Analysis and Simulation of Z-source Inverter Control
Techniques with Different Modes of Operations
Jitendra Patil
Vikas Kulkarni
Dept. of Electrical Engg.
AISSMS COE
Pune, India
jitendrapatil0911@yahoo.com
Dept. of Electrical Engg.
AISSMS COE
Pune, India
vvkulkarni@aissmscoe.com
Abstract— In this paper two different control techniques of
modified pulse width modulation schemes discovered to control
the output power of Z-source inverter, analysed with the help of
MATLAB simulink. Different modes of operations of Z-source
inverter also described here in brief. When the input dc voltage
to inverter is sufficient to drive the load easily then it is
preferable to use traditional PWM scheme, but if the input dc
voltage is not enough to generate the desired ac output, in that
case modified PWM scheme plays important role to increase
efficiency of inverter. Normally there are only two modes of
operations in Z-source inverter but in case if the current is
discontinuous conduction mode and power factor is very poor
then additional three modes will comes in picture.
factor is also high, i.e. there are only two modes of operations.
But if the inductance and power factor of inverter is very poor,
there can be three additional modes of operations.
In this paper the analysis has been done for the common
modulation index and boost factor with simple boost control and
maximum boost control technique. In traditional converters,
shoot-through state is forbidden but in Z-source inverter it
provides the unique feature like ability to buck and boost
inverter voltage without change in circuit configuration. To
verify the theoretical concepts, simulation has been performed.
Figure 1. Z-source inverter
Keywords—Modified PWM; Z-source inverter; Shoot-through;
Simple boost control; Maximum boost control.
Ι. INTRODUCTION
Previously, there existed only two traditional
converters, which are voltage-source inverter (VSI) and
current-source inverter (CSI), but they are having no. of
theoretical barriers and limitations [1]. The important
limitation of traditional VSI is it is buck converter for dc-to-ac
conversion and it will get short circuited if two switches in any
phase leg turned on simultaneously, which will destroy the
device. To overcome all theoretical limitations and barriers in
traditional converters, the cost effective solution is Z-source
inverter [1], [3]-[5]. It employs unique LC network connected
in X shape to boost output voltage of inverter at desired level
as shown in figure (1). By controlling the boost factor we can
vary the output voltage of inverter at required level. It uses
two split capacitors C1 and C2 and two split inductors L1 and
L2 which are connected in X shape to provide impedance
source to inverter [1], [5], [8].
Z-source inverter utilise the shoot-through state to
produce output voltage of inverter which may be greater than
the input dc rail. During shoot-through state energy is
transferred from capacitor to inductor. All the analysis is done
by considering the inductance of inductor is high and power
ΙΙ. DIFFERENT MODES OF OPERATION
The basic operating principle of Z-source inverter is
described by assuming the inductor current is large and almost
constant [2]. When inductance used in Z source network is too
small then the output current of inverter contains high ripples
i.e. current is in discontinues conduction mode then Z-source
inverter having five operating modes instead of two. Same
case happens in case of load power factor is also too poor.
Mode 1: In this mode Inverter Bridge is producing one of
shoot-through state as shown in figure (2). If two switches
(one from upper side and one from lower side) from any phase
leg are gated on simultaneously then the sum of two capacitor
voltages i.e. VC1 and VC2 becomes greater than the input dc
voltage, as a consequence the current flows in opposite
direction and the diode (D) in figure (1) reverse biased. During
this period the energy stored in capacitors is transferred
towards the inductors [1]-[2], [4].
Figure 2. Shoot-through mode
𝑉𝐿1 =𝑉𝐶1 and 𝑉𝐿2 = 𝑉𝐶2
(1)
Assume that capacitor voltage is constant, hence inductor
current increase linearly. Because of circuit symmetry in Zsource network (L1=L2=L and C1=C2=C),
𝑉𝐿1 = 𝑉𝐿2 =𝑉𝐿 , 𝑖𝐿1 = 𝑖𝐿2 = 𝑖𝐿 (2)
And
𝑉𝐶1 = 𝑉𝐶2 =𝑉𝐶 , 𝑖𝐶1 = 𝑖𝐶2 = 𝑖𝐶
(3)
As a result (eqn.6), the input current becomes zero and diode
becomes reverse bias. For the inverter load is highly inductive
(greater than the inductance used in inverters), inverter voltage
𝑣𝑖 is equal to capacitor voltage𝑉𝐶 [2].
Mode 4: When inverter bridge is producing one of two
traditional zero states, shorting through either upper three
device or lower three device (𝑖𝑖 = 0). At that case, inverter
acting as an open circuit viewed from Z-source network.
Hence Z-source network isolated from both ac and dc sides.
Mode 2: In this mode inverter bridge is producing one of six
traditional active states and two traditional zero states.
Figure 5. When inverter bridge is producing one of two zero state
The inductor current remains in zero level until next switching
action takes place [2].
Figure 3. When inverter bridge is producing one of six active states
and two zero state
In this mode the inductor current i L is greater than the
half of output current ii. The input current is,
𝑖𝑖𝑛 >
𝑖𝑖
2
(4)
This is given by𝑖𝑖𝑛 = 𝑖𝐿1 +𝑖𝐶1 = 𝑖𝐿1 + (𝑖𝐿2 − 𝑖𝑖 ) = 2𝑖𝐿 -𝑖𝑖 > 0
Mode 5: The mode 5 is not intentionally created by control
signals and depends on load current and inductor current at the
time of switching. It is freewheeling diode shoot-through state.
If inverter is switched on in an active state with inductor
current is less than half of inverter current then, the inverter
cannot goes directly into an active state because, the available
dc current (2𝑖𝑙 ) is not sufficient to supply load current (𝑖𝑖 ). At
that time this mode comes in picture [2].
(5)
Since the input current is not zero, the diode is
conducting and the difference between voltages V0 and VC
appears across VL which is negative because in previous shootthrough state the capacitor voltage (VC) is boosted above the
input voltage. Assuming the capacitor voltage is constant,
inductor current decreases linearly up to the level where the
condition (4) can no longer the same and it decreases to zero.
At mode 2 ends, inverter enters into anew mode of operation.
Mode 3: In this mode the inverter bridge is producing one of
two traditional zero vectors. In this mode the inductor current
is given by,
𝑖𝐿 =
𝑖𝑖
2
(6)
Figure 6. When inverter bridge is in freewheeling shoot-through state
In this mode the inductor current linearly increases
and it continuous until it becomes equal to half of inverter
current or next switching action takes place.
ΙΙΙ. MODIFIED PWM WITH SIMPLE BOOST AND
MAXIMUM BOOST CONTROL
The shoot-through states are inserted before and after the
active states by keeping the time period of active states
constant. The sinusoidal PWM technique is used due to its no.
of advantages. For the same modulation index, switching
frequency, boost factor and dc input, the output voltage,
output current and THD analysis is done which is loaded by
same 3 phase RL load [9].
Figure 4. When inverter bridge is producing one of six active states

SIMPLE BOOST CONTROL
Simple boost control employs two straight lines, one from
upper side and one from lower side as shown in figure (7).
When carrier wave i.e. saw tooth wave is greater than the
upper envelope or less than lower envelope, then circuit turns
into shoot-through state otherwise, it operates just like
traditional PWM control.
shoot-through duty ratio (𝐷0 ) is given by for the interval
𝜋 𝜋
[ , ],
6
2
𝐷0 =
2𝜋−3√3𝜋
(12)
2𝜋
Figure 8. Modified PWM with Maximun boost control
Figure 7. Modified PWM with simple boost control
‘
If TS is the total switching period, T0 is the zero
state time period , 𝑚𝑎 is the modulation index, B is the boost
factor and D0 is the shoot-through duty ratio which is given
by,
𝑇0
𝐷0 = 𝑇
Boost factor is given by,
1
1−2𝐷0
=
1
𝑇
1−2 0
(8)
𝑇𝑠
G is the voltage gain of inverter, 𝑣𝑎𝑐 is the output ac voltage
and 𝑣𝑑𝑐 is the input dc voltage to the inverter, which is given
by,
G=
𝑣𝑎𝑐
𝑣𝑑𝑐 /2
𝑚𝑎
= 𝑚𝑎 . B = 1−2(𝐷
0)
And,
𝑣𝑎𝑐 = 𝑚𝑎 . B.
𝑣𝑑𝑐
2
𝐷0 = (1- 𝑚𝑎 )
(9)
𝑚𝑎
1−2(𝐷0 )
=
𝑚𝑎 .𝜋
3√3.𝑚𝑎 −𝜋
(13)
Then,
B=
3√3𝐺−𝜋
𝜋
(14)
To minimize the voltage stress, we have to minimize boost
factor and maximize modulation index to achieve maximum
voltage gain. As increasing the shoot-through duty ratio the
voltage gain is increased in that proportion.
The difference between simple boost control and
maximum boost control is, in simple boost control carrier
wave (i.e. saw tooth wave here) is compared with reference
wave (i.e. 2 envelopes, one from upper side and one from
lower side) as shown in figure (7) and in maximum boost
control the carrier wave is being compared with 3 phase sine
wave to generate shoot-through duty ratio.
IV. PARAMETERS USED AND SIMULATION RESULTS
(10)
(11)
The method is very simple; however the resulting
voltage stress across device is more because some zero vectors
are not utilized properly.

G=
(7)
𝑠
B=
The relationship between modulation index and gain is given
by,
MAXIMUM BOOST CONTROL
In maximum boost control, all the traditional zero vectors
are converted into the shoot-through states to overcome
aforementioned problem of voltage stress in simple boost
control as shown in figure (8). Thus maximum boost factor
and duty cycle obtained for any modulation index. The shootthrough state repeats after n/3 period. Assume that switching
frequency is much higher than modulation frequency. The
Traditional voltage-source inverters and current-source
inverters use capacitors and inductors to store energy and
filtering element to suppress voltage and current ripples
respectively. Here Z-source inverter is used, which uses both
two split capacitors and inductors to store energy which boosts
voltage and acts as a second order filter. 𝐿1 ,𝐿2 , 𝐶1 and 𝐶2 has
same values with respect to each others because of circuit
symmetry [1]-[3]. Table I and II shows the parameters used
for simple RL load and Z-source inverter respectively. Also
the simulation graphs are given for analysis purpose. All
reference values of Z-source network are tabulated below [5].
TABLE I
PARAMETERS USED FOR RL LOAD
S.No.
1
2
Parameters
Load resistance, 𝑅𝑙
load inductance, 𝐿𝑙
Specification
5Ω
2 mH
TABLE II
Z-SOURCE NETWORK PARAMETERS
S.
No.
1
2
3
4
5
6
7
Parameters
Dc supply
𝐿1 =𝐿2 =𝐿
𝐶1 =𝐶2 =𝐶
Switching frequency
Modulation index, 𝑚𝑎
Shoot through duty ratio, 𝐷0
Initial capacitor voltage, 𝑉𝐶1 and
𝑉𝐶2
Value
250 V
160 𝜇𝐻
1000 μ𝐹
5 kHz
0.8
0.2
335 V
The comparative analysis is done for two methods
i.e. for simple boost control and the maximum boost control
with the help of MATLAB/simulink. The shoot-through state
should be inserted in such a way that, equal null (zero)
intervals are again maintained at the start and end of switching
cycle to achieve the same optimal harmonic performance.
The input dc voltage to the Z-source inverter is 250V
with 0.8 modulation index. For simple boost control the output
voltage waveforms and output current waveforms in are given
below in figures (9) and (10) respectively.
The output voltage and current waveforms from
inverters for maximum boost control techniques also carried
out with the help of MATLAB/simulink, which are shown in
figure (11) and (12) respectively. For the same modulation
index, switching frequency, boost factor and input supply, and
loaded by same ratings the variation shown in output voltages
and currents also. For maximum boost control, 250 V input it
boosted up to 800 V (all values are with respect to positive
and negative sides), but in simple boost it is up to 600 V. The
voltage stress is also greatly reduced in maximum boost
control because all zero states are utilised properly. The motor
current is varies in between 0 to 100 Amps.
Figure 11. Line voltage in maximum boost
Figure 12. Line current of any one phase in maximum boost
Figure 9. Load voltage (Line-to-Line) in simple boost
The total harmonic distortion (THD) analysis is also
done with the help of FFT analysis. THD presents in output
voltages and currents for both methods (simple boost and
maximum boost) is discovered which is tabulated below.
TABLE – III
THD ANALYSIS
Method used
Figure 10. 3 Phase load current in simple boost
Simple boost
control
Maximum
boost control
THD in output
voltage in (%)
THD in output
current in (%)
88.63 %
2.460 %
92.56 %
2.740 %
Note that all THD analysis is done without any filtering of
output voltage and current. It can be reduced in great amount
with the help of low pass LC filter. It can be seen that the THD
in voltage is increased in maximum boost control than the
simple boost control.
VI. CONCLUSION
The Z-source inverter can produce any desired output
voltage which is required for application which may be greater
than the input voltage level with the help of modulation index
and shoot-through duty ratio. Modes of operations of Z-source
inverters are increased if the inductance used in Z-source
network is very smalls or the power Factor of inverter is too
poor, which is described in this paper briefly. This additional
modes of operations can be eliminated by using bidirectional
switch during traditional all active and zero states instead of
diode (D). This operation can also provide bidirectional power
flow capacity of the inverter. Circuit operations under
different conditions with modified PWM for simple boost
control and maximum boost control technique. In this work
theoretical analysis and simulation results are described.
[8] B. K. Bose, “Modern Power Electronics and AC Drives”, Upper Saddle
River, NJ: Prentice – Hall PTR, 2002.
[9] Holtz, J., 1992, “Pulse Width Modulation-a Survey”, IEEE Transaction
on Industrial Electronics, vol.39, pp.410-420.
Jitendra Patil was born in Sangli,
Maharashtra, India on December 23,
1991. He received the dipl. from the
Dept. of Electrical Engg. at the Latthe
Polytechnic (MSBTE) of Kupwad,
Maharashtra, India in 2010 and Engg.
Degree from the dept. of Electrical
Engg. at the R.I.T. Islampur, Shivaji
University, Maharashtra, India in
2013. He is currently Working
toward the M.E. Degree in power
electronics and drives at the SPPU,
Pune.
His special interests are Power Electronics and drives with
special emphasis on Electrical Machinery Analysis, HVDC
Transmission, FACT’s devices and simulation of Power
converters.
REFERENCES
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Zhiguo Pan, Eduardo Ortiz-Rivera and Yi Huang, “Z-Source Inverter for
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K.srinivasan and Dr.S.S.Dash, “Performance Analysis of a Reduced
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Computer and Electrical Engineering, vol.2,no. 4, August 2010.
S. Thangaprakash and A.krishnan, “Comparative evalution of modified
pulse width modulation schemes of Z-source inverter for various
applications and demands”, International journal of Engineering,
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N. Mohan, W. P. Robbin, and T.Underland, “Power Electronics:
converters Applications, and Design”, 2nd ed. New York: Wiley, 2003.
M. H. Rashid, “Power Electronics”, 3rd ed.Englewood Cliffs, NJ:
Prentice – Hall, 2004.
Vikas Kulkarni was born in Pune,
Maharashtra, India on October 24,
1975. He received the Engg. Degree
from the dept. of Electrical Engg. at
the AISSMS COE, Pune University,
Maharashtra, India in 1998 and M.E.
Degree from the dept. of Electrical
Engg. At the PVG COET, Pune
University in 2006. He is currently
Working toward the Ph.D. at the
Govt. COE, Aurangabad.
His special interests are PV based systems & DC-DC
converters.