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

Fig. 1 |

_{1 }= Primary winding resistance

_{1 }= Primary leakage reactance

_{2 }= Secondary winding resistance

_{2 }= Secondary leakage reactance

_{L }= Load impedance

_{1}= Primary current

_{2 }= Secondary current = I

_{L }= Load current

_{1}= Ī

_{o}+ Ī

_{2}'

_{o }= No load current

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

_{2}where K is transformer component

_{1 }has now three components,

_{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 load

2. 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}

__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 inphase

4. Assume V

_{2 }in a particular direction

5. 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}.

_{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.2

Fig. 2 Phasor diagram for unity power factor load |

__Lagging Power Factor Load, cos Φ__

_{2}_{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}_{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. 4

Fig. 4 Phasor diagram for leading power factor |

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