Modeling and Ride-Through Control of Dfig

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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: [email protected]; [email protected]).

S. R. Silva is with the Federal University of Minas Gerais, Belo Horizonte,MG, 31270-901 Brazil (e-mail: [email protected]).

B. C. Rabelo is with Voith Hydro Ocean Current Technologies, Heidenheim89510, Germany (e-mail: [email protected]).

W. Hofmann is with the Department of Electrical Machines and Drives,Dresden University of Technology, 01069 Dresden, Germany (e-mail: [email protected]).

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

0885-8969/$26.00 2011 IEEE


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1162 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 26, NO. 4, DECEMBER 2011

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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MENDES et al.: MODELING AND RIDE-THROUGH CONTROL OF DFIGs DURING SYMMETRICAL VOLTAGE SAGS 1163

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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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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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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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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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.

Modeling and Ride-Through Control of Dfig

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