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Losses in Transformers

Updated on August 28, 2014

Losses can be considered as the difference between the Input power and the output power. All electrical machines has certain losses. There is no equipment which has zero loss or whose output power is equal to the input. Losses occur in all electrical equipment and these losses are dissipated in the form of heat.

Transformer is the most efficient electrical machine. Since the transformer has no moving parts, its efficiency is much higher than that of rotating machines. The various losses in a transformer are enumerated as follows:

1. Core loss

2. Copper loss

3. Load (stray) loss

4. Dielectric loss


Of these four losses the first two i.e) the constant core (iron) loss and the variable copper loss are the major losses. Lets see about each one of then in detail.


Transformer core

1. Core loss

When the core of the transformer undergoes cyclic magnetization power losses occur in it. There losses are together called as core loss. There are two kinds of core losses namely hysteresis loss and eddy current loss. Core loss is important in determining heating, temperature rise, rating and efficiency of transformers.The core losses comprises of two components:

  • Hysteresis loss
  • Eddy current loss

A complete Electrical Engineering reference guide

Hysteresis loop

Hysteresis loss

This phenomenon of lagging of magnetic induction behind the magnetising field is called hysteresis.

In the process of magnetisation of a ferromagnetic substance through a cycle, there is expenditure of energy. The energy spent in magnetising a specimen is not recoverable and there occurs a loss of energy in the form of heat. This is so because, during a cycle of magnetisation, the molecular magnets in the specimen are oriented and reoriented a number of times. This molecular motion results in the production of heat. It has been found that loss of heat energy per unit volume of the specimen in each cycle of magnetisation is equal to the area of the hysteresis loop.
The shape and size of the hysteresis loop is characteristic of each material because of the differences in their retentivity, coercivity, permeability, susceptibility and energy losses etc.

Hysteresis loop

Click thumbnail to view full-size

The net unrecoverable energy lost in the process is area of abco which is lost irretrievably in the form of heat is called the hysteresis loss. the total hysteresis loss in one cycle is easily seen to be the area of one complete loop abcdefa.

If wh indicates the hysteresis loss/ unit volume, then hysteresis loss in volume V of material when operated at f Hz is given by the following equation.

Ph=whVf W

Steinmetz gave an emprical formula to simplify the computation of the hysteresis loss based on his experimental studies. The formula given by him is as follows:

Ph=khfBnm W

where kh is a characteristic constant of the core material, Bm is the maximum flux density and n is caller steinmetz constant


Permissible core losses in transformer

kVA
Core loss (W)
16
155
25
195
40
260
50
295
63
350
75
385
88
400
100
500
125
570
160
670
200
800
250
950
315
1150
400
1380
500
1660
860
1980
900
2400
1000
2800
All the above losses are subjected to positive or negative variation of 10%

Eddy current Loss


When the magentic core flux varies in a magnetic core with respect to time, voltage is induced in all possible paths enclosing the flux. This will result in the production of circulating currents in the transformer core. These currents are known as eddy currents. These eddy currents leads to power loss called Eddy current loss. This loss depends upon two major factors. The factors affecting the eddy currents are:

Resistivity of the core and
Length of the path of the circulating currents for a given cross section.

The eddy currents can be expressed as

Pe = kef2B2 W/m3
ke = ke'd2/p

Where,

d is the thickness of the lamination
p is the resistivity of material of the core

Pe = ke'd2f2B2/p W/m3

Hence from the above equations it is evident that Eddy current loss is directly proportional to the square of the thickness of the lamination and that of the frequency of supply voltage.


Total core loss

Total core loss = Hysteresis loss + Eddy current loss.

Reduction of Eddy Current Loss

Reduction of eddy current loss can be achieved by using core with high resistivity and increasing the path of circulating currents.

By increasing the length of the path, the resistance offered by the material to the induced voltages will increase, resulting in the reduction of Eddy current loss.

High resistance can be achieved by using silicon steel cores. The resistance of the steel can be increased by adding silicon to it. The cores can be laminated along the flow of flux. Each lamination is insulated from the adjoining one. This increases the path length of the circulating currents with consequent reduction in Eddy current loss.

Permissible copper losses at 75 degree Centigrade

kVA
Copper losses (W)
16
500
25
700
40
975
50
1180
63
1400
75
1600
88
1650
100
2000
125
2350
160
2840
200
3400
250
4000
315
4770
400
5700
500
6920
860
8260
1000
11880
All the above losses are subjected to positive or negative variation of 10%

Copper Loss

It is a well known fact that whenever there is a resistance to the flow of current in a conductor, power loss occurs in the conductor due to its resistance. Copper loss occurs in the winding of the transformer due to the resistance of the coil. When the winding carries current, power loss occurs due to its internal resistance. This loss is known as copper loss. The copper loss can be expressed as below

Pcu = I2R

Where I is the current through the winding and R is the resistance of the winding.

Copper loss is proportional to the square of current flowing through the winding.

Stray Loss.

Stray loss results from leakage fields including Eddy currents in the tank wall and conductors. The winding of the transformers should be designed such that the stray loss is small. This can be achieved by the spliting of conductors in to small strips to reduce Eddy currents in the conductors. The radial width of the strips should be small and they should be transposed.


Dielectric Loss

This loss occurs in the transformer oil and other solid insulating materials in the transformer.

The major losses occurring in the transformer are Core loss and copper loss. Rest of the losses are very small compare to these two. All the losses occurring in transformer are dissipated in the form of heat in the winding, core, insulating oil and walls of the transformer. Efficiency of the transformer increases with decrease in the losses.

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