From the SelectedWorks of suresh L
2012
MODELING AND SIMULATION OF ZSOURCE INVERTER
suresh L
Available at: http://works.bepress.com/suresh_l/1/
MODELING AND SIMULATION OF Z-SOURCE INVERTER
1
SURESH L., G.R.S. NAGA KUMAR, and M.V. SUDARSAN
Abstract— Z – source inverters have been recently proposed as an
alternative power conversion concept as they have both voltage buck and
boost capabilities. These inverters use a unique impedance network,
coupled between the power source and converter circuit, to provide both
voltage buck and boost properties, which cannot be achieved with
conventional voltage source and current source inverters. To facilitate
understanding of Z – source inverter, this paper presents a detailed
analysis, showing design of impedance network, implementation of simple
Boost control PWM technique and simulation of Z – source inverter for
different values of modulation indices.
Index Terms—PWM Technique, SBC, Z – source inverter.
An output LC filter is needed, which causes additional
losses and control complexity.
B. Current inverter (CSI) source
CSI is 3-Ø bridge inverter fed from current source i.e a voltage
source in series with large inductor as shown in fig 2. Six switches are used;
each composed of Insulate Gate Bipolar Transistor (IGBT) or Metal Oxide
Semiconductor Field Effect Transistor (MOSFET) with series diode to
provide unidirectional current flow and bidirectional voltage blocking. Unlike
VSI, CSI has nine switching states in those six are active states and three are
zero states. The AC output voltage is greater than DC input voltage.
I. INTRODUCTION
There exists two traditional converters, voltage-source (or voltagefed) and current-source (or current-fed) converters, either rectifier or inverter
depending on power flow directions. There are some limitations in those two
inverters.
A.Voltage source inverter (VSI)
VSI is a 3-Ø bridge inverter fed from DC voltage source (or) AC
voltage source with diode rectifier as shown in fig 1. A large capacitor is
connected at the input terminals tends make the input DC voltage constant.
Six switches are used in the main circuit; each composed of power transistor
and an antiparallel diode to provide bidirectional current flow and
unidirectional voltage blocking capability. It has eight switching states. In
those eight states, six are active states and two are zero states. VSI can be
operated as a stepped wave inverter or pulsewidth modulated (PWM) inverter.
Fig 2: Current Source Inverter
However, the current-source inverter has the following conceptual
and theoretical limitations:
It is a boost inverter i.e, the output AC current is greater than the
input current it cannot be used as buck inverter.
The cost of CSI is high.
The operating power factor is poor on line side.
CSI is vulnerable to EMI noise in terms of reliability.
The dynamic response is slow.
II Z-SOURCE INVERTER
The main objective of static power converters is to produce an AC
output waveform from a dc power supply. Impedance source inverter is an
Fig .1:Voltage Source Inverter
It has the following conceptual and theoretical barriers.
The AC output voltage is limited below and cannot
exceed the DC input voltage.
inverter which employs a unique impedance network coupled with the inverter
main circuit to the power source. This inverter has unique features in terms of
voltage (both buck & boost) compared with the traditional inverters. A twoport network that consists of a split-inductor and capacitors that are connected
External equipment is needed to boost up the voltage,
in X shape is employed to provide an impedance source (Z-source) coupling
which increases the cost and lowers the overall system
the inverter to the dc source, or another converter. The DC source/load can be
efficiency.
either a voltage or a current source/load. Therefore, the DC source can be a
There is a possibility for the occurrence of short
through which destroys the devices.
battery, diode rectifier, thyristor converter, fuel cell, PV cell, an inductor, a
capacitor, or a combination of those [1]. Switches used in the converter can be
a combination of switching devices and anti-parallel diode as shown in Fig. 3
Mr. SURESH L. is with the Vignan’s Lara Institute of Technology& Science, Vadlamudi, INDIA
(phone:
7702759430; e-mail:suresh.201@gmail.com).
Mr. G.R.S. NAGA KUMAR is with Vignan’s Lara Institute of Technology & Science, Vadlamudi,
INDIA. He is now with the Department of EEE.(e-mail: naga01013ee022@gmail.com).
Mr. M.V. SUDARSAN is with the Electrical Engineering Department, Vignan’s Lara Institute of
Technology & Science, Vadlamudi, INDIA (e-mail: mvsudarsan.eee@gmail.com).
2
voltage, which means shoot-through only replaces some or all of the
traditional zero states.
Let us briefly examine the Z-source inverter structure. In Fig. 3,
the three-phase Z-source inverter bridge has nine permissible switching states
(vectors) unlike the traditional three-phase V-source inverter that has eight.
The traditional three-phase V-source inverter has six active vectors when the
DC voltage is impressed across the load and two zero vectors when the load
Fig. 3: ZSI Using the Antiparallel Combination of Switch and Diode
terminals are shorted through either the lower or upper three devices,
respectively. However, three-phase Z-source inverter bridge has one extra
Six switches are used in the circuit; each is traditionally composed
zero state (or vector) when the load terminals are shorted through both the
of a power transistor and an antiparallel (or freewheeling) diode to provide
upper and lower devices of any one phase leg (i.e., both devices are gated on),
bidirectional current flow and unidirectional voltage blocking capability. The
any two phase legs, or all three phase legs. This shoot-through zero state (or
commonly used switches are Metal Oxide Semi-Conductor Field Effect
vector) is forbidden in the traditional V-source inverter, because it would
Transistor (MOSFET), Insulated Gate Bipolar Transistor (IGBT), Bipolar
cause a shoot-through. We call this third zero state (vector) the shoot-through
Junction Transistor (BJT), Silicon Controlled Rectifier (SCR), and Gate Turn
zero state (or vector), which can be generated by seven different ways: shoot-
off Thyristor (GTO) etc. Here we employed IGBT as the switch as it
through via any one phase leg, combinations of any two phase legs, and all
combines the advantages of both BJT and MOSFET.
three phase legs.
The Z-source network makes the shoot-through zero state possible.
A.
Impedance Network
The Z-source concept can be applied to all DC-to-AC, AC-to-
DC, AC-to-AC and DC-to-DC power conversion. It consists of voltage source
from the DC supply, Impedance network, and three phase inverter and with
AC motor load. AC voltage is rectified to DC voltage by the three phase
rectifier. In the rectifier unit consist of six diodes, which are connected in
bridge way. This rectified output DC voltage fed to the Impedance source
This shoot-through zero state provides the unique buck-boost feature to the
inverter. The Z-source inverter can be operated in three modes which are
explained in below.
Mode I:
In this mode, the inverter bridge is operating in one of the six
traditional active vectors; the equivalent circuit is as shown in figure 4.
network which consists of two equal inductors (L1, L2) and two equal
capacitors (C1, C2).The network inductors are connected in series arms and
capacitors are connected in diagonal arms .The impedance network is used to
buck or boost the input voltage depends upon the boosting factor .This
network also act as a second order filter .This network should require less
Fig.4: Equivalent Circuit of the ZSI in one of the Six Active States
inductance and smaller in size. Similarly capacitors required less capacitance
and smaller in size. This impedance network, constant impedance output
The inverter bridge acts as a current source viewed from the DC
voltage is fed to the three phase inverter main circuit. Depending upon the
Gating signal, the inverter operates and this output is fed to the 3-phase AC
load or AC motor.
link. Both the inductors have an identical current value because of the circuit
symmetry. This unique feature widens the line current conducting intervals,
thus reducing harmonic current.
B. Equivalent Circuit and Operating Principle
Mode II:
The Z-source inverter is analyzed using voltage source inverter.
The unique feature of the Z-source inverter is that the output ac voltage can be
The equivalent circuit of the bridge in this mode is as shown in the
fig. 5
any value between zero and infinity regardless of the input DC voltage. That
is, the Z-source inverter is a buck–boost inverter that has a wide range of
obtainable voltage. The traditional V- and I-source inverters cannot provide
such feature.
The main feature of the Z-source is implemented by providing gate
pulses including the shoot-through pulses. Here how to insert this shootthrough state becomes the key point of the control methods. It is obvious that
during the shoot-through state, the output terminals of the inverter are shorted
and the output voltage to the load is zero. The output voltage of the shootthrough state is zero, which is the same as the traditional zero states, therefore
the duty ratio of the active states has to be maintained to output a sinusoidal
Fig. 5: Equivalent Circuit of the ZSI in one of the Two Traditional Zero States
The inverter bridge is operating in one of the two traditional zero
vectors and shorting through either the upper or lower three device, thus
acting as an open circuit viewed from the Z-source circuit. Again, under this
mode, theinductor carry current, which contributes to the line current’s
harmonic reduction as shown in below fig 6.
3
Where Vo is the DC source voltage and
The average voltage of the inductor over one switching period
should be zero in steady state, thus,
We have
Fig. 6: Equivalent Circuit of the ZSI in the Non Shoot-Through States.
Mode III:
The inverter bridge is operating in one of the seven shoot-through states.
The equivalent circuit of the inverter bridge in this mode is as shown in the
below figure 7. In this mode, separating the dc link from the ac line. This
shoot-through mode to be used in every switching cycle during the traditional
zero vector period generated by the PWM control. Depending on how much a
voltage boost is needed, the shoot-through interval (T0) or its duty cycle (T0/T)
is determined. It can be seen that the shoot-through interval is only a fraction
of the switching cycle.
Similarly the average DC link
voltage across the inverter bridge
can be found as follows.
From equation 4:
From equation 6:
Fig. 7: Equivalent Circuit of the ZSI in the Shoot-Through State.
The peak DC-link voltage across the inverter bridge is
C. Analysis of Impedance Network
The equivalent circuit of the impedance network [3] is shown in fig. 8
Where
B is a boost factor
The output peak phase voltage from the inverter
Where M is the modulation index
In this source
Fig. 8: Equivalent Circuit of Impedance Network
For simplicity, assuming that the inductors L1 and L2 and
capacitorsC1 and C2 have the same inductance and capacitance respectively,
the Z-source network become symmetrical.
From the symmetry and the equivalent circuits, we have
(1)
The output voltage can be stepped up and down by choosing an
appropriate buck - boost factor B*
B*= B.M (it varies from 0 to α)
(11)
The capacitor voltage can be expressed as
(2)
The boost factor B is determined by the modulation index M. The
Given that the inverter bridge is in the shoot-through zero state for an interval
ofT0, during a switching cycle, T and from the equivalent circuit, Fig. 8, one
has
boost factor B can be controlled by duty cycle of the shoot-through zero state
over the non-shoot through states of the PWM inverter. The shoot-through
zero state does not affect PWM control of the inverter. Because, it
equivalently produces the same zero voltage to the load terminal, the available
shoot- through period is limited by the modulation index.
Now consider that the inverter bridge is in one of the eight non shoot-through
states for an interval of T1, during the switching cycle. From the equivalent
D. Advantages of Z-source Inverter
The following are the advantages of Z-source inverter
circuit, Fig. 8, one has
when compared to the two traditional inverters i.e. voltage source inverter
and current source inverter.
)
4
Secures the function of increasing and decreasing of the voltage in
same high frequency triangular signal. Comparator compares these two
the one step energy processing. (lower costs and decreasing
signals and produces pulses (when Vsin>Vtri, on and Vsin<Vtri, off). These
losses)
pulses are then sent to gates of the power IGBT’s through isolation and gate
Resistant to short circuits on branches and to opening of the circuits.
drive circuit. Figure 10 shows the pulse generation of the three phase leg
Improve resistant to failure switching and EMI distortions.
switches (S1, S3 and S5-positive group/upper switches and S2, S4 and S6-
Relatively simple start-up (lowered current and voltage surges).
negative group/lower switches).This method is much uncomplicated;
Provide ride-through during voltage sags without any additional
however, the resulting voltage stress across the device is relatively high
circuits.
because some traditional zero states are not utilized either partially or fully.
Improve power factor reduce harmonic current and common-mode
voltage.
This characteristic will restrict the obtainable voltage gain because of the
limitation of device voltage rating. For a complete switching period, Tis total
Provides a low-cost, reliable and highly efficient single stage for
buck and boost conversions.
Has low or no in-rush current compared to VSI.
switching period, T0is the zero state time period and Dois the shoot-through
duty ratio. In this paper, the control of ZSI is done by this control technique
(SBC).
III PWM TECHNIQUES
The number of control methods to control Z-source inverter, that
include the sinusoidal PWM techniques, three types of PWM control
algorithms: simple boost control (SBC), maximum boost control (MBC),
constant boost control (CBC).
The modulation index also called as amplitude modulation ratio (M) which
is the main control factor is defined as the ratio of amplitude of reference
wave to the amplitude of carrier wave
The linearity between the modulation index and the output voltage is
achieved by under modulation index (M < 1).
A. Simple Boost Control [5, 8]
Actually, this control strategy inserts shoot through in all the
PWM traditional zero states during one switching period. This maintains
the six active states unchanged as in the traditional carrier based PWM.
The implementation of simple boost control method [7] is illustrated in
Fig 10: PWM Signals from Simple Boost Control
Fig. 9. Two straight lines are employed to realize the shoot through duty
ratio (Do). The first one is equal to the speak value of the three-phase
Important mathematical expressions are:
sinusoidal reference voltages while the other one is the negative of the first
(12)
one. When the triangular carrier waveforms is greater than the upper
envelope, Vp, or lower than the bottom envelope, Vn, the circuit turns into
(13)
shoot-through state. Otherwise it operates just as traditional carrier-based
Where
PWM.
G is inverter voltage gain;
M is modulation index;
B is boost factor.
(15)
The voltage stress across the inverter devices is given by
Fig 9: Implementation Diagram of SBC
Shoot-through pulses are inserted into the switching waveforms by
logical OR gate. To produce switching pulses, three phase reference wave
forms having peak value with modulation index (M) are compared with the
IV SIMULATION & RESULTS
5
Here a 3-phase RLC parallel load is connected to ZSI. The 3-phase output
The Z-source inverter can be operated in both boost and buck
voltage across load is shown in fig 15.
operations depending on values of ‘M’. If M is greater than 0.5 it acts as boost
Three phase load voltage for M=0.8
500
inverter, if M is less than 0.5 then it acts as buck inverter. The following block
300
diagram figure 11 shows the SIMULINK implementation of Z – Source
200
Voltage...(V)
inverter.
phase 'a'
phase 'b'
phase 'c '
400
100
0
-100
-200
-300
-400
-500
0
0.05
0.1
0.15
Time...(sec)
0.2
0.25
0.3
Fig 15: Three Phase Load Voltage across Load for M=0.8.
B. Buck Operation Results
Fig. 11: Implementation Diagram of Z – source inverter
In this mode of operation the modulation index is reduced to 0.4
A. Boost Operation Results
we get by varying the amplitude of the carrier wave.
By considering inverter output voltage we can say boost or buck
operation. The inverter output voltage is shown in fig 12, for M=0.8.
The inverter output voltage for M-=0.4 is shown in fig 16. In this figure we
observe that the inverter output voltage decreases when comparing as in the
case M=0.8.
Inverter line voltage for M=0.8
2000
1500
Inverter llline voltage for M=0.4
voltage...(V)
1000
800
500
600
0
-1500
-2000
400
Voltage...(V)
-500
-1000
0
0.01
0.02
0.03
Time...(sec)
0.04
0.05
Fig 12: Inverter Output Voltage for M=0.8
200
0
-200
-400
0
The corresponding input to inverter circuit is output of diode bridge
0.02
rectifier is fig 13.
0.04
0.06
Time...(sec)
0.08
0.1
Fig 16: Inverter Output Line Voltage for M=0.4
Rec tifier output voltage for M=0.8
The corresponding diode rectifier output voltage is shown in fig 17.
1800
Rec tifier output voltage for M=0.4
1400
900
1200
800
1000
700
800
600
Voltage...(V)
Voltage...(V)
1600
600
400
200
0
-200
500
400
300
200
0
0.01
0.02
0.03
Time...(sec)
0.04
0.05
100
0
Fig 13: Diode Bridge Rectifier Output Voltage for M=0.8
-100
The voltage across the capacitor is shown in fig 13. Initially the capacitor
voltage rises to maximum value after it reaches to constant value.
0
0.01
0.02
0.03
Time...(sec)
0.04
0.05
Fig 17: Diode Bridge Rectifier Output Voltage for M=0.4
The voltage across capacitor reaches maximum voltage at the time of
starting, for the application of high starting torque. The typical wave form is
Voltage across capac itor for M=0.8
900
shown in fig 18.
800
Vo
ltage...(V)
700
600
500
400
300
200
100
0
0
0.1
0.2
0.3
Time...(sec)
0.4
Fig 14: Voltage across Capacitor for M=0.8.
0.5
6
voltage across capacitor for M=0.4
450
400
350
Voltage...(V)
300
250
REFERENCES
200
150
[1]
100
50
[2]
0
-50
0
0.01
0.02
0.03
Time...(sec)
0.04
0.05
[3]
Fig 18: Voltage across Capacitor for M=0.4.
The output three phase load voltage wave forms is shown in fig 19.
[4]
Three phase output load voltage for M=0.4
200
phase 'a'
phase 'b'
phase 'c'
150
Voltage...(V)
100
[5]
50
[6]
0
-50
-100
[7]
-150
-200
0
0.05
0.1
0.15
Time...(sec)
0.2
0.25
0.3
Fig 19: Three Phase Voltage across Load for M=0.4.
The inverter line voltages for different values of modulation index are
tabulated as follows which shows that both boost and buck operations are
possible in Z-source inverter.
Table 1 Load Voltage Profile for Different values of ‘M’
Inverter
S.NO.
Modulation
Output Peak
Index (M)
Voltage
(volts)
1
0.8
1150
2
0.6
1050.3
3
0.4
142.6
4
0.2
30
V CONCLUSION
This paper presents, the theoretical analysis and design of Z-source inverter is
studied. The Z-source inverter employs a unique impedance network to couple
the inverter main circuit to the power source and thus providing unique
feature. The control methods with the insertion of shoot-through states of Zsource inverter have been studied. The proposed scheme under simple boost
control is simulated with the help of MATLAB/SIMULINK and the
simulation results are obtained for different values of modulation indices. The
simulation results shows that both buck and boost operations can be obtained
in Z-source inverter by varying Modulation index (M) or Boost factor (B)
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