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ELEN 3441 Fundamentals of Power Engineering Spring 2008

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Instructor:

Dr. Gleb V. Tcheslavski

Contact:

gleb@ee.lamar.edu

Office Hours:

TBD; Room 2030

Class web site: MyLamar

Lecture 3: Three!hase !ower circuits

mailto:gleb@ee.lamar.edumailto:gleb@ee.lamar.edu

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Intro"uction

lmost all ele!tri! power generation and most of t"e powertransmission in t"e world is in t"e form of t"ree#p"ase $

!ir!uits% t"ree#p"ase $ s&stem !onsists of t"ree#p"ase

generators' transmission lines' and loads%

("ere are two ma)or ad*antages of t"ree#p"ase s&stems o*er

a single#p"ase s&stem+

1,-ore power per .ilogram of metal form a t"ree#p"ase

ma!"ine;

2,Power deli*ered to a t"ree#p"ase load is !onstant at all time'instead of pulsing as it does in a single#p"ase s&stem%

("e first t"ree#p"ase ele!tri!al s&stem was patented in 1882

/& o"n op.inson #ritis" p"&si!ist' ele!tri!al engineer'

Fellow of t"e Ro&al So!iet&%

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#. Generation of three!hase

volta$es an" currents

t"ree#p"ase

generator !onsists of

t"ree single#p"ase

generators wit"

*oltages of eualamplitudes and

p"ase differen!es of

1200%

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#. Generation of three!hase

volta$es an" currents

Ea!" of t"ree#p"ase

generators !an /e

!onne!ted to one of t"ree

identi!al loads%

("is wa& t"e s&stem would

!onsist of t"ree single#p"ase

!ir!uits differing in p"ase

angle /& 1200%

("e !urrent flowing to ea!"

load !an /e found as

VI

Z

= 3%4%1,

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#. Generation of three!hase

volta$es an" currents

("erefore' t"e !urrents flowing in ea!" p"ase are

0

0

0

0

120120

240240

A

B

A

V

I IZ

VI I

Z

VI IZ

= =

= =

= =

3%5%1,

3%5%2,

3%5%3,

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#. Generation of three!hase

volta$es an" currents

7e !an !onne!t t"e negati*e ground, ends of t"e t"ree single#

p"ase generators and loads toget"er' so t"e& s"are t"e !ommon

return line neutral,%

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#. Generation of three!hase

volta$es an" currents

("e !urrent flowing t"roug" a neutral !an /e found as

0 0

0 0 0 0

0 0 0 0

120 240

cos( ) sin( ) cos( 120 ) sin( 120 ) cos( 240 ) sin( 240 )

cos( ) cos( 120 ) cos( 240 ) sin( ) sin( 120 ) sin( 240 )

cos(

N A B CI I I I I I I

I jI I jI I jI

I jI

I

= + + = + +

= + + + + +

= + + + + +

= 0 0 0 0

0 0 0 0

) cos( )cos(120 ) sin( )sin(120 ) cos( )cos(240 ) sin( )sin(240 )

sin( ) sin( )cos(120 ) cos( )sin(120 ) sin( )cos(240 ) cos( )sin(240 )jI

+ + + +

+ + +

1 3 1 3cos( ) cos( ) sin( ) cos( ) sin( )2 2 2 2

1 3 1 3sin( ) sin( ) cos( ) sin( ) cos( )

2 2 2 2

0

NI I

jI

= +

+ +

=

7"i!" is+

3%%1,

3%%2,

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#. Generation of three!hase

volta$es an" currents

s long as t"e t"ree loads are eual' t"e return !urrent in

t"e neutral is 9ero:

Su!" t"ree#p"ase power s&stems eual magnitude' p"ase differen!es

of 1200' identi!al loads, are !alled /alan!ed%

n a /alan!ed s&stem' t"e neutral is unne!essar&:

P"ase Seuen!eis t"e order in w"i!" t"e *oltages in t"e indi*idual

p"ases pea.%

abc acb

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amined%

4% ("e s&stem power fa!tor at t"at point using t"e

power triangle relations"ip%

5% Line and p"ase !urrents at t"at point%

7e !an treat t"e line *oltage as !onstant and use t"e power triangle met"od to

ui!.l& !al!ulate t"e effe!t of adding a load on t"e o*erall s&stem and power fa!tor%