a 12-sector space vector switching scheme for … · 3804 ieee transactions on power electronics,...

3804 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 30, NO. 7, JULY 2015

A 12-Sector Space Vector Switching Schemefor Performance Improvement

of Matrix-Converter-Based DTC of IM DriveS. Sina Sebtahmadi, Member, IEEE, Hossein Pirasteh, S. Hr. Aghay Kaboli, Ahmad Radan, Member, IEEE,

and Saad Mekhilef, Senior Member, IEEE

Abstract—This paper presents a direct torque control (DTC)switching scheme based on the direct matrix converter (DMC) us-ing a 12-side polygonal space vector for variable speed control ofan induction motor (IM). The conventional DTC scheme-basedmatrix converter (MC) is limited by 60° sectors of both flux andvoltage vectors, which introduce a high torque ripple. The proposedmethod utilizes twelve 30° sectors of both flux and voltage vectorsto increase the degrees of freedom for selection of proper vectorsand reduce the torque ripple. The proposed switching scheme forthe MC-based DTC of an IM drive select the appropriate switch-ing vectors for control of torque with small variations of the statorflux within the hysteresis band. This improves the degrees of free-dom in selecting the vector algorithm and the torque ripple aswell. Furthermore, during the large torque demand, the probabili-ties of transgressing reference vector limits, which are enclosed by12-side polygonal space vector, are reduced. Extensive simulationand experimental results are presented to verify the effectivenessof the 12-sector space vector switching scheme for the DTC of anIM fed by the DMC.

Index Terms—Direct torque control (DTC), induction motor(IM), matrix converter (MC), space vector, switching scheme,torque ripple.

NOMENCLATURE

Hϕ Flux hysteresis output controller.HTe Torque hysteresis output controller.K Flux vector sector number.L Voltage vector sector number.Lm Mutual inductance.Lr Rotor leakage inductance.

Manuscript received March 14, 2014; revised May 26, 2014; accepted July30, 2014. Date of publication August 21, 2014; date of current version February13, 2015. This work was supported by the High Impact Research of Universityof Malaya—Ministry of Higher Education of Malaysia under Project UM.C/HIR/MOHE/ENG/17. Recommended for publication by Associate Editor A. M.Trzynadlowski.

S. S. Sebtahmadi and S. Mekhilef are with the Power Electronics and Re-newable Energy Research Laboratory (PEARL), Department of Electrical En-gineering, University of Malaya, 50603 Kuala Lumpur, Malaysia (e-mail:[email protected]; [email protected]).

H. Pirasteh and A. Radan are with the Faculty of Electrical and ComputerEngineering, K. N. Toosi University of Technology, 19697 Tehran, Iran (e-mail:[email protected]; [email protected]).

S. H. A. Kaboli is with the UM Power Energy Dedicated Advanced Centre(UMPEDAC), University of Malaya, 50603 Kuala Lumpur, Malaysia (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2014.2347457

Ls Stator leakage inductance.P Number of polesSk Switching states.Te Electromagnetic torque of the induction ma-

chines.T ∗

e Torque command.ΔTe Variation of electromagnetic torque.ΔTe,pu Torque variation in per unit.Vm Rated voltage.Vsm1 Minimum vector voltage for conventional (60°)

scheme.Vsm2 Minimum voltage vector for proposed (30°)

scheme.Vsr and Vst Radial and tangential components of stator-

voltage space vector.�Vs Stator-voltage space vector.Vsα and Vsβ α and β components of stator voltage, respec-

tively.k1 and k2 Flux and torque variation coefficient, respec-

tively.kT Constant value.t0 Initial time.Δt Time interval.v+1 andv−1 Voltage vector first order in (+)ve and (−)ve

regions, respectively.α and β Real and imaginary components of the transfor-

mation from three-phase stationary coordinatesystem to the two-phase coordinate system.

γ Load angle.γ1 Angle between stator and rotor-flux vectors.Δγ Variation of load angle.Δζ Variation of rotor-flux vector angle.θθ Angle of stator-flux vector.Δθ Variation of stator-flux vector angle.σ Leakage factor.ψm Maximum flux of stator.�ψs Stator-flux vector.�ψr Rotor-flux vector.ψ̂∗

s Stator-flux command.−−→Δψs Stator-flux vector variation.

Δ∣∣∣ �ψs

∣∣∣pu

Stator flux variation in per unit.

ws Synchronous speed.Note: All the motor parameters are referred to stator side.

0885-8993 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications standards/publications/rights/index.html for more information.

SEBTAHMADI et al.: 12-SECTOR SPACE VECTOR SWITCHING SCHEME FOR PERFORMANCE IMPROVEMENT 3805

I. INTRODUCTION

T he requirement of torque control to adjust the speed inindustrial applications resulted in the high demand for a

controlling scheme with fast transient, less torque ripple, andaccurate control of torque for an induction motor (IM) withcompact and high reliability adjustable speed drive [1]. A ma-trix converter (MC) enables the control of torque and flux viavarious vector-selection criteria give rise to various switchingstrategies, each affecting drive torque ripple, current ripple, andswitching frequency. The MC has been an apposite candidatefor interfacing of two ac systems with a compact and reliabledesign [2] as compared to the voltage source inverters (VSI),which conventionally are utilized to drive IM [3]. In addition,the MC has a long lifetime and can operate in hostile envi-ronments due to the absence of dc-link electrolytic capacitors[4]; these features of MC could offer advantages in military[5], transportation, renewable energy [6] and aerospace appli-cations, where weight, volume, and reliability are importantcriteria [7].

While, the researches chiefly concern direct matrix converters(DMCs), an indirect matrix converter (IMC) can be consideredas an option for the DMC [8], [9]. Still, the main circuit of theIMC has drawbacks compared to the DMC, e.g., power losses ofthe IMC are larger with most loading situations. In addition, itsoutput/input voltage ratio is more nonlinear than the ratio of theDMC, which reduces its suitability to the speed sensor-less driveof IM [10]. One of the biggest difficulties in the operation of thisconverter was the commutation of the bidirectional switches.This problem has been solved by introducing intelligent and softcommutation techniques, giving new momentum to research inthis area, while with a suitable modulation method, there is noneed for special commutation methods of MCs [11]. The mostrelevant modulation methods developed up to now, for the MC,are the scalar techniques and pulse width modulation (PWM)methods. These MC modulations are efficient, but complex tounderstand and synthesize, compared to the three-phase VSImodulations, thereby heavy to implement in digital processors.An alternative solution conventionally in use is to apply spacevector modulation (SVM) for MCs [3], [12]–[14].

The two elegant and powerful controlling methods currentlyused to control the speed of IM fed by the MC, are field-orientedcontrol and direct torque control (DTC). The advantages of DTCare no requirements for coordinate transformations and decou-pling processes for both voltage and currents, robust and fasttorque response, robustness against parameter variation, no re-quirements for PWM pulse generation and current regulators[15]. However, the main drawback of the DTC scheme is thehigh current and torque ripple. The disadvantages of the DTCscheme also include variable switching frequency, and difficult-to-control torque and flux at very low speeds [16]. In the con-ventional DTC, the circular locus is divided into six sectors anda total of eight voltage vectors are used. However, the discreteinverter switching vectors cannot always generate exact statorvoltage required to obtain the demanded electromagnetic torqueand stator flux linkages. This results in production of ripples inthe flux as well as torque.

The researchers have reported various voltage-vector-selection strategies for MC-based DTC scheme [17]–[19]. Theadvantages of the MC were combined with the advantages of theDTC schemes in [17]. The use of MC input voltages with differ-ent amplitudes in order to reduce the inherent torque ripple thatappears when direct torque control is applied to drive PMSMwas investigated in [18]. An improved DTC-SVM method forsensor-less MC drives using an over modulation strategy anda simple nonlinearity compensation was proposed in [19] toovercome the degradation of the dynamic torque response ascompared to the basic DTC method and improve the phase-current distortion due to the nonlinearity of the MC. However, inall the aforementioned researches, the authors utilized the con-ventional (60°-sector) voltage vector selection algorithm, whichlimits the degrees of freedom to select voltage vectors. Thus,the torque ripple is significant, which may not be acceptable forhigh-performance drives.

Lately, researchers have proposed the switching strategy bydividing the space vector into twelve 30° sectors [20]–[27].The switching loss for the three-phase VSI by recarving thesix sectors up into twelve ones were minimized in [20]. Thetotal harmonic distortion (THD) of line-to-line output voltageand peak value of the common-mode voltage for an RL loadpowered through the MC was reduced [21]. In [22] and [23], aneutral-point-clamped multilevel inverter combined with 12 sec-tor methodology was performed for the DTC of an IM drive. In[24], a novel DTC of MC-Fed permanent-magnet synchronousmotor drives using duty-cycle control for the torque ripple re-duction was proposed. In [25]–[27], the authors applied 12-sidedpolygonal space-vector-based instead of hexagonal-based volt-age vectors for an IM drive by implementing a voltage sourceinverter (VSI). However, in all listed publications, the focus hasnot been on the development of the switching strategy for theMC-based DTC of an IM drive. Moreover, the development ofthe switching strategy, switching time table, stator flux varia-tion, torque variation, and improvement of degrees of freedomare not discussed profoundly.

In this paper, to take advantage of the DMC based on DTCwith SVM and reduce the torque ripple of an IM at the sametime, a novel switching strategy is developed based on twelve30° sectors for the circular locus of space vector to increase thedegrees of freedom in selecting voltage and flux vectors, hence,the torque ripple is reduced. The simulation and experimental re-sults demonstrate that the proposed switching strategy providesadditional degrees of freedom to select voltage vectors; conse-quently, the torque ripple reduces significantly. Additionally, theperformance of the proposed switching strategy is compared tothat of the hexagonal boundary SVM-based direct MCs for theDTC of IMs.

II. MODELING OF IM FOR THE PROPOSED DTC SCHEME

Neglecting stator-resistance voltage drop, an induction ma-chine’s flux equation can be expressed as

−−→Δψs = �Vs · Δt. (1)


Fig. 1. Variation of flux vectors pre and post applications of voltage vector inthe corporation with DTC-based IM drive.

Radial component (Vsr ) of the stator-voltage space vector(�Vs) changes the stator-flux magnitude, and the tangential com-ponent (Vst) changes the stator-flux angle as shown in Fig. 1.They can be expressed as

Vsr = Vsα cos θ + Vsβ sin θ (2)

Vst = −Vsα sin θ + Vsβ cos θ (3)

where θ is the angle of stator-flux vector �ψs .After applying a new voltage vector �Vsfor Δt time, the dif-

ferential change in stator-flux linkage can be written as

Δ | �ψs | = | �ψs2 | − | �ψs1 | ∼= Vsr · Δt. (4)

Substituting Vsr from (2) into (4) gives

Δ| �ψs | = (Vsα cos θ1 + Vsβ sin θ1) · Δt (5)

which reveals the influencing characteristics of each voltagevector on magnitude variation of the stator-flux vector.

The developed electromagnetic torque of an IM can be ex-pressed by

Te =32· P

2· Lm

σ · Ls · Lr· | �ψr | · | �ψs | sin γ (6)

where γ and σ are load angle and leakage factor, respectively.In order to see the torque variation caused by applying volt-age space vector �Vs during Δt, (6) is differentiated, assumingconstant magnitude for rotor-flux vector during Δt owing torotor’s large time constant [27]. Thus, the following equation isobtained:

ΔTe = kT · | �ψr | ·(

d| �ψs |dt

· sin γ

+d ( sinγ)

dt· | �ψs |

) ∣∣∣∣t0

· Δt (7)

where t0 is the initial time, which is the time just before applyingvoltage vector. kT is a constant defined as

kT =32· P

2· Lm

σ · Ls · Lr. (8)

Fig. 2. Matrix converter. (a) DMC configuration. (b) Active voltage vectorsproduced by the matrix converter.

Rearranging (7) gives

ΔTe = kT · | �ψr | ·(

d| �ψs |dt

∣∣∣∣∣t0

sin γ1 +dγ

dt

∣∣∣∣t0

cos γ1

·| �ψs1 |)

· Δt (9)

where subscript “1” indicates the magnitude of specified vari-ables at exactly t0 .

Equation (5) leads to

d| �ψs |dt

∣∣∣∣∣t0

= Vsα cos θ1 + Vsβ sin θ1 (10)

where θ1 is the angle of stator-flux vector just before applyingvoltage vector �Vs .

During Δt, variation of load angle Δγ is given by

Δγ = Δθ − Δζ (11)

where Δθ and Δζ are variation of stator and rotor flux angle,respectively, due to the application of the new voltage vector,Vs .

Again

Δ|�ψs | = Δθ · |�ψs1 | ∼= Vst · Δt. (12)


TABLE I3 × 3 MATRIX CONVERTER SWITCHING CONFIGURATION

Switching Combinations On Switches Voltage-Vector Values α Component Value β Component Value

vo αo

+1 SA a SB b SB c 2/3vA B 0 2/√

3 Vm cos(ωt + π/6) 0−1 SB a SA b SA c −2/3vA B 0 −2/

√3 Vm cos(ωt + π/6) 0

+2 SB a SC b SC c 2/3vB C 0 2/√

3 Vm cos(ωt − π/2) 0−2 SC a SB b SB c −2/3vB C 0 −2/

√3 Vm cos(ωt − π/2) 0

+3 SC a SA b SA c 2/3vC A 0 2/√

3 Vm cos(ωt + 5π/6) 0−3 SA a SC b SC c −2/3vC A 0 −2/

√3 Vm cos(ωt + 5π/6) 0

+4 SB a SA b SB c 2/3vA B 2π/3 −1/√

3 Vm cos(ωt + π/6) Vm cos(ωt + π/6)−4 SA a SB b SA c −2/3vA B 2π/3 1/

√3 Vm cos(ωt + π/6) −Vm cos(ωt + π/6)

+5 SC a SB b SC c 2/3vB C 2π/3 −1/√

3 Vm cos(ωt − π/2) Vm cos(ωt − π/2)−5 SB a SC a SB c −2/3vB C 2π/3 1/

√3 Vm cos(ωt − π/2) −Vm cos(ωt − π/2)

+6 SA a SC b SA c 2/3vC A 2π/3 −1/√

3 Vm cos(ωt + 5π/6) Vm cos(ωt + 5π/6)−6 SC a SA b SC c −2/3vC A 2π/3 1/

√3 Vm cos(ωt + 5π/6) −Vm cos(ωt + 5π/6)

+7 SB a SB b SA c 2/3vA B 4π/3 −1/√

3 Vm cos(ωt + π/6) −Vm cos(ωt + π/6)−7 SA a SA b SB c −2/3vA B 4π/3 1/

√3 Vm cos(ωt + π/6) Vm cos(ωt + π/6)

+8 SC a SC b SB c 2/3vB C 4π/3 −1/√

3 Vm cos(ωt − π/2) −Vm cos(ωt − π/2)−8 SB a SB b SC c −2/3vB C 4π/3 1/

√3 Vm cos(ωt − π/2) Vm cos(ωt − π/2)

+9 SA a SA b SC c 2/3vC A 4π/3 −1/√

3 Vm cos(ωt + 5π/6) −Vm cos(ωt + 5π/6)−9 SC a SC b SA c −2/3vC A 4π/3 1/

√3 Vm cos(ωt + 5π/6) Vm cos(ωt + 5π/6)

0A SA a SA b SA c 0 . . . 0 00B SB a SB b SB c 0 . . . 0 00C SC a SC b SC c 0 . . . 0 0

Substituting Vst from (3) into (12) yields

Δθ =−Vsα sin θ1 + Vsβ cos θ1

|�ψs1 |· Δt. (13)

Hence

dθ

dt

∣∣∣∣t0

=−Vsα sin θ1 + Vsβ cos θ1

|�ψs1 |. (14)

Considering rotor flux rotating with synchronous speed ωs

while magnitude remains nearly constant during Δt, Δζ can bewritten as

Δζ = ωs · Δt ⇒ dζ

dt

∣∣∣∣t0

= ωs. (15)

Equations (11), (14), and (15) can be written as

dγ

dt

∣∣∣∣t0

=dθ

dt

∣∣∣∣t0

− dζ

dt

∣∣∣∣t0

=−Vsα sin θ1 + Vsβ cos θ1

|�ψs1 |− ωs.

(16)By substituting (10) and (16) into (9), expression for the

torque variation becomes

ΔTe = kT · |�ψr | · (x − y) · Δt (17)

where x and y are

x = (Vsα cos θ1 + Vsβ sin θ1) · sin γ1

y =(

Vsα sin θ1 − Vsβ cos θ1 + ωs |�ψs1 |)

· cos γ1 .(18)

For normalization of (5) and (17), rating values of the machinecan be selected as base values

Vm = ω · ψm ⇒ ψbase =Vbase

ωbase=

Vm

ω(19)

and

Te,base =32

· P

2· Lm

σ · Ls · Lr· |�ψr,base |

· |�ψs,base | · sin γbase (20)

where the subscript “base” indicates the base value

Δ|�ψs |pu =Δ|�ψs |ψbase

=(Vsα cos θ1 + Vsβ sin θ1) · Δt

Vbase/ωbase. (21)

The per-unit equation for flux variation results

Δ|�ψs |pu = (Vsα,pu cos θ1 + Vsβ ,pu sin θ1) · k1 (22)

where k1 = ωbase · Δt.Torque variation can be expressed in per unit from (6) and

(17) as follows:

ΔTe,pu =ΔTe

Te,base=

kT ·∣∣∣�ψr

∣∣∣ · (x − y) · Δt

kT ·∣∣∣�ψr,base

∣∣∣ ·

∣∣∣�ψs,base

∣∣∣ sin γbase

(23)

ΔTe,pu = |�ψr,pu | · (xpu − ypu) · Δt

where

xpu = (Vsα,pu cos θ1 + Vsβ ,pu sin θ1) · sin γ1

sin γbase· ωbase

ypu = ((Vsα,pu sin θ1 − Vsβ ,pu cos θ1) · ωbase

+ωs ·∣∣∣�ψs1

∣∣∣pu

)

· cos γ1

sin γbase. (24)

Equation (23) for torque variation per-unit can be rewrittenas


Fig. 3. Block diagram of the proposed DTC-based switching strategy by the MC.

TABLE IISPECIFICATIONS AND PARAMETERS OF THE THREE-PHASE TEST INDUCTION

MOTOR, REFERRED TO THE STATOR SIDE

Rated power S 1100 VARated Torque Te , b a s e 6.3 NmRated Voltage Vl−l 380 VNumber of Poles 2P 2rated frequency f 50 HzStator Resistance Rs 1.405 ΩStator Reactance Xl s 1.834 ΩMutual Reactance Xm 54.09 ΩRotor Resistance R ′

r 1.395 ΩRotor Reactance X ′

l r 1.834 ΩFriction Factor J 0.0131 kg/m2

ΔTe,pu = |�ψr,pu | ·{

Δ|�ψs |pu ( sinγ1)pu

− ((Vsα,pu sin θ1 − Vsβ ,pu cos θ1)

+ (2/p) · ωs,pu · |�ψs1 |pu

)

·√

k2 − ( sin γ1)2pu · k1

}

.

(25)

where k2 = 1( sin γb a s e )2 .

Expression (25) is applicable to any size IM drive, but becauseof its dependence on γbase , influencing characteristics of voltagevectors can differ in low- and high-power applications.

III. FUNDAMENTALS OF MC-BASED DTC SCHEME

The DMC as shown in Fig. 2(a) is of the highest practicalinterest as it connects a three-phase voltage source with a three-phase load (typically a motor). There are 27 possible switchingconfigurations, but only 21 of them are useful in the DTC al-gorithm, which are given in Table I. Fig. 2(b) shows the first18 active voltage vectors having fixed directions. As shown inTable I, the magnitudes of voltage vectors depend on the in-put voltages. The fourth and fifth columns of Table I show real

(α) and imaginary (β) components of the MC’s output voltagevectors in a stationary reference frame. The last three switchingconfigurations correspond to zero-output voltage vectors.

Based on the earlier torque and flux equations, the blockdiagram of the proposed MC-based DTC scheme for an IMdrive is shown in Fig. 3.

IV. EFFECT OF VOLTAGE VECTOR ON FLUX AND TORQUE

A. Effect of Voltage-Vector on Flux

The IM parameters used for simulation are shown in Table II.For flux variation in different voltage vectors, α and β com-ponents of each vector were substituted based on per unit, andequations obtained. For example, voltage vector of first order in(+)ve region is obtained from

v+1 =23vAB ∠0 =

23

(vA − vB ) · ( cos (0) + j. sin t(0)) .

(26)The aforementioned equation converted into per unit based

on machine’s rated voltage (Vbase); α and β components of v+1yields

⎧

⎨

⎩

v+1α,pu =v+1α

Vm=

2√3

cos(

ωt +π

6

)

v+1β ,pu = 0.(27)

From (22) and (27), the flux variation can be obtained as

Δ|−→ψs |pu,+1 =2√3· cos (ωt + π/6)

×( cos θ1) · ((120π) × 10−6 . (28)

In (28), rated frequency of the motor is considered as 50 Hz,and sampling time-interval is considered 1 μs. The comparisonof stator flux variation between the conventional (60° sector)and the proposed (30° sector) switching schemes is shown inFigs. 4 and 5, respectively. It is seen from Figs. 4(a) and 5(a)that the peak-to-peak flux variation in both the conventional andproposed switching scheme is the same. However, there is 180°phase difference between Figs. 4(a) and 5(a) by applying voltagevectors v+1 and v−1 , respectively. In Fig. 4(b), the colored area


Fig. 4. Stator-flux vector variation of the conventional (60° sector) DTC scheme under the rated condition of the motor for v+1 (NU = NoUse). (a) Stator fluxvariation. (b) Stator-flux vector behavior characteristic.

Fig. 5. Stator-flux vector variation of the proposed (30° sector) DTC scheme under rated condition of the motor for v−−1 . (a) Stator flux variation. (b) Sator-fluxvector behavior characteristic.

Fig. 6. Instantaneous basic voltage vectors for both conventional (60° sector)and proposed (30° sector) switching scheme, and the zoom-in view of the firstsector.

indicates the (+)ve (Δ|−→ψs |pu ≥ 0) variation and white area in-dicates the (−)ve b(Δ|−→ψs |pu < 0) variation of stator flux. Notethat in some sectors, applying the voltage vector when the spacevector is divided into six 60° sectors is impossible because theflux increases and decreases at the same time in the sectors. Forexample, (when ωt < 120° and 60°< θ < 120°), flux in one halfof this sector is positive, which means that v+1 increases the sta-tor flux, while in the other half, it is negative, which means thatv+1 decreases the stator flux. So, the use of v+1 in this sector isnot allowed. Hence, for the conventional switching scheme thedegree of freedom to choose the stator-voltage vector is limited.Fig. 5(b) shows flux vector variations of voltage vector v+1 forthe proposed 30° sector-based switching scheme. It is clearlyseen from the figures that there is no sector when the flux is in-creasing and decreasing simultaneously. Thus, the stator-voltage


Fig. 7. Torque variation for the proposed (30° sector) DTC-based IM drive under the rated condition of the motor. (a) Torque variation for voltage vector v+1 .

(b) Torque behavior characteristic for v+1 . (c) Torque variation for voltage vector v+2 . (d) Torque behavior characteristic for v+2 .

vector can be applied for each sector for the proposed 30° sec-tor scheme. Therefore, the degrees of freedom to choose thestator-voltage vector with the proposed 30° sector switchingscheme is increased significantly as compared the conventional60° sector scheme. For stator-voltage vector v-1 , the stator fluxvariation is exactly opposite to that of voltage vector v+1 . Thisstatement is true for all stator-voltage vectors (e.g., v+5 andv−5 , etc.)

Fig. 6 compares instantaneous basic voltage vectors of theproposed (30°- sector) method with the conventional (60°-sector) method. As it is evident in Fig. 6, the magnitude ofvoltage vector for the proposed scheme is always higher thanor at least equal to that of the conventional scheme. Thus,the voltage ripple could reduce with the proposed scheme.Moreover, the probability of stator voltage reference transgressduring large torque demand may reduce because the voltage

reference vector limitations are enclosed by 12-side polyg-onal rather than hexagonal boundary. According to Fig. 6,the maximum value of reference voltage vector for 12-sidepolygonal space vector is Vsm2 = r cos (ϑ), and the maximumvalue of reference voltage vector for hexagonal boundary isVsm1 = r cos(ϑ

2 ). While ϑ = π/6, the maximum value of refer-ence voltage vector for 12-side polygonal space vector is Vsm2 =1.11(Vsm1).

B. Effect of Voltage-Vector on Torque

Torque variation by applying vectors v+1 and v+2 are shownin Fig. 7(a) and (c), respectively, for the proposed switchingscheme. It is clearly seen from these figures that the torque vari-ation not defected when the voltage vector switches from v+1 tov+2 . The corresponding torque variations on θ1 − ωt plane are


TABLE IIIDEGREES OF FREEDOM IN SELECTING APPROPRIATE VOLTAGE VECTOR FOR THE PROPOSED DTC SCHEME

Proper Vectors for k as an Odd Number (k = 1,3,5,7,9,11)

Hϕ +1 −1

HTe +1 −1 +1 −1

L = 1 (3k+9)/2 (3k−1)/2, (3k+1)/2, (3k+33)/2, (3k+3)/2, (3k+29)/2, (3k+31)/2 (3k+15)/2 (3k+23)/2, (3k+25)/2, (3k+19)/2, (3k+27)/2L = 2 (3k+9)/2 (3k−1)/2, (3k+1)/2, (3k+33)/2, (3k+3)/2, (3k+29)/2, (3k+31)/2 (3k+15)/2 (3k+23)/2, (3k+25)/2, (3k+17)/2, (3k+27)/2L = 3 (3k+7)/2 (3k+1)/2, (3k+11)/2, (3k+33)/2, (3k+17)/2, (3k+3)/2, (3k+31)/2 (3k+13)/2 (3k−1)/2, (3k+25)/2, (3k+5)/2, (3k+27)/2L = 4 (3k+7)/2 (3k+1)/2, (3k+11)/2, (3k+33)/2, (3k+17)/2, (3k+3)/2, (3k+31)/2 (3k+13)/2 (3k+21)/2, (3k+25)/2, (3k+5)/2, (3k+27)/2L = 5 (3k+23)/2 (3k+1)/2, (3k+21)/2, (3k+11)/2, (3k+17)/2, (3k+31)/2, (3k+15)/2 (3k+29)/2 (3k+25)/2, (3k+9)/2, (3k+3)/2, (3k+5)/2L = 6 (3k+23)/2 (3k+1)/2, (3k+21)/2, (3k+11)/2, (3k+17)/2, (3k+31)/2, (3k+15)/2 (3k+29)/2 (3k+25)/2, (3k+9)/2, (3k+19)/2, (3k+5)/2

Proper Vectors for k as an Even Number (k = 2,4,6,8,10,12)

Hϕ +1 −1

HTe +1 −1 +1 −1

L = 1 (3k+8)/2 (3k+12)/2 (3k−4)/2, (3k−2)/2, 3k/2 − (3k+2)/2, (3k+20)/2, (3k+22)/2, (3k+26)/2, (3k+28)/2, (3k+24)/2L = 2 (3k+10)/2 (3k+12)/2 (3k−4)/2, (3k−2)/2, 3k/2 − (3k+2)/2, (3k+20)/2, (3k+22)/2, (3k+26)/2, (3k+28)/2, (3k+24)/2L = 3 (3k+10)/2 (3k+12)/2 (3k−2)/2, (3k+14)/2, 3k/2 − (3k+8)/2, (3k+30)/2, (3k+22)/2, (3k+28)/2, (3k+2)/2, (3k+24)/2L = 4 (3k+10)/2 (3k+26)/2 (3k−2)/2, (3k+14)/2, 3k/2 − (3k+8)/2, (3k+30)/2 (3k+22)/2, (3k+28)/2, (3k+2)/2, (3k+24)/2L = 5 (3k+10)/2 (3k+26)/2 (3k−2)/2, (3k+18)/2, (3k+14)/2 − (3k+8)/2, (3k+22)/2, (3k+6)/2, (3k+28)/2, (3k+12)/2, (3k+2)/2L = 6 (3k+30)/2 (3k+26)/2 (3k−2)/2, (3k+18)/2, (3k+14)/2 − (3k+8)/2, (3k+22)/2, (3k+6)/2, (3k+28)/2, (3k+12)/2, (3k+2)/2

TABLE IVMATRIX CONVERTER SWITCHING STATUS FOR PROPOSED SWITCHING SCHEME

Switching Code Vector Number On Switches Equivalent Vector Code in Odd Sectors Equivalent Vector Code in Even Sectors

1 v+ 1 SA a SB b SC b (3k−1)/2 (3k−4)/22 v+ 2 SA b SB c SC c (3k+1)/2 (3k−2)/23 v−3 SA a SB c SC c (3k+3)/2 3k/24 v−7 SA a SB a SC b (3k+5)/2 (3k+2)/25 v−8 SA b SB b SC c (3k+7)/2 (3k+4)/26 v+ 9 SA a SB a SC c (3k+9)/2 (3k+6)/27 v+ 4 SA b SB a SC b (3k+11)/2 (3k+8)/28 v+ 5 SA b SB b SC c (3k+13)/2 (3k+10)/29 v−6 SA b SB a SC c (3k+15)/2 (3k+12)/210 v−1 SA b SB a SC a (3k+17)/2 (3k+14)/211 v−2 SA c SB b SC b (3k+19)/2 (3k+16)/212 v+ 3 SA b SB a SC a (3k+21)/2 (3k+18)/213 v+ 7 SA b SB b SC a (3k+23)/2 (3k+20)/214 v+ 8 SA b SB c SC b (3k+25)/2 (3k+22)/215 v−9 SA b SB c SC a (3k+27)/2 (3k+24)/216 v−4 SA a SB b SC a (3k+29)/2 (3k+26)/217 v−5 SA b SB c SC b (3k+31)/2 (3k+28)/218 v+ 6 SA a SB c SC a (3k+33)/2 (3k+30)/219 0a SA a SB a SC a 19 1920 0b SA b SB b SC b 20 2021 0c SA c SB c SC c 21 21

shown in Fig. 7(b) and (d), respectively. In Fig 7(b) and (d), twocolor pericyles indicate the (+)ve torque variation and the whitearea indicates the (−)ve torque variation. The area of colored re-gions is same in both Fig. 7(b) and (d) except their positions arechanged. In other words, with the application of various voltagevectors, there is no additional torque variation. It means that withapplying a different voltage vector, the torque ripple remainsconstant.

It is found that the developed torque of the motor is sta-ble at different load and speed conditions. Additionally, it isclearly seen from these figures that the torque for v+1 andv+2 have same space-dependent expression, and for time-

dependent expression. The torque variation by applying vectorsv+2 lags the torque variation as a result of applying v+1 byπ/3.

V. VECTORS SUITABLE FOR CONTROL

To examine the effect of 18 active voltage vectors produced bythe MC on the flux and torque, a procedure similar to that appliedfor v+1 is applied. Voltage vectors with stable characteristic inthe 30° sectors are then chosen as suitable for control of motortorque and flux. Based on the earlier result analysis, the proposedswitching technique is extracted, and shown in Table III. Hϕ andHT e are the outputs of flux and torque hysteresis controllers,


Fig. 8. Responses comparison of the proposed switching method with conventional switching method at rated speed (1473 r/min), rated load (6.3 Nm), and 20%of rated load. (a) Speed. (b) Torque response of the proposed method under rated load. (c) Torque response of the conventional method under rated load. (d) Torqueresponse of the proposed method under 20% of rated load. (e) Torque response of the conventional method under 20% of rated load. (f) Input current and its THDspectrum of the proposed method under rated load. (g) input current and its THD spectrum of the conventional method under rated load. (h) Input current and itsTHD spectrum of the proposed method under 20% of rated load. (i) Input current and its THD spectrum of the conventional method under 20% of rated load.

respectively, shown as follows:

{Te < T ∗

e ,HTe= +1

Te > T ∗e ,HTe

= −1(29)

{φ < φ∗,Hφ = +1

φ > φ∗,Hφ = −1.(30)

Table III is produced for the stator flux in the first and thesecond sectors, but owing to symmetry conditions in spacevector the results are valid also for the remaining sectors. Itis to be noted that Hϕ = +1 indicates the flux needs to in-crease and Hϕ = − 1 indicate the flux needs to decrease. Simi-larly, HT e = +1 indicate that the torque needs to increase andHT e = −1 indicate that the torque needs to decrease.

Table III lists the results for the first six sectors of the inputvoltage. The results for the six remaining sectors contrast, thoseof the first six sectors, e.g., in seventh sector (L = 7) the voltagevector is −9, while the voltage vector is +9 in the first voltagesector (L = 1) and this logic is true for all remaining sectors(L = 7, 8, 9, . . . , 12).

Table IV shows the switching scheme codes correspondingto each voltage vector.

VI. SELECTION OF OPTIMUM VECTORS TO MINIMIZE

THE SWITCHING LOSSES

As can be seen from Table III, there are multiple vectors forswitching selection in some sectors, which increases the degreesof freedom in the selection of the space-vector voltage for theDTC of an IM by the MC.


Fig. 9. Responses of the proposed DT-based IM drive for step changes of load condition. (a) Speed. (b) Electromagnetic torque. (c) Stator flux. (d) Stator-phasecurrents.

Fig. 10. Responses of the proposed DTC based IM drive for step changes of command speed. (a) Speed. (b) Electromagnetic torque. (c) Stator flux.(d) Stator-phase currents. (e) Output voltage and its THD spectrum of the proposed method. (f) Output voltage and its THD spectrum of the conventionalmethod.


TABLE VCOMPARISON OF PROPOSED SWITCHING METHOD

AND CONVENTIONAL METHOD

Parameters of Comparison Proposed Method Conventional Method[3]

THD of MC Input Current 5.15% 8.56%THD of MC Output Voltage 61.9% , harmonics are

mainly in the vicinity ofthe switching frequency

(10 kHz)

58.1%, harmonics aremainly distributed withinthe range of (0.5—6 kHz)

Torque Ripple Reduction 60% reduction fixedMaximum Limit of ReferenceVoltage Within CircularLocus of Space VectorsWithout Over Modulation

V sm 1 × 1.11 V sm 1

Degrees of Freedom to SelectAppropriate Voltage VectorsFor DTC

intensified fixed

The enhanced degrees of freedom improve the IM drive per-formance. In addition, the proposed 12-sector switching methodis independent of the load and speed variation, in the ex-pense of introducing of no use sectors, which are included inTable III when k is equal to an even number, Hϕ = −1 andHT e = +1. These redundancies of vectors for switching se-lection provide an additional option, to optimize the switchinglosses by the proposed 12-sector method compares to the con-ventional switching. While the switching is fixed in the con-ventional method and there is no redundancy of vectors forswitching selection, the proposed method can provide the op-timum switching losses due to existence of multiple vectorsfor switching selection. In order to obtain minimum switch-ing frequency, which provides optimum switching loss, thespace-vector voltage with lowest flux variation is selected fromTable III as the best switching vector. This selection increasesthe switching period by extending time to reach the hystere-sis band in both flux and torque. Accordingly, the switch-ing frequency is optimized, hence, the switching losses arediminished.

The lowest average values in each sector of the contour-map are chosen for switching by comparing the variation ratesof the flux correspond to each input voltage in different fluxsectors.

VII. SIMULATION RESULT OF THE PROPOSED

DTC-BASED IM DRIVE

The proposed DTC-based IM drive is simulated extensivelyat different operating conditions using MATLAB/Simulink soft-ware. The sample results are presented below.

Fig. 8 compares the starting responses of the DTC-based IMdrive at rated speed under full load and 20% of load condi-tions for the proposed (30° sector) and conventional (60° sec-tor) switching scheme, respectively. Fig. 8(a) depicts how actualspeed follows the reference speed. It is seen from Fig. 8(b) and(c) that the torque ripple is less for the proposed switchingscheme as compared to the conventional switching under fullload terms and also in Fig. 8(d) and (e) the comparison has beenapplied between suggested and conventional methods for 20%

Fig. 11. .Photograph of the experimental setup.

of loading conditions. Thus, the proposed switching schemeintroduces lower vibration to the motor. As the input currentof the MC is an important variable that should be monitored,the waveform of input current and its harmonic spectrum inthe steady-state operation of the motor for both proposed andconventional methods at rated load are shown in Fig. 8(f) and(g), respectively, and then, for 20% of rated load illustrated inFig. 8(h) and (i). The components of the input filter are in-ductance (Lr = 4 mH) and capacitor (Cr = 40 μF). It can beseen that the distortion of the input current for the conventionalmethod is more severe than that of the proposed method. TheTHDs of the conventional and proposed methods under full loadcondition are 8.56% and 5.15%, respectively, as well as one-fifthof the rated load are similarly 24.19% and 40.27%.

Fig. 9 shows the responses of the proposed DTC-based IMdrive at step changes of load conditions. It is seen from Fig. 9(a)that the motor can follow the command speed in spite of changesof the load from no-load to full-load conditions. Thus, the pro-posed drive is insensitive to load variations. It is also seen fromFig. 9(b) that the torque ripple is very low at different load con-ditions. It is found that the flux remains constant while the loadchanges and the stator current changes with load, accordingly.Fig. 9(c) and (d) shows the produced flux and stator currents,respectively.

It is found that the motor can follow the command speed evenif it changes to the reverse direction. Therefore, the performanceof the proposed switching-based MC for an IM drive is foundrobust at different operating conditions. Fig. 10 shows the speed,produced electromagnetic torque, flux, and stator currents, re-spectively.

It is clear that the motor can reverse rotation directionsmoothly without any overshoot/undershoot or steady-state er-ror. In addition, the waveform of the output voltage and its har-monic spectrum in the steady-state operation of the motor forboth proposed and conventional methods are shown in Fig. 10(e)and (f), respectively. It can be seen that the harmonics of theproposed method are mainly in the vicinity of the switching


Fig. 12. Experimental waveforms of steady-state performance of proposedmethod at rated speed (1473 r/min) and rated load (6.3 Nm). (a) Output voltage.(b) Stator current. (c) Input current. (d) Electromagnetic torque. (e) Speed.

frequency (10 kHz) as shown in Fig. 10(e), while the harmonicsof the conventional method are mainly distributed within therange of 0.5–6 kHz as shown in Fig. 10(f). The result shows thatthe output voltage THDs of the conventional and proposed meth-ods are 58.1% and 61.9%, respectively. To evaluate performance

Fig. 13. Experimental waveforms of dynamic performance of the proposedmethod for speed reference step change, with speed reference increasing from1/3 rated speed (1473/3 r/min) to 1/2 rated speed (1473/2 r/min) at rated load(6.3 Nm). (a) Speed. (b) Electromagnetic torque. (c) Stator current.

of the proposed method precisely and entirely, the comparisonof the proposed method and the conventional switching methodis summarized and tabulated in Table V.

VIII. EXPERIMENTAL RESULTS

To verify the feasibility and effectiveness of the proposedDTC scheme based on 12-side polygonal space vector of volt-age and flux, an MC connected to three-phase network througha variable ac power supply to feed a 1-kw three-phase IM wasimplemented. The experimental setup is shown in Fig. 11, whilethe motor parameters are same as the parameters for simulationand listed in Table II. In order to attenuate the harmonics ofswitching, an LC input filter was designed based on the valuesextracted from simulation. The MC bidirectional switching isconfigured using IGBTs as in Fig. 1. The proposed control al-gorithm is implemented by using TMS320F28335 digital signalprocessor (DSP).

A. Steady-State performance

Fig. 12 presents the steady-state performance of the proposedswitching scheme under rated conditions of the motor, speed(1473 r/min) and load (6.3 Nm). The there-phase waveform ofthe output voltage and stator current are shown in Fig. 12(a)and (b), respectively. Fig. 12(c) shows the three-phase input


Fig. 14. Experimental waveforms of dynamic performance of the proposedmethod for load torque step change, with load torque increasing from no-load (0 Nm) to rated load (6.3 Nm) at rated speed (1473 r/min). (a) Speed.(b) Electromagnetic torque. (c) Stator current.

currents of the MC at the steady - state performance under ratedconditions of an IM. The electromagnetic torque and speedwaveforms of an IM at rated condition are shown in Fig. 12(d)and (e), respectively. As it is evident in the zoom-in view, theripples for both speed and electromagnetic torque are ratheracceptable despite of high-frequency ripples.

B. Dynamic Performance

Fig. 13 shows the waveforms of the speed, electromagnetictorque, and stator current of the IM drove by the proposedmethod with speed reference value stepping up from 500 to 1000r/min at full-load condition (6.3 Nm). It is evident that with thestep change of speed reference value, the electromagnetic torquesteps up within a short period. Once the actual speed reaches tothe reference value, the electromagnetic torque reaches to thenominate value for a short period of time. It is concluded thatthe proposed method has the advantage of fast torque, dynamicresponse with acceptable ripples.

Fig. 14 shows the waveforms of the speed, electromagnetictorque, and stator current of the IM drove by the proposedmethod with load torque step up from no-load to full-load, whilethe reference speed is kept constant at rated speed of 1475 r/min.The experimental results show that with the abrupt change of

load, the electromagnetic torque increases rapidly and the speedreaches to the reference value only after a short period of time.

IX. CONCLUSION

A novel space vector modulation based on twelve 30° sec-tors of both flux and voltage vectors within a circular locusof the space vector for the speed control of an IM fed by anMC-based DTC was developed. The performance of the pro-posal switching strategy was compared to the hexagonal bound-ary space vector modulation-based MC for the direct torquecontrol of an IM. The method provides additional degrees offreedom to select appropriate voltage vectors, which resulted in60% reduction of torque ripple. The simulation and experimen-tal results verify the applicability of the 12-sector space vectorswitching scheme for the direct torque control of an IM fed byan MC for different industrial application where there is highdemand for fast transient response of controlling scheme, lesstorque ripple, and accurate control of torque with compact andhigh reliability adjustable speed drive.

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S. Sina Sebtahmadi (S’12–M’14) received theB.Eng. (Hons.) degree in electronics engineering andthe M.Sc. degree in industrial electronics and con-trol from the University of Malaya, Kuala Lumpur,Malaysia, in 2012, where he is currently workingtoward the Ph.D. degree in Power Electronics engi-neering at Power Electronics and Renewable EnergyResearch Laboratory.

He has been a Research Assistant with the Univer-sity of Malaya, since 2012. His research interests in-clude industrialization of Matrix Converter, Z-source

Matrix Converter, DTC-based machine drives, and optimizing the power con-verters in terms of energy conversion.

Hossein Pirasteh received the B.Eng. degree inelectrical engineering from Islamic Azad University,Saveh, Iran, in 2005, and the M.Sc. degree from theK.N.Toosi University of Technology, Tehran, Iran, in2008.

He is currently a Lecturer of Daneshestan Institute,Saveh. His research interests include new topologyof matrix converter, controlling techniques of powerconverters, grid connected ac/ac drives.

S. Hr. Aghay Kaboli received the B.Eng. degree inelectrical engineering from Islamic Azad University,Esfahan, Iran, in 2009, and the M.Eng. degree fromthe University of Malaya, Kuala Lumpur, Malaysia,in 2012.

Since 2011, he has been a High Impact ResearchAssistant for Campus Network Smart Grid for EnergySecurity project with the University of Malaya. Hisresearch interests include ac/ac converters and dc/acmachine drives and smart grid.

Ahmad Radan (M’00) received the B.Sc. degreefrom Ferdowsi University, Mashhad, Iran, in 1987,the M.Sc. degree from Tehran University, Tehran,Iran, in 1991, and the Ph.D. degree from the Techni-cal University of Munich, Munich, Germany, in 2000,all in electrical engineering.

He is a currently an Associate Professor at theDepartment of Power and the Head of Power Elec-tronics Laboratory, K.N.Toosi University of Tech-nology, Tehran. His research interests include high-power converters and drives, modulation strategies,

control of power electronics converters, wind and solar energy applications ofpower electronics, and electric hybrid vehicles.

Saad Mekhilef (M’01–SM’12) received the B.Eng.degree in electrical engineering from the Univer-sity of Setif, Setif, Algeria, in 1995, and theM.Eng.Sci. and Ph.D. degrees from the University ofMalaya, Kuala Lumpur, Malaysia, in 1998 and 2003,respectively.

He is currently a Professor with the Departmentof Electrical Engineering, University of Malaya. Heis the author and coauthor of more than 200 publica-tions in international journals and proceedings. He isactively involved in industrial consultancy for major

corporations in the power electronics projects. His research interests includepower conversion techniques, control of power converters, renewable energy,and energy efficiency.

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