Making the Case for Applications of Switched ... - IEEE Xplore

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The main debate over the adequacy of switched reluctance drives in automotive applications ... excitation technologies which improve efficiency, freewheeling.

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 21, NO. 3, MAY 2006

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Making the Case for Applications of Switched Reluctance Motor Technology in Automotive Products Mahesh Krishnamurthy, Student Member, IEEE, Chris S. Edrington, Member, IEEE, Ali Emadi, Senior Member, IEEE, Peyman Asadi, Student Member, IEEE, Mehrdad Ehsani, Fellow, IEEE, and Babak Fahimi, Senior Member, IEEE

Abstract—Switched reluctance machines (SRM) offer attractive attributes for automotive applications. These include robustness to harsh operational conditions, rugged structure, fault resilient performance, and a wide range of speed. The main debate over the adequacy of switched reluctance drives in automotive applications has often focused on efficiency and position sensorless control over the entire speed range, adaptation of control algorithms in the presence of parameter variations, and high levels of acoustic noise and vibration. The present paper demonstrates three key technologies developed over the past few years that have resulted in tangible improvements in the performance of SRM/generators (SRM/G) as related to the above areas of interest. This paper intends to illustrate the new possibilities and remaining challenges in applications of SRM in automotive industry. The proposed technologies have been validated by simulation and experimental results. Index Terms—Acoustic noice, switched reluctance machines (SRM), vibration.

I. INTRODUCTION

A

UTOMOTIVE applications form an ever-growing market for power electronic and adjustable speed motor drive technologies [1], [2]. These applications require high-grade performance, robustness to harsh ambient conditions, rugged yet quiet and bump-free operation, and they should be at an affordable price [1]–[5]. Switched reluctance drives (SRD) inherently satisfy a number of these somewhat contradictory criterions. A modular and rugged structure, wide speed range, and insensitivity to high temperatures have put SRD among the prominent contenders for automotive applications. Although there is significant compatibility between natural characteristics of SRD and requirements of the automotive industry, the progress in introduction of this emerging technology has been relatively sluggish. The main questions surrounding the use of SRD for automotive applications are focused on: • need for an external position sensor for high-grade control [6]–[8];

Manuscript received March 15, 2005; revised October 26, 2005. Recommended by Associate Editor J. Shen. M. Krishnamurthy and B. Fahimi are with the Electrical Engineering Department, University of Texas, Arlington, TX 76019 USA. C. S. Edrington is with the College of Engineering, Arkansas State University, Jonesboro, AR 72467 USA. A. Emadi is with Grainger Power Electronics and Motor Drives Laboratory, Illinois Institute of Technology, Chicago, IL 60616–3793 USA (e-mail: [email protected]). P. Asadi and M. Ehsani are with the Electrical Engineering Department, Texas A&M University, College Station, TX 77843 USA. Digital Object Identifier 10.1109/TPEL.2006.872371

• improvement of efficiency for generating and motoring modes of operation [9]–[12]; • mitigation of acoustic noise and vibration [5]; • need for adaptation in control to cope with parameter variations [13]. The ultimate success of SRD technology seems to be closely tied to how effectively the above questions are answered. Over the past decade, there have been several researches that have attempted to offer feasible answers to the above questions. The present paper explains three key technologies that offer solutions for the above issues, thereby, making a case for the use of SRD technology in vehicular applications. These are bipolar excitation technologies which improve efficiency, freewheeling control strategy to boost productivity while operating as a generator, self-tuning, and four quadrant sensorless controls over the entire speed range. These technologies are explained in detail and are supported with simulation and experimental results for validation purposes. Experimental results are obtained from two different switched reluctance machine (SRM) prototypes that have been primarily designed and developed for electrically assisted power steering (12/8, 2[kW], 42[V]) and electric coolant pump (8/6, 2[kW], 42[V]). II. FUNDAMENTALS OF MOTORING AND GENERATING VIA SWITCHED RELUCTANCE MACHINE Electromagnetic torque in SRMs is produced by polarized rotor poles tending to align with the excited stator poles (see Fig. 1). The resulting mechanical work in motoring is provided by the magnetic field via excitation of the machine coils from an electric source. During generation, on the other hand, mechanical energy supplied by prime mover is mostly responsible for build up of magnetic field and generated electric power. The electromagnetic torque can be expressed in terms of co-energy as follows:

(1) The electromechanical exchange of energy results in an induced voltage in machine coils that opposes the increase of current during motoring. The same induced voltage contributes to the increase of current in generating mode of operation. It must be noted that due to its singly excited structure, during generation, the initial magnetizing flux should be supplied by an

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and resistive voltage drop, (4) can be rewritten as given in (5) for motoring and generating, respectively

(5) where stands for number of rotor poles. It must also be noted that for generation purposes, stator coils are turned ON around the aligned position and turned off well before unaligned position. This has been presented with a phase shift in (5). Equation (5) can be used to arrive at an expression for current. The solutions are approximately expressed as Fig. 1. Cross section of a 12/8 SRM along with the flux lines at aligned position.

external source. The induced voltage, also known as motional back-emf, can be expressed in terms of magnetic co-energy

(2) Owing to saliency of the SRM geometry, there exists an inherent dependency between all major magnetic parameters and rotor position. Therefore, in order to achieve good performance, the impact of geometry has to be incorporated. This, in fact, shifts the burden from development of complex geometries to sophisticated control algorithms, a quality encouraged by the existing trend in digital signal processor (DSP)-based processors. Switched reluctance machines can operate either as a motor or generator. This is apparent from the analytical expression for electromagnetic torque

(3) With no loss of generality, saturation effects have been neglected. According to the above formula, while the generated torque does not depend on the sign of phase current, the relative positioning of phase current with respect to inductance profile can determine the mode of operation, per motoring or generating. As a result, by locating the current pulse in a region with negative slope of inductance, one can generate electric power. Consequently, the generated power depends upon magnetic design and shape of the current pulse. The phase voltage equation for an SRM can be written as follows:

(4) where , , , , , and stand for phase voltage, phase current, phase inductance, rotor position, speed, and stator resistance, respectively. Neglecting nonlinear effects of saturation

(6) This equation shows that for a given speed, symmetric commutation, and a fixed bus voltage, current waveforms in motoring and generating modes of operation are a mirror image of each other. This means that while motional back-emf tends to limit the current in SRM, during generation—it acts as a source that increases the current even after turn-off instant. Indeed at higher speeds, a substantial motional back-emf forms the essence of generation in the drive. Since efficient operation of switched reluctance generators (SRG) occurs at high speeds, there is a need for control strategies to tune commutation instants as a function of speed. The main objective of such strategies needs to be to control and maintain bus voltage and phase current, thereby, enhancing cost, packaging, and thermal management of semiconductor devices. Fig. 2 shows a typical phase current in a SRG. In the first part of the current pulse (indicated as magnetizing), the converted mechanical energy contributes to the build up of induced voltage and hence, phase current. After the turn-off instant, i.e., the second portion of the current pulse, the converted mechanical energy is solely responsible for build up of the current. As a result of change in the current path in the converter, sign of current from the dc link changes at turn-off instant. In other words, the phase current is fed back to the source after turn-off instant, a region indicated by generating. It is also critical to note that, in single pulse mode of operation during motoring, turn-on instant is solely responsible for the peak value of current. During generation, however, both turn-on and turn-off instants contribute to the peak value of phase current. This has been demonstrated by simulating the behavior of our experimental SRM as shown in Fig. 3. As can be seen, for a fixed turn-on instant, significantly different peak currents can be achieved by altering the turn-off instant. This point should be

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Fig. 4. Finite element field solution with phase overlap under long flux path excitation. Fig. 2. Applied current pulse in relation to inductance profile in generation mode.

Fig. 3. Variation of the phase current with respect to the turn-off instant in SRG.

taken into account when designing optimal or protective control strategies. III. BIPOLAR EXCITATION OF SRM DRIVES In order to efficiently operate an SRM drive, use of substantial overlap between two phases is commonly practiced. Creation of an overlap, once properly tuned, contributes to higher torque productivity and mitigation of torque pulsation. In an 8/6 SRM a maximum overlap of 15 (mechanical) is allowed. Fig. 4 shows the distribution of flux density in the SRM under multiphase excitation. Notably, a part of the back iron, located between two excited stator phases, exhibits a very low flux density. This is due to the fact that fluxes generated by each phase oppose each other within this region. In the remaining 75% of the back iron, on the other hand, fluxes generated by two stator phases are added. This explains the existence of a relatively high flux density in this part of the back iron. This pattern of magnetization has been referred to as “long flux path excitation (LFPE).”

Fig. 5. Finite element field solution with phase overlap under short flux path excitation.

Fig. 5 shows the distribution of flux density which changes once in every electrical cycle in the SRM for conventional winding in the stator coils under unipolar excitation. This pattern of magnetization is referred to as “short flux path excitation (SFPE).” This means that in an 8/6 SRM, within every electrical cycle, there exist three LFPE and one SFPE. Since SRM drives are usually operated under heavy saturation, one can observe certain differences between the performances of the machine under each mode of operation. For instance, it is known that with identical excitations applied to every phase of the SRM, one of the phases generates more torque. This in turn results in an increase in the torque pulsation, a major origin of audible noise in SRM drives. Similarly, during generation, it is observed that with an identical magnetizing current, one of the phases would generate more electricity. These observations can be linked to the above observation. In order to evaluate the impact of the SFPE in SRM under multiphase excitation, review of the phase voltage equation is

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necessary. Phase voltage equation for a conventional 8/6 SRM drive can be formulated as:

(7)

where , , , , ,and denote phase current, flux linkage, self/mutual inductance, rotor position, phase voltage, and stator phase resistance, respectively. As can be seen during SFPE, there exists a significant coupling between adjacent phases (mutual terms are shown in bold). Due to changes in the magnetic circuit and under the assumption of a saturated stator pole, one can expect lower reluctance under SFPE which results in a higher inductance as compared to LFPE. In addition, mutual effects under the LFPE are not very significant and reportedly have been neglected by many researchers. As can be seen, in the presence of a significant overlap and under SFPE, mutual flux can no longer be ignored. To take a full advantage of this observation, a new bipolar excitation scenario has been proposed which guarantees SFPE at each instant of time. In other words using the proposed excitation (as shown in Fig. 6), there are four SFPE within each electrical cycle of an 8/6 SRM. In order to provide bipolar excitation to the SRM, a new series of inverter topologies have been introduced. Primary focus has been given to circuit topologies that can provide flexibility in control, versatility in operation, and survivability. Fig. 7 illustrates the conventional asymmetric bridge used in unidirectional drives along with those targeted topologies intended for bipolar SR drives. Circuit topology shown in Fig. 7(b) is formed using four identical H-bridges which provides maximum flexibility in motoring and generating modes of operation. The SR-drive remains modular and any failure in one of the phases can be isolated from the other phases. This portrays a fault tolerant topology which is desired in many high impact automotive applications. There are 16 switches as compared to eight switches and eight diodes used in asymmetric bridge. One may note that although there is an additional cost and real estate associated with the gate driver circuitry, the price of a fast recovery diode is comparable to that of a metal-oxide-semiconductor field-effect transistor (MOSFET) (especially for current intensive applications such as automotive products). The circuit shown in Fig. 7(c) portrays a hybrid combination of asymmetric bridge and 8-b topology in which the direction of mismatched fields (mmf) for the first three phases has been adequately alternated such that a SFPE is achieved by a unidirectional excitation. The last phase, however, is required to change polarity once per electrical cycle. In this topology, ten switches and six diodes are incorporated. Finally, using a star connected stator and by the compliment of two auxiliary switches a new topology for a bipolar SRM is developed. The auxiliary switches are employed whenever the sum of all phase

Fig. 6. Proposed excitation for maintaining a SFPE at all times: (a) conventional excitation and (b) proposed pattern of excitation.

current does not equal zero. In spite of the employment of ten switches, there is a reduction of fault tolerance as the modular structure of the SRM is lost. IV. FREEWHEELING TECHNIQUE TO ENHANCE GENERATION CAPABAILITY IN SRG In order to improve the productivity of the SRG drive, a new switching strategy has been proposed. This method incorporates an intermediate freewheeling period with optimal timing. In the descending portion of the inductance profile, the stator phases can be excited. Initially the magnetizing current is established by turning on both switches (see Fig. 8). This current not only establishes a magnetizing flux in the core but also generates a braking torque which works against the torque generated by

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Fig. 8. Establishment of the magnetizing flux.

Fig. 9. Freewheeling mode of operation to boost the magnetizing current.

Fig. 7. Asymmetric bridge for unidirectional SR drives along with three topologies for bipolar SR drives: (a) asymmetric bridge for four-phase SR, (b) H-bridge configuration for bipolar excitation, (c) hybrid configuration (three asymmetric legs, one H-bridge) for bipolar excitation, and (d) star connected configuration for bipolar excitation

the prime mover. In this region, dc link voltage and motional back-emf contribute to the build up of the current. It must be

noted that the motional back-emf is the product of the electromechanical energy conversion. Turn-on instant is selected in the neighborhood of aligned position. Notably, turn-on instant is used for phase advancing at higher speeds to allow enough time for build up of magnetizing current. This phase advancing may as well be extended into the motoring region to allow for a satisfactory operation at very high speeds. Once the magnetizing current reaches its targeted value at po, one of the switches is opened (in the case shown in sition Fig. 9 the upper transistor has been opened). This causes freewheeling of phase current within a short-circuited path comprising of a diode and the lower switch. In this region motional back-emf further boosts the build up of current. Notably, in this region no current is taken from or injected into the dc link. In this region, part of the converted mechanical energy is consumed in the form of silicon and copper losses. However, since the dc link voltage does not oppose the build up of current, a higher rate of increase is expected here. Once the second targeted level of current has been reached at position , the second transistor is opened (see Fig. 10). This action imposes the negative dc link voltage on the active stator phase. At this time, mechanical energy of the rotor converted into electrical form is sent back to the dc link. Due to a substantial back-emf, current continues to rise thereby further boosting the motional back-emf. This trend continues until a drastic change in the slope of inductance occurs, resulting in a significant reduction in the motional back-emf. At this time,

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In this expression, , , and represent phase current, time, and time index, respectively; while, , , and represent analytical function/matrices of phase current and commutation instants. Once the commutation angles are issued, coefficient matrices ( and ) are calculated as follows:

(11)

Fig. 10. Generating mode of operation.

negative dc link voltage dominates the dynamics of the coil and the phase current starts its downhill path. This process quickly clears the respective stator phase from any residual current. It must be noted that extension of the current into the motoring region must be prohibited to avoid inefficient operation of the SRG drive. By optimal selection of three commutation instants, overall productivity of the SRG can be enhanced. This translates to an improved compactness, which is key to the successful implementation of this emerging technology. V. POSITION SENSORLESS CONTROL TECHNIQUE A balance probe forms the essence of the sensorless control techniques in this paper. Depending on the operational region of the SRM, an appropriate version of the phase voltage equation is selected. The selected version of the phase voltage equation is then used to form a balance probe. This incorporates an analytical model of the phase inductance/flux linkage as shown below [14]–[16] (8) , , and denote polynomials, which reflect the where nonlinear effects of saturation. Equations (9a) and (9b) express the integral and differential forms of the phase voltage equation

(9a) (9b) where , , , , , , and denote phase voltage, phase current, phase resistance, phase inductance, phase flux linkage, angular speed, and rotor position, respectively. Notably, certain terms in differential form of the phase voltage equation are to be modified according to the region in which SRM operates. The general form of a balance probe is given as

(10)

By online measurement of phase current/voltage and time, both sides of (10) are monitored. Upon observing a balance, a commutation command to the phases is issued. Although the proposed sensorless technique has the same generic formulation over the entire speed range, three technologies have been adopted that cover sensorless control at standstill, near zero speed, and high-speed regions. A. Detection of Operational Region Due to the synchronous nature of SRM, at very low speeds, each pulse of current takes a relatively longer time to complete. Considering the fact that our balance probe technique at high speeds relies on computation of flux linkage, accumulation of errors in measurement of terminal quantities viz. phase current and voltage at low speeds can lead to creation of a drift which consequently impairs the practicality of the method. Indeed, the following inequality can be used as a measure for finding a speed below which significant inaccuracies can be expected: (12) where , , , , , , , , and , stand for interrupt frequency, scaling factor in flux calculation, permitted error in flux calculation (in percentage), maximum phase current, coil resistance, threshold for flux linkage, number of bits in analog to digital (A/D) conversion, and number of inaccurate least significant bits (LSBs) in current measurement, respectively. In order to detect the operational region of the SRM drive, a diagnostic approach is implemented. The detection system injects pulses of voltage with a sufficiently short duration into idle phases of the SRM (after completion of each commutation). By measuring the time it takes for current to be completely removed from the phase and its comparison to the injection period, one can predict the extent of back-emf contribution. For instance, assuming and to stand for rise and fall times, respectively, the following equation for a sufficiently small pulse holds:

(13) where denotes effective motional back-emf. Since motional back-emf is directly proportional to the speed, this has been used as the foundations for detecting of operational region. Fig. 11 shows a decision-making chart based on the proposed diagnostic method. Once reaches a certain percentage of the dc bus voltage, defined as region threshold, the switching of the sensorless routine takes place in the next upcoming phase. It must be noted that threshold for transition from low speed to

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Fig. 12. Existence of a double value function in detected flux during generation.

Fig. 11. Detection methodology for operational region (H: high speed, L: low speed).

high speed are deliberately chosen different from that assigned for detecting a transition from high speed to low speed . This removes the chance of falling into a limit cycling between the two regions. Operation in all four quadrants of torque versus speed plane is a requirement for many applications. This is to operate the machine as a motor or generator during clockwise and counterclockwise motions. It is well known that, in order to achieve motoring, the stator windings should be excited when the rotor is moving from unaligned to aligned position. Generation on the other hand, is achieved by excitation of stator windings when the rotor moves from aligned position toward unaligned position. Given the symmetrical shape of the inductance profile with respect to aligned position, for a given conduction band and at a constant speed, one can expect current waveforms during motoring and generating to be mirror image of each other. However, one should note that motional back-emf during generation acts as a voltage source resulting in an increase of phase current even after a phase is turned OFF. In order to alter the direction of rotation, the only necessary step is to change the sequence of excitation. Notably the sequence of excitation among stator phases is opposite to the direction of rotation. The transition between the two modes needs to be quick and smooth. Upon the receipt of a command requesting a change in direction, the excited phase needs to be turned OFF to avoid generation of additional torque. Simultaneously, a regenerative braking needs to be performed. This requires detection of a phase in which inductance profile has a negative slope. The operation in generating mode continues until speed decays to zero (or a tolerable near zero speed). At this time, all the phases are cleared and a new sequence of excitation can be implemented. Speed reversal during generation is not a usual case since direction of the rotation is dictated by the prime mover. In case speed reversal is initiated by the prime mover, machine controller needs to be notified. Otherwise, a mechanism for detection of direction of rotation should be in place. Such mechanism would detect any unexpected change of mode, i.e., motoring to generating.

Notably, to perform these procedures, continuous access to the rotor position is necessary. Under a sensorless format, where an explicit access to the rotor position is replaced by an electromagnetic quantity such as flux linkage or inductance, certain steps need to be added. For instance, the balance probe method presented in this paper is based on the existence of a single value flux linkage. As can be observed from Fig. 12. such condition is not valid during generation. During generation, unlike motoring, the flux linkage initially starts to increase. However, after entering the hysteresis control, the net flux decreases. In order to explain this, one needs to note that motional back-emf, during generation, acts as an additional voltage source forcing the current to increase. Therefore, in each triangle caused by hysteresis control, the time for current to reach the maximum, i.e., ON-time, would be less than the amount of time it takes for current to reach the minimum band, i.e., OFF-time. Flux linkage is therefore given by (14) where indicates the flux at the beginning of the hysteresis current control and experiences a decrease. As a result, searching for a single threshold needs to be combined with a secondary condition to prevent a false decision as shown graphically in Fig. 12. A proper condition would be detection of a decreasing trend before the occurrence of the final balance. Once a robust sensorless operation during generation and motoring is established, same procedures for transition between various modes of operation can be followed using the balancing method and implicit access to the rotor position. Given the fact that SRM is a synchronous machine, electrical frequency of the excitation can be used in order to estimate the speed. VI. AUTO-CALIBRATING MODEL OF SRM DRIVES The following formula provides an analytical expression in terms of a truncated Fourier series for inductance profile in SRM. The self-inductance is thus given as

(15) This illustrates the important fact that self-inductance is dependent upon both the rotor angle and phase current.

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midway-to -aligned, and unaligned inductances. The relationship between the coefficients of inductance profile in (15) and inductance at aligned, unaligned and midway from aligned are given as

Fig. 13. Inductance at aligned position as a function of phase current.

(16)

Fig. 14. Inductance at midway from aligned position as a function of phase current.

Fig. 15. Inductance at the unaligned position as a function of phase current.

can be obtained through experiments or finite element analysis (FEA). Various curve-fitting routines provide ways to yield analytical expressions for . A fifth order polynomial curve fit was chosen to express . Fig. 13 shows the aligned inductance calculated using a two dimensional finite element analysis for the experimental 8/6 SRM plotted versus current. From Fig. 13, one can note that the machine becomes saturated as current increases and thus the inductance decreases. The variation of inductance at the midway-to-aligned position versus phase current is shown in Fig. 14. It is once again seen that the inductance seen at this position decreases as current increases, due to the effect of saturation. Finally Fig. 15 shows the inductance versus phase current for the unaligned position. Note that the inductance does not change with respect to phase current due to the dominating reluctance of a large air-gap. In calculating self-inductance of the machine, one can completely characterize inductance by measuring the aligned,

Mutual inductance, like self-inductance is both a function of the rotor angle, and phase current. In the literature a method to calculate mutual inductance offline is given. This method in essence includes applying a voltage to a phase and then solving the phase voltage equations of the other phases by applying Faraday’s law. However, this methodology does not address the effect of saturation on mutual inductances, nor the case when phase overlap is present, but merely addresses the mutual inductance in a nonexcited phase that arises due to excitation of an adjacent phase. It must be noted that the effects of mutual inductances are more salient when the machine starts to saturate (In order to accurately model the machine, mutual inductance must be characterized for the cases in which the machine is saturated in the stator/rotor poles and stator back-iron. As in the case of self-inductance, we may model the mutual inductance by a truncated Fourier series expansion. However, in the self-inductance case the Fourier series coefficients could be obtained in terms of , , and . With respect to the mutual inductance, only values of the mutual inductance at aligned and midway will be used. This is due to the fact that mutual inductance with a quadrature phase would be zero due to a dominant air-gap, nonexistence of mutual flux path, as well as a lack of coupling between windings. Thus as in the case with self-inductance we can represent the mutual inductance as

(17) The magnitude of the mutual inductance may change drastically due to the formation of a short flux path within an electric cycle which would introduce an asymmetry in the profile that has not been mathematically reflected in the above expression. This is better described in the next section. However, by proper monitoring of the magnetic pattern in the machine this phenomenon can be effectively incorporated into the dynamic model. Although self and mutual inductances can be measured and stored offline, it is important to adopt an auto-calibrating approach to keep these inductances up-to-date. This is owing to the fact that inductances of an SRM are subject to alteration due to relaxed manufacturing tolerances, aging effects, and operating conditions. A time efficient modeling approach has been developed for extraction of inductances at aligned, unaligned and midway to aligned positions in SRM drives [17].

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Fig. 16. Current versus time for a single excited phase.

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Fig. 17. Rotor position versus time.

This method has been experimentally verified for our targeted 8/6 SRM drives. As mentioned earlier this particular configuration can render significant simplicity in allowing access to align, midway, and unaligned rotor positions. It has been noted earlier that when one phase of an 8/6 SRM is aligned, the other two phases are automatically located at midway and unaligned positions. To extract the inductances at these targeted positions, we submit a solid pulse of voltage to the phase of interest and allow current to grow up to a maximum rated current. Upon reaching the maximum value, phase is turned OFF and the current is removed. By collecting the induced voltage in the coil and current values one can compute the flux linkage and thus the inductance as a function of current. In the proposed method, one phase is aligned and the above diagnostic approach is performed in a sequence on other phases. Our simulation shows that due to the existing separation between mechanical, electrical and control time constants, rotor does not move. Mechanical time constant for the experimental SRM is described as

(18) where is the moment of inertia of the rotor assembly, and is the dynamic friction. Electrical time constant is given as

(19) where is the self-inductance and is the winding resistance. Taking the ratio of to we obtain:

(20) Therefore, it folows that the machine is virtually at standstill during one electrical time constant. This fact is illustrated in the following figures. Fig. 16 shows phase current in the SRM. Current rises from its zero value to its regulated peak at 60 A in approximately 0.9 ms. This rise time is 2.45% of . Since current can be used during this time to calculate the flux-linkage

and thus inductance we can essentially say that the ratio between and is (21) To illustrate that the rotor indeed does not move over this brief time period, a plot of the rotor position versus time has been shown during the same time period over which current ramps from its zero value to its regulated peak value. From the graph in Fig. 17, it can be seen that rotor position changes from its initial value of 0 to a value of 0.0009 . This change in rotor angle small enough to allow calculations to be made assumping the rotor to be at standstill. This is a significant result with respect to online parameter estimation. Using the above analysis, an update for the model can be obtained in a matter of a few milliseconds. However, completion of the model requires a high performance processor. To address this issue, the DSP computation time becomes the driving factor. The auto-tuning procedure relies on the sensing of phase currents and voltages, and therecore necessitates A/D conversion. VII. SIMULATION AND EXPERIMENTAL VERIFICATION A. Bipolar Excitation In order to validate the results of finite-element (FE) analysis a series of experiments were performed on the targeted SRM drive. Fig. 18 illustrates a block diagram of our experimental setup. The system comprises of an 8/6, 42[V], and 2[kW] SRM, a programmable permanent magnet synchronous motor (PMSM) drive acting as a four quadrant dynamometer, an inline torque meter, an optical encoder, a bipolar power electronic converter, and a DSP based controller. The entire control routine for the SRM is developed in assembly language of the TMS320F2407A DSP processor. This processor offers a speed of 40 millions of instructions per second (MIPS), a 10-b A/D conversion at a speed of 800[ns] which is adequate for our control purposes. The current in each phase of the machine is controlled via hysteresis control algorithm. Two 42[V], 3[KW] switching power supplies provide the dc link voltage for the converter. The inline torque meter provides analog outputs corresponding to the difference between the torques supplied

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Fig. 18. Experimental test setup used for the investigation.

Fig. 20. Improvement of the torque density in the targeted SRM at 70 A for three different positions.

Fig. 19. Improvement of the torque density at three different positions due to bipolar excitation of the SRM.

by the SRM and PMSM drive as well as the speed of rotation. The dc link current and voltage are also sampled and stored to monitor the input power to our SRM drive system. In order to compare the static torque generated by bipolar and conventional excitation the following procedure was performed. Using an index head the rotor of the SRM was locked at specific positions starting ranging from aligned position to unaligned position (torquemeter is located between the index head and the SRM). While exciting phase-a by current of 30[A], current in the adjacent phases was varied between 0 70[A] and the inline torque meter was used to measure generated torque under conventional and bipolar excitation. Fig. 19 illustrates the percentage of increase in the measured electromagnetic torque at three distinct positions namely, aligned, 5 from aligned and 10.5 from the aligned position. Notably at 10.5 there exists a large airgap between the rotor and stator pole of the neighboring phase resulting in a negligible difference between the two techniques. However at aligned and 5 positions there exists a significant improvement in the generated torque by the virtue of the short flux path excitation. By increasing the current in phase-a from 30[A] to 70[A] the same trend has been observed (70[A] is the highest current that

Fig. 21. Experimentally obtained torque profile of the SRM using bipolar and conventional excitations.

could be reached using our power supplies). However, due to the significant saturation in the back iron of the machine a relatively smaller gain in the generated torque has been observed. This is in agreement with the results of our FE analysis. The results of this test are shown in Fig. 20. To illustrate the overall gain in torque density in the bipolar SRM drives, the measured torque profile of the SRM at 30[A] under two bipolar and conventional excitations are shown in Fig. 21. As can be observed there exists a substantial increase in the torque productivity of the machine while offering a balanced torque profile with smaller pulsation. In order to compare the efficiency of the SRM drive, a series of tests were performed under bipolar and conventional unipolar

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Fig. 23. Improvement of efficiency by using bipolar excitation at two different voltage levels.

Fig. 22. Sample phase current waveforms at 1500[rpm] using (a) conventional and (b) bipolar excitation.

excitations. The input and output powers were measured using the following relationships:

(22) , , , and denote torque generated where by SRM, torque generated by the PMSM, and torque measured by the inline torque-meter and electrical period of the drive system. The torque generated by the PMSM drive was available through a built in torque estimator. The accuracy of the estimated torque has been verified. In addition the dc link current and dc link voltage was measured using adequate sensors. In order to perform each test, the PMSM drive was set in a speed control mode running at a speed of interest. At this time SRM was started in the same direction of rotation and the magnitude of the current in the phases are set at desired value. This configuration prohibits a sudden reversal of the direction

of motion. Under these conditions the input and output average powers were monitored and recorded. Using the recorded values of input and output powers the overall efficiency of the system (incorporating silicon, copper, core losses etc.) was measured. Fig. 22 shows sample recorded current waveforms under conventional and bipolar excitations at 1500[rpm]. The existing ripple in the current waveform is caused by the digital hysteresis current control taking into account small phase inductances and limited switching frequency of the power electronics devices. Fig. 23 depicts the experimentally measured improvement in the efficiency of the SRM under bipolar control strategy for two different dc link voltages with a phase current of 15[A]. The experiment was performed up to 4000 [rpm] which is well above the base speeds of 1500[rpm] for 12[V] and 3000[rpm] for the 24[V] dc link voltages. One can note that in constant power region where the iron losses play a dominant role a maximum enhancement in the efficiency has been achieved. At lower speeds the bipolar SRM presents a superior efficiency thanks to the added torque density. Finally Fig. 24 illustrates the improvement in efficiency at various levels of current. It was noted that by increasing current, the improvement in efficiency persisted although with a smaller magnitude. One should also note that the copper and silicon losses play a dominant role in the low speed region and a better efficiency should be expected at higher speeds owing to a significant drop in core losses in bipolar SRM drive. B. Freewheeling Switching Strategy In order to show the practicality of the proposed technique detailed simulation verifications have been performed [18]. In order to simulate the switching strategy in Simulink, first a switching function was defined as follows: On Off

On

(23)

off where and denote the upper and lower switches in an asymmetric bridge converter. A detailed dynamic simulation

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Fig. 26. Classic control of SRG drives.

Fig. 24. Comparison of the efficiency improvement in bipolar SRM at various current levels.

Fig. 25. Simplified block diagram of the system incorporating the proposed switching method. Fig. 27. Proposed switching method.

model of the SR machine was incorporated for investigating the practicality of the proposed technique. The differential equation describing phase voltage for the 8/6 SRM is defined in (7). Phase inductance for an 8/6 SRM model can effectively be described using (8). This description of inductance accounts for the effects of saturation but does not include mutual effects that have been mentioned earlier in this paper and does not utilize the auto-calibration model for the estimation of inductance. Fig. 25 shows an upper level of our dynamic model as used in developing the switching strategy of our interest. To demonstrate the feasibility and effectiveness of the proposed technique the following study was conducted. The stator phase was excited slightly before aligned position , i.e., 4 . This allowed for build up of magnetizing current which is necessary at high speeds. Once the magnetizing current reached the desired value, 9 both switches were turned OFF and the current was directed toward dc link via freewheeling diodes. The net electricity generated in this process was the difference between areas denoted by regions I and II in Fig. 26. Running the simulation again with the same value for and using the same magnetizing current as before, i.e., 9 , the freewheeling diode was allowed to conduct for a pre-calculated period yielded the following results (see Fig. 27). In this case, the second switching function takes place at 14 . For this switching strategy no electricity was drawn from the power source or generated during region II so the net electricity

generated was equal to the area under the current curve for region III minus the area under the current curve for region I. For both of these plots the area in region I is the same. However, it is easy to see that area under the curve for the generated current is much larger when using the freewheeling switching method. Another benefit of using the freewheeling switching technique is the reduction of current ripple. This translates into a smaller dc link capacitor, which in turn enhances the compactness of the drive electronics. Using (24) to calculate the net current generated, and (25) to calculate the percentage of current ripple, the freewheeling current ripple was found to be approximately two-thirds that of the current ripple calculated using the traditional switching method (24) where phases

,

, and

stand for switching functions of the stator

(25) This reduction in ripple was experimentally verified. For a range of free wheeling angles between 1 to 9 , dc link ripple

KRISHNAMURTHY et al.: APPLICATIONS OF SWITCHED RELUCTANCE MOTOR TECHNOLOGY

Fig. 28. Variation of ripple factor with free-wheeling angle for proposed switching scheme.

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Fig. 30. RMS value of Phase current versus 

1.

Fig. 29. Measured current in one of the phases and a bus capacitor of the ar8 . rangement for 



was measured for fixed turn ON and turn OFF angles, 10 and 12 . Fig. 28 shows the results obtained from this study. From this figure, the optimal rotor position for the start of freewheeling can be established in order to reduce the ripple factor. It can also be noted from Fig. 28 that by the varying the angle of start of freewheeling, the ripple factor in the dc-link can be mitigated for the same positions of turn-ON and turnOFF angles. For the given set of conditions set to obtain maximum output power, dc-link ripple is least for a freewheeling angle of approximately 6 from aligned position. Fig. 29 shows measured current in one of the phases along with the current through one of the bus capacitors for a of approximately 8 from aligned position. Fig. 30 shows the variation of the RMS current through one of the phases with the angle of freewheeling under the current switching scheme. Figs. 31 and 32 show the variation of the dc average and RMS bus current versus the freewheeling angle. The reduction of ripple in the dc-link current is also apparent in the plots for both the classic and freewheeling net current waveforms as shown in Fig. 33(a) and (b) which show a significant reduction upon using the proposed freewheeling scheme as compared to the classic switching strategy. This study was further extended to evaluate the variation of output power of the system with respect to change freewheeling angle as shown in Fig. 34. For performing this study, various

Fig. 31. Average of dc bus current versus 

1.

Fig. 32. RMS value of bus current versus 

1.

combinations of , , and were tried and the output electric power was calculated for each combination. This information was then used to set the turn-on and turn-off angles to reach the maximum output power. With reference set

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 21, NO. 3, MAY 2006

Fig. 34. Output power versus 

.

Fig. 33. Simulated current waveforms comparing classic switching strategy to the proposed switching strategy. (a) Net current for a classic switching strategy. (b) Net current for freewheeling switching strategy.

at aligned position, fixed mechanical angles were set for the test with 10 and 12 . Speed of operation was set at 1500 for a bus voltage of 125[V]. It was thus concluded that the freewheeling switching strategy results in a higher output power than conventional schemes.

Fig. 35. Experimental results form Sensorless estimation of rotor position. (a) Estimated position from sensorless technique starting from standstill. (b) Comparison between estimated and actual rotor positions.

C. Sensorless Control To prove the functionality of the proposed sensorless scheme, the following tests were performed. By implementing the proposed sensorless technique, the experimental SRM was started from standstill and, at an approximate speed of 250[rpm], a transition to high-speed sensorless technique was found to occur. The SRM drive then accelerated to a steady state speed of 1150[rpm] as shown in Fig. 35(a). Fig. 35(b) illustrates a comparison between the estimated and actual rotor positions. The estimated rotor position was performed using the estimated commutation instants to detect rotor position via a reverse transformation and interpolation within each mechanical degree of rotation. Since the actual and estimated rotor positions were measured from digital to analog (DAC) outputs of the

DSP, there exists a significant noise due to DAC circuitry. In general the performance of the sensorless method was found satisfactory in terms of accuracy and a precision of 1.5 [mechanical] was maintained over the entire speed range. The error met its maximum at low speeds and at higher speeds was very limited. The hysteresis control of phase current was done in the software and with additional circuitry being used. All of the routines were developed in assembly language of TMS320F240 DSP and implemented on a 2[kW], 48[V], 12/8 SRM drive. The power electronic driver was a classic two-switch per phase driver. In the next step, a spin down experiment using regenerative braking was performed. As can be seen in Fig. 36, the SRM was

KRISHNAMURTHY et al.: APPLICATIONS OF SWITCHED RELUCTANCE MOTOR TECHNOLOGY

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Fig. 36. Spin down test with and without regenerative braking (measured speed).

Fig. 38. Torque reversal in sensorless SRM drive, vertical axis (measured torque [1 N-m/div]), horizontal axis (time [5 s/div]).

Finally, the transition between motoring and generating at a constant speed with sensorless control was verified. In these experiments, system was driven by an ac permanent magnet drive in closed loop speed control. The SRM was then started as a motor moving in the same direction. The ac permanent magnet drive operating under speed control absorbed the surplus torque on the shaft. After 15 s operating as a motor, a command for operation as a generator was issued (in the same direction). Fig. 38 depicts the torque trajectory under this experiment. The result of our experiment showed that torque control in motoring and generating modes of operation with sensorless control is feasible. D. Auto-Calibration of the Inductance Model

Fig. 37. Speed reversal test under sensorless control. (a) 1700 [rpm]. (b) 60 [rpm].

running at almost 2000[rpm] when a reversal command was issued. Speed response was recorded with and without regenerative braking. Notably, it would take a relatively long time for speed to decay in friction braking whereas regenerative braking accomplished the task in the matter of a few tens of millisecond. In addition, the braking torque during regeneration can be adjusted to further accelerate this process. Speed reversal test was also performed to verify the practicality of the proposed system. Fig. 37 shows the speed trajectory in both directions. During this test, an SRM drive operating as a motor starts in clockwise direction and after certain number of revolutions, it would stop and then start in the opposite direction. This test was performed at 1700[rpm] and 60[rpm] to represent the performance of the system at high and low speeds. The speed information was collected using an external speed sensor on the PM load. The SRM drive system is accommodating this action with high reliability and consistency.

A comprehensive model for the accurate estimation of inductance in an SRM requires inclusion of factors such as saturation, mutual effects and formation of short flux paths in the machine. Although self and overlap inductances can be measured and stored offline, it is important to adopt an auto-calibrating approach to keep these inductances up-to-date. This ensues from the fact that inductances of the SRM are subject to alteration due to relaxed manufacturing tolerances and operating conditions. A time efficient modeling approach including the above-mentioned factors was developed modeling approach for extraction of inductances at aligned, unaligned and midway-to-aligned positions in an 8/6 SRM. To perform this analysis, a solid pulse of voltage was submitted to the phase of interest and current allowed to increase up to a maximum rated value. Upon reaching this preset value, the phase excitation was turned OFF and current was allowed to decay to zero. By measuring the current and induced voltage in the coil during the region of rising current, the flux linkage was calculated thereby obtaining inductance as a function of current. Implementation was carried out by aligning one phase and performing the above diagnostic approach in a sequence on the other phases, which are at midway-from-aligned and unaligned respectively. Thus inductance values at these three positions were obtained. Change in rotor position during the process was found to be very small 0.001 .Thus all calculations were made under the assumption that the rotor is at standstill. This is a significant result with respect to online parameter estimation. For the above analysis, an update for the model can be ob-

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describing inductance incorporated in this model have been described in (8). Fig. 39 illustrates the sequence of model identification by exciting the three stator phases in our experimental 8/6 SRM drive at three unique rotor positions. As can be observed in either case the movement of the shaft due to the excitation current (70 A) is negligible and hence the shaft can be assumed as motionless. It must be noted that the dc link current has been used for monitoring of the phase currents. Therefore there exists a negative current when a stator phase is being cleared. VIII. CONCLUSION Three key technologies for enhancement of efficiency, productivity, and elimination of position sensors in SRDs have been presented in this paper. The sensorless method has been devised with an auto-calibrating modeling approach, which does not require any extra hardware or memory. The ability to update the model enhances the self-tuning attributes of the sensorless technique. Additional benefits of incorporating the proposed methods include reduction of torque pulsation, mitigation of dc-link current ripple in generation mode, and capability to reconfigure in the event of failure in position sensing. It is hoped that the presented technologies will bring a renewed attention to the switched reluctance technology for automotive applications. REFERENCES

Fig. 39. Diagnostic current waveforms for collection of data for auto-calibration at various rotor position along with the movement of the rotor: (a) diagnostic currents at aligned position, (b) diagnostic currents at 5 position, and (c) diagnostic currents at 22.5 position.

tained within a matter of a few milliseconds which can further be improved with the use of faster processors. The equations

[1] A. Emadi, Handbook of Automotive Power Electronics and Motor Drives. New York, Marcel Dekker, May 2005. [2] A. Emadi, M. Ehsani, and J. M. Miller, Vehicular Electric Power Systems: Land, Sea, Air, and Space Vehicles. New York: Marcel Dekker, Dec. 2003, 0-8247-4751-8. [3] A. Emadi, K. Rajashekara, S. S. Williamson, and S. M. Lukic, “Topological overview of hybrid electric and fuel cell vehicular power system architectures and configurations,” IEEE Trans. Veh. Technol., vol. 54, no. 3, pp. 763–770, May 2005. [4] K. M. Rahman, B. Fahimi, G. Suresh, A. V. Rajarathnam, and M. Ehsani, “Advantages of switched reluctance motor applications to EV and HEV: design and control issues,” IEEE Trans. Ind. Appl., vol. 36, no. 1, pp. 119–121, Jan./Feb. 2000. [5] B. Fahimi, G. Suresh, K. M. Rahman, and M. Ehsani, “Mitigation of acoustic noise and vibration in switched reluctance motor drive using neural network based current profiling,” in Proc. IEEE 1998 Ind. Appl. Soc. Annu. Meeting, St. Louis, MO, Oct. 1998, pp. 715–722. [6] P. P. Acarnley, R. J. Hill, and C. W. Hooper, “Detection of rotor position in stepping and switched reluctance motors by monitoring of current waveforms,” IEEE Trans. Ind. Electron., vol. IE-32, no. 3, pp. 215–222, Aug. 1985. [7] G. Suresh, B. Fahimi, K. M. Rahman, and M. Ehsani, “Inductance based position encoding for sensorless SRM drives,” in Proc. 30th IEEE Power Electron. Spec. Conf., Charleston, SC, Jul. 1999, pp. 832–837. [8] C. C. Chan and Q. Jiang, “Study of starting performances of switched reluctance motors,” in Proc. Int. Conf. Power Electron. Motor Drive Syst., Singapore, Feb. 1995, vol. 1, pp. 174–179. [9] J. M. Miller, P. J. McClear, and J. H. Lang, “Starter-alternator for hybrid electric vehicle: comparison of induction and variable reluctance machines and drives,” in Proc. 33rd IEEE Ind. Appl. Soc. Annu. Meeting, Oct. 1998, pp. 513–523. [10] D. A. Torrey, “Switched reluctance generators and their control,” IEEE Trans. Ind. Electron., vol. 49, no. 1, pp. 3–14, Feb. 2002. [11] E. Mese, Y. Sozer, J. M. Kokernak, and D. A. Torrey, “Optimal excitation of a high speed switched reluctance generator,” in Proc. IEEE Appl. Power Electron. Conf., 2000, pp. 362–368. [12] B. Fahimi, A. Emadi, and R. B. Sepe, “A switched reluctance machine based starter/alternator for more electric cars,” IEEE Trans. Energy Conv., vol. 19, no. 1, pp. 116–124, Mar. 2004. [13] P. Tandon, A. V. Rajarathnam, and M. Ehsani, “Self-tuning control of a switched-reluctance motor drive with shaft position sensor,” IEEE Trans. Ind. Appl., vol. 33, no. 4, pp. 1002–1010, Jul./Aug. 1997.

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[14] B. Fahimi, A. Emadi, and R. B. Sepe, “Four-quadrant position sensorless control in SRM drives over the entire speed range,” IEEE Trans. Power Electron., vol. 20, no. 1, pp. 154–163, Jan. 2005. [15] M. Ehsani and B. Fahimi, “Elimination of position sensors in switched reluctance motor drives: state of the art and future trends,” IEEE Trans. Ind. Electron., vol. 49, no. 1, pp. 40–48, Feb. 2002. [16] B. Fahimi, G. Suresh, J. Mahdavi, and M. Ehsani, “A new approach to model switched reluctance motor drive application to dynamic performance prediction, design and control,” in Proc. IEEE Power Electron. Spec. Conf., Fukuoka, Japan, May 1998, pp. 2097–2102. [17] C. S. Edrington and B. Fahimi, “An auto-calibrating model for switched reluctance motor drives: application to design and control,” in Proc. IEEE Power Electron. Spec. Conf., Acapulco, Mexico, Jun. 2003, pp. 409–415. [18] S. Dixon and B. Fahimi, “Enhancement of output electric power in switched reluctance generators,” in Proc. IEEE Int. Elect. Machines Drives Conf., Jun. 2003, vol. 2, pp. 849–856. Mahesh Krishnamurthy (S’97–S’04) received the B.E. degree from Amrawati University, Amrawati, India, the M.S. degree from the University of Missouri, Rolla, in 2004, and is currently pursuing the Ph.D. degree in the Electrical Engineering Department, University of Texas, Arlington. His areas of interest include design, analysis, and control of adjustable speed drives at microscopic and macroscopic levels.

Chris S. Edrington (S’94–M’04) was born in Paragould, AR, in 1968. He received the B.S. degree in engineering from Arkansas State University, Jonesboro, in 1999, and the M.S. and Ph.D. degrees in electrical engineering from the University of Missouri, Rolla, in 2001 and 2004, respectively. Since 2004, he has been with the College of Engineering, Arkansas State University. His current research is in the areas of magnetic modeling of switched reluctance and induction machines, applied power electronics, and control of electromechanical drive systems. Ali Emadi (S’98–M’00–SM’03) is the Director of the Electric Power and Power Electronics Center, Illinois Institute of Technology (IIT), Chicago. He is the author/co-author of over 160 journal and conference papers as well as several books including Vehicular Electric Power Systems (New York: Marcel Dekker, 2003), Energy Efficient Electric Motors (New York: Marcel Dekker, 2004), Uninterruptible Power Supplies and Active Filters (Boca Raton, FL: CRC Press, 2004), and Modern Electric, Hybrid Electric, and Fuel Cell Vehicles (Boca Raton, FL: CRC Press, 2004). He is also the Editor of the Handbook of Automotive Power Electronics and Motor Drives (New York: Marcel Dekker, 2005). Dr. Emadi received the 2005 Richard M. Bass Outstanding Young Power Electronics Engineer Award from the IEEE Power Electronics Society, the Ralph R. Teetor Educational Award from the Society of Automotive Engineers (SAE) in 2005, the 2002 University Excellence in Teaching Award from IIT as well as the 2004 Sigma Xi/IIT Award for Excellence in University Research, and was named the Eta Kappa Nu Outstanding Young Electrical Engineer of the Year in 2003. He was the General Chair of the 2005 IEEE Vehicle Power and Propulsion and SAE Future Transportation Technology Joint Conference.

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Peyman Asadi (S’05) received the B.S. degree from the Iran University of Science and Technology, Tehran, in 1996 and the M.S. degree from the University of Tehran, Tehran, Iran, in 1999, both in electrical engineering, and is currently pursuing the Ph.D. degree at Texas A&M University, College Station. He has been doing research on the control of motor drives since 1997. His research interests are mainly advanced control methods in motor drives, intelligent and robust control systems, and industrial electronics.

Mehrdad Ehsani (S’70–M’81–SM’83–F’96) has been at Texas A&M University, College Station, since 1981 where he is the Robert M. Kennedy Professor of electrical engineering and Director of Advanced Vehicle Systems Research Program. 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 co-author of several books on power electronics, motor drives, vehicle power and propulsion systems, and a contributor to an IEEE Guide for Self- Commutated Converters in 1990, as well as many monographs. He is the author of over 20 U.S. and EC patents. Dr. Ehsani received the Prize Paper Awards in Static Power Converters and motor drives at the IEEE-Industry Applications Society in 1985, 1987, and 1992 Annual Meetings, was named the Halliburton Professor in the College of Engineering at A&M in 1992, was named the Dresser Industries Professor in the same college in 1994, was named the Dow Chemical Faculty Fellow of the College of Engineering at Texas A&M University in 2001, received the James R. Evans Avant Garde Award from the IEEE Vehicular Technology Society in 2001, the IEEE Field Award in Undergraduate Teaching in 2003, and became the holder of Robert M. Kennedy Endowed Chair of Engineering at Texas A&M University in 2004.

Babak Fahimi (S’96–M’00–SM’02) received the Ph.D. degree in electrical engineering from Texas A&M University, College Station, in 1999. Currently, he is with the Department of Electrical Engineering, University of Texas, Arlington, as an Assistant Professor. His areas of interest include microscopic analysis of electromechanical energy conversion, digital control of adjustable speed motor drives, and design and development of power electronic converters.

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