Concept of Rotating Magnetic Field

CONCEPT OF ROTATING MAGNETIC FIELD

If a balanced 3ϕ voltage is applied to a balanced 3ϕ winding, it produced a rotating magnetic field of constant amplitude. This speed is called synchronous speed.

The speed of the rotating magnetic field is

N_s = 120ƒ/P

f- is the frequency of the supply

P - is the number of stator poles

The stator may be star or delta connected. The 3ϕ windings are displaced from each other by an angle 120°.

Fig. 3.88 shows that the 3ϕ windings are supplied by a balanced 3f supply having phase sequence RYB.

The current through the windings are displaced from each other by an angle of 120°.

The instantaneous values of three fluxes are

ϕ_R = ϕ_m m sin ωt ………(1)    

ϕ_Υ = ϕ_m sin (ωt - 120°) ………..(2)

ϕ_В = ϕ_m sin (ωt - 240°) …..…….(3)

The resultant flux is

Case 1

If ωt = Ɵ = 0

Substitute ωt = 0 in equations (1), (2) and (3)

ϕ_R = ϕ_m sin 0 = 0

ϕ_Y = ϕ_m sin (0-120°) = - 0.866 ϕ_m

ϕ_B= ϕ_m (0-240°) = + 0.866 ϕ_m

Fig. shows the phasor addition of fluxes

From the above fig

OD = DA = ϕRes/2

ϕ_Res = 2 × 0.866 ϕ_m × cos 30°

= 1.5 ϕ_m

The magnitude of ϕ_Res is 1.5 ϕ_m and it is vertivally placed.

Case 2

If ωt = Ꮎ = 60°

Substitute Ɵ = 60° in equations (1), (2) and (3)

ϕ_R = ϕ_m sin 60° = 0.866 ϕ_m

ϕ_Υ = ϕ_m sin (60° - 120°) = - 0.866 ϕ_m

ϕ_В = ϕ_m sin (60° - 240°) = 0

Fig.3.90 shows the phasor addition of the above three fluxes

From the fig

OD = DA = ϕRes/2

ϕ_Res = 2 × 0.866 ϕ_m × cos 30°

= 1.5 ϕ_m

The magnitude of ϕ_Res is 1.5 ϕ_m and it is rotated through 60° in  space in clockwise

direction compared to its previous position

Case 3

ωt = Ө = 120°

Substitute Ɵ = 120° in equations (1), (2) and (3)

ϕ_R = ϕ_m sin 120° = + 0.866 ϕ_m

ϕ_Y = ϕ_m sin (120° - 120°) = 0

ϕ_B = ϕ_m (120° - 240°) = - 0.866 ϕ_m

Fig.3.91 shows the phasor addition of the above three fluxes

From the fig

OD = DA = ϕRes/2

ϕ_Res = 2 × 0.866 ϕ_m × cos 30°

= 1.5 ϕ_m

The magnitude of ϕ_Res is 1.5ϕ_m and it is rotated through 120° in space on clockwise direction compared to its previous position.

Case 4

ωt = Ө = 180°

Substitute Ɵ = 180° in equations (1), (2) and (3)

ϕ_R = ϕ_m sin 180° = 0

ϕ_Y = ϕ_m sin (180° - 120°) = + 0.866 ϕ_m

ϕ_B = ϕ_m (180° - 240°) = - 0.866 ϕ_m

Fig. 3.92 shows the phasor addition of the above three fluxes

From the fig

OD = DA = ϕRes/2

ϕ_Res = 2 × 0.866 ϕ_m × cos 30°

= 1.5 ϕ_m

The magnitude of ϕ_Res is 1.5 ϕ_m, and is rotated through 180° in space in clockwise direction compaced to its previous position.