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Running head: COMPUTERS AND OPERATION RESEARCH Computers and operation research Name Institution 1 COMPUTERS AND OPERATION RESEARCH 2 Computers and operation research usually meet in a vast number of scientific fields. Most of them are currently a vital concern to our troubled society. These include transportation, safety, ecology, urban planning, economics, reliability, investment strategy, inventory control, and military analysis. This journal gives an international forum for operations research and computer applications techniques to problems in the selected fields. The common aspect in all these scientific areas which this journal addresses is the methodology for evaluating viable solutions to these problems by the use of computers and the operations research techniques. The mathematical methodology is not however the only one that is of interest. Both applications are equally important and are manually supportive because understanding of the application helps one greatly in comprehending the mathematical methods that are used and vice versa. This journal will discuss the scientific fields of application and will be broad in scope of the subject of the matter. The language, form and content of the journal will take cognizance of this span of applications and of the resulting fact, which many readers may not be expert in the given scientific field to which the author applies the operations research and computer techniques. The journal will also publish some articles that are containing some interesting application despite the fact that there may be no new technique that is involved. Therefore, it is important there be actual or real cases of interest and significance which the author was asked to analyze. The presentation and content of the international journal is to give maximum utility to teachers, practitioners and researchers who have a given interest in operations research, computers and the subject of the matter of the application fields served by these. Special features to be included from time to time include descriptions of computer programs that may be of immediate value to researchers. These programs will be tabulated in adequate detail for immediate use. COMPUTERS AND OPERATION RESEARCH References Stefan, N. (2013). Computers & operations research and their application to problems of world concern. Journal of computer and operations research Vol. 5, pp. 14 – 38. 3 Literature Critique Format: The literature critique is a brief summary of an article from a ‘refereed’ journal. Critiques must be word-processed, single spaced and at most one page. Also, you must have a minimum margin size of 0.75 inch and a maximum margin size of 1inch on all sides (i.e., where the top, left and rights sides are basically even) of your submitted assignment. Occasionally, your article may not fully reach the bottom margin due to the writing of your summary; thus, if this occurs, you must not leave more than a 1.5” margin at the bottom in any case. If necessary, write a longer summary! Minimum acceptable font size is 10 pt and the maximum is 12 pt. In the final paragraph, briefly discuss one point or idea from the article that really made you think or really impressed you. Only the last paragraph can be written from the first person point of view, but not in any other location of the literature critique should 1st or 3rd person be used. See my posted critique for an example of this. A proper bibliographic reference MUST appear at the top of the paper. Although many reference styles exist, the only style that will be accepted in this class is the APA-style as shown below: First Author’s Last Name, First Initial. Middle Initial., & Second Author’s Last Name, First Initial. Middle Initial. (year of publication). Title of the article with only the first letter of the first word in title or sub-title as well as proper nouns and acronyms are capitalized. Name of Journal in Italics, volume in italics (issue number in parenthesis and not in italics if known), first page number-last page number. e.g. Pitts, Jr., R.A., & Ventura, J.A. (2009). Scheduling manufacturing cells using Tabu Search. International Journal of Production Research, 47(24), 6907-6928. Jerald, J., Asokan, P., Prabaharan, G., & Saravanan, R. (2005). Scheduling optimization of flexible manufacturing systems using particle swarm optimization algorithm. International Journal of Advanced Manufacturing Technology, 25(1), 964-971. Note: If more than 2 authors have written the article, ALL authors names must be listed in the bibliographical reference as in the example above. www.DownloadPaper.ir 130 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL 21, NO, 1, MARCH 2006 Control of Permanent-Magnet Generators Applied to Variable-Speed Wind-Energy Systems Connected to the Grid Mónica Chinchilla, Member, IEEE, Santiago Arnaltes, Member, IEEE, and Juan Carlos Burgos, Member, IEEE Abstract—Wind energy is a prominent area of application of variable-speed generators operating on the constant grid frequency. This paper describes the operation and control of one of these variable-speed wind generators: the direct driven permanent magnet synchronous generator (PMSG). This generator is connected to the power network by means of a fully controlled frequency converter, which consists of a pulsewidth-modulation (PWM) rectifier, an intermediate dc circuit, and a PWM inverter. The generator is controlled to obtain maximum power from the incident wind with maximum efficiency under different load conditions. Vector control of the grid-side inverter allows power factor regulation of the windmill. This paper shows the dynamic performance of the complete system. Different experimental tests in a 3-kW prototype have been carried out to verify the benefits of the proposed system. Index Terms—Permanent-magnet generators, pulsewidthmodulated (PWM) power converters, wind energy. I. INTRODUCTION ARIABLE-SPEED power generation enables operation of the turbine at its maximum power coefficient over a wide range of wind speeds, obtaining a larger energy capture from the wind. One of the problems associated with variable-speed wind systems today is the presence of the gearbox coupling the wind turbine to the generator. This mechanical element suffers from considerable faults and increases maintenance expenses. To improve reliability of the wind mill and reduce maintenance expenses the gearbox can be eliminated. Permanent magnets can be used to replace the excitation winding of synchronous machines because of due to magnet price reduction and magnetic material characteristic improvement [1]. Permanent-magnet excitation allows us to use a smaller pole pitch than do conventional generators, so these machines can be designed to rotate at rated speeds of 20–200 r/min, depending on the generator rated power [2]. Several wind generator manufacturers incorporate multipole permanent-magnet generators into their wind turbines (e.g., Jeumont, Lagerwey). The overall system (see Figs. 1 and 3) consists of a surface mounted permanent-magnet generator with a frequency con- V Manuscript received December 17, 2002; revised May 4, 2004. This work was supported by the Spanish government under the PB98-0032 project of the “Programa Sectorial de Promoción General del Conocimiento” of the MEC. Paper no. TEC-00281-2002. The authors are with the Electrical Engineering Department, Universidad Carlos III, Leganes 28911, Spain (e-mail: mchin@ing.uc3m.es; arnalte@ing. uc3m.es; jcburgos@ing.uc3m.es). Digital Object Identifier 10.1109/TEC.2005.853735 Fig. 1. Rectifier control schemes. verter which allows variable-speed operation. By adapting the turbine speed to wind variations, it is possible to obtain maximum power from the incident wind. The main aim of this work is the precise selection of the system components (generator, converter, grid filter) as well as the control loop design and implementation, in order to extract maximum power from the wind. To achieve this objective, appropriate active generator current components are imposed [3], [4]. Variable-speed wind-energy conversion systems have been widely discussed in the bibliography. In [3], the control of a variable-speed wind-turbine with a doubly fed induction generator is presented with experimental results. The power converter in such generators needs only to be rated to handle rotor power (power converter rating is related to speed range). In [4], the control of a variable-speed permanent-magnet generator with a diode rectifier followed by a dc chopper is shown. With this configuration the control of the generator power factor is not possible, which in turn, affects generator efficiency. Also, high harmonic distortion currents are obtained in the generator that reduce efficiency and produce torque oscillations. In [5], three different alternatives for generator power factor rating are given in order to obtain an optimum rating of a permanent-magnet generator and its power converter. In [6], the optimal magnetizing current leading to the highest efficiency of an induction generator is obtained online through a fuzzy system. The main difference between these works and the work presented in this paper is that, in this paper, the generator reactive current component is calculated and imposed on the generator in order to minimize power losses, both in the generator and power converter, along the whole operating range. In this paper, an active and reactive power control for the inverter used for 0885-8969/$20.00 © 2006 IEEE Authorized licensd use limted to: IE Xplore. Downlade on May 10,2 at 19:0345 UTC from IE Xplore. Restricon aply. www.DownloadPaper.ir CHINCHILLA et al.: CONTROL OF PERMANENT-MAGNET GENERATORS grid connection is also provided. The power capability of such an inverter is also discussed. A deeper study of inverter operation may be found in [7]. Different experimental tests in a 3-kW prototype system have been carried out. A digital signal processor (DSP)-based board has been used to implement control algorithms. II. PROTOTYPE DESCRIPTION AND CONTROL IMPLEMENTATION A. Permanent-Magnet Generator and Grid Connection The permanent-magnet synchronous generator used was 3 kW, 220 V (wye three-phase stator winding), and 375 r/min (16 poles). NdFeB magnets provide proper flux density in the air gap. The winding resistance and inductance (obtained through laboratory tests) are, respectively, RS = 2.4 Ω and LS = 51 mH. Rotor position is obtained through an encoder giving 1500 pulses per revolution. The frequency converter consists of two back-to-back insulated gate bipolar transistors (IGBTs) bridges; the one connected to the generator works as a pulse rectifier; the other one, connected to the grid, works as a pulsewidth-modulation (PWM) inverter. Both of them have six IGBTs (600 V, 15 A). The dc link incorporates a 600-µF, 800-V capacitor. An inductive filter has been designed to limit harmonic current injection into the grid complying with IEC 61000-3-2 regulations. The switching frequency was 3 kHz. A transformer (400/230 V) was used for grid connection to allow the operation of the inverter with leading power factor. The resulting inductance in the grid connection, including the transformer short circuit reactance, was 4 mH. B. Wind Turbine Emulation The emulation of the wind turbine is implemented by means of a dc motor drive with torque control. In the prototype, a 4.4 kW, 1980 r/min dc motor was used. A computer program reads the wind input file, which has been obtained in different test conditions, and calculates the wind turbine torque, by taking into account wind velocity, turbine rotational speed, and the wind turbine power coefficient curve (a lookup table in the computer was used). The control algorithms for turbine emulation are implemented in a control board dSPACE DS1102. This board is a commercial system designed for rapid prototyping of real control algorithms; it is based on the Texas Instruments TMS320C31 floating-point DSP and includes four A/D input channels, 16 digital I/O channels, an eight-channel capture/compare unit, and a six-channel PWM generation module. The DS1102 board is hosted by a personal computer. C. Power Converter Control Real-time control was implemented in two dSPACE boards, one for each power converter. The sampling time for generator control (175 µs) is longer than that of the grid inverter control, as the former provides the turbine torque reference besides the corresponding PWM pulse signals. Also, the generator controller board has to obtain the reference angle position and the Authorized licensd use limted to: IE Xplore. Downlade on May 10,2 at 19:0345 UTC from IE Xplore. Restricon aply. 131 generator speed from the pulse encoder signals. Inverter control calculations are simpler, as the reference angle needed for vector control is obtained from the line voltage zero crossing, that allows a reduction of the sampling time (130 µs). Hall sensors are used to capture necessary current and voltage signals. III. CONTROL OF THE PERMANENT-MAGNET GENERATOR-SIDE CONVERTER In order to get a dynamical model for the electrical generator that easily allows us to define the generator control system, the equations of the generator are projected on a reference coordinate system rotating synchronously with the magnet flux. The dynamic model of the surface-mounted permanent-magnet generator in the magnet flux reference system is diS d + LS ωiS q dt diS q − LS − LS ωiS d + ωΨ dt uS d = −RS iS d − LS uS q = −RS iS q (1) where LS and RS are the generator inductance and resistance, respectively, ω is the generator speed, and Ψ is the magnet flux. The above equations show how to control current components by means of the applied voltage. The electromagnetic torque is given by Te = 3 pΨiS q 2 (2) where p is the pole pair number. Equation (2) shows that the generator torque may be controlled directly by the quadrature current component. Fig. 1 shows the schematic diagram of the control loops of the permanent-magnet generator-side converter. direct-axis current component reference is obtained through a calculator f (Ω), in order to minimize power losses. The required d–q components of the rectifier voltage vector are derived from two proportional plus integral (PI) current controllers: one of them controlling the d-axis component of the current and the other one the q-axis component. Compensation terms are added to improve the dynamic response. The control requires the measurement of the stator currents, dc voltage, and rotor position. Space-vector modulation (SVM) is used to generate the switching signals for the power converter semiconductors. A. Efficiency Optimization In a variable-speed wind turbine, maximum power is a cubic function of rotational speed. To maximize efficiency, losses for a given load must be minimized. A stator q-axis current component is used to develop generator torque, but a freedom degree remains to set direct current. A direct-axis current component can be set at zero to minimize current for a given torque, and therefore, minimize resistive losses [8], but d-axis current component can also be used to reduce stator flux as  (3) ΨS = (LS iS q )2 + (Ψ + LS iS d )2 and minimize core losses. 132 www.DownloadPaper.ir IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL 21, NO, 1, MARCH 2006 The optimum value for iS d is obtained offline from   min Ploss = min(PFe + PCu + Pmec + Prectifier ). (4) The value of iS d resulting from (4) is tabulated as a function of generator speed, which is expressed as the function f (Ω) in Fig. 1. B. Control-Loop Design From (1), the transfer function of the stator winding is F (s) = IS d (s) 1 IS q (s) = = ′ US′ d (s) US q (s) RS + LS s (5) ′ ′ where Usd and Usq are the voltage components in the d–q axes that control the corresponding current components, and s is the Laplace operator. The converter can be modeled as a pure delay of one sampling period. Conventional design techniques are used to calculate √ the controller parameters. Choosing a damping factor ξ = 1/ 2 to maintain overshooting lower than 5%, the resulting controller transfer function is 0.0201s + 1 . (6) R(s) = 46 0.0201s Cross frequency of the current control loops is 1414 Hz. In the experimental rig, a sampling frequency of 3 kHz is used, which is not high enough, so continuous Laplace domain design is not justified. The current controller in the z domain for the aforementioned sampling frequency results as follows: R(z) = 46z − 45.2 . z−1 (7) C. Rectifier Operating Limits As said, to achieve maximum efficiency for each load, the proper direct current must be injected. Nevertheless, some limits exist on the controller rectifier. These limits are due to the following. 1) Maximum Current Limit: It is due to the generator rated current or admissible IGBTs current. 2) Maximum Voltage Limit: To achieve a given direct and quadrature current a certain armature voltage is needed. So current component limits may be expressed as a function of the maximun allowable rectifier voltage. Maximum rectifier voltage U1 lim depends on dc voltage and on the amplitude modulation index. With SVM, the rms voltage value of the fundamental voltage component can be expressed as 1 U1 = √ √ ma Udc 3 2 (8) where ma is the amplitude modulation index [7]. When choosing ma = 1, the maximum voltage is 0.408 times the maximum dc link voltage. Neglecting RS in (1), it follows that in steady state, the rectifier current limit may be expressed by 2  2  U1 lim E 2 = − IS d (9) IS q + XS XS where E is the generator electromotive force (EMF). Authorized licensd use limted to: IE Xplore. Downlade on May 10,2 at 19:0345 UTC from IE Xplore. Restricon aply. Fig. 2. Real-time response of generator current components. D. Experimental Results Fig. 2 shows generator current response under a quadrature current step at 185 r/min. A fast and decoupled response is obtained. For the test, zero d-axis current command is set. Fig. 2 shows that the response of the q-axis current does not affect the d-axis current response. IV. CONTROL OF THE LINE-SIDE CONVERTER The dynamic model of the grid connection when selecting a reference frame rotating synchronously with the grid voltage space vector is did + ωLiq dt diq − ωLid uq = uiq − Riq − L (10) dt where L and R are the grid inductance and resistance, respectively, and uid and uiq are the inverter voltage components. If the reference frame is oriented along the supply voltage, the grid voltage vector is ud = uid − Rid − L u = ud + j0. (11) Then active and reactive power may be expressed as 3 ud id . (12) 2 3 Q = ud iq . (13) 2 Active and reactive power control can be achieved by controlling direct and quadrature current components, respectively. The control of this converter is quite similar to that of the generator. Two control loops are used to control the active and reactive power, respectively [3] (Fig. 3). An outer dc voltage control loop is used to set the d-axis current reference for active power control. This assures that all the power coming from the rectifier is instantaneously tranferred to the grid by the inverter. P = www.DownloadPaper.ir CHINCHILLA et al.: CONTROL OF PERMANENT-MAGNET GENERATORS 133 B. Inverter Sizing Fig. 3. Inverter control schemes. The second channel controls the reactive power by setting a q-axis current reference to a current control loop similar to the previous one. The current controllers will provide a voltage reference for the inverter that is compensated by adding rotational EMF compensation terms. All controllers are PI and are tuned using the symmetrical optimum method. A. Mathematical Formulation of the Inverter P-Q Capability The inverter operating limits represent the maximum active and reactive power inverter capability. These limits depend on the following constraints. 1) The rated current of the power switches or any other limiting element in the grid interface (Imax ) P 2 + Q2 = (3U Imax )2 . (14) 2) The maximum root mean square (rms) voltage of the fundamental component of the inverter voltage, which in turn depends on the dc-link voltage, on the modulation technique used and on the maximum amplitude modulation index allowed in steady-state conditions. Once the last two are fixed, the reactive power capacity depends on the inverter dc-link voltage. Neglecting grid resistance in (10) and taking into account (12) and (13), it follows that in steady state, the resulting inverter limits may be expressed by the circumference [7]  P2 + Q + 3U X 2 2  = 3 2 UDC ma X 2  (15) where X is the grid reactance. This situation is quite similar to that of a synchronous machine, in which the active and reactive power capability limits depend on the field current. In the inverter, for a given dc-link voltage, the amplitude modulation index plays the role of the field current. Power references laying out of the converter domain will produce highly distorted current waveforms. Authorized licensd use limted to: IE Xplore. Downlade on May 10,2 at 19:0345 UTC from IE Xplore. Restricon aply. The inverter P-Q capability depends mainly on the following: 1) converter dc-link voltage; 2) grid filter inductance; 3) grid rms voltage. Of course, the rating of the power switches or any other physical devices, like the filter, will limit the power capability of the grid connection. For sizing the inverter, the following considerations have to be taken into account. 1) The maximum active power the inverter can inject into the grid, for a given power factor, increases with dc voltage. 2) The inverter may be used as a reactive power compensator. The maximum reactive power the inverter can inject into the grid, with a certain power factor, increases with dc voltage. 3) Higher inductance of the filter leads to lower current totalharmonic distortion (THD) values, but the inverter power capability decreases. 4) Grid voltage plays an important role in the inverter operating limits. Sometimes, it could be useful to connect the inverter to the grid through a step-up transformer. The maximum active power that the inverter can inject into the grid, with unity power factor, increases as the turn ratio increases. The same is true for reactive power capability. V. MAXIMUM POWER TRACKING A. Wind Turbine The mechanical power delivered by a wind turbine is expressed as Pmec = 1 ρAcp vw3 2 (16) where ρ is the air density, A is the area swept out by the turbine blades, vw is the wind velocity, and cp is the power coefficient defined as the ratio of turbine power to wind power; cp is a function of the pitch angle β and of the tip speed ratio λ defined as the ratio of turbine speed at the tip of a blade to wind velocity (vw ) λ= ΩRt vw (17) where Rt is the turbine radius, and Ω is the turbine speed. In a wind turbine, there is an optimum value of tip speed ratio λopt that leads to maximun power coefficient (cp max ). From (16) and (17), we get [9] Pmax = 1 5 2 ρπRt cp max 3 Ωopt . λ3opt (18) This equation shows the relationship between turbine power and turbine speed at maximum power. When regulating the system under the specification of maximum power, it must be taken into account that turbine power must never be higher than generator rated power. Once generator rated power is reached 134 www.DownloadPaper.ir IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL 21, NO, 1, MARCH 2006 Fig. 4. Regulation stages. Fig. 5. Wind velocity v (in meters per second). at rated wind velocity (vr ), output power must be limited. For variable-speed wind turbines, a mechanical actuator is usually employed to change the pitch angle of the blades in order to reduce power coefficient (cp ) and maintain the power at its rated value. In some wind turbines, when working with the maximum power coefficient, rated speed is obtained at a wind velocity lower than that of generator rated power, because the choice of the generator rating is an optimization process between energy capture for the wind system and system cost [10]. When rated turbine speed is reached at a wind velocity vW 1 , control strategy must be changed so that a higher wind velocity no longer increases turbine speed but increases generated power until generator rated power; increases in rotor speed of about 10% are allowed during transients because of the slow pitch control response. To prevent structural damage, the turbine is shut down over the so-called furling wind speed (vcut−off ). Also under cut-in wind speed (vcut−in ), the turbine is shut down because the power is so low that it is hardly worth working with. So in order to regulate Authorized licensd use limted to: IE Xplore. Downlade on May 10,2 at 19:0345 UTC from IE Xplore. Restricon aply. Fig. 6. Experimental results. (a) Generator speed n (in revolutions per minute). (b) Actual power P (in Watts). (c) Reference and actual q-axis current component iS q (in Amps). (d) Power coefficient cp . www.DownloadPaper.ir CHINCHILLA et al.: CONTROL OF PERMANENT-MAGNET GENERATORS the system, different stages can be distinguished, depending on the wind velocity (Fig. 4). Taking into account these stages, the control strategy is the following 1) When Wind Velocity Is Between Cut-In and vw 1 : An optimal speed reference is applied in order to obtain maximum power from the incident wind. Speed reference is obtained from measured power taking into account (18). A speed control loop provides quadrature axis current reference as this current is proportional to generator torque. The blade pitch angle is set at an optimal value that allows the turbine to extract maximum energy from incident wind. Speed control loop bandwidth must be as low as possible (around 2 rad/s) in order to obtain a smooth power output [11]. An efficient generator control means also minimizing the power losses. To achieve this objective, not only active but reactive generator current component is imposed by the power converter (Section III). 2) When Wind Velocity Is Greater Than vw 1 : Generator speed is held at its rated value by limiting speed reference. The speed control loop will act on the quadrature-axis current component (proportional to generator torque) to achieve this objective. Rated torque is obtained at rated wind velocity. 3) When Wind Velocity Is Higher Than Rated: Power is limited by pitch control. To avoid over rated power excursions due to wind gusts, a constant power reference is obtained by reducing torque (with the increase of rotational speed). B. Experimental Results Fig. 6 shows experimental results for the wind velocity shown in Fig. 5. Fig. 6(a) shows shaft speed; it can be observed that the system tracks the maximum power point until rated generator speed is achieved. Fig. 6(c) shows reference and actual values of quadrature axis current, which is proportional to generator torque. Note that the speed control loop does not impose any abrupt change in torque reference, resulting in low-power fluctuations [see Fig. 6(b)]. Power coefficient cp [see Fig. 6(d)] is close to its maximum value until the generator gets its rated power; then, the pitch angle is changed to limit power and speed. VI. CONCLUSION This work shows the performance of a direct-driven permanent-magnet synchronous generator used in variablespeed wind-energy systems. When exciting the system with a real wind profile, the system is able to track maximum power using generated power as input. The speed controller sets the generator torque command, which is achieved through a current control loop. An efficient generator control has been proposed. To achieve this objective, the optimum generator d-axis current component is imposed by the power converter, i.e., the current that leads to the minimum losses. The proposed system has been implemented in a real-time application, with a commercial permanent-magnet synchronous generator and a dc drive that emulates the wind turbine behaviour. The real-time process is running in a dSPACE board that includes a TMS320C31 Authorized licensd use limted to: IE Xplore. Downlade on May 10,2 at 19:0345 UTC from IE Xplore. Restricon aply. 135 floating-point DSP. Experimental results show the appropriate behavior of the system. REFERENCES [1] A. Grauers, “Efficiency of three wind energy generator systems” IEEE Trans. Energy Convers, vol. 11, no. 3, pp. 650–657, Sep. 1996. [2] E. Spooner and A. C. Williamson, “Direct coupled, permanent magnet generators for wind turbine applications,” Proc. Inst. Elect. Eng.—Elect. Power Appl., vol. 143, no. 1, pp. 1–8, 1996. [3] R. Peña, J. C. Clare, and G. M. Asher, “Doubly fed induction generator using back-to-back PWM converters and its application to variable-speed wind-energy generation,” Proc. Inst. Elect. Eng.—Elect. Power Appl., vol. 143, no. 3, pp. 231–241, May 1996. [4] Z. Chen and E. Spooner, “Simulation of a direct drive variable speed energy converter,” in Proc. Int. Conf. Electrical Machines, Istanbul, Turkey, 1998, pp. 2045–2050. [5] A. Grauers “Design of direct driven permanent magnet generators for wind turbines,” M.S. thesis, Chalmers Univ. Technol., Göteborg, Sweden, 1996. [6] M. G. Simoes and B. K. Bose, “Design and performance evaluation of fuzzy-logic-based variable-speed wind generation system,” IEEE Trans. Ind. Appl., vol. 33, no. 4, pp. 956–965, Jul./Aug. 1997. [7] M. Chinchilla, S. Arnalte, J. C. Burgos, J. Sanz, and J. L. Rodrı́guez, “Active and reactive power limits of three-phase PWM voltage source inverter connected to the grid,” in Proc. EPE-PEMC, Dubrovnik, Croatia, Sep. 2002. [8] W. Leonhard, Control of Electrical Drives. New York: Springer, 1997. [9] G. Johnson, Wind Energy Systems. Englewood Cliffs, NJ: Prentice-Hall, 1990. [10] A. Miller, E. Muljadi, and D. S. Zinger, “A variable speed wind turbine power control,” IEEE Trans. Energy Convers, vol. 12, no. 2, pp. 181–186, Jun. 1997. [11] E. N. Hinrichsen “Variable Rotor Speed for Wind Turbines: Objectives and Issues,” Elect. Power Res. Inst., Palo Alto, CA, EPRI Rep. AP-4261, Sep., 1985. Mónica Chinchilla (M’02) was born in 1970. She received the degree in industrial engineering and the Ph.D. degree from the Universidad Carlos III de Madrid, Leganes, Spain, in 1995 and 2001, respectively. Since 2001, she has been an Associated Professor in the Electrical Engineering Department, Universidad Carlos III. Her main area of interest is permanent-magnet synchronous generator control and wind energy. Santiago Arnaltes (M’02) was born in 1963. He graduated in 1984 and received the Ph.D. degree in 1989 from the Escuela Técnica Superior de Ingenieros Industriales de Madrid, Madrid, Spain. Since 1997, he has been an Associate Professor at the Universidad Carlos III de Madrid, Leganes, Spain. His main area of interest is the control of ac electrical machines, mainly for applications of wind energy. Juan Carlos Burgos (M’01) was born in 1955. He graduated in 1980 and received the Ph.D. degree in 1987 from the Escuela Técnica Superior de Ingenieros Industriales de Madrid, Madrid, Spain. In 1980, he joined the Escuela Tecnica Superior de Ingenieros Industriales as an Associate Professor. Since 1994, he has been an Associate Professor at the Universidad Carlos III de Madrid, Leganes, Spain. He has been the Director of the Electrical Engineering Area since 2003. His main area of interest is transformer fault prevention, but he also works in dynamic control of ac electrical machines and control of variable-speed electrical generators for wind turbines.
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