Hybrid PWM control for Z-source Matrix Converter

Qin Lei, ECE department of Michigan State University, East Lansing, MI, leiqin8512@gmail.com; Baoming Ge, ECE department of Michigan State University, East Lansing, MI, gebm@msu.edu;

Fang. Z. Peng, ECE department of Michigan State University, East Lansing, MI, fangzpeng@gmail.com Abstract- This paper proposes four control strategies for Z-source

matrix converter: simple maximum boost control, maximum boost control, maximum gain control and hybrid minimum stress control. The maximum gain control can obtain the maximum gain at the same modulation index among all four; and the hybrid minimum voltage stress control can obtain the minimum voltage stress at the same voltage gain. The relationship of voltage gain to modulation index and the relationship of voltage stress to voltage gain have been analyzed in detail for each method and verified by simulation and experiments.

I. INTRODUCTION

Fig. 1.Voltage-fed Z-source matrix converter

'a

'b

'c

Fig. 2.Equivalent circuit of VF ZS-MC

The matrix converter (MC) is a direct ac/ac converter with sinusoidal input/output waveforms and controllable input power factor [1-4]. It has less passive component compared to the existing back-to-back converter. Its control methods, circuit operation and possible applications have been investigated in paper [5-24]. It has a good perspective especially when the reverse-blocking IGBT is available now. In a traditional matrix converter, the three switches on the

same output phase leg can not be gated on at the same time because doing so would cause a short circuit(shoot through) to occur, which would destroy the converter. In addition, the maximum voltage gain can not exceed 0.866. These limitations can be overcome by Z-source matrix converter [25], shown in Fig. 1, which adds an impedance network (Z-network) in the

input phase lines. The Z-source matrix converter advantageously utilizes the shoot through states to boost the ac voltage by gaiting on all the three switches on the same output phase leg. Therefore, the Z-source matrix converter can boost the voltage to be greater than the input voltage. in addition, the reliability of the converter is greatly improved because the shoot through states can no longer destroy the circuit. Also the current commutation steps can be simplified. Therefore, it provides a low-cost, reliable, and highly efficient structure for buck and boost ac/ac conversion. Pulsewidth-modulation (PWM) control for traditional matrix

converter has to be modified to utilize the shoot-through states for voltage boost. It can be inherient from the control methods for Z-source inverter [26-27]. A simple maximum boost control is proposed in section II which inherits the straight lines of the simple boost control; a maximum boost control is proposed in section III which utilizes all available zero states. More important, two control methods to achieve maximum gain at certain modulation index and to achieve minimum voltage stress across the switch at certain voltage gain respectively have been proposed to provide two advanced PWM control method to provide a more efficient solution for this converter. All the analysis about voltage gain and stress will be investigated and verified by simulation and experiments.

II. BASIC PWM CONTROL METHODS

A. Simple maximum boost control In MC, the maximum envelope of the three input phase

voltages MX and the minimum envelope MN can be considered as the positive level and negative level of the equivalent dc link voltage respectively, as shown in Fig.3. So each output phase voltage is switched between these two levels, as shown in Fig.3, according to the comparison between carrier voltage which is enveloped by MX and MN and the output reference voltage in each phase. In this method the maximum output reference voltage can not exceed half of the input phase peak voltage, which also means the modulation index can only go up to 0.5.

978-1-4577-0541-0/11/$26.00 ©2011 IEEE 246

Fig.3. Simple maximum boost control

For ZS-MC, the principle of applying shoot through state is to replace some of the zero state of the converter by shoot through state, in order to not affect the output voltage. The zero output voltage state in MC is corresponding to the switching state that all three output phases are connected to the same input phase. It happens when all three phase output voltages are either higher or lower than the carrier voltage. So the shoot through reference voltage should be either higher than the maximum reference voltage or lower than the minimum reference voltage. The simple boost shoot through reference voltages are two straight lines which bound the reference voltage maximum and minimum envelopes, as shown in blue line in Fig.3. In this case, the reference voltage is a constant value at a certain modulation index; however, the shoot through duty ratio varies with time, thus it is different from the simple boost control in Z-source inverter. The introduction of Z-source network into the conventional

matrix converter is equivalent to cascade a boost converter in the front stage. The boost ratio of Z-source network can be obtained by using the state average model of the equivalent simplified ZS matrix converter circuit shown in Fig. 2. There are two basic operation states of this equivalent circuit: shoot through state and non-shoot through state. In shoot through state, the three output switches S1, S2 and S3 are all turned on to short the three phase terminals Vsa’, Vsb’ and Vsc’ together; and at the same time the front switches S0 are turned off simultaneously. In non-shoot through state, the three switches switch like the conventional matrix converter and the front stage switches are turned on. The voltage boost ratio can be derived by applying the volt-seconds balance on the Z-source inductors [28]. In one switching cycle Tsw, the average voltage on the inductor

of Z-network is equal to zero, neglecting the small fundamental voltage drop because of the big ratio between switching frequency and fundamental frequency. Thus:

' '

0 ' ' 0

' '

0 0

(1 )

(1 )

La Ca a b Ca

Lb Cb b c Cb

Cc c a CcLc

ac Cc Ca

ba Ca Cb

cb Cb Cc

V V V VV D V V D V

V V VV

V V VD V V D V

V V V

� � −� � � �� � � � � �= − − +� � � � � �� � � � � �−� � � �� �� �+� � � �

� � � �= − + +� � � �� � � �+� � � �

(1)

This equation can be solved by adding the square of the three elements in one column together on both sides, and applying the trigonometric functions, such as:

2 2 22 2sin ( ) sin ( ) sin ( ) 3 / 23 3i i it t tπ πω ω ω+ − + + = . So the boost

ratio between Vlm (amplitude of Va’b’ ) and Vlm( amplitude of Vab ) can be obtained:

2

0 0

' 1

3 3 1lm

lm

VBV D D

= =− +

(2)

It can be found that the maximum boost ratio 2 happens at 0 0.5D = , as shown in Fig. 4. Similarly to Z-source inverter, the voltage conversion ratio between output line voltage amplitude Vom and input Vlm is:

om

lm

VG MBV

= = (3)

Fig. 4.Voltage boost ratio B vs D0

In practice, to get the voltage gain at a certain M, the relationship between M and D0 is required. In simple control, D0 is a function of time, thus the average value is used to calculate the voltage gain, which can be obtained by average the integration over time. Assume the input phase peak voltage is equal to per unit 1,

then the output phase peak voltage is equal to M. The height of the shoot through reference is also M. Assume the input three phase voltages are:

sin( )2sin( )3

2sin( )3

ia

b im i

ci

tVV V tV

t

ωπω

πω

� �� �

� � � �� � � �= −� � � �� � � �� �

� �+� �� �

(4)

And the output three phase reference voltages are:

247

sin( )2sin( )3

2sin( )3

oxo

yo om o

zoo

tVV V t

Vt

ω απω α

πω α

� �� �+� � � �� � � �= + −� � � �� � � �� � � �+ +� �� �

(5)

In simple boost control, to get the instantaneous shoot through

duty ratio, take the area of input phase a angle within [ , ]6 2π π

as an example, as shown as the shadow area in Fig.3, thus:

0sin( )

( )2sin( ) sin( )3

i

i i

t MMX MD tMX MN t t

ωπω ω

−−= =− − −

(6)

Due to the symmetry, the average value of D0 in one output reference voltage fundamental cycle is equal to the average value in 60 degrees wide shadow area, which is:

/2

0/

6

sin( ) 2( ) 12 3 3sin( ) sin( )3

i

i

i

i i

t MD t dt M

t t

π ωπ ω

ω ππω ω

−= = −

− −� (7)

From equation (2), (3), (7), the boost factor and voltage conversion ratio sG can be derived

2

2

1

2 4193

B

M Mπ π=

− +

(8)

2 22 2

1

2 4 11 ( )9 93 3

sMG

M MM

π π π π= =

− + − +

(9)

Thus the maximum voltage gain 0.955 can be obtained at 0.552M = . Since the maximum modulation index is 0.5, so the maximum voltage gain can only go to 0.944 at M=0.5 here.

B. Maximum boost control

0 0.005 0.01 0.015-1.5

-1

-0.5

0

0.5

1

1.5

t (s)

MX MXo(Vsh1)

Va Vb VcMN MNo(Vsh2)

Fig. 5. Maximum boost control

Inherit from the concept in Z-source inverter, maximum boost control in ZS-MC refers to the case that all the zero states are transferred into shoot through state. The shoot through reference curves are identical to the maximum and minimum envelopes of the output reference voltage, shown in blue line in Fig. 5. The instantaneous shoot through duty cycle thus can be

calculated as:

0( ( ) ( )) ( ( ) ( ))( )

( ) ( )MX t MXo t MNo t MN tD t

MX t MN t− + −=

−

(10) , where ( )MXo t and ( )MNo t are the maximum envelope

and minimum envelope of the output three phase voltages. The instantaneous D0(t) is not a periodic function like the simple boost, because the different frequencies and phase angle between input and output. However, the maximum envelope is a periodic function which repeats every 1/3 of the input fundamental period. Similarly, MN repeats every 1/3 period. MXo and MNo are periodic functions with period of 1/3 of output fundamental cycle. In order to get the accurate average value of D0(t), the integration has to be conducted in integer times of the periodic unit of both input and output envelopes. Assume the total integration time is:

1 2 1 23 3i o

t m nπ πω ω

= ⋅ = ⋅ (11)

, in which m and n are integers. Due to the symmetry, the upper half plane integration of D0(t) is the same as the lower half plane, therefore from equation (10):

0

( ( ) ( )) ( ( ) ( ))( )( ) ( )

MX t MXo t MNo t MN tD tMX t MN t

− + −=−

(10)

00

0

0

0

(( ( ) ( )) ( ( ) ( )))( )

( ( ) ( ))

2 ( ( ) ( ))

2 ( )

t

t

t

t

MX t MXo t MNo t MN t dtD t

MX t MN t dt

MX t MXo t dt

MX t dt

− + −=

−

−=

��

��

(12)

The integration on the right hand side of equation (12) can be either divided into m subsections that each section is one periodic unit of input voltage, or into n subsections that each section is one periodic unit of output voltage. Thus:

5 /6

0 /6

( ) sin( ) 3 /i

i

ti iMX t dt m t dt m

π ωπ ω

ω ω= ⋅ =� � (13)

5 /6

0 /6

( ) sin( ) 3 /o

o

to oMXo t dt n M t dt nM

π ωπ ω

ω ω= =� � (14)

The average D0(t) thus can be derived from equations (11)-(14):

0 ( ) 1D t M= − (15) , which indicates that average shoot through duty ratio in

maximum boost control is a constant value at a fixed modulation index, regardless of the frequency and phase angle differences. In conclusion, the average shoot through duty ratio in maximum boost control in general case is shown in equation (15). The boost factor in this control strategy is:

2

' 1

3 3 1lm

lm

VBV M M

= =− +

(16)

248

The voltage conversion ratio of ZS-MC mG is:

2 2

11 3 33 3 1 ( )

2 4

mMG

M MM

= =− + − +

(17)

Thus the maximum voltage gain is 2 / 3 at 2 / 3M = . However, the basic modulation of MC requires that M<=0.5, as shown in Fig.3. So the maximum gain 1.155 at M=0.667 is not available. To solve this problem, a third harmonic injection strategy based on the waveform shifting is proposed in the next section to increase M to 0.866.

C. Third harmonic injection The third harmonic injection is composed of two steps: (1)

Shift the input envelope curve to maximum utilize the available equivalent dc link voltage; (2) add the third harmonic of output voltage to the reference. The original envelope MX and MN can be considered as a set

of shifted dc link voltage. If they are shifted back to make the MN identical to y=0 line, which is called MN’, the upper envelope MX becomes (MX-MN). Then the space between MX and MN can be best utilized. The new output reference voltage Vxo’ can be created under this equivalent dc link as shown in Fig.6. The lowest point of the upper envelope MX’ is 1.5, thus the maximum available modulation index M is increased to 0.75. The sinusoidal reference waveform Vxo’ will not keep the same when it is changed back to the original frame. However, since all three phase voltages have been shifted by the same voltage level, the line to line voltage waveform still keeps the sinusoidal shape with the desired M. Thus the change of frame doesn’t affect the output.

0 0. 005 0. 01 0. 015 0. 02 0. 0250

0. 20. 40. 60. 81

1. 21. 41. 61. 82

Shift

ed e

nvel

ope

and

refe

renc

es

t(s)

Vxo'Vxo2'

MX'MN'

Vxoh'

Fig.6. Shifted envelopes and references with third harmonic injection

In the new frame the expression of the reference voltage is: ' sin( ) 0.75xo oV M tω α= + + (18)

, in which [0,0.75]M ∈ . In addition, 1/6 of the third harmonic of Vxo’ can be injected to

bring M up to 1.15 times of the previous maximum value, which is 0.866. As shown in Fig.6, the sinusoidal voltage with M=0.866 is Vxo2’; after the third harmonic injection, it becomes the new reference Vxoh’, whose expression is:

1' sin( ) 0.75 sin(3 )6

[0,0.866]

xoh o oV M t M t

M

ω α ω= + + +

∈(19)

The relationship between the original frame [x, y] and the new

frame [x, y’] is:

''

x xy y MN

== −

(20)

Thus the corresponding reference voltage in the original frame is:

1sin( ) 0.75 sin(3 )6

[0,0.866]

xoh o oV M t M t MN

M

ω α ω= + + + +

∈ (21)

, as shown in red line in Fig.7. Thus the maximum modulation index for non-shoot through control, maximum control can go up to 0.866.

0

-1-0. 8-0. 6-0. 4-0. 2

00. 20. 40. 60. 8

1

0. 005 0. 01 0. 015 0. 02 0. 025t(s)R

efer

ence

with

3rd

har

mon

ic (p

u)

MX VxohMN

Fig.7. Input voltage envelope and output phase x reference with 3rd harmonic

injection

III. MAXIMUM VOLTAGE GAIN CONTROL In ZS-MC, the boost factor B is not a monofonic function of

D0 like the traditional Z-source inverter, thus the maximum voltage gain is not necessarily achieved at maximum available D0., as illustrated in Fig. 4. In ZS-MC, voltage gain is the function of M and D0, as shown in equation (2) and (3), with the restriction that 0( ) 1D t M≤ − , in which the equal sign can only be obtained at maximum boost control. To get the maximum G, assume that 0( ) 1D t k M= − ⋅ ( k ≥ ),

thus:

2 22

1 13 [( ) ]2 12

MG MBM k

M M

= =− +

(22)

The maximum G happens at 12

kM

= , which leads

0( ) 0.5.D t = Considering the restriction 0( ) 1D t M≤ − , when

M>0.5, 0( )D t should be the maximum available 0( )D t , which is 1-M, because B is a monotone increasing function at [ ]0 0,0.5D ∈ ; thus the control strategy is identical to

maximum boost control. When M<0.5, 0( )D t should be equal to 0.5. So the maximum gain control law is:

0

0

( ) 0.5 ( 0.5)

( ) 1 ( 0.5)

D t M

D t M M

= ≤�

= − >� (23)

249

And the voltage gain gG equations are:

2

2 ( 0.5)

( 0.5)3 3 1

g

g

G M M

MG MM M

= ≤� = >

− +�

(24)

As shown in the green line in Fig.8.

0 0. 2 0. 4 0. 6 0. 80

1

1. 5

M

Vol

tage

Gai

n G

Simple Maximum BoostNon-shoot-through

Maximum gainMaximum boost

0. 5

0. 94

1. 155

Fig.8. Maximum voltage gain vs. M

To implement the constant D0 at M<0.5, the shoot through reference curve has to be located between MX and MXo, or between MNo and MN, while keeping 0( )D t =0.5. Assume the upper and lower reference curves for maximum gain control at M<0.5 is 1shV and 2shV , thus:

1 20

( ) ( )( ) 1 ( ) 0.5

( ) ( )sh shV t V t

D tMX t MN t

−= − =

− (25)

Similar to the maximum boost control case, one choice of the two curves are MXo and MNo at a constant M=0.5. So, the Vsh1, Vsh2 equations for maximum gain control are:

1

2

( , , ) ( 0.5)

( , , ) (0.5 0.866)sh xo yo zo

sh xo yo zo

V Max V V V M

V Min V V V M

= ≤

= < < (26)

They are compared with the triangle to generate the shoot through PWM, as shown in Fig.9. the red line is reference curve at M<0.5. The shadow part is the available shoot through area.

0 0. 005 0. 01 0. 015 0. 02 0. 025

- 1- 0. 8- 0. 6- 0. 4- 0. 2

00. 20. 40. 60. 8

1 Vsh1 Vsh2MX MXo MNo

t(s)

MN

Fig.9. Shoot through references to generate 0( ) 0.5D t =

IV. HYBRID MINIMUM VOLTAGE STRESS CONTROL At a given target voltage gain, one criterion to select the

control strategy is to minimize the voltage stress on the switch. From Fig. 1, the voltage stress in ZS-MC is equal to B times the input line to line voltage. Different from traditional Z-source inverter, B here is not a monotonic function of D0 thus the

minimum voltage stress is not necessarily achieved at maximum available D0. From equation(3), to minimize voltage stress ratio B for a

defined G, M is required to be the biggest available M. From the G-M curves in Fig. 10 for four control strategies,

different control strategy can be selected during different voltage gain range to obtain the maximum modulation index. The dot symbols show the selection of different curves in different sections. The executive law of this kind of hybrid control is illustrated in Table I according to the cross points of the four G-M curves.

TABLE I. CONTROL STRATEGY FOR DIFFERENT G Control strategy Range of G Non-shoot-through [0,0.866]G ∈ Constant M [0.866,1.073]G ∈ Maximum Boost [1.073,1.155]G ∈

In the second range, M is fixed to be 0.866, thus G is

proportional to B and D0 can be selected in the range [0,1-M]; in the third range, G=f(M) function becomes a quadratic function of which the maximum M is obtained in the section of

[ ]0.667, 0.866M ∈ at the same voltage gain.

M

Volt

age

Gain

GSi mpl e Maxi mum Boost Maxi mum Boost Non-Shoot -Through

Maxi mum Gai n

0. 667 0. 8660. 442 0. 542

1. 155

0. 8661. 073

Hybr i d Cont rol

Fig. 10. Hybrid minimum voltage stress control

0 0.2 0.4 0.6 1.41

1.2

1.4

1.6

1.8

2

G

B

1.1550.866 1.073

Simple Max BoostMaximum Boost

Maximum gainHybrid minimum stress control

Fig. 11. Voltage stress comparison of different control methods.

From equation (16) (17), the voltage stress ratio of the hybrid control hB is:

2

1 ( [0,0.866])

( [0.866,1.073])0.866

3 4 3 ( [1.073,1.155])2

h

h

h

B GGB G

G GB G

= ∈ = ∈� − − = ∈�

(27)

250

The voltage stresses across the devices with different control strategies are shown in Fig. 11. As can be seen, the hybrid control has the smallest voltage stress at the whole voltage gain range.

V. SIMULATION AND EXPERIMENTAL RESULTS To verify the theory analysis of the four control strategies, the

simulations are conducted with the following parameters: 170 , 60 , 30 , 1 ,

330 , 20 , 1 .im i o

o o

V V f Hz f Hz L mHC uF L mH R

= = = == = = Ω

A. Demonstration of voltage gain equations To demonstrate the G-M curves in Fig.8, simulation

waveforms of different voltage gains at M=0.661 and M=0.2 of four control strategies (non-shoot-through, simple maximum boost, maximum boost and maximum gain) are shown in Fig. 12(a)(b), where the voltage gain is represented by the load current. Moreover, the corresponding experimental results are shown in Fig. 13 and Fig. 14. Table I lists the theoretical voltage gains and measured

simulation and experimental voltage gains. It can be seen that the simulation and experimental results are consistent with the theory analysis at both M>0.5 and M<0.5 cases. It also demonstrates that at certain M, the voltage gain satisfies:

( 0.5)

(0.5 0.866)g s m n

g m n

G G G G M

G G G M

> > > ≤� = > < <�

(28)

, which are consistent with Fig.8.

Fig. 12 (a). Voltage gain comparison at M=0.661: non-shoot-through control at

[0,0.1]t ∈ and maximum gain control at [0.1,0.2]t ∈ .

Fig. 12.(b). Voltage gain comparison at M=0.2: non-shoot-through control

at [0,0.1]t ∈ ; maximum boost control at [0.1,0.2]t ∈ ; simple maximum boost control at [0.2,0.3]t ∈ and maximum gain control at [0.3,0.4]t ∈ .

Vab 100V/div

Vxy 100V/div

Ia 50A/div

Ix 2A/div

Fig. 13. Experimental results of Fig. 12 (a)

100V/div

Vxy 100V/div

Ia 50A/div

Ix 2A/div

' 'a bV

Fig. 14. Experimental results of Fig. 12 (b) from non-shoot-through to

maximum gain control

B. Demonstration of voltage stress equations

251

Fig. 15(a) Voltage stress comparison at G=1.073: maximum boost control with M=0.542 at [0,0.1]t ∈ ; hybrid minimum voltage stress control with M=0.866

at [0.1,0.2]t ∈ .

Fig.15.(b). Voltage stress comparison at G=0.8: maximum gain control at [0,0.1]t ∈ ; simple maximum boost control at [0.1,0.2]t ∈ ; maximum boost

control at [0.2,0.3]t ∈ ; hybrid minimum voltage stress control at [0.3,0.4]t ∈

100V/div

Vxy 100V/div

Ia 50A/div

Ix 2A/divT1 T2

' 'a bV

Fig. 16. Experimental voltage stress comparison at G=1.073: T1(hybrid

minimum voltage stress control) to T2(maximum boost control at M=0.542)

100V/div

Vxy 100V/div

Ia 50A/div

Ix 2A/divT1 T2 T3 T4

' 'a bV

Fig. 17. Experimental voltage stress comparison at G=0.8: T1(hybrid minimum voltage stress control) to T2(maximum boost control) to T3(simple maximum

boost control) to T4(Maximum gain control) To demonstrate the B-G curves in Fig. 11, simulation

waveforms with different voltage stresses at the same voltage gain G=1.073 and G=0.8 respectively are shown in Fig. 15(a)(b), in which the switch voltage stress is represented by

' 'a bV . And the corresponding experimental results are shown in Fig. 16 and Fig. 17. The theory analysis, measured simulated results and

experimental results are shown in Table III and they are consistent with each other. It also can be seen that the hybrid control can achieve less voltage stress than other control strategies at both G>0.866 and G<0.866 cases. In conclusion, the simulation and experiment results

demonstrate that maximum gain can be achieved at the maximum gain control and minimum voltage stress across the switch can be achieved through hybrid minimum voltage stress control.

TABLE II. VOLTAGE GAIN COMPARISON AT CERTAIN M N-S M S-M M-G

M=0.661

Theory G 0.661 1.155 -- 1.16

Simulation G 0.685 1.2 -- 1.2

Experiment G 0.721 1.149 -- 1.15

M=0.2

Theory G 0.2 0.28 0.3 0.4

Simulation G 0.22 -- -- 0.39

Experiment G 0.234 -- -- 0.35

252

TABLE III. VOLTAGE STRESS COMPARISON AT CERTAIN G

N-SM

S-M M-GM1 M2

G=1.073

Theory B -- 1.696 1.24 -- --

Simulation B -- 1.923 1.42 -- --

Experiment B -- 1.73 1.442 -- --

G=0.8

Theory B 1 -- 1.921 1.997 2

Simulation B 1 -- 1.91 2.08 2.01

Experiment B 1.08 -- 1.89 2.13 2.13

VI. CONCLUSION In Z-source matrix converter, the simple maximum shoot

through control which uses two straight lines as the shoot through generation reference, and maximum boost control, which utilizes all the zero state, can be used as the shoot through control strategies. However, the maximum voltage gain is not achieved at both strategies due to the non-monotonic characteristics of the G-M curve. Also the minimum voltage stress is not obtained at maximum shoot through duty cycle. As analyzed and demonstrated in the paper, the maximum voltage gain can be achieved at each M can be achieved by using maximum gain control. The minimum voltage stress can also be achieved by applying hybrid minimum voltage stress control.

REFERENCES [1] P. W. Wheeler, J. Rodriguez, J. C. Clare, L. Empringham and A.

Weinstein, “Matrix converters: A technological review”, IEEE Transactions on Industrial Electronics, Vol. 49, No. 2, pp. 276-288, April, 2002. [2] Bradaschia, F., et al., A Modulation Technique to Reduce Switching Losses

in Matrix Converters. Industrial Electronics, IEEE Transactions on, 2009. 56(4): p. 1186-1195. [3] Arias, A., et al., Elimination of Waveform Distortions in Matrix Converters

Using a New Dual Compensation Method. Industrial Electronics, IEEE Transactions on, 2007. 54(4): p. 2079-2087. [4] Domenico Casadei, Giovanni Serra, Angelo Tani, and Luca Zarri, Optimal

Use of Zero Vectors for Minimizing the Output Current Distortion in Matrix Converters, IEEE Transactions On Industrial Electronics, Vol. 56, No. 2, February 2009, pp.326-336. [5] Glinka, M. and R. Marquardt, A new AC/AC multilevel converter family.

Industrial Electronics, IEEE Transactions on, 2005. 52(3): p. 662-669. [6] Meng Yeong, L., P. Wheeler, and C. Klumpner, Space-Vector Modulated

Multilevel Matrix Converter. Industrial Electronics, IEEE Transactions on, 2010. 57(10): p. 3385-3394. [7] Muller, S., U. Ammann, and S. Rees, New time-discrete modulation

scheme for matrix converters. Industrial Electronics, IEEE Transactions on, 2005. 52(6): p. 1607-1615. [8] Domenico Casadei, Giovanni Serra, Angelo Tani, Andrew Trentin,

andLuca Zarri, Theoretical and Experimental Investigation on the Stability of Matrix Converters, IEEE Transactions on Industrial Electronics, Vol. 52, No. 5, October 2005, pp.1409-1419. [9] Domenico Casadei, Jon Clare, Lee Empringham, Giovanni Serra, Angelo

Tani, Andrew Trentin, Patrick Wheeler, and Luca Zarri, Large-Signal Model for the Stability Analysis of Matrix Converters, IEEE Transactions on Industrial Electronics, Vol. 54, No. 2, April 2007, pp.939-950. [10] Kyo-Beum Lee, and Frede Blaabjerg, An Improved DTC-SVM Method

for Sensorless Matrix Converter Drives Using an Overmodulation Strategy and a Simple Nonlinearity Compensation, IEEE Transactions on Industrial Electronics, Vol. 54, No. 6, December 2007, pp.3155-3166.

[11] Fabrício Bradaschia, Marcelo C. Cavalcanti, Francisco A. S. Neves, Member, and Helber E. P. de Souza, A Modulation Technique to Reduce Switching Losses in Matrix Converters, IEEE Transactions on Industrial Electronics, Vol. 56, No. 4, April 2009, pp.1186-1195. [12] Hoang M. Nguyen, Hong-Hee Lee, Member, IEEE, and Tae-Won Chun,

Input Power Factor Compensation Algorithms Using , a New Direct-SVM Method for Matrix Converter, IEEE Transactions On Industrial Electronics, In press. [13] Hossein Hojabri, Hossein Mokhtari, Liuchen Chang, A Generalized

Technique of Modeling, Analysis and Control of a Matrix Converter Using SVD, IEEE Transactions On Industrial Electronics, in press. [14] Fang Lin Luo and Zhi Yang Pan, “Sub-Envelope Modulation Method to

Reduce Total Harmonic Distortion of AC/AC Matrix Converters,” the 1ST IEEE Conference on Industrial Electronics and Applications, Page(s):1 – 7, 24-26 May 2006 [15] Pfeifer, M. and G. Schroder. New commutation method of a matrix

converter. in Industrial Electronics, 2009. ISIE 2009. IEEE International Symposium on. 2009. [16] Xu, L., et al. Capacitor clamped multi-level matrix converter: Space

vector modulation and capacitor balance. in Industrial Electronics, 2008. IECON 2008. 34th Annual Conference of IEEE. 2008. [17] Hongwu She, Student Member, IEEE, Hua Lin, Member, IEEE, Xingwei

Wang, Limin Yue, Xing An, and Bi He, Nonlinear Compensation Method for Output Performance Improvement of Matrix Converter, IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, in press. [18] Andreu, J., et al., New Protection Circuit for High-Speed Switching and

Start-Up of a Practical Matrix Converter. Industrial Electronics, IEEE Transactions on, 2008. 55(8): p. 3100-3114. [19] Gupta, R.K., et al., Direct-Matrix-Converter-Based Drive for a

Three-Phase Open-End-Winding AC Machine With Advanced Features. Industrial Electronics, IEEE Transactions on, 2010. 57(12): p. 4032-4042. [20] Zanchetta, P., et al., Control Design of a Three-Phase

Matrix-Converter-Based AC&#x2013;AC Mobile Utility Power Supply. IEEE Transactions on Industrial Electronics, 2008. 55(1): p. 209-217. [21] Patrick W. Wheeler, Jon C. Clare, Maurice Apap, and Keith J. Bradley,

Harmonic Loss Due to Operation of Induction Machines From Matrix Converters, IEEE Transactions on Industrial Electronics, Vol. 55, No. 2, February 2008, pp.809-816. [22] Roberto Cárdenas, Rubén Peña, Patrick Wheeler, Jon Clare, and Greg

Asher, Control of the Reactive Power Supplied by a WECS Based on an Induction Generator Fed by a Matrix Converter, IEEE Transactions on Industrial Electronics, Vol. 56, No. 2, February 2009, pp.429-438. [23] Roberto Cárdenas, Rubén Peña, Germán Tobar,Jon Clare, Patrick Wheeler,

and Greg Asher, Stability Analysis of a Wind Energy Conversion System Based on a Doubly Fed Induction Generator Fed by a Matrix Converter, IEEE Transactions on Industrial Electronics, Vol. 56, No. 10, October 2009, pp.4194-4206. [24] Saúl López Arevalo, Pericle Zanchetta, Patrick W. Wheeler, Andrew

Trentin, and Lee Empringham, Control and Implementation of a Matrix-Converter-Based AC Ground Power-Supply Unit for Aircraft Servicing, IEEE Transactions on Industrial Electronics, Vol. 57, No. 6, June 2010, pp.2076-2084. [25]. Fang Zheng, P., Z-source inverter. Industry Applications, IEEE

Transactions on, 2003. 39(2): p. 504-510. [26]. Fang Zheng, P., S. Miaosen, and Q. Zhaoming, Maximum boost control

of the Z-source inverter. Power Electronics, IEEE Transactions on, 2005. 20(4): p. 833-838. [27]. Shen, M., et al. Maximum constant boost control of the Z-source inverter.

in Industry Applications Conference, 2004. 39th IAS Annual Meeting. Conference Record of the 2004 IEEE. 2004. [28]. Fan, Z., et al. A new three-phase ac-ac Z-source converter. in

Applied Power Electronics Conference and Exposition, 2006. APEC '06. Twenty-First Annual IEEE. 2006.

253