armature reaction in ac machine ppt and modern trends in ac machine ppt
HelenBoyle,Greece,Researcher
Published Date:14-07-2017
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AC Machine AC Machine F Fundamental ndamental
618 221 Basic Electric Machines
Mr. Mr. Kittithuch Kittithuch Paponpen Paponpen
Electronic and Computer System Engineering
Department ofi f Electrical Engiineeriing
Faculty of Engineering and Industrial Technology¾¾¾¾¾¾¾¾
Outline Outline
A simple loop in a uniform magnetic field
The Voltage Induced In A Simple Rotating Loop
The Torque Induced In A Current The Torque Induced In A Current-Carrying Loop Carrying Loop
The Rotating Magnetic Filed
The Relationship Between Electrical Frequency And The
S Speed d Of M Of Magnet ti i F c Fil ild ed R Rot tat ti ion
Mag gnetomotive Force And Flux Distribution On AC Machine¾¾¾¾¾¾¾¾¾¾
Outline Outline
The Induced Voltage In Coil On A Two-Pole Stator
The Ind The Induced Voltage ced Voltage In A Three In A Three-Phase Set Of Coils Phase Set Of Coils
The RMS Voltag ge In A Three-Phase Stator
Induced Torque In An AC Machine
AC Machine Power Flows And Losses
The Power-Flow i Diagram
Voltage Regulation And Speed Regulation Voltage Regulation And Speed RegulationOutline Outline
AC M AC Machi hines
Synchronous Machines Induction Machines
Magnetic filed current, I , Filed current is supplied by
F
is supplied by a separate dc magnetic induction
power source (transformer action) into
their filed windings their filed windings.
The filed circuits are located on their rotors.¾¾¾¾¾¾
A Simple Loop In A Uniform Magnetic Field A Simple Loop In A Uniform Magnetic Field
A lA large statiionary magnet prod duci ing an essentil ialll y constant d and
uniform magnetic filed
Rotating loop of wire within that filed.
The rotating part of the machine is called the “rotor” The rotating part of the machine is called the “rotor”
The stationary part of the machine is called the “stator”¾¾¾¾¾¾¾¾¾
The Voltage Induced In A Simple The Voltage Induced In A Simple Rotating Loop Rotating Loop
The voltage The voltage on each segment on each segment is is
e = vBוl
( )
ind
Segment ab:
Point into page
ev = vBוl=Bl sinθ
( ( ) )
ba ab
ee =× =× vB vB••ll== 0 0
( ( ) )
Segment bc: Segment bc:
cb
vB × ⊥l
e = vBוl= 0
Segment da: ( )
ad
Point out of page
Segment Segment cd: cd:
ev =× vB•l=Bl sinθ
( )
dc cd
¾¾¾
The Voltage Induced In A Simple The Voltage Induced In A Simple Rotating Loop Rotating Loop
Total Total induced induced voltage voltage on on the the loop loop
ee=+e+e+e =vBl sinθ +vBl sinθ
ind ba cb dc ad ab cd
and
sinθ = sin 180 −θ
θ = 180 −θ ( ( ) )
Note that
ab ab ccdd
ev =2sBlinθ
ind
If the loop is rotating at a constant ω, the angle θ of the
θ = ωt.
loop will increase with time,
vr = ω
The tangential velocity v of the edge of the loop:
er =2s ωBlinωt
ind
Area of the loop:
φ = AB
eA = ωBsinωφt = ω sinωt
A = 2rl
max
ind maxThe Voltage Induced In A Simple The Voltage Induced In A Simple Rotating Loop Rotating Loop
The The voltage voltage generated generated i in n t the he loop loop is is a a s sinusoid inusoid.
eA = ωBsinωφt = ω sinωt
ind max
¾
The Voltage Induced In A Simple The Voltage Induced In A Simple Rotating Loop Rotating Loop
eA = ωBsinωφt = ω sinωt
ind max
VVg oltage in anyy real machine will deppend on three factors:
The flux in machine (B)
The speed of rotation (ω)
A constant representing the construction of the machine
(the number of loopp, s, etc)¾¾
The Torque Induced In A Current The Torque Induced In A Current- -Carrying Loop Carrying Loop
If a current flows in the loop, then a torque
will be induced on the wire loop p.
Fl =i ×B
( ( ) )
Torque on the segment will then be
τ =rF ×
τθ τθ== == Fr Fr sin sin rrFF s sin inθθ
( ( ) )( ( ) )
θ is the ang gle between the vector r and vector FÆ
Æ
Æ
The Torque Induced In A Current The Torque Induced In A Current- -Carrying Loop Carrying Loop
Fi = l×B
( )
Left-hand rule
Index finger Field direction
Middle fing ger Current direction
thump Force direction¾¾
The Torque Induced In A Current The Torque Induced In A Current- -Carrying Loop Carrying Loop
segment ab:
( (d d down di irect ti ion) )
Fl =ii ×=BlB
( ( ) )
( (clockwise clockwise) )
τθ τθ== == Fr Fr sin sin rriillFF s sin inθθ
( ( ) )( ( ) )
ab ab ab
segment bc:
(into the page)
Fl =×= i B ilB
()
τθ =Fr sin = 0
( )( )
bc bc
(b (both R th R and d F F it point i it nto ththe page) )¾¾
The Torque Induced In A Current The Torque Induced In A Current- -Carrying Loop Carrying Loop
segment cd:
Fl Fl =×ii ii ×BB =llBB ( (up) )
( ( ) )
τ = F r sinθθ =rilF sin
( ( ) )( ( ) )
( (co clocckw wise se) )
cd cd cd cd cd cd
segment da:
(out of the page)
Fl =×= i B ilB
( )
τθ =Fr sin = 0
( )( )
da da
(Both R and F point out of the page)¾¾
The Torque Induced In A Current The Torque Induced In A Current- -Carrying Loop Carrying Loop
T Tl otal i ind duced d torque on th he l loop
τ =+ ττ +τ +τ =rilBsinθ +rilBsinθ
ind ab bc cd da ab cd
Note that:
θ =θθ =
ab cd
τ =2s rilBinθ
ind
A = 2rl
τθ τθ = = ABi ABi sin sin
ind¾¾
The Torque Induced In A Current The Torque Induced In A Current- -Carrying Loop Carrying Loop
If there is current in the loop, that current will generate a
magnetic flux density B with the direction shown.
loop
µi
BG
loop
B =
i =
loop
G
µ
G is a factor that depends on the geometry of the loop
µ is magnetic permeability of material
Substitutinggq these into induced torque eq quation
AG
τ== BB sinθθ kB B sin
ind loop s loop s
µ µ
τ =kBB ×
τ = ABi sinθ
ind loop s
ind¾¾¾¾¾¾
The Rotating Magnetic Filed The Rotating Magnetic Filed
τ τ=× =× kkBB BB
ind loop s
If two magnetic fields are present in a machine, then a torque will If two magnetic fields are present in a machine, then a torque will
B
be created.
S
If one magnetic field is produced by the stator and the other one is
B
R
produced by the rotor, then a torque will be induced in the rotor.
τ =kBB ×
ind R S
Thi i i s induced torque cause the rotor to turn and ali ign i itself f wi ith
the stator magnetic filed.
B
R
B
S¾¾¾
The Rotating Magnetic Filed The Rotating Magnetic Filed
If stator magnetic filed rotate, then the induced torque in the rotor
would cause it to constantly “chase” the stator magnetic filed
around in the cycle.
B
R
B B
S
This is the basic principle of all AC motor operation.¾¾¾
The Rotating Magnetic Filed The Rotating Magnetic Filed
How can the stator magnetic field be made to rotate?
“If a three phase set of current flows in a three If a three phase set of current flows in a three- -phase winding phase winding,
then it will produce a rotating magnetic filed of constant
magnitude”
Æ
Æ
The Rotating Magnetic Filed The Rotating Magnetic Filed
From magnetic filed principle: I mmf, F = Ni H = F/l
H tH = sinωt∠0 Aiturns/m
( ( ) )
it =II siA in ωt A
/
( ( ) )
M
/
aa
M
aa
The Rotating Magnetic Filed The Rotating Magnetic Filed
H H tH tH=∠ =∠ si sin nω ωtt 0 0 A Aiit turns/ urns/m m
( ( ) )
it it = =II sin sinω ωtt A A /
( ( ) ) M
/
aa
M
aa
it=− I sin ωt 120 A
( )
/ ( )
M
bb
it =I sin ωt − 240 A
( )
/
( ( ) )
M
cc
H tH=− sin ωt 120∠120 Aiturns/m
()
/ ()
M
bb
H tH=− sin ωt 240∠240 Aiturns/m
( )
/ ( )
M
cc
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