Transformer Phasor Diagram

Exact equivalent circuit of a transformer (with lagging load) is shown below.

Let the lagging load has impedance angle ϴ₂ .

Applying KVL in secondary circuit.

Draw   I₂R₂  parallel to I₂ ,   jI₂X₂   perpendicular and 90⁰ ahead of I₂ .

Add  I₂   and   jI₂X₂   phasors to phasor V₂  to get E₂  , as per equation  (1)  above.

Let  Ф = Ф_m sinwt   be the flux linking both windings. Therefore,

By observing above E₁ and E₂  equations,  we find that E₁ and E₂  lead flux Ф by 90⁰ , therefore, draw  Ф phasor 90⁰ behind E₂ . Draw E₁ along E₂ .

Current I₀ is made of two components  I_c and I_m .

As the central part (in exact equivalent circuit of a transformer) is an ideal transformer, therefore, by relation

We find I_p to be in phase with  I₂ . Further resultant of I₀ and I_P gives I₁ .

Apply KVL in primary circuit.

Draw I₁R₁ parallel to I₁ , jI₁X₁ perpendicular to I₁ and 90⁰ ahead of it and add these to E₁ to get V₁ as per equation (2).

This is the complete phasor diagram for a lagging power factor load. Exactly similarly, phasor diagram for leading power factor load can be drawn by taking I₂ ahead of V₂  i.e  ϴ₂  in opposite direction.

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