Parallel Operation of Two Ideal Transformer

Parallel Operation of  Two Ideal Transformer
       Now we will consider ideal case of two transformers having the same voltage ratio and their voltage triangles are equal in size and shape. The circuit shown in the Fig. 1 consists of two transformers in parallel.
Fig. 1

      The corresponding phasor diagram is shown in the Fig. 2.
      As seen from the Fig. 2  the impedance voltage triangles of both the transformers is same. IA and IB are the currents flowing through transformers A and B which are in parallel. These currents are in phase with the load current and are inversely proportional to the respective impedances.
Fig. 2

      Applying KCL,
                     I = I1 + I2
      Secondary voltage,
                    V2 = E - IA ZA = E - IB ZB
      Also        I1 Z1 = I2 Z2
                     I1 / I2 = Z2 / Z1
      Applying current divider formulae,
                    I1 = I Z2 / (Z1 + Z2 )
and               I2 = I Z1 /(Z1 + Z2)

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