Shifting Impedance in a Transformer

SHIFTING IMPEDANCE IN A TRANSFORMER

Transformer windings has resistance R₁ and R₂ in primary and secondary of the transformer shown in Figure 1.24. Both resistance and reactance of the windings can be shifted any one side of the two windings using the factor k². It makes the calculations easy by doing it one side only. 

Effective Resistance of Transformer referred to Primary:

Whenever the impedance is transferred to primary, it is divided by K². Then it is called equivalent secondary resistance and reactance referred to primary and it is represented as R₂' and X₂'.

Referred to Secondary

If primary and secondary resistance and reactance is transferred to secondary, both resistance and reactance should be multiplied by k². R₁' and X₁' are the equivalent primary resistance and reactance respectively, referred to secondary.

Equivalent Resistance (referred to Secondary)

Primary side doesn't have any impedance which is shown in above Figure 1.26.

Example 1.11:

A 20 kVA, 2000/200 V, single phase, 50 Hz transformer has a primary resistance of 2.5 Ω and reactance of 4.8 Ω. The secondary resistance and reactance are 0.01 Ω and 0.018 Ω respectively. Find

(i) Equivalent reactance referred to primary

(ii) Equivalent impedance referred to primary

(iii) Equivalent resistance, reactance and impedance referred to secondary

(iv) Total copper loss of the transformer.

Solution:

Given data:

(i) Equivalent resistance referred to primary (R₀₁):

(ii) Equivalent reactance referred to primary (X01):

(iii) Equivalent resistance referred to secondary (R₀₂):

(iv)Total Copper Losses:

Example 1.12:

A 100 kVA, 1100/200 V single phase transformer has the following parameters R₁ = 0.1Ω, X₁ = 0.3 Ω, R₂ = 0.004 Ω, X₂ = 0.012 Ω. Find equivalent resistance and leakage reactance as referred to high voltage winding.

Solution

Transformer rating = 100 kVA,

V₁ = 1100 V,

V₂ = 200 V

R₁ = 0.1 Ω,

X₁ = 0.3 Ω,

R₂ = 0.04 Ω,

X₂ = 0.012 Ω.

Transformation ratio, k = (V₂/V₁) = 200/1100 = 0.1818

1100 is the high voltage side which is primary side.

Equivalent resistance referred to primary: