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3528 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 7, JULY 2013

DTC Scheme for a Four-Switch Inverter-FedInduction Motor Emulating the Six-Switch

Inverter OperationBassem El Badsi, Badii Bouzidi, and Ahmed Masmoudi

AbstractThis paper proposes a novel direct torque control(DTC) strategy for induction motor (IM) drives fed by a four-switch three-phase inverter (FSTPI). The introduced strategy isbased on the emulation of the operation of the conventional six-switch three-phase inverter (SSTPI). This has beenachieved thanksto a suitable combination of the four unbalanced voltage vectorsintrinsically generated by the FSTPI, leading to the synthesis of thesix balanced voltage vectors of the SSTPI. This approach has beenadopted in the design of the vector selection table of the proposedDTC strategy which considers a subdivision of the Clarke plane

into six sectors. Simulation results have revealed that, thanks tothe proposed DTC strategy, FSTPI-fed IM drives exhibit interest-ing performance. These have been experimentally validated andcompared to the ones yielded by the Takahashi and the basic DTCstrategies dedicated to the SSTPI and to the FSTPI, respectively.

Index TermsBalanced voltage vectors, direct torquecontrol (DTC), four-switch/six-switch three-phase inverter(FSTPI/SSTPI), induction motor (IM) drive, vector selectiontable.

I. INTRODUCTION

IN RECENT years, direct torque control (DTC) strategies

of induction motor (IM) drives have been widely imple-mented in industrial variable speed applications. Introduced in

the middle of the 1980s, the first DTC strategy involves a simple

control scheme which makes it possible rapid real-time imple-

mentation [1]. Since then, several investigations carried out in

order to improve the performance of the original DTC strategy.

The major focused features are the uncontrolled switching fre-

quency of the inverter and the high torque ripple resulting from

the use of flux and torque hysteresis controllers.

Currently and more than two decades of investigation, several

DTC strategies have been proposed so far [2][5]. These could

be classified within four major categories: 1) strategies consid-

ering variable hysteresis band controllers [6]; 2) strategies withspace vector modulation (SVM)-based control of the switch-

ing frequency [7], [8]; 3) strategies using predictive control

Manuscript received April 13, 2012; revised June 5, 2012; acceptedOctober 6, 2012. Date of current version December 24, 2012. The work wassupported by the Allison Transmission Division of General Motors, Indianapo-lis, IN. Recommended for publication by Associate Editor P. Chi-Kwong Luk.

The authors are with the Department of Electromechanical Engineering,Sfax Engineering School, University of Sfax, 3029 Sfax, Tunisia (e-mail:[email protected]; [email protected]; [email protected]).

Digital Object Identifier 10.1109/TPEL.2012.2225449

schemes [9][11]; and 4) strategies built around intelligent con-

trol approaches [12], [13]. Nevertheless, the gained performance

is allied to significant increase of implementation schemes.

Commonly, the voltage source inverter (VSI) feeding IM un-

der DTC is the six-switch three-phase inverter (SSTPI). This

said, some applications such as electric and hybrid propulsion

systems, should be as reliable as possible. Within this require-

ment, the reconfiguration of the SSTPI into a four-switch three-

phase inverter (FSTPI), in case of a switch/leg failure, is cur-rently given an increasing attention [14][16]. A DTC strategy

dedicated to FSTPI-fed IM drives has been proposed in [17].

In spite of its simplicity, this strategy is penalized by the low

dynamic and the high ripple of the torque. These drawbacks are

due to the application of unbalanced voltage vectors to control

flux and torque with a subdivision of the Clarke plane limited

to four sectors.

Recently, an attempt to discard the previously described dis-

advantages has been proposed in [18] where a DTC scheme

using a 16-sector vector selection table has been implemented.

Nevertheless, it has been noted that the drive performance re-

mains relatively low due to the increase of the CPU time which

is linked to the complexity of the involved vector selection ta-ble. In order to achieve a constant switching frequency and

to decrease the torque ripple, many DTC schemes based on

SVM, using the FSTPI as a VSI, dedicated to control induction

and permanent-magnet synchronous motors have been reported

in the literature [19], [20]. These strategies offer high perfor-

mance in terms of torque ripple reduction allied to the control

of the inverter switching losses. However, these performances

are compromised by the complexity of their implementation

schemes.

This paper proposes a new DTC strategy dedicated to FSTPI-

fedIM drives. It is based on theemulation of theSSTPI operation

thanks to the synthesis of an appropriate vector selection table,which is addressed by hysteresis controllers. The resulting sim-

plicity of the implementation scheme makes the strategy very

attractive in many applications, such as the automotive one.

II. DTC OF FSTPI-FED IM DRIVES: BACKGROUND

A. DTC Basis

DTC strategies allow a direct control of the motor variables

through an appropriate selection of the inverter control signals,

in order to fulfill the requirements as whether the stator flux and

torque need to be increased, decreased, or maintained. These

decisions are achieved according to the output c of the flux

0885-8993/$31.00 2012 IEEE


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EL BADSI et al.: DTC SCHEME FOR A FOUR-SWITCH INVERTER-FED INDUCTION MOTOR EMULATING 3529

induction

motor

V ector

Selection

Ta ble

InductionMotor

s

s

sTorqueEstimator

Stator FluxEstimator

si

Clarke

Tr ansform

si

SpeedControlle r

(PI)

c

-+s*Two-Level

FluxController

mm*

+-

c

+ -Tem*

Tem Two-LevelTorque

Controlle r

S2

Vdc

2

Vdc

2

S 1

s

a

bo

c

Fig. 1. Implementation scheme of the DTC strategy dedicated to FSTPI-fedIM drives.

hysteresis controller, the output c of the torque hysteresis con-troller, and the angular displacement s of the stator flux vectors in the Clarke () plane.

The dynamic ofs is governed by the stator voltage equation

expressed in the stationary reference frame, as follows:

d

dts = Vs rsIs (1)

where Vs , Is , and rs are the stator voltage vector, current vec-tor, and resistance, respectively. Neglecting the voltage drop

rsIs across the stator resistance, and taking into account thatthe voltage vector is constant in each sampling period Ts , thevariation of the stator flux vector turns to be proportional to the

applied voltage vector.

Maintaining the stator flux constant, the variation of the elec-

tromagnetic torque Tem depends on the direction of the appliedvoltage vector, such that:

Tem = NpM

lr ls M2ssr sin (2)

where sr is the rotor flux vector referred to the stator, is theangular shift between the stator and rotor fluxes, Np is the polepair number, and ls , lr , andMare the stator self-inductance, the

rotor self-inductance, and the mutual inductance, respectively.The implementation scheme of the DTC strategy dedicated

to a FSTPI-fed IM, shown in Fig. 1, has the same layout as the

one of the basic DTC strategy initially proposed in [1], except

that

1) the SSTPI inverter is reconfigured to a FSTPI. Such a

reconfiguration is carried out by adding to the former three

extra TRIACs with three fast acting fuses [21][24],

2) the three-level hysteresis controller in the torque loop is

substituted by a two-level hysteresis controller. As will

be depicted in Section III, this substitution is motivated

by the fact that no zero voltage vector is involved in the

proposed DTC scheme.

TABLE ISWITCHING STATES, STATOR PHASE VOLTAGES, THEIR Clarke COMPONENTS

AND CORRESPONDING VOLTAGE VECTORS

(S1 S2) Vas Vbs Vcs Vs Vs Vi

(0 0) Vdc6 Vdc6

Vdc3

Vdc2

6 Vdc

2

2V1

(1 0) Vdc2 Vdc2 0 3Vdc26 Vdc22 V2

(1 1) Vdc6Vdc6

Vdc3

Vdc2

6Vdc

2

2V3

(0 1) Vdc2Vdc2 0

3Vdc2

6Vdc

2

2V4

V 3 (1 1)

V 1 (0 0)

V 4 (0 1)

V 3T s

V 1T s V 2T s

V 4T s

s

V 2 (1 0)

III

IV

II

I

+

Fig. 2. Unbalanced active voltage vectors generated by the FSTPI.

B. Intrinsic Voltage Vectors of the FSTPI

The FSTPI topology consists of a two-leg inverter as illus-

trated in Fig. 1. Two among the three phases of the motor areconnected to the FSTPI legs, while the third one is connected to

the middle point of the dc-bus voltage.

Let us assume that the states of the four insulated-gate bipolar

transistors (IGBTs) of the FSTPI are denoted by the binary

variables S1 to S4 , where the binary 1 corresponds to an ONstate and the binary 0 indicates an OFF state. The IM statorvoltages are expressed in terms of the states (S1 and S2 ) of theupper IGBTs, as follows:

Vas

Vbs

Vcs

=

Vdc6

4 2 12 4 1

2 2 2

S1

S2

1

. (3)

The Clarke transform applied to the stator voltages yields:

Vs

Vs

=

2

3

1

12 12

0

3

2

32

VasVbs

Vcs

(4)

Four combinations of the states of the upper IGBTs are char-

acterized by four active voltage vectors (V1 to V4) in the plane, which are given in Table I.

Fig. 2 shows the four active voltage vectors represented in

the plane. These vectors have unbalanced amplitudes and

are shifted by an angle of2 . Indeed, vectors V1 and V3 have


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TABLE IIVECTOR SELECTION TABLE OF THE BASIC DTC STRATEGY

c +1 +1 1 1c +1 1 +1 1

Sector I V3 V2 V4 V1

Sector II V4 V3 V1 V2

Sector III V1 V4 V2 V3

Sector IV V2 V1 V3 V4

an amplitude of Vdc /

6, while vectors V2 and V4 have anamplitude ofVdc /

2.

C. Limitations of the Basic DTC of a FSTPI-Fed IM

The basic DTC of an IM fed by the FSTPI is based on the

subdivision of the plane into four sectors [17], limited bythe four active voltage vectors as shown in Fig. 2. The vector

selection table corresponding to the basic strategy is presentedin Table II.

Accounting for the symmetry of the four sectors, the follow-

ing analysis of the torque and flux variations, will be limited to

sector I, considering two cases:

1) the initial stator flux vector s1 is held by vector V2 ;

2) the initial stator flux vector s1 is held by vector V3 .

Equation (1) could be rewritten as follows:

is2 = s1 + (Vi rsIs)Ts (5)where Vi (1 i 4) is the voltage vector generated by theFSTPI.

Fig. 3 shows different phasor diagrams of (5), consideringboth cases previously cited with four scenarios selected from

the vector selection table, for each. One can notice the following

remarks which deal with the torque dynamic.

1) The application of voltage vectors V1 or V3 leads to a

low torque dynamic if:

a) s1 is close to vector V2 due to the low amplitude

ofV1 and V3 [see Fig. 3(a1) and (a3)];

b) s1 is close to vectorV3 due to the low angular shift

of the flux vector [see Fig. 3(b1) and (b3)]. It is to

be noted that the torque command c of the controlcombinations (c = 1, c = +1) corresponding tosector II and (c = +1, c = +1) corresponding to

sector I could not be achieved by the application ofvectors V1 and V3 , respectively.


low torque dynamic ifs1 is close to vector V2 due to

the low angular shift of the flux vector [see Fig. 3(a2)

and (a4)]. One can notice that the control combina-

tions (c = +1, c = +1) corresponding to sector IV and(c = 1, c = +1) corresponding to sector I could notbe achieved with the application of voltage vectors V2and V4 , respectively.


high torque dynamic ifs1 is located near vector V3 [see

Fig. 3(b2) and (b4)].

Concerning the flux dynamic, one can notice the following.

1) High flux variations leading to overshoots or undershoots

outside the flux hysteresis band with:

a) the application of voltage vectors V1 or V3 ifs1is close to vector V3 [see Fig. 3(b1) and (b3)];

b) the application of voltage vectors V2 or V4 ifs1is close to vector V2 [see Fig. 3(a2) and (a4)].

2) The flux command c is not achieved with the applicationof:

a) vector V1 in sector IV corresponding to the control

combination (c = +1, c = 1) as illustrated inFig. 3(a1);

b) vector V2 in sector I corresponding to the control

combination (c = +1, c = 1) as illustrated inFig. 3(b2);

c) vector V3 in sector I corresponding to the control

combination (c = +1, c = +1) as illustrated inFig. 3(a3);

d) vector V4 in sector II corresponding to the control

combination (c = +1, c = +1) as illustrated inFig. 3(b4).

From the previous analysis, one can clearly notice that the

basic DTC strategy presents different limitations. These could

be eradicated considering the introduced DTC strategy which

will be developed in the following section.

III. PROPOSED DTC STRATEGY

A. Approach to Generate Balanced Voltages by the FSTPI

The proposed DTC strategy is based on the emulation of

SSTPI operation by the FSTPI. This has been achieved through

the generation of six balanced voltage vectors using the fourintrinsic ones of the FSTPI. The generated vectors have the

same amplitude and angular shift as those of the SSTPI.

Basically, the active voltage vectors Vk , with 1 k 6,yielded by the SSTPI have an amplitude Vk equal to

23Vdc ,

where Vdc is the dc-bus voltage. For the same value of Vdc , thevoltage vectors Vi , with 1 i 4, generated by the FSTPI,present unbalanced amplitudes Vi , such that:

V1 = V3 =Vdc

6= 12Vk

V2 = V4 =Vdc

2=

3

2 Vk .(6)

Therefore, a dual application of the voltage vector V1 (re-

spectively, V3) of the FSTPI, leads to the generation of the

voltage vector V11 (respectively, V33 ), as shown in Fig. 4. It

is to be noted that V11 and V33 are identical to two vectors

among the six generated by the SSTPI.

Now, let us call Vij the voltage vectors resulting from the

sums of successive voltage vectors Vi and Vj , with 1 i 4and 1 j 4. As far as the angular shift between two succes-sive voltage vectors is equal to 2 , the amplitude Vij of vectorsVij can be expressed as follows:

Vij

= Vi

2 + Vj

2 = 16

+1

2V

dc= 2

3V

dc= V

k. (7)


4/11


Fig. 3. Phasor diagrams describing the evolution of the stator flux vector in the case where it is located in the limits of sector I. Legend: (a) initial flux vectors1 held by the voltage vector V2 , (b) initial flux vector s1 held by the voltage vector V3 .

Fig. 4. Generation of the SSTPI active voltage vectors using the four unbal-anced voltage ones of the FSTPI.

One can notice that the voltage vectorsVij have the same ampli-

tude as the ones generated by the SSTPI. Beyond the amplitude,

the four generated vectors, named V12 , V23 , V34 , and V41 , as

shown in Fig. 4, share the same phases with the four remaining

active voltage vectors of the SSTPI. Table III summarizes the

Clarke components of the six voltage vectors generated by the

FSTPI considering the previously described approach.

TABLE IIIClarke COMPONENTS OF THE GENERATED VOLTAGE VECTORS

Vij V23 V33 V34 V41 V11 V12

Vs

23Vdc Vdc6 Vdc6

23Vdc Vdc6 Vdc6

Vs 0Vdc

2Vdc

20 Vdc

2Vdc

2

Following the generation of six balanced active voltage vec-

tors (V23 , V33 , V34 , V41 , V11 , and V12 ), the plane turnsto be subdivided into six symmetric sectors as illustrated in

Fig. 4. Moreover, zero voltage vectors can be achieved through

the application of two opposite intrinsic ones.

The previously described approach represents a great control

benefit so far as several DTC strategies implemented in SSTPI-

fed IM drives could be applied to FSTPI-fed IM ones.

B. Vector Selection Table of the Proposed DTC Strategy

The proposed DTC strategy is inspired from the earlier one

introduced by Takahashi [1]. For the sake of reduction of the

switching frequency as well as the torque ripple, the control

combinations (c = 1, c = 0) are omitted using a two-levelhysteresis controller in the torque loop.

The synthesis of the vector selection table of the proposed

DTC strategy is based on the approach described in the previ-

ous paragraph. Reaching this advanced step, one can wonder:

how the control combinations (c = 1, c = 1) could be


5/11


Fig. 5. Applied voltage vectors in the case wheres is located in sector I.

achieved applying the generated balanced voltage vectors? Toanswer this question, the following approach has been adopted.

1) The application ofV1 (respectively, V3) during two suc-

cessive sampling periods 2Ts allows the generation ofV11 (respectively, V33 ),

2) The application of two consecutive voltage vectorsVi and

Vj during two successive sampling periods leads to the

generation ofVij .

As a result, the equivalent voltage vectors per sampling period

Ts generated by the FSTPI, considering the adopted approach,can be expressed as:

V11H =12V11 = V1

V33H =12V33 = V3

VijH =12Vij

(8)

where subscript H indicates the half of the corresponding volt-

age vector.

In what follows, the synthesis of the vector selection table

will be limited to sector I (6 s 6 ). In this case and asshown in Fig. 5, the following voltage vectors are applied dur-

ing a sampling period, according to the corresponding control

combinations:

V3 for (c = +1, c = +1)

V12H for (c = +1, c = 1)V34H for (c = 1, c = +1)V1 for (c = 1, c = 1).

In order to emulate the operation of the SSTPI, each control

combination (c , c) should be maintained during two samplingperiods 2Ts , which yields the application of:

V33 for (c = +1, c = +1) V3 then V3V12 for (c = +1, c = 1) V1 then V2V34 for (c = 1, c = +1) V3 then V4V11 for (c = 1, c = 1) V1 then V1 .

Fig. 6. Control combinations (c , c ), desired voltage vectors per Ts , equiv-alent voltage vectors during 2Ts , and applied voltage vectors per Ts .

TABLE IVDESIRED VECTOR SELECTION TABLE

c +1 +1

1

1

c +1 1 +1 1Sector I V3 V12H V34H V1

Sector II V34H V23H V41H V12H

Sector III V41H V3 V1 V23H

Sector IV V1 V34H V12H V3

Sector V V12H V41H V23H V34H

Sector VI V23H V1 V3 V41H

TABLE VIMPLEMENTED VECTOR SELECTION TABLE

c +1 +1 1 1c +1 1 +1 1

Periods Ts 1st 2nd 1st 2nd 1st 2nd 1st 2nd

Sector I V3 V1 V2 V3 V4 V1

Sector II V3 V4 V2 V3 V4 V1 V1 V2

Sector III V4 V1 V3 V1 V2 V3

Sector IV V1 V3 V4 V1 V2 V3

Sector V V1 V2 V4 V1 V2 V3 V3 V4

Sector VI V2 V3 V1 V3 V4 V1

An illustration of the previously described control scenarios is

provided in Fig. 6. An extension of thesynthesis to theremaining

sectors has led to the vector selection table given in Table IV.

The inputs (c , c, and s ) of the vector selection table shouldbe maintained during 2Ts which yields the implemented vectorselection table provided in Table V. It is to be noted that both

intrinsic and compoundedvoltage vectors are involved in sectors

I, III, IV, and VI, while in sectors II and V, only the compounded

voltage vectors are applied. Thus, one can expect an increase of

the switching frequency in sectors II and V, with respect to the

one in the remaining sectors.


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2.84 2.86 2.88 2.9 2.92 2.94300

200

100

0

100

200

300

StatorVoltageV

as(V)

2.84 2.86 2.88 2.9 2.92 2.94

1

2

34

5

6

Sectors

)d()a(

2.84 2.86 2.88 2.9 2.92 2.94300

200

100

0

100

200300

StatorVoltageV

cs(V

)

2.84 2.86 2.88 2.9 2.92 2.941

1.1

1.2

StatorFlux(Wb)

)e()b(

2.84 2.86 2.88 2.9 2.92 2.942

1

0

1

2

Time (s)

StatorCurrents(A)

2.84 2.86 2.88 2.9 2.92 2.940

1

2

Time (s)

Torque(Nm)

)f()c(

Fig. 7. Simulated steady-state variables yielded by the introduced DTC strategy for a reference speed m = 50 rad/s and a load torque Tl = 1 Nm. Legend:(a) stator a-phase voltage, (b) stator c-phase voltage, (c) stator phase currents, (d) sector succession described in the plane, (e) stator flux amplitude and itsreference, (f) electromagnetic torque.

IV. SIMULATION-BASED INVESTIGATION OF PERFORMANCE

OF THE DTC STRATEGY

The ratings and parameters of the induction machine, used in

the simulation as well as in the experimental study, are listed in

Tables VII and VIII of the Appendix.

The sampling period Ts is equal to 100 s, except for the fluxand torque controllers as well as the function enabling the local-

ization ofs in the plane, where the sampling period is keptequal to 2Ts . Considering the power invariant Clarke transfor-mation, the amplitude of the reference stator flux is kept constant

equal to

3 times its rated value. A bandwidth of the stator fluxcontroller is equal to 0.02 Wb which represents 1.8% of thereference stator flux. A bandwidth of the electromagnetic torque

controller is equal to0.04 Nm which represents1.6% of therated torque. For the sake of a safe operation of the inverter,

the dc-bus voltage Vdc is limited to 400 V in both experimentaltests and simulation works. Under this value ofVdc , it has beennoticed that the maximum stator frequency is limited to 40 Hz

(0.1 Hz/V) in the case of the SSTPI and to 20 Hz (0.05 Hz/V)

in the case of the FSTPI. These ratio are directly linked to the

amplitude of the applied voltage vectors. Indeed, the amplitude

of the equivalent voltage vectors generated by the FSTPI is the

half of the one of the voltage vectors generated by the SSTPI,

as depicted in (8).

Fig. 7 shows some features characterizing the steady-state

operation of the IM under the control of the proposed DTC

strategy, for a mechanical speed m = 50 rad/s and a constantload torque Tl = 1 Nm. Fig. 7(a) and (b) illustrates the wave-forms of the stator phase voltages Vas and Vcs , respectively.Fig. 7(c) shows the stator phase currents. As can be noticed, the

stator phase currents are almost balanced, although the stator

phase voltage Vcs has an amplitude lower than the one ofVas .

Fig. 7(d)(f) shows the sector succession, the stator flux,

and the electromagnetic torque, respectively. The analysis of

Fig. 7(e) with respect to Fig. 7(d) clearly highlights that a demag-

netization appears at the beginning of each sector. For instance,

ifs is located in the beginning of sector I, the corresponding

control combination (c = +1, c = +1) is achieved by the ap-plication of the voltage vectorV3 . This leads to a decrease of the

stator flux due to the voltage drop. Such a phenomenon also oc-

curs in the Takahashi DTC strategy implemented in SSTPI-fed

IM drives [1].

Referring to Fig. 7(d), and (f), one can notice the increasing

of the torque ripple frequency in sectors II and V. Indeed, during

these sectors and as depicted in Table V, each control combi-

nation (c , c) is achieved by the application of two differentvoltage vectors, yielding a compounded voltage vector.

In order to highlight the appropriateness of the application of

the compounded voltage vectors to achieve the corresponding

control combinations, these have been kept unchanged during

4Ts through the increase of the hysteresis bands of the torqueand flux controllers. The resulting flux and torque responses are

illustrated in Fig. 8 with s located in sector I.Fig. 8(a) treats the case where the sequence of voltage vectors

V1 ;V2 is applied. One can notice an increase of the average

value of the flux and a decrease of the torque one. This state-

ment confirms the appropriateness of such a sequence to achieve

the control combination (c = +1, c = 1) as synthesized inTable V. The same reasoning has been adopted in the case of the

sequence of voltage vectors V3 ;V4 . The obtained results are

illustrated in Fig. 8(b) where a decrease of the average value of

the flux and an increase of the torque one are noticed. Thus, the

desired control combination (c = 1, c = +1) is achievedby the applied sequence.


7/11


(a) (b)

Fig. 8. Evolutions of the stator flux and the electromagnetic torque over four sampling periods in the case wheres is located in sector I. Legend: (a) applicationof the voltage vector sequence V1 ;V2 ;V1 ;V2 to achieve the control combination (c = +1, c = 1), (b) application of the voltage vector sequenceV3 ;V4 ;V3 ;V4 to achieve the control combination (c = 1, c = +1).

Fig. 9. Schematic block diagram of the developed experimental platform.

V. EXPERIMENTAL VALIDATION

For the sake of validation, the proposed DTC strategy has

been implemented in a test bench built around a TMS320F240DSP-based digital controller. A schematic block diagram of the

experimental platform is shown in Fig. 9.

The sampling period, the amplitude of the reference stator

flux, the bandwidths of the controllers, and the dc-bus voltage

have been kept the same as in the simulation corresponding

to Fig. 7. The presented experimental results characterize the

steady-state operation of the IM.

A. Analysis of the Performance of the Proposed DTC Strategy

In what follows is considered the operation of the IM under

a low and a high values of the speed. The corresponding exper-

imental results are presented in Fig. 10 with subscript 1 form = 7 rad/s (stator frequency fs=2.5 Hz) and subscript 2for m = 62 rad/s (fs=20 Hz).

The stator a-phase voltage Vas and current ias are shown inFig. 10(a). The stator c-phase voltage Vcs and current ics areshown in Fig. 10(c). From the waveforms of the stator phase

voltages, one can notice the effect of the unbalanced capacitor

voltages affecting the experimental results especially at high

speeds. This effect is highlighted by the difference between the

waveforms of ias and ics . Obviously, this drawback does notaffect simulation results as illustrated in Fig. 7.

The harmonic spectra of ias and ics are shown in Fig. 10(b)

and (d), respectively. Under low-speed operation (fs=2.5 Hz),

TABLE VIRATIO OF THE AMPLITUDES OF THE INFLUENT HARMONICS WITH RESPECT TO

THE FUNDAMENTAL ONE

ias icsHarmonic 2nd 3rd 5th 2nd 3rd 5th

fs=2.5Hz 8% 13.8% 9.5% 11%fs=20Hz 12% 13% 12.5% 7% 4% 8.5%

the second and the third harmonics present higher amplitudes

compared to the ones of the other ranks. While in the case of

high-speed operation (fs=20 Hz), the second, the third, andthe fifth harmonics present higher amplitudes compared to the

ones of the other ranks. Table VI summarizes the ratio of the

amplitudes of the influent harmonics to the fundamental one.

B. Comparative Study

In order to highlightthe performance gainedby theintroducedDTC scheme, the resulting steady-state features are compared

to the ones obtained following the implementation of the basic

DTC strategy. Fig. 11 illustrates the waveforms ofVas , ias , Vcs ,and ics and the harmonic spectra of ias and ics following theimplementation of the proposed DTC strategy (subscript 1)

and the basic DTC one (subscript 2) for m = 50 rad/s andTl = 1 Nm.

The considered comparison criterion is the total harmonic

distortion (THD) of currents ias and ics , which is expressed as:

THD =n= 1

I2n

I1 (9)

where I1 and In are the amplitudes of the fundamental and thenth harmonic ranks ofias and ics , with n = 2, 3, 5, and 7.

From the analysis of Fig. 11(b) and (d), it has been found that

the THD of ias is equal to 11% and 17.4% in the case of theproposed DTC strategy and the basic DTC one, respectively.

While, the THD ofics reaches 12.5% and 14.6% in the case ofthe proposed DTC strategy and the basic DTC one, respectively.

Now, let us consider the common-mode voltage which is

defined as follows:

Vco m =

Vao + Vbo + Vco

3 (10)


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Fig. 10. Steady-state experimental results under the proposed DTC strategy considering two values of the stator frequencyfs . Legend 1: (subscript 1) Case of

fs =2.5 Hz and (subscript 2) case of fs =20 Hz. Legend 2: (a) stator a-phase voltage Vas (200 V/div) and current ias (0.5 A/div and 1 A/div), (b) harmonicspectrum ofias (10 db/div), (c) stator c-phase voltage Vcs (200 V/div) and current ics (0.5 A/div and 1 A/div), (d) harmonic spectrum of ics (10 db/div).

Fig. 11. Steady-state experimental results for a reference speed m = 50 rad/s and a load torque Tl = 1 Nm. Legend 1: (subscript 1) Case of the proposedDTC strategy and (subscript 2) case of the basic DTC strategy. Legend 2: (a) stator a-phase voltage Vas (200 V/div) and current ias (1 A/div), (b) harmonicspectrum ofias (10 db/div), (c) stator c-phase voltage Vcs (200 V/div) and current ics (1 A/div), (d) harmonic spectrum of ics (10 db/div).

where Vao , Vbo ,and Vco denote the voltages between the inverteroutputs to the middle point of the dc-bus. It is to be noted that

Vco is null in the case of the FSTPI.Fig. 12 shows the waveforms ofVco m in the case of the pro-

posed DTC strategy [seeFig. 12(a)], in the case of the basic DTC

strategy [see Fig. 12(b)] and in the case of the Takahashi DTC

strategy [1] with the IM fed by a SSTPI [see Fig. 12(c)]. One can

notice that Vco m is equal to 0 andVd c3 in the case of the FSTPI,while it is equal to Vd c6 and Vd c2 in the case of the SSTPI.

The comparison study between the three DTC schemes is

extended to the analysis of the sector succession, the stator flux

amplitude, and locus in the plane, and the electromagnetic

torque.

Fig. 13(a1), (b1), and (c1) illustrates the sector successionand the stator flux amplitude yielded by the proposed DTC

strategy, the basic DTC scheme, and the Takahashi DTC one,

respectively. Referring to Fig. 13(a1), it can be noticed that the

proposed DTC strategy offers the lowest stator flux ripple which

is confirmed by the locus described by the extremity ofs in

the plane shown in Fig. 13(a2), (b2), and (c2).Fig. 13(a3), (b3), and (c3) illustrates the sector succession

and the electromagnetic torque yielded by the proposed DTC

strategy, the basic DTC scheme, and the Takahashi DTC one,

respectively. One can clearly notice that the proposed DTC

strategy exhibits a torque ripple which has the lowest ampli-

tude and frequency. From Fig. 13(a3) and (c3), it is to be noted


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Fig. 12. Steady-state experimental results corresponding to the common-mode voltage Vco m (100 V/div) for a reference speed m = 50 rad/s and a load torqueTl = 1 Nm. Legend: (a) Case of the proposed DTC strategy, (b) case of the basic DTC strategy, and (c) case of the Takahashi DTC strategy.

Fig. 13. Steady-state experimental results for a reference speed m = 50 rad/s and a load torque Tl = 1 Nm. Legend 1: (a) Case of the proposed DTC strategy,(b) case of the basic DTC strategy, and (c) case of the Takahashi DTC strategy. Legend 2: (subscript 1) sector succession (2 sectors/div) and stator flux amplitude(0.2 Wb/div), (subscript 2) s extremity-locus described in the plane (0.5 Wb/div), and (subscript 3) sector succession (2 sectors/div) and electromagnetictorque (1 Nm/div).


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TABLE VIIINDUCTION MACHINE RATINGS

Power 0.37kW Efficiency 77%Voltage 230V/400V Current 1.7A/1ATorque 2.56N.m Stator flux (rms) 640mWbSpeed 1380rpm Frequency 50Hz

TABLE VIIIINDUCTION MACHINE PARAMETERS

rs = 24 .6 ls = 984mH M = 914mH J = 2 .5g.m2

rr = 17.9 lr = 984mH Np = 2 f=6mN.m.s

that the frequency of the torque ripple is lower in the case of

the proposed DTC scheme than the one yielded by the Taka-

hashi DTC strategy which is in full harmony with the approach

adopted in the synthesis of the vector selection table treated in

Section III-B. The high torque ripple noticed in Fig. 13(b3)

during the sector commutations from I to II and from III to IV

confirms the phasor analysis shown in Fig. 3.

VI. CONCLUSION

This paper dealt with a new DTCstrategy dedicated to FSTPI-

fed IM drives. The proposed DTC strategy is based on the emu-

lation of the operation of the conventional SSTPI. This has been

achieved thanks to suitable combinations of the four unbalanced

voltage vectors intrinsically generated by the FSTPI, leading to

the synthesis of the six balanced voltage vectors yielded by the

SSTPI. This approach has been adopted in the design of the vec-

tor selection table which is simply addressed by hysteresis con-

trollers, considering a subdivision of the Clarke plane into six

sectors. Simulation-based investigations of the IM steady-statefeatures have revealed the high performance of the introduced

DTC strategy. These performances have been the subject of an

experimental validation along with a comparison against those

yielded by Takahashi and the basic DTC strategies dedicated to

the SSTPI and to the FSTPI, respectively.

APPENDIX

The ratings and parameters of the three-phase induction ma-

chine, considered in both simulation and experiments, are pro-

vided in Tables VII and VIII, respectively, at the top of the

page.

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Bassem El Badsi received the B.S. degree in elec-tromechanical engineering, and the M.S. and Ph.D.degrees both in electrical engineering from the SfaxEngineering School (SES), University of Sfax, Sfax,Tunisia, in 2004, 2005, and 2009, respectively.

Since 2009, he has been an Associate Professorof power electronics and drives at SES. He is a mem-ber of the Research Unit on Renewable Energies andElectric Vehicles, University of Sfax. His major re-search interests include the analysis and the imple-mentation of advanced control strategies in ac motor

drives applied to automotive systems.

Badii Bouzidi received the B.S. degree in electrome-chanical engineering, and the M.S. and Ph.D. degreesin electrical engineering from the Sfax EngineeringSchool (SES), University of Sfax, Sfax, Tunisia, in2005, 2006, and 2011, respectively.

He is currently an Associate Professor of power

electronics and drives at the Department of Elec-tromechanical Engineering, SES. He is a member ofthe Research Unit on Renewable Energies and Elec-tric Vehicles, University of Sfax. His research inter-ests include the analysis and the implementation of

DTC strategies in ac motor drives applied to automotive systems.

Ahmed Masmoudi received the B.S. degree fromSfax Engineering School (SES), University of Sfax,Sfax, Tunisia,the Ph.D. degree from Pierreand MarieCurie University, Paris, France, and the ResearchManagement Ability degree from SESin 1984,1994,and 2001, respectively, all in electrical engineering.

In 1988, he joined the Tunisian University wherehe held different positions involved in both educationand research activities. He is currently a Professor ofelectric power engineering at SES. He is the Man-ager of the Research Unit on Renewable Energies

and Electric Vehicles, University of Sfax. His main research interests includethe design of new topologies of ac machines allied to the implementation ofadvanced and efficient control strategies in drives and generators, applied toautomotive as well as in renewable energy systems.

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