Tuesday, July 19, 2011

Losses in a Transformer

1. Losses in a Transformer
       In a transformer, there exists two types of losses.
i) The core gets subjected to an alternating flux, causing core losses.
ii) The windings carry currents when transformer is loaded, causing copper losses.
1.1 Core or Iron Losses
       Due to alternating flux set up in the magnetic core of the transformer, it undergoes a cycle of magnetisation and demagnetisation. Due to hysteresis effect there is loss of energy in this process which is called hysteresis loss.
        It is given by,             hysteresis loss = Kh Bm1.67 f v watts
where                       Kh = Hysteresis constant depends on material.
                                 Bm = Maximum flux density.
                                 f = Frequency.
                                 v = Volume of the core.
       The induced e.m.f. in the core tries to set up eddy currents in the core and hence responsible for the eddy current losses. The eddy current loss is given by,
                       Eddy current loss = Ke Bm2 f2 t2 watts/ unit volume
where                 Ke = Eddy current constant 
                          t = Thickness of the core
       As seen earlier, the flux in the core is almost constant as supply voltage V1 at rated frequency f is always constant. Hence the flux density Bm in the core and hence both hysteresis and eddy current losses are constants at all the loads. Hence the core or iron losses are also called constant losses. The iron losses are denoted as Pi.
      The iron losses are minimized by using high grade core material like silicon steel having very low hysteresis loop by manufacturing the core in the form of laminations.
1.2 Copper Losses
       The copper losses are due to the power wasted in the form of  I2 R loss due to the resistances of the primary and secondary windings. The copper loss depends on the magnitude of the currents flowing through the windings.
       Total Cu loss = I12 R1 + I22 R2 = I12 ( R1 + R2' )= I22 ( R2 +R1' )
                           = I12 R1e = I22 R2e
       The copper looses are denoted as. If the current through the windings is full load current, we get copper losses at full load. If the load on transformer is half then we get copper losses at half load which are less than full load copper losses. Thus copper losses are called variable losses. For transformer VA rating is or. As is constant, we can say that copper losses are proportional to the square of the KVA rating.
       So,     Pcu  α  I2α   (KVA)2
       Thus for a transformer,
       Total losses = Iron losses + Copper losses
                          = Pi  + Pcu 

Key point : It is seen that the iron losses depend on the supply voltage while the copper losses depend on the current. The losses are not dependent on the phase angle between voltage and current. Hence the rating of the transformer is expressed as a product of voltage and current and called VA rating of transformer. It is not expressed in watts or kilo watts. Most of the times, rating is expressed in KVA.

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