ee-260 lecture 20 ac machinery

8/9/2019 EE-260 Lecture 20 AC Machinery

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EE-260 : Electro-Mechanical Systems(EMS)EE-260 : Electro-Mechanical Systems(EMS)Lecture#20Lecture#20

4.2 The rotating Magnetic Field (Page238)

The Relationship between Electrical Freqenc! and "peed o# MagneticField Rotation

(page 242)

Text Book: ha!ter 0" (Ste!hen $ ha!man "th E%)

&nstructor: Miss 'eelma 'a

lass: BEE " *

School o+ Electrical En,ineerin,an% om!uter Science

*e!artment o+ ElectricalEn,ineerin,

1


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1: The Rotating Magnetic Field (1/7)A rotating magnetic field induces three phase set of voltages in the three-phase

indings of a stator

!hat happens if three-phase set of voltages are applied to the threeindings of the stator"

Fundamental principle of ac machine operation


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http$%%www.teslasociet!.co


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How the stator magnetic field be made to rotate?

The fundamental principle of ac machine operation is that:

IF a 3-phase set of currents, each of equal magnitude and

differing in phase by 1200, flows in a 3-phase winding, then it willproduce a rotating magnetic field of constant magnitude (1.5

times the peak value).

1: The Rotating Magnetic Field (#/7)


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To understand the concept of the

rotating magnetic field, apply a set of

currents to the stator of the machine

shown in the Figure and see what

happens at specific instants of timei!e! "t#$o, "t#%$o&

' The rotating magnetic field concept is illustrated by an empty

stator containing (ust three coils, 1)$o apart!

' *ince such a winding produces only one north and one south

magnetic pole, it is a two pole winding!

1: $roduction of Rotating Magnetic

Field (%/7)


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( )

A

A

A

)#&'()(

)1#'()(

°−=

°−=

=

′

′

′

t Sin I t i

t Sin I t i

t Sin I t i

M cc

M bb

M aa

ω

ω

ω

A.turn/m

A.turn/m

A.turn/m

°∠°−=

°∠°−=

°∠=

′

′

#&')#&'()(

1#')1#'()(

')(

t Sin H t H

t Sin H t H

t Sin H t H

M cc

M bb

M aa

ω

ω

ω

The resultant flux density is given by:

( )

T

T

T

T

°∠°−=

°∠°−=

∠=

=

′

′

#&')#&'()(

1#')1#'()(

')(

t Sin Bt B

t Sin Bt B

t Sin Bt B

H B

M cc

M bb

M aa

ω

ω

ω

µ

The three phase current are gi+en by:

The current produces magnetic field intensity:

1: The Rotating Magnetic Field (&/7)


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1* +'

net aa bb cc

net M

B B B B

B B

′ ′ ′′= + +

= ∠ − °

°∠=°∠°−=

°∠−=∠°−=

=

′

′

#&'#

%#&')#&'(

1#'#

%1#')1#'(

'

M M cc

M

o

M bb

aa

BSin B B

BSin B B

B

t "t#$o

Flux densities at variousinstants of time

( )

( ) ' T

( ) ( 1#' ) 1#' T

( ) ( #&' ) #&' T

aa M

bb M

cc M

B t B Sin t

B t B Sin t

B t B Sin t

ω

ω

ω

′

′

= ∠

= − ° ∠ °

= − ° ∠ °

1: The Rotating Magnetic Field (*/7)


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Flux densities at variousinstants of time

( )

( ) ' T

( ) ( 1#' ) 1#' T

( ) ( #&' ) #&' T

aa M

bb M

cc M

B t B Sin t

B t B Sin t

B t B Sin t

ω

ω

ω

′

′

= ∠

= − ° ∠ °

= − ° ∠ °

t "t#%$o

°∠°−=

°∠°−=

°∠=

′

′

′

#&')1*'(

1#')%'(

'+'

Sin B B

Sin B B

Sin B B

M cc

M bb

M aa

'* 1#' '* #&'

1* '

net aa bb cc

M M M

net M

B B B B

B B B

B B

′ ′ ′= + +

= − ∠ ° − ∠ °

= ∠

1: The Rotating Magnetic Field (,/7)


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imilarl. at t01'o and at t0#7'o2 the net magnetic field is:

1)* +'net M B B= ∠ ° 1* 1'net M B B= ∠ °

3 Thus the direction of 4net changes

5ut magnitude remains constantThe net magnetic field is rotating

in a circle

3 This rotating magnetic field in the

stator can 5e represented asrotating north and south poles

and

1: The Rotating Magnetic Field (7/7)


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3 ;f the inding pattern is repeated tice<

a-c=-5-a=-c-5= - a-c=-5-a=-c-5=

!hen the % phase current is applied2 to

north and to south poles ill 5e created

3 A pole moves onl. half a. around the stator

surface in one electrical c.cle

#

#

#

e m

e m

e m

f f

θ θ

ω ω

=

=

=

#: Relationship 5eteen 6lectrical Freuenc. and peed of

Magnetic Field Rotation (#/%)

3 The indings on the to pole stator occur in

the order (ta>en counter cloc>ise): a-c=-5-a=-c-5=

' The electrical freuenc. of the

current is tice the mechanical

freuenc. of rotation


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3 The electrical freuenc. in hert can 5e related to the resulting

mechanical speed of the magnetic fields in revolution per minute

< <

# # #e m e m e m

P P P f f θ θ ω ω = = =

P

f n em

1#'=

#: Relationship 5eteen 6lectrical Freuenc. and

peed of Magnetic Field Rotation (%/%)3 ;f $ are the magnetic poles then $/# are repetition of indings

seuence around the inner surface of the stator

3 The electrical and mechanical uantities on the stator are related as:

;f nm is revolution per minute

/ sec,'

mm

n f rev=

# ,'

me

n P f = ×


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onclusion

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4.2 The rotating Magnetic Field(Page 238) The Relationship between Electrical

Freqenc! and "peed o# MagneticField Rotation

(page242)

ee-260 lecture 20 ac machinery

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