Phasor Diagram of Transformer

## Phasor Diagram

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

Â Â Â Â Â Â  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                    Äª1 = Äªo + Äª2

where                 I= No load current

I2‘= Load component of current decided by the load

= 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, cosÎ¦2 = 1       As load power factor is unity, the voltage Vand Iare in phase. The steps to draw the phasor diagram are,
1. Consider flux Î¦ as a reference
2. E1 lags Î¦ 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 Î¦1 and cosÎ¦1 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 Î¦2:

Â Â Â Â Â Â  As the load power factor is lagging cosÎ¦2, the current I2Â lags V2Â by angle Î¦2. So the only change in drawing the phasor diagram is to draw I2Â laggingÂ V2Â by Î¦2Â in step 5 discussed earlier. Accordingly direction of I2Â R2, I2Â X2, I2′, I1, I1Â R1Â and I1X1Â will change. Remember that whatever may be the power factor of load, I2X2Â leads I2Â by 90oÂ and I1X1Â leads I1Â by 90o.Â Â Â Â Â Â  The complete phasor diagram is shown in Fig. 3.

As the load power factor is leading, the current I2 leads V2 by angle Î¦2. So change is to draw I2 leading I2  by angle Î¦2. All other steps remain the same as before. The complete phasor diagram is shown in Fig. 4

### Aanchal Gupta

Welcome to my website! I'm Aanchal Gupta, an expert in Electrical Technology, and I'm excited to share my knowledge and insights with you. With a strong educational background and practical experience, I aim to provide valuable information and solutions related to the field of electrical engineering. I hold a Bachelor of Engineering (BE) degree in Electrical Engineering, which has equipped me with a solid foundation in the principles and applications of electrical technology. Throughout my academic journey, I focused on developing a deep understanding of various electrical systems, circuits, and power distribution networks.