A High-Performance Z-source Inverter with Low
Capacitor Voltage Stress and Small Inductance
Liqiang Yang, Dongyuan Qiu, Bo Zhang and Guidong Zhang
School of Electric Power, South China University of Technology
Guangzhou, Guangdong, P. R. China
Email: epdyqiu@scut.edu.cn
Abstract—A novel high-performance Z-source inverter is
proposed in this paper. It can obtain the same voltage gain with
low Z-source network capacitor voltage stress than conventional
one and has inherent limitation to inrush-current at startup.
Moreover, it can work in a very wide range load even with small
inductance of the Z-source network inductor. Therefore,
compared with the conventional Z-source inverters, the
proposed converter not only has lower cost but also has smaller
weight and size. The operating principle and parameters design
of the proposed converter are analyzed. Simulation and
experimental results are presented to verify the validity of the
proposed high-performance Z-source inverter.
I. INTRODUCTION
The Z-source inverter proposed in recent years has drawn
extensive attentions due to its remarkable merits, such as: (1)
it utilizes the shoot-through zero state to boost dc voltage and
produce an output voltage greater than the input dc voltage
without an additional dc-dc boost converter; (2) it can avoid
the shoot-through problem caused by the EMI and eliminate
the harmful influence caused by the dead-time of the switches
due to the introduction of the Z-source network [1-8]. The
Z-source inverter which is illustrated in Fig.1 is very suitable
for the renewable generation system, because the
photovoltaic arrays and fuel cells normally need a high
voltage gain inverter to boost their voltages to the grid level.
However, there are three disadvantages in the traditional
Z-source inverter.
(1) Its load capacity is poor when it operates with small
inductance of the Z-source network inductor. The peak value
of the dc-link voltage is increasing infinitely and there is
distortion of the dc-link voltage when the inverter operates in
light-load or low power factor with small inductance which
will cause the output voltage uncontrollable and the system
unstable [2].
(2) The voltage stress of the Z-source network capacitor is
very high, which will bring some problems in the selection of
capacitors and make the whole system heavier and larger.
(3) Its startup inrush-current is very large. As shown in Fig.
2, there is a startup current path existed in the converter
inherently. Since the initial voltage of the Z-source network
This work was supported by National Natural Science Foundation of
China (NSFC) (51277079).
Fig. 1.
The traditional Z-source inverter
Fig. 2.
The current path at startup of the traditional Z-source inverter
capacitors are zero, a large inrush-current will charge the
capacitors to half of the input voltage V0 immediately. Then,
the capacitors and inductors of the Z-source network start to
resonate, which will result in large voltage and current surges
[3].
In order to overcome the above three disadvantages of the
traditional Z-source inverter, a novel high-performance
Z-source inverter has been proposed in this paper. The rest of
the paper is organized as follows. The proposed Z-source
inverter is introduced in section II. The operating principle
and circuit analysis of the proposed Z-source inverter are
introduced in Section III. In Section IV, voltage relationships
and parameters design of the proposed inverter are analyzed.
Simulation and experimental results are presented in Section
V and a conclusion is given in Section VI.
II. THE PROPOSED HIGH-PERFORMANCE Z-SOURCE
INVERTER
The proposed high-performance Z-source inverter is
illustrated in Fig. 3. As can be seen, the first difference
between the proposed inverter and the traditional Z-source
inverter is the connection way. In the traditional inverter, the
inverter bridge is in parallel with the Z-source network, while
in the proposed inverter, the inverter bridge is in series with
the Z-source network. The second difference between them is
that the proposed inverter has added a controllable switch
SW7 and the switch is in parallel with the Z-source network.
The third difference between them is the connection of the
Z-source network capacitors are inversed which results in the
polarity of the capacitors voltages in proposed converter
remains the same with the polarity of the input voltage source.
At last, considering the reverse current from the inverter
bridge and unidirectional current of some applications, a
capacitor Cin has been added behind diode D8 in the proposed
converter. Since the Z-source network of the proposed
inverter is in series with the inverter bridge, the Z-source
network inductors can limit the inrush-current at startup.
Therefore, the proposed inverter has inherent inrush-current
limitation ability.
III. OPERATING PRINCIPLE AND CIRCUIT ANALYSIS
A.Operating Principle and Circuit Analysis
For simplicity, it is assumed that all the components are
ideal and the capacitor voltage is a constant value due to the
large capacitance.
Denote the clockwise as the forward direction of the circuit
current. And due to the symmetry of the Z-source network:
capacitors C1 = C2, inductors L1 = L2, inductors currents
satisfy with iL1 = iL2 = iL, inductors voltages satisfy with vL1 =
vL2 = vL and capacitors voltages satisfy with VC1 = VC2 = VC.
The three-phase Z-source inverter bridge has nine
permissible switching states including one shoot through zero
state, two traditional zero states and six active states [1].
Therefore, the Z-source inverter can be analyzed in terms of
shoot through zero state, traditional zero states and active
states. And then according to the flowing states of current of
the inverter’s other parts, there are 8 possible operation
modes in the proposed high-performance Z-source inverter,
which are shown in Fig. 4, respectively. In addition, it uses a
current source to equivalent the inverter bridge in Fig. 4.
[Mode 1] The inverter is in shoot through zero state, and
switch SW7 is in off-state. As shown in Fig. 4(a), although the
inverter is in shoot through zero state, the inductor current is
flowing in reverse way and it cannot change suddenly.
Therefore, the inductor current is conducted by the
freewheeling diodes of the inverter bridge switches. And the
dc-link voltage vi is clamped to zero. Hence, the inductor
voltage vL is equal to V0 + VC and the inductor current iL is
decreasing linearly in reverse way.
[Mode 2] The inverter is in shoot through zero state, and
switch SW7 is in off-state. Due to the switches of the inverter
bridge are on, the input capacitor together with the Z-source
network capacitors are charging the inductors and the
inductors currents are increasing linearly in forward way. The
dc-link voltage vi is equal to zero.
[Mode 3] The inverter is in one of the traditional zero
Fig. 3.
The proposed high-performance Z-source inverter.
states and input current ii of the Z-source network is zero. The
input capacitor Cin is charging from input voltage source V0
and the Z-source network capacitors are charging from the
inductors. The inductor voltage vL is equal to -VC and the
dc-link voltage vi is equal to V0 + 2VC.
[Mode 4] The inverter is in one of the active states and
inductor current and the current of SW7’s freewheeling diode
iD meets the following inequalities
iD  0, iL  ii
(1)
Therefore, the input voltage source V0 supplies the load
directly, the Z-source network capacitors are charging from
the inductors and vL is to equal to -VC. The dc-link voltage vi
is equal to V0 + 2VC as well.
[Mode 5] The inverter is in one of the active states but
inductor current meets the following inequality
1
ii  iL  ii
2
(2)
Therefore, the inductor current iL cannot affordable the input
current ii of Z-source network and the Z-source network
capacitors begin to supply the load. Switch SW7’s
freewheeling diode is conducting and vL is equal to -VC.
The dc-link voltage vi is equal to V0 + 2VC.
[Mode 6] The inverter is in one of the active states but
inductor current meets the following inequality
1
0  iL  ii
2
(3)
Therefore, in order to supply input current ii of the Z-source
network, the discharging currents of the Z-source network
capacitors should be greater than ii / 2, which results in the
freewheeling diode of switch SW7 is off and switch SW7 is on.
The voltage vL is clamped to –VC and current iL is decreasing.
The dc-link voltage vi is equal to V0 + 2VC.
[Mode 7] The inverter is in one of the active states and
switch SW7 is conducting. However, the inductor current iL is
flowing in reverse way and increasing linearly in reverse way
due to the voltage vL is equal to -VC. Therefore, the Z-source
network capacitors are discharging to both the load and
Fig. 4.
Possible operation modes of the proposed converter
inductors. The dc-link voltage vi is equal to V0 + 2VC.
[Mode 8] The inverter is in one of the traditional zero
states (ii = 0). The input capacitor Cin is charging from the
voltage source V0 and switch SW7 is conducting. The inductor
current is flowing in reverse way and increasing linearly in
reverse way due to the voltage vL is equal to -VC. Therefore,
the Z-source network capacitors are discharging to the
inductors. The dc-link voltage vi is equal to V0 + 2VC as well.
Under different control methods and circuit parameters, the
proposed inverter can operate with different combination and
sequence of the above 8 modes. According to the above
analysis, it can be seen that the dc-link voltage vi is always
equal to a constant value (V0 + 2VC) when the inverter
operates in non-shoot through zero states including active
states and traditional zero states. Therefore, the dc-link
voltage is normal in all operating modes, eliminating the
possibility of the dc-link voltage distortion which may
happen when the traditional Z-source inverter operates in
light-load with small inductance.
B.Control Strategy for SW7
According to the above analysis, it can be seen that the
function of switch SW7 is to provide the reverse current path
for iD, which makes the output current of the Z-source
network to meet current ii. In Fig. 4, SW7 is conducting in
modes 6, 7 and 8, while SW7 has to turn off during the
inverter in its shoot-through zero states including modes 1
and 2. In modes 3, 4 and 5, the current is conducted by the
SW7’s freewheeling diode rather than SW7, but it is hard to
determine the instant to turn on SW7 due to the different
operation conditions of the inverter. Therefore, to simplify the
control strategy, SW7 is only turned off during the inverter’s
shoot through zero state. Namely, the control signal of SW7 is
complemented with the shoot-through signal of the inverter
bridge.
Fig. 5 shows how to generate the control signal of SW7.
Therein, vtri is the triangle-carrier wave: vra， vrb, and vrc are
the three phase modulating waves respectively; straight lines
LP and LN are the positive and negative references which
regulate the duty cycle of the shoot-through signal,
respectively; G0 is the shoot-through control signal and Gs
is the control signal of SW7. It can be seen that the control
strategy for SW7 is very easy to realize based on the simple
As shown in Fig. 7, when the proposed inverter operates
into steady state, the inductor current will experience two
same process during a switching period Ts. Therefore, only
half of the switching period Ts has to be considered to deduce
the voltage relationships.
During the period dTs / 2, the inverter is in the shoot
through state which corresponds to Fig. 6(a), then the voltage
relationship can be derived as
vL  V0  VC
(4)
During the period (1-d)Ts / 2, the inverter is in the
non-shoot through states including the active states and
traditional zero states which corresponds to Fig. 6(b), the
voltage relationships can be derived as
vL  VC
Fig. 5.
The generation principle of the control signal of SW7
boost control strategy.
IV. VOLTAGE RELATIONSHIPS AND PARAMETERS DESIGN
A.Equivalent Circuit and Voltage Relationship
As shown in Fig. 4, the proposed Z-source inverter has 8
operation modes from the view of the current relationships.
However these 8 operation modes can be generalized as 2
basic modes in view of the voltage relationships, which are
shoot-through mode and non-shoot through mode in Fig. 6.
Denote the switching period by Ts and the shoot through
duty cycle by d. Then the main voltage relationships of the
proposed converter can be deduced below.
(5)
Vi  V0  VC  vL  V0  2VC
(6)
therein, Vi is the peak value of the dc-link voltage.
According to the voltage-second constant theory, one has
dTs
2
0

Ts
(Vi  VC )dt  dT2s (VC )dt  0
(7)
2
Therefore, it can be derived as
VC 
d
V0
1  2d
(8)
Then, from (6) and (8), it can be derived as
Vi  2VC  V0 
1
V0
1  2d
(9)
and the output peak phase voltage from the inverter can be
expressed as
vˆac  M
Fig. 6.
The basic two equivalent operation modes: (a) shoot through
state; (b) non-shoot through states
Fig. 7.
Variation of the inductor current during a switching period Ts
Vi
M

V0
2 2(1  2d )
(10)
where M is the modulation index and vˆac is the peak value of
the output ac phase voltage.
According to the above analysis and the voltage
relationships of the traditional Z-source inverter, it can be
seen that the expressions of Vi and vˆac of the proposed
inverter are same to those of the traditional converter. The
difference between them is the capacitor voltage VC.
As described in [1], the Z-source network capacitor voltage
of the traditional converter equals to [(1-d) / (1-2d)]V0.
Compared with (8), it can be seen that the capacitor voltage
VC in traditional converter is greater than that of the proposed
converter. Therefore, the proposed converter has lower
voltage stress of the Z-source network capacitors than the
traditional converter when they obtain the same boost voltage
and output ac voltage with same input voltage V0.
According to the voltage relationships of the proposed
converter, the voltage stresses of each device can be obtained
in Tab. I. Diode D8 is not included in Tab. I due to it is used to
prevent the reverse current flowing into the input voltage
source and its voltage stress is so small that can be neglected.
where the current ripple iL can be determined by the
following equation generally
TABLE I. Voltage stresses of devices in the proposed inverter
Devices
iL  xL %I Ldc
Voltage Stress
1
V0
1  2d
Switches of inverter bridge
Switch SW7
1
V0
1  2d
Capacitors C1 and C2
d
V0
1  2d
Capacitor Cin
V0
and xl % represents the permitted fluctuation range of ILdc.
Then substituting (14) into (13), the inductance L can be
further expressed as
L
The selection of devices in the proposed converter must meet
with the voltage stresses listed in Tab. I.
B.Current Ripple and Inductance
For the three-phase voltage type inverter and considering
the high frequency carrier of the inductor current as triangle,
it can be derived the dc component of the inductor current is
I Ldc 
3vˆac iˆac cos 
2V0
(11)
where iˆac is the peak value of the ac output line current, and
cos  is the load power factor.
Except the dc component of the inductor current, the ripple
of the inductor current also has a significant influence on the
stability of the converter and determines the value of the
inductance. According to the circuit analysis of the proposed
converter, the voltage across the Z-source network inductor is
always equal to VC and the current decreases linearly when
the proposed converter in its non-shoot through zero state. As
shown in Fig. 7, the inductor current experiences a same
process every half a switching period Ts. Therefore, the
inductor current ripple can be expressed as
iL 
(1  d )VC
(1  d )dV0

2 Lf s
2(1  2d ) Lf s
(12)
where L is the inductance of the inductor and fs is the
switching frequency.
In the design of the Z-source network inductors, the
inductance should not be too large, because large inductance
will cause resonance of the Z-source network inductors and
capacitors and result in low frequency oscillation in the
system. For the traditional Z-source inverter, the inductance
of inductor cannot be too small at the same time, because too
small inductance will lead the system to operate into the
abnormal operating situation which described in [2]. However,
the inductance of the proposed inverter is usually only needed
to make the inductor current ripple meets the system
requirement and the inductance could be as smaller as
possible without considering the abnormal operating situation
which usually caused by the load condition. Therefore,
according to (12), the inductance can be calculated as
L
(1  d )dV0
2(1  2d )iL f s
(14)
(13)
(1  d )dV0
2 xL % I Ldc (1  2d ) f s
(15)
Therefore, compared with the traditional Z-source inverter,
the size of the proposed Z-source inverter can be reduced
significantly due to the small inductance. Furthermore, the
load capacity of the proposed converter will not be weakened
with small inductance of the inductor, on the contrary, the
load capacity is greatly enhanced.
C.Voltage Ripple and Capacitance
According to the circuit analysis of the proposed converter,
the proposed converter is the same with the traditional one
that the Z-source network inductor current is equal to the
capacitor current during the inverter’s shoot-through state. As
shown in Fig. 7, similar to the inductor current, the capacitor
voltage also experiences a same process every half a
switching period Ts when the inverter operates in steady state.
Therefore, the voltage ripple across the capacitors in
proposed converter can be expressed as
VC 
I Ldc d
2Cf s
(16)
where C is the capacitance of the capacitor.
The main function of the Z-source capacitor is to absorb
current ripples, thus to obtain the stable voltage. Therefore,
the capacitance of the Z-source network capacitor should be
satisfied with
C
I Ldc d
2VC f s
(17)
Similar to the calculation of inductance, the voltage ripple
of capacitor voltage VC can be determined by the
following equation
VC  xC %VC
(18)
where xC % represents the permitted fluctuation range of
VC. Then, substituting (8) and (18) into (17), the capacitance
can be derived as
C
I Ldc (1  2d )
2 xC %V0 f s
(19)
However, the selection of the Z-source capacitors has to
consider the voltage stress of the capacitor expects the
capacitor voltage ripples. According to above analysis, the
proposed Z-source inverter has much smaller capacitor
voltage stress than the traditional Z-source inverter under the
same ac output voltage and input voltage V0. Low voltage
stress of the capacitor means small size of the capacitor.
Therefore, the size of the proposed Z-source inverter will be
smaller than that of the traditional Z-source inverter.
V. SIMULATION AND EXPERIMENTAL RESULTS
A.Simulation Result
The proposed high-performance Z-source inverter is firstly
verified by MATLAB®. The simulation circuit is in Fig. 3
and simulation parameters are: V0 = 100V, d = 0.15, Cin =
470uF, fs = 100kHz and M = 0.8. According to the design of
inductors and capacitors in section IV, the parameters of
Z-source network are: L1 = L2 = 500uH and C1 = C2 = 470uF.
Fig. 11. Simulation results of the proposed high-performance Z-source
inverter. (a) waveforms of the dc-link voltage vi, capacitor voltage VC,
inductor current iL and ac output voltage vac, (b) enlarged view of dc-link
voltage vi and inductor current iL. (R = 300Ω, Lf = 10mH).
Fig. 8.
3mH)
Dc-link voltage vi and the capacitor voltage VC ( R = 10Ω, Lf =
Fig. 9.
Simulation results of the traditional Z-source inverter. (a)
waveforms of the dc-link voltage vi, capacitor voltage VC, inductor current
iL and ac output voltage vac, (b) enlarged view of dc-link voltage vi and
inductor current iL. (R = 300Ω, Lf = 10mH).
Fig. 10.
Firstly, set the load R = 10Ω, filter inductor Lf = 3mH and
filter Cf = 15uF. According to [2], the traditional Z-source
inverter can work normally under this load condition. Fig. 8
shows the simulation results of the dc-link voltage vi and the
capacitor voltage VC of the traditional converter and the
proposed converter, respectively. It can be seen that the
dc-link voltage vi of both the traditional converter and
proposed converter are exactly the same when they are
operating under same condition. However, the capacitor
voltage VC of the proposed converter is much smaller than
that of the traditional converter and the difference between
them is the value of the input voltage V0, which is in
accordance with the theoretical analysis. Furthermore, it can
be seen that the proposed converter almost has no inrush
voltage at startup and has better dynamic performance when
compared to the traditional converter.
In order to verify the improved performance of the
proposed inverter when the inverter operates in light load
with small inductance of the Z-source network inductors, set
R = 300Ω, Lf = 10mH and Cf = 15uF, while other parameters
and control strategy are keep same. According to [2] and [4],
the load condition is beyond the load range of the traditional
converter, and the traditional converter will operate
abnormally. The simulation results of the traditional Z-source
inverter are shown in Fig. 9. It can be seen that the peak value
of the dc-link voltage vi becomes more and more higher if the
duty cycle d is unchanged, and vi drops down when the
inductor current iL is in the discontinuous mode during the
non-shoot through states.
The corresponding waveforms of the proposed converter
under the same load condition are shown in Fig. 10. It can be
seen that the peak value of the dc-link voltage vi maintains
steady even the inductor current iL is negative during the
non-shoot through states. Therefore, the proposed converter
can operate normally in light-load with small inductance.
B.Experimental Results
A prototype has been built to verify the validity of the
proposed high-performance Z-source inverter. In this
experimental, we used the RT-LAB equipment to provide
some function of the inverter. With the help of the RT-LAB
equipment, the control circuit of the inverter can be realized
by the MATLAB/SIMULINK instead of by building a
hardware circuit or writing complex program with a digital
signal processor (abbreviated DSP). I.e., the RT-LAB can
provide the desired control signal of the inverter main power
circuit which should build by hardware. Therefore, it largely
reduced the experimental time and simplified the circuit
design when to verify the performance of a novel circuit. The
experimental parameters are same to the simulation
parameters. The dc-link voltage vi, the capacitors voltage VC,
the inductor current iL and one of the output phase voltage vac
waveforms of the prototype when it is working in light-load
with small inductance are shown in Fig. 11(a). It can be seen
that the experimental results are in according with the
simulation results, the peak value of the dc-link voltage vi, the
and maintain constant, the inductor current iL has negative
value which corresponds to the above operation modes
concept of the proposed converter.
VI. CONCLUSIONS
A novel high-performance Z-source inverter is proposed in
this paper which can overcome the disadvantages and
maintain all the original merits of the traditional Z-source
inverter. Though, a switch added in the proposed converter,
the control strategy of the inverter does not become
complicity, just an additional control signal which is
complemented with the shoot-through control signal for this
switch. Moreover, it is this switch that significantly enhanced
the load capacity of the proposed inverter by providing a path
for the reverse current after the current of the switch’s
freewheeling diode becomes to zero. In addition, the
proposed high-performance Z-source inverter also owns two
merits: one is low voltage stresses of the Z-source network
capacitors and the other is inherent limitation to inrush
current and voltage at startup. The proposed Z-source inverter
is suitable not only for the renewable generation system
whose input voltage is very low, but also for the power
supply or power generation system whose load changes in
wide range.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
Fig. 10. Experimental results of the proposed high-performance
Z-source inverter. (a) waveforms of the dc-link voltage vi, capacitor
voltage VC, inductor current iL and ac output voltage vac, (b) enlarged view
of dc-link voltage vi and inductor current iL. (R = 300Ω, Lf = 10mH).
Fig. 11. .voltage VC and inductor current iL maintain constant.
capacitor
From Fig. 11(b), the peak value of the dc-link voltage vi does
not occur distortion during the non-shoot through zero states
F.Z. Peng, “Z-source inverter”, IEEE Trans. Ind. Appl., vol.39, no.2,
pp.504-510, Mar./Apr., 2003.
X.P. Ding, Z.M. Qian, S.T. Yang, B. Cui and F.Z. Peng, “A
High-performance Z-source Inverter Operating with Small Inductor at
wide-Range Load”, IEEE Trans. Power Electron., vol.22, no.5,
pp.615-620, Mar., 2007.
Y. Tang, S.J. Xie, C.H. Zhang and Z.G. Xu, “Improved Z-source
Inverter With Reduced Z-Source Capacitor Voltage Stress and
Soft-Start Capability”, IEEE Trans. Power Electron., vol.24, no.2,
pp.409-415, Feb., 2009.
M.S. Shen and F.Z. Peng, “Operation Modes and Characteristics of the
Z-source Inverter With Small Inductance or Low Power Factor,” IEEE
Trans. Ind. Appl., vol.55, no.1, pp.89-96, Jan., 2008.
M.S. Shen, J. Wang, A. Joseph, F.Z. Peng, L.M. Tolbert, and D.J.
Adams, “Constant Boost control of the Z-source inverter to minimize
current ripple and voltage stress”, IEEE Trans. Ind. Appl., vol.42, no.3,
pp.770-777, May/Jun., 2006.
M. Shen, A. Joseph, J. Wang, F.Z. Peng, and D.J. Adams, “Comparison
of traditional inverters and Z-source inverter for fuel cell vehicles”, in
Proc. Power Electron. Transp., 2004, pp.125-132.
F.Z. Peng, M. Shen, and K. Holland, “Application of Z-source inverter
for traction drive of fuel cell-battery hybrid electric vehicles”, IEEE
Trans. Power Electron. , vol.22, no.3, pp.1054-1061, May., 2007.
J.B. Liu, J.G. Hu, and L.Y. Xu, “Dynamic modeling and analysis of
Z-source converter-derivation of AC small signal model and
design-oriented analysis”, IEEE Trans. Power Electron., vol.22, no.5,
pp.1786-1796, Sep., 2007.
M.S Shen, Alan Joseph, J. Wang, F.Z. Peng and Donald J.Adams,
“Comparison of Traditional Inverters and Z-source Inverter for Fuel
Cell Vehicles”, IEEE Trans. Power Electron., vol.22, no.4,
pp.1453-1463, July., 2007.