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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 4, DECEMBER 2004 715 Optimal Efciency Control Strategy for Interior Permanent-Magnet Synchronous Motor Drives Christos Mademlis  , Member, IEEE , Iordanis Kioskeridis, and Nikos Margaris  , Member, IEEE  Abstract—In this paper , the problem of efc ienc y optimiza- tion in vect or-c ontr olled inter ior permanent -magne t (PM) syn- chronous motor drives is investigated. A loss model controller is intr oduce d that deter mines the op timal -axis componen t of the stator current that minimizes power losses. For the implementa- tion of the suggested controller, the knowledge of the loss model is not requir ed sinc e an expe rime ntal proced ure is foll owed 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 propose d metho d and demon strate the operatio nal improvements.  Index T erms— Loss es, optimal cont rol, optimizati on metho ds, 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 ux. 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 coefcient. Stray loss coefcient. Mechanical loss coefcient. Manuscript received January 3, 2003; revised July 31, 2003. Paper no. TEC- 00296-2002. The auth ors are with the Depar tmen t of Elect rical and Comp uter Engineering, Aristotle University of Thessaloniki, Thessaloniki GR-54 124, Greece (e-mail: [email protected]). Digital Object Identier 10.1109/TEC.2004.83 7282 I. INTRODUCTION P ERMANENT-MAGNET (PM) sync hronou s motor ad-  just able speed drives offe r signi cant adv antag es over induction motor drives in a wide variety of industrial appli- catio ns (i.e., high-p owe r densi ty, high efc ienc y, impro ved dynamic performance, and reliability) [1]. Since vector control in PM synch ronous motors provides fast dynamic respo nse with a less complex and nonparameter-dependent controller, PM motor drives can be an attractive alternative choice [2]. Improvement of PM motor efciency is a most important pri- ority, especially in cases where drives are powered by a battery source. Therefore, signicant efforts are taken to improve their efciency. Since there are a great variety of PM motor congu- rations, the efforts are mainly focused on the search for the op- timum rotor structure [3]–[7]. However, efciency can also be improved by intervening in the motor operation principle with automatic control techniques. Se veral control met hod s ha ve bee n pro pos ed in ord er to reduce the loss of PM motor drives and improve their perfor- mance. The copper loss can be minimized by the maximum torque -per-a mpere curre nt control [8]. In surface PM motor drives, maximum torque-per-ampere current ratio is attained by keep ing the -axis co mpone nt of the stato r current eq ual to zero ( ) [9], [ 10]. Si nce the “ control” pr eve nts th e demagnetization of the PM, it is often employed in interior PM motor driv es. However, the curren t th at provi des maximu m torque -per-a mpere current ratio in inter ior PM motor driv es is a fun ction of the cur ren t and o pposes the e xci tat ion eld of the PM [8]–[11]. Several attempts to minimize both copper and iron losses have been recently presented [12]–[14]. However, the proposed los s minimi zat ion condit ion s are comple x and can onl y be implemented usi ng of in e made loo kup tables. The ref ore, a number of cos tly and time-c ons umi ng mea sur eme nts are required. A control method, described in [15], improves ef- ciency of PM motors and is implemented using a voltage source inverter. The efciency 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 losse s are not minimized. An adapt ive search control ler for interior PM motors was developed in [ 16]. Finally, an approach that spe cies the opt imal -axis cur rent for minimi zing inte rior PM motor losses was presented in [17]. This paper presents an optimal efciency method for vector- con tro lled int eri or PM syn chr onous mot or dri ve s. The los s minimization is accomplished with a loss model controller that is based on the op timal -axis cur rent cond ition , as present ed 0885-8969/04$20.00 © 2004 IEEE

Transcript of Stray Loss 2

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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

0885-8969/04$20.00 © 2004 IEEE

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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)

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)

currentand input power and (b)

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.

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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.