Grid connection of the Doubly-Fed Induction Machine ...

Grid connection of the Doubly-Fed Induction Machine withoutposition sensor

I. KORTABARRIA, I. MARTINEZ de ALEGRIAJ. ANDREU, J.L. MARTIN

University of the Basque CountryDepartment of Electronics and Telecommunications

Alameda Urquijo s/n, 48013, BilbaoSPAIN

[email protected]

J.L. VILLATERobotiker, Energy Unit

TECNALIA48170, ZAMUDIO

[email protected]

Abstract: In the present paper the complete process of grid connection of a Doubly Fed Induction Machine (DFIM)based wind energy generation system without position sensors is described in detail. A sensorless position estima-tion algorithm based on axes transformation is used. The sensorless algorithm has been tested in all the differentstages, from acceleration, through grid connection to active power extraction. A new grid synchronization methodwithout position sensors is proposed.

Key–Words: Position-sensorless control, Doubly Fed Induction Machine, Grid connection

List of symbolsVgridabc

Three-phase grid voltagesVsabc

, VrabcThree-phase stator and rotor voltages

~Vs, ~Vr Stator and rotor voltage space vectorisabc

, irabcThree-phase stator and rotor currents

~is,~ir Stator and rotor current space vector~ims Stator flux magnetizing current space

vector~φs, ~φr Stator and rotor flux space vectorWv Wind speedωm Mechanical angular frecuency of rotor,

electrical rad/sΩm Mechanical speed of rotor, r/minωs, ωr Angular frecuency of stator and rotor,

electrical rad/sωg Angular frecuency of the grid, electrical

rad/sLs, Lr Stator and rotor self inductanceLm Mutual inductanceRs Stator resistancetr Transformation ratiop Number of pole pairsSuperscripts:s Stator (stationary) reference framer Rotor reference frameg Grid voltage synchronous reference

framee Stator flux synchronous reference frame∗ Reference value

Subscripts:(d, q) Direct and quadrature vector components

1 IntroductionDuring the last years, mainly because of the problemsof fossil fuel dependency, and volatility of the price ofpetrol, renewable energy sources, and specially windenergy, have increased their share in the energy sector.In countries such as Germany and Spain predictionsfor the wind energy market are very optimistic [1, 2].It is expected that offshore wind farms will contributeto reach a very high penetration of the wind energyin European grids. Wind turbines for offshore windfarms need to be highly reliable, because maintenancework in the sea is expensive and slow. In this con-text, sensorless position estimation algorithms may beuseful, because the use of encoders in such a harshenvironment as the sea reduces the reliability of windturbines. Anyway, the application of sensorless algo-rithms will only be possible if the position and speedcan be estimated with accuracy in all the working con-ditions of the wind turbine, included start up and gridsynchronization.

The process of grid synchronization has been pre-viously studied by other research groups [3] - [5].

[3] analyzes the grid connection of a DFIM withthe use of an encoder for position and speed measure-ment.

[4] describes the grid connection of a DFIM with-out the use of an encoder, but the stage from a rest

Proceedings of the 6th WSEAS/IASME Int. Conf. on Electric Power Systems, High Voltages, Electric Machines, Tenerife, Spain, December 16-18, 2006 188

Position sensorless algorithm θm

DC Bus

V gridabc

Grid

Power control algorithm

Grid synchronization algorithm

Rotor-side converter control

DFIG PWM

sync

V sabc

isabc

V r∗abc

irabc

Figure 1: Schematic block diagram of the studied control scheme

position until the instant when the turbine reaches aminimum speed when the synchronization is possiblebecause it is inside an allowable slip range is not des-cribed s ≤ 0.3.

[5] describes the grid connection of a DFIM with-out the use of an encoder, using an axes transforma-tion position estimation algorithm. In this work theDFIM accelerates making the generator work in mo-toring mode, drawing energy from the grid. The sta-tor is short circuited and the DFIM works as a Squi-rrel Cage Motor. Starting a wind turbine working asa motor is problematic, because some Grid Codes donot allow to draw power from the grid, and also me-chanical problems may arise.

The present paper describes the whole grid syn-chronization problem of a wind turbine with DFIMusing the wind as the only source of power for theacceleration.

The circuit topology is a classical wind turbinewith DFIM (figure 1). The stator is connected to thegrid using a conmutator, and the rotor is connectedto a Voltage Source Inverter (VSI). The VSI controlsthe active and reactive power of the stator during nor-mal operation (power extraction) or the stator voltage(grid synchronization). The VSI is usually connected

to a second VSI using a common DC bus forming aback-to-back converter. This second converter is incharge of keeping constant the DC bus voltage by ex-changing active power with the grid [6]. The mainadvantage of this system is the low power rating ofthe converters, usually a 30% of the rated power ofthe wind turbine.

The control of the second VSI (connected to thegrid) is totally independent of the control described inthis paper and the DC bus voltage is assumed to beconstant.

The results of this study where obtained using thesystem equations described in section 2 for a DFIM of30kW and a constant wind speed of Wv = 8.67m/susing the MATLAB-SIMULINK environment.

2 Mathematical modelUsing the Clark-Park transformations, the followingvector equations define the stator and rotor voltagesand fluxes of the DFIM in a reference frame linked tothe stator (’s’ reference frame).

Stator and rotor voltages are:

~V ss = Rs ·~iss +

d~φss

dt(1)


~V sr = Rr ·~isr +

d~φsr

dt− j · ωm · ~φs

r (2)

Stator and rotor fluxes are:

~φss = Ls ·~iss + Lm ·~isr (3)

~φsr = Lr ·~isr + Lm ·~iss (4)

and the electromagnetic torque developed by theDFIM is:

Te =32· p · Lm · ((−isds · isqr) + (isqs · isdr)) (5)

This set of equations form the model of the DFIMunder control.

3 Grid Connection Process

Before connecting the stator to the grid, the controllermust apply the necessary rotor voltages in order forthe stator voltage to be in phase and have the sameamplitude as the grid voltage. If it fails to do so,very high currents may damage the generator and thepower converters. The grid connection process is di-vided in three stages, as shown in figure 2.

|s| ≤ 0.3

t

Synchronization

Power extraction

Stage 3

Stage 1

Speed estimation

Synchronization

Stage 2

Speed

Ωmmin

Ωs

Ωmmax

Figure 2: Stages of the grid connection process

The grid connection process starts when the windhas reached a minimum speed or cut in wind speed.At this moment, the DC bus is charged to its nomi-nal voltage, and immediately after, the brake is re-leased and the turbine accelerates using the torqueprovided by the wind. The stator is open circuited.When an encoder is used the rotor is open circuitedbut when position sensorless algorithm is used the ro-tor must be connected to the VSI in order to generatecurrents for a correct position estimation. It will takesome time before the wind turbine reaches a rotationalspeed enough for a safe synchronization with the grid.This stage is the Speed Estimation Stage

The rotor and stator voltage are related by the fo-llowing equation

|Vr| = tr · s · |Vs| (6)

Bearing in mind that the maximum rotor voltage|Vrmax | depends on the DC bus voltage VDC :

|Vrmax | = K · VDC (7)

the maximum allowable slip is:

smax =K · VDC

tr · |Vs|(8)

and, thus, the minimum speed Ωmmin for the synchro-nization process is:

Ωmmin =ωs · (1− smax)

p(9)

While the DFIM rotor spins at a speed belowΩmmin the synchronization process cannot start, be-cause the rotor voltage is not enough to guarantee thatthe necessary stator voltage amplitude (close to thegrid voltage amplitude) will be obtained.

When an encoder is used, the controller onlyneeds to read the speed to determine when the syn-chronization stage can take place and there is no needto apply voltage to the rotor until the synchronizationprocess starts. But if the encoder is not used, the con-troller must apply voltage in the rotor, otherwise thereis not enough information for speed estimation. Therotor voltages generate rotor currents and stator vol-tages and these variables will be used in the positionsensorless algorithm for the obtention of rotor posi-tion θm and speed Ωm = 1

p ·dθmdt that will allow the

controller to decide when to start the synchronizationprocess.

Once the speed is high enough for the synchro-nization process, the controller will determine the ne-cessary rotor voltages for the VSI that induce the co-rrect stator voltages synchronous to the grid voltage.This stage is the Synchronization Stage.

Once the error between the stator and grid volta-ges are small enough, the stator can be connected tothe grid and normal operation with active power ex-traction can begin. This stage is the Power extractionStage.

Depending on the stage of the grid connectionprocess, the controller must use different rotor voltagecontrol strategies.

3.1 Speed estimation stage

In the first stage, the controller will apply a rotor vol-tage vector ~V r

r with the only purpose of generating


Grid

d, q

~V ss

arctan

φsqs =

∫V s

qs − Rsisqsdt

φsds =

∫V s

ds − Rsisdsdt

+

θm

−

e−jθs

~φas

arctan

γ

−

arctan δ +

θr

DFIG

~irr

d, q

θs

Figure 3: Position sensorless algorithm scheme at stage 1

currents for the estimation of the DFIM speed. Thespeed estimation is necessary in order to detect theminimum speed Ωmmin for the start of the synchro-nization stage.

The position estimation algorithm, based in axestransformation, is described in the ROTODRIVE sys-tem [5]. As described in [8], this algorithm is stableat synchronism speed an it can start without previousknowledge of the initial position of the rotor. Themain drawback is the dependence of the precision ofthe estimation on the machine parameters (Ls, Rs).

In figure 3 a block diagram of the position sen-sorless algorithm is shown. During this stage thereare no stator currents ~iss. The stator flux is obtainedfrom integration of the induced stator voltages. In or-der to avoid saturation of the integral terms, the ωr

frequency of the rotor voltage vector ~V rr applied by

the controller cannot be too low, because at low rotorspeed ωm ≈ 0 this will be close to the frequency ωs ofthe stator voltage vector ~V s

s , and low stator frequencycan lead to saturation of the integral terms. The fo-llowing rotor voltage vector has been used:

~V rr = |10| · e−j60 V (10)

In figure 5 the stator voltages and rotor currentsobtained with ~V r

r from equation (10) are shown. Theposition sensorless algorithm estimates the rotor posi-tion θm and speed Ωm as shown in figure 4.

The controller will apply the rotor voltage vector~V r

r until the the minimum speed Ωmmin for startingthe synchronization process is reached (Stage 2).

t (s)

Spee

d(r

.p.m

)

Ωmreal

Ωmest

t (s)

Posi

tion

(rad

)

θmreal

θmest

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

2

4

6

0

100

200

300

Figure 4: Speed and position estimation at stage1

3.2 Synchronization stage

During this stage the position sensorless algorithmneeds to estimate the rotor position θm, as well as therotor speed ωm = Ωm · p for a proper operation of thesynchronization algorithm in figure 6 as described in[5].

The synchronization algorithm uses a referenceframe linked to the grid voltage (′g′ reference frame).Each component of the rotor current (igdr, i

gqr) con-

trols the corresponding stator voltage component(V g

ds, Vgqs).

As shown in figure 7 the reference voltages(V g∗

ds , V g∗qs ) in reference frame ′g′, start as a ramp for


Vgds

V gqs

3/2

e−jθg e

−jθg

(ωg − ωmest) ∗ Lr ∗ i

gdr

~Vgg

~irr

(ωg − ωmest) ∗ Lr ∗ igqr

V g∗qs = |~Vg|

Vg∗ds = 0

DFIGirabc

+

2/3

3

Vrabc

V rdr

V rqr

-

+

-

-

+

VgridabcVsabc

θg

ig∗qr

ig∗dr

igqr igdr

e−j(θg−θmest

)

Vgdr

V gqr

ej(θg−θmest

)

~Vss

3/2 3/2

Figure 6: Synchronization algorithm schematic block diagram

t (s)

Vs(V

)

Vsds

Vs

qs

t (s)

I r(A

)

Irdr

Irqr

0 0.5 1 1.5 2

0 0.5 1 1.5 2

-0.5

0

0.5

-10

-5

0

5

10

Figure 5: Stator voltages and rotor currents at stage1

a smooth transition between stage 1 and stage 2. Fi-gure 8 shows the synchronization of phase ’a’ of thestator voltage and the grid voltage. Stage 2 finisheswhen the difference between each of the componentsof the stator voltage and the grid voltage are smallerthan the limit set by the controller. At that momentthe controller connects the stator to the grid and thegrid connection process steps to the next stage (Powerextraction stage).

During this stage there is no need for a very accu-rate estimation of the rotor position θm from the posi-tion sensorless algorithm. The synchronization algo-rithm can obtain a smooth connection to the grid evenif there is a stationary error (offset) in the estimation

t (s)

|Vds|(V

)

STAGE1 STAGE2

Vg∗

dsVds

t (s)

|Vqs|(V

)

STAGE1 STAGE2

Vg∗qs

Vqs

3.4 3.45 3.5 3.55 3.6 3.65 3.7

3.4 3.45 3.5 3.55 3.6 3.65 3.7

-400

-200

0

200

400

600

-400

-200

0

200

400

600

Figure 7: Stator voltage control in the grid voltage syn-chronous reference frame ′g′

of the rotor position θm.

3.3 Power extraction stage

After a correct connection to the grid, the wind turbinecan start extracting power from the wind. This stagehas been thoroughly described in many papers. In thispaper the stator-flux-oriented vector control has beenused for power extraction [7]. In a reference framelinked to the stator flux (′e′ reference frame) the mag-


Ve

qr

ωs

e−jθs e−jθs

3/2

Vr

qr

2/3Te

ωmest

ω∗

m Wv

Vgridabc

mod

| ~Vs|

isabc

ieds

Ec. 11

~iems

DFIGirabc

~irr

e−j(θs−θmest)

ieqr

iedr

3

Vrabc

Q∗

s = 0

Ec. 13ie∗dr

+

-

-ie∗qr

+

Ec. 12

P ∗

s

+

(ωs − ωmest) ∗ Lr ∗ i

edr

- Ve

dr

(ωs − ωmest) ∗ Lr ∗ i

eqr

ej(θs−θmest)

Vr

dr

3/2 3/2

Figure 9: Stator-flux-oriented vector control schematic block diagram

t (s)

(V)

FASE1 FASE2

VgridaVsa

3.4 3.45 3.5 3.55 3.6 3.65 3.7

-800

-600

-400

-200

0

200

400

600

800

Figure 8: Stator voltage control. Phase ′a′

netizing current vector~iems is:

~iems =~φs

e

Lm=

(Ls

Lm

)ieds + iedr (11)

The stator resistance Rs can be omitted, and thestator active power Ps and the stator reactive powerQs are defined as

Ps =32

(Lm

Ls

)|~Vs|ieqr (12)

Qs =32|~Vs|

Lm

Ls(iems − iedr) (13)

As shown in equations 12 and 13, controlling eachof the rotor current components (iedr, i

eqr), a decou-

pled control of the stator active and reactive power(Qs, Ps) is achieved.

In opposition to stages 1 and 2, in stage 3 the posi-tion sensorless algorithm must estimate the rotor posi-tion with a very high accuracy. The controller is verysensitive to rotor position estimation errors, speciallyduring accelerations, because the speed regulator willsaturate at zero active power reference. Positive ac-tive power references cannot be used because grid co-nnection regulations do not allow this operating mode.When the speed regulator is saturated, the controllercannot compensate errors in the estimation of the ro-tor position θm and this leads to errors in Ps and Qs.

In figure 10 we can appreciate a slight deviationof θm from the reference signal.

4 Simulation results

A simulation of the estimated rotor speed for thewhole grid connection process of the wind turbinewith DFIM is shown in figure 11. During stages 1and 2 the wind turbine accelerates with the torqueprovided by the wind, and the DFIM remains withthe stator open circuited and there is no electromag-netic torque (Te = 0 Nm). When the DFIM entersstage 3, the error in the estimated speed (ω∗

m − ωm)is high enough for the speed regulator to saturate and


t (s)

ε θm

(rad)

STAGE 1 ST

AG

E2

STAGE 3

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.50

0.05

0.1

0.15

0.2

0.25

Figure 10: θm estimation error

P ∗s = 0 kW . As a result the wind turbine still acce-

lerates as in the previous stages. As soon as the speedregulator exits saturation, the speed of the DFIM Ωm

follows the its reference signal Ω∗m. Ω∗

m is set toobtain maximum power extraction by an MaximumPower Point Tracker (MPPT).

In figure 12 the components d,q of the rotor cu-rrent reference signals ie∗dr,ie∗qr and of the real rotor cu-rrents iedr,ieqr are shown in a reference frame linked tothe stator flux. The vector control current loops makethe rotor current follow with high precision their refe-rences. Figure 13 shows that there is no appreciabletransients between the three operating stages, whichproofs the applicability of the proposed control andestimation process.

t (s)

Spee

d(r

.p.m

)

Ω∗

m

STAGE 1

ST

AG

E2

ST

AG

E3

Ωmreal

Ωmest

t (s)

Spee

d(r

.p.m

)

STAGE 1 STAGE 2 STAGE 3

Ωmreal

Ωmest

3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5

1000

1100

1200

0

500

1000

1500

Figure 11: Speed estimation in the grid connection process

t (s)

ie dr

(A)


ie∗dr

iedr

t (s)

ie qr

(A)


ie∗qr

ieqr

3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5 5.2

3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5 5.2

-10

0

10

20

-10

0

10

20

Figure 12: Rotor currents control in the stator flux syn-chronous reference frame ′e′

t (s)

i ra

bc(A

)

STAGE 2 STAGE 3

ira

irb

irc

3.4 3.6 3.8 4 4.2 4.4-40

-30

-20

-10

0

10

20

30

Figure 13: Rotor currents

5 ConclusionsPosition sensorless algorithms offer advantages inwind turbines because they increase robustness andreliability. This is specially interesting in offshorewind farms. But this algorithms will only be usefulif they can obtain an accurate estimation of the posi-tion and speed in all the operating stages of the windturbine.

All the stages of operation of a wind turbine withDFIM have been analyzed. In order to obtain thenecessary position θm and speed ωm of the machinea position sensorless algorithm developed for everyoperating stage of connection to the grid.

Simulation results show that position and speedestimation sensorless techniques can be used in aWind Turbine with DFIM, in all operating stages,without affecting the quality of the control of the sys-


tem.

Acknowledgements: The present paper has been fi-nanced by “Ministerio de Educacion y Ciencia” and“FEDER” within the research project ENE 2004-07881-C03-01/ALT.

References:

[1] E. De Vries. Market predictions. WindEn-ergy Study 2006. Renewable Energy World,9(3):112–123, May - June 2006.

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[3] Byoung-Chang Jeong, Tae-Hwa Kwon, Seung-Ho Song, and Eel-Hwan Kim. Grid connect-ion algorithm for doubly-fed induction generatorusing rotor side PWM inverter-converter. Trans-actions of the Korean Institute of Electrical En-gineers, B, 52(10):528 – 34, October 2003.

[4] U. Radel, D. Navarro, G. Berger, and S. Berg.Sensorless field-oriented control of a slipring in-duction generator for a 2.5 MW wind powerplant from Nordex energy GmbH. 9th EuropeanConference on Power Electronics and Applica-tions. EPE 2001, 2001.

[5] L. Morel, H. Godfroid, A. Mirzaian, and J.M.Kauffmann. Double-fed induction machine:converter optimisation and field oriented con-trol without position sensor. IEE Proceedings-Electric Power Applications, 145(4):360 – 8,July 1998.

[6] R.J. Koessler, S. Pillutla, L.H. Trinh, and D.L.Dickmander. Integration of large wind farmsinto utility grids pt. i - modeling of dfig. 2003IEEE Power Engineering Society General Meet-ing (IEEE Cat. No.03CH37491), 3:1512 – 19,2003.

[7] P. Vas. Sensorless vector and direct torque con-trol. Oxford University Press, 1998.

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