The phasor diagram of loaded induction motor is similar to the loaded transformer. The only difference is the secondary of induction motor is rotating and short circuited while transformer secondary is stationary and connected to load. The load on induction motor is mechanical while load on transformer is electrical. Still by finding electrical equivalent of mechanical load on the motor, the phasor diagram of induction motor can be developed.

Let Φ = Magnetic flux links with both primary and secondary.

There is self induced e.m.f. E

_{1}in the stator while a mutually induced e.m.f. E_{2r}in the rotor. Let R

_{1}= Stator resistance per phase. X

_{1}= Stator reactance per phase The stator voltage per phase V

_{1}has to counter balance self induced e.m.f. E_{1}and has to supply voltage drops I_{1}R_{1}and I_{1}X_{1}. So on stator side we can write, The rotor induced e.m.f. in the running condition has to supply the drop across impedances as rotor short circuited.

The value of E

_{2r}depends on the ratio of rotor turns to stator turns. The rotor current in the running condition is I

_{2r}which lags E_{2r}by rotor p.f. angle Φ_{2r}. The reflected rotor current I

_{2r}**'**on stator side is the effect of load and is given by, I

_{2r}**'**= K I_{2r} The induction motor draws no load current I

_{o }which is phasor sum of I_{c }and I_{m}. The total stator current drawn from supply is, Ī

_{1}= Ī_{o}+ Ī_{2r}**'** The Φ

_{1}is angle between V_{1}and I_{1}and cos Φ_{1}gives the power factor of the induction motor. Thus using all above relations the phasor diagram of induction motor on load can be obtained.

The steps to draw phasor diagram are,

1. Takes Φ as reference phasor.

2. The induced voltage E

_{1}lags Φ by 90^{o}.3. Show - E

_{1}by reversing voltage phasor.4. The phasor E

_{2r}is in phase with E_{1}. So I_{2r}show lagging E_{2r}i.e. E_{1}direction by Φ_{2r}.5. Show I

_{2r}R_{2 }in phase with I_{2r}and I_{2r }X_{2r }leading the resistive drop by 90^{o}, to get exact location of.6. Reverse I

_{2r}to get I_{2r}**'**.7. I

_{m}is in phase with Φ while Ic is at leading with. Add I_{m}and Ic to get I_{o}.8. Add I

_{o}and I_{2r}**'**to get I_{1}.9. From tip of - E

_{1}phasor, add I_{1}R_{1 }in phase with I_{1}and I_{1}X_{1 }at 90^{o}leading to I_{1}to V_{1 }get phasor.10. Angle between V

_{1 }and I_{1}is Φ_{1}. The phasor diagram is shown in the Fig. 1.

Fig. 1 On load phasor diagram of induction motor |

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Nice to come across your site sir.Really thankful to you sir. I have started a blog Electrical Engineering Info but could not be successful.Can you help me sir

ReplyDeletethanku so much sir.....but let me know what is Ic and Im

ReplyDeleteIc is the core current , and Im is the magnetizing current.

DeletePlease tell me particular side

ReplyDeletePlease tell me particular side

ReplyDeleteThis comment has been removed by the author.

ReplyDeleteHi...When we are changing E1 to +ve X Axis it becomes -E1....but why not rotor current becoming -I2 when it changing to Primary side?

ReplyDelete