Pulsewidth Modulation of Z-Source Inverters With Minimum Inductor Current Ripple

98 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 61, NO. 1, JANUARY 2014
Pulsewidth Modulation of Z-Source Inverters
With Minimum Inductor Current Ripple
Yu Tang, Shaojun Xie, and Jiudong Ding
Abstract—This paper proposes the pulsewidth modulation
(PWM) strategy of Z-source inverters (ZSIs) with minimum in-
ductor current ripple. In existing PWM strategy with single-phase
shoot-through, the shoot-through time interval is divided into
six equal parts, therefore the three phase legs bear the equal
shoot-through time interval. In this manner, the allotment and
arrangement of the shoot-through state is easy to realize, but
the inductor current ripple is not optimized. This causes to use
relatively large inductors. In the proposed PWM strategy, the
shoot-through time intervals of three phase legs are calculated
and rearranged according to the active state and zero state
time intervals to achieve the minimum current ripple across the
Z-source inductor, while maintaining the same total shoot-through
time interval. The principle of the proposed PWM strategy is
analyzed in detail, and the comparison of current ripple under
the traditional and proposed PWM strategy is given. Simulation
and experimental results on the series ZSI are shown to verify the
analysis.
Index Terms—Current ripple, pulsewidth modulation (PWM),
single-phase shoot-through (SPST), Z-source inverter (ZSI).
I. INTRODUCTION
THE voltage-source inverter (VSI) performs only the volt-
age buck conversion, which limits its application in the
fields with wide input voltage, such as the renewable energy
system. To extend the suited input voltage range, a boost
converter is usually inserted as the front stage. Such two-stage
structure needs an additional active switch either with separated
controller and drive system for the two stages. By introducing
a passive network composed two inductors and two capacitors
into the voltage-source inverter, the Z-source inverter (ZSI) can
buck and boost its output voltage in a single stage without
additional active switch [1]–[3]. The additional shoot-through
state which is forbidden in VSI is utilized to boost the voltage in
ZSI. Compared to the two-stage structure, the system structure
of ZSI is simplified.
In the ZSI, the introduced Z-source network influences the
system weight and volume greatly. The system power density
Manuscript received January 6, 2012; revised April 19, 2012 and June 2,
2012; accepted July 11, 2012. Date of publication January 16, 2013; date of
current version July 18, 2013. This work was supported in part by the Priority
Academic Program Development of Jiangsu Higher Education Institutions and
in part by the Research Fund for the Doctoral Program of Higher Education of
China (20093218120017).
The authors are with the Jiangsu Key Laboratory of New Energy Gen-
eration and Power Conversion, Nanjing University of Aeronautics and As-
tronautics (NUAA), Nanjing 210016, China (e-mail: tangyu@nuaa.edu.cn;
eeac@nuaa.edu.cn; jiudong@163.com).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TIE.2013.2240632
can be improved by minimizing the size of Z-source network.
The size of the Z-source capacitors can be minimized by the
improvement of ZSI topology. Recently, two improved ZSI
topologies have been presented [4]–[6], called as the embed-
ded and series ZSI, respectively. The power source is series
connected with the Z-source inductor in embedded ZSI, shows
the merits such as continuous input current and reduced voltage
across one capacitor. In series ZSI, the power source is series
connected with the inverter bridge and shows the reduced volt-
age across both capacitors with soft start capability. Compared
to traditional ZSI, the improved ZSI topologies can reduce
the size and cost of the capacitor in Z-source network with
higher power density. By minimizing the size of the inductors
in Z-source network, the system power density can be higher.
Recently, this topic has not been discussed yet.
When the upper and lower switches in the same phase legs
are turned on simultaneously, named the shoot-through state.
All the ZSI topologies utilize the shoot-through state to boost
the voltage [7]–[9]; therefore, they can be modulated with
the same pulsewidth modulation (PWM) strategies. Various
PWM strategies have been developed and can be classified
as three-phase shoot-through (TPST) and single-phase shoot-
through (SPST). In the TPST type, the shoot-through state is
inserted into the center of zero state. It is simple in realiza-
tion, but the switching times are doubled, and the equivalent
operating frequency of the Z-source network is only twice
the carrier frequency, which causes to use large inductors. In
the SPST type, the shoot-through state is inserted into the
transit time of switching while maintaining the same active state
time without introducing additional switching times. There are
six shoot-through states in one carrier period, therefore the
equivalent frequency of Z-source network is higher compared
in TPST type, which is beneficial on minimizing the size of
inductors.
In existing SPST manner, the shoot-through time is dis-
tributed to the three phases in equal time [10]. The calculation
and arrangement of the shoot-through time in phase legs is
easy to realize, but the inductor current ripple is not optimized
[11]–[17].
This paper reveals the characteristic of the inductor current
in traditional SPST PWM strategy and then proposes a new
SPST PWM strategy with minimum inductor current ripple.
The operational principle of the proposed PWM strategy is
analyzed in detail, and the comparison of current ripple under
traditional and proposed PWM strategy is given. Simulation
and experimental results on the series ZSI topology are given
to verify the analysis.
0278-0046/$31.00 © 2013 IEEE

TANG et al.: PWM OF Z-SOURCE INVERTERS WITH MINIMUM INDUCTOR CURRENT RIPPLE 99
Fig. 1. Traditional ZSI.
Fig. 2. Derivation of embedded and series ZSI. (a) Embedded ZSI;
(b) series ZSI.
II. DERIVATION AND EQUIVALENCE OF ZSI TOPOLOGIES
For traditional ZSI shown in Fig. 1, the dc source and the
inverter bridge is located at two sides of the Z-source network
[11]–[15].
The embedded and series ZSI can be derived from the
traditional topology, as shown in Fig. 2. By inserting the power
source into the Z-source network, this topology is the embedded
ZSI in which the power source is series connected with the
inductor, shown in Fig. 2(a). For series ZSI topology, the power
source is series with the inverter bridge, shown in Fig. 2(b).
From the above derivation, we can see that the operational
principle and modulation strategy of the three ZSI topologies
is the same. The waveform of the inductor current in three
topologies is exactly the same; the difference is the capacitor
voltage and has been discussed in detail in published papers
[4]–[6]. The analysis on inductor current ripple can take the
series topology as an example.
Fig. 3. Series ZSI.
Fig. 4. Equivalent circuits of Series ZSI. (a) Shoot-through state. (b) Non-
shoot-through state.
For series ZSI shown in Fig. 3, the Z-source capacitor voltage
VC and the peak dc-link voltage ˆvi is calculated by
VC =
Dsh
1 − 2Dsh
Vdc ˆvi = 2VC + Vdc =
1
1 − 2Dsh
Vdc (1)
where Vdc is the dc source voltage, Dsh is the shoot-through
duty ratio. Fig. 4 shows the equivalent circuits. When in
the shoot-through state shown in Fig. 4(a), the inductors are
charged and the capacitors are discharged, the energy is trans-
ferred from the power source to the inductor, the inductor
current can be described as
diL
dt
=
Vdc + VC
L
=
(1 − Dsh)ˆvi
L
(2)
where iL is the inductor current, L is the inductance. When in
the non-shoot-through state as shown in Fig. 4(b), the inductors
are discharged and the capacitors are charged, the energy is
transferred from the power source to the load, the inductor
current is
diL
dt
=
−VC
L
=
−Dshˆvi
L
. (3)
III. SPST PWM STRATEGY OF ZSI
TheswitchingsequenceofVSIandZSIwithSPSTisshownin
Fig. 5. By inserting the shoot-through states into the switching

Fig. 5. Switching sequence of VSI and ZSI.
Fig. 6. Inductor current ripple.
transits in VSI, the PWM strategy of ZSI can be derived,
discussed in [10]. As can be seen, there are six shoot-through
states T in one carrier period. Fig. 6 shows the waveform of
inductor current ripple. In shoot-through state, the inductor
current rises; while in non-shoot-through state, the inductor
current decreases.
Noting the symmetry of the switching signal around TS/2,
the switching transit time t1 − t6 and instantaneous current at
t1 − t6 can be expressed as the following:
⎧
⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩
i(t1) = IL −
Dshv∧
i
L t1 t1 = T0
4 − 3
2 T
i(t2) = i(t1) +
(1−Dsh)v∧
i
L (t2 − t1) t2 = T0
4 − 1
2 T
i(t3) = i(t2) −
Dshv∧
i
L (t3 − t2) t3 = t2 + 1
2 T
i(t4) = i(t3) +
(1−Dsh)v∧
i
L (t4 − t3) t4 = t3 + T
i(t5) = i(t4) −
Dshv∧
i
L (t5 − t4) t5 = t4 + 1
2 T2
i(t6) = i(t5) +
(1−Dsh)v∧
i
L (t6 − t5) t6 = t5 + T
(4)
where IL represents the average value of inductor current. The
inductor current ripple can be expressed as
ΔiL = 2 max (|i(t1) − IL| , |i(t2) − IL| , |i(t3) − IL|
|i(t4) − IL| , |i(t5) − IL| , |i(t6) − IL|) . (5)
IV. PROPOSED PWM STRATEGY WITH MINIMUM
INDUCTOR CURRENT RIPPLE
A PWM strategy with minimum inductor current ripple is
proposed. For ZSI, the boost factor is determined by the total
shoot-through time; therefore, the boost ability and ac output
voltage of ZSI keeps the same while maintaining the same
total shoot-through time. The arrangement of the shoot-through
inﬂuences the inductor current obviously; thus, by careful allot-
ment of the shoot-through time in three phase legs, the inductor
current ripple can be optimized. The switching sequence of the
proposed PWM strategy is shown in Fig. 7. The shoot-through

Fig. 7. Switching sequence of proposed PWM strategy.
Fig. 8. Inductor current ripple with proposed PWM strategy.
time of the phases is reassigned as Ta, Tb, Tc, respectively,
while keeping the sum of the three unchanged to get the same
voltage boost. Ta, Tb, Tc is designed according to the active
state time and zero state time to minimize the inductor current
ripple. The active state time, the total shoot-through time, and
zero state time can be calculated instantaneously and is deﬁnite;
therefore, the decreased value of inductor current in active state
and zero state is also deﬁnite. The inductor current ripple is
shown in Fig. 8.
The instantaneous value of inductor current meets the follow-
ing rules:
⎧
⎨
⎩
|i(t2) − IL| + |i(t3) − IL| = a
|i(t4) − IL| + |i(t5) − IL| = b
|i(t1) − IL| = |i(t6) − IL| = c/2
(6)
where a, b, c is the decreased value of the inductor current in
active state 1, active state 2, and zero state, respectively. The
inductor current ripple can be expressed as
ΔiL = 2 max (|i(t1) − IL| , |i(t2) − IL| , |i(t3) − IL| ,
|i(t4) − IL| , |i(t5) − IL| , |i(t6) − IL|)
= 2 max [max (|i(t2) − IL| , |i(t3) − IL|) ,
max (|i(t4) − IL| , |i(t5) − IL|) , c/2] . (7)
Combining (6) and (7), we can obtain
ΔiL ≥ 2 max (a/2, b/2, c/2) . (8)
When |i(t2) − IL| = |i(t3) − IL| = a/2 & |i(t4) − IL| =
|i(t5) − IL| = b/2. The current ripple reaches its minimum
value
ΔiL_min = max(a, b, c). (9)
Therefore, to get the minimum inductor current ripple, the
shoot-through time of the three phases Ta, Tb, Tc is designed to
guarantee that
i(t2) − IL = IL − i(t3) = a/2
i(t4) − IL = IL − i(t5) = b/2.
(10)
The increased value of the inductor current in shoot-through
time Ta, Tb, Tc is
⎧
⎨
⎩
ΔiL_Ta
= c/2 + a/2
ΔiL_Tb
= a/2 + b/2
ΔiL_Tc
= b/2 + c/2.
(11)
The increased value is equal to the decreased value; there-
fore, the shoot-through time of the three phases Ta, Tb, Tc can

be calculated as
⎧
⎪⎨
⎪⎩
Ta = c/2+a/2
a+b+c
Tsh
2
Tb = a/2+b/2
a+b+c
Tsh
2
Tc = b/2+c/2
a+b+c
Tsh
2
(12)
where a, b, c is proportional to the time interval of active
state 1, active state 2, and zero state, described as
a : b : c =
T1
2
:
T2
2
:
T0 − Tsh
2
. (13)
By combining the above two equations, Ta, Tb, Tc can be
derived as
⎧
⎪⎨
⎪⎩
Ta = Tsh
4(Ts−Tsh) (T0 +T1 −Tsh)=k(T0 +T1 −Tsh)
Tb = Tsh
4(Ts−Tsh) (T1 +T2)=k(T1 +T2)
Tc = Tsh
4(Ts−Tsh) (T0 +T2 −Tsh)=k(T0 +T2 −Tsh)
(14)
where k is proportional to the ratio of the shoot-through time to
non-shoot-through time, expressed as
k =
Tsh
4(Ts − Tsh).
(15)
According to (14) and (15), the switching transit time t1 − t6
can be derived easily.
A prototype of series ZSI is designed with the parameters
given in the following.
1) input voltage Vdc: 200 V–400 V;
2) output voltage: 3 phase, 110 V/50 Hz AC;
3) rated capacity: 3 kVA;
4) switching frequency: 13.5 kHz;
5) Z-source network: L = 500 μH, C = 2000 μF;
6) output ﬁlter: Lf = 1000 μH, Cf = 15 μF.
In the control strategy, the dc-link voltage is boost to 370 V,
when Vdc is less than 370 V, shoot-through state is introduced,
while Vdc is larger than 370 V, shoot-through state is not
inserted into the switching state.
The product of ripple current and inductance of the Z-source
inductor ΔiL · L is related to Vdc and the phase angle of
reference vector θ, and the calculated value is shown in Fig. 9
with previous and proposed PWM scheme, respectively. As can
been seen, the product ΔiL · L is decreased greatly with the
new PWM scheme; thus, smaller inductors can be utilized while
maintaining the same ripple current.
V. SIMULATION AND EXPERIMENTAL RESULTS
Simulation results are given with the parameters given above.
The Z-source inductance is L = 500 μH, the output power
is 3 kW.
Fig. 10 shows the simulation waveforms with previous PWM
scheme when Vdc = 200 V in line frequency and carrier fre-
quency. From top to bottom shows the dc-link voltage, the
Z-source inductor current, Z-source capacitor voltage, and
output phase voltage, respectively. The peak dc-link voltage
is controlled at 370 V; the capacitor voltage is 85 V; the
maximum current ripple through the inductor is about 6 A.
The current ripple reaches its maximum value when the phase
Fig. 9. Relationship of ΔiL · L with Vdc and θ. (a) Previous PWM strategy.
(b) Proposed PWM strategy.
output voltage is maximum (θ = 0◦
). There are 6 equal shoot-
through states in each switching period seen from Fig. 10(b),
which is in accordance with PWM scheme discussed in Fig. 5.
Fig. 11 shows the simulation waveforms when Vdc = 300 V.
The peak dc-link voltage is controlled at 370 V; the capacitor
voltage is 35 V; the maximum ripple in this condition is
about 3 A.
Fig. 12 shows the simulation waveforms with proposed
PWM scheme when Vdc = 200 V in line frequency and car-
rier frequency. The peak dc-link voltage is also controlled at
370 V; the capacitor voltage is 85 V; the maximum current
ripple through the inductor is about 4 A, which has been
decreased greatly compared to traditional PWM strategy as
shown in Fig. 10. The current ripple reaches its maximum value
when the phase output voltage is maximum (θ = 0◦
). The time
intervals of the six shoot-through states is different as seen in
Fig. 12(b), which is discussed in Fig. 7.
Fig. 13 shows the simulation waveforms with proposed
PWM scheme when Vdc = 300 V. The peak dc-link voltage is
controlled at 370 V; the capacitor voltage is 35 V; the maximum
ripple in this condition is about 1.9 A, which has been de-
creased greatly compared to traditional PWM strategy as shown
in Fig. 11.
A prototype has been built to verify the proposed system
and control method. TMS320LF2407DSP is used to realize the
control strategy. Fig. 14 shows the power board and controller
board utilized in the experimental veriﬁcation.

Fig. 10. Simulation waveforms with previous PWM scheme when Vdc =
200 V. (a) Waveform in line period; (b) waveform in carrier period.
Fig. 11. SimulationwaveformswithpreviousPWMschemewhenVdc =300 V.
Fig. 12. Simulation results with proposed PWM scheme when Vdc = 200 V.
(a) Waveform in line period. (b) Waveform in carrier period.
Fig. 15 shows the experimental waveforms with previous
PWM scheme when Vdc = 200 V in line frequency and carrier
frequency. The ripple current is about 6 A, six equal shoot-
through states exist in one switching cycle, which is coincide
with the simulation results. Fig. 16 shows the experimental
waveforms with previous PWM scheme when Vdc = 300 V.
The measured ripple current is about 3 A. Fig. 17 shows the
experimental waveforms with proposed PWM scheme when
Vdc = 200 V in line frequency and carrier frequency. In this
condition, the ripple current is decreased to 4 A, and the time
intervals of the six shoot-through states is not equal to each
other seen in Fig. 17(b). The dc-link voltage and output voltage
is the same as in Fig. 15. Fig. 18 shows the experimental
waveforms with proposed PWM scheme when Vdc = 300 V.
The ripple current is decreased to 1.9 A.

Fig. 13. Simulation results with proposed PWM scheme when Vdc = 300 V.
Fig. 14. Prototype in experiments. (a) Power board. (b) Control board.
The experimental results coincide with the simulations well.
With the proposed PWM scheme, the ripple current is dramat-
ically reduced by 33% compared with the previous method,
while keeping the same voltage boost and output voltage.
Fig. 15. Previous PWM scheme when Vdc = 200 V. (a) Waveform in line
period. (b) Waveform in carrier period.
Fig. 16. Previous PWM scheme when Vdc = 300 V.
The tested ripple current under different Vdc is shown in
Fig. 19. The upper curve is with the previous PWM scheme,
and the bottom curve is with the proposed PWM scheme. The
ripple current is reduced by 33% under different Vdc conditions,
thus can reduce the inductance.

Fig. 17. Proposed PWM scheme when Vdc = 200 V. (a) Waveform in line
period. (b) Waveform in carrier period.
Fig. 18. Proposed PWM scheme when Vdc = 300 V.
VI. CONCLUSION
A PWM scheme with minimum inductor current ripple for
ZSI has been proposed in this paper. The ripple current was an-
alyzed in detail under the present and proposed PWM scheme,
Fig. 19. Tested ripple current with the two PWM scheme under different Vdc.
and the realization of the proposed PWM scheme was de-
rived. The comparison of ripple current under these two PWM
schemes was given. Analysis, simulation, and experimental
results reveal that the proposed PWM scheme can reduce the
ripple current greatly, and thus smaller inductors can be utilized
in ZSI.
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Yu Tang received the B.S. and the Ph.D. de-
grees in electrical engineering from Nanjing Uni-
versity of Aeronautics and Astronautics (NUAA),
Nanjing, China, in 2003 and 2008, respectively.
He joined the Electrical Engineering Department
of NUAA in 2008 as a lecturer. He has published
more than 20 papers in journals and conference pro-
ceedings, and holds two China patents. His research
interests include power electronics in renewable en-
ergy generation.
Shaojun Xie was born in Hubei, China, in 1968. He
received the B.S., M.S., and Ph.D. degrees in elec-
trical engineering from Nanjing University of Aero-
nautics and Astronautics (NUAA), Nanjing, China,
in 1989, 1992, and 1995, respectively.
In 1992, he joined the Faculty of Electrical En-
gineering, Teaching and Research Division, and is
currently a Professor in the College of Automation
Engineering, NUAA. He has authored more than
80 technical papers in journals and conference pro-
ceedings. His main research interests include avia-
tion electrical power supply systems and power electronics conversion.
Jiudong Ding received the M.S. degree in electrical
engineering from Nanjing University of Aeronautics
and Astronautics, Nanjing, China, in 2011.
His research interests include power electronics in
renewable energy generation.

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