ee2351 psa im 2013

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EE2351 POWER SYSTEM ANALYSIS

UNIT-I INTRODUCTION

1. Explain the modeling of generator, load, transmission line and transformer for power

flow, short circuit and stability studies.

Refer - modeling chart

2. Draw the per unit reactance diagram for the power systems shown below. Neglect

resistance and use a base of 100MVA, 220KV in 50 ohms line. The ratings of the

generator, motor and transformers are

G: 40MVA, 25KV, X’’ = 20%

M: 50MVA, 11KV, X’’ = 30%

T1: 40MVA, 33 Y/ 220Y KV, X = 15%

T2: 30MVA, 11 ∆ / 220Y KV, X = 15%

Load: 11KV, 50MW+j68 MVAR

3. Draw the reactance diagram using a base of 50MVA and 13.8KV on generatorG1

G1: 20MVA, 13.8KV, X’’=20% ; G2: 30MVA, 18.0KV, X’’=20%

G3: 30MVA, 20.0KV, X’’=20% ; T1: 25MVA, 220/13.8 KV, X =10%

T2:3Single phase unit each rated 10MVA, 127/18 KV, X =10%

T3: 35MVA, 220/22 KV, X =10%

4. A simple power system is shown in fig. Redraw this system where the per unit

impedance of the components are represented on a common 5000 VA base and

common system base voltage of 250V.

j 50Ω G1 M

T1 T2

G1 G3

G2

T1 T3

T2

Line 1 Line 2

j80Ω j100Ω



5. The single line diagram of a three phase power system is shown in fig. Select a common

base of 100MVA and 13.8KV on the generator side. Draw per unit impedance diagram

G: 90MVA, 13.8KV, X=18% ; T1 :50MVA, 13.8/220KV, X=10%

T2:50MVA, 220/11KV, X=10% ; T3 :50MVA, 13.8/132KV, X=10%

T4:50MVA, 132/11KV, X=10% ; M : 80MVA, 10.45KV, X=20%

LOAD : 57MVA, 0.8 p.f lagging at 10.45 KV ; Line 1 = j 50Ω ; Line 2 = j 70Ω

6. A three phase line has an impedance of 2+j 4 ohm as shown in figure

7. The line feeds two balance three phase loads that are connected in parallel. The first load

is star connected and has an impedance of 30+j40 ohm/phase. The second load is delta

connected and has an impedance of 60-j45 ohm/phase. The line is energized at the

sending end from a three phase balanced supply of line voltages 207.85 V. taking the

phase voltage Va as reference, determine.

Z=40 + j 150Ω

G1 T1 T2

G2

Load

1000VA

250V

Z = j0.2 p.u

2000VA

250V

Z = j0.3 p.u

4000VA

250/800V

Z = j0.2 p.u

8000VA

1000/500V

Z = j0.06 p.u

2500VA

400V

j 50Ω

T1 T2

2

j70Ω

G M T3

T4

4



a. The current, real power and reactive power drawn from the supply.

b. The line voltage at the combine loads

c. The current per phase in each load

d. The total real and reactive power in each load and the line (16)

8.. The one line diagram of a three phase power system is shown in figure. Select a

common base of 100 MVA and 22 KV on the generator side. Draw an impedance

diagram with all impedance including the load impedance marked in per unit. The

manufacturer’s data for each device is given as follow

G: 90 MVA 22KV X=18%

T1: 50 MVA 22/220KV X=10%

T2: 40 MVA 220/11KV X=6.0%

T3: 40 MVA 22/110KV X=6.4%

T4: 40 MVA 110/11KV X=8.0%

M: 66.5 MVA 10.45 KV X=18.5%

The three phase load at bus 4 absorbs 57MVA, 0.6 power factor lagging at 10.45 KV.

Line 1 and Line 2 have reactance of 48.4 and 65.43 ohms respectively. (16)

9. A 345-KV, three phase transmission line is 130km long. The resistance per phase is

0.036 ohm per km and the inductance per phase is 0.8 mH per km. The shunt

capacitance is 0.0112 microfarad per km. the receiving end load is 270 MVA with 0.8

power factor lagging at 325 KV. Use the medium line model to find the voltage and

power at the sending end and the voltage regulation (16)

10. (a) (i) The terminal voltage of a Y – connected load consisting of three equal impedance

of 20∟30° Ω is 4.4 KV line to line. The impedance of each of the three lines

connecting the load to a bus at a substation is ZL = 1.4 ∟75° Ω. Find the line to line

voltage at the substation bus. (6)

(ii) List out the advantages of per unit computations. (4)

(iii) A single - phase transformer is rated 110/440 V, 2.5 KVA. Leakage reactance

measured from the low-voltage side is 0.06 Ω. Determine leakage reactance in per

unit.(6)

11.The single line diagram of an unloaded power system is shown in fig. Reactances of the

two sections of the transmission line are shown on the diagram. The generator and

transformers are rated as follows:

Generator G1: 20 MVA, 13.8 KV, X” = 20%





Transformer T1 : 25 MVA, 220 Y / 13.8 ∆ KV, X = 10%

Transformer T2 :3 single phase units each rated at : 10 MVA, 127/18 KV,X = 10%

Transformer T3: 35 MVA, 220 Y / 22 Y KV, X = 10%

Draw the reactance diagram using a base of 50 MVA and 13.8 KV on generator G1 (16)

12. (i) Explain the need for system analysis in planning and operation of power system. (6)

(ii) Discuss about per phase analysis of symmetrical three phase system (10)

13. Draw the structure of an electrical power system and describe the components of the

system with typical values. (16)

14. Draw thereactance diagram using a base of 100 MVA, 220 KV in 50 ohm line.

Generator : 40 MVA, 25 KV, X” = 20%

Transformer : 50 MVA, 11 KV, X” = 20%

Star – Star transformer : 40 MVA, 33 / 220 KV, X = 15%

Star – Delta transformer : 30 MVA, 11 / 220 KV, X = 15% (16)

15. A 120 MVA, 19.5 KV generator has a synchronous reactance of 0.15 p.u and it is

connected to a transmission line through a transformer rated 150 MVA, 230/18 KV

(star/delta) with X = 0.1 p.u.

(i) Calculate the p.u reactance by taking generator rating as a base values (5)

(ii) Calculate the p.u reactance by taking transformer rating as a base values. (5)

(iii) Calculate the p.u reactance for a base value of 100 MVA and 220 KV on H.T

side of ransformer. (6)

UNIT-II POWER FLOW ANALYSIS

1.Find out the Y matrix of the sample power system as shown in fig. Data for this system is

given in table.

2. Find out the Y matrix of the sample power system network diagram as shown in fig.



3. Consider the system shown in fig. It shows a transmission network with impedance of

transmission lines all in p.u as shown. Compute Ybus matrix.

4. Find the bus admittances matrix for the system. Use the values of 220 KV and 100

MVA as base quantities. Express all impedances and admittance in per unit it is given

that all the lines are characterized by a series impedances of 0.1+j0.7 ohm/km and shunt

admittance of j0.35 ×10-5 mho/km. lines are rated at 220 KV. (16)

5. a. Derive static load equations for ‘n’ bus system. (10)

b. Compare Gauss seidal, Newton raphson and fast decoupled for load flow solution (6)

6. Draw the flowchart of gauss seidal method for load flow analysis when PV bus is present

7. The figure below shows the one line diagram of a simple three bus power system with

generators at buses 1 and 3. The magnitude of voltage at bus 1 is adjusted to 1.05 .u.

voltage magnitude at bus 3 is fixed at 1.04 p.u 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 by the gauss seidal method at the end of first

iteration (16)

8. Figure shows the one line diagram of a simple four bus system. Table gives the line

impedances identified by the buses on which these terminate. The shunt admittance at all

buses on which these terminate. The shunt admittance at all buses is assumed negligible.

a. Fine YBUS assuming that the line dotted is not connected. What modifications need

to be carried out in YBUS if the line shown dotted is connected? (16)

Line, Bus to Bus R, pu X, pu

1-2 0.05 0.15

1-3 0.10 0.30

2-3 0.15 0.45

2-4 0.10 0.30

3-4 0.05 0.15

0.02+j0.04

0.0125+j0.025 0.01+j0.03

1 2

3



9. Derive load flow algorithm using Gauss – Seidal method with flow chart and discuss the

disadvantages of the method (16)

10. Derive load flow algorithm using Newton – Raphson method with flow chart and state

the importance of the method. (16)

11. With a neat flow chart explain the computational procedure for load flow solution using

fast decoupled method when the system contain all types of buses. (16)

12. For the network shown in fig. form the bus admittance matrix. Determine the reduced

admittance matrix by eliminating node 4. (16)

13. Using Singular transformation method, Determine YBUS for the network shown in Fig.

Where the impedance labeled in p.u (16)

14. The following is the system data for a load flow solution :

Bus code Admittance

1-2 2.0 -j8.0

1-3 1.0 – j3.0

2-3 0.6 – j2.0

2-4 1.0 –j4.0

3-4 2.0 –j8.0

The schedule of active and reactive power is

Bus code P Q V Remarks

1 - - 1.05+j0.0 Slack

2 0.5 0.2 1.0+j0.0 PQ

3 0.4 0.3 1.0+j0.0 PQ

4 0.3 0.1 1.0+j0.0 PQ

Determine the voltage at the end of first iteration Using Gauss – Seidal method.

Take acceleration factor = 1.4. (16)

15. (i) Explain the formation of YBUS by Singular transformation with one example.

(ii) Draw a one line diagram of a sample power system using synchronous machines,

transformers, and transmission lines. (4)



UNIT- III FAULT ANALYSIS - BALANCED FAULT

1. A 25 MVA, 11 KV generator with Xd’’=20% is connected through a transformer to a

bus which supplies four identical motors as shown in figure. Each motor has Xd’’

=20% and Xd’=25% on a base of 5 MVA, 6.6 KV. The three phase rating of the

transformer is 25 MVA, 11/6.6 KV with a leakage reactance of 10%. The bus voltage at

the motors is 6.6 KV when a three phase fault occurs at point P. for the faults specified,

Calculate (i) the sub transient current in the fault (ii) the sub transient current in breaker

A. (iii) momentary current in breaker A. (16)

2. 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

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, one 10000 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 (a) at the high voltage terminals of the

transformers (b) at load end of transmission line (16)

3. Determine the Z bus for the system whose reactance diagram is shown in the Fig. where

the impedance is given in p.u (16)

4. Explain the step by step procedure of the formation of ZBUS by bus building algorithm

5. Determine the Z bus for the system whose reactance diagram is shown in the Fig. where

the impedance is given in p.u (16)



6. Explain the step by step procedure for systematic fault analysis using bus impedance

matrix. (16)

7. A synchronous generator and a synchronous motor each rated 25 MVA, 11 KV having

15% sub – transient 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 at a terminal voltage of

10.6 KV. When a symmetrical three phase fault occurs at the motor terminals. Find the

sub – transient current in the generator,Motor and Fault.

(i) Find the bus impedance matrix for the system whose reactance diagram is shown fig.

All the impedance are in p.u (10)

(ii) Derive the Π – model for a transformers with off - nominal tap – ratio. (6)

8. Using building algorithm method, determine ZBUS for the network shown in Fig where

the impedances are labeled are shown in per unit. (16)

9. A generator is connected through a transformer to a synchronous motor. The subtransient

reactance of generator and motor are 0.15 p.u. and 0.35 p.u.respectively. The leakage

reactance of the transformer is 0.1p.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 generator is 1 p.u. and 0.8 p.f. leading. Find the subtransient current in p.u. in the

fault, generator and motor. Use the terminal voltage of generator as a reference vector.

10. (i) The currents flowing in the lines towards a balanced load connected in ∆ are Ia =

100∟0°, Ib = 141.4 ∟225°, Ic = 100∟∟90°. Find the symmetrical components of

the given line currents and draw phasor diagram of the positive and negative

sequence line and phase currents. (8)

(ii) Derive the expression of three phase power in terms of symmetrical components (8)



11.For the radial Network shown below, a three phase fault occurs at F. Determine the fault

current and the line voltage at 11KV bus under fault conditions. (16)

UNIT- IV FAULT ANALYSIS – SYMMETRICAL COMPONENTS AND

UNBALANCED FAULT

1. Explain the sequence impedance of synchronous machine, transmission lines and star

connected loads. (16)

2. Draw the transformer zero sequence equivalent circuits for the various winding

connections (16)

3. A 25MVA, 11KV, three phase generator has a sub transient reactance of 20%. The

generator supplies two motors over a transmission line with transformers at both

ends as shown in one line diagram a of figure. The motors have rated inputs of 15

and 7.5 MVA both 10KV with 25% sub transient reactance. The three phase

transformers are rated 30MVA, 10.8/121KV, and connection delta-star with leakage

reactance of 10% each. The series reactance of the line is 100 ohms. Draw the

positive and negative sequence networks of the system with reactance marked in

per unit. (16)

4. Develop the sequence network for a double line to ground (LLG) fault. (16)

5. Draw the Zero sequence diagram for the system whose one line diagram is shown in

fig. (16)

6. (i) A salient pole generator without dampers is rated 20 MVA, 13.6 KV and has direct

axis sub – transient reactance of 0.2 per unit. The negative and zero sequence

reactances are, respectively, 0.35 and 0.1 per unit. The neutral of the generator is

solidly grounded. With the generator operating unloaded at rated voltage with Ean =

1.0 ∟0° per unit, a single line to ground fault occurs at the machine terminals, which

then have per – unit voltage to ground,



Va = 0; Vb = 1.013∟-102.25°;

Vc = 1.013∟102.25°

Determine the sub transient current in the generator and the line to line voltage for

sub transient conditions due to the fault. (16)

7. Derive the expression for fault current in single line to ground fault on unloaded

generator. Draw an equivalent network showing the inter connection of networks to

simulate single line to ground fault (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)

9. Derive the expression for fault current in line to line fault on unloaded generator. Draw

an equivalent network showing the inter connection of networks to simulate double line

to line fault (16)

10. An unloaded star connected solidly grounded 10 MVA, 11 KV, generator has Positive,

Negative and zero sequence impedances as j 1.3 ohms, J 0.8 ohms and j 0.4 ohms

respectively. Single line to ground fault occurs at terminals of the generator.

(i) Calculate the fault current.

(ii) Determine the value of the inductive reactance that must be inserted at the

generator neutral to limit the fault current to 50% of the value obtained in

(i) Determine the fault current and MVA at faulted bus for a line to ground (solid)

fault at

bus 4 as shown in fig

G1, G2 : 100 MVA, 11 KV, X+ = X - 15%, Xn = 6%

T1, T2 : 100 MVA, 11 KV/220 KV, Xleak = 9%

L1, L2 : X+ = X - = 10% on a base of 100 MVA. Consider Fault at

phase ‘a’ (16)

UNIT- V POWER SYSTEM STABILITY

1. Derive swing equation used for stability studies in power system. (16)

2. Describe the equal area criterion for transient stability analysis of a system. (16)

3. Write the computation algorithm for obtaining swing curves using modified Euler’s

method (16)

4. Write a short note on i. Factors influencing transient stability,ii. Voltage collapse (16)

5. Given the system of figure below where a three phase fault is applied at a point P as

shown (16)

6. Find the critical clearing angle for clearing the fault with simultaneous opening of the

breakers 1 and 2. The reactance vales 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 above figure. (16)

7. Explain in detail the equal area criterion. (16)

8. (i) Derive Expression for critical clearing angle. (8)

(ii) A 150 MVA generator – transformer unit having an overall reactance of 0.3 p.u. is

delivering 150 MW to infinite bus bar over a double circuit 220 KV line having

reactance per phase per circuit of 100 ohms. A 3 - phase fault occurs midway along

one of the transmission lines. Calculate the maximum angle of swing that the

generator may achieve before the fault is cleared without loss of stability. (8)

9. A 50 Hz, 500 MVA, 400 KV generator (with transformer) is connected to a 400 KV

infinite bus bar through an interconnector. The generator has H = 2.5 MJ/MVA,

Voltage behind transient reactance of 450 KV and is loaded 460 MW. The transfer

reactances between generator and bus bar under various conditions are :

Prefault 0.5 Pu

During Fault 1.0 Pu

Post fault 0.75 Pu

Calculate the swing curve using intervals of 0.05 sec and assuming that the fault is

cleared at 0.15 sec. (16)

10. Explain the modified Euler method of analyzing multi machine power system for

stability, with neat flow chart. (16)

ee2351 psa im 2013

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