Losses in the Transformer

The following losses are occurs in the transformer.

Core Loss

• The core loss depends upon the supply voltage. 
• The coreloss 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.

( I ) Hysteresis 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

        W_h = hB_max^1.6fV Joule / second or watt

Where h = Steinmetz constant, its value depends on the core material

     B_max = Maximum flux density in weber / meter²

            f = Supply frequency in Hz

          V = Volume of the core in meter³

( II ) Eddy current loss

• 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 B_max^1.6f²t²  

Where K = Constant

     B_max = Maximum flux density in weber / meter²

            f = Supply frequency in Hz

            t = Thickness of lamination 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 winding.

• 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 ( W_c ) = 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 W_c α ( I )²

• It means that copper loss varies as square of the current.

Total copper losses at half load

W_c  α ( I / 2 )² R

        =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

       W_c α ( 2I )² R

             = 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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