Estimation of Effective Wind Speed for Fixed-Speed Wind Turbines ...

IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 3, NO. 1, JANUARY 2012

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Estimation of Effective Wind Speed for Fixed-Speed Wind Turbines Based on Frequency Domain Data Fusion Zhiqiang Xu, Member, IEEE, Qinghua Hu, Member, IEEE, and Mehrdad Ehsani, Fellow, IEEE

Abstract—The rotator of the wind turbine is subject to a spatially and temporally distributed wind field; the wind speed varies significantly at different points over the blades plane. This makes a direct measurement of effective wind speed impossible. We analyze the spectrums of the measurement of the anemometer and generator power of a wind turbine, and point out that the characteristics of these two signals are complementary in the frequency domain. Then an observer for effective wind speed is proposed based on frequency-domain data fusion. The observer design is formulated as a mixed-sensitivity problem with linear matrix inequalities (LMIs). Simulations were carried out to assess the performance under a realistic wind speed profile. The simulation results show that the observer can not only guarantee the static accuracy, but also improve the dynamic accuracy of the measurements of the effective wind. Index Terms—Data fusion, effective wind speed, linear matrix inequalities, observers, spectral analysis, wind turbines.

I. INTRODUCTION

O

WING to concern over the environment, there is much interest in renewable sources of electrical power generation, of which the most promising is wind power. Wind turbines exploit this energy source to directly generate electrical power [1], [2]. As the wind is not a stable source of energy (its speed and direction is kept changing all the time), a control system is necessary to regulate the wind turbines. Typical objectives of the control system are to maximize energy capture in low wind speeds, to maintain the generated power and the rotational turbine speed within safe limits during high wind speeds, and to avoid lightly damped resonant modes in the closed loop system [3]–[6]. The wind speed is a key feedback signal for the control system of the wind turbines. Unlike traditional energy conversion systems, where the energy input can be controlled, the Manuscript received November 29, 2010; revised May 25, 2011; accepted July 14, 2011. Date of publication July 22, 2011; date of current version December 16, 2011. This work was supported by the National Natural Science Foundation of China under Grant 50606008 and by the National Basic Research Program of China (973 Program) under Grant 2012CB215201. Z. Xu was with Texas A&M University, College Station, TX 77843 USA. He is now with the School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, China (e-mail: [email protected]). Q. Hu is with the School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, China (e-mail: [email protected]). M. Ehsani is with the Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX 77843 USA (e-mail: ehsani@ece. tamu.edu). Digital Object Identifier 10.1109/TSTE.2011.2162638

Fig. 1. Wind speeds at different points of the wind turbine blades swept area [20].

speed of the wind cannot be controlled. Thus, knowing the wind speed ahead of time is useful in controlling a wind turbine [7]. Currently, the wind speed used in the control system is usually measured with an anemometer which is installed at the top of the cabin, known as the point wind speed [8]. However, since the rotator of the wind turbine is subject to a spatially and temporally distributed wind field, the wind speed will vary significantly at different points over the blades swept area (Fig. 1). There is no such thing as the “wind speed” experienced by a wind turbine; it may be considered to experience an effective wind speed which, in some sense, is the average speed over the blades that produce the same aerodynamic torque. It is impossible to measure the effective wind speed [6], [9]. In order to solve the problem of measuring effective wind speed, some researchers have proposed to indirectly estimate the effective wind speed through other signals which are easy to measure, such as the generator electric power, the electric torque, or the rotator speed of the generator. The effective wind speed can be then estimated through system identification [9], [10], state observer [11], data mining [12], [13], and fuzzy techniques [14]–[16]. Dynamic observers for estimating the effective wind speed have not been intensively investigated as the above-mentioned methods. The main trend on this topic is to design a linear Kalman filter for estimating the aerodynamic torque and then calculate the effective wind speed [2]. These methods can be considered as using the impeller of the wind turbine as a giant “anemometer” for measurement of the effective wind speed. Then, a variety of control strategies for the wind turbine that do not require the wind speed sensor were proposed [9], [12]. On the other hand, since the blades of the large-scale wind turbine are very heavy and long, the inertia of the wind turbine rotator is very large. Then response speed of the generator is very slow if the wind speed changes. As we know, the changes

1949-3029/$26.00 © 2011 IEEE

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of the wind speed are usually very fast. It is difficult for the generator power or rotator speed to follow the changes in wind speed [5]. The problem becomes more severe as the capacity of the wind turbine increases. The problem can be then be summarized to find an accurate and rapid feedback signal of the effective wind speed. The wind speed feedback signals currently in use cannot take the accuracy and response speed into account simultaneously: The response speed of an anemometer to changes of the wind speed is rather high. But it is susceptible to factors such as the wind turbulence, tower, wind shear, and the roughness of ground. The static accuracy of an anemometer is poor. On the other hand, the static precision of measurement of generator signals is good. However, because of the large lag and delay of the rotator, the dynamic response speed of the generator signals is slow. Fortunately, the characteristics of these two kinds of signals are complementary in the frequency domain. Therefore, if these two observations are correctly associated, the combination of the two sensors data provides an improved determination of speed than could be obtained by either of the two independent sensors. This will result in a reduced error in the fused or combined effective wind speed estimate. The data fusion of multisensor data provides significant advantages over single source data. In addition to the statistical advantage gained by combining same-source data, the use of multiple types of sensors may increase the accuracy with which a quantity can be observed and characterized [17], [18]. This paper proposes a method for the estimation of the effective wind speed of a wind turbine. The observer can provide additional freedom that can make use of the complementary characteristics in the frequency domain between generator power and the measurement of anemometer [19]. Since the generator power is easy to measure, the paper focuses on the fusion of the measurement of the generator power and the anemometer. This paper is structured as follows. In Section II, the frequency characteristics of the wind speed measurement signals are discussed, and then the idea of the observer is presented. In Section III, the design of the effective wind speed observer is discussed. Then, in Section IV, an effective wind speed observer is proposed for a fixed-speed fixed-pitch wind turbine, and computer simulations are conducted to evaluate the performance of the proposed observer. Finally, the conclusions and future works are given in Section V. II. MOTIVATIONS As the wind speed changes, the energy available for energy capture increases at roughly cubic with the wind speed. The generator power represents the actual energy captured by the wind turbine. Thus, in some sense, both the wind speed signals measured by the anemometer and the generator power signal can be thought of as the measurements of the wind energy at different stages during the procedure of the energy conversion. Then they can be regarded as two measurements for the same signal subjected to different disturbances. Typically, as the size and inertia of an anemometer are small, the response speed of the measurement results of the anemometer to the change of the wind speed is very fast.

Fig. 2. Schematic diagram of the effective wind speed filter.

However, due to factors such as wind turbulence, tower, wind shear, and the roughness of ground, the wind speed will vary significantly at different points of the blade plane (Fig. 1). The static accuracy of the measurement is poor. The measurement outputs of the anemometer can be considered as the effective wind speed signal with low-frequency disturbance signals. On the other hand, by neglecting the mechanical losses and generator losses, all the wind energy captured by the blade will be converted to the electric power of the generator. The electric power of the generator is able to accurately represent the steady value of the effective wind speed (effective wind energy that is captured by the turbine) over the blades. However, the inertia of the wind turbine blade is so large that its response speed to the effective wind speed is slow. The time constant is usually up to ten seconds, even tens of seconds. The electric power signal of the generator can be considered as the effective wind speed signal with a high-frequency noise. To sum up, these two measurements for the effective wind speed have their own advantages and disadvantages. They do not meet the requirements for the wind speed measurement of the control system by use of either one of these two signals alone. However, it is notable that the disturbances of the two signals are at different frequency ranges: one is at low frequency domain; the other is at high frequency domain. Thus we can combine the high-frequency components of wind speed signal measured by the anemometer, with the low-frequency components of the generator electric power signals into one signal. The combination of the two sensors data would provide an improved estimation of effective wind speed. The improved one can not only ensure the static accuracy, but also improve the dynamic response speed (Fig. 2). This is just the basic idea of the information fusion theory (also known as Multisensor Data Fusion) [18]. Data fusion techniques combine data from multiple sensors, and related information from associated databases, to achieve improved accuracies and more specific inferences than could be achieved by the use of a single sensor alone. The most fundamental characterization of data fusion involves a hierarchical transformation between observed energy or parameters (provided by multiple sources as input) and a decision or inference (produced by fusion estimation and/or inference processes) regarding the location, characteristics, and identity of an entity, and an interpretation of the observed entity in the context of a surrounding environment and relationships

XU et al.: ESTIMATION OF EFFECTIVE WIND SPEED FOR FIXED-SPEED WIND TURBINES

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According to Fig. 3, the power of the generator can be written as (3) The estimation of generator power can be written as (4) Then the estimation of the effective wind speed can be written as

Fig. 3. Structure of the Observer.

to other entities. The definition of what constitutes an entity depends upon the specific application under consideration [17].

(5) Substituting the (4) into (5)

III. DESIGN OF THE EFFECTIVE WIND SPEED OBSERVER

(6)

A. Structure of the Observer There are several causes of the wind speed variations such as: wind shear caused by wind speed variations over the rotor height, tower shadow caused by the support structure interfering with the air flow, and yaw misalignment caused by the alignment error between the turbine shaft and the wind speed direction. The disturbance observer takes these disturbances as the output of another system driven by white noise, which represents a dynamic model of the disturbance signal. The goal of the disturbance observer is to estimate the state of the disturbance system. The results of the estimation can be used to compensate the disturbance on the measurement. Considering the reliability as well as flexibility of system implementation, the observer of the effective wind speed is composed based on the generalized state observer. This approach provides additional freedom, which can be used in data frequency fusion for different signals [21]. It is applicable to the tasks where the statistical properties of the signals are known. The structure of the observer is shown in Fig. 3. In Fig. 3, is the wind turbine. is the nominal model of wind turbine. Usually is a lower degree approximation of the plant. is the dynamic compensator. The output of is the estimation of the disturbances of wind speed, e.g., the disturbances to be eliminated. is the effective wind speed, and is the measurement signal of the anemometer. As mentioned above, due to the measuring principle of the anemometer, the measurement results of the anemometer can be regarded as the effective wind speed signal superimposed with a low-frequency disturbance (1) is the disturbance. The spectrum of is mainly diswhere tributed at the lower-frequency range. is the measurement of the electric power of generator. It can be regarded as the actual electrical power superimposed with a high-frequency measurement noise (2) where

is the high-frequency measurement noise.

where . It is worth noting that, and are just the sensitivity function and complementary sensitivity function of the system, respectively. They are also the weighting functions for the wind speed measurement and generator power measurement , respectively. Both of them can be determined by the nominal plant model and the dynamic compensator . Therefore, when the nominal plant model is determined, the influence of the disturbance in wind speed measurement and the noise in generator power measurement can be restrained simultaneously by proper design of . Noting that the disturbance in wind speed measurement distributed in the low frequency range, in order to reduce the influences of disturbances on wind speed measurement , the gain of sensitivity function in low frequency should be reduced. On the other hand, the measurement noise in generator power measurement is mainly in the high frequency range. To attenuate the noise in generator power measurement , the gain of complementary sensitivity function in high frequency should be restrained. Then the problems can be attributed to the design of the dynamic compensator , e.g., considering which can be determined by requirement of control system, to design the dynamic compensator , such that, when ; when . B. Design of the Dynamic Compensator 1) Constraints for : The design objective of in lower-frequency is to attenuate the disturbances in measurement of anemometer. It can be seen from Fig. 3 that is in fact the closed-loop transfer function from disturbance to the estimation of effective wind speed . The singular values of determine the disturbance attenuation performance. Thus a disturbance restrain performance specification may be written as (7)

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where is the desired disturbance weighting function. Since depends on frequency , we can obtain different attenuation performance for a different frequency . 2) Constraints for : Considering the measurement noise of the generator power , the estimation error of the generator power can be written as (8) where . In (8), the first item of the right side represents the attenuation performance for the plant perturbations, while the second item is the attenuation performance for the measurement noise. The influences of the two impacts will be discussed as follows. As to the first item of the right side of (8), taking the upper boundary of the measurement noise of the generator power, e.g., . Thus a noise attenuation performance specification is written as (9) where is the -norm. Plant model uncertainty arises from many sources. There may be small unmodeled time-delays or stray electrical capacitance. Imprecisely understood actuator time constants, or, in mechanical systems, high frequency torsional bending modes, and similar effects can be responsible for plant model uncertainty [22]. Given an approximate model of a plant , the multiplicative uncertainty of the model is defined as (10) where is the effect of all plant uncertainty lumped into a single fictitious multiplicative perturbation. Usually the left side of (10) is unknown. Only the nominal model and the margin of the model uncertainty are known. Assume the margin of model uncertainty is , e.g., (11) The complementary sensitivity function determined the stability margin for multiplicative perturbations . Then the constraint for estimation robustness under model uncertainty can be written as (12) where is the -norm. Considering both the requirement for noise attenuation and robustness against model uncertainty, we choose the weighting function as (13) The constraints for complementary sensitivity function can be then written as (14)

Fig. 4. Wind energy conversion system (WECS).

The performance and stability robustness specifications (9) and (14) can be combined into a single infinity norm specification of the form (15) This is in fact a mixed-sensitivity problem. It penalizes both sensitivity and complementary sensitivity . Loop shaping is achieved when we choose to have the target loop shape for frequencies , and to be the target for . Thus, , determine the shapes of sensitivity and complementary sensitivity . Typically, is chosen to be small inside the desired control bandwidth to achieve good disturbance attenuation (i.e., performance), and is chosen to be small outside the control bandwidth, which helps to ensure good stability margin (i.e., robustness) [21]. It should be noted that the compensate loop itself is also a feedback loop. The bandwidth of the observer should be restricted by the robust stability constraints. Therefore, the bandwidth of should not be too wide. It should be a trade-off between disturbance attenuation performance and robust stability. IV. CASE STUDY

FIXED-SPEED FIXED-PITCH ANGLE WIND TURBINE

OF

In order to evaluate the proposed method, an effective wind speed observer has been designed for a fixed-speed fixed-pitch angle wind turbine. Simulations have been conducted to evaluate the performance of the observer. The mechanical and wind speed models are described in detail in [23]. A. System Description A three-bladed 200-kW fixed-speed induction generator based wind turbine power plant is considered in this paper. The wind turbine considered in this work consists of a wind turbine, an induction generator, and an electronic converter. The last of these controls the generator torque. A gearbox adapts the rotational speeds of the wind turbine and the electric generator. The system is connected to a stiff grid which can absorb all the power supplied by the wind turbine without considerable change in either voltage or frequency. The structure of the wind turbine power plant is given in Fig. 4.


VARIABLES

TABLE I PARAMETERS OF THE MODEL REFERRED LOW-SPEED SIDE OF THE SYSTEM

AND

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Linearizing the model around the design operation point TO THE

(21) where

,

,

,

,

Parameters corresponding to the fixed-speed fixed- pitch angle wind turbine are , m, tm , tm , t m /s, and t m /s . The dominant dynamics usually lie in the mechanical subsystem. Therefore, wind turbines are generally modeled as flexible structures undergoing exogenous torques from the wind and generator [24]. 1) Model of the Wind Turbine Energy Conversion System: A wind turbine with only one dominant resonant mode is considered, modeled as a series of inertias linked by flexible shafts with friction. In this case, the dynamic equations for the wind energy conversion system are (16) (17) (18) where and are the moments of inertia of the wind turbine and the generator, respectively. is the stiffness coefficient, is the friction coefficient. is the shaft torque. is the rotational turbine speed, and is the generator speed (all parameters are assumed on the turbine side). The aerodynamic torque has the expression (19) where is the air density. is the turbine ratio. is the wind speed. is the tip speed ratio, defined as , and is the torque coefficient. Under the reasonable assumption that the mechanical dynamics is dominant compared with the electric one, the steady state model of the generator is adequate for torque calculation. Assuming small slip and a constant voltage-frequency relationship, the generator torque is linear in , i.e., (20) where and are the linearization coefficients and is the synchronic frequency in squirrel-cage configurations or the control signal of the converter in DFIG configurations. This is a third degree nonlinear model, which has been used for study on LPV gain-scheduling control of wind energy conversion systems [3], [4]. The variables and parameters involved in the model are tabulated in Table I.

2) Model of the Anemometer: The anemometer of the wind turbine is usually installed on top of the cabin, while the blade of the wind turbine is installed upstream of the cabin. Therefore, the output of the anemometer is the wind speed after the blade. Since parts of the energy are absorbed by the turbine, the wind speed measured by the anemometer is lower than the actual wind speed. According to [25], the maximum power that can be captured from the wind with the speed and power can be written as (22) where is the theoretical power coefficient defined as the ratio between the power captured by the wind turbine and the available wind power. It is the turbine efficiency to convert the kinetic energy of the wind into mechanical energy (23) are the wind speed before and after the blades where and of the wind turbine, respectively. And . is the Betz limit. It can be seen from (23) if the theoretical power coefficient is known, the wind speed after the blades can be calculated from the wind speed before the blades . Within the range of the value of , (23) can be written as [10] (24) , . where The theoretical power coefficient can be obtained from the real power coefficient and the optimal power coefficient

(25) both and are functions of tip speed ratio . They can be obtained through the characteristics of wind turbines.

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Fig. 5. Frequency responses of

and

.

Fig. 6. Measurement of the anemometer.

B. Design of the Observer The weighting functions

and

are chosen as (26) (27)

weights the effort with the aim of penalizing the higher-frequency components of the measurement of anemometer. On the other hand, stresses the importance of the lower-frequency components of the generator power. Once the weighting functions are defined, the compensator is designed using any of the available computer packages [22]. So do the sensitivity functions and complementary sensitivity functions . The frequency responses of and are presented in Fig. 5. It can be seen that the gain of is very small in lower frequency and large in higher frequency. Thus can be regarded as a high-pass filter. It attenuate the components of the measurement of the anemometer, and passes the signals . On the other hand, the frequency response characteristics of are the opposite to . It can be regarded as a low-pass filter. It retains the higher frequency components of the generator power. C. Simulation Results In this section, some simulation results that illustrate the effectiveness of the proposed observer are presented. The realistic wind profile employed in the simulations was generated considering the cyclic fluctuations caused by the spatial distribution of the wind speed field. The wind speed varies between 7 and 12 m/s, with an average wind speed of about 8.5 m/s. It should be pointed out that the real wind speed is not necessary during design and calculating of the observer. The wind speed is used just for simulations. Because of the characteristics of the induction generator, the rotate speed keeps nearly constant during the simulation. The inputs of the simulation system are effective wind speed ; and

Fig. 7. Results of observer-based estimation.

the outputs are the measurement of the anemometer and generator power . Figs. 6 and 7 show the response of the observer to a wind speed profile. The performance of an estimator designed on the basis of a Kalman filter is also given in Fig. 8. The method is described in detail in [2]. It can be observed from Fig. 6 that the measurements of the anemometer can follow the rapid fluctuations in the effective wind speed signals. But there exist relative large steady errors. However, the outputs of the observer fit the effective wind speed signal very well, and there is no obvious lag in phase (Fig. 7). It can be observed from Figs. 7 and 8 that the estimation of effective wind speed is improved slightly against the method based on Kalman filters. And when comparing standard deviations, it can be concluded that there is an improved performance. The power spectral density curve (Fig. 9) shows that within the bandwidth that can affect the design of the control system, the outputs of the observer and realistic wind profile fit very


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using broadly available numerical algorithms. The proposed method provides a useful and simple tool to design an observer exhibiting robust performance against the mode perturbations. Simulations were carried out to assess the performance under a realistic wind speed profile. The simulation results show the ability of the observer to follow the changes of the realistic wind speed within a wide frequency range. Theoretically, the concepts presented in this word can be used for other types of wind turbine generators, but one of the purposes of measuring the effective wind speed is to use it as the feedback signal for the control of the pitch angle of the blade. The change of the pitch angle would change the generator power. This would add an extra close-loop to the system. The problem will be fully discussed in the future. REFERENCES Fig. 8. Results of Kalman filter-based estimation.

Fig. 9. Power spectral density of wind speeds.

well. It shows that the proposed method can effectively improve the accuracy of the wind speed measurement. It can also be seen from Fig. 9 that there is a large variation near 8.5 Hz. Although the size and inertia of the anemometer is small, its bandwidth is still limited. In the higher frequency range, the anemometer cannot follow the changes of the wind speed. However, it is beyond the system bandwidth; it would have little effect on the control system design. V. CONCLUSION AND FUTURE WORK The purpose of this paper is to investigate the measurement method for the effective wind speed of a wind turbine. In this paper, we focused on the estimation of fixed-speed fixed-pitch wind turbines. An observer for effective wind speed has been proposed based on frequency-domain data fusion theory. In this context, the observer design is formulated as a mixed-sensitivity problem with linear matrix inequalities (LMIs), which is solved

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[18] B. V. Dasarathy, “Information fusion—What, where, why, when, and how?,” Inf. Fusion, vol. 2, no. 2, pp. 75–76, 2001, DOI: 10.1016/S1566-2535(01)00032-X. [19] D. R. Yu, Y. Fan, and Z. Q. Xu, “Reconstruction for fuel signal of once-through boiler based on distributed data fusion,” in Proc. CSEE, 2004, vol. 24, no. 2, p. 5. [20] H. Camblong, M. Vidal, and J. Puiggali, “Principles of a simulation model for a variable-speed pitch-regulated wind turbine,” Wind Eng., vol. 28, no. 2, pp. 157–175, 2004. [21] J. R. Ryoo, T. Doh, and M. J. Chung, “Robust disturbance observer for the track-following control system of an optical disk drive,” Control Eng. Practice, vol. 12, no. 5, pp. 577–585, 2004, DOI: 10.1016/S09670661(03)00140-0. [22] J. E. Speich and M. Goldfarb, “An implementation of loop-shaping compensation for multidegree-of-freedom macrocmicroscaled telemanipulation,” IEEE Trans. Control Syst. Technol., vol. 13, no. 3, pp. 459–464, May 2005. [23] F. D. Bianchi, D. B. H. , and M. R. , Wind Turbine Control Systems: Principles, Modelling and Gain Scheduling Design. Berlin, Germany: Springer-Verlag, 2006. [24] F. D. Bianchi, H. De Battista, and R. J. Mantz, “Optimal gain-scheduled control of fixed-speed active stall wind turbines,” IET Renewable Power Generation, vol. 2, no. 4, pp. 228–238, 2008. [25] W. Leithead and B. Connor, “Control of variable speed wind turbines: Dynamic models,” Int. J. Control, vol. 73, no. 13, pp. 1173–1188, 2000. Zhiqiang Xu (M’09) received the B.E., M.E., and Ph.D. degrees from Harbin Institute of Technology, Harbin, China, in 1994, 1996, and 2002, respectively. Since 1996, he has been at the School of Energy Science and Engineering, Harbin Institute of Technology. His main research is in modeling, simulation, and control of power plants and power systems. During 2009–2010, he was a visiting scholar at the Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX, and had been engaging in collaborative research on the regulation of a wind turbine generator power plant with Prof. M. Ehsani.

Qinghua Hu (M’10) received the B.E., M.E., and Ph.D. degrees from Harbin Institute of Technology, Harbin, China, in 1999, 2002, and 2008, respectively. Now he is an Associate Professor with Harbin Institute of Technology and a postdoctoral fellow with the Hong Kong Polytechnic University. His research interests are focused on intelligent modeling, data mining, knowledge discovery for classification, and regression. He is a PC cochair of RSCTC 2010 and serves as referee for a great number of journals and conferences. He has published more than 70 journal and conference papers in the areas of pattern recognition and fault diagnosis.

Mehrdad Ehsani (S’73–M’75–SM’84–F’96) has been at Texas A&M University, College Station, TX, since 1981, where he has been the Robert M. Kennedy Professor of electrical engineering and Director of Advanced Vehicle Systems Research Program since 2004. He is the author of over 300 publications in specialty power systems, pulsed-power supplies, high-voltage engineering, power electronics and motor drives, and automotive power and propulsion systems. He is the coauthor of several books on power electronics, motor drives, vehicle power and propulsion systems, and a contributor to an IEEE Guide for Self-Commutated Converters and many monographs. He is the author of over 20 U.S. and EC patents. His current research work is in power electronics, motordrives, hybrid electric vehicles, and vehicle power systems. Dr. Ehsani is a Fellow of the SAE.