adaptive observer for sensorless control of stand-alone doubly fed induction generator

4174 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 10, OCTOBER 2009

Adaptive Observer for Sensorless Control ofStand-Alone Doubly Fed Induction Generator

Daniel G. Forchetti, Guillermo O. García, Senior Member, IEEE, and María Inés Valla, Senior Member, IEEE

Abstract—A sensorless control strategy for a doubly fed (woundrotor) induction machine working in variable-speed stand-alonepower systems without using mechanical sensors is presented inthis paper. Stator voltage magnitude and frequency are regulatedusing two field-oriented control loops. A Luenberger observeris used to estimate the stator flux, while an adaptive schememodifies the rotor position required in the stator flux estimation.Stator voltage magnitude and frequency control loops behave verywell for steady state as well as for transient states like startup,speed variations, or electric load changes. Experimental results arepresented to validate this proposal.

Index Terms—Adaptive observers, doubly fed induction ma-chine (DFIM), stand-alone generation.

I. INTRODUCTION

THE doubly fed induction machine (DFIM) is one of themost used machines in generation systems connected to

the grid or working in stand-alone mode. The main advantagein using a DFIM, working in a stand-alone generation systemwith variable (restricted) speed, is that the rotor side needsa small power electronic converter [1], [2]. This makes thegeneration system suitable for variable speed diesel hydro- andwind-energy turbine applications.

Stand-alone systems must be able to provide the users withregulated voltage and frequency [3]. In these cases, the DFIMpresents several advantageous characteristics [4]. Stator voltageand frequency regulation can be achieved using two back-toback converters connected to the rotor windings (RC) and statorwindings (FEC), respectively, as shown in Fig. 1. RC is usedto control the rotor currents in order to achieve the desiredstator voltage and frequency control of the DFIM. The FEC

Manuscript received September 30, 2008; revised January 20, 2009. Firstpublished February 18, 2009; current version published September 16, 2009.This work was supported in part by the Universidad Nacional de Río Cuarto,in part by the Universidad Nacional de La Plata, in part by FONCyT-ANPCyT,and in part by the Consejo Nacional de Investigaciones Científicas y Técnicas(CONICET).

D. G. Forchetti is with the Grupo de Electrónica Aplicada, Facultad deIngeniería, Universidad Nacional de Río Cuarto, 5800 Río Cuarto, Argentina(e-mail: [email protected]).

G. O. García is with the Consejo Nacional de Investigaciones Científicasy Técnicas, 1033 Buenos Aires, Argentina, and also with the Grupo de Elec-trónica Aplicada, Facultad de Ingeniería, Universidad Nacional de Río Cuarto,5800 Río Cuarto, Argentina (e-mail: [email protected]).

M. I. Valla is with the Consejo Nacional de Investigaciones Científicas yTécnicas, 1033 Buenos Aires, Argentina, and also with the Laboratorio deElectrónica Industrial, Control e Instrumentación, Departamento de Electrotec-nia, Facultad de Ingeniería, Universidad Nacional de La Plata, 1900 La Plata,Argentina (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIE.2009.2014907

Fig. 1. Stand-alone variable-speed generation system.

can be controlled to regulate the dc-link voltage and to filterharmonic currents originated by the nonlinear loads connectedto the system [5], [6].

Most DFIM control strategies require knowing the rotorposition to achieve the orientation of rotor currents. Usually,a position sensor like a shaft encoder is employed. The elim-ination of this position sensor reduces size, costs, wiring, andmaintenance of the drive. On the contrary, it increases thesystem reliability and noise immunity. In conclusion, sensorlessschemes appear to be very attractive and have been in constantevolution in the last years.

Sensorless strategies usually estimate the machine flux usingsome kind of observer. Several of these proposed observersare open loop estimators since they have no error correctionmechanism. Such estimators are not able to either modifytheir speed of convergence or ensure stable convergence underparameter uncertainties or measurement noise [7]–[9].

The classical model reference adaptive systems (MRAS) ap-proach compares the reference model outputs with the adaptivemodel outputs to obtain an estimation error used by the adaptivelaw to achieve the convergence of the adaptive model to thereference model [10], [11]. Using this kind of observer theconvergence of the adaptive model to the reference model canbe ensured, although, the reference model must be an exactdescription of the actual system. Other MRAS approaches usethe real-system measurements as the reference model outputsavoiding reference model errors. This kind of systems comparesthe adaptive model output with real-system output measure-ments to obtain the estimation error used by the adaptive law[12], [13].

Other authors proposed adaptive Luenberger observers toestimate some machine parameters and the rotor speed for theinduction machine used as motor [14]–[16]. Observers of thistype have shown better performance than others when used ininduction motor applications [17].

In this paper, a control strategy to regulate the frequencyand voltage of a DFIM working as a variable speed stand-alone generating system is developed. An adaptive Luenbergerobserver has been used to estimate the stator flux and rotor

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FORCHETTI et al.: ADAPTIVE OBSERVER FOR SENSORLESS CONTROL OF DOUBLY FED INDUCTION GENERATOR 4175

position in [18]. In that paper, simulation results were presentedto evaluate the behavior of the control loops and the observerunder load and speed changes, as well as parameters mismatch.In this paper, experimental results are introduced. They validatethe performance of the proposed control.

In detail, this paper is organized as follows. The DFIM modelis presented in Section II-A. The field oriented control loopsdeveloped to regulate stator voltage magnitude and frequencyare presented in Sections II-B and C. An adaptive Luenbergerobserver to estimate stator flux and rotor position is presentedin Section III. The observer behavior is evaluated throughsimulations which are shown in Section IV. The completesystem performance is evaluated through experimental resultswhich are shown in Section V. Finally, conclusions are given inSection VI.

II. DFIM CONTROL

The main objective in developing the control strategy pre-sented is to implement a stand-alone generation system thatsupplies regulated stator voltage magnitude and frequency us-ing a DFIM without a position sensor. Two independent controlloops are designed to regulate the stator voltage magnitude andfrequency.

The frequency control loop consists in aligning the statorflux with a reference frame rotating with synchronous speed.This frequency control strategy is preferred since the estimatedflux offers smoother signals than the measured voltages. On theother hand, the voltage magnitude is directly controlled using aPI control loop built-up using the stator voltage measurements.

A. DFIM Model

The DFIM can be described by the following equation usinga reference frame rotating at arbitrary speed ωdq [19]:

λs = ωdqJλs − rsis + vs (1)

where rs is the stator resistance, and λs, vs, and is are thestator flux, voltage, and current vectors referred to an arbitraryreference frame, respectively, and

λs =[

λqs

λds

]vs =

[vqs

vds

]is =

[iqsids

]J=

[0 −11 0

].

For this paper, ωdq is considered equal to the desired statorfrequency (50 Hz) so the arbitrary reference frame becomes thedesired synchronous one. The stator flux can also be obtainedfrom stator and rotor currents like

λs = Lsis + M ir (2)

where Ls is the stator inductance, M is the magnetizing induc-tance, and ir (ir = [iqr, idr]T) is the rotor current referred to thesynchronous reference frame. This stator flux current model canalso be expressed as follows:

λs = Lsis + MKdqr irr (3)

Fig. 2. Block diagram of stator voltage magnitude and frequency control.

where irr (irr = [irqr, irdr]

T) is the rotor current referred to a ref-erence frame fixed to the rotor which can be directly measured,and

Kdqr =

[cos(θdq − θr) − sin (θdq − θr)sin(θdq − θr) cos (θdq − θr)

](4)

is the transformation matrix, where θr is the rotor positiondefined as the angular displacement between the rotor and statorcircuits and θdq is the angular position of the synchronousreference frame.

B. Stator Frequency Control Loop

The angular speed of the stator flux space vector must beconstant in order for a constant frequency of the stator voltageto be generated. The frequency control is achieved by defining asynchronous reference frame and forcing the stator flux vectorto be aligned with its d-axis, so that

λqs = 0 λqs = 0. (5)

The frequency control loop can be implemented using aPI controller with q-component stator flux reference definedas λ∗

qs ≡ 0. The frequency control loop error, defined aseλqs = λ∗

qs − λqs can be calculated using the q-component

stator flux estimation λqs obtained from the stator flux observerproposed in Section III. The rotor current q-component (i∗qr), isused as the actuation variable, so

eλqs = − λqs (6)

i∗qr =KPfeλqs + KIf

∫eλqsdt. (7)

This control loop is shown at the bottom of the block diagramshown in Fig. 2. The frequency control loop bandwidth shouldsatisfy a tradeoff between load perturbation rejection and noisemeasurement rejection capabilities.

The angular position of the reference frame (θdq) is obtainedfrom a free-running integral as follows:

θdq =∫

ωdqdt. (8)

θdq is used to transform back and forth currents and voltages,as shown in Fig. 2.


Fig. 3. Simplified block diagram of the proposed observer.

C. Stator Voltage Magnitude Control Loop

The stator voltage magnitude control loop is designed toregulate the voltage magnitude (V ) of the DFIM stator voltagevector, defined as follows:

V =√

v2qs + v2

ds (9)

where vqs and vds are the quadrature and direct axis componentsreferred to a synchronous reference frame.

The stator voltage control loop is implemented using a PIcontroller where the voltage error (eVs) can be defined as

eVs = V ∗ − V. (10)

This control loop mainly aims to reject the voltage variationsproduced by electric load or speed changes.

The d-component of the rotor current (idr) modifies thed-component of the stator flux which also modifies the statorvoltages as can be deduced from (1) and (2). Then, this rotorcurrent component is used as the actuation variable for thestator voltage control loop, so

i∗dr = KPveVs + KIv

∫eVsdt. (11)

The stator voltage magnitude control loop is shown at the topof the simplified block diagram shown in Fig. 2. The bandwidthof this control loop should satisfy a tradeoff between loadperturbation and noise measurement rejection capabilities.

III. OBSERVER

An adaptive observer for estimating the stator flux and rotorposition is designed and presented in this section. The statorflux estimation is obtained with a Luenberger observer usingstator voltage and current measurements.

The angular difference between the estimated and the mea-sured rotor current vectors is used to build an adaptive law to es-timate the rotor position. The correction term of the Luenbergerobserver is calculated using this rotor position estimation. Fig. 3shows a block diagram of the proposed observer.

A. Stator Flux Estimation

The stator flux is estimated using a Luenberger observer asfollows:

˙λs = ωdqJλs − rsis + vs − G(λs − λs) (12)

where λs is the estimated stator flux and G is the error correc-tion matrix

G = σI − ωdqJ (13)

where σ is the observer gain. The design of the error correctionmatrix can be found in [20].

For this kind of observer, the convergence transient of the es-timation error (eλs = λs − λs) is exponential and the observergain is used to set the desired speed of convergence.

Since the real stator flux cannot be measured, it is calculatedusing

λs = Lsis + MKdqr irr (14)

where Kdqr is the same transformation matrix used in (4) with

θ = θr − θdq, where θr is the rotor position estimation obtainedas described in the next section.

B. Rotor Position Estimation

First, an estimation of the rotor currents in a reference framefixed to the rotor (irr) is obtained using the stator flux estimationfrom (12) and (14)

irr =(Kdq

r

)−1

(λs − Lsis)/M (15)

then, the rotor position can be estimated using the angulardifference (ξ) between the estimated rotor current (irr) and themeasured rotor current (irr).

It is not simple to calculate the angular difference betweentwo vectors when the vector angles are defined within a largerange (−π, π). Some proposed observers use the cross productbetween two vectors (ξ× = λαsλβs − λαsλβs) as the error termto estimate rotor position on induction machines [10], [11]. Inthese cases, the error depends on the magnitude of the vectors tobe aligned [12], [13]. Moreover, the cross product is a nonlinearfunction of the angular difference (α) between both vectors(ξ× ∼= sin(α)) which is less sensitive to big angular errors, asthose above π/2.

This dependence can be avoided by normalizing the crossproduct with the dot product of both vectors. In this way, abetter estimation for the angular error is calculated as

ξ = tan−1(∥∥∥irr × irr

∥∥∥ / (irr · irr

)). (16)

Using (16) requires only one tan−1 for solving the angular dif-ference and then the programming algorithm becomes simplerand better defined than the one that uses the angular differ-ence directly. Solving the angular difference directly requirestwo tan−1 for solving individual angles, and in consequence,additional calculus must be done to obtain results within therange (−π, π). Moreover, (16) offers a simple way of gettingthe required angular difference independently of the vectormagnitude in the whole range.

Fig. 4 shows both error signals. From Fig. 4, it is clear thatan angular difference near ±π radians means a value of ξ× nearzero when only the cross product is used.


Fig. 4. Angular error estimation comparison ξ× ∼= sin(α).

Fig. 5. Observer startup (simulation test).

This angular difference can be driven to zero by using a PIcontroller as follows:

ωr = KPωξ + KIω

∫ξdt (17)

where ωr is the estimated rotor speed.The rotor position estimation is obtained integrating ωr

θr =∫

ωrdt. (18)

IV. OBSERVER PERFORMANCE

In order to test the developed observer, simulations werecarried out using SIMULINK/MATLAB. For this particularcase, the proposed control loops use the real stator flux androtor position as feedback signals. Simulations are preferred atthis instance because the real stator flux cannot be measured(without using flux sensors or special machine). Therefore,simulation results are provided to compare the real stator fluxwith the estimated one.

A. Observer Startup

This test shows the observer startup process. First, the gen-eration system is turned on. At t = 0.04 s, the observer startsthe estimation process, as shown in Fig. 5. The rotor speedis set to 0.6 p.u., and the rated stator electric load is fixed to1 p.u. The estimated stator flux converges to the actual value inless than 20 ms. This is clearly shown in Fig. 5(a).

At the beginning, the rotor position estimation process showsa very fast transient due to the PI convergence speed as shownin Fig. 5(b). Then, the slow evolution is due to the stator flux

Fig. 6. Angular position estimation error rejection test (simulation test).

convergence speed as a right rotor position estimation dependson correct estimation of stator flux.

B. Angular Position Estimation Error Rejection Test

This test shows the rejection capabilities of the observerwhen a rotor position error is introduced. The observer hasalready converged to the actual values when the estimated rotorposition is changed so (eθ(0.15) = −π/2) as shown in Fig. 6.

The angular error (eθ) is defined as the difference betweenthe estimated rotor position (θr) and actual one (eθ = θr − θr)while the rotor current angular error (ξ) is given by (16).

Fig. 6(a) shows the angular error (eθ) and the rotor currentangular error (ξ) while Fig. 6(b) shows the estimation errors ofthe stator flux dq-components. The rotor current angular error(ξ) reaches zero very fast. On the contrary, the angular error(eθ) shows a very fast initial decrease, but a small error remainsuntil flux error reaches zero. This behavior can be explainedas a cross coupling between the stator flux and rotor positionestimation mechanisms. This is due to gains chosen for theobserver, given by σ, KPω

, and KIω.

C. Estimated Flux Error Rejection Test

This test shows the rejection capabilities of the observerwhen stator flux dq-components errors are introduced as shownin Fig. 7. The observer has already converged to the actual val-ues when the estimated stator flux dq-components are changedso that eλqs = 0.1 p.u. and eλds = −0.1 p.u., at t = 0.03 s.

Fig. 7(a) shows the angular error (eθ) and the rotor currentangular error (ξ) while (b) shows the stator flux dq-componentserrors. The estimated flux error decreases exponentially asstated on Section III-A reaching zero in less than 20 ms. Theinstantaneous change of the estimated stator flux components,produces an instantaneous change of the rotor current angularerror (ξ). Since the estimated rotor position is obtained as aresult of a free-running integral, the angular error (eθ) does notchange instantaneously, as shown in Fig. 7(a). It is also shownthat ξ reaches zero very fast but eθ only reaches zero when theestimated stator flux converge to its actual value.

Parameter mismatch should also be considered when thewhole control system performance is evaluated. The stator


Fig. 7. Estimated flux error rejection test (simulation test).

Fig. 8. Test rig used to obtain experimental results.

flux estimation depends on the stator resistance rs and statorinductance Ls. This resistance varies with temperature whichcan change for load condition and rotor speed. A detailedanalysis through simulation results can be found in [18].

V. EXPERIMENTAL RESULTS

The performance of the proposed control system is evaluatedthrough extensive experimental results within a wide range ofoperating conditions. The test rig used to obtain the experimen-tal results is shown in Fig. 8.

The RC is implemented using a bang-bang current controlover a voltage source inverter to impose the DFIM rotor cur-rents. In this paper, the FEC shown in Fig. 1 is not implemented,and the dc-link voltage is achieved using a full-bridge rectifierconnected to the machine stator terminals through a trans-former. In addition, a dump resistive load is connected to dc-link to dissipate the generated energy during supersynchronousspeed operation. Stand-alone systems require initial energy forexcitation. In this paper, a standard battery connected to the dc-link through a diode is used to initialize the system, as shownin Fig. 8.

A capacitor bank, connected to the generator terminals(C = 50 μF) is designed taking three premises into account:1) to filter high-frequency commutation noise induced by theRC; 2) to smooth the voltage peak that appears after a suddenchange of load on the generator terminals; and 3) to provide partof the magnetizing current that reduces the current required bythe rotor windings.

A purely resistive load was applied to the generator termi-nals. This load may be fixed in two values corresponding to

TABLE IMACHINE PARAMETERS (RATED VALUES)

TABLE IICONTROLLER AND OBSERVER GAINS

Fig. 9. Load change response.

0.5 and 1 p.u. of the generator rated load. The rotor speed is setusing an adjustable speed drive (ASD). A standard PC is used tosolve the observer and control equations. A National Instrumentconversion board (NI-LAB-PC+, with 200-μs sampling time) isused to acquire the signals obtained from current and voltagesensors. The machine parameters are listed on Table I. Thegains of the PI controllers and the observer are listed onTable II.

A. Load Rejection Capabilities

This test shows the system startup and its behavior forload changes, with the DFIM rotor speed set to 0.6 p.u. Theestimated stator flux and rotor position are used as feedback


Fig. 10. Stator voltage during load changes.

Fig. 11. System response to speed change.

signals in control loops. The system is turned on with 1 p.u. ofrated load connected on the stator terminal. At t = 0.118 s, thestator load is changed to 0.5 p.u., and at t = 0.18 s, the load isset back to 1 p.u. Fig. 9 shows the stator phase currents (a), thestator phase voltages (b), the stator voltage control loop error(c), the stator flux d- and q-component (d) and the estimatedrotor position error (e) along the whole test.

The stator voltage shows no significant perturbation underthe load changes as shown in Fig. 10(a) and (b). The controlloop errors reaches zero in less than 40 ms. The control errordynamics depends on the control gains, the sampling time, andthe inverter switching frequency plus the load dynamics.

B. Speed Rejection Capabilities

This test shows the system rejection capabilities to speedchanges. The generating system is working with 1-p.u.-ratedload connected to the stator terminals and the rotor speed forcedto follow the profile shown in Fig. 11(e).

Speed changes are designed to evaluate the system under avery hard condition (acceleration 2400 r/min/s). The controlloop error corresponding to the stator voltage magnitude is not

Fig. 12. Steady-state stator voltage waveform at constant speed (fundamentalfrequency is 1 p.u.).

Fig. 13. Steady-state stator voltage waveform for speed variations (fundamen-tal frequency is 1 p.u.).

affected by a speed change, as shown in Fig. 11(a) and (b). Thevariations of the flux q-component shown in Fig. 11(c) indicatethe frequency control loop error. From the same figure, it canbe deduced that there is no significant perturbation in d- or inq-components during speed changes. Commutation noise maskthe frequency and voltage control loop, and angular estimationerrors as shown in Fig. 11(b)–(d). However, all errors remain atsmall values as can be seen from experimental results.

C. Steady-State Performance

This test shows the quality of the energy provided by thegeneration system through a rated load connected on the statorterminal while the DFIM rotor speed is set to 0.6 p.u. A statorphase voltage is shown in Fig. 12(a). It can be seen that statorvoltage is a sinusoidal waveform with a small amount of thirdharmonic components in Fourier spectral decomposition, asshown in Fig. 12(b).

Stator voltage during speed variations is also shown inFig. 13(a). This stator voltage waveform is obtained from azoom at Fig. 11(a). In this case, stator voltage is very similarto that obtained at constant speed. This is easily verified by theFourier spectrum shown in Fig. 13(b).


VI. CONCLUSION

A sensorless control strategy for a DFIM working withvariable-speed variable-load in stand-alone power system hasbeen presented. An adaptive Luenberger observer is designedto estimate the stator flux and the rotor position of the DFIM.Experimental results have validated this proposal. These resultshave shown very good performance of the whole system evenfor load and speed variations.

Moreover, this control strategy can be used successfully forsynchronizing the generation system to connect it to the grid.Synchronism can be achieved by aligning the stator flux refer-ence frame with a fictitious grid flux vector obtained from gridvoltages [21]. In this case, control loops should be adjusted towork properly controlling active and reactive power as requiredfor grid connection [22]. The stator flux observer can be usedon either working condition with no modifications.

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Daniel G. Forchetti received the Electrical Engineerdegree from the Universidad Nacional de Río Cuarto,Río Cuarto, Argentina, in 1999. He is currentlyworking toward the Ph.D. degree at the UniversidadNacional de La Plata, La Plata, Argentina.

Since 1996, he has been with the Grupo deElectrónica Aplicada, Universidad Nacional de RíoCuarto. His research interests are in electric gener-ator control, sensorless induction machine control,and renewable energy generation.

Mr. Forchetti is a member of the AutomaticControl Association of Argentina.

Guillermo O. García (M’86–S’90–M’95–SM’01)received the Electrical and Electronics Engineeringdegree from the Universidad Nacional de Córdoba,Córdoba, Argentina, in 1981, and the M.Sc. andDr. degrees in electrical engineering from theCoordenação dos Programas de Pós-graduaçãode Engenharia, Universidade Federal do Rio deJaneiro, Rio de Janeiro, Brazil, in 1990 and 1994,respectively.

Since 1994, he has been with the UniversidadNacional de Río Cuarto, Río Cuarto, Argentina,

where he is currently Director of the Grupo de Electrónica Aplicada. He isalso with the Consejo Nacional de Investigaciones Científicas y Técnicas,Córdoba. His research interests are in power electronics and renewable energyconversion.

María Inés Valla (S’79–M’80–SM’97) received theElectronics Engineer and Doctor in Engineeringdegrees from the National University of La Plata(UNLP), La Plata, Argentina, in 1980 and 1994,respectively.

She is currently a Full Professor in the Electri-cal Engineering Department, Engineering Faculty,UNLP. She is also with the Consejo Nacional de In-vestigaciones Científicas y Técnicas, Buenos Aires,Argentina. She is engaged in teaching and researchon power converters and ac motor drives.

Dr. Valla is a member of the Buenos Aires Academy of Engineering inArgentina. Within IEEE she is a Senior Member of the Administrative Com-mittee of the IEEE Industrial Electronics Society.

adaptive observer for sensorless control of stand-alone doubly fed induction generator

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