6 November 2017

Transformer Efficiency and Condition for Maximum Efficiency

EFFICIENCY OF TRANSFORMER

Efficiency = ( Output power / Input power ) × 100%

                 = ( Output power / Output power + Losses ) × 100%
                 = ( Output power / Output power + Iron losses + Copper losses
                                                                                                            × 100%
                 = kVA Cos F / ( kVA Cos F + Wi + Wcu ) × 100%
Where

Why the efficiency of the transformer is much higher than any other rotating machines?
  • There are no moving or rotating parts in the transformer i.e. the mechanical losses are zero so the transformer efficiency is much higher than any other rotating device.
How the efficiency of transformer varies with load current?
  • The efficiency of transformer increases as the load current increases from no load to full load. 
  • It becomes maximum at full load. 
  • The efficiency is practically constant from about 115% load current to 120% load current. 
  • The transformer efficiency becomes poor at light loaded and over loaded conditions.

CONDITION FOR MAXIMUM EFFICIENCY
  • The transformer iron losses are practically constant at constant voltage, but copper losses varies as square of load current therefore the efficiency is affected by the factor load current. Let us find out the condition for maximum efficiency.

Efficiency = ( Output power / Input power ) × 100 %
                 = ( Input power – Total losses / Input power ) × 100 %
             h  = [ ( V1I1 Cos F – Wcu – Wi ) / V1I1 Cos F ] × 100 %
             h  = [ ( V1I1 Cos F – I12R01 – Wi ) / V1I1 Cos F ] × 100 %
                 = ( V1I1 Cos F / V1I1 Cos F ) – ( I12R01 / V1I1 Cos F ) –  ( Wi
                                                                                                   V1I1 Cos F )
                 =  1 – ( I1R01 / V1 Cos F ) –  ( Wi / V1I1 Cos F )
As the load current is variable parameter, the transformer efficiency becomes maximum when
   dh / dI1 = 0
                 = 0 – ( R01 / V1 Cos F ) + ( Wi / V1I12 Cos F )
( R01 / V1 Cos F ) = ( Wi / V1I12 Cos F )
                  I12 R01 = Wi
                     Wcu  = Wi
The transformer efficiency becomes maximum when total copper losses are equal to iron losses
At what load current efficiency becomes maximum?
For maximum efficiency Wcu  = Wi
I12 R01 = Wi
I22 R02 = Wi
I2 = √ ( Wi / R02 )
I2 = [ I2full / I2full ] √ ( Wi / R02 )
   = I2full √ ( Wi / I2full2 R02 )
   = I2full √ ( Wi / Wcu )
   = I2full √ ( Iron losses / Full load Copper losses )
At what kVA rating the efficiency of transformer becomes maximum?
       I2 = I2full √ ( Wi / Wcu )
V2I2   = V2 I2full √ ( Wi / Wcu )
V2I2 / 1000   = [ V2 I2full / 1000 ] √ ( Wi / Wcu )
kVA = kVAfull √ ( Wi / Wcu )
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