Distributed Power Systems ELCT 908 by iqbiU0h7

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									 Modeling of Power
   Transformers


A Static Device
      Transformers
   The transformer enables us to utilize different voltage
    levels across the system for the most economical
    value.
   Stepping up the generator voltage to high voltage, is
    done through power transformers to minimize losses
    and increase the transmission capacity of the lines.
   This transmission voltage level is then stepped down in
    many stages for distribution and utilization purposes.
          General Theory

   A transformer contains two or more windings linked by a
    mutual field.
   The primary winding is connected to an alternating
    voltage source.
   The input current results in an alternating flux whose
    magnitude depends on the voltage and number of turns
    of the primary winding.
   The alternating flux links the secondary winding and
    induces a voltage in it with a value that depends on the
    number of turns of the secondary winding.
         Transformers

          Primary winding        Secondary winding



Supply                    NP       NS                    Load




                      Laminated iron core
          Basic components of single phase transformer
  Transformers
                                          Primary
                                          Winding



Multi-layer
Laminated                                        Secondary
Iron Core                                         Winding


                                          X1
                                          X2
                                  H1 H2

                                                Winding
                                               Terminals




     5.2 Single phase transformer arrangement
                          Transformers
                     H2                   X2                               H2                         X1

                     Vp                   Vs                               Vp                         Vs


                     H1                   X1                               H1                         X2

           100                                                   100


Vp ( t )                                              Vp ( t )

             0                                                     0
Vs( t )                                               Vs( t )




           100                                                   100
                 0        5     10         15   20                     0        5           10         15   20
                                 t                                                           t
                              milli  s                                                   milli  s

                              (a)                                                   (b)

                                          Polarity for transformer
Transformers
                                                 Iron core




                                                              Insulation

                                                             Secondary
                                                              winding




                                     Terminals


           Small transformer construction
   a) Lamination        b) Iron core with winding
Transformers




Dry-type three-phase transformer
        Transformers
                                          Bushing




                                                    Steel
   Iron core                                        tank
behind the steel
      bar




               Winding




                         Insulation


                                       Radiator



                   Oil Insulated and cooled transformer
Power Transformers
Transformation ratio




Primary (supply)       Secondary (Load)
            Transformers at no load
                                                         Ic                E1
            IF
                                                         Qc


            E1                                                If
                                                Im
                                                 f                    IF



                                                                   Ic Im
The no load current If is needed to supply the no load
losses and to magnetize the transformer core.
Loaded Transformer




               Z2’ is the load impedance
               referred to the primary
    Transformer losses
   The transformer losses are divided into electrical losses
    (copper losses) and Magnetic losses (Iron losses).
   Copper losses in both the primary and secondary windings.

                         I12 R1  I 2 R2
                                    2


   Magnetic losses, these losses are divided into eddy current
    losses and hysteresis losses.

           Pmag  Peddy  Physterises  V1I m
  Equivalent circuit




V1: Primary voltage (supply)
I1 : Primary current.
V2: Secondary voltage (load)
I2: : Secondary current
Exact Circuit
      Approximate Circuit




          (a)                                          (b)


The no load current ranges from 1% to 3% of the full load current.
Therefore, the circuit can be simplified to circuit (b).
Phasor Diagram




  V1  V2
        '
             I 2 ( Req
                '
                           jX eq )
      Performance Measures

   The percent regulation




   The transformer efficiency
Voltage Regulation




VR  V1  V2'  I 2 Req cosf  I 2 X eq sin f
                  '              '
       Example


A 100-kVA, 400/2000 V, single-phase transformer has the following
   parameters
               R1 = 0.01                R2 = 0.25 ohms
               X1 = 0.03 ohms           X2 = 0.75 ohms
The transformer supplies a load of 90 kVA at 2000 V and 0.8 PF lagging.

 Calculate the primary voltage and current using the simplest
  equivalent circuit.
 Find also the V.R. and efficiency for the transformer

								
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