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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 26, NO. 4, DECEMBER 2011 1161
Modeling and Ride-Through Control of DoublyFed Induction Generators During Symmetrical
Voltage SagsVictor Flores Mendes, Clodualdo Venicio de Sousa, Selenio Rocha Silva, Member, IEEE,
Balduino Cezar Rabelo, Jr., and Wilfried Hofmann, Senior Member, IEEE
AbstractModern grid codes determine that wind generationplants must not be disconnected from the grid during some levelsof voltage sags and contribute to network stabilization. Wind en-ergy conversion systems equipped with the doubly fed inductiongenerator (DFIG) are one of the most frequently used topologies,but they are sensitive to grid disturbances due to the stator directconnection to the grid. Therefore, many efforts have been donein the last few years in order to improve their low-voltage ride-through capability. This paper analyzes the behavior of the DFIG
during symmetrical voltage sags using models in the frequency do-main. A new strategy, the machine magnetizing current control, isproposed in order to enhance the system response during balanceddips. The method is derived on a theoretical basis and numericallyinvestigated by means of simulation. Experimental results are pre-sented and validate the proposed strategy. Finally, the practicalaspects of the use of this strategy are discussed.
Index TermsDoubly fed induction generator (DFIG), low-voltage ride-through capability (LVRT), voltage sags and windconversion systems.
I. INTRODUCTION
THE NUMBER of wind energy conversion systems(WECS) has increased rapidly in the last few years. The
massive investment in the development of new WECS technolo-
gies has decreased the equipment cost, thus becoming its use
more attractive.
With higher penetration of wind power plants into the inter-
connected electrical system, power system operators have de-
Manuscript received February 10, 2011; revised May 31, 2011; acceptedJuly 5, 2011. Date of publication September 22, 2011; date of current versionNovember 23, 2011. This work was supported by CAPES (Brazilian Agencyfor Higher Education Improvement) and DAAD (German Academic ExchangeService) through the PROBRAL cooperation program, CNPQ (Brazilian Na-tional Council for Scientific and Technological Development) and FAPEMIG(Minas Gerais Research Foundation). Paper no. TEC-00068-2011.
V. F. Mendes and C. V. de Sousa are with the Federal University of Ita-juba, Rua Um, Distrito Industrial II, Itabira - MG, 35903-081 Brazil, and alsowith the Graduate Program in Electrical Engineering, Federal University ofMinas Gerais, Belo Horizonte, MG, 31270-901 Brazil (e-mail: victormendes@unifei.br; clodualdosousa@unifei.br).
S. R. Silva is with the Federal University of Minas Gerais, Belo Horizonte,MG, 31270-901 Brazil (e-mail: selenios@dee.ufmg.br).
B. C. Rabelo is with Voith Hydro Ocean Current Technologies, Heidenheim89510, Germany (e-mail: balduino.rabelo@voith.com).
W. Hofmann is with the Department of Electrical Machines and Drives,Dresden University of Technology, 01069 Dresden, Germany (e-mail: wilfried.hofmann@tu-dresden.de).
Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TEC.2011.2163718
Fig. 1. Wind conversion system with the DFIG topology.
veloped grid codes with specific requirements for regulating the
connection of wind power plants to the electrical network [1].
One of these is the system low-voltage ride-through (LVRT)
capability, i.e., the ability of the power plant to remain con-
nected to the grid during voltage sags [2], [3]. In most of the
cases, power plants are also required to supply reactive power
to the grid in order to guarantee voltage support during voltagesags [3].
WECSs using DFIG drive topologies, as depicted in Fig. 1, are
the most commercialized ones over the world. This technology
consists of a wound rotor induction generator with the stator
terminals directly connected to the grid and the rotor supplied
by a back-to-back converter, allowing a broader slip frequency
range and, thus, variable speed. Its main advantage is the use
of converters dimensioned for a small parcel of the generator
rated power (normally 30%), thereby reducing the equipment
cost. Nevertheless the advantages of the DFIG, due to the direct
connection of the stator to the grid, it is more susceptible to grid
disturbances than WECSs using full-scale power converters [4].
During voltage sags, overvoltages and overcurrents are inducedin the rotor circuit of the DFIG technology which may damage
the rotor-side converter (RSC) [5], [6].
Within this context, it is important to study the behavior of the
DFIG drive duringthe voltage sags, in order to analyze cause and
effect chains, identifying the system weaknesses and developing
new strategies to improve the DFIG LVRT capability.
In the last few years, several papers on this topic have been
published. Papers [5][8] model the DFIG during the sags, scru-
tinizing the behavior of the fluxes, currents, and voltages in the
generator, but the control influence on the machine behavior is
not strictly analyzed. This study intends to go one step further
carrying out the modeling of the DFIG behavior during the sags
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using the frequency domain and including the control effect in
the system modeling.
Most papers dealing with strategies to improve the LVRT ca-
pability describe different ways to implement and actuate the so-
calledcrowbar device. In [5]and [9], thecrowbaris implemented
using a resistance inserted in parallel with the rotor circuit dur-
ing the sags in order to avoid that the high currents flow through
the converter. With this solution, the DFIG acts as an equiva-
lent squirrel cage generator during the sag, consuming reactive
power. Therefore, Meegahapola et al. [10] show the use of the
grid-side converter (GSC) to compensate the consumed reactive
power, acting as a static synchronous compensator. Furthermore,
this paper calculates the optimal crowbar resistance. In [11], the
crowbar actuation strategy is described and the RSC is discon-
nected from the machine and put in parallel with the GSC, both
injecting reactive power into the grid. In order to avoid the dis-
connection of the RSC during the dip, Yang et al. [12] propose
the implementation of the crowbar in series with the rotor cir-
cuit while Rahimi and Parniani [13] propose that of the crowbar
in series with the stator, both showing the advantages of thesemodifications.
The use of the crowbar requires the addition of extra hard-
ware, thereby increasing system complexity and costs. There-
fore, software modifications in the control strategy are preferred,
enhancing the system behavior during the dips.
Lopez et al. [14] calculate new rotor current references using
the stator flux linkage for increasing the damping of this flux, but
a deeper analysis of the strategy results is missing. In [15], the
rotor current references are also modified according to the stator
flux linkage and an analysis of the feasible conditions when the
strategy can ride through the sag is shown. The reduction of
the rotor currents during the sag is also performed in [16] usingfeed-forward compensators to deal with the rotor voltages and
currents transients caused by the voltage sag, but it is shown
that the flux damping is reduced. Papers [14][16] have the dis-
advantage of the necessity of flux estimation. The feed-forward
compensator calculation is simpler in [17] since only the stator
currents are used as the new control references. This strategy re-
duces the rotor overcurrents, but the stator flux oscillation is not
analyzed. In [18], a nonlinear behavior of the classical control
under some voltage sag conditions is demonstrated, leading the
system to unstable operations, so it proposes the use of nonlinear
controllers.
The previous discussed papers show results for the symmet-
rical voltage sags, but the majority of the dips in the powersystem are unbalanced. The operation of the DFIG during un-
balanced conditions is dealt in [19][25]. In [19], feed-forward
compensation is employed in order to decrease the torque pulsa-
tion caused by the negative-sequence current. The use of a dual
PI structure to control separately the positive-sequence current
and negative-sequence current is proposed in [20] and [21].
In [22] and [23], both sequences are controlled using pro-
portional + integral (PI) resonant controllers. Resonant con-
trollers are also employed in a stator stationary reference frame
in [24] and [25]. All these papers show the reduction in the
electromagnetic torque pulsation due to the negative sequence,
but the transient caused by the voltage sag is not analyzed
since only permanent voltage unbalances in the network are
addressed.
Although the unbalanced voltage sags are more common, this
paper treats only the balanced case in order to analyze the DFIG
behavior caused by the voltage transient. As the balanced sags
are particular cases of the unbalanced [6], the study developed
here can be extended in future works for asymmetrical voltage
conditions.
Besides the analysis for the classical control, here a new con-
trol strategy is proposed to increase the flux damping and help
the system to ride through the balanced voltage sags. Simula-
tion results in a 2-MW system and experimental results in a
small-scale 4-kW test bench are presented to show the DFIG
behavior during symmetrical voltage sags and validate the pro-
posed strategy. Details about the simulation, the test bench, and
the classical control are found in [5] and [26].
This section discusses the motivation and objectives of this
study and presents the state of the art. In Section II, the analysis
of the classical DFIG control is carried out, and the simulation
and experimental results are presented to show the DFIG be-havior during the symmetrical sags. The new control strategy is
proposed and validated in Section III. Finally, the conclusions
are presented in Section VI.
II. CLASSICAL CONTROL
The classical control structure of the DFIG drive employs
internal loops controlling the rotor currents and external loops
regulating the active and reactive stator power, both using con-
ventional PI controllers [5], [26]. In this paper, the orientation
in the angle of the stator voltage is used.
The following parts analyze the DFIG behavior during volt-
age sags through mathematical modeling, and simulation andexperimental results.
A. Mathematical Analysis
The following classical dynamic equations of induction ma-
chines in the synchronous reference frame are used:
vs = Rsis +d s
dt+ js s (1)
vr = Rrir +d r
dt+ jr r (2)
s = Lsis + Lmir (3)r = Lrir + Lmis (4)
where the variables have their usual meanings, all in the stator
reference frame, and s , r , are the stator, the slip, and themachine electrical angular frequencies, respectively.
Neglecting the voltage drop in the stator resistance, which
is generally small, and solving the differential equation (1),
it is seen that during stator voltage transients the stator flux
linkage is composed of two components: the forced response,
due to the remaining voltage, and the natural response, due to
the voltage transient. The latter has higher amplitude and decays
exponentially. As demonstrated in [5] and [6], the main problem
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Fig. 2. Root locus of the direct stator flux linkage transfer function (10).
during the symmetrical sags is caused by this stator flux natural
component.
Applying the Laplace transformation in (1)(4) and decou-pling these equations in dq components, the transfer functions
of the stator flux linkage are given by
sd =(s + (1/s ))
(s2 + 2(1/s )s + 2s )Vsd +
(Lm /s ) (s + (1/s ))
(s2 + 2(1/s )s + 2s )Ird
(5)
sd =s
(s2 + 2(1/s )s + 2s )Vsd +
(Lm /s )(s + (1/s ))
(s2 + 2(1/s )s + 2s )Irq
(6)
where s = Ls/Rs is the stator time constant. s is the derivative
operator of Laplace and the capital letters means the Laplacetransformation of the variables with the dependence ofs omitted
to simplify the notation.
One can notice that the stator flux linkage depends on the
stator voltage and the rotor current components. During stator
voltage transients, if the rotor current is kept constant (perfect
current control), the stator flux linkage describes a second-order
response. The flux oscillation is the natural behavior, described
earlier, and analyzing (5) and (6), it is seen that this component
has the stator frequency and decays exponentially with the stator
time constant. This flux behavior was also reported in the open
rotor analysis carried out in [5] and [6].
Perfect current control is theoretically possible, but actuallynot feasible. Depending on the rotor currents behavior, imposed
by thecontrol action, thestator fluxlinkage oscillation frequency
and damping can be modified. Using (2)(4), the rotor currents
can be expressed by
Ir =1
Lr s + RrVr
(Lm /Ls )s
Lr s + Rrs
jr
Lr Ir + (Lm /Ls ) s
Lr s + Rr
(7)
where = 1 (L2m /Ls Lr ). In this equation, the last term,
called cross-coupling term, may be neglected since its effect
is reduced using feed-forward compensators in the current con-
trol structure. Using PI current controllers and considering an
ideal converter, (7) is rewritten as
Ird , q =1
Lr s + Rr
Kp s + Ki
s
Ird , q Ird , q
sLmLs
sd , q
(8)
with the superscript indicating the reference values. Kp and
Ki are the proportional and integral gains of the rotor current
controllers, respectively.
It is interesting to analyze only the stator flux linkage and
rotor current natural components (oscillatory response) since
the forced component can be easily obtained from the steady-
state analysis. Therefore, null rotor current reference can be
assumed and from (8) the natural rotor current is given by
Inrd , q (s) =s2 (Lm /Ls )
Lr s2 + (Kp + Rr )s + Kinsd , q (s) (9)
where the superscript n represents the natural or oscillatory
response component.
Substituting (9) into (5) and (6), the natural stator flux linkage
is calculatedthrough (10) and (11) at the bottom of the nextpage.
These equations represent two fourth-order transfer functions
relating the stator voltage to the natural stator flux linkage. It
is not an easy task to simplify these equations using the literalform, but substituting the real numeric values of a typical DFIG
generator and choosing acceptable controller gains, one can
notice that the system may be reduced to second-order transfer
functions. The pole and zero cancellation can be seen in Fig. 2,
where the root locus of (10) is shown using the parameters of
the 2-MW WECS described in the Appendix. One can notice
that the control parameters values affect the stator flux linkage
damping and oscillation frequency as described later.
If the controller zero is much smaller than the grid frequency
s , the controller will not affect the phase angle between theinput and output, so the rotor current will be lagging the voltage
by 180
(negative feedback). In this situation, the flux damping
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1164 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 26, NO. 4, DECEMBER 2011
Fig. 3. Bode diagram of the PI controller (2-MW gains).
depends on the controller gain in the grid frequency. The smaller
the gain, the higher the flux damping. Cases 1 and 2 in Fig. 3
illustrate the Bode diagram of the PI controller with high and
small gains, respectively, in the case without phase displacement
in the frequency s . The gains for the 2-MW system listed inTable II of the Appendix were used as base values.
When the controller zero is higher than the frequency s ,the controller inserts a phase angle between the rotor current
and voltage. In this case, the flux damping is slowed down.
The higher the phase shift, the smaller the damping. The worst
case happens when there is a phase lag of 90. This situation is
depicted as Case 3 in Fig. 3.
Fig. 4 depicts the natural direct stator flux linkage in the three
cases mentioned earlier. These graphs were obtained using (10)
with the 2-MW parameters. The results of Fig. 4 and the pole
analyses of (10) and (11) lead to important conclusions.
1) The flux damping is accelerated when the current control
is adjusted to a small bandwidth. Although a small control
bandwidth means a slow system response, during volt-
age sags the currents will be extremely high, because the
inverter will not answer fast to counteract the high electro-
motive force (EMF) induced in the rotor. In this situation,
the RSC may be destroyed.
2) A priori, in the normal operation the implementation offast controllers is desirable, because it can reject the sys-
tem disturbances, but during the voltage sags a fast con-
troller implies a slower flux damping. Although the ro-
tor currents are smaller than those in the case with slow
control, a decrease in the flux damping is not desirable,
Fig. 4. Direct stator flux linkage (2 MW, 50% three-phase voltage sag).
because the flux oscillations affect the electromagnetic
torque causing high mechanical stresses in the drive train.
In order to avoid problems like those, it is necessary to imple-
ment control strategies in such a way that the system behavior
is not dependent on the current control adjustment. It is also
mandatory to limit the rotor current to avoid the damage of the
RSC.
The experimental results for the validation of the theoreti-
cal development and analysis of the DFIG behavior during the
symmetrical voltage dips are shown next.
B. Experimental Results
For the experimental tests, the following conditions were con-
sidered in the test bench, which parameters are listed in Table I
of the Appendix.
1) The quadrature grid and rotor current references are equal
to zero.
2) The stator active power reference is following the maxi-
mum power point tracking (MPPT).
3) During the voltage sag, the active power control is de-
activated and the current reference is kept constant. This
procedure is used in order to avoid the influence of the
power control that can complicate the analysis. Further-
more, the power control is slow; therefore, its influencecan be neglected without significant errors in the analysis.
4) The generator speed is equal to 1750 r/min (slip = 0.15)and does not change during the sag, because the mechani-
cal dynamic is considered slower than the electromagnetic
transient.
nsd (s) =(s + (1/s ))
Lr s
2 + (Kp + Rr ) s + Ki
(s2 + 2(1/s )s + 2s ) (Lr s2 + (Kp + Rr ) s + Ki ) + (1/s )(L2m /Ls )s
2 (s + (1/s ))Vsd (s) (10)
nsq (s) =s
Lr s
2 + (Kp + Rr ) s + Ki
(s2 + 2(1/s )s + 2s ) (Lr s2 + (Kp + Rr ) s + Ki ) + (1/s )(L2m /Ls )s
2 (s + (1/s ))Vsd (s). (11)
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Fig. 5. Calculated and measured dq rotor currents.
5) An 85% (remaining voltage) three-phase voltage sag is
applied, starting at t= 0 s and during 1 s. The used voltagesag has a small depth in order to avoid harmful system
operation.
The most important variable to be analyzed is the rotor cur-
rents, shown in Fig. 5, since it is a consequence of the rotor
voltages and, consequently, of the stator flux linkage. It is seen
that during the voltage sag, the rotor currents reach high values
when compared with the value before the sag. These high val-
ues are caused by the natural stator flux that induces high rotor
voltages [5] and this component oscillates with approximately
50 Hz (natural component). One can notice that the natural com-ponent extinguishes in approximately 0.2 s, indicating that the
control increases the flux damping (the stator time constant is
0.15 s).
Fig. 5 also shows the rotor current obtained simulating the
transfer functions (9)(11). Both theoretical and experimental
results are in good agreement with a small difference between
the responses mainly in the phase. The error probably comes
from approximations assumed during the mathematical devel-
opment, but does notinvalidate themodelingsinceit is important
to calculate the maximum current values and approximate the
damping. It is important to highlight that (9)(11) only give
the natural response, so in order to compare the responses the
forced current before the sag (steady-state value) was added tothe calculated result.
One phase of the voltage imposed by the RSC is depicted in
Fig. 6. An ideal converter was considered for the mathemati-
cal development, i.e., without delays and infinite capability of
imposing voltage. In the case when the RSC current control
saturates, i.e., the RSC is operating in overmodulation, the rotor
currents will be higher and the risk for the converter is increased
if no protections are implemented.
The rotor currents and stator flux linkage oscillations due
to the natural component cause vibration in the machine elec-
tromagnetic torque (see Fig. 7), so the mechanical parts are
submitted to high stresses. These oscillations also reflect the
Fig. 6. Phase A of the rotor voltage.
Fig. 7. Estimated electromagnetic torque.
power supplied to the grid, causing a decrease in the system
power quality already degraded by the voltage sag.
The use of the controller gains designed by traditional pole
allocation criteria, listed in the Appendix, increases the flux
damping because in this case the controller gain evaluated in thegrid frequency is small. Increasing the integral gain in such a
way that the controller inserts a phase between the rotor current
and voltage and keeping the same conditions of the previous
test, Fig. 8 shows the rotor current for this new condition. It is
seen that natural damping is decreased and the rotor currents
are increased what it is undesirable. In this case, (9)(11) also
describe adequately the current behavior.
Only the behavior in the sag beginning was analyzed here, but
the natural flux response also appears in the voltage recovering
due to the voltage transient. Therefore, the analysis carried out
is also valid for the sag end transient, during voltage recovery
period.
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1166 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 26, NO. 4, DECEMBER 2011
Fig. 8. Calculated and measured dq rotor currents, Kp = 50 and Ki =10 000.
It is important to highlight that high-power machines have
the stator time constant much higher than a small-power one,
as in the test bench, since the stator resistance in the first is
much smaller. Therefore, the natural component of the stator
flux linkage generally will take more time to extinguish. This
fact must be considered when analyzing the results of a small-
power test rig compared with high-power WECS.
In order to improve the DFIG behavior during the sags and
avoid the dependence of the damping on the current control
adjustment, the use of the magnetizing current control (MCC)
is proposed next.
III. MAGNETIZING CURRENT CONTROL
As demonstrated previously, the oscillations in the rotor cur-
rents come from the natural component of the stator flux linkage.
With the model orientation in the angle of the stator voltage, the
stator flux linkage is induced from the quadrature components
of the rotor and stator currents. The sum of these currents is
called magnetizing current
Im =
Irq + Isq
. (12)
The proposed strategy intends to control the generator magne-
tizing current in order to increase the damping of the stator flux
linkage oscillations (natural component), thereby reducing thetorque and power pulsation during the sag.
In order to control the magnetizing current, thus the stator flux
linkage, it is possible to manipulate the rotor current quadrature
component. Fig. 9 shows the block diagram of the magnetizing
current control. As depicted, this control works in parallel with
the reactive power control and external to the quadrature rotor
current control. This structure offers two main advantages.
1) It is not necessary to detect the voltage sag for the control
actuation, because the magnetizing control can be always
active.
2) It is possible to control the reactive power even during the
sag. This fact is important because the machine can inject
reactive current into the network as required in the modern
grid codes.
The objective of the magnetizing current control (MCC) is to
control only the oscillatory parcel of the magnetizing current.
Thus, as can be seen in Fig. 9, the magnetizing current is filtered
using a band-pass filter shown in
Gf(s) = s ss2 + s s + 2s
. (13)
Only the natural part, i.e., the oscillatory response, is used for
the control. With this artifice, the reference of the control can be
kept equal to zero. Furthermore, only a proportional controller
Kim is required, since steady-state zero error is not the control
objective.
A. Mathematical Analysis
For the mathematical analysis of the MCC for the sake of
simplicity, the following conditions are assumed.
1) Neglect the reactive power control, because generally it
has slow dynamic.
2) The rotor currents control (internal loop) is much faster
than the magnetizing current control and has no limits.
Although it was demonstrated previously that during the volt-
age sag perfect control of the rotor current generally is not pos-
sible, in this case one can notice that the reference generated
by the MCC will be approximately the rotor current oscilla-
tions multiplied by the gain Kim . Therefore, the error of the
quadrature current control will be smaller than the case without
the MCC strategy and a perfect control may be possible. This
fact is similar to decrease the current control gain during the
sag thereby increasing the flux damping, as Case 2 described
in Section II. More strictly, the MCC acts like a feed-forwardcompensator.
Proceeding in the same way for the obtainment of (10) and
(11), the stator flux linkage natural components, with the use of
the MCC strategy, are given by
nsd (s) =(s + (1/m ))
s2 + ((1/s ) + (1/m )) s + 2sVsd (s) (14)
nsq (s) =s
s2 + ((1/s ) + (1/m )) s + 2sVsd (s) (15)
where m = (Kim Ls + Ls Kim Lm )/(Rs (1 + Kim )).Plotting the time constant of the transfer functions (14) and
(15) as a function of the MCC gain using the 2-MW systemparameters, Fig. 10 shows that by increasing the controller gain,
the flux damping is increased. Therefore, the oscillations in
the currents, torque, and power extinguish faster. On the other
hand, by increasing the MCC gain, the total rotor current is
increased. Fig. 11 shows the comparison between the simu-
lated rotor current behavior without and with the MCC strategy
(Kim = 15). An increase in the damping of the natural compo-nent, but a correspondent increase in the quadrature current is
seen.
Fig. 12 shows the simulation result of the maximum rotor
current for different voltage sags varying the MCC gain when
the system is operating at the rated power. One can notice that
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Fig. 9. Magnetizing current control block diagram.
Fig. 10. Time constant of the stator flux natural component varying the MCCgain (2-MW system parameters).
Fig. 11. Simulated dq rotor currents (2-MW system, rated operation, 50%three-phase voltage sag).
the deeper the sag, the greater the increase of the current with
the rising gain.
It is necessary to make balance between the desired damping
and the maximum current limit of the converter. In Figs. 10 and
12, one can notice that, for this case, it is possible to increase
Fig. 12. Maximum rotor current simulated varying the MCC gain (2-MWparameters, rated operation).
Fig. 13. Maximum rotor voltage simulated varying the MCC gain (2-MWparameters, rated operation).
considerably the damping without exceeding the current by 2
p.u., a value generally acceptable by the IGBTs since the peak
value is transitory.
Another important variable for the correct control of the mag-
netizing current is the rotor voltage. Fig. 13 shows that the
maximum voltage varies with the sag depth and it has a small
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Fig. 14. Maximum rotor voltage simulated varying the speed (2-MW param-eters, MPPT curve).
dependence on the gain. As can be seen in Fig. 14, the maximum
required voltage has a greater dependence on the slip frequency.
Therefore, the effectiveness of the MCC strategy is dependent
on the converter voltage capability. In Fig. 14, it is seen that for
deep voltage sags and high turbine speeds the demanded voltage
can reach almost 3 p.u. The high voltage is the main drawback
of this strategy and will be discussed hereafter.
B. Experimental Results
In order to validate experimentally the MCC strategy, the
following conditions were tested.1) An 85% three-phase voltage sag is applied.
2) The machine is operating at 1750 r/min.
3) During the sag, the active power is set to zero in order to
reduce the rotor current and the machine starts to supply
reactive power to the grid.
4) The rotor current control is adjusted for Kp = 50 andKi = 10 000. This change in the gains was used for abetter visualization of the MCC effect.
Fig. 15 compares the behavior of the stator flux linkage with
and without the MCC strategy. The increase in the damping
of the natural flux component is seen, thereby reducing the
oscillations of the rotor currents (see Fig. 16) and voltages,
consequently, of the electromagnetic torque and the generatedpower (see Fig. 17).
Due to undesired fluctuation in the stator voltage, Figs. 15
17 show low-frequency oscillations after the natural component
clearance.
It is important to highlight that in the test bench the use of the
MCC seems to be not so useful, because the stator time constant
is small, thereby the natural oscillation disappears relatively fast.
Furthermore, the rotor control adjustment in the small-power
systems influences much more the damping than in a high-
power system. Generally, it is interesting to improve the LVRT
of high-power WECS, case when the MCC is more effective, as
the simulation results show.
Fig. 15. Estimated stator flux in the test bench with and without the MCC
strategy (1750 r/min, Kp = 50, Ki = 10 000, and Km = 3).
Fig. 16. dq rotor currents in the test bench using the MCC strategy(1750 r/min, Kp = 50, Ki = 10 000, and Km = 3).
Here, only the behavior of the strategy in the sag beginning
was demonstrated, but it is also useful during the voltage re-
covering in the end of voltage sag, because in this instant thenatural response of the stator flux linkage also appears. Further-
more, the MCC can also be employed during the connection
of the generator to the grid, because the voltage transient in
the machine stator also causes oscillatory flux response, thereby
causing undesired torque and power oscillations.
C. Application Issues
Figs. 1214 show that the use of the MCC strategy is restric-
tive due to the high demanded RSC currents and voltages.
In fact, Fig. 12 is plotted for the rated operation without any
change in the direct (active) current reference during the sag.
It is possible to reduce the maximum rotor current by reducing
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MENDES et al.: MODELING AND RIDE-THROUGH CONTROL OF DFIGs DURING SYMMETRICAL VOLTAGE SAGS 1169
Fig. 17. Active and reactive stator power in the test bench using the MCCstrategy (1750 r/min, Kp = 50, Ki = 10 000, and Km = 3).
the active power reference, as demonstrated in the experimental
result in Fig. 16. Even with this reduction, the demanded rotor
current may be high depending on the MCC adjustment, so it is
necessary to choose the gain in such a way that the flux damping
is increased, but the current is not so high. Another fact to be
evaluated is the capability of the converter to supply reactive
power to the grid. The reactive power control also increases the
rotor current.
The main issue for the application of the MCC strategy lies in
the RSC voltage capability. The observations for the currents are
generally true in the case when the converter voltage limit is not
exceeded. As shown in Fig. 14, the RSC has to apply high volt-ages depending on the voltage sag amplitude and the machine
speed. If the converter is not capable of imposing the demanded
voltage, the correct control of the magnetizing control will not
be attained, reducing the strategy effectiveness. Furthermore,
as described in Section II, the rotor currents will also increase,
increasing the probability of the system to trip.
In order to use the MCC strategy theoretically, it is not neces-
sary to increase the converter current limits if the methodologies
mentioned earlier are used, but the voltage limits must be higher
to improve the system performance for deep voltage sags. The
RSC voltage capability may be improved, increasing the dc-
link voltage until the IGBTs limit voltage. If it is necessary to
increase the voltage beyond this limit, the strategy becomes eco-
nomically unviable and it can be used only to shallow voltage
sags or the transient during the connection of the generator to
the grid.
The proposed strategy does not intend to be a unique solution
of ride-through, but it can improve the system performance and
it may be combined to others strategies.
IV. CONCLUSION
In this paper, the DFIG behavior during symmetrical voltage
sags was analyzed through mathematical, simulation, and ex-
perimental results. It was shown that the main problem during
balanced dips is caused by the natural response of the stator flux
linkage that causes high oscillatory rotor voltages and currents,
and, consequently, electromagnetic torque and generated power
oscillations.
The mathematical development and the experimental results
show that the control adjustment influences the damping of the
natural flux. The higher the rotor current control bandwidth, the
higher the decrease in the stator flux linkage damping and the
system may become unstable during voltage sag transients.
In order to increase the damping of the natural flux, the use
of the magnetizing current control was proposed. Through a
mathematical analysis, and simulation and experimental results,
it was demonstrated that the strategy increases the flux damping
by improving the system behavior during the sag. This strategy
shows improvement in the system response during the sag, but
it demands high rotor voltages that depend on the machine
operation points that are not feasible for the converter.
This paper only addressed the balanced case, but the behav-
ior described here is also present in the unbalanced voltage sags
with the addition of the negative-sequence influence. The math-ematical analysis developed here is also valid for the unbalanced
case and the magnetizing current control strategy can also be
used in combination with other strategies, subject of further
works.
APPENDIX
TABLE ISYSTEM PARAMETERS
TABLE IICONTROLLER GAINS
ACKNOWLEDGMENT
The authors gratefully acknowledge the contribution of the
Brazilians and Germans colleagues involved in the cooperation
between UFMG and TU Dresden supported by CNPQ/CAPES
and DAAD with contribution of FAPEMIG.
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Victor Flores Mendes received the B.E.E. degree incontrol and automation engineering and the M.E.E.degree in electricalengineering fromthe Federal Uni-versity of Minas Gerais, Belo Horizonte, Brazil, in2008 and 2009, respectively.
He is an Assistant Professor at the Federal Univer-sity of Itajuba, Itabira, Brazil. Since 2009,he hasbeen
the Doctor Student at Federal University of MinasGerais, Belo Horizonte, Brazil, where his researchfocuses on the development of new strategies to im-prove the ride-through fault capability of the doubly
fed induction wind generators. In 2010, he developed part of his thesis, whichfocuses on the experimental implementation of the ride-through strategies, atDresden University of Technology (TU Dresden), Dresden, Germany. His mainresearch interests include ac motor drives, power electronics, renewable sources,and variable-speed generators for wind turbines.
Clodualdo Venicio de Sousa received the B.E.E.degree from Centro Univesitario de Minas Gerais,
Coronel Fabriciano, Brazil and the M.E.E. degreefrom the Federal University of Minas Gerais), BeloHorizonte, Brazil, both in electrical engineering, in2001 and 2007, respectively.
Since 2009, he has been an Assistant Professor atthe Federal University of Itajuba, Itabira, Brazil, andsince 2007,he hasbeen theDoctor Student at FederalUniversity of Minas Gerais, Belo Horizonte, Brazil,with the topic Using back-to-back converters to test
transformers. His main research interests include ac motor drives, power elec-tronics, and transformers.
Selenio Rocha Silva (M93) received the B.E.E. andM.E.E. degrees in electrical engineering from theFederal University of Minas Gerais (UFMG), BeloHorizonte, Brazil, in 1980 and 1984, respectively,and the Ph.D. degree from Campina Grande FederalUniversity, Campina Grande, Brazil, in 1988.
Since 1982, he has been with the Department ofElectrical Engineering, UFMG, where, in 1995, hebecame a Full Professor. He has published more than200 technical papers and advised more than 40 post-graduatestudents. His mainresearchinterestsinclude
ac motor drives, power quality variable-speed generators for wind turbines, andgrid integration of DG.
Prof. Silva is a member of the Brazilian Power Electronics Association, theBrazilian Automatic Control Association, and the IEEE Industry ApplicationSociety.
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MENDES et al.: MODELING AND RIDE-THROUGH CONTROL OF DFIGs DURING SYMMETRICAL VOLTAGE SAGS 1171
Balduino Cezar Rabelo, Jr. received the B.Sc. andM.Sc. degrees from the Federal University of MinasGerais, Belo Horizonte, Brazil, and the Dr.-Ing. de-greein electrical engineering fromthe Chemnitz Uni-versity of Technology, Chemnitz, Germany.
From 2008 until 2010, he was a Research Assis-tant at the Department of Electrical Machines andDrives, TU Dresden. Since 2010, he has been withthe Voith Hydro Ocean Current Technologies, Hei-denheim, Germany, where he was involved in thedevelopment of submarine tidal current turbines. His
main research interests include control of electrical drives, power electronics,and renewable energy sources.
Wilfried Hofmann (SM11) received the Dipl.-Ing.and Dr.-Ing. degrees in electrical engineering fromthe Dresden University of Technology(TU Dresden),Dresden, Germany in 1978 and 1984, respectively.
He was a Development Engineer and ProjectLeader with Elpro AG and Docent at BerlinLichetnberg Engineering School, Berlin, Germany.From 1992 to 2007, he was the Chair of the De-partment of Electrical Machines and Drives, Chem-nitz University of Technology, Chemnitz, Germany.Since 2007, he has been the Head of the Department
of Electrical Machines andDrives,TU Dresden. He haspublished more than 260papers and 60 patents and is the author or coauthor of four technical books. Hismain research interests include electromagnetic energy conversion, mechatron-ics and motion control, control of ac machines, power electronics, and renewableenergy conversion systems.
Dr. Hofmann is a member of the German Academy of Science and Engineer-ing (acatech), the Saxonia Academy of Science, Verband der Elektrotechnik(VDE), Verein Deutscher Ingenieure (VDI), Steering Committee of EuropeanPower Electronics and Drives Association (EPE). He is a member in 1992 andthe senior member in 2011 of the IEEE Industrial Applications Society, IEEEPower Electronics Society, and the IEEE Industrial Electronics Society.