196 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 1, MARCH 2004 Sensorless Vector Control of Induction Machines for Variable-Speed Wind Energy Applications Roberto Cárdenas, Member, IEEE, and Rubén Peña, Member, IEEE Abstract—A sensorless vector-control strategy for an induction generator in a grid-connected wind energy conversion system is presented. The sensorless control system is based on a model reference adaptive system (MRAS) observer to estimate the rotational speed. In order to tune the MRAS observer and compensate for the parameter variation and uncertainties, a separate estimation of the speed is obtained from the rotor slot harmonics using an algorithm for spectral analysis. This algorithm can track fast dynamic changes in the rotational speed, with high accuracy. Two back-to-back pulse-width-modulated (PWM) inverters are used to interface the induction generator with the grid. The front-end converter is also vector controlled. The dc link voltage is regulated using a PI fuzzy controller. The proposed sensorless control strategy has been experimentally verified on a 2.5-kW experimental set up with an induction generator driven by a wind turbine emulator. The emulation of the wind turbine is performed using a novel strategy that allows the emulation of high-order wind turbine models, preserving all of the dynamic characteristics. The experimental results show the high level of performance obtained with the proposed sensorless vector-control method. Index Terms—Fuzzy logic, induction generator, induction motor drives, spectral analysis, wind energy. NOMENCLATURE A. General , , , Air density. Pitch angle. Wind turbine blade radius. Electrical torque. Inertia and viscous friction. Wind velocity. Magnetizing, rotor, stator inductance. Rotor, stator resistance. Induction machine leakage coefficient. DC link voltage. Rotor flux. Number of pole pairs. Induction machine rotational speed. Turbine rotational speed. Electrical frequency (in radians per second). Electrical frequency (in Hertz). Rotor time constant. Number of rotor slots. Forgetting factor. Manuscript received September 12, 2002. This work was supported in part by the Chilean Research Council Conicyt under Grant 1000979 and in part by internal grants from the University of Magallanes. The authors are with the Electrical and Electronics Engineering Department, University of Magallanes, Punta Arenas, Chile (e-mail: [email protected]). Digital Object Identifier 10.1109/TEC.2003.821863 Shaft compliance. Shaft viscous fiction. B. Superscripts Estimated value. Reference value. C. Subscripts Stator fixed coordinates. Synchronous rotating coordinates. Rotor or stator quantities. Turbine or generator quantities. I. INTRODUCTION T HE advantages of cage induction machines are well known. These machines are relatively inexpensive, robust, and require low maintenance. When induction machines are operated using vector-control techniques, fast dynamic response and accurate torque control are obtained . All of these characteristics are advantageous in variable-speed wind energy conversion systems (WECS). The control systems for the operation of indirect rotor flux-oriented (IRFO) vector-controlled induction machines for variable-speed wind energy applications have already been discussed in –. In , the number of transducers, rating of the power converters and control schemes suitable to operate cage and doubly fed induction machines are discussed. In  and , cage induction machines are considered and a fuzzy control system is used to drive the WECS to the point of maximum energy capture for a given wind velocity. The induction machine is connected to the utility using back-to-back converters. In –, speed encoders are used to implement the vectorcontrol strategies. The use of this encoder implies additional wiring, extra cost, extra space, and careful mounting which detracts from the inherent robustness of cage induction machines –. In this paper, a sensorless control structure based on a direct rotor flux-oriented (DRFO) vector-control system, for variablespeed wind energy applications, is discussed. A speed estimation, obtained from a model reference adaptive system (MRAS) , is used to control the electrical torque of the induction machine. A V/F control strategy is used in the low-speed region for starting and driving the WECS set into the speed operating range. In order to tune the MRAS system and compensate for the variation of the machine parameters, an estimation of the rotational speed is obtained from the rotor slot harmonics (RSH) , . The spectral analysis method used in this publication can track the rotational speed not only in steady state but also when 0885-8969/04$20.00 © 2004 IEEE CÁRDENAS AND PEÑA: SENSORLESS VECTOR CONTROL OF INDUCTION MACHINES Fig. 1. 197 Control system proposed. the WECS is subjected to fast dynamic changes. To the best of our knowledge, this is the first publication discussing a sensorless vector-control method, including tuning of the MRAS observer, for a WECS. The system proposed in this paper is shown in Fig. 1. An induction generator is driven from an emulated variable-speed wind turbine. A microprocessor-based system is used to implement the DRFO algorithms, the V/F control strategy, the MRAS rotational speed observer, the spectral estimation algorithm, the control of the front-end converter, and the emulation of the wind turbine. The front-end converter supplies the electrical energy into the grid. This converter controls the dc link voltage of the back-to-back configuration using a fuzzy PI controller. currents and voltages of the induction machine are The referred to a reference frame aligned to the rotor flux. These currents take dc values in steady state. The rotor flux is calculated from the machine voltages and currents (“Voltage model” in Fig. 1). The – components of the flux are used to calculate the electrical angle for the vector rotators. In Sections II–VII, the control system shown in Fig. 1 is discussed. Experimental results obtained from a 2.5-kW prototype will be presented and fully analyzed. II. WIND TURBINE MODELING is the torque coefficient and where ratio defined as is the tip-speed (2) The power captured from the wind turbine is obtained as (3) is the power coefficient. The value, which where maximizes the power coefficient, is the optimal tip-speed ratio . For the experimental work of this paper, the curve reported in  has been used. This curve is shown in Fig. 2 for . The model of a typical variable-speed wind turbine  is shown in Fig. 3. A. Torque Control of the Induction Generator In the experimental work presented in this paper, the electrical torque is controlled according to the well-known control strategy for below rated wind speed (BRWS) operation which, in steady state, drives the WECS to the point of maximum energy capture  (4) There are several models appropriate for wind turbines depending on the size, blade radius, nominal power, shaft stiffness, losses, gear box ratio, etc. –. The mechanical torque produced by the blades is given by depends on In (4), the losses have been neglected and the blade aerodynamics and wind turbine parameters. The electrical torque of the DRFO induction machine is calculated as (1) (5) 198 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 1, MARCH 2004 III. MRAS OBSERVER A MRAS observer is used to estimate the rotational speed of the induction machine. This observer is based on two models, the voltage model and the current model . The voltage model is used to obtain the rotor flux as (8) The rotor flux is also calculated from the stator current, speed and machine inductances. The flux from the current model is obtained as (9) Fig. 2. C versus curve ( = 0). where the 2/3 arises from the 2–3 axes scaling and is the torque producing current. Using (4–5) the reference for the torque current can be obtained as In the MRAS observer, the flux obtained from (8) is used as the reference. By adjusting the rotational speed, it is possible to reduce the error between the reference flux and the flux estimated from (9). The error in – components is usually defined as (10) (6) For sensorless control, the estimated rotational speed the MRAS observer is used in (6). from B. Wind Turbine Emulation From Fig. 3, the discrete state equations of the wind turbine can be obtained as Equations (8)–(10) are used to implement the MRAS speed observer. The error calculated using (10) is driven to zero by a PI controller (see Figs. 1 and 4). The output of this PI controller used in (6). The implemenis the estimated rotational speed tation of the MRAS observer is shown in Fig. 4. The voltage model is used to obtain the rotor flux using a band-pass filter as a modified integrator to block the dc components of the measured voltages and currents. From the voltage model, the elecis calculated using the – components of the trical angle rotor flux. At the bottom of Fig. 4 is the current model and the estimated speed . A. Detuning of the Machine Parameters (7) where is the sampling time. The mechanical torque on the blades is calculated from (1) and the electrical torque is calculated using the current [see (5)]. In (7) , , , , , and have been referred to the generator side of the gearbox and the high-speed part of the shaft is considered very stiff. A wind turbine emulation method, which preserves all of the dynamic characteristics of a wind turbine, is obtained by implementing (7) in a microprocessor board . The values of , , and are calculated by the microprocessor in each sampling time. A speed control system, implemented using a dc machine driving the induction machine, is used to force the generator speed to follow the value of calculated from (7). With this emulation technique, the induction machine rotates at the same speed as that of a generator driven by a real wind turbine. Further information about the wind turbine emulation strategy used in this work can be found in , . The dynamic performance of a MRAS observer has been studied in – and . Using a small-signal model, it can be shown that when the machine parameters are correctly estimated and the MRAS speed estimator is implemented using a relatively large close loop bandwidth, the transfer function is a first-order low-pass filter . In this case, the effects of the MRAS observer in the control system dynamics are negligible. However, a MRAS observer with incorrect parameters can be considered as an encoder with inherent ripple , producing oscillations and even instability. Besides the dynamic effects, incorrect parameters in the MRAS observer lead to an estimated speed with a steady-state error , , . The steady-state speed error may give rise to the following. 1) Reduced Power Capture for BRWS Operation: Because of steady-state speed error, the control strategy of (6) will not drive the WECS to the point of maximum power capture. Using (3), the reduction on the captured power, for BRWS operation is calculated as (11) CÁRDENAS AND PEÑA: SENSORLESS VECTOR CONTROL OF INDUCTION MACHINES 199 Fig. 3. Modeling of a typical wind turbine. the wind velocity for ARWS operation. In , a wind speed observer is proposed for BRWS control, and in , a torque observer is presented for BRWS operation. Therefore, it is important to have accurate speed estimation for ARWS/BRWS operation. In Section V, a novel method for obtaining the speed from the RSH is discussed. This method can be used to tune the MRAS observer and compensate for parameter variations IV. SPEED ESTIMATION USING ROTOR SLOT HARMONICS Fig. 4. MRAS observer implemented. where is the quiescent tip-speed ratio and is the rotational speed for optimal energy capture. From (11), the reduction in the power captured depends both on the steady speed error and the variation of the power coefficient in respect to the tip-speed ratio. 2) Incorrect Pitch Control Operation: Pitch control of the blades is used to avoid overloading the wind turbine for ARWS operation as reported in  and . The pitch angle is controlled using a rotational speed signal. When the rotational speed , the torque is controlled is below a given rotational speed according to (4) [BRWS operation]. When the rotational speed , the pitch angle of the blade is controlled to reis above duce the power capture (ARWS operation). Because the power capture is a function of the cube of the wind velocity, incorrect switching between control strategies may produce overloading or reduced power capture. In  and , a hysteresis band of only 2% of the nominal speed is used to switch between ARWS/BRWS control. Therefore, an accurate estimation of the rotational speed is necessary in this application. 3) Incorrect Operation for Other Control Systems: There are other control schemes which require an accurate rotational speed signal. For instance in , the speed is used to estimate In a squirrel cage induction machine, the rotor slots produce airgap permeance waves with a spatial distribution dependent on the number of slots in the machine , . The rotor slots interact with the magnetizing component of the airgap MMF, generating harmonics that are dependent on the machine rotational speed. The frequencies of the rotor slot harmonics are defined from the following equation: (12) where is the slip frequency and is an integer. In this is used. In Fig. 5, application, only the first-order RSH the RSH and PWM harmonics obtained experimentally for 600 r/min, 30% of full load are shown. A. Tracking of the RSH There are several methods which can be used to estimate the position of the RSH. The fast Fourier transforms (FFTs) and the interpolated FFT  can yield very accurate speed estimates but rely on long record lengths and cannot be used to track fast speed changes. There is also a high computational burden associated with a FFT with good resolution. In this paper, the RSH are tracked using a recursive maximum likelihood adaptive tracking filter (RML-ATF) , . Based on the principle of maximum likelihood estimation , the method uses an adaptive notch filter that is adaptively moved to minimize or eliminate a particular RSH. The filter is realized by  (13) 200 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 1, MARCH 2004 Fig. 5. RSH obtained from the experimental rig. where is the filter input, is the filter output, and , are parameters updated recursively. The notch frequency is obtained as cos (14) The bandwidth of the notch filter is related to as (15) Therefore, if the bandwidth is infinitely narrow. If is reduced, the bandwidth is increased. The adaptive notch is tuned to eliminate the largest sinusoidal component in the is adapted by a input signal. To achieve this, the parameter recursive maximum likelihood (RML) algorithm through which (16) is minimized. The parameter is the forgetting factor. The full algorithm implemented in the microprocessor is (17) The residual prediction error is given by (18) The error covariance is (19) The parameter estimate is (20) the prediction error update is obtained solving the difference equation of (13) (21) the forgetting factor cording to and the notch width are updated ac- (22) Fig. 6. Control system proposed for the tracking of the RSH. where and determine the rate at which the forgetting factor and the notch width converge toward the final values , .A computer model is used to select the initial values of the forget, , using experimental line current ting factor, as well as data. This model also tests the performance of the RML-ATF algorithm for fast dynamic transients and steady-state operation. The adaptive RML-AT notch filter is fully explained in  and . This filter is computationally efficient because 13 multiplications, 14 additions, and 1 division are required for iteration. The implementation of the RML-ATF algorithm takes 30 in the experimental rig described in Section VI. The convergence of the filter is also fast because the notch frequency is established in few iterations, provided the RSH is clearly the largest signal. In Fig. 6, the implementation of the proposed RSH tracking scheme, for the sensorless control system of Fig. 1, is shown. From the voltage model, the electrical angle and the electrical frequency is obtained. A second-order filter, not shown in A fourth-order Fig. 6, is used to eliminate the noise from high-pass filter eliminates the fundamental and the low-order harmonics from the current. Because the induction machine used in the experimental prototype has 14 rotor slots per pole pair, from (12), the upper (considlimit for the position of the first-order RSH is ). The lower limit is obtained assuming operaering tion at nominal slip and considering that it is unlikely to operate the machine below 250 r/min (because of the BRWS operating range of a typical wind turbine, for example, ). Considering the lower limit for the position of the first-order . RSH, the cutoff frequency of the high-pass filter is set to With this cutoff frequency, the fundamental and low-order harmonics are eliminated from the current without attenuating the RSH tracked by the RML-ATF algorithm. After the high-pass filter, a band-pass filter is used to isolate the first-order RSH. The center frequency of this filter is calculated considering the electrical frequency and an estimation of the slip frequency derived from . The band-pass area of this filter must be narrow to avoid harmonics produced by the PWM but wide enough to avoid filtering the tracked RSH when, because of parameter variations, the slip frequency is incorrectly estimated. Finally, in Fig. 6, the RML-ATF is used to obtain the CÁRDENAS AND PEÑA: SENSORLESS VECTOR CONTROL OF INDUCTION MACHINES 201 frequency of the RSH through a lookup table implementation of is obtained from (12). (14). The speed estimation To obtain a speed estimation with high accuracy and lownoise contents, the forgetting factor and the notch width must converge to near unity values. However, because of the narrow bandwidth and reduced weighting given to past values, the dynamic response of the RML-ATF is rather poor when and are close to unity values. In order to improve the dynamic response of the RML-ATF, a slope detector has been included in the RSH tracking control system. When a transient is detected, the parameters and are reduced, increasing the notch filter bandwidth and reducing the weight given to past samples. A simple algorithm is implemented to reset the forgetting factor is and the notch bandwidth to their initial values when above a given threshold. B. Tuning of the Parameters Using RSH Tracking In WECS, the generator is not required to operate at very low rotational speeds. Therefore, most of the problems related with the use of a MRAS observer in the low-speed range are avoided because the fundamental voltage applied to the machine is relatively large and the small voltage drop produced in the stator resistance is negligible. Unless the stator resistance is really overestimated, the stability of the system is not compromised . Therefore, tuning of the stator resistance is not considered in this work. Also because the induction machine is operating at fixed flux, tuning of the machine inductances is not necessary. (or ) is the most For this application, the parameter important factor to determine the accuracy of the speed estimate. In order to implement a tuning algorithm, the following relationship between the real and estimated slip frequencies is used: (23) Assuming that , and are measured or estimated without error, the following equation is obtained: (24) From (24), using and yield (25) Therefore, it is possible to reduce the speed error to zero by to zero correcting the rotor time constant and forcing , . Fig. 1 shows the control system for parameter tuning obtained from the RSH (i.e., ). with the speed A PI controller is used to regulate the time constant . This controller processes the error between the speed estimated from . The output is which is added the MRAS observer and to drive the estimation of the rotor time constant to the to correct value. The tuning algorithm is switched off for fast speed changes to avoid the relatively large speed errors produced at the output Fig. 7. Supply-side converter control schematic. of the RML-AT filter (in practice, this does not take place very often because of the large inertia of WECS). Due to the reduced slip at light load, small errors in the estimated speed may produce a large variation in the estimated rotor time constant [see (25)]. To avoid this, the tuning algorithm is also switched off when the current is small. V. CONTROL OF THE FRONT-END CONVERTER The aim of the boost-type PWM converter is to regulate supplying the energy generated from the dc link voltage the WECS into the grid. Furthermore, the use of vector-control techniques allows to control the ac currents with high bandwidth. In this application, the reference frame is oriented along the supply voltage rotating vector. Therefore, the power supplied into the grid is controlled using the direct current. The reactive power is controlled using the quadrature current. For this application, the system shown in Fig. 7 is proposed  for the control of the front-end converter. A fuzzy logic controller is used because the transfer function between the dc link voltage and the current is nonlinear and because the generating condition is unknown and varies with the wind speed in a wide range. The fuzzy controller is augmented by a feedforward compensupsation term that relates the current with the current plied from the WECS or from other generation sources or loads connected to the dc link capacitors. The feedforward compensation term is calculated from the power balance between the dc link side and the front-end converter output. The relationship is between and (26) where is the grid voltage and arises from the 2–3 axes scaling. To further discuss the control of the front-end converter is beyond the scope of this paper and more information can be found in . 202 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 1, MARCH 2004 Fig. 8. Experimental system. VI. EXPERIMENTAL RESULTS A 2.5-kW, 380-V, 50-Hz, four-pole cage induction machine is utilized in the experimental prototype. The machine parameters are given in the Appendix. Two 5-kW commercial inverters with a 1-kHz switching frequency are used. The supply-side converter is connected to the grid via three 12-mH single-phase inductors. The dc link voltage is regulated to 550 V. A speed encoder of 10 000 ppr is used to calculate the system speed. This speed is not used in the control algorithms and it is only used for comparison purposes and the emulation of the wind turbine. In the machine side, two line currents and two line voltages are measured. Also, in the front-end converter, two line currents and two line voltages are measured together with the dc link voltage and the current . The experimental rig is shown in Fig. 8. The generator is driven by a speed-controlled dc motor drive speed is calculated that emulates a wind turbine. The in each sampling time from (7) and sent to the dc machine control system which regulates the shaft speed. A lookup table is characteristic in the microprocessor. used to store the Additional lookup tables are used to implement (14), the abc transformations, the calculation of the electrical angle , to etc. The control strategies proposed in this paper have been tested with several wind profiles (obtained from ) and similar results have been achieved. Fig. 9 shows a typical wind profile with a 0.1-s sampling time for the wind velocity. The results in this section have been obtained using this profile. The performance of the RML-ATF algorithm has been investigated emulating wind turbines of different inertia, friction coefficient, and compliance. The most challenging test for the RML-ATF algorithm is the emulation of wind turbines with stiff shaft because in this case the shaft is not absorbing part of the speed fluctuations. For this reason, only the emulation of wind turbines with stiff shafts is considered in this paper. The torque current is controlled according to (6). The response of the MRAS observer and RML-ATF is shown in Fig. 10 for a wind step between 6 to 9 m/s when a wind tur- Fig. 9. Fig. 10. Wind profile used in the experimental rig. System response to a wind step between 6 to 9 m/s. bine of kgm is emulated. A wind step is not very realistic but it is the most drastic change from the control system point of view. In Fig. 10, the rotor time constant is correctly estimated and the estimated speeds from the MRAS observer and RML-ATF algorithm are very good with a negligible tracking e Fig. 11 shows the performance of the MRAS and RML-ATF kgm is emulated. In algorithm when a wind turbine of this test, the rotor time constant is underestimated by 50% and the tuning algorithm is off. The top graphic in Fig. 11 shows the speed obtained from the encoder, MRAS and RML-ATF for the whole wind profile. The speed is tracked by the RML-ATF with a negligible error during CÁRDENAS AND PEÑA: SENSORLESS VECTOR CONTROL OF INDUCTION MACHINES Fig. 11. Sensorless control using an untuned MRAS observer. Fig. 12. Sensorless control using the tuning control system. the whole wind profile. The MRAS observer tracks the real speed with a relatively large error. The bottom graphic in Fig. 11 to 60 s). Note that the shows the speeds during 40 s ( real speed is closely tracked by the estimation obtained from the RSH. Fig. 12 shows the performance of the control system when the tuning algorithm is on. In this case, the MRAS observer and the RML-ATF are tracking the real speed during the whole wind profile with very small error. The error between the estimated speed from the MRAS observer and the real speed from the encoder is almost negligible. Fig. 13 shows the speed tracking error corresponding to Fig. 12. The top graphic in Fig. 13 shows the tracking error of the RML-ATF algorithm and the bottom graphic shows the tracking error of the MRAS observer when the tuning of the rotor time constant is on. Fig. 13 shows that the error of the RML-ATF algorithm is r/min with some peaks of up to 7 r/min. approximately The corresponding tracking error of the MRAS observer is 203 Fig. 13. Speed estimation errors. Fig. 14. Control system response of the parameter-tuning algorithm. r/min. The tracking error of the MRAS is smaller than the error from the RML-ATF because the tuning algorithm has a reduced bandwidth, which eliminates the fast and noisy variations at the output of the RML-ATF, and also because the tuning algorithm is switched off when fast dynamic changes are detected. Fig. 14 shows the performance of the parameter-tuning algo, the algorithm is activated and the speed from rithm. In the MRAS observer is driven to the real speed. After 2 s, the speed error is negligible. The system is operating with a wind m/s. speed of The performance of the RML-ATF algorithm and MRAS observer for wind turbines of different inertia is shown in Table I. , Using the wind profile of Fig. 9, wind turbines of 1.75, and 3 kgm are emulated and the error of the MRAS and RML-ATF estimations are obtained. Table I shows the average and the standard deviation of the error . value of the error 204 Fig. 15. IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 1, MARCH 2004 Control system response of the RML-ATF for several inertia values. TABLE I SPEED ERRORS FOR MRAS AND RML-ATF For all of the wind turbines emulated in this work, the value of is smaller for the MRAS error than that from the RML-ATF. As mentioned previously, this is mainly because the small bandwidth of the parameter-tuning algorithm eliminates the high-frequency components of the RML-ATF. When the turbine inertia is increased, the speed tracking errors from the MRAS observer and RML-ATF algorithm are reduced. For inertia values higher than 3 kgm the improvement in performance is negligible. Fig. 15 shows the real speed and the speed obtained from the RML-ATF algorithm, when the wind profile is used. Curves a,b,c correspond to inertia values of 0.9 kgm , 1.75 kgm , and 3 kgm , respectively. The tracking of the RML-ATF algorithm is very good even for a small inertia of 0.9 kgm . current of The top graphic in Fig. 16 shows the the front-end converter when the wind profile is used kgm . The bottom graphic of Fig. 16 shows the corresponding dc link voltage. Despite the large and relatively fast variations in the wind speed with its corresponding variation in V the generated power, the dc link voltage varies less than for the whole wind profile. Finally, Fig. 17 shows the waveform for the line current , and the dc link voltage for the equivalent phase voltage the supply side of the front-end converter when the WECS is in steady state. The system operates at the optimum tip-speed ratio with a wind velocity of 8 m/s with the front-end converter current set to zero for close-to-unity power factor operation. VII. CONCLUSION This paper has presented a new sensorless vector-control strategy for an induction generator in a variable-speed WECS Fig. 16. Front-end converter i current and dc link voltage. Fig. 17. Voltage and current waveforms for the supply side. using a MRAS observer to estimate the rotational speed of the induction generator. In the sensorless system, the application of a novel RML adaptive tracking filter for the estimation of the RSH has been discussed. The dynamic performance of this adaptive filter is very good and can be used to obtain an accurate estimation of the rotational speed not only in steady state but also when fast input changes as wind steps are applied to the WECS. Using the speed estimated from the RML-ATF algorithm, a parameter tuning control system has been implemented to improve the accuracy of the MRAS observer. When the tuning of the rotor time constant is enabled, the MRAS observer can track the speed of the wind turbine with an error of less than r/min for the whole speed range. The experimental results show that the RML-ATF algorithm could be used to tune the rotor time constant not only during steady state but also during speed transients. CÁRDENAS AND PEÑA: SENSORLESS VECTOR CONTROL OF INDUCTION MACHINES Experimental results have been obtained using a wind turbine emulator and an induction machine of 2.5 kW. A novel method for the emulation of high-order wind turbine models has been implemented. This emulation strategy has been used to emulate wind turbines with inertias between 0.9 kgm and 3 kgm . 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Specialist Conf., vol. 2, Vancouver, BC, Canada, June 2001, pp. 730–735.  “Wind profiles, 2s sampling time,” Rutherford Appleton Laboratory, Chilton Didcot, Oxfordshire, U.K. Roberto Cárdenas (S’95–M’97) was born in Punta Arenas, Chile. He received the electrical engineering degree from the University of Magallanes, Punta Arenas, Chile, in 1988, and the M.Sc. and Ph.D. degrees from the University of Nottingham, Nottingham, U.K., in 1992 and 1996, respectively. Currently, he is with the Electrical Engineering Department at the University of Magallanes. From 1989 to 1991, he was a Lecturer at the University of Magallanes. His research interests include control of electrical machines for wind energy applications and variable-speed drives. 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. Currently, he is with the Electrical Engineering Department at the University of Magallanes, Chile, where he was a Lecturer from 1985 to 1991. His main research interests are in control of power electronics converters, ac drives, and renewable energy systems.