ECE320, Spring 2010, Exam 4a 12th April, 2010

Name

PID Number

Problem Max Point Point

1 40

2 30

3 30

!otal 100

Intru"tion#

• Closed book, but you are allowed to have one-page single-sided handwritten notes.

• $rite %our olution an& tep neatl% an& or&erl%' No "re&it (or ran&om i&e

)riting'

• *ox %our (inal an)er+alue )hen nee&e&'

Problem 1.

a) Draw the equivalent circuit o an !", label each parameter and its meaning. !ndicatewhich elements #or parameters) represent the copper losses and mechanical output,

respectively. #$% pts)

S-./!I-N#

& s ' (tator winding resistance

ls ' (tator leakage inductance

lr ' &otor leakage inductance

m ' "agneti*ing inductance& r ' &otor winding resistance

!r $+& r ##1-s)s) ' mechanical output power

!s$+& s ' (tator winding loss

!r $+& r ' &otor winding loss

!s$+& s !r

$+& r ' Copper oss.

!r $+& r ##1-s)s) ' mechanical output power.

b) /ill out the ollowing blanks to complete the sentences. #$% pts)

/or an !", the stator current consists o two components0 magneti*ing current and torque

current. he magneti*ing current is determined by the stator 2oltage and

stator requency .

he magneti*ing current produces a &otating "agnetic /ield . he

torque current component is related to the &otor current.

3hen the rotor is rotating at its synchronous speed, the rotor current becomes *ero ,

the torque produced becomes *ero , and the stator current becomes the

magneti*ing current component only. 3hen the rotor is rotating slightly slower than

the synchronous speed with a slip, the rotor current starts to low and torque is produced.

he torque produced at a speed near the synchronous speed is proportional to the slip speed

#or slip requency) .

4n !"5s parameters can be determined by ocked &otor and 6o oad 7 tests, which are

equivalent to transormer5s (hort Circuit and 77 8pen Circuit tests, respectively.

Problem $ a) 4 9-phase !" is ed by a :% ;* power and operating at a slip o s ' %.%<, the

rotor current #reerred to the stator side), I 2 is 1$ 4, and rotor resistance is $ Ω, determine

i) the mechanical output power #= pts), rotor speed #= pts), and shat torque #$ pts), given

that the !" is a $-pole machine, and

ii) the mechanical output power #$ pts), rotor speed #$ pts), and shat torque #$ pts), giventhat the !" is a =-pole machine.

S-./!I-N#

i)$ $1 1 .%<

9. . 9 . $ . . 1$ 1:=1:.%<

out r r

s P R I W

s

− −= = Ω =

( ) ( )1 . 1 .%< . :% <>rotor synW s W Hz Hz = − = − =

Nm P

T rotor

out shaft ?<.=<

$<>

=1:,1:=

⋅==

π ω

ii) out P same=

<> <>$?.<

$

$

rotor

Hz Hz W Hz

P = = =

÷

. ) $#=<.?<) @1.> .$

shaft shaft

P T T in i N m

= = = ÷

b) 4 9-phase $-pole :%-;* !" is rated at $=% 2, 9%4 and 1% k3 and its stator connection is

delta and its rate rotor speed is 9,9%% rpm. 3hat are the rated voltage, rated current, rated

speed, and rated power ater reconigured to A connectionB #1= pts)

S-./!I-N#

&ated voltage 0 :@$.=1<9$=% =

&ated current 0 A9$1.1>9,9% =

&ate speed0 9,9%%rpm #same)

&ated power 0 1% 3 #same)

Problem 9. #9% points) S-./!I-N#

a) he circuit below shows a single-phaseinverter circuit using our switches to

convert a dc voltage into ac to power an

inductive load. Draw a control sequenceor each o the our switches by using

logic %E #or o) and 1E or on,

respectively, to complete the waveormigure. #$% pts)

b) !n the given circuit below, assume the switch is used to dim the light by turning on and o at1 k;*. 3hen the switch is turned on or 1%%F o each switching period #i.e., turn on the

switch all the time), the light bulb consumes :% 3. 3hat is the duty cycle o the switch when

the light is dimmed to $% 3B #he duty cycle is deined as onsw, the ratio o turn-oninterval, on versus the switching period, sw) #1% pts)

S-./!I-N#

3hen ( is on, P L ' :% 3, and when o, P L ' % 3.

hereore, the average power, P L ' $% 3 ' DG#:% 3) and D ' $%:% ' 19.

Load

S1

S2 S4

S3

v dc v ac

0

Vdc

0

Vdc

-Vdc

Vac

S1

S2

S3

S4

V dc

Light

Bulb

R L

i S S

v S