Question #226502

Show that the per unit impedance referred to the circuits connected by a transformer is same, if same base MVA is taken for both circuits and base KVs have ratio equal to the transformation ratio.

Expert's answer

If windings 1 and 2 have N_{1} and N_{2} turns, respectively, then:

\frac{v_1}{N_1}=\frac{v_2}{N_2}

One of the ideal transformer relations is that there can be no energy absorbed, stored, or

lost in the device. Whatever complex power enters one winding must leave the other.

Therefore, we have

v_1 i_1^*=v_2 i_2^*

and \frac{i_1}{i_2}=\frac{N_2}{N_1}

The transformer also tends to transform impedances. Some impedance is

connected to one side of the ideal transformer. We can find an equivalent impedance Z.'

viewed from the other side of the transformer.

I_2=\frac{N_1}{N_2}I_1

The ratio between the input voltage and current is:

V_1=Z'I_1=\frac{N_1}{N_2}V_2=(\frac{N_1}{N_2})^2ZI_1

We may derive the expression of the equivalent impedance viewed from the primary side

of the transformer:

Z'=(\frac{N_1}{N_2})^2Z

Hence, per unit impedance referred to the circuits connected by a transformer is the same.

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