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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI10.1109/TPEL.2015.2429593, IEEE Transactions on Power Electronics

1

A Novel Quasi-Z-Source Inverter Topology WithSpecial Coupled Inductors For Input Current

Ripples CancellationAlexandre Battiston, Member, IEEE, El-Hadj Miliani, Member, IEEE, Serge Pierfederici, Farid Meibody-Tabar

Abstract—This paper proposes an inductors coupling tech-nique to cancel input current ripples of a quasi-Z-source inverterwithout adding any additional components. This means thesuppression of input filters that are used to protect voltagesources, and this whatever the voltage boost factor value. Thiscancellation property is made possible by a suitable coupling ofthe two existing quasi-Z-source inductors according to mathemat-ical condition. The considered system in this paper is an electricdrive system composed of a motor fed by the proposed coupledquasi-Z-source inverter. An experimental prototype to validateboth the theoretical and simulation analyses has been developed.The results have validated the proposed coupling strategy andshow that it does not degrade the global efficiency of the system.

Index Terms—high-frequency ripples, quasi-Z-source inverter,coupled inductors, battery current, electric drive system

I. INTRODUCTION

IN the last decade, the number of electric drives systemsfor hybrid/electric vehicles as well as renewable-energy

applications have increased significantly and involved thedevelopment of cost-effective, high-efficient converters. Thepower is thus modulated and converters are controlled bymeans of power electronics switches. Generally, a boost-typearchitecture is required to convert energy and link the sourcevoltage to the DC-AC inverter. This allows working at highrange of voltage by stepping up the low source voltage (forinstance that of a battery). Furthermore, continuous currentswith minimum high-frequency ripples are generally requiredin some applications such as embedded or renewable-energyapplications. Indeed, the lifetime of storage sources (battery,fuel cells, ...) is influenced by current ripples. DC-DC boostconverter is traditionally adopted to step up source voltagewhen isolation is not required [1]–[4]. However, some isolatedversions can be found with input current ripples cancellationtechniques [5].

In 2002, a promising DC-AC converter, also known as Z-source inverter (ZSI), has been proposed by Prof. Fang ZhengPeng [6], [7]. In Fig. 1, a bidirectional version (the diode Dis replaced by a bidirectional switch K,D) of the original Z-source inverter is presented in an electric drive system feed-ing an electrical machine. This inverter possesses particularimpedance-source input that allows extra shoot-through statesof the inverter legs (the upper and lower switches of a sameinverter’s leg are turned-ON) to step up the source voltage vs.Such an impedance-source offers advantages for the inverterin terms of both robustness and reliability. Indeed, incorrect

Z-source inverterDC-source

voltage Motor

iL1L1

vC2

L2

C1

vDC

vC1vs

iL2

K,D Iinv

C2

Fig. 1. Bidirectional Z-source inverter in an electric drive system.

IGBT turned-ON switching no longer destroy the inverter.However, one drawback that can be pointed out concerns thediscontinuous input current flowing through the bidirectionalK,D switch (see Fig. 1). To overcome this problem, bulkycapacitor and inductor are generally used as LC passivefilter to protect the voltage source against current ripples.As a consequence, this filter increases both the volume andcost of the system, which are often limited in embeddedapplications. This represents a great disadvantage comparedwith classical DC-DC boost converter, which possesses inputinductive current. However, the minimization of the inputcurrent ripple is combined with the use of large inductoror ripple cancellation techniques. In all cases, this leads tocomplexity of the architecture and additional passive elements[8]–[14]. In [15], authors show that boost converter with ripplecancellation network (RCN) takes advantage on classical boostconverter from a weight point of view. Interesting results arealso obtained in [16] where the authors manage to cancel theinput current ripples of a boost-type converter architecture.Some disadvantages of this proposal can be pointed out. Forinstance, it uses additional active and passive components andis slightly dependent on the operating point of the system.Other papers focus on coupled impedance-source invertertopologies but they do not aim at canceling the input currentripples [17], [18]. Most of the time, they present a reductionof 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 originalZ-source inverter [7]. Using quasi-Z-source inverter allowsworking with continuous input current. Thus, there is noneed to use additional passive filter if the inductors are well-



2

designed. This topology is interesting as it naturally containstwo inductors, which can be coupled or not. The coupledquasi-Z-source inverter (CQZSI) is presented in Fig. 2 inan electric traction system application that will be used inboth simulation and experiment. One takes advantage of thisproperty to propose in this paper a suitable coupling of theinductors that leads to the cancellation of the input currentripples. The advantages of the presented method in comparisonwith the other ones in the literature can be enumerated asfollows:

1) There is no need to add other passive or active compo-nents. Only the coupling techniques of the inductors aremodified according to the geometry used.

2) The proposed technique is not dependent on the operat-ing point. Theoretically, it is valid for the entire rangeof the duty cycle.

3) The current flowing through the battery is theoreticallyperfectly continuous.

In the next part, the modeling of the studied system isdetailed before giving a mathematical point of view of theproposed input current ripple cancellation technique in partIII. The realization of the coupling is studied in part IV. basedon commercialized ferrite cores. Simulation and experimentalvalidations are given in parts V. and VI. respectively beforegiving a conclusion in part VII.

II. PRESENTATION OF THE STUDIED SYSTEM

In Fig. 2, the Coupled quasi-Z-source inverter (CQZSI) ispresented in a global electric traction system with an inputsource voltage and a motor. The source voltage vs can thusbe stepped up by means of inserting extra shoot-through zerostates in the inverter PWM scheme [23]–[25]. By consideringiL1, iL2, vC1 and vC2 as state variables, the CQZSI can bemodeled as follows using the logical command u ∈ 0, 1.This latter indicates the state of the inverter (traditional orshoot-through state). When u = 1, inverter is shorten (shoot-through state) whereas u = 0 means it operates in its classical

Coupled Quasi Z-source inverterDC-source

voltage

Motor

iL1

L1

C2

vC2

L2

C1vDC

vC1vs

iL2K,D

Iinv

Fig. 2. Bi-directional coupled quasi-Z-source inverter in an electrical tractionsystem.

active or zero-sequence states.

L1diL1

dt+M

diL2

dt= vs + vC2 u− vC1 (1− u)

L2diL2

dt+M

diL1

dt= vC1 u− vC2 (1− u)

C1dvC1

dt= −iL2 u+ iL1 (1− u)− Iinv (1− u)

C2dvC2

dt= −iL1 u+ iL2 (1− u)− Iinv (1− u)

(1)

M represents the mutual inductance. By averaging the twofirst equations in (1), the elevating ratio of CQZSI is given by(2) noting vDC = vC1 + vC2:

vDC

vs=

1

1− 2 d(2)

where d ∈ [0, 0.5] represents the duty cycle of the short-circuitstates during a switching period T . It is thus the mean valueof the logical variable u.

III. MATHEMATICAL CONDITION OF INPUT CURRENTRIPPLES CANCELLATION

It is assumed the capacitors C1 and C2 are well-sizedto consider the voltages vC1 and vC2 close to their meanvalues vC1 and vC2 respectively. These quantities are givenby averaging (1):

vC1 ' vC1 =1− d

1− 2 dvs (3)

vC2 ' vC2 =d

1− 2 dvs (4)

Let vL1 and vL2 be the voltages across the two inductors. Onehas:

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

vL2 = vC1(7)

And with the assumption that vC1 ' vC1 and vC2 ' vC2, (7)is given by (8) according to (3) and (4). vL1 '

1− d1− 2 d

vs ' vC1

vL2 = vC1

(8)

Thus, one obtains that for u = 1, vL1 ' vL2. The samemathematical description is made by considering the secondsequence for which u = 0. One has:

vL1 = vs − vC1

vL2 = −vC2(9)

And, according to (3) and (4), (9) is given by: vL1 '−d

1− 2 dvs ' −vC2

vL2 = −vC2

(10)

As a result, vL1 ' vL2 on this second sequence. The voltagesacross the two inductors can be thus considered equal for all



3

time. From (1), by considering current ripples on an operatingsequence, the equality (11) can be expressed.

L1∆iL1

∆T+M

∆iL2

∆T= L2

∆iL2

∆T+M

∆iL1

∆T(11)

with ∆T the duration of a sequence when u = 1 or u = 0.This latter is theoretically known. (11) leads to the expressionof the input current ripple:

∆iL1 =L2 −ML1 −M

∆iL2 (12)

One finally obtains the mathematical cancellation conditiongiven by:

L2 = M (13)

IV. MAGNETIC CONDITION OF INPUT CURRENT RIPPLESCANCELLATION

This part now focuses on the magnetic realization of thecoupled inductors with respect on the above mathematicalcondition. An E magnetic core is for instance considered withtwo sets as illustrated in Fig. 3. In order to present results ingeneral case, three different lengths l1, l2 and l3 as well asthree different air gap e1, e2 and e3 are taken into account.The third dimension length is noted lz . A permeance network

l1 l2 l3

lz iron

air

e1 e2 e3

vL2

vL1

iL1

iL2

Fig. 3. Geometry of the considered magnetic core.

modelling the magnetic geometry in Fig. 3 is presented inFig. 4. This representation allows pre-dimensioning the systemand will be verified by means of finite elements methodsin the following lines. The two windings are replaced byAmpereturns n1 iL1 and n2 iL2 with n1 and n2 the turnsnumber on the primary and secondary side of the coupledinductors. The magnetic fluxes in the different legs are notedϕ1 and ϕ2. Magnetic reluctances < are given by:

<material =1

µmaterial

l

A(14)

with l the length of the circuit in meters, µmaterial the perme-ability of the material (air or iron) and A the cross-sectionalarea of the circuit in square meters. From this concept and theanalogy 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:

ϕ1 =n2<air2

(<air2 + <air3) (<air1 + <air2)−<2air2

iL2

+n1 (<air2 + <air3)


iL1

ϕ2 =n1<air2


iL1

+n2 (<air1 + <air2)


iL2

(17)From an electrical circuit point of view, the total fluxes φ1 andφ2 through the primary and secondary sides of the inductorsare given by:

φ1 = n1 ϕ1 = L1 iL1 +M iL2

φ2 = n2 ϕ2 = L2 iL2 +M iL1(18)

From (17) and (18), one finally obtains the expressions of theinductances L1, L2 and the mutual inductance M :

L1 =n21 (<air2 + <air3)


(19)

L2 =n22 (<air1 + <air2)


(20)

M =n1 n2<air2


(21)

The mathematical equality (13) is finally geometrically givenby:

n2 =<air2

<air1 + <air2n1 (22)

From the definition (14) of magnetic reluctance, (22) gives acondition on the turns numbers n1 and n2:

n1 =

(1 +

A2

A1

e1e2

)· n2 (23)

with A1 = l1 · lz and A2 = l2 · lz . By considering symmetricalcommercialized ferrite cores, with l1 = l3 = l2

2 and e1 =e2 = e3 the above condition becomes:

n1 = 3 · n2 (24)



4

Designing the experimental coupled inductors in compliancewith condition (24), input current ripples are theoreticallycanceled. The values of inductances and mutual (19), (20)and (21) becomes with this technique and for the chosen coregeometry:

L2 =3

4

n22<air1

(25)

M = L2 (26)L1 = 9L2 (27)

Theoretical design has been obtained according to the per-

(a) with n1 = n2.

(b) with n1 = 3n2.

Fig. 5. Finite elements results: flux lines in the magnetic circuit plotted forthe two considered configurations.

meance network in Fig. 4 under hypothesis. The mean valueof the two inductive currents being the same ( ¯iL1 = ¯iL2),ϕ1 = ϕ2 with n1 = n2. This comes from (15) and (16)with the considered geometry. By contrast, with n1 = 3n2,(15) and (16) lead to ϕ2 = 3/5ϕ1. This property is thusverified using a finite elements software which takes intoaccount iron reluctance or boundaries effects. The resultsobtained in Fig. 5 for the two configurations are comply withtheoretical expectation. For the first configuration (n1 = n2),the results show that the flux lines share between the twosides of the magnetic material (inductions are equal in the airgaps |B1| = |B2| = 0.025T ). For the second configuration

(n1 = 3n2), the ratio 3/5 is validated according to theinductions values for the considered point in the air gaps(|B1| = 0.061T and |B2| = 0.037T ).

V. SIMULATION RESULTS

Simulation parameters as well as experimental ones aregiven in TABLE I. A simulation of electrical system in Fig.

TABLE ISIMULATION AND EXPERIMENTAL PARAMETERS

Symbol Description Value

vs source voltage 65V

vDC DC-bus voltage 100V

L1 = L2 inductors 230µH

C1 = C2 capacitors 680µF

Pmax0 PM-motor power < 500W

2 is conducted. The CQZSI is controlled by means of SlidingMode Control and the source voltage vs = 65V is stepped upto vDC = 100V . The control diagram will not be detailed inthis paper. The mechanical speed of the machine is controlledby means of PI regulators. In Fig. 6, the DC-bus voltage vDC

0.07 0.0701 0.0702 0.0703 0.07040

50

100

150

DC

−bu

s vo

ltage

0.07 0.0701 0.0702 0.0703 0.0704

1

2

3

4

simulation time (s)

Indu

ctiv

e cu

rren

ts

iL2

(A)

iL1

− 1A (A)

vDC

(V)

Fig. 6. Simulation results: inductive currents waveforms in steady state withL1 = L2 = 230µH .

and the inductive currents iL1 and iL2 are presented. The DC-bus voltage evolves between two values, vmax

DC , which repre-sents the DC-bus voltage reference (100V ) and zero when ashoot-through zero state is added in the inverter PWM scheme.In simulation, four shoot-through states are added during theswitching period T = 10−4 s (see [7] for more details). Inthis figure, the currents waveforms are obtained with simplecoupling n1 = n2. Thus, the inductive currents are equal so asthe high-frequency ripples (about 1A according to the figure).In Fig. 7, the proposed coupling strategy is investigated withrespect to condition (24). As expected, this result validates theinput current ripples cancellation (iL1). The input current isthus perfectly continuous and does not contain high-frequencyripples. A third test in Fig. 8 is conducted and focuses on



5

0.09 0.09 0.0901 0.0901 0.0902 0.0902 0.0903 0.0904 0.09040

50

100

150D

C−

bus

volta

ge

0.09 0.09 0.0901 0.0901 0.0902 0.0902 0.0903 0.0904 0.09041

2

3

4

5

6

Indu

ctiv

e cu

rren

ts

iL2

(A)

iL1

(A)

vDC

(V)

Fig. 7. Simulation results: inductive currents waveforms in steady state withL1 = 9 · L2 (n1 = 3n2) and L2 = M = 230µH .

0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.360

50

100

150

DC

−bu

s vo

ltage

0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36

500

1000

Spe

ed

0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36

−2

0

2

4

6

8

10

simulation time (s)

Indu

ctiv

e cu

rren

ts

vDC

(V)

Ω* (rpm)

iL1

−4A (A)

iL2

(A)

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 resultallows validating the proposed coupling technique even intransient state. The input current does not have any high-frequency ripples. One advantage of the proposed strategyusing a quasi-Z-source inverter is that it is valid on the entirerange of duty cycle. It does not depend on the boost ratiovDC/vs. The simulation results in Fig. 9 allow proving thisfor two tested duty cycles (d = 10% and d = 30%).

VI. EXPERIMENTAL RESULTS

A. Presentation of the test bench

The experimental test bench is presented in Fig. 10. It iscomposed of a PM-motor fed by a CQZSI with two capacitors(C1 = C2) and two coupled inductors with the proposedcoupling strategy (n1 = 3n2). In order to present results forthe two considered coupling techniques, two coupled inductors

(a) d = 10%. (b) d = 30%.

Fig. 9. DC-bus voltage and currents for two operating points depending onthe duty cycle d value.

L1= 9 L2

C1 = C2

Motor

inverter

Alternator

Fig. 10. Test bench for validation.

n1=3n2 n2

n1=n2n2

Fig. 11. Two coupling techniques for comparison and validation.

are built according to the turns numbers in primary and sec-ondary sides (n1 = n2 or n1 = 3n2). The two configurationsare presented in Fig. 11. The typical waveforms of inductivecurrents with classical coupling n1 = n2 are given in Fig. 12.When a shoot-through zero state is added, the DC-bus voltageequals zero and the inductive currents iL1 and iL2 increase.These waveforms are obtained by inserting four short-circuits



6

vDC (100V/div)

iL2 (1A/div)

iL1 (1A/div)

Fig. 12. Experimental results: inductive currents iL1 and iL2 waveforms insteady state for L1 ' L2 (n1 = n2).

Ω (500 rpm/div)

vDC (100V/div)

iL2 (1A/div)

iL1 (1A/div)

Fig. 13. Experimental results: inductive currents iL1 and iL2 waveforms insteady state for L1 = 9L2 (n1 = 3n2) and L2 = M .

states during a switching period T [7]. The waveforms withthe proposed coupling strategy are presented in Fig. 13 bykeeping 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 inFig. 12. This confirms the simulation results obtained above.The Fig. 14 presents the inductive currents iL1 and iL2 withthe proposed coupling strategy after a speed step from 500to 1000 rpm. This validates the behavior of the two currentsand confirms the ripples cancellation of iL1. A zoom in Fig.14 when Ω = 1000 rpm is given in Fig. 15 for severalswitching periods to point out the effectiveness of the couplingtechnique. In Fig. 16, the transient response of the inductivecurrents is given after a voltage step from 80V to 100V

Ω (500 rpm/div)

vDC (100V/div)

iL2 (1A/div)

iL1 (1A/div)

Fig. 14. Experimental results: inductive currents waveforms after a speedstep (from 500 to 1000 rpm) with the proposed couplig strategy.

Ω (500 rpm/div)

vDC (100V/div)

iL2 (1A/div)

iL1 (1A/div)

Fig. 15. Experimental results: inductive currents waveforms in steady statefor Ω = 1000 rpm with the proposed coupling strategy.

with constant speed Ω. This test represents the worst caseof using quasi-Z-source inverter as it is preferable to adaptthe DC-bus voltage to the mechanical speed of the machineso that the efficiency is better [26]. Indeed, the referencevoltage v∗DC generally evolves with the same dynamic as thatof the mechanical speed. Nevertheless, the experimental resultsremains interesting and show that the coupling strategy is stillvalid.

VII. EFFICIENCY RESULTS ON THE TEST BENCH

It is interesting in this part to study the effect of the couplingstrategy (n1 = 3n2) over the efficiency of the global system.Note that n2 is always constant in the two configurations andonly n1 is modified (see Fig. 11). With vs = 100V andvDC = 180V , experimental efficiencies are plotted in Fig 17.



7

vDC* (50 V/div)

vDC (100V/div)

iL1 (5A/div)

iL2 (5A/div)

Fig. 16. Experimental results: inductive currents waveforms after a voltagestep from 80V to 100V .

200 400 600 800 1000 1200 1400 1600 18000.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

Mechanical speed Ω (rpm)

Effi

cien

cy

with classical coupling strategy (n1=n

2)

with proposed coupling strategy (n1=3 n

2)

Fig. 17. Experimental results: Efficiency comparison between proposed andclassical inductors coupling with vs = 100V and vDC = 180V .

For this test, the efficiency is given for different mechanicalspeeds of the machine and for the two coupling techniques.The efficiency is calculated according to the ratio of the powerabsorbed by the machine Pm = Ts ·Ω over the power providedby the source Ps = iL1·vs. Ts represents the shaft torque givenby an Luenberger estimator not detailed in this paper. It is aviscous-type load torque that is generated according to a three-phase resistor fed by an alternator coupled in the same machineshaft. The calculated efficiency thus takes into account all thelosses in the system (machine losses, switching and conductionlosses in the inverter, resistive and iron losses in the coupledinductors, resistive losses in the capacitors ...). The resultsshow that the proposed coupling strategy does not seem tohave high influence on efficiency. However, it can be pointedout that a slight advantage is given to the proposed coupling

in low speed range. A remark can be expressed as regardsthe efficiency values that evolve between 45 to 80 %. Theselow values can be explained by the fact the source voltage vsis always stepped up to 180V . Thus, shoot-through states arealways added and increase losses in the inverter even when thesource voltage is high enough to control the machine. Usinga quasi-Z-source inverter, it is preferable to adapt the DC-busvoltage to the power demand of the machine so that lossesare reduced [26]. Nevertheless, the worst case study has thusbeen considered to plot the efficiency.

VIII. CONCLUSION

In this paper, an input current ripples cancellation techniqueis presented using a DC-AC coupled quasi-Z-source inverter.The mathematical derivation is established by consideringcommercialized E ferrite core. Others geometries can be usedand may be optimized. The validation has been conductedon an electric traction prototype composed of a PM-motorfed by a quasi-Z-source inverter. Experimental results are inaccordance with simulation ones. The input current is thus”perfectly” continuous (without high-frequency ripples), henceinterest as regards voltage sources (battery, fuel cell, ...) froma lifetime point of view. Other advantages can be pointed outin comparison with widely used boost-type architecture. Forinstance, there is no need to use additional components inthe system as the two inductors exists in the quasi-Z-sourcetopology. Furthermore, as the input current high-frequencyripples are canceled, no passive filter is necessary to protect thesource, which is interesting in such applications like embeddedor renewable-energy ones. Finally, in addition to be valid forall dudty cycle d, the coupling strategy does not impact theefficiency, which is slightly the same as the classical quasi-Z-source topology.

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