**Phasor Diagrams for Transformer on Load**Consider a transformer supplying the load as shown in the Fig. 1.

Fig. 1 |

The various transformer parameters are,

R

_{1 }= Primary winding resistance X

_{1 }= Primary leakage reactance R

_{2 }= Secondary winding resistance X

_{2 }= Secondary leakage reactance Z

_{L }= Load impedance I

_{1}= Primary current I

_{2 }= Secondary current = I_{L }= Load currentnow Ī

_{1}= Ī_{o}+ Ī_{2}'where I

_{o }= No load current I

_{2}'= Load component of current decided by the load = K I

_{2}where K is transformer component The primary voltage V

_{1 }has now three components,1. -E

2. I

3. I

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

1. V

2. I

3. I

As load power factor is unity, the voltage V

1. Consider flux Φ as reference

2. E

3. E

4. Assume V

5. I

6. Add I

7. Reverse I

8. Add I

9. Add I

_{1}, the induced e.m.f. which opposes V_{1}2. I

_{1}R_{1}, the drop across the resistance, in phase with I_{1}3. I

_{1}X_{1}, the drop across the reactance, leading I_{1}by 90^{o}The secondary induced e.m.f. has also three components,

1. V

_{2}, the terminal voltage across the load2. I

_{2}R_{2}, the drop across the resistance, in phase with I_{2}3. I

_{2}X_{2}, the drop across the reactance, leading I_{2}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, cosΦ__

_{2}= 1_{2 }and I_{2 }are in phase. Steps to draw the phasor diagram are,1. Consider flux Φ as reference

2. E

_{1 }lags Φ by 90^{o}. Reverse E_{1 }to get -E_{1}.3. E

_{1 }and E_{2 }are inphase4. Assume V

_{2 }in a particular direction5. I

_{2 }is in phase with V_{2}.6. Add I

_{2 }R_{2 }and I_{2 }X_{2 }to to get E_{2}.7. Reverse I

_{2 }_{ }to get I_{2}**'**.8. Add I

_{o }and I_{2}**'**_{}to get I_{1}.9. Add I

_{1 }R_{1 }and to -E_{1 }to get V_{1}. Angle between V

_{1 }and I_{1}is Φ_{1}and cosΦ_{1}is primary power factor. Remember that I_{1}X_{1 }leads I_{1 }direction by 90^{o}and I_{2}X_{2 }leads I_{2}by 90^{o}as current through inductance lags voltage across inductance by 90^{o}. The phasor diagram is shown in the Fig.2Fig. 2 Phasor diagram for unity power factor load |

__Lagging Power Factor Load, cos Φ__

_{2} As load power factor is lagging cosΦ

The complete phasor diagram is shown in the Fig. 3._{2}, the current I_{2 }_{ }lags V_{2 }_{ }by angle Φ_{2}. So only changes in drawing the phasor diagram is to draw I_{2 }_{ }lagging V_{2 }_{ }by Φ_{2}in step 5 discussed earlier. Accordingly direction of I_{2 }R_{2}, I_{2 }X_{2}, I_{2}**'**, I_{1}, I_{1 }R_{1 }and I_{1}X_{1 }will change. Remember that whatever may be the power factor of load, I_{2}X_{2 }leads I_{2 }by 90^{o }and I_{1}X_{1 }leads I_{1}by 90^{o}.Fig. 3 Phasor diagram for lagging power factor |

__Loading Power Factor Load, cos Φ__

_{2} As load power factor is leading, the current I

_{2}leads V_{2 }by angle Φ_{2}. So change is to draw I_{2 }leading I_{2 }by angle Φ_{2}. All other steps remain same as before. The complete phasor diagram is shown in the Fig. 4Fig. 4 Phasor diagram for leading power factor |

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Very good information!!!! Thank you, Erik Arckens

ردحذفThanks. U're Awesome :)

ردحذفthere are two inductances on primary side one is that of Py winding and other due to leakage reactance. lenz's law is applicable on both inductors.i.e there should be -ve sign with E1 as well as I1X1 drop. but we have used with only E1 not with the other inductor.please explain with very basic concepts so that I can get the idea.further with applied signs both should be voltage drop across the inductor and should have same sign?

ردحذفplease post the picture of phasor diagram of ideal transformer with capacitive load

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ردحذفBob

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Nice information

ردحذفThis was really helpful... Thank u so much.

ردحذفPlease explain the expression for volt ampere and reactive volt ampere in three phase system

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Sir, In the practical transformer case, what is criteria for drawing the V2 phasor? How much angle the V2 phasor is lagging or leading the E2 phasor?

ردحذفSir, actually V2 is not leading or lagging by E2 because two voltages never leads or lags behind / over themself.

حذفActually V2 is drawn as per our load conditions

Let me clear....

I2 is drawn as reference of I2'and than V2 is drawn as per the load condition. (Lagging/leading/unity).

If our load is lagging than we draw V2 leading by I2 (or I2 lagging by V2), If our load is unity than V2 is in phase of I2 , If our load is leading than draw the V2 lagging by I2 (or I2 leading by V2). As shown in phasors.

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