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UNIVERSITY OF MAURITIUS

FACULTY OF ENGINEERING

PAPER NO

BEEEE/06S/10

EXAMINATION

Second Semester 2006/07

BEng (Hons) Electrical andElectronic / Electronic and

Communication EngineeringLevel 2

DATE

Monday28 May 2007

SERIES

May 2007

PAPER

Electrical Machines[ELEC 2006Y(3)]

TIME

9:30 12:30 Hours

This paper contains SIX (6) Questions. Candidates are required to answerANY FIVE (5) Questions.

Figure 2 for Question 1 is attached.

INSTRUCTION TO CANDIDATES:

Students attempting Question 1 are requested to detach Figure 2 and use itto attempt Question 1. Figure 2 should then be attached to the answerbooklet used for Question 1 and handed over.

Graph paper is required for Question 3. Graph paper used should beattached to the booklet used to answer Question 3.

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Question 1

(a) Explain the meaning of the following terms:

(i) Residual flux density, Br

(ii) Coercivity of a magnetic core, Hc[3 + 3 = 6 marks]

(b) An inductor is made of two coils, A and B, having 300 and 200 turnsrespectively. The coils are wound on a cast steel core and in directions asshown in Figure 1. The two coils are connected in series to a dc voltage.

(i) Determine the 2 possible values of current required in the coils toestablish a flux density of 0.6 T in the air gap. [6 marks]

(ii) Determine the self-inductances LA and LB of the two coils. Neglectmagnetic leakage and fringing. [2 marks]

(iii) If the coil B is now disconnected and the current in coil A is adjusted to2 A, determine the mean flux density in the air gap. [6 marks]

Figure 1: All dimensions are in cm, NA = 300, NB = 200

o = 4 x 10-7 Hm-1

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Question 2

(a) A single phase, 300 kVA, 11 kV / 2.2 kV, 60Hz transformer has the followingequivalent circuit parameters referred to the high voltage side:

Rc(HV) = 50.0 k, Xm(HV) = 17.0 k

Req(HV) = 2.9 Xeq(HV) = 7.5

Determine

(i) No-load current as a percentage of full-load current.

(ii) No-load power loss (i.e. core loss).

(iii) No-load power factor.

(iv) Full-load copper loss.

[2 + 2 + 2 + 2 = 8 marks]

If the load impedance on the low-voltage side is Zload = 8 30 0 , determinethe voltage regulation using the approximate equivalent circuit.

[5 marks]

(b) A 50 kVA, 2400/240 V transformer has a core loss Pc = 200W at rated voltageand a copper loss Pcu = 300W at full load. It has the following load cycle.

Table 1: Load Cycle

Load (%) 0.0% 50% 75% 100% 110%

Power Factor - 1 0.6 lag 0.8 lag 0.9

Hours 6 6 6 3 3

Determine the all-day efficiency of the transformer, AD . [7 marks]

Question 3

(a) Explain clearly what you understand by the term armature reaction.[5 marks]

(b) What are the THREE conditions that need to be satisfied for voltage build-upin a self-excited d.c generator? [3 marks]

(Continued next page)

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Question 3(Continued)

(c) A d.c machine (10 kW, 250V, 1000rpm) has Ra = 0.2 , Rfw = 133. Themachine is self-excited and is driven at 1000rpm. The data for themagnetisation curve are

Table 2: Magnetisation data at 1000rpm

If (A) 0.0 0.1 0.2 0.3 0.4 0.5 0.75 1.0 1.5 2.0

Ea (V) 10 40 80 120 150 170 200 220 245 263

(i) Determine the generated voltage with no field current.[2 marks]

(ii) Determine the critical field circuit resistance.[2 marks]

(iii) Determine the value of the field control resistance (Rfc) if the no-loadterminal voltage is 250V. [2 marks]

(iv) Determine the value of the no-load generated voltage if the generator isdriven at 800rpm and Rfc = 0. [3 marks]

(v) Determine the speed at which the generator is to be driven such thatno-load voltage is 200V with Rfc = 0. [3 marks]

Question 4

(a) Use the approximate equivalent circuit to derive an expression for the slip atwhich maximum torque occurs in a wound rotor induction machine.

[6 marks]

(b) A 3 phase, Y-connected, 18kW, 50Hz, 415V, 6 poles, wound rotor Inductionmotor with stator / rotor turns of 2 has the following per phase parameters

Stator resistance = 0.3723

Stator reactance = 1.434 Rotor resistance = 0.1

Rotor reactance = 0.5

Determine

(i) The maximum torque developed.[4 marks]

(ii) The rheostat resistance / phase required to operate the machine atrated torque and 900 rpm. [10 marks]

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Question 5

(a) From a construction and operation point of view, give 3 ways in whichsynchronous motors and induction motors differ.

[3 marks]

(b) State any 2 synchronous motor applications.[2 marks]

(c) A 3300V, 1.5 MW, 3 phase, Y-connected synchronous motor hasXd = 4 /phase and Xq = 3 /phase. Neglecting all losses, calculate

(i) The excitation emf when the motor supplies rated load at unity powerfactor.

[7 marks]

(ii) The maximum mechanical power which the motor would develop forthis field excitation.

[8 marks]

Question 6

(a) Derive the relationship between governor droop and speed regulation.

[5 marks]

(b) With the help of a diagram, explain how synchronous generators withdifferent governor droops share on-coming bus loads. [5 marks]

(c) Three 25Hz turbine generators A, B and C are connected in parallel andoperating at 25Hz, 2400V. Generator A is rated at 600 kW and has a speedregulation of 2.0%. Generator B is rated at 500 kW and has a speed regulationof 1.5%. Generator C has a rating of 1000 kW and has a speed regulation of4.0%. The loads on machines A, B and C are 200 kW, 300 kW and 400 kW

respectively. If an additional 800 kW is connected to the bus, determine

(i) The new frequency[7 marks]

(ii) The load on each generator[3 marks]

END OF QUESTION PAPER

sg/

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Candidates ID:

Figure 2 for Question 1 [AttachmentTo be submitted with the answer booklet]

Figure 2: Magnetisation curve

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