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1
A Novel Quasi-Z-Source Inverter Topology With
Special Coupled Inductors For Input Current
Ripples Cancellation
Alexandre Battiston, Member, IEEE, El-Hadj Miliani, Member, IEEE, Serge Pierfederici, Farid Meibody-Tabar
Abstract—This paper proposes an inductors coupling technique to cancel input current ripples of a quasi-Z-source inverter
without adding any additional components. This means the
suppression of input filters that are used to protect voltage
sources, and this whatever the voltage boost factor value. This
cancellation property is made possible by a suitable coupling of
the two existing quasi-Z-source inductors according to mathematical condition. The considered system in this paper is an electric
drive system composed of a motor fed by the proposed coupled
quasi-Z-source inverter. An experimental prototype to validate
both the theoretical and simulation analyses has been developed.
The results have validated the proposed coupling strategy and
show that it does not degrade the global efficiency of the system.
K,D i
L1
vs
DC-source
voltage
C2
L1
Iinv
C1
vC2
vC1
vDC
iL2 L2
Z-source inverter
Motor
Fig. 1. Bidirectional Z-source inverter in an electric drive system.
Index Terms—high-frequency ripples, quasi-Z-source inverter,
coupled inductors, battery current, electric drive system
I. I NTRODUCTION
I
N the last decade, the number of electric drives systems
for hybrid/electric vehicles as well as renewable-energy
applications have increased significantly and involved the
development of cost-effective, high-efficient converters. The
power is thus modulated and converters are controlled by
means of power electronics switches. Generally, a boost-type
architecture is required to convert energy and link the source
voltage to the DC-AC inverter. This allows working at high
range of voltage by stepping up the low source voltage (for
instance that of a battery). Furthermore, continuous currents
with minimum high-frequency ripples are generally required
in some applications such as embedded or renewable-energy
applications. Indeed, the lifetime of storage sources (battery,
fuel cells, ...) is influenced by current ripples. DC-DC boost
converter is traditionally adopted to step up source voltage
when isolation is not required [1]–[4]. However, some isolated
versions can be found with input current ripples cancellation
techniques [5].
In 2002, a promising DC-AC converter, also known as Zsource inverter (ZSI), has been proposed by Prof. Fang Zheng
Peng [6], [7]. In Fig. 1, a bidirectional version (the diode D
is replaced by a bidirectional switch K,D) of the original Zsource inverter is presented in an electric drive system feeding an electrical machine. This inverter possesses particular
impedance-source input that allows extra shoot-through states
of the inverter legs (the upper and lower switches of a same
inverter’s leg are turned-ON) to step up the source voltage vs .
Such an impedance-source offers advantages for the inverter
in terms of both robustness and reliability. Indeed, incorrect
IGBT turned-ON switching no longer destroy the inverter.
However, one drawback that can be pointed out concerns the
discontinuous input current flowing through the bidirectional
K, D switch (see Fig. 1). To overcome this problem, bulky
capacitor and inductor are generally used as LC passive
filter to protect the voltage source against current ripples.
As a consequence, this filter increases both the volume and
cost of the system, which are often limited in embedded
applications. This represents a great disadvantage compared
with classical DC-DC boost converter, which possesses input
inductive current. However, the minimization of the input
current ripple is combined with the use of large inductor
or ripple cancellation techniques. In all cases, this leads to
complexity of the architecture and additional passive elements
[8]–[14]. In [15], authors show that boost converter with ripple
cancellation network (RCN) takes advantage on classical boost
converter from a weight point of view. Interesting results are
also obtained in [16] where the authors manage to cancel the
input current ripples of a boost-type converter architecture.
Some disadvantages of this proposal can be pointed out. For
instance, it uses additional active and passive components and
is slightly dependent on the operating point of the system.
Other papers focus on coupled impedance-source inverter
topologies but they do not aim at canceling the input current
ripples [17], [18]. Most of the time, they present a reduction
of the high-frequency ripples.
In this paper, one focuses on DC-AC quasi-Z-source inverter
[19]–[22]. This topology is an improvement of the original
Z-source inverter [7]. Using quasi-Z-source inverter allows
working with continuous input current. Thus, there is no
need to use additional passive filter if the inductors are well-
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designed. This topology is interesting as it naturally contains
two inductors, which can be coupled or not. The coupled
quasi-Z-source inverter (CQZSI) is presented in Fig. 2 in
an electric traction system application that will be used in
both simulation and experiment. One takes advantage of this
property to propose in this paper a suitable coupling of the
inductors that leads to the cancellation of the input current
ripples. The advantages of the presented method in comparison
with the other ones in the literature can be enumerated as
follows:
1) There is no need to add other passive or active components. Only the coupling techniques of the inductors are
modified according to the geometry used.
2) The proposed technique is not dependent on the operating point. Theoretically, it is valid for the entire range
of the duty cycle.
3) The current flowing through the battery is theoretically
perfectly continuous.
In the next part, the modeling of the studied system is
detailed before giving a mathematical point of view of the
proposed input current ripple cancellation technique in part
III. The realization of the coupling is studied in part IV. based
on commercialized ferrite cores. Simulation and experimental
validations are given in parts V. and VI. respectively before
giving a conclusion in part VII.
II. P RESENTATION OF THE STUDIED SYSTEM
In Fig. 2, the Coupled quasi-Z-source inverter (CQZSI) is
presented in a global electric traction system with an input
source voltage and a motor. The source voltage vs can thus
be stepped up by means of inserting extra shoot-through zero
states in the inverter PWM scheme [23]–[25]. By considering
iL1 , iL2 , vC1 and vC2 as state variables, the CQZSI can be
modeled as follows using the logical command u ∈ {0, 1}.
This latter indicates the state of the inverter (traditional or
shoot-through state). When u = 1, inverter is shorten (shootthrough state) whereas u = 0 means it operates in its classical
vC2
C2
iL1
L1
vs
DC-source
voltage
1
vDC
=
vs
1 − 2d
(2)
where d ∈ [0, 0.5] represents the duty cycle of the short-circuit
states during a switching period T . It is thus the mean value
of the logical variable u.
III. M ATHEMATICAL CONDITION OF INPUT CURRENT
RIPPLES CANCELLATION
It is assumed the capacitors C1 and C2 are well-sized
to consider the voltages vC1 and vC2 close to their mean
values v̄C1 and v̄C2 respectively. These quantities are given
by averaging (1):

1−d

vs
(3)
 vC1 ' v̄C1 =
1 − 2d
d

 vC2 ' v̄C2 =
vs
(4)
1 − 2d
Let vL1 and vL2 be the voltages across the two inductors. One
has:
vL1 = vs + vC2 u − vC1 (1 − u)
(5)
vL2 = vC1 u(t) − vC2 (1 − u)
(6)
Thus, for the sequence corresponding to u = 1, one has:
vL1 = vs + vC2
(7)
vL2 = vC1
And with the assumption that vC1 ' v̄C1 and vC2 ' v̄C2 , (7)
is given by (8) according to (3) and (4).

1−d

vs ' vC1
vL1 '
(8)
1 − 2d
 v =v
L2
C1
Thus, one obtains that for u = 1, vL1 ' vL2 . The same
mathematical description is made by considering the second
sequence for which u = 0. One has:
vL1 = vs − vC1
(9)
vL2 = −vC2
Iinv
K,D iL2 L2
vC1 C
vDC
1
Coupled Quasi Z-source inverter
active or zero-sequence states.

diL2
diL1

+M
= vs + vC2 u − vC1 (1 − u)
L1



dt
dt


di
di
L2
L1

 L2
+M
= vC1 u − vC2 (1 − u)
dt
dt
(1)
dv
C1
 C

=
−i
u
+
i
(1
−
u)
−
I
(1
−
u)

1
L2
L1
inv

dt



 C dvC2 = −i u + i (1 − u) − I (1 − u)
2
L1
L2
inv
dt
M represents the mutual inductance. By averaging the two
first equations in (1), the elevating ratio of CQZSI is given by
(2) noting vDC = vC1 + vC2 :
Motor
And, according to (3) and (4), (9) is given by:

−d

vL1 '
vs ' −vC2
1 − 2d
 v = −v
L2
Fig. 2. Bi-directional coupled quasi-Z-source inverter in an electrical traction
system.
(10)
C2
As a result, vL1 ' vL2 on this second sequence. The voltages
across the two inductors can be thus considered equal for all
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time. From (1), by considering current ripples on an operating
sequence, the equality (11) can be expressed.
∆iL2
∆iL2
∆iL1
∆iL1
+M
= L2
+M
(11)
∆T
∆T
∆T
∆T
with ∆T the duration of a sequence when u = 1 or u = 0.
This latter is theoretically known. (11) leads to the expression
of the input current ripple:
L1
∆iL1 =
L2 − M
∆iL2
L1 − M
(12)
One finally obtains the mathematical cancellation condition
given by:
L2 = M
(13)
IV. M AGNETIC CONDITION OF INPUT CURRENT RIPPLES
CANCELLATION
This part now focuses on the magnetic realization of the
coupled inductors with respect on the above mathematical
condition. An E magnetic core is for instance considered with
two sets as illustrated in Fig. 3. In order to present results in
general case, three different lengths l1 , l2 and l3 as well as
three different air gap e1 , e2 and e3 are taken into account.
The third dimension length is noted lz . A permeance network
iL1
vL1
air
lz
iron
vL2 l1
e1
e2
l2
e3
l3
iL2
Fig. 3. Geometry of the considered magnetic core.
modelling the magnetic geometry in Fig. 3 is presented in
Fig. 4. This representation allows pre-dimensioning the system
and will be verified by means of finite elements methods
in the following lines. The two windings are replaced by
Ampereturns n1 iL1 and n2 iL2 with n1 and n2 the turns
number on the primary and secondary side of the coupled
inductors. The magnetic fluxes in the different legs are noted
ϕ1 and ϕ2 . Magnetic reluctances < are given by:
<material =
l
1
µmaterial A
(14)
with l the length of the circuit in meters, µmaterial the permeability of the material (air or iron) and A the cross-sectional
area of the circuit in square meters. From this concept and the
analogy with electrical circuit, one has on the assumption that
<iron ' 0:
n1 iL1 = <air1 ϕ1 + <air2 (ϕ1 − ϕ2 )
(15)
n2 iL2 = <air3 ϕ2 + <air2 (ϕ2 − ϕ1 )
(16)
Fig. 4. Permeance network model of the magnetic core.
From (15) and (16), the expression of the fluxes ϕ1 and ϕ2
are given by:

n2 <air2

ϕ1 =
iL2



(<air2 + <air3 ) (<air1 + <air2 ) − <2air2




n1 (<air2 + <air3 )


+
iL1



(<air2 + <air3 ) (<air1 + <air2 ) − <2air2


n1 <air2


ϕ2 =
iL1

2

(<
+
<
)

air2
air3 (<air1 + <air2 ) − <air2




n2 (<air1 + <air2 )


iL2
+
(<air2 + <air3 ) (<air1 + <air2 ) − <2air2
(17)
From an electrical circuit point of view, the total fluxes φ1 and
φ2 through the primary and secondary sides of the inductors
are given by:
φ1 = n1 ϕ1 = L1 iL1 + M iL2
(18)
φ2 = n2 ϕ2 = L2 iL2 + M iL1
From (17) and (18), one finally obtains the expressions of the
inductances L1 , L2 and the mutual inductance M :

n21 (<air2 + <air3 )


L1 =
(19)



(<air2 + <air3 ) (<air1 + <air2 ) − <2air2



n22 (<air1 + <air2 )
L2 =
(20)

(<air2 + <air3 ) (<air1 + <air2 ) − <2air2




n1 n2 <air2


(21)
M=
(<air2 + <air3 ) (<air1 + <air2 ) − <2air2
The mathematical equality (13) is finally geometrically given
by:
<air2
n2 =
n1
(22)
<air1 + <air2
From the definition (14) of magnetic reluctance, (22) gives a
condition on the turns numbers n1 and n2 :
A2 e 1
n1 = 1 +
· n2
(23)
A1 e 2
with A1 = l1 · lz and A2 = l2 · lz . By considering symmetrical
commercialized ferrite cores, with l1 = l3 = l22 and e1 =
e2 = e3 the above condition becomes:
n1 = 3 · n2
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(24)
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Designing the experimental coupled inductors in compliance
with condition (24), input current ripples are theoretically
canceled. The values of inductances and mutual (19), (20)
and (21) becomes with this technique and for the chosen core
geometry:

3 n22


(25)
 L2 =
4 <air1
(26)
 M = L2


L1 = 9 L2
(27)
(n1 = 3 n2 ), the ratio 3/5 is validated according to the
inductions values for the considered point in the air gaps
(|B1 | = 0.061 T and |B2 | = 0.037 T ).
V. S IMULATION RESULTS
Simulation parameters as well as experimental ones are
given in TABLE I. A simulation of electrical system in Fig.
TABLE I
S IMULATION AND EXPERIMENTAL PARAMETERS
Theoretical design has been obtained according to the perSymbol
Description
Value
vs
source voltage
DC-bus voltage
inductors
capacitors
PM-motor power
65 V
100 V
230 µH
680 µF
< 500 W
vDC
L1 = L2
C1 = C2
P0max
2 is conducted. The CQZSI is controlled by means of Sliding
Mode Control and the source voltage vs = 65 V is stepped up
to vDC = 100 V . The control diagram will not be detailed in
this paper. The mechanical speed of the machine is controlled
by means of PI regulators. In Fig. 6, the DC-bus voltage vDC
(a) with n1 = n2 .
DC−bus voltage
150
vDC (V)
100
50
0
0.07
0.0701
0.0702
0.0703
iL2 (A)
4
Inductive currents
0.0704
iL1 − 1A (A)
3
2
1
0.07
(b) with n1 = 3 n2 .
Fig. 5. Finite elements results: flux lines in the magnetic circuit plotted for
the two considered configurations.
meance network in Fig. 4 under hypothesis. The mean value
¯ = iL2
¯ ),
of the two inductive currents being the same (iL1
ϕ1 = ϕ2 with n1 = n2 . This comes from (15) and (16)
with the considered geometry. By contrast, with n1 = 3 n2 ,
(15) and (16) lead to ϕ2 = 3/5 ϕ1 . This property is thus
verified using a finite elements software which takes into
account iron reluctance or boundaries effects. The results
obtained in Fig. 5 for the two configurations are comply with
theoretical expectation. For the first configuration (n1 = n2 ),
the results show that the flux lines share between the two
sides of the magnetic material (inductions are equal in the air
gaps |B1 | = |B2 | = 0.025 T ). For the second configuration
0.0701
0.0702
simulation time (s)
0.0703
0.0704
Fig. 6. Simulation results: inductive currents waveforms in steady state with
L1 = L2 = 230 µH.
and the inductive currents iL1 and iL2 are presented. The DCmax
bus voltage evolves between two values, vDC
, which represents the DC-bus voltage reference (100 V ) and zero when a
shoot-through zero state is added in the inverter PWM scheme.
In simulation, four shoot-through states are added during the
switching period T = 10−4 s (see [7] for more details). In
this figure, the currents waveforms are obtained with simple
coupling n1 = n2 . Thus, the inductive currents are equal so as
the high-frequency ripples (about 1 A according to the figure).
In Fig. 7, the proposed coupling strategy is investigated with
respect to condition (24). As expected, this result validates the
input current ripples cancellation (iL1 ). The input current is
thus perfectly continuous and does not contain high-frequency
ripples. A third test in Fig. 8 is conducted and focuses on
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DC−bus voltage
150
vDC (V)
100
50
0
0.09
0.09
0.0901
0.0901
0.0902
0.0902
0.0903
0.0904
0.0904
Inductive currents
6
iL2 (A)
5
i
L1
4
(A)
3
2
1
0.09
0.09
0.0901
0.0901
0.0902
0.0902
0.0903
0.0904
0.0904
(a) d = 10%.
Speed
DC−bus voltage
Fig. 7. Simulation results: inductive currents waveforms in steady state with
L1 = 9 · L2 (n1 = 3 n2 ) and L2 = M = 230 µH.
(b) d = 30%.
Fig. 9. DC-bus voltage and currents for two operating points depending on
the duty cycle d value.
150
C1 = C2
inverter
100
vDC (V)
50
0
0.18
0.2
0.22
0.24
0.26
0.28
0.3
0.32
0.34
Alternator
0.36
1000
Ω* (rpm)
500
Inductive currents
0.18
10
0.2
0.22
8
iL1−4A (A)
6
iL2 (A)
0.24
0.26
0.28
0.3
0.32
0.34
Motor
0.36
4
L1= 9 L2
2
0
−2
0.18
0.2
0.22
0.24
0.26
0.28
0.3
simulation time (s)
0.32
0.34
0.36
Fig. 10. Test bench for validation.
Fig. 8. Simulation results: study of transient state after a speed step.
transient state after a speed step from 500 rpm to 1000 rpm.
The two currents have been shifted for convenience. The result
allows validating the proposed coupling technique even in
transient state. The input current does not have any highfrequency ripples. One advantage of the proposed strategy
using a quasi-Z-source inverter is that it is valid on the entire
range of duty cycle. It does not depend on the boost ratio
vDC /vs . The simulation results in Fig. 9 allow proving this
for two tested duty cycles (d = 10% and d = 30%).
n1=n2
n2
n1=3n2
n2
Fig. 11. Two coupling techniques for comparison and validation.
VI. E XPERIMENTAL RESULTS
A. Presentation of the test bench
The experimental test bench is presented in Fig. 10. It is
composed of a PM-motor fed by a CQZSI with two capacitors
(C1 = C2 ) and two coupled inductors with the proposed
coupling strategy (n1 = 3 n2 ). In order to present results for
the two considered coupling techniques, two coupled inductors
are built according to the turns numbers in primary and secondary sides (n1 = n2 or n1 = 3 n2 ). The two configurations
are presented in Fig. 11. The typical waveforms of inductive
currents with classical coupling n1 = n2 are given in Fig. 12.
When a shoot-through zero state is added, the DC-bus voltage
equals zero and the inductive currents iL1 and iL2 increase.
These waveforms are obtained by inserting four short-circuits
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vDC (100V/div)
vDC (100V/div)
Ω (500 rpm/div)
iL1 (1A/div)
iL2 (1A/div)
iL2 (1A/div)
iL1 (1A/div)
Fig. 12. Experimental results: inductive currents iL1 and iL2 waveforms in
steady state for L1 ' L2 (n1 = n2 ).
Fig. 14. Experimental results: inductive currents waveforms after a speed
step (from 500 to 1000 rpm) with the proposed couplig strategy.
vDC (100V/div)
Ω (500 rpm/div)
iL2 (1A/div)
vDC (100V/div)
Ω (500 rpm/div)
iL2 (1A/div)
iL1 (1A/div)
iL1 (1A/div)
Fig. 13. Experimental results: inductive currents iL1 and iL2 waveforms in
steady state for L1 = 9 L2 (n1 = 3 n2 ) and L2 = M .
states during a switching period T [7]. The waveforms with
the proposed coupling strategy are presented in Fig. 13 by
keeping n2 constant and modifying n1 according to (24).
These results are presented in steady state for Ω = 1000 rpm.
As expected, the high-frequency ripples of input current iL1
have been canceled in comparison with previous results in
Fig. 12. This confirms the simulation results obtained above.
The Fig. 14 presents the inductive currents iL1 and iL2 with
the proposed coupling strategy after a speed step from 500
to 1000 rpm. This validates the behavior of the two currents
and confirms the ripples cancellation of iL1 . A zoom in Fig.
14 when Ω = 1000 rpm is given in Fig. 15 for several
switching periods to point out the effectiveness of the coupling
technique. In Fig. 16, the transient response of the inductive
currents is given after a voltage step from 80 V to 100 V
Fig. 15. Experimental results: inductive currents waveforms in steady state
for Ω = 1000 rpm with the proposed coupling strategy.
with constant speed Ω. This test represents the worst case
of using quasi-Z-source inverter as it is preferable to adapt
the DC-bus voltage to the mechanical speed of the machine
so that the efficiency is better [26]. Indeed, the reference
∗
voltage vDC
generally evolves with the same dynamic as that
of the mechanical speed. Nevertheless, the experimental results
remains interesting and show that the coupling strategy is still
valid.
VII. E FFICIENCY RESULTS ON THE TEST BENCH
It is interesting in this part to study the effect of the coupling
strategy (n1 = 3 n2 ) over the efficiency of the global system.
Note that n2 is always constant in the two configurations and
only n1 is modified (see Fig. 11). With vs = 100 V and
vDC = 180 V , experimental efficiencies are plotted in Fig 17.
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vDC (100V/div)
vDC* (50 V/div)
iL1 (5A/div)
in low speed range. A remark can be expressed as regards
the efficiency values that evolve between 45 to 80 %. These
low values can be explained by the fact the source voltage vs
is always stepped up to 180 V . Thus, shoot-through states are
always added and increase losses in the inverter even when the
source voltage is high enough to control the machine. Using
a quasi-Z-source inverter, it is preferable to adapt the DC-bus
voltage to the power demand of the machine so that losses
are reduced [26]. Nevertheless, the worst case study has thus
been considered to plot the efficiency.
VIII. C ONCLUSION
iL2 (5A/div)
Fig. 16. Experimental results: inductive currents waveforms after a voltage
step from 80 V to 100 V .
0.8
0.75
0.7
Efficiency
0.65
0.6
0.55
0.5
with classical coupling strategy (n1=n2)
with proposed coupling strategy (n1=3 n2)
0.45
0.4
200
In this paper, an input current ripples cancellation technique
is presented using a DC-AC coupled quasi-Z-source inverter.
The mathematical derivation is established by considering
commercialized E ferrite core. Others geometries can be used
and may be optimized. The validation has been conducted
on an electric traction prototype composed of a PM-motor
fed by a quasi-Z-source inverter. Experimental results are in
accordance with simulation ones. The input current is thus
”perfectly” continuous (without high-frequency ripples), hence
interest as regards voltage sources (battery, fuel cell, ...) from
a lifetime point of view. Other advantages can be pointed out
in comparison with widely used boost-type architecture. For
instance, there is no need to use additional components in
the system as the two inductors exists in the quasi-Z-source
topology. Furthermore, as the input current high-frequency
ripples are canceled, no passive filter is necessary to protect the
source, which is interesting in such applications like embedded
or renewable-energy ones. Finally, in addition to be valid for
all dudty cycle d, the coupling strategy does not impact the
efficiency, which is slightly the same as the classical quasi-Zsource topology.
R EFERENCES
400
600
800
1000
1200
Mechanical speed Ω (rpm)
1400
1600
1800
Fig. 17. Experimental results: Efficiency comparison between proposed and
classical inductors coupling with vs = 100 V and vDC = 180 V .
For this test, the efficiency is given for different mechanical
speeds of the machine and for the two coupling techniques.
The efficiency is calculated according to the ratio of the power
absorbed by the machine Pm = Ts ·Ω over the power provided
by the source Ps = iL1 ·vs . Ts represents the shaft torque given
by an Luenberger estimator not detailed in this paper. It is a
viscous-type load torque that is generated according to a threephase resistor fed by an alternator coupled in the same machine
shaft. The calculated efficiency thus takes into account all the
losses in the system (machine losses, switching and conduction
losses in the inverter, resistive and iron losses in the coupled
inductors, resistive losses in the capacitors ...). The results
show that the proposed coupling strategy does not seem to
have high influence on efficiency. However, it can be pointed
out that a slight advantage is given to the proposed coupling
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