502 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 28, NO.

3, SEPTEMBER 2013

Asymmetrical Low-Voltage Ride Through of

Brushless Doubly Fed Induction Generators
for the Wind Power Generation
Teng Long, Member, IEEE, Shiyi Shao, Member, IEEE, Ehsan Abdi, Member, IEEE,
Richard A. McMahon, and Shi Liu

Abstract—Compared with the Doubly fed induction generators δ Differential operator, i.e., d/dt.
(DFIG), the brushless doubly fed induction generator (BDFIG) sn Slip of the BDFIG, defined in (16).
has a commercial potential for wind power generation due to its superscripts
lower cost and higher reliability. In the most recent grid codes, wind
generators are required to be capable of riding through low voltage +, − Positive and negative synchronous reference
faults. As a result of the negative sequence, induction generators frames.
response differently in asymmetrical voltage dips compared with subscripts
the symmetrical dip. This paper gave a full behavior analysis of p, n Forward and backward sequence.
the BDFIG under different types of the asymmetrical fault and d, q Rotating dq frame axis.
proposed a novel control strategy for the BDFIG to ride through
asymmetrical low voltage dips without any extra hardware such α1 , β1 Stationary axis of PW.
as crowbars. The proposed control strategies are experimentally α2 , β2 Stationary axis of CW.
verified by a 250-kW BDFIG.
Index Terms—AC generators, doubly fed induction generators
(DFIG), fault ride-through, wind energy. I. INTRODUCTION
HE brushless doubly fed induction generator (BDFIG) is
NOMENCLATURE T attractive for wind power, especially offshore. In common
with the doubly fed induction generator (DFIG), it has the ben-
PW, CW Power winding and control winding. efit of a low-cost converter but does not have brushgear, promis-
V, I, Ψ Voltage, current, and flux vectors. ing low maintenance costs, and high robustness [1]. A recent
F Arbitrary vector. study predicts a significant increase in reliability [2]. A 20-kW
v, i, ψ Voltage, current, and flux scalars. BDFIG-based wind turbine has been erected and experience to
P, Q Active and reactive power. date confirms expectations [3].
ω Angular frequency of the arbitrary rotating ref- Wind power has become ever more popular during recent
erence frame. decades. With its increasing penetration, requirements for grid
ω 1 , ω2 , ωr Angular frequency of PW, CW, and rotor. connection have been established. Among these, low-voltage
θ 1 , θr Angular position of PW flux frame and rotor. ride-through (LVRT) capability is regarded as one of the most
p1 , p2 Pole pair numbers of PW and CW. challenging requirements that is found in contemporary grid
R 1 , R2 , Rr Resistances of PW, CW, and rotor. codes [4]. For example, the requirement defined in the Chinese
L1 , L2 , Lr Self-inductance of PW, CW, and rotor. grid code [5], [6] is shown in Fig. 1. During voltage dips, wind
L1r , L2r Coupling inductance between stator windings generators are expected to remain connected, i.e., to ride through
and rotor. the low-voltage fault.
Generally, two types of grid faults can be defined. One in-
volves symmetrical voltage dips (all three phases short circuited
Manuscript received July 14, 2012; revised October 12, 2012 and January to the ground) and the other asymmetrical voltage dips. This pa-
21, 2013; accepted March 3, 2013. Date of publication June 19, 2013; date of per concentrates on the latter case.
current version August 16, 2013. T. Long and S. Shao contributed equally to
this work. Paper no. TEC-00299-2012. The DFIG has become the most widely used generator for
T. Long is with the GE Power Conversion, Rugby, Warwickshire CV21 1BU, wind turbines, principally because it achieves variable speed
U.K. (e-mail: teng.long@ge.com). operation with only a fractionally rated converter [7], [8]. How-
R. A. McMahon is with the Department of Engineering, University of Cam-
bridge, Cambridge CB3 0FA, U.K. (e-mail: ram1@cam.ac.uk). ever, the brushes and slip rings present in the DFIG result in a
S. Shao is with the CSE Electric Technology Ltd., China Ship Industry significant maintenance cost, particularly, for wind turbines in
Cooperation, Beijing 100097, China (e-mail: shaoshiyi@gmail.com). remote places such as offshore wind farms [2], [9]. The DFIG
E. Abdi is with the Wind Technologies Ltd., Cambridge CB4 0EY, U.K.
(e-mail: ehsan.abdi@windtechnologies.com). is also very sensitive to asymmetrical voltage dips [10]. With-
S. Liu is with the School of Control and Computer Engineering, North China out extra hardware, the DFIG cannot ride through the most
Electric Power University, Beijing 102206, China (email: liushidr@yahoo.com). severe asymmetrical faults even with very complex LVRT con-
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org. trollers [11]. Generally speaking, crowbar protection is required
Digital Object Identifier 10.1109/TEC.2013.2261818 to limit transient overcurrents [12]–[14]. Other solutions using
0885-8969 © 2013 IEEE
LONG et al.: ASYMMETRICAL LOW-VOLTAGE RIDE THROUGH OF BRUSHLESS DOUBLY FED INDUCTION GENERATORS 503

III. DYNAMIC VECTOR MODEL OF THE BDFIG

The vector model of the BDFIG, aligned in the PW stationary
reference frame, is expressed as [18]
dΨ1
V1 = R 1 I 1 + (2)
dt
dΨ2
V2 = R 2 I 2 + − j((p1 + p2 )ωr )Ψ2 (3)
dt
dΨr
Vr = R r I r + − jp1 ωr Ψr (4)
dt
Ψ1 = L1 I1 + L1r Ir (5)
Ψ2 = L2 I2 + L2r Ir (6)
Fig. 1. Grid fault pattern, the solid line is from the Chinese grid code, and the Ψr = Lr Ir + L1r I1 + L2r I2 (7)
dash line is the voltage fault used in this paper.
where R1 , R2 , L1 , L2 , Lr , L1r , L2r are the PW resistance, CW
resistance, PW self-inductance, CW self-inductance, rotor self-
hardware protective circuit such as a stator damping resistor inductance, mutual inductance between PW and rotor, and mu-
(SDR) controllers [11], or a dynamic voltage restorer [15], [16], tual inductance between CW and rotor, respectively.
or a series grid-side converter [17] all increase the system cost The power winding is connected to the grid. Hence, in the
and complexity. steady state, all vectors rotate at the power winding synchronous
To date, no research has been carried out on the asymmetrical speed ω1 , which is set by the frequency of the grid. For example,
LVRT performance of the BDFIG. This paper aims to fill this V1 can be expressed as
gap. The dynamic behavior of the BDFIG will be analyzed, and
V1 = |V1 |ej ω 1 t (8)
a crowbarless scheme will be proposed, with experimental val-
idation based on a 250-kW prototype BDFIG. The low voltage where |V1 | is the magnitude of the power winding voltage.
fault emulated in this paper, shown in the dash line in Fig. 1, From (4) to (7), the CW flux linkage in terms of the PW flux
is more severe than the Chinese gird code with a deeper low linkage and CW current is
voltage drop and a longer fault time. The experimental result
L1r L2r
shows the proposed asymmetric LVRT method is able to meet Ψ2 = − Ψ1
this severe grid requirement. L1 Lr − L21r + δ −j
L1 Rr
p1 ωr

L1 L2 Lr − L1 L22r − L2 L21r + L1 L2 Rr
δ −j p 1 ω r
+ I2 (9)
II. BDFIG OPERATION L1 Lr − L21r + L1 Rr
δ −j p 1 ω r
The stator of the BDFIG has two separate windings with d
where δ represents the differential operator dt .
different pole pair numbers chosen to avoid direct coupling be-
The term δ − jp1 ωr is very large compared with other terms
tween the windings. The rotor employs a special design enabling
in the aforementioned expression, so its reciprocal can be ne-
it to couple to both stator windings. The power winding (PW)
glected. By substituting (9) into (3), V2 becomes
is connected to the grid directly, whereas the control winding
(CW) is connected to the grid through a bidirectional variable V2 = R 2 I 2
voltage, variable frequency (VVVF) converter handling only a
L1 L2 Lr − L21r L2 − L1 L22r
fraction of the rated power [1]. + (δ − j(p1 + p2 )ωr )I2
The BDFIG is normally operated in the synchronous (doubly L1 Lr − L21r
fed) mode, in which the shaft angular velocity is determined by L1r L2r
(δ − j(p1 + p2 )ωr )Ψ1
the excitation frequencies of the two stator windings, indepen- L21r − L1 Lr
dent of the torque exerted on the machine, and can be expressed
= EΨ 1 + Vx2 . (10)
as
From (10), the converter output voltage V2 can be split into
ω1 + ω2 two terms: EΨ 1 that is the induced EMF due to the rate of
ωr = (1)
p1 + p2 change of Ψ1 , and VR 2 + VL l which is the voltage drop across
the CW resistance and an equivalent leakage inductance. These
where ω1 and ω2 are the excitation angular frequencies supplied terms are shown in an equivalent circuit in Fig. 2, in which
to the two stator windings.
When the CW angular frequency ω2 equals to zero, the angu- Vx2 = (R2 + Ll (δ − j(p1 + p2 )ωr ))I2 (11)
lar velocity of the shaft is defined as the natural angular velocity L1r L2r
EΨ 1 = (δ − j(p1 + p2 )ωr )Ψ1 (12)
ωn . L21r − L1 Lr
504 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 28, NO. 3, SEPTEMBER 2013

as

|V1 |ej ω 1 t (t < t0 )
V1 = −j ω 1 t
(20)
|V1p |e jω1 t
+ |V1n |e (t ≥ t0 ).
The forward and backward sequences, subscripted by p and
n, respectively, are decomposed as
Fig. 2. Equivalent circuit of BDFIG control winding. ⎡ ⎤
    V1u
|V1p |
2π 4π
j j
1 1 e 3 e 3 ⎢ ⎥
= · · ⎣ V1v ⎦ (21)
L1 L2 Lr − L21r L2 − L1 L22r |V1n | 3 4π
1 ej 3 ej 3
2π

Ll = . (13) V1w
L1 Lr − L21r
For simplicity, the PW resistance is ignored in this section where V1u = V sin(ω1 t) and V1v = V sin(ω1 t + 23 π), V1w =
for analyzing the behavior of the BDFIG under asymmetric V sin(ω1 t + 43 π).
low-voltage faults. However, the resistance is considered when The forward sequence component generates a flux rotating at
estimating the PW flux linkage for designing and implementing the synchronous speed and the backward sequence component
the control scheme in the Section VI. produces a flux rotating at the synchronous speed but in a reverse
Hence, (2) can be simplified as direction. In the steady state, these two fluxes can be expressed
as
dΨ1
V1 = = jω1 Ψ1 . (14) |V1p | j ω 1 t
dt Ψ1p = e (22)
Substituting (8) and (14) into (12) gives jω1
|V1n | −j ω 1 t
L1r L2r ω1 − (p1 + p2 )ωr Ψ1n = e . (23)
EΨ 1 = |V1 |ej ω 1 t −jω1
L21r − L1 Lr ω1
L1r L2r The forward and backward sequences of the PW flux linkage
= sn |V1 |ej ω 1 t (15) in the steady state vary with the type of the faults. Three types
L1r − L1 Lr
2
of asymmetrical low voltage faults are discussed in this paper:
where sn is defined as the slip of the BDFIG: phase to phase short circuit (p-p), one phase to the ground short
circuit (p-n), and phase to phase to the ground short circuit
ωn − ωr ω1 − (p1 + p2 )ωr
sn = = . (16) (p-p-n). When the PW of the machine is Δ connected, the PW
ωn ω1 voltage and flux linkages are given as
The induced EMF EΨ 1 can be also expressed in the CW refer- phase to phase short circuit (p-p):
ence frame, as indicated as superscript (2) ⎡ ⎤
0
L1r L2r ⎡ ⎤ ⎢√ ⎥
sn |V1 |e−j (ω 1 −(p 1 +p 2 )ω r )t .
(2)
EΨ 1 = (17) V1u ⎢ 3 3 ⎥
L21r − L1 Lr ⎢ ⎥ ⎢ 2⎢ V sin ω t + π ⎥
⎣ V1v ⎦ = ⎢
1
2 ⎥ (24)
⎥
Similarly, the voltage drop due to the CW current is ⎢√  ⎥
V1w ⎣ 3 1 ⎦
(2) (2) V sin ω1 t + π
Vx2 = (R2 + j(ω1 − (p1 + p2 )ωr )Ll )I2 . (18) 2 2
⎡ 1 ⎤
Hence, from the viewpoint of the converter (CW stationary   V ej ω 1 t
Ψ1p 1 ⎢ 2 ⎥
reference frame), the CW voltage in terms of the PW flux and = ·⎣ ⎦ (25)
the voltage drop caused by the CW current becomes Ψ1n jω 1 1 −j ω 1 t
Ve
(2) (2) (2)
2
V2 = EΨ 1 + Vx2. (19)
phase to ground short circuit (p-n):
Equations (17), (18), and (19) show that for normal operation ⎡ √ ⎤
(2) 3 π
of the BDFIG, the magnitude of V2 depends on the PW voltage
⎡ ⎤ ⎢ 3 V sin(ω1 t + 6 ⎥
|V1 | and its gain is proportional to the CW frequency which is V1u ⎢ ⎥
⎢ ⎥
determined by the rotor angular velocity ωr .With a −0.3 to 0.3 ⎢ ⎥ ⎢ 4 ⎥
⎣ V1v ⎦ = ⎢ V sin(ω1 t + π) ⎥ (26)
slip range, a fractionally rated converter is sufficient. ⎢ 3 ⎥
V1w ⎢√ ⎥
⎣ ⎦
3 π
IV. BEHAVIOR UNDER ASYMMETRICAL VOLTAGE DIP V sin(ω1 t + )
3 2
In the following analysis, the CW is taken to be open circuited, ⎡ 2 jω1 t ⎤
  Ve
i.e., I2 = 0. Under asymmetrical conditions, the sequence com- Ψ1p 1 ⎢ 3 ⎥
ponent theory can be used [19], [20]. Considering an asymmet- = ·⎣ ⎦ (27)
Ψ1n jω1 1 −j (ω 1 t− 4 π )
rical voltage drop at t = t0 , the PW voltage can be expressed Ve 3
3
LONG et al.: ASYMMETRICAL LOW-VOLTAGE RIDE THROUGH OF BRUSHLESS DOUBLY FED INDUCTION GENERATORS 505

phase to phase to ground short circuit (p-p-n): scaling factor can be much larger that of the forward sequence
⎡ ⎤ and its maximum value is 2.3 when the machine is running at
0
⎡ ⎤
V1u ⎢√ ⎥ the highest speed, i.e., 130% of the natural speed. The backward
⎢ 3 3 ⎥ sequence component of the grid fault voltage |V1n | is smaller
⎢ ⎥ ⎢ V sin(ω1 t + π) ⎥
⎣ V1v ⎦ = ⎢ 3 2 ⎥ (28) than the prefault rated voltage.
⎢√ ⎥
V1w ⎣ ⎦ (2) (2)
Transient zero sequence of EΨ 1 z : This sequence of EΨ 1 z
3 1
3
V sin(ω1 t + π)
2 rotates with an angular velocity of −(p1 + p2 )ωr with a scaling
⎡ 1 ⎤ factor of |1 − sn | which is also much larger than that of the
  V ej ω 1 t forward one with a maximum value of 1.3. According to (31), the
Ψ1p 1 ⎢ 3 ⎥
= ·⎣ ⎦. (29) magnitude of the zero sequence of the CW voltage is determined
Ψ1n jω1 1 −j ω 1 t by the time when the grid fault happens and decays with a time
Ve
3 L L −L 2
constant τ1 which can be expressed as 1 R r1 L r 1 r .
During the transient, the PW flux linkage must be continuous
from one state to the other state and a transient zero sequence
component is produced to link these two states at t = t0 although V. CONTROL WINDING OVERCURRENT ANALYSIS WHEN THE
the PW voltage has a step change when the fault happens [21], MACHINE-SIDE CONVERTER IS CONNECTED
[22]. This transient flux linkage is the zero sequence flux linkage
Ψ1z The aforementioned analysis assumes the CW current is zero.
In normal operation, however, the CW of the BDFIG is fed with
Ψ1p + Ψ1n + Ψ1z = Ψ1 . (30) a voltage source converter. During an asymmetrical fault, the
Substituting (22) and (23) into (30), in the PW stationary converter ideally should balance all three sequence components
reference frame, the zero sequence flux linkage is expressed as of the induced EMF in the CW to control the current. From
  the last section, it is shown that the backward and the zero se-
 (|V1 | − |V1p |)ej ω 1 t 0 − |V1n |e−j ω 1 t 0  −( t −t 0 )
Ψ1z =   e τ1 . quence component of the induced EMF, EΨ 1n and EΨ 1n , are
jω1  much greater than the converter voltage rating due to the scaling
(31) factors. Thus, the converter is not able to supply enough volt-
Since the CW current is assumed to be zero, the CW voltage age to balance the backward and zero sequence components of
is the induced EMF. From the view of the CW stationary refer- the induced EMF. Uncontrollable overcurrents occur simulta-
ence frame, combining (12), (19), (30), and (31), the voltage is neously and become an issue for LVRT [23]. In this section, the
expressed as steady-state analysis of the backward sequence current and the
(2)
V2
(2) (2)
= EΨ 1 p + EΨ 1 n + EΨ 1 z
(2)
(32) transient analysis of the zero sequence current are given.

where
(2) L1r L2r A. Backward Sequence Component of the CW Current
EΨ 1 p = sn |V1p |ej s n ω 1 t (33)
L21r− L1 Lr in the Steady State
L1r L2r Assuming the converter does not supply the backward se-
(2 − sn )|V1n |e−j (2−s n )ω 1 t
(2)
EΨ 1 n = (34) quence voltage, V2n = 0, from (19), the backward sequence
L21r − L1 Lr
EMF appears across the equivalent impedance, i.e., EΨ 1n =
L1r L2r −( t −t 0 )
−Vx2n . When the generator is initially running at 650 r/min, in
(1 − sn )ω1 |Ψ1z |e−j (1−s n )ω 1 t e τ 1 .
(2)
EΨ 1 z =
L21r− L1 Lr an asymmetrical fault, from (34), the scaling factor of the back-
(35) ward sequence EMF becomes 2.3 which is 7.7 times greater
than the prefault value. The converter is not able to compensate
From the converter side, the open-circuited voltages contains this voltage [10], [24].
all three sequence components during an asymmetrical fault, for Nevertheless, in the steady state, the backward sequence EMF
t ≥ t0 . will not introduce any overcurrent to the converter. Combining
(2)
Steady-state forward sequence of EΨ 1 p : This sequence of (18), (19), and (34), ignoring the CW resistance, R2 , the back-
(2)
EΨ 1 p rotates with an angular velocity of ω1 − (p1 + p2 )ωr , ward sequence of the CW current is expressed as
with a scaling factor of |sn |. It is aligned with the prefault EMF
but has a smaller magnitude because the forward sequence of 
(2) L1r L2r (2 − sn )|V1n | −j ((2−s n )ω 1 t+ 1 π )
the grid fault voltage, |V1p |, is smaller than the prefault rated I2n = e 2 .
L1r − L1 Lr
2 (2 − sn )ω1 Ll
voltage |V1 |. The BDFIG for a wind turbine is usually designed
(36)
with a ±30% speed range, so the slip is from −0.3 to 0.3 and
The equivalent impedance, shown in Fig. 2, is also increased
the maximum scaling factor for normal operation is 0.3.
(2) with the same scaling factor of the induced EMF shown as the
Steady-state backward sequence of EΨ 1 n : This sequence of appearance of the (2 − sn ) at the denominator in (36). Thus the
(2)
EΨ 1 n rotates with an angular velocity of −ω1 − (p1 + p2 )ωr enlargement of the EMF from the scaling factor is cancelled by
with a scaling factor of |2 − sn |. It should be noted that its the impedance.
506 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 28, NO. 3, SEPTEMBER 2013

TABLE I (19), and (35):

FORWARD, BACKWARD, AND ZERO SEQUECNES OF THE PW FLUX LINKAGE  t
(p.u) SUMMARY 1 −( ν −t 0 )
Λ|Ψ1z |e−j (1−s n )ω 1 ν e
(2)
I2 =− τ1
dν (38)
Ll t0

where Λ = L 2L 1−L
r L2r
1 Lr
(1 − sn )ω1 .
1r
As shown in (38), the magnitude of the current depends on
the equivalent inductance Ll which is mainly the leakage in-
ductance of the rotor. For the conventional DFIG, the equivalent
inductance can be also derived and it is mainly contributed by the
leakage inductance of the stator and the rotor of the DFIG [25],
[27]. However, the BDFIG, compared to the conventional DFIG,
For comparison, in normal operation, the forward sequence has a much larger rotor leakage inductance, arising from rotor
of the CW is also given as harmonic inductance inherent in the special rotor design [28].
Hence, the equivalent inductance is much lager than that found
  in the DFIG. Because of this larger equivalent inductance Ll ,
(2) |V2 | L1r L2r sn |V1p | 1
I2p = − ej (s n ω 1 t− 2 π ) . the current from the zero sequence component can be reduced
ω1 Ll L1r − L1 Lr
2 sn ω1 Ll
(37) to an acceptable value for the converter and the extra overcur-
From (36), it is seen that the CW backward current will not be rent protection equipment such as crowbars are not needed [29],
increased because the increased scaling factor appear at both the [30].
EMF and the impedance. Associating (23) and (36), the back-
ward current is only proportional to the PW backward flux link- VI. CONTROL SCHEME DEVELOPMENT
age, i.e., the backward grid voltage as |Ψ1 n| = |Vω11n | . Accord- A. Basic Control Loops in Normal Conditions
ing to (24), (26), and (28), the steady-state negative sequence
PW flux linkages in all three different asymmetrical faults are As has been discussed previously, only the forward sequence
less than half of the rated, thus the backward sequence current is component needs to be considered. Therefore,
predicted to have a smaller magnitude to the forward sequence Ψ+ + + +
1 = ψ1dp + jψ1q p = ψ1dp . (39)
current although the backward sequence current shows larger
frequencies than the forward one as shown in (36) and (37) . The PW real and reactive powers can be expressed as
Thus, the backward sequence current in the CW is not a major 3 + + 3 + +
p i1q p ] ≈ v1q p i1q p
+ +
issue for the BDFIG during asymmetric low-voltage faults. P1 = [v i + v1q (40)
2 1dp 1dp 2
3 3 + +
p i1dp ] ≈ v1q p i1dp .
+ + + +
Q1 = [−v1dp i1q p + v1q (41)
2 2
B. Zero Sequence Component of the CW Current
During the Transient Therefore, the real and reactive powers of the power winding
can be regulated by i+ +
1q p and i1dp , respectively. However, the
The flux linkage must be continuous between periods of the power winding current cannot be controlled directly as the grid
prefault and the asymmetrical faults, and the zero sequence flux voltage is fixed. From [31] and [32], mathematical analysis
is the transient component linking those two steady states. shows that i+ + + +
1q p and i1dp can be controlled by i2q p and i2dp with
From (24) to (28), in the steady state for p-p and p-p-n faults, a linear gain K1p and perturbation terms D1dp and D1q p arising
the backward sequence components have the same magnitude from cross coupling from the BDFIG:
as the forward sequence components so the the resultant flux
linkages during the faults are pulses. In the steady-state p-n fault, i+ +
1dp = K1p i2dp + D1dp (42)
the backward sequence component is smaller than the forward
i+ +
1q p = K1p i2q p + D1q p . (43)
one and the resultant flux trajectory is an ellipse. The flux linkage
magnitude of the zero sequence depends on the timing of an Mathematical expressions for K1p , D1dp , and D1q p can be found
asymmetrical fault and the type of the fault. According to (24)– in [31].
(31), the zero sequence of the flux linkage in different faults is Similarly, the relationship between I+ +
2 and V2 in the two-axis
summarized in Table. I. The experimental result, illustrated in (dq) form can be written as
Fig. 3, has shown the PW flux linkage trajectory from prefault
to the asymmetrical fault in three types of faults. All faults i+ +
2dp = K2p v2dp + D2dp (44)
occurred at the the point where the largest zero sequence of PW i+ +
2q p = K2p v2q p + D2q p . (45)
fluxes were generated.
From (35), the zero sequence of the PW flux linkage results Expressions for K2p , D2dp , and D2q p can also be found in [31].
a large EMF on the CW, which decays exponentially, and the Considering (42), (43), (44), and (45), a cascaded control
converter is not able to compensate the zero sequence EMF [25], loop can be designed. The outer loop is called the power loop,
[26]. Similar to the analysis of the negative sequence current, in which i+∗ +∗
2dp and i2q p are generated by two PI controllers from
+∗
the zero sequence of the CW current is given by combining (18), active and reactive power errors. The inner loop generates v2dp
LONG et al.: ASYMMETRICAL LOW-VOLTAGE RIDE THROUGH OF BRUSHLESS DOUBLY FED INDUCTION GENERATORS 507

(a) (b) (c)

Fig. 3. PW flux-linkage trajectory experimental results in different faults. The prefault condition is full load, 625 r/min and unity power factor. (a) PW flux-linkage
trajectory for p-p fault. (b) PW flux-linkage trajectory for p-n fault. (c) PW flux-linkage trajectory for p-p-n fault.

+∗
and v2q p , and is called the current loop. Note that, compared to
the outer loop, the current control loop generally requires much
faster dynamics.

B. Control System During Asymmetrical Dips

During asymmetrical dips, (40) and (41) will not be valid due
to the appearance of backward and zero sequence components.
In contrast to the controller proposed by [11], this paper proposes
a simple and robust control strategy which is to control I+ 2p to
+
zero in the positive frame. In other words, V2p is supplied to
balance E+ Ψ1p . Fig. 4. Derivative equivalent circuit model for asymmetrical LVRT.
The effect of the backward sequence CW current I2n − is not
considered. The backward sequence of PW flux linkages, which In normal grid conditions, both the power loop and current
are proportional to backward sequence CW currents, are less loop will operate. During an asymmetrical fault, however, the
than or equal to half of the prefault rated value (see Table. I); power loop will be switched out and the forward sequence of
thus, the backward current is not the major issue of protecting the CW current reference is set to be zero. Only the backward
the converter from the catastrophic overcurrent. sequence component will appear in the converter current with
Due to the large equivalent inductance Ll the CW zero se- the decay of the zero sequence component.
quence current can be reduced to an acceptable value. As the
zero sequence current of asymmetrical low faults is smaller than
C. Flux Estimation and Phase Locked Loop (PLL)
that found in the symmetrical low voltage fault [29], [30], so
the asymmetrical LVRT without a crowbar is considered to be The purpose of the PLL is to synchronize the forward se-
viable. quence to the positive PW reference frame. For the PW flux
Therefore, the control chain for asymmetrical LVRTs is pre- linkage, this can be expressed as
sented as 
Ψ+1dq = +
(V1dq − R 1 I+
1dq )dt
2dp ⇒ v2dp
0 ⇒ i+ +

−
+
= [ψdp + ψdn cos(2ω1 t) + ψq−n sin(2ω1 t)]
0 ⇒ i+
2q p ⇒ v2q p
+

−
− + j[ψq+p − ψdn sin(2ω1 t) + ψq−n cos(2ω1 t)]. (46)
0 ⇒ v2dn
− The flux linkage estimated by (46) contains a dc component
0 ⇒ v2q n
from the forward sequence and a 100 Hz component from the
and the derivative equivalent model with the control strategy backward sequence. Without loss of generality, there may be
for asymmetrical LVRTs is illustrated in Fig. 4. The complete a transient 50 Hz component from the zero sequence in the
control scheme is shown in Fig. 6. The PW voltages and currents positive reference frame [10].
are used to estimate the angle of the forward sequence of the A PLL containing two band-stop filters is used, shown in
PW flux linkage through the phase locked loop (PLL) that will Fig. 5, to trap components at 50 Hz for the zero sequence and
be discussed later. 100 Hz for the backward sequence [33], so that only Ψ+ p =
508 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 28, NO. 3, SEPTEMBER 2013

Fig. 5. PLL block diagram.

Fig. 6. Schematic of the control system.

+ TABLE II
ψdp + jψq+p remains in (46). The forward sequence is locked to
PROTOTYPE MACHINE SPECIFICATIONS
the positive reference frame when ψq+p = 0, implemented by a
PI controller.

D. Fault Detector
A fault detector is designed to sense an asymmetrical fault.
The index used is the magnitude of the backward sequence
component of the PW voltage

− − −
|V1n |= (v1nd )2 + (v1nq )2 . (47)

−
−
Ideally, |V1n | should be zero if there is no unbalance. It is im- switched back to the normal operation mode when |V1n | is less
portant to distinguish between the asymmetric low voltage fault than 10% of the nominal grid voltage.
and the steady-state small voltage unbalance which is common
for wind generators connecting to a weak power system. In the VII. EXPERIMENTAL RESULTS
latter case, the wind generator is required to operate normally. A
special control scheme for operating the BDFIG under a steady- A. Experimental Setup
state small voltage unbalance was investigated in [34]. In this An experimental setup was used to evaluate the performance
paper, the low voltage detector is designed to avoid switching of the proposed control scheme using a 250-kW BDFIG, be-
the control loop into the asymmetric LVRT mode when a small lieved to be the largest built to date, the specifications of which
steady-state voltage unbalance is present, as occurs in normal are given in Table II.
grid operation. The thresholds for the low voltage fault and its This paper focuses on the control algorithm of the machine-
−
clearance is hysteresis-comparator based. When |V1n | exceeds side converter, assuming that the grid- side converter stabilizes
20% of the nominal grid voltage, the control loop is switched the dc-link voltage well enough during asymmetric grid fault
to the asymmetric LVRT mode and the control loop will be condition [35]. A commercial inverter supplied from control
LONG et al.: ASYMMETRICAL LOW-VOLTAGE RIDE THROUGH OF BRUSHLESS DOUBLY FED INDUCTION GENERATORS 509

(a) (b)

Fig. 7. Schematic and photo of the LVRT test rig. (a) Schematic of the LVRT test rig.(b) Photo of the test rig.

(a) (b) (c)

Fig. 8. Experimental results of asymmetrical LVRT in different faults. The pre-fault condition is full load, 625 r/min and unity power factor. (a) Phase to phase
LVRT. (b) One phase to ground LVRT. (c) Phase-phase to ground LVRT.
510 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 28, NO. 3, SEPTEMBER 2013

techniques (Unidrive SP6601) embedded with a dc-link damper 1/2, 1/3, and 1/3 of the rated forward CW current (the prefault
is able to stabilize the dc-link voltage for the experiment reported current). Because the zero sequence CW current decays expo-
in this paper. The coordinated control scheme combining both nentially with a small time constant, the fault current is mainly
the grid- and machine- side converters is beyond the scope of from the backward sequence CW current except the beginning
this paper and will be investigated in the future. of the fault so the fault current during the most of the period
In the test, the grid-side converter was always connected to of an asymmetrical low voltage fault is smaller than the normal
the grid bypassing the grid fault hardware. prefault current. This behavior is verified by the experimental
The prototype BDFIG was coupled to an induction machine results shown in Fig. 8.
equipped with a commercial ac drive (ABB ACS800). The drive
was set to operate at constant speed and the BDFIG was in a
power control mode. An incremental encoder with 10 000 pulses VIII. CONCLUSION
per revolution was used to measure the shaft rotational speed.
This paper has thoroughly analyzed the behavior of the BD-
The voltages and currents of each stator phase were measured
FIG under asymmetrical low voltage faults in cases of the phase
by LEM LV 25-p and LEM LTA 100-p transducers, respectively.
to phase, phase to ground, and phase to phase to ground short
The line currents of the power winding were also obtained.
circuits. Analysis shows that the major issue for an asymmet-
The control algorithm was implemented in MATLAB
rical low voltage fault is from the zero sequence of the CW
Simulink in an xPC Target computer which receives all the
current but not the backward sequence current. The severity of
measurements and generates PWM signals for the machine-side
these three types of asymmetrical faults has been compared.
converter. The sampling time of the control loop was 0.5 ms.
This paper has also introduced a practical control scheme for
The test rig schematic and photograph are shown in Fig. 7.
the BDFIG to ride through asymmetrical LVRT. Experimental
results have shown that the BDFIG with the proposed controller
B. Experimental Results has potential to ride through asymmetrical low voltage faults
without extra hardware such as crowbars. The BDFIG-based
As has been mentioned, the main concern during LVRT is
wind turbine with the proposed control scheme is able to show
the converter current. It is widely accepted that the IGBTs in
high stability and a low cost of grid integration.
a converter can withstand a 2 p.u. peak current for 1 ms, and
therefore 2 p.u. current has become a benchmark [11].
The first experiment was a p-p circuit test, as shown in
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for DFIG of grid connected wind turbines,” IEEE Trans. Ind. Electron., Teng Long (S’10–M’13) received the B.Eng degree
vol. 58, no. 99, pp. 1–1, 2010. from Huazhong University of Science and Technol-
[15] C. Wessels, F. Gebhardt, and F. Fuchs, “Fault ride-through of a DFIG ogy, Wuhan, China, and the B.Eng (first class Hons.)
wind turbine using a dynamic voltage restorer during symmetrical and degree from the University of Birmingham, Birming-
asymmetrical grid faults,” IEEE Trans. Energy Convers., vol. 26, no. 99, ham, U.K, in 2009. He was an exchange student in
pp. 1–1, Mar. 2011. Hong Kong Polytechnic University, Hong Kong, in
[16] L. Meegahapola, T. Littler, and D. Flynn, “Decoupled-DFIG fault ride- 2008. He received the Ph.D degree in electrical en-
through strategy for enhanced stability performance during grid faults,” gineering from the University of Cambridge, Cam-
IEEE Trans. Sustainable Energy, vol. 1, no. 3, pp. 152–162, Oct. bridge, U.K, in 2013.
2010. He is currently with the GE Power Conversion,
[17] P. Flannery and G. Venkataramanan, “A fault tolerant doubly fed induction U.K., as a Power Electronics Engineer in the Global
generator wind turbine using a parallel grid side rectifier and series grid Technology and Engineering team. His research interests include power elec-
side converter,” IEEE Trans. Power Electron., vol. 23, no. 3, pp. 1126– tronics, electric machines, drive and control, energy efficiency, and renewable
1135, May 2008. energy.
[18] J. Poza, E. Oyarbide, D. Roye, and M. Rodriguez, “Unified reference
frame DQ model of the brushless doubly fed machine,” Electr. Power
Appl. IEE Proc., vol. 153, no. 5, pp. 726–734, Sep. 2006. Shiyi Shao (M’10) received the B.Eng. and M.Phil
[19] K. Lee, T. Jahns, and T. Lipo, “New control method including state ob- degrees from Shanghai Jiao Tong University, Shang-
server of voltage unbalance for grid voltage-source converters,” IEEE hai, China, in 2003 and 2006, respectively, and the
Trans. Ind. Electron., vol. 57, no. 6, pp. 2054–2065, Jun. 2010. M.Phil and Ph.D. degrees in electrical engineering
[20] H. de Souza, F. Bradaschia, F. A. S. Neves, M. C. Cavalcanti, from the University of Cambridge, Cambridge, U.K,
G. M. S. Azevedo, and J. O. de Arruda, “A method for extracting the in 2008 and 2010 respectively.
fundamental-frequency positive-sequence voltage vector based on simple He was the Chief Engineer of the Wind Tech-
mathematical transformations,” IEEE Trans. Ind. Electron., vol. 56, no. 5, nologies, Cambridge, U.K. He is currently with CSE
pp. 1539–1547, May 2009. Electric Technology Ltd., China Ship Industry Co-
[21] J. Morren and S. DeHaan, “Ridethrough of wind turbines with doubly-fed operation, Beijing, China, as a Chief Engineer. His
induction generator during a voltage dip,” IEEE Trans. Energ. Convers., research interests include power electronics, electric
vol. 20, no. 2, pp. 435–441, Jun. 2005. machine, electric system design, drive and control, energy efficiency, and re-
[22] G. Pannell, D. Atkinson, and B. Zahawi, “Minimum-threshold crowbar newable energy.
for a fault-ride-through grid-code-compliant DFIG wind turbine,” IEEE
Trans. Energy Convers., vol. 25, no. 3, pp. 750–759, Sep. 2010.
[23] F. Lima, A. Luna, P. Rodriguez, E. Watanabe, and F. Blaabjerg, “Ro- Ehsan Abdi (M’13) received the B.Sc. degree in elec-
tor voltage dynamics in the doubly fed induction generator during grid trical engineering from the Sharif University of Tech-
faults,” IEEE Trans. Power Electron., vol. 25, no. 1, pp. 118–130, Jan. nology, Tehran, Iran, in 2002, and the M.Phil. and
2010. Ph.D. degrees in electrical engineering from Cam-
[24] J. Morren and S. W. H. de Haan, “Short-circuit current of wind turbines bridge University, Cambridge, U.K., in 2003 and
with doubly fed induction generator,” IEEE Trans. Energy Convers., 2006, respectively.
vol. 22, no. 1, pp. 174–180, Mar. 2007. He is currently with Wind Technologies, Cam-
[25] G. Pannell, D. Atkinson, and B. Zahawi, “Analytical study of grid-fault bridge, aiming at exploiting the Brushless Doubly
response of wind turbine doubly fed induction generator,” IEEE Trans. Fed Machine for commercial applications. He is also
Energy Convers., vol. 25, no. 4, pp. 1081–1091, Dec. 2010. an Embedded Researcher at Electrical Engineering
[26] J. López, E. Gubia, E. Olea, J. Ruiz, and L. Marroyo, “Ride through Division, Cambridge University, and his main re-
of wind turbines with doubly fed induction generator under symmetrical search interests include electrical machines and drives, wind power generation,
voltage dips,” IEEE Trans. Ind. Electron., vol. 56, no. 10, pp. 4246–4254, and electrical measurements and instrumentation.
Oct. 2009.
[27] J. Lopez, P. Sanchis, X. Roboam, and L. Marroyo, “Dynamic behav-
ior of the doubly fed induction generator during three-phase voltage
dips,” IEEE Trans. Energy Convers., vol. 22, no. 3, pp. 709–717, Sep.
2007. Richard A. McMahon received the B.A. degree in
[28] X. Wang, R. McMahon, and P. Tavner, “Design of the brushless doubly- electrical sciences and the Ph.D. degree from the Uni-
fed (induction) machine,” in Proc. IEEE Int. Electr. Mach. Drives Conf., versity of Cambridge, Cambridge, U.K., in 1976 and
May 2007, vol. 2, pp. 1508–1513. 1980, respectively.
[29] T. Long, S. Shao, P. Malliband, E. Abdi, and R. McMahon, “Crowbarless He has been with the Department of Engineering,
fault ride through of the brushless doubly fed induction generator in a University of Cambridge, where he was a University
wind turbine under symmetrical voltage dips,” IEEE Trans. Ind. Electron., Lecturer in electrical engineering in 1989, follow-
vol. 60, no. 7, pp. 2833–2841, Jul. 2013. ing his Postdoctoral work on semiconductor device
[30] T. Long, S. Shao, E. Abdi, P. Malliband, M. E. Mathekga, R. A. Mcmahon, processing, and became a Senior Lecturer in 2000.
and P. J. Tavner, “Symmetrical low voltage ride-through of a 250 kw His research interests include electrical drives, power
brushless dfig under a symmetrical full voltage dip,” in Proc. 6th IET Int. electronics, and semiconductor materials.
Conf. Power Electron. Mach. Drives,, Mar. 2012, pp. 1–6.
[31] S. Shao, E. Abdi, F. Barati, and R. McMahon, “Stator-flux-oriented vector
control for brushless doubly fed induction generator,” IEEE Trans. Ind.
Electron., vol. 56, no. 10, pp. 4220–4228, Oct. 2009. Shi Liu received the B.Eng and M.Sc degrees from
[32] K. Protsenko and D. Xu, “Modeling and control of brushless doubly-fed Chongqing University, Chongqing, China, and the
induction generators in wind energy applications,” IEEE Trans. Power Ph.D degree from the University of Cambridge, Cam-
Electron., vol. 23, no. 3, pp. 1191–1197, May 2008. bridge, U.K.
[33] L. Xu and Y. Wang, “Dynamic modeling and control of DFIG-based He was the Research Professor with the Chi-
wind turbines under unbalanced network vonditions,” IEEE Trans. Power nese Academy of Sciences in 1998, and has been
Electron., vol. 22, no. 1, pp. 314–323, Feb. 2007. with North China Electric Power University, Beijing,
[34] S. Shao, T. Long, E. Abdi, and R. McMahon, “Dynamic control of China, since 2007. His research interests include sys-
the brushless doubly fed induction generator under unbalanced opera- tem integration of renewable energy and forecast of
tion,” IEEE Trans. Ind. Electron., vol. 60, no. 6, pp. 2465–2476, Jun. renewable energy power generation.
2013.