Dynamic analysis of the Brushless Doubly-Fed Induction Generator during symmetrical three-phase voltage dips

Abstract

The Brushless Doubly-Fed Induction Generator (BDFIG) shows commercial promise as replacement for doubly-fed slip-ring generators for wind power applications by offering reduced capital and operational costs due to its brushless operation. In order to facilitate its commercial deployment, the capabilities of the BDFIG system to comply with grid code requirements have to be assessed. This paper, for the first time, studies the performance of the BDFIG under grid fault ride-through and presents the dynamic behaviour of the machine during three-phase symmetrical voltage dips. Both full and partial voltage dips are studied using a vector model. Simulation and experimental results are provided for a 180 frame BDFIG.

Full text

Dynamic Analysis of the Brushless Doubly-Fed Induction Generator during
Symmetrical Three-Phase Voltage Dips
Shiyi Shao Ehsan Abdi
Electrical Engineer Division
Cambridge University
9 JJ Thomson Avenue, Cambridge
CB3 0FA, United Kingdom
ram1@cam.ac.uk
Richard McMahon
Abstract – The Brushless Doubly-Fed Induction Generator
(BDFIG) shows commercial promise as replacement for doubly-
fed slip-ring generators for wind power applications by offering
reduced capital and operational costs due to its brushless
operation. In order to facilitate its commercial deployment, the
capabilities of the BDFIG system to comply with grid code
requirements have to be assessed. This paper, for the first time,
studies the performance of the BDFIG under grid fault ride-
through and presents the dynamic behaviour of the machine
during three-phase symmetrical voltage dips. Both full and
partial voltage dips are studied using a vector model. Simulation
and experimental results are provided for a 180 frame BDFIG.
Index Terms—Brushless Doubly-Fed Induction Generator,
voltage dips, vector model
I. INTRODUCTION
The Brushless Doubly-Fed Induction Generator (BDFIG),
also known as the Brushless Doubly-Fed Machine (BDFM),
promises significant advantages as a variable speed generator
for wind power applications due to its fractionally rated
converter and brushless operation [1], [2]. These advantages
become even more important as there is continuous attempt
to reduce the capital and operational costs of wind turbines as
well as improve their reliability.
In order to realise the BDFIG’s advantages and deploy it in
commercial wind farms, its performance at the system level
such as inverter rating [3], system control [5] and grid code
compliance have to be assessed. The latter is particularly
important as the share of wind power generation has been
increasing over the recent years and new grid codes are being
introduced in countries with a large installed wind capacity
such as Germany.
The grid fault ride-through capability of wind turbines
with doubly-fed induction generators (DFIGs) has been
studies in several publications, for example, [6], [7]. These
have led to improvements in the performance of DFIG
systems through utilising various methods such as crowbar
solutions.
However, to date, no such studies exist for the BDFIG.
This paper presents a preliminary study of the BDFIG
performance under partial and full symmetrical three-phase
voltage dips using the methods widely used for DFIGs [6],
[7]. The analysis is based on a simplified vector model
developed for the BDFIG with a nested-loop type of rotor.
For this work, the multiple rotor loops in each nest are
reduced to one effective loop in the vector model using the
approach presented in [8].
The analysis presented in this paper for partial and full
voltage dips can be utilised to assess inverter rating and grid
code compliance for BDFIG-based wind turbines.
Fig. 1. BDFIG configuration
II. BDFIG OPERATION ANALYSIS
The BDFIG comprises two stator windings with different
pole numbers to avoid direct coupling, and a special type of
rotor which couples to both stator fields. The nested-loop
type of rotor is the most well known [1]. One winding, called
the power winding (PW), is connected to mains and the other,
called the control winding (CW), is fed with a fractionally-
rated power electronics converter as shown in Fig. 1. The
shaft angular speed ωr is determined by the stator angular
frequencies as:
21
21
pp
r+
+
=
ω
ω
ω
(1)
p1, p2 and ω1 and ω2 are the pole pair numbers and angular
frequencies of the two stator windings respectively. The
BDFIG is characterised by the so-called natural speed when
the control winding is supplied with DC:
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21
1
pp
n+
=
ω
ω
(2)
A vector model aligned with the power winding stationary
frame is used in this paper for the machine operation analysis
[4], [8]. The model can be expressed as:
dt
d
iRv s
1
111
ψ
+= (3)
221
2
222 )(
ψω
ψ
rs ppj
dt
d
iRv +−+= (4)
rr
r
rrr jp
dt
d
iRv
ψω
ψ
1
−+= (5)
rrss iLiL 1111 +=
ψ
(6)
rrss iLiL 2222 +=
ψ
(7)
2211 iLiLiL rsrsrrr ++=
ψ
(8)
The parameters in the above equations are described in
Table I.
TABLE I
DEFINITION OF VECTOR MODEL PARAMETERS
Parameters Power winding Control winding
Rotor
Resistance Rs1 Rs2 Rr
Self inductance Ls1 Ls2 Lr
Mutual inductance Ls1r Ls2r -
Voltage vector v1 v2 vr
Current vector i1 i2 ir
Flux linkage vector φ1 φ2 φr
The power winding is connected to the grid. Hence, in
steady state, all vectors rotate at the power winding
synchronous speed ω1, which is set by the frequency of the
mains. For example, v1 can be expressed as:
tj
eVv 1
|| 11
ω
= (9)
where |V1| is the magnitude of the power winding voltage.
From (5) and (8),
0)(
)(])([
221
1111
=−+
−+−+=
iLjps
iLjpsiLjpsiRv
rsr
rsrrrrrrr
ω
ω
ω
(10)
Considering (6) and (10), ir and i1 can be expressed as:
r
rs
rsrs
rssrs
r
jps
RL
LLL
iLLL
i
ω
ψ
1
1
1
2
1
22111
−
−−
+
=
(11)
r
rs
rsrs
rsrs
r
r
r
jps
RL
LLL
iLL
jps
R
L
i
ω
ψ
ω
1
1
2
11
2211
1
1
)(
−
+−
+
−
+
= (12)
Substituting (11) to (7):
2
1
1
2
11
1
21
2
12
2
2121
1
1
1
2
11
21
2
i
jps
RL
LLL
jps
RLL
LLLLLLL
jps
RL
LLL
LL
r
rs
rsrs
r
rss
rssrssrss
r
rs
rsrs
rsrs
ω
ω
ϕ
ω
ϕ
−
+−
−
+−−
=
−
+−
−=
(13)
Noting that s-jp1ω1 is larger both in steady state and transient,
1
ψ
v
l
L
v
2s
R
v
2
v
2s
R
2
i
l
L
Fig. 2. Equivalent circuit of BDFIG control winding
then its reciprocal can be neglected. Hence, substituting (13)
to (4), v2 can be expressed as:
1
111
1
2
1
21
211
2
11
2
212
2
121
222
2
))((
))((
ψ
ψω
ω
vvv
ppjs
LLL
LL
ippjs
LLL
LLLLLLL
iRv
ls LR
r
rsrs
rsrs
r
rsrs
rsssrsrss
s
++=
+−
−
+
+−
−
−−
+
=
(14)
From (14), the converter output voltage v2 can be split into
two terms: vψ1 that is the induced back EMP due to the rate of
change of ψ1, and vRs2+vLl which is effectively the voltage
drop across the control winding resistance and an equivalent
leakage inductance. These terms are shown in an equivalent
circuit in Fig. 2, in which:
22
2iRv sRs= (15)
221122 ))(( iLppjiLjv lrlLl
ωωω
+−=−= (16)
2
11
2
212
2
121
rsrs
rsssrsrss
lLLL
LLLLLLL
L−
−−
= (17)
Ignoring the effect of the power winding resistance, (3)
can be simplified as:
1
1
1
ωψ
ψ
j
dt
d
v== (18)
Substituting (18) to (14), then:
tj
rsrs
rsrs
tj
r
rsrs
rsrs
eV
LLL
LL
eV
pp
LLL
LL
v
1
1
1
||
||
)(
1
1
2
1
2
1
21
1
1
111
1
2
1
21
ω
ω
ψ
ω
ω
ω
ω
ω
−
=
+
−
−
= (19)
In a well designed BDFIG, the voltage drops across the
control winding resistance Rs2 and equivalent inductance Ll
are relatively small, thereby, in normal operation vRs2+vLl can
be neglected compared to vψ1. The control winding voltage
can hence be derived by transferring (19) which is in the
power winding stationary reference frame into the control
winding stationary reference frame:
tppj
rsrs
rsrs r
eV
LLL
LL
vv ))((
1
1
2
1
2
1
21
)2(
1
)2(
2
211
||
ωω
ψ
ω
ω
+−
−
=≈ (20)
Equation (20) shows that for normal operation of the BDFIG,
the magnitude of )2(
2
v has a correlation with power winding
voltage |V1| and its gain is proportional to the control winding
frequency which is determined by the rotor speed ωr.
Therefore, only a partially-rated converter is needed if
operating speed range is limited.
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III. BDFIG PERFORMANCE UNDER FULL VOLTAGE DIP
In the following analysis, the control winding is assumed
to be open-circuited, i.e. i2 = 0. In literature, this mode is
referred to as idle operation [9] which facilitates the
investigation of the grid fault effects by decoupling the
control winding supply.
The grid voltage profile can be expressed as below when a
full voltage dip occurs at t = t0:
⎩
⎨
⎧
≥
<
=)(0
)(||
0
01
1
1
tt
tteV
v
tj
ω
(21)
Substituting (12) and (21) into (3) and setting i2 = 0, ψ1
can be calculated as:
⎪
⎪
⎩
⎪
⎪
⎨
⎧
≥
<
=−−
)(
||
)(
||
0
1
/)(
1
0
1
1
11001
1
tt
j
eeV
tt
j
eV
tttj
tj
ω
ω
ψ
τω
ω
(22)
τ1 is a time constant defined as:
rs
rsrs
LR
LLL
1
2
11
1
−
=
τ
(23)
From (22), when a fault occurs at t = t0, ψ1 becomes frozen
at the direction 01tj
e
ω
and with a magnitude of |V1|/jω1, then
decays exponentially with time constant τ1. From (20) and
(22), the open-loop control winding voltage in the power
winding stationary reference frame can be expressed as:
1001
1
/)(
1
1
21
1
1
2
1
21
121
1
2
1
21
||
)(
1
))((
τω
ψ
ω
ω
τ
ϕω
tttj
r
rsrs
rsrs
r
rsrs
rsrs
eeV
j
ppj
LLL
LL
ppjs
LLL
LL
v
−−
+−−
−
=
+−
−
≈
(24)
Generally, 1/τ1 is small relative to j(p1+p2)ωr, hence (24) can
be simplified as:
1001
1001
1
/)(
1
1
21
2
11
21
/)(
1
1
21
2
11
21
||
||
)(
τω
τω
ψ
ω
ωω
ω
ω
tttj
rsrs
rsrs
tttj
r
rsrs
rsrs
eeV
LLL
LL
eeV
pp
LLL
LL
v
−−
−−
+
−
=
+
−
= (25)
By transferring vψ1 to the control winding stationary frame,
(25) becomes:
tppj
tttj
rsrs
rsrs
tt
r
eeeV
LLL
LL
v
ω
τω
ψ
ω
ωω
)(
/)(
1
1
21
2
11
21
)2(
)(
21
1001
01 || +−
−−
≥
+
−
=(26)
From (26), the maximum transient voltage |Vψ1
(2)|max
occurs at t = t0 and its amplitude is:
|||| 1
1
21
2
11
21
max)(
)2(
01 V
LLL
LL
v
rsrs
rsrs
tt
ω
ωω
ψ
+
−
=
≥ (27)
which is larger compared to its value before the grid fault,
given by (20):
|||| 1
1
2
2
11
21
)(
)2(
01 V
LLL
LL
v
rsrs
rsrs
tt
ω
ω
ψ
−
=
< (28)
It should be noted from (27) that the maximum induced
voltage is latger if the machine operates above the natural
speed i.e. when ω2 > 0, as compared to the case that the shaft
speed is below the natural speed i.e. when ω2 < 0. Moreover,
(26) indicates that the post-fault induced voltage has a higher
angular frequency (ω2 = - (p1 + p2) ωr) than normal operation,
which causes transient torque oscillations. Similar effects can
be observed in DFIG systems [10].
The above analysis is based on the control winding being
open circuit. However, in practical applications, the control
winding is connected to a frequency converter and thereby i2
≠ 0. If the converter is capable of providing the required v2 in
grid fault situations to balance the transient vψ1, the control
winding currents would remain within their rating limit.
Otherwise, the voltage difference between v2 and vψ1 would
cause increased currents.
IV. BEHAVIOUR OF THE BDFIG UNDER A PARTIAL VOLTAGE
DROP
In this section, the performance of the BDFIG under a
partial voltage dip is analysed. Similar to the preceding
analysis, it will be assumed that control winding is open
circuit. The profile of a voltage dip occurring at t = t0 is given
as:
⎩
⎨
⎧
≥−
<
=)(||)1(
)(||
01
01
11
1
tteVa
tteV
vtj
tj
ω
ω
(29)
where a is defined as dip depth. When a = 1, (29) is
equivalent to the full voltage dip which is a special case of
the partial voltage dip. The power winding flux linkage can
be obtained from (3) as:
⎪
⎪
⎩
⎪
⎪
⎨
⎧
≥+
−
<
=−−
)(
||||)1(
)(
||
0
1
/)(
1
1
1
0
1
1
11001
1
1
tt
j
eeVa
j
eVa
tt
j
eV
tttjtj
tj
ωω
ω
ψ
τωω
ω
(30)
From (30), the post-fault flux linkage comprises two
components: the first term has fixed amplitude and rotates at
the synchronous speed ω1, and the second term is frozen in
the power winding stationary frame and decays exponentially.
Substituting (30) into (20), the control winding open-loop
voltage can be obtained as:
tj
rsrs
rsrs
tttj
rsrs
rsrs
tj
r
rsrs
rsrs
tttj
r
rsrs
rsrs
eVa
LLL
LL
eeVa
LLL
LL
eVa
pp
LLL
LL
eeVa
pp
LLL
LL
v
1
1001
1
1001
||)1(
||
||)1(
)(
||
)(
1
1
2
2
11
21
/)(
1
1
21
2
11
21
1
1
211
2
11
21
/)(
1
1
21
2
11
21
1
ω
τω
ω
τω
ψ
ω
ω
ω
ωω
ω
ωω
ω
ω
−
−
+
+
−
=
−
+−
−
+
+
−
≈
−−
−−
(31)
If (31) is expressed in the control winding stationary
reference frame, then:
tppj
rsrs
rsrs
tppjtttj
rsrs
rsrs
r
r
eVa
LLL
LL
eeeVa
LLL
LL
v
))((
1
1
2
2
11
21
)(/)(
1
1
21
2
11
21
)2(
1
211
21
1001
||)1(
||
ωω
ωτω
ψ
ω
ω
ω
ω
ω
+−
+−−−
−
−
+
+
−
= (32)
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Similar to ψ1 given in (30), vψ1
(2) comprises two vectors, the
first term
||)1( 1
1
2
2
11
21 Va
LLL
LL
rsrs
rsrs −
−
ω
ω
(33)
has a fixed amplitude determined by the depth of the voltage
dip and rotates at the same frequency as the pre-fault
condition, i.e. ω1 - (p1 + p2) ωr. The second term
|| 1
1
21
2
11
21 Va
LLL
LL
rsrs
rsrs
ω
ω
ω
+
−
(34)
decays exponentially with an oscillation frequency of (p1 + p2)
ωr.
Therefore, the steady-state value of the post-fault control
winding open-loop voltage is:
tppj
rsrs
rsrs
t
r
eVa
LLL
LL
v))((
1
1
2
2
11
21
)2(
)(
211
1||)1(
ωω
ψ
ω
ω
+−
∞→ −
−
= (35)
From (33) and (34), if the machine is operating above the
natural speed i.e. ωr > 0, both vectors have the same initial
phase, hence (32) reaches its maximum value at t = t0.
However, when the shaft speed is below the natural speed, i.e.
ωr < 0, (33) and (34) have opposite direction at t = t0. Since
(34) rotates faster than (33), at t = t0 + π / ω1, the two vectors
will be aligned, but the amplitude of (33) has reduced by a
damping factor of 11
/
τωπ
−
e. As a conclusion, when the BDFIG
operates at below natural speed and a partial voltage dip
occurs, (32) may reach its maximum transient value at either
t0 or t0 + π / ω1, depending on the dip depth a.
It should be noted that (32) is a general expression which
can be used to analyse full voltage dip by setting a = 1
(identical to (26)), as well as pre-fault operation by setting a
= 0 (identical to (20)).
V. EXPERIMENTAL AND SIMULATION RESULTS
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A. Experimental setup
In order to verify the analysis presented in previous
sections, an experimental rig has been set up on a 180 frame
size BDFIG with specifications shown in Table II. Tests were
carried out in the following conditions:
1) The power winding was connected to a PWM-driven
converter which can simulate balanced three-phase
voltage dips.
2) The control winding was open circuited and )2(
1
ψ
v
was measured from the control winding terminals.
3) A DC machine was mechanically coupled to drive
the BDFIG at constant speeds.
B. Full voltage dip test
The BDFIG was first tested under a full voltage dip. As
shown in Fig. 3(a), when supply to the power winding is
disconnected at t = 0.2 s, the power winding voltages
disappear immediately. However, due to the inductive nature
of the windings, the power winding currents vanish with a
time constant as shown in Fig. 3(b).
TABLE II
PROTOTYPE MACHINE SPECIFICATIONS
Parameter Value Parameter Value
Frame size D180 Ls1 0.3498 H
PW pole-pairs 2 Ls2 0.3637 H
CW pole-pairs 4 Ls1r 0.0031 H
Natural speed 500 rpm Ls2r 0.0022 H
Stator / rotor slots 48 / 36 Lr 4.4521×10-5 H
PW rated voltage 240 (at 50 Hz) Rs1
1 2.3 Ω
CW rated voltage 240 (at 50 Hz) Rs2 4 Ω
PW rated current 7 A Rr 1.2967×10-5 Ω
CW rated current 7 A J 0.53 kgm2
Rated rorque 100 Nm Rotor design Nested-loop [8]
When Nr = 400 rpm, from (20) the steady-state control
winding voltage is:
7.43||23.0|| 1max)(
)2(
01 ==
<VV tt
ψ
V
and its angular frequency, from (1), is:
102
)(2 0×−=
<
πω
tt rad/s
During the voltage dip, the maximum )2(
1
ψ
v can be calculated
from (26):
9.172||91.0|| 1max)(
)2(
01 ==
≥VV tt
ψ
V
with the angular frequency calculated from (26):
402
)(2 0×
=
≥
π
ω
tt rad/s
For the operation above the natural speed when Nr = 600
rpm. max)(
)2(
01 || tt
V<
ψ
and )(
20
tt<
ω
have the same values as
calculated above, but the maximum transient inducted control
winding voltage during full voltage dip is: max)(
)2(
01 || tt
V<
ψ
=1.33|V1|=252.7 V and its angular frequency is )(
20
tt≥
ω
= 2π
× 40 rad/s. Both are larger than their equivalent values in
below-natural speed operation. The simulated waveforms of
)2(
1
ψ
v are shown in Fig. 3(c) and 3(d).
The power winding time constant can be calculated from
(23) as:
033.0
1=
τ
s
Indicating that the transient regime disappears in 3τ1 = 0.099
s which can also be observed from Fig. 3(c) and 3(d).
The experimental results are shown from Fig. 3(e) to 3(h),
demonstrating close agreement with simulation results.
C. Partial voltage dip test
A 50 % voltage drop at t = 0.2 s is generated by the
converter as shown in Fig. 4(a). The power winding currents
are shown in Fig. 4(b).
At Nr = 400 rpm, the control winding has the same steady
1 Rs1 was set to 4.055 Ω in simulation. The additional value of 1.755 Ω is
due to the converter output resistance which is connected in series with the
power winding.
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467

state value and frequency as the previous test. During the
voltage dip, as discussed in the previous section, the
maximum value of )2(
1
ψ
v may occur at either t0 or t0 + π / ω1
and can be calculated from (32):
6.64||)1(23.0||91.0|| 11)(
)2(
01 =−−=
=VaVaV tt
ψ
V
45.75||)1(23.0||56.0|| 11)/(
)2(
101 =−+=
+= VaVaV tt
ωπψ
V
Therefore,
45.75|||| )/(
)2(
max)(
)2(
10101 == +=≥
ωπψψ
tttt VV V
From (34), the angular frequency of the transient regime is
(p1 + p2) ωr = 2π × 40 rad/s and from (33), the angular
frequency of the post-fault steady-state control winding
voltage is -ω1 + (p1 + p2) ωr = -2π × 10 rad/s.
For above-natural speed test, Nr = 600 rpm and
2.148||)1(23.0||33.1|| 11max)(
)2(
01 =−+=
≥VaVaV tt
ψ
V
The transient and steady-state angular frequencies are 2π ×
60 rad/s and 2π× 10 rad/s respectively.
In both under and above natural speed operations, the
damping time constant τ1 is the same as calculated for the
previous test with full voltage dip.
The simulated control winding voltage waveforms are
shown in Fig. 4(c) and 4(d). Experimental results are
provided in Fig. 4(e) and 4(h).
D. Voltage dip test when control winding is supplied
In normal BDFIG operation, the control winding is fed
from a converter. The voltage dip leads to a high induced vψ1
on the control winding terminals. If the converter is capable
of generating enough voltage v2 to balance the induced vψ1,
then i2 would be restricted ensuring safe operation. Otherwise,
high currents will be induced in the control winding as a
result of the voltage difference between v2 and vψ1 exerted on
Rs2 and Ll, shown in Fig. 2. This is similar to the case for
DFIG systems. However, the BDFIG typically has a larger Ll,
so the transients in the converter may not be as severe as for
the DFIG.
The short-circuit currents are shown from simulation in
Fig. 5. The BDFIG is equipped with a vector controller [5],
(a) Simulated PW voltages
0 0.1 0.2 0.3 0.4 0.5
−300
−200
−100
0
100
200
300
Time (s)
PW Voltage (V)
U Phase
V Phase
W Phase
0 0.1 0.2 0.3 0.4 0.5
−10
−5
0
5
10
Time (s)
PW Current (A)
U Phase
V Phase
W Phase
0 0.1 0.2 0.3 0.4 0.5
−300
−200
−100
0
100
200
300
Time (s)
CW Voltage (V)
U Phase
V Phase
W Phase
0 0.1 0.2 0.3 0.4 0.5
−400
−300
−200
−100
0
100
200
300
400
Time (s)
CW Voltage (V)
U Phase
V Phase
W Phase
0 0.1 0.2 0.3 0.4 0.5
−300
−200
−100
0
100
200
300
Time (s)
PW Voltage (V)
U Phase
V Phase
W Phase
(b) Simulated PW currents (c) Simulated CW induced
voltages (400 rpm)
(d) Simulated CW induced
voltages (600 rpm)
0 0.1 0.2 0.3 0.4 0.5
−10
−5
0
5
10
Time (s)
PW Current (A)
U Phase
V Phase
W Phase
0 0.1 0.2 0.3 0.4 0.5
−300
−200
−100
0
100
200
300
Time (s)
CW Voltage (V)
U Phase
V Phase
W Phase
0 0.1 0.2 0.3 0.4 0.5
−400
−300
−200
−100
0
100
200
300
400
Time (s)
CW Voltage (V)
U Phase
V Phase
W Phase
(e) Experimental PW voltages (f) Experimental PW currents (h) Experimental CW induced
voltages (600 rpm)
(g) Experimental CW induced
voltages (400 rpm)
Fig. 3: Simulation and experimental results from the full voltage dip test. Power winding is delta connected and supplied with 190 V rms, control
winding is open circuit. Full voltage dip occurs at t = 0.2 s.
0 0.1 0.2 0.3 0.4 0.5
−20
−15
−10
−5
0
5
10
15
20
Time (s)
CW Current (A)
U Phase
V Phase
W Phase
0 0.1 0.2 0.3 0.4 0.5
−20
−15
−10
−5
0
5
10
15
20
Time (s)
CW Current (A)
U Phase
V Phase
W Phase
(a) Simulated CW currents at
400 rpm
(b) Simulated CW currents at
600 rpm
Fig. 5 Simulation results from a full voltage dip test. The power
winding is delta connected and supplied with 190 V rms. The control
winding is connected to a converter regulated by a vector controller
when Q1* = 500 VAR (lagging ) and Tl = 0. The full voltage dip occurs
at t = 0.2 s.
PEDS2009
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and full voltage drop occurs at t = 0.2 s. The transient
currents are higher for over-natural speed operation, which
reasonably agrees with the theory presented in the paper.
VI. CONCLUSION
This paper has presented an analysis of the performance of
the BDFIG during symmetrical three-phase voltage dips.
Substantial voltage is induced at the control winding
terminals as a result of grid faults. The transient and steady-
state behaviour of such voltages have been derived in detail.
It has been shown that the induced voltage is large,
particularly at over-natural speed operation, leading to large
currents induced in the control winding. Hence, the system
will require an increase in the inverter rating. The amplitude
of the induced currents is limited by the effective series
impedance of the machine. In the BDFIG, this impedance is
typically larger than an equivalent DFIG, hence the currents
may have lower magnitudes.
REFERENCES
[1] R. A. McMahon, X. Wang, E. Abdi, P. J. Roberts and M. Jagiela, "The
BDFM as a generator in wind turbines," Power Electronics and Motion
Control Conference, 12th International, pp. 1859-1865, Aug. 2006.
[2] R. A. McMahon, P. C. Roberts, X. Wang, P. J. and Tavner,
"Performance of BDFM as generator and motor," Electrical Power
Applications, IEE Proceedings. Antennas Propagat., pp. 290-299, Mar.
2006.
[3] X. Wang, P. C. Roberts, and R. A. McMahon, "Studies of inverter
ratings of bdfm adjustable speed drive or generator systems," 6th
International Conference on Power Electronics and Drive Systems, Vol.
1, pp. 337-342, Dec. 2005.
[4] J. Poza, E. Oyarbide, D. Roye, and M. Rodriguez, "Unified reference
frame dq model of the brushless doubly fed machine," Electrical Power
Applications, IEE Proceedings. Vol. 146, no. 6, pp. 726-734, Sep. 2006.
[5] S. Shao, E. Abdi, and R. A. McMahon, "Vector control of the brushless
doubly-fed machine for wind power generation," IEEE International
Conference on Sustainable Energy Technologies, pp. 322-327, Nov.
2008.
[6] J. Lopez, P. Sanchis, X. Roboam, and, L. Marroyo, "Dynamic
behaviour of the doubly fed induction generator during three-phase
voltage dips," IEEE Transactions on Energy Conversion, vol. 22, no. 3,
pp. 707-717, Sep. 2007.
[7] J. Lopez, E. Gubia, P. Sanchis, X. Roboam, and, L. Marroyo, "Wind
turbines based on doubly fed induction generator under asymmetrical
voltage dips," IEEE Transactions on Energy Conversion, vol. 23, no. 1,
pp. 321-330, Mar. 2008.
[8] P. C. Roberts, "A study of Brushless Doubly-Fed (Induction)
Machines," Ph.D. dissertation, University of Cambridge, 2004.
[9] J. Morren, and S. Haan, "Short-circuit current of wind turbines with
doubly fed induction generator," IEEE Transactions on Energy
Conversion, vol. 22, no. 1, pp. 174-180, Mar. 2007.
[10] I. Erlich, H. Wrede and C. Felter "Dynamic behaviour of DFIG-based
wind turbines during grid faults," IEEE Power Conversion Conference,
vol. 22, no. 1, pp. 1195-1200, Apr. 2007.
(a) Simulated PW voltages (b) Simulated PW currents (c) Simulated CW induced
voltages (400 rpm)
(d) Simulated CW induced
voltages (600 rpm)
(e) Experimental PW voltages (f) Experimental PW currents (h) Experimental CW induced
voltages (600 rpm)
(g) Experimental CW induced
voltages (400 rpm)
Fig. 4: Simulation and experimental results from 50% voltage dip test. Power winding is delta connected and supplied with 190 V rms, control
winding is open circuit. Full voltage dip occurs at t = 0.2 s.
0 0.1 0.2 0.3 0.4 0.5
−300
−200
−100
0
100
200
300
Time (s)
PW Voltage (V)
U Phase
V Phase
W Phase
0 0.1 0.2 0.3 0.4 0.5
−10
−5
0
5
10
Time (s)
PW Current (A)
U Phase
V Phase
W Phase
0 0.1 0.2 0.3 0.4 0.5
−150
−100
−50
0
50
100
150
Time (s)
CW Voltage (V)
U Phase
V Phase
W Phase
0 0.1 0.2 0.3 0.4 0.5
−300
−200
−100
0
100
200
300
Time (s)
CW Voltage (V)
U Phase
V Phase
W Phase
0 0.1 0.2 0.3 0.4 0.5
−300
−200
−100
0
100
200
300
Time (s)
PW Voltage (V)
U Phase
V Phase
W Phase
0 0.1 0.2 0.3 0.4 0.5
−10
−5
0
5
10
Time (s)
PW Current (A)
U Phase
V Phase
W Phase
0 0.1 0.2 0.3 0.4 0.5
−150
−100
−50
0
50
100
150
Time (s)
CW Voltage (V)
U Phase
V Phase
W Phase
0 0.1 0.2 0.3 0.4 0.5
−300
−200
−100
0
100
200
300
Time (s)
CW Voltage (V)
U Phase
V Phase
W Phase
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