Hardware Reference
In-Depth Information
then the currents i a , i b and i c form a 3-phase sinusoidal current set, which is
symmetric in the time domain. In this case, the airgap MMF generated by the
windings changes to
F g (θ,t)=F a1 (θ,t)+F b1 (θ,t)+F c1 (θ,t)
3KI m
cos(ωt −pθ)=F m1 cos(ωt −pθ)
Equation 4.37 is a typical expression of traveling wave, and its phase angle
τ is determined by
τ = ωt −pθ.
Therefore, if an MMF value or a phase angle τ is given at certain time
instant t, the position of the traveling wave θ at that phase angle can be
determined using equation 4.38. It is clear that this position θ is a function of
For a gi ven τ,differentiating both sides of equation 4.38 yields
that is,
Ω =
dt = ω
p = 2πf
where Ω is the angular speed of the traveling wave whose unit is radian per
second, and f the frequency of the current in Hz (Hertz).
Conventional practice in engineering expresses rotational speed in units of
revolution per minute or RPM and uses the symbol n to describe it. From
4.40, it can be shown that,
n = 60Ω
= 60f
It shows that, the rotational speed of the MMF or of the airgap fl ux density
is proportional to the frequency of the current, and inversely proportional to
the pole-pair of the magnetic fi eld. In other words, a rotating magnetic fi eld
can be generated by inputting the 3-phase time-symmetric alternating currents
into the 3-phase space-symmetric windings. This is an electrical method to
realize the rotational fi eld. The fi eld speed can be adjusted by changing the
frequency of the current. Otherwise, for a given frequency of the current in
the winding, the speed of the rotating fi eld can be designed with a suitable
magnetic pole-pair in the motor design stage.
We can also know from equation 4.31 that, besides the fundamental MMF,
the winding-A, winding-B and winding-C also contain harmonic fi elds. It is
not difficult to prove that, when the input currents are symmetric in the time
domain, the m th order harmonic fi elds produced by the 3-phase winding can
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