TAP CHi KHOA

TAP CHi KHOA Hpc & CONG NGHg CAC TRUftNG DAI HQC KY THU^T • S6 91 - 2012

ANALYSIS OF SWITCHING PATTERNS IN SPACE VECTOR MODULATION METHOD FOR Z SOURCE INVERTERS

PHAN TICH tVlAU XUNG TRONG PHU'ONG PHAP BIEN DIEU VECTOR KHONG GIAN CHO BQ BIEN DOI N G U 6 N Z

Tran Trong Minh, Vu Hoang Phuong Hanoi University of Science and Technology Received February 29,2012; accepted August 01,2012

ABSTRACT

Pulse width modulation plays a crucial role In determining characteristics as well as work efficiency of the Z-source inverter In this paper three switching patterns, applied in space vector modultlon for Z-source inverter, were analyzed in term of: 1) utilizing DC voltage, (2) the peak dc-link voltage across the inverter bridge and (3) bi-directional energy exchange. The analysis the shows algebraic formula and the suitable switching pattern to implement on modern microcontrollers of a particular Z-source inverter design Finally, the analytical results were verified by Matlab/Simulink simulation.

T 6 M TAT

Luit phit xung c6 y nghta quan trong quyit dinh din dac tinh. cung nhw hi$u qui lim viSc cua nghich luv ngudn Z. Bii bio niy phin tich vi khio sit ba loai miu xung ip dung trong phuang phip biin di&u vector khdng gian cho nghich luv ngudn Z vi. (1) khi ning tin dung di$n ip ngudn mot chiiu; (2) diin ip dat l^n nhinh van nghich Iwu; (3) trao dii ning Iwgng theo hai chiiu. Qui trinh phin tich chi ra cic phip tinh toin thuin dai s6 vi miu xung phu hgp de cii dat trin cic vi diiu khiin hiin dai trong thiit ki nghjch luu ngudn Z cho mdt wng dung. Cic phin tich trin dugc kiim chimg bing md phdng Matlab/Simulink cho h$ thing diiu khiin phit xung cha nghich Iwu ngudn Z.

NOMENCLATURE

ZSI Z source inverter CSI BZSI Bidirectional Z source inverter SVM VSI Voltage source inverter PWM

Current source inverter Space vector modulation Pulse width modulation L INTRODUCTION

The ZSI employs a unique impedance network which is coupled between a power source (voltage source type in this case) and an inverter circuit. This two-port impedance network consists of split-inductor (Ll and L2) and capacitors (Cl and C2) connected in X shape. This unique impedance network allows the ZSI to buck and boost its output voltage, and also provides unique features that cannot be achieved with conventional VSI and CSI [1].

Addition of antiparallel S7 allows possible energy exchange between DC and AC side in both directions Fig.l.

Several PWM control methods have been developed and used for the ZSI [3]. However, space vector modulation has been widely used

in industrial inverter because of less harmonic distortion in the output voltage and more efficient use of supply voltage. This paper presents a space vector modulation method which is suitable to be implemented on microcontrollers of Z-source inverters. Also, an analysis of three switching patterns was carried out to distinguish performance on inverter switching: (1) utilizing DC voltage; (2) the peak dc-link voltage across the inverter bridge;

(3) bi-directional energy exchange. Based on analysis performance the paper shows the scope of a particular Z-source design,

2. SPACE VECTOR MODULATION FOR Z SOURCE INVERTER

Space vector modulation method for ZSI is carried out similar to VSI. However, unlike

T/SP CHi KHOA IIQC & C6NG NGlIp CACTRUING D^l HQC KY THU^T * S6 91 - 2012 VSI, the SVM for ZSI has an additional zero

state called shoot through state. Shoot through state can appear in any one phase leg, in combination of any two phase legs, or in all three phase legs. This shoot through zero state

provides the unique buck - boost feature to the inverter. Hence, the ZSI has nine permissible switching (states) vectors comparing to eight of VSI. The vectors (ui to ug) divide the plane into six sectors in stationary ap frame Fig.2.

Fig. 1 Topology of Z source inverter

Hence, the first step in implementing SVM is to identify the sector of the reference voltage vector u„f supplied by the external controller. Then this vector is detected by comparing the phase-voltage components based on tbe algorithm Fig.3.

Fig. 3 Algorithm to determine position reference vector in each sector

This paper shows a general method to determine the duty ratio in which only algebra formula present such that it is easier to be implemented in microcontrollers [4]. u,tf is generated by two adjacent active vectors and zero vectors as the following.

T T

•^r.f=Y^.,+Y^n*v=d^u„+d^vi„^, (n=l--5)

(1) Or it can be rewritten in stationary ap frame as follows.

Fig. 2 The eight space vectors in stationary o^

frame

[::l-[;:]-[:]-[;:;H

(2) [x„ yo] are the values of Un at stationary ap frame, so are the [xp yp] with respect to u^,.

From (2), duty ratios for active state can be obtained as

(3)

Duty ratio for zero state (do) is

d^=\-d,-d^ (4)

From the duty ratios do, d|, di the next step is to identify the duty ratio for each transistor. It is necessaiy to build switching pattern for each sector. Because of an additional stage, i.e. shoot through, it will resuh in many more switching patterns. Each switching pattern contains specific characteristics related to activities ZSI. In this paper, an analysis of three switching patterns was carried out to indicate the application scope of a particular ZSI design.

3. COMPARISON OF SWTTCHING PATTERN IN SVM METHOD

The shoot through duty ratio (d^h) can be supplied by capacitor voltage controller and is kept constant over the switching period Tj [5].

It is divided into six equal portions Fig.4^ Fig.5

TAP CHi KHOA HQC & C O N G NGlIf CAC T R I / O N G DAI HOC KY TIIU^T * S6 91 - 2012 or four equal portions in the switching period

Fig.6 [2],[3]. The shoot through states is inserted in the transition of each phase leg or in zero state time intervals without changing the active state time interval in the space vector

modulation algorithm. How to insert this shoot through state becomes the key point of the PWM control methods for the ZSI.

[ : 1

^ - ^ — I

•: B ;B

::k^

Fig 4 First switching pattern Fig. 5 Second switching patter Fig. 6 Third switching pattern u in sector I (SPI) in sector I (SP2) sector 1 (SP3)

From switching patterns, the duty ralio for each transistor is determined. Six duty ratios should be controlled independently. Noted that the polarity of PWM channel must be set properly, for example in Fig.5.

• d s , = d , / 4 - d , | , / 4 d s j = d , / 4 + d , / 2 - d „ / 1 2 d s 3 = d „ / 4 + d , / 2 + d , / 2 + d , i / 1 2 d s . = d „ / 4 - d „ / 1 2

ds, = d „ / 4 + d , / 2 + d , j / 1 2 d s j = d „ / 4 + d , / 2 + d , / 2 + d , j / 4 In Fig. 4 the shoot through time limitation is 3/4 zero state time (To). The maximum shoot through duty ratio (dsh) can be obtained as

(5)

<',,.

³ ₍₆₎

The shoot through duty ratio can be calculated by modulation index (ma) [3].

3^/3w„

.4o-

2a-

_-)

⁽⁷⁾

The value of boost factor (B) fl 1 _ 4;r

l-2rf,„ 9 s / 3 m , - 2 ; The voltage gain (G)

G = 2a-(B + 2)

(8)

(9) The peak dc-lin!c voltage across the inverter bridge (Upn)

2ff (10) In Fig.5, Fig.6 the shoot through time

limitation is zero state time (To). Tbe maximum shoot through duty ratio (d^h) can be obtained

" , / - - " o (11) The shoot through duty ratio can be

calculated by modulation index (m^).

' ' , , , = ( 1 3^/3m.

In (12)

TAP cni KIIOA Hpc & C6NG NGIie CAC TRU'dNG DAI HQC K? THUAT * S6 91 - 2012 The value of boost factor (B)

1 "

l-2rf,j 373m„

The voltage gain (G) a-(B +

3VJ

(13)

(14) The peak dc-link voltage across the inverter bridge (Upn)

U^ = B.EJ-:^^^E

^ (15) The SP2, SP3 show the higher boost

factor (B) and lower peak dc-link voltage across the inverter bridge (Upn) in comparison with the SPI under the same conditions of DC voltage source (E) and desired line-to-line output voltage as shown in Fig.7, Fig.8. The SP2, SP3 have wider operation region than the SPI as shown in Fig.9, Fig.lO.

The shoot through duty ratio (d,h) is divided into six equal portions in the switching period, so the operating frequency of Z network is six times faster than the switching frequency of the main bridge. As a result the size of passive elements are reduced significantly, especially inductors (L, and Lj). The fact that a Diode operates faster than switching frequency is acceptable, but operation of S7 with six-time faster frequency is questionable. Therefore, the pulses in Fig. 6 can be considered as a more feasible solution when utilizing for the BZSI because the equivalent frequency is smaller in the case of Fig. 4, Fig. 5. One of the trends is to represent the minimum switching number in order to make the S7 frequency equal to switching frequency to improve the converter efficiency [6]. However, this will result in a decrease in the voltage boosting capability of BZSI because the maximum of shoot through duty ratio (djh) is just equal to a half of duty ratio for zero state (do).

Fig. 7 Characteristic boost factor Fig. 8 Characteristic peak dc-link voltage across the inverter bridge

Fig. 9 Operation region for ZSI with SPI Fig 10 Operation region for ZSI with SP2, SP3

TAP CHi KHOA HQC & C6NG NGHC CAC TRITONG D^l HQC KY THU^T * S6 91 - 2012 4. SIMULATION RESULTS

The Space vector modulation method for ZSI with three switching patterns is simulated and tested by Matlab/Simulink/Simpower Software. Parameters used for the simulation are shown as follows

DC voltage source AC line to line voltage Switching frequency

E=310V 380 V U=5 kHz

Impedance components ZSI output filter Load resistance/phase

C, = CI =235 uF L,=L,.1.4mH C,= 40uF Lr = 0.8mH R,= i o n Following [7] using unified control technique for ZS! with equations (6-^8) of SPI and equations (11-13) of SP2, SP3, the simulation results are shown in Fig.ll to Fig.

15.

VI ,1. ?.' " •

Fig 11 do and d,h with SPI Fig. 12 do anddshwilh SP2. SP3 Fig 13 Duty ratios of e transistor f

Fig. 14a Capacitor voltage Uc Fig. 14b DC-link voltage across Fig. 14c AC output voltage and E ihe inverter bridge

Fig 14 Simulation results with SPI

Fig 15a Capacitor andE

Uc Fig. 15b DC-link voltage across Fig. 15c. AC output the inverter bridge

Fig 15 Simulation results wilh SP2. SP3

TAP CHi KIIOA HOC & C6NG NGHf CAC TRUING DAI HQC KV THU^T • SO 91 - 2012 From the simulation results, it is clear implemented on microcontroller. The results that when E=310V and the desired line-to-line from theory and simulation showed output voltage is 380V, the capacitor voltage Uc characteristic of each switching pattern. Using requiresavalueof660V leading to the peak dc- the SP2, SP3 in ZSI control configuration will link voltage across the inverter bridge (Upn) reduce the loss of the inverter because the peak reaches lOlOV in case of implementing ZSI dc-link voltage across the inverter bridge is with switching pattern in Fig. 4. On the other lower than when using the SPI. However the hand, with switching patterns in F(i'.5, F/i'.tfuc SP2 showed some disadvantages when being and Upn require smaller values, i.e. uc =535V, applied to BZSI, Hence, the SP3 becomes an Up„=760V. appropriate solution. The above analysis leads to a novel approach on pulse generation melhod to improve the efficiency of the BZSI and this The paper presents a simple space vector problem will be addressed in the future modulation for ZSI, which is easy to be researches.

5. CONCLUSION

REFERENCES

1. Fang Zheng Peng.; Z-source inverter; IEEE transactions on industry applications, vol.39, no.2, March/April, 2003.

2. U.Shajilh Ali, V.Kamaraj; A novel space vector PWM for Z-source inverter ; Electrical Energy Systems - 2011 1st International Conference on.

3. S.Thangaprakash, n. Krishnan; Comparative evaluation of modified pulse width modulation schemes of Z-source inverter for various applications and demands; Intemational Joumai of Engineering, Science and Technology Vol, 2, No, 1,2010, pp. 103-115.

4. Dao Phuong Nam, Vu Hoang Phuong, Nguyen Minh Long; Some problems of space vector modulation for three-phase four leg inverter; Joumai of Automatic Control Engineering, June - 2007.

5. Tran Trong Minh, Vu Hoang Phuong; Design method of backstepping control for closed loop DC voltage of Z source inverter; papes 696 - 702, The first VietNam conference on control and automation - VCCA-2011.

6. Rabkowski. J, Bariik.R, Nowak.M; Pulse width modulation methods for bidirectional/High- Performance Z source inverter; Power Electronics Specialists Conference, 2008.

7. Sbuitao Yang, Xinping Ding, Fan Zhang, F. Z. Peng, and Zhaoming Qian; Unified Control Technique for Z-Source Inverter; Power Electronics Specialists Conference, 2008.

Author's address: Vu Iloang Phuong - Tcl.:0989258854-Email: phuong. vuhoang@hust.edu.vn Hanoi University of Science and Technology

No. 1 Dai Co Viet Str., Ha Noi, Viet Nam