To make the calculations easy, the reactance of the two windings can be transferred to any one side. The reactance from one side to the other is transferred in such a manner that percentage voltage drop remains the same when represented on either side.
Let the primary reactance X1 be transferred to the secondary, and the new value of this reactance is 
called equivalent reactance of primary referred to secondary, as shown in Figure 10.22(a).
Fig. 10.22 (a) and (b) Equivalent reactance when referred to secondary side (c) and (d) Equivalent reactance when referred to primary side
Then,
or
∴Total equivalent reactance referred to secondary.
Xes = X2 + = X2 + K2 X1
Now, let us consider secondary reactance X2 when it is transferred to primary side its new value is 
called equivalent reactance of secondary referred to primary, as shown in Figure 10.22(c).
Then,
∴ Total equivalent reactance referred to primary.
A 63 kVA, 1100/220 V single-phase transformer has R1 = 0.16 ohm, X1 = 0.5 ohm, R2 = 0.0064 ohm and X2 = 0.02 ohm. Find equivalent resistance and reactance as referred to primary winding.
(P.T.U. May 2009)
Solution:
Here, transformer rating = 63 kVA; V1 = 1100 V; V2 = 220 V
R1 = 0.16 ohm; X1 = 0.5 ohm; R2 = 0.0064 ohm; X2 = 0.02 ohm
Transformation ratio,
Equivalent resistance referred to secondary side,
Res = R2 + 
= R2 + R1 × K2 = 0.0064 + 0.16 × (0.2)2 = 0.0128 ohm
Equivalent reactance referred to secondary side,
Xes = X2 + = X2 + X1 × K2 = 0.02 + 0.5 × (0.2)2 = 0.04 ohm
Example 10.15
A 33 kVA, 2200/220 V, 50 Hz single-phase transformer has the following parameters. Primary winding resistance r1 = 2.4 Ω, Leakage reactance x1 = 6 Ω Secondary winding resistance r2 = 0.03 Ω Leakage reactance x2 = 0.07 Ω. Then, find primary, secondary, and equivalent resistance and reactance.
(P.T.U. Dec. 2009)
Solution:
Here, rating of transformer = 33 kVA; V1 = 2200 V; V2 = 220 V
f = 50 Hz; R1 = 2.4Ω; X1 = 6Ω; R2 = 0.03Ω; X2 = 0.07Ω
Transformation ratio,
Transformer resistance referred to primary side
Transformer reactance referred to primary side
Transformer resistance referred to secondary side
Res = R2 + = R2 + R1 × K2 = 0.03 + 2.4 × (0.1)2 = 0.054Ω
Transformer reactance referred to secondary side
Xes = X2 + = X2 + X1 × K2 = 0.07 + 6 × (0.1)2 = 0.054Ω
A single-phase transformer having voltage ratio 2500/250 V (primary to secondary) has a primary resistance and reactance 1.8 ohm and 4.2 ohm, respectively. The corresponding secondary values are 0.02 and 0.045 ohm. Determine the total resistance and reactance referred to secondary side. Also, calculate the impedance of transformer referred to secondary side.
Solution:
Here,
R1 = 1.8 Ω; X1 = 4.2 Ω; R2 = 0.02 Ω; X2 = 0.045 Ω
Transformation ratio,
Total resistance referred to secondary side,
Res = R2 + = R2 + R1 × K2 = 0.02 + 1.8 × (0.1)2 = 0.038Ω
Total reactance referred to secondary side,
Xes = X2 + = X2 + X1× K2 = 0.045 + 4.2 × (0.1)2 = 0.087Ω
Impedance of transformer referred to secondary side,
Leave a Reply