**NJR/KS/18/4599**

**Time : Three Hours**

** Max. Marks : 80**

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**Notes : 1. All questions carry marks as indicated.**

**2. Solve Question 1 OR Questions No. 2.**

**3. Solve Question 3 OR Questions No. 4.**

**4. Solve Question 5 OR Questions No. 6.**

**5. Solve Question 7 OR Questions No. 8.**

**6. Solve Question 9 OR Questions No. 10.**

**7. Solve Question 11 OR Questions No. 12.**

**8. Due credit will be given to neatness and adequate dimensions.**

**9. Assume suitable data whenever necessary.**

**10. Illustrate your answers whenever necessary with the help of neat sketches.**

**11. Use of non programmable calculator is permitted.**

1. a) Derive an expression of symmetrical component powers and show that the symmetrical component transformation is power invariant. ** [06 M] **

b) The line to ground voltages on the high voltage side of a step-up transformer are 100 kV, 33 kV and 38 kV on phases a, b and c respectively. The voltage of phase a leads that of phase b by 100º and lags that of c by 176.5º. Determine analytically the symmetrical components of voltage. **[07 M]**

**OR
**

2. a) Describe positive, negative and zero sequence impedances of a synchronous generator.

b) For a power system shown in fig. draw zero sequence networks. The generators and transformers are rated as follows. **[08 M]
**

Generator 1 : 25 MVA, 11 kV, X0 = 3% pu.

Generator 2 : 15 MVA, 11 kV, X0 = 5% pu.

Synchronous motor 3 : 25 MVA, 11 kV, X

Transformer 1 : 25 MVA, 11Δ/120Y kV, X = 10%

2 : 12.5 MVA, 11Δ/120Y kV X=10%

3 : 10 MVA, 120Y/11Y kV X = 10%

Choose a base of 50 MVA, 11 kV in the circuit of Generator 1. Zero sequence reactance of each line is 250% of its positive sequence reactance.

3. a) Symmetrical short circuit current in transmission line contributes steady state current and DC offset current. Explain**. [06 M]**

b) A 63 MVA, 11 kV synchronous generator is connected to a 75 MVA, 11/132 kV delta-star transformer. The subtransient direct axis reactance of generator is 0.15 pu and transformer reactance is 0.1 pu. The generator is unloaded. The symmetrical fault suddenly occurs on 132 kV side of transformer. Find symmetrical subtransient fault current and also calculate fault MVA. **[07 M] **

**OR**

4. a) Explain the following.

i) Circuit breaker rating. **[03 M]
**

ii) Necessity of current limiting reactors and their types.

b) The estimated short circuit MVA at the bus bars of a generating station is 1000 MVA and of another is 670 MVA. The generated voltage at each station is 11 kV calculate the possible short circuit MVA at each station when they are interconnected by a reactance of 0.4Ω/phase. **[06 M] **

5. a) Derive an expression for fault current if L-L-G fault is occured with a fault impedance Z_{f} . Also draw the sequence network. ** [07 M] **

b) A synchronous generator is rated 25 MVA 11 kV. It is star connected with the neutral point solidly grounded. The generator is operating at no load at rated voltage. Its reactances are X”= X_{2}=0.20 pu and X_{0}=0.08 pu. Calculate the symmetrical subtransient line currents for

i) Single line-to-ground fault.

ii) Double line fault.

iii) Double line to ground fault.

Compare these currents and comment**. [07 M] **

**OR**

6. a) Write a short note on open conductor faults. **[06 M] **

b) A synchronous machine 1 generating 1 pu voltage is connected through a Y/Y transformer of reactance 0.1 pu to two transmission lines in parallel. The other ends of the lines are connected through a Y/Y transformer of reactance 0.1 pu to a machine 2 generating 1 pu voltage for both transformer X_{1}=X_{2}=X_{0}.

Calculate the current fed into a double line to ground fault on the line side terminals of the transformer fed from machine 2. The star points of machine 1 and of the two transformer are solidly grounded. The reactances of the machines and lines referred to a common base are ** [08 M]
**

X

Machine 1 0.35 0.25 0.05

Machine 2 0.30 0.20 0.04

Line (each) 0.40 0.40 0.80

7. a) Differentiate clearly the meaning of steady state, dynamic and transient stability referred to power system. **[07 M] **

b) A synchronous generator of reactance 1.20 pu is connected to an infinite bus bar (|U|=1.0 pu) through transformer and a line of total reactance of 0.60 pu. The generator no load voltage is 1.20 pu and its inertia constant H = 4 mW-S/MVA.

The resistance and machine damping may be assumed negligible. The system frequency is 50 Hz. ** [07 M]**

Calculate the frequency of natural oscillation if the generator is loaded to

i) 50% and ii) 80% of its maximum power limit.

**OR**

8. a) Explain the concept of equal area criterion. How it can be used to study transient stability? **[07 M]
**

b) Determine the critical clearing angle for the network shown in fig. below. A three phase fault takes place at B. And breakers A and B operate simultaneously. The generator is delivering 1 pu power before the fault takes place.

9. a) Discuss the following.

i) Equality and inequality constraints.** [03 M] **

ii) Penalty factor and its significance. **[03 M]
**

b) The fuel inputs per hour of plants 1 and 2 are given as

F

F

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 transmission losses are neglected. If the load equally shared by both the units. Determine the saving obtained by loading the units as per equal incremental production cost.

**OR**

10. a) Derive the co-ordination equation for economic load scheduling of power plants including transmission losses. Give the algorithm for solution of co-ordination equations. **[07 M] **

b) A power system has two plants and power is being dispatched economically with P_{1}=130 mW and P_{2}=200 mW loss coefficients are

B_{11}=0.1 x 10^{-2} mW^{-1}

B_{22}=0.13 x 10^{-2} mW^{-1}

B_{12}= -0.01 x 10^{-2} mW^{-1}

To raise the total load on the system by 1 mW will cost additional Rs. 5 per hour. Find **[06 M] **

i) Total losses in the system.

ii) Penalty factor of plant 1.

iii) Additional cost per hour to increase the output of this plant by 1 mW.

11. a) Discuss the advantages and disadvantages of grounding the neutral of the power system.** [06 M] **

b) Derive an expression for the reactance of the Peterson coil in terms of the capacitance of the protected line. Calculate the reactance of the coil suitable for a 33 kV, 3 phase transmission system of which the capacitance to earth of each conductor is 5 μF. **[07 M] **

**OR
**

12. a) Necessity of compensation in power system. Different types of compensating devices. Explain.

b) Explain the following.

i) Zig-zag transformer. **[03 M] **

ii) Arcing grounding and its method. **[03 M]**