Phasor Diagrams for Transformer on Load

Phasor Diagrams for Transformer on Load

AU: Dec.-02,17, May-06,10,14

• Consider a transformer supplying the load as shown in the Fig. 6.12.1.

The various transformer parameters are,

R₁ = Primary winding resistance,

X₁ = Primary leakage reactance

R₂ = Secondary winding resistance,

X₂ = Secondary leakage reactance

Z₁ = Load impedance, I₁ = Primary current

I₂ = Secondary current = I_L = Load current

whereI₀ = No load current

I '₂ = Load component of current decided by the load

= K I₂ where K is transformation ratio

The primary voltage V₁ has now three components,

1. - E₁, the induced e.m.f. which opposes V₁

2. I₁ R₁, the drop across the resistance, in phase with I₁

3. I₁X₁, the drop across the reactance, leading I₁ by 90°

• The secondary induced e.m.f. E₂ has also three components,

1. V₂, the terminal voltage across the load

2. I₂ R_2', the drop across the resistance, in phase with I₂

3. I₂ X_2', the drop across the reactance, leading I₂ by 90°

• The phasor diagram for the transformer on load depends on the nature of the load power factor. Let us consider the various cases of of the load power factor.

1. Unity Power Factor Load, cos ϕ2 = 1

• As load power factor is unity, the voltage V₂ and I₂ are in phase. Steps to draw the phasor diagram are,

1. Consider flux ϕ as reference

2. E₁ lags ϕ by 90°. Reverse E₁ to get - E₁.

3. E₁ and E₂ are in phase.

4. Assume V₂ in a particular direction.

5. I₂ is in phase with V₂.

6. Add I₂ R₂ and I₂ X₂ to V₂ to get E₂.

7. Reverse I₂ to get I'₂.

8. Add I₀ and I'₂ to get I₁.

9. Add I₁ R₁ and I₁ X₁ to - E₁ to get V₁.

Angle between V₁ and I₁ is ϕ₁ and cos ϕ₁ is primary power factor. Remember that I₁X₁, leads I₁ direction by 90° and I₂ X₂ leads I₂ by 90° as current through inductance lags voltage across inductance by 90°. The phasor diagram is shown in the Fig. 6.12.2.

2. Lagging Power Factor Load, cos ϕ₂

As load power factor is lagging cos ϕ₂, the current I₂ lags V₂ by angle ϕ₂. So only change in drawing the phasor diagram is to draw I₂ lagging V₂ by ϕ₂ in step 5 discussed earlier. Accordingly directions of I₂R₂, I₂X₂, I'₂, I₁,I₁R₁, and I₁ X₁, will change. Remember that whatever may be the power factor of load, I₂X₂ leads I₂, by 90° and IX1 leads I1 by 90°. The complete phasor diagram is shown in the Fig. 6.12.3.

3. Leading Power Factor Load, cos ϕ₂

 • As load power factor is leading, the current I₂ leads V₂ by angle ϕ₂. So the change is to draw I₂, leading V₂ by angle ϕ₂. All other steps remain same as before. The complete phasor diagram is shown in the Fig. 6.12.4.

Review Question

1. Draw a phasor diagram to represent conditions in a single phase transformer supplying load at: 1) Unity p.f. 2) Lagging p.f. and 3) Leading p.f. AU: Nov.-02, Dec.-17, May-06, 10, 14, Marks 8