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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 4, DECEMBER 2004 715
Optimal Efficiency Control Strategy for InteriorPermanent-Magnet Synchronous Motor Drives
Christos Mademlis , Member, IEEE , Iordanis Kioskeridis, and Nikos Margaris , Member, IEEE
Abstract—In this paper, the problem of efficiency optimiza-
tion in vector-controlled interior permanent-magnet (PM) syn-
chronous motor drives is investigated. A loss model controller is
introduced that determines the optimal -axis component of the
stator current that minimizes power losses. For the implementa-tion of the suggested controller, the knowledge of the loss model
is not required since an experimental procedure is followed to
determine its parameters. Furthermore, it is shown that the loss
model of the interior PM motor can be used as a basis for deriving
loss minimization conditions for surface PM synchronous motors
and synchronous reluctance motors as well. Experimental results
of an interior PM motor are presented to validate the effective-
ness of the proposed method and demonstrate the operationalimprovements.
Index Terms—Losses, optimal control, optimization methods,permanent-magnet (PM) motors, variable-speed drives.
NOMENCLATURE
Stator resistance.
, - and -axis magnetizing inductances.
Stator leakage inductance.
Supply frequency.
Motor speed.
Stator voltage.
Air-gap voltage.
Air-gap magnetic flux.
Stator current.
, - and -axis components of stator current.
Magnetizing current.
, -and -axis components of magnetizing
current.
Equivalent excitation current of the perma-
nent magnet (PM).
Electromagnetic torque.
Total power losses.
Copper losses.
Iron losses.Stray losses.
Mechanical losses.
Iron loss coefficient.
Stray loss coefficient.
Mechanical loss coefficient.
Manuscript received January 3, 2003; revised July 31, 2003. Paper no. TEC-00296-2002.
The authors are with the Department of Electrical and Computer Engineering,Aristotle University of Thessaloniki, Thessaloniki GR-54 124, Greece (e-mail:[email protected]).
Digital Object Identifier 10.1109/TEC.2004.837282
I. INTRODUCTION
PERMANENT-MAGNET (PM) synchronous motor ad-
justable speed drives offer significant advantages over
induction motor drives in a wide variety of industrial appli-
cations (i.e., high-power density, high efficiency, improved
dynamic performance, and reliability) [1]. Since vector control
in PM synchronous motors provides fast dynamic response
with a less complex and nonparameter-dependent controller,
PM motor drives can be an attractive alternative choice [2].
Improvement of PM motor efficiency is a most important pri-
ority, especially in cases where drives are powered by a batterysource. Therefore, significant efforts are taken to improve their
efficiency. Since there are a great variety of PM motor configu-
rations, the efforts are mainly focused on the search for the op-
timum rotor structure [3]–[7]. However, efficiency can also be
improved by intervening in the motor operation principle with
automatic control techniques.
Several control methods have been proposed in order to
reduce the loss of PM motor drives and improve their perfor-
mance. The copper loss can be minimized by the maximum
torque-per-ampere current control [8]. In surface PM motor
drives, maximum torque-per-ampere current ratio is attained
by keeping the -axis component of the stator current equal to
zero ( ) [9], [10]. Since the “ control” prevents thedemagnetization of the PM, it is often employed in interior PM
motor drives. However, the current that provides maximum
torque-per-ampere current ratio in interior PM motor drives is
a function of the current and opposes the excitation field of
the PM [8]–[11].
Several attempts to minimize both copper and iron losses
have been recently presented [12]–[14]. However, the proposed
loss minimization conditions are complex and can only be
implemented using offline made lookup tables. Therefore,
a number of costly and time-consuming measurements are
required. A control method, described in [15], improves ef-
ficiency of PM motors and is implemented using a voltagesource inverter. The efficiency improvement is attained with
appropriate control of stator voltage in order to keep power
factor equal to unity. However, although the real-to-apparent
power ratio (kW/kVA) of the PM motor is maximized, power
losses are not minimized. An adaptive search controller for
interior PM motors was developed in [16]. Finally, an approach
that specifies the optimal -axis current for minimizing interior
PM motor losses was presented in [17].
This paper presents an optimal efficiency method for vector-
controlled interior PM synchronous motor drives. The loss
minimization is accomplished with a loss model controller that
is based on the optimal -axis current condition, as presented
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716 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 4, DECEMBER 2004
Fig. 1. Per-unit equivalent circuits of interior PM synchronous motor.
in [17]. For the implementation of the proposed controller, an
experimental procedure is followed to adjust its parameters
without requiring the knowledge of the exact motor model.Additionally, a further investigation of the loss model of the
interior PM motor is conducted and it is shown that this model
can be used as a basis for deriving loss minimization expres-
sions for surface PM synchronous motors and synchronous
reluctance motors (SynRMs).
The contents of the paper are organized as follows. In Sec-
tion II, the basic equations of an interior PM synchronous motor
drive are given and the motor loss model is presented. The loss
minimization condition is derived in Section III. The imple-
mentation of the optimal interior PM motor drive with search
controller (SC) and loss model controller (LMC) is described
in Section IV. The experimental results are presented in Sec-tion V. In Section VI, comparisons between the performance of
the optimum control, conventional “ control,” and max-
imum torque-per-ampere current control are presented. Loss
minimization conditions for surface PM synchronous motors
and SynRM, derived from the interior PM loss model, are pre-
sented in Section VII. Finally, conclusions are drawn in Sec-
tion VIII.
II. BASIC EQUATIONS—LOSS MODEL
Fig. 1 shows the - and -axis equivalent circuits of the inte-
rior PM synchronous motor in the synchronously rotating ref-
erence frame [18]. The equivalent circuits are given in the per-unit system and the effects of iron and stray losses are ignored.
The phasor diagram in the synchronously rotating - reference
frame is illustrated in Fig. 2. In the figure, the current is nega-
tive (demagnetizing current) and results in field weakening. The
- and -axis components of the magnetizing current are given,
respectively, by
(1)
and
(2)
Since the magnetic permeability of the PM is close to air,the interior PM synchronous motor presents inverse saliency.
Fig. 2. Phasor diagram of interior PM synchronous motor.
Consequently, the -axis inductance of the interior PM motor
exceeds the -axis inductance [9]
(3)
The electromagnetic (EM) torque of the motor is given by [9]
(4)
where is the saliency ratio
(5)
The main losses of the PM synchronous motor are the
following:
A. Copper Losses
These are due to current flow through the stator windings and
are given by
(6)
B. Iron Losses
These are due to hysteresis and eddy currents and are given
by the following empirical formula [9], [19]:
(7)
where . Substituting (1) and (2) in (7), iron losses
are given by
(8)
C. Stray Losses
These arise on the copper and iron of the motor and are given
by [20]
(9)
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718 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 4, DECEMBER 2004
Fig. 3. Power loss versusI
current in a 3.4-kW interior PM motor drive(experimental results).
TABLE I3.4-kW INTERIOR PM SYNCHRONOUS MOTOR PARAMETERS
Fig. 4. Variation of the optimalI
current versus speed for various load
torques (simulation results).
IV. IMPLEMENTATION OF THE LOSS MINIMIZATION CONDITION
The block diagram of the optimal interior PM motor drive is
shown in Fig. 6. The loss minimization can be accomplished
with an SC or an LMC. The SC measures the input power to the
drive and adjusts the current searching for the minimum input
power. The LMC measures the speed and the current and
specifies the optimal current through the loss minimization
condition (23).
Although the use of SC could be the obvious way for lossminimization, experiments prove that the drive performance is
Fig. 5. Optimal (I , I ) trajectories for various speeds and load torques(simulation results).
Fig. 6. Optimal vector-controlled interior PM synchronous motor drive.
Fig. 7. Performance of the optimal PM motor drive with SC (experimental
results).
not satisfactory. As shown in Fig. 7, the drive does not reach
a steady state, causing undesirable torque disturbances. Alsoduring transient operation, the SC should remain disabled and is
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MADEMLIS et al.: OPTIMAL EFFICIENCY CONTROL STRATEGY FOR INTERIOR PM SYNCHRONOUS MOTOR DRIVES 719
setting [16]. Generally, the SC approach has several dis-
advantages and such performance is expected from the relevant
literature [14], [22]. On the contrary, the LMC offers superior
performance; hence, it is preferable for the implementation of
the optimal controller.
Substituting (12) and (13) in (23), the equation of the LMC
that specifies the optimal current is given by
(24)
where
(25)
(26)
(27)
and
(28)
From (25)–(27), it is concluded that the following relation holds:
(29)
In order to calculate the optimal current from (24), the
motor speed and the current are required. Since loss min-
imization is accomplished at steady-state, the command signals
of the speed and current can be used. The LMC parameters
can be adjusted experimentally as follows.
1) A three-phase wattmeter is used for measuring the total
input power of the drive.
2) The motor rotates at low speed, about 15%–25% of its
nominal value. Since , condition (24) becomes
(30)
and the gain is adjusted so that the minimum
wattmeter indication is obtained.
3) Speed is increased up to 50%–70% of its nominal value
and the motor rotates with no load. In this case, the
current could be taken as approximately equal to zero and
using (29), condition (24) is reduced to
(31)
TABLE IILMC PARAMETERS
The current is adjusted so that the minimum wattmeter
indication is accomplished. Two measurements for two
different speed values give an equation system with un-
known parameters and . The solution of the equa-
tion system gives the values of and . Parameter
is then calculated by (29).
4) Speed is maintained equal to the value of the previous
step. Load torque is increased up to 40%–55% of its nom-
inal value. Parameter is adjusted so that the minimum
wattmeter indication is accomplished.
5) Steps 2)–4) are repeated until the desired accuracy is
obtained.
The -axis magnetizing inductance varies due to satura-
tion [9]. Since the gain and parameters , , and de-
pend on , their values are affected by saturation. Therefore,
is an increasing function of the load torque and Step 2) must
be repeated for medium- and high-load torques. Additionally,
the variation of parameters , , and are partially compen-
sated by the increase of .
The armature resistance and excitation current vary de-
pending on the temperature [1]. The gain decreases as load
torque increases and, consequently, the temperature increases.
On the contrary, due to saturation, increases as load torque
increases and, therefore, the temperature variation of is par-
tially compensated. Additionally, parameters to are af-
fected by temperature variations. However, to are varied
by temperature in both numerator and denominator of each frac-
tion of (24) and, consequently, the variation of is narrow.
Thus, parameters variation is considered by means of depen-
dency on current. Furthermore, successful approximation of
the minimum is possible since loss curves, as shown in Fig. 3,
are smooth and flat around the minimum. The above is consis-
tent to the approach presented in [12].
The conclusion is that, in practice, knowledge of the loss
model is not required. Furthermore, no additional feedback sig-nals from the motor are required, beyond those already used in
the pre-existing control (i.e., and control signals). There-
fore, the LMC controller does not affect the cost and the com-
plexity of the drive. Moreover, due to experimental adjustment
of the LMC parameters, the LMC minimizes not only the PM
motor losses, but also the whole drive losses.
V. EXPERIMENTAL RESULTS
For the experimental verification of the theoretical results and
the effectiveness of the LMC operation, a 3.4-kW interior PM
synchronous motor was used. The LMC parameters that have
been adjusted experimentally, according to the rules describedin Section IV, are given in Table II.
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720 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 4, DECEMBER 2004
Fig. 8. Performance of the optimal PM motor drive with LMC: (a) I currentand input power and (b) I current and stator voltage (experimental results).
Fig. 8 shows the performance of the suggested LMC. Com-
paring Fig. 7 to Fig. 8, it is concluded that the optimal controlscheme performs better with an LMC than with an SC. In Fig. 8,
the command of the LMC decreases at a low rate in order to
avoid strong armature current and torque disturbances.
Fig. 9 illustrates the LMC performance to an abrupt torque
demand. It can be seen that at any torque disturbance, the LMC
reacts almost immediately and after equilibrium is established,
the LMC reaches its new optimal current value.
VI. COMPARISONS BETWEEN THE OPTIMUM CONTROL AND
OTHER CONTROL METHODS
The current for producing maximum torque-per-ampere
current is given by [10], [11]
(32)
Substituting (20) in (32) yields
(33)
Fig. 10(a) provides the power saving of the suggested LMC
method against the conventional “ control” and the “max-imum torque-per-ampere current control” methods, for various
Fig. 9. LMC response to load torque demand: (a)I
current and speed and(b)
I
current and power input (experimental results).
speeds and load torques. Fig. 10(b) provides the ratio of the op-
timal ef ficiency of the suggested LMC method, to the conven-tional “ control” and the “maximum torque-per-ampere
current control” methods, for various speeds and load torques.
Finally, the performances of the LMC and the “maximum
torque-per-ampere current controller” are compared in Fig. 11.
Power losses are reduced by “maximum torque-per-ampere cur-
rent control,” however, are minimized by LMC.
VII. LOSS MINIMIZATION CONDITIONS FOR ALL
SYNCHRONOUS MOTOR TYPES
It iswell knownthat the model of an interior PMmotor can be
regarded as a general-type motor model. The equivalent circuits
and the equations that describe the behavior of a surface PMmotor or a SynRM are derived from that of an interior PM motor
if equal inductances in - and -axis are obtained (
and, therefore, ) or rotor excitation is eliminated ( ),
respectively. Therefore, based on the analysis for ef ficiency op-
timization of the interior PM motor, as presented in Section III,
loss minimization expressions for the surface PM motor and the
SynRM can be derived.
Specifically, condition (18) as rewritten
(34)
is modified to obtain the loss minimization expression for eachspecific motor.
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MADEMLIS et al.: OPTIMAL EFFICIENCY CONTROL STRATEGY FOR INTERIOR PM SYNCHRONOUS MOTOR DRIVES 721
Fig. 10. Comparisons of the LMC against “I = 0
control” and maximumtorque-per-ampere current control: (a) power saving and (b) ef ficiency improve-
ment (experimental results).
A. Optimal Efficiency Locus of Interior PM Motor
From (34), it is concluded that the optimal ef ficiency locus of
an interior PM motor is a hyperbola, as described by
(35)
with center at
and (36)
and the slopes of the asymptotes are
(37)
For a given speed value, the intersection of the hyperbola with
a motoring load torque curve corresponds to an operating point
[point A, Fig. 12(a)], in which interior PM motor optimal ef fi-
ciency is attained for that particular load torque. Note that the
hyperbola that corresponds to points with positive current
does not intersect the load torque curve. These are points that
correspond to the first solution of (19) and, as explained inSection III, solution is rejected.
Fig. 11. Comparison of the LMC and maximum torque-per-ampere currentcontroller performances in a 3.4-kW interior PM motor drive: (a)
I
currentand input power and (b)
I
current and stator current (experimental results).
B. Optimal Efficiency Locus of Surface PM Motor
Substituting saliency ratio equal to unity ( ) in (34), the
loss minimization condition for a surface PM motor is derived
[11], [12], [22]
(38)
The optimal ef ficiency locus of a surface PM motor is a straight
line [Fig. 12(a)]. This can also be derived from the optimal ef fi-
ciency locus of the interior PM motor. As saliency ratio tends
to unity, the slope of the asymptotes increases and the center of
the hyperbola moves to infinity. Thus, for , the left part of
hyperbola that corresponds to accepted operating points is re-
duced to a straight line, as specified by (38).
In surface PM motor, the EM torque (4) becomes [9]
(39)
For a given speed value, the intersection of the line (38) with a
motoring load torque curve corresponds to an operating point, in
which surface PM motor optimal ef ficiency is attained for that
particular load torque [point B, Fig. 12(a)].
C. Optimal Efficiency Locus of SynRM
Eliminating the rotor excitation ( ) in (34), the solution
that gives the optimal -axis current for a SynRM is
(40)
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722 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 4, DECEMBER 2004
Fig. 12. Optimal ef ficiency locus of: (a) interior and surface PM synchronousmotors and (b) synchronous reluctance motors.
The solutions (40) correspond to straight lines that are parallel
to the asymptotes of the hyperbola of the interior PM optimal
ef ficiency locus.
In SynRM, the EM torque (4) becomes [9]
(41)
Since , the saliency ratio is less than unity ( ).The solution isrejectedsince inmotoring operation( )
results in negative EM torque and in braking operation in posi-
tive EM torque. Thus, the optimal -axis current for a SynRM
is given by the first solution [11], [23]
(42)
As for the PM motors, at a given speed value, the intersec-
tion of the locus of (42) with a motoring load torque curve cor-
responds to an operating point [point C, Fig. 12(b)], in which
SynRM optimal ef ficiency is attained for that particular loadtorque.
VIII. CONCLUSION
This paper has described a method for minimizing the losses
in vector-controlled interior PM synchronous motor drives. An
LMC for determining the optimal current was presented. The
suggested controller uses the command signals of the speed and
current, and for its implementation, the knowledge of the loss
model is not required. The LMC parameters were determinedby following a simple experimental procedure. Additionally,
the controller does not affect significantly the cost, complexity,
and dynamic performance of the drive. The performance of the
loss model controller was compared against the conventional
“ control” and the “maximum torque-per-ampere current
control.” Finally, based on the interior PM motor loss model, the
loss minimization conditions for surface PM synchronous mo-
tors and synchronous reluctance motors were also derived.
REFERENCES
[1] J.K. Gierasand M.Wing, Permanent Magnet Motor Technology:Design
and Applications. New York: Marcel-Dekker, 1997.[2] B. K. Bose, Power Electronics and AC Drives. Englewood Cliffs, NJ:
Prentice-Hall, 1986.
[3] P. Viarouge, M. Lajoie-Mazenc, and C. Andrieux, “Design and construc-
tion of a brushless permanent magnet servomotor for direct-drive appli-cation,” IEEE Trans. Ind. Applicat., vol. IA-23, pp. 526–531, May/June
1987.
[4] G. R. Slemon, “On the design of high-performance surface-mounted
PM motors,” IEEE Trans. Ind. Applicat., vol. 30, pp. 134–140, Jan./Feb.
1994.[5] L. Xu, L. Ye, L. Zhen, and A. El-Antably, “A new design concept of
permanent magnet for flux weakening operation,” IEEE Trans. Ind. Ap-
plicat., vol. 31, pp. 373–378, Mar./Apr. 1995.
[6] J. D. La Ree and N. Boules, “Magnet shaping to reduce induced voltage
harmonics in PM machines with surface magnets,” IEEE Trans. Energy
Conversion, vol. 6, pp. 155–161, Mar. 1991.[7] W. L. Soong, D. A. Staton, and T. J. Miller, “Design of a new axi-
ally-laminated interior permanent magnet motor,” IEEE Trans. Ind. Ap- plicat., vol. 31, pp. 358–367, Mar./Apr. 1995.
[8] T. M. Jahns, G. B. Kliman, and T. W. Neumann, “Interior permanent-
magnet synchronous motors for adjustable-speed drives,” IEEE Trans.
Ind. Applicat., vol. IA-22, pp. 738–747, July/Aug. 1986.
[9] S. A. Nasar, I. Boldea, and L. E. Unnewehr, Permanent Magnet, Reluc-
tance and Self-Synchronous Motors. Boca Raton, FL: CRC, 1993.
[10] S. Morimoto, Y. Takeda, T. Hirasa, and K. Taniguchi, “Expansion of
operating limits for permanent magnet motor by current vector control
considering inverter capacity,” IEEE Trans. Ind. Applicat., vol. 26, pp.
866–871, Sept./Oct. 1990.[11] B. J. Chalmers, L. Musaka, and D. F. Gosden, “Variable-frequency syn-
chronous motor drives for electric vehicles,” IEEE Trans. Ind. Applicat.,
vol. 32, pp. 896–903, July/Aug. 1996.
[12] S. Morimoto, Y. Takeda, and T. Hirasa, “Loss minimization control of
permanent magnet synchronous motor drives,” IEEE Trans. Ind. Elec-
tron., vol. 41, pp. 511–517, Oct. 1994.[13] F. F. Bernal, A. Garcí a-Gerrada, and R. Faure, “Model-Based loss min-
imization for DC and AC vector-controlled motors including core satu-
ration,” IEEE Trans. Ind. Applicat., vol. IA-36, pp. 755–763, May/June
2000.
[14] R. B. Colby and D. W. Novotny, “An ef ficiency-optimizing permanentmagnet synchronous motor drive,” IEEE Trans. Ind. Applicat., vol. 24,
pp. 462–469, May/June 1988.
[15] Y. Nakamura, T. Kudo, F. Ishibashi, and S. Hibino, “High-ef ficiency
drive due to power factor control of a permanent magnet synchronous
motor,” IEEE Trans. Power Electron., vol. 10, pp. 247–253, Mar. 1995.
[16] S. Vaez and M. A. Rahman, “An on-line loss minimization controller for
interior permanent magnet motor drives,” IEEE Trans. Energy Conver-
sion, vol. 14, pp. 1435–1440, Dec. 1999.
[17] C. Mademlis and N. Margaris, “Loss minimization in vector-controlled
interior permanent-magnet synchronous motor drives,” IEEE Trans. Ind.
Electron., vol. 49, pp. 1344–1347, Dec. 2002.[18] P. C. Krause, Analysis of Electric Machinery. New York: McGraw-Hill, 1986.
8/3/2019 Stray Loss 2
http://slidepdf.com/reader/full/stray-loss-2 9/9
MADEMLIS et al.: OPTIMAL EFFICIENCY CONTROL STRATEGY FOR INTERIOR PM SYNCHRONOUS MOTOR DRIVES 723
[19] V. B. Hosinger, “Performance of polyphase permanent magnet ma-chines,” IEEE Trans. Power App. Syst., vol. PAS-99, pp. 1510–1518,July/Aug. 1980.
[20] S. A. Nasar, Handbook of Electric Machines. New York: McGraw-Hill, 1987.
[21] F. Fernández-Bernal, A. Garcí a-Cerrada, and R. Faure, “Determinationof parameters in interior permanent-magnet synchronous motors withiron loss without torque measurement,” IEEE Trans. Ind. Applicat., vol.
37, pp. 1265–1272, Sept./Oct. 2001.[22] C. Mademlis, J. Xypteras, and N. Margaris, “Loss minimization in sur-face permanent-magnet synchronous motor drives,” IEEE Trans. Ind.
Electron., vol. 47, pp. 115–122, Feb. 2000.[23] I. Boldea, Reluctance Synchronous Machines and Drives. Oxford,
U.K.: Clarendon Press, 1996, pp. 26–30.
Christos Mademlis (S’96–A’00–M’04)was bornin Arnea Chalkidikis,Greece,on February 7, 1964. He received the Diploma degree in electrical engineering(Hons.) and the Ph.D. degree in electrical machines from the Aristotle Univer-sity of Thessaloniki, Thessaloniki, Greece, in 1987 and 1997, respectively.
Since 1990, he hasbeen with theElectrical Machines Laboratory, Departmentof Electrical and Computer Engineering, Aristotle University of Thessalonikias a Research Associate. He was recently appointed as a Lecturer in the sameDepartment. His research interests are in the areas of electrical machines and
drives, especially in machines design and control optimization.
Iordanis Kioskeridis was born in Thessaloniki, Greece, on January 29, 1965.He received the Diploma degree in electrical engineering and the Ph.D. degreein asynchronous motors loss minimization from Aristotle University of Thessa-loniki, Thessaloniki, Greece, in 1989 and 1994, respectively.
Currently, he is with the Technological Educational Institute of Thessaloniki,where he teaches power electronics andelectrical machines.From 1995to 2000,he was Superintendent Engineer with the Natural Gas Project in the North Sec-tion of Greece. His research activities include power-electronic converters, con-
trol, and modeling of adjustable speed drives.
Nikos Margaris (M’00) was born in Athens, Greece, on February 10, 1949. Hereceived the Diploma in physics, the Postgraduate degree in electronics and thePh.D. degree in automatic control from the Aristotle University of Thessaloniki,Thessaloniki, Greece, in 1972, 1975, and 1982, respectively.
Since 1977, he has been with the Electrical and Computer Engineering De-partment, Aristotle University of Thessaloniki, teaching graduate and postgrad-uate courses in electronics, automatic control, power electronics, and circuittheory. From 1992to 1994, he wasthe Director of the Electronics and ComputerDivision and from 1993 to 1995, he was the Vice President of the Electrical andComputer Engineering Department. His current research interests include theloss minimization in variable and constant speed drives, the study of nonlinearoscillations, the analysis and design of switch mode dc-dc converters, and the
robust control theory.