Induction-motor sensorless vector control with online ... - IEEE Xplore

154

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 53, NO. 1, FEBRUARY 2006

Induction-Motor Sensorless Vector Control With Online Parameter Estimation and Overcurrent Protection Mario J. Durán, Member, IEEE, José L. Durán, Francisco Pérez, and José Fernández

Abstract—Sensorless drive control has been widely studied in recent years due to the numerous advantages regarding potential failures of position sensors, especially in applications such as automotive or aerospace. Among vector-control drives, indirect rotor-flux-oriented control (IRFOC) type is one of the most popular and tested options. However, it is still a challenging field since several aspects can be improved, such as the low-speed behavior, parameter detuning, and current control. The present scheme includes temperature estimation to correct the deviation in steady state, a new control scheme with skin-effect estimation to improve the transient accuracy, and overcurrent protection to be able to control the stator currents while allowing a good performance. The parameter estimation is carried out using lumped-parameter models, the control scheme is modified and is able to account for static friction, and the overcurrent protection improves the performance allowing transient currents over the rated value. The validity and usefulness of the proposed scheme is experimentally tested on a TMS320C31 digital signal processor (DSP) from the Simulink/Matlab environment. Index Terms—Deep-bar effect, parameter estimation, thermal effect, vector control.

N OMENCLATURE bs , br , bsr Cs , Cr Gs , Gr , Gsr id , iq imr , ωmr J, αf kH , kF Lr , Lm P, p Rs , Rr Tm , Te

Stator environment, rotor environment, and stator–rotor convection coefficients. Stator and rotor thermal capacitances. Stator environment, rotor environment, and stator–rotor thermal conductances. Instantaneous values of direct and quadrature axis of stator-current components. Modulus and angular speed of rotor magnetizing current space phasor. Moment of inertia and friction coefficient. Hysteresis- and eddy-current coefficients. Rotor self-inductance and magnetizing inductance. Number of poles pairs and derivative operator, respectively. Stator and rotor resistance. Load and electrical torque.

Manuscript received June 25, 2004; revised November 17, 2004. Abstract published on the Internet November 25, 2005. M. J. Durán, J. L. Durán, and F. Pérez are with the Departamento de Ingeniería Eléctrica, Universidad de Málaga, 29013 Málaga, Spain (e-mail: [email protected]; [email protected]). J. Fernández is with the Departamento de Ingeniería Eléctrica, Universidad de Jaén, 23700 Linares, Spain (e-mail: [email protected]). Digital Object Identifier 10.1109/TIE.2005.862302

Ts , Tr , Ts θs , θr ω, ωs , ωr

Subscripts abc d, q s, r

Stator and rotor time constants and stator transient time constant, respectively. Stator and rotor representative temperature. Motor speed and angular speed of stator and rotor currents, respectively.

Three-phase instantaneous values. Direct and quadrature components of a space phasor, respectively. Stator and rotor, respectively.

Superscripts an, app Analytical and approximate solution. ∗ Reference values in the controller. I. I NTRODUCTION

B

ASED on the pioneering work of Blashke [1], many high-performance induction-motor drives have been developed, focusing in recent years in speed sensorless-control methods. Two main trends can be considered: those based on the field orientation principles to carry out the control flux-oriented control (FOC) [1] and the direct torque control (DTC) [2], which is inherently a sensorless method. Both have their own weaknesses, and a lot of research work has been done trying to solve them. Among the former, the indirect type indirect rotor FOC (IRFOC) is widely used in high-performance drives because of its simplicity and linearity of its steady-state torque-slip characteristic. It is a feedforward method that is very sensitive to motor-parameter variation [3] and its performance at very low speed is poor [4]. Some sensorless schemes estimate the speed directly from motor model [5], though many other approaches such as model reference adaptive system (MRAS) [6], Kalman-filter-based methods [7], or stator spectrum analysis with fundamental or separate excitation signals [8] have been implemented. Similar approaches have been used for the estimation of motor parameters together with the speed estimation to improve the sensorless performance [3]. Apart from the control accuracy, the motor protection and current limitation is another important aspect for the drive performance. This issue is usually solved by adding a current limiter that directly saturates the stator reference currents provided by the controller [9]. However, demanding tasks of high-performance drives sometimes require high currents to provide the necessary

0278-0046/$20.00 © 2006 IEEE

DURÁN et al.: INDUCTION-MOTOR SENSORLESS VECTOR CONTROL WITH ONLINE PARAMETER ESTIMATION

torque, and in such cases, a better design in the overcurrent protection also leads to a better performance. On the other hand [9], a simple but nonconservative protection that allows transient currents over the rated value is proposed in this paper. If the reference overcurrents do not exceed an energy threshold, a desired behavior, which otherwise would not be possible, is obtained. Concerning the speed and parameter estimate, the approach adopted is to use a novel speed estimator from the motor model and the mechanical equation, but to use lumped-parameter models for the different phenomena obtaining an independent parameter estimation, instead of using other previously proposed approaches [3]. For the skin effect, there are finite-element solutions [10] and improved models [11], but they are time consuming and need more parameters to be determined during the commissioning, respectively. In this paper, a classical model is used, but instead of considering fixed parameters in an improved model [11], variable rotor parameters are considered, obtaining a simpler and quicker solution. These parameters are updated from an approximated lumped-parameter solution that uses a previously developed general solution [12]. To take into account the thermal variations, detailed solutions [13] are not valid for this application, and the approach is to directly model the motor heating, but focusing on the calculation of representative temperatures both for the stator and rotor. The step size of the thermal model can be higher, if necessary, than the electrical one, due to the higher thermal time constant. Finally, both models are integrated in a global estimator that updates the values of the stator resistance, and the rotor resistance and inductance. II. C ONTROL S CHEME For sensorless-control speed, estimators that substitute direct measurements are required. Using three from the four wellknown rotor-flux-oriented equations [10], it is possible to build an estimator obtaining the speed from one of the rotor electrical equations. In this paper, a different proposal is made including the dynamical equation into the estimator together with the four RFOC equations, obtaining the following set of equations: ud + ωmr Ts iq − (Ts − Ts ) p|imr | Rs uq − ωmr Ts id − (Ts − Ts ) |imr | Ts piq + iq = Rs

Ts pid + id =

Tr p|imr | + |imr | = id ωmr = ω +

iq Tr |imr |

P L2m 2 2 iq |imr | = Tm + Jpω + αf ω . 2 Lr P P

(1)

Speed is obtained from the mechanical equation, and this allows considering a variable friction torque that takes into account the static friction that exists when the movement is starting (Fig. 1). From the set of equations in (1), the motor speed can be calculated using an estimator whose inputs are the voltage components and the load torque. Since these are the real inputs of

155

Fig. 1. Variable friction torque considered.

Fig. 2. Control scheme using the simulated motor as a speed estimator with adaptive load-torque estimation.

an induction machine, the estimator is further called simulated motor. Voltage components can be measured or reconstructed from the stator equations, but the torque must be estimated since it is not a measured variable. In order to estimate the load torque, an adaptive scheme is adopted considering that the motor torque is proportional to iq . This component can be easily measured and can also be obtained from the speed estimator. The difference between them is due to the fact that the information of the load torque that the estimator is using is not correct, and so a controller can be used to update this torque value. In Fig. 2, the complete control scheme is shown, where a digital filter is used for the measurements of the currents before considering the transformation matrix into the dq values. The speed and flux target values are compared with the estimated ones obtaining target currents that are transformed into target voltages using (1). Three antiwind-up controllers are involved, as is usual in this kind of vector control, with one for the flux comparison obtaining the direct component id and two for the speed and torque comparison obtaining the quadrature component iq . The rotor-flux reference decreases in inverse proportion to the speed of rotation in the field-weakening region, while it is constant and equal to rated rotor flux in the base speed region.

156


TABLE I RESULTS FOR THE THERMAL TESTS

Fig. 3.

Rotor equivalent circuit considering three sections.

The model proves to be accurate and is fast enough to be included in a real-time application. B. Deep-Bar-Effect Model III. P ARAMETER E STIMATION Until now, a speed estimator and a control scheme have been proposed, but the parameter-variation problem that is common to any vector control [including DTC and stator-flux-oriented control (SFOC)] remains the same. In order to overcome this problem, two of the main influencing factors are considered: thermal and deep-bar effects. A. Thermal Model In a previous paper [14], a thermal model that takes electrical RFOC variables as inputs and provides stator and rotor representative temperatures was developed. The aim of the thermal model is not to obtain a full picture of the thermal state, but to find stator and rotor representative temperatures with a fast model. In the model proposed, three parts are considered: stator, rotor, and environment. The losses considered both in the stator and rotor are due to the Joule effect, hysteresis, and eddy currents. The heat evacuation is modeled through thermal conductances and capacitances for the massive elements. The conductances consider both conduction and convection, which is proportional to the motor speed. The balance equations are dθs + Gsr (θs − θr ) dt dθr + Gsr (θr − θs ) Rr i2r + kHr ωr + kFr ωr2 = Gr θr + Cr dt G = G0 (1 + b · ω). (2)

Rs i2s + kHs ωs + kFs ωs2 = Gs θs + Cs

The model parameters are obtained from three tests: blockedshaft, dc, and ac tests. For the offline temperature measurements, type K thermocouples and infrared equipment have been used. Measurements at different points have been taken, searching for the stator and rotor representative temperatures that provide the correct resistance. For the stator, it is a value between the temperature measured in a hole near the end winding and another hole made in the center of the carcass at 1 mm from the stator slots. For the rotor, it is the value of the temperature measured in the frontal ring. The simulated and experimental steady-state results for the tests are summarized in Table I.

To account for the deep-bar effect, finite-element-method solutions are not possible for a real-time application, and both analytical [15] and lumped-parameter [16] previous solutions are only valid for rectangular rotor bars. In a previous work [12], a generalization of the analytical solution was carried out, considering the contribution of the sides when using Ampère’s law and when integrating the Poynting’s flux to obtain the rotor parameters

h

P + jQ = EH (0)b(0) + 2

EH (z)b(z)dz

0

I 2 Lr = Ir2 Rr + j r 2

(3)

with b(z) being the width of the rotor bar. All in all, a general analytical solution is obtained, whose main weakness is its being time consuming due to hyperbolic functions. The skin effect is then considered, courtesy of an approximate lumped-parameter solution that calculates the values of the different parameters by comparing the results with the previously developed analytical solution. This solution considers the lumped-parameter π equivalent circuit shown in Fig. 3, and minimizes the error using a Nelder–Mead direct search with the following error function: 2 1 1 an calc 2 + Prl · Rr − Rr · Xran − Xrcalc Error = cr cl f f (4) with cr and cl being weight coefficients that improve the solution performance at low or high frequencies, Prl a coefficient that allows a better adjustment of resistance or inductance, and F the frequency range. The initial parameters, necessary for the iterative process, are taken from the ones obtained for the rectangular solution, which are near the sought values. For a Boucherot-type rotor bar and considering the equivalent circuit with three sections shown in Fig. 3, six resistances and three inductances are needed. The final parameters obtained choosing weight values of cr = 2; cl = 2 : 5, and Prl = 100 are summarized in Table II. For the three-section case, which involves a low number of calculations, the rotor-resistance variation in the analytical and approximate solutions can be compared, as shown in Fig. 4.


157

TABLE II EQUIVALENT CIRCUIT PARAMETERS: RESISTANCES IN OHMS PER CENTIMETER AND INDUCTANCES IN MICROHENRY PER CENTIMETER

Fig. 6. Three-phase currents during acceleration transient. Fig. 4.

Three-phase currents during acceleration transient.

thermal effect since the rotor representative temperature θr is one of its inputs. IV. M OTOR P ROTECTION

Fig. 5.

Global estimation scheme.

The ladder-network approximate solution presents a good precision versus simplicity characteristic, and is the method selected to take into account the skin effect. C. Global Estimation Scheme Considering the relationship between both phenomena, previous models can be included into a global estimator that is added to the simulated motor to take parameter variation into account, obtaining the scheme shown in Fig. 5. It must be noticed that the motor heating influences the deepbar model due to the electrical-conductivity variation, but the motor temperature is not practically affected by the additional losses caused by the skin effect. As a consequence, the stator resistance is estimated just using the stator temperature provided by the thermal model since the skin effect in the stator can be neglected. The rotor parameters are updated by the outputs of the deep-bar model, which already takes into account the

Vector control provides high performance to drives, but to achieve a good transient response, a high electrical torque is required, and it means high currents flowing in the machine. Apart from the achievement of decoupled and optimal control, it is also necessary to protect the motor against overcurrents. In general, there are two reasons why the motor would need to consume high currents: high accelerations (hence, great inertia torque) or high load torque. In Fig. 6, the stator-current evolution when the reference speed is increased in a rampwise manner with high accelerations is shown, and it is clear that in this transient, currents over the rated value are required. The inverter used is a voltage source inverter (VSI) type, and therefore, to carry out a proper control, target voltages are supplying the motor, but without any current control. For this reason, it is convenient to include current protection in the software design. It is relatively easy to have control over the currents in field-oriented control compared with other schemes such as DTC, since it is only necessary to control the quadrature component of the stator space vector iq . The obvious solution is just to saturate this component in the control scheme. However, the aim is to design nonconservative protection that allows transient currents above the rated value. Traditionally, for steady-state operation, manufacturers provide the maximum time for a certain value over the rated current so that the motor is not damaged. For a vector-control application, the motor works in transient state, but a protection based on energy considerations can also be used. The method proposed is to use an energy meter that starts to rise when the

158


Fig. 7. Proposed protection.

Fig. 8. Experimental rig.

current is over the rated value, integrating this current. When the energy meter is over a certain energy threshold, then the protection acts by limiting the quadrature current iq to its rated value. Some considerations have to be made in order to make the system work: The integration for the energy meter must be limited, and if the current is below the rated value, the integration must continue with a negative value until the energy meter is set to zero. This means that if a repetitive cycle occurs (Fig. 7), the protection finally acts, even if the energy of the each cycle is below the limit. V. E XPERIMENTAL R IG A schematic diagram showing the major components of the experimental rig is given in Fig. 8. The experimental systems consists of a 1-kW induction motor (AEG eAM 90SY 4Ex), a Semikron Skiip with integrated rectifier and VSI inverter, a dynamo and a bank resistor for load tests, and a digital signal processor (DSP) (TMS320C31) main control board. The control design is carried out in Simulink/Matlab and compiled to be executed in the DSP. For the acquisition data, two types can be considered: the control and the verification data. Control data are the currents necessary to estimate the motor speed, which need printed circuit boards (PCBs) specifically designed with Hall-effect trans-

Fig. 9. Speed evolution with current limiter and proposed overcurrent protection.

ducers to obtain proper voltages that can be introduced in the DSP courtesy of a 16-bit A/D converter. Moreover, the speed is also measured in order to have a verification tool, and so it is vital to carry out the measurement with high precision. For this purpose, the TTL pulses from a 1024 cycles per revolution (CPR) encoder are filtered and counted into the DSP obtaining the shaft position. In order to obtain the real speed, a simple algorithm with variable integration step is designed and an accurate measurement is achieved. Since the measured speed is captured by Simulink, it is of immediate concern to compare it with the reference so that the control can be rigorously tested. Tuning of the PI controllers and filters is performed using experimental data from no-load and loaded tests in the base speed region. VI. E XPERIMENTAL R ESULTS In the experimental results, tests are carried out to see the performance in the steady state, transient state, and overcurrent states, so that the different aspects of the proposed scheme can be tested. A. Motor Protection It was shown that large accelerations can lead to overcurrents in the machine, but these currents can also be necessary when the load torque is over the rated value. With the aim of testing the proposed protection, tests are carried out by applying a load torque such that the motor consumes a current over the rated value. Two similar tests are considered, one limiting the value of iq to its rated value and the other with the designed protection. The results, setting a target speed of 1000 r/min, are shown in Fig. 9. It can be noticed that using a dc limiter, the target speed is never reached since there is no sufficient electrical torque. On the other hand, the proposed protection allows a transient overcurrent and the machine achieves the target speed providing the necessary torque. When the energy meter reaches the energy threshold, the protection acts by limiting the motor current to the rated value. At this moment, the speed of the machine must be reduced to


159

Fig. 10. Constant-load test. Fig. 12. Load test.

Fig. 11. Speed test. Fig. 13. iq evolution in the load test.

provide a higher torque and balance the mechanical equation, reaching the same steady-state value as in the previous case. In some occasions, the necessary torque is reduced before reaching the energy threshold and so the target speed is followed, improving the drive performance. B. Steady-State Behavior In order to verify the steady-state behavior, and the influence of the motor heating on the control precision, it is necessary to perform a test for sufficient time to reach a constant temperature. The effect of parameter detuning cannot be observed if there is no sufficient time for the physical phenomenon to influence the parameters, and so the test is carried out for 4000 s, a period that in the thermal tests proved to be sufficient to reach the thermal balance. The test is carried out with a target speed of 1000 r/min and a load torque of half the rated value, and it is made with and without the inclusion of the thermal model in the control scheme. The results of both tests are shown in Fig. 10, where the vertical lines are due to the reset of the incremental encoder position counter. If the thermal effect is neglected and constant parameters are considered, there is a deviation due to the effect of the motor heating. On the contrary, if the thermal effect is considered, the parameters are updated with their correct value as the motor

temperature increases. It makes the motor follow the target speed without deviation. C. Acceleration Test A requirement of the dynamical behavior is the response when sudden changes in the target speed occur. In order to be demanding with the control features, a test with a target speed linearly ramped from 0 to 1000 r/min for the first 1.3 s, maintaining a constant reference speed afterwards, is considered. Fig. 11 shows that even with this acceleration, the motor follows the target speed just with some oscillations in the starting at 7.2 s and braking at 8.5 s. Carrying out the same test without considering the proposed scheme with the skin-effect estimation leads to higher oscillations and poorer transient response, and not considering the static friction in the mechanical equation makes the motor oscillate more during starting. D. Load Test A usual test to observe the dynamical performance of the control is to apply a sharp load torque to verify the system response. In this case, during a few seconds, a rated load torque acting manually on the resistor bank was applied. At

160


approximately the 28th second, the load torque was released and so the motor is instantaneously accelerated. The maximum error in this test, as shown in Fig. 12, is 16 r/min, and the motor speed quickly recovers the target value of 1000 r/min. In the control scheme, when the torque is applied, the measured value of iq changes and so the controller provides the correct information of the external conditions. In Fig. 13, the estimated and measured quadrature currents are shown. The evolution is similar, so that the correct information about the load torque is being provided to the speed estimator. The rapid change in the quadrature current when changes in the load torque occur is the clue to obtain a quick response of the control. Until the 28th second, the torque is gradually being increased and this information is introduced in the controller through the measured quadrature current. When the torque is released, the quadrature component is also suddenly changed by the control following the target speed in this way.

VII. C ONCLUSION The scheme that has been proposed improves the performance of the drive in several ways. On the one hand, the thermal-state estimation can correct the steady-state deviation in the motor speed that otherwise is produced when the motor is heated and parameter detuning occurs. Though the hot spots are not calculated, the thermal model could also be used for monitoring purposes since the temperatures obtained are representative of the motor thermal state. The scheme also includes a skin-effect estimation courtesy of a lumped-parameter model valid for any rotor-bar shape and the consideration of the static friction showing a good performance in the transient state, both against target-speed or load-torque changes. Since, apart from the control characteristics, it is necessary to avoid overcurrents, the proposed protection proves that it permit transient currents over the rated value, improving the drive performance. Not saturating the current directly helps the motor reach the target values even when a high transient torque is required. All in all, a control scheme with a protection module, adaptive torque estimation, and a new speed estimator that takes into account thermal and deep-bar effects has been experimentally tested, showing that the control can be achieved in a secure manner with great accuracy, both in the steady and nonsteady state.

[5] A. M. Trzynadlowski, The Field Orientation Principle in Control of Induction Machines. Norwell, MA: Kluwer, 1994. [6] M. Rashed, F. Stronach, and P. Vas, “A new stable MRAS-based speed and stator resistance estimators for sensorless vector control induction motor drive at low speeds,” in Proc. 38th IEEE-IAS Annu. Meeting, Salt Lake City, UT, Oct. 2003, vol. 2, pp. 1181–1188. [7] M. Barut, M. Gokasan, and O. S. Bogosyan, “An extended Kalman filter based sensorless direct vector control of induction motors,” in Proc. IEEE 29th Annu. Conf. Industrial Electronics Society (IECON), Roanoke, VA, Nov. 2003, vol. 1, pp. 318–322. [8] M. W. Degner and R. D. Lorenz, “Position estimation in inductionmachines utilizing rotor bar slot harmonics and carrier frequency signal injection,” in Proc. Power Conversion Conf. (PCC), Nagaoka, Japan, 1997, pp. 69–72. [9] P. Vas, Sensorless Vector and Direct Torque Control. London, U.K.: Oxford Univ. Press, 1998. [10] S. Williamson and D. R. Gersh, “Finite element calculation of doublecage rotor equivalent circuit parameters,” IEEE Trans. Energy Convers., vol. 11, no. 1, pp. 41–48, Mar. 1996. [11] R. C. Healey, S. Williamson, and A. C. Smith, “Improved cage rotor models for vector control induction motors,” IEEE Trans. Ind. Appl., vol. 31, no. 4, pp. 812–822, Jul./Aug. 1995. [12] M. J. Durán, J. L. Durán, F. Pérez, and J. Fernández, “Improved sensorless induction machine vector control with on-line parameter estimation taking into account deep-bar and thermal effects,” in Proc. IEEE 28th Annu. Conf. Industrial Electronics Society (IECON), Seville, Spain, 2002, pp. 1716–1721. [13] J. Xypteras and V. Hatziathanassiou, “Thermal analysis of an electrical machine taking into account the iron losses and the deep-bar effect,” IEEE Trans. Energy Convers., vol. 14, no. 4, pp. 996–1003, Dec. 1999. [14] J. Fernández, F. Pérez, and M. J. Durán, “Realization of tests to determine the parameters of the thermal model of induction machine,” Proc. Inst. Elect. Eng.—Electr. Power Appl., vol. 148, no. 5, pp. 392–397, Sep. 2001. [15] P. L. Alger, Induction Machines. New York: Gordon and Breach, 1970. [16] W. Levy, C. F. Landy, and M. D. McCulloch, “Improved models for the simulation of deep bar induction motors,” IEEE Trans. Energy Convers., vol. 5, no. 4, pp. 393–400, Jun. 1990.

Mario J. Durán (M’04) was born in Bilbao, Spain, in 1975. He received the M.Sc. (Eng) and Ph.D. degrees in electrical engineering from the University of Málaga, Málaga, Spain, in 1999 and 2003, respectively. In 2001, he joined the Electrical Engineering Department of the University of Málaga, and in 2004, he joined the University of Seville, developing both teaching and research activities. Since then, he has been lecturing on the subjects of electrical machines and electromagnetism, on which he has authored several books and teaching software. He is the author of many publications both in conference proceedings and relevant journals and his current research interests are directed towards the modeling and control of multiphase machines and variable-speed drives.

R EFERENCES [1] F. Blashke, “The principle of field-orientation as applied to the new transvector closed-loop control system for rotating field machines,” Siemens Rev., vol. 34, no. 5, pp. 217–220, 1972. [2] T. Naguchi and I. Takahashi, “A new quick-response and high efficiency control strategy of an induction motor,” IEEE Trans. Ind. Appl., vol. IA-22, no. 5, pp. 820–827, Sep./Oct. 1986. [3] H. Toliyat, E. Levi, and M. Raina, “A review of RFO induction motor parameter estimation techniques,” IEEE Trans. Energy Convers., vol. 18, no. 2, pp. 271–283, Jun. 2003. [4] J. Holtz and J. Quan, “Sensorless vector control of induction motors at very low speed using a nonlinear inverter model and parameter identification,” IEEE Trans. Ind. Appl., vol. 38, no. 4, pp. 1087–1095, Jul./Aug. 2002.

José L. Durán was born in Cáceres, Spain, in 1945. He received the M.Sc. (Eng) degree from the University of Bilbao, Bilbao, Spain, and the Ph.D. degree from the University of Málaga, Málaga, Spain, in 1970 and 1997, respectively, both in electrical engineering. In 1988, he joined the Electrical Engineering Department, University of Málaga, where he is now a Professor of Engineering, lecturing on electromagnetism and electrical power systems. He has written several books and developed both teaching and research software in these fields. His principal research interests are state estimation of power systems and variable-speed drives.


Francisco Pérez was born in Málaga, Spain, in 1955. He received the M.Sc. (Eng) degree from the Polytechnic University of Madrid, Madrid, Spain, and the Ph.D. degree from the University of Málaga, Málaga, Spain in 1989 and 1993, respectively, both in electrical engineering. Since 1995, he has been a Professor of Engineering in the Electrical Engineering Department, University of Málaga, teaching electrical machines and power electronics. He is currently the Head of the Investigation Group at the university and his principal research topics are focused on the design of variable-speed drives, HVdc active filters, and artificial intelligence (AI) applied to motor control.

161

José Fernández was born in Jaén, Spain, in 1945. He received the M.Sc. (Eng) degree from the University of Cataluña, Barcelona, Spain, and the Ph.D. degree from the University of Málaga, Málaga, Spain, in 1975 and 2001, respectively, both in electrical engineering. He worked in automation engineering from 1975 to 1996 at several international companies. In 1988, he joined the Electrical Engineering Department of the University of Jaén, Linares, Spain, where he is currently a Professor of Engineering. His main research interests include electrical machines modeling, variable-speed drives, and flexible ac transmission systems (FACTS) technology.