POWER SYSTEM ANALYSIS
UNIT – 1
PART – A (2 MARKS)
1. What is single line diagram?
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.
2. What are the components of power system?
The components of power system are Generators, power Transformers,
Transmission lines, Substation Transformers, Distribution Transformers and Loads.
3. Define per unit value.
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.
Actual Value
Per unit Value = 
Base Value
4. What is the need for base values?
The components or 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 components of power system are expressed with
reference to a common value called base value. Hence for analysis purpose a base value
is chosen for voltage, power, current and impedance. Then all the voltage power, current and impedance ratings of the components are expressed as a percent or per unit of the
base value.
9. What is impedance and reactance diagram?
The impedance diagram is the equivalent circuit of power system in which the
various components of power system are represented by their approximate or simplified
equivalent circuits. The impedance diagram is used for load flow studies. The reactance
diagram is the simplified equivalent circuit of power system in which the various
components are represented by their reactance. The reactance diagram can be obtained
form impedance diagram if all the resistive components are neglected. The reactance
diagram is used for fault calculations.
10. What are the factors that need to be omitted for an impedance diagram to reduce it to a
reactance diagram?
(or)
What are the approximations made in reactance diagram?
The following approximations are made in reactance diagram.
1. The neutral reactances are neglected.
2. Shunt branches in the equivalent circuits of transformer are neglected
3. The resistances are neglected.
4. All static loads and induction motors are neglected.
5. The capacitances of the transmission lines are neglected.
11. What is a bus?
The meeting point of various components in a power system is called a bus. The
bus is a conductor made of copper or aluminum having negligible resistance. The buses
are considered as points of constant voltage in a power system.
12. What is bus admittance matrix?
The matrix consisting of the self and mutual admittances of the network of a power
system is called bus admittance matrix. It is given by the admittance matrix Y in the node
basis matrix equation of a power system and it is denoted as Ybus
. The bus admittance
matrix is symmetrical.
13. What is bus impedance matrix?
The matrix consisting of driving point impedances and impedances of the network
of a power system is called bus impedance matrix. It is given by the inverse of bus
admittance matrix and it is denoted as Zbus
. The bus impedance matrix is symmetrical.
14. Write the four ways of adding an impedance to an existing system so as to modify bus
impedance matrix.
To modify a bus impedance matrix, a branch of impedance Zb can be added to
original system in the following four different ways.
Case 1: Adding a branch of impedance Zb from a new busp to the reference bus.
Case 2: Adding a branch of impedance Zb from a new busp to the existing busq.
Case 3: Adding a branch of impedance Zb from an existing busq to the reference bus.
Case 4: Adding a branch of impedance Zb
between two existing buses h and q.
15. How the Zbus is modified when a branch of impedance Zb is added from a new busp to
the reference bus?
When a branch of impedance Zb is added from a new busp to the reference bus, the
order of the bus impedance matrix increases by one.
Let the original bus impedance matrix have an order of n and so the new bus
impedance matrix have an order of (n+1). The first n x n sub matrix of new bus impedance
matrix is the original bus impedance matrix. The elements of (n+1)th column and row are all
zeros except the diagonal. The (n+1) diagonal element is the added branch impedance Zb .
16. What are symmetrical components?
An unbalanced system of N related vectors can be resolved into N systems of
balanced vectors. The N – sets of balanced vectors are called symmetrical components.
Each set consists of N – vectors which are equal in length and having equal phase angles
between adjacent vectors.
17. What are sequence impedance and sequence networks?
The sequence impedances are 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 the
current of any one sequence only is called sequence network.
PART  B
UNIT – 2
PART – A (2 MARKS)
1. What is power flow study or load flow study?
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 linelosses.
2. 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.
(i) Representation of the system by single line diagrams.
(ii) Determining the impedance diagram using the information in single line
diagram.
(iii) Formulation of network equations.
(iv) Solution of network equations.
3. List the quantities specified and the quantities to be determined 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.
4. Define Voltage controlled bus.
A bus is called voltage controlled bus if the magnitude of voltage 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.
5. What is PQbus?
A bus is called PQbus or load bus when real and reactive components of power
are specified for the bus. In a load bus the voltage is allowed to vary within permissible
limits.
6. What is swing bus (or slack bus)?
A bus is called swing bus for (or slack 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.
7. What is the need for slack bus?
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.
8. Write the expression for complex power injected to a bus.
The complex power injected to busp of a nbus system is given by
11. Discuss the effect of acceleration factor in the load flow solution algorithm. How will
you account for voltage controlled buses in this algorithm?
In load flow solution by iterative methods, the number of iterations can be
reduced if the correction voltage at each bus is multiplied by some constant. The
multiplication of the constant will increase the amount of correction to bring the
voltage closer to the value it is approaching. The multipliers that accomplish this
improved convergence are called acceleration factors. An acceleration factor of 1.6 is
normally used in load flow problems. Studies may be made to determine the best
choice for a particular system.
The acceleration factor is a real quantity and it modifies the magnitude of
voltage alone. Since in voltage controlled bus (generator bus), the magnitude of bus
voltage is not allowed to change, the acceleration factor is not used for voltage
controlled bus. (i.e acceleration factor is used only for load bus)
12. Why do we go for iterative methods to solve flow problems?
The load (or power) flow equations are nonlinear equations and so explicit
solution is not possible. The solution of nonlinear equations can be obtained only by
iterative numerical techniques.
13. What will be the reactive power and bus voltage when the generator bus is treated as
load bus?
When the generator bus is treated as load bus the reactive power of the bus is
equated to the limit it has violated, and the previous iteration value of bus voltage is used
for calculating current iteration value.
14. Compare the GS and NR methods of load flow solutions.
15. How the convergence of NR method is speeded up?
The convergence can be speeded up in NR method by using Fast Decoupled
Load Flow (FDLF) algorithm. In FDLF method the weak coupling between P and QV
are decoupled and then the equations are further simplified equations are further
simplified using the knowledge of practical operating conditions of a power system.
16. How the disadvantages of NR method are overcome?
The disadvantage of large memory requirement can be overcome by decoupling the
weak coupling between P and QV. (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.
17. What is the need for voltage control in a power system?
The various components of power system (or equipments connected to power
system) are designed to work satisfactorily at rated voltages. If the equipments are not
operated at rated voltages then the performance of the equipments will be poor and the
life of the equipment will reduce. Hence the voltages are various points in a power
system should be maintained at rated value. (Specified value).
18. Mention the various methods of voltage control employed in power system.
The various methods of voltage control in a power system are.
1. Voltage control by adjusting the excitation of generators.
2. Voltage control using shunt capacitors.
3. Voltage control using series capacitors.
4. Voltage control by synchronous capacitors.
5. Voltage control by tapchanging transformer.
6. Voltage control by regulating and booster transformer.
19. What is infinite bus?
A bus is called infinite bus if its voltage remains constant and does not alter by any
changes in generator excitation.
20. How the reactive power of a generator is controlled?
The reactive power of a generator is controlled by varying the magnitude and
phase of induced emf, which in turn varied by varying excitation. For an increase in
reactive power the magnitude of induced emf is increased and its phase angle is
decreased. For a reduction in reactive power the magnitude of induced emf is decreased
and its phase angle is increased.
21. What are the drawbacks in voltage control using generator excitation?
The generators have a limit for excitation variation. Reducing the excitation
below a certain limit may result in instability and increasing the excitation above a limit
may result in over heating of the generator rotor. Hence larger reactive power demand
cannot be met by excitation control. Also, the voltage regulation by varying excitation is
limited to permissible voltage rise at the sending end.
22. What is the disadvantage in reactive power compensation by shunt capacitors and
how it is overcome?
The disadvantage in reactive power compensation by shunt capacitors is that
with the fall in bus voltage the reactive power supplied by capacitor reduces. Similarly on
light loads, when the reactive power required is less the capacitor output will be large.
This disadvantage can be eliminated by connecting number of capacitors in parallel and
then the capacitance can be varied by switching ON or OFF depending on the
requirement.
23. What is the drawback in series connected capacitor?
The drawback in series connected capacitor is the high voltage produced
under short circuit (fault) conditions. This high voltage may damage the capacitor.
Therefore the capacitor has to be protected using a spark gap with a high speed
contactor.
24. Compare the reactive power compensation by shunt and series capacitors.
1. The voltage boost due to a shunt capacitor is evenly distributed over the
transmission line whereas the series capacitor provide a sudden change in
voltage at the point where it is connected.
2. It can be proved that for same voltage boost the reactive power capacity of
shunt capacitor is greater than that of a series capacitor.
3. The shunt capacitor improves the power factor of the load but the series
capacitor has little effect on the power factor.
4. The series capacitors are effective in improving the system stability when
introduced in long transmission lines.
25. What are the advantages of synchronous capacitors over static capacitors?
1. In synchronous capacitors the reactive power can be smoothly varies
whereas in static capacitors only stepped variation is possible.
2. The synchronous capacitors can deliver or absorb reactive power but the
static capacitors can only deliver reactive power and cannot absorb
reactive power.
3. The synchronous capacitors can be overloaded for short periods, whereas
the static capacitors cannot be overloaded.
4. For large reactive power outputs synchronous capacitors are less costlier
than the static capacitors.
26. What is the main difference in voltage control by capacitors and transformers?
When capacitors are employed the voltage control is achieved by injecting or
absorbing reactive power at appropriate points in power system. But in voltage control by
transformers, the voltage is regulated by providing a small boost or buck to the
transmission line voltages by altering the voltage ratios of the transformer.
27. What is regulating transformer and booster transformer?
A type of transformer designed for small adjustment of voltage rather than for
changing the voltage levels is called a regulating transformer.
The booster transformer (or series transformer) is a transformer used for
boosting or bucking the voltages in a transmission line by connecting one of the winding
in series with the line. Usually the other winding of booster transformer is excited by
regulating transformer.
28. What is offnominal transformer ratio? Draw the equivalent circuit of a transformer
with offnominal transformer ratio connected to a transmission line.
When the Voltage or turns ratio of a transformer is not used to decided the ratio of
base kV then its voltage or turns ratio is called offnominal turns ratio. Usually the voltage
ratio of regulating transformer will be offnominal ratios.
The equivalent circuit of a transformer with offnominal ratio, and connected to a
transmission line of admittance y is shown below
PART – B
1. Derive load flow algorithm using Gauss – Seidel method with flow chart and discuss
theadvantages of the method.
(16)
2. Derive load flow algorithm using NewtonRaphson method with flow chart and state the
importance of the method.
(16)
3. Explain clearly the algorithmic steps for solving load flow equation using Newton –
Raphson method (polar form) when the system contains all types of buses. Assume
that
the generators at the PV buses have adequate Q Limits.
(16)
4. Explain the step by step procedure for the NR method of load flow studies.
(16)
5. Find the bus admittance matrix for the given network. Determine the reduced admittance
matrix by eliminating node 4. The values are marked in p.u.
(16)
6. Find the bus impedance matrix for the system whose reactance diagram is shown in fig.
All the impedances are in p,u.
(16)
7. (i) Derive the power flow equation in polar form.
(8)
(ii)Write the advantages and disadvantages of GaussSeidel method and
NewtonRaphson method.
(8)
8. The parameters of a 4bus system are as under:
Draw the network and find bus admittance matrix.
(16)
9. With a flow chart, explain the NR Iterative method for solving load flow problem.
(16)
10. (i) Compare GaussSeidel method and NewtonRaphson method of load flow studies
(6)
(ii) Fig.12 shows a three bus power system.
Bus 1 : Slack bus, V= 1.05/00 p.u.
Bus 2 : PV bus, V = 1.0 p.u. Pg = 3 p.u.
Bus 3 : PQ bus, Pl = 4 p.u., Ql = 2 p.u.
Carry out one iteration of load flow solution by Gauss Seidel method. Neglect limits on
reactive power generation.
UNIT – III
PART – A (2 MARKS)
1. 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.
2. How the faults are classified?
In one method of classification, the faults are classified as shunt and series
faults. The shunt faults are due to short circuits in conductors and the series faults are
due to open conductors.
In another method of classificat6ion, the faults are classified into symmetrical and
unsymmetrical faults. In symmetrical faults the fault currents are equal in all the phases
unbalanced and so they can be analyzed only using symmetrical components.
3. List the various types of shunt and series faults.
The various types of shunt faults are
(i) Linetoground fault
(ii) Linetoline fault
(iii) Double linetoground fault
(iv) Three phase fault.
The various types of series faults are
(i) One open conductor fault
(ii) Two open conductor fault.
4. Name the main differences in representation of power system for load flow and short
circuit studies.
(i) For load flow studies both the resistances and resistances are reactance
are considered whereas for fault analysis the resistances are neglected.
(ii) For load flow studies the bus admittance matrix is useful whereas for short
circuit studies bus impedance matrix is used.
(iii) The load flow study is performed to determine the exact voltages and
currents whereas in short circuit studies the voltages can be safely
assumed as 1 pu and the prefault current can be neglected.
5. For a fault at a given location, rank the various faults in the order of severity. In a
power system relatively the most severe fault is three phase fault and less severe
fault is open conductor fault.
The various faults in the order of decreasing severity are given below.
(i) 3Phase fault
(ii) Double linetoground fault
(iii) Linetoline fault
(iv) Single linetoground fault
(v) Open conductor faults.
6. What is the need for short circuit studies or fault analysis?
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.
7. 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.
8. 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.
9. 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.
10. Define sub transient reactance.
The sub transient reactance is the ratio of induced emf on noload and the sub
transient symmetrical rms current, (i.e, it is the reactance of a synchronous machine
under transient condition)
11. What is the significance of subtransient 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.
12. How symmetrical faults are analyzed?
The symmetrical faults are analyzed using per unit reactance diagram of the
power system. Once the reactance diagram of the power system is formed then the fault
is simulated by short circuit (or by connecting the fault impedance at the fault point). The
currents and voltages at various parts of the system can be estimated by any one of the
following method.
(i) Using Kirchoff’s laws
(ii) Using Thevenin’s theorem
(iii) By forming bus impedance matrix.
13. What are the main factors to be considered to select a circuit breaker?
The choice of a circuit breaker for particular application depends on the following
ratings of the circuit breaker.
i.) Normal working power level specified as rated interrupting current or rated
interrupting MVA.
ii.) The fault level specified as either rated short circuit interrupting current or rated
short circuit interrupting MVA.
iii.) Momentary current rating.
iv.) Speed of circuit breaker.
14. Why the circuit breaker interrupting current is asymmetrical?
The interrupting current of circuit breaker is the sum of symmetrical short circuit
current and dcoffset current. The presence of dcoffset current makes the interrupting
current as asymmetric.
15. What is momentary current rating of circuit breaker? How it si estimated?
The momentary current rating is the maximum current that may flow through a
circuit breaker for a short duration. It is estimated by multiplying the symmetrical subtransient
fault current by a factor of 1.6 (The factor 1.6 accounts for dcoffset current
during subtransient period).
16. Define short circuit interrupting MVA of a circuit breaker.
The short circuit interrupting MVA of a circuit breaker is the voltamperes (power)
flowing through it at the moment of opening its contacts due to a fault.
It is estimated by the following equations.
PART – B
reactance 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.u. The output current of generator is 1 p.u. and 0.8 p.f. leading. Find the
sub transient current in p.u. in the fault, generator and motor. Use the terminal voltage of
generator as reference vector.
(16)
2. Explain the step by step procedure for systematic fault analysis using bus impedance
matrix.
(16)
3. A 60 MVA, Y connected 11 KV synchronous generator is connected to a 60 MVA, 11/132
KV /Y transformer. The sub transient reactance X”d 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. 3 Find the
sub transient symmetrical fault current in p.u. amperes and actual amperes on both side of
the transformer. Phase to neutral voltage of the generator at no load is 1.0 p.u.
(16)
4. A three –phase transmission line operating at 33 KV and having a resistance and
reactance of 5 Ohms and 15 Ohms respectively is connected to the generating station busbar
through a 5000 KVA step up transformer which has a reactance of 0.05 p.u. Connected to
the busbars 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.
(16)
5. A synchronous generator and a synchronous motor each rated 25 MVA, 11 KV having 15%
subtransient reactance are connected through transformers and a line as shown in fig. The
transformers are rated 25 MVA< 11/66 KV and 66/11 KV with leakage reactance of 10%
each. The line has a reactance of 10% on a base of 25 MVA, 66 Kv. The motor is drawing 15
MW at 0.5 power factor leading and a terminal voltage of 10.6 KV. When a symmetrical 3
phase fault occurs at the motor terminals. Find the subtransient current in the generator,
motor and fault.
6. A three phase power of 700 MW is to be transmitted to a substation located 315 kM from
the source of power. For a preliminary line design assume the following parameters:
Vs = 1.0 p.u., Vr + 0.9 p.u. = 5000 km ; zc = 320
, and S = 36.870 .
(i) Based on the practical line load ability equation, determine a nominal voltage level
for
the transmission line.
(8)
(ii) For the transmission voltage level obtained in (i) Calculate the theoretical maximum
power that can be transferred by the transmission line.
(8)
7. A 25,000 KVA, 13.8 kV generator with X”d = 15% is connected through a transformer to a
bus which supplies four identical motors as shown in Fig. 7 The sub transient reactance X”d of each motor is 20% on a base of 5000 KVA, 6.9 kV. The threephase rating of the transformer
is 25,000 KVA, 13.8/6.9 kV, with a leakage reactance of 10%. The bus voltage at the motors
is 6.9 kV when a threephase fault occurs at point p. for the fault specified, determine (i) the
sub transient current in the fault (ii) the sub transient current in breaker A and (iii) the
symmetrical shortcircuit interrupting current in the fault and in breaker A.
(16)
8 Determine Zbus for the network shown below in Fig. 8 where the impedances labeled 1
through 6 are shown in per unit. Preserve all buses.
(16)
Fig. 8 Branch impedances are in p.u. and branch numbers are in parentheses.
8. With a help of a detailed flowchart, explain how a symmetrical fault can be analyzed using
Zbus ?
(16)
8. (i) For the radial network shone below a three phase fault occurs at F. Determine the fault
current and the line voltage at 11 kV bus under fault conditions.
(6)
(ii) Explain the procedure for making shortcircuit studies of a large power system networks
using digital computers.
(10)
9. Two synchronous machines are connected through three phase transformers to the
transmission line shown in Fig.11 the ratings and reactance of the machines and
transformers are
Machine 1 and 2 : 100 MVa, 20kV; X”d = X1 = X2 = 20%
X0 = 4%, Xn = 5%
Transformers T1 and T2 : 100 MVA, 20 /345 YkV ; X = 8%.
On a chosen base of 100 MVA, 345 kV in the transmission line circuit the line reactances
are X1 = X2 = 15% and X0 = 50%. Draw each of the three sequence networks and find the
zero sequence bus impedance matrixes by means of Zbus building algorithm.
(16)
UNITIV
PART – A (2 MARKS)
1. Name the various unsymmetrical faults in a power system.
The unsymmetrical faults in a power system are.
(i) Single line –toground fault
(ii) Line–toline fault
(iii) Double linetoline ground fault
(iv) Open conductor fault.
2. Name the faults which the zero sequence currents flowing
In line to line faults the zero sequence current do not flow.
3. Define positive sequence impedance.
PART B
1. Derive the expression for fault current in LinetoLine fault on an unloaded generator in
terms of symmetrical components.
(16)
2. Determine the fault current and MVA at faulted bus for a line to ground (solid) fault at
bus 4 as shown in Fig.2
3. A single line to ground fault occurs on bus 4 of the system shown in Fig.3
(i) Draw the sequence networks and
(12)
(ii) Compute the fault current.
(4)
4.. Draw the Zero sequence diagram for the system whose one line diagram is shown in
fig.
(16)
5. Two synchronous machines are connected through threephase transformers to the
transmission line as given below in Fig. 5. The ratings and reactance of the machines
and transformers are
Machines 1 and 2 : 100 MVA, 20 Kv; X”d = X 1 = X2 = 20%
X0 = 4%; Xn = 5%.
Transformers T1 and T2 : 100 Mva, 20y/345 YkV ; X= 8%
Both transformers are solidly grounded on two sides. On a chosen base of 100 MVA,
345 kV in the transmission line circuit the line reactance are X1 =X2 = 15% and X0 =
50%. The system is operating at nominal voltage without prefault currents when a
bolted (Zf = o) single linetoground fault occurs on phase A at bus (3) Using the bus
impedance matrix for each of the three sequence networks, determine the sub
transient current to ground at the fault. (16)
6. Determine the positive, negative and zero sequence networks for the system shown in
Fig. 6. Assume zero sequence reactance for the generator and synchronous motors as
0.06 p.u. current limiting reactors of 2.5
are connected in the neutral of the generator
and motor No.2 The zero sequence reactance of the transmission line is j 300
.
(10)
7. Develop the connection of sequence network when a line to line fault occurs in a power
network.
(16)
8. Derive the expression for fault current in double line to ground fault on unloaded
generator. Draw an equivalent network showing the inter connection of networks to
simulate double line to ground fault
(16)
UNIT – V
PART – A (2 MARKS)
1. Define Steady state stability.
The steady state stability is defined as the ability of a power system to remain
stable (i.e, without loosing synchronism) for small disturbances.
2. Define transient stability.
The transient stability is defined as the ability of a power system to remain stable
(i.e., without loosing synchronism) for large disturbances.
3. What is steady state stability limit?
The steady stability limit is the maximum power that can be transmitted by a
machine (or transmitting system) to a receiving system without loss of synchronism. In
study state the power transferred by synchronous machine 9or power system) is always
less than the steady state stability limit.
4. What is transient stability limit?
The transient stability limit is the maximum power that can be transmitted by a
machine 9or transmitting system) to a fault or a receiving system during a transient state
without loss of synchronism. The transient stability limit is always less than the steady
state stability limit.
5. How stability studies are classified, what are they?
The stability studies are classified depending on the nature of the disturbance.
Depending on the nature of disturbance the stability studies can be classified into the
following three types.
1. Steady state stability
2. Dynamic stability
3. Transient stability.
6. In a 3 machine system having ratings G1’ G2 and G 3 and inertia constants M1’ M2 and
M3’ what is the inertia constants M and H of the equivalent system.
7. Define synchronizing coefficient. For what value of synchronizing coefficient the system
remains stable.
The term Pmax cos o is called synchronizing coefficient is positive. It is positive
when O
o /2.
8. Define swing curve. What is the use of swing curve?
The swing curve is the plot or graph between the power angle and t.
It is usually plotted for a transient state to study the nature of variation in for a sudden
large disturbance. From the nature of variations of the stability of a system for any
disturbance can be determined.
9. Give the simplified power angle equation and the expression for Pmax
The simplified power angle equation for a generator feeding energy to infinite bus is
given by,
10. Define power angle.
The power angle (or torque angle) is defined as the angular displacement of the
rotor from synchronously rotating reference frame.
11. Define critical clearing time and critical clearing angle and give equations for both.
The critical clearing angle, cc is the maximum allowable change in the power
angle
before clearing the fault, without loss of synchronism. The time corresponding to this
angle
is called critical clearing time, tcc. The critical clearing time, tcc can be defined as the
maximum time delay that can be allowed to clear a fault with out loss of synchronism.
12. List the methods of improving the transient limit of a power system.
The following are the methods used to improve the transient stability of a system.
(i) Increase of system voltage and use of AVR (Automatic Voltage
Regulation)
(ii) Use of high speed excitation systems.
(iii) Reduction in system transfer reactance.
(iv) Use of high speed enclosing breakers.
13. State equal area criterion.
The equal area criterion for stability states that the system is stable if the area
under Pa – curve reduces to zero at some value of .
This is possible only if the positive (accelerating) area under Pa – curve for a finite
change in . Hence this stability criterion is called equal area criterion.
14. A 50Hz, 4 pole turbo generator of rating 20 MVA, 13.2 kV has an inertia constant of H =
9 kW – sec/kVA. Find the kinetic energy stored in the rotor at synchronous speed.
15. Find the frequency of oscillation for a synchronizing coefficient of 0.6, inertia constant,
H = 4 and system frequency of 50 Hz .
PART B
1. Derive swing equation used for stability studies in power system.
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2. Explain the modified Euler method of analyzing multi machine power system for
stability with a neat flow chart.
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3. (i) Derive swing equation for a synchronous machine.
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(ii) 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
reactance between the generator and the infinite bus to 500% of the value before the
fault. When the fault is isolated, the maximum power that can be delivered is 75% of
the original maximum value. Determine the critical clearing angle for the condition
described.
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4. Find the critical clearing angle for clearing the fault with simultaneous opening of the
breakers 1 and 2. The reactance values of various components are indicated on the
diagram. The generator is delivering 1.0 p.u. power at the instant preceding the fault.
The
fault occurs at point p as shown in the figure.
5 In the system shown in Fig. 5 a three phase static capacitive reactor of reactance 1 p.u.
per phase in connected through a switch at motor bus bar. Calculate the limit of steady
state power with and without reactor switch closed. Recalculate the power limit with
capacitance reactor replaced by an inductive reactor of the same value.
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Assume the internal voltage of the generator to be 1.2 pu. and motor to be1.0 p.u.
6. Describe the RungeKutta method of solution of swing equation for multimachine
systems.
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7. (i) Derive the swing equation of a synchronous machine swinging against an infinite
bus. Clearly state the assumption in deducing the swing equation.
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(ii) The generator shown in Fig. 7 is delivering power to infinite bus. Take Vt = 1.1 p.u.
Find the maximum power that can be transferred when the system is healthy.
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9. (i) A 2pole 50 Hz, 11kV turbo alternator has a ratio of 100 MW, power factor 0.85
lagging. The rotor has a moment of inertia of 10,000 kgm2. Calculate H and M.
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(ii)A three phase fault is applied at the point P as shown below. Find the critical
clearing angle for clearing the fault with simultaneous opening of the breakers 1 and 2.
The reactance values of various components are indicated in the diagram. The generator is delivering 1.0 p.u. power at the instant preceding the fault.
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10. Describe the equal area criterion for transient stability analysis of a system.
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