Efficiency of Transformer

The transformer is a vital link between the load and the supply. The efficiency of transformer is very important in view of energy saving.The transformer supplies the required power to the load at the specified voltage. The Various loads are connected to the transformer and the loading on the transformer varies according to the running hours of the different loads connected to the secondary of the transformer.The efficiency of the transformer varies when the loading on the transformer is increased or decreased.

Under unload condition, the transformer draws only magnetizing current and the current that represents the core loss. The primary and secondary current increase with increased loading on secondary of the transformer. The output power of the transformer can’t be equal to the input power because of the no load core losses and the copper loss. The certain amount of electrical energy is lost in the form of the heat.The higher the losses, the lesser the efficiency of the transformer. 

 Efficiency of the transformer is defined as the ratio of output power to input power at any load.
Efficiency η = Output Power / Input Power
                     = (Input Power-Losses)/ Input Power
 Efficiency η =  (1- Losses)/Input Power
The efficiency of the transformer can be expressed in terms of output power and losses.
 Efficiency η =  output power/(output power+losses)
Efficiency η can be expressed in percentage as
Efficiency η = (Output Power / Input Power) x 100 %
The  losses take place in a transformer at given loads is required to be calculated for determining the efficiency of the transformer. The following losses occurs in a transformer.
1. No load losses
2. Primary Copper loss
3. Secondary Copper loss 
4. Stray loss
5. Dielectric loss
No Load or Iron/ core Loss:
No load loss can be categorized into – Eddy current loss and Hysteresis loss .
The eddy current loss occurs because of the induced voltage in the steel parts and the eddy current starts flowing in the steel parts of the core.The eddy current loss is the power loss takes place in the lamination. The eddy current loss can be expressed by following mathematical expression.
t is the thickness of the lamination. The eddy current loss can be reduced by use of thin lamination.
The hysteresis loss occurs because of cyclic magnetization of the dipoles. The energy required to align the dipoles in the core is dissipated as heat energy. The hysteresis loss can be expressed as;
The total core loss is the sum of eddy current loss plus hysteresis loss. The core loss can be calculated by the open circuit test of the transformer.
Primary and secondary Copper Loss or Load Losses :
The copper loss in the transformer is load dependent and the loss increases with an increased loading on the transformer.

The primary and secondary copper loss takes place due to flow of electric current in the winding. The heat loss(I^2 x R) takes place in the winding because the winding has certain resistance. The total copper loss is ;
Pc= I2p  x Rp  + I2s  x Rs
Pc= I2e Re  
Re = total resistance of the primary and secondary
Ie   =  sum of primary and the secondary current
The copper loss is obtained by short circuit test.
The resistance must be corrected for the operating temperature of the transformer. The temperature of the winding resistance should be corrected for 75 °C. The corrected resistance  at 75 °C is;
[(235 +75)/(235+ ambient temp)] x Resistance at ambient. temperature
Stray loss:
Stray loss occurs due to leakage  flux in the transformer. When the transformer is at full load some amount of the flux gets linked to the other parts of the transformer.
Dielectric loss:
Dielectric loss occurs in the insulation of the transformer. The loss can be obtained by tanδ test.

Efficiency Calculation of the Transformer:

The major loss in the transformer is copper loss and the core loss. The core loss is voltage and frequency dependent the loss remains more or less constant for the constant voltage and frequency.The core loss is also known as constant loss. It is independent of the load and the core loss is fairly constant for 0-100 % loading on the transformer.
The copper loss of the transformer depends on the loading on the transformer and it increase as the loading on the transformer is increased. The copper loss is known as variable loss.
Let KVA rating of the transformer is S. The percentage loading on the transformer is x % of the transformer’s full load KVA rating and the power factor is Cosθ2.
The output power of the transformer
Po = x S Cosθ2  
The copper loss in the transformer
Pc = xPcufl
Where,   Pcufl   – Copper loss at full load
Efficiency η =  output power/(output power+losses)
                    η x S Cosθ / ( x S Cosθ2  +Pix2  Pcufl )

Condition of maximum efficiency:

The copper loss is a variable loss. The maximum efficiency of the transformer occurs when the variable loss is equal to the constant loss.
x2Pcufl = Pi
x= √ (Pi / Pcufl )
Putting value of copper loss(Pc)
η  = x S Cosθ2   / ( x S Cosθ2  +Pix2  Pcufl )
η(Max)  = x S Cosθ2   / ( x S Cosθ2  +2Pi )  
The maximum efficiency of the transformer is obtained when the core loss is equal to the copper loss.
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