1
1
1
Wound Rotor Induction
Generators (WRIGs):
Steady State
1.1
Introduction .
......................................................................
1
1
1.2
Construction Elements .
.....................................................
1
4
Magnetic Cores
•
Windings and Their mmfs
•
SlipRings
and Brushes
1.3
SteadyState Equations.
......................................................
1
9
1.4
Equivalent Circuit .
...........................................................
1
11
1.5
Phasor Diagrams .
.............................................................
1
13
1.6
Operation at the Power Grid.
..........................................
1
18
Stator Power vs. Power Angle
•
Rotor Power vs. Power Angle
•
Operation at Zero Slip (S
=
0)
1.7
Autonomous Operation of WRIG.
.................................
1
22
1.8
Operation of WRIG in the Brushless Exciter Mode.
.....
1
28
1.9
Losses and Efﬁciency of WRIG.
......................................
1
33
1.10
Summary.
..........................................................................
1
34
References.
...................................................................................
1
36
1.1
Introduction
Wound rotor induction generators (WRIGs) are provided with three phase windings on the rotor and
on the stator. They may be supplied with energy at both rotor and stator terminals. This is why they are
called doubly fed induction generators (DFIGs) or double output induction generators (DOIGs). Both
motoring and generating operation modes are feasible, provided the power electronics converter that
supplies the rotor circuits via sliprings and brushes is capable of handling power in both directions.
As a generator, the WRIG provides constant (or controlled) voltage
V
s
and frequency
f
1
power through the
stator, while the rotor is supplied through a static power converter at variable voltage
V
r
and frequency
f
2
.
The rotor circuit may absorb or deliver electric power. As the number of poles of both stator and rotor
windings is the same, at steady state, according to the frequency theorem, the speed
ω
m
is as follows:
(1.1)±
where
p
1
is the number of pole pairs
Ω
R
is the mechanical rotor speed
ωωωω
mm
R
p
=±
=⋅
12
1
;
Ω
© 2006 by Taylor & Francis Group, LLC
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Variable Speed Generators
The sign is positive (
+
) in Equation 1.1 when the phase sequence in the rotor is the same as in the
stator and
ω
m
<
1
, that is, subsynchronous operation. The negative (
−
) sign in Equation 1.1 corresponds
to an inverse phase sequence in the rotor when
m
>
1
, that is, supersynchronous operation.
For constant frequency output, the rotor frequency
2
has to be modiﬁed in step with the speed
variation. This way, variable speed at constant frequency (and voltage) may be maintained by controlling
the voltage, frequency, and phase sequence in the rotor circuit.
It may be argued that the WRIG works as a synchronous generator (SG) with threephase alternating
current (AC) excitation at slip (rotor) frequency
2
=
1
−
m
. However, as
1
≠
ω
m
, the stator induces
voltages in the rotor circuits even at steady state, which is not the case in conventional SGs. Additional
power components thus occur.
The main operational modes of WRIG are depicted in Figure 1.1a through Figure 1.1d (basic conﬁg
uration shown in Figure 1.1a). The ﬁrst two modes (Figure 1.1b and Figure 1.1c) refer to the already
deﬁned subsynchronous and supersynchronous generations. For motoring, the reverse is true for the
rotor circuit; also, the stator absorbs active power for motoring. The slip
S
is deﬁned as follows:
(1.2)
FIGURE 1.1
Wound rotor induction generator (WRIG) main operation modes: (a) basic conﬁguration, (b) subsynchro
nous generating (
r
<
1
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 ........., Power factor, Taylor & Francis Group, WRIGs

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