IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 1, JANUARY 2012 93

A Research on Space Vector Modulation Strategyfor Matrix Converter Under Abnormal

Input-Voltage ConditionsXingwei Wang, Hua Lin, Member, IEEE, Hongwu She, Student Member, IEEE, and Bo Feng

Abstract—The matrix converter is a single-stage ac–ac powerconversion device without dc-link energy storage elements. Anydisturbance in the input voltages will be immediately reflected tothe output voltages. In this paper, a modified space vector mod-ulation strategy for matrix converter has been presented underthe abnormal input-voltage conditions, in terms of unbalance,nonsinusoid, and surge (sudden rising or sudden dropping). Byusing the instantaneous magnitude and phase of input-voltagevector to calculate the voltage modulation index and input-currentphase angle, this modified modulation strategy can eliminate theinfluence of the abnormal input voltages on output side without anadditional control circuit, and three-phase sinusoidal symmetricalvoltages or currents can be obtained under normal and abnormalinput-voltage conditions. The performance of the input currentsis analyzed when the matrix converter uses different modulationstrategies. Some numerical simulations are presented to confirmthe analytical results. Tests are carried out on a 5.5-kW matrixconverter prototype. Experimental results verify the validity of theproposed strategy.

Index Terms—Abnormal input, matrix converter, modulationindex, modulation strategy, space vector modulation (SVM).

I. INTRODUCTION

MATRIX converter offers a number of advantages, includ-ing simple and compact power circuit, generation of

load voltage with arbitrary amplitude and frequency, sinusoidalinput and output currents, and operation with unity power factorfor any load [1]–[3]. It has found more and more applicationsin motor drive, power supply, wind generation, dynamic voltagerestorer, etc. [4]–[7].

Three approaches are widely used when developing mod-ulation strategies for matrix converters. The first one is theAlesina–Venturini modulation strategy based on transfer func-tion analysis and has been proposed in [8] and [9]. The secondone is the space vector modulation (SVM) strategy, including

Manuscript received December 6, 2010; revised March 28, 2011; acceptedApril 28, 2011. Date of publication May 23, 2011; date of current versionOctober 4, 2011. This work was supported in part by the Natural ScienceFoundation of Hubei Province, China, under Grant 2009CDB413 and in partby the National Basic Research Program of China (973 Program) under Grant2010CB227206.

The authors are with the College of Electrical and Electronic Engineering,Huazhong University of Science and Technology, Wuhan 430074, China(e-mail: wxw@mail.hust.edu.cn; lhua@mail.hust.edu.cn; hongwu.she@ieee.org; fengbohust@163.com).

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

Digital Object Identifier 10.1109/TIE.2011.2157288

indirect SVM and direct SVM proposed in [10] and [11],respectively. The SVM modulation strategy is often used inmatrix converter for it has some advantages, such as immediatecomprehension of the required commutation processes, a sim-plified control algorithm, and maximum voltage transfer ratiowithout adding third harmonic components [1]. The third oneis based on the double input line-to-line voltages and has beenproposed in [12].

However, these conventional modulation strategies are de-rived under the assumption that the input voltages are wellbalanced and sinusoidal. In practice, the matrix converter mayoperate under abnormal input-voltage conditions, in terms ofunbalance, nonsinusoid, and surge (sudden rising or suddendropping). Due to lack of dc-link capacitors for energy storage,the matrix converter is highly sensitive to disturbances in theinput voltages. For most of the modulation strategies, the unbal-anced and nonsinusoidal input voltages can result in unwantedoutput harmonic voltages. The short-time input-voltage surgecould bring the voltage surge on the load side instantly [13],[14]. Several techniques that reduce this influence of the abnor-mal input voltages for these conventional modulation strategieshave been reported.

For the Alesina–Venturini modulation strategy, by incorpo-rating the characteristics of the supply voltage into the com-putation and adjusting the calculated duty cycles accordingly[15]–[17], the modified strategy can synthesize the desiredoutput voltages when the supply voltages are either unbalancedor distorted. Another strategy using a single output-voltagecontrol loop employing a repetitive controller has been imple-mented [18]. This controller can attenuate the intermodulationharmonic components generated at the output of a matrixconverter.

In [19], an improved double input line-to-line voltagesynthesis strategy is developed to improve the input andoutput performances of matrix converter when the input volt-ages are unbalanced, and it has been applied to industries byYASKAWA [20].

An effective modified SVM is proposed in [21] for theindirect SVM. The output-voltage waveforms are improved ob-viously by adding negative sequence components into the mod-ulation vector of fictitious rectifier. This method can improvethe output-voltage performance, but it is too complex and onlyused under the unbalanced input voltages. Two compensationtechniques are proposed to improve the output performance ofthe matrix converter. The first one is a feedback compensation

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94 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 1, JANUARY 2012

Fig. 1. Schematic diagram of a three-phase/three-phase matrix converter.

method using closed-loop control of output currents [22], [23].The other technique is a feedforward compensation method[22]–[25], which is based on the instantaneous values of thethree-phase input voltages. In [22] and [24], the inverter stagemodulation index is adjusted adaptively according to the varia-tion of the virtual dc-link voltage, and this method can be onlyused with indirect SVM, whereas the modulation index with thewhole matrix converter is calculated using actual input voltagesto compensate the distortion presented in [23] and [25]. Thefeedforward compensation method can reduce the load currentdistortion considerably but not totally if the supply voltages aredistorted [23]. To achieve sufficient compensation, a combi-nation of feedback and feedforward compensation methods isproposed in [23].

A simple modified strategy is proposed in [26] for the space-vector-modulated matrix converter, including indirect SVM anddirect SVM. In this method, not only the modulation indexis calculated using instantaneous vector magnitude of outputvoltages and input voltages but also the input-current vectorangle is calculated using the actual input-voltage vector angle.

In this paper, the derivation process of the proposed SVMstrategy is presented in detail based on [26], and the modifiedcalculation of the sector angle of the input-current vector isanalyzed further compared with various input-voltage condi-tions. First, a review of the conventional SVM theory for matrixconverters is presented in Section II. Then, in Section III,the modified strategy is derived from the conventional SVM.The numerical simulations compared with different modulationmethods have been carried out in Section IV. Moreover, theperformance of the input currents is analyzed when the matrixconverter uses different modulation strategies in Section V.Finally, a prototype has been built to testify the validity ofthe modified method. The validity of the theoretical analysisand the performance of the modulation strategy have beenconfirmed.

II. REVIEW OF SVM FOR A MATRIX CONVERTER

In a three-phase/three-phase matrix converter, the nine bidi-rectional switches allow any output phase to be connected toany input phase, as schematically shown in Fig. 1.

Fig. 2. Emulation of the (a) VSR and (b) VSI conversions.

When the input voltages are purely symmetric and sinu-soidal, the input phase voltages can be expressed as

ui =

⎡⎣ ua

ub

uc

⎤⎦ = Uim

⎡⎣ cos(ωit)

cos(ωit − 2π/3)cos(ωit + 2π/3)

⎤⎦ (1)

where ωi is the input angular frequency and Uim is the ampli-tude of input phase voltages.

If it is desired that the local-averaged output line voltages besinusoidal, i.e.,

uol =

⎡⎣uAB

uBC

uCA

⎤⎦=

√3Uom

⎡⎣ cos (ωot−ϕo+π/6)

cos (ωot−ϕo+π/6−2π/3)cos (ωot−ϕo+π/6+2π/3)

⎤⎦ (2)

where Uom is the amplitude of output phase voltages, ωo isthe output angular frequency, and ϕo is the load displacementangle.

It has been proved that the indirect and direct SVM ap-proaches, although seems apparent, can be regarded as a uniquemodulation approach [27]. Indirect SVM approach is adoptedin this paper for it is simplicity in realization. The emulationof virtual voltage source rectifier (VSR) and voltage sourceinverter (VSI) converters of three-phase/three-phase matrixconverter is shown in Fig. 2(a) and (b), respectively.

Consider the virtual VSI in Fig. 2(b) as a stand-alone invertersupplied by a dc voltage source udc. In order to avoid opencircuit of the load, there exist six active switching configura-tions which yield nonzero output voltages and two switchingconfigurations which yield zero voltages.

In virtual VSI modulation, switching configuration “1, 0, 0”represents that the output phase A is connected to the anodeof the dc power supply and the output phases B and C areconnected to the cathode of the dc power supply, which are thesame to other switching configurations. The six active switch-ing configurations and their corresponding output-voltage vec-tors are shown in Fig. 3(a).

The complex plane is divided into six sectors by six activevoltage vectors. In each output-voltage sector, the referenceoutput-voltage vector can be synthesized by two adjacent activevoltage vectors. If the reference output-voltage vector is lyingin Sector 1 and the duty cycles of the two active voltage vectors

WANG et al.: RESEARCH ON SVM STRATEGY FOR MATRIX CONVERTER UNDER ABNORMAL CONDITIONS 95

Fig. 3. Synthesis of the output-voltage vector and the input-current vector.(a) VSI hexagon and (b) VSR hexagon.

are dα and dβ in counterclockwise, the relationship of referenceoutput-voltage vector and the duty cycles is

|uo|ej(θo−π/6) = dα(2udc/3)e−jπ/6 + dβ(2udc/3)ejπ/6 (3)

where dα + dβ ≤ 1, 0 ≤ dα ≤ 1; 0 ≤ dβ ≤ 1.Using the law of sine, the duty cycles are{

dα = mv sin(π/3 − θo)dβ = mv sin(θo)

(4)

where mv is the VSI modulation index

mv =|uo|

udc/√

3, 0 ≤ mv ≤ 1. (5)

Moreover, θo is the output-voltage vector angle within thecorresponding sector. At any sampling instant, θo is known asreference quantities. Furthermore, for Sector 1

0 ≤ θo ≤ π/3, θo = ωot − ϕo + π/6 + π/6. (6)

Then, consider the virtual VSR in Fig. 2(a) as a stand-aloneVSR loaded by a dc current generator idc. The VSR input-current SVM is completely analogous to the VSI output-voltageSVM. The VSI subscripts α, β, and o are replaced with the VSR

subscripts μ, γ, and i, respectively. The VSR hexagon is shownin Fig. 3(b), and the duty cycles are{

dμ = mc sin(π/3 − θi)dγ = mc sin(θi)

(7)

where mc is the VSI modulation index

mc = |ii|/idc, 0 ≤ mc ≤ 1. (8)

Moreover, θi is the input-current vector angle within the corre-sponding sector. In addition, for Sector 1

0 ≤ θi ≤ π/3, θi = αi − ϕi + π/6 (9)

where αi is the input-voltage vector angle and ϕi is the input-current displacement angle.

The input active power of VSR is equal to the output activepower

udcidc =32

12

(u∗iii + uii

∗i ) (10)

where the symbol ∗ denotes the complex conjugate.Then, the output dc voltage of the VSR can be obtained

from (10)

udc =32|ui|mc cos ϕi. (11)

The combination of two switching configurations in thevirtual VSR and two switching configurations in the virtualVSI results in four matrix converter switching configurations.The final duty cycles of the four active and one zero switchingconfigurations can be obtained from (4), (5), (7), and (11)

dαμ = dαdμ =2√

3 cos ϕi

|uo||ui|

sin(π/3 − θo) sin(π/3 − θi)

dαγ = dαdγ =2√

3 cos ϕi

|uo||ui|

sin(π/3 − θo) sin(θi)

dβμ = dβdμ =2√

3 cos ϕi

|uo||ui|

sin(θo) sin(π/3 − θi)

dβγ = dβdγ =2√

3 cos ϕi

|uo||ui|

sin(θo) sin(θi)

d0 = 1 − dαμ − dαγ − dβμ − dβγ . (12)

The zero voltage vectors are applied to complete the switch-ing cycle period. Moreover, it can be verified that (12) has ageneral validity.

In general, the conventional modulation strategy is derivedunder the assumption that input voltages are sinusoidal andbalanced. Thus, θi can be achieved by detecting the zerocrossing of one input phase voltage and by using a software-implemented phase-lock loop (PLL) [23]. It is calculated as

θi = mod(ωit − ϕi + π/6, π/3) (13)

where the mod(x, y) function returns the remainder when x isdivided by y.

Moreover, the modulation index m is usually defined as

m =Uom

Uim(14)

96 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 1, JANUARY 2012

where Uim and Uom represent the constant values of the inputand output phase voltage amplitudes.

The modulation index m can be calculated according to theamplitude of the desired three-phase output line voltages. If theamplitude of the output voltages remains as a constant value,then the voltage modulation index m is fixed. The desiredoutput voltages of matrix converter can be acquired basedon (12).

Unfortunately, when abnormal input-voltage conditions arepresented, the influences of input-voltage disturbances on theoutput behavior of matrix converter are significant and un-desirable. From (11), the virtual dc-link voltage udc includesthe harmonic content. Thus, the strategy cannot synthesizethe desired reference output voltages and generates low-orderharmonics.

For example, in the case of unbalanced supply voltages,(2ωi + ωo) and (2ωi − ωo) frequency components are con-cluded in the output voltage of the synchronous reference framewhen the fixed modulation index m is used to calculate theduty cycles [13]. Similar to the unbalanced condition, it canbe derived for this case also that, if the input power-supplyvoltages contain the harmonics on the order of k, the harmoniccomponents with the frequency of (k − 1)ωi ± ωo and (k +1)ωi ± ωo will be introduced in output voltages [13].

III. MODIFIED SVM STRATEGY

Several strategies mentioned in Section I reduce the influenceof the abnormal input voltage by measuring the instantaneousvalue of the input voltages or load currents. However, theoutput-voltage waveforms are only improved at a certain extentby these strategies. This paper modifies the conventional SVMalso by incorporating the characteristics of the input voltageinto the computation and adjusting the calculated duty cyclesaccordingly. It is carried out by adjusting both the voltagemodulation index m and the input-current vector angle θi

according to the input voltages.It is found that, when the SVM is employed in the matrix

converter, the voltage modulation index m should be calculatedusing the instantaneous values of the output- and input-voltagevector magnitudes according to the voltage space vector syn-thesis principle. That is

m =|uo||ui|

. (15)

If using the following Clarke’s transformation:

Cabcαβ =

[1 − 1

2 − 12

0√

32 −

√3

2

](16)

so ⎧⎨⎩

|uo| =√

u2oα + u2

oβ = 32Uom

|ui| =√

u2iα + u2

iβ , uiαβ = Cabcαβ ui.

(17)

With the normal supply voltage, |ui| can be expressed by

|ui| =32Uim. (18)

TABLE ILOCAL-AVERAGED OUTPUT VOLTAGES

In particular, the amplitude ratio of the voltage vector equalsto the amplitude ratio of the phase (or line) voltage, and thevoltage modulation index is fixed.

Whereas for unbalanced nonsinusoidal power supply, thevoltage modulation index m is not constant and can be adjustedaccording to the input voltages. This make the modulationprocess adaptive to the characteristics of the input voltages,hence enabling the output voltages to track closely their ref-erence counterpart when the supply voltages are abnormal.

As under abnormal conditions, the synchronization of thecurrent reference vector defined with PLL is no longer ap-plicable, and the input-current vector angle θi should also becalculated as

θi = mod(αi − ϕi + π/6, π/3) (19)

where

αi =

⎧⎪⎪⎨⎪⎪⎩

arctan uiβ

uiα, when uiα > 0

arctan uiβ

uiα+ π, when uiα < 0

π2 , when uiα = 0, uiβ > 03π2 , when uiα = 0, uiβ < 0.

By using the instantaneous vector magnitude of input voltageto calculate the modulation index m and introducing (19) in(12) lead to modified SVM strategy.

In order to explain the modulation strategy, the output-voltage vector uo and input-current vector ii are assumed tobe both lying in Sector 1, without missing the generality of theanalysis.

With the VSI output-voltage SVM, the local-averaged outputvoltages are [10]⎡

⎣ uAB

uBC

uCA

⎤⎦ =

⎡⎣ dα + dβ

−dα

−dβ

⎤⎦ udc. (20)

Moreover, the local-averaged output voltage in other output-voltage sectors is summarized in Table I.

With the VSR input-current SVM, the local-averaged inputcurrents are [10] ⎡

⎣ iaibic

⎤⎦ =

⎡⎣ dμ + dγ

−dμ

−dγ

⎤⎦ idc. (21)

Moreover, the local-averaged input current in other input-current sectors is summarized in Table II.

WANG et al.: RESEARCH ON SVM STRATEGY FOR MATRIX CONVERTER UNDER ABNORMAL CONDITIONS 97

TABLE IILOCAL-AVERAGED INPUT CURRENTS

Thus, the local-averaged output voltages with the input volt-age can be obtained from (20) and (21)⎡⎣uAB

uBC

uCA

⎤⎦=

⎡⎣dα + dβ

−dα

−dβ

⎤⎦⎡⎣dμ + dγ

−dμ

−dγ

⎤⎦

T⎡⎣ua

ub

uc

⎤⎦

=

⎡⎣ 1−d0 −dαμ−dβμ −dαγ−dβγ

−dαμ−dαγ dαμ dαγ

−dβμ−dβγ dβμ dβγ

⎤⎦⎡⎣ua

ub

uc

⎤⎦ .

(22)

Using the same procedure, the local-averaged output voltagesin other output-voltage sectors and input-current sectors can bederived.

If the input three-phase voltages are unbalanced and nonsi-nusoidal, they can be written in Fourier series as

ui =

⎡⎣ua

ub

uc

⎤⎦

⎡⎢⎢⎢⎢⎢⎣

∞∑k=1

Uak cos(kωit)∞∑

k=1

Ubk cos(kωit − k 2π/3)∞∑

k=1

Uck cos(kωit + k 2π/3)

⎤⎥⎥⎥⎥⎥⎦

. (23)

Substituting ui = [Cabcαβ ]−1uiαβ in (22) becomes

⎡⎣uAB

uBC

uCA

⎤⎦=

⎡⎢⎣

(1−d0)uiα+√

33 (−dαμ−dβμ+dαγ +dβγ)uiβ

−(dαμ+dαγ)uiα+√

33 (dαμ−dαγ)uiβ

−(dβμ+dβγ)uiα+√

33 (dβμ−dβγ)uiβ

⎤⎥⎦ .

(24)

With the input-current and output-voltage vectors laid inSector 1, with θo = ωot − ϕo + π/3 and θi = θi − ϕi + π/6,and substituting (12) in (24), we can deduce⎡

⎣ uAB

uBC

uCA

⎤⎦ =

2m√3 cos ϕi

× [uiα(cos θi cos ϕi + sin θi sin ϕi)

+ uiβ(sin θi cos ϕi − cos θi sin ϕi)]

·

⎡⎣ cos(ωot − ϕo + π/6)

cos(ωot − ϕo + π/6 − 2π/3)cos(ωot − ϕo + π/6 + 2π/3)

⎤⎦ . (25)

Substituting sin θi = (uiβ/|ui|), cos θi = (uiα/|ui|), and(15) in (25), the output line voltages of this converter could beexpressed by⎡⎣ uAB

uBC

uCA

⎤⎦ =

√3Uom

⎡⎣ cos(ωot − ϕo + π/6)

cos(ωot − ϕo + π/6 − 2π/3)cos(ωot − ϕo + π/6 + 2π/3)

⎤⎦ . (26)

It is clear from the aforementioned equation that the modifiedmethod can restrain the disturbance of the input voltages. Thus,the output line voltages keep with the reference voltages underthe abnormal input voltages.

Although the analysis presented is based on the indirectSVM, the proposed method is valid for both indirect SVM anddirect SVM.

IV. SIMULATION ANALYSIS UNDER THE ABNORMAL

INPUT-VOLTAGE CONDITIONS

In order to verify the effectiveness of the modified method,numerical simulations have been carried out on the matrixconverter by using MATLAB. In the simulations, Y-connectedR–L loads are with resistors of 10 Ω and inductors of 10 mH.The fundamental amplitude of input-voltage sources Uim is311 V, and the input frequency fin is 50 Hz. The output-voltageamplitude and frequency are set at 100 V and 30 Hz.

The simulations have been carried out assuming a samplingperiod of 200 μs and ideal switching devices.

A. Simulation of the Modified Modulation Under Abnormaland Sudden-Dropping Input Voltages

The simulated tests under unbalanced and nonsinusoidalinput voltages are carried out with the modified SVM strategy.

Supposed that the steady input voltage ui is unbalanced andcontains harmonic components, expressed as

ui =

⎡⎣ua

ub

uc

⎤⎦ =

⎡⎣ Uim cos(ωit)

1.4Uim cos(ωit − 2π/3)0.6Uim cos(ωit + 2π/3)

⎤⎦

+

⎡⎣ 0.5Uim cos (3(ωit + π/20))

0.4Uim cos (3(ωit − 2π/3 + π/20))0.4Uim cos (3(ωit + 2π/3 + π/20))

⎤⎦

+

⎡⎣ 0.3Uim cos (5(ωit + π/15))

0.2Uim cos (5(ωit − 2π/3 + π/15))0.2Uim cos (5(ωit + 2π/3 + π/15))

⎤⎦ . (27)

The input voltages, the input-current vector angle, the voltagemodulation index, R-load voltages, and spectrum of A-phaseR-load voltage under unbalanced and nonsinusoidal input volt-ages are shown in Fig. 4(a)–(e), respectively.

Under the abnormal input-voltage conditions, owing to themodified method, the duty cycles of the power switches arenot constant anymore and are variable according to the distur-bance in the input voltages. Thus, the output voltages can bekept balanced and sinusoidal even in abnormal input-voltageconditions.

98 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 1, JANUARY 2012

Fig. 4. Simulation waveforms under unbalanced and nonsinusoidal input volt-ages. (a) Input voltages. (b) Input-current displacement angle. (c) Voltage mod-ulation index. (d) R-load voltages. (e) Spectrum of A-phase R-load voltage.

Similar to the simulations under unbalanced and nonsi-nusoidal input voltages, the simulated tests under sudden-dropping input voltages are also carried out with the modifiedSVM strategy.

When 0 ≤ time < 0.03 s, the input voltages are balanced andsinusoidal in 311 V/50 Hz, and when 0.03 s ≤ time < 0.06 s,the amplitude of the input voltages Uim decreases to 80% of therated value. The input voltages, the input-current displacementangle, the voltage modulation index, R-load voltages, andspectrum of A-phase R-load voltage under sudden-droppinginput voltages are shown in Fig. 5(a)–(e), respectively.

The simulation results show that the voltage modulationindex can be adjusted quickly according to the variation of

Fig. 5. Simulation waveforms under sudden-dropping input voltages.(a) Input voltages. (b) Input-current displacement angle. (c) Voltage modulationindex. (d) R-load voltages. (e) Spectrum of A-phase R-load voltage.

input voltages, and the output voltages remain the same whenthe input voltages decrease. The proposed method improves theperformance of the matrix converter effectively.

B. Comparison of Simulation in Terms of Three Conditions

The simulated tests under unbalanced and nonsinusoidalvoltages are carried out in terms of three conditions: Method 1with the conventional SVM, Method 2 with the modified volt-age modulation index, and Method 3 with the modified voltagemodulation index and input-current vector angle.

Fig. 6 shows the R-load voltages of the matrix converter inthe condition that the amplitude values of ua, ub, and uc are311, 373, and 249 V, respectively.

WANG et al.: RESEARCH ON SVM STRATEGY FOR MATRIX CONVERTER UNDER ABNORMAL CONDITIONS 99

Fig. 6. Simulation waveforms of R-load voltages under unbalanced input voltages. (a) With Method 1. (b) With Method 2. (c) With Method 3.

Fig. 7. Simulation waveforms of R-load voltages under nonsinusoidal input voltages. (a) With Method 1. (b) With Method 2. (c) With Method 3.

The simulation results show that the low-order harmoniccomponents in output voltages are reduced obviously by theuse of the modified method. Furthermore, the control effectof the modified method with the voltage modulation index

and input-current vector angle is better than that of the simplesynchronization method.

Fig. 7 shows the R-load voltages of the matrix converterin the condition that each of the three-phase input voltages

100 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 1, JANUARY 2012

Fig. 8. Simulation waveforms of input currents under unbalanced input voltages. (a) With Method 1. (b) With Method 2. (c) With Method 3.

contains 30% fifth-order harmonic component with the initialphase angle of 15◦.

The main low-order harmonics in output voltages resultedfrom fifth-order input voltages are the harmonic componentswith frequencies of 330 and 270 Hz. From the simulationresults, it can be seen that, when the input voltages containfifth-order harmonics, the distortion occurs in the output volt-ages with the conventional SVM. However, using the modifiedtechnique, the output waveforms could be improved effectively.

V. PERFORMANCE OF INPUT CURRENTS UNDER THE

UNBALANCED INPUT-VOLTAGE CONDITIONS

There is, however, an important issue to be noted. Althoughthe aforementioned modified strategy results in sinusoidal out-put voltages under abnormal supply, it will generate distortedinput currents.

In the case of unbalanced supply voltages, also with 20%unbalance with the input peak–peak voltages in phases a, b,and c being 311, 373, and 249 V , respectively, the fundamentalnegative sequence component which appears causes variationsin both magnitude and angular velocity of the input-voltagevector: The input-voltage vector trajectory changes from cir-cular to elliptical.

The simulation of the input currents under unbalanced volt-ages is also carried out in terms of three conditions: Method 1with the conventional SVM, Method 2 with the modified volt-age modulation index, and Method 3 with the modified voltagemodulation index and input-current vector angle.

Fig. 8 shows the results with unity input power factor. Ascan be seen, the input currents have the harmonic content underunbalanced voltages in terms of three conditions. Fig. 8 alsoshows the harmonic spectrum of the input a-phase current. Asthe spectrum indicates, the third-order harmonic componentis very large with the modified voltage modulation index andinput-current vector angle method.

In order to reduce or eliminate the harmonic content of theinput currents under unbalanced conditions, a strategy proposedin [28] and [29] is used.

As in the previous modulation strategy, the input-currentvector is kept in phase with the input-voltage vector. Thus,the input-current vector displacement angle ϕi is constant andequal to a reference value. In addition, the input-voltage vectorangle is quite easily determined by synchronizing a timer tothe zero crossing of the voltage or measuring the instantaneousvalues of the input voltages.

However, in [28] and [29], the strategy is defined with thepurpose of reducing the harmonic content of the input currentsunder unbalanced supply voltage conditions. Moreover, theinput-current displacement angle ϕi is dynamically modulatedas a function of positive and negative sequence componentsof the input voltages. Thus, this strategy does not lead to aninstantaneous unity input power factor under unbalanced supplyvoltage conditions.

The simulations in Fig. 9 show the input-current controlperformance and the output voltages of the matrix converterunder unbalanced grid voltages with the proposed strategy in[28] and [29].

WANG et al.: RESEARCH ON SVM STRATEGY FOR MATRIX CONVERTER UNDER ABNORMAL CONDITIONS 101

Fig. 9. Simulation waveforms with the method of reducing the harmonic content of the input currents. (a) Input currents. (b) R-load voltages.

Fig. 10. Top view of the matrix converter prototype.

The waveforms show that, using this unbalanced compensa-tion technique, there are no significant harmonic componentsapart from the fundamental. However, the input currents arealso unbalanced, and the total harmonic distortion of the outputvoltages is larger than that of the modified strategy. Therefore,it can be concluded that the harmonic components in the outputvoltages and the input-current spectrum cannot be eliminated atthe same time under the abnormal input conditions.

VI. EXPERIMENTAL RESULTS

In order to verify the modified SVM modulation strategyunder the abnormal input conditions, a 5.5-kW experimentalprototype of matrix converter, as shown in Fig. 10, has been im-plemented to feed a three-phase R–L load and a three-phase in-duction motor. The hardware configuration for matrix converteris shown in Fig. 11. The instantaneous input voltages of thematrix converter are sampled by three high-precision voltagetransducers and a high-speed 16-b A/D converter (ADS8361from Texas Instruments Incorporated), which is controlled bya field-programmable gate array (FPGA) (EP2C8 from Altera).

Fig. 11. Hardware structure of the matrix converter prototype.

The input-voltage signals are also transferred to a microcon-troller (TMS320LF2407A from Texas Instruments Incorpo-rated) for modulation algorithm; the data of switching statesand their duty cycles are then transferred back to the FPGA forpulsewidth modulation pulse generation. The input filter is athree-phase LC filter with a damping resistor, and the parame-ters are Lf = 1 mH, Cf = 10 μF, and Rf = 51 Ω, respectively.

A. R–L Load

A three-phase R–L load (R = 37 Ω, L = 50 mH) with starconnection is used to verify the modified modulation strategy.Moreover, the output voltage is set at 88 V, and the frequencyis 30 Hz.

For the purpose of generating various power-supply voltages,a three-phase variac is used in the experiments. The three-phasevariac outputs are connected to the three-phase symmetrical380 VAC/50 Hz while the inputs are open circuited. The variaccontactors are moved when the core is saturation, and then, thethird-order harmonic component can be obtained at the variacneutral point. It is added into the input c-phase voltage. Theinput line voltages are shown in Fig. 12(a). The output phasevoltage waveform using the conventional SVM method and thatusing the modified method are shown in Fig. 12(b) and (d),respectively.

102 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 1, JANUARY 2012

Fig. 12. Experimental waveforms under abnormal input-voltage conditions.(a) Input line voltage. (b) Output voltage with the conventional strategy.(c) Modulation index with the modified strategy. (d) Output voltage with themodified strategy.

Fig. 12 shows the steady-state performance of the three-phase output voltage using the conventional SVM and themodified method proposed in this paper. Within the distortedinput voltages, Fig. 12(b) shows that distortion occurs in theoutput voltages, measured across R of the Y-connected R–Lloads, whereas Fig. 12(d) shows that the output voltages are

Fig. 13. Experimental waveforms under sudden-dropping input-voltage con-ditions. (a) Input line voltage. (b) Output voltage with the conventional strategy.(c) Modulation index with the modified strategy. (d) Output voltage with themodified strategy.

unaffected from the abnormal input voltages with the instanta-neous voltage modulation index.

The magnitude of the input voltages decreases to 55% of therated value by adjusting the variac. Fig. 13 shows the outputvoltages using the two methods.

WANG et al.: RESEARCH ON SVM STRATEGY FOR MATRIX CONVERTER UNDER ABNORMAL CONDITIONS 103

TABLE IIIPARAMETERS OF INDUCTIVE MOTOR

Fig. 14. Experimental waveforms of induction motor drive system at600 r/min. (a) With the conventional strategy and (b) with the modified strategy.Waveforms from top to bottom: rotor speed n and stator current is.

In Fig. 13(b), when the input voltages are sudden dropping,the amplitude of output voltages has also notable variety withthe conventional SVM method. In Fig. 13(d), the amplitude ofoutput voltages is steady with the proposed method.

B. Induction Motor Drive Application

The modified modulation strategy is then applied to a1.1-kW induction motor drive system. The parameters ofinductive motor are given in Table III.

The control experiments in the two cases (same as R–Lload experiments) are implemented: 1) with the conventionalstrategy and 2) with the modified strategy.

Fig. 14(a) and (b) shows the experimental results of thesteady-state performance of the induction motor at 600 r/min.It can be seen from this result that there are some ripples onthe rotor speed and stator current waveforms in case 1), andthe stator current is more distorted. This will result in poorperformance of the drive system. Moreover, in case 2), thestator current waveform quality is significantly modified, andthe ripples on rotor speed are significantly eliminated. It canbe said that the motor performance is improved by using themodified modulation strategy.

VII. CONCLUSION

This paper has proposed a modified SVM strategy for amatrix converter under abnormal conditions. In this strategy,the instantaneous vector magnitude of output voltages and inputvoltages is used to calculate the voltage modulation index andinput-current phase angle. Thus, the duty cycles of the switchstates can be adjusted according to the distortion of the inputvoltages in time. By using this strategy, the output voltages cankeep with the reference voltages under normal and abnormalinput-voltage conditions. The validity of the theoretical analysisand the performance of the modulation strategy have beenconfirmed by simulations and experimental results.

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Xingwei Wang was born in Hubei, China, in 1980.He received the B.S. and M.S. degrees in electricalengineering from Huazhong University of Scienceand Technology (HUST), Wuhan, China, in 2002and 2005, respectively, where he is currently workingtoward the Ph.D. degree.

From 2005 to 2007, he was with the MindrayMedical International Limited, Shenzhen, China, asa Research and Development Engineer. Since 2007,he has been with the College of Electrical and Elec-tronic Engineering, HUST, where he is currently a

Faculty Member. His research interests include matrix converter and ac motordrive.

Hua Lin (M’10) was born in Wuhan, Hubei, China,in 1963. She received the B.S. degree in industrialautomation from the Wuhan University of Technol-ogy, Wuhan, in 1984, the M.S. degree in electricalengineering from the Naval University of Engi-neering, Wuhan, in 1987, and the Ph.D. degree inelectrical engineering from Huazhong University ofScience and Technology (HUST), Wuhan, in 2005.

From 1987 to 1999, she was with the Departmentof Electrical Engineering, Naval University of Engi-neering, as a Lecturer and Associate Professor. Since

1999, she has been with the College of Electrical and Electronic Engineering,HUST, where she became a Full Professor in 2005. In October 2010, she wasa Visiting Scholar at the Center for Advanced Power Systems, The FloridaState University, Tallahassee. She has been engaged in research and teaching inthe field of power electronics and electric drive. Her research interests includehigh-power high-performance ac motor drives and novel power converters andtheir control. She has authored or coauthored more than 50 technical papers injournals and conferences.

Dr. Lin was a recipient of the Second-Grade National Scientific and Techno-logical Advance Prize of China in 1996 and 2003.

Hongwu She (S’09) was born in Hubei, China, in1982. He received the B.S. degree in electrical en-gineering from the Naval University of Engineering,Wuhan, China, in 2004, the M.S. degree in electricalengineering from Huazhong University of Scienceand Technology (HUST), Wuhan, in 2007, where heis currently working toward the Ph.D. degree.

His research interests include matrix converter andinduction motor drive.

Bo Feng was born in Hubei, China, in 1987. Hereceived the B.S. degree in electrical engineeringfrom Huazhong University of Science and Technol-ogy (HUST), Wuhan, China, in 2009, where he iscurrently working toward the Ph.D. degree.

His research interests include matrix converter anddirect torque control.