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DESK NUMBER: UNIVERSITY OF NEWCASTLE STUDENT NUMBER : STUDENT NAME:

SCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE EXAMINATION

Semester 2 2010

ELEC3130 ELECTRIC MACHINES AND POWER SYSTEMS FINAL EXAMINATION

This paper is for Callaghan students

Examination duration: 3 hours

Reading time: 10 minutes

This examination has 4 pages.

This examination has 10 questions.

Materials supplied by examinations: 1 4 Page Booklet 1 12 Page Booklet Any non-programmable calculators are allowed

Special Instructions: Students must answer four (4) questions from Part A and three (3) questions from Part B. Part A is valued at 40%. Part B is valued at 60%. All questions of Part A are of equal value. All questions of Part B are of equal value.

ELEC3130 Electric Machines and Power Systems

Part A: Answer any four(4) questions

1. A DC shunt generator gave the following results in the open circuit test at a speed of 800rpm:

Field Current (A): 1 2 3 4 6 8 10E.M.F (V): 90 185 251 290 324 345 360

Under the load condition the field resistance is adjusted to 50 and the terminal voltage is300 V. The armature resistance is 0.1 .

Assuming that the flux is reduced by 5% due to armature reaction, find the load current suppliedby the generator.

(10 Marks)

2. A 50 Hz, 8 pole induction motor has a full load slip of 4%. The rotor resistance is 0.001 per phase and the stand still reactance is 0.005 per phase. Find the ratio of maximum torqueto full load torque and the speed at which the maximum torque occurs. Stator resistance, corelosses and friction and windage losses may be ignored.

(10 Marks)

3. The rotor emf of a 3-phase, 6 pole, 400 V, 50 Hz induction motor alternates at 3 Hz.Compute the speed and percentage slip of the rotor. Find the rotor copper loss per phase ifthe full input to the rotor is 111.9 kW.

(10 Marks)

4. The synchronous reactance per phase of a 3-phase, star-connected, 6600 V, round rotor,synchronous motor is 10 . For a certain load, the input is 900 kW and the induced line to linee.m.f is 8900 V. Evaluate the line current. Neglect armature resistance.

(10 Marks)

5. A resultant current space vector has a peak magnitude of 15.4 amperes and an angle of13 relative to the a-phase magnetic axis, which has been taken as the reference axis. Findthe a, b and c phase components of the resultant current space vector.

(10 Marks)

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ELEC3130 Electric Machines and Power Systems

Part B: Answer any three(3) questions

6. When operated at rated voltage, a 230 volt shunt motor runs at 1800 rpm at full loadand at no-load. The full load armature current is 50 amps, the shunt field winding has 1500turns per pole and the resistance of the armature circuit is 0.2 .

The magnetisation characteristic at 1800 rpm is:

generated emf 200 210 220 230 240 250field current 0.53 0.59 0.65 0.73 0.81 0.95

(a) Compute the demagnetising effect of armature reaction at full load in ampere-turns perpole.

(b) A long shunt cumulative series winding having six turns per pole and a resistance of 0.055 is added to the machine. Compute the speed at full load current and rated voltage,with the same shunt field circuit resistance as in part (a).

(c) With the series field winding of part (b) installed, compute the internal starting torqueif the starting armature current is limited to 90 amps and the shunt field current has itsnominal value. Assume that the corresponding demagnetising effect of armature reactionis 230 ampere-turns/pole.

(20 Marks)

7. A 3 phase, 6 pole, 220 V, 60 Hz induction motor has an effective rotor to stator turns ratioNre/Nse of 0.8. Regard the machine as ideal. A balanced wye-connected load of 3 resistancein parallel with 2200 F capacitance in each phase is connected to the rotor terminals. Themotor is rotating at 350 rev/min. Determine

(a) The effective impedance per phase as seen from the stator side.

(b) The total power delivered by the supply.

(c) The power delivered to the rotor load.

(d) The mechanical power.

(e) The shaft torque.

(20 Marks)

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ELEC3130 Electric Machines and Power Systems

8. A 440 volt, 6 pole, three phase, star connected, synchronous motor has a resistance of0.6 /phase and a synchronous reactance of 5 /phase. The machine takes a current of 30 Aat a power factor of 0.8 leading. Find the excitation voltage and the machine angle.

If the machine angle on no-load is two mechanical degrees what is the net torque developed bythe motor.

(20 Marks)

9. A 750-kV line utilizes a bundling arrangement of four conductors per phase, as shown inFigure 1.

Figure 1: Physical dimensions of 750-kV line for Question 9.

(a) Compute the reactance per phase of this line at 60 Hz. Each conductor carries 25 percentof the phase current, and we assume transposition.

(b) Find the cable dimensions of a hypothetical single-conductor that would have the sameinductance as the given line.

(c) Compute the shunt capacitance per phase of the given line. Assume that the chargeper phase divides equally between the four conductors. Neglect the effect of earth oncapacitance.

(20 Marks)

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ELEC3130 Electric Machines and Power Systems

10. Draw the impedance diagram for the power system shown in Figure 2. Mark impedancesin per unit. Neglect resistance, and use a base of 50,000 kVA, 138 kV in the 40 line.

The ratings of the generators, motors, and transformers are:

Generator 1: 20,000 kVA, 13.2 kV, X = 15%

Generator 2: 20,000 kVA, 13.2 kV, X = 15%

Synchronous Motor 3: 30,000 kVA, 6.9 kV, X = 20%

Three-phase Y-Y transformers: 20,000 kVA, 13.8Y-138Y kV, X = 10%

Three-phase Y- transformers: 15,000 kva, 6.9-138Y kV, X = 10%

All transformers are connected to step up the voltages of the generators to the transmissionline voltages.

Figure 2: One line diagram for Question 10.

(20 Marks)

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