Rotating Magnetic Field


Production of Rotating Magnetic Field :


     When the three phase uniformly distributed winding suitably wound on the stator is supplied with 3-φ a.c supply, a rotating magnetic field of constant magnitude rotating at synchronous speed is produced.



 Proof : 


     Consider 3-phase, 2 pole stator having three similar windings aa'bb', and ccdisplaced in space by 120°, supplied with 3-φ a.c supply.

Rotating Magnetic Field

     Due to current flowing in each phase of the stator produces an alternating flux which is assumed to be sinusoidal in nature. Let these fluxes be φ1φ2, and φ3 and are displaced from each other by 120°.

     The instantaneous values of fluxes with respect to time is given by

φ1 =  φm Sin θ

φ2  =  φm Sin ( θ - 120⁰ )

φ3  =  φm Sin ( θ - 240⁰ )

Where,

      φm  =  Maximum value of the flux due to any phase. 


     The wave forms of these fluxes and their phase representation is shown below.

Rotating Magnetic Field

Phasor Diagram :


Rotating Magnetic Field

     The three fluxes together gives rise to an effect of rotating flux called as Rotating Magnetic Field.



Let us see Four Different Instants :


     The resultant flux, φr at any instant is the phasor sum of the fluxes of the three phases at that instant.


(i) when θ  =  0⁰  ( At point ' 0 ' ) 



Rotating Magnetic Field

     The resultant of φ2 and φ3 can be found out by reversing φ2 and adding it with φ3.

From the figure Resultant flux, 


(ii) when θ  =  60  ( At point ' 1 ' ) 




Rotating Magnetic Field

From the figure Resultant flux,


     Hence φr  = 1.5 φm but has rotated clockwise through as angle of  60⁰


(iii) when θ  =  120  ( At point ' 2 ' ) 



Rotating Magnetic Field

From the figure Resultant flux,




     Hence φr  = 1.5 φm but has rotated clockwise through as angle of  60⁰ or 120⁰ from the start.


(iv) when θ  =  180⁰  ( At point ' 3 ' ) 




Rotating Magnetic Field

From the figure Resultant flux,


     Hence φr  = 1.5 φm but has rotated clockwise through as angle of  60⁰ or 180⁰ from the start.



From the above, we can say that


(i) The resultant flux is of constant magnitude and having value 1.5 φm i.e., φr  = 1.5 φm.

(ii) The resultant flux rotates at the synchronous speed, Ngiven by  

Ns  =  120f / P  rpm

Where

   f  =  Supply frequency and

   P  =  Number of poles of the stator winding.


Therefore,

     When 3-φ supply is fed to 3-φ stator winding, a rotating magnetic field of constant magnitude rotating at synchronous speed is produced.



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