INDUCTION MACHINES I

4. The rotor is driven and the sinusoidally distributed flux rotates at
rotational (angular) speed ω. In effect there are electromotive forces
induced in stator windings:
e
u
e
v
e
w
=
=
=
2E
f
sinωt
⎛ 2 ⎞
2E
f
sin⎜ωt
− π ⎟
⎝ 3 ⎠
⎛ 4 ⎞
2E
f
sin⎜ωt
− π ⎟
⎝ 3 ⎠
Ef – rms value of emf in stator winding
due to rotor flux
E 4 . 44Nf
k Φ
f
1
f
= 1
w
pn1
= f
60
5. In the closed circuit of stator windings the currents flow due to emfs:
i
i
i
u
v
w
=
=
=
1
f
=
ω
2π
2I
sin
( ωt
− Ψ)
⎛ 2 ⎞
2I
sin⎜ωt
− π − Ψ ⎟
⎝ 3 ⎠
⎛ 4 ⎞
2I
sin⎜ωt
− π − Ψ ⎟
⎝ 3 ⎠
Such 3-phase symmetrical currents flowing in 3-phase symmetrical
stator windings produce rotating magnetic field of stator – sinusoidally
distributed in space. Direction of rotation – accordingly to phase
sequence, i.e. in the same direction as rotor rotates. The field is called
60f1
armature reaction field. Its rotational speed n1
= is of the same
p
value as rotor speed.
Summary: rotor, rotor field and stator (armature) field rotate
synchronously (with the same speed n1) ⇒ SYNCHRONOUS
MACHINE!
PHASOR REPRESENTATION
Armature reaction flux induces emf Ea
E = cΦ
= c I E = − c I = −jX
I
U
a
or
a
a
a
1
a
j 1
= jX
I − voltage drop at the reactance X
Xa – armature reaction reactance (reactance of the stator winding
corresponding to the armature reaction flux).
E – total emf induced by total (resultant) flux Φ. It is also called the airgap
emf (as it corresponds to resultant air-gap flux).
a
a
SM1- 2
Ψ - angle of displacement
between emf Ef and current I
in stator winding.
Symmetry of load is
assumed.
In normal steady-state
operation everything rotate
synchronously.