Transformer 2W2

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    08-Feb-2016
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Transcript of Transformer 2W2

  • 2

  • E.m.f. equation of transformer2

    m

    m

    mm

    mmm

    mmm

    m

    fNEfNE

    NfNfEsmrNfNE

    tEtNtdtdNe

    tdtdNde

    ==

    ==

    ==

    ===

    =

    =

    22

    11

    44.444.4

    44.42

    2...

    2

    coscos)sin(

    sin

    pi

    pi

  • Ideal Transformer

    Conditions for the ideal transformer.a) no leakage fluxb) all core losses (both hysteresis and eddy) are zero

    c) the windings have zero resistanced)the permeability of the core is infinite ( the exciting current is negligible)

    1

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  • 5Ideal Transformer Relation between current that flows in the primary

    winding, ip(t) and current that flows in the secondary winding, is(t):

    atiti

    tiNtiN

    S

    P

    SSPP

    1)()(

    )()(

    =

    =

    aII

    aVV

    S

    P

    S

    P

    1=

    =(2)

    (3)

    (4)

    (5)

  • 6Transformer Impedance Primary Impedance:

    Primary Voltage:

    Primary Current:

    Primary impedance in terms of secondary impedance

    P

    PL I

    VZ ='

    SP aVV =

    a

    II SP =

    LL

    S

    S

    S

    S

    P

    PL

    ZaZIV

    aaI

    aVIVZ

    2

    2

    '

    /'

    =

    ===

    (15)

    (16)

    (17)

    (18)

  • 7Example 1

    A transformer coil possesses 4000 turns and links an ac flux having a peak value of 2 mWb. If the frequency is 60 Hz, calculate the effective value of the induced voltage E.

    Ans: 2131V

  • 8Example 2

    A coil having 90 turns is connected to a 120V, 60 Hz source. If the effective value of the magnetizing current is 4 A, calculate the following:

    a. The peak value of fluxb. The peak value of the mmfc. The inductive reactance of the coild. The inductance of the coil.

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    Equivalent Circuit a) referred to primary side b) referred to secondary side

  • 14

    Approximate equivalent circuit

    Approximate equivalent circuit c) Referred to primary side (no exicitation) d) Referred to secondary side (no excitation).

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    Example 3A not-quite-ideal transformer having 90 turns on the primary

    and 2250 turns on the secondary is connected to a 120 V, 60 hz source. The coupling between the primary and the secondary is perfect but the magnetizing current is 4 A. calculate:

    a. The effective voltage across the secondary terminalsb. The peak voltage across the secondary terminals.c. The instantaneous voltage across the secondary when the

    instantaneous voltage across the primary is 37 V.

    Ans: 3000V, 4242 V, 925 V.

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    Example 4An ideal transformer having 90 turns on the primary and 2250

    turns on the secondary is connected to a 200 V, 50 Hz source. The load across the secondary draws a current of 2 A at a power factor of 80 per cent lagging. Calculate :

    a. The effective value of the primary currentb. The instantaneous current in the primary when the

    instantaneous current in the secondary is 100 mA.c. The peak flux linked by the secondary winding.

    Ans: 50 A, 2.5 A, 10 mWb.

  • 21

    Example 5Calculate voltage E and current I in the circuit

    of Fig. shown below, knowing that the ideal transformer T has a primary to secondary turns ratio of 1;100.

    Ans: 800 V, 2 A.

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    Determination of transformer parameters: Short Circuit Test

    Magnitude of series impedance:

    Power factor:

    SC

    SCSE I

    VZ =

    SCSC

    SC

    IVPPF == cos

    000

    00

    =

    =

    SC

    SC

    SC

    SCSE I

    VIVZ

    )()( 22 SPSPSEeqeqSE

    XaXjRaRZjXRZ

    +++=

    +=

  • 27

    Three Phase Transformer Three phase transformer consists of 3 transformers. It is connected independently or in combination of 3

    transformers. Primary and secondary windings can be connected as wye

    (Y) or delta () Thus, there are 4 types of connections:

    Wye wye (Y-Y) Wye delta (Y-) Delta wye (-Y) Delta delta (-)

  • 28

    3 phase Transformer

    3 phase transformer connected independently

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    Three Phase Transformer

    Three phase transformer connected to a common core with three legs

  • 30

    Connection Y-Y

    Three Phase transformer Y-Y connection

  • 31

    Transformer Connection Y-Y

    aVV

    VV

    S

    P

    LS

    LP==

    33

  • 32

    Transformer Y- Connection

    aVV

    VV

    VV

    LS

    LP

    S

    P

    LS

    LP

    3

    3

    =

    =

  • 33

    Transformer -Y Connection

    aVV

    VV

    VV

    LS

    LP

    S

    P

    LS

    LP

    3

    3

    =

    =

  • 34

    Transformer - Connection

    aVV

    VV

    S

    P

    LS

    LP==

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