ΦΦΦΦAbstract—One of the most important research topics in drive

train topologies applied to electric/hybrid vehicles is the

efficiency analysis of the power train components, including the

global drive efficiency. In this paper, two basic traction electric

drive systems of electric/hybrid vehicles are presented and

evaluated, with a special focus on the efficiency analysis. The first

topology comprises a traditional pulse-width-modulation battery-

powered inverter while in the second one, the battery is

connected to a bidirectional dc-dc converter, which supplies the

inverter. Furthermore, a variable voltage control technique

applied to this second topology is presented, which allows to

improve the drive overall performance. Some simulation results

are presented considering both topologies and a permanent

magnet synchronous motor. An even more detailed analysis is

performed through the experimental validation. Particular

attention is given to the evaluation of the main drive components

efficiency, including the global drive efficiency, presented in the

form of efficiency maps. Other parameters such as motor

voltages distortion and power factor are also considered. In

addition, the comparison of the two topologies takes into account

the drive operation under motoring and regenerative braking

modes.

Index Terms—Electric vehicles, automotive applications,

permanent magnet machines, energy efficiency, power

conversion, voltage control, dc-dc power converters, bidirectional

power flow, machine vector control.

I. NOMENCLATURE

vd, vq dq axes voltage components

id, iq dq axes current components

icd, icq dq axes iron losses current components

imd, imq dq axes magnetizing current components

Rs Stator winding resistance

! Stator currents frequency

Ld, Lq dq axes inductance components

ÃPM Flux linkage due to the rotor magnets

Copyright (c) 2012 IEEE. Personal use of this material is permitted.

However, permission to use this material for any other purposes must be

obtained from the IEEE by sending a request to pubs-permissions@ieee.org.

This work was supported by the Portuguese Government through the

Foundation for Science and Technology (FCT) under Project No.

SFRH/BD/40286/2007 and Project No. PTDC/EEA-ELC/105282/2008.

Jorge O. Estima is with the Department of Electrical and Computer

Engineering, University of Coimbra, 3030-290 Coimbra, Portugal, and also

with the Instituto de Telecomunicações, 3030-290 Coimbra, Portugal (email:

jestima@ieee.org).

A. J. Marques Cardoso is with the Dep of Electromechanical Engineering,

University of Beira Interior, 6201-001 Covilhã, Portugal, and also with the

Instituto de Telecomunicações, 3030-290 Coimbra, Portugal (email:

ajmcardoso@ieee.org).

!r Rotor mechanical speed

J Moment of inertia

Te Electromagnetic torque

D Damping coefficient

TL Load torque

µ Rotor electrical position

p Pole pairs number

PCu Stator winding copper power losses

PFe Stator iron power losses

´ Efficiency

Pin Input power

Pout Output power

Plo Power losses

Xrms Waveform rms value

X1 Waveform fundamental component rms value

II. INTRODUCTION

ONSIDERING the high oil consumption rate of the

transportation sector and due to the arising concerns

about global warming and energy resource constraints,

government agencies and organizations are imposing more

stringent regulations for fuel consumption and emissions.

With this increasing demand for environmentally friendlier

and higher fuel economy vehicles, the automotive companies

are focused on the development of new technologies such as

hybrid electric vehicles, electric vehicles, fuel cell vehicles

and plug-in vehicles [1]. Although electric and fuel cell

vehicles represent a possible solution for this problem,

presently, they have some limitations which make them a less

attractive option than the others [2].

For these automotive traction systems, the electric motor is

one of the most important key components. The major

requirements for these applications include high torque and

power density, high starting torque, high efficiency over wide

torque and speed ranges, a very wide speed range, including

constant torque and constant power regions, high intermittent

overload capability and reasonable cost [3]-[7]. In this

context, permanent magnet synchronous motors (PMSM) are

becoming more and more attractive. These machines have

inherent features such as high power density and high

efficiency, which make them very suitable for these

applications.

Regarding the traction electric drive system, there are two

basic configurations [8]-[10]. The first comprises a traditional

PWM battery-powered inverter (Fig. 1a), while in the second

Efficiency Analysis of Drive Train Topologies

Applied to Electric/Hybrid Vehicles

Jorge O. Estima, Member, IEEE, and A. J. Marques Cardoso, Senior Member, IEEE

C

one the battery is connected to a bidirectional dc-dc converter,

typically a boost converter, which supplies the inverter (Fig.

1b). The use of a bidirectional dc-dc converter, to connect the

battery and the inverter, has several advantages over the

configuration where the battery directly powers the inverter.

Beyond the possibility to minimize the stress of the inverter

with an extra dc stage, it is possible to improve the motor

output by increasing and controlling the inverter supply

voltage (system voltage) without increasing the battery cost

and size, due to the requirement of building up a higher cell

number, keeping simultaneously the same motor size [11].

This topology also permits to separately design the system

voltage and battery, allowing for flexible system designs for

vehicles with different output characteristics. System voltage

design can be based on motor output and withstanding voltage

of parts, and for battery voltage design the number of cells can

be altered to match the required battery output and capacity

[12]-[13]. However, this configuration has some

disadvantages such as power losses in the dc-dc converter and

the increase of system complexity and cost. This also arises

the concern about the power components physical dimensions.

Despite the battery size reduction, it must be taken into

account the additional inductor and power switches, which

may require the optimization and size reduction of the power

electronics components. The reliability issues due to the

introduction of an additional component must also be taken

into account.

An important aspect in the selection of these topologies is

the system cost versus the cost of use relation. The second

topology requires a smaller battery, and therefore its cost can

be reduced. Nevertheless, the cost regarding the extra power

components and more complex design issues can compensate

for the cheaper battery. Considering the cost of use, beyond

the drive system efficiency, it strongly depends on the

maintenance aspects. As a consequence, important issues such

as battery life-time, its corresponding cost and the reliability

levels associated to the topologies complexity must be taken

into account for an accurate analysis.

Other configurations can be obtained by combining these

topologies with different energy storage technologies. In [14]

and [15], a high voltage battery pack directly supplies the

inverter, supported by an ultracapacitor bank, connected to the

battery bus through bidirectional dc-dc converters. Parallel

converters were considered, which allow to reduce the

inductor current ripple and improve the global efficiency. The

same power sources can also be connected together to a dc-dc

converter, which supplies the high voltage bus [16].

The combination of batteries and fuel cells can also be used

for the drive train of hybrid/electric vehicles. In [17] it was

addressed the integration of these power sources with several

topologies of isolated and non-isolated dc-dc converters. This

subject, as well as other different configurations, were also

investigated in [18].

The advantages of fuel cells can also be combined with the

great dynamic response and power density of ultracapacitors

for these electric traction systems [19]-[21]. The presented

results allow to conclude that with an appropriate power

management control technique, this hybrid source is able to

provide any load demand. Furthermore, by using bidirectional

dc-dc converters, it is possible to achieve a better control over

the fuel cell voltage during transients. Considering the

combination of these hybrid sources and using several dc-dc

converters, an energy management strategy based on flatness

and fuzzy logic control techniques was presented in [22]. As a

main advantage, it is pointed out that the power management

is carried out with a single general control algorithm in

different operating modes.

Due to the great importance of bidirectional dc-dc

converters in advanced transportation systems, a novel

capacitor-switched regenerative snubber for dc-dc boost

converters was proposed in [23]. The resulting topology

allows to reduce the switching losses so that high switching

frequency operation can be achieved. As a consequence,

higher efficiency values can be obtained and the overall

converter mass can be significantly reduced.

The literature review shows that, despite of all the existing

work done by several authors concerning the study of electric

drive systems for electric/hybrid vehicles, there is a lack of

research regarding the detailed efficiency analysis of different

power train configurations for these specific applications.

Accordingly, and considering the work previously reported in

[24], this paper provides an in-depth analysis of two basic

electric drive topologies based on a PMSM (Fig. 1), with a

special focus on the efficiency analysis. Furthermore,

considering the topology T2 (Fig. 1b), an improved variable

voltage control technique for the dc-dc converter is described

and implemented, allowing to dynamically adjust the system

voltage, thus contributing to achieve higher efficiency values

and improve the drive overall performance. Some simulation

results are presented using a PMSM dynamic model which

takes the iron losses into account. An even more detailed

analysis is performed through the experimental validation

+

-

Inverter

PMSM

(a)

+

-

DC-DC Converter Inverter

PMSM

(b)

Fig. 1 – Basic traction electric drive topologies for electric/hybrid vehicles:

(a) topology T1; (b) topology T2.

where efficiency maps are obtained for each drive component,

including the efficiency maps of both topologies global

efficiency. In addition, motor voltages distortion and power

factor results are also evaluated. Finally, a comparison of the

two topologies is provided for the drive operation under

motoring and regenerative braking modes trough a drive cycle

analysis.

III. PMSM DYNAMIC MODEL WITH IRON LOSSES

Typical PMSM mathematical models found in the literature

do not take iron losses into account. For this reason, in order

to obtain a more accurate modeling, especially for the iron

losses, a dedicated parameter has been considered aimed at

accounting for the iron losses in the stator core, specifically

the eddy current losses. These are modeled by a resistor Rc

which is inserted in parallel with the magnetizing branch, so

that the power losses depend on the air-gap flux linkage [25]-

[30]. Thus, the dq axes currents (id, iq) are divided into the

iron loss currents (icd, icq) and the magnetizing currents (imd,

imq), as shown in Fig. 2.

Considering this, and assuming that the saturation is

neglected, the electromotive force is sinusoidal, and a cageless

rotor, the state equations of the dynamic model of the PMSM

in the synchronous reference frame, also taking into account

the iron losses, are given by:

dimd

dt=

1

Ld

(vd ¡Rsid + !Lqimq) (1)

dimq

dt=

1

Lq

(vq ¡Rsiq ¡ !Ldimd ¡ !ÃPM ) (2)

d!r

dt=

1

J(Te ¡D!r ¡ TL) (3)

dµ

dt= ! = !rp (4)

where

id =1

Rc

µ

Ld

dimd

dt¡ wLqimq +Rcimd

¶

(5)

iq =1

Rc

µ

Lq

dimq

dt+ !Ldimd + !ÃPM +Rcimq

¶

(6)

icd = id ¡ imd ; icq = iq ¡ imq (7)

Te =3

2p [ÃPM imq + (Ld ¡ Lq) imdimq] (8)

By referring equations (1), (2), (5) and (6) to a steady-state

condition, it is possible to define a mathematical expression

for the power losses in the stator windings. These can be

calculated according to following expression:

PCu =3

2Rs

¡

i2

d + i2

q

¢

(9)

In a similar way, the power losses that are caused by the

fundamental component of the total flux linkage in the iron

stack can be calculated as:

PFe =3

2Rc

¡

i2cd + i2cq¢

=3

2

!2

Rc

h

(Lqimq)2 + (ÃPM + Ldimd)

2

i (10)

Although not considered in this work, hysteresis losses can

also be taken into account. These losses are proportional to the

machine phase currents frequency. Therefore, in order to

include them into the machine model, the iron losses

resistance Rc is usually treated as a function of !.

IV. VARIABLE VOLTAGE CONTROL

Considering the topology T2, and by adjusting the inverter

supply voltage through a variable voltage control strategy

applied to the bidirectional dc-dc boost converter, the system

minimum losses can be achieved, according to the motor

operating conditions. When the motor is operating below its

base speed, the system voltage does not need to be equal to

the rated inverter supply voltage. Therefore, it can be

concluded that to minimize the overall system losses, the

system voltage must be proportional to the PMSM back-EMF.

Taking into account that the back-EMF generated by a PMSM

is typically proportional to its mechanical speed, the required

system voltage can be then obtained according to the curve

shown in Fig. 3.

When the motor speed is low, the inverter supply voltage

will be the lowest voltage of the boost converter, which is

Rs

!Lqimq

LdRc

id imd

icd

vd

(a)

Rs

!Ldimd

LqRc

iq imq

icq

vq

!ÃPM

(b)

Fig. 2 – dq axes equivalent circuits for the PMSM model taking iron losses

into account: (a) d-axis; (b) q-axis.

imposed by the battery. Above the motor base speed, in the

constant power zone, the dc-dc converter is controlled in

order to supply the inverter with the rated system voltage. For

the intermediate range, the system voltage changes

dynamically in accordance with the machine mechanical

speed.

The overall performance can be even more improved if the

system voltage also takes into account the PMSM load level.

These two fundamental goals can be simultaneously

considered if the system voltage is controlled according to the

modulation index m of the inverter space-vector pulse-width-

modulation (SV-PWM) technique. Since directly it depends

on the amplitude of the reference voltage vector and on the

inverter supplying voltage Vdc, the dc-dc converter can be

controlled in order to impose a system voltage that maintains

the inverter modulation index at a specific reference value, as

shown in Fig. 4. By doing this and assuming a large value for

the reference modulation index, it is possible to dynamically

adjust and optimize the system voltage according to the motor

mechanical operating conditions. Therefore, the overall drive

performance can be greatly improved by reducing the voltage

and currents distortion values and increasing the efficiency

levels.

V. SIMULATION RESULTS

The modeling and simulation of the PMSM drive systems

shown in Fig. 1, was carried out using the Matlab/Simulink

environment, in association with the Power System Blockset.

This software toolbox provides a great number of several

power electronics mathematical models that were used for the

simulation. The PMSM model described in Section III was

implemented in Simulink, as well as the battery model. This

last one is based on the work published in [31].

For both topologies, a rotor field oriented control strategy

employing PI current controllers and a SV-PWM technique

was applied to the inverter in order to control the PMSM

mechanical speed. The PMSM parameters are summarized in

Table VI, included in Appendix.

The switching frequency of the SV-PWM was chosen to be

equal to 6 kHz. Regarding the topology in Fig. 1a, the inverter

is directly supplied by the battery with a rated voltage of 384

V. Considering the other topology, the system voltage is

controlled by the bidirectional dc-dc converter within the

range of 168 V (corresponding to the battery rated voltage) to

384 V. Assuming that the rated system voltage is 384 V, the

battery voltage for topology T2 can be selected according to

several criteria. Beyond the size limitation, an important

aspect is the desired global drive maximum efficiency

operating point. Therefore, by choosing a battery voltage near

to the system rated voltage, allows to achieve maximum

efficiency at high speeds. On the other hand, a lower battery

voltage allows to achieve high efficiency at low speed values.

For both topologies, the same IGBT inverter and PMSM

were considered. The control system implemented is

described in Fig. 4. A value of 9 kHz was chosen for the

switching frequency of the PWM technique. Regarding the

modulation index control loop, it is controlled within the

linear range between 0 and 1 (over-modulation is not

considered). Therefore, and taking also into account that

lower harmonic distortion is obtained for a high modulation

index [32], a reference value of 0.93 was assumed.

Two distinct operating conditions were considered: when

the machine operates as a motor (motoring mode) and when it

operates as a generator (regenerative braking). For both cases,

several results are presented with the aim to establish a

performance comparison of both topologies.

In order to analyze all the considered cases, several

performance parameters are calculated. The efficiency values

of the main drive components, i.e. the dc-dc converter, the

inverter and the machine, are presented as well as the global

drive efficiency values. All the efficiency values and power

losses are calculated by the analysis of the drive power flow,

using the input and output power of each component:

´ =Pout

Pin

£ 100% (11)

Plo = Pin ¡ Pout (12)

Regarding the PMSM, beyond the analysis of its power

factor, the harmonic distortion values of its supplying voltages

are also investigated. In order to take into account the dc

component and all the sub-harmonics, the distortion of the

waveforms is more properly evaluated by calculating the Total

System

Voltage

Rated

Voltage

Battery

Voltage

Constant Torque Constant Power

Mechanical

Speed

Base

Speed

Variable Voltage

Control Range

Fig. 3 – Required system voltage with variable voltage control.

+-

dq

αβ

+-

+- SV-PWM

Speed

Controller

iq

!¤

r

i¤

d

id

v¤

q

v¤

d

v¤

®

v¤

¯

µ

!r

dq

abciaibic

+-

+-

m¤

+-

V¤

dc

m Modulation Index

Controller

Vdc

PMSM

DC

DCPWM

Fig. 4 – Block diagram of the control strategy for topology T2.

Waveform Distortion (TWD) defined as:

TWD =

p

X2rms

¡X2

1

X1

£ 100% (13)

Finally, for all the considered operating conditions, a

constant torque equivalent to 50% of the PMSM rated torque

is assumed, together with a reference speed of 600 revolutions

per minute. Considering these speed and load values, the dc-

dc converter variable voltage control adjusts the system

voltage to a reference value of approximately 177 V.

Table I and Table II present the efficiency results of the

drive system main components for topologies T1 and T2,

under motoring and regenerative braking operating modes,

respectively. These results clearly demonstrate that higher

global efficiency results can be achieved by the topology T2.

Furthermore, the results also show that the inverter is the

mostly affected device since its efficiency varies considerably

when comparing both topologies. Considering topology T1,

the inverter is supplied by its the rated voltage, corresponding

to the battery voltage. This means that, for the considered

operating conditions, the modulation index is relatively low

and, as a consequence, the inverter switching losses are larger

when compared to the ones obtained for the topology T2.

Regarding to the voltage distortion values, the results in

Table III show that for both motoring and regenerative

braking modes, with topology T2 the TWD values can be

approximately reduced by one-half. This also leads to the

reduction of the motor phase currents distortion, as shown in

Fig. 5. These lower TWD values are justified by the fact that

the system voltage imposed by the dc-dc converter is

controlled by taking into account the chosen reference

modulation index. This also leads to the improvement of the

machine power factor. By reducing the voltage TWD, their

corresponding rms values will also decrease, as well as the

PMSM apparent power, subsequently increasing its power

factor.

VI. EXPERIMENTAL RESULTS

The experimental setup basically comprises a battery pack,

two IGBT Semikron power modules SKiiP 132GD120-3DU,

one for the inverter and the other for the dc-dc converter, a

dSPACE DS1103 digital controller and a Yaskawa PMSM

coupled to a four-quadrant servomotor test system (Fig. 6).

TABLE I

EFFICIENCY RESULTS (%), UNDER MOTORING OPERATION, FOR 50% OF THE

PMSM RATED TORQUE

Topology T1 Topology T2

600

rpm

900

rpm

1200

rpm

600

rpm

900

rpm

1200

rpm

DC-DC

Converter − − − 98.1 97.4 96.6

Inverter 92.9 95.0 96.2 97.2 97.4 97.3

PMSM 85.8 86.9 87.2 88.6 88.8 88.9

Global 79.7 82.6 83.9 84.5 84.2 83.6

TABLE II

EFFICIENCY RESULTS (%), UNDER REGENERATIVE BRAKING OPERATION, FOR

50% OF THE PMSM RATED TORQUE

Topology T1 Topology T2

600

rpm

900

rpm

1200

rpm

600

rpm

900

rpm

1200

rpm

DC-DC

Converter − − − 97.9 97.6 96.7

Inverter 89.7 93.3 95.1 97.2 97.6 97.4

PMSM 83.7 84.7 85.1 86.9 87.4 88.0

Global 75.1 79.0 80.9 82.7 83.3 82.9

TABLE III

TWD AND POWER FACTOR RESULTS FOR 600 RPM AND 50% OF THE

PMSM RATED TORQUE

Topology T1 Topology T2

Motoring

Mode

TWD (%) 150.91 69.39

Power Factor 0.551 0.796

Regenerative

Braking Mode

TWD (%) 170.16 90.74

Power Factor 0.467 0.718

0.44 0.45 0.46 0.47 0.48 0.49 0.5−3

−2

−1

0

1

2

3

Time (s)

PM

SM

Ph

ase

Cu

rren

ts (

A)

0.44 0.45 0.46 0.47 0.48 0.49 0.5−3

−2

−1

0

1

2

3

Time (s)P

MS

M P

has

e C

urr

ents

(A

)

ia ib ic

ia ib ic

(b)

(a)

Fig. 5 – Time-domain waveforms of the PMSM phase currents for 600 rpm

and 25% of the motor rated torque: (a) topology T1; (b) topology T2.

Fig. 6 – General view of the experimental setup.

The PMSM parameters can be found in Appendix. For the

dc-dc converter, an inductor of 10 mH was used, together with

an output filter capacitor of 1100 µF. The battery pack

comprises several 12 V 12 Ah lead-acid batteries connected in

series (32 and 14 batteries for topologies T1 and T2,

respectively). Due to the limited number of dedicated PWM

outputs available at the controller, the modulation strategies

were implemented by software. The switching frequencies for

the inverter SV-PWM and the dc-dc converter PWM

techniques were therefore chosen to be of 6 kHz and 9 kHz,

respectively.

The real-time interface board library for the DS1103

controller is designed as a common Matlab/Simulink Blockset

that provides blocks to implement the I/O capabilities in

Simulink models. The dSPACE ControlDesk software

provides functions for real-time control and monitoring,

allowing simultaneously to capture data files that can be

plotted using the Matlab (Fig. 7).

The control system was implemented for the DS1103 board

using a sampling time of 25 µs. The voltage and current

signals as well as all the IGBTs gate commands are connected

to the dSPACE controller trough interface and isolation

boards (Fig. 8). Two digital power analyzers Yokogawa

WT3000 were connected in series in the power circuit in order

to obtain the required data such as power flow, power factor,

efficiency and rms values. The rotor position is obtained by an

incremental encoder with 1024 pulses per revolution, being

the PMSM mechanical speed obtained by filtering the

derivative of the rotor position.

For the topology T1, the inverter is directly supplied by a

rated system voltage of 384 V. On the other side, considering

the second topology, the drive system is supplied by a battery

pack with a rated voltage of 168 V. The system voltage is

dynamically adjusted by the dc-dc converter within the range

of 168 V to 384 V. For the modulation index control, a

reference value of 0.93 is assumed again. The same inverter

power module was also used for both topologies.

Experimental results are presented considering the drive

operation under motoring and regenerative braking modes. In

order to compare both topologies, a particular attention is

given to the efficiency analysis of the drive main components,

including the global efficiency values. The PMSM voltages

TWD and power factor results are also presented.

A. Motoring Operation

Fig. 9 presents an acceleration test for 50% of the PMSM

rated load torque, showing the behavior of the variable

voltage control for the topology T2. At t=1 s, a change of the

reference speed from 500 rpm to 800 rpm is introduced, with

an acceleration rate of 100 rpm/s. The system voltage is kept

constant and equal to 168 V when the motor operates below

550 rpm. Under these conditions, the modulation index is

lower than the imposed reference value and the dc-dc

converter will fed the inverter with the lowest voltage value,

corresponding to the battery voltage. When the machine

accelerates above 550 rpm, the modulation index becomes

equal to the reference value and the variable voltage control is

enabled. Then, the system voltage increases proportionally to

the PMSM speed until the new reference speed is reached.

The results in Fig. 10 to Fig. 15 present the efficiency maps

of the inverter and the PMSM, including the global drive

efficiency values for the topologies T1 and T2.

Comparing the inverter efficiency maps for both topologies in

Fig. 10 and in Fig. 11, it can be clearly seen that with the

Fig. 7 – General view of the real-time interface and measuring equipment.

Fig. 8 – Block diagram with the main components of the experimental setup.

0 1 2 3 4 5 6400

500

600

700

800

900

Time (s)

PM

SM

Mec

han

ical

Spee

d (

rpm

)

160

180

200

220

240

260

Syst

em V

olt

age

(V)

System Voltage

PMSM Speed

Fig. 9 – Time-domain waveforms of the PMSM mechanical speed and system

voltage for a change of the reference value from 500 rpm to 800 rpm.

topology T2, it is possible to obtain significantly higher

efficiency values for the inverter. Moreover, for the operating

points above 600 rpm, the inverter efficiency is relatively high

and constant when compared to the topology T1. This is

justified by the fact that the drive is operating in the variable

voltage control zone, and consequently the inverter losses,

especially the switching losses, are minimized. Below this

speed value, the inverter efficiency starts to decrease more

rapidly because the system voltage is imposed by the battery

and the modulation index control is no longer possible.

Nevertheless, the efficiency values in this zone are still

significantly higher for topology T2.

Regarding the PMSM, Fig. 12 and Fig. 13 present its

efficiency maps for the two considered topologies T1 and T2,

respectively. For high speed and load levels, the PMSM

presents similar efficiency values for both topologies since the

system voltage is practically the same. However, the most

important difference is observed for load levels below 50% of

the motor rated torque, where the PMSM efficiency for

topology T2 becomes higher than for topology T1. Once

more, thanks to the variable voltage control, the global

machine efficiency can be improved, particularly for low

speed and torque values. By adjusting the inverter supplying

voltage through the control of its modulation index, the

PMSM voltage rms values are minimized, reducing the

machine losses, namely the iron losses in the stator stack.

Fig. 14 and Fig. 15 present the efficiency maps of the

global drive efficiency for topologies T1 and T2, respectively.

Comparing these results, it can be concluded that, despite

of the higher efficiency values of the inverter and the motor

for topology T2, due to the dc-dc converter losses, the global

efficiency is negatively affected when the PMSM operates at

high speed and load levels. Under these conditions, the

modulation index for topology T1 is naturally high. Therefore,

and taking also into account that there are losses only in the

inverter and in the machine, the overall efficiency values will

be higher than for topology T2. However, for low speed

values or in particular for load levels below 50% of the motor

rated torque, the global drive efficiency for topology T2

becomes much higher than for topology T1. Under these

operating conditions, the modulation index control allows to

decrease the system voltage, resulting in lower losses in all

drive components and higher efficiency values.

From these tests, the maximum global drive efficiency was

68.5

69.8

71.1

72.4

73.7

75.1

76.4

79

79

80.3

80.3

81.6

81.6

82.9

82.9

84.2

84.2

85.5

85.5

86.9

86.9

88.2

88.2

89.5

89.5

90.8

90.8

92.2

Speed (rpm)

Lo

ad T

orq

ue

(Nm

)

300 400 500 600 700 800 900 1000 1100 12001

2

3

4

5

6

7

8

9

10

11

12

70

75

80

85

90

Fig. 12 – PMSM efficiency map for topology T1.

68.9

70.2

71.5

72.9

74.2 75.9

78.2

79.5

79.5

80.9

80.9

82.2

82.2

83.5

83.5

84.9

84.9

86.2

86.2

87.5

87.5

88.9

88.9

90.2

90.2

91.5

91.5

92.9

92.9

Speed (rpm)

Load

Torq

ue

(Nm

)

300 400 500 600 700 800 900 1000 1100 12001

2

3

4

5

6

7

8

9

10

11

12

70

75

80

85

90

Fig. 13 – PMSM efficiency map for topology T2.

75

77.4

78.6

79.8

81

82.2

83.4

84.6

85.8

87

88.2

89.4

90.6

91.8

93

94.2

95.4

96.6

Speed (rpm)

Lo

ad T

orq

ue

(Nm

)

300 400 500 600 700 800 900 1000 1100 12001

2

3

4

5

6

7

8

9

10

11

12

75

80

85

90

95

Fig. 10 – Inverter efficiency map for topology T1.

90

90.9

91.3

91.7

92.2

92.6

93

93.5

93.9

94.3

94.8

95.2

95.6

96.1

96.5 9

6.9

97.3

Speed (rpm)

Load

Torq

ue

(Nm

)

300 400 500 600 700 800 900 1000 1100 12001

2

3

4

5

6

7

8

9

10

11

12

75

80

85

90

95

Fig. 11 – Inverter efficiency map for topology T2.

achieved for topology T2 at 600 rpm and 3 Nm, with a value

of 90.2%. Considering topology T1, a value of 89.9% was

achieved at 1200 rpm and 4 Nm.

The PMSM supplying voltages distortion can be significantly

improved for topology T2, using the variable voltage control

technique. This can be clearly seen in Fig. 16 and Fig. 17,

where the TWD values of the motor phase-to-phase voltages

for topologies T1 and T2 are, respectively, presented. When

the system voltage is directly imposed by the battery

(topology T1), the voltage distortion values are relatively high

for low speed operation since the inverter modulation index is

low. As the mechanical operation speed increases, the

modulation index also increases, and as a result, the TWD

values decrease. It is also noticed that for a given speed, the

distortion values are lower for higher load levels due to the

small increasing of the modulation index. As far as topology

T2 is concerned, it can be concluded that the overall distortion

values are significantly lower than the ones obtained for

topology T1, being in some cases reduced by more than 50%.

It is worth mentioning that for the variable voltage control

zone, approximately between 600 rpm and 1200 rpm, all the

TWD values are relatively constant and low. As a result of the

inverter modulation index control, the system voltage is

constantly adjusted in order to maintain the modulation index

60.161.763.465 66.7

68.3 70 71.7

73.3

73.3

75

75

76.6

76.6

78.3

78.3

79.9

79.9

81.6

81.6

83.3

83.3

84.9

86.6

88.2

Speed (rpm)

Lo

ad T

orq

ue

(Nm

)

300 400 500 600 700 800 900 1000 1100 12001

2

3

4

5

6

7

8

9

10

11

12

60

65

70

75

80

85

90

Fig. 14 – Global drive efficiency map for topology T1.

64.4

65.8

67.168.569.871.272.5

73.9

73.9

75.3

75.3

76.6

76.6

78

78

79.3

79.3

80.7

80.7

82.1

82.1

83.4

83.484.8

84.886.1

86.1

87.5

88.8

Speed (rpm)

Load

Torq

ue

(Nm

)

300 400 500 600 700 800 900 1000 1100 12001

2

3

4

5

6

7

8

9

10

11

12

60

65

70

75

80

85

90

Fig. 15 – Global drive efficiency map for topology T2.

3

6

9

12300

600900

1200

0

50

100

150

200

250

Load Torque (Nm)Speed (rpm)

Volt

age

TW

D V

alues

(%

)

Fig. 16 – PMSM phase-to-phase voltage TWD values for topology T1.

3

6

9

12300

600900

1200

0

50

100

150

200

250

Load Torque (Nm)Speed (rpm)

Volt

age

TW

D V

alues

(%

)

Fig. 17 – PMSM phase-to-phase voltage TWD values for topology T2.

0 0.01 0.02 0.03 0.04 0.05 0.06−3

−2

−1

0

1

2

3

Time (s)

PM

SM

Phas

e C

urr

ents

(A

)

0 0.01 0.02 0.03 0.04 0.05 0.06−3

−2

−1

0

1

2

3

Time (s)

PM

SM

Phas

e C

urr

ents

(A

)

ia ib ic

ia ib ic

(b)

(a)

Fig. 18 – Time-domain waveforms of the PMSM phase currents for 600 rpm

and 25% of the motor rated torque: (a) topology T1; (b) topology T2.

in its reference value. Thus, the voltage distortion is kept at

relatively low values, independently of the PMSM operating

conditions.

The voltage distortion also affects the PMSM phase

currents, particularly for low speed and torque values, as

shown in Fig. 18. Therefore, the distortion of the motor phase

currents for topology T1 (Fig. 18a) will be larger than for

topology T2 (Fig. 18b).

An important issue related to the distortion of the PMSM

supplying voltages and currents is their impact on the machine

efficiency and its lifetime. Hysteresis and eddy current losses

are part of the iron losses that are produced in the machine

core due to the alternating magnetic field. Hysteresis losses

are proportional to the frequency while eddy current losses

vary with its square value. Therefore, high frequency voltage

components produce additional losses in the PMSM core,

which in turn, increase the operating temperature of the core

itself and also of the surrounding windings.

As seen before, the application of a non-sinusoidal voltage

to the motor results in harmonic current circulation in its

windings. As a consequence, due to the skin effect, they will

contribute even more to the decrease of the machine

efficiency. These additional power losses also affect

negatively the PMSM temperature, contributing in this way to

the reduction of its lifetime.

Another important issue related to the harmonic distortion

is the noise generation. This aspect is particularly important in

electric/hybrid vehicles applications since it is required to

keep the noise levels to the minimum in order to assure the

passengers comfort. Accordingly, by reducing the PMSM

supplying voltages TWD values with topology T2, it is

possible to decrease the machine generated of noise.

Finally, Fig. 19 presents the PMSM power factor results for

several mechanical speed values and for a load torque

equivalent to 50% of the motor rated value. It is clearly seen

that higher power factor values can be obtained for topology

T2, since the variable voltage control allows to reduce the

voltage rms values and therefore the apparent power.

A. Regenerative Braking Operation

Table IV presents the main drive components efficiency for

topologies T1 and T2, including the global drive efficiency,

for a load level equivalent to 50% of the PMSM rated torque,

under regenerative braking operation.

As expected, comparing both configurations, higher

efficiency values can be obtained for topology T2, especially

for low operating speeds. Under these conditions, it can be

seen that the global drive efficiency can be significantly

improved for the topology T2, despite of the power losses in

the dc-dc converter. In a similar way to the motoring mode

operation, high efficiency values can be obtained for the drive

main devices, and in particular for the inverter. For low

mechanical speeds, the variable voltage control imposes a

lower system voltage in order to maintain the defined

modulation index. As a consequence, the inverter losses,

namely the switching losses, are reduced. This control strategy

also allows to decrease the motor voltage rms values, which

lead to the subsequent decreasing of the machine losses,

especially the iron losses. However, for higher PMSM speed

values, the global efficiency for topology T2 is lower than for

topology T1. Although the inverter and PMSM efficiency

values are higher for topology T2, under these conditions, the

dc-dc converter efficiency is negatively affected, contributing

to the decrease of the drive overall efficiency.

Table V presents the PMSM power factor and phase-to-

phase voltage TWD values for both topologies and for a load

level equivalent to 50% of the machine rated torque. Once

again, it can be verified that with the variable voltage control

applied to topology T2, it is possible to obtain lower distortion

values for the motor voltages, and therefore for its phase

currents, as well as higher power factor values.

B. Drive Cycle Analysis

In order to evaluate the drive dynamic behavior, for both

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

PM

SM

Pow

er F

acto

r

T1

T2

600 rpm 900 rpm 1200 rpm

Fig. 19 – Power factor results for topologies T1 and T2 for 50% of the PMSM

rated torque under motoring operation.

TABLE IV

EFFICIENCY RESULTS (%), UNDER REGENERATIVE BRAKING OPERATION, FOR

50% OF THE PMSM RATED TORQUE

Topology T1 Topology T2

600

rpm

900

rpm

1200

rpm

600

rpm

900

rpm

1200

rpm

DC-DC

Converter − − − 98.8 97.8 95.7

Inverter 91.1 94.8 96.1 95.9 97.6 97.8

PMSM 81.4 82.9 83.7 82.2 83.6 84.1

Global 74.2 78.7 80.5 77.9 79.8 78.7

TABLE V

TWD AND POWER FACTOR RESULTS, UNDER REGENERATIVE BRAKING

OPERATION, FOR 50% OF THE PMSM RATED TORQUE

Topology T1 Topology T2

600 rpm TWD (%) 186.89 97.93

Power Factor 0.477 0.712

900 rpm TWD (%) 133.21 68.22

Power Factor 0.602 0.820

1200 rpm TWD (%) 75.39 69.75

Power Factor 0.703 0.821

topologies, under motor and regenerative braking modes, a

whole driving cycle analysis is also presented.

Fig. 20 presents the drive cycle used for this purpose. This

profile is similar to ECE 15 urban drive cycle, also integrated

in the first part of the New European Drive Cycle (NEDC)

[33]-[34].

Based on this drive cycle, Fig. 21 presents the time-domain

waveforms of the power drawn from the battery for both

topologies T1 and T2. During the acceleration periods the

power required by the drive system increases proportionally to

the machine speed and reaches larger values than for the

steady-state operation. In steady-state, the PMSM is operating

with a constant mechanical speed and the electromagnetic

torque is less significant. As a consequence, the power drawn

from the battery is constant and relatively low. During the

deceleration periods, a braking torque is developed by the

machine, resulting in a negative power that charges the

battery. Comparing the two considered drive topologies (Fig.

21) it becomes clear that topology T1 requires more battery

output power than topology T2.

Finally, considering the drive energy consumption results

shown in Fig. 22, it can be observed that the energy increases

when the system operates under the motoring mode and

decreases due to the kinetic energy recovery under

regenerative braking. However, the most important conclusion

is that, as expected, topology T2 is the more efficient one for

the considered drive cycle, consuming about 5.62 Wh in

opposition to 5.98 Wh consumed by topology T1. If a drive

cycle corresponding to an extra-urban profile is considered,

the PMSM will operate at higher speeds. Under these

conditions, and taking into account the global drive efficiency

maps presented in Fig. 14 and Fig. 15, the topology T1 will

perform better than topology T2.

VII. CONCLUSIONS

A detailed efficiency analysis of two basic drive train

topologies based on a PMSM and applied to electric/hybrid

vehicles has been presented in this paper. The first topology

comprises a traditional PWM battery-powered inverter, while

in the second one the battery is connected to a bidirectional

dc-dc converter, which supplies the inverter. In addition,

considering this second topology, a variable voltage control

technique applied to the dc-dc converter was presented with

the aim to optimize the global drive performance.

The presented results, in the form of efficiency maps,

provide a very good perspective about the torque/speed

combinations at which a specific propulsion motor drive or

device is most efficient. This allows for better design of these

advanced vehicular systems that make use of electric traction

motors for propulsion, and allow for choosing and optimize

the right kind of technology, in order to improve the system as

a whole.

Regarding the obtained results, it can be concluded that

with the variable voltage control, applied to the second

topology, the inverter efficiency can be significantly

improved, as compared to the first topology. The PMSM

efficiency can also be enhanced, especially for low load

values. As to the global drive efficiency, it is concluded that

for the considered operating conditions, higher efficiency

values can be obtained for the second topology at low speeds

and partial load. However, the inclusion of a dc-dc converter

brings some disadvantages such as increased complexity, cost

and size. Comparing both topologies, it can also be concluded

0 20 40 60 80 100 120 140 160 180 2000

200

400

600

800

1000

Time (s)

PM

SM

Mec

han

ical

Sp

eed

(rp

m)

Fig. 20 – Considered drive cycle.

0 20 40 60 80 100 120 140 160 180 200−300

−200

−100

0

100

200

300

400

500

600

700

Time (s)

Bat

tery

Ou

tpu

t P

ow

er (

W)

T1

T2

Fig. 21 – Time-domain waveforms of the battery output power for topologies

T1 and T2 and for the considered drive cycle.

0 20 40 60 80 100 120 140 160 180 2000

1

2

3

4

5

6

7x 10

−3

Time (s)

Dri

ve

En

erg

y C

on

sum

pti

on

(k

Wh

)

T1

T2

Fig. 22 – Time-domain waveforms of the drive energy consumption for

topologies T1 and T2 and for the considered drive cycle.

that the maximum efficiency value for the first topology is

achieved at high speeds, while for the second one it is reached

at low speeds.

The presented voltage distortion and power factor results

also allow to demonstrate that a better performance can be

obtained for the second topology with the variable voltage

control technique. The obtained distortion results are

particularly important since high acoustic noise levels are

typically associated with high distortion values. Hence, this

topology also allows to reduce the overall acoustic noise

generated by the traction motor.

Finally, considering all this and taking into account that for

an urban driving cycle a traction machine operates most

frequently at light loads and low speeds [5], the electric drive

train system should be designed to operate at maximum

efficiency and minimum acoustic noise in this region.

Therefore, the presented variable voltage control technique,

applied to the second topology, allows to fulfill these

requirements.

APPENDIX

TABLE VI

PARAMETERS OF THE USED PMSM

Power P 2.2 kW

Torque T 12 Nm

Voltage V 316 V

Current I 5.3 A

Number of pole pairs p 5

Armature resistance Rs 1.72 Ω

Iron losses resistance Rc 700 Ω

Magnet flux linkage ÃPM 0.244 Wb

d-axis inductance Ld 20.5 mH

q-axis inductance Lq 20.5 mH

Moment of inertia J 0.007 Kg.m2

REFERENCES

[1] A. Y. Saber and G. K. Venayagamoorthy, “Plug-in vehicles and

renewable energy sources for cost and emission reductions”, IEEE

Transactions on Industrial Electronics, vol. 58, no. 4, pp. 1229-1238,

April 2011.

[2] C. C. Chan, A. Bouscayrol and K. Chen, “Electric, hybrid, and fuel-cell

vehicles: architectures and modeling”, IEEE Transactions on Vehicular

Technology, vol. 59, no. 2, pp. 589-598, February 2010.

[3] K. T. Chau, C. C. Chan and L. Chunhua, “Overview of permanent-

magnet brushless drives for electric and hybrid electric vehicles”, IEEE

Transactions on Industrial Electronics, vol. 55, no. 6, pp. 2246-2257,

June 2008.

[4] M. Zeraoulia, M. E. H. Benbouzid and D. Diallo, “Electric motor drive

selection issues for HEV propulsion systems: a comparative study”,

IEEE Transactions on Vehicular Technology, vol. 55, no. 6, pp. 1756-

1764, November 2006.

[5] Z. Q. Zhu and D. Howe, “Electrical machines and drives for electric,

hybrid, and fuel cell vehicles”, Proceedings of the IEEE, vol. 95, no. 4,

pp. 746-765, April 2007.

[6] K. I. Laskaris and A. G. Kladas, “Internal permanent magnet motor

design for electric vehicle drive”, IEEE Transactions on Industrial

Electronics, vol. 57, no. 1, pp. 138-145, January 2010.

[7] C. Liu, K. T. Chau and J. Z. Jiang, “A permanent-magnet hybrid

brushless integrated starter–generator for hybrid electric vehicles”, IEEE

Transactions on Industrial Electronics, vol. 57, no. 12, pp. 4055-4064,

December 2010.

[8] M. Shen and F. Z. Peng, “Converter systems for hybrid electric

vehicles”, International Conference on Electrical Machines and

Systems, pp. 2004-2010, 8-11 October, 2007.

[9] J. S. Lai and D. J. Nelson, “Energy management power converters in

hybrid electric and fuel cell vehicles”, Proceedings of the IEEE, vol. 95,

no. 4, pp. 766-777, April 2007.

[10] C. C. Chan, “The state of the art of electric, hybrid, and fuel cell

vehicles”, Proceedings of the IEEE, vol. 95, no. 4, pp. 704-718, April

2007.

[11] A. Kawahashi, “A new-generation hybrid electric vehicle and its

supporting power semiconductor devices”, International Symposium on

Power Semiconductor Devices and ICs, pp. 23-29, 24-27 May, 2004.

[12] K. Asano, Y. Inaguma, H. Ohtani, E. Sato, M. Okamura and S. Sasaki,

“High performance motor drive technologies for hybrid vehicles”,

Power Conversion Conference, pp. 1584-1589, 2-5 April, 2007.

[13] E. Sato, “Permanent magnet synchronous motor drives for hybrid

electric vehicles”, IEEJ Transactions on Electrical and Electronic

Engineering, vol. 2, no. 2, pp. 162-168, 2007.

[14] Z. Amjadi and S. S. Williamson, “A novel control technique for a

switched-capacitor-converter-based hybrid electric vehicle energy

storage system”, IEEE Transactions on Industrial Electronics, vol. 57,

no. 3, pp. 926-934, March 2010.

[15] M. B. Camara, H. Gualous, F. Gustin, A. Berthon and B. Dakyo,

“DC/DC converter design for supercapacitor and battery power

management in hybrid vehicle applications − polynomial control

strategy”, IEEE Transactions on Industrial Electronics, vol. 57, no. 2,

pp. 587-597, February 2010.

[16] Z. Amjadi and S. S. Williamson, “Power-electronics-based solutions for

plug-in hybrid electric vehicle energy storage and management

systems”, IEEE Transactions on Industrial Electronics, vol. 57, no. 2,

pp. 608-616, February 2010.

[17] F. H. Khan, L. M. Tolbert and W. E. Webb, “Hybrid electric vehicle

power management solutions based on isolated and nonisolated

configurations of multilevel modular capacitor-clamped converter”,

IEEE Transactions on Industrial Electronics, vol. 56, no. 8, pp. 3079-

3095, August 2009.

[18] A. Emadi, Y. J. Lee and K. Rajashekara, “Power electronics and motor

drives in electric, hybrid electric, and plug-in hybrid electric vehicles”,

IEEE Transactions on Industrial Electronics, vol. 55, no. 6, pp. 2237-

2245, June 2008.

[19] T. Azib, O. Bethoux, G. Remy, C. Marchand and E. Berthelot, “An

innovative control strategy of a single converter for hybrid fuel

cell/supercapacitor power source”, IEEE Transactions on Industrial

Electronics, vol. 57, no. 12, pp. 4024-4031, December 2010.

[20] S. Williamson, M. Lukic and A. Emadi, “Comprehensive drive train

efficiency analysis of hybrid electric and fuel cell vehicles based on

motor-controller efficiency modeling”, IEEE Transactions on Power

Electronics, vol. 21, no. 3, pp. 730-740, May 2006.

[21] A. S. Samosir and A. H. M. Yatim, “Implementation of dynamic

evolution control of bidirectional DC–DC converter for interfacing

ultracapacitor energy storage to fuel-cell system”, IEEE Transactions on

Industrial Electronics, vol. 57, no. 10, pp. 3468-3473, October 2010.

[22] M. Zandi, A. Payman, J.-P. Martin, S. Pierfederici, B. Davat and F. M.

Tabar, “Energy management of a fuel cell/supercapacitor/battery power

source for electric vehicular applications”, IEEE Transactions on

Vehicular Technology, vol. 60, no. 2, pp. 433-443, February 2011.

[23] J. Bauman and M. Kazerani, “A novel capacitor-switched regenerative

snubber for DC/DC boost converters”, IEEE Transactions on Industrial

Electronics, vol. 58, no. 2, pp. 514-523, February 2011.

[24] J. O. Estima and A. J. M. Cardoso, “Performance analysis of a PMSM

drive for hybrid electric vehicles”, International Conference on

Electrical Machines, 6 pp., 6-8 September 2010.

[25] S. Morimoto, Y. Tong, Y. Takeda and T. Hirasa, “Loss minimization

control of permanent magnet synchronous motor drives”, IEEE

Transactions on Industrial Electronics, vol. 41, no. 5, pp. 511-517,

October, 1994.

[26] N. Urasaki, T. Senjyu and K. Uezato, “A novel calculation method for

iron loss resistance suitable in modeling permanent-magnet synchronous

motors”, IEEE Transactions on Energy Conversion, vol. 18, no. 1, pp.

41- 47, March 2003.

[27] Y. K. Chin and J. Soulard, “Modeling of iron losses in permanent

magnet synchronous motors with field weakening capability for electric

vehicles”, International Journal of Automotive Technology, vol. 4, no. 2,

pp. 87-94, March, 2003.

[28] N. Urasaki, T. Senjyu and K. Uezato, “Relationship of parallel model

and series model for permanent magnet synchronous motors taking iron

loss into account”, IEEE Transaction on Energy Conversion, vol. 19, no.

2, pp. 265-270, June, 2004.

[29] J. O. Estima and A. J. M. Cardoso, “Performance evaluation of DTC-

SVM permanent magnet synchronous motor drives under inverter fault

conditions", IEEE Industrial Electronics Conference, Porto, Portugal,

pp. 1228-1233, 3-5 November, 2009.

[30] S. Bolognani, L. Peretti, M. Zigliotto and E. Bertotto, “Commissioning

of electromechanical conversion models for high dynamic PMSM

drives”, IEEE Transactions on Industrial Electronics, vol. 57, no. 3, pp.

986-993, March 2010.

[31] O. Tremblay, L.-A. Dessaint and A.-I. Dekkiche, “A generic battery

model for the dynamic simulation of hybrid electric vehicles”, IEEE

Vehicle Power and Propulsion Conference, pp. 284-289, 9-12

September 2007.

[32] J. Holtz, “Pulsewidth modulation − a survey”, IEEE Transactions on

Industrial Electronics, vol. 39, no. 5, pp. 410-420, October 1992.

[33] P. H. Nguyen, E. Hoang, M. Gabsi, L. Kobylanski and D. Condamin,

“Permanent magnet synchronous machines: performances during driving

cycles for a hybrid electric vehicle application”, IEEE International

Symposium on Industrial Electronics, pp. 1432-1438, 4-7 July 2010.

[34] A. Froberg and L. Nielsen, “Efficient drive cycle simulation”, IEEE

Transactions on Vehicular Technology, vol. 57, no. 3, pp. 1442-1453,

May 2008.

Jorge O. Estima was born in Aveiro, Portugal in

1984. He received the E. E. diploma from University

of Coimbra, Portugal, in 2007. Since then, he has

been a PhD student at the Department of Electrical

and Computer Engineering of the Faculty of Sciences

and Technology of the University of Coimbra,

Portugal. His research interests are focused on

condition monitoring and diagnostics of power

electronics and AC motor drives, fault-tolerant

variable speed AC drives, traction motor drives

applied to electric/hybrid vehicles and wind energy conversion systems.

Antonio J. Marques Cardoso (S’89, A’95, SM’99)

was born in Coimbra, Portugal, in 1962. He received

the Electrical Engineering diploma, the Dr. Eng.

degree and the Habilitation degree, all from the

University of Coimbra, Coimbra, Portugal, in 1985,

1995 and 2008, respectively. From 1985 until 2011

he was with the University of Coimbra, Coimbra,

Portugal, where he was Director of the Electrical

Machines Laboratory. Since 2011, he has been with

the University of Beira Interior (UBI), Covilhã,

Portugal, where he is a Full Professor at the Department of Electromechanical

Engineering. His teaching interests cover electrical rotating machines,

transformers, and maintenance of electromechatronic systems and his research

interests are focused on condition monitoring and diagnostics of electrical

machines and drives. He is the author of a book entitled Fault Diagnosis in

Three-Phase Induction Motors (Coimbra, Portugal: Coimbra Editora, 1991),

(in Portuguese) and about 300 papers published in technical journals and

conference proceedings.