IEEE ICSET 2010

6-9 Dec 2010, Kandy, Sri Lanka

Generalized Multi-Cell Switched-Inductor and

Switched-Capacitor Z-source Inverters
Ding LI1, Miao ZHU2, Poh Chiang LOH1, Feng GAO3 and Frede Blaabjerg4
1
School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore
2
Experimental Power Grid Centre, Institute of Chemical and Engineering Sciences (ICES), A*STAR, Singapore
3
School of Electrical Engineering, Shandong University, China
4
Institute of Energy Technology, Aalborg University, Denmark

Abstract- High performance voltage and current-source traditional active and null states, then allows the Z-source
inverters (VSI and CSI) are widely required in various inverter to boost its output voltage without causing
industrial applications such as servo-motor drives, special power damagingly large current to flow through the shorted phase,
supplies, distributed power systems and hybrid electric vehicles. as long as the duration is not considerably long. The Z-source
However, the traditional VSI and CSI have been seriously
inverter is therefore a safer topology that does not require
restricted due to their narrow obtainable output voltage range,
short-through problems caused by misgating and some other dead-time protection, unlike the traditional VSI.
theoretical difficulties due to their bridge-type structures. The As an extension, the current-type Z-source inverter,
Z-source inverter was proposed to overcome the problems representing the dual of the voltage-type Z-source inverter,
associated with the traditional inverters, in which the functions
of the traditional dc-dc boost converter and the bridge-type
was studied in [2, 3], and drawn in Fig.2. In addition to the
inverter have been successfully combined. To further widen the traditional nine active and null states, the added impedance
operational range or gain of the Z-source inverter in both the network allows current following into the dc-link of the
voltage and current type configurations, the generalized inverter bridge to be broken to create an open-circuit state
switched-inductor and switched-capacitor impedance networks without causing severe overvoltage (e.g. by turning OFF all
are proposed hereon. Both simulation and experimental testing switches of the CSI bridge). This open-circuit state is
have been conducted for validating the extra boosting responsible for introducing voltage-buck (or current-boost)
introduced with some representative results captured and functionality to the otherwise voltage-boost (or current-buck)
presented near the end of the paper. only CSI. So far, the current-type Z-source inverter has not
been as popular as its voltage-type variant, which has already
been tested for motor drives, photovoltaic (PV) and fuel cell
I. INTRODUCTION
powered systems [4-6], where either a wide input or output
The voltage-type Z-source inverter shown in Fig.1 was first variation range is needed. Regardless of that, knowledge on
proposed in [1], where unlike the traditional voltage-source how to realize a current-type Z-source inverter might still be
inverter (VSI) and current-source inverter (CSI), it supports
both voltage-buck and boost operating modes. Surely, these
two operating modes can also be obtained by connecting a dc-
dc boost converter to a dc-ac inverter to form a distinctly
distinguishable two-stage configuration, having no reduction
in switches. The Z-source inverter, in contrast, introduces
buck-boost functionalities by including a unique X-shaped
LC impedance network between its input dc source and rear-
end inverter circuitry. To an observable extent, it merges
some semiconductor switching actions of the front-end dc-dc
converter with the rear-end dc-ac inverter bridge.
To show how the merging has been introduced, the Fig. 1. Voltage-type Z-source inverter
voltage-boost operating mode is considered, during which an
inductive element must in principle be shorted across either a
voltage source or a capacitive element. For the two-stage
converter, the necessary shorting action can be introduced by
turning on the relevant switch found in the front-end dc-dc
converter with the rear-end inverter switches less untouched.
In contrast, shorting of a Z-source inverter is triggered by
turning on any two switches from the same phase (e.g. SA
and SA’ in Fig.1) of the rear-end inverter, hence allowing it
to exclude the otherwise needed front-end active switch. The
inserted shoot-through state, together with the eight Fig. 2. Current-type Z-source inverter.

978-1-4244-7191-1/10/$26.00 ©2010 IEEE

of interest, judging from some recent attempts to use CSI for boost ratio B can also be explicitly expressed as
PV energy harnessing [7-8]. 1 ⁄ ⁄ 1 3 ⁄ , which strictly is larger than the
expression of 1⁄ 1 2 ⁄ [1], derived earlier for the
Besides dc-ac topological variations, another recent path of
traditional Z-source inverter shown in Fig. 1, if the same
development pursued for Z-source inverter is to investigate
shoot-through duration is applied.
on ways to further raise its voltage or current gain. An
From the switched-L cell, the dual switched-C cell can also
example commonly quoted that needs such high voltage gain
be derived with its application now directed to the current-
is in the grid connection of low voltage green sources like PV
type Z-source inverter drawn in Fig. 2 for further enhancing
panels and fuel cells, if their series connection or the explicit
its current gain. Instead of using the layout shown in Fig. 2
inclusion of a bulky transformer is not recommended.
directly, its orientation is rotated before replacing the Z-
Particularly in [9], the switched-inductor (switched-L in short)
source capacitors with two switched-C cells. The resulting
concept, originally developed for dc-dc converters [10], has
configuration is shown in Fig. 4, which matches the layout of
been applied to the Z-source inverter, whose resulting
its corresponding switched-L inverter in Fig. 3, but has its
outcome is a further boost in voltage gain. Although [9]
input source orientation reversed, as compared to that shown
demonstrated that the direct replacement of the Z-source
in Fig. 2. Analyzing the operating states of this switched-C
inductors by two switched inductor-diode networks can
inverter then leads to the following:
indeed raise the inverter gain, it stops short of generalizing
• Open-Circuit: Introduced by turning off all switches
the concept to obtain an even higher gain, which to some
of the CSI bridge with diode D then conducting naturally. In
extent goes again the original intention of that paper. Also not
addition, D1, D2, D1’ and D2’ are off, while D3 and D3’ are on,
attempted is the exploration of the switched-capacitor
hence giving rise to two series-connected capacitors per cell
(switched-C in short) network, which by duality, should
with their capacitive current expressed as
apply to the Z-source current-type inverter for boosting its
.
current gain. Yet another issue not addressed is the technical
comparison of the switched-L and C techniques with two • Non-Open-circuit: Referred to any of the nine
earlier cascaded techniques proposed in [11], which when not traditional active and null states of a CSI. In this state, D, D3
done, does not bring out their respective advantages for the and D 3 ’ block, while D 1 , D 2 , D 1’ and D2’ conduct, hence

consideration of readers. These not yet addressed shortfalls giving rise to two parallel-connected capacitors per cell. Their
are now investigated with findings explicitly verified in capacitive current is then expressed as /2.

simulation and experiment. Averaging the capacitive current to zero per switching
cycle then results in the following current governing
II. ELEMENTARY SWITCHED-L AND C Z-SOURCE INVERTERS equations for relating the network inductive IL, peak dc-link ̂
Fig.3 shows the topology of the elementary switched-L Z-
source inverter proposed in [9], which in principle, is simply
derived by replacing the Z-source inductors found in Fig. 1
with the switched-L cell proposed in [10]. Operation of the
inverter after such modification can be analyzed as follows:
• Shoot-Through: Introduced by turning on two
switches from at least a phase-leg of the inverter bridge.
While doing so, the far-left diode D reverse-biases, and
within the two switched-L cells, diodes D1, D2, D1’ and D2’
conduct, while D3 and D3’ turn off naturally. The two
inductors per cell therefore appear to be parallel-connected,
and their inductive voltage is expressed as
.
• Non-Shoot-Through: Referred to any of the eight Fig.3. Switched-L Z-source inverter.
traditional active and null states of a VSI. In this state, diode
D is forward conducting, and within the switched-L cells, D1,
D2, D1’ and D2’ block, while D3 and D3’ start conducting. The
two inductors per cell are thus series-connected, leading to
the expression of /2.
Averaging vL over a switching period and equating it to
zero then give rise to the following voltage governing
expressions for relating the network capacitive VC, peak dc-
link and peak ac output voltages in terms of the source
voltage Vdc:
⁄ ⁄ ⁄
⁄
; ⁄
; ⁄
(1)
where m ≤ 1.15 and T0 / T ≤ 1 represent the inverter
modulation ratio with triplen offset taken into consideration Fig.4. Switched-C Z-source inverter.
and normalized shoot-through duration, respectively. The
and peak ac output ̂ currents in terms of the input current • Open-Circuit: Introduced by turning off all switches
Idc: of the CSI bridge with diodes D and D3n conducting, and
⁄ ⁄ ⁄ diodes D3n-1 and D3n-2 blocking. The capacitors are therefore
⁄
; ̂ ⁄
; ̂ ⁄
(2)
charging in series with their capacitive current expression
where T’0 / T represents the normalized open-circuit written as .
duration, and the computed current boost factor of
• Non-Open-circuit: Represented by any of the nine
1 ⁄ ⁄ 1 3 ⁄ is again proved to be larger than the
traditional active and null states of a CSI. In this state, diodes
earlier derived expression of 1⁄ 1 2 ⁄ [3] for the
D and D3n block, while D3n-1 and D3n-2 conduct to discharge
traditional current-type Z-source inverter drawn in Fig. 2.
the capacitors in parallel for obtaining a higher dc-link
current. The capacitive current can then be deduced as
III. EXTENDED SWITCHED-L AND C Z-SOURCE INVERTERS / .
As mentioned earlier, the switched-L and C Z-source Performing the same averaging-to-zero process per
inverters are developed by replacing either the Z-source switching cycle for the capacitive current then leads to the
inductors or capacitors by the switched-L or switched-C cells. following equations for governing the inverter operation:
These replacements are better generalized in Fig. 5 and 6, ⁄
; ̂
⁄
;
which also infer that other enhanced Z-source topologies can ⁄ ⁄
⁄
be derived by replacing the inductive impedance blocks in ̂ ⁄
(4)
Fig. 5 or capacitive impedance blocks in Fig. 6 by newly The current gain of 1 1 ⁄ ⁄ 1 1 ⁄
designed impedance layouts or those directly borrowed from is again much higher, as intended.
dc-dc converters, which are after all more developed than dc- The voltage or current boost factor (B) of switched-L or C
ac inverters. The generalized layouts also make possible some with n=1,2,3,4… normalized with reference to that of
extension options like those shown in Fig. 7 and 8, where the conventional z-source(n=1) are plotted in the Fig. 9. It is
relevant inductive and capacitive impedance blocks have obvious that the boost factor increased intensely as the
been duplicated and cascaded N times (in other words, N cells number of cascaded cells increasing.
in cascaded using n = N + 1 inductors). Besides providing high gain, the switched-L inverter might
Beginning with the extended multi-cell structure shown in still have some convincing advantages over those existing Z-
Fig. 7, the generalized concept is to introduce more inductors source inverters, when they are commanded to produce the
in parallel during shoot-through charging and more inductors same output voltage from the same given input voltage. From
in series during non-shoot-through discharging. These Fig.10 it is clear that the multi-cell switched-L network
orientations can indeed be guaranteed by the diode layout results in a reduction of the capacitive voltage stress. The
found within each switched-L cell. figure shows the capacitor voltage within the network with
• Shoot-Through: Introduced by turning on two n=1,2,3 while producing the same input-to-output voltage
switches from a phase-leg of the inverter bridge. Doing so gain as the conventional Z-source network.
causes diodes D and D3n to turn off, while D3n-1 and D3n-2
starts conducting. All the inductors are then connected in
D ii
shunt for charging by the two Z-source capacitors, and their Inductance
Components
idc
common voltage expression is written as . iC1 iC2
SA SB SC
• Non-Shoot-Through: Represented by one of the vd C1 C2 Va ioa
eight traditional active and null VSI states. In this state, D and Vdc vi Vb
Vc
iob
ioc
D3n conduct, while D3n-1 and D3n-2 reverse-bias, causing all
the inductors to series-discharge their energy to the external Inductance SA’ SB’ SC’
ac load. The common inductive voltage expression is then Components

expressed as / .
Averaging vL over a switching period and equating it to
zero again lead to the following generalized voltage
expressions for governing the multi-cell switched-L inverter:
⁄ ⁄
⁄
; ⁄
; Fig. 5. Generalized single-cell voltage-type Z-source inverter.
⁄
⁄
(3)
Clearly, the boost factor extracted from (3), and written as
1 1 ⁄ ⁄ 1 1 ⁄ is much higher than any
of the gain expression written earlier, but of course at the
expense of using more inductors and diodes. Justifications for
these additional components and their comparison with other
cascading techniques are discussed in the following section.
Similar operating state analysis can also be performed on
the multi-cell switched-C inverter shown in Fig. 8, whose
derived current expressions are discussed, as follows:
Fig. 6. Generalized single-cell current-type Z-source inverter.
 IV. COMPARISON WITH OTHER HIGH GAIN CASCADED Z- As anticipated, with a boosted dc-link voltage of about 300
SOURCE INVERTERS V available for powering the rear-end inverter bridge, its ac
Other cascaded techniques for developing Z-source current amplitude is boosted to around 3 A, which is shown
inverters with exceptionally high gain are described in [11] in Fig.14. The measured dc gain is around 3 which is
with one possible circuit drawn in Fig. 11 for illustration. The however lower than that calculated theoretically 3.25,
first comparison is performed when the two kind of cascaded because of system parasitic found in the not yet optimized
networks producing the same boost factor when the same experimental setup. The relative capacitor voltage inductor
cascaded levels (n=N) are applied and printed in Fig. 12, current and dc-link current is shown in Fig.15.
noting that the inductor numbers are different, the multi-cell The LC components are then rearranged with capacitors
switched-L network holds n-1 more inductors than the cascaded to perform the current type cascaded network. The
alternative cascaded network. The multi-cell switched-L voltage source connected in series with a large inductor
network observed a lower shoot-through duty ratio, which forming a current source to power the rear-end CSI bridge
indicates a higher maximum modulation index leading to a was then tested under current-boost operation with M = 0.85
lower output voltage harmonic induced and a lower voltage × 1.15 and T0/T = 0.15. The corresponding experimental
stress the semiconductors bears. waveforms obtained are printed in Fig.16 and 17.
The next factor of interest for comparison is the sizing of
each inductor, which rightfully should be chosen to avoid
those additional unwanted states identified in [12]. Those
additional states surface when the diodes D in multi-cell
switched-L or any of the diodes in alternative cascaded
networks unintentionally block when in the non-shoot-
through state. Obviously, that happens when the diode current
falls to zero. That then means the condition to avoid the
unwanted states is:
∆ ⁄2 ⁄2 ⇒ ∆ 2 (5)
where is the peak ac output current fixed by the load
and represents the worst case value for . is the average
inductive current and ∆ is the peak-to-peak inductive
current ripple. The average current flow through all the
inductor during shoot-through and non-shoot-through should
be the same in two networks because of a same input-to-
output gain premised. The inductor current increase linearly
during shoot-through state and decrease during non-shoot-
.
through state, the current ripple can be calculated by ∆
· / , with assuming the same current ripple experienced Fig. 7. Generalized multi-cell switched-L Z-source inverter.
by all the inductors, the smallest inductances needed by the
two networks, normalized with reference to that of the
traditional single-network Z-source inverter, are plotted in Fig.
13. The figure shows the advantages of multi-cell switched-L
Z-source inverter which requires smaller inductances.

V. EXPERIMENTAL RESULTS
For testing the extended multi-cell cascading topologies,
the voltage type inverter with three inductor cell cascaded
(six inductors in total and n=3) were assembled in hardware
followed by the current type one with three capacitor cell
cascaded. (six capacitors in total and n=3) The inductance
and capacitance values used for each network were L = 3 mH
and C = 2200 μF, respectively.
The voltage type cascaded network assembled was then
powered by a single 100 V dc source, and terminated by a
two-level VSI bridge, was then tested under voltage-boost
operation with M = 0.85 × 1.15 and T0/T = 0.15. The
corresponding experimental waveforms obtained are printed
in Fig.14 and 15. Fig. 8. Generalized multi-cell switched-C Z-source inverter.
 The input current is about 0.9 A, with a boosted dc-link theoretically 3.25, because of system parasitic found in the
current of about 3 A available for powering the rear-end not yet optimized experimental setup. The relative capacitor
inverter bridge, its ac current amplitude is boosted to around voltage inductor current and dc-link current is shown in
1.4 A, which is shown in Fig.16. The measured dc gain is Fig.17.
around 3.18 which is however lower than that calculated
0.35

0.3
10

Shoot-through duty ratio

0.25
The boost ratio (B) of voltage or current

(Traditional Z)
8 N=4 N=3 N=2 N=1
... 0.2

6 0.15

Alternative Switched-L
0.1
4 Cascaded

0.05

2
0
0 2 4 6 8 10
Voltage boost ratio
0
0 0.1 0.2 0.3 0.4 0.5 Fig.12. Shoot-through duty ratio versus the voltage boost ratio
Shoot-through or Open-circuit Duty ratio (D)
with the same cascaded level (N=n). Solid, dashed and dot lines
Fig. 9. The boost ratio versus shoot-through or open-circuit duty represent N = 2, 3 and 4, respectively.
ratio D. Bold, solid dashed and dot lines represent N = 1,2,3 and
4 respectively. 0.7

0.6

1
Normalized DC-Link Voltage of Switched-L Z-source

0.5

Normalized Inductance
Alternative
0.95
Cascaded
0.4
0.9 Switched-L

0.3
0.85 N=2

0.8 0.2

0.75 . N=3
0.1

0.7
.
. 0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
0.65 Duty ratio of tradition Z-source
N=4
Fig.13. Minimum inductance of alternative cascaded and multi-
0 0.05 0.1 0.15 0.2 0.25 0.3
Duty ratio of traditinal Z-source
0.35 0.4 0.45 0.5 cell switched-L networks normalized to tradition Z-source
network versus traditional Z-source duty ratio D when producing
Fig.10. DC-link voltage ratios versus traditional Z-source duty the same voltage gain. Solid dashed and dot lines represent N =
ratio when producing the same voltage gain. Solid, dashed and 2, 3 and 4, respectively.
dot lines represent N = 2, 3 and 4, respectively.

VI. CONCLUSION
From extending the switched-L Z-source inverter circuit,
the generalized multi-cell switched-L and C Z-source
inverters are derived. Their operating principles have been
explained, and their gains have been shown to be much larger
than those produced by traditional Z-source inverters. Even if
the same input-to-output gain is demanded, the switched-L
and C inverters can still be proven to have advantages over
the traditional Z-source inverters. Comparison with normal Z-
source inverter and other high gain cascaded Z-source
inverters has also been performed with the switched-L and C
circuitries again shown to have a number of favorable
advantages. These advantages and operating features of the
proposed inverters have already been confirmed in simulation
before all the circuits are verified through experimental
testing.
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Fig.14 Experimental dc-link voltage line voltage and output current waveforms Fig.15 Experimental capacitor voltage inductor current and dc-link current
of a n=3 switched-L Z-source inverter with M = 0.8×1.15 and D=0.15 waveforms of a n=3 switched-L Z-source inverter with M = 0.8×1.15 and
D=0.15

Fig.16 Experimental input current load voltage line current and output current Fig.17 Experimental capacitor voltage inductor current and dc-link current
waveforms of a n=3 switched-C Z-source inverter with M = 0.8×1.15 and waveforms of a n=3 switched-C Z-source inverter with M = 0.8×1.15 and
D=0.15 D=0.15