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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 18, NO. 1, JANUARY 2003
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Restructuring of First Courses in Power Electronics
and Electric Drives That Integrates Digital Control
Ned Mohan, Fellow, IEEE, William P. Robbins, Member, IEEE, Paul Imbertson, Member, IEEE,
Tore M. Undeland, Fellow, IEEE, Razvan C. Panaitescu, Amit Kumar Jain, Student Member, IEEE,
Philip Jose, Student Member, IEEE, and Todd Begalke
Index Terms—Digital control, education, electric drives, laboratories, power electronics.
I. INTRODUCTION
C
signal processors. These developments necessitate that courses
be structured such that students learn the basic principles on
which these devices and components operate in order to control
them optimally in exciting new applications. This restructuring
has the added benefit of drawing students to these fields where
otherwise, due to lack of student interest, courses are often
cancelled and eventually dropped from the curriculum.
At the University of Minnesota, restructuring of these courses
began in 1994 through NSF funding and has been successful
in nearly tripling student enrollments in these courses. This restructuring has also been the topic of four NSF sponsored workshops held in 1994, 1997, 1998, and 2002 [1]. This paper will
describe the structure of the first courses in Power Electronics
and Electric Drives, the associated simulation software, and the
hardware laboratories that are still under refinement, and how
this restructuring allows digital control to be integrated.
This course restructuring has several objectives. The first
courses should prepare students for industry as well as advanced courses and research and development oriented careers.
They should be appealing and exciting so students are drawn to
them. These courses should provide requisite information about
power electronics and electric drives in a way that provides
motivation and allows time to take related courses in areas such
as digital signal processing applications, programmable logic,
and digital control. This way, students will learn what is needed
to meet industry needs and be able to create opportunities for
future engineers by starting new companies.
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Abstract—Since 1994, the University of Minnesota has been undertaking a long overdue restructuring of power electronics and
electric machines/drives courses. This restructuring allows digital
control to be integrated into first courses, thereby teaching students what they need to learn, making these courses appealing,
and providing a seamless continuity to advanced courses. By a concise presentation in just two undergraduate courses, this restructuring motivates students to take related courses in programmable
logic controllers, microcontrollers and digital signal processor applications. This ensures a first-rate education that is meaningful
in the workplace as well as in graduate education leading to a research and development oriented career. This restructuring has
several components to it. Outdated topics that waste time and mislead students are deleted. To integrate control in the first courses,
unique approaches are developed to convey information more effectively. In the first course in power electronics, a building block
is identified in commonly used power converter topologies in order
to unify their analysis. In the field of electric drives, the use of
space vectors is introduced on a physical basis to describe operation of ac machines in steady state in the first course, and to discuss their optimum control under dynamic conditions in the advanced course. Appropriate simulation software and software-reconfigurable hardware laboratories using a DSP-based rapid prototyping tool are used to support the analytical discussion.
OURSES in power electronics and electric machines/drives have not changed in several decades.
In a fast changing economy where power electronic converters
and electric drive components are becoming commodity items,
the role of graduating engineers in these fields would likely be
to integrate these components into systems and control them
for optimum performance. These commodity items would need
flexible control, which is easily implemented digitally using
programmable logic controllers, microcontrollers, or digital
Manuscript received February 3, 2002; revised October 21, 2002. This
work was supported in part by the National Science Foundation under Grants
9414044, 9619312, 9729197, 9952704 and 0004201, and NASA under Grants
NASA/NAG3-246. Recommended by Associate Editor S. B. Leeb.
N. Mohan, W. P. Robbins, P. Imbertson, R. C. Panaitescu, A. K. Jain, P.
Jose, and T. Begalke are with the Department of Electrical and Computer
Engineering, University of Minnesota, Minneapolis, MN 55455 USA (e-mail:
[email protected];
[email protected];
[email protected];
[email protected];
[email protected];
[email protected];
[email protected]).
T. M. Undeland is with the Department of Electrical Power Engineering,
Norwegian Institute of Science and Technology, Trondheim N-7491, Norway
(e-mail: [email protected]).
Digital Object Identifier 10.1109/TPEL.2002.807120
II. COURSE OFFERINGS AND THEIR SEQUENCE
These courses are designed carefully using a top-down approach where the topology and control are described in the context of applications. To provide continuity to advanced courses,
fundamental concepts are included with illustrations of design
examples that are helpful in industry. The courses are divided
into modules [1] which are sequenced appropriately to maintain interest and to allow practicing engineers the flexibility to
choose the requisite topics. Using an approach that is based on a
common underlying theme, as illustrated by the subsequent discussion of courses, saves valuable course time and clearly shows
the basic principles of operation. To reinforce theory, all topics
are tightly coupled with simulations and hardware laboratories.
Fig. 1 describes the course offerings at the University of Minnesota, where the first courses on Power Electronics and Electric Drives are aimed at college seniors, but can also be taken for
credit by graduate students. The converse is true for advanced
0885-8993/03$17.00 © 2003 IEEE
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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 18, NO. 1, JANUARY 2003
various converter topologies, allowing them to be discussed in
a short period of time.
A. Power-Pole Building-Block Approach
Fig. 1. Course sequence at the University of Minnesota.
The building-block of power electronic converters is the
two-port power-pole as shown in Fig. 2. It has a voltage-port and
a current-port with voltages and currents related by the switch
position. Given an input voltage, an “instantaneous average” of
the output voltage is synthesized by pulse-width-modulating
the switch. In the continuous-conduction mode (CCM) with
, the average values, indicated by “ ” on top, are
related by the switch duty-factor
and
This allows the switching two-port to be represented on an
average basis by means of a controllable turns-ratio ideal transformer as shown in Fig. 2(b). For example, in a buck converter
the power-pole building-block is identified in Fig. 3(a). Here
corresponds to the average input voltage, while
corresponds to the average inductor current. The average representation of the buck converter is obtained in Fig. 3(b) by simply replacing the power-pole by its average representation. In the discontinuous conduction mode (DCM), the average CCM model
of Fig. 2(b) is augmented by a dependent voltage source and
a dependent current source—both expressed conditionally—to
make this model valid for CCM and DCM [3]. This average
model has several benefits:
1) it provides an insight to synthesis of output using PWM;
2) it allows linearization for feedback controller design;
3) it results in much faster simulation times for dynamic performance analysis.
A flow chart for covering various topics using this building
block approach is shown in Fig. 4. The modules shown in Fig. 4
were described at a recent NSF workshop [1], and a detailed
description of this approach is available in an article on the IEEE
Power Electronics Society website [4].
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Fig. 2. Two-port power-pole building block: (a) switching and (b) average
model in CCM.
Fig. 3. Buck converter modeling: (a) power-pole building block and PWM
synthesis and (b) average representation.
courses. The first courses are stand-alone so they can be taken
in any sequence and require, as prerequisites, knowledge in circuits and systems, electronics and basic electromagnetic field
theory usually discussed in physics courses.
III. POWER ELECTRONICS FIRST COURSE
In the past, power electronics courses were organized on the
assumption that most students would take two such courses to
get a complete picture. However, what is needed now is a complete overview as well as complete coverage of the fundamentals
in the very first course, as most students are now likely to take
only one course in this field; they can supplement their knowledge by taking advanced courses later. Such a course needs to
include various converter topologies, their control and some design aspects. Therefore, it is important that it is taught using a
building-block approach [2], [3], which brings cohesion to the
(1)
B. PSpice® Based Simulations and Controller Design
As seen in Fig. 4, the use of PSpice (or another simulator with
similar capabilities) in such a course is interwoven throughout.
Such a program can, for example, quickly calculate the transfer
function for a converter in CCM or DCM, thus allowing the design of its feedback controller to be included in the first course.
1) Example: Design of a Voltage Mode Controller for a Buck
Converter: Fig. 5(a) shows the average representation of the
buck converter with the power-pole replaced by its average representation [Fig. 5(b)] that is valid in DCM and CCM. Bode
plots of the linearized converter for different values of the load
resistance are easily obtained by running a parametric sweep
with ac analysis in PSpice. Fig. 6(a) shows the plots obtained for
both DCM and CCM modes. Fig. 6(b) shows the corresponding
bode plots obtained experimentally by means of a frequency analyzer [5]. The experimental plots have lower overall gain and
more damping due to the effect of parasitic resistances which
are not included in the PSpice simulations.
For DCM, simulation and experimental results match well
below one third of the switching frequency (100 kHz) where
MOHAN et al.: RESTRUCTURING OF FIRST COURSES IN POWER ELECTRONICS AND ELECTRIC DRIVES
Flow chart of topics in the first power electronics course.
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Fig. 4.
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Fig. 5. (a) Average representation of buck coverter and (b) two port model that
is valid for both CCM and DCM.
the average model is valid. Since the controller is designed for a
much lower crossover frequency (1 kHz) the model is adequate.
The voltage mode controller is designed using the -factor
approach [6] which is based on simple bandwidth and phase
margin requirements and carried out in the continuous time domain-topics which students are familiar with from their circuits
and systems courses. A crossover frequency of 1 kHz is chosen.
The controller transfer function and the parameter values obtained for the particular example are
(2)
with
,
rad/s,
rad/s.
Simulated dynamic response of the closed loop system for a
step change in load is seen in Fig. 7. The load is changed from
100 to 9 (by connecting a 10 resistance in parallel) at
s, then back to 100 at
ms. The converter operates
Fig. 6. Control voltage to output voltage small signal transfer function: (a)
from PSpice and (b) experimentally using a frequency analyzer.
in CCM for the 9 load and in DCM for the 100 load. As
seen, the controller acts to regulate the voltage in both modes.
C. Hardware Laboratory for the Power Electronics Course
A hardware lab based on the building-block approach has
recently been developed [7], where there is an option to control these converters digitally using a rapid prototyping tool
described in connection with the electric drives courses (Section IV-C). The circuit board used for this laboratory is shown in
Fig. 8. The controllers can be implemented using analog circuits
as is common for dc–dc converters. Alternately they can be implemented digitally as transfer-function blocks in Simulink and
downloaded to a digital signal processor using the rapid prototyping tool, without the prerequisite of digital control theory.
In the first course, sampling issues—discretization and quantization, and computational delay are not important. Sample
times, even with general purpose rapid prototyping tools, are
sufficiently small to achieve the desired controller bandwidth in
the laboratory experiments. With increasing processor speeds,
computational delays will be even less significant. Quantization
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Fig. 7. Simulated dynamic response for a step change in the load.
Fig. 10. (a) Simulink block diagram of controller. (b) Dynamic response for a
step change in the load.
Fig. 8.
Circuit board for a flexible power electronics laboratory.
Fig. 11.
Fig. 9. Experimentally obtained dynamic response for a step change in the
load using an analog controller.
errors due to ADC and PWM resolution are important for practical applications, however, the performance achieved is more
than adequate for the first course. Digital implementation using
a rapid prototyping tool allows not only control of dc–dc converters but also of power-factor-correction circuits, a topic that
is often left out of first courses. There is a separate board for the
power factor correction circuit, where the controller can be implemented digitally as a modification of the one described in [8].
Experiments dealing with converters for dc and ac motor drives
Main subsystems in the first course on electric drives.
are included based on the setup for the electric drives laboratory
described later on in Section IV-C.
1) Example: Voltage Mode Controller for a Buck Converter: The controller described above (Section III-B) is
implemented using analog components, and a step response
similar to the simulated response (Fig. 9) is obtained using the
power electronics circuit board. The same controller is implemented as transfer function blocks in Simulink [Fig. 10(a)] and
downloaded to a DSP using a rapid prototyping system. In the
latter, the controller as well as the PWM synthesis is carried
out in the DSP. A sampling time of 100 s is used. Fig. 10(b)
shows the step response obtained with the digital controller. All
the responses obtained [Figs. 7, 9, and 10(b)] show very good
correlation. Since the digitally implemented controllers can be
changed by simply changing parameters or transfer functions
MOHAN et al.: RESTRUCTURING OF FIRST COURSES IN POWER ELECTRONICS AND ELECTRIC DRIVES
Average model of a three-phase ac motor drive converter.
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Fig. 12.
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Fig. 13. Physical basis of space vectors, representing sinusoidally distributed
mmfs in the air gap.
Fig. 15. Speed control of a dc motor: (a) Simulink block diagram; (b)
simulated step response.
in Simulink, this approach is ideal for trying out different
controllers for experiments in a power electronics laboratory.
IV. ELECTRIC MOTOR DRIVES COURSES
Fig. 14.
Torque calculation using space vectors in a PMAC motor drive.
Exciting new applications of electric drives can be discussed
by covering this subject in an integrative manner, as shown
in Fig. 11 where all three subsystems—power electronic
converters, electric machines, and feedback controllers are
covered in a single semester course. An important aspect in
structuring such a course is to delete irrelevant topics which
waste valuable course time and worse yet give students the
wrong impression that these practices may still be relevant. A
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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 18, NO. 1, JANUARY 2003
tures where the torque is calculated in a very physical manner
(Fig. 14) as follows.
The flux density “seen” by the stator windings is
(3)
Then, from
(4)
Fig. 16.
Specially designed 42 V machines for the electric drives laboratory.
since there are
considered in Fig. 14.
Integrating (4)
turns in the small angle
(5)
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Notice the remarkable similarity of the torque expression to that
of dc machines. It can further be proven that the voltage constant
is equal to .
The Space Vector approach [10] has several advantages:
1) clearly shows that ac and dc machines have a voltage con;
stant equal to their torque constant, i.e.,
2) in induction machines the squirrel-cage rotor need not be
replaced by three equivalent phase windings;
3) it clearly shows how the induction machine operation
goes from the motoring mode to the generating mode by
reversal of currents in the rotor bars.
Fig. 17. Hardware implementation of digital control of dc and ac machines for
the electric drives laboratory.
detailed description of the proposed approach is available on
the IEEE Power Electronics Society website [9].
In this course, power electronics converters, based on the
power-pole building-block approach mentioned earlier, are described in terms of their functionality by means of controllable
turns-ratio ideal transformers. For illustration, the converter for
a three-phase motor drive is represented as shown in Fig. 12.
Electrical machines, without assuming any prior knowledge, are
described using the fundamental principles governing the production of electromagnetic torque and the generation of voltage.
Such a presentation, in contrast with the circuit-oriented approaches used in traditional courses for describing uncontrolled
line-fed operation, clearly shows the mechanism on which electric machines operate and how they ought to be controlled for
optimum performance.
A. Use of Space Vectors for Analysis of AC Machines
A significant component of the integrated approach is the
use of space vectors (leading to digital control) in this very
first course. Usually space vectors are introduced in advanced
courses and on a highly mathematical basis. Here space vectors are introduced to represent flux density and mmf distributions in the air gap of the machine (Fig. 13) thus attaching to
them a physical basis on which terminal quantities such as currents can also be represented. This allows ac machines such as
permanent-magnet ac drives to be covered in a couple of lec-
B. Control Concepts in the First Course
Integration of controls in first course is possible by describing
control of dc motor for torque, speed, and position in typical
cascade connection [10] where each control loop is designed
using bandwidth and phase margin considerations similar to that
discussed for switched mode dc power converters. In advanced
courses, discussion of controller design provides seamless continuity to designing vector-controllers/direct-torque controllers
in ac motor drives. Simulink is adopted for simulation due to its
control systems oriented environment and availability of rapid
prototyping tools which can be used to translate Simulink block
diagrams into DSP code for digital implementation. In the advanced course in electric drives, where simulation is essential,
having introduced Simulink in the first course (having a very
short learning curve) is helpful.
1) Example: Speed Controller for a DC Motor: Fig. 15(a)
shows the Simulink block diagram for the speed control of a
dc motor with an inner current loop. The current loop has a
PI controller with gains calculated to cancel the pole due to
the electrical time constant of the dc motor, and to give the required bandwidth—chosen as 1 kHz for this example. The speed
controller also has a PI controller designed to achieve a phase
margin of 60 and a bandwidth of 1 Hz. Simulated response for
a step change in speed is shown in Fig. 15(b).
C. Electric Drives Laboratory Using DSP-Based Control
A software reconfigurable hardware laboratory for this course
has been developed using a rapid prototyping system [11]. The
MOHAN et al.: RESTRUCTURING OF FIRST COURSES IN POWER ELECTRONICS AND ELECTRIC DRIVES
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tronics board. In the laboratory context the advantages of a highlevel rapid prototyping tool such as the one from dSPACE [13]
are several:
1) no knowledge of coding in C or assembly language is
needed;
2) the same simulation blocks used in Simulink are used in
the hardware implementation (see Fig. 17);
3) an easy-to-use graphical interface which allows users
real-time monitoring and parameter adjustments.
Such a laboratory also has many possibilities for other undergraduate courses, research, and student projects in electrical and
mechanical engineering. The proposed laboratory will be invaluable to show the correspondence between simulation results
and their verification experimentally in topics like field-oriented
control and direct torque control of induction motor drives [14].
1) Example: Speed Control of DC Motor: Fig. 18(a) shows
the Simulink block diagram which was used for hardware implementation of speed control of a dc motor. Comparing with
Fig. 15(a), the dc motor and the average converter models have
been replaced by the PWM duty cycle block of the DSP which in
turn sends the PWM signals to a power electronic drive that runs
the dc motor. The speed is sensed using an optical encoder, and
the current is sensed and fed to one of the ADC channels of the
DSP board. The controller designed earlier (Section IV-B) for
simulation is used here for implementation. This block diagram
is compiled and downloaded to the DSP and used for control
of the actual machine using the power electronic board. A step
change in the speed reference was given using the graphical real
time interface. The response obtained in Fig. 18(b) matches the
simulated response obtained in Simulink (the noise seen on the
current waveform is actually the current ripple which is aliased
due to slow sampling) thus showing the capability of going from
theory to simulations to real-time digital control implementation
using the outlined approach.
V. CONCLUSION
Fig. 18. Digital implementation of speed control for a dc motor: (a) Simulink
block diagram; (b) step response obtained from the real time interface.
dc bus voltage is chosen to be 42 V for safety reasons as well as
recognizing the new automotive standards [12]. The load sends
power back to the bus so that only the stray losses in the overall
system need to be supplied by the small DC power supply. The
load is actively controllable in all four quadrants, opening up
possibilities for experiments that cannot be done in traditional
machine labs. Small motors, shown in Fig. 16, were specially
designed and built for the laboratory. The hardware setup in this
electric drives laboratory is also intended to demonstrate converter operation for dc drives, three-phase ac drives and uninterruptible power supply applications.
For experiments, from very simple to very sophisticated, the
controller is designed in Simulink and then downloaded to a
DSP, which provides the switching signals to the power elec-
Structuring of power electronics and electric machines/drives
courses in the manner outlined in this paper allows control, and
in particular digital control, to be brought into first courses,
thereby teaching students what they need to learn, generating
excitement and providing a seamless continuity to advanced
courses. Students are motivated to take related courses in programmable logic controllers, microcontrollers and digital signal
processor applications, thus receiving a first-rate education that
is meaningful in the workplace as well as in graduate school,
leading to a research and development oriented career.
REFERENCES
[1] Proc. NSF-Sponsored Faculty Workshop Teaching Courses Power Electron. Elect. Drives, Tempe, AZ, Jan. 3–5, 2002, Online. [Availiable]:
http://www.ece.umn.edu/groups/workshop2002.
[2] N. Mohan, G. Shanmugavel, P. Holenarsipur, and G. Nirgude, “First
course on power electronics simplified by unifying analysis of PWM
converters as cycle-by-cycle averaged two-ports, and by PSpice-based
simulations,” in Proc. 8th Eur. Conf. Power Electron. Applicat., Lausanne, Switzerland, 1999, p. 8.
[3] G. Nirgude, R. Tirumala, and N. Mohan, “A new, large-signal average
model for single-switch DC–DC converters operating in both CCM and
DCM,” in Proc. IEEE Power Electron. Spec. Conf., vol. 3, Vancouver,
BCf, Canada, 2001, pp. 1736–1741.
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[4] [Online]. Available: Link on PELS website: www.pels.org/Comm/Education/Tutorials/tutorial.htm.
[5] Analog Network Analyzer Operator’s Manual: A. P. Instruments, 2002.
factor: A new mathematical tool for stability
[6] H. D. Venable, “The
analysis and synthesis,” in Proc. Powercon10, San Diego, CA, 1983.
[7] W. Robbins, N. Mohan, C. Henze, and T. Undeland, “A building-blockbased power electronics instructional laboratory,” in Proc. IEEE Power
Electron. Spec. Conf., vol. 2, Cairns, Australia, 2002, pp. 467–472.
[8] M. O. Eissa, S. B. Leeb, G. C. Verghese, and A. M. Stankovic, “A fast
analog controller for a unity-power factor AC/DC converter,” in Proc.
9th Annu. IEEE Appl. Power Electron. Conf. Expo., vol. 2, New York,
NY, 1994, pp. 551–555.
[9] N. Mohan, M. Riaz, P. Imbertson, and T. Brekken, “A strategy for the
revival of electrical machines and drives courses,” Tech. Rep., IEEE
Power Electronics Society Educational Activities Committee website,
under Tutorials and Educational Materials: Online. [Availiable]:
www.pels.org/Comm/Education/Tutorials/PELS_ED_Article.pdf.
[10] N. Mohan, Electric Drives: An Integrative Approach. Minneapolis,
MN: MNPERE, 2001. [Online]. Available: www.mnpere.com.
[11] R. C. Panaitescu, N. Mohan, W. Robbins, T. Undeland, E. Persson, P.
Jose, T. Begalke, and C. Henze, “An instructional laboratory for the
revival of electric machines and drives courses,” in Proc. IEEE Power
Electron. Spec. Conf., vol. 2, Cairns, Australia, 2002, pp. 455–460.
[12] J. G. Kassakian, “Automotive applications of power electronics,” in
Proc. NSF-Sponsored Faculty Workshop Teaching Courses Power
Electron. Elect. Drives, Tempe, AZ, January 3–5, 2002. [Online].
Available: http://www.ece.umn.edu/groups/workshop2002.
[13] dSPACE Company. Solutions For Control. Tech. Rep. [Online]. Available: www.dspaceinc.com
[14] N. Mohan, Advance Electric Drives. Minneapolis, MN: MNPERE,
2001. [Online]. Available: www.mnpere.com.
Razvan C. Panaitescu received the B.Eng., M.S.,
and Ph.D. degrees in electrical engineering from the
Transilvania University of Brasov, Romania.
He was a Post-Doctoral Research Associate,
Department of Electrical Engineering and Computer
Science, University of Minnesota. His research
interests are digital processing for real-time control,
power electronics, and electric drives. He has
published in major conference proceedings and was
Sr. Lecturer, Transilvania University of Brasov.
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Tore M. Undeland (M’86–SM’92–F’00) is Professor of power electronics, Norwegian University
of Science and Technology, Trondheim, Norway,
teaching since 1972, as a Professor since 1984.
He has published in the field of power converters,
snubbers, and control in power electronics. He has
co-written the book Power Electronics: Converters,
Applications, and Design (New York: Wiley, 2003).
Dr. Undeland was the Chairman of the EPE 1997
Conference, Trondheim, and is presently Vice President of EPE. He is active as AcCom Member, IEEE
Power Electronics Society, where he also has been a Distinguished Lecturer.
Ned Mohan (S’72–M’73–SM’91–F’96) is Oscar A.
Schott Professor of Power Electronics, University of
Minnesota, Minneapolis, where he has taught since
1976. He has numerous patents and publications in
the field of power electronics. He has written the
books Power Electronics: Converters, Applications,
and Design (New York: Wiley, 2003) Electric
Drives: An Integrative Approach (Minneapolis, MN:
MNPERE, 2001), and Advanced Electric Drives,
Analysis, Control and Modeling Using Simulink
(Minneapolis, MN: MNPERE, 2001).
Dr. Mohan received the Distinguished Teaching Award.
Amit Kumar Jain (S’97) received the M.Tech. degree in electrical engineering from the Indian Institute of Technology, Bombay, in 1996 and the M.S.
degree in electrical engineering from the University
of Minnesota, Minneapolis, in 2000 where he is currently pursuing the Ph.D. degree in the Department
of Electrical Engineering.
His research interests include electric motor drives,
dc–dc converters for power supplies, and grid connection of distributed power generation sources.
William P. Robbins (S’62–M’70) received the B.S.
and M.S. degrees in electrical engineering from the
Massachusetts Institute of Technology, Cambridge,
in 1963 and 1965, respectively, and the Ph.D. degree
in electrical engineering from the University of
Washington, Seattle, in 1971.
He joined the University of Minnesota, Minneapolis, in 1969 and is a Professor of electrical
and computer engineering. His research interests
are ultrasonics, sensors, and microelectromechanical
devices. He is coauthor of Power Electronics:
Converters, Applications, and Design (New York: Wiley, 2003).
Dr. Robbins is a member of the American Physical Society and Sigma Xi.
Philip Jose (S’00) received the B.Tech. degree in
electrical engineering from the Indian Institute of
Technology, Madras, in 1998 and the M.S. degree
from the University of Minnesota, Minneapolis,
in 2002 where he is currently pursuing the Ph.D.
degree.
He has experience in automotive electrical systems
design and testing with research interests in automotive power electronics and electric/hybrid vehicles.
Paul Imbertson (S’91–M’92–S’92–M’99) received
the B.S., M.S., and Ph.D. degrees in electrical
engineering from the University of Minnesota,
Minneapolis, in 1983, 1994, and 1997, respectively.
He worked in power electronics for military
avionics and is an Assistant Professor in the
Electrical and Computer Engineering Department,
University of Minnesota. His current interests are
wide ranging topics of energy and deciphering the
minds of electrical engineering students.
Todd Begalke received the B.S. degree in electrical
engineering from the University of Minnesota, Minneapolis, in 2000 where he is currently pursuing the
M.S. degree.
His experience includes power electronics and
electric machine design for solar vehicles. Current
research interests are electric drives and wind
generation systems.