Previous VTU Question Papers withSuggested Scheme of Answers/ Solutions

SUBJECT: Computer Techniques in Power Systems EE72

VTU QUESTION PAPER of Dec.06 / Jan.07

Note: 1. Answer any five questions.

2. Assume missing data suitably.

1. a. Explain the significance of primitive network and hence get the performance

equations in both impedance and admittance form. (5 Marks)

b. Derive an expression for obtaining the bus admittance matrix using singular

transformations. (7 Marks)

c. Determine the bus admittance matrix using the singular transformations for the

sample power system with the line data shown in table below. (8 Marks)

Line No. 1 2 3 4 5

Bus-code p-q 0 -1 1 - 2 2 -3 3 - 0 2 - 0

Impedance pu) 0.8 0.5 0.4 0.5 0.25

2. a. Obtain the generalized algorithmic expression for bus impedance matrix

elements when a link is added to the partial network. Also discuss the special

cases. (14 Marks)

b. Explain the steps to modify the ZBUS for removal of a line or modification of the

line impedance. (6 Marks)

3. a. What are different types of buses considered during power system load flow

analysis? Explain briefly. (5 Marks)

b. Determine the voltages at the end of first iteration using GS method for the

system data given below. Assume an acceleration factor of 1.6. (15 marks)

i) Line Data

Bus Code 1 - 2 1 - 3 2 - 3 2 - 4 3 - 4

Admittance 2 – j 8 1 – j 4 0.66 – j 2.664 1 – j 4 2 – j 8

ii) Bus Data

Bus No. P Q V Remarks

1 - - 1.060 SLACK

2 0.5 0.2 1+ j 0 PQ

3 0.4 0.3 1+ j 0 PQ

4 0.3 0.1 1+ j 0 PQ

2

4. a. Solve the non linear equations below using NR method for 2 iterations.

y2 - 4x - 4 = 0

2y – x – 2 =0

Assume initial values of: x(0) = -1 and y(0) = 1. (10 Marks)

b. Explain with the help of a flow chart the NR method of LFA in a power system.

(10 Marks)

5. a. The fuel costs per hour for plants 1 and 2 are given by

F1 = 0.2 P12 + 40 P1 + 120 Rs./Hr.

F2 = 0.25 P22 + 30 P2 + 150 Rs./Hr.

Determine the economic operating schedule and the corresponding cost of

generation if the maximum and minimum loading on each unit is 100 MW and

25 MW, the demand is 180 MW and the transmission losses are neglected. If the

load is equally shared by both the units, determine the saving obtained by loading

the units as per equal incremental production cost. (10 Marks)

b. What are transmission line loss coefficients? Obtain the general expression Bmn

with usual notations. (10 Marks)

6. a. What is load frequency control? Explain with a block diagram model of load

frequency control for an isolated power system. (10 Marks)

b. Explain the basic concepts of two interconnected control areas in LFC, with

relevant block diagram models and equations. (10 Marks)

7. a. With the help of a block diagram explain simplified representation of a speed

governor. (8 Marks)

b. With the help of a flow chart and equation explain the transient stability analysis

using modified Euler’s method. (12 Marks)

8. Write brief notes any four of the following:

a. Representation of tap changing of transformers in load flow studies

b. Automatic voltage regulators

c. Runge- Kutta method for transient stability analysis

d. Representation of synchronous machines fro transient stability analysis

e. Fast decoupled load flow analysis.

(20 Marks)

3

Suggested scheme of answers/ solutions

SUBJECT: Computer Techniques in Power Systems EE72

VTU QUESTION PAPER of Dec.06 / Jan.07

1. a. Definition of primitive network (set of unconnected elements)

Diagram for impedance representation

v + e = [z] i

Diagram for admittance representation

i + j = [y] v (1+2+2 Marks)

b. Expression for bus admittance matrix by singular transformations.

To derive as: YBUS = At [y] A (7 Marks)

c. Oriented Graph : 02 Marks

Matrices A and A : 02 Marks

Matrix YBUS : 04 Marks

2. a. Algorithmic expression for ZBUS when a link is added to the partial network.

To derive for elements zli and zll. (8 Marks)

Modification by removing nodel l (2 Marks)

Discussion on special cases. (4 Marks)

b. Sequential steps to modify ZBUS for

(i) Removal of a line

(ii) Modification of line impedance. (3+3 Marks)

3. a. Classification of buses for LFA (5 Marks)

b. YBUS =

3- j 12 -2 + j 8 -1 + j 4 0.0-2 + j 8 3.67-j14.67 -0.67+j2.66 -1 + j 4-1 + j 4 -0.67+j2.66 3.67-j14.67 -2 + j 80.0 -1 + j 4 -2 + j 8 3- j 12

(5 Marks)LFE’s with =1.6 used to get I iterated values as:

V2(1) = 0.01187 – j 0.02888

V3(1) = 0.994119 – j 0.029248

V4(1) = 0.9716032 – j 0.064684 (10 Marks)

4. a. f(x) = Y2 - 4x - 4 = 0 ; g(x) = 2y – x – 2 =0

k=0; First Iteration:

x(0)=-1, y(0)=1; f(0)=1, g(0)=1; (1 Mark)

f/x=-4; f/y=2y-2; g/x=-1 ; g/y=-2 ; (2 Marks)

Thus, the linearised NR equations are :

1 - 4 Δx + 2 Δy = 0 and 1- Δx + 2 Δy = 0; (1 Marks)

Solving, we get; x=0 and y=-0.5; and hence, x(1)=-1 and y(1)=0.5; (2 Marks)

k=1; Second Iteration:

similar to the procedure above, we get at the end of second iteration:

x(2) = - 0.92857 and y(2) = 0.53571. (4 Marks)

4

b. Flow chart of the NRLFA in a power system- using YBUS, or explanation of the

step by step procedure to be furnished (10 Marks)

5. a. F1 = 0.2 P12 + 40 P1 + 120 Rs./Hr.; F2 = 0.25 P2

2 + 30 P2 + 150 Rs./Hr.

dF1/dP1 = 0.4 P1 + 40; dF2/dP2 = 0.5 P2 + 30 (2 Marks)

Equating dF1/dP1 and dF2/dP2 and since P1 + P2 = 180, by solving, we get,

P1 = 88.89 MW and P2 = 91.11 MW. (3 Marks)

Thus, F1 = 5255.88 Rs./Hr. and F2 = 4958.55 Rs./Hr.

Therefore, total cost of generation = F1 + F2 = 10214.43 Rs./ Hr. (2 Marks)

If now, the load is 90 MW, then, the costs of generation would be;

F1 = 5340 Rs./Hr. and F2 = 4875 Rs./Hr., so that the total cost of generation is;

F1 + F2 = 10215 Rs./ Hr.

Thus saving in cost is: Rs.0.57 per hour of operation. (3 Marks)

b. Definition of transmission line loss coefficients (2 Marks)

General expression for Bmn with usual notations. ( 8 Marks)

6. a. Definition of load frequency control (2 Marks)

Block diagram model of load frequency control (5 Marks)

Explanation with PI controls (3 Marks)

b. Block diagram for two area CS in LFC (7 Marks)

Tie line bias explanation (3 Marks)

7. a. Block diagram (5 Marks)

Equations of dynamics of speed governor. (3 Marks)

b. Flow chart or procedural steps wrt transient stability analysis by using modified

Euler’s method (10 Marks)

Explanation with equations involved (2 Marks)

8. Write brief notes any four of the following:

a. Representation of tap changing of transformers in load flow studies:

for fixed or TCUL case – any one to be briefly arrived at with π – equivalent

model along with equations for π - parameters. (5 Marks)

b. Automatic voltage regulators (5 Marks)

c. Runge- Kutta method for transient stability analysis: the procedural steps with

equations to be furnished (5 Marks)

d. Representation of synchronous machines for transient stability analysis: the

models with appropriate sketches/ vector diagrams, and brief explanation to be

given (5 Marks)

e. Fast decoupled load flow analysis: Flow diagram or procedural steps, brief

explanation with list of assumptions made, to be covered. (5 Marks)