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. I_A and I_B 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 - I_A Z_A = E - I_B Z_B

      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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