0195136047.pdf

12.3 ROTATING MAGNETIC FIELDS 525

Phase a

Phase a

Phase b

Phase b

Phase c

Phase c

Total

(a)

(b)

Total

θ

− 90 ° − 30 ° 0 ° 30 ° 90 ° 150 ° 210 ° 270 °

θ

150 ° 210 ° 270 °

120 °

30 ° 90 °

− 30 °

0 °

− 90 °

F

Instant in time

ia

ib

ic

Instant in time

ic

ia

ib

Figure 12.3.2Generation of a rotating mmf.(a)Spatial mmf distribution at the instant in time when the
a-phase current is a maximum.(b)Spatial mmf distribution at the instant in time when theb-phase current
is a maximum.

rotating in opposite directions at the same angular velocity given bydθ/dt=ω. The vertical
components of the two rotating vectors in Figure 12.3.3(b) always cancel, and the horizontal
components always yield a sum equal toBmcosωt, the instantaneous value of the pulsating
vector.
This principle is often used in the analysis of single-phase machines. The two rotating fluxes
are considered separately, as if each represented the rotating flux of a polyphase machine, and
the effects are then superimposed. If the system is linear, the principle of superposition holds
and yields correct results. In a nonlinear system with saturation, however, one must be careful in
reaching conclusions since the results are not as obvious as in a linear system.