Download - 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,
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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)