Department of Electrical EngineeringIndian Institute of Technology, Kharagpur

Electrical Machines(EE2l002) Date: 25th April, 2016 AN2nd Year EE Exam Halls: F116, F142, NR221,NR222 & NR321 104 studentsTime: 3 hours. Spring End Semester Exam. 2015-2016 Full Marks: 100

Instructions: Attempt ANY FIVE questions. Intermediate calculation steps must be shown.

1. (a) With reference to a 3-phase synchronous generator, explain with phasor diagram the conceptof armature reaction reactance. Why is this reactance called a fictitious reactance? [5]

(b) Draw the phasor diagram of an over-excited non-salient pole synchronous motor having perphase z, = ra + jxs. [5]

(c) Draw the phasor diagram of salient pole over excited synchronous motor having negligiblearmature resistance and direct and quadrature axis reactances are Xd and xq. [5]

(d) A Salient pole synchronous generator has negligible armature resistance and with direct &quadrature axis reactances Xd and xq. The generator is working steadily connected to the buswith zero excitation. Under this condition it is delivering maximum power. Draw the phasordiagram and find out the power factor at which it is operating. [5]

2. A 3-phase, star connected, 6 pole, 50 Hz synchronous generator has the following data:

Diameter of the inner bore:Length of the machine:Phase spread:Total number of slots:Number of conductors/slot:Coils are short chorded:

30 em25 em60°7210by one slot pitch

Air gap flux density distribution is given to be:

b = 0.9 sine + 0.2 sin3e + 0.1 sin5e Wb/m2

(a)(b)

(c)

(d)

calculate flux per pole due to fundamental, 3rd harmonic and 5th harmonic components. [3]

calculate distribution factors for fundamental, 3rd harmonic and 5th harmonic components. [3]

calculate the pitch factors due for fundamental, 3rd harmonic and 5th harmonic components. [3]

ponents.

(e) Also calculate the line to line voltage.

calculate per phase induced voltages due to fundamental, 3rd harmonic and 5th harmonic com-[8][3]

3. (a) Explain the basis of Blondel's two reaction theory for analyzing a salient pole synchronousmachine. [5]

(b) A salient pole synchronous generator has per phase reactances Xd and Xq along d and q axisrespectively with armature resistance raper phase. The generator is supplying to the bus anarmature current of fa at a power factor angle e lagging. Assume the per phase bus voltage tobe V. Draw the phasor diagram showing bus voltage, excitation voltage and voltage drops inra, Xd and xq. Also explain clearly how the position of d and q axis can be ascertained fromthe knowledge of bus voltage, armature current and e. Also find out an expression for powerdelivered to the bus in terms of E, V, 6, Xd and xq. [15]

Please Turn Over

1

4. (a) A 6 pole, 50 Hz, 3 phase induction motor has a rotor resistance of 0.20 per phase and amaximum torque of 160 m at 875 rpm. Calculate: (i) the torque for a full load slip of 4percent and the (ii) resistance to be added to the rotor circuit per phase to obtain 90 percentof full load torque at starting. Neglect stator impedance. [6]

(b) Draw the circle diagram for a 5 hp, 200 V (L-L), 50 Hz, 4 pole, 3-phase, star connected inductionmotor from the following test results:

o load test:Blocked rotor test:

Line Voltage Line current200V 5A100V 26A

Total Input power350W1700W

Estimate from the diagram for full load conditions, the line current and power factor; also themaximum torque and the starting torque in terms of full load torque. At standstill, the rotorcopper loss is half the total copper loss. [14]

5. (a) A 230 V, 50 Hz, 4-pole, single phase induction motor has rl = 100, r; = 130, Xl = x~= 140and Xm = 290 O.Calculate the input current, power factor, output power, efficiency of the motor when it runsat a slip of 4%. Also calculate the ratio of forward and backward field strengths. [10]

(b) The standstill impedances of main and auxiliary windings of a 220 V, 50 Hz single phaseinduction motor are respectively ZM = 47.83 L79.75° 0 and Z A = 75 L58.15° O. Assume themain & auxiliary winding turns ratio to be unity.

(i) Estimate the value of the capacitance (graphically or otherwise), to be connected in erieswith the auxiliary winding to make main and auxiliary currents in quadrature at starting.

[5](ii) Estimate the value of the capacitance (graphically or otherwise), to be connected in series

with the auxiliary winding for getting maximum starting torque. [5]

6. (a) Speed of a 3-phase induction motor is to be controlled over a wide range (very low to rated speedand above the rated speed). Suggest a suitable method with schematic diagram and explain themethod critically by torque-speed characteristics. [10]

(b) What are the conditions to be satisfied to synchronize an incoming alternator with the bus.With the help of a neat circuit diagram and relevant phasor diagram explain how successfulsynchronization can be accomplished. [10]

*****-*****

2