Answer to Question 7

 

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A 250 kVA  transformer has a full load copper loss of 3.0 kW and an iron loss of 2.0 kW.  It has a power factor of 0.80.  Calculate:

(a) The output apparent power at which the efficiency of the transformer is at a maximum;

(b) The maximum percentage efficiency.

 

(a) Let x be the fraction of the load at which the efficiency is at a maximum:

Copper loss = 3.0 kW x2

Copper loss = iron loss = 2.0 kW

x2 = 2.0 kW 3.0 kW = 0.667

x = 0.8165

 

The output apparent power S = 0.8165 250 kVA = 204.1 kVA

 

(b) Now work out the useful power:

P = 0.80 204.1 kVA = 163.3 kW

 

Total loss = 2.0 kW  + 2.0 kW = 4.0 kW

 

Input power = 163.3 kW + 4.0 kW = 167.3 kW

 

Efficiency = 1 - (4.0 kW 167.3 kW) = 0.9755 = 97.55 %