## Phasor Diagram

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

The various transformer parameters are,

R= Primary winding resistance

X= Primary leakage reactance

R= Secondary winding resistance

X= Secondary leakage reactance

I1= Primary current

I= Secondary current = I= Load current

now                    Ī1 = Īo + Ī2

= K I2 where K is the transformer component

The primary voltage Vhas 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 90o

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 90o

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 Vand Iare 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. Iis in phase with V2.
6. Add IRand IXto to get E2.
7. Reverse Ito get I2.
8. Add Iand I2 to get I1.
9. Add IRand to -Eto 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 Φ2:

As the load power factor is lagging cosΦ2, the current I2 lags V2 by angle Φ2. So only changes 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.