114.MET January 2021 Q.9

 A 20 kVA , 2000/220 V single-phase transformer has a primary resistance of 2.1 ohms and a secondary resistance of 0.026 ohms. The corresponding leakage reactance are 2.5 and 0.03 ohms. Estimate the regulation at full load under power factor condition of a) Unity b) 0.5 (lagging) and c) 0.5 (leading)

Given

kVA = 20

V1 = 2000

V2 = 220

R1 =2.1

R2 = 0.026

X1 = 2.5

X2 = 0.03

To find

Estimate the regulation at full load under power factor condition of 

a) Unity 

b) 0.5 (lagging)  

c) 0.5 (leading)

Solution

We know that turn ratio = N1/N2 = V1/V2

So Turn ratio = 2000/220 = 9.09

Full load secondary current I2 = VA/V

                                                 = 20000 / 220

                                                 = 90.9 A

Equivalent resistance, R2' = R2 + R1 x (N2/N1)²

                                          = 0.026 + 2.1 x (1/9.09)² 

                                          = 0.026 + 0.0255

                                          = 0.0515 ohm

Equivalent reactance, X2' = X2 + X1 x (N2/N1)²

                                          = 0.03 + 2.5 x (1/9.09)² 

                                          = 0.03 + 0.0302

                                          = 0.0602 ohm