Analysis and Design of Bi-Directional Z-Source Inverter for Electrical Vehicles

Haiping Xu1,2 , Fang Z. Peng1 , Lihua Chen1, Xuhui Wen2 1ECE department, Michigan state University, East Lansing, MI 48824,USA

2Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing, China

Email: hpxu@mail.iee.ac.cn, fzpeng@egr.msu.edu

Abstract- A new topology Bi-directional Z-source inverter is proposed. It can overcome the uncontrollable and unstable limitations of the Z-source inverter in DCM mode. The operational principle, design guidelines of Z-source networks and power devices are provided. A DC clamp snubber circuit is developed to limit the voltage spike on power device. Power loss analysis and 3-D design for Z-source inverter system are presented. A prototype of 55kVA bi-directional Z-source inverter is designed to verify the principle and performance of the proposed topology.

Keywords: Z-source inverter, DCM mode

I. INTRODUCTION The recently proposed Z-source inverter [1], which is

suitable for electrical vehicles, utilizes a unique LC network to handle shoot through states and boost the output voltage. The Z-source inverter can boost and buck the output voltage with a single stage structure. The shoot through caused by EMI can no longer destroy the inverter, which increases the reliability of the inverter greatly. Because of no dead time is required, perfect sinusoidal output waveform is obtainable.

However, all the descriptions and analysis are based on an assumption that the inductance of inductor in the Z-source network is great enough to maintain the inductor current almost constant, and the Z-source inverter work in CCM mode. In some applications, the inductance should be minimized in order to reduce cost, volume, and weight. In the case of Z-source inverter with small inductance or light-load operation, The CCM critical condition IL>1/2Iin is not satisfied [2]. The Z-source inverter work in DCM mode, the dc-link voltage is increasing infinitely, the output voltage will be uncontrollable and the system is unstable.

This paper proposes a new topology bi-directional Z-source inverter to overcome the above limitations. The operational principle and operate modes are analyzed thoroughly in section II. The design guidelines of Z-source networks and couple inductor are deducted in section III. In section IV, the voltage and current stress on power devices are analyzed. To limit the high spike on power devices, a novel dc clamp circuit was designed. In section V, the power loss of the system is evaluated. Based on the thermal simulation, 3D design of the inverter will be provided. Finally, a prototype of 55kVA bi-directional Z-source inverter is designed to verify the principle and performance of the proposed topology in section VI.

II. THE PRINCIPLE OF BI-DIRECTIONAL Z-SOURCE INVERTER

By proper design of the Z-source networks and proper control, one can avoid DCM condition in the certain degree. However, it is impossible to completely avoid these modes with the Z-source inverter. Figure 1 shows a new topology of Bi-directional Z-source inverter. By using this topology, the inverter is able to completely avoid the unwanted operation modes by turning on the switch S during all active states and traditional zero states. Furthermore, this topology provides the circuit bi-directional power flow function.

S1

S4

S5

S3

S6

S2

S7

Vo

C1

C2

L2

L1

ACload

Figure 1. Bi-directional Z-source inverter

The operation principle of Bi-directional Z-source

inverter: Fig. 2 shows the possible operation modes of the Bi-

directional Z-source inverter with the simple control strategy. In one cycle, it has seven operation modes.

iL1

iL2

+ +_ _vc1 v c 2

+

_vo

i L 1

iL 2

+

_

v i

+ +_ _v c1 v c2

+

_v o

iiiin i c 1ic 2

s7

978-1-4244-1874-9/08/$25.00 ©2008 IEEE 1252

i L 1

iL 2

+

_

v i

+ +_ _v c1 v c2

+

_v o

iiiin i c 1ic 2

s7

i L 1

iL 2

+

_

v i

+ +_ _v c 1 v c 2

+

_v o

i iii n i c 1i c 2

s 7

i L 1

iL 2

+

_

v i

+ +_ _v c 1 v c 2

+

_v o

i iii n i c 1i c 2

s 7

i L 1

iL 2

+

_

v i

+ +_ _v c 1 v c 2

+

_v o

i iii n i c 1i c 2

s 7

i L 1

iL 2

+

_

v i

+ +_ _v c 1 v c 2

+

_v o

i iii n i c 1i c 2

s 7

Figure 2. The possible operation modes of the Bi-ZSI

[Mode 1]: The circuit is in a switch shoot-through zero state when the two switches in any of the three phase legs are turned on at the same time, the sum of the two capacitors’ voltage is greater than the dc source voltage (VC1+VC2 > V0), the diode is reverse biased, and the capacitors charge the inductors. The voltages across the inductors are:

2L211 V , CCL VVV == . (1) The inductor current increases linearly. Because of the

symmetry (L1=L2=L and C1=C2=C) of the circuit, vL1=vL2=vL, iL1=iL2=iL, and VC1 = VC2 = VC. [Mode 2]: The inverter is in a non-shoot through state and the inductor current meets the following inequation,

iL ii21

> . (2)

Again because of the symmetry of the circuit, the capacitor current iC1 and iC2 and the inductor current iL1 and iL2 should be equal to each other respectively. In this mode, the input current from the dc source becomes:

02)( 2111 >−=−+=+= iLiLLcLin iiiiiiii (3)

Therefore, the diode is conducting and the voltage source and capacitor C supplies the inverter, the Z-source network capacitors C1 and C2 are charging. The voltage across the inductor is

CoL VVv −= , (4)

Which is negative, thus the inductor current decreases linearly. [Mode 3]: As time goes on, the inductor current keeps decreasing to a level that no longer the condition of (5.2) can be met

iL ii21

< . (5)

The Z-source network capacitors are discharged to the load. The input current, iin is still satisfied the inequation (4). [Mode 4]: The inverter is in one of the 2 traditional zero states (ii=0) and at the end of Mode 3, the inductor current decreases to zero, thus a new operation mode appears. In Mode 4, the inverter is an open circuit to the Z-source network because of ii=0. The inductor current becomes zero and maintains zero until the next switching action. Capacitors (C1 and C2) are charging from source.

[Mode 5:]: With the inductor current continue decreasing, the inductor current is becomes reverse-flow. The switch SW7 is conducting, the input current Iin becomes no larger than zero and Iin also becomes reverse-flow. [Mode 6]: At the end of Mode 5, the inductor current begins to increase, the inductor current is also reverse-flow, while the switch SW7 is in its on-state.

,0<ini ,0<Li (6)

inLi iii −=2 It is also charged energy from capacitors (C1 and C2) to

input source instead of the inductors (L1 and L2). [Mode 7]: The inverter is in one of the traditional zero states (Ii=0). Z-source network is isolated from the load. The inductor current decreases to zero, and the input current is reverse-flow. Capacitors C1,C2 are discharged to source.

O p e r a t io nm o d e 1 2 5

i LI p k

4

T 0 T 1 T 2 T 7T s t

2iI

6

73

Figure 3 The inductor current for the Bi-ZSI

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Fig 3 shows the inductor current and period of each operation mode for ZSI in bi-directional Z-source inverter. From Fig 3, considered voltage relationship, only two modes of Bi-directional Z-source inverter is left in Fig 4.

i L 1

i L 2

+ +_ _vc 1 v c 2

+

_vo

i L 1

iL 2

+

_

v i

+ +_ _v c 1 v c 2

+

_v o

iiiin i c 1i c 2

Figure 4. The simplified operation modes of the Bi-ZSI

021 211 V

DDVVV

s

sccc −

−=== (7)

0)21(2ˆ V

DMV

sac −= (8)

III. Z SOURCE NETWORKS: COUPLED INDUCTOR AND CAPACITOR

The specification of Z-source inverter for Fuel Cell Electrical Vehicle as follows; Fuel cell open voltage is 420 V, the rated power of Fuel cell is 30kW at 305V, the maximum output current is 220 A at peak power of 55 kW and 250 V. The target maximum output power of the inverter is 55 kW. The components to be designed or selected include the two inductors, L1 & L2; the two capacitors, C1, C2, the inverter switches S1~S6 and bi-directional switch S7.

The purpose of the inductors is to limit the current ripple through the devices during boost mode with shoot-through. The purpose of the capacitor in the Z-source network is to absorb the current ripple and maintain a fairly constant voltage so as to keep the output voltage sinusoidal.

In order to decrease the size and weight of indictor and capacitor, the ripple current and voltage should be limited; the changes of capacitor voltage and inductor current can be assumed as linear. The waveforms are shown in Fig 5. During shoot-though as shown in Fig.5, the capacitor charges the inductors, the inductor current increases linearly, and the voltage across the inductor is equal to the voltage across the capacitor, the current through the capacitor equals to the current through the inductor. During non-shoot-through modes (six active modes and the two traditional zero modes), the inductor current decreases linearly and the voltage across the inductor is the difference between the input voltage and the capacitor voltage.

IL

(1-Ds)Ts DsTs

LI

LL II Δ−

LL II Δ+Active state

Shoot_throughstate

t

Vc

(1-Ds)Ts DsTs

CV

CC VV Δ−

Active stateShoot_through

state

t

CC VV Δ+

Fig 5. Waveforms of inductor current (a) and capacitor voltage (b)

In the shoot-through period,

c

ssl

VTdI

CΔ

=2

(9)

l

ssc

ITdV

LΔ

=2

(10)

Define the ripple coefficient of voltage and current as

vK , iK , and peak line voltage as 2

im

VMV = .

. For simple boost control,

MS

SC VV

dd

V 221

10 =−

−= (11)

0211

Id

dI

S

SL −

−= (12)

The capacitance and inductance can be determined with equations,

)4(2)2(

00

00

VVVKVVTI

Cmv

ms

−−

= , (13)

)4(2

)2(

00

00

VVIKVVTV

Lmi

ms

−−

= (14)

For 55kW bi-directional Z-source inverter, with the voltage ripple coefficient Kv equals to 2.5%, current ripple coefficient Ki equals to 20%. L=53uH, C=375uF. To minimize the size and weight of the inductors, the couple inductor is designed for the system, and film capacitor AVX FFB56J0136K is selected.

The two inductors are built together on one core as shown in Fig. 6. For a single coil on one core, the flux through the core is

1254

PNi=φ , (15) Where P is a constant related to the core material and

dimension, N is the number of turns of the coil, and i is the current through the coil. The inductance of the coil is

2PNi

NL ==φ

. (16) For the two inductors in the Z-source, because of the

symmetry of the circuit, the current through the inductors are always exactly the same. For two coils on one core with exactly the same current, i, the flux through the core is

PNi2=φ . (17) The resulted inductance of each coil when supplying

exactly the same current to the two coils is 22PN

iNL ==φ

. (18) i1

i2φ

v1

v2

N

N

Fig. 6. Coupled inductors.

The inductance of each coil is doubled. Metglas AMCC_63 and AMCC_100 core pair are selected to reduce the loss.

IV. POWER SWITCHES STRESS ANALYSIS AND SNUBBER CIRCUIT DESIGN

The semiconductor devices are selected based on the current through them and the maximum voltage across them. The voltage rating of the IGBT main switches (S1~S6) are, 0)1(2 VVKV cvigbt −+=

The peak current of the dc-link of Inverter Bridge occurred in the shoot-through state, the peak current of IGBT main switches (S1~S6) is,

s

cacacli Lf

dVViv

II2

cosˆˆ32

0

+==φ

(19)

s

cacacigbt Lf

dVV

ivI

6cosˆˆ

0

+=φ

(20)

With the voltage ripple coefficient Kv equals to 2.5%, current ripple coefficient Ki equals to 20%, peak power 55kW at 250V. The maximum voltage across the switches is 420V. The maximum voltage across the switches is limit to 400 V. The peak current through the switches occurred at the peak power, the maximum current through the switches is 297A.

The voltage and current rating of Bi-switch S7 are,

cvs VkV )1(27 += (21)

))(1(2 07 IIkI lis −+= (22)

And mc VV 2= , 00 /2 VIVI ml = The maximum voltage across the Bi-switch S7 is limit to

400 V. The current through the inductor is 286A at peak power 55kW. The peak current through the S7 is twice the inductor current during traditional zero states, therefore, the peak current through the S7 is 552 A.

The following devices were selected, considering the high temperature requirement: a 600V/600A six-pack IPM PM600CLA060 for the inverter bridge, and IPM PM800HSA060 for the bi-directional switch S7.

Design a snubber circuit for Z-source inverter for high power application is really a big challenge. Because of shoot through state, there can not be any dc capacitors right across the PN of the inverter bridge, otherwise huge loss will occur during shoot through, thus the normal snubber circuit cannot be applied in ZSI. In order to reduce the overshoot of the devices, a dc rail clamp circuit is developed as shown in Fig.7.

Two pairs of Capacitor and diode combination, which Capacitor Cs1 and diode D1 in series, Capacitor Cs2and diode D2 in series, are parallel connected right across PN of the inverter bridge. Another two resistors, rs1 and rs2, are connected to the main device and power source forming a discharge loop. From Fig.7 (b), when the current to the inverter, Ii, has a step change, the dc rail clamping circuit provides an extra absorbing path for the extra current maintained by the parasitic inductance of the main bus-bar, thus helping to reduce the overshoot voltage across the device. Fig.7 (c) shows the two paths for discharging the two capacitors, Cs1 and Cs2, in the clamping circuit. Cs1 can be discharged through D1, and Cs2 can be discharged through D2. The capacitors used in the clamp circuit are 0.18uF/1000V ceramic capacitors, and the diodes D1, D2 are IXYS fast recovery epitaxial diode DESI 2*101 with SOT-227B packages.

S1 S5S3L1

S7

S4 S6 S2L2

ACload

rs2

rs1

C1

C2

Vo

Cs1

Cs2

D2

D1

(a) DC clamp circuit

ACload

S1 S5S3L1S7

S4 S6 S2L2

C1C2

Vo rs1

rs2

Cs2

D2

D1

Cs1

(b) Charging mode

1255

S1

S5

S3

L1

S7

S4

S6

S2L

2

ACload

C1

D1

Vo

C2

Cs1

Cs2

D2

rs1

rs2

(c) Discharging mode

Fig 7. Snubber circuit for Bi-Z Source Inverter

V. POWER LOSS ANALYSIS AND 3D DESIGN The power loss includes conduction loss and switching

loss. Since Bi-directional Z-source inverter has shoot-through state and active state, the switching loss and the conduction loss of the switches are different from traditional PWM inverters.

There are two parts of switching and conduction losses: active loss (switching actions between active states) and shoot through loss (switching states between shoot through state and traditional states).

))(1( ___ diodeonigbtonacton PPdP +−= (23)

Lsatceshooton IdVP32*__ = (24)

)sin21sin)((

21 6

5

60_ ∫∫

−

−−+=

a

aswoffswonswactsw dxxxdxEEfP

π

π

π

π

(25)

)(21

_ swoffsswonsswshootsw EEfP += (26)

Where Eswons and Eswoffs are the turn on and turn off energy loss corresponding to switching current of LI*2/3 . The calculated loss of the inverter at 55kW is 1.4kW; the temperature rise of the IPM junction to the heat sink can be calculated from the thermal resistance of the IPM.

The 3-D design of the inverter is shown in Fig.8. The final dimension of the inverter is 11”*12”*4.5”.

Fig8. 3-D design of the Bi-ZSI inverter

VI. PROTOTYPE & EXPERIMENTAL RESULTS A 55kW Bi-Directional Z-Source Inverter Prototype for

Electrical Vehicles is developed, shown in Fig 9. Fig. 10 (a) simulation shows that Z-source DC link voltage Vpn and output voltage are uncontrollable in DCM condition, while Bi-directional Z-source inverter can keep the Vpn and output voltage constant, shown in Fig 10 (b). The experiment waveforms of the Z-Source Inverter operating in DCM condition are shown in Fig 11. When the power factor is low or the load current is small, the current of inductor is discontinuous, the Z-Source Inverter operating in DCM condition. The DC link voltage Vpn across the device is boosted to 240V with input voltage at 150V, which is much higher than CCM condition 190V. This means the voltage stress on power switches much higher than CCM condition. The voltage Vpn also oscillates during DCM period, which impairs the stability of inverter system. The equation (8) is not satisfied anymore, and the output voltage loses of control.

Fig 12 is shown the experiment results of the Bi-Directional Z-Source Inverter. Fig 12 (a) show the PWM signal for inverter IPM switch and bi-directional switch S7. Fig 12 (b) shows the inverter operates in boost mode with shoot-through. The PN voltage Vpn across the device is boosted to 190V with input voltage at 150V. The inductor current IL is continuous and the direction of current can be reverse, which confirms that the Bi-directional Z source inverter can eliminate DCM condition and provide the circuit bi-directional power flow function. Fig 12 (c) shows the output line-to line voltage Vab and phase current Ia with RL load. Fig 12 (d) shows the spike on Vpn and voltage on snubber resistance Vsrn. The spike on Vpn is clamped to less than 10%, and power loss of snubber circuit is less than 1W, which confirm the snubber circuit is valid. The experimental results verify the principle and performance of the proposed Bi-directional Z-source inverter.

Fig 9. 55kW Bi-Directional Z-Source Inverter Prototype

Figure 10 (a) Vpn & IL of ZSI in DCM condition

1256

Figure 10 (b) Vpn & IL of Bi-ZSI

Figure 10. Simulation of ZSI in DCM and Bi-ZSI Upper: Vpn, Middle: IL, Lower: Vpn (zoom in)

IL:10A/div

Vin:100V/div

Vpn:100V/div

Ia:10A/div

Figure 11. ZSI in DCM condition

PWM

S1

S7

(a) PWM signal

IL:10A/div

Vin:100V/div

Vpn:100V/div

Ia:10A/div

(b) DC-link voltage Vpn and inductor current IL

Vab:100V/div

Vin:100V/div

Vpn:100V/div

Ia:10A/div

(c) Output voltage Vab and current Ia

IL:10A/div

Vsm:25V/div

Vpn:100V/div

Ia:10A/div

(d) Vpn and voltage on snubber resistance Vsrn

Figure 12. Experiment results of the Bi-ZSI

VII. CONCLUSION In this paper, a new topology bi-directional Z-source

inverter is proposed. It can operate in DCM condition with small inductor; overcomes the uncontrollable and unstable limitations of the Z-source inverter in DCM mode. Furthermore, the new topology provides the circuit with bi-directional power flow ability. The operational principle and seven modes of bi-directional Z-source inverter are analyzed. The design guidelines of Z-source networks and main circuit power devices are provided. A novel DC clamp snubber circuit is effective to reduce the voltage spike on IGBT less than 10%. The power loss analysis and 3-D design are presented for a prototype of 55kVA bi-directional Z-source inverter. The experimental results verify the principle of the proposed Bi-directional Z-source inverter. It can be widely used in the electrical vehicle, as well as the renewable energy application.

ACKNOWLEDGMENT The author would like to thank the fund and support of

Oak Ridge National Laboratory and Department of Energy.

REFERENCES [1] Fang Zheng Peng; “Z-source inverter” IEEE Transactions on Industry

Applications Volume 39, Issue 2, March-April 2003, pp.504 – 510.

[2] Miaosen Shen, and Fang Z. Peng, “Operation Modes and Characteristics of the Z-Source Inverter with Small Inductance,” IEEE IAS 2005, pp. 1253-1260

[3] J. Liu, J. Hu, and L. Xu;” A Modified Space Vector PWM for Z-Source Inverter - Modeling and Design” in Proc. of International Conference on Electrical Machines and Systems, 2005. Volume 2, pp.1242 – 1247, 27-29 Sept. 2005.

[4] 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” in Proc. of IEEE Industry Applications Society Annual Meeting, Volume 4, pp. 2782-2789, 2-6 Oct. 2005.

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