Losses in a Transformer

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. Core or Iron losses

• Due to alternating flux set up in the magnetic core of the transformer, it undergoes a cycle of magnetisation demagnetisation. Due to hysteresis effect there is loss of energy in this process which is called hysteresis loss.

It is given by, Hysteresis loss = K_h B_m^1.67 f v watts

K_h = Hysteresis constant depends on material and

B_m = Maximum flux density

f = Frequency and 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 = K_e B_m² f²t² watts/unit volume

where K_e = Eddy current constant and 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 gato 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 P_i.

• The iron losses are minimized by using high grade core material like silicon steel having very low hysteresis loop and by manufacturing the core in the form of laminations.

2. Copper losses

• The copper losses are due to the power wasted in the form of I²R loss due to the resistances of the primary and secondary windings. The copper loss depends on the magnitude of the currents flowing how through the windings.

• Total Cu loss = I₁² R₁ +I₂² R₂ = I₁² (R₁ + R'₂) = I₂² (R₂ +R'₁) = I₁² R_1e = I²₂ R_2e

• The copper losses are denoted as P_Cu. 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.

• Copper losses are proportional to the square of the current and square of the kVA rating as voltage is constant.

 So,  P_Cu ∞ I² (kVA)²

Thus for a transformer,

Total losses = Iron losses + Copper losses = P_i + P_Cu

• The copper losses are kept minimum by designing the windings with low resistance values.

Review Question

1. Explain the various losses in a transformer and how to minimize them? On what factors they depend? Give the equations for these losses.