit current with time is due to the characteristics of the synchronous
generators. Thus the synchronous impedance is more than transient reactance.

UNIT 5 – STABILITY ANALYSIS IN POWER SYSTEM
1. Define swing curve. What is the use of Swing curve? (A/M 2017)
2
( . ) ( . )2 m p u e p u
H d
P P
f dt


 
The graphical display of δ versus t is called the swing curve. The plot of swing curves of all
machines tells us whether machines will remain in synchronism after a disturbance.
2. State equal area criterion. (A/M 2017)
 The equal area criterion for stability states that the system is stable if the area under Pa – δ
curve reduced to zero at some value of δ.
 This is possible if the positive (acceleration) are under Pa – δ curve is equal to the negative
(deceleration) area under Pa – δ curve for a finite change in δ. Hence the stability criteria is
called equal area criterion.
3. Define voltage stability. (N/D 2016)
 Ability of power system to maintain steady acceptable voltages at all buses in power system
under normal operating conditions and after being subjected to a disturbance.
 Reactive power balance
4. State few techniques to improve the stability of the power system. (N/D 2016)
 Increase of the system voltage and use of AVR
 Use of high speed excitation systems.
 Reduction in system transfer reactance
 Use of high speed reclosing
5. Define transient stability of a power system. (A/M 2016)
It is the ability of the system to bring it to a stable condition after a large disturbance. Large
disturbance can occur due to the occurrence of fault, sudden outage of a line, sudden loss of
excitation, sudden application or removal of loads, etc.
6. How are power system stability classified? (N/D 2015)
Power system stability can be classified into as follows
 Rotor angle stability
 Voltage stability
 Frequency stability
7. Define critical clearing angle. (N/D 2015)
For any given initial load in the case of a fault clearance on a synchronous machine connected
to an infinite bus bar, there is a critical clearing angle. If the actual clearing angle is greater than the

critical value, the system is unstable, otherwise the system is stable. Maximum allowable angle for
a system to remain stable.
8. What is steady state stability limit? (Nov/Dec- 14)
The gradual increase of the generator power output is possible until the maximum
electrical power is transferred. This maximum power is referred to as the steady state stability
limit.
9. Define dynamic stability with an example. (May/June -14)
It is the ability of the system to remain in synchronism when it is subjected to sustained
oscillations followed by transient state.
10. Differentiate between voltage stability and rotor angle stability. (N/D 2013)
Voltage Stability Rotor angle stability
 Ability of power system to maintain
steady acceptable voltages at all
buses in power system under
normal operating conditions and
after being subjected to a
disturbance.
 Reactive power balance
 Ability of inter – connected
synchronous machines of a power
system to remain in synchronism.
 Torque balance of synchronous
machines
11. Define swing curve? What is the use of this curve. (N/D 2013)
2
( . ) ( . )2 m p u e p u
H d
P P
f dt


 
The graphical display of δ versus t is called the swing curve. The plot of swing curves of all
machines tells us whether machines will remain in synchronism after a disturbance.
12. What are the causes of oscillatory and non-oscillatory instabilities in power systems?
(A/M 10)
Oscillatory :
 Due to insufficient damping torque
 Due to unstable control action
Non – oscillatory :
 Due to insufficient synchronous torque
13. Write the power angle equation of a synchronous machine connected to an infinite bus
and also the expression for maximum power transferable to the bus.
1 1 2 2
eq
b b
M S M S
M
S S
 
1 11
12
max
| '|| |
| '| sin
sin
e
e C
E V
P P E G
X
P P P
Thisequationiscalled power angleequation


  
 
Expression for Maximum Power transfer:-
max
12
| '|| |
sin
E V
P
X


14. Define infinite bus in a power system. (M/J 13)
The substation bus voltage and frequency is assumed to remain constant. This is called as
infinite bus, since its characterized do not change regardless of the power supplied or consumed
by any device connected to it.
15. What is an infinite bus?
The substation bus voltage and frequency is assumed to remain constant. This is called
as infinite bus, since its characterized do not change regardless of the power supplied or
consumed by any device connected to it.
16. What are the methods used to solve swing equation? (M/J 09)
 Modified Euler’s method
 Runge-Kutta method.
17. Give the expression for critical clearing time. (N/D 07)
Critical time margin = critical clearing time – clearing time specified
( )cr critical spec
spec
t t
where
t Specified clearing time
 

18. Distinguish between small disturbance and large disturbance.
Small disturbance Large disturbance
 The disturbances that cause small
and gradual infinitesimal variation
in system variables such as rotor
angle, voltage, etc., are classified as
small disturbance.
 Any disturbance that causes a
change in the admittance matrix
encountered in stability is classified
as large disturbance
 Eg – Fault occurring, removal of
line
19. What is meant by synchronism and damping torques?
The component of electrical torque proportional to rotor angle deviation from initial value is
referred to as synchronizing torque and that proportional to speed deviation from initial value is
called damping torque.
Assume initially, the machine is in steady state, then
Machine speed = Rated speed = synchronous speed
Then Initial speed deviation = 0
20. Define power or torque angle.
Under normal operating conditions, the relative position of the rotor axis and the resultant
magnetic field are fixed. The angle between the two is known as the power angle or torque
angle.

Vel Tech High Tech Dr.Rangarajan Dr.Sakunthala Engg. College EE6501 – Power System Analysis
Prepared by Prabaakaran K AP/EEE Page |1
UNIT – 2 POWER FLOW ANALYSIS
1. Compare Newton Raphson and Gauss Seidal methods of load flow solutions. (A/M 2017)
Gauss Seidal method Newton Raphson method
Variable is expressed in rectangular
coordinates.
Variables are expressed in polar
coordinates.
Computation time per iteration is less Computation time per iteration is more.
It has linear convergence
characteristics.
It has quadratic convergence characteristics.
The number of iterations required for
convergence increases with size of the
system.
The numbers of iterations are independent of the size
of the system.
The choice of slack bus is critical. The choice of slack bus is arbitrary.
2. Write the quantities that are associated with each bus in a system.(A/M 2017)
Each bus in a power system is associated with four quantities and they are
i. real power
ii. reactive power
iii. magnitude of voltage, phase angle of voltage.
3. What is Jacobian Matrix? (N/D 2016)
The matrix formed from the first derivatives of load flow equation is called jacobian
matrix and it is denoted by J.
The elements of jacobian matrix will change in every iteration .the elements of the jacobian matrix
are obtain matrix are obtained by partially differentiating the load flow equation with respect to a
unknown variable and then evaluating the first derivative as using the solution of previous iteration.
4. Write the need for slack bus in load flow analysis. (N/D 2016) A/M 2017, 2018
The slack bus is needed to account for transmission line losses. In a power
system the total power generated will be equal to sum of power consumed by loads and losses. In a power
system only the generated power and load power are specified for buses. The slack bus is assumed to
generate the power required for losses. Since the losses are unknown the real and reactive power are not
specified for slack bus. They are estimated through the solution of load flow equations.
5. What is the need for load flow analysis? (A/M 2016) N/D 2017
The study of various methods of solution to power system network is referred to as load flow study.
The solution provides the voltages at various buses, power flowing in various lines and line-losses.
The load flow study of a power system is essential to decide the best operation of existing system
and for planning the future expansion of the system. It is also essential for designing a new power
system.
6. Mention the various types of buses in power system with specified quantities for each bus. (A/M
2016) N/D 2017
The buses of a power system can be classified into three types based on the
quantities being specified for the buses, which are as follows:
 Load bus or PQ bus (P and Q are specified)
 Generator bus or voltage controlled bus or PV bus (P and V are specified)
 Slack bus or swing bus or reference bus (|V| and δ are specified)
7. Write the static load flow equation. (N/D 2015)
𝑁
𝑗=1 −𝛿𝑖)
𝑁
𝑗=1 −𝛿𝑖)

8. State the role of acceleration factor in GS method. (N/D 2015) A/M 2018
In Gauss Seidal method, the number of iteration required for convergence can be reduced if the
voltage computed at each iteration is multiplied by a factor greater than unity called acceleration factor to
bring the voltage closer to the value to which it is converging. The range of 1.3 to 1.6 is found to be
satisfactory for the typical systems.
𝑉𝑖
𝑛𝑒𝑤
= Vi
old
+ ∝ [𝑉𝑖
𝑛𝑒𝑤
− Vi
old
]
Where Vi
old
= Voltage value obtained in previous iteration
𝑉𝑖
𝑛𝑒𝑤
= New value of Voltage value obtained in current iteration
∝ = Acceleration factor
9. Why the load flow studies are important for planning the existing system as well as its future
expansion?
The load flow studies are very important for planning, economic scheduling, control and operation
of existing systems as well as planning its future expansion depends upon knowing the effect of
interconnections, new loads, new generating stations, or new transmission lines, etc. before they
installed.
10. What is swing bus? (N/D 2013)
A bus is called swing bus when the magnitude and phase for bus voltage are specified for it. The
swing bus is the reference bus for load flow solution and it is required for accounting line losses.
Usually one of the generator bus selected as the swing bus.
Swing bus is also called as Slack bus.
11. When the generator buses are treated as load bus? (N/D’13, M/J’14)
If the reactive power constraints of a generator bus violates the specified limits then the generator is
treated as load bus.
If Qi > Qi(max), substitute Qi = Qi(max)
If Qi
cal
< Qi(min) , substitute Qi= Qi(min)
12. What is meant by flat voltage start?
In iterative methods of load flow solution, the initial voltages of all buses exept slack bus are assumed
as 1+j0 pu. This is referred as flat voltage profile.
V = |𝑉𝑠𝑝𝑒𝑐| 0 for slack bus
V = |𝑉𝑠 𝑝𝑒𝑐| 0 for generator bus
V = 1 0 for load bus
13. What are the works involved in a load flow study? ( Or) How a load flow study is
performed?
The following work has to be performed for a load flow study.
 Representation of the system by single line diagrams.
 Determining the impedance diagram using the information in single line diagram.
 Formulation of network equations.
 Solution of network equations.

14. List the quantities specified and the quantities to be determined from load flow study for
various types of buses.
The following table shows the quantities specified and to be obtained for various types of buses.
Bus type Quantities specified Quantities to be obtained
Load bus P,Q │V│, δ
Generator bus P, │V│ Q, δ
Slack bus │V│, δ P,Q
15. Why bus admittance matrix is used in load flow instead of bus impedance matrix? (M/J 2014)
Using bus admittance matrix is amenable to digital computer analysis, because it could be formed
and modified for network changes in subsequent cases. Bus admittance matrix is used in Gauss seidal
method because of the following reasons.
 It requires less computation time
 Less memory allocation
16. What are the operating Constrains imposed in load flow studies?
The operating constraints imposed in load flow studies are reactive power limits for generator buses
and allowable change in magnitude of voltage for load buses.
17. What is infinite bus?
A bus is called infinite bus if its voltage remains constant and does not altered by any
changes in generator excitation.
18. Define Voltage control bus?
A bus is called voltage controlled bus if the magnitude of |V| and real power (P) are specified for it. In a
voltage controlled bus the magnitude of the voltage is not allowed to change. The other names for voltage
controlled bus are generator bus and PV bus.
19. Why do we go for iterative methods to solve load flow problems?
The load flow equations are nonlinear algebraic equation and so explicit solution is not possible. The
solution of nonlinear equations can be obtained only by iterative numerical techniques.
20. How the disadvantages of N-R method are overcome?
The disadvantage of large memory requirement can be overcome by decoupling the weak coupling
between P-δ and Q-V. (i.e., using decoupled load flow algorithm). The disadvantage of large
computational time per iteration can be reduced by simplifying the decoupled load flow equations. The
simplifications are made based on the practical operating conditions of a power system.
PART – B
1. Derive the development of load flow model in complex variable form and polar variable form.
(13) (M/J’14)
The power flow or load flow model in complex form is obtained by writing one complex power
matching equation at each bus for the figure shown below. (4)
Net power injected into the bus i.
Si = SGi – SDi
= PGi + jQGi – (PDi + jQDi)
= Pi + jQi

We know,
Pi + jQi = Vi Ii
*
Consider two bus system with I1 and I2 as net current entering into bus 1 and 2.
[I]= [Y][𝑉]
[
I1
I2
] = [
𝑌11 𝑌12
𝑌21 𝑌22
] [
𝑉1
𝑉2
] (4)
𝑌11 = 𝑦10 + 𝑦12
𝑌22 = 𝑦20 + 𝑦21
𝑌12 = 𝑌21 = - 𝑦21
In general, Yij = |𝑌𝑖𝑗|∠𝜃𝑖𝑗
I1 = 𝑌11 𝑉1+ 𝑌12 𝑉2
I2 = 𝑌21 𝑉1+ 𝑌22 𝑉2
In general , the net current entering into ith
bus
Ii = Yi1V1 + Yi2V2+………………………………..+ YiNVN = ∑ Y𝑖𝑗 𝑉𝑗
𝑁
𝑗=1
Substituting the value of Ii in power flow eqn we get.
Si = Pi + jQi = Vi Ii
*
Si = Pi - jQi = Vi Ii
*
Pi - jQi = Vi
*
∑ Y𝑖𝑗 𝑉𝑗
𝑁
𝑗=1 where i = 1,2,3…………..N (4)
There are N complex variable equations for which the N unknown complex variables V1,V2…….VN can be
determined.
Substituting Yij from the above eqn, we get.
Pi - jQi = Vi
*
∑ |𝑌𝑖𝑗|∠𝜃𝑖𝑗 𝑉𝑗
𝑁
𝑗=1
Where Vi = |𝑉𝑖|∠𝛿𝑖 , Vi
*
= |𝑉𝑖|∠ − 𝛿𝑖,
Vj = |𝑉𝑗|∠𝛿𝑗
Therefore net power equations can be written as
Pi - jQi = ∑ |𝑉𝑖||𝑌𝑖𝑗||𝑉𝑗|∠(𝜃𝑖𝑗 + 𝛿𝑗 − 𝛿𝑖 )𝑁
𝑗=1
Equating real and reactive parts, (4)
Pi = ∑ |𝑉𝑖||𝑌𝑖𝑗||𝑉𝑗| 𝑐𝑜𝑠 (𝜃𝑖𝑗 + 𝛿𝑗 − 𝛿𝑖 )𝑁
𝑗=1
Qi = - ∑ |𝑉𝑖||𝑌𝑖𝑗||𝑉𝑗| 𝑠𝑖𝑛 (𝜃𝑖𝑗 + 𝛿𝑗 − 𝛿𝑖 )𝑁
𝑗=1
We can write the above equation as
Pi = |𝑉𝑖|2 |𝑌𝑖𝑖| 𝑐𝑜𝑠 𝜃𝑖𝑖 ∑ |𝑉𝑖||𝑌𝑖𝑗||𝑉𝑗| 𝑐𝑜𝑠 (𝜃𝑖𝑗 + 𝛿𝑗 − 𝛿𝑖 )𝑁
𝑗=1
Qi = - |𝑉𝑖|2 |𝑌𝑖𝑖| 𝑠𝑖𝑛 𝜃𝑖𝑖 ∑ |𝑉𝑖||𝑌𝑖𝑗||𝑉𝑗| 𝑐𝑜𝑠 (𝜃𝑖𝑗 + 𝛿𝑗 − 𝛿𝑖 )𝑁
𝑗=1
The above equations are called as polar form of the power flow equations.
2. Write the step-by-step algorithm for load flow solution by Gauss-seidal method. (13)
Step 1 : form Y-Bus (4)
Step 2 : Assume Vk = Vk(spec) ∠00
at all generator buses.
Step 3 : Assume Vk = 1∠00
= 1+j0 at all load buses.
Step 4 : set iteration count = 1 (iter = 1)
Step 5 : let bus number i = 1 (4)
Step 6 : If ‘i’ refers to generator bus go to step no. 7, otherwise go to step 8.
Step 7(a) : If ‘i’ refers to slack bus go to step no. 9, otherwise go to step 7(b).
Step 7(b) :compute Qi using
Qi
cal
= - Im [ ∑ 𝑁
𝑗=1 𝑉𝑖
∗
𝑌𝑖𝑗 Vj ]

QGi = Qi
cal
+ QLi
Check for Q limit violation (6)
If Qi(min) < QGi < Qi(max), then Qi(spec) = Qi
cal
If Qi(min) < QGi, then Qi(spec) = Qi(min) - QLi
If Qi(max) < QGi, then Qi(spec) = Qi(max) - QLi
If Qlimit is violated, then treat this bus as P-Q bus till convergence is obtained.
Step 8 : Compute Vi using eqn.
𝑉𝑖
𝑛𝑒𝑤
=
1
𝑌𝑖𝑖
[
𝑃 𝑖− 𝑗𝑄 𝑖
𝑉𝑖
𝑜𝑙𝑑∗ − ∑ 𝑗−1
𝑖=1 𝑌𝑖𝑗 Vj
new
- ∑ 𝑁
𝑖=𝑗+1 𝑌𝑖𝑗 Vj
old
Step 9 : If i is less than number of buses, increment I by 1 and go to step 6.
Step 10 : Compare two successive iteration values for Vi
If 𝑉𝑖
𝑛𝑒𝑤
- 𝑉𝑖
𝑜𝑙𝑑
< tolerance, go to step 12.
Step 11 : Update the new voltage as
Vnew
= Vold
+ ∝ (Vnew
- Vold
)
Vnew
= Vold
Iter = iter +1; go to step 5.
Step 12: Compute relevant quantities. (2)
Slack bus power, S1 = V*I = Vi
*
∑ 𝑁
𝑗=𝑖 𝑌𝑖𝑗 Vj
line flow losses, Sij = Pij + jQij
Real power loss, Ploss = Pij + Pji
Reactive power loss, Qloss = Qij + Qji
Step 13 : Stop the execution.

3. Write the Procedure for load flow solution by Newton Raphson method. (13) (N/D’08, M/J’12,
N/D’14)
Step 1 : Form Y-Bus (8)
Step 2 : Assume flat start voltage solution
𝛿𝑖
0
= 0, for i = 1…..N
|𝑉𝑖
0
|=1.0,
|𝑉𝑖| = |𝑉𝑖|spec
Step 3 : for load buses, calculate Pi
cal
and Qi
cal
Step 4 : for PV bus, Check for Q limit violation
If Qi(min) < Qi
cal
< Qi(max), the bus acts as PV bus
If Qi
cal
> Qi(max), then Qi(spec) = Qi(max)
If Qi
cal
< Qi(min) , then Qi(spec) = Qi(min) , the PV bus will act as PQ bus.
Step 5 : Compute mismatch vector using. (8)
∆Pi = Pi(spec) - Pi
cal
∆𝑄i = Qi(spec) - Qi
cal
Step 6 : Compute ∆Pi(max) = max |∆P𝑖| i = 1,2……….N except slack
∆Qi(max) = max |∆𝑄𝑖| i = M+1……….N
Step 7 : compute jacobian matrix using J = [
𝜕𝑃 𝑖
𝜕𝛿
𝜕𝑃 𝑖
𝜕|𝑉|
𝜕𝑄 𝑖
𝜕𝛿
𝜕𝑄 𝑖
𝜕|𝑉|
]
Step 8 : Obtain state correction vector [
∆V
∆𝛿
] = [J]-1
[
∆𝑃
∆𝑄
]
Vnew
= Vold
+∆V
𝛿 new
= 𝛿 old
+∆𝛿
Step 9 : Update state vector using .
Vnew
= Vold
+∆V
𝛿 new
= 𝛿 old
+∆𝛿
Step 10 : This procedure is continued until
|∆P𝑖| < 𝜀 and |∆𝑄𝑖| < 𝜀, otherwise go to step 3.

4. Derive the load flow equation using Newton Raphson method. (13)
The most widely used method for solving simultaneous non linear algebraic equation is the Newton
Raphson method. (4)
from the fig the complex power balance at bus i is given by

PIi + jQIi = Pi + jQi ………………………………………………………..…(1)
Complex power injection at the ith
bus PIi + jQIi
= (PGi - PDi ) + (jQGi - jQDi) (4)
Since the bus generation and demand are specified, the complex the complex power injection is a specified
quantity and is given by,
PIi(spec) + jQIi(spec) = [PGi(spec) - PDi(spec)] +j[QGi(spec) - QDi(spec)] ………………(a)
The current entering bus i is given by,
Ii = ∑ Y𝑖𝑗 𝑉𝑗
𝑁
𝑗=1
In polar form
Ii = ∑ |𝑌𝑖𝑗||𝑉𝑖|∠(𝜃𝑖𝑗 + 𝛿𝑗
𝑁
𝑗=1 ) ………………………………………………….(b)
[Y𝑖𝑗 = |𝑌𝑖𝑗|∠𝜃𝑖𝑗 ; 𝑉𝑗 = |𝑉𝑖|∠𝛿𝑖]
Complex power at bus i
Pi - jQi = Vi
*
Ii = Vi
*
∑ Y𝑖𝑗 𝑉𝑗
𝑁
𝑗=1 (4)
Substituting from eqn (b), we get
Pi - jQi = |𝑉𝑖|∠−𝛿𝑖 ∑ |𝑌𝑖𝑗||𝑉𝑗|∠(𝜃𝑖𝑗 + 𝛿𝑗
𝑁
𝑗=1 )
= ∑ |𝑉𝑖||𝑌𝑖𝑗||𝑉𝑗|∠(𝜃𝑖𝑗 + 𝛿𝑗
𝑁
𝑗=1 −𝛿𝑖)
Equating the real and imaginary parts
𝑁
𝑗=1 −𝛿𝑖)………………………(c) (4)
𝑁
𝑗=1 −𝛿𝑖) ………………………………………….(d)
The above eqn constitute a set of nonlinear algebraic equations in terms of the independent variables.
Substitute eqn (a),(c),(d) in (1) we get power balance eqns.
Pi (δ,V) - PIi(spec) = 0
Qi (𝛿,V) - QIi(spec) = 0
5. For the system shown in Fig., determine the voltages at the
end of the first iteration by Gauss – seidel method and also
find the slack bus power, line flows, transmission line loss.
Assume base MVA as 100. (13) (N/D’13)
Solution:
Bus No. Voltage
Generator Load Qmin
MVAR
Qmax
MVARP Q P Q
1. 1.050 p.u. - - - - - -
2. 1.02 p.u. 0.3 p.u. - - - -10 100
3. - - - 0.4 p.u. 0.2 p.u. - -

Step – 1: From Y-bus. (4)
Ybus =
[
1
Y11
−1
Y12
−1
Y13
−1
Y21
1
Y22
−1
Y23
−1
Y31
−1
Y32
1
Y33
]
=
[
1
j0.4
+
1
j0.3
−1
j0.4
−1
j0.3
−1
j0.4
1
j0.4
+
1
j0.2
−1
j0.2
−1
j0.3
−1
j0.2
1
j0.3
+
1
j0.2]
Ybus = [
−j5.8333 j2.5 j3.3333
j2.5 −j7.5 j5
j3.3333 j5 −j8.3333
]
Step – 2: Initialize bus voltages.
V1
old
= 1.050 p.u. [Bus 1 is a slack bus i.e., V and  is specified]
V2
old
= 1.020 p.u. [Bus 2 is a PV bus i.e., P and V is specified]
V3
old
= 1.0 p.u. [Bus 3 is a load bus i.e., P and Q is specified]
For Slack bus, the specified voltage will not change in any iteration.
For generation bus, calculate Vi
new
using the formula and write
Vi
new
= Vspecifiedcalculated value
Step 3 : Calculate Q value for all generator buses. (4)
Qi
cal
= - Im {Vi
old
*[∑ Yij Vjnewi−1
j=1 + ∑ Yij VjoldN
j=i ]}
Q2
cal
= - Im {V2
old
*[Y21V1
new
+Y22V2
old
+ Y23V3
old
]}
Q2
cal
= - Im {1.020 *[j2.51.050 +(-j7.51.020) + j5  10]}
Q2
cal
= - Im {1.020 *j2.625-j7.65+j5]}
Q2
cal
= 0.025 p.u.
Now Q2(min)  Q2
cal
Q2(max)
i.e., Q2
cal
is within the specified limit.
Step – 4: Calculate Vi
new
.
Vi
new
= 1.050 p.u.
Vi
new
=
1
Yii
[
Pi−jQi
Vi
old*
− ∑ Yij Vj
newi−1
j=1 − ∑ Yij Vj
oldN
J=i+1 ]
V2
new
=
1
Y22
[
P2−jQ2
V2
old*
− Y21V1
new
− Y23 V3
old
]
P2 = 0.3 p.u. (Given); Q2= 0.025 p.u.
V2
new
=
1
−j7.5
[
0.3−j0.025
1.020
− j2.5 X 1.050 − j5 X 10]
= 1.0199+j0.0392
V2
new
= 1.02072.2
V2
new
= V2(spec)2
cal
= 1.022.2 = 1.0192 + j0.0392
P3 = PG3 – PL3 = 0- 0.4 = -0.4 p.u.
Q3= QG3 – QL3 = 0 – 0.2 = -0.2 p.u.
V3
new
=
1
Y33
[
P3−jQ3
V3
old*
− Y31V1
new
− Y32 V2
new
]
V3
new
=
1
−j8.3333
[
−0.4+j0.2
1.00
− j3.3333 X 1.050 − j5 X 1.022.2]
=
1
−j8.3333
[−0.4 + j0.2 − j3.4999 − j5.096 + 0.196]
= 1.0075 – j0.0244 = 1.0078 -1.39
V3
new
= 1.0075 – j0.0244 = 1.0078  -1.39

6. Perform two iteration of Newton Raphson load flow method and determine the power flow
solution for the given system. Take base MVA as base 100. (13)
Solution:
Line Data:
Line Bus R(p.u.) X(p.u.) Half line charging
admittance (p.u.)From To
1 1 2 0.0839 0.5183 0.0636
Bus Data:
Bus PL QL
1 90 20
2 30 10
Step – 1: Ybus = [
0.3044 − j1.816 −0.3044 + j1.88
−0.3044 + j1.88 0.3044 − j1.816
] (4)
Ybus = [
1.842 − 1.405 1.9041.7314
1.9041.7314 1.842 − 1.405
] {Note: Use in rad mode}
Step – 2: Assume the initial value i.e., =0, V=1.0
[X] = [
2
V2
] = [
0
1.0
]
Step – 3: Calculate P2
cal
, Q2
cal
, P2 and Q2.
P2
cal
= |V2|{|V1||Y2| cos(12 + 2 − 1) + |V2||Y22|cos(22 + 2 − 2) }
= 1.0[1.05 X 1.904 cos(1.7314) + 1.842 cos(-1.405)]
= 1.05 X 1.904(-0. 15991) + 1.842(0.16503)
= -0.015 p.u.
P2(spec) = PG2 – PL
= 0 -
30
100
= - 0.3 p.u.
P2(spec) = - 0.3 p.u.
P2 = P2(spec) – P2
cal
= -0.3 – (-0.015)= - 0.285
Q2
cal
= - V2{|V1||Y21| sin(12 + 1 − 2) + |V2||Y22| sin(22 + 2 − 2)}
= - 1.0[1.05 X 1.904 sin(1.7314)+ 1.0 X 1.842 sin(-1.405)]
= - 0.157 p.u.
Q2 = Q2(spec) – Q2
cal
= - 0.1 – ( -0.157)
= 0.057
Step – 4: Form Jacobian matrix (4)
[
∂P2
∂2
∂P2
∂V2
∂Q2
∂2
∂Q2
∂V2
] [
2
V2
] = [
P2
Q2
]
∂P2
∂2
= |V2||V1||Y12| sin(12 + 1 − 2) + |V2|2
|Y22|X 0
= 1.0 X 1.05 X1.904 sin(1.7314)
= 1.973
∂P2
∂V2
= |V1||Y21| cos(12 + 1 − 2) + 2|V2||Y22| cos(22)
= 1.05 X 1.904 cos(1.7314) + 2 X 1.842 cos(-1.405)
= 0.289

-1
-1
∂Q2
∂2
= |V2||V1||Y21| cos(12 + 1 − 2) − |V2|2
|Y22|X 0
= 1.05 X 1.904 cos(1.7314)
= - 0.3197
∂Q2
∂V2
= −|V1||Y21| sin(12 + 1 − 2) − 2|V2||Y22| sin(22)
= - 1.05 X 1.904 sin(1.7314) – 2 X 1.842 sin(-1.405)
= 1.66
Step – 5: Compute x, (4)
[
2
V2
] = [
∂P2
∂2
∂P2
∂V2
∂Q2
∂2
∂Q2
∂V2
]  [
P2
Q2
]
= [
1.973 0.289
−0.3196 1.66
] x [
−0.285
0.057
]
= [
0.493 −0.086
0.0949 0.586
] [
−0.285
0.057
]
[
2
V2
] = [
−0.145
0.0064
]
X = X + X = [
0
1.0
] + [
−0.145
0.0064
] = [
−0.145
0.0064
]
UNIT 3 – SYMMETRIC FAULT ANALYSIS
1.What is the significance of sub transient reactance and transient reactance in short circuit studies?
(A/M 2017)
The sub-transient reactance can be used to estimate the initial value of fault current immediately
on the occurrence of the fault. The maximum momentary short circuit current rating of the circuit
breaker used for protection or fault clearing should be less than this initial fault current.
2. For a fault at a given location, rank the various fault in the order of severity.(A/M 2017)
Types of fault Relative frequency of occurrence of faults
Three phase fault 5%
Double line to ground fault 10%
Line to Line fault 15%
Line to ground fault 70%
3.How shunt and series fault are classified ? (N/D 2016)
 Shunt faults - due to short circuits in conductors
 Series faults - due to open conductors.
 The shunt fault is also called as short circuit faults.
4.What is the need for short circuit study? (N/D 2016)
The short circuit studies are essential in order to design or develop the protective schemes for
various parts of the system. The protective scheme consists of current & voltage sensing devices, protective
relays and circuit breakers. The selection (or proper choice) of these device mainly depends on various
currents that may flow in the fault conditions.
5.State and explain symmetrical fault. (A/M 2018, 16)
The fault on the power system which gives rise to symmetrical fault currents (i.e. equal fault current
in the lines with 1200
displacement) is called as symmetrical faults. The symmetrical fault occurs when all
the three conductors of phase are brought together simultaneously in short circuit condition.

6.What is bolted fault or solid fault? (N/D 2017, A/M 2016)
A Fault represents a structural network change equivalent with that caused by the addition of
impedance at the place of a fault. If the fault impedance is zero, the fault is referred as bolted fault or solid
fault.
7.Define short circuit capacity. (N/D 2015)
Short circuit capacity or short circuit MVA of fault level at a bus is defined as the product of the
magnitudes of the perfect bus voltage and the post fault current.
SCC = |𝐸 𝑇ℎ||𝐼𝑓| =
|𝐸 𝑇ℎ|2
𝑋 𝑇ℎ
p.u. MVA
8.What is meant by a fault?
A fault in a circuit is any failure which interferes with the normal flow of current. The faults are
associated with abnormal change in current, voltage and frequency of the power system. The faults may
cause damage to the equipments if it is allowed to persist for a long time. Hence every part of a system has
been protected by means of relays and circuit breakers to sense the faults and to isolate the faulty part from
the healthy part in the event of fault.
9.Why fault occurs in a power system?
In a power system the fault may occur due to the following reasons.
 Insulation failure of equipments.
 Flashover of lines initiated by a lightning stroke.
 Switching surges.
 Sudden releasing of heavy loads at same instant of time.
 Due to accidently faulty operation of power system operators.
10.What are the objectives of short circuit analysis.
 To check the MVA ratings of the existing circuit breaker’s, when new generation are added
into system.
 To select the rating for fuses, circuit breaker’s and switch gear in addition to set up of
protective relays.
 To determine the magnitudes of currents flowing through out the power system at various
time intervals after a fault occurs.
11.State the applications of short circuit analysis.
Short circuit studies are used
 For proper relay setting and co ordination.
 To obtain the rating of the protective switch gears.
 To select the circuit breakers.
 To perform whenever system expansion is planned.
12.What are symmetrical components?
An unbalanced system of N related vectors can be resolved into N systems of balanced vectors called
symmetrical components. The various symmetrical components are as follows.
 Positive sequence components
 Negative sequence components
 Zero sequence components

13.Why delta connected load will not have any zero sequence components
The current in the neutral is three times the zero sequence line current. A delta connected load
provides no path to neutral and hence the line currents flowing to a delta connected load contain zero
component. Hence the delta connected load will not have any zero sequence components.
14. What is symmetrical components of three phase system.
Symmetrical components of three phase system is given as
For voltage
[
𝑉𝑎
𝑉𝑏
𝑉𝑐
] = [
1 1 1
1 𝑎2
𝑎
1 𝑎 𝑎2
] [
𝑉𝑎0
𝑉𝑎1
𝑉𝑎2
]
For current.
[
𝐼 𝑎
𝐼 𝑏
𝐼𝑐
] = [
1 1 1
1 𝑎2
𝑎
1 𝑎 𝑎2
] [
𝐼 𝑎0
𝐼 𝑎1
𝐼 𝑎2
]
15.What is meant by doubling effect?
If a symmetrical fault occurs when the voltage wave is going through zero then the maximum
momentary short circuit current will be double the value of maximum symmetrical short circuit current.
This effect is called doubling effect.
16. What is synchronous reactance? N/D 2015
The synchronous reactance is the ratio of induced emf and the steady state rms current (i.e. it is the
reactance of a synchronous machine under steady state condition). It is the sum of leakage reactance and the
reactance representing armature reaction.
It is given by, Xs = Xl + Xa
Where,Xs = Synchronous reactance, Xl = Leakage reactance, Xa = Armature reaction reactance.
17.What is the reason for transients during short circuits?
The faults or short circuits are associated with sudden change in currents. Most of the
components of the power system have inductive property which opposes any sudden change in currents
and so the faults (short circuit) are associated with transients.
18. What are the advantages of symmetrical components.
 This method is simple.
 This method leads to accurate prediction of system behavior.
 Unsymmetrical faults on the transmission system are studied by the method of symmetrical
components.
 They suitable to determine the currents and voltages in all parts of the power system after
the occurrence of fault.
19.What are the needs of sequence network in power system.
 Sequence network in power system are very much useful in computing unsymmetrical faults
at different points of the power system network.
 Positive sequence network is necessary foe load flow studies.
 Negative and zero sequence networks are for stability studies involving unsymmetrical fault.
20.What are sequence impedances and sequence networks?
 The sequence impedances are the impedances offered by the devices or
components for the like sequence component of the current.
 The single phase equivalent circuit of a power system consisting of impedances
to current of any one sequence only is called sequence network.

21. What is meant by fault calculation? A/M 2018
Fault calculations are one of the most common types ofcalculation carried out during the design and
analysis of electrical systems. These calculations involve determining the current flowing through circuit
elements during abnormal conditions – short circuits and earthfaults.
22. What are all the assumption to be made to simplify the short circuit study? A/M 2018
 Representing each machine by constant voltage source behind proper reactance.
 Prefault load currents are neglected.
 Transformer taps are assumed to be nominal.
 Shunt elements & core loss in transformer are neglected.
 A symmetric three phase power system is considered.
 Shunt capacitance & Series resistance are neglected.
23. How the shunt & series fault are classified? N/D 2016
Shunt : LLLG, LG, LL, LLG Fault
Series : Open conductor fault , Two open conductor fault.
24. Draw the oscillogram of short circuit current when an unloaded generator is subjected to
symmetrical fault. A/M 2015
25. A motor is drawing 10000 kW at 0.85 pf leading and a terminal voltage of 10kV. Determine the
load current.
Load Current, IL =
10000
√3 ×0.85 ×12
∠cos-1
0.85 = 566 ∠31.8o
26. What is circuit breaker?
A circuit breaker is an automatically operated electrical switch designed to protect an electrical
circuit from damage caused by excess current from an overload or short circuit. Its basic function is to
interrupt current flow after a fault is detected. Unlike a fuse, which operates once and then must be
replaced, a circuit breaker can be reset (either manually or automatically) to resume normal operation.
27. What are the main factors to be considered for selection of circuit breaker?
 Normal working power level specified as rated interrupting current or rated interrupting MVA.
 The fault level specified as either rated short circuit interrupting current or rated short circuit
interrupting MVA.
 Momentary current rating
 Normal working voltage
 Speed of circuit breaker.

28. Why the circuit breaker interrupting current is asymmetrical?
The interrupting current of circuit breaker is the sum of symmetrical short circuit current and dc –
offset current. The presence of dc – offset makes the interrupting current as asymmetric.
PART – B
1. Algorithm & Flowchart for symmetrical fault analysis using Zbus
Step 1 : Start.
Step 2 : Read line impedance,
generator impedance and fault
impedance.
Step 3 : Form the Zbus matrix using
step by step assembly using 4 types
of modifications.
Step 4 : Set all bus voltages as
10 p.u.
Step 5 : Connect Zf in series with
faulted bus.
Step 6 : Calculate fault current for
ith
bus.
Ii(F) =
𝑉𝑖(𝑜)
𝑍 𝑖𝑖+𝑍 𝑓
Step 7 : Calculate the generator
current IG = Zeq IGi
Step 8 : Calculate change in
voltage ∆𝑉𝑖 and Vi(F)
Vi(F) = 𝑉𝑖(𝑜) + ∆𝑉𝑖
Step 9 : Calculate Vj(F) = 𝑉𝑗(𝑜) = -∑ 𝑍𝑖𝑗 𝐼𝑖(𝐹)𝑛
𝑗=1
≠𝑖
Step 10 : Calculate Iij(F) =
𝑉𝑖(𝐹)−𝑉 𝑗(𝐹)
𝑍 𝑖𝑗
Step 11 : Print the result.
Step 12 : Stop.
2. A symmetrical fault occurs on bus 4 of system shown in fig. Determine the fault current, post fault
voltages and line currents. G1, G2 : 100 MVA, 20 KV, X+=15%. Transformer: Xleak=9%,
L1, L2: X+=10%.

Solution.
Step 1: draw reactance diagram
Step 2: form Z-bus using building algorithm.
Zbus = [j0.15]
Zbus =[
j0.15 j0.15
j0.15 j0.24
]
Zbus =[
j0.15 j0.15 j0.15
j0.15 j0.24 j0.24
j0.15 j0.24 j0.29
]
Zbus =[
j0.15 j0.15 j0.15 j0.15
j0.15 j0.24 j0.24 j0.24
j0.15 j0.24 j0.29 j0.29
j0.15 j0.24 j0.29 j0.38
]
Zbus =
[
j0.15 j0.15 j0.15 j0.15 j0.15
j0.15 j0.24 j0.24 j0.24 j0.24
j0.15 j0.24 j0.29 j0.29 j0.29
j0.15 j0.24 j0.29 j0.38 j0.38
j0.15 j0.24 j0.29 j0.38 j0.53]
Eliminate node 5 using the relation.
Zij new = Zij old -
𝑍 𝑖(𝑛+1) 𝑍(𝑛+1)𝑗
𝑍(𝑛+1)(𝑛+1)

= [
j0.1075 j0.172 j0.068 j0.0424
j0.172 j0.13 j0.108 j0.068
j0.068 j0.108 j0.13 j0.082
j0.0424 j0.13 j0.082 j0.075
]
Step 3: fault current
If =
𝑉0
𝑍 𝑞𝑞+𝑍 𝑓
=
1∠00
𝑗0.1075
= 9.3∠ − 900
p.u
If = 9.3∠ − 900
p.u
Actual current in KA = p.u value x base current.
= 9.3∠ − 900
x
𝑀𝑉𝐴
√3 𝑥 𝐾𝑉
= 9.3∠ − 900
x
100
√3 𝑥 20
= 26.85 KA
Actual current in KA = 26.85 KA
Step 4 : Post fault bus voltages:
𝑉1
𝑓
= 𝑉0
- 𝑍14 𝑍𝑓
= 1∠00
- j0.042 x 9.3∠ − 900
= 0.6056 p.u
𝑉2
𝑓
= 𝑉0
- 𝑍24 𝑍𝑓
= 1∠00
- j0.068 x 9.3∠ − 900
= 0.3686 p.u
𝑉3
𝑓
= 𝑉0
- 𝑍34 𝑍𝑓
= 1∠00
- j0.082 x 9.3∠ − 900
= 0.2374 p.u
𝑉4
𝑓
= 𝑉0
- 𝑍44 𝑍𝑓
= 1∠00
- j0.1075 x 9.3∠ − 900
= 0 p.u
𝑉1
𝑓
= 0.6056 p.u
𝑉2
𝑓
= 0.3686 p.u
𝑉3
𝑓
= 0.2374 p.u
𝑉4
𝑓
= 0 p.u
Step 5 : Post fault line currents.
𝐼𝑖𝑗
𝑓
=
𝑉𝑖
𝑓
−𝑉𝑗
𝑓
𝑍 𝑖𝑗 𝑠𝑒𝑟𝑖𝑒𝑠
; 𝐼12
𝑓
=
𝑉1
𝑓
−𝑉2
𝑓
𝑍12
=
0.6056−0.3686
𝑗 0.09
|𝐼12
𝑓
| = 2.634 p.u
𝐼23
𝑓
=
𝑉2
𝑓
−𝑉3
𝑓
𝑍23
=
0.3686−0.2374
𝑗 0.05
|𝐼23
𝑓
| = 2.63 p.u.
𝐼34
𝑓
=
𝑉3
𝑓
−𝑉4
𝑓
𝑍34
=
0.2374−0
𝑗 0.09
|𝐼34
𝑓
| = 2.637 p.u.

3. A 3 phase transmission line operating at 33kv and having resistance and reactance of 5 ohms and
15 ohms respectively is connected to the generating station bus-bar through a 5000 KVA step up
transformer which has a reactance of 0.05 p.u. Connected to the bus-bars are two alternators, are
10,000 KVA having 0.08 p.u. reactance and another 5000 KVA having 0.06 p.u. reactance. Calculate
the KVA at a short circuit fault between phases occurring at the high voltage terminals of the
transformers.
Solution :
Base MVA = 10 MVA
Base KV = 33KV
Transmission line :𝑍 𝑝.𝑢
𝑛𝑒𝑤
=
𝑍 𝑝.𝑢
𝑜𝑙𝑑
𝐾𝑉𝑏
2 x MVA
=
5+𝑗15
332
x10 = 0.0459 +j0.1377 p.u
𝑍 𝑝.𝑢
𝑛𝑒𝑤
= 0.0459 +j0.1377 p.u
Transformer : 𝑘𝑉𝑏,𝑛𝑒𝑤 = 33KV
Zp.u. new = Zpu,given x [
𝑘𝑉 𝑏,𝑔𝑖𝑣𝑒𝑛
]2
x [
𝑀𝑉𝐴 𝑏,𝑔𝑖𝑣𝑒𝑛
]
Zp.u. new =j 0.05 x(33/33)2
x(10/5)
Znew = j 0.1 p.u
Generator 1: 𝑘𝑉𝑏,𝑛𝑒𝑤 = 11KV
]2
x [
]
= j 0.08 x(33/33)2
x(10/10)
Znew = j 0.08 p.u
]2
x [
]
= j 0.06 x(33/33)2
x(10/5)
Znew = j 0.12 p.u

Reactance diagram:
a. Total impedance upto the fault F1, Z1 p.u = - j0.148 p.u
Short circuit KVA fed into the fault at F1 = |𝐾𝑉𝐴1 𝑆.𝐶| =
|𝐾𝑉𝐴 𝑏|
|𝑍1 𝑝.𝑢|
=
10,000
0.148
= 67567.56 KVA
= 67.568 MVA
Short circuit KVA fed into the fault at F1 = 67.568 MVA
a. Total impedance upto the fault F2, Z2 p.u = 0.0459 +j0.2857 p.u
|𝑍2 𝑝.𝑢| = 0.289 p.u
Short circuit KVA fed into the fault at F2 = |𝐾𝑉𝐴2 𝑆.𝐶| =
|𝐾𝑉𝐴 𝑏|
|𝑍2 𝑝.𝑢|
=
10,000
0.289
= 34602 KVA
= 34.602 MVA
Short circuit KVA fed into the fault at F2 = 34.602 MVA
4. For the radial network shown in the figure, three phase fault occurs at F. Determine the fault
current and the line voltage at 11KV bus under fault conditions.

Solution.
Base MVA = 10 MVA
Base KV = 11KV
]2
x [
]
= j 0.15 x(11/11)2
x(10/10)
Znew = j 0.15 p.u
]2
x [
]
= j 0.125 x(11/11)2
x(10/10)
Znew = j 0.125 p.u
Transformer 1: primary side 𝑘𝑉𝑏,𝑛𝑒𝑤 = 11KV
Zp.u. new =j 0.1 x(11/11)2
x(10/10)
Znew = j 0.1 p.u
Transmission line: 𝑘𝑉𝑏,𝑛𝑒𝑤 = 11 x (33/11) = 33 KV
Z =
𝑍 𝑎𝑐𝑡𝑢𝑎𝑙
𝑍 𝑏𝑎𝑠𝑒
=
𝐾𝑉𝑏
2 x 𝑀𝑉𝐴 𝑏
𝑍 𝑎𝑐𝑡𝑢𝑎𝑙 = 0.27 + j0.36 Ω/km = (0.27 + j0.36) x 30 Ω
𝑍 𝑛𝑒𝑤 =
0.27+𝑗0.36
332
x 10 x 30 = 0.0744 +j0.0992 p.u
𝑍 𝑛𝑒𝑤 = 0.0744 + j0.0992 p.u
Transformer 2 : 𝑘𝑉𝑏,𝑛𝑒𝑤 = 33 KV (PY)
Zp.u. new =j 0.08 x(33/33)2
x(10/5)
Znew = j 0.16 p.u
Cable : 𝑍 𝑎𝑐𝑡𝑢𝑎𝑙 = (0.135 + j0.08) Ω/km = (0.135 + j0.06) x 3 Ω
Z =
=
𝐾𝑉𝑏
2 x 𝑀𝑉𝐴 𝑏 =
0.135 +𝑗0.08
6.62
x 3 x 10 = 0.093 +j0.0055 p.u

Fault current If =
𝐸 𝑇ℎ
𝑍 𝑇ℎ
=
1∠00
0.1674 + 𝑗0.4822
= 0.6425 - j1.85
= 1.959 ∠−70.850
p.u
Fault current If = 1.959 ∠−70.850
p.u
Base current, IB =
𝑀𝑉𝐴 𝑏
√3 𝑥 𝐾𝑉 𝑏
=
10 𝑥 103
√3 𝑥 6.6
= 874.77 Amp
IB = 874.77 Amp
[𝑘𝑉𝑏 for cable because fault point at F]
If = 1.959 ∠−70.850
p.u. x IB
= 1.959 ∠−70.850
x 874.77 =1714 Amp
If = 1714 Amp
Voltage at 11 KV bus : ZAF = j0.1 + 0.0744 +j0.0992 + j0.16 + 0.093 + j0.55
= 0.1674 + j0.4142
= 0.447 ∠67.990
p.u
Voltage at 11 KV bus = ZAF p.u x If p.u
= 0.447 ∠67.990
x 1.959 ∠−70.850
= 0.874 – j0.0436 = 0.875 p.u
= 0.875 x Base voltage
= 0.875 x11 = 9.615 KV
Voltage at 11 KV bus = 9.615 KV
5. A 25 MVA, 11 KV, 3φ generator has a subtransient reactance of 20 %. The generator supplies two
motors over a transmission line with transformers at both ends as shown in fig. The motors have rated
input of 15 and 7.5 MVA, both 10 KV and 20% subtransient reactance. The 3φ transformers are both
rated 50 MVA, 10.8/121 KV with delta-star connection with leakage reactance of 10% each. The series
reactance of the line is 80 Ω. Draw the impedance diagram of the system with reactances marked in
p.u. when symmetrical fault occurs at bus 2 and calculate fault current. (16)
Generator values:
G = 25 MVA; 11KV;𝑿 𝒅
′′
=20% M1 = 15 MVA; 10KV; 𝑿 𝒅
′′
=20% M2 = 7.5 MVA; 10KV; 𝑿 𝒅
′′
=20%
Transformer rating:
X=50MVA, 10.8/121 KV;Xd =10%
Transmission line rating : X = 80 Ω, MVAbnew = 25, MVAb =11KV

Generator
]2
x [
]
= j 0.2 x (11/11)2
x(25/25)
Znew = j 0.2 p.u
Transformer 1: (referred to primary)
KVb =11KV
]2
x [
]
= j 0.1 x (10.8/11)2
x(25/50)
Znew = j 0.0482 p.u
Transmission line:
KVb,new = KVb old x
𝐻.𝑇 𝑟𝑎𝑡𝑖𝑛𝑔 𝑜𝑓 𝑡𝑟𝑎𝑛𝑠𝑓𝑜𝑟𝑚𝑒𝑟 1
𝐿.𝑇 𝑟𝑎𝑡𝑖𝑛𝑔 𝑡𝑟𝑎𝑛𝑠𝑓𝑜𝑟𝑚𝑒𝑟 1
= 11 x
121
10.8
=123.24 KV
KVb,new =123.24 KV
Zp.u. new =
=
𝑗 80
𝐾𝑉𝑏
2 x MVAb =
𝑗 80 𝑥 25
123.242
= j0.1316 p.u
Zp.u. new = j0.1316 p.u
Transformer 2: (referred to primary)
]2
x [
]
= j 0.1 x (121/123.4)2
x(25/50)
Znew = j 0.482 p.u
Motor 1 :
KVb,new = KVb old x
𝐿.𝑇 𝑟𝑎𝑡𝑖𝑛𝑔 𝑜𝑓 𝑡𝑟𝑎𝑛𝑠𝑓𝑜𝑟𝑚𝑒𝑟 2
𝐻.𝑇 𝑟𝑎𝑡𝑖𝑛𝑔 𝑡𝑟𝑎𝑛𝑠𝑓𝑜𝑟𝑚𝑒𝑟 2
= 123.24 x
10.8
121
=11 KV
Zp.u. new = j 0.2 x (10/11)2
x(25/11)
= j0.2755 p.u
Zp.u. new = j0.2755 p.u
Motor 2 :
Zp.u. new = j 0.2 x (10/11)2
x(25/50)
= j0.551 p.u
Zp.u. new = j0.551 p.u

Impedance diagram
Fault occurs at bus 2, the circuit becomes.
Find ZTh.
ZTh =
𝑗0.2482 𝑥 [𝑗0.6136+𝑗0.1837]
𝑗0.2482 + 𝑗0.6136+𝑗0.1837
= j0.1893 p.u
ZTh = j0.1893 p.u
If =
𝐸 𝑇ℎ
𝑍 𝑇ℎ+𝑍 𝑓
=
1∠00
𝑗0.1893
= -j5.28 = 5.28 ∠ − 900
p.u
If = 5.28 ∠ − 900
p.u
Base current Ibase =
𝑀𝑉𝐴 𝑏
√3 𝑥 𝐾𝑉 𝑏
=
25 𝑥 106
√3 𝑥 123.24 𝑥 103
[𝐾𝑉𝑏 for secondary of transformer 1 or transmission line]
= 117.119 Amp.
Base current Ibase = 117.119 Amp.
Actual fault current = If x Ibase = 5.28 x 117.119 = 618.388 Amp.
Actual fault current = 618.388 Amp.

6. A 3-phase, 5 MVA, 6.6 kV alternator with a reactance of 8% is connected to a feeder of series
impedance of 0.12+j0.48 ohms/phase per km. The transformer is rated at 3 MVA, 6.6kV/3.3 kV 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.
Solution:
The single line diagram of the power system and the prefault reactance diagram are shown in fig
respectively. Let the point F be the point where fault occurs.
Let us choose generator rating as base values.
MVAb = 5 MVA and kVb = 6.6 kV
To find Eg and Vpf:
Here the generator is not delivering any load current and so the induced emf of the generator will be
same as operating voltage.
Actual value of induced emf, Eg = 6.9 kV
p.u. value of induced emf =
=
6.9
6.6
= 1.0455 p.u.
p.u. value of induced emf = 1.0455 p.u.
The prefault voltage, Vpf at the fault point F can be obtained using the transformer ratio as below.
Actual value of prefault voltage, Vpf = 6.9×
33
6.6
= 34.5 kV
The base kV referred to HT side of transformer = 6.6×
33
6.6
= 33 kV
 The p.u. value of the prefault voltage, Vpf =
=
34.5
33
= 1.0455 p.u.
Vpf = 1.0455 p.u.
Note: The open circuit p.u. value of voltage is same at every point in a series path irrespective of their actual
voltages.
To find generator reactance:
Since the rating of the generator is chosen as base value, the p.u. reactance of the generator will be
same as the specified value.
 p.u. reactance of the generator, Xd = 8% = 0.08 p.u.
Xd = 8% = 0.08 p.u.
To find transformer reactance:
The transformer reactance can be computed with respect to the new base using the following
equation.
Xpu,new = Xpu,old × (
𝑘𝑉b old
𝑘𝑉b new
)2
×
𝑀𝑉𝐴b,new
𝑀𝑉𝐴b,old
Here Xpu,old = 5% =0.05 p.u.
p.u. reactance of transformer, XT = 0.05×
66
6.6
×
5
3
= 0.0833 p.u.
XT = 0.0833 p.u.

To find feeder reactance:
The base impedance, Zb =
(𝑘𝑉b)2
𝑀𝑉𝐴b
=
(33)2
5
= 217.8 /phase.
Actual impedance of the feeder for a length of 15km, Zfeed = impedance/km  length
Zfeed = (0.12+j0.48)15 = 1.8+j7.2/phase
 p.u. value of the impedance of the feeder, Zfeed =
𝐴𝑐𝑡𝑢𝑎𝑙 𝑖𝑚𝑝𝑒𝑑𝑎𝑛𝑐𝑒
𝐵𝑎𝑠𝑒 𝑖𝑚𝑝𝑒𝑑𝑎𝑛𝑐𝑒
=
1.8+𝑗7.2
217.8
Zfeed = 0.0083+j0.0331 p.u.
To find fault current:
The prefault reactance diagram can be represented by Thevenin’s equivalent circuit shown. Here the
Thevenin’s voltage is the prefault voltage is the prefault voltage at fault point F and the Thevenin’s
impedance is the sum of three impedances in series.
Zth = jXd + jXT + Zfeed = j0.08 + j0.0833+ j0.0083 + j0.0331
= 0.0083 + j0.1964 p.u. = 0.196687.6 p.u.
Zth = 0.196687.6 p.u.
The fault in the feeder can be represented by a short circuit as shown. Now the current If through the
short circuit is the fault current.
p.u. value of fault current, If =
𝑉th
𝑍th
=
1.04550
0.196687.6
= 5.3179-87.6 p.u.
Note: The solution can also be attempted by neglecting the resistance of the feeder. In this case,
Zth = j0.1964 = 0.196490 p.u. and
If = 5.3233-90 p.u.
It is important to note that the error in neglecting the resistive component is negligible.
Base current, Ib =
𝑘𝑉𝐴b
√3𝑘𝑉b
=
𝑀𝑉𝐴b ×1000
√3𝑘𝑉b
=
5×1000
√3 ×33
= 87.4773 A.
Ib = 87.4773 A.
 Actual value of fault current, If = p.u. value of If  Ib = 5.3179-87.6  87.4773
If= 465.2-87.6 amps.
Result:
Fault current = 5.3179-87.6 p.u. or 465.2-87.6 A.

UNIT IV FAULT ANALYSIS – UNBALANCED FAULTS
PART - A
1. What is meant by symmetrical fault? (A/M 2018)
The fault is called symmetrical, if the fault current is equal in all the phases.
i.e. Ia = Ib = Ic
2. Explain the concept of sequence impedance and sequence networks. (A/M 2018)
One of the most powerful tools for dealing with unbalanced polyphase circuits is the method of
sequential components. An unbalanced system of n related phasors can be resolved into n systems of
balanced phasors called sequential components. Sequential newtorks are positive, negative and zero
sequence components.
3. What are the features of zero sequence current? N/D 2017, M/J 2014
It consists of three phasors equal in magnitude and with zero phase displacement from each other.
Zero sequence phasors a,b,c can be written as
0 0 0
a b cI I I 
Where 0 0 0
, ,a b cI I I are the sequence components of ,a b c
I I and I
4. Write down the equation to determine symmetrical currents from unbalance current.
N/D 2017, M/J 2016
 
0
2
2
0
2
2
,
1 1 1
1
1
3
1
1
3
1
3
1
3
a a
a b
a c
a a b c
a a b c
a a b c
Thesymmentrical componetsof currents are
I I
I a a I
I a a I
I I I I
I I aI a I
I I a I aI




     
          
         
  
    
    
5. Express the unbalance current in terms of symmetrical components. (A/M 2017)
0
0
2
2
2
, , .
, , .
1 1 1
1
1
1 120 1 240
a b c
a a a
a a
b a
c a
Let I I I betheunbalanced phasecurrents
Let I I I bethesymmetrical componentsof phase
I I
I a a I
I a a I
wherea and a
 


    
         
         
     
6. Draw the zero sequence network of Y - ∆ transformer with neutral ungrounded. (A/M 2017)

7. Why the neutral grounding impedance Zn appears as 3Zn in zero sequence equivalent circuit?
(N/D 2016)
Voltage drop is ZN*IN=ZN*3*I0
=I0
*3ZN. Therefore, to obtain the correct voltage drop seen
in the neutral conductor with a flow of only, model the zero sequence impedance as 3Zn.
8. What are symmetrical components of a 3ph system? (M/J 2016)
One of the most powerful tools for dealing with unbalanced polyphase circuits is the method
of symmetrical components. An unbalanced system of n related phasors can be resolved into n systems
of balanced phasors called symmetrical components. Symmetrical components are positive, negative
and zero sequence components.
9. State Fortescue theorem. (N/D 2015)
Fortescue's Theorem for a Three-Phase Unbalanced System. In 1918, C. L. Fortescue stated his
theorem: unbalanced phasors can be represented by systems of balanced phasors. Sequence
components were created to facilitate calculations in unbalanced circuits and systems.
10. Which type of fault is very common in power system? (N/D 2015)
Single line to ground fault is most common occurrence fault in power system.
It occurs about nearly 70 % in fault conditions.
11. What are the observation made from the analysis of various fault ? Nov/Dec 2013
 Finding out the value of Fault current under different fault conditions
 Zero sequence is not presence in LL fault conditions
 Positive and negative sequence component of currents are opposite and equal to each other in
LL fault condition
 Positive and negative sequence component of voltage are equal in LLG fault condition
12. Write the boundary condition for the single line to ground fault. Nov/Dec 2013
 If the generator is solidly grounded, Zn = 0 and for bolted fault or solid fault,
Zf = 0.
 If the neutral of the generator is ungrounded, the zero sequence network is open circuited.
0
0a a a fI I I and I 
   
13. Define negative sequence impedance. May/June 2013
Impedance offered to the flow of negative sequence current is known as negative sequence impedance
and it is denoted by Z-
. The negative sequence impedance is occurred in all the fault condition and it
is important to find the fault current.
14. What is positive, negative and zero sequence impedance?
 Impedance offered to the flow of positive sequence current is known as positive sequence
impedance and it is denoted by Z+
 Impedance offered to the flow of negative sequence current is known as negative sequence
impedance and it is denoted by Z-
 Impedance offered to the flow of zero sequence current is known as Zero sequence impedance
and it is denoted by Z0
15. What is the assumption made in short circuit studies?
 Representing machines by reactance namely X’’
, X’ and X
 Prefault load current are neglected
 Transformer tap are assumed to be nominal
 Shunt capacitance and series resistance are ignored and neglected

16. Find the fault current whose impedance are j0.2 & j015 in series and in parallel with j0.35 if
prefault voltage at the fault point is 0.97 p.u.?
Ans:
j0.2 and j0.15 are in series
Its becomes, j0.2 + j0.15 = j0.35
j0.35 is in parallel with j0.15.
0.35 0.15
0.105 . .
0.5 0.15
0.97
9.238 . .
0.105
Th
Th
f
Th
j j
Z j p u
j j
V
Fault current I j p u
Z j

 

  
17. Name the method of reducing short circuit capacity and uses of short circuit capacity.
 By introducing artificial series reactors
 By providing neutral reactance
 By introducing a large value of shunt reactance between buses.
18. What are the reactances used in synchronous machines?
"
'
1. tan
2. tan
3. tan .
d
d
d
Subtransient reac ce X
Transient reac ce X
Synchronous reac ce X
19. Define transient reactance.
It is the ration of induced emf on no-load and the transient symmetrical rms current.
It is given by,
'
| | 1
tan ,
1 1| '|
tan
tan
tan
g
d l
a f
l
f
a
E
Transient reac ce X X
I
X X
where X Leakagereac ce
X Field winding reac ce
X Armaturereactionreac ce
  




20. What is the significant of transient reactance in short circuit studies?
The subtransient reactance can be used to estimate the initial value of fault current immediately on the
occurrence of the fault. The maximum momentary short circuit current rating of the circuit breaker
used for protection or fault clearing should be less than this initial fault current.
21. Difference between Load flow and short circuit studies.
Load flow Studies Short circuit studies
The resistance and reactance are considered The resistance are neglected
To solve load flow analysis, the bus admittance
matrix is used
To solve short circuit analysis, the bus
impedance matrix is used
It is used to determine the exact voltage and
currents
Prefault voltage are assumed to be1 p.u. and the
prefault current can be neglected.
22. Why synchronous impedance more than transient reactance?
The short circuit is of larger magnitude than the current measured half a second later. This mean that
magnitude of Z will have a minimum value immediately following the fault and then grow. This
change of the short circuit current with time is due to the characteristics of the synchronous generators.
Thus the synchronous impedance is more than transient reactance.

PART – B
1. Explain the detail derivation for Sequence networks analysis of single line to ground(LG Fault)
N/D 2017, M/J 2016
Suppose a line to ground fault is occurs on phase a connected to ground through impedance Zf.
0
2
2
0
0 (1)
1 1 1
1
1 (2)
3
1
0,
1 1 1
1
1
3
a f a
b c
f a
a a
a b
a c
b c
a
a
a
V Z I
I I
I I
Symmetrical componetsofcurrents are
I I
I a a I
I a a I
Substitute for I I symmetrical componentsof currents are
I
I a a
I





 

     
          
         
 
 
 
 
 
 
2
2
0 (3)
1 0
aI
a a
   
   
   
      
0
0
(3),
3
3
3 3
(4)
3
a
a
a
a
fa
a
a
a a a
Fromeq we get
I
I
I
I
II
I
I
I I I


 


 
  

0
2
2
1 1 1
1 (6)
1
a a
b a
c a
The phasevoltageare givenby
V V
V a a V
V a a V


    
         
         
0
0
.(6) ,
a a a a
a f a
a a a f a
Fromeq we get
V V V V
FromtheconditionV Z I
V V V Z I
 
 
  

   
0
0
,
(7)
3
3
3
3
a
a
KK KK KK f
a
f a a
KK KK KK f
Substituting thesymmetrical components we get
E
I
Z Z Z Z
The fault current is
E
I I I
Z Z Z Z

 

 

  
  
  
2. Explain the derivation for Sequence networks analysis of line to line (LL Fault)
N/D 2016, A/M 2016
0( )
, 0, :
b c
a
b c f b c b f b
b c a
I I
I unloaded generator
V V Z I V V Z I
Substitute for I I I thesymmetrical componentsof current are


    
  
0
2
2
1 1 1
1
1
3
1
a a
a b
a c
I I
I a a I
I a a I


     
          
         
0 0 0
0 0 0 0
,
0 0 0
0 0
0 0 0
(5)
a KK a
a a KK a
a KK a
a KK a KK a
a a KK a
a KK a KK a
From sequencenetwork of generator symmetrical
voltages are givenby
V Z I
V E Z I
V Z I
V Z I Z I
V E Z I
V Z I Z I
  
  

  
   
      
             
            
   
 
   

0
2
2
1 1 1 0
1
1
3
1
a
a b
a b
I
I a a I
I a a I


     
          
         
2 2
,
( ) ( )
b
a a a f
a a
Substitutethevalueof I we get
a a V V a a I Z
V V
  
 
     

 0
2
2
0
1
0 0
3
1
3
1
3
0
a b b
a b b
a b b
a a a
I I I
I aI a I
I a I aI
I I and I


 
   
   
   
  
0
2 2
2 2
2 2
2 2
1 1 1 1 1 1 0
1 1
1 1
0, ( )
( )
a a
b a a
c a a
a b a a a
c a a a b
The Phasecurrent are givenby
I I
I a a I a a I
I a a I a a I
I I a I aI I a a
I aI a I I a a I
 
 
  
  
        
                 
                
    
     
2
2
0
2
2
1 1 1 0
1
1
0
a
b a
c a
a
a a a
b a a
c a a
The Phasevoltageare
V
V a a V
V a a V
V
V V V
V a V aV
V aV a V


 
 
 
     
          
          

 
 
 
2
,
( )
b c f b
b c
a a f b
FromtheconditionV V Z I
SubstitutingV andV we get
a a V V Z I 
 
    
2 2
,
( ) ( )
b
a a a f
a a
Substitutethevalueof I we get
a a V V a a I Z
V V
  
 
     

0
, , ,
0
a a
a K K f a
a
a
K K f
a a
a
SubstitueV V we get
E Z Z Z I
E
I
Z Z Z
I I
I
 
  

 
 
    

 
 


0
2 2 2
2 2 2
2
min
1 1 1 0 0
1 0 ( ) ( )
1 0 ( ) ( )
( )
( 0.5 0.866 0.5 0
a a a a
b a a a
c a a a
b c a
Current phasedo e
I I I I
I a a I a a I a a I
I a a I a a I a a I
The fault current is I I a a I
j j
 
  
  

         
                    
                   
   
     .866) 1.732
3
a a
a
I j I
j I
 

 
 
,
3
a
a
f b
KK KK f
Substituting I we get
j E
I I
Z Z Z

 

 
 
3. Explain the derivation for Sequence networks analysis of Double line to ground fault (LLG
Fault) N/D 2015, A/M 2015
A three phase generator with a fault on phases b and c through an impedance Zf to ground.
0
( ) (1)
:
a
b c f
b c f f f b c
I
I I I
V V Z I Z I I
Thesymmetrical componentsof voltageare

 
   
0
2
2
1 1 1
1
1 (2)
3
1
a a
a b
a c
V V
V a a V
V a a V


     
          
         
Substitute Vb =Vc in equation (2), we get
0
2
2
1 1 1
1
1
3
1
a a
a b
a b
V V
V a a V
V a a V


     
          
         

0 1
( 2 )
3
1
( )
3
1
( )
3
(3)
a a b
a a b
a a b
a a
V V V
V V V
V V V
V V


 
 
 
 

0
2
2
0
0 2
0 2
0 2 0 2
0 2 2
1 1 1
1
1
2 ( ) ( ) (4)
a a
b a
c a
a a a a
b a a a
c a a a
f b c a a a a a a
a a a
The Phasecurrent are givenby
I I
I a a I
I a a I
I I I I
I I a I aI
I I aI a I
I I I I a I aI I aI a I
I I a a I a a


 
 
 
   
 
    
         
         
  
  
  
       
    
0
0
0
( ) (5)
(5) (6),
3
, 3 (6)
a a a
b c a
b f a
I I I
substituting in we get
I I I
Fromthecondition V Z I
 
  
 

0
2
2
0
0 2
0 0
1 1 1
1
1
3 (7)
a a
b a
c a
a a a a
b a a a a a
b a a b f a
The Phasevoltageare
V V
V a a V
V a a V
V V V V
V V a V aV V V
V V V V Z I


 
   

    
         
         
  
     
     
0 0 0
(8)
a KK a
a a KK a
a KK a
Thesymmetrical componentsvoltageis givenby
V Z I
V E Z I
V Z I
  
  
 
 
 
0
0
[ ]
(9)
3
a KK a
a
KK f
E Z I
Then I
Z Z
 
 


[ ]
(10)a KK a
a
KK
E Z I
I
Z
 


 

0
0
a a a
a a a
I I I
I I I
 
 
  
  

0
0
( 3 )
3
a
a
KK KK f
KK
KK f KK
onby solving we get
E
I
Z Z Z
Z
Z Z Z







 
00
0
3
( 3 )3
3
KK a
f a
KK KK fKK f
KK
KK KK f
Z E
I E
Z Z ZZ Z
Z
Z Z Z




 
 
  
 
 
   
4. Determine the fault current and MVA at faulted bus for a line to ground (solid) fault at bus 4 as
shown in fig. A/M 2018, N/D 2017, A/M 2017
G1,G2: 100MVA, 11KV, X+
= X-
=15%, X0
=5%, Xn
=6%
T1,T2: 100 MVA, 11 KV/220KV, Xleak= 9%
L1,L2: X+
= X-
=10%, X0
=10%, on a base of 100 MVA.Consider a fault at phase ‘a’
Sol :-
Step 1 : Positive sequence thevenin equivalent viewed from bus 4:
Step 2: Negative sequence thevenin equivalent viewed fron bus 4:

. 2
2
0.121
0.121
100 0.1
11
0.1 0.1 .
0.1 0.1
0.05
0.1 0.1
new
p u
Actual value j
For transmissionlineZ BaseMVA
Basevalue Base KV
j
j
j and j arein parallel
j j
j
j j
  
  



0
0
0
0
44 44 44
.
1 0
1 0
0.1075 0.1075 0.1533
2.7152
3 3 2.7152
8.1455 .
( )
100
8.1455 42.75
3 11
3
a
a a a
f
f a
f p u
prefault voltage E V
I I I
V
Z Z Z Z
j j j
j
I I j
j p u
Actual fault current KA I Basecurrent
KA
Fault MVA KV
 
 

   
 

  
 

 
 
   
 
 
  

 
3 11 42.75 814.55
KA
   

EE6501 - Power System Analysis

EE6501 - Power System Analysis

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