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Phasor Diagram of Transformer

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.

Fig. 1

       The various transformer parameters are,

                        R= Primary winding resistance

                        X= Primary leakage reactance

                        R= Secondary winding resistance

                        X= Secondary leakage reactance

                         Z= Load impedance

                         I1= Primary current

                          I= Secondary current = I= Load current 

now                    Ī1 = Īo + Ī2

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, 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


Fig. 2  Phasor diagram for unity power factor load

Lagging Power Factor Load, cos Φ2:

       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.

Fig.  3  Phasor diagram for lagging power factor

Loading Power Factor Load, cos Φ2:

       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

Fig. 4  Phasor diagram for leading power factor

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.

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