Research Article Control of DFIG Wind Turbines Based on

Hindawi Publishing CorporationAdvances in Power ElectronicsVolume 2013 Article ID 157431 11 pageshttpdxdoiorg1011552013157431

Research ArticleControl of DFIG Wind Turbines Based onIndirect Matrix Converters in Short Circuit Mode toImprove the LVRT Capability

Ahmad Khajeh and Reza Ghazi

Electrical Engineering Department Faculty of Engineering Ferdowsi University of Mashhad PO Box 9177948974 Mashhad Iran

Correspondence should be addressed to Ahmad Khajeh ahmad khajeh79yahoocom

Received 29 August 2013 Revised 8 October 2013 Accepted 9 October 2013

Academic Editor C M Liaw

Copyright copy 2013 A Khajeh and R Ghazi This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Nowadays the doubly-fed induction generators (DFIGs) based wind turbines (WTs) are the dominant type of WTs Traditionallythe back-to-back converters are used to excite the rotor circuit of DFIG In this paper an indirect matrix converter (IMC) isproposed to control the generator Compared with back-to-back converters IMCs have numerous advantages such as higher levelof robustness reliability and reduced size and weight due to the absence of bulky electrolytic capacitor According to the recent gridcodes wind turbines must have low voltage ride-through (LVRT) capability In this paper a new crowbar system is proposed so thatalong with the control system it protects the IMC from large fault currents and supports the grid voltage dips during grid faultsThis crowbar system is provided using the existing converter switches to establish a short circuit mode without any extra circuitryEven in severe fault conditions the duration of short circuit mode is quite small so the control system will be activated shortly afterthe fault to inject reactive power as required by new LVRT standards Therefore the new LVRT standards are well satisfied withoutany extra costs PSIM simulation results confirm the efficiency of the proposed method

1 Introduction

Wind energy has been found as the fastest growing renewablepower generation resources over theworld Government sup-port and advancement in technology of WT have acceleratedthis rapid growth Based on estimation thewind power capac-ity becomes double every three years [1]

Due to their superior characteristics most of the grid-connected WTs operate at a variable speed Among thedifferent variable speed types theDFIG is themost promisingone The stator winding of DFIG is directly connected tothe grid while the rotor winding is connected to the gridthrough an ac-ac power electronic converter having bidirec-tional switches Traditionally the back-to-back converters areused to excite the rotors of DFIGs The presence of the dc-link capacitor in this arrangement is a serious drawback asit increases the costs and reduces the overall lifetime of thesystem and also makes the system bulky [2]

In this paper the back-to-back converter arrangement isreplaced by an indirect matrix converter (IMC) to controlthe generator as shown in Figure 1 The main advantages of amatrix converter are robustness reliability with less size andweight due to the absence of the bulky electrolytic capaci-tor controllable input power factor nearly sinusoidal inputcurrent and output voltage with only switching frequencyharmonics along with bidirectional power flow The directmatrix converter (DMC) encounters the commutation prob-lems requiring a complex control circuitry While in IMC allswitches at the line side will turn on and off at zero current sothe commutation problems are eliminated [3] Therefore theIMCs are the most promising devices for wind energy appli-cations regarding their robustness reliability and reducedsize

In the past based onmost grid codes wind turbines wereallowed to be disconnected from the grid during the griddisturbances and the abnormal voltage reduction With the

2 Advances in Power Electronics

DFIG

Supply

WindGear Box

sim

Figure 1 Wind Turbine based on the DFIG excited by indirect ma-trix converter

increased capacity of wind powers in the power systems overthe years the sudden loss of wind turbines during the gridfaults resulting from turbines disconnection could generatecontrol problems of frequency and voltage in the system soleading to the voltage collapse in worst cases The increasedpenetration of wind energy into the power system over thelast decade has therefore led to a serious concern about itsinfluence on the dynamic behavior of the power system Tohandle this issue the grid codes are revised by system opera-tors in several countries [4] According to the new grid codesthe wind turbines must be remain connected to the networkon the occurrence of grid faults and tolerate the resultingvoltage drops This feature is known as the low voltageride-through (LVRT) capability of a power plant The LVRTrequirement defines a specific voltage profile with limitingcurves depending on the grid voltage dip depth Moreoverin some grid codes such as Germany wind turbines shouldalso inject reactive power to help the grid voltage recovery

Because of direct connection of stator winding to thegrid and the small rating of power electronic converter inthe rotor side DFIG based wind turbine is very sensitiveto grid disturbances especially to voltage dips during gridfaults Grid faults even those occurring far from the windturbines can cause voltage drops at the point of wind turbineconnection The abrupt drop of the grid voltage will makean increase in the current of stator windings of the DFIGBecause of the magnetic coupling between stator and rotorthis current will also flow in the rotor circuit and the powerconverter At present the back-to-back converter is the mostfrequently used power electronic converter in the windturbines industryTherefore the most of research works havebeen done to enhance the LVRT ability of DFIG utilizing thistype of converters So the grid faults cause over current inthe rotor windings and over voltage in the dc-link capacitorhence the proper protection should be provided to safekeepthe converter Various solutions have been proposed to solvethe problem Some of them are briefly reviewed as follows

The most popular and reliable method is based on theuse of a protective circuit known as crowbar The crowbarconsists of resistors connected to the rotorwindings bymeansof electronic switches In active crowbar the switches arecontrollable such as IGBTs whereas in passive one they areantiparallel thyristors The active crowbar allows openingthe circuit when the currents reach safe region The passivecrowbar allows closing the circuit but not opening it until

the crowbar currents reach zero Therefore according to thenew grid codes the passive crowbar is not appropriate forthe modern wind turbines When a fault occurs the rotorwindings get connected to the crowbar while the converteris tripped Several papers have discussed the implementationand control of crowbar [5ndash12] Different types of crowbarsrealization are shown in Figure 2The crowbar can effectivelyprotect the rotor converter under serious grid faults But itsmain drawback is that when the crowbar is activated therotor converter cannot control the active and reactive powerduring crowbar activation so the DFIG operates as a cageinduction generator absorbing extra reactive power from thegrid and deteriorates the grid voltage profile

Another approach is to modify the rotor-side convertercontrol system to limit the fault currents without using anyextra hardware circuit [13ndash21] In this method at seriousgrid faults the required voltage in the rotor-side converterbecomes too large and exceeds its voltage capability There-fore the rotor current greatly increases thus leading toconverter destructionThismethod is beneficial as it does notrequire any additional hardware but it is suitable formoderatefaults

Another solution for LVRT is to use an additional energystorage system (ESS) connected to the dc link [22ndash26] TheESS can balance the extra power that goes through the rotorcircuit during a grid fault transient but it also requires a rotorside converter with higher current ratings having extra costand more system complexity

Utilizing matrix converters in DFIG wind turbines is stillin research phase Most of the works have dealt with theirnormal operation [27ndash30] The control of a DFIG using anindirect matrix converter for dynamic performance evalua-tion under normal grid condition is presented in [27] Sigma-delta modulator to control IMC switches of DFIG basedWT is proposed in [28] By using this modulation methodtorque pulsations and harmonic content of currents arereducedTherefore the power quality ofWT is improvedThecapability of the input converter to generate different virtualdc-link voltage levels is also proposed in [29] This methodreduces both the commutation losses of output converterand common mode voltage Due to small voltage requiredaround the synchronous speed this strategy is suitable inDFIG applications

Dynamic performance of DFIG using two-stage IMCunder voltage dip condition has been discussed in [30] with-out providing any protection As simulation results show for80 terminal voltage sag the stator current reaches 25 puWithout any protection method this high current coulddamage the IGBT switches of the IMC According to newLVRT standards the reactive power injection to the grid ismandatory to improve the voltage recovery Results of [30]indicate that during the fault about 07 pu reactive poweris absorbed from the grid which makes the voltage deeperTherefore the existing controller which is designed for nor-mal operating condition is ineffective during fault conditions

To solve these drawbacks and satisfy the new LVRTstandards in present paper a new method is proposed toprotect the IMC with DFIG following the grid faults In thismethod a new short circuit mode is proposed to control

Advances in Power Electronics 3

DFIG

sim

sim =

=

(a)

DFIG

sim

sim =

=

(b)

DFIG

sim

sim=

=

(c)

Figure 2 Different types of crowbar realization

the short circuit currents of the DFIG wind turbines basedon IMC In addition to protect the IMC against large faultcurrents the proposedmethod alsomakes it possible to injectreactive power during grid faults to improve voltage recoveryso the new LVRT standards are well satisfied The PSIMsimulation results confirm the efficiency of the proposedmethod

This paper is organized as follows In Section 2 LVRTrequirement of a German transmission system operator isdiscussed Modeling and control of the DFIG based windturbine is presented in Section 3 The vector control of theDFIG is briefly discussed in Section 4 In Section 5 theproposed method is presented and analyzed The simulationresults are provided in Section 6 Finally Section 7 concludesthe paper

2 LVRT Requirement

The German transmission system operator EON Netz wasthe first power system operator which introduced grid codesfor wind turbines and is followed now bymany other networkoperators in several countries EON introduces a voltageprofile and the limiting curves and regions defining theLVRT requirement as shown in Figure 3 Accordingly windturbines must stay connected even when the voltage at thepoint of common coupling (PCC) drops to zero The 150msdelay shown in Figure 3 accounts for the normal operatingtime of protection relays Three-phase short circuits or fault-related symmetrical voltage dips must not lead to instabilityabove the limit line 1 in Figure 3 or disconnection of thewind turbines from the grid Within the shaded area andabove limit line 2 in Figure 3 LVRT is also required but incase of instability a short term interruption (STI) is allowedBelow the limit line 2 in Figure 3 no LVRT is required and STIfrom the grid is always permissible Here resynchronizationtimes of more than 2 seconds and an active power increase

Limit line 1 Limit line 2100

70

45

15

0 150 700 1500

Time when a fault occursTime (ms)

Highest value of the three line-to-line grid voltage

UU

N(

)

Figure 3 EON Netz LVRT requirement

following fault clearance of less than 10 of the rated powerper second are also possible According to the EON Netzgrid code wind turbines have to provide amandatory voltagesupport during voltage dips Wind turbines have to supply1 pu reactive current when the voltage falls below 05 pu

3 Modeling and Control ofDFIG Based Wind Turbine

In this section dynamic model of DFIG based wind turbineis providedThe stator winding of DFIG is directly connectedto the grid and the rotor winding is coupled via an IMCTheIMC must handle the slip power that is about 30 of therated power of wind turbineThe speed range of the generatoris typically plusmn30 of synchronous speed thus providing flex-ibility to operate in both sub- and supersynchronous modesdepending on the wind conditions The inverter of the IMC


is used to control the active and reactive power of the DFIGThe rectifier of the IMC is often operated at unity powerfactor Depending on the rotor speed the IMC will eitherabsorb power (subsynchronous) from grid or inject power(supersynchronous) to the grid Therefore the IMC musthave the ability of bidirectional power flow to the network

31 Turbine Model The mechanical power extracted by awind turbine from the wind is expressed by

119875 =1

2

119860 sdot 120588 sdot 119862119901 (120582 120573) sdot V3

120596 (1)

where 119860 is the area covered by the rotor blades 120588 is the airdensity 119862119901 is the power coefficient representing the amountof power the turbine can extract and V120596 is thewind speedThepower available in the wind cannot be extracted completelyTheoretically the maximum captured power is 59 of thepower available in the wind The power coefficient is afunction of the tip-speed ratio 120582 and the pitch angle of therotor blades 120573 The tip-speed ratio is defined by

120582 =119877Ω119905

V120596 (2)

where 119877 is the radius of the rotor blades andΩ119905 is the angularspeed of the blades For each pitch angle of the rotor bladesthere is an optimum tip-speed ratio120582opt forwhich119862119901(120582opt 120573)takes a maximum value Therefore for wind speeds belowrated value the existing power is below the rated power sopower coefficient is optimized by adjusting the tip-speed ratioto achieve the maximum power coefficient The pitch angleis kept constant in this region which is called the maximumpower point tracking (MPPT) of wind turbines On contraryat wind speeds above rated value the extracted wind powerhas to be limited bymeans of blade pitching In this paper theMPPT is accomplished through a look-up table The MPPTtable ensures the plant operation at maximum power forpartial loads and specifies that the rated speed is achievedat rated power According to [4] coordination between thecontrol of the mechanical and the electrical system exists

32 DFIG Model For DFIG modeling a fifth-order dynamicmodel of the DFIG is used in this paper [31] The model in atwo-axis 119889-119902 synchronous reference frame is given by

V119904119889119902 = 119877119904119894119904119889119902 +

119889120595119904119889119902

119889119905

+ 119895120596119904120595119904119889119902

V119903119889119902 = 119877119903119894119903119889119902 +

119889120595119903119889119902

119889119905

+ 119895 (120596119904 minus 120596119903) 120595119903119889119902

119879119890119898 =119901

2

(120595119903119902119894119903119889 minus 120595119903119889119894119903119902)

(3)

120595119904119889119902 = 119871 119904119894119904119889119902 + 119871119898119894119903119889119902

120595119903119889119902 = 119871119898119894119904119889119902 + 119871119903119894119903119889119902

119871 119904 = 119871 119897119904 + 119871119898

119871119903 = 119871 119897119903 + 119871119898

(4)

In these equations 119877119904 119877119903 119871 119904 119871119903 119871 119897119904 and 119871 119897119903 are theresistors and inductors of the stator and rotor windings 119871119898is the magnetizing inductance V119904119889119902 V119903119889119902 119894119904119889119902 119894119903119889119902 120595119904119889119902 and120595119903119889119902 are the space vectors of the stator and rotor voltagescurrents and fluxes respectively120596119904 is the synchronous speedof the generator 120596119903 is the electrical speed of the rotor and 119901

is the number of poles

33 Indirect Matrix Converter Due to the numerous advan-tages of matrix converters over back-to-back converters inthis paper the IMC is used to control the DFIG An IMCconsists of a rectification part on the input side and aninversion part on the output side connected via fictitious dclink as shown in Figure 4 For purposes of analysis we canassume that the switching frequency is far greater than thefundamental frequency of both the input voltage and outputcurrent Thus during each switching cycle it is assumed thatboth input voltage and output current are constant

The rectifier has six bidirectional switches with theability of conducting current and blocking voltage in bothdirectionsThe rectifier side objective is to achieve maximumpositive voltages at the fictitious dc-link and sinusoidal inputcurrents Usually the grid side converter of DFIG exchangeszero reactive power at the grid point In order to obtainmaximum dc-link voltage the input phase voltage which hasthe highest absolute value is connected to the positive ornegative rail of the dc link at 60 degree intervals dependingon its polarity To achieve sinusoidal current and unity powerfactor at the input side regardless of the load type theother two phase voltages are modulated so that the referencecurrent space vector be in phase with the voltage space vectorSpace vectors of the input current are shown in Figure 5Assume the input voltages are

V119886 = 119881119898 cos 120579119886 = 119881119898 cos (120596119894119905)

V119887 = 119881119898 cos 120579119887 = 119881119898 cos(120596119894119905 minus2120587

3

)

V119888 = 119881119898 cos 120579119888 = 119881119898 cos(120596119894119905 +2120587

3

)

(5)

where119881119898 is themaximumof the input phase voltage and120596119894 isthe angular frequency In order to achieve unity power factorat the input side the input currents must be in phase with theinput voltages Therefore input currents are as follows

119868119886 = 119868119898 cos (120596119894119905)

119868119887 = 119868119898 cos(120596119894119905 minus2120587

3

)

119868119888 = 119868119898 cos(120596119894119905 +2120587

3

)

(6)

where 119868119898 is the maximum of the input current On therectifier side always two switches one from top and anotherfrom the bottom are ON and the others are OFF

To calculate the duty cycle of each switch first the angleof the input voltage space vector is obtained This is thereference angle of the current space vector to obtain the unity


C

B

Aa

bc

P

N

Figure 4 Indirect matrix converter topology

23

4

5 6

1

Vb

Vc

Va

I3(bc)

I2(ac)

I1(ab)

I6(cb)

I5(ca)

I4(ba)

120579ref

Iref

Figure 5 Space vectors of the input current

power factor Regarding the angle of current space vector itscorresponding sector is determined from Figure 5 Then thecurrent reference vector can be built using two adjacent vec-tors of each section For example when the reference currentspace vector is located in the first section two adjacent vectorsare ldquo119886119887rdquo and ldquo119886119888rdquo In this section voltage of phase ldquo119886rdquo has thehighest absolute value Therefore in 60 degree duration ofthis section the top switch of phase ldquo119886rdquo is ON and the bottomswitches of phases ldquo119887rdquo and ldquo119888rdquo get modulated Vector ldquo119886119887rdquomeans that the top switch of phase ldquo119886rdquo and the bottom switchof phase ldquo119887rdquo are ON and ldquo119886119888rdquo means that the top switch ofphase ldquo119886rdquo and the bottom switch of phase ldquo119888rdquo are ON and soon

So in one period of switching frequency in this sectioninput currents are as follows

119894119886 = (119889119886119887 + 119889119886119888) 119894119889119888 119894119887 = minus119889119886119887119894119889119888 119894119888 = minus119889119886119888119894119889119888 (7)

where 119889119886119887 and 119889119886119888 are the duty cycles of 1198681(119886119887) and 1198682(119886119888)respectively and 119894119889119888 is the dc-link current As only the activevectors are used the following relationships hold

119889119886119887 + 119889119886119888 = 1 997904rArr 119894119886 = 119894119889119888 (8)

Therefore the duty cycles of active vectors in section oneare given by

119889119886119887 = minus119894119887

119894119886

119889119886119888 = minus119894119888

119894119886

(9)

The duty cycles in the other sections are obtained simi-larly Based on this modulation method in the rectifier stagethe average fictitious dc-link voltage in each period is

119881119889119888 =3 sdot 119881119898

2 sdot1003816100381610038161003816cos (120579in)

1003816100381610038161003816

1003816100381610038161003816cos (120579in)

1003816100381610038161003816= max (1003816100381610038161003816cos (120579119886)

10038161003816100381610038161003816100381610038161003816cos (120579119887)

10038161003816100381610038161003816100381610038161003816cos (120579119888)

1003816100381610038161003816)

(10)

where 120579in is the angle of the input voltage space vector On theoutput stage the space vector modulation (SVM) is used togenerate the required rotor voltage space vector by currentscontrollers Inverter voltage space vectors along with thereference vector are shown in Figure 6

Duty cycles of active vectors on the inverter stage are asfollows

119889120572 = 119896 sdot sin (60∘minus 120579119894) 119889120573 = 119896 sdot sin (120579119894) (11)

where 119896 is the modulation index and is given by

119896 =

2 sdot1003816100381610038161003816cos (120579in)

1003816100381610038161003816sdot 119903

radic3 sdot 119881119898

(12)

where119881119903 is the absolute of the reference voltage Consideringmodulation of both the input and output sides the final dutycycles of active vectors are

119889120572120574 = 119889120574 sdot 119889120572 119889120573120574 = 119889120574 sdot 119889120573

119889120572120575 = 119889120575 sdot 119889120572 119889120573120575 = 119889120575 sdot 119889120573

(13)

where 119889120574 is the first vector of the rectifier section and 119889120575 is thesecond vector of the rectifier section Finally the duty cyclesof the zero vectors are calculated as

1198890 = 1 minus (119889120574 + 119889120575) sdot (119889120572 + 119889120573)

1198890120574 =

119889120574

(119889120574 + 119889120575)

1198890 1198890120575 =119889120575

(119889120574 + 119889120575)

1198890

(14)

The overall switching scheme in one period is depictedin Figure 7 Fictitious dc-link voltage for simulated IMC isshown in Figure 8

4 Vector Control of DFIG

The goal of the DFIG controller is the independent controlof the stator active and reactive power The active powerreference is determined by MPPT algorithm and the reactivepower is set in order to achieve the desired power factorStator flux 119889-119902 reference frame is the most widely used DFIGvector control in the wind turbine applications Thus theinverter of IMC is controlled in a stator flux 119889-119902 reference


2

3

4

5

6

1120579ref

V3(010)

V1(100)

V4(011)

V5(001)

V6(101)

V2(110)

Vref

VA

VB

VC

Figure 6 Space vectors of the output voltage

120574R 120575R

0120574

2

0120574

2

0120575

2

0120575

2120573120574 120573120575 120572120575120572120574In

vRe

c

Ts

tcom

Figure 7 Switching scheme in one period

frame with the 119889-axis oriented along the stator flux vectorposition For this reference frame selection the DFIG modelcan be written as

120595119904 = 120595119904119889 0 = 120595119904119902 (15)

Substituting (15) into (4) we obtain

119894119889119904 =1

119871 119904

(120595119904 minus 119871119898119894119889119903) 119894119902119904 = minus119871119898

119871 119904

119894119902119903

120595119889119903 = 120590119871119903119894119889119903 +119871119898

119871 119904

120595119904 120595119902119903 = 120590119871119903119894119902119903 120590 = 1 minus

1198712

119898

119871 119904119871119903

(16)

where 120590 is the leakage factor In DFIG the rotor voltages arecontrol variables which control the rotor currents Substitut-ing (16) into (3) rotor voltages can be written as

V119889119903 = 119877119903119894119889119903 +119889

119889119905

(120590119871119903119894119889119903 +119871119898

119871 119904

120595119904) minus (120596119904 minus 120596119903) (120590119871119903119894119902119903)

V119902119903 = 119877119903119894119902119903 +119889

119889119905

(120590119871119903119894119902119903) + (120596119904 minus 120596119903) (120590119871119903119894119889119903 +119871119898

119871 119904

120595119904)

(17)

0002 0004 0006 0008 001 0012 0014 0016 0018 0020

200

400

600

800

1000

1200

Time (s)

Volta

ges (

V)

VdcVabVbcVca

VbaVcbVca

Figure 8 Fictitious dc-link voltage

In dynamic performance analysis of the overall systemcross-coupling terms in (17) are added to control loopsas feed-forward compensation terms The stator active andreactive power can be calculated as

119875119904 =3

2

(V119889119904119894119889119904 + V119902119904119894119902119904) 119876119904 =3

2

(V119902119904119894119889119904 minus V119889119904119894119902119904) (18)

In steady state the stator flux is proportional to the gridvoltage Neglecting the small voltage drop in the stator resis-tance yields

119881119904 = V119902119904 0 = V1198891199041003816100381610038161003816119881119904

1003816100381610038161003816≃ 120596119904

1003816100381610038161003816120595119904

1003816100381610038161003816 (19)

Thus when orienting the 119889-axis with the stator flux thevoltage aligns with the 119902-axis Combining (19) and (16) with(18) we obtain

119875119904 =3

2

V119889119904119894119889119904 = minus3

2

119881119904

119871119898

119871 119904

119894119902119903

119876119904 =3

2

V119902119904119894119889119904 =3119881119904

2119871 119904

(120595119904 minus 119871119898119894119889119903)

(20)

The above equations clearly show that under the statorflux orientation the active and reactive powers are decoupledand can be controlled via the rotor currents By means of119894119902119903 we can control the active power while the reactive powercan be controlled via the 119894119889119903 Using the above equations thereference currents can be calculated from the desired powersThe schematic diagram of stator flux based vector control ofDFIG along with MPPT algorithm is shown in Figure 9

5 New LVRT Scheme Based onthe Short Circuit Mode

51 Operation and Implementation In wind turbines basedon back-to-back converters using the crowbar is the most


DFIG

Stator

PI

PI

fluxcalculation

MatrixconverterSV

M

MPPT

23

23

23

+

+

+

+

+

+

++ minus

minus

minus

minus

120595s

120579s

120596s

120596r120596slip

i120572si120573s120572s120573s

abs bcs

ias ibs

120579r

120579slip = 120579s minus 120579r

ddt

i120572r iar ibr

i120573ridr

idrlowast

iqrlowast

iqr

dr

dr998400

qr

qr998400

120573r

120572r

Plowasts

Qlowasts

eminusj120579slip

ej120579slip

Vwind or 120596r

minus120596slip120590LriqrPlowasts = minus

3

2Vs

Lm

Ls

iqrlowast

120596slip (120590Lridr +Lm

Ls

120595s)

Qlowasts = minus

3Vs2Ls

(120595s minus Lmidr)lowast

Figure 9 Schematic diagram of vector control of DFIG

popular and reliable scheme to relieve the problems of overcurrent in rotor windings and over voltage at dc link Asshown in Figure 2 these schemes employ extra circuitry to dothe job However in patent [32] for back-to-back convertera scheme is presented using only the existing converterswitches In this scheme the crowbar function is performedby handling the fault currents through applying zero vectorsby inverter part of the converter Simultaneous zero vectorsare achieved by means of turning on 3 upper switches orlower switches Here due to the presence of dc-link capacitorturning on both switches of a leg is prohibited to prevent itfrom short circuit

In the present paper based on this concept a new crowbarscheme is proposed and applied on DFIG excited by anindirect matrix converter (Figure 10) In the indirect matrixconverter due to the absence of dc-link capacitor the limita-tion of simultaneous switching of two switches of each leg isremovedTherefore in the occurrence of large voltage dips alloutput stage switches of IMC are turned on and those of inputstage are turned off simultaneously This mode is known asshort circuit mode and could do the crowbar task Thereforea new low-cost crowbar is realized that does not require anyadditional hardware Activation of the short circuit mode isbased on the output of a comparator The comparator blockcompares the maximum absolute value of the rotor currentswith a threshold value If the output of the comparator is zerothen the gate pulses generated by SVM modulator will applyto the IMC In case of occurring faults the rotor currents willexceed the threshold value and comparator output value willchange to one Hence the controller switches to the shortcircuit mode and apply the new crowbar Furthermore inIMC there are six switches in this mode (Figure 10) So eachswitch in this scheme should tolerate half the current of back-to-back converter case Therefore it can work well in DFIGbased on IMC even for severe faults

52 Dynamic Performance The dynamic performance of theproposed scheme is investigated during the paperTheoreticalanalysis of the dynamic behavior of the DFIG during three-phase voltage dips has been investigated in previous worksespecially in [14 15] Both of them proposed inserting extraresistances in stator circuit along with control modificationto improve the behavior of the DFIG During faults theproposed method could be considered as a crowbar havinga small resistance In normal operating condition the spacevector of the stator flux inDFIG rotates at synchronous speedReferenced to rotor it rotates at the slip speed and inducessmall voltages in it Due to continuity principle of the statorflux when the DFIG experiences a voltage dip the stator fluxencompasses two components an ac component correspondsto the remaining voltage of the DFIG terminal and a dccomponent to maintain flux continuity The dc componentis fixed to the stator but it is seen by the rotor as a fluxthat rotates at the rotor speed Note that the rotor speed issignificantly greater than the slip speed and so the inducedvoltages in rotor are much greater Therefore it is desired toincrease the damping of the dc term to improve transientperformance of the DFIG Impact of the proposed methodon the stator flux dynamic is investigated to compare withdisconnecting the converter as follows

If the converter is disconnected from the rotor the dy-namic equation of the stator flux based on (3) and (4) can becalculated by

119894119904119889119902 =

120595119904119889119902

119871 119904

997904rArr

119889120595119904119889119902

119889119905

= minus119877119904

119871 119904

120595119904119889119902 minus 119895120596119904120595119904119889119902 + V119904119889119902 (21)

The pole of the above equation is 119904 = minus119877119904119871 119904 minus 119895120596119904 Thedamping coefficient of this pole is 120572 = minus119877119904119871 119904 and is equalto minus038 for the studied DFIG Therefore the pole is close toimaginary axis with poor damping The dynamic equation of


[0 0 0 0 0 0]

[1 1 1 1 1 1]

DFIG

Supply

Rec gatepluses

Inv gatepluses

SVMmodulation

Referencegeneration

from PIcontrollers

Comparator

ITH0 normal mode1 short circuit mode

Mode selector

1

1

0

0Vd

Vq

Iar

Ibr

Icr

IarIbrIcr

gt

sim

MaxIar Ibr Icr

Figure 10 New crowbar structure

the stator flux in case of applying the proposed method willchange to

119894119904119889119902 =

119871119903120595119904119889119902 minus 119871119898120595119903119889119902

119871 119904119871119903 minus 1198712119898

997904rArr

119889120595119904119889119902

119889119905

= minus119877119904

120590119871 119904

120595119904119889119902 minus119877119904

120590119871119903

120595119903119889119902 minus 119895120596119904120595119904119889119902 + V119904119889119902

(22)

The pole of the new equation is 119904 = minus119877119904120590119871 119904 minus 119895120596119904 Thedamping coefficient is modified to 120572 = minus119877119904120590119871 119904 and forthe studied DFIG it becomes minus256 which is quite greaterthan the previous damping coefficient Therefore in the pro-posed method not only the fault current distributed inmore switches but the damping of the stator flux is also greatlyincreased

6 Simulation Results

In this section the performance of a DFIG wind turbine issimulated under a severe fault condition Simulations arecarried out in PSIM environment to investigate the effects ofswitching As was mentioned in Section 2 according to LVRTstandard of Germany wind turbines must remain connectedto grid following occurrence of grid faults Moreover theymust also inject reactive power to help the grid for voltagerecovery To simulate the fault condition at 119905 = 07 s thegrid voltages are dropped to 02 pu for 300ms as shownin Figure 11 Figure 12 shows the rotor currents in this casewithout any protection For such a severe voltage dip therotor currents are increased to 28 pu In the absence of anytype of protecting method these high currents can damagethe IGBT switches of the IMC Figure 13 shows the rotor


06 07 08 09 1 11 12 13minus15

minus1

minus05

0

05

1

15

Time (s)

Term

inal

vol

tage

(pu)

Figure 11 Grid voltages

06 07 08 09 1 11 12 13minus3

minus2

minus1

0

1

2

3

Time (s)

Roto

r cur

rent

s (pu

)

Figure 12 Rotor currents in fault condition with the controllerdesigned for normal operation

currents when the proposed method is in operation Shortcircuit activation signal is obtained from comparison ofrotor currents with a threshold value In this simulation thethreshold value is set to 15 pu When the rotor current isgreater than the threshold value the short circuit mode isactivated It means that all of the output stage switches areturned on As was mentioned in the previous section herethe high fault currents of the rotor are distributed betweenoutput switches

Figure 14 shows the currents flowing in IGBT switchesin time interval from 119905 = 072 s up to 119905 = 077 s duringactivation of the short circuit mode As shown in Figure 14the currents through all switches are in the safe operatingarea (SOA) Furthermore the duration of short circuit modeis less than 20ms so there is a chance for reactive powerinjection as required by new LVRT standards Short circuitmode activation signal is presented in Figure 13 It impliesthat the short circuit mode will be instantly activated if therotor currents exceed the threshold value The short circuitmode is active only for a short time so for most of thetime during fault the control system of DFIG is in operationto inject reactive power to grid In order to meet the newLVRT standards during fault the references of the active andreactive powers are set to 00 pu and 10 pu respectively Ascan be seen fromFigure 13 injection of 10 pu reactive currentis realized in compliance with LVRT standard

06 07 08 09 1 11 12 13minus3

minus2

minus1

0

1

2

3

Time (s)

r

r(p

u)

rlowast

id

i d

id

(a)

06 07 08 09 1 11 12 13minus3

minus2

minus1

0

1

2

3

Time (s)

Roto

r cur

rent

s (pu

)

(b)

06 07 08 09 1 11 12 13minus05

0

05

1

15

Time (s)

Crow

bar a

ctiv

atio

n sig

nal

(c)

Figure 13 Rotor currents in fault condition with the proposedmethod

7 Conclusion

To enhance the LVRT capability of DFIGwind turbines basedon indirect matrix converters (IMCs) in this paper a newcrowbar system is proposedThis crowbar system is based onusing the existing converter switches in short circuit mode toprotect the IMC against large fault currents Therefore thismethod is interesting as it does not require any additionalhardware Even in severe fault conditions the short circuitmode is active only for short time so the control system can


072 0725 073 0735 074 0745 075 0755 076 0765 077

minus2

0

2

IGBT

curr

ents

(pu)

Time (s)

I1I2I3

I4I5I6

(a)

072 0725 073 0735 074 0745 075 0755 076 0765 077minus05

005

115

Time (s)

Crow

bar s

igna

l

(b)


be in operation at most of the fault duration Therefore thereactive power injection is realized to help voltage recovery inorder to satisfy the new LVRT standards Simulation resultsconfirm the efficiency of the proposed method

Appendix

Parameters of the studied system are as followsWind turbine

119875nom = 15MWBase wind speed = 12msMoment of inertia 12M kgsdotm2

Gearbox11989911198992 = 1100

DFIG119875nom = 15MW 119881nom = 690V119891nom = 50Hz 119877119904 = 103mΩ119877119903 = 828mΩ 119871 119897119904 = 02801mH119871 119897119903 = 01177mH 119871119898 = 2696mH119875 = 6 119869 = 116Kgsdotm2

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] ldquoWorld wind energy report 2010rdquo Tech Rep World WindEnergy Association Bonn Germany 2011 httpwwwwwind-eaorg

[2] T Friedli J W Kolar J Rodriguez and P W Wheeler ldquoCom-parative evaluation of three-phase AC-AC matrix converterand voltage DC-link back-to-back converter systemsrdquo IEEETransactions on Industrial Electronics vol 59 no 12 pp 4487ndash4510 2012

[3] L Wei and T A Lipo ldquoA novel matrix converter topology withsimple commutationrdquo in Proceedings of the 36th IAS AnnualMeeting of Industry Applications Conference vol 3 pp 1749ndash1754 Chicago Ill USA September 2001

[4] G Michalke Variable speed wind turbinesmdashmodeling controland impact on power systems [PhD thesis] Riso National Lab-oratory Roskilde County Denmark 2008

[5] Z Lu J Xinmin andZ Liangyu ldquoAnovel LVRT control strategyof DFIG based rotor active crowbarrdquo in Proceedings of the Asia-Pacific Power and Energy Engineering Conference (APPEEC lsquo11)pp 1ndash6 Wuhan China March 2011

[6] W Maoze X Wei J Hongjie and Y Xinghuo ldquoA novel methodto optimize the active crowbar resistance for low voltage ridethrough operation of doubly-fed induction generator based onwind energyrdquo in Proceedings of the IEEE International Symposi-um on Industrial Electronics (ISIE rsquo12) pp 957ndash962 HangzhouChina May 2012

[7] R Lohde S Jensen A Knop and F W Fuchs ldquoAnalysis ofthree phase grid failure and doubly fed induction generatorride-through using crowbarsrdquo in Proceedings of the EuropeanConference on Power Electronics and Applications pp 1ndash8Aalborg Denmark September 2007

[8] P Ling B Francois and L Yongdong ldquoImproved crowbarcontrol strategy of dfig based wind turbines for grid fault ride-throughrdquo in Proceedings of the 24th Applied Power ElectronicsConference and Exposition (APEC rsquo09) pp 1932ndash1938Washing-ton DC USA February 2009

[9] W Zhang P Zhou and Y He ldquoAnalysis of the by-pass resis-tance of an active crowbar for doubly-fed induction generatorbased wind turbines under grid faultsrdquo in Proceedings of theInternational Conference on Electrical Machines and Systems(ICEMS rsquo08) pp 2316ndash2321 Wuhan China October 2008

[10] J Yang D G Dorrell and J E Fletcher ldquoA new converter pro-tection scheme for doubly-fed induction generators duringdisturbancesrdquo in Proceedings of the 34th Annual Conference ofthe IEEE Industrial Electronics Society (IECON lsquo08) pp 2100ndash2105 Orlando Fla USA November 2008

[11] Z Zhong Y Geng and G Hua ldquoShort circuit current analysisofDFIG-typeWGwith crowbar protection under grid faultsrdquo inProceedings of the IEEE International Symposium on IndustrialElectronics (ISIE lsquo12) pp 1072ndash1079 Hangzhou China May2012

[12] J Zhai B Zhang KWang andW Shao ldquoThree-phase symmet-rical short circuit current characteristic analysis of doubly fedinduction generator with crowbar protectionrdquo in Proceedingsof the IEEE Innovative Smart Grid TechnologiesmdashAsia (ISGTAsia rsquo12) pp 1ndash5 Tianjin China May 2012

[13] X Shuai Y Geng Z Honglin and G Hua ldquoAn LVRT controlstrategy based on flux linkage tracking for DFIG-basedWECSrdquoIEEE Transactions on Industrial Electronics vol 60 no 7 pp2820ndash2832 2013

[14] M Rahimi and M Parniani ldquoEfficient control scheme of windturbines with doubly fed induction generators for low-voltageride-through capability enhancementrdquo IET Renewable PowerGeneration vol 4 no 3 pp 242ndash252 2010

[15] I Esandi X Juankorena J Lopez and L Marroyo ldquoAlter-native protection system for wind turbines with doubly fed


induction generatorrdquo in Proceedings of the 2nd InternationalConference on Power Engineering Energy and Electrical Drives(POWERENG rsquo09) pp 501ndash506 Lisbon Portugal March 2009

[16] M Rahimi and M Parniani ldquoGrid-fault ride-through analysisand control of wind turbines with doubly fed induction genera-torsrdquo Electric Power Systems Research vol 80 no 2 pp 184ndash1952010

[17] F K A Lima A Luna P Rodriguez E H Watanabe and FBlaabjerg ldquoRotor voltage dynamics in the doubly fed inductiongenerator during grid faultsrdquo IEEE Transactions on PowerElectronics vol 25 no 1 pp 118ndash130 2010

[18] J Liang W Qiao and R G Harley ldquoDirect transient controlof wind turbine driven DFIG for low voltage ride-throughrdquo inProceedings of the IEEE Power Electronics andMachines inWindApplications (PEMWA rsquo09) pp 1ndash7 Lincoln Neb USA June2009

[19] X Shuai G Hua Z Honglin and Y Geng ldquoAnalysis of thecontrol limit for rotor-side converter of doubly fed inductiongenerator-based wind energy conversion system under variousvoltage dipsrdquo Renewable Power Generation vol 7 no 1 pp 71ndash81 2013

[20] O Gomis-Bellmunt A Junyent-Ferre A Sumper and JBergas-Jane ldquoRide-through control of a doubly fed inductiongenerator under unbalanced voltage sagsrdquo IEEE Transactions onEnergy Conversion vol 23 no 4 pp 1036ndash1045 2008

[21] Y Zhou P Bauer J A Ferreira and J Pierik ldquoOperation of grid-connected DFIG under unbalanced grid voltage conditionrdquoIEEE Transactions on Energy Conversion vol 24 no 1 pp 240ndash246 2009

[22] D Li and H Zhang ldquoA combined protection and control strat-egy to enhance the LVRT capability of a wind turbine drivenby DFIGrdquo in Proceedings of the 2nd IEEE International Sympo-sium on Power Electronics for Distributed Generation Systems(PEDG rsquo10) pp 703ndash707 Hefei China June 2010

[23] L Qicheng and L Yuping ldquoAn integration of super capacitorstorage research for improving low-voltage-ride-through inpower grid with wind turbinerdquo in Proceedings of the Asia-PacificPower and Energy Engineering Conference (APPEEC rsquo12) pp 1ndash4 Shanghai China March 2012

[24] W Guo L Xiao and S Dai ldquoEnhancing low-voltage ride-through capability and smoothing output power of DFIGwith asuperconducting fault-current limiterndashmagnetic energy storagesystemrdquo IEEE Transactions on Energy Conversion vol 27 no 2pp 277ndash295 2012

[25] A Chakraborty S K Musunuri A K Srivastava and A KKondabathini ldquoIntegrating statcom and battery energy storagesystem for power system transient stability a review andapplicationrdquoAdvances in Power Electronics vol 2012 Article ID676010 12 pages 2012

[26] K Ibrahima andC Zhao ldquoModeling of wind energy conversionsystem using doubly fed induction generator equipped batteriesenergy storage systemrdquo in Proceedings of the 4th InternationalConference on Electric Utility Deregulation and Restructuringand Power Technologies (DRPT rsquo11) pp 1780ndash1787 WeihaiChina July 2011

[27] E Reyes R Pena R Cardenas P Wheeler J Clare and RBlasco-Gimenez ldquoApplication of indirect matrix converters tovariable speed doubly fed induction generatorsrdquo in Proceedingsof the 39th IEEE Annual Power Electronics Specialists Conference(PESC rsquo08) pp 2698ndash2703 Rhodes Greece June 2008

[28] J Amini R Kazemzahed and H Madadi Kojabadi ldquoPerfor-mance enhancement of indirectmatrix converter based variable

speed Doubly-fed induction generatorrdquo in Proceedings of the1st Power Electronic amp Drive Systems amp Technologies Conference(PEDSTC rsquo10) pp 450ndash455 Tehran Iran February 2010

[29] E Reyes R Pena R Cardenas J Clare andPWheeler ldquoControlof a doubly-fed induction generator with an indirect matrixconverter with changing DC voltagerdquo in Proceedings of the IEEEInternational Symposium on Industrial Electronics (ISIE rsquo10) pp1230ndash1235 Bari Italy July 2010

[30] W Deng Z Chen L Zhou and Y Yang ldquoResearch on the per-formance of low voltage ride-through for doubly fed inductiongenerator excited by two-stagematrix converterrdquo in Proceedingsof the IEEE 6th International Power Electronics and MotionControl Conference (IPEMC rsquo09) pp 638ndash643 Wuhan ChinaMay 2009

[31] G D Marques and D M e Sousa ldquoA new sensorless MRASbased on active power calculations for rotor position estimationof a DFIGrdquo Advances in Power Electronics vol 2011 Article ID970364 8 pages 2011

[32] J DrsquoAtre A Klodowski A Ritter et al ldquoSystem and method forpower control in wind turbinerdquo US Patent 0024059 2007

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



DFIG

Supply

WindGear Box

sim

Figure 1 Wind Turbine based on the DFIG excited by indirect ma-trix converter

increased capacity of wind powers in the power systems overthe years the sudden loss of wind turbines during the gridfaults resulting from turbines disconnection could generatecontrol problems of frequency and voltage in the system soleading to the voltage collapse in worst cases The increasedpenetration of wind energy into the power system over thelast decade has therefore led to a serious concern about itsinfluence on the dynamic behavior of the power system Tohandle this issue the grid codes are revised by system opera-tors in several countries [4] According to the new grid codesthe wind turbines must be remain connected to the networkon the occurrence of grid faults and tolerate the resultingvoltage drops This feature is known as the low voltageride-through (LVRT) capability of a power plant The LVRTrequirement defines a specific voltage profile with limitingcurves depending on the grid voltage dip depth Moreoverin some grid codes such as Germany wind turbines shouldalso inject reactive power to help the grid voltage recovery

Because of direct connection of stator winding to thegrid and the small rating of power electronic converter inthe rotor side DFIG based wind turbine is very sensitiveto grid disturbances especially to voltage dips during gridfaults Grid faults even those occurring far from the windturbines can cause voltage drops at the point of wind turbineconnection The abrupt drop of the grid voltage will makean increase in the current of stator windings of the DFIGBecause of the magnetic coupling between stator and rotorthis current will also flow in the rotor circuit and the powerconverter At present the back-to-back converter is the mostfrequently used power electronic converter in the windturbines industryTherefore the most of research works havebeen done to enhance the LVRT ability of DFIG utilizing thistype of converters So the grid faults cause over current inthe rotor windings and over voltage in the dc-link capacitorhence the proper protection should be provided to safekeepthe converter Various solutions have been proposed to solvethe problem Some of them are briefly reviewed as follows

The most popular and reliable method is based on theuse of a protective circuit known as crowbar The crowbarconsists of resistors connected to the rotorwindings bymeansof electronic switches In active crowbar the switches arecontrollable such as IGBTs whereas in passive one they areantiparallel thyristors The active crowbar allows openingthe circuit when the currents reach safe region The passivecrowbar allows closing the circuit but not opening it until

the crowbar currents reach zero Therefore according to thenew grid codes the passive crowbar is not appropriate forthe modern wind turbines When a fault occurs the rotorwindings get connected to the crowbar while the converteris tripped Several papers have discussed the implementationand control of crowbar [5ndash12] Different types of crowbarsrealization are shown in Figure 2The crowbar can effectivelyprotect the rotor converter under serious grid faults But itsmain drawback is that when the crowbar is activated therotor converter cannot control the active and reactive powerduring crowbar activation so the DFIG operates as a cageinduction generator absorbing extra reactive power from thegrid and deteriorates the grid voltage profile

Another approach is to modify the rotor-side convertercontrol system to limit the fault currents without using anyextra hardware circuit [13ndash21] In this method at seriousgrid faults the required voltage in the rotor-side converterbecomes too large and exceeds its voltage capability There-fore the rotor current greatly increases thus leading toconverter destructionThismethod is beneficial as it does notrequire any additional hardware but it is suitable formoderatefaults

Another solution for LVRT is to use an additional energystorage system (ESS) connected to the dc link [22ndash26] TheESS can balance the extra power that goes through the rotorcircuit during a grid fault transient but it also requires a rotorside converter with higher current ratings having extra costand more system complexity

Utilizing matrix converters in DFIG wind turbines is stillin research phase Most of the works have dealt with theirnormal operation [27ndash30] The control of a DFIG using anindirect matrix converter for dynamic performance evalua-tion under normal grid condition is presented in [27] Sigma-delta modulator to control IMC switches of DFIG basedWT is proposed in [28] By using this modulation methodtorque pulsations and harmonic content of currents arereducedTherefore the power quality ofWT is improvedThecapability of the input converter to generate different virtualdc-link voltage levels is also proposed in [29] This methodreduces both the commutation losses of output converterand common mode voltage Due to small voltage requiredaround the synchronous speed this strategy is suitable inDFIG applications

Dynamic performance of DFIG using two-stage IMCunder voltage dip condition has been discussed in [30] with-out providing any protection As simulation results show for80 terminal voltage sag the stator current reaches 25 puWithout any protection method this high current coulddamage the IGBT switches of the IMC According to newLVRT standards the reactive power injection to the grid ismandatory to improve the voltage recovery Results of [30]indicate that during the fault about 07 pu reactive poweris absorbed from the grid which makes the voltage deeperTherefore the existing controller which is designed for nor-mal operating condition is ineffective during fault conditions

To solve these drawbacks and satisfy the new LVRTstandards in present paper a new method is proposed toprotect the IMC with DFIG following the grid faults In thismethod a new short circuit mode is proposed to control


DFIG

sim

sim =

=

(a)

DFIG

sim

sim =

=

(b)

DFIG

sim

sim=

=

(c)




2 LVRT Requirement



70

45

15

0 150 700 1500



UU

N(

)








119875 =1

2

119860 sdot 120588 sdot 119862119901 (120582 120573) sdot V3

120596 (1)


120582 =119877Ω119905

V120596 (2)



V119904119889119902 = 119877119904119894119904119889119902 +

119889120595119904119889119902

119889119905

+ 119895120596119904120595119904119889119902

V119903119889119902 = 119877119903119894119903119889119902 +

119889120595119903119889119902

119889119905

+ 119895 (120596119904 minus 120596119903) 120595119903119889119902

119879119890119898 =119901

2

(120595119903119902119894119903119889 minus 120595119903119889119894119903119902)

(3)

120595119904119889119902 = 119871 119904119894119904119889119902 + 119871119898119894119903119889119902

120595119903119889119902 = 119871119898119894119904119889119902 + 119871119903119894119903119889119902

119871 119904 = 119871 119897119904 + 119871119898

119871119903 = 119871 119897119903 + 119871119898

(4)





V119886 = 119881119898 cos 120579119886 = 119881119898 cos (120596119894119905)

V119887 = 119881119898 cos 120579119887 = 119881119898 cos(120596119894119905 minus2120587

3

)

V119888 = 119881119898 cos 120579119888 = 119881119898 cos(120596119894119905 +2120587

3

)

(5)


119868119886 = 119868119898 cos (120596119894119905)

119868119887 = 119868119898 cos(120596119894119905 minus2120587

3

)

119868119888 = 119868119898 cos(120596119894119905 +2120587

3

)

(6)




C

B

Aa

bc

P

N


23

4

5 6

1

Vb

Vc

Va

I3(bc)

I2(ac)

I1(ab)

I6(cb)

I5(ca)

I4(ba)

120579ref

Iref




119894119886 = (119889119886119887 + 119889119886119888) 119894119889119888 119894119887 = minus119889119886119887119894119889119888 119894119888 = minus119889119886119888119894119889119888 (7)


119889119886119887 + 119889119886119888 = 1 997904rArr 119894119886 = 119894119889119888 (8)


119889119886119887 = minus119894119887

119894119886

119889119886119888 = minus119894119888

119894119886

(9)


119881119889119888 =3 sdot 119881119898

2 sdot1003816100381610038161003816cos (120579in)

1003816100381610038161003816

1003816100381610038161003816cos (120579in)

1003816100381610038161003816= max (1003816100381610038161003816cos (120579119886)

10038161003816100381610038161003816100381610038161003816cos (120579119887)

10038161003816100381610038161003816100381610038161003816cos (120579119888)

1003816100381610038161003816)

(10)





119896 =

2 sdot1003816100381610038161003816cos (120579in)

1003816100381610038161003816sdot 119903

radic3 sdot 119881119898

(12)


119889120572120574 = 119889120574 sdot 119889120572 119889120573120574 = 119889120574 sdot 119889120573

119889120572120575 = 119889120575 sdot 119889120572 119889120573120575 = 119889120575 sdot 119889120573

(13)


1198890 = 1 minus (119889120574 + 119889120575) sdot (119889120572 + 119889120573)

1198890120574 =

119889120574

(119889120574 + 119889120575)

1198890 1198890120575 =119889120575

(119889120574 + 119889120575)

1198890

(14)





2

3

4

5

6

1120579ref

V3(010)

V1(100)

V4(011)

V5(001)

V6(101)

V2(110)

Vref

VA

VB

VC


120574R 120575R

0120574

2

0120574

2

0120575

2

0120575

2120573120574 120573120575 120572120575120572120574In

vRe

c

Ts

tcom



120595119904 = 120595119904119889 0 = 120595119904119902 (15)


119894119889119904 =1

119871 119904

(120595119904 minus 119871119898119894119889119903) 119894119902119904 = minus119871119898

119871 119904

119894119902119903

120595119889119903 = 120590119871119903119894119889119903 +119871119898

119871 119904

120595119904 120595119902119903 = 120590119871119903119894119902119903 120590 = 1 minus

1198712

119898

119871 119904119871119903

(16)


V119889119903 = 119877119903119894119889119903 +119889

119889119905

(120590119871119903119894119889119903 +119871119898

119871 119904

120595119904) minus (120596119904 minus 120596119903) (120590119871119903119894119902119903)

V119902119903 = 119877119903119894119902119903 +119889

119889119905

(120590119871119903119894119902119903) + (120596119904 minus 120596119903) (120590119871119903119894119889119903 +119871119898

119871 119904

120595119904)

(17)

0002 0004 0006 0008 001 0012 0014 0016 0018 0020

200

400

600

800

1000

1200

Time (s)

Volta

ges (

V)

VdcVabVbcVca

VbaVcbVca



119875119904 =3

2

(V119889119904119894119889119904 + V119902119904119894119902119904) 119876119904 =3

2

(V119902119904119894119889119904 minus V119889119904119894119902119904) (18)


119881119904 = V119902119904 0 = V1198891199041003816100381610038161003816119881119904

1003816100381610038161003816≃ 120596119904

1003816100381610038161003816120595119904

1003816100381610038161003816 (19)


119875119904 =3

2

V119889119904119894119889119904 = minus3

2

119881119904

119871119898

119871 119904

119894119902119903

119876119904 =3

2

V119902119904119894119889119904 =3119881119904

2119871 119904

(120595119904 minus 119871119898119894119889119903)

(20)





DFIG

Stator

PI

PI

fluxcalculation

MatrixconverterSV

M

MPPT

23

23

23

+

+

+

+

+

+

++ minus

minus

minus

minus

120595s

120579s

120596s

120596r120596slip

i120572si120573s120572s120573s

abs bcs

ias ibs

120579r

120579slip = 120579s minus 120579r

ddt

i120572r iar ibr

i120573ridr

idrlowast

iqrlowast

iqr

dr

dr998400

qr

qr998400

120573r

120572r

Plowasts

Qlowasts

eminusj120579slip

ej120579slip

Vwind or 120596r


3

2Vs

Lm

Ls

iqrlowast


Ls

120595s)

Qlowasts = minus

3Vs2Ls







119894119904119889119902 =

120595119904119889119902

119871 119904

997904rArr

119889120595119904119889119902

119889119905

= minus119877119904

119871 119904

120595119904119889119902 minus 119895120596119904120595119904119889119902 + V119904119889119902 (21)



[0 0 0 0 0 0]

[1 1 1 1 1 1]

DFIG

Supply

Rec gatepluses

Inv gatepluses

SVMmodulation

Referencegeneration

from PIcontrollers

Comparator


Mode selector

1

1

0

0Vd

Vq

Iar

Ibr

Icr

IarIbrIcr

gt

sim

MaxIar Ibr Icr



119894119904119889119902 =

119871119903120595119904119889119902 minus 119871119898120595119903119889119902

119871 119904119871119903 minus 1198712119898

997904rArr

119889120595119904119889119902

119889119905

= minus119877119904

120590119871 119904

120595119904119889119902 minus119877119904

120590119871119903

120595119903119889119902 minus 119895120596119904120595119904119889119902 + V119904119889119902

(22)





06 07 08 09 1 11 12 13minus15

minus1

minus05

0

05

1

15

Time (s)

Term

inal

vol

tage

(pu)


06 07 08 09 1 11 12 13minus3

minus2

minus1

0

1

2

3

Time (s)

Roto

r cur

rent

s (pu

)




06 07 08 09 1 11 12 13minus3

minus2

minus1

0

1

2

3

Time (s)

r

r(p

u)

rlowast

id

i d

id

(a)

06 07 08 09 1 11 12 13minus3

minus2

minus1

0

1

2

3

Time (s)

Roto

r cur

rent

s (pu

)

(b)

06 07 08 09 1 11 12 13minus05

0

05

1

15

Time (s)

Crow

bar a

ctiv

atio

n sig

nal

(c)


7 Conclusion



072 0725 073 0735 074 0745 075 0755 076 0765 077

minus2

0

2

IGBT

curr

ents

(pu)

Time (s)

I1I2I3

I4I5I6

(a)

072 0725 073 0735 074 0745 075 0755 076 0765 077minus05

005

115

Time (s)

Crow

bar s

igna

l

(b)



Appendix



Gearbox11989911198992 = 1100




References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










DFIG

sim

sim =

=

(a)

DFIG

sim

sim =

=

(b)

DFIG

sim

sim=

=

(c)




2 LVRT Requirement



70

45

15

0 150 700 1500



UU

N(

)








119875 =1

2

119860 sdot 120588 sdot 119862119901 (120582 120573) sdot V3

120596 (1)


120582 =119877Ω119905

V120596 (2)



V119904119889119902 = 119877119904119894119904119889119902 +

119889120595119904119889119902

119889119905

+ 119895120596119904120595119904119889119902

V119903119889119902 = 119877119903119894119903119889119902 +

119889120595119903119889119902

119889119905

+ 119895 (120596119904 minus 120596119903) 120595119903119889119902

119879119890119898 =119901

2

(120595119903119902119894119903119889 minus 120595119903119889119894119903119902)

(3)

120595119904119889119902 = 119871 119904119894119904119889119902 + 119871119898119894119903119889119902

120595119903119889119902 = 119871119898119894119904119889119902 + 119871119903119894119903119889119902

119871 119904 = 119871 119897119904 + 119871119898

119871119903 = 119871 119897119903 + 119871119898

(4)





V119886 = 119881119898 cos 120579119886 = 119881119898 cos (120596119894119905)

V119887 = 119881119898 cos 120579119887 = 119881119898 cos(120596119894119905 minus2120587

3

)

V119888 = 119881119898 cos 120579119888 = 119881119898 cos(120596119894119905 +2120587

3

)

(5)


119868119886 = 119868119898 cos (120596119894119905)

119868119887 = 119868119898 cos(120596119894119905 minus2120587

3

)

119868119888 = 119868119898 cos(120596119894119905 +2120587

3

)

(6)




C

B

Aa

bc

P

N


23

4

5 6

1

Vb

Vc

Va

I3(bc)

I2(ac)

I1(ab)

I6(cb)

I5(ca)

I4(ba)

120579ref

Iref




119894119886 = (119889119886119887 + 119889119886119888) 119894119889119888 119894119887 = minus119889119886119887119894119889119888 119894119888 = minus119889119886119888119894119889119888 (7)


119889119886119887 + 119889119886119888 = 1 997904rArr 119894119886 = 119894119889119888 (8)


119889119886119887 = minus119894119887

119894119886

119889119886119888 = minus119894119888

119894119886

(9)


119881119889119888 =3 sdot 119881119898

2 sdot1003816100381610038161003816cos (120579in)

1003816100381610038161003816

1003816100381610038161003816cos (120579in)

1003816100381610038161003816= max (1003816100381610038161003816cos (120579119886)

10038161003816100381610038161003816100381610038161003816cos (120579119887)

10038161003816100381610038161003816100381610038161003816cos (120579119888)

1003816100381610038161003816)

(10)





119896 =

2 sdot1003816100381610038161003816cos (120579in)

1003816100381610038161003816sdot 119903

radic3 sdot 119881119898

(12)


119889120572120574 = 119889120574 sdot 119889120572 119889120573120574 = 119889120574 sdot 119889120573

119889120572120575 = 119889120575 sdot 119889120572 119889120573120575 = 119889120575 sdot 119889120573

(13)


1198890 = 1 minus (119889120574 + 119889120575) sdot (119889120572 + 119889120573)

1198890120574 =

119889120574

(119889120574 + 119889120575)

1198890 1198890120575 =119889120575

(119889120574 + 119889120575)

1198890

(14)





2

3

4

5

6

1120579ref

V3(010)

V1(100)

V4(011)

V5(001)

V6(101)

V2(110)

Vref

VA

VB

VC


120574R 120575R

0120574

2

0120574

2

0120575

2

0120575

2120573120574 120573120575 120572120575120572120574In

vRe

c

Ts

tcom



120595119904 = 120595119904119889 0 = 120595119904119902 (15)


119894119889119904 =1

119871 119904

(120595119904 minus 119871119898119894119889119903) 119894119902119904 = minus119871119898

119871 119904

119894119902119903

120595119889119903 = 120590119871119903119894119889119903 +119871119898

119871 119904

120595119904 120595119902119903 = 120590119871119903119894119902119903 120590 = 1 minus

1198712

119898

119871 119904119871119903

(16)


V119889119903 = 119877119903119894119889119903 +119889

119889119905

(120590119871119903119894119889119903 +119871119898

119871 119904

120595119904) minus (120596119904 minus 120596119903) (120590119871119903119894119902119903)

V119902119903 = 119877119903119894119902119903 +119889

119889119905

(120590119871119903119894119902119903) + (120596119904 minus 120596119903) (120590119871119903119894119889119903 +119871119898

119871 119904

120595119904)

(17)

0002 0004 0006 0008 001 0012 0014 0016 0018 0020

200

400

600

800

1000

1200

Time (s)

Volta

ges (

V)

VdcVabVbcVca

VbaVcbVca



119875119904 =3

2

(V119889119904119894119889119904 + V119902119904119894119902119904) 119876119904 =3

2

(V119902119904119894119889119904 minus V119889119904119894119902119904) (18)


119881119904 = V119902119904 0 = V1198891199041003816100381610038161003816119881119904

1003816100381610038161003816≃ 120596119904

1003816100381610038161003816120595119904

1003816100381610038161003816 (19)


119875119904 =3

2

V119889119904119894119889119904 = minus3

2

119881119904

119871119898

119871 119904

119894119902119903

119876119904 =3

2

V119902119904119894119889119904 =3119881119904

2119871 119904

(120595119904 minus 119871119898119894119889119903)

(20)





DFIG

Stator

PI

PI

fluxcalculation

MatrixconverterSV

M

MPPT

23

23

23

+

+

+

+

+

+

++ minus

minus

minus

minus

120595s

120579s

120596s

120596r120596slip

i120572si120573s120572s120573s

abs bcs

ias ibs

120579r

120579slip = 120579s minus 120579r

ddt

i120572r iar ibr

i120573ridr

idrlowast

iqrlowast

iqr

dr

dr998400

qr

qr998400

120573r

120572r

Plowasts

Qlowasts

eminusj120579slip

ej120579slip

Vwind or 120596r


3

2Vs

Lm

Ls

iqrlowast


Ls

120595s)

Qlowasts = minus

3Vs2Ls







119894119904119889119902 =

120595119904119889119902

119871 119904

997904rArr

119889120595119904119889119902

119889119905

= minus119877119904

119871 119904

120595119904119889119902 minus 119895120596119904120595119904119889119902 + V119904119889119902 (21)



[0 0 0 0 0 0]

[1 1 1 1 1 1]

DFIG

Supply

Rec gatepluses

Inv gatepluses

SVMmodulation

Referencegeneration

from PIcontrollers

Comparator


Mode selector

1

1

0

0Vd

Vq

Iar

Ibr

Icr

IarIbrIcr

gt

sim

MaxIar Ibr Icr



119894119904119889119902 =

119871119903120595119904119889119902 minus 119871119898120595119903119889119902

119871 119904119871119903 minus 1198712119898

997904rArr

119889120595119904119889119902

119889119905

= minus119877119904

120590119871 119904

120595119904119889119902 minus119877119904

120590119871119903

120595119903119889119902 minus 119895120596119904120595119904119889119902 + V119904119889119902

(22)





06 07 08 09 1 11 12 13minus15

minus1

minus05

0

05

1

15

Time (s)

Term

inal

vol

tage

(pu)


06 07 08 09 1 11 12 13minus3

minus2

minus1

0

1

2

3

Time (s)

Roto

r cur

rent

s (pu

)




06 07 08 09 1 11 12 13minus3

minus2

minus1

0

1

2

3

Time (s)

r

r(p

u)

rlowast

id

i d

id

(a)

06 07 08 09 1 11 12 13minus3

minus2

minus1

0

1

2

3

Time (s)

Roto

r cur

rent

s (pu

)

(b)

06 07 08 09 1 11 12 13minus05

0

05

1

15

Time (s)

Crow

bar a

ctiv

atio

n sig

nal

(c)


7 Conclusion



072 0725 073 0735 074 0745 075 0755 076 0765 077

minus2

0

2

IGBT

curr

ents

(pu)

Time (s)

I1I2I3

I4I5I6

(a)

072 0725 073 0735 074 0745 075 0755 076 0765 077minus05

005

115

Time (s)

Crow

bar s

igna

l

(b)



Appendix



Gearbox11989911198992 = 1100




References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119875 =1

2

119860 sdot 120588 sdot 119862119901 (120582 120573) sdot V3

120596 (1)


120582 =119877Ω119905

V120596 (2)



V119904119889119902 = 119877119904119894119904119889119902 +

119889120595119904119889119902

119889119905

+ 119895120596119904120595119904119889119902

V119903119889119902 = 119877119903119894119903119889119902 +

119889120595119903119889119902

119889119905

+ 119895 (120596119904 minus 120596119903) 120595119903119889119902

119879119890119898 =119901

2

(120595119903119902119894119903119889 minus 120595119903119889119894119903119902)

(3)

120595119904119889119902 = 119871 119904119894119904119889119902 + 119871119898119894119903119889119902

120595119903119889119902 = 119871119898119894119904119889119902 + 119871119903119894119903119889119902

119871 119904 = 119871 119897119904 + 119871119898

119871119903 = 119871 119897119903 + 119871119898

(4)





V119886 = 119881119898 cos 120579119886 = 119881119898 cos (120596119894119905)

V119887 = 119881119898 cos 120579119887 = 119881119898 cos(120596119894119905 minus2120587

3

)

V119888 = 119881119898 cos 120579119888 = 119881119898 cos(120596119894119905 +2120587

3

)

(5)


119868119886 = 119868119898 cos (120596119894119905)

119868119887 = 119868119898 cos(120596119894119905 minus2120587

3

)

119868119888 = 119868119898 cos(120596119894119905 +2120587

3

)

(6)




C

B

Aa

bc

P

N


23

4

5 6

1

Vb

Vc

Va

I3(bc)

I2(ac)

I1(ab)

I6(cb)

I5(ca)

I4(ba)

120579ref

Iref




119894119886 = (119889119886119887 + 119889119886119888) 119894119889119888 119894119887 = minus119889119886119887119894119889119888 119894119888 = minus119889119886119888119894119889119888 (7)


119889119886119887 + 119889119886119888 = 1 997904rArr 119894119886 = 119894119889119888 (8)


119889119886119887 = minus119894119887

119894119886

119889119886119888 = minus119894119888

119894119886

(9)


119881119889119888 =3 sdot 119881119898

2 sdot1003816100381610038161003816cos (120579in)

1003816100381610038161003816

1003816100381610038161003816cos (120579in)

1003816100381610038161003816= max (1003816100381610038161003816cos (120579119886)

10038161003816100381610038161003816100381610038161003816cos (120579119887)

10038161003816100381610038161003816100381610038161003816cos (120579119888)

1003816100381610038161003816)

(10)





119896 =

2 sdot1003816100381610038161003816cos (120579in)

1003816100381610038161003816sdot 119903

radic3 sdot 119881119898

(12)


119889120572120574 = 119889120574 sdot 119889120572 119889120573120574 = 119889120574 sdot 119889120573

119889120572120575 = 119889120575 sdot 119889120572 119889120573120575 = 119889120575 sdot 119889120573

(13)


1198890 = 1 minus (119889120574 + 119889120575) sdot (119889120572 + 119889120573)

1198890120574 =

119889120574

(119889120574 + 119889120575)

1198890 1198890120575 =119889120575

(119889120574 + 119889120575)

1198890

(14)





2

3

4

5

6

1120579ref

V3(010)

V1(100)

V4(011)

V5(001)

V6(101)

V2(110)

Vref

VA

VB

VC


120574R 120575R

0120574

2

0120574

2

0120575

2

0120575

2120573120574 120573120575 120572120575120572120574In

vRe

c

Ts

tcom



120595119904 = 120595119904119889 0 = 120595119904119902 (15)


119894119889119904 =1

119871 119904

(120595119904 minus 119871119898119894119889119903) 119894119902119904 = minus119871119898

119871 119904

119894119902119903

120595119889119903 = 120590119871119903119894119889119903 +119871119898

119871 119904

120595119904 120595119902119903 = 120590119871119903119894119902119903 120590 = 1 minus

1198712

119898

119871 119904119871119903

(16)


V119889119903 = 119877119903119894119889119903 +119889

119889119905

(120590119871119903119894119889119903 +119871119898

119871 119904

120595119904) minus (120596119904 minus 120596119903) (120590119871119903119894119902119903)

V119902119903 = 119877119903119894119902119903 +119889

119889119905

(120590119871119903119894119902119903) + (120596119904 minus 120596119903) (120590119871119903119894119889119903 +119871119898

119871 119904

120595119904)

(17)

0002 0004 0006 0008 001 0012 0014 0016 0018 0020

200

400

600

800

1000

1200

Time (s)

Volta

ges (

V)

VdcVabVbcVca

VbaVcbVca



119875119904 =3

2

(V119889119904119894119889119904 + V119902119904119894119902119904) 119876119904 =3

2

(V119902119904119894119889119904 minus V119889119904119894119902119904) (18)


119881119904 = V119902119904 0 = V1198891199041003816100381610038161003816119881119904

1003816100381610038161003816≃ 120596119904

1003816100381610038161003816120595119904

1003816100381610038161003816 (19)


119875119904 =3

2

V119889119904119894119889119904 = minus3

2

119881119904

119871119898

119871 119904

119894119902119903

119876119904 =3

2

V119902119904119894119889119904 =3119881119904

2119871 119904

(120595119904 minus 119871119898119894119889119903)

(20)





DFIG

Stator

PI

PI

fluxcalculation

MatrixconverterSV

M

MPPT

23

23

23

+

+

+

+

+

+

++ minus

minus

minus

minus

120595s

120579s

120596s

120596r120596slip

i120572si120573s120572s120573s

abs bcs

ias ibs

120579r

120579slip = 120579s minus 120579r

ddt

i120572r iar ibr

i120573ridr

idrlowast

iqrlowast

iqr

dr

dr998400

qr

qr998400

120573r

120572r

Plowasts

Qlowasts

eminusj120579slip

ej120579slip

Vwind or 120596r


3

2Vs

Lm

Ls

iqrlowast


Ls

120595s)

Qlowasts = minus

3Vs2Ls







119894119904119889119902 =

120595119904119889119902

119871 119904

997904rArr

119889120595119904119889119902

119889119905

= minus119877119904

119871 119904

120595119904119889119902 minus 119895120596119904120595119904119889119902 + V119904119889119902 (21)



[0 0 0 0 0 0]

[1 1 1 1 1 1]

DFIG

Supply

Rec gatepluses

Inv gatepluses

SVMmodulation

Referencegeneration

from PIcontrollers

Comparator


Mode selector

1

1

0

0Vd

Vq

Iar

Ibr

Icr

IarIbrIcr

gt

sim

MaxIar Ibr Icr



119894119904119889119902 =

119871119903120595119904119889119902 minus 119871119898120595119903119889119902

119871 119904119871119903 minus 1198712119898

997904rArr

119889120595119904119889119902

119889119905

= minus119877119904

120590119871 119904

120595119904119889119902 minus119877119904

120590119871119903

120595119903119889119902 minus 119895120596119904120595119904119889119902 + V119904119889119902

(22)





06 07 08 09 1 11 12 13minus15

minus1

minus05

0

05

1

15

Time (s)

Term

inal

vol

tage

(pu)


06 07 08 09 1 11 12 13minus3

minus2

minus1

0

1

2

3

Time (s)

Roto

r cur

rent

s (pu

)




06 07 08 09 1 11 12 13minus3

minus2

minus1

0

1

2

3

Time (s)

r

r(p

u)

rlowast

id

i d

id

(a)

06 07 08 09 1 11 12 13minus3

minus2

minus1

0

1

2

3

Time (s)

Roto

r cur

rent

s (pu

)

(b)

06 07 08 09 1 11 12 13minus05

0

05

1

15

Time (s)

Crow

bar a

ctiv

atio

n sig

nal

(c)


7 Conclusion



072 0725 073 0735 074 0745 075 0755 076 0765 077

minus2

0

2

IGBT

curr

ents

(pu)

Time (s)

I1I2I3

I4I5I6

(a)

072 0725 073 0735 074 0745 075 0755 076 0765 077minus05

005

115

Time (s)

Crow

bar s

igna

l

(b)



Appendix



Gearbox11989911198992 = 1100




References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










C

B

Aa

bc

P

N


23

4

5 6

1

Vb

Vc

Va

I3(bc)

I2(ac)

I1(ab)

I6(cb)

I5(ca)

I4(ba)

120579ref

Iref




119894119886 = (119889119886119887 + 119889119886119888) 119894119889119888 119894119887 = minus119889119886119887119894119889119888 119894119888 = minus119889119886119888119894119889119888 (7)


119889119886119887 + 119889119886119888 = 1 997904rArr 119894119886 = 119894119889119888 (8)


119889119886119887 = minus119894119887

119894119886

119889119886119888 = minus119894119888

119894119886

(9)


119881119889119888 =3 sdot 119881119898

2 sdot1003816100381610038161003816cos (120579in)

1003816100381610038161003816

1003816100381610038161003816cos (120579in)

1003816100381610038161003816= max (1003816100381610038161003816cos (120579119886)

10038161003816100381610038161003816100381610038161003816cos (120579119887)

10038161003816100381610038161003816100381610038161003816cos (120579119888)

1003816100381610038161003816)

(10)





119896 =

2 sdot1003816100381610038161003816cos (120579in)

1003816100381610038161003816sdot 119903

radic3 sdot 119881119898

(12)


119889120572120574 = 119889120574 sdot 119889120572 119889120573120574 = 119889120574 sdot 119889120573

119889120572120575 = 119889120575 sdot 119889120572 119889120573120575 = 119889120575 sdot 119889120573

(13)


1198890 = 1 minus (119889120574 + 119889120575) sdot (119889120572 + 119889120573)

1198890120574 =

119889120574

(119889120574 + 119889120575)

1198890 1198890120575 =119889120575

(119889120574 + 119889120575)

1198890

(14)





2

3

4

5

6

1120579ref

V3(010)

V1(100)

V4(011)

V5(001)

V6(101)

V2(110)

Vref

VA

VB

VC


120574R 120575R

0120574

2

0120574

2

0120575

2

0120575

2120573120574 120573120575 120572120575120572120574In

vRe

c

Ts

tcom



120595119904 = 120595119904119889 0 = 120595119904119902 (15)


119894119889119904 =1

119871 119904

(120595119904 minus 119871119898119894119889119903) 119894119902119904 = minus119871119898

119871 119904

119894119902119903

120595119889119903 = 120590119871119903119894119889119903 +119871119898

119871 119904

120595119904 120595119902119903 = 120590119871119903119894119902119903 120590 = 1 minus

1198712

119898

119871 119904119871119903

(16)


V119889119903 = 119877119903119894119889119903 +119889

119889119905

(120590119871119903119894119889119903 +119871119898

119871 119904

120595119904) minus (120596119904 minus 120596119903) (120590119871119903119894119902119903)

V119902119903 = 119877119903119894119902119903 +119889

119889119905

(120590119871119903119894119902119903) + (120596119904 minus 120596119903) (120590119871119903119894119889119903 +119871119898

119871 119904

120595119904)

(17)

0002 0004 0006 0008 001 0012 0014 0016 0018 0020

200

400

600

800

1000

1200

Time (s)

Volta

ges (

V)

VdcVabVbcVca

VbaVcbVca



119875119904 =3

2

(V119889119904119894119889119904 + V119902119904119894119902119904) 119876119904 =3

2

(V119902119904119894119889119904 minus V119889119904119894119902119904) (18)


119881119904 = V119902119904 0 = V1198891199041003816100381610038161003816119881119904

1003816100381610038161003816≃ 120596119904

1003816100381610038161003816120595119904

1003816100381610038161003816 (19)


119875119904 =3

2

V119889119904119894119889119904 = minus3

2

119881119904

119871119898

119871 119904

119894119902119903

119876119904 =3

2

V119902119904119894119889119904 =3119881119904

2119871 119904

(120595119904 minus 119871119898119894119889119903)

(20)





DFIG

Stator

PI

PI

fluxcalculation

MatrixconverterSV

M

MPPT

23

23

23

+

+

+

+

+

+

++ minus

minus

minus

minus

120595s

120579s

120596s

120596r120596slip

i120572si120573s120572s120573s

abs bcs

ias ibs

120579r

120579slip = 120579s minus 120579r

ddt

i120572r iar ibr

i120573ridr

idrlowast

iqrlowast

iqr

dr

dr998400

qr

qr998400

120573r

120572r

Plowasts

Qlowasts

eminusj120579slip

ej120579slip

Vwind or 120596r


3

2Vs

Lm

Ls

iqrlowast


Ls

120595s)

Qlowasts = minus

3Vs2Ls







119894119904119889119902 =

120595119904119889119902

119871 119904

997904rArr

119889120595119904119889119902

119889119905

= minus119877119904

119871 119904

120595119904119889119902 minus 119895120596119904120595119904119889119902 + V119904119889119902 (21)



[0 0 0 0 0 0]

[1 1 1 1 1 1]

DFIG

Supply

Rec gatepluses

Inv gatepluses

SVMmodulation

Referencegeneration

from PIcontrollers

Comparator


Mode selector

1

1

0

0Vd

Vq

Iar

Ibr

Icr

IarIbrIcr

gt

sim

MaxIar Ibr Icr



119894119904119889119902 =

119871119903120595119904119889119902 minus 119871119898120595119903119889119902

119871 119904119871119903 minus 1198712119898

997904rArr

119889120595119904119889119902

119889119905

= minus119877119904

120590119871 119904

120595119904119889119902 minus119877119904

120590119871119903

120595119903119889119902 minus 119895120596119904120595119904119889119902 + V119904119889119902

(22)





06 07 08 09 1 11 12 13minus15

minus1

minus05

0

05

1

15

Time (s)

Term

inal

vol

tage

(pu)


06 07 08 09 1 11 12 13minus3

minus2

minus1

0

1

2

3

Time (s)

Roto

r cur

rent

s (pu

)




06 07 08 09 1 11 12 13minus3

minus2

minus1

0

1

2

3

Time (s)

r

r(p

u)

rlowast

id

i d

id

(a)

06 07 08 09 1 11 12 13minus3

minus2

minus1

0

1

2

3

Time (s)

Roto

r cur

rent

s (pu

)

(b)

06 07 08 09 1 11 12 13minus05

0

05

1

15

Time (s)

Crow

bar a

ctiv

atio

n sig

nal

(c)


7 Conclusion



072 0725 073 0735 074 0745 075 0755 076 0765 077

minus2

0

2

IGBT

curr

ents

(pu)

Time (s)

I1I2I3

I4I5I6

(a)

072 0725 073 0735 074 0745 075 0755 076 0765 077minus05

005

115

Time (s)

Crow

bar s

igna

l

(b)



Appendix



Gearbox11989911198992 = 1100




References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










2

3

4

5

6

1120579ref

V3(010)

V1(100)

V4(011)

V5(001)

V6(101)

V2(110)

Vref

VA

VB

VC


120574R 120575R

0120574

2

0120574

2

0120575

2

0120575

2120573120574 120573120575 120572120575120572120574In

vRe

c

Ts

tcom



120595119904 = 120595119904119889 0 = 120595119904119902 (15)


119894119889119904 =1

119871 119904

(120595119904 minus 119871119898119894119889119903) 119894119902119904 = minus119871119898

119871 119904

119894119902119903

120595119889119903 = 120590119871119903119894119889119903 +119871119898

119871 119904

120595119904 120595119902119903 = 120590119871119903119894119902119903 120590 = 1 minus

1198712

119898

119871 119904119871119903

(16)


V119889119903 = 119877119903119894119889119903 +119889

119889119905

(120590119871119903119894119889119903 +119871119898

119871 119904

120595119904) minus (120596119904 minus 120596119903) (120590119871119903119894119902119903)

V119902119903 = 119877119903119894119902119903 +119889

119889119905

(120590119871119903119894119902119903) + (120596119904 minus 120596119903) (120590119871119903119894119889119903 +119871119898

119871 119904

120595119904)

(17)

0002 0004 0006 0008 001 0012 0014 0016 0018 0020

200

400

600

800

1000

1200

Time (s)

Volta

ges (

V)

VdcVabVbcVca

VbaVcbVca



119875119904 =3

2

(V119889119904119894119889119904 + V119902119904119894119902119904) 119876119904 =3

2

(V119902119904119894119889119904 minus V119889119904119894119902119904) (18)


119881119904 = V119902119904 0 = V1198891199041003816100381610038161003816119881119904

1003816100381610038161003816≃ 120596119904

1003816100381610038161003816120595119904

1003816100381610038161003816 (19)


119875119904 =3

2

V119889119904119894119889119904 = minus3

2

119881119904

119871119898

119871 119904

119894119902119903

119876119904 =3

2

V119902119904119894119889119904 =3119881119904

2119871 119904

(120595119904 minus 119871119898119894119889119903)

(20)





DFIG

Stator

PI

PI

fluxcalculation

MatrixconverterSV

M

MPPT

23

23

23

+

+

+

+

+

+

++ minus

minus

minus

minus

120595s

120579s

120596s

120596r120596slip

i120572si120573s120572s120573s

abs bcs

ias ibs

120579r

120579slip = 120579s minus 120579r

ddt

i120572r iar ibr

i120573ridr

idrlowast

iqrlowast

iqr

dr

dr998400

qr

qr998400

120573r

120572r

Plowasts

Qlowasts

eminusj120579slip

ej120579slip

Vwind or 120596r


3

2Vs

Lm

Ls

iqrlowast


Ls

120595s)

Qlowasts = minus

3Vs2Ls







119894119904119889119902 =

120595119904119889119902

119871 119904

997904rArr

119889120595119904119889119902

119889119905

= minus119877119904

119871 119904

120595119904119889119902 minus 119895120596119904120595119904119889119902 + V119904119889119902 (21)



[0 0 0 0 0 0]

[1 1 1 1 1 1]

DFIG

Supply

Rec gatepluses

Inv gatepluses

SVMmodulation

Referencegeneration

from PIcontrollers

Comparator


Mode selector

1

1

0

0Vd

Vq

Iar

Ibr

Icr

IarIbrIcr

gt

sim

MaxIar Ibr Icr



119894119904119889119902 =

119871119903120595119904119889119902 minus 119871119898120595119903119889119902

119871 119904119871119903 minus 1198712119898

997904rArr

119889120595119904119889119902

119889119905

= minus119877119904

120590119871 119904

120595119904119889119902 minus119877119904

120590119871119903

120595119903119889119902 minus 119895120596119904120595119904119889119902 + V119904119889119902

(22)





06 07 08 09 1 11 12 13minus15

minus1

minus05

0

05

1

15

Time (s)

Term

inal

vol

tage

(pu)


06 07 08 09 1 11 12 13minus3

minus2

minus1

0

1

2

3

Time (s)

Roto

r cur

rent

s (pu

)




06 07 08 09 1 11 12 13minus3

minus2

minus1

0

1

2

3

Time (s)

r

r(p

u)

rlowast

id

i d

id

(a)

06 07 08 09 1 11 12 13minus3

minus2

minus1

0

1

2

3

Time (s)

Roto

r cur

rent

s (pu

)

(b)

06 07 08 09 1 11 12 13minus05

0

05

1

15

Time (s)

Crow

bar a

ctiv

atio

n sig

nal

(c)


7 Conclusion



072 0725 073 0735 074 0745 075 0755 076 0765 077

minus2

0

2

IGBT

curr

ents

(pu)

Time (s)

I1I2I3

I4I5I6

(a)

072 0725 073 0735 074 0745 075 0755 076 0765 077minus05

005

115

Time (s)

Crow

bar s

igna

l

(b)



Appendix



Gearbox11989911198992 = 1100




References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










DFIG

Stator

PI

PI

fluxcalculation

MatrixconverterSV

M

MPPT

23

23

23

+

+

+

+

+

+

++ minus

minus

minus

minus

120595s

120579s

120596s

120596r120596slip

i120572si120573s120572s120573s

abs bcs

ias ibs

120579r

120579slip = 120579s minus 120579r

ddt

i120572r iar ibr

i120573ridr

idrlowast

iqrlowast

iqr

dr

dr998400

qr

qr998400

120573r

120572r

Plowasts

Qlowasts

eminusj120579slip

ej120579slip

Vwind or 120596r


3

2Vs

Lm

Ls

iqrlowast


Ls

120595s)

Qlowasts = minus

3Vs2Ls







119894119904119889119902 =

120595119904119889119902

119871 119904

997904rArr

119889120595119904119889119902

119889119905

= minus119877119904

119871 119904

120595119904119889119902 minus 119895120596119904120595119904119889119902 + V119904119889119902 (21)



[0 0 0 0 0 0]

[1 1 1 1 1 1]

DFIG

Supply

Rec gatepluses

Inv gatepluses

SVMmodulation

Referencegeneration

from PIcontrollers

Comparator


Mode selector

1

1

0

0Vd

Vq

Iar

Ibr

Icr

IarIbrIcr

gt

sim

MaxIar Ibr Icr



119894119904119889119902 =

119871119903120595119904119889119902 minus 119871119898120595119903119889119902

119871 119904119871119903 minus 1198712119898

997904rArr

119889120595119904119889119902

119889119905

= minus119877119904

120590119871 119904

120595119904119889119902 minus119877119904

120590119871119903

120595119903119889119902 minus 119895120596119904120595119904119889119902 + V119904119889119902

(22)





06 07 08 09 1 11 12 13minus15

minus1

minus05

0

05

1

15

Time (s)

Term

inal

vol

tage

(pu)


06 07 08 09 1 11 12 13minus3

minus2

minus1

0

1

2

3

Time (s)

Roto

r cur

rent

s (pu

)




06 07 08 09 1 11 12 13minus3

minus2

minus1

0

1

2

3

Time (s)

r

r(p

u)

rlowast

id

i d

id

(a)

06 07 08 09 1 11 12 13minus3

minus2

minus1

0

1

2

3

Time (s)

Roto

r cur

rent

s (pu

)

(b)

06 07 08 09 1 11 12 13minus05

0

05

1

15

Time (s)

Crow

bar a

ctiv

atio

n sig

nal

(c)


7 Conclusion



072 0725 073 0735 074 0745 075 0755 076 0765 077

minus2

0

2

IGBT

curr

ents

(pu)

Time (s)

I1I2I3

I4I5I6

(a)

072 0725 073 0735 074 0745 075 0755 076 0765 077minus05

005

115

Time (s)

Crow

bar s

igna

l

(b)



Appendix



Gearbox11989911198992 = 1100




References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










[0 0 0 0 0 0]

[1 1 1 1 1 1]

DFIG

Supply

Rec gatepluses

Inv gatepluses

SVMmodulation

Referencegeneration

from PIcontrollers

Comparator


Mode selector

1

1

0

0Vd

Vq

Iar

Ibr

Icr

IarIbrIcr

gt

sim

MaxIar Ibr Icr



119894119904119889119902 =

119871119903120595119904119889119902 minus 119871119898120595119903119889119902

119871 119904119871119903 minus 1198712119898

997904rArr

119889120595119904119889119902

119889119905

= minus119877119904

120590119871 119904

120595119904119889119902 minus119877119904

120590119871119903

120595119903119889119902 minus 119895120596119904120595119904119889119902 + V119904119889119902

(22)





06 07 08 09 1 11 12 13minus15

minus1

minus05

0

05

1

15

Time (s)

Term

inal

vol

tage

(pu)


06 07 08 09 1 11 12 13minus3

minus2

minus1

0

1

2

3

Time (s)

Roto

r cur

rent

s (pu

)




06 07 08 09 1 11 12 13minus3

minus2

minus1

0

1

2

3

Time (s)

r

r(p

u)

rlowast

id

i d

id

(a)

06 07 08 09 1 11 12 13minus3

minus2

minus1

0

1

2

3

Time (s)

Roto

r cur

rent

s (pu

)

(b)

06 07 08 09 1 11 12 13minus05

0

05

1

15

Time (s)

Crow

bar a

ctiv

atio

n sig

nal

(c)


7 Conclusion



072 0725 073 0735 074 0745 075 0755 076 0765 077

minus2

0

2

IGBT

curr

ents

(pu)

Time (s)

I1I2I3

I4I5I6

(a)

072 0725 073 0735 074 0745 075 0755 076 0765 077minus05

005

115

Time (s)

Crow

bar s

igna

l

(b)



Appendix



Gearbox11989911198992 = 1100




References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










06 07 08 09 1 11 12 13minus15

minus1

minus05

0

05

1

15

Time (s)

Term

inal

vol

tage

(pu)


06 07 08 09 1 11 12 13minus3

minus2

minus1

0

1

2

3

Time (s)

Roto

r cur

rent

s (pu

)




06 07 08 09 1 11 12 13minus3

minus2

minus1

0

1

2

3

Time (s)

r

r(p

u)

rlowast

id

i d

id

(a)

06 07 08 09 1 11 12 13minus3

minus2

minus1

0

1

2

3

Time (s)

Roto

r cur

rent

s (pu

)

(b)

06 07 08 09 1 11 12 13minus05

0

05

1

15

Time (s)

Crow

bar a

ctiv

atio

n sig

nal

(c)


7 Conclusion



072 0725 073 0735 074 0745 075 0755 076 0765 077

minus2

0

2

IGBT

curr

ents

(pu)

Time (s)

I1I2I3

I4I5I6

(a)

072 0725 073 0735 074 0745 075 0755 076 0765 077minus05

005

115

Time (s)

Crow

bar s

igna

l

(b)



Appendix



Gearbox11989911198992 = 1100




References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










072 0725 073 0735 074 0745 075 0755 076 0765 077

minus2

0

2

IGBT

curr

ents

(pu)

Time (s)

I1I2I3

I4I5I6

(a)

072 0725 073 0735 074 0745 075 0755 076 0765 077minus05

005

115

Time (s)

Crow

bar s

igna

l

(b)



Appendix



Gearbox11989911198992 = 1100




References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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