Sensorless Control of Doubly-Fed Induction Generators ... - IEEE Xplore

330

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 1, JANUARY 2008

Sensorless Control of Doubly-Fed Induction Generators Using a Rotor-Current-Based MRAS Observer Rubén Peña, Member, IEEE, Roberto Cárdenas, Senior Member, IEEE, José Proboste, Greg Asher, Fellow, IEEE, and Jon Clare, Senior Member, IEEE

Abstract—This paper presents a new sensorless method for the vector control of Doubly-Fed Induction Machines (DFIMs) without using speed sensors or rotor position measurements. The proposed sensorless method is based on the Model Reference Adaptive System (MRAS) estimating the rotor position and speed from the machine rotor currents. The method is appropriate for both stand-alone and grid-connected operation of variable speed DFIMs. To design the MRAS observer with the appropriate dynamic response, a small signal model is derived. The sensitivity of the method for variation in the machine parameters is also analyzed. Speed catching on the fly and synchronization of the Doubly-Fed Induction Generator with the utility are also addressed. Experimental results obtained from a 3.5-kW prototype are presented and fully analyzed. Index Terms—AC generators, induction motors, sensorless control, wind power generation.

I. I NTRODUCTION

T

HE DOUBLY-FED Induction Generator (DFIG) has many advantages for variable speed generation at medium- and high-power applications. The machine is robust and requires little maintenance. The power converter is connected to the rotor and, for restricted speed range applications, is rated at only a fraction of the machine nominal power [1]–[3]. The DFIG can be used as a variable speed generator for stand-alone and grid-connected applications. In both cases, the use of sensorless vector control is desirable, because an encoder has drawbacks in terms of cost, robustness, and cabling. The sensorless control of Doubly-Fed Induction Machines (DFIMs) has been addressed by several researchers [4]–[12]. The earliest research proposed the use of magnetizing current supplied from the rotor and stator to estimate the rotor position and speed. However, only simulation results were presented in this publication and the observer design and its dynamics were not addressed. A sensorless control method, for the subsynchronous stand-alone operation of DFIGs, is proposed Manuscript received February 20, 2006; revised March 30, 2006. This work was supported by Fondecyt Chile under Contract 1050592 and the University of Magallanes, Chile. R. Peña, R. Cárdenas, and J. Proboste are with the Electrical Engineering Department, University of Magallanes, Punta Arenas 01855, Chile (e-mail: [email protected]; [email protected]; [email protected]). G. Asher and J. Clare are with the School of Electrical and Electronic Engineering, University of Nottingham, NG7 2RD Nottingham, U.K. (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TIE.2007.896299

in [5] and [6] in which the error between the stator voltage vector and a reference rotating vector is processed to obtain an estimation of the rotor angle. However, only the operation at subsynchronous speed is considered and the observer design is not analyzed. In [7], a rotor-flux-based sensorless scheme is reported, where the rotor flux is obtained by the integration of the rotor back-electromotive force. This approach suffers from integration problems, with poor performance when the machine operates about synchronous speed, because the rotor is excited with low frequency voltages. The sensorless methods presented in [8]–[12] are open-loop based on rotor current estimators in which the estimated and measured currents are compared to obtain the rotor position, and the rotational speed is obtained by differentiation. None of these address the design of the rotor position estimator bandwidth and the effect of parameter error in the position accuracy. Moreover, obtaining the speed via differentiation of the rotor position may produce a noisy speed estimation [12]. Although the Model Reference Adaptive System (MRAS) observer is a well known method for the sensorless control of cage induction machines [13]–[15], there are few reports related to the use of MRAS observers for sensorless control of DFIMs. A simulation study of a stator-flux DFIM MRAS observer operating at very low speed has been reported in [16], but the design, observer dynamics or parameter sensitivity were not addressed. A stator flux MRAS observer for standalone DFIG operation was presented by the authors in [17] and [18] and covered a small signal model design procedure and experimental verification. However, in [17] and [18] it is shown that the stator flux MRAS observer design is dependent on the magnetizing current supplied from the rotor of the DFIG making this sensorless method inappropriate for grid-connected applications when the DFIG magnetizing current is entirely supplied from the stator [18]. This paper presents a rotor current MRAS observer for the control of variable speed DFIGs. Because the rotor current is a measured quantity, the implementation of a rotor-currentbased MRAS observer is simple. The measured rotor current is compared to an estimation of the rotor current obtained from the stator voltages and currents. A proportional-integral (PI) control adjusts the speed, driving the error between the measured and estimated currents to zero. The proposed method is appropriate for both stand-alone and grid-connected DFIG operation. Also, the proposed observer performance is robust,

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PEÑA et al.: SENSORLESS CONTROL OF DFIGs USING A ROTOR-CURRENT-BASED MRAS OBSERVER

Fig. 1.

331

Sensorless vector control scheme for a stand-alone DFIG.

does not suffer from integrator drift at low excitation frequency, and is not dependent on resistance parameters. The rest of this paper is organized as follows. Section II introduces the DFIG vector control systems for stand-alone and grid-connected operation. Section III presents the rotor currentbased MRAS observer, describing a small signal model, the effects of incorrect parameter estimation, synchronization of the DFIG to the grid, and speed catching operation. Section IV presents experimental results. Finally, an appraisal of the rotor current MRAS observer is presented in the conclusions.

II. V ECTOR C ONTROL OF DFIG A. Vector Control of the DFIG for Stand-Alone Operation The proposed control system for the stand-alone operation of a DFIG is shown in Fig. 1. As is appropriate for stand-alone application, the vector control scheme is indirect [1] and contains demands for frequency ωe and magnetizing current to regulate the load voltage and frequency irrespective of the shaft speed. The machine equations written in a synchronously rotating d−q frame are [1], [2] λds = Ls ids + Lm idr = Lm ims

(1)

λqs = Ls iqs + Lm iqr

(2)

λdr = Lm ids + Lr idr

(3)

λqr = Lm iqs + Lr iqr

(4)

dλds − ωe λqs dt dλqs + ωe λds = Rs iqs + dt

vds = Rs ids +

(5)

vqs

(6)

dλdr − (ωe − ωr )λqr dt dλqr + (ωe − ωr )λdr vqr = Rr iqr + dt p Lm (iqs idr − ids iqr ) Te = 3 2

vdr = Rr idr +

(7) (8) (9)

where λs is the stator flux, Ls , Lm and Lr are the stator, magnetizing and rotor inductances, respectively, ωe is the electrical frequency, v s and is are the stator voltages and currents, Rr and Rs are the rotor and stator resistances, respectively and ims is the magnetizing current. For stand-alone operation, the equivalent stator magnetizing current ims is supplied entirely from the rotor. Aligning the d–q axis of the reference frame on the stator flux vector gives iqr = −

Ls iqs . Lm

(10)

Eliminating ids using the definition for ims given in (1) and eliminating iqs using (10) yields, with λqs = 0 τms

dims 1 + σs + ims = idr + vds dt Rs p L2 m Te = − 3 ims iqr 2 Ls

(11) (12)

where τms = Ls /Rs and σs = ls /Ls with ls as the stator leakage inductance. Since the last two terms in (5) are zero for constant flux operation, vds is seen to be small, and from (11) it is thus seen that ims can be controlled using idr . The rotor current iqr can be controlled according to i∗qr = −

Ls iqs Lm

(13)

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Fig. 2. Sensorless vector control scheme for a grid-connected DFIG.

which forces the orientation of the reference frame along the stator flux vector position. The demodulation of the rotor demand voltages uses the slip angle derived from θslip = θe − θˆr =

ωe∗ dt − θˆr

(14)

where θˆr is estimated from the rotor current MRAS observer. For stand-alone operation, the electrical angle θe is derived from a free running integral of the stator frequency demand ωe∗ . This has the advantage that the orientation is shielded from measurement noise and stator voltage harmonics, which may be a problem in a stand-alone application [1]. Using α–β components, the stator flux is obtained from the stator voltages and currents as [13], [18]–[21] λαs = λβs =

(vαs − Rs iαs )dt (vβs − Rs iβs )dt

(15)

the electrical angle θe is used to obtain the d–q components of the stator flux (see Fig. 1). When the vector control system is oriented along the stator flux vector, λqs = 0 and ims = λds /Lm . In Fig. 1, the MRAS observer is represented by the block diagram inside the dotted box. Its output is the rotor angle used to modulate and demodulate the rotor currents and reference voltages. The structure of the MRAS observer is discussed in Section III. Since the sensorless control system is not affected by the operation of the pulsewidth modulation (PWM) frontend converter [1], [19], the control of this converter is considered outside the scope of this paper.

B. Vector Control of the DFIG for Grid-Connected Operation For grid-connected generation, the DFIG vector control system is also oriented along the stator flux vector. The electrical angle is obtained from the α–β components of the stator flux as shown in (16) λβs . (16) θe = tan−1 λαs For grid-connected operation, ims can be supplied from the DFIG rotor or stator. The rotor current idr can be also used to supply reactive power to the grid [19], or even to compensate the harmonics produced by nonlinear loads [8]. For gridconnected operation the power supplied to the grid is regulated using iqr [19]. The control system for a grid-connected DFIG is shown in Fig. 2. Again the MRAS observer is represented by the block diagram inside the dotted box. In the experimental implementation of (15), a Band-Pass Filter (BPF) is used as a modified integrator to block the dc component of the measured voltages and currents [19], [20]. The BPF is designed with cutoff frequencies of 0.1 and 1 Hz. The frequency response of this filter is shown in Fig. 3. For frequencies above ≈3 Hz, the difference between the response of the BPF and that of an ideal integrator (1/s in Fig. 3) is insignificant. Therefore, because v s and is are 50 Hz signals, the performance deterioration from integral action is negligible. III. MRAS O BSERVER FOR DFIG S In this paper, an MRAS observer estimates the DFIG rotor speed and position. This observer is based on an adaptive model and a reference model or signal [13], [18], [21]. In this paper, the reference model is the measured rotor current ir which is filtered by a second-order low-pass antialising filter. An


Fig. 3.

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Frequency response of the BPF used to replace the ideal integrator.

estimation of ir can be obtained using is and vs . In the stationary frame the stator flux is obtained as λs = Ls is + Lm ir ejθr .

(17)

From (17), the rotor current is obtained as ir =

λs − Ls is −jθr e . Lm

(18)

Replacing θr in (18), an estimation of the rotor current is obtained as îr = λs − Ls is e−j θˆr Lm

(19)

Fig. 4. Rotor-current-based MRAS observer. (a) Small signal model of the proposed MRAS observer. (b) Implementation of the proposed MRAS observer.

slip frequency (ωe − ωr ). Therefore, îr is rotating at (ωr − ω ˆr) with respect to ir . Neglecting the initial conditions, the angle θerror is obtained as θerror =

ˆr ωr − ω s

(21)

where the rotational speeds ω ˆ r and ωr are defined as dθˆr /dt and dθr /dt, respectively. A small signal model of (20) is derived assuming that all the machine parameters are correctly identified and, at the quiescent point, ir0 = îr0 and θerror = 0. Linearizing (20), the small signal model is obtained as

where θˆr is the position estimated by the MRAS observer. The error in α–β components between the estimated and measured rotor current is defined as the cross product between ir and îr

∆ε = |ir0 |2 cos(θerror0 )∆θerror ⇒ ∆ε

ξ = îαr iβr − iβrîαr = |ir ||îr | sin(θerror )

Fig. 4(a) shows the small signal model. The PI controller drives the error of (20) to zero by adjusting ω ˆ r . The implementation of the rotor current MRAS observer is shown in Fig. 4(b) in which the stator flux is calculated using is and vs (15) and where the block labeled “X” denotes cross product (20). The output of the PI controller is the estimated speed which is integrated to obtain the rotor angle. Since |ir | varies with the DFIG output power, there is a variable gain in the transfer function of (22), [see Fig. 4(a)]. To compensate for this, a variable gain |ir |−2 (for ir > 0) is used in the MRAS controller. The small signal model of (22) could be modified to include some nonlinear effects as sampling delays, and distortion in the DFIG voltages and currents. A design methodology, to design the PI controller of a PLL structure considering nonlinearities, is presented in [22] and [23].

(20)

where θerror is the angle between the vectors ir and îr. Correct estimation of rotor angle and speed are achieved when θerror = 0. As discussed previously by Schauder in [13], the MRAS observer could be interpreted as a vector Phase-Locked Loop (PLL) in which the measured current is the reference vector, and the estimated current of (19) is a vector phase-shifter controlled by the estimated rotor position. This is because the error ξ of (20) is defined as the cross product between the output of the adaptive model and that of the reference model. Therefore, during normal operation of the DFIG, the error ξ is driven to zero when the phase angle between ir and îr is also zero. A discussion of the advantages of using the cross product to define the error ξ of (20) is considered outside the scope of this paper and the interested reader is referred elsewhere [13]. A. Small Signal Model The small signal model for the MRAS observer is derived from (19) and (20). The estimated current of (19) is rotating at ˆ r ) with respect to the rotor frame and ir is rotating at the (ωe − ω

= |ir0 |2

(∆ωr − ∆ˆ ωr ) . s

(22)

B. Machine Parameter Sensitivity For the proposed rotor current MRAS observer, incorrect estimation of the machine inductances produces an incorrect estimation of the rotor angle. This angle is used to demodulate the rotor currents and the demanded rotor voltages (see Figs. 1 and 2). The rotor angle estimation error can be obtained using

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C. Speed Catching Operation of the MRAS Observer

Fig. 5. Position error produced by the variation of K.

a small-signal model. From (19), the d–q components of îr are obtained as îdr = 1 (λds − Ls ids ) Lm îqr = 1 (−Ls iqs ). Lm

It is desirable for a sensorless DFIG to be able to catch the rotational speed of an already spinning machine [10]. For the proposed system, the speed catching procedure considers the DFIG operating in stand-alone mode with scalar control and rotor current limitation. For the speed catching procedure, a circuit breaker is used to disconnect the load/grid from the stator. The voltage supplied to the rotor is demodulated using the estimated slip frequency calculated from ωe∗ (see Fig. 1) and the speed estimated from the MRAS observer. Since the stator frequency is not equal to ωe∗ when the estimated speed differs from the real speed, then the absolute error of the stator frequency with respect to the reference can be used as an indicating parameter for the MRAS convergence. Using (α–β) coordinates for the stator voltage and flux, the electrical frequency can be estimated as [20]

(23) ω ê =

(Vβs − Rs iβs )λαs − (Vαs − Rs iαs )λβs λ2αs + λ2βs

(26)

Assuming that the stator flux is well regulated, and defining K = Ls /Lm , a small signal model of (23) is obtained as

and the absolute value of the stator frequency error is given by

∆îdr = −(∆Kids0 + K∆ids )

ωe,error = |ωe∗ − ω ê| .

∆îqr = −(∆Kiqs0 + K∆iqs ).

(24)

If the machine is operating at steady-state and a variation is introduced in the MRAS observer parameters, then the phase of the estimated current îr will change, introducing a phase error ∆θ between ir and îr (see Fig. 5). This phase error is corrected by the observer PI controller which drives the phase error between ir and îr to zero. However, this introduces an offset ∆θ in the estimation of the rotor angle. Therefore, an incorrect estimation of the term Ls /Lm is equivalent to use a position encoder with an offset in the measured position. From (24) and the vector diagram of Fig. 5, the error ∆θ can be calculated as ∆θ = tan

−1

i∗qr + ∆îqr i∗ + ∆îdr dr

− tan

−1

(27)

i∗qr i∗dr

.

(25)

In Section IV, it is experimentally demonstrated that the variation in idqs is negligible for small changes in K. If this is the case, ∆ids and ∆iqs can be neglected in (24) and ∆θ is obtained from (25). Small deviations in estimated Ls /Lm do not affect the accuracy of the steady-state speed obtained from the MRAS observer. This is because the error of (20) is driven to a zero steady-state value only when both the estimated and measured rotor currents have the same phase and frequency. From (18) and (19), it is easily concluded that ir and îr have the same frequency and phase only when ω ˆ r = ωr . The observer is mainly affected by incorrect estimation of Lm /Ls . The estimated rotor current obtained from (19) is robust against variations in the stator resistance and the MRAS observer is not affected by rotor resistance variations because the rotor current is a measured quantity.

A first-order low-pass filter is used to eliminate the high frequency noise in ωe,error . Once the MRAS observer has estimated the rotational speed correctly, the vector control of idqr may be enabled and the machine connected to the load, or synchronized to the grid. In this paper, it is considered that the MRAS observer converges to the correct speed and rotor position when the filtered values of ωe,error < 0.5 Hz. During the speed catching procedure, the stator frequency ˆ r + ωr , and ωe > ωe∗ when ω ˆ r < ωr . If the iniis ωe = ωe∗ − ω tial estimated speed is assumed to be ω ˆ r = 0, then the stator frequency is above the demanded value before MRAS convergence. Therefore, during the entire speed catching procedure, the DFIG stator frequency is not close to the BPF cutoff frequencies, and the performance deterioration from integral action is again negligible even when relatively large variations in the DFIG stator frequencies are produced. This is further corroborated from the experimental results presented in Section IV. D. Grid Synchronization of the DFIG For the grid-connected operation of the DFIG, the speed catching operation described above is performed first. When the stator electrical frequency has converged to the correct value, and the correct estimation of the rotor angle θˆr is obtained at the output of the MRAS observer, the control system shown in Fig. 6 is used to synchronize and connect the DFIG to the grid. In Fig. 6, the stator and grid voltages are measured and transformed into a d–q axis. The control system is oriented on a fictitious grid flux vector obtained by integrating the grid α–β voltages. The electrical angle is obtained from the α–β components of this flux vector [see (16)]. To synchronize the DFIG to the grid, the phase and magnitude of the stator voltage


Fig. 6.

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Control system used to synchronize and connect the DFIG to the grid.

are regulated using the voltages supplied to the rotor. Using (5) and (6), the open loop rotor voltages are obtained as vdr =

ωsl Lr Rr vdG + vqG ωe Lm ωe Lm

vqr = −

Rr ωsl Lr vdG + vqG ωe Lm ωe Lm

(28)

Fig. 7. Experimental system.

(29)

where vdG and vqG are the d–q components of the grid voltage. Using (28) and (29), synchronism is achieved and the DFIG may be connected to the grid. Vector control mode is then changed to direct stator flux orientation [19]. IV. E XPERIMENTAL R ESULTS The control system of Figs. 1 and 2 have been implemented using a 3.5-kW DFIM driven by a cage machine. This cage induction machine can be used to emulate a wind turbine or another prime mover using the modeling and emulation techniques presented in [24] and [25]. The experimental rig is shown in Fig. 7. Two PWM back-to-back inverters are connected to the machine rotor. Current transducers are used to measure the rotor and stator currents and for the control of the front-end converter. Two voltage transducers measure the stator voltage. A position encoder of 10 000 ppr is used to measure the rotor angle and rotational speed. This encoder is used only for comparison purposes and to control the cage machine. A microprocessor board is used to implement the rotor current MRAS observer and the whole sensorless vector control system. The MRAS observer bandwidth is approximately 10 Hz, which, considering the high inertia of wind turbines, is sufficient for DFIG sensorless control for wind energy applications. The parameters of the whole system, including control loop parameters, are given in the Appendix. With the DFIG operating as a stand-alone generator (see Section II-A), Fig. 8 shows the measured and observed speed for speed variations between 650 to 1350 r/min and 1350 to 650 r/min in approximately 6 s. The acceleration is about 140 r/min/s, which is more than typical for a wind energy conversion system. During the speed variation, a resistive load

Fig. 8. Estimated and real speed for speed variations between 650 and 1350 r/min.

step of 1.65 kW (≈50% of nominal load) is connected and disconnected from the stator. Despite the relatively large speed variations and load impacts, the performance of the MRAS observer is very good with an error of less than ±15 r/min when the load impact is applied, and less than ±3 r/min under steady loading operation. Under constant speed and constant load operation, the speed error is zero. Fig. 9 shows the system performance for a load step of ≈1.7 kW. The DFIG is operating at 700 r/min sourcing a standalone load. Fig. 9(a) shows the real and estimated speeds, and the speed error. Even for this relatively large load step, the estimation at the output of the observer is good, with a speed error of less than ±15 r/min when the load impact is applied. Fig. 9(b) shows the load voltage modulus, calculated from the d–q axis components. Since ims is well regulated, the voltage variation at the load is small, with a dip and overshoot of less than 15 V (≈10% of the demanded value) for the load step connection/disconnection. Finally, Fig. 9(c) shows the ims and iqr currents. The regulation of ims is good, with small variations produced when the load step is connected/disconnected. The rotor current iqr , regulated according to (13), is controlled with a good dynamic response. Fig. 10 shows the speed catching operation and grid synchronization. For this test, the rotational speed of the DFIG

336


Fig. 9. Control system performance for a load impact. (a) Estimated, real speed and speed error for a load step of 1.7 kW. (b) Load voltage corresponding to Fig. 9(a). (c) Magnetizing and torque current corresponding to Fig. 9(a).

is varying. The machine is synchronized to the grid using the control system presented in Fig. 6. Initially, the circuit breaker is opened and the machine is under stand-alone configuration (see Section II-A and Fig. 1). A voltage ramp is applied to the DFIG rotor with the rotor current limit set to ≈5 A. Fig. 10(a) shows the estimated and real rotational speeds. The observer converges to the correct value of speed and rotor position in less than 10 s, after which the speed error is negligible. Fig. 10(b) shows the frequency error. As discussed in Section III-C, the frequency error is used as an indicating parameter for the ˆ r and ω ˆ e = MRAS convergence. From t = 0 to t ≈ 9.5 s ωr = ω ˆ e obtained from (26). After approximately 9.5 s, ωe∗ , with ω ωe,error [see (27)] is below 0.5 Hz and the correct rotational speed and rotor angle are obtained at the at the output of the MRAS observer. The rotor position error is shown in Fig. 10(c). At the start of this test, the rotor position error varies between ±180◦ . In t ≈ 9.5 s, after the convergence of the MRAS observer, the rotor position error is negligible. Fig.10(d) shows the stator and rotor currents. Initially the stator currents are zero because the circuit breaker (see Fig. 6) is opened. From t = 0 to t ≈ 4 s, the rotor current is linearly increased from ir = 0 to ir ≈ 5 A. The MRAS convergence is produced when the frequency error is below 0.5 Hz, in t ≈ 9.5 s [see Fig. 10(c)]. After convergence, the d–q components of the rotor voltage are set to the values obtained from (28) and (29), driving the stator voltage to the grid value. At t ≈ 12.2 s, the breaker (see Fig. 6) is manually closed and the rotor currents are vector controlled.

Fig. 10. Speed catching on the fly and grid synchronization. (a) Rotational speeds for speed catching and DFIG synchronization to the grid. (b) Frequency error corresponding to Fig. 10(a). (c) Rotor position error corresponding to Fig. 10(a). (d) Rotor and stator currents corresponding to Fig. 10(a).

After synchronization, iqr is regulated to zero, idr is regulated to 3 A and the remaining magnetizing current is supplied from the DFIG stator (ids ≈ 2.5 A). Fig. 11 shows the speeds and rotor current for steady-state grid-connected operation at synchronous speed. Unlike the previous work [7], the estimation of the rotor speed is very good at synchronous speed, since no integration of the rotor voltage or current is performed. Fig. 11(a) shows the dynamic performance across the synchronous speed. The current control is operating with good dynamic response and the sensorless control system is tracking the real speed with a negligible error. Fig. 11(b) shows steady state operation at synchronous speed. The rotor current is a dc signal with some PWM switching noise. Again the observer is tracking the real speed very well. The rotor position error for steady-state operation at synchronous speed is shown in Fig. 12. Negligible steady state error in the rotor angle is seen when the machine parameters


337

Fig. 13. Rotor position error for variations in Ls /Lm .

Fig. 11. Operation at synchronous speed. (a) Speeds and currents for dynamic operation across synchronous speed. (b) Steady-state operation at the synchronous speed.

Fig. 14. Control system performance for step changes in the rotor currents.

Fig. 12. Rotor position error for the proposed MRAS observer. TABLE I EXPERIMENTAL RESULTS FOR THE ROTOR POSITION ERROR ∗ = 7 A, I ∗ = 0 A, V = 190 V CONSIDERING ωr = 700 r/min, Iqr s dr

are correctly identified. For transient operation, the error in the rotor position angle is dependent on the observer bandwidth. As discussed in Section III-B, the variation of K = Ls /Lm introduces an error ∆θ in the estimation of the rotor position. It has been found experimentally that the variation on ∆ids and ∆iqs [see (24)] is negligible for small changes in ∆K. In this case the calculation of (25) becomes simplified and the rotor position error is obtained with a maximum error of ≈1◦ for ∆K variations below ±10%. This is shown in Table I where the estimated rotor position error is calculated from (25) with variations on ∆ids and ∆iqs neglected. Fig. 13 shows the rotor angle error for an estimation error of ±20% in the value of Ls /Lm . For this test, the DFIG is grid-connected, the speed is ≈700 r/min and iqr ≈ 7 A. For this machine, the position error is about −30◦ electrical for a variation in the quotient Ls /Lm of ≈−20%.

The effect of incorrect estimation of Ls /Lm was studied for speeds of 1000 and 1300 r/min with similar results to those shown in Fig. 13 and Table I. In addition, to study the effects of incorrect estimation of the machine inductances, the performance of the MRAS observer has been experimentally tested for ±100% estimation errors in the stator resistance. There was no noticeable effect in performance. The dynamic performance of the grid-connected sensorless controlled DFIG is also tested using step variations on the rotor current. This is shown in Fig. 14. The machine is operating at 600 r/min and step changes between 4 to 10 A are applied to the d–q components of the rotor currents. The dynamic performance of the proposed sensorless vector control system is good with a fast response for both current control loops. The DFIG performance has also been studied for the gridconnected operation of the DFIG, considering variable speed generation over a wide speed range. For this test the DFIG is driven by a 4-kW wind turbine emulator [24]. To increase the effects of the wind speed fluctuations on the rotational speed, the emulated wind turbine inertia is approximately one third of that of a real wind turbine for this power range (see the Appendix). For this application the DFIG electrical torque is controlled according to the well-known control law in which the iqr demand is proportional to the square of the estimated speed [19], [21]. Further discussion of wind turbine emulation and variable control strategies is outside the scope of this paper and the reader is referred elsewhere [1], [2], [11], [19], [21], [24], [25]. Fig. 15(a) shows the wind profile, used by the turbine emulation, and the electrical power generated at the DFIG output. The power has been calculated using the stator voltage and the stator and front-end converter currents. For this test the maximum power generated is ≈ 3.5 kW (100% of nominal value). Fig. 15(b) shows the estimated and real rotational speed and the speed error. The average speed error for the whole wind profile

338


catching on the fly, and synchronization to the grid of the variable speed generator has also been proposed. The proposed sensorless control method has been experimentally validated for operation under both stand-alone and grid-connected variable speed generation. Experiments verify the operation of the rotor current MRAS observer with the magnetizing power supplied from the machine stator or rotor. Moreover, dynamic and steady operation at the synchronous speed has also been demonstrated. Several tests, including load impact, fast speed transients and DFIG operation when driven by a wind turbine emulator have been presented, showing the excellent performance of the speed tracking system. Moreover, the experimental results are in broad agreement with the small-signal models proposed in this paper. It has been experimentally shown that the performance of the proposed sensorless method, for the control of DFIG, can provide a dynamic response that is as good as that obtained from a sensored drive. A PPENDIX

Fig. 15. Operation of the DFIG driven by an emulated wind turbine. (a) Wind speed and corresponding power capture. (b) Rotational speed and speed error corresponding to Fig. 15(a). (c) d–q axis rotor and stator currents corresponding to Fig. 15(a).

is 0.017 r/min with a dispersion coefficient σω of 2.28 r/min. The dispersion coefficient is calculated as N 1 σω =

(ωr − ω ˆ r )2i (30) N 1 where N is the total number of samples in the wind profile. A real wind profile, measured at the Rutherford Appleton Laboratory, U.K., (with a sampling frequency of 10 Hz) is used. Fig. 15(b) also shows the percentage of the speed error, which remains below 1% during this test. Fig. 15(c) shows the DFIG stator and rotor currents; the magnetization is supplied from the grid and i∗dr = 0 and ids ≈ 9 A for the whole wind profile. The q-axis rotor current is proportional to ω ˆ r2 and is varying between 5 to 9.2 A. As expected from (13), the variation in −iqs is similar to that of iqr . From Figs. 9(c), 10(d), and 15(c) it is concluded that good operation of the proposed sensorless scheme is obtained when the DFIG magnetization is supplied from the rotor and/or stator. V. C ONCLUSION This paper has presented an analysis and discussion of DFIG sensorless control using a rotor-current-based MRAS observer. A small signal model has been derived for the analysis and design of the observer, as well as for understanding the effects of incorrect parameter estimation. A methodology for speed

Parameters of the experimental rig: DFIM: Stator 220 V delta, rotor 250 V star, 3.5 kW, six poles, 960 r/min, Rr = 0.525 Ω, Rs = 0.398, Ls = 0.0835 H, Lm = 0.0796, Lr = 0.0825. External inductances of 30 mH have been added to the rotor. A start connected capacitor bank of 20 µF/phase is connected to the stator for harmonics filtering. Turn ratio Nr /Ns ≈ 1.4. Control loops: iqr and idr control loops, designed with a natural frequency of ωn ≈ 70 Hz, damping coefficient ≈0.8. MRAS observer designed for a bandwidth of ≈10 Hz. Wind turbine emulation: A small wind turbine of ≈4 kW is emulated, nominal speed ≈1200 r/min, blade inertia J ≈ 0.8 kg · m2 , B ≈ 0.01 N · m · s. R EFERENCES [1] R. S. Pena, G. M. Asher, and J. C. Clare, “A Doubly Fed induction generator using back to back PWM converters supplying an isolated load from a variable speed wind turbine,” Proc. Inst. Electr. Eng.—Power Appl., vol. 143, no. 5, pp. 380–387, Sep. 1996. [2] B. Rabelo and W. Hofmann, “Power flow optimisation and grid integration of wind turbines with the Doubly-Fed induction generator,” in Proc. Power Electron. Spec. Conf., Recife, Brazil, 2005, pp. 2930–2936. [3] F. Bonnet, P. Vidal, and M. Pietrzak-David, “Dual direct torque control of Doubly Fed induction machine,” IEEE Trans. Ind. Electron., vol. 54, no. 5, pp. 2482–2490, Oct. 2007. [4] O. A. Mohammed, Z. Liu, and S. Liu, “A novel sensorless control strategy of Doubly Fed induction motor and its examination with the physical modelling of machines,” IEEE Trans. Magn., vol. 41, no. 5, pp. 1852– 1855, May 2005. [5] G. Iwanski and W. Koczara, “Sensorless stand-alone variable speed system for distributed generation,” in Proc. Power Electron. Spec. Conf., Aachen, Germany, 2004, pp. 1915–1921. [6] G. Iwanski and W. Koczara, “Sensorless direct voltage control of the stand-alone slip-ring induction generator,” IEEE Trans. Ind. Electron., vol. 54, no. 2, pp. 1237–1239, Apr. 2007. [7] L. Xu and W. Cheng, “Torque and reactive power control of a doublyfed induction machine by position sensorless scheme,” IEEE Trans. Ind. Appl., vol. 31, no. 3, pp. 636–641, May/Jun. 1995. [8] M. Abolhassani, P. Niazi, H. Toliyat, and P. Enjeti, “A sensorless integrated Doubly-Fed electric alternator/active filter (IDEA) for variable speed wind energy system,” in Conf. Rec IEEE IAS Annu. Meeting, Salt Lake City, UT, 2003, vol. 1, pp. 507–514.


[9] R. Datta and V. T. Ranganathan, “A simple position sensorless algorithm for rotor side field oriented control of wound rotor induction machine,” IEEE Trans. Ind. Electron., vol. 48, no. 4, pp. 786–793, Aug. 2001. [10] L. Morel, H. Godfroid, A. Mirzaian, and J. M. Kauffmann, “DoubleFed induction machine: Converter optimisation and field oriented control without position sensor,” Proc. Inst. Electr. Eng.—Power Appl., vol. 145, no. 4, pp. 360–368, Jul. 1998. [11] E. Bogalecka and Z. Krzeminski, “Sensorless control of a double-fed machine for wind power generators,” in Proc. Power Electron. Motion Control, Dubrovnik, Croatia, 2002. [12] B. Hopfensperger, D. J. Atkinson, and R. A. Lakin, “Stator-flux oriented control of a doubly-fed induction machine without position encoder,” Proc. Inst. Electr. Eng.—Power Appl., vol. 147, no. 4, pp. 241–250, Jul. 2000. [13] C. Schauder, “Adaptive speed identification for vector control of induction motors without rotational transducers,” IEEE Trans. Ind. Appl., vol. 28, no. 5, pp. 1054–1061, Oct. 1992. [14] M. Comanescu and L. Xu, “Sliding-mode MRAS speed estimators for sensorless vector control of induction machine,” IEEE Trans. Ind. Electron., vol. 53, no. 1, pp. 146–153, Dec. 2005. [15] D. P. Marcetic and S. N. Vukosavic, “Speed-sensorless AC drives with the rotor time constant parameter update,” IEEE Trans. Ind. Electron., vol. 54, no. 5, pp. 2618–2625, Oct. 2007. [16] R. Ghosn, C. Asmar, M. Pietrzak-David, and B. De Fornel, “A MRASLuenberger sensorless speed control of Doubly Fed induction machine,” in Proc. Eur. Power Electron. Conf., Toulouse, France, 2003. [17] R. Cardenas, R. Pena, J. Proboste, G. Asher, and J. Clare, “Sensorless control of a doubly-fed induction generator for stand alone operation,” in Proc. Power Electron. Spec. Conf., Aachen, Germany, 2004, pp. 3378–3383. [18] R. Cárdenas, R. Peña, G. Asher, J. Clare, and J. Cartes, “MRAS observer for doubly-fed induction machines,” IEEE Trans. Energy Convers., vol. 19, no. 2, pp. 467–468, Jun. 2004. [19] R. S. Pena, J. C. Clare, and G. M. Asher, “Doubly-fed induction generators using back-to-back PWM converters and its applications to variablespeed wind-energy generation,” Proc. Inst. Electr. Eng.—Power Appl., vol. 153, no. 3, pp. 231–241, May 1996. [20] X. Xu and D. Novotny, “Implementation of direct stator flux orientation control on a versatile DSP system,” IEEE Trans. Ind. Appl., vol. 27, no. 4, pp. 694–700, Jul./Aug. 1991. [21] R. Cardenas and R. Peña, “Sensorless vector control of induction machines for variable-speed wind energy applications,” IEEE Trans. Energy Convers., vol. 19, no. 1, pp. 196–205, Mar. 2004. [22] V. Kaura and V. Blasko, “Operation of a phase locked loop system under distorted utility conditions,” IEEE Trans. Ind. Appl., vol. 33, no. 1, pp. 58– 63, Jan./Feb. 1997. [23] S. Pavljaevic and F. Dawson, “Synchronization to disturbed utilitynetwork signals using a multirate phase-locked loop,” IEEE Trans. Ind. Electron., vol. 53, no. 5, pp. 1410–1417, Oct. 2006. [24] R. Cárdenas, R. Peña, G. Asher, and J. Clare, “Emulation of wind turbines and flywheels for experimental purposes,” in Proc. Eur. Power Electron. Conf., Graz, Austria, 2001. [25] A. Mirecki, X. Roboam, and F. Richardeau, “Architecture complexity and energy efficiency of small wind turbines,” IEEE Trans. Ind. Electron., vol. 54, no. 1, pp. 660–670, Feb. 2007.

Rubén Peña (S’95–M’97) was born in Coronel, Chile. He received the electrical engineering degree from the University of Concepcion, Concepcion, Chile, in 1984 and the M.Sc. and Ph.D. degrees from the University of Nottingham, Nottingham, U.K., in 1992 and 1996, respectively. From 1985 to 1991 he was a Lecturer in the University of Magallanes, Punta Arenas, Chile. He is currently with the Electrical Engineering Department, University of Magallanes. His main interests are in control of power electronics converters, ac drives and renewable energy systems.

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Roberto Cárdenas (S’95–M’97–SM’07) was born in Punta Arenas, Chile. He received the electrical engineering degree from the University of Magallanes, Punta Arenas, in 1988 and the M.Sc. and Ph.D. degrees from the University of Nottingham, Nottingham, U.K., in 1992 and 1996, respectively. From 1989 to 1991 he was a Lecturer in the University of Magallanes. He is currently with the Electrical Engineering Department, University of Magallanes. His main interests are in control of electrical machines, variable speed drives and renewable energy systems. Dr. Cárdenas is the Principal Author of the paper that received the Best Paper Award from the Industrial Electronics Society, for the best paper published in the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS during 2004.

José Proboste was born in Puerto Natales, Chile, on March 21, 1976. He received the electrical engineering degree from the University of Magallanes, Punta Arenas, in 2004. He is currently a Research Assistant at the Electrical Engineering Department, University of Magallanes. His main interests are in control of power electronics converters and ac drives.

Greg Asher (M’98–SM’05–F’07) received the degree in electrical and electronic engineering and the Ph.D. degree in bond graph structures and general dynamic systems from Bath University, Bath, U.K., in 1976 and 1979, respectively. He was appointed Lecturer in Control in the School of Electrical and Electronic Engineering at University of Nottingham, Nottingham, U.K., in 1984 where he developed an interest in motor drive systems, particularly the control of ac machines. He was appointed Professor of Electrical Drives in 2000 and is currently Head of the School of Electrical and Electronic Engineering at Nottingham. He has published over 180 research papers, has received over $5M in research contracts and has supervised 29 Ph.D. students. He is currently Chair of the Power Electronics Technical Committee for the Industrial Electronics Society. Dr. Asher was a member of the Executive Committee of European Power Electronics Association until 2003. He is a member of the Institution of Electrical Engineers and is an Associate Editor of the IEEE Industrial Electronics Society.

Jon Clare (M’90–SM’04) was born in Bristol, U.K. He received the B.Sc. and Ph.D. degrees in electrical engineering from The University of Bristol, Bristol, U.K. From 1984 to 1990 he worked as a Research Assistant and Lecturer at The University of Bristol involved in teaching and research in power electronic systems. Since 1990 he has been with the Power Electronics, Machines and Control Group at the University of Nottingham, Nottingham, U.K. and is currently Professor in power electronics and Head of the Research Group. His research interests are: power electronic converters and modulation strategies, variable speed drive systems and electromagnetic compatibility. Dr. Clare is a member of the Institution of Electrical Engineers and is an Associate Editor for IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS.