07 rr320203 modelling of power system components

8/9/2019 07 Rr320203 Modelling of Power System Components

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Code No: RR320203 Set No. 1

III B.Tech II Semester Regular Examinations, Apr/May 2007MODELLING OF POWER SYSTEM COMPONENTS

(Electrical & Electronic Engineering)Time: 3 hours Max Marks: 80

Answer any FIVE QuestionsAll Questions carry equal marks

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1. (a) Define the following terms with suitable example: Basic

i. tree

ii. branches

iii. linksiv. co-tree

v. loop

(b) Write the relation among the number of nodes, number of branches, numberof Links and number of elements.

(c) For the graph given in figure 1 below, draw the tree and the correspondingco-tree. Choose a tree of your choice, and hence write the cutest schedule.

[5+2+9]

Figure 1

2. (a) Derive the expression for the loop impedance Z loop using singular transforma-

tion in terms of primitive impedance matrix z and the basic loop incidencematrix C.

(b) Derive an expression for Z loop for the oriented graph shown in Figure 2below.[8+8]

Figure 2

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3. Describe the procedure of modification of Zbus by adding mutually coupled branchfrom existing buses (p) and (k). [16]

4. (a) Two branches connected between buses 2-3 and 3-1 having impedances

equal to j0.25 pu are coupled through mutual impedance Zm = j0.15 pu. Findthe nodal admittance matrix for the mutually coupled branches and write thecorresponding nodal admittance equations.

(b) What is primitive admittance and impedance matrix. Bring out the signifi-cance of system admittance matrix. [8+8]

5. (a) For the power system network shown Figure 5a obtain bus incidence matrixin three phase representation.

Figure 5a

(b) Find the sequence impedance matrix of an element whose phase componentimpedance matrix is: [8+8]

zabc pq

=

j0.5 j0.2 j0.1 j0.1 j0.7 j0.4 j0.2 j0.3 j0.8

Derive the formula used.

6. Derive the relevant models for steady state and transient modes of operation of synchronous generator with relevant phasor diagrams and equations. Take saliencyinto consideration. [16]

7. (a) Develop the mathematical model of primary and secondary Control Loops andderive the transfer functions of each block.

(b) Determine the primary Automatic load frequency control loop parameters forthe following system data:Total rated area capacity = 2000 MwNormal operating load = 1000 MwInertia constant = 5 sec.Regulation = 2.4 hz/ p.u. MwAssume load frequency depending is linear. [10+6]

8. (a) Why AVR is required for Generator?

(b) Give alternator voltage regulator scheme with the help of a neat schematicdiagram. Explain the importance of all the components in an AVR.

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(c) Give block diagram of automatic voltage regulator scheme and hence explainvarious blocks in it. [4+6+6]

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1. (a) Define the following terms with suitable example: Basic

i. tree

ii. branches

iii. links

iv. co-tree

v. loop

(b) Write the relation among the number of nodes, number of branches, numberof Links and number of elements.

(c) For the graph given in figure 1 below, draw the tree and the correspondingco-tree. Choose a tree of your choice, and hence write the cutest schedule.

[5+2+9]

Figure 1

2. Derive the expressions for Bus admittance and impedance matrices by singulartransformation. [16]

3. (a) St arting from Zbus for a partial network, describe step-by-step how you

will obtain the Zbus for the modified network when a new line is to be addedbetween two buses of the existing network.

(b) What are the advantages of Zbus building algorithm? Explain what is prim-itive network, primitive admittance matrix and primitive impedance matrix.Explain by giving an example. [7+9]

4. In a four bus system, a generator connected to bus- 3 and a motor connected tobus-4 having reactance equal to 0.15 pu are connected through their respectivetransformers havingX T = 0.1 pu. Generated e.m.f. of generator connected to bus-3is 1.25 00 and internal voltage of motor is 0.85

−450. Line reactances connecting

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buses are X 31 = X 23 = 0.25 pu, X 21 = 0.125 pu, X 24 = 0.2 pu, X 14 = 0.4 pu. Developthe nodal admittance matrix for each of the network branches and then write thenodal admittance equations of the system. [16]

5. (a) Explain the primitive network three phase representation of a component inimpedance form.

(b) Show that for a stationary element, the phase impedances matrix of a com-ponent is diagonalised using symmetrical component transformation.

(c) Define the bus incidence matrix of a Power system network whose graph isshown in figure 5. [6+6+4]

Figure 5

6. (a) Define characteristic load parameters and give their typical values for commonload types. Obtain the characteristic load parameters of a composite load ata particular bus in a power system.

(b) Derive the relation between the inertia constant H and angular momentumM. State the units for H & M. [10+6]

7. (a) Explain the functions of various blocks of speed governing system.

(b) Explain the turbine model and hence discuss transfer functions of reheat andnon-reheat models. [8+8]

8. Explain the functional blocks of Automatic voltage regulator. [16]

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1. (a) Explain the following terms.

i. Basic loops

ii. cut-set

iii. basic cut-set

iv. loop

by taking an oriented connected graph. Verify the following relationsAbk

t. UB1.A1k

t

(b) Show the basic loops and the basic cut sets of the Figure 1 shown below andverify the relation asked in (a). (Take 1 -2 -3 -4 as tree) [8+8]

Figure 1

2. (a) For the network shown below, draw its graph and mark also a tree. Give

the total number of edges (i.e. elements), nodes, buses and branches for thisgraph. Write also its nodal equations and determine the elements of Y Bus

matrix directly by inspection.

(b) For the same network, write the loop equations and hence determine the el-ements of Z loop matrix directly by inspection. Values shown are currents &admittances Figure 2 [12+4]

Figure 2

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3. Describe the procedure of modification of Zbus by adding mutually coupled branchfrom existing buses (p) and (k). [16]

4. (a) Write a detail note on tap-changing and regulating transformer.

(b) Explain the necessity of transformer modelling for power system studies. [10+6]

5. (a) Explain the primitive network three phase representation of a component inimpedance form.

(b) Show that for a stationary element, the phase impedances matrix of a com-ponent is diagonalised using symmetrical component transformation.

(c) Define the bus incidence matrix of a Power system network whose graph is

shown in figure 5. [6+6+4]

Figure 5

6. (a) Derive the swing equation of a synchronous machine connected to an infinitebus.

(b) Derive the electrodynamic equations for modeling an induction motor. [8+8]

7. (a) Develop the mathematical model of primary and secondary Control Loops andderive the transfer functions of each block.

(b) Determine the primary Automatic load frequency control loop parameters forthe following system data:

Total rated area capacity = 2000 MwNormal operating load = 1000 MwInertia constant = 5 sec.Regulation = 2.4 hz/ p.u. MwAssume load frequency depending is linear. [10+6]


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1. (a) What do you understand by “branch-path incidence matrix K”? And what arethe elements of the matrix K? And what is the nature of this matrix? What isthe relation between the branch-path incidence matrix K and the submatrixAb

of the bus incidence matrix A, (Ab

is of dimensions b×

(n-l).(b) Taking node ‘O’ as the reference, write down the branch-path incidence matrix

K for the Figure 1 given below. (Take 1-2-3-5 as tree). [10+6]

Figure 1

2. Derive the expressions for Bus admittance and impedance matrices by singulartransformation. [16]

3. How do you modify Zbus by adding mutually coupled Zbus between existing bus(p) to new bus (q)? Describe the algorithm by giving suitable example. [4+8+4]

4. (a) What is nominal and off-nominal transformer tap settings? Derive the rela-tionships between primary inputs and secondary outputs of a transformer on

nominal ratio using admittances in matrix form.(b) What is phase shifting transformer? Bring out its significance in power system.

Draw basic equivalent circuit of phase shifting transformer with nominal tapratio and solve this circuit for terminal currents bringing out their relationshipwith input and output voltages. [8+8]

5. Develop the expressions for formation of Z BUS in three phase network represen-tation for the element which is added between an existing bus and a bus beingcreated. [16]

6. (a) What is a “Composite load”? Develop a mathematical model for such a load

and sketches the static characteristics of a composite load.

(b) Derive the swing equation of a synchronous machine connected to infinite bus.State assumptions made if any. [10+6]

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7. (a) Explain the complete block diagram of speed governing system and derivetransfer function.

(b) Two generators are supplying power to a system. Their rating are 50 and500Mw respectively. The frequency is 50Hz and each generator is half loaded.The system load increased by 110Mw and as a result frequency drops to49.5Hz. What must be the individual regulations be if two generators shouldincreased their turbine powers in properties to their ratings. Also express theregulation in p.u.Hz and p.u.Mw. [11+5]


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07 rr320203 modelling of power system components

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