This paper proposes a reactive current assignment and control strategy for a doublyfed induction generator (DFIG) based windturbine generation system under generic grid voltage sag or swell conditions. The system’s active and reactive power constrains during grid faults are investigated with both the grid and rotorside convertors (GSC and RSC) maximum ampere limits considered. To meet the latest grid codes, especially the low and highvoltage ridethrough (LVRT and HVRT) requirements, an adaptive reactive current control scheme is investigated. In addition, a torqueoscillation suppression technique is designed to reduce the mechanism stress on turbine systems caused by intensive voltage variations. Simulation and experiment studies demonstrate the feasibility and effectiveness of the proposed control scheme to enhance the fault ridethrough (FRT) capability of DFIGbased wind turbines during violent changes in grid voltage.
I. INTRODUCTION
Doubly fed induction generators (DFIGs) have been recognized as the most promising technology in wind energy conversion systems
[1]
,
[2]
. When compared to other types of wind turbines (WTs), the DFIGbased turbines have some attractive advantages, such as small convertor capacity, relatively wide operation speed region, competitive durability and so on. However, DFIGs have also been found to be more vulnerable to grid disturbances, especially voltage sag and swell events. Since the number and capacity of WTs integrated into the electric networks is increasing, their dynamic behavior has become critical to the stability of power systems. As a result, modern grid codes have to stringently specify some voltage profiles, above which WTs must remain connected to the grid. This is commonly referred to as the low voltage ridethrough (LVRT) requirement. In fact, the updated grid codes in Germany, Australia, UK, etc., even require WTs to withstand severe voltage swell conditions, which is usually referred to as the high voltage ridethrough (HVRT) regulation
[3]
. Technically, LVRT and HVRT can be generally referred to as fault ridethrough (FRT).
In terms of voltage sag scenarios, reported as the most common grid disturbance in industrial power systems, there have been many studies focusing on the electromagnetic transient process
[4]

[7]
and LVRT enhancement technologies
[8]

[17]
for DFIGbased WTs. The most commonly accepted technical solution applied in engineering can be summarized as follows: 1) for a mild voltage dip, only modified control strategies for gridside and rotorside converters (GSC and RSC) are applied, such as the flux demagnetizing approach
[10]
; 2) for a depth voltage drop, additional hardware devices, such as resistances connected in parallel with the RSC (the so called crowbar
[11]
,
[12]
) or with the dclink capacitor (the so called chopper
[13]
). On the one hand, they are equipped to suppress the inrush currents through the converters; on the other hand, the DFIG systems should be controlled to inject reactive current into the grid as soon as possible
[3]
. There are other solutions to protect convertors from destructive overcurrents, which enhances the uninterrupted operation ability of turbines. For example, static synchronous compensators (STATCOMs)
[15]
, static var compensators (SVCs)
[16]
and dynamic voltage restorers (DVRs)
[17]
, which have already been shown to be ideal auxiliary equipment to increase the FRT capability of a WT during grid voltage sag conditions.
However, in the case of voltage swells, the matters concerning the HVRT of DFIGbased WTs have not been so adequately explored in the literature. Voltage swell is a common grid anomaly and it usually emerges when the reactive power exceeds the needs in a power system. It was reported that 598 WTGs disconnected from the grid in Gansu Province, China, on February 24, 2011. Among these disconnections, 46% were caused by voltage sags and 54% were caused by voltage swells due to installed reactive compensators being unable to cutoff in time
[18]
. Consequently, in addition to LVRT, the HVRT behavior and its related technology for DFIGbased WTs need to be carefully considered and investigated. The transient process of DFIGbased WTs during voltage swells has been studied in
[19]

[23]
. A resonant controller, as a supplementary part of a traditional PI regulator, is introduced in
[19]
to improve the dynamic performance of current controller during voltage swell conditions. In
[20]
and
[21]
, the application of hysteretic controllers are said to be more effective in improving the dynamic response of the system. Similarly, STATCOMs and DVRs have also been suggested as alternatives for the HVRT operation of WTs by compensating the line voltage back to its normal level
[22]
,
[23]
. Obviously, this will significantly increase the hardware costs. In addition, the active and reactive power constraints during voltage swells have not been fully studied in the aforementioned studies. As a result, such proposed strategies are obviously unable to meet the strict grid code regulations.
For this reason, this paper proposes a reactive current assignment and comprehensive control approach for DFIGbased WT systems under grid voltage sag and swell conditions. The active and reactive power constrains of a system during grid faults are investigated while considering the maximum ampere limits of both the GSC and the RSC. To enhance its LVRT and HVRT capability, an adaptive reactive current control strategy is suggested with only traditional crowbar and dcbus chopper protectiondevices applied. In order to reduce the mechanism stress on the turbine shaft system caused by torque oscillations during grid voltage abnormalities, a torqueoscillation suppression technique is introduced. This paper is organized as follows. In Section II, the capability of the reactive current support for a DFIG system is analyzed. Section III then proposes a control scheme for both the GSC and RSC to meet grid codes during voltage sag or swell events. Simulation studies and experimental validations are presented in Sections IV and V, respectively. Finally, Section VI summarizes some valuable conclusions.
II. REACTIVE CURRENT LIMIT OF A DFIG SYSTEM
In order to put forward a control scheme capable of meeting the latest grid codes, it is necessary to evaluate the reactive power support capability for a DFIG system during grid voltage dip and swell conditions. As is well known, the active and reactive powers can be output from both the statorand gridsides of the DFIG system. In principle, the statorside power of a DIFG is controlled by the RSC while the gridside power is determined by the GSC. This means that the reactive power limitation of a DFIGbased WT is dominated by the capacity of the two converters.
The structure of a DFIG system with its power distribution (by motor convention) is shown in
Fig. 1
. From this the following power equations can be formulated:
where
P_{t}
,
P_{s}
and
P_{g}
represent the active powers of the overall system, the statorside and the gridside, respectively, with
Q_{t}
,
Q_{s}
and
Q_{g}
being their corresponding reactive powers.
The structure of a DFIGbased wind turbine.
Furthermore, if the copper and core losses of the DFIG windings are ignored, the stator and gridside active powers can be expressed in terms of the total active power and the slip ratio, i.e.:
where
s
= (
ω_{s}

ω_{r}
) /
ω_{s}
is the slip ratio.
Based on the above power equations, the reactive current limitations for the GSC and RSC can be deduced. The voltage swell case will be paid more attention since the sag case has been discussed more often in the literature
[8]

[17]
.
 A. Current Limit of the GSC
The stability of the dcbus voltage is the premise of the uninterruptible operation for DFIG systems during grid voltage disturbances. Thus, the reactive and active current constrains of the GSC will be studied in this section.
The steadystate voltage equation of the GSC in the synchronously rotating coordinate can be expressed as:
where
U_{gd}
and
U_{gq}
are the d and qaxis grid voltages.
I_{gd}
and
I_{gq}
are the d and qaxis grid currents.
L_{g}
and
R_{g}
are the input inductance and resistance of the GSC, respectively.
Meanwhile, the dcbus voltage should obey the following power balance relationship, i.e.:
According to Eq. (3), the steadystate voltage space vector diagram of the GSC can be depicted as in
Fig. 2
, with
φ
being the power factor angle. From
Fig. 2
, it can be concluded that the terminal of the output voltage vector
V_{g}
should always fall on the hypotenuse of the impedance triangle with its magnitude restricted by the rated operational voltage across the dcbus capacitor. This is actually based on the voltage space vector modulation theory, which states that without overmodulation the modulation ratio m needs to meet the following equation:
The spatial relationship of GSC steady voltage vectors.
If grid voltage orientation (SVO) is adopted,
U_{gd}
=
U_{g}
and
U_{gq}
=0, where
U_{g}
is the magnitude of the grid phase voltage vector and is equal to
U_{s}
according to
Fig. 1
. Meanwhile, if the small voltage drop across
R_{g}
is ignored, Eq. (3) can be further simplified as:
Substituting (6) into (5), it can be derived that:
Equation (7) gives the operation constrains of the GSC with the dcbus voltage, grid voltage, inductor and load currents being the main parameters. It can be found that the minimum value of the dcbus voltage should be no less than the grid line voltage, i.e.,
when the GSC is operated in unity power factor (UPF) mode, i.e.,
I_{gq}
=0. Actually, this is caused by the natural attribute of the GSC boost circuit. Based on the above discussion, the GSC reactive current limit can then be analyzed and acquired for voltage sags and swells.
1) Voltage Sag:
For convenient analysis, a 3MW DFIG system is taken as an example with the parameters shown in
TABLE I
of the Appendix. The rated line voltage of the DFIG is 690V, while the normal dcbus voltage is set to 1050V. When a voltage sag fault occurs,
U_{g}
will be brought down. Thus, Eq. (7) is easy to satisfy if the currents flowing through the GSC are not beyond the maximum ampere limit. In this case, the maximum reactive current output from the gridside can be calculated as:
where
I
_{gmax}
is the maximum ampere limit of the GSC and equal to 0.45p.u. in the example.
According to Eq. (8), it is obvious that the reactive power supporting capability of the GSC is determined by both the overall active power of the system and the slip ratio for a given maximum ampere limit.
Fig. 3
shows the curves of the reactive current vs. the total active power and grid voltage for a given maximum generator speed, i.e.,
s
= –0.3p.u. From this, it can be observed that the maximum reactive current is around 0.45p.u. when the total active power is set to zero.
The curves of GSC reactive current vs. the total active power and grid voltage.
2) Voltage Swell:
It is worth pointing out that although the reactive current injection is helpful for the voltage recovery of a faulty power system, it is not the premise to satisfy the operation principle of the boost circuit for the GSC during voltage sags. In other words, the GSC reactive current can be set to zero under this circumstance if the reactive current required by the grid codes can be adequately provided through the statorside of a DFIG system. However, this assignment is no longer valid for the voltage swell case. For example, if the GSC continues to operate in the UPF mode, the dcbus voltage has to be increased to more than 1296V when the PCC voltage swells to 1.3p.u., which goes far beyond the rated operational voltage of dcbus capacitor, i.e., 1050V. Thankfully, the GSC reactive current usually possesses an inductive property, which is useful for reducing the required dcbus voltage.
According to Eq. (7), the required minimum reactive current during a voltage sag can be calculated as:
which clearly indicates that the minimum reactive current depends on both the grid voltage (
U_{g}
) and the active current (
I_{gd}
) of the GSC, as illustrated in
Fig. 4
.
The curves of the GSC reactive current vs. its active one and grid voltage.
Meanwhile, it can be found from
Fig. 4
that the minimum reactive current is mainly determined by the grid voltage. It is scarcely influenced by the active power. Hence, Eq. (9) can be further simplified as:
Eq. (10) presents the minimum reactive current constrained by the natural attribute of the boost circuit.
Once the minimum reactive current is obtained, the active current of the GSC can be restricted by:
As a result, the output minimum reactive power and the maximum active power can be integrated as:
where:
 B. Current Limit of the RSC
The stator active and reactive powers of the DFIG can be expressed as
[19]
:
From Eq.(14), the magnitude of the rotor current can then be calculated as:
Consequently, by substituting (2) into (15), the statorside reactive current
I_{sq}
can be obtained as:
Likewise, from Eq. (16) it can be found that once the maximum rotor current is determined, the output stator reactive current mainly depends on the total active power, the slip radio and the terminal voltage.
Fig. 5
thus graphically shows the relationship of the stator reactive current vs. the total active power and grid voltage during a voltage sag at the maximum generator speed, i.e.,
s
= –0.3p.u., with the maximum rotor current being 1.5p.u. (referred to the stator). By this curve, the maximum stator reactive current for a given stator voltage can be easily determined. For example, the calculated
I_{sq}
could reach up to 1.396p.u. (capacitive) for a grid voltage dip down to 26% of the rated value, with the total active power being equal to zero. Meanwhile, the maximum stator reactive current during voltage swell conditions can be obtained similarly from Eq. (16), but with the opposite polarity.
The curves of stator reactive current vs. the total active power and grid voltage.
III. PROPOSED CONTROL SCHEME
 A. Current Assignment
In the previous section, the maximum reactive currents of both the grid and statorsides of a DFIG system under voltage sag and swell conditions have been discussed in detail. In order to meet the grid codes, the reactive current references of the GSC and RSC will be preferentially assigned in this section. Moreover, the active current references of the two convertors will also be designed properly so as to maintain system stability. For the sake of convenience, the reactive power support requirement enforced by the German Grid Code is selected here as the standard to be discussed.
1) Voltage Sag:
According to the German Grid Code, WTs are required to provide capacitive reactive current as:
where
I_{Q}
is defined as the required reactive current, and
I_{N}
is the rated current of the system, which is assumed to be 1.3p.u. in this paper.
Assume the maximum continuous currents of the GSC and RSC, i.e.,
I
_{gmax}
and
I
_{rmax}
to be 0.45p.u. (the rated value is defined as 0.3p.u.) and 1.5p.u. (the stator and the rated value are defined as 1p.u.), respectively. Thus, according to Eq. (16), the maximum stator reactive power can then be calculated approximately as:
Obviously, the reactive current required by the grid code can be adequately provided by the statorside of the DFIG. Then the reactive current reference of the RSC can be set as:
It is worth noting that if the reactive current of the RSC is not beyond its limit, the active power should be controlled to restrain the generator speed upsurge. Accordingly, the RSC active current can be assigned as:
Since the reactive current on this condition is entirely provided by the RSC, the GSC can be consequently controlled in the UPF state, i.e.,
I^{*}_{gq}
= 0 , with
I^{*}_{gd}
being the PI output of its voltage loop.
2) Voltage swell [25]:
Similarly, during grid voltage swell conditions, WTs are required to inject current into the power system with the same intensity as for the voltage sag case, but of inductive property. As a result, the total required reactive current can be expressed as:
Considering that the GSC has to inject a certain inductive current to ensure the safe operation of the capacitor, the reactive current required can be preferentially provided by the GSC.
Fig. 6
illustrates the currentvoltage curves obtained from Eqs. (10) and (21), from which it can be seen that the magnitude of the reactive current required by the inherent operation principle of the boost circuit is smaller than that required by the grid code. Hence, the partial required reactive current, marked by the slashed area in
Fig. 6
, should be supplemented by the statorside of the DFIG.
Currentvoltage curves obtained from Eqs. (10) and (21).
As a result, the GSC output reactive current can be assigned as:
with its maximum active current limited by:
As far as the RSC is concerned, the output stator reactive current can be determined as:
Consequently, the RSC reactive current should be computed as follows:
According to
Fig. 1
, if the copper loss of the generator windings is ignored, the relationship between the grid and statorside powers of the DFIG system can be simplified as:
where
P_{r}
is the output active power of the RSC.
Due to the fact that the current capacity of the RSC is usually designed a littler larger than that of the GSC, the output active power of the RSC during the voltage swell cases should be set so that it is not more than that of the GSC. Thus, according to Eqs. (14) and (26), the maximum active current of the RSC can be constrained as:
Meanwhile, if the current limit of the RSC is considered, the maximum active current reference of the RSC can be further limited by:
 B. Current Controller Design
Once the reactive and active current references are acquired as requested by the grid regulations, a precise current controller must be properly designed to regulate them accurately and rapidly. Since it is capable of gaining zero steadystate error for the dc components, the traditional PI controller is usually applied in the vector control of distributed power generation systems. However, due to its limited bandwidth, the PI controller is not able to achieve a very effective response to the ac components, which usually occur during voltage sag or swell scenarios
[11]
,
[23]
. It is wellknown that without a proper control design, the ac components in the currents will lead to destructive oscillations in the electromagnetic torque for DFIGbased WTs
[24]
. As a result, they should be inhibited to the greatest extent possible. Thus, a torqueoscillation suppression approach needs to be investigated, which can be commenced from setting the auxiliary current references.
In the synchronously rotating reference frame, the stator flux vector of the DFIG can be expressed as:
Consequently, there is:
Meanwhile, the stator voltage vector can be calculated by the stator flux vector as:
where the subscripts “+” and “0” represent the respective positive and dcsequence components.
In this manner, the electromagnetic power can be calculated as:
where:
As a result, the auxiliary dc current references of
I^{*}
_{rd0}
and
I^{*}
_{rq0}
can be acquired by setting
P
_{ecos}
= 0 and
P
_{esin}
= 0 in Eq. (30):
To simultaneously regulate both the dc and ac components, a compound of a PI regulator plus a resonant controller (PIR) is introduced here with its transfer function being:
where
K_{p}
,
K_{i}
and
K_{r}
are the proportional, integral and resonant parameters, respectively, and with
ω_{c}
being the cutoff frequency, introduced into the resonant part of the controller to reduce its sensitivity to slight frequency variations at the resonant pole
[26]
. It is worth noting that the proposed PIR controller is insensitive to parameter variations, which has been demonstrated in
[27]
,
[28]
. Since the resonant controller is tuned at the synchronous frequency, the PIR can nullify the errors of the dc components as well as the ac components at the frequency of
ω_{s}
.
 C. Control Logic
Once the reactive current control strategy for DFIG based windturbine systems under generic grid voltage sag and swell conditions is founded, the concrete control logic to implement the proposed scheme seems to be predominant, and a schematic diagram of it is shown in
Fig. 7
. It is clear that the control scheme is designed with three operation modes: 1) mode I: maximum power point tracing (MPPT) mode
[29]
, where the active and reactive current references of the GSC and RSC are assigned so that the system operates approximately in UPF; 2) mode II: LVRT operation; and 3) mode III: HVRT operation, where the fundamental active and reactive current references of the two convertors are given respectively as in part A of section III, with their auxiliary current references set as in part B of the same section. Furthermore, the reactive and active current references are momentarily changed to proper values with their corresponding modes according to the grid voltage
U_{s}
. Additionally, a group of protective devices, consisting of a traditional crowbar and a dcbus chopper, are also equipped to suppress the inrush rotor currents if necessary (judged by
I_{rabc}
and
V_{dc}
).
The schematic diagram of the proposed control scheme.
IV. SIMULATION STUDIES
To validate the feasibility and effectiveness of the proposed control strategies, simulation studies were conducted with Matlab/Simulink. The simulated DFIG is rated at 3MW. Its parameters are listed in
TABLE I
and the system schematic diagram is shown in
Fig. 1
. The switching frequencies for both the RSC and GSC are 3kHz with the sampling frequencies set as 10kHz. Considering that the mechanical time constant is much larger than the electromagnetic one, the rotor speed is conditionally assumed to be fixed at 1.2p.u. in the simulation. In addition, a programmable ac source module was employed to emulate an irregular grid.
Fig. 8
shows the simulated results for both the voltage sag and swell cases, with the three different control modes adopted and compared.
THE REQUIRED AND OUTPUTTED REACTIVE CURRENTS WITH DIFFERENT CONTROL MODES
THE REQUIRED AND OUTPUTTED REACTIVE CURRENTS WITH DIFFERENT CONTROL MODES
Simulated results of the DFIG system with different operation modes under voltage sag and swell transients.
As can be seen in
Fig. 8
, under Mode I, where the grid voltage is 1p.u. (
Fig. 8
(a)), the total active and reactive powers of the system are 1.15p.u. and 0.08p.u. (capacitive), respectively (
Fig. 8
(b)). This means that the system was operated approximately at unity power factor. However, when a voltage dip fault is detected, the system’s control mode switches immediately to Mode II. According to the grid code, the DFIG system needs to output 1.3p.u. of capacitive reactive current into the power network. This can be entirely provided by the DFIG statorside, as shown as
I_{sq}
in
Fig. 8
(e). Consequently, the DFIG active current
I_{sd}
should set to be zero due to the limited current capacity of the RSC, while the GSC is operated nearly in the UPF state, as displayed in
Fig. 8
(f). Meanwhile, the crowbar and chopper (indicated in
Figs. 8
(g) and
8
(h), with “1” denoting “activated”) are activated respectively for tens of milliseconds according to the detected rotor currents and dcbus voltage (as shown in
Figs. 8
(c) and (j)). Thanks to the optimization current assignment and valid controller design, the system is able to keep uninterruptable operation during such grid faults and inject the required current into the grid, which naturally meets the requirements of the grid code. Once the grid fault is cleared, the system’s operation switches mildly from Mode II to Mode I with its active current setting gradually returning to its normal value in order to reduce the torque strike, as shown in
Fig. 8
(i).
Similarly, when a voltage swell fault occurs, the system’s control mode switches quickly to Mode III, where the inductive reactive current is provided by both the GSC and RSC, with the former in priority. Unlike the voltage dip case, the final active power in the voltage swell case almost equals its normal value, as shown in
Fig. 8
(b). Although the GSC currents become much bigger than its normal value in this case, they are still lower than its maximum, as seen in
Fig. 8
(d).
Table I
summarizes the reactive currents required by the grid code and output from the GSC and stator of the DFIG. It can be seen that the total output reactive current is a little smaller than that required since the stator voltage has been compensated to a relatively higher or lower level during grid faults, as shown in
Fig. 8
(a). After all, the reactive current requirement is well satisfied.
To thoroughly understand the importance of the reactive current assignment during a voltage swell,
Fig. 9
illustrates the simulated results of the same DFIG system with null reactive current injection. It is obvious that although the chopper is effectively activated for a long time, the dcbus voltage still rises to an unacceptable value due to the boost circuit characteristics of the GSC. As a result, it is essential to inject a certain reactive current into the grid by the GSC during a voltage swell. This is equally valuable for grid recovery. Furthermore, simulation tests were conducted with a traditional PI controller to evaluate the effectiveness of the torqueoscillation suppression scheme, as shown in
Fig.10
. When compared to the corresponding waveforms in the same duration in
Fig. 8
, it is obvious that proposed method is valid for eliminating the destructive pulsations in electromagnetic torque. In addition, the scheme can also be used to suppress ripples in the dcbus voltage and to reduce overcurrent in the GSC.
Simulated results of the GSC with UPF operation during voltage swell condition.
Simulated results for the DFIG system with a traditional PI current controller during voltage swell conditions.
V. EXPERIMENT VALIDATIONS
In order to evaluate the feasibility and validity of the proposed control strategy in practice, experimental tests were carried out on a 5.5kW DFIG setup, the parameters of which are listed in
TABLE II
of the Appendix. The RSC and GSC are controlled by two TI TMS320F2812 DSPs and the switching frequencies for both converters are set at 2.5kHz with a sampling frequency of 10kHz.
Figs.11
(A) and (B) display the measured waveforms of the tested DFIG system during grid voltage sag and swell scenarios, respectively, with grid faults lasting for 300ms. The average output stator active and reactive powers during normal operation, i.e., Mode I, are set at
P^{*}_{s}
= 2
k
W and
= 0.5
k
var (inductive), respectively. In addition, the DFIG speed is fixed at 800r/min during the whole test process with the corresponding synchronous speed being 1000r/min. As can be seen from
Fig.11
(A), when a grid fault occurs the operation mode of the system is switched immediately from Mode I to Mode II, i.e., once the overcurrent of the RSC (waveform (i)) is detected, the RSC is deactivated promptly and the crowbar is activated simultaneously (waveform (j)). If the over current is discharged to an acceptable extent by the crowbar device (about 30ms later), the RSC is reactivated with the reactive power supporting (the active power is set to zero) as required, as shown in waveforms (c) and (d). Meanwhile, the GSC is operated in the UPF state since the required reactive current can be entirely provided by the stator of the DFIG, as displayed in waveforms (f) and (g). When the fault is cleared, the system operation mode is then switched from Mode II back to Mode I with the active power gradually controlled up to its normal value. Since the dclink capacitor used in the tested setup is a little larger than it needs to be, the oscillations in the dcbus voltage are not so obvious (waveform (b)) as predicted by the simulation.
Fig. 11
(B) shows the high voltage ridethrough process of the DFIG system. Compared to
Fig. 11
(A), the required reactive current is injected simultaneously from both the statorside and the GSC of the system, while the output active power is kept the same as its normal value. Nevertheless, the feasibility and effectiveness of the proposed control scheme have been well validated by the experiment results.
Experiment results of the DFIG prototype during voltage sag and swell scenarios.
Further tests were carried out under different voltage sag and swell cases. The measured waveforms behaved similar to those shown in
Fig. 11
. However, they are not provided here due to space limitation.
VI. CONCLUSIONS
In order to meet the latest grid code, a reactive current assignment and control strategy, with its feasibility and effectiveness validated by simulation and experiment results, is proposed to enhance the FRT capability of WTs. As a result, some valuable conclusions can be summarized as follows.

1) In addition to uninterrupted operation, reactive power support during voltage disturbances is another stringent and important regulation in the latest grid codes. To put forward a control scheme capable of meeting the extended regulations, it is necessary to evaluate the reactive power support capability of a DFIG system during grid voltage dips and swells. During grid voltage sag events, the reactive current can be provided mainly or even entirely by the statorside of the DFIG system. However, in the voltage swell case, the required reactive current should be injected from both the gridand statorsides of the system, with the former in priority.

2) The proposed control scheme is implemented with a very simple structure that can be easily and completely transplanted to the existing LVRT application of installed DFIGbased WTs. No extra protection devices are needed in the proposed control but a lowcost crowbar and a chopper, which are usually contained in WTs for LVRT operation. This feature offers the possibility of forming a comprehensive FRT scheme for handling the grid faults of voltage revulsion.

3) Due to limited bandwidth, the traditional PI controller is not able to achieve an effective response to the ac components in current controlloops during voltage sags and swells, which leads to destructive pulsations in the electromagnetic torque if no proper control design is adopted. To simultaneously regulate both the dc and ac components, a compound of a PI regulator plus a resonant controller (PIR) is introduced with the auxiliary current references calculated. This has been shown to be capable of achieving a more smooth operation. In addition, pitch angle control usually needs to be carefully designed to restrain surges in a turbine’s speed under such grid faults, especially during serious voltage sag conditions.
Acknowledgements
The authors want to thank the Natural Science Foundation of Zhejiang Province, China for the financial support (Project No. Y13E070001).
BIO
Hailiang Xu was born in China, in 1985. He received his B.S. degree in Electrical Engineering from China University of Petroleum, Dongying, China, in 2008, and his Ph.D. degree in Electrical Engineering from Zhejiang University, Hangzhou, China, in 2014. He has been an postdoctorate student with Academy of Armored Force Engineering, Bejing, China, since 2014. His current research interests include wind power generation systems and electric vehicle drives .
Xiaojun Ma was born in China, in 1963. He received his B.S. degree from Shenyang University of Industry in Industrial Automation, Shenyang, China, in 1985, his M.S. degree from Academy of Armored Force Engineering in Electrical Engineering, Beijing, China, in 1988, and his Ph.D. degree from Tsinghua University in Power System and Automation, Beijing , China, in 1998. In 1988, he joined the Department of Control Engineering, Academy of Armored Force Engineering, where he has been a Professor, since 2000. His current research interests include vehicle electric drive technology and weapon system motion control.
Dan Sun was born in China, in 1971. She received her B.S. degree from Shenyang Jianzhu University, Shenyang, China, in 1997, her M.S. degree from Hehai University, Nanjing, China, in 2000, and her Ph.D. degree from Zhejiang University, Hangzhou, China, in 2004, all in Electrical Engineering. In 2004, she joined the College of Electrical Engineering, Zhejiang University, where she has been an Associate Professor, since 2007. From 2002 to 2004, she was a Visiting Researcher in the University of Technology, Sydney, Australia. From 2009 to 2011, she was a Visiting Professor in the University of Wisconsin, Madison, WI, USA. Her current research interests include advanced electric machine drives and control for wind power generation systems.
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