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8/14/2019 part 3 emachines EEP 3243
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ELECTRICAL MACHINE
EEP 3243
Lt Cdr Ong Khye Liat RMN
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RECAP/ADDITION
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Transformer Types
• Power transformers• Instrument transformers
• Pulse transformers
• RF transformers
• Audio transformers
–
–
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Operating Principle
• A voltage willinduce acrosssecondary coil
according toFaradays laws of electromagnetic
induction.
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Ideal Transformer
,B y d e fin itio n a n id e a l tra n sfo rm e r h a s n o lo sse s a n d it co re is in fin ite ly
.p e rm e a b le T h e fo llo w in g p o in ts o f id e a l
:tra n sfo rm e r sh o u ld b e n o te d
– .N o w in d in g re sista n ce
– .N o le a ka g e flu x
– .N o iro n lo sse s
– Its co e fficie n t o f co u p lin g is.u n ity
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Voltage induced in a coil
• T h e flu x a lte rn a te s sin u so id a lly a t
fre q u e n cy f , +periodically reaching ve-and ve peaks Ø max .
• The alternating flux induces a sinusoidal,ac voltage in the coil whose effective
value is given by
= .E 4 44fNØmax V
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Cont. = .E 4 44fNØmax V
where
= E effective voltage induced
= f frequency of the flux N = # of turns on the coil
Ømax = peak value of the flux
. =4 44 a constant of•
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EXAMPLE 1
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Cont.•
• Flux is increasingwith time, the rateof change is
greater than zeroand the voltage is+ve.
• Flux is decreasing
with time, the rateof change is lessthan zero and thevoltage is -ve.
Fig 1: A sinusoidal flux induces asinusoidal voltage.
•
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Applied Voltage and Induced Voltage
• The coil has areactance X m and
draws a current Im. If the
resistance of thecoil is negligible,the current isgiven by
Im = Eg /X m
:Fig 2 The voltage E induced in a coil is equal to the applied voltage Eg .
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Cont.• The sinusoidal current Im produces a sinusoidal
mmf (NIm), which icreates a sinusoidal flux, Ø.
• Im is called the magnetizing current and Ø max is
the peak value of this ac flux.
• The applied voltage Eg and the induced voltage
E must be identical.
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Cont.
# ,For a g iven freq u en cy an d of tu rn s Ø max varies in
proportion to the applied voltage E g .
= = .E Eg 4 44fNØmax V
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EXAMPLE 2
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Cont.
• For insert an iron coreinto the coil Eg, E,
Ø max will retain its
original value.
• The magnetizingcurrent Im is much
smaller.
• To produce the sameflux, a smaller mmf is needed with aniron core than with
an air core.
:Fig 3 T h e flu x in th e co ilre m a in s con sta n t a s lo n g a s Eg .isconstant
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Elementary Transformer
• If second coil closeto the first, it will
surround a portionØm1 of the total
flux.
• An ac voltage E2 is
induced in thesecond coil.
:Fig 4 Vo lta g e in d u ced in a seco n d a ry
.co il
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Cont.
• Voltage only existsonly btw terminal 1-2 and 3-4. Novoltage exists btw
primary andsecondary terminal (electrically isolated).
• The flux, Ø can bebroken up intomutual flux Øm1 and
the leakage flux Øf1.
•
:Fig 4 Vo lta g e in d u ced in a seco n d a ry
.co il
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Cont.• Coupling btw the 2
coils is weak whenthey are far apartand the mutual fluxis very smallcompared to thetotal flux.
• Better coupling can
obtain by bringing 2coils closer, buteven bring andtouch the 2 coils the
mutual flux still
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Ideal Transformer at No-LoadVoltage Ratio
• This idealtransformer hasprimary and
secondary coilsrespectivelyposses N1 and N2
turns.
• The mutual flux iscompletely linkedby the primaryand secondary
coils.
: - .Fig 5 T h e id e a l tra n sfo rm e r a t n o lo a d
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Cont.
• According to the previousequation, we can write:
E1 = 4.44fN1 Ø max and E2 =
4.44fN2 Ø max
• The above equations canbe deduce for voltage
ratio and turn ratio, a of an ideal transformer :
•
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Cont.
• E2 is in phase with
phasor E1, current
Im lags 90o behind
applied voltage Eg
and flux Ø m also in
phase with Im.
•
:Fig 6 Phasor relationships at- .no load
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EXAMPLE 3
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END OF PART 3
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Reactance• C ircu it e le m e n t's o p p o sitio n to a n a lte rn a tin g
,cu rre n t ca u se d b y th e b u ild u p o f e le ctric o r m a g n e tic fie ld s in th e e le m e n t d u e to th e
.current
• R e a cta n ce is th e im a g in a ry p a rt o f e le ctrica lim p e d a n ce , used to compute amplitude and p h a se ch a n g e s o f sin u so id a l a lte rn a tin g
current .g o in g th ro u g h th e circu it e le m e n t
• ,B oth rea ctan ce X an d ,re sista n ce R a re re q u ire d to ca lcu la te th e , .im p e d a n ce Z
•
•
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Cont.
• If >X 0 , the reactance is said tob e inductive
• If =X 0, then the impedance is
purely resistive • If <X 0 , the reactance is said tobe capacitive
•
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Cont.
• C a p a citiv e re a cta n ce
•
•
• C o n d u ctive re a cta n ce
•