Page 733 - Basic Electrical Engineering

The double or two revolving field theory is explained with the help of
vector representations as in Fig. 9.2. The alternating magnetic field is
represented by a vector, ϕ, which varies from its positive maximum value to

negative maximum value, in every half cycle of current flow through the
stator winding. This maximum of ϕ as ϕ has been shown by two vectors
m

the sum of these two vectors will always be equal to ϕ . As the
m

flux produced varies sinusoidally, it will be observed that this magnetic flux
at every instant of time is the vector sum of two rotating magnetic fields.

In Fig. 9.2 is shown the stator winding connected to a single-phase supply
voltage V. The current flown and the flux produced have been shown. As the

current changes its polarity every half cycle, the flux produced in the air gap
will change sinusoidally varying from maximum of +ϕ to negative
m
maximum of –ϕ . Let us consider different instants of time on the flux wave,
m
say at θ = 0°, 90°, 180°, 270°, and 360°. We have considered ϕ as the sum
m

of two vectors , the sum of which at every instant of time will be

equal to ϕ . Two component vectors have been represented in the figure as
m

represents forward field rotating in anticlockwise

direction and represents backward field rotating in the clockwise

direction at the same speed. The speed of rotation of the two fields is the

same and is synchronous with the alternating magnetic field. At θ = 0, the
two fields are shown opposite to each other so that the resultant flux ϕ = 0. At

θ = 90°, the two flux vectors have rotated by 90° in opposite directions and
the resultant flux is +ϕ . At θ = 180°, the two component flux vectors have
m