The Control Technology Research of the Z-source Three-phase Four-bridge Arm Inverter

doi:10.4236/epe.2013.54B142

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Energy and Power Engineering, 2013, 5, 733-739

doi:10.4236/epe.2013.54B142 Published Online July 2013 (http://www.scirp.org/journal/epe)

The Control Technology Research of the Z-source

Three-phase Four-bridge Arm Inverter

Xiangli Li, Zhaoyang Yan , Keke Pan, Chenghao Ma, Hanhong Qi

Key Lab of Power Electronics for Energy Conservation and Motor Drive of Hebei Province,

Yanshan university, Qinhuangdao, China

Email: [email protected]

Received March, 2013

ABSTRACT

Z-source inverter can boost the voltage of the DC-side, allow the two switches of the same bridge arm conducting at the

same time and it has some other advantages. The zero-sequence current flows through the fourth leg of the three-phase

four-leg inverter so the three-phase four-leg inverter can work with unbalanced load. This paper presents a Z-source

three-phase four-leg inverter which combines a Z-source network with three-phase four-leg inverter. The circuit uses

simple SPWM modulation technique and the fourth bridge arm uses fully compensated control method. The inverter

can maintain a symmetrical output voltage when the proposed scheme under the unbalanced load.

Keywords: Z-source Inverter; Three-phase Four-leg inverter; Unbalanced Load; Imbalanced Voltage

1. Introduction

Z-source inverter[1-5] with Buck-Boost characteristic

can boost the low DC power to a specified high voltage,

and the two switches of the same bridge arm can conduct

at the same time. Then there is no longer necessary to

add the dead zone, thereby Z-source inverter can reduce

the harmonic content because of the dead zone setting,

and improve the quality of the power conversion. The

traditional three-phase inverter can not provide pathways

for the zero sequence current which is generated by un-

balanced load, It is only suitable for balanced load.

Three-phase four-bridge arm inverter[6-7] increases a

bridge arm on the basis of the traditional three-bridge

arm inverter structure. And this bridge arm constitutes

midline and then eliminates the need of the midpoint

transformer when the load is unbalanced, reduces the

volume and weight of the system. Dq0 rotating coordi-

nate variables are mutually orthogonal, there is no cou-

pling, they can be individually controlled, but the disad-

vantage of this method is the large amount calculation of

the coordinate transformation and coordinate inverse

transformation[8]. The paper separates the fourth bridge

arm from the other control coupled bridge arm. The

fourth bridge arm is individually controlled. Based on the

advantages of the Z-source network and three-phase

four-bridge arm inverter, this paper presents Z source

three-phase four- bridge arm inverter, and it can improve

the voltage pressure, under the unbalanced load it is able

to maintain a good symmetrical output voltage.

2. Analysis of the Main Circuit

2.1. The Main Circuit

The main circuit is shown in Figure 1. Z-source imped-

ance network is provided by the diode D, capacitor C1,

C2 and inductors L1, L2.In the design of the Z imped-

ance network, the capacitance value of C1, C2 is equal

and the inductance value of L1, L2 is equal. And the

formula is C1 = C2 = C, L1 = L2 = L.

The fourth bridge arm of the three-phase four- bridge

arm inverter is added to the traditional three-phase three

arms. The fourth bridge arm consists of switching tube

Q7, Q8. The midpoint of the bridge arm connects the in-

ductor Ln to the load neutral point. The main function of

the inductance Ln is to filter the switching ripple of the

neutral current. Z-source network and three-phase four-

bridge arm inverter are combined to form a Z -source

three-phase four-bridge arm inverter. The DC voltage

Udc boost by the Z-source network then changes into

alternating current through the four-leg inverter then the

alternating current powers the unbalanced load through

the LC filter.

2.2. Working Principle of Z-source Inverter

Z-source inverter has two working conditions which are

the active state and the shoot-through state. The inverter

can be equivalent to a controlled current source iin.

Figure 2(a) shows the active working state of the Z-

source inverter’s equivalent circuit diagram. When the

X. L. LI ET AL.

734

switching state is one of the active state or the traditional

zero vector, the input of the diode D is conducting, the

power source and the inductors L1, L2 simultaneously

power the load, capacitor Cl and C2 are charging status.

Figure 2( a) can be obtained:

12 21

11 21

dc CLCL

inCL C L CL

uuuuu

uuuuuuu





Calculate the above two formulas,we can obtain:

inC dc

uuu

where uin is the DC side input voltage .

Figure 2(b) shows the shoot-through working state of

the Z-source inverter’s equivalent circuit diagram. Diode

D is cutoff. Inductor and capacitor exchange energy. Ca-

pacitance charges inductance .We can obtain from Fig-

ure 2 (b):

12 12

in 0

CCCLL

uuuuuu





The inductor L1 (L2) should satisfy the volt-second

characteristic within a switching period Ts (the average

storage energy of a switching cycle is zero). During a

switching cycle, anti-shoot-through state works time is

T1, shoot- through state works time is T0,and T1 + T0 =

Ts, d0 is the straight-through duty cycle. Then we can

obtain:

10 0

() 0

dc CC

Cdc

in dc

uuTuT

TT d













It can be seen that when T 0 varies within the range of

0-0.5T, Uin / Udc is theoretical from 1 to infinity.

2.3. The Simple Boost SPWM Modulation Me-

thod

The basic idea of the Z source three-phase inverter SPWM

modulation is as follows. When Z-source inverter works

in traditional zero vector state and shoot-through zero

vector state, the three-phase load is short-circuited. Re-

place the part time of the traditional zero vector time

with the shoot-through zero vector time, keep the effec-

tive vector works time the same, and then can increase

the output voltage value of the Z-source inverter. The

modulation principle is shown in Figure 3.

Figure 1. The main circuit topology of Z-source three-phase four-leg inverter.

Figure 2. The status of the Z-source inverter.

X. L. LI ET AL. 735

Figure 3. Simple boost SPWM modulation technology sche matic .

In Figure 3, Vp is equal to or greater than the peak

value of the three-phase reference voltage, and Vn is

equal to or smaller than the carrier negative peak voltage.

They are used to control the straight duty cycle. When

the carrier amplitude is higher than Vp or lower than Vn,

the inverter operates in the shoot-through zero state,

when the carrier amplitude is between Vp and Vn, the

inverter is in the traditional SPWM modulation state.

Can be obtained, D0 will be reduced when the modula-

tion factor M increases. The maximum value of D0 of is

(1-M), when M is 1, D0 is 0. The output phase voltage

amplitude of inverter is:

dc dc

uMMB G 

a,b,c 2

122 1

BdM





(1)

*21

GMB



 (2)

Uin is the DC side of the inverter input voltage. B is the

boosting factor. M is the modulation factor of the in-

verter. G is a gain factor.

By the formula (1) and formula (2), knowing that the

arbitrary size’s AC output voltage can be obtained by

controlling the d0 and M. It expands the conversion range

of the entire system, and is applicable to more applica-

tions.

2.4. The Fourth Leg Control Principle

Figure 4 is a circuit diagram of the three-phase four-

bridge arm inverter.

ia + ib + ic = 0 when three-phase three- bridge arm in-

verter with three-phase linear balanced load. uan, ubn, ucn

are determined by ua, ub, uc. ia + ib + ic ≠ 0. When the

three-phase four-bridge arm inverter with unbalanced

load, uan, ubn, ucn are jointly decided by ua, ub, uc and un.

Assumptions:

asin( )

sin(2/ 3)

sin(4/ 3)

um t



 













(3)

Ln = L, by the formula (3) can be obtained

3(/)

a b cnAGBGCG

uuuLdi dtuuu

uLdidt

 



)

If ua + ub + uc = 0, then

/()3( /)

nAGBGCGn

Ldi dtuuuuLdi dt



 

If the fourth bridge arm’s un is designed to be

n4/3* /

uLdi dt





Then

AG BG CG

uuu





Output voltage is balanced.

X. L. LI ET AL.

736

In the actual control, k (AG BG) items is add

to adjust the three-phase asymmetry.

uuu

3. Three-phase Output Voltage Control

3.1. Mathematical Model of the Three-phase

Four-leg Inverter under the Three-phase

Rotating Coordinate System (d, q, 0)

Differential equations of the three-phase four-bridge arm

according to Fig u r e 4 can be listed as follows:

ana

bn nbBG

cnc

IId

LILIdU

dt dt

IId

 

 



 

 

(4)

AGa oa

Gbob

CGc oc

UII

CUI I

dt UII

















(5)

Among them da, db, dc are three-phase phase voltage

duty cycles, Ia, Ib, Ic are output phase current of the in-

verter. Ioa, Iob and Ioc are three-phase load current. In is the

neutral inductor current. Uin is the DC side input voltage

of the inverter.

Stationary coordinate system (a, b, c) changes to the

rotating coordinate system (d, q, 0) coordinates. The

transformation matrix is as follows.

abc/ 0

sinsin() sin()

coscos() cos()

1/ 21/21/ 2

tt t

Tttt



 



 



















(6)

The correspondence relationship between the abc co-

ordinate physical quantity with dq0 coordinate physical

quantity is as follows.

0abc/0

o0abc/0

0abc/0

d qdqAG BGCG

dqdq abc

doqodqoa ob oc

dqdq abc

UUUTUUU

IIITIII

IIIT III

ddd Tddd

























(7)

Consolidate the formula (4) (5) (6) (7) can be ob-

tained.

000

ddd

qqq

IdU

Md MUI

dt IdU



  

  



  

  

 

(8)

qdq

CU CUII

dt UI





 













 





 





(9)

where the matrix M is

100









































(10)

From the formula (8) and (9) we can obtain the cou-

pling between the dq axis, 0 axes is independent. Feed

forward compensation is used to release the coupling

between the dq axis, after decoupling, after decoupling,

d-axis, q-axis, 0 axes are the three single-input single-

output independent control system.

Under the dq0 rotated coordinate system, inductor cur-

rent loop is the inner loop; the capacitor voltage loop is

the outer loop. The controlled schematic diagram is

shown in Figure 5 as below:

Figure 4. Three-phase four-leg inverter structure diagram.

X. L. LI ET AL. 737

Figure 5. dq0 axis control schematic structure diagram.

3.2. Z-source Network Capacitor Voltage

Control Design Idea

Here is the controlled method of Z-source network ca-

pacitor voltage. The Z-source network capacitor voltage

control block diagram is shown in Figure 5. In the de-

sign of the capacitor voltage out loop, the current inner

loop is regarded as a gain link in the out loop path. Ig-

noring the inverter bridge own loss under the condition

of unity power factor, the active power of the inverter

AC side is equal to the active power of the inverter cir-

cuit DC side, then we can obtain the formula (11).

333

222

in inadq

uiuiuiui

(11)

In order to simplify the design of the controlled system,

q axis vector voltage was regarded as the 0 vector volt-

age in the two-phase synchronous rotating coordinate

system (d, q). so formula (11) is converted into formula

(12).

in inad

uiui ui

(12)

There are formulas (13), (14) of the Z-source network

as follows.

212

inc dcdc

uuu u



 (13)

inZL C

iii



 (14)

According to formula (13) and formula (14), formula

15 can be obtained. Where uin is the DC side of the in-

verter input voltage, iin is the DC side of the inverter in-

put current, udc is the power supply of the system. iZL is

the current in the inductor Z-source network.

(1 2)

dd dd

cZLinZL ZL

in dc

uiui d

iii ii



 (15)

So capacitor current ic of the voltage loop can be con-

trolled by controlling the load AC current id and thus

control the capacitor voltage.

4. The Simulation Results

System simulation parameters are as follows:

Three-phase output phase voltage: 1102/50 Hz

Input voltage of the DC side: 330 V

Three-phase filter inductor: 1 mH

Midline inductance: 1mH

Filter capacitor: 25



Z-source network inductance: 2 mH

Z-source network capacitor: 3300



The next two cases were analyzed: (1) the Z source

three-phase three-leg with unbalanced load (two-phase

no-load, one phase with a load of 50 ohms) (2) Z-source

three-phase four-leg with unbalanced load(two-phase no-

load, one phase with a load of 50 ohms).

From Figure 6, we can see the output waveforms

quality is poor and the load voltage is unbalanced when

Z-source three-phase three-bridge arm inverter circuit is

with unbalanced load.

X. L. LI ET AL.

738

00.02 0.04 0.060.080.10.12

-5

t /s

Out put c urrent/A

00.02 0.04 0.060.080.10.12

-500

500

t /s

Out put voltage/V

Figure 6. Three-phase three-leg simulation waveforms with unbalanced load.

0.10.11 0.12 0.13 0.14 0.150.16 0.17 0.18 0.19 0.2

-4

-2

t /s

Output current

0.10.11 0.12 0.130.14 0.15 0.160.17 0.18 0.19 0.2

-200

-100

100

200

t/s

Output v oltage

Figrue 7. Three-phase four-le g with unbalanced load simulation.

From Figure 7, we can see the waveforms in the Z-

source three-phase four-bridge arm inverter system with

the same load have been greatly better. The degree of

imbalance of output voltage is small. But the amplitude

does not have a very good stability in expectation; there

is a growing trend, so the control mode needs to improve.

5. Conclusions

This paper presents a Z-source three-phase four-bridge

arm inverter which combines a Z-source network with

three-phase four-leg inverter. The circuit uses simple

SPWM modulation technique. The three-phase four-

bridge arm use PI control in synchronous rotating coor-

dinate system, the fourth bridge arm use independent

methods to control. The simulation results demonstrate

the Z-source three-phase four-bridge arm inverter can

output three-phase sine wave voltage under unbalanced

load conditions.

REFERENCES

[1] F. Z. Peng, X. P. Fang, B. Gu, et al., “Z-Source Con-

verter,” Transactions of China Electrotechnical Society,

Vol. 19, No. 2, 2004, pp. 47-51.

[2] M. S. Shen, J. Wang, F. Z. Peng, et al., “Maximum Con-

stant Boost Control of the Z-source Inverter,” IEEE In-

dustry Applications Society Annual Meeting, 2004, pp.

142-147.

[3] E. Wit and J. McClure, “Statistics for Microarrays: De-

sign, Analysis, and Inference,” 5th Edition, John Wiley &

Sons Ltd., Chichester, 2004. doi:10.1002/0470011084

[4] X. P. Ding，Z. M. Qian，B. Cui，et al., “Fuzzy PID

Controller for DC-link Boost Voltage in Z-source In-

X. L. LI ET AL. 739

verter,” Proceedings of the CSEE, Vol. 28, No. 24, 2008,

pp. 31-38.

[5] P. C. Loh, D. M. Vilathgamuwa, C. J. Gajanayake, Y. R.

Lim and C. W. Teo, “Transient Modeling and Analysis of

Pulse-Width Modulated Z-Source Inverter,” EEEE Trans-

action on Power Electronics, Vol. 22, No. 2, 2009, pp.

498-507.

[6] L. B. Li, Z. G. Zhao, et al., “Study on three-phase photo-

voltaic grid-connected inverter system based on composi-

tive control,” Power System Protection and Control, 2010,

Vol. 38, No. 21, pp. 44-47.

[7] L. Jun, T. C. Green and C. Feng, “Increasing Voltage

Utilization inSplit-Link, Four-Wire Inverters,” IEEE

Trans. on Power Electronics,” Vol. 6, No. 24, 2009, pp.

1562-1569.

[8] P. C. Loh, D. M. Vilathgamuwa, C. J. Gajanayake,

L. T. Wong, C. P. Ang, “Z-Source Current—Type

Inverters: Digital Modulation and Logic Imple-

mentation,” IEEE Transactions on Power Electron-

ics, Vol. 22, No. 1, 2007, pp. 169-177.

doi:10.1109/TPEL.2006.886618