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DHANALAKSHMI COLLEGE OF ENGINEERING

CHENNAI

Department of ELECTRICAL AND ELECTRONICS ENGINEERING

EE 2351 – POWER SYSTEM ANALYSIS

Year / Semester: III/VI

UNIT – I

PART A

1. What is meant by transient and steady state conditions?

2. Draw the equivalent circuit of a three winding transformer.

3. What are the components of a power system?

4. If the reactance is 15 ohm, find the p.u. value for a base of 15 kVA and 10 kV.

5. What is meant by single line diagram?

6. How are the loads represented in reactance or impedance diagram?

7. What are the different types of buses in power systems? What are the quantities specified in each bus?

8. What is the need for system analysis in planning and operation of power system?

9. Draw the single line diagram showing the essential parts in the power system network.

10. A Generator rated at 30 MVA, 11 kV has a reactance of 20% calculate it’s per unit reactance for a base of 50 MVA and 10 kV.

PART B

16marks

1. (i) The one-line diagram of a power system is shown below.

G1:80 MVA 22 kV X = 9%

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

T2: 40 MVA 220/22 kV X = 6.0%

T3, T4: 40 MVA 22/110 kV X = 6.4%

Line 1 200 kV X = 121

Line 2 110 kV X = 42.35

M: 68.85 MVA 20 kV X = 22.5%

Load: 10 MVA 4 kV Δ – Connected Capacitor

Draw an impedance diagram showing all impedances in per unit on a 100 MVA base. Choose 22 kV as the voltage base for generator.

[pic]

ii) State the applications of bus admittance matrix. (16)

1. Form the bus impedance matrix for the network shown by building algorithms. (16)

[pic]

1. (i) What are the advantages of per unit computations?

(ii) 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

Generator : 40 MVA, 25 kV, X11 = 20%

Synchronous motor : 50 MVA, 11 kV, X11 = 30%

Y- Y transformer : 40 MVA, 33/220 kV, X = 15%

Y- Δ transformer : 30 MVA, 11/220 kV (Δ/Υ) (16) [pic]

2. Find the bus impedance matrix for the 4-bus system shown in figure. Consider bus 4 as the reference bus. (16)

[pic]

3. (i) The parameters of a 4 – bus system are as under.

|Bus code |Line impedance (p.u.) |Charging admittance |

| | |(p.u.) |

|1-2 |0.2 + j 0.8 |j 0.02 |

|2-3 |0.3+j0.9 |j 0.03 |

|2-4 |0.25+j1 |j 0.04 |

|3-4 |0.2+j0.8 |j 0.02 |

|1-3 |0.1+j0.4 |j 0.01 |

Draw the network and find bus admittance matrix.

(ii) A three phase, Δ/Υ transformer with rating 100 kVA, 11 kV / 400 V has its primary and secondary leakage reactance as 12 Ω / phase and 0.05 Ω / respectively. Calculate the p.u. reactance of transformer. (16)

4. Determine Zbus for system whose reactance diagram is shown in figure. Where the impedance is given in p.u. preserve all the nodes. (16)

[pic]

5. (i) Derive the Π model for a transformer with off nominal tap-ratio. (8)

(ii) Sketch and explain electric power system and mark the voltage level at various points from generator to load. (8)

6. Describe the modern power system in detail. (16)

7. Determine the positive, negative and zero sequence networks for the system shown in figure. Assume zero sequence reactance for the generator and synchronous motors as 0.06 p.u. Current limiting reactors of 2.5 Ω are connected in the neutral of the generator and motor number 2. The Zero sequence reactance of the transmission line is j300 Ω. (16)

[pic]

8. (i) Fine the by impedance matrix for the system whose reactance diagram is shown in figure. All the impedances are in p.u.

[pic]

(ii) Explain briefly about bus incidence matrix with an illustration. (16)

UNIT – II

PART A

1. What is the need for swing bus?

2. What is meant by acceleration factor in load flow solution? What is its best value?

3. List out the advantages of Gauss-Siedal method.

4. List out the advantages of Newton-Raphson method.

5. What is meant by P-Q bus in power flow analysis?

6. Define – Primitive matrix

7. Define – Load bus

8. How is load flow study performed?

9. What is meant by slack bus?

10. List the disadvantages of Gauss-Siedal method.

PART B

16marks

1. Derive load flow algorithm using Gauss-Siedel method with flow chart and discuss the advantages of the method.

2. Derive load flow algorithm using Newton-Raphson method with flow chart and state the importance of the method.

3. Explain with a flow chart, the GS method of load flow analysis with PQ and PV buses.

4. Derive load flow algorithm using Fast Decoupled method with flow chart and write the advantages of the method.

5. Illustrate the Newton-Raphson algorithm for the solution of the load flow problem, when no PV buses are present. Show how the technique may be modified to handle PV buses also.

6. Describe formulation of power flow equations using Y – matrix.

7. Solve for load flow solution for the given three bus system by Gauss-Siedal method. Carry out 2 iterations. Also neglect limits on reactive power.

Bus data:

Bus 1: Slack bus, V = 1.05 (0( 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.

Line data:

|Line No. |From |To |Impedance |

|1 |1 |2 |j0.4 |

|2 |2 |3 |j0.2 |

|3 |1 |3 |j0.3 |

8. The following are the system data for a load flow solution. The line admittances are as follows:

|Line No. |From |To |Admittance |

|1 |1 |2 |2 – j8.0 |

|2 |2 |3 |0.606 – j2.664 |

|3 |1 |3 |1 – j4.0 |

|4 |2 |4 |1 – j4.0 |

|5 |3 |4 |2 – j8.0 |

The schedule of active and reactive powers are as follows:

|Bus Code |P |Q |V |Remarks |

|1 |-- |-- |1.06 |Slack |

|2 |0.5 |0.2 |1 + j0.0 |PQ |

|3 |0.4 |0.3 |1 + j0.0 |PQ |

|4 |0.3 |0.1 |1 + j0.0 |PQ |

Determine the bus voltages at the end of first iteration using Newton-Raphson method.

9. The following are the system data for a load flow solution. The line admittances are as follows:

|Line No. |From |To |Admittance |

|1 |1 |2 |2 – j8.0 |

|2 |2 |3 |0.606 – j2.664 |

|3 |1 |3 |1 – j4.0 |

|4 |2 |4 |1 – j4.0 |

|5 |3 |4 |2 – j8.0 |

The schedule of active and reactive powers are as follows:

|Bus Code |P |Q |V |Remarks |

|1 |-- |-- |1.06 |Slack |

|2 |0.5 |0.1 ( Q2 ( 1.0 |1.04 |PV |

|3 |0.4 |0.3 |1 + j0.0 |PQ |

|4 |0.3 |0.1 |1 + j0.0 |PQ |

Determine the bus voltages at the end of first iteration using Newton-Raphson method.

10. For the following system solve load flow using Fast Decoupled method.

Bus data:

|Bus Code |P |Q |V |Remarks |

|1 |-- |-- |1.05 |Slack |

|2 |3 |0.1 ( Q2 ( 1.0 |1.00 |PV |

|3 |4 |2 |1 + j0.0 |PQ |

Line data:

|Line No. |From |To |Impedance in Ω |

|1 |1 |2 |j0.4 |

|2 |2 |3 |j0.2 |

|3 |1 |3 |j0.3 |

UNIT – III

PART A

1. List out the various types of faults occur in a power system.

2. What is the need for short circuit studies or fault analysis?

3. What is meant by symmetrical fault or balanced three phase fault?

4. What is meant by doubling effect?

5. What is meant by synchronous reactance or steady state condition reactance?

6. What is meant by sub transient reactance?

7. What is meant by transient reactance?

8. Define – Short circuit capacity

9. Define – DC off set current

10. What is meant by bolted fault or solid fault?

PART B

16marks

1. A generator is connected through a transformer to a synchronous motor. The sub transient reactances 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 the 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.

2. Derive the expression for fault current in Line-to-Line fault on an unloaded generator in terms of symmetrical components.

3. Explain symmetrical fault analysis using Z-bus matrix with neat flow chart

4. A 11 kV, 100 MVA alternator having a sub-transient reactance of 0.25 p.u. is supplying a 50 MVA motor having a sub-transient reactance of 0.02 p.u. through a transmission line. The line reactance is 0.05 p.u. on a 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 3-phase fault occurs at the generator terminals. Calculate the total current in generator and motor under fault conditions.

5. A 3 phase, 5 MVA, 6.6 KV alternator with a reactance of 8% is connected to a feeder of series impedance of (0.12 + j 0.48) ohm/phase/km. The transformer is rated at 3MVA, 6.6 KV/ 33 KV and has a reactance of 5%. Determine the fault current supplied by the generator operating under no-load with a voltage of 6.9 kV, when a 3 phase symmetrical fault occurs at a point 15 km along the feeder.

6. The bus impedance matrix of 4-bus system with values in p.u is given by ,

0.15 0.08 0.04 0.07

0.08 0.15 0.06 0.09

Z ‭bus = j 0.04 0.06 0.13 0.05

0.07 0.09 0.05 0.12

In this system generators are connected to buses 1 and 2 and their sub-transient reactances were included when finding Z bus. If pre-fault current is neglected, find sub-transient current in p.u. for a 3 phase fault on bus-4. Assume pre fault voltage as 1 p.u. if the sub transient reactance of generator bus-2 is 0.2 p.u., find the sub transient fault current supplied by generator.

7. (i) What are the basic assumptions made in fault calculations?

(ii) How can the fault current be determined using Zbus?

8. Explain with the help of a detailed flow chart, how can a symmetrical fault be analyzed using Z-bus?

9. Explain the procedure for making short-circuit studies of a large power system networks using digital computers.

10. Derive the equations to find the π-equivalent circuit of transformer with off-nominal tap ratio.

11. Explain the modelling of generator, load, shunt capacitor and transmission line for short circuit studies.

UNIT – IV

PART A

1. What are the symmetrical components of a 3 phase system?

2. What are the positive sequence components?

3. What are the negative sequence components?

4. What are the zero sequence components?

5. What is meant by sequence operator?

6. What is meant by sequence impedance and a sequence network?

7. Draw the positive, negative and zero sequence network of all power system components

8. Write the equation to determine fault current for L-G, L-L and L-L-G fault with impedance.

9. Write the equations to convert symmetrical currents into unbalanced phase currents.

10. Write the equations to convert unbalanced phase currents into symmetrical components.

PART B

16marks

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

2. What are the assumptions to be made in short circuit studies? Deduce and thaw the sequence network for a line to line fault at the terminals of an unloaded generator.

3. Two 11 kV, 20 MVA, 3-phase, star connected generators operate in parallel as shown in figure 14.b : the positive, negative and zero sequence reactance’s of each being, respectively, j0.18, j0.15, j0.10 pu. The star point of one of the generators is isolated and that of the other is earthed through a 2 ohms resistor. A single line to ground fault occurs at the terminals of the generators.

Estimate

i) the fault current,

ii) current in grounding resistor, and

iii) the voltage across grounding resistor.

4. (i) Derive the necessary equation to determine the fault current for a single line to ground fault. Draw a diagram showing the inter connection of sequence networks. (ii) A 30 MVA, 11 KV generator has Z1 = Z2 =j0.2 p.u. Z0 = j 0.05 p.u. 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.

5. A 50 MVA, 11 KV, 3-ph alternator was subjected to different types of faults. the fault currents are ; 3-ph fault 1870 A, line to line fault 2590 A, single line to ground fault 4130 A. The alternator neutral is solidly grounded. find the p.u values of the three sequence reactances of the alternator

6. Draw the sequence network connected for a double line to ground fault at any point in a power system and from that obtain an expression for the fault current.

7. (i) Derive an expression for the total power in a three phase system in terms of sequence components of voltages and currents.

(ii) Explain in detail about the sequence impedances of transmission lines.

8. A 30 MVA, 11 kV generator has Z1=Z2=j.02 pu. A line to ground fault occurs on the generator terminals. Find the fault current and line to line voltages during limit 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.

9. Derive the expression for three phase power in terms of symmetrical components.

10. The currents flowing in the lines toward a balanced load connected in delta are Ia = 100(0ْ, Ib = 141.4(225ْ and Ic = 100(90ْ. Find the symmetrical components of the given line currents and draw phasor diagrams of the positive and negative sequence line and phase currents.

11. Derive the equations of fault currents in terms of symmetrical components when there is a L-L-G fault

12. Draw the zero sequence equivalent circuits for the various possible transformer connections

UNIT – V

PART A

1. How is the power system stability classified?

2. What is meant by rotor angle stability?

3. What is meant by transient stability?

4. What is meant by steady state stability limit?

5. What is meant by dynamic stability?

6. Define – Critical Clearing Angle

7. Write the power angle equation and draw the power angle curve.

8. Write the swing equation for a SMIB (Single Machine connected to an Infinite Bus bar) system.

9. Define – Swing Curve

10. What is meant by Equal Area Criterion

PART B

16marks

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

2. Explain in detail, the modified Euler method of analyzing multi-machine power system for stability.

3. Explain in detail, the Runge-Kutta method of solving swing equation for multi-machine systems.

4. Derive an expression for the critical clearing angle and clearing time.

5. Derive the power angle equation for SMIB system. Also draw the power-angle curve.

6. A 3 phase generator delivers 1.0 p.u., power to an infinite bus through a transmission network when a fault occurs. The maximum power which can be transferred during pre-fault and post fault conditions is 1.75 p.u., 0.4 p.u., 1.25 p.u. find critical clearing angle

7. Explain in detail, the equal area criterion. How can the equal area criterion be applied to find the maximum additional load that can be suddenly added?

8. Derive the swing equation of a single machine connected to an infinite bus system and explain the steps of solution by Runge-Kutta method

9. A generator is operating at 50 Hz delivers 1 p.u. power to an infinite bus through a transmission circuit in which resistance is ignored. A fault takes place reducing the maximum power transferable to 0.05 p.u. whereas before the fault, this power was 2.0 p.u. and after the clearance of the fault, it is 1.5 p.u. By the use of equal area criterion, determine the critical clearing angle.

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