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**Assignment 1**

NOTE: This assessment carries 15% of the final unit total. Each question in the assessment will be marked out of 20, and the total will be scaled down to a mark out of 15 to be added to the unit total

Students need to score more than 40% (6/15) to pass this assessment item

**Question 1 20 Marks**

(a) A 20 kV source delivers power to 48 Ω resistive load and a 550 kW electric boiler (connected in parallel). Draw the equivalent per unit circuit diagram and calculate the per unit line voltage, resistance, and power for 50 kV base voltage and 100 MVA base power. (10 Marks)

(b) A magnetic circuit has dimensions Ac = Ag = 9 cm2, g = 0.060 cm, LC = 60 cm and N = 600 turns. Find the reluctances Rc and Rg with μr = 70,000. Find the flux and current for core flux density Bc = 1 T. (10 Marks)

**Question 2 20 Marks**

(a) A 3-phase 50 Hz synchronous generator operating at no load has a generated voltage of 11.2 kV at rated frequency. If the pole flux is decreased by 15% and the speed is increased by 10%. Determine-

(i) The induced voltage. (4 Marks)

(ii) The frequency. (4 Marks)

(b) A 3-phase, 1500-KVA, 13.2 kV, wye connected synchronous generator has an armature resistance of 0.6 Ω and a synchronous reactance of 11 Ω. The generator supplies rated load at rated voltage.

(i) Calculate the generated voltage at 0.9 PF leading and lagging. (4 Marks)

(ii) Calculate the generated voltage at 0.85 PF leading and lagging. (4 Marks)

(iii) Calculate the voltage regulation for unity PF, 0.9 PF, and 0.8 PF. (4 Marks)

**Question 3 20 Marks**

(a) A motor drives a flywheel having a moment of inertia of 5 kg. m2 . The speed increases from 1600 r/min to 1800 r/min in 8 s. Calculate:

(i) The torque developed by the motor. (4 Marks)

(ii) The energy in the flywheel at 1800 r/min. (4 Marks)

(b) A 4-pole 250 kW, 750 V DC generator has a lap winding on the armature. Calculate the following:

(i) The full load current of the generator. (6 Marks)

(ii) The current carried by the armature coil. (6 Marks)

**Question 4 20 Marks**

(a) A 3-phase, 8-pole, squirrel-cage induction motor, connected to a 50 Hz line, possesses a synchronous speed of 800 r/min. The motor absorbs 65 kW, the copper and iron losses in the stator are 5 kW and 1 kW, respectively. Determine the active power to the rotor, the torque developed by the motor, and mechanical power delivered to the load (assume the windage and friction losses are equal to 2.2 kW). (8 Marks)

(b) A large 3-phase, 4000 V, 50 Hz, squirrel-cage induction motor draws a current of 385 amp and a total active power of 2344 KW at full load. The measured speed is 709.2 r/min. The stator is connected to wye and the resistance between two stator terminals is 0.10 Ω. The total iron losses are 23.4 kW, and the windage and friction losses are 12 kW. Determine the following:

(i) The power factor at full load. (4 Marks)

(ii) The active power supplied to the rotor. (4 Marks)

(iii) The total I^{2}R losses in the rotor. (4 Marks)

**Question 5 20 Marks**

(a) A 240 kW, 500 V, 1850 r/min separately excited DC generator has an overall efficiency of 94%. The shunt field resistance is 60 Ω and the rated current is 4.7 amp. The I^{2}R loss in the armature is 0.023 pu. Determine-

(i) The rated armature current. (3 Marks)

(ii) The total losses in the machine. (3 Marks)

(b) A separately excited DC generator running at 1400 r/min produces an induced voltage of 127 V. The armature resistance is 2 Ω and the machine delivers a current of 10 amp.

**Determine-**

(i) The terminal voltage. (3 Marks)

(ii) The heat dissipated in the armature. (4 Marks)

(c) A 3-phase, 20-pole induction motor is connected to a 600 V, 50 Hz source. Calculate:

(i) Synchronous speed. (3 Marks).

(ii) If the voltage is reduced to 300 V, will the synchronous speed change? (4 Marks).

**Assessment Criteria:**

Each section of questions will be marked according to criteria below

- Correct procedure and steps toward correct solutions: 80%
- Correct answers and units: 10%
- Professional presentation and layout: 10%