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1 ELECTRICAL MACHINE EEP 3243  Lt Cdr Ong Khye Liat RMN

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1

ELECTRICAL MACHINE

EEP 3243

 

Lt Cdr Ong Khye Liat RMN

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2

RECAP/ADDITION

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3

Transformer Types

•  Power transformers•  Instrument transformers

•  Pulse transformers

•  RF transformers

•  Audio transformers

 –

 –

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4

Operating Principle

• A voltage willinduce acrosssecondary coil

according toFaradays laws of electromagnetic

induction.

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5

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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6

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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8

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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10

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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12

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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13

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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18

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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22

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