Phasor Diagram of transformer | Phasor diagram for leading, lagging power factor | Phasor diagram for unity power factor load

Phasor Diagram

Consider a transformer supplying the load as shown in Fig. 1.

       The various transformer parameters are,

                        R₁ = Primary winding resistance

                        X₁ = Primary leakage reactance

                        R₂ = Secondary winding resistance

                        X₂ = Secondary leakage reactance

                         Z_L = Load impedance

                         I₁= Primary current

                          I₂ = Secondary current = I_L = Load current 

now                    Ī₁ = Ī_o + Ī₂‘

where                 I_o = No load current 

                           I₂‘= Load component of current decided by the load

                               = K I₂ where K is the transformer component

       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. I₁ X₁, the drop across the reactance, leading I₁ by 90^o

       The secondary induced e.m.f. has also three components,
 1. V₂, the terminal voltage across the load
2. I₂ R₂, the drop across the resistance, in phase with I₂
3. I₂ X₂, the drop across the reactance, leading I₂ by 90^o

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

1.1 Unity power factor load, cosΦ₂ = 1       As load power factor is unity, the voltage V₂ and I₂ are in phase. The steps to draw the phasor diagram are,
1. Consider flux Φ as a reference
2. E1 lags Φ by 90o. Reverse E1 to get -E1.
3. E1 and E2 are inphase
4. Assume V2 is in a particular direction
5. I₂ is in phase with V₂.
6. Add I₂ R₂ and I₂ X₂ to to get E₂.
7. Reverse I₂ to get I₂‘.
8. Add I_o and I₂‘ to get I₁.
9. Add I₁ R₁ and to -E₁ to get V₁.

       The angle between V1 and I1 is Φ1 and cosΦ1 is the primary power factor. Remember that I1X1 leads I1 direction by 90o and I2 X2 leads I2 by 90o as current through inductance lags voltage across inductance by 90o. The phasor diagram is shown in Fig.2

Lagging Power Factor Load, cos Φ_2:

       As the load power factor is lagging cosΦ2, the current I2 lags V2 by angle Φ2. So the only change in drawing the phasor diagram is to draw I2 lagging V2 by Φ2 in step 5 discussed earlier. Accordingly direction of I2 R2, I2 X2, I2′, I1, I1 R1 and I1X1 will change. Remember that whatever may be the power factor of load, I2X2 leads I2 by 90o and I1X1 leads I1 by 90o.       The complete phasor diagram is shown in Fig. 3.

Loading Power Factor Load, cos Φ_2:

       As the load power factor is leading, the current I2 leads V2 by angle Φ2. So change is to draw I2 leading I2  by angle Φ2. All other steps remain the same as before. The complete phasor diagram is shown in Fig. 4