Modeling and Control of a Wind Turbine Driven Doubly Fed Induction Generator

194 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 18, NO. 2, JUNE 2003 Modeling and Control of a Wind Turbine Driven Doubly Fed Induction Generator Arantxa Tapia, Gerardo Tapia, J. Xabier Ostolaza, and José Ramón Sáenz Abstract This paper presents the simulation results of a grid-connected wind driven doubly fed induction machine (DFIM) together with some real machine performance results. The modeling of the machine considers operating conditions below and above synchronous speed, which are actually achieved by means of a double-sided PWM converter joining the machine rotor to the grid. In order to decouple the active and reactive powers generated by the machine, stator-flux-oriented vector control is applied. The wind generator mathematical model developed in this paper is used to show how such a control strategy offers the possibility of controlling the power factor of the energy to be generated. Index Terms Doubly fed induction machine, power converter, power factor, vector control, wind power generation. I. NOMENCLATURE Stator side power factor. Wind turbine net power factor. Grid frequency. Stator magnetising current space phasor modulus., Direct- and quadrature-axis stator magnetising current components respectively, expressed in the stationary reference frame. Rotor current space phasor modulus., Direct- and quadrature-axis rotor current stationary reference frame., Direct- and quadrature-axis rotor current stator-flux-oriented reference frame., Reference values of the rotor current and components, respectively., Direct- and quadrature-axis rotor current rotor natural reference frame., Direct- and quadrature-axis stator current stationary reference frame. Manuscript received February 5, 2001; revised December 4, 2001. This work was supported by the electric generation company IBERDROLA S.A. A. Tapia, G. Tapia, and J. X. Ostolaza are with the Systems Engineering and Control Department, University of the Basque Country, Donostia-San Sebastián, 20011, Spain (e-mail: isptaota@sp.ehu.es). J. R. Sáenz is with the Electrical Engineering Department, University of the Basque Country, Bilbao, 48013, Spain (e-mail: iepsaruj@bi.ehu.es). Digital Object Identifier 10.1109/TEC.2003.811727, Direct- and quadrature-axis stator current stator-flux-oriented reference frame.,, Inner loop vector controller PI compensator parameters.,, Outer control-loop PI compensator parameters. Magnetizing inductance., Rotor and stator inductances, respectively. Rotor transient inductance., Wind turbine net active and reactive powers. Sum of the stator and rotor side active and reactive powers, respectively., Rotor side active and reactive powers, respectively., Stator side active power actual and reference values, respectively., Stator side reactive power actual and reference values, respectively., Stator and rotor phase winding resistances, respectively., Direct- and quadrature-axis rotor decoupling voltage components, respectively, expressed in the stator-flux-oriented reference frame., Direct- and quadrature-axis rotor voltage components, respectively, expressed in the stator-flux-oriented reference frame., Direct- and quadrature-axis rotor voltage rotor natural reference frame. Stator voltage space phasor modulus., Direct- and quadrature-axis stator voltage components, respectively, expressed in the stationary reference frame. Rotor electrical angle. Phase angle of stator flux-linkage space phasor with respect to the direct-axis of the stationary reference frame. Rotor electrical speed. Angular slip frequency. II. INTRODUCTION WIND energy is one of the most important and promising sources of renewable energy all over the world, mainly because it is considered to be nonpolluting and economically viable. At the same time, there has been a rapid development of related wind turbine technology [1] [3]. 0885-8969/03$17.00 2003 IEEE

TAPIA et al.: MODELING AND CONTROL OF A WIND TURBINE DRIVEN DOUBLY FED INDUCTION GENERATOR 195 Nevertheless, this kind of electric power generation usually causes problems in the electrical system it is connected to, because of the lack or scarcity of control on the produced active and reactive powers. Several designs and arrangements have been implemented so as to cope with this difficulty [4] [8]. As far as variable-speed generation is concerned, it is necessary to produce constant-frequency electric power from a variable-speed source [1], [3], [4], [9]. This can be achieved by means of synchronous generators, provided that a static frequency converter is used to interface the machine to the grid. An alternative approach consists in using a wound-rotor induction generator fed with variable frequency rotor voltage. This allows fixed-frequency electric power to be extracted from the generator stator. Consequently, the use of doubly fed induction machines is receiving increasing attention for wind generation purposes [6], [7], [10], [11]. One of the main advantages of these generators is that, if rotor current is governed applying stator-flux-oriented vector control carried out using commercial double-sided PWM inverters, decoupled control of stator side active and reactive powers results. The ability to generate electricity with power factors different to one would reduce the costs of introducing additional capacitors for reactive power regulation, and would be especially advantageous for both producers and distributors in charge of transmission systems. This paper aims to show the techniques followed to control a DFIM power factor. Several significant simulation results, obtained after modeling both the generator and its overall control system in MATLAB/SIMULINK, validated with real machine performance results are also presented. III. WIND TURBINE MODEL Several models for power production capability of wind turbines have been developed and can be found throughout the bibliography [4], [7], [9], [12]. The mechanical power, captured by a wind turbine, depends on its power coefficient given for a wind velocity and can be represented by where and correspond to the air density and the radius of the turbine propeller, respectively. The power coefficient can be described as the portion of mechanical power extracted from the total power available from the wind, and it is unique for each turbine. This power coefficient is generally defined as a function of the tip-speed-ratio which, in turn, is given by where represents the rotational speed of the wind turbine. Fig. 1 shows a typical relationship between the power coefficient and the tip-speed-ratio. It should be noted that there is a value of to ensure a maximum of. Thus, it can be stated that, for a specified wind velocity, there is a turbine rotational speed value that allows capturing the maximum mechanical power attainable from the wind, and this is, precisely, the turbine speed to be followed. (1) (2) Fig. 1. Fig. 2. Typical power coefficient versus tip-speed-ratio curve. DFIM configuration. The method followed in this paper in order to reach the optimum tip-speed-ratio at each wind velocity consists in, based on the generator rotor speed, estimating and, therefore, trying to achieve the optimum active power to be generated by means of the rotor current stator-flux-oriented vector control. Specifically, assuming that the optimum power coefficient and, as a result, the optimum tip-speed-ratio values for the particular wind turbine employed are properly identified, the stator side active power reference value which is made equal to is established starting from the turbine angular speed through (1) and (2). This operation principle is only effective below the rated wind speed, where the available wind power does not exceed the rated capacity of the generator. However, above the rated wind speed pitch regulation is applied so as to limit the attainable wind power, hence leaving the optimal power coefficient operation. IV. DOUBLY FED INDUCTION GENERATOR ELECTRICAL MODEL The basic configuration of a DFIM is sketched in Fig. 2. The most significant feature of this kind of wound-rotor machine is that it has to be fed from both stator and rotor side. Normally, the stator is directly connected to the grid and the rotor is interfaced through a variable frequency power converter. In order to cover a wide operation range from subsynchronous to supersynchronous speeds, the power converter placed on the rotor side has to be able to operate with power flowing in both directions. This is achieved by means of a back-to-back PWM inverter configuration. The operating principle of a DFIM can be analyzed using the classic theory of rotating fields and the wellknown model, as well as both three-to-two and two-tothree axes transformations.

196 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 18, NO. 2, JUNE 2003 TABLE I DFIG ELECTRIC PARAMETERS system outputs. As a result, the state equations implemented in MATLAB are the following: Fig. 3. Stator and rotor side reference frames for the Quadrature-Phase Slip-Ring model. In order to deal with the machine dynamic behavior in the most realistic possible way, both stator and rotor variables are referred to their corresponding natural reference frames in the developed model. In other words, the stator side current and voltage components are referred to a stationary reference frame, while the rotor side current and voltage components are referred to a reference frame rotating at rotor electrical speed, see Fig. 3. The machine electrical model expressed in such reference frames is referred to as the Quadrature-Phase Slip-Ring model [8]. When aiming to express the induction machine electrical model in the above-mentioned reference frames, it is first necessary to perform the Clarke s transformation from the three-phase to the current and voltage system, through the equations given in the Appendix. In this way, taking the general three-phase model of the electric machine dynamic performance as starting point, the Quadrature-Phase Slip-Ring model for the DFIM might be expressed through the following matrix equation See equation (3) at the bottom of the page. where represents the Laplace differential operator. The roles of current and voltage components in (3) need to be interchanged so as to treat voltages as independent variables system inputs and currents as dependent variables system outputs, as corresponds to a voltage doubly fed induction generator (DFIG). On top of this, each of the equations included in (3) is rewritten according to a nonlinear state equation, in order to achieve expressions whose structure is compatible with that of S-function-type C-MEX files. The states to be considered,,, and correspond to where all inductances are assumed to remain constant. In order to obtain the electric parameters needed to completely define the dynamic model of a four-pole 660 kw wound-rotor induction generator, different experimental tests were performed in a test-bed placed in the origin factory. From those standard tests, the parameter values referred to a 20 C ambient temperature, collected in Table I, were obtained. (4) (5) (6) (7) (3)

TAPIA et al.: MODELING AND CONTROL OF A WIND TURBINE DRIVEN DOUBLY FED INDUCTION GENERATOR 197 Therefore, the parameters defined for the dynamic model are computed as follows: mh mh mh (8) V. THERMAL STUDY Since the main objective of this research work consists in designing a controller so as to let the DFIG work with different power factors, the operating limits of the machine in regard to active and reactive powers need to be accounted for. One of the main aspects to be considered when trying to govern the reactive power generated or absorbed by a DFIG, is directly related to the temperature heat reached on the rotor side because of the high rotor currents the back-to-back PWM converter may drive. Such currents may cause damage to the insulation of the rotor windings, hence reducing the machine life span. As a result, while the working temperature increases, the amount of heat that can be removed out from the machine diminishes and, consequently, the value of the highest current that is allowed to be driven into or out of the DFIG rotor also decreases. In order to obtain an analytical expression relating the stator side active and reactive powers with the rotor side current maximum value, the following expressions are considered [8]: (9) Fig. 4. Generator P Q limits for several operating temperatures. capability, several limit curves, shown in Fig. 4, have been derived from the DFIM heating test by considering different operating temperatures 30, 50, and 60 C, exactly, which lead to different values of the maximum permissible rotor current. The solid curve at the top of Fig. 4, which has been derived by considering that the bidirectional PWM is able to handle currents up to 400 A, reflects the limitation imposed just by this rotor side converter. It has also to be stated that it can feed the DFIG rotor with instantaneous voltages up to 380 V. Generated active and reactive powers are considered to be positive. Consequently, considering the induction generator operating limits provided in the curves above, a control strategy has to be designed in order to govern separately the active and reactive powers interchanged with the grid through the stator. This can be achieved by implementing a stator-flux-oriented vector control algorithm on the rotor side, which requires the determination of both the stator flux-linkage space phasor position and rotor electric angle at each moment. (10) Based on (9) and (10), the equation for load curves given next is derived (11) where corresponds to the rotor current maximum value. According to (11), the radius and eccentricity of any load curve can be easily computed as and, respectively. As already mentioned, the limitation curve given in (11) is directly related to the rotor side current maximum value. Therefore, as the ambient temperature increases, the radius of the semicircle becomes smaller since, the highest current that is allowed to flow through the DFIG rotor, decreases. On the other hand, the eccentricity inherent to load curves is caused by the inductive nature of induction machines. Based on (11), and considering the restrictions imposed by rotor slip-rings and brushes, as well as those due to converter VI. CONTROL SCHEME The DFIM control structure shown in Fig. 5 contains two cascaded control-loops. The outer one governs both the stator side active and reactive powers, so that the power factor setpoint value demanded by the electric energy distribution company is complied with as accurately as possible. Simultaneously, it would be convenient to employ profitably the whole active power generation capability provided by the wind at each moment, from the income-yield capacity point of view. On the other hand, the inner control-loop task consists in controlling independently the rotor current direct and quadrature components expressed according to the reference frame fixed to the stator flux-linkage space phasor. In order to implement this inner control-loop, the stator-flux-oriented vector control method based on two identical PI controllers is used. It has to be pointed out that Tustin s trapezoidal method [13] has been used to discretise the PI controllers in both inner and outer control-loop algorithms. Consequently, a hybrid model containing a continuous induction machine and discrete controllers has been developed in MATLAB/SIMULINK using S-function type C-MEX files. Furthermore, as the controllers used are PI type, anti wind-up algorithms have also been implemented so as to prevent converter saturation.

198 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 18, NO. 2, JUNE 2003 Fig. 5. Overall control structure for the DFIM. Particularly, if the control signals originally computed in the inner or outer loops exceed the bidirectional converter capability, they are limited in such a way that priority is given to active power set-point achievement, rather than attempting to ensure the reactive power reference value demanded. A. Vector Control Implementation As stated in (9) and (10), when governing a stator-flux-oriented vector-controlled generator, it can be proved that variations in rotor current real and imaginary components, are directly reflected on their corresponding stator current components, provided that they are all referred to the reference frame fixed to the stator flux-linkage space phasor [8]. Therefore, and are used to control the stator reactive and active powers, respectively. Thus, the steps followed to model and implement this vector control algorithm are described below and can also be identified in Fig. 5. 1) Three-to-two phase Clarke s transformation of measured stator and rotor side currents in their corresponding natural reference frames. 2) Estimation of the stator flux-linkage space phasor angular position with respect to the stationary direct axis. Since the rotor side current components need first to be changed from their natural axes to the stationary reference frame, it is necessary to measure the rotor angle. The equations to be followed are given next 3) Expression of the rotor current space phasor in the reference frame fixed to the stator flux-linkage space phasor, so as to compare its and components with their corresponding and set-point values. Based on the errors in both current components, the voltage and components to be applied to the rotor side are generated by means of two identical PI controllers, as shown below (13) For this particular case, both PI controllers in (13) have been tuned applying the pole assignment method, in an attempt to reach a critically damped inner loop response with a 40-ms settling time. Furthermore, inclusion of parameter allows placing independently not only the inner loop poles, but also the unique zero inherent to the PI controller. Particularly, if is made equal to zero, the PI controller zero is placed at and, as a result, its influence on the closed-loop time response is cancelled out. 4) In order to improve the decoupling between and axes, the and decoupling voltage components given below are added to and, respectively (14) (12) where,, and. The resultant voltages in both axes will be referred to as and.

TAPIA et al.: MODELING AND CONTROL OF A WIND TURBINE DRIVEN DOUBLY FED INDUCTION GENERATOR 199 Fig. 6. Three-phase voltages applied to the rotor. Fig. 8. Time response of the rotor current i component. Fig. 7. Rotor three-phase currents. Fig. 9. Generated active power performance. 5) Expression of and according to the rotor natural reference frame as follows: (15) 6) Clarke s inverse transformation of rotor voltage and components from two-to-three phases. It is worth pointing out that replacing the voltage-controlled back-to-back PWM sketched in the control scheme proposed in Fig. 5 with a current-controlled rotor converter, this inner control-loop PI controllers and computation of decoupling voltages could be avoided. Actually, it would be sufficient to apply the reference frame change and the two-to-three phase transformation, given in steps 5. and 6. respectively, to current components and provided by the outer loop, in order to generate the three-phase current signals to be demanded to the rotor converter. Some results obtained when simulating the described model are provided in Figs. 6 12. These results correspond to a test carried out according to Table II, in which, keeping wind conditions constant m/s and kg/m, six changes Fig. 10. Time response of the rotor current i component. in rotor current and reference values were performed. First, two changes affected both components simultaneously, while last four involved only one of them. Figs. 6 and 7 show the three-phase voltages applied to the rotor side through the converter and the resulting rotor threephase currents. On the other hand, the correlation existing between the rotor current and components and the stator

200 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 18, NO. 2, JUNE 2003 Fig. 11. Reactive power performance. side active and reactive powers, respectively, can be clearly observed in Figs. 8 11, where both generated active and reactive powers have been assumed to be negative. The time response of rotor side- as well as wind turbine net active and reactive powers are also displayed in Figs. 9 and 11, respectively. At this point, it is convenient to highlight that, even though wind conditions do not alter during the whole test, the amount of generated active power can be varied just by modifying the current component value, provided that the outer control-loop shown in Fig. 5 is not yet implemented. Moreover, the machine rotor accelerations and decelerations observed in Fig. 12 correspond to current component setpoint changes. In fact, it has to be considered that wind energy is employed not only to generate electric power, but also to produce rotational mechanical energy, which is associated to rotor speed. Therefore, since the wind power provided to the turbine remains constant during this test, generated active power increases and decreases, shown in Fig. 9, give rise to rotor decelerations and accelerations, respectively. In addition, Figs. 9 and 12 prove that, below the synchronous speed, the rotor side power flows from the grid to the DFIG, whereas, at supersynchronous speeds, it flows in the opposite direction. This slip power management, which is closely related to slip frequency control, allows to generate electric energy at synchronous frequency permanently, in spite of rotor angular speed significant variations. As a result, it can be stated that the implemented vector control algorithm achieves very good decoupling of the stator side active and reactive powers, thus making it possible to follow either stator side or net different power factor reference values just by adding an outer control-loop which performs a relatively simple control strategy. Fig. 12. Rotor angular speed time response. TABLE II SET-POINT VALUES FOR i AND i CURRENT COMPONENTS DURING THE TEST B. Outer Control-Loop Design Once the vector control algorithm has been implemented on the induction generator, it is required to design the outer loop control law, which is responsible for providing the power generation process with the desired power factor. The steps followed by the designed control algorithm are summarized next: 1. Calculation of the optimum active power to be generated from the instantaneous rotor angular speed. It should be noticed that, once this outer control-loop has been correctly implemented, the amount of active power interchanged between the grid and the DFIG through its rotor side, turns out to be only a short fraction of the wind turbine net active power. Consequently, the stator side active power does not differ significantly from. 2. Computation of the stator side reactive power to be generated or absorbed, based on the instantaneous active power set-point obtained in the previous step and the desired either stator side or net power factor or, respectively. If the specification to be complied with corresponds to the stator side power factor, the calculation of is straightforward (16) On the other hand, if a wind turbine net power factor is specified as set-point, is derived as follows: (17) where the rotor side active and reactive powers might be either measured or estimated as (18)

TAPIA et al.: MODELING AND CONTROL OF A WIND TURBINE DRIVEN DOUBLY FED INDUCTION GENERATOR 201 As far as the sign of is concerned, it has necessarily to be established by considering the nature of the requested power factor. Accordingly, leading capacitive and lagging inductive power factors should give rise to reactive power generation and consumption, respectively. In addition, it is checked whether the resulting produces an operating point within the limits defined by the DFIG load curve or not. If not, it is limited according to this restriction. 3. Application of two identical PI compensators to the previously decoupled stator side active and reactive power controlloops, in order to generate the reference and rotor current components to be followed by the inner control-loop see Fig. 5 as Fig. 13. Generator net power factor time response. (19) Since, according to (9) and (10), it turns out that signals and as well as and exhibit contrary signs at any time [8], it is essential to note that, for this outer loop, the error signals fed into its PI controllers are obtained by subtracting the setpoint of the variable to be controlled or from its actual value or, respectively. Similarly to the inner loop case, these two PI controllers are again tuned following the pole assignment method. In particular, a monotonically increasing time response with no overshooting and a 70-ms settling time is demanded for the outer control-loop. The function of factor is equivalent to that satisfied by parameter in the inner loop. The stator side actual active and reactive powers are measured by means of a digital power analyzer, so that their corresponding error signals are fed into the PI controllers given in (19). During the test, whose simulation results are collected in Figs. 13 20, in addition to changing the wind turbine net power factor set-point four times, sudden wind speed variations were applied in order to evaluate the overall control-system performance under wind gusts. Nevertheless, since the wind speed did not exceed its rated value all through the test, no pitch regulation took place. As shown in Table III, throughout the first four test stages, the wind speed and the net power factor set-point were alternatively varied, while in the last two both variables were simultaneously changed. In addition, the DFIG net power factor was kept lagging during these last two stages. Fig. 13 shows the fast wind generator response to DFIG net power factor set-point changes. It should also be noted that, once the outer control-loop is put into operation, only wind speed changes can cause the generated active power to vary, since rotor angular velocity, which establishes, depends on wind speed. Thus, the overall control-system designed allows the generator to work properly either under subsynchronous or supersynchronous conditions, as shown in Fig. 14. Once again, the relationship between the and rotor current components and the stator side active and reactive powers Fig. 14. Rotor angular speed time response. Fig. 15. Rotor current i component time response. becomes evident in Figs. 15 18, where generated active and reactive powers have been taken as negative. As stated before, Fig. 16 reveals that, provided that the outer control-loop works properly, the DFIG net and stator side active powers turn out to be very similar. Finally, the three-phase rotor voltages and currents corresponding to this test are also displayed in Figs. 19 and 20, respectively.

202 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 18, NO. 2, JUNE 2003 Fig. 16. Generated active power performance. Fig. 19. Rotor three-phase voltages. Fig. 17. Rotor current i component time response. Fig. 20. Rotor three-phase currents. TABLE III NET POWER FACTOR SET-POINT AND WIND SPEED VALUES DURING THE TEST Fig. 18. Reactive power performance. VII. COMPARISON BETWEEN REAL AND SIMULATED RESULTS In order to validate the wind generator model performance when the designed control law for stator active and reactive power decoupling is applied, some graphs comparing real and simulation results are presented. Figs. 21 and 22 show the dynamic behavior of a real 660-kW generator working in a wind farm when, generating 300 kw as a result of the wind speed at the moment with a, sudden stator side power factor set-point changes take place. In both cases, this new set-point corresponds to a power factor, leading in Fig. 21, and lagging in Fig. 22. Generated active and reactive powers are considered to be positive. Since wind conditions remain constant during the whole test, it can be seen that generated stator active power does not change, while stator side reactive power varies rapidly so as to track the power factor new set-point. On the other hand, the simulated dynamic performance of the wind generator model described throughout this paper is shown

TAPIA et al.: MODELING AND CONTROL OF A WIND TURBINE DRIVEN DOUBLY FED INDUCTION GENERATOR 203 Fig. 21. case. Dynamic performance of a real wind generator. Leading power factor Fig. 24. Simulated dynamic performance of the wind generator model. Lagging power factor case. Fig. 22. case. Dynamic performance of a real wind generator. Lagging power factor paper, correspond strictly to those of a real doubly fed induction generator working in a wind farm. Even if working conditions and, consequently, the optimum of active power to be generated vary because of changes in wind speed, the designed control laws are capable of keeping track of the desired power factor in the wind generator. Nevertheless, it is worth pointing out that the above-mentioned curve, which provides the optimum active power to be generated for each wind speed, could be optimized and tested using the developed wind generator model. Since the simulation results obtained so far are really satisfactory, it would be especially interesting to build a wind farm model based on the wind generator model described in this paper, so as to design and analyze possible power factor control laws for the overall wind farm system. APPENDIX Any three-phase stator or rotor electrical magnitude can be expressed according to its natural reference frame stationary, if it is a stator side quantity, and rotating at rotor electrical speed if it is a rotor side quantity direct, quadrature, and zerosequence components as follows: Fig. 23. Simulated dynamic performance of the wind generator model. Leading power factor case. in Figs. 23 and 24. The simulation reproduces the real test conditions so that, for a constant wind speed, a sudden change in the stator side power factor set-point is introduced, thus varying its reference value from to a leading Fig. 23 or lagging Fig. 24. Since simulation results obtained in these and other diverse tests are completely according to the wind generator real behavior, the reliability of the developed model is proved. VIII. CONCLUSION The simulation results obtained when running the wind generator and its overall control-system model presented in this (20) where represents the stator or rotor side voltage, current or flux-linkage. Equation (20) is referred to as Clarke s transformation. Similarly, the Clarke s inverse transformation from to three-phase quantities can be carried out just by applying the matrix equation given next (21)

204 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 18, NO. 2, JUNE 2003 ACKNOWLEDGMENT We would especially like to thank R. Criado and J. Soto from the electric generation company IBERDROLA for their helpful comments. The authors are also grateful to the induction generator manufacturing company, INDAR, and the control systems company, INGETEAM, for their contribution in providing the electric machine characteristics and all the test results needed for this research work; special thanks to G. Rivas, J. Garde, and J. Mayor. Arantxa Tapia was born in San Sebastián, Spain, on September 24, 1963. She received the electrical engineering degree from the School of Industry Engineers, University of Navarra, Spain, in 1987. She received the Ph.D. degree in 1992 from the Univeristy of Basque Country. Currently, she is Full Professor in Control at the University of Basque Country. She joined the University of the Basque Country in the Systems Engineering and Control Department. She worked for five years in the Electronics and Control Department in CEIT, a research center in the Basque Country. Her current research interests include control and monitoring of different processes as ac machines and different industrial multivariable processes. REFERENCES [1] D. J. Leith and W. E. Leithead, Appropriate realization of gain-scheduled controllers with application to wind turbine regulation, Int. J. Contr., vol. 65, no. 2, pp. 223 248, 1996. [2] D. Levy, Stand alone induction generators, Elect. Power Syst. Res., vol. 41, pp. 191 201, 1997. [3] B. T. Ooi and R. A. David, Induction-generator/synchronous-condenser system for wind-turbine power, Proc. Inst. Elect. Eng., vol. 126, no. 1, pp. 69 74, Jan. 1979. [4] W. E. Leithead, M. C. M. Rogers, D. J. Leith, and B. Connor, Progress in control of wind turbines, in Proc. 3rd Europe. Contr. Conf., Rome, Italy, Sept. 1995, pp. 1556 1561. [5] C.-M. Liaw, C.-T. Pan, and Y.-C. Chen, Design and implementation of an adaptive controller for current-fed induction motor, IEEE Trans. Ind. Electron., vol. 35, pp. 393 401, Aug. 1988. [6] M. G. Simões, B. K. Bose, and R. J. Spiegel, Fuzzy logic based intelligent control of a variable speed cage machine wind generation system, IEEE Trans. Power Electron., vol. 12, pp. 87 95, Jan. 1997. [7] R. Spee, S. Bhowmik, and J. H. R. Enslin, Novel control strategies for variable-speed doubly fed wind power generation systems, Renewable Energy, vol. 6, no. 8, pp. 907 915, 1995. [8] P. Vas, Vector Control of AC Machines. New York: Oxford Univ. Press, 1990. [9] A. Miller, E. Muljadi, and D. Zinger, A variable speed wind turbine power control, IEEE Trans. Energy Conversion, vol. 12, pp. 181 186, June 1997. [10] D. J. Atkinson, R. A. Lakin, and R. Jones, A vector-controlled doubly-fed induction generator for a variable-speed wind turbine application, Trans. Inst. Meas. Contr., vol. 19, no. 1, pp. 2 12, 1997. [11] R. S. Peña, J. C. Clare, and G. M. Asher, Vector control of a variable speed doubly-fed induction machine for wind generation systems, EPE J., vol. 6, no. 3-4, pp. 60 67, Dec. 1996. [12] T. Tanaka, T. Toumiya, and T. Suzuki, Output control by hill-climbing method for a small scale wind power generating system, Renewable Energy, vol. 12, no. 4, pp. 387 400, 1997. [13] K. J. Åström and T. Hägglund, PID Controllers: Theory, Design and Tuning, USA: Instrument Soc. America, 1995. [14] S. Wade, M. W. Dunnigan, and B. W. Williams, Modeling and simulation of induction machine vector control with rotor resistance identification, IEEE Trans. Power Electron., vol. 12, pp. 495 506, May 1997. Gerardo Tapia was born in San Sebastián, Spain, on April 22, 1970. He received the electrical engineer degree from the University of Navarra, Spain, in 1995, and the M.Sc. degree in digital systems engineering from Heriot-Watt University, U.K., in 1996. He received the Ph.D. degree from the University of the Basque Country Systems Engineering and Control Department, in 2001. During the first half of 1997, he was an Assistant Researcher with Ikerlan Research Center, Spain. Currently, he is Full Lecturer in control and digital electronics with the University of the Basque Country Systems Engineering and Control Department. His current research interests include wind power generation and control of electric drives based on vector and direct torque control schemes. J. Xabier Ostolaza was born in San Sebastián, Spain, on October 23, 1968. He received the degree in Electrical Engineering from University of Navarra, Spain, in 1993. He worked for five years in the Electronics and Control Department of CEIT Research Centre, until he awarded a Ph.D. in 1998. After that, he joined the University of the Basque Country in its Systems Engineering and Control Department, where nowadays he is full lecturer in System Modeling and Control. His current research interests include Frequency-based Robust QFT Control, Distributed Electrical Generation Control and Process Automation. José Ramón Sáenz was born on January 12, 1954. He received the Ph.D. degree in electrical engineering from University of Navarra, Spain, in 1980. Currently, he is Full Professor in the electrical engineering department (University of the Basque Country) and Head of the Department. He leads an appreciable number of research groups and projects in areas such as wind energy, electric energy systems, deregulated electric markets, and electrical machinery.