1 November 2017

Losses in the Transformer

  • There are following losses occures in the transformer.
( a ) Core loss
  • The core loss depends upon the supply voltage. 
  • The core loss practically remains constant for all loads because the core flux remains constant at any load conditions. 
  • This loss includes hysteresis loss and eddy current loss.

  • This loss is due to rapid reversal of magnetism due to alternating flux. 
  • It depends on the loop area of the material. The hysteresis loss is given by
        Wh = hBmax1.6fV Joule / second or watt
        Where h = Steinmetz constant, its value depends on the core material
             Bmax = Maximum flux density in weber / meter2
                   f = Supply frequency in Hz
                  V = Volume of the core in meter3
  • An emf is induced in the core due to alternating flux in the core according to the laws of electromagnetic induction. 
  • Although this emf is small, it sets up large current in the core due to small core resistance. 
  • The loss due to this current is known as eddy current loss. The eddy current loss is given by
        We = K Bmax1.6f2t2  
        Where K = Constant
              Bmax = Maximum flux density in weber / meter2
                    f = Supply frequency in Hz
                    t = thickness of laminations in mm
  • The eddy current loss varies as ( I ) Square of maximum flux density ( II ) Square of supply frequency ( III ) Square of thickness of lamination
  • If the supply voltage keeps constant, the core loss remains constant. The core loss does not depend on the load current. 
  • The value of core loss can find out by open circuit test.
( b ) Copper losses
  • These losses are due to ohmic resistances of the transformer windings.
        Copper losses in the primary winding = I12 R1
        Copper losses in the secondary winding = I22 R2
        Total copper losses = I12 R1 + I22 R2
  • Total copper losses at full load ( Wc ) = I12 R01
                                                                 = I22 R02
        Where R01 = Transformer winding resistance as referred to primary side
                   R02 = Transformer winding resistance as referred to secondary  side
        \ Copper losses Wc a I2
  • It means that copper loss varies as square of the current.
Total copper losses at half load
        Wc a ( I / 2 )2 R 
              a  I2R / 4 
  • Therefore total copper loss at half load is reduced four time that of full load copper losses.
Total copper losses at twice full load
       Wc a ( 2I )2 R 
             a  4I2 R
  • Therefore total copper loss at twice full load is four times that of full load copper losses. 
  • The copper loss depends on the value of square load current and its value can find out by short circuit test.
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