Transformer Losses

Transformer Losses

Among all electrical machines, the transformer is the most efficient electrical machine. As shown in  working of the transformer, it is a static device. Hence, friction and windage losses are not present in the case of the transformer. The transformer losses are variable or constant loss.

There are four types of losses occurred in the transformer and that is,

  1. Copper loss
  2. Iron loss
  3. Stray loss
  4. Dielectric loss

Out of above-mentioned losses, copper loss and iron loss considered as major losses and stray loss and dielectric loss considered as minor losses. Let’s explain this in details.

1) Copper loss:

There are two winding in the transformer; primary winding and a secondary winding. The copper loss is nothing but, the losses occur due to the winding resistance. The copper loss is also known as I^2R loss or CU loss.

If primary winding resistance is R_1 and secondary winding resistance is R_2, then

(1)   \begin{equation*} Total\:copper\:loss\:in\:transformer = I_1^2 R_1 + I_2^2 R_2 \end{equation*}

Where I_1 is the load current at primary side

I_2 is the load current at secondary side

From the above equation, it is clear that the copper loss is directly proportional to the square of the load current. Value of the load current depends on the load. If the load varies, the value of the load current is also varied. Hence, the copper loss is a variable loss.

2) Iron loss:

This loss takes place in the core of the transformer due to the time-varying nature of flux in the core. Hence, the iron loss known as core loss. The total iron loss divides into two parts;

  • hysteresis loss
  • eddy current loss

(A) Hysteresis loss:

Whenever it subjected to the alternating nature of the magnetizing force, the hysteresis loss occurs due to the reversal of magnetization of the transformer core. After every half cycle, the domain present in the magnetic material will change their orientation. The power consumed by this change of orientation after every half cycle is known as hysteresis loss.

The magnetic reversal of the transformer core plotted with the help of the BH curve and it represents as below figure.

BH curve
BH curve

The hysteresis loss occurs in one cycle is equal to the area enclosed with the one hysteresis loop.The hysteresis loss can be determined with the Steinmetz’s formula. Which is given as

(2)   \begin{equation*}  W_h = \eta B^x_m_a_x f v \end{equation*}

Where \eta = Steinmetz coefficient = range 1.5 to 2.5

f = supply frequency

v = volume of core

x = Steinmetz exponent = 1.6 for silicon steel

(B) Eddy current loss:

Due to the production of the eddy current in the core, the eddy current loss is the I^2R loss present in the core of the transformer. The eddy current produced because of the conductivity of the core.

The eddy current loss is directly proportional to the conductivity (\sigma) of the core. R_s_e = the resistance offered by the core to flow of eddy current. R_s_e is inversely proportional to the conductivity. By reducing the conductivity, the eddy current can be reduced. It is possible to reduce conductivity without affecting magnetic properties by adding silica content and by using laminated core.

3) Stray loss:

There are two types of stray losses;

  • copper stray loss
  • iron stray loss.

(A) Copper stray loss:

Due to the leakage flux, Copper stray loss occurs under full load condition. This loss considered as the additional I^2R loss due to the stray current within the conductor. Instead of the solid conductor, the stranded conductors used to reduce the copper stray loss. Hence, by this way, the skin effect of winding is also reduced. The copper stray loss considers as a variable loss.

(B) Iron stray loss:

Due to the auxiliary iron parts, the iron stray loss is the additional iron loss occurred in the transformer. These auxiliary iron parts are the transformer tank, steel channels, and conservation tank. In this auxiliary iron parts, the iron stray loss occurred due to the leakage flux. This loss is less in shell type transformer compared to the core type transformer. The leakage flux is directly proportional to the load current. So, this loss also considered as a variable loss. The iron stray loss is just 0.5% of full load output.

4) Dielectric loss:

This loss produced in the insulating material of the transformer. An insulating material, the free electrons are not available. When a voltage applied, a small amount of current will flow through this due to the conversion of atoms. There is displacement of charges and the current produce due to this known as displacement current.

The process of conversion of atoms into electric dipole known as polarization. The dielectric loss is depending on the applied voltage and it is independent of load current. So, this loss considered as a constant loss. This loss is 0.25% of full load output.

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Transformer: Construction and Classification

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