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Ain Shams Engineering Journal (2016) xxx, xxx–xxx

Ain Shams University

Ain Shams Engineering Journal

www.elsevier.com/locate/asejwww.sciencedirect.com

ELECTRICAL ENGINEERING

Matrix converters and three-phase inverters fed

linear induction motor drives—Performance

compare

* Corresponding author. Tel.: +20 1060707573.E-mail addresses: [email protected]

(E.E.M. Mohamed), [email protected] (M.A. Sayed).

Peer review under responsibility of Ain Shams University.

Production and hosting by Elsevier

http://dx.doi.org/10.1016/j.asej.2016.02.0022090-4479 � 2016 Faculty of Engineering, Ain Shams University. Production and hosting by Elsevier B.V.This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Please cite this article in press as: Mohamed EEM, Sayed MA, Matrix converters and three-phase inverters fed linear induction motor drives—Performanpare, Ain Shams Eng J (2016), http://dx.doi.org/10.1016/j.asej.2016.02.002

Essam E.M. Mohamed *, Mahmoud A. Sayed

Electrical Engineering Department, Faculty of Engineering, South Valley University, Qena, Egypt

Received 23 March 2015; revised 19 January 2016; accepted 21 February 2016

KEYWORDS

Linear induction motors

(LIM);

Three-phase inverter;

Matrix converters;

Space-vector PWM;

Indirect field oriented control

(IFOC)

Abstract In this paper, the system of the Linear Induction Motor (LIM) driven by direct AC–AC

matrix converter is presented and its dynamic performance is briefly compared with the conven-

tional LIM drives based on AC–DC–AC converter. Space-vector pulse-width modulation (SVM)

and indirect field oriented control (IFOC) are applied to control the two employed converters.

For the sake of comparison, the PI controllers are applied to control the primary (mover) speed

and current considering the same parameter settings. The objective of this paper was to compare

theoretically the dynamic performance of linear induction motor (single-sided LIM) drives driven

by three-phase voltage source inverters and the direct AC/AC matrix converters. The study com-

pares the dynamic performance in addition to the harmonics content and THD of the input and

output voltage and current for both converters. The simulation of each system has been imple-

mented using the MATLAB/SIMULINK platform.� 2016 Faculty of Engineering, Ain Shams University. Production and hosting by Elsevier B.V. This is an

open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

Linear motors are special electrical machines, in which

electrical energy is converted directly into linear mechanicalmovement without the need for rotary to linear conversion.There are many types of linear motors such as; DC motors,

permanent magnet motors, synchronous motors, and steppingmotors. Among these types, The Linear Induction Motor

(LIM) is considered one of the most promising types of linearmotors due to its high-starting thrust force, high-speed opera-tion, simple mechanical construction, no need for a gear

between motor and motion devices, reduction of mechanicallosses and size of motion devices, silence operation, easy main-tenance, no backlash, low friction, and suitability for both lowand high speed applications [1]. Therefore, LIMs are now

widely used in many industrial applications with satisfactoryperformance including transportation, conveyor systems, actu-ators, material handling, pumping of liquid metals, sliding

door closers, robot base movers, office automation, drop tow-ers, and elevators [2,3].

ce com-

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http://dx.doi.org/10.1016/j.asej.2016.02.002


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Nomenclature

kdr � kqr d–q secondary flux components

/i phase angle of the input waveform/o phase angle of the output waveformkar � kbr a–b secondary flux componentsh reference vector position

r leakage coefficientD viscous friction and iron-loss coefficientF1 end-effect force disturbance

Fe electromagnetic forceFL external force disturbanceh pole pitch

ias � ibs a–b primary current componentsisx supply input current, x denotes for r, s, or ticx converter input current, x denotes for r, s, or tKf force constant

Lm magnetizing inductance per phaseLr secondary inductance per phaseLs primary inductance per phase

M total mass of the moving element

np number of pole pairs

p differential operatorRr secondary resistance per phaseRs primary winding resistance per phaseT0 ON interval of zero vectors

Tn ON intervals of active vectorsTr secondary time constantTs switching period

V0: V7 switching vectorsVdc dc link voltageVenv instantaneous value of the rectified input volt-

age envelopeV�

s reference vectorV�

as � V�bs a–b reference voltage components

Vas � Vbs a–b primary voltage components

v primary (mover) linear velocityve synchronous linear velocityvsl slip velocity

2 E.E.M. Mohamed, M.A. Sayed

In the past few decades, Indirect Field Oriented Control oflinear induction machines has been tremendously applied

through the literature to resemble the ideal performance ofseparately excited DC machines by decoupling the flux currentcomponent and the force current component to separate

between secondary flux and motion dynamics. By doing so,the secondary flux-magnetizing current component is kept nulland the secondary force producing current component is kept

constant; hence, high dynamic performance is gained [4–7].Voltage source inverters (VSIs) are extensively applied to

study the performance of linear induction motor drives. Theauthors in [4,8–11] studied the performance of new vector con-

trol algorithms applying machine models that consider theend-effect. In [12] Hamedani and Shoulaie studied the LIMperformance applying IFOC using five-level Cascaded H-

bridge (CHB) inverter with multi-band hysteresis modulation.The Adaptive Fuzzy Sliding Mode Control of LIM has beenexamined experimentally using hysteresis current control

(HCC) and IFOC by Chin et al. in [13]. In [14], Liu et al. stud-ied the performance of Sliding Mode Current Control usingVSI and IFOC. In [15–17], the performance of LIM is studied

Figure 1 Structure of an experimental LIM [24].

Please cite this article in press as: Mohamed EEM, Sayed MA, Matrix converters apare, Ain Shams Eng J (2016), http://dx.doi.org/10.1016/j.asej.2016.02.002

using voltage-source inverters incorporated with new directthrust controller algorithms. Traditional voltage source invert-

ers have some drawbacks: the two stage operation that reducesthe reliability of the system, the bulky short life-time capacitoron the rectification stage, high power losses, and high input

current THD [18].On the other hand, direct AC/AC matrix converter over-

comes the previous mentioned drawbacks of traditional VSI.

The AC/AC matrix converters are applied to provide fullycontrollable output voltages in a single conversion stage. Fea-tures of matrix converters that make them an attractive solu-tion for some applications include the following: bulky DC

capacitors free, which improves the system reliability, bidirec-tional switches used in matrix converters which enable regener-ative power process, unity input power factor which can be

obtained at the input side, decreased THD of input and outputcurrents in addition to the output voltage, and unlimited out-put frequency range [18]. At the same time, matrix converters

have some drawbacks: the maximum ratio between the inputand output is limited to 86.7%, as well as the complexity ofthe controller and converter structure [18]. In [19], the authorsproposed the use of carrier based PWM matrix converters in

controlling the LIM speed.Space-vector pulse width modulation (SV-PWM), intro-

duced in [20] based on the principles of space-vectors, is

intended to approximate the demanded voltage based on theVolt. Second. The operation of space-vector PWM has beenanalyzed and detailed in [21]. The duty of SV-PWM is to gen-

erate the power converter controlling signals according to thereference d–q voltage components calculated by the speed andcurrent control loops.

This paper presents a comparison of the linear inductionmotor drive performance fed by a conventional three-phaseinverter and matrix converter drives. In both converters, theswitching signals have been obtained based on SVM and the

LIM speed is controlled based on IFOC. Section 1 providesan introduction to LIM drives and control. Section 2 presents

nd three-phase inverters fed linear induction motor drives—Performance com-


(a) block diagram

(b) VSI

Vdc

+

PI

abc/dq

PI

PIdq/αβ SV-PWM

VSI v*

v

Fig.3θe

θe

6Switching

signals

Vαs

Vβs

Load force and end effect

FL+Fl

--

-

DSP

v

VSI LIM

v

iqs*iqs*

ids*

ids*

Vqs*

Vds*

*

*

Cdcvr

vs

vt

Vdc

va

vb

vc Sx

S1 S3 S5

S4 S6 S2Ci

Ri

Li

isr icr

iss ics

ist ict

Figure 2 VSI fed LIM drive.

v

Σvsl ve

θe

π/h ∫

np

iqs*

ids*Tr

iqs*

ids*

Figure 3 Calculation of electrical position, he [12].

β

α

(100)

(110)(010)

(011)

(001) (101)

(000-111)

vs*v1

v2v3

v4

v5 v6

v0-v7

III

III

IVV

VI

(a) Switching and reference vectors

Figure 4 SVM topolog

Matrix converters and three-phase inverters 3


the dynamic model of the LIM considering the end effect. Sec-tion 3 describes the Indirect Field Oriented Control of LIM.Section 4 explains the Linear Induction Motor convertertopologies. Simulation results are given in Section 5. Finally,

Section 6 presents the conclusions.

2. Dynamic model of LIM taking end effect into consideration

A three-phase LIM is shown in Fig. 1. The primary (mover) issimply a cut open and rolled flat rotary-motor primary. Thesecondary, usually consists of an aluminum sheet conductor

with an iron back for the return path of magnetic flux. Theprimary and the secondary form a single-sided LIM. A simple

(b) Synthesis of reference vector

β

α

vs

θ

*

2/3Vdc

(T1/Ts)V1

(T2/Ts)V2

(T0/Ts)V0

y for VSI drives [21].




linear encoder is employed to provide feedback of the primaryposition. The electrical dynamic model of the LIM is modifiedfrom the traditional model of a three phase, Y-connected

induction motor in stationary a–b frame and can be describedby the following differential equations [22]:

(a) block dia

(b) MC

abc/d

PI

PIdq/αβ

SV-PWMMC

θe

9Switching signals

-

MC

αβ/abc

Vqs*

Vds*

Vαs*

Vβs*

vr

vs

vt

Sxy

Ci

Ri

Li

isr icr

iss ics

ist ict

Figure 5 Matrix conve

(a) Switching and reference vector

β

α

(CAA)(ABB)(BCC)

III

III

IV V

VI

vs*

(AAB)(BBC)(CCA)

(ACA)(BAB)(CBC)

(BAA)(CBB)(ACC)

(ACC)(BBA)(CCB)

(ABA)(BCB)(CAC)(AAA)

(BBB)(CCC)

Figure 6 SVM topology


pias ¼ � Rs

rLs

þ 1� rrTr

� �ias þ Lm

rLsLrTr

kar þ npLmprLsLrh

vkbr

þ 1

rLs

Vas ð1Þ

gram

PI

q

v

Fig. 3θe

Load force and end effect

--

DSP

v

LIMFL+Fl

iqs*iqs*

ids*

ids* v*

a

b

c

va

vb

vc

Sra

Ssa

Sta

Srb

Ssb

Stb

Src

Ssc

Stc

rter fed LIM drive.

(b) Synthesis of reference vector

β

α

θ

vs*

v1

v6

for MC drives [28,29].



0

200

400

olta

ge (V

)


pibs ¼ � Rs

rLs

þ 1� rrTr

� �ibs þ Lm

rLsLrTr

kbr � npLmprLsLrh

vkar

þ 1

rLs

Vbs ð2Þ

pkar ¼ Lm

Tr

ias � 1

Tr

kar � npph

vkbr ð3Þ

pkbr ¼ Lm

Tr

ibs � 1

Tr

kbr þ npph

vkar ð4Þ

pv ¼ 1

MFe � D

Mv� 1

MFL ð5Þ

where Tr ¼ Lr=Rr and r ¼ 1� ðL2m=LsLrÞ.

The longitudinal end-effect is approximated by Taylor’sseries and can be taken as an external load force, Fl, [22,23]:

Fl ¼ h1 þ h2vþ h3v2 ð6Þ

where h1, h2, and h3 are constants. This end-effect increaseswith the speed of the primary (mover) [4,8]. Taking F1 into

consideration, Eq. (5) is rewritten as follows:

pv ¼ 1

MFe � D

Mv� 1

MðFL þ F1Þ ð7Þ

0 0.1 0.2 0.3 0.4 0.5-400

-200

Sup

ply

v

0 0.1 0.2 0.3 0.4 0.5-15-10-505

1015

Sup

ply

0 0.1 0.2 0.3 0.4 0.5-15-10-505

1015

Mot

or

0 0.1 0.2 0.3 0.4 0.50

5

10

15

d-q

axis iqs & i*

qs

ids & i*ds

0 0.1 0.2 0.3 0.4 0.50

400

8001000

Forc

e (N

) Fe

FL & Fl

0 0.1 0.2 0.3 0.4 0.5-0.5

0

0.5

1

Time (s)

Spe

ed (m

/s)

v*

v

v

curr

ents

(A)

curr

ents

(A)

curr

ents

(A)

3. Indirect field oriented control of a LIM

In the field oriented control method, the dynamics of thehighly coupled nonlinear structure of the induction machine

becomes linearized and decoupled. The decoupled relationshipis obtained by proper selection of state coordinates, under thehypothesis that the rotor flux is kept constant [1]. Therefore,

the rotor speed is only asymptotically decoupled from therotor flux, and is linearly related to the torque current onlyafter the rotor flux becomes in the steady state. The flux model

of the LIM can be described in the d–q synchronous frame as[24] follows:

pkdr ¼ Lm

Tr

ids � 1

Tr

kdr þ phve � npp

hv

� �kqr ð8Þ

pkqr ¼ Lm

Tr

iqs � 1

Tr

kqr � phve � npp

hv

� �kdr ð9Þ

In an ideally decoupled induction motor, the secondary fluxlinkage axis is forced to be aligned with the d-axis, and the fieldorientation conditions can be applied. It follows that:

kqr ¼ 0 and pkdr ¼ pkqr ¼ 0 ð10ÞUsing (10), the desired secondary flux linkage in terms of idscan be found from Eq. (8) as follows:

kdr ¼ Lmids ð11ÞMoreover, Eq. (8) can be combined with Eqs. (9) and (10) togive the feed-forward slip velocity signal as follows:

vsl ¼ phve � npp

hv ¼ iqs

Tridsð12Þ

The electromagnetic force can be described in the d–q syn-chronous frame as [24] follows:

Fe ¼ kfðkdriqs � kqridsÞ ð13Þ


where kf is the force constant which is equal to: kf ¼ 3npLmp2Lrh

.

With the implementation of the field oriented control, Eq.

(13) can be rewritten using Eqs. (10) and (11) as follows:

Fe ¼ KFiqs ð14Þwhere KF ¼ kfLmids.

If the d-axis primary current (flux current component) is

kept constant at rated value, the electromagnetic force isdirectly proportional to the q-axis current. In this case, if theq-axis current is rapidly changed in response to the load vari-ation, this will be followed by a rapid change in the motor

developed force and the LIM will exhibit a high dynamicperformance.

4. Linear induction motor converter topologies

The performance of the LIM is examined by two differentpower converters, i.e. the VSI and the MC; hence, speed con-

Figure 7 Dynamic performance of the VSI drive.




trol loop and the d–q current regulators are kept unchanged.For the two cases, the Clarke and Park transformations areapplied based on the description given in [25]. The electrical

position, he, used in Clarke and Park transformations is calcu-

0.3 0.302 0.304 0.306 0.308 0.31-1000

-500

0

500

1000

Time (sec)

Line

vol

tage

(V)

0.3 0.302 0.304 0.306 0.308 0.31-15

-10

-5

0

5

10

15

Time (sec)

Mot

or c

urre

nt (A

)

0.3 0.305 0.31 0.315 0.32 0.325 0.33 0.335 0.34-15

-10

-5

0

5

10

15

Time (sec)

Sup

ply

curr

ent (

A)

0.3 0.305 0.31 0.315 0.32 0.325 0.33 0.335 0.34-15

-10

-5

0

5

10

15

Time (sec)

Inpu

t cur

rent

(A)

Figure 8 VSI steady


lated as shown in Fig. 3 [24,26,27]. The difference between thetwo cases is in the SV-PWM block, which is changed accordingto the employed power converter and the number of switches

as detailed below.

102

103

104

105

10-2

10-1

100

101

102

Frequency (Hz)

FFT

(%)

fs

f1=222 Hz, THD=86.7%

102

103

104

105

10-2

10-1

100

101

102

Frequency (Hz)

FFT

(%)fs

f1=222 Hz, THD=5.1%

101

102

103

104

105

10-6

10-4

10-2

100

102

Frequency (Hz)

FFT

(%)

fs

f5&f7

f1=50 Hz, THD=38 %

101

102

103

104

105

10-4

10-2

100

102

Frequency (Hz)

FFT

(%)

state performance.



0 0.1 0.2 0.3 0.4 0.5-400

-200

0

200

400

Sup

ply

volta

ge (V

)

0 0.1 0.2 0.3 0.4 0.5-15-10-505

1015

Sup

ply

0 0.1 0.2 0.3 0.4 0.5-15-10-505

1015

Mot

or

0 0.1 0.2 0.3 0.4 0.50

5

10

15

d-q

axis

ids & i*ds

iqs & i*qs

0 0.1 0.2 0.3 0.4 0.50

400

8001000

Forc

e (N

) Fe

FL & Fl

0 0.1 0.2 0.3 0.4 0.5-0.5

0

0.5

1

Time (s)

Spe

ed (m

/s)

v*

v

v

curr

ents

(A)

curr

ents

(A)

curr

ents

(A)

Figure 9 Dynamic performance of the MC drive.


4.1. Voltage source inverter drives

Conventional three-phase voltage source inverters (VSIs)have been traditionally applied to develop controlled magni-tude and frequency AC voltage. Fig. 2(a) shows a block dia-

gram of VSI fed LIM drive. Fig. 2(b) depicts the rectifierand the VSI stage. The input supply voltages are rectifiedand smoothed using a three-phase full-wave rectifier andsmoothing capacitors respectively. The VSI consists of six

switches connected as three-leg bridge inverter. The controlsignals of the VSI are obtained by the control loops whichconsist of a speed PI controller, and two d–q axis currents

PI regulators. The d–q voltage references are then employedto calculate the switching periods of the VSI using the a–btransform and the SV-PWM VSI block. The SV-PWM

VSI block is implemented based on the description givenin [21]. While the voltage reference vector represents a rotat-ing vector with variable magnitude, the three-phase voltage

source inverter can compose specific eight switching statevectors according to eight switching patterns as depicted inFig. 4.

The duty cycles of the inverter are calculated according to

the space-vectors theory proposed by Broeck et al. [21]. Thereference voltage vector is approximated in average Volt. Sec-ond by applying the two active state vectors and two zero state

vectors. For reference vector V�s\h, as shown in Fig. 4, the ON

intervals of two adjacent vectors and two zero-vectors are cal-

culated so that [21]:

V�s ¼ Vn

Tn

Ts

þ Vnþ1

Tnþ1

Ts

þ V0

T0

Ts

ð15Þ

The ON intervals of the active vectors (Vn and Vnþ1) and zerovector (V0) can be calculated as follows:

Tn ¼ffiffiffi3

pTs

jV�s j

Vdc

sinp3� h

� �ð16Þ

Tnþ1 ¼ffiffiffi3

pTs

jV�s j

Vdc

sinðhÞ ð17Þ

T0 ¼ Ts � ðTn þ Tnþ1Þ ð18Þwhere

V �s ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiV �2

as þ V �2bs

q.

Tn and Tn+1: ON intervals of active vectors.

Ts: Switching period.T0: ON interval of zero vectors (divided equally between V0

and V7).

4.2. Three-phase AC/AC matrix converter

Fig. 5(a) shows the control block diagram of a three-phase tothree-phase matrix converter fed linear induction motor drive.Fig. 5(b) shows the matrix converter configuration, which con-sists of nine bidirectional switches that allow any output phase

to connect with any input phase. Each output phase is con-nected to the three input phases through three bi-directionalswitches, Sxy. For the nine bi-directional switches of matrix

converters, the available switching states equal 29, i.e. 512switching state. Applying the two contrarians given in (19)


and (20), the switching states reduce to 27 switching state.These switching states are presented in a regular hexagon asshown in Fig. 6. These states will be subdivided into three

groups [28,29]. First group (six states): when each input phaseis connected to only one of the output phases. The producedvectors have the same amplitude and different angles. This

group of switching states is unused. Second group (eighteenstates): when two of the output phases share the same inputphase, the output vectors have the same angle with different

amplitudes. Third group (three states): when all the outputphases share one input phase, which produce zero vectors.Fig. 6 presents the eighteen active vectors in addition to thethree zero vectors. Each sector has six different switching

states located at the edges and three zero states in the center.The MC controlling signals are calculated by the speed andcurrent regulators control loops as applied in the previous sec-

tion. The SV-PWM MC is implemented to approximate thereference voltage vector V�

s in a time averaging fashion. In each




sampling period, two active adjacent vectors and one zero vec-tor are selected from the 27 possible converter output vectors[28,29]. The ON intervals of the active and zero vectors can

be calculated by (19)

0.3 0.302 0.304 0.306 0.308 0.31-750

-500

-250

0

250

500

750

Time (sec)

Line

vol

tage

(V)

0.3 0.302 0.304 0.306 0.308 0.31-15

-10

-5

0

5

10

15

Time (sec)

Mot

or c

urre

nt (A

)

0.3 0.31 0.32 0.33 0.34 0.35 0.36-15

-10

-5

0

5

10

15

Time (sec)

Supp

ly c

urre

nt (A

)

0.3 0.305 0.31 0.315 0.32 0.325 0.33 0.335 0.34-15

-10

-5

0

5

10

15

Time (sec)

Inpu

t cur

rent

(A)

Figure 10 MC steady


T1 ¼ jVsjVenv

Ts sinðhÞ

T6 ¼ jVsjVenv

Ts sinp3� h

� �

T0 ¼ Ts � T1 � T6

ð19Þ

102

103

104

105

10-2

10-1

100

101

102

Frequency (Hz)

FFT

(%)

f1=218 Hz, THD=89.6%

fs/2fs

102

103

104

105

10-2

10-1

100

101

102

Frequency (Hz)

FFT

(%)

f1=218 Hz, THD=9.1%

fs/2

fs

101

102

103

104

105

10-2

10-1

100

101

102

Frequency (Hz)

FFT

(%)

f1=50 Hz, THD=21.5 %

f10

101

102

103

104

105

10-4

10-2

100

102

Frequency (Hz)

FFT

(%)

state performance.




whereT1 and T6, ON time of the two adjacent active vectors.

T0, ON time of zero vector.Venv, the instantaneous value of the rectified input voltage

envelope.

The Indirect Space Vector Modulation proposed by [30]and further described in [28,29] applied to calculate the exis-

tence function for each switch is expressed as follows:

SlmðtÞ ¼1 Slm closed

0 Slm opened

�l&m 2 1; 2; 3f g ð20Þ

In order to avoid short circuit that might be occurred between

the input phases and open circuit of the output phases, one andonly one switch per column must be ON.

Sm1 þ Sm2 þ Sm3 ¼ 1 m 2 1; 2; 3gf ð21ÞThe input three-phase voltage can be formulated as follows:

er

es

et

264

375 ¼ Vm

cosðxtþ /iÞcosðxtþ /i � 2p=3Þcosðxtþ /i þ 2p=3Þ

264

375 ð22Þ

where /i is the phase angle of the input waveform.The output three-phase voltage can be formulated as

follows:

va

vb

vc

264

375 ¼ Vm

cosðxtþ /oÞcosðxtþ /o � 2p=3Þcosðxtþ /o þ 2p=3Þ

264

375 ð23Þ

where /o is the phase angle of the output waveform.The relation between the input and the output waveforms

can be formulated as follows:

va

vb

vc

264

375 ¼

Sra Ssa Sta

Srb Ssb Stb

Src Ssc Stc

264

375

er

es

et

264

375 ð24Þ

The input current equation is obtained as follows:

ir

is

it

264

375 ¼

Sra Ssa Sta

Srb Ssb Stb

Src Ssc Stc

264

375

Tia

ib

ic

264

375 ð25Þ

0.3 0.32 0.34 0.36 0.38 0.4-400

-200

0

200

400

Sup

ply

volta

ge (V

)

0.3 0.32 0.34 0.36 0.38 0.4-10

-5

0

5

10

Time (sec)

Sup

ply

curre

nt (A

) VSIMC

Figure 11 Supply currents for MC and VSI converters.


5. Simulation results and discussion

5.1. System configuration

Figs. 2 and 5 depict the block diagram of linear inductionmotor fed by a conventional three-phase VSI and a three-

phase direct AC/AC matrix converter, respectively. AppendixA gives the parameters of the LIM, and the PI controllersand the settings of the Simulink models. For the sake of com-

parison, the simulation has been performed under the samemodeling parameters and simulation settings, i.e. the same PIcontroller parameters, the same Simulink settings, and thesame load and speed profiles. Appendices B and C present

the Matlab Simulink models of the MC and the VSI drive sys-tems respectively.

5.2. Dynamic performance of the LIM driven by VSI

Fig. 7 shows the simulation results of the supply voltage, LIMthree-phase current, reference and actual d–q axis currents, and

the supply current, the load force and electromagnetic devel-oped force, and reference and actual LIM speed. It is clearthat, the load force and the electromagnetic developed force

agree well.Also, the reference and actual LIM speed in addition to the

reference and actual d–q axis current of the LIM are in closeagreement. Fig. 8 shows the harmonic spectrum of the LIM

line voltage, LIM line current, the supply current, and theVSI input current. It is clear that the harmonic spectrum ofthe line voltage has high frequency components resulting in

THD equals 86.7%. Also, the LIM line current is sinusoidalwaveforms and its harmonic spectrum shows low THD, of5.1%. Since the first stage has uncontrolled rectifier the supply

current has significant low order odd harmonics of 5th, 7th,11th, 13th, . . ., due to the limited effect of the input filter onthe VSI input current as it has been designed to remove highswitching harmonics; hence, about 27% of 5th harmonic and

10% of 7th harmonic are present in both the supply currentand input current of the VSI drive with 38% of THD.

5.3. Dynamic performance of the LIM driven by matrixconverter

The LIM driven by matrix converter is carried out in the Mat-

lab Simulink environment in order to investigate its dynamicperformance. Fig. 9 shows the simulation results of the refer-ence and actual LIM speed, LIM three-phase currents, refer-

ence and actual d–q axis currents, supply currents andvoltages and the load force and electromagnetic developedforce. It is clear that there is a closed agreement between thewaveforms of the load force and the electromagnetic developed

force, the reference and actual LIM speed, and the referenceand actual d–q axis current of the LIM. Moreover, the unityinput power factor at the supply side has been achieved since

the supply current and voltage are almost in-phase as shownin Fig. 11. Fig. 10 shows the harmonic spectrum of the matrixconverter output line-to-line voltage, LIM line current, the

supply current, and the MC input current. It is clear that theharmonic spectrum of the line voltage has high frequency com-ponents with little higher magnitude resulting in THD equals




89.6%. In addition, the LIM line currents have sinusoidalwaveforms and its harmonic spectrum shows a THD of9.1%. The supply current has a near sinusoidal waveform with

lower THD of 21.5%. It can be seen in Fig. 10 that, the inputfilter improves the supply current shape of the MC drive,where the MC input current has a quasi-square switched and

the supply current has near sinusoidal waveforms.

5.4. Features comparison

Comparing the two drives dynamic performance shown inFigs. 7 and 9, it can be seen that the two drives track boththe speed and load demands. The supply current of the VSI

drive has a non-sinusoidal waveform with high harmonic con-tents due to the uncontrolled rectifier action. On the otherhand, high force ripples are noticed in the developed force ofthe matrix converter drive, which can be related to the high

switching ripples found in the d–q current components dueto the rough nature of the MC switching operation. However,the d–q current components track well their demanded refer-

ences. In addition, the THD of the supply current is smallerthan that in case of using conventional VSI. The supply cur-rent of the matrix converter has a sinusoidal waveform and

unity input power factor operation has been gained.

6. Conclusions

This paper has presented the matrix converter for the linearinduction motor drives. The dynamic performance of thematrix converter has been compared with conventional AC/DC/AC converter in order to investigate its validity in control-

ling the LIM speed. Both converters have been controlledusing field oriented control. The SVM has been used to gener-ate the proper PWM signals of both converters. MATLAB/

SIMULINK software has been used to simulate both convert-ers with the LIM model. Simulation results prove that thematrix converter as a LIM drive has shown better THD in

the output voltage and the input current than that in the con-ventional drives. However, the dynamic performance of bothconverters looks the same.

Discrete,Ts = 5e-06 s.

powerguiV*

Vabc

Iabc

A

B

C

a

b

c

Vabc

Iabc

A

B

C

a

b

c

Vd_Ref

Vq_Ref

theta

MC-SVPWM

a

b

c

A

B

C

Input filter

V

v *

v

Vd*

Vq*

theta

CONTROLLER

Appendix B. Linear induction motor drive SIMULINK MODEL-M


Appendix A. Linear induction motor drive parameters

C

n

LIM

Stator

resistance, Rs

g1

g2

g3

g4

g5

g6

g7

g8

g9

R

S

T

Matrix Co

Stw

Ssw

Srw

Stv

Ssv

Srv

Ssu

Stu

Sru

d three-phase invert

5.37 Ω

U

V

W

nverter

ers fed linear i

Pole pitch, h

fl

fl vabc

iabc

v

fe

vess

va

vb

vc

van

vbn

vcn

LIM

nduction motor drives—Perfo

0.027 m

Mover

resistance, Rr

3.75 Ω
Total mass of the
mover, m

2.78 kg

Primary

inductance, Ls

0.02846 H
Viscous friction and
iron-loss coefficient, D

36.045 kg/

s

Secondary

inductance, Lr

0.02846 H
Force constant, kf 593.35 N/
Wb A

Magnetizing

inductance, Lm

0.02419 H
Rated secondary flux, 0.056 Wb
Number of

poles, np

8
Rated line current, Ir 14.2 A
Rated load
650 N –
Converters

MC
VSI
Input side filter

inductance, Li

7.3 mH
Input side filter
inductance, Li

rm

7.3 mH

Input side filter

inductance, Ci

13.2 lF
Input side filter
inductance, Ci

13.2 lF

Input side filter

resistance, Ri

47 Ω
Input side filter
resistance, Ri

47 Ω

–
Smoothing capacitor,
Cdc

200 lF

PI controllers

Speed regulator
d–q axis current regulators
kp
3 500
ki
500 1000
SIMULINK

Sampling time, Ts
5 ls Phase supply voltage,
Vs

an

220 V

Switching frequency,

Fs

10 kHz
Supply frequency, f 50 Hz
ce com-


v*Discrete,Ts = 5e-06 s.

powergui

A

B

C

+

-

g

A

B

C

+

-

Vabc

Iabc

A

B

C

a

b

c

Vabc

IabcA

B

C

a

b

c

+

fl vabc

iabc

ves

fe

V

va

vb

vc

van

vbn

vcn

LIM

A

B

C

a

b

c

Input filter

V

v*

v

gates

CONTROLLER

Appendix C. Linear induction motor drive SIMULINK MODEL-VSI


References

[1] Loukianov A, Rivera J, Alanis A, Raygoza J. Super-twisting

sensorless control of linear induction motors. In: Electrical

engineering, computing science and automatic control (CCE),

2012 9th international conference on; 2012. p. 1–5.

[2] Bucci G, Meo S, Ometto A, Scarano M. The control of LIM by a

generalization of standard vector techniques. In: Industrial

electronics, control and instrumentation, 1994. IECON’94, 20th

international conference on; 1994. p. 623–26.

[3] Zhang Z, Eastham TR, Dawson GE. Peak thrust operation of

linear induction machines from parameter identification. In:

Industry applications conference, 1995. Thirtieth IAS annual

meeting, IAS’95., Conference Record of the 1995 IEEE; 1995. p.

375–79.

[4] da Silva EF, dos Santos CC, Nerys JWL. Field oriented control of

linear induction motor taking into account end-effects. In:

Advanced motion control, 2004. AMC ’04. The 8th IEEE

international workshop on; 2004. p. 689–94.

[5] da Silva EF, dos Santos EB, Machado PCM, de Oliveria MAA.

Vector control for linear induction motor. In: Industrial technol-

ogy, 2003 IEEE international conference on, vol. 1; 2003. p. 518–

23.

[6] Rathore AK, Mahendra SN. Direct secondary flux oriented

control of linear induction motor drive. In: Industrial technology,

2006. ICIT 2006. IEEE international conference on; 2006. p.

1586–90.

[7] Motlagh S, Fazel SS. Indirect vector control of linear induction

motor considering end effect. In: Power electronics and drive

systems technology (PEDSTC), 2012 3rd; 2012. p. 193–98.

[8] Jeong-Hyoun S, Kwanghee N. A new approach to vector control

for a linear induction motor considering end effects. In: Industry

applications conference, 1999. Thirty-fourth IAS annual meeting.

Conference record of the 1999 IEEE, vol. 4; 1999. p. 2284–89.

[9] Jianqiang L, Fei L, Hu S, Zheng TQ. Optimal efficiency control of

linear induction motor for linear metro. In: Power electronics

specialists conference, 2008. PESC 2008. IEEE; 2008. p. 673–77.

[10] Kang G, Nam K. Field-oriented control scheme for linear

induction motor with the end effect. In: Electric power applica-

tions, IEE proceedings, vol. 152; 2005. p. 1565–72.

[11] Jianqiang L, Fei L, Zhongping Y, Zheng TQ. Field oriented

control of linear induction motor considering attraction force &

end-effects. In: Power electronics and motion control conference,

2006. IPEMC 2006. CES/IEEE 5th international; 2006. p. 1–5.

[12] Hamedani P, Shoulaie A. Indirect field oriented control of Linear

Induction Motors considering the end effects supplied from a

Cascaded H-Bridge inverter with multiband hystersis modulation.


In: Power electronics, drive systems and technologies conference

(PEDSTC), 2013 4th; 2013. p. 13–9.

[13] Chin IH, Kou-Cheng H, Hsin-Han C, Kuang-Yang K, Tsu-Tian

L. Adaptive fuzzy sliding mode control of linear induction motors

with unknown end effect consideration. In: Advanced mecha-

tronic systems (ICAMechS), 2012 international conference on;

2012. p. 626–31.

[14] Liu J, You X, Zheng TQ. Sliding-mode variable structure current

controller for field oriented controlled linear induction motor

drive. In: Power electronics and motion control conference, 2009.

IPEMC’09. IEEE 6th international; 2009. p. 1036–39.

[15] Susluoglu B, Karsli VM. Direct thrust controlled linear induction

motor including end effect. In: Power electronics and motion

control conference, 2008. EPE-PEMC 2008. 13th; 2008. p. 850–54.

[16] Usta MA, Akyazi O, Akpinar AS. Simulation of direct thrust

control for linear induction motor including end-effect. In:

Innovations in intelligent systems and applications (INISTA),

2012 international symposium on; 2012. p. 1–5.

[17] Byung-Il K, Kyung-Il W, Kim S. Finite element analysis of direct

thrust-controlled linear induction motor. Mag, IEEE Trans

1999;35:1306–9.

[18] Casadei D, Grandi G, Tani A. Space vector control of matrix

converters with unity input power factor and sinusoidal input/

output waveforms. In: Fifth European conference on power

electronics and applications; 13–16 September 1993. p. 170–75.

[19] Sayed MA, Mohamed EE, Mohamed TH, Takeshita T. Field

oriented control of sensorless linear induction motor using matrix

converter. In: Power electronics conference (IPEC-Hiroshima

2014 – ECCE-ASIA), 2014 international; 2014. p. 3877–84.

[20] Pfaff G, Weschta A, Wick AF. Design and experimental results of

a brushless AC servo drive. IEEE Trans Ind Appl 1984;IA-

20:814–21.

[21] Van Der Broeck HW, Skudelny HC, Stanke GV. Analysis and

realization of a pulsewidth modulator based on voltage space

vectors. IEEE Trans Ind Appl 1988;24:142–50.

[22] Kuang-Yow L, Cheng-Yao H, Chian-Song C, Li-Chen F. Robust

adaptive control of linear induction motors with unknown end-

effect and secondary resistance. Energy Convers, IEEE Trans

2008;23:412–22.

[23] Chin IH, Ko-Lo C, Hou-Tsan L, Li-Chen F. Nonlinear adaptive

backstepping motion control of linear induction motor. In:

American control conference, 2002. Proceedings of the 2002,

vol. 4; 2002. p. 3099–04.

[24] Lin F-J, Shieh H-J, Shyu K-K, Huang P-K. On-line gain-tuning

IP controller using real-coded genetic algorithm. Electr Power

Syst Res 2004;72:157–69, 12/1.

[25] Instruments T. Clarke & park transforms on the TMS320C2xx.

Application Report BPRA, vol. 48; 1996.


http://refhub.elsevier.com/S2090-4479(16)00031-9/h0085


















[26] Hassan A, Mohamed Y, Mohamed T. Robust control of a field

oriented linear induction motor drive. In: Power systems confer-

ence, 2006. MEPCON 2006. Eleventh international middle east;

2006. p. 41–7.

[27] Hassan AAE, Sayed Y, Hiyama MT, Mohamed TH. Model

predictive control of a speed sensorless linear induction motor

drive. In: The 14th international middle east power systems

conference, MEPCON’10; December 19–21, 2010.

[28] Dabour SM, Rashad EM. Analysis and implementation of space-

vector-modulated three-phase matrix converter. IET Power Elec-

tron 2012;5:1374–8.

[29] Wheeler PW, Rodriguez J, Clare JC, Empringham L, Weinstein

A. Matrix converters: a technology review. In: Industrial elec-

tronics, IEEE transactions on, vol. 49; 2002. p. 276–88.

[30] Huber L, Borojevic D. Space vector modulator for forced

commutated cycloconverters. In: Industry applications society

annual meeting, 1989., conference record of the 1989 IEEE; 1989.

p. 871–76.

Essam E.M. Mohamed was born in Qena,

Egypt, in 1974. He received the BSc and the

MSc degrees in electrical power and machines

engineering from Faculty of Energy Engi-

neering, Aswan University, Aswan, Egypt, in

1997 and 2003 respectively. He received the

Ph.D. degree in electrical engineering from the

University of Sheffield, Sheffield, United

Kingdom in 2011. In 1999, he joined the

Department of Electrical Engineering, Faculty

of Energy Engineering, Aswan University, as

a Demonstrator, as a Lecturer Assistant in 2003, and as a Lecturer in


2011. Since 2013, he has been with the Department of Electrical

Engineering, Faculty of Engineering, South Valley University, Qena,

Egypt. His current research interests include power electronics, elec-

trical machines design and control, electric drives design and control,

multi-phase electrical machines, and renewable energy systems. He is a

member of IEEE and founder and manager of the South Valley

University IEEE student branch.

Mahmoud A. Sayed was born in Qena Pre-

fecture, Egypt, in 1974. He received the B.Sc.

and M.Sc. degree in Electrical Engineering

from Minia University, El-Minia, Egypt, in

1997 and 2001, respectively, and the Ph.D.

degree from the Nagoya Institute of Tech-

nology, Nagoya, Japan, in 2010. Since 1999,

he has been with the Department of Electrical

Engineering, Faculty of Energy Engineering,

Aswan University, Aswan, Egypt. Currently,

he is an Assistant Professor in the Department

of Electrical Engineering, Faculty of Engineering, South Valley

University, Qena, Egypt. His research interests include series and shunt

compensation of electrical distribution systems for voltage regulation

and loss reduction using series and shunt PWM converters in addition

to renewable energy applications and machine drives. He is a member

of the IEEE Power Electronics Society.






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