LETTERS
International Journal of Recent Trends in Engineering, Vol 2, No. 6, November 2009
Modified Space Vector Pulse Width Modulation
for Z-Source Inverters
S. Thangaprakash1 and A. Krishnan2
1
Sri Shakthi Inst. of Engg. & Tech.,/ Department of Electrical Engineering, Coimbatore, India
Email: s_thangaprakash@rediffmail.com
2
K.S.R. College of Engineering /Dean (Academic), Tiruchengode, India.
Abstract— This paper presents a Modified control method
for Space Vector Modulated (SVM) Z - Source inverters.
Proposed algorithm provides a modified voltage vector with
single stage controller having one degree of freedom
wherein traditional controllers have two degrees of freedom.
Through this method of control, the full utilization of the dc
link input voltage and keeping the lowest voltage stress
across the switches with variable input voltage could be
achieved. The SVM control algorithm presented in this
paper is implemented through Matlab/Simulink tool and
experimentally verified with Z - source inverter prototype in
the laboratory.
Index Terms— Shoot through, Z-Source Inverter, Space
Vector Modulation, Harmonics.
I. INTRODUCTION
Z source inverter overcomes the problems in the
Traditional VSI and CSI. Several control methods for the
Z-Source inverter have been developed since the ZSource inverter was proposed in 2002 [1]-[3]. In these
control strategies, the capacitor voltage is controlled by
the shoot-through duty ratio and the output voltage is
controlled by the modulation index, respectively. Both of
the two controllers are designed separately, thus the
whole system is controlled by two degree of freedom.
Furthermore, it cannot make full use of the input dc link
voltage, which results in low control voltage margin. The
voltage boost is inversely related to the shoot through
duty ratio, therefore the ripple in shoot through duty ratio
will result in ripple in the current through the inductor as
well as the voltage in the capacitor.
mentioned above simultaneously, this paper aims
presenting a modified voltage space vector for the ZSource inverters based on Space Vector Modulation
technique. This algorithm provides a Modified Voltage
Space Vector with single stage control having one degree
of freedom and allows the inverter to be operated in wide
modulation index with improved output voltage.
II. MODIFIED VOLTAGE SPACE VECTOR MODULATION
A. Modified SVM
For a three-phase-leg two level VSI, both continuous
switching (e.g., centered SVM) and discontinuous
switching (e.g., 60 – discontinuous PWM) are possible
with each having its own unique null placement at the
start and end of a switching cycle and characteristic
harmonic spectrum. The same strategies with proper
insertion of shoot through modes could be applied to the
three-phase-leg z–source inverter with each having the
same characteristic spectrum as its conventional
counterpart [4].
Figure 2. Voltage space vectors with shoot through states for z
source inverter
Figure 1. Z-Source inverter system
Modified Voltage Space Vector has been presented for
effective AC output control with DC boost but it still
depends two stage controllers. However the operation of
the Z-Source inverter with wide modulation index range
and the effective DC link voltage boost has not been
evidently reported. To address the different shortcomings
There are fifteen switching states of a three-phase-leg
z-source inverter. In addition to the six active and two
null states associated with a conventional VSI, the zsource inverter has seven shoot-through states
representing the short-circuiting of a phase-leg (E1), two
phase-legs (E2) or all three phase-legs(E3). These shootthrough states again boost the dc link capacitor voltages
and can partially supplement the null states within a fixed
switching cycle without altering the normalized volt–sec
average, since both states similarly short-circuit the
inverter three-phase output terminals, producing zero
voltage across the ac load. Shoot-through states can
therefore be inserted to existing PWM state patterns of a
conventional VSI to derive different modulation
136
© 2009 ACADEMY PUBLISHER
LETTERS
International Journal of Recent Trends in Engineering, Vol 2, No. 6, November 2009
strategies for controlling a three-phase-leg z-source
inverter.
The continuous centered SVM state sequence of a
conventional three-phase-leg VSI, where three state
transitions occur (e.g., null (000) → active(100) →
active (110) → null (111) ) and the null states at the start
and end of a switching cycle Ts span equal time intervals
to achieve optimal harmonic performance [5]. With threeT
state transitions, three equal-interval ( 0 ) shoot-through
3
states can be added immediately adjacent to the active
states per switching cycle for modulating a Z–Source
inverter where T0 is the shoot through time period in one
switching cycle. Preferably, the shoot-through states
should be inserted such that equal null intervals are again
maintained at the start and end of the switching cycle to
achieve the same optimal harmonic performance. The
middle shoot-through state is symmetrically placed about
the original switching instant. The traditional switching
pattern for sector-I is shown in fig.3 and modified
switching pattern for sector-I is shown in fig.4.
Figure 3. Traditional switching pattern for Z-Source inverter
Vmin( sn ) = Vmin + Voff − 2T
(6)
{sp, sn} = {1, 4},{3, 6},{5, 2}
T
Where T = 0 shoot through duty ratio.
3
In the case of traditional pulse width modulation
methods of Z-Source Inverters reported in [2], all the
T
switching functions are altered with 0 either added with
3
the active time or take out from them. But in MSVM, the
active states of two switches remain unaltered neither
added nor reduced by the shoot through.
B. Modified Voltage Vector
As aforementioned, the modulation signal produced by
the conventional VSI method cannot produce voltage
3
and Z-Source inverters need two stage
vector beyond
2
controllers separately for boost mode and non-boost
mode. A modified Voltage Vector is presented in this
section to allow the voltage vector to be operated beyond
3
with single stage controller block. Normally the
2
shoot through duty ratio is defined as follows,
D0 = min(
Tz
) ; for θ = 0 → 2π
Ts
ur
π
) V sin(θ + )Ts
3
3
2
= (1 −
(7)
Further D0 could be related with the modulation index M
as,
D0 = 1 − M
Figure 4. Modified switching pattern for Sector I of Z-Source inverter
The active states {100} and {110} are left/right shifted
T
accordingly by ( 0 ) with their time intervals kept
3
constant, and the remaining two shoot-through states are
lastly inserted within the null intervals, immediately
adjacent to the left of the first state transition and to the
right of the second transition. This way of sequencing
inverter states also ensures a single device switching at all
transitions, and allows the use of only shoot-through
states E1, E2, and E3. The other shoot-through states
cannot be used since they require the switching of at least
two phase-legs at every transition. The modulating signal
for the modified SVM strategy could be derived from the
following equations,
Vmax( sp ) = Vmax + Voff + T
(1)
Vmax( sn ) = Vmax + Voff
(2)
Vm id ( sp ) = Vm id + Voff
(3)
Vm id ( sn ) = Vm id + Voff − T
(4)
Vmin( sp ) = Vmin + Voff − T
(5)
© 2009 ACADEMY PUBLISHER
V =
3
2
M;M =
V
2
3
2
D0 = 1 −
B=
(8)
then
V ;
3
1
1
=
4
1 − 2 D0
V −1
3
(9)
In boost mode of operation, shoot through periods for
shoot through vector are acquired from the traditional
zero vector and is calculated by (8). In non-boost mode of
operation, z-source inverter operates as a traditional VSI
and the boost factor (B) constantly equals one. So the
new vector which is accomplished by both the operating
modes non-boost as well as boost could be defined as,
uur
ur
V ' = B.V and
uur
V '=
4
(10)
V −1
3
uur ur
V ' =V ;
137
ur
.V ; for boost mode
1
for non-boost mode
(11)
LETTERS
International Journal of Recent Trends in Engineering, Vol 2, No. 6, November 2009
Cap. Voltage (V)
uur
The length of the modified voltage vector V ' could be
Current (A)
3
with proper placement of shoot
extended beyond
2
through time as (1)–(6). Trajectory of the Modified space
vector V’ for Z-Source inverter is shown in fig.2.
m agnitude (v )
1
0.5
200
100
0
0
0.05
0.1
Time (s)
0.15
0.2
20
0
-20
0
0.02
0.04
0.06
0.08
0.1
0.12
Time (s)
0.14
0.16
0.18
0.2
Figure 7. Simulation results of capacitor voltage and current
through inductors of the z-source inverter
-0.5
-1
300
0
0.5
1
1.5
2
time (s)
2.5
4
x 10
Figure 5. Modulation signal of proposed MSVM algorithm
The modulation signal (Vref) for carrier wave
comparison to generate pulses to the Power IGBT’s by
Modified Voltage Space Vector with modulation
index=0.7 and shoot through = 0.2 is depicted in Fig.5.
Figure 8. Experimental
waveform of the inverter
switching
line
voltage
and
current
V. SIMULATION AND RESULTS
The traditional modulation concepts and proposed
control based implementation have been verified through
simulation by Matlab / Simulink for three bridge-two
level Z-Source inverters with 5kW load. System
parameters for computer simulation is shown in Table-I
and the results are shown in figures 6 through 8.
Figure 9. Prototype of z-source inverter
TABLE I – SYSTEM PARAMETERS FOR SIMULATIONS
Output current (A)
Output voltage (V)
Parameter
DC Supply
m and f0
Switching frequency
Shoot through
C1=C2=C
L1=L2=L
Specification
150
0.7 and 50 Hz
1000
0.2
1000
1
VI. CONCLUSION
Unit
V
Hz
µF
mH
This paper presents a Modified Space Vector to control
the capacitor voltage (boost factor) of the z-source
inverter to be operated beyond m = √3/2 with one degree
of freedom. Simulations as well as experimental results
are given to validate the algorithm. This presented model
greatly improves the voltage boost and utilizes the DC
link voltage effectively than classical SVPWM methods.
200
REFERENCES
0
-200
0
0.02
0.04
0.06
0.08
0.1
0.12
Time (s)
0.14
0.16
0.18
0.2
0
0.02
0.04
0.06
0.08
0.1
0.12
Time (s)
0.14
0.16
0.18
0.2
20
0
-20
Figure 6. Simulation results of output voltage and current of the zsource inverter with output filter (cut-off frequency=1kHz)
Experimental verification using a three bridge-two level zsource inverter prototype (shown in fig.9) has been
performed to validate the simulation results. The hardware
inverter is controlled digitally using a Texas Instruments
TMS320F240 digital signal processor (DSP) with
composed C codes for generating the required references.
© 2009 ACADEMY PUBLISHER
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