ECE320, Spring 2006, Exam 4c 17th April, 2006

Name
PID Number
Problem / Max Points / Points
1 / 40
2 / 30
3 / 30
Total / 100

Instructions:

·  Closed book, but you are allowed to have one-page single-sided handwritten notes and your exam_1 notes.

·  You can have 3 pages of blank papers for calculation purpose.

·  Write your solutions and steps neatly and orderly. No credits for random side writings.

·  Box your answers.


Problem 1.

a)  Draw the equivalent circuit of an IM, label each parameter and its meaning. Indicate which elements (or parameters) represent the copper losses. (20 pts)

SOLUTION:

Rs and Rs and Is 2 . Rs and Ir 2. Rr represent copper losses

b) Fill out the following blanks to complete the sentences. (20 pts)

For an IM, the stator current consists of two components: magnetizing current and torque current. The magnetizing current is determined by the stator Voltage and

stator frequency .

The magnetizing current produces a rotating magnetic field . The torque current component reflects the current that flows in the rotor .

When the rotor is rotating at its synchronous speed, the rotor current becomes zero_____ , the torque produced becomes zero , and the stator current becomes the

magnetizing current component only. When the rotor is rotating slightly slower than the synchronous speed with a slip, the rotor current starts to flow and torque is produced. The torque produced at a speed near the synchronous speed is proportional to the slip (frequency).

An IM’s parameters can be determined by locked rotor and no load tests, which are equivalent to transformer’s short circuit and open circuit tests, respectively.


Problem 2 a) A 3-phase IM is fed by a 50 Hz power and operating at a slip of s = 0.05, the rotor current (referred to the stator side), I2 is 20 A, and rotor resistance is 1 W, determine

i) the mechanical output power (4 pts), rotor speed (4 pts), and shaft torque (2 pts), given that the IM is a 2-pole machine, and

ii) the mechanical output power (2 pts), rotor speed (2 pts), and shaft torque (2 pts), given that the IM is a 8-pole machine.

SOLUTION:

i)

ii) 8 pole :

b) A 3-phase IM is rated at 460 V and 10 kW and its stator connection is Y. What are the rated voltage, rated current, and rated power after reconfigured to delta connection? (14 pts)

SOLUTION:

Rated voltage :

Rated current : 21.73 A

Rated power : 10 KW (same)
Problem 3. (30 points)

a) The circuit below shows a single-phase inverter circuit using four switches to convert a dc voltage into ac to power an inductive load. Draw a control sequence for each of the four switches by using logic “0” (for off) and “1” for on, respectively, to complete the waveform figure. (20 pts)

SOLUTION:

b) In the given circuit below, assume the switch is used to dim the light by turning on and off at 1 kHz. When the switch is turned on for 100% of each switching period (i.e., turn on the switch all the time), the light bulb consumes 60 W. What is the duty cycle of the switch when the light is dimmed to 20 W? (The duty cycle is defined as Ton/Tsw, the ratio of turn-on interval, Ton versus the switching period, Tsw) (10 pts)

SOLUTION:

Duty cycle D

When S is on, pL = 60 W, and when off, pL = 0 W.

Therefore, the average power, PL = 20 W = D·(60 W) and D = 20/60 = 0.333.