PALLAVAN COLLEGE OF ENGINEERING - THIMMASAMUDRAM
DEPARTMENT OF ELECTTICAL AND ELECTRONICS ENGINEERING
EE2351 - POWER SYSTEM ANALYSIS.
UNIT 1
PART
A 2 Marks
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
What is meant by percentage reactance
Define per unit Quantity. Write equation for base impedance with respect to 3 phase system
What are the approximation used to draw an impedance diagram
Define load factor
Define single line diagram
What is the need for analysis planning and operation of a power system
What are the advantage of per unit system
What are the two methods available to find Y bus
List the different components of a power system
What are the approximation used to draw an reactance diagram
What is power system analysis?
Draw the π circuit representation of a transformer with off nominal tap ratio
Write the equation for converting the per unit impedance expressed in one base to another
base.
14. What is the new per unit impedance if the new base MVA is twice the old base MVA?
15.How the generator is represented in transient analysis?
16. What is the advantage of building algorithm over other methods of forming Z bus?
17. Give the methods available for forming bus impedance matrix
18. What is bus?
19. What are the applications of Y bus and Z bus matrix?
20. What do you meant by transient and steady state conditions?
21.What is the need for finding the YBUS Matrix?
22. Draw the equivalent circuit for a three winding transformer
23. How the loads are represented in reactance or impedance diagram?
24. Explain the four cases of bus building algorithm
25. Draw the simple per phase model for a cylindrical rotor synchronous machine
26. what condition on base and rated voltage should be satisfied to give equal pu impedance
viewed from either side of two winding transformer
27. If the reactance in ohms is 15 ohms, find the per unit value for a base of 15 kVA and 10kV.
28. A 3 phase generator with rating 1000 KVA 33 KV has its armature resistance and
synchronous reactance 20 ohm/phase and 70 ohm/phase calculate per unit impedance of
Generator
29. The reactance of a generator designated X’’ is given as 0.2 per unit based on the generator’s
name plating of 20 kV, 500 MVA. The base for calculations is 22kV, 100 MVA. Find X’’ on
the new base.
PART B – 16 marks
1. The one line diagram of a power system is shown in figure. The three phase power and line
to line ratings are given below.
(Nov/Dec
2012)
G
:
80 MVA
22kV
X=9%
T1
:
50 MVA
22/220kV
X=10%
T2
:
40 MVA
220/22kV
X=6%
T3, T4 :
40 MVA
22/110kV
X=6.4%
Line 1 :
200kV
X=121Ω
Line 2 :
110kV
X=42.35Ω
M
:
68.85 MVA
20kV
X=22.5%
Load :
10 MVAr
4kV
Δ connected capacitor
Draw the impedance diagram showing all impedances in per unit on a 100 MVA base.
Choose 22 kV as the voltage base for generator.
(12)
2. Draw the reactance diagram for the power system shown in figure. Neglect resistance and
use a base of 100 MVA, 220 kV in 50Ω line. The ratings of the generator, motor and
transformer are given below.
(May/June 2012)
Generator
: 40 MVA, 25 kV, X’’ =20%
Synchronous motor
: 50 MVA, 11 kV, X’’ =30%
Y-Y Transformer
: 40 MVA, 33/220 kV, X=15%
Y-Δ Transformer
: 30 MVA, 11/220 kV, X =15%
3. The single line diagram of an unloaded power system is shown in Figure. Reactances of the
two sections of the transmission line are shown on the diagram. The generators and
transformers are rated as follows:
Generator 1:
20 MVA, 11 kV, Xd’’= 0.25 Per unit
Generator 2:
30 MVA, 18 kV, Xd’’= 0.25 Per unit
Generator 3:
30 MVA, 20 kV, Xd’’= 0.21 Per unit
Transformer 1: 25 MVA, 220/13.8 kV, X= 0.15 Per unit
Transformer 2: single phase units, each rated 10 MVA 127/18 kV, X= 0.15 Per
unit
Transformer 3: 35 MVA, 220/22 kV, X= 0.15 Per unit
Draw the impedance diagram with all reactance’s marked in per unit. Choose a base of 50
MVA, 11 kV in the circuit of generator 1.
(Nov/Dec
2007)
4. Write short notes on
(April/May 2008)
i. Single line diagram
ii. Change of base
iii. Reactance of synchronous machines.
5. Eliminate bus 4 for the given admittance matrix and form the new bus admittance matrix
(5)
(5)
(5)
6. Draw an impedance diagram for the electric power system shown in the figure showing all the
impedances in the per unit on a 100 MVA base choose 20 KV as the voltage base for generator. The
three phase power and line ratings are given below
(Apr/ May
2011)
G1: 90 MVA 20 KV X= 9 %
T1: 80 MVA 20/200 KV X=16 %
T2: 80 MVA 200/20 KV X=20%
G2: 90 MVA 18 KV
X= 9%
Line 200 KV X=120 Ohm
Load: 200 KV S=48MW+J64 MVAR
7. Determine the Z bus for the system whose reactance diagram is shown in fig. where the
impedance is given in per unit (Nov/Dec 2011)
8. The parameters of a 4 bus system are as under:
Bus
Line
Code
impedance(pu)
1-2
0.2+j0.8
2-3
0.3+j0.8
2-4
0.25+j1
3-4
0.2+j0.8
1-3
0.1+j0.4
Draw the network and find the bus admittance matrix.
Charging
Admittance(pu)
j0.02
j0.03
j0.04
j0.02
j0.01
(Nov/Dec 2011)
9. Find the bus impedance matrix for the 4 bus system shown in below figure. Consider bus 4 as
reference.
(May/June 2012)
10.Draw the reactance for the system shown in figure and mark all the reactance in per unit on 20
MVA, 6.6kV basis.
(April/ May 2008)(16)
Generator G1= 10 MVA, 6.6 kV, 0.1p.u.
Generator G2= 20 MVA, 11.5 kV, 0.1p.u.
Transformer T1= 10 MVA, 3 phase, 6.6kV/115 kV, 0.15 p.u.
Transformer T2= three single phase units, each 10 MVA, 7.5 kV/75 kV, 0.1
p.u.
10. With the help of a single line diagram, explain the basic components of a power system. (April/
May 11)
11. Using building algorithm method determine the Z BUS for the network shown in the below figure
where the impedances labeled are shown in per unit.
12. Draw the per unit reactance diagram for the system shown in Fig. and mark all
reactances in per unit on 50 MVA, 13.8 KV on generator G1.(May/June 2006)
G1 : 20 MVA, 13.8 KV, X’’=20%
G2 : 30 MVA, 18 KV, X’’=20%
G3 : 30 MVA, 20 KV, X’’=20%
T1 : 25 MVA, 220/13.8KV, X=10%
T2 :three single phase units each 10 MVA, 127/18 KV , X=10%
T3 : 35 MVA, 220/22 KV, X=10%
13. Explain the following
i.
ii.
iii.
(Nov/Dec 2010)
Generator model
Transformer model
Transmission line model
14. Determine Z bus for the network shown in figure, where the impedances are marked in per unit
(Nov/Dec 12)
15. Determine the Z BUS for the network shown, where the impedance are labeled (1) through
(6) are shown in pu .
16. For the system shown in fig determine the generator voltage. take a base of 100 MVA
and 210 KV in the transmission line (May/ Jun 2013)
17. Form the bus impedance matrix for the network shown in fig by bus building algorithm
(May/ Jun 2013)
UNIT 2
PART A -2 MARKS
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
What is the need for slack bus or swing bus in a power system?
Compare Gauss Seidal and N-R method
Explain bus classification in power flow analysis with their known and unknown quantities
What is meant by acceleration factor in Gauss Seidal load flow solution and its best value?
What is Jacobian matrix?
What do you mean by flat voltage start?
What are the information’s that are obtained from a power flow study?
What is bus admittance matrix?
State at least four applications of load flow studies in the planning and operation of power
system
What are the data required for load flow study
How are the disadvantages of NR method overcome
What is slack bus
Describe primitive network. give an example
what is the need for load flow study
What is load flow?
State practical load flow problem.
Write the general power flow equation
Why bus admittance matrix is preferred in load flow?
What are advantages and disadvantages of gauss siedal method?
At what condition the generator bus is treated as load bus
What are advantages and disadvantages of Newton Raphson method?
Write the formula for finding line flows in a power system?
Write the formula for finding the slack bus power?
PART B 16 marks
1. With neat flow chart explain the computational procedure for load flow solution
using fast decoupled method when the system contains all types of buses. (Nov/Dec
2011)
2. Explain Classification of buses in load flow analysis.(6)
3. Derive the development of load flow problem in complex variable form and polar
variable form. (10)
4. Explain the flow chart and algorithm of gauss seidal method of load flow studies.
(May/Jun 2013)
5. 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.
(May/Jun 2012)
6. Give the comparisons of Gauss Seidal, Newton Raphson and Fast Decoupled load flow
methods (Nov/Dec 12)
7. Figure shows the single line diagram of simple three bus power system with generators at
buses 1 and 3. The magnitude of bus 1 is adjusted to 1.05 pu. Voltage magnitude at bus 3 is
fixed at 1.04 pu with a real power generation of 200 MW. A load consisting of 400 MW and
250 MVAR is taken from bus 2. Line impedances are marked in per unit on a 100 MVA base,
and the line charging susceptances are neglected. Obtain the power flow solution using
Newton Raphson method upto one iteration
8. Figure shows the single line diagram of simple three bus power system with generators at
buses 1 and 3. The magnitude of bus 1 is adjusted to 1.05 pu. Voltage magnitude at bus 3 is
fixed at 1.04 pu with a real power generation of 200 MW. A load consisting of 400 MW and
250 MVAR is taken from bus 2. Line impedances are marked in per unit on a 100 MVA base,
and the line charging susceptances are neglected. Obtain the power flow solution using fast
decoupled method upto one iteration. (April/May 2007)
9. For the sample system shown in figure the generator are connected at all four busses,
while the loads are at buses 2 and 3. Values of real and reactive power are listed in
the table. Bus 2 be a PV bus with V2=1.04 and bus 3 and bus 4 are PQ bus. Assuming
a flat voltage start, find the bus voltages and bus angles at the end of first iteration
using gauss seidal method. And consider the reactive power limits as 0.2≤Q2≤1
Bus
Pp p.u
Qp p.u
Vp p.u
Remarks
1
-
-
1.04∟0º
Slack bus
2
0.5
-
1.04
PV bus
3
-1.0
0.5
-
PQ bus
4
0.3
-0.1
-
PQ bus
10. Figure shows the single line diagram of simple three bus power system with generators at
buses 1 and 3. The magnitude of bus 1 is adjusted to 1.05 pu. Voltage magnitude at bus 3 is
fixed at 1.04 pu with a real power generation of 200 MW. A load consisting of 400 MW and
250 MVAR is taken from bus 2. Line impedances are marked in per unit on a 100 MVA base,
and the line charging susceptances are neglected. Obtain the power flow solution using
gauss seidal method up to one iteration including line flows and line losses. (Nov/Dec 2010)
11. Obtain the power flow solution (one iteration) for the system shown in fig. the line
admittances are in per unit on a 100 MVA base. Use fast decoupled load flow method
12. For the system shown in figure determine the voltages at the end of the first iteration by
Gauss Siedal method and also find the slack bus power, line flows and Transmission losses.
Assume base MVA as 100.
1
2
1.05∟0 pu
1.02 pu
Generator
P
Q
0.3 pu
-
3
-
-
Bus
Voltage
o
0.4 pu
Load
P
0.4 pu
Q
0.2
pu
Qmin(MVAR)
Qmin(MVAR)
-10
100
-
-
13. A five bus power system is given below. Each line has an impedance of (0.05+j0.15) pu.
The line shunt admittance may be neglected. The bus power and voltage specifications are
given in the table.
(May/June 2012)
i.
Find Y BUS
ii.
Find Q2, δ2, V3, V4 and V5 after the first iteration using Gauss Siedal method.
Assume Q2 min= 0.2 pu and Q2 max= 0.6 pu
Bus
PL/PD
QL/PD
PG
QG
V
Bus
Specification
1
1.0
0.5
Not specified
Not specified
1.02∟0o
Slack Bus
2
0
0
2
Not specified
1.02
PV Bus
3
0.5
0.2
0
Not specified
PQ Bus
4
0.5
0.2
0
Not specified
PQ Bus
5
0.5
0.2
0
Not specified
PQ Bus
UNIT 3
PART A -2 Marks
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Define short circuit MVA
How do short circuits occurs in a power system
What is bolted or solid fault?
Define negative sequence impedance
What is the need for short circuit studies?
Distinguish between symmetrical and unsymmetrical faults .
List the symmetrical and unsymmetrical faults that occur in a power system
List the various types of shunt and series faults
what is synchronous reactance
How the circuit breakers can be selected?
what are the approximation made in short circuit studies
What is a fault?
What is meant by fault level
explain the term momentary current and interrupting current
The Z bus method is very suitable for fault studies on large system. why?
PART B 16 Marks
1. A symmetrical fault occurs on bus 4 of system shown in fig. determine the fault current,
post fault voltages and line currents using thevenins method.
2.
For a radial network shown a 3 phase fault occurs at F. determine the fault current and
the line voltage at 11 KV bus under fault conditions (Nov/Dec 12)
3.
Explain the computational procedure of fault analysis using bus building algorithm
(May/ Jun 2013)
4.
A synchronous generator and motor are rated 30 MVA , 13.2 kv and both have sub
transient reactance of 20%. The line connecting them has a reactance of 10% on the
base of machine rating. The motor is drawing 20000 KW at 0.8 pf lagging and terminal
voltage of 12.8 KV. When a symmetrical 3 phase fault occurs at the midpoint of the
transmission line. Find the subtransient current in the generator, motor and fault by
using the internal voltage of the machines.(Nov/Dec 2009)
5.
A synchronous generator rated rated at 500 KVA, 440V, 0.1 p.u subtransient reactance
is supplying a passive load of 400 KW at 0.8 pf lagging. Calculate the intial
symmetrical RMS current for a 3 phase fault at the generator terminals.
6.
Figure shows two generating stations feeding a 132 KV system. Determine the total
fault current, fault level and fault current supplied by each alternator for a 3 phase solid
fault at the receiving bus. The length of the transmission line is 150 km. (Nov/Dec 2011)
7.
The generators at bus 1 and 3 of the network have impedances of j1.5 .if a 3 phase short
circuit fault occurs at bus 3 and at bus 2 when there is no load. Find the initial
symmetrical current in fault, line Flows and the post fault voltages using bus building
algorithm.
8.
A symmetrical fault occurs on bus 4 of system shown in fig. determine the fault current,
post fault voltages and line currents using bus building algorithm.
9.
A three phase 5 MVA, 6.6kV alternator with a reactance of 8% I connected to a feeder
of series impedance of 0.12+j0.48 ohm/phase/km through a step up transformer. The
transformer is rated at 3MVA, 6.6/33kV and has a reactance of 5%. Determine the fault
current supplied by the generator operating under no load with a voltage of 6.9kV, when
a 3 phase symmetrical fault occurs at a point 15km long the feeder (May/June 2012)
10.
Two generators G1 and G2 opposite to each other are connected to two transformers T1
and T2 respectively through a transmission line of 60km long, each conductor ha a
reactance 0.92Ω/ km . Generator G 1 and G2 are identical and rated as 11kV, 30 MVA and
have a transient reactance of 0.3 pu at on MVA base. The transformers T 1 and T2 are
identical and are rated 11/66kV, 10 MVA and have a reactance of 0.075 per unit to their
own base. The three phase fault is assumed at point F, which is 25km from generator G 1.
Find the short circuit current.
11.
A 11 KV, 100 MVA alternator having a sub-transient reactance of 0.25 pu is supplying a
50 MVA motor having a sub-transient of 0.2 pu through a transmission line. The line
reactance is0.05 pu on the base of 100 MVA. The motor is drawing 40 MW at 0.8 p.f
leading with a terminal voltage of 10.95 KV when a three phase fault occurs at the
generator terminals. Calculate the total current in generator and motor under fault
condition. (16) (Apr/May 2011)
12.
Two synchronous motor are connected to the bus of large system through a short
transmission line. the ratings of various components are motor(each) : 1 MVA
440V 0.1 PU transient reactance , Line: 0.05 ohm (reactance) large system :
short circuit MVA as its bus at 440.V is 8 . when the motors are operating at
440V calculate the short circuit current (symmetrical) fed into a three phase fault
at motor bus.(Apr/May 2010)
UNIT 4
PART A 2 Marks
1.
2.
3.
4.
5.
Write the symmetrical components of a 3 phase system
What is the significance of ‘a’ operator?
Draw the equivalent sequence network for a L-L bolted fault in a power system
What is sequence network?
Draw the sequence networks for a Δ-Δ connected transformer
6. Write the matrix notations of the operator ‘a’ which relates the phasorsV a, Vb,andVc with Va0,
Va1 and Va2 ?
7. Name the faults which do not have zero sequence currents flowing.
8. Name the faults in which all the three sequence component currents are equal and in which
positive and negative sequence currents together is equal to zero sequence current.
9. Give the reason for L-G fault
10. Why the neutral grounding impedance Zn appears as 3Zn in zero sequence equivalent
circuit?
11. Draw the zero sequence network for Y-Δ connected transformer
12. The line currents in 3 phase supply to an unbalanced load are Ia, Ib, Ic. The pahse sequence
is abc. Determine the sequence components of currents
13.write down the equation to convert symmetrical components into phase quantities
14. write down the relative frequency of occurrence of various types of faults
15. what are unsymmetrical faults
16. Draw the sequence network for a L-G bolted fault in a power system
17. Draw the sequence network for a LL-G bolted fault in a power system
18. Draw the sequence network for a L-L fault to ground through an impedance in a power
system
19. Draw the sequence network for a L-G fault to ground through an impedance in a power
system
20. Draw the sequence network for a LL-G fault to ground through an impedance in a power
system
PART B 16 marks
1. Draw the sequence network connection for double line to ground fault at any point of in a
power system and from that obtain the expression for the fault current (Nov/Dec 2012)
2. Derive the expression for L-G fault and L-L fault which is grounded through impedance Z f.
(May/ June 12)
3. Derive the expression for LL-G fault which is grounded through impedance Z f.
4. What are the assumptions to be made in short circuit studies. Deduce and draw the sequence
network for a line to line fault & L-G at the terminals of an unloaded generator and from
that obtain the expression for the fault current (solidly grounded) (Apr/May 2011)
5. Determine the fault current for the following faults using bus impedance matrix
i.
ii.
Balanced 3 phase fault at bus 3 through fault impedance Z f.=0.1j
Single line to ground fault at bus 3 through fault impedance Z f.=0.1j
6. A 50 MVA, 11 kV, 3φ alternator was subjected to different types of faults. The fault currents
are 3φ fault 1870 A, line to line fault 2590 A, single line to ground fault 4130 A. The
alternator neutral is solidly grounded. Find the pu values of the three sequence reactance’s of
the alternator. (May/June 2012)
7. A 30 MVA, 11 kV generator has Z 1=Z2=j0.2 pu and Z0=j0.05 pu. A line to ground fault
occurs on the generator terminals. Find the fault current and line to line voltages during fault
conditions. Assume that the generator neutral is solidly grounded and that the generator is
operating at no load and at rated voltage at the occurrence of fault. (May/June 2012)
8. Discuss in detail about the sequence impedance of and networks of synchronous machine,
transformer, transmission line and loads (May/June 2013)
9. Derive an expression for the total power in a three phase system interms of sequence
components of voltages and currents (Nov/Dec 2012)
10. A single line diagram is shown in the fig. generator grounding reactance is 0.5 pu. draw the
sequence networks and calculate the fault current for line to line fault on phase b and c at
point Q assume prefault voltage is 1.0 pu (May/Jun 2013)
UNIT 5
PART A 2 Marks
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
What is power system stability?
Write the swing equation and explain the terms involved in it
What is the use of swing equation? What are the methods used to solve it
What is an infinite bus?
Define transient stability and transient stability limit
Give the expression for swing equation. Explain each term along with their units
Write the need for swing equation?
State two techniques to improve stability of power systems.
What is meant by critical clearing time?
What is critical clearing angle?
State equal area criterion
On what basis do you conclude that a given synchronous machine has lost stability?
State the cause for voltage instability
What is meant by power angle curve
Define voltage stability
Define steady state stability
What are the causes of oscillatory and non oscillatory instabilities in power system
18. 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?
19. In equal area criterion how will you represent the graph during fault?
Part B -16 marks
1. Describe R.K method of solution of swing equation for SMIB system
(16)
(Apr/May
2011)
2. Derive an expression for critical clearing angle and clearing time
2011)
(16)
(Apr/May
3. Derive the swing equation for a single machine connected to an infinite bus system.
(May/June 2013)
4. State and explain equal area criterion. Indicate how you will apply equal area criterion
to find maximum additional load that can be suddenly added. (May/June 2013)
5. With a neat flow chart, explain how the transient stability study can be made by
modified Euler method. (Nov/Dec 2012)
6. A three generator delivers 1 pu, power to an infinite bus through a transmission network when
a fault occurs. The maximum power which can be transferred during pre fault, during fault
and post fault conditions is 1.75 pu, 0.4 pu, 1.25 pu. Find critical clearing angle (May/June
2012)
7. Derive the power angle equation for a (May/June 2012)
(i) SMIB System. Also draw the power angle curve.
(ii) A generator having Xd = 0.7 pu delivers rated load at a power factor of 0.8
lagging. Find Pe, Qe, E and δ.
8. Discuss the methods by which transient stability can be improved (Nov/Dec 2011)