 B. Boost Mode Operation ( Vi
In the boost mode, a shootthrough interval occurs at the gate signal, and energy is stored in the qZsource inductors. The wellknown voltage equations in the shootthrough (boost) mode are as follows:
where
D_{sh}
is the switch shootthrough duty ratio of the converter that is defined as
D_{sh}
=1−
D
.
Therefore, the voltage gain of the proposed converter in the boost mode is expressed as follows:
Given that
D_{sh}
=1−
D
, Equation (5) can be rewritten as follow:
Fig. 5
shows the voltage gain plot of the proposed converter as
D
varies when
n
=1. As expected, the desired buck and boost functions can be achieved by modulating D.
Fig. 4
shows the key waveforms of the proposed converter in both buck and boost modes. Given the interleaving effect, the output (or input) current ripple is reduced. However, all inductor current ripples are not reduced even with the interleaving action. Thus, they remain bulky and heavy. A coupled inductor is used in this study to decrease inductor current ripples.
Key waveforms of the proposed parallelconnected qZsource FB DCDC converter.
Voltage gain of the proposed converter (n=1).
III. THE COUPLED INDUCTOR AND ITS EFFECTS
This section discusses the effect of the coupled inductor on decreasing ripple currents.
Fig. 3
shows that, the four inductors in the qZsource networks and the two inductors in the output filter are coupled. The two output filter inductors (
L
_{o1}
,
L
_{o2}
) are first selected for the analysis because their operation is similar to that of the conventional twophase interleaved buck converter
[7]

[13]
.
The two main issues of interest in the interleaved buck converter is the inductor (phase) current ripple and output current ripple, which is the sum of the two inductor currents. The current ripples in a noncoupled inductor are first analyzed to compare the ripple reduction effect.
 A. NonCoupled Inductor
Fig. 6
shows the voltage waveforms across
L
_{o1}
and
L
_{o2}
. Four operating states are observed. The detailed voltage and current direction in each state is summarized in
Table I
by assuming that
v
_{rec1}
=
v
_{rec2}
=
nV_{pn}
.
Voltage waveform of the output filter inductor.
OUTPUT INDUCTOR CURRENT VARIATION OF A NONCOUPLEDINDUCTOR
OUTPUT INDUCTOR CURRENT VARIATION OF A NONCOUPLEDINDUCTOR
Given that the two inductors are noncoupled, no interaction occurs between them and the inductor current ripple is calculated as follows:
If
L
_{o1}
=
L
_{o2}
=
L
,then the inductor current ripple in a noncoupled case is expressed as follows:
Considering that the output current is the sum of
i
_{L1}
and
i
_{L2}
, then it increases in State 1 and decreases in State 2. This cycle is repeated in States 3 and 4. Consequently, the output current ripple occurs twice at a given period
T_{s}
. The equation for the output current ripple is as follows:
Equations (7) to (10) are valid when
D
<0.5. When
D
>0.5, the equations can be derived similarly as summarized in
Table II
[7]
. The inductor and output current ripples of the twophase interleaved converter are compared with those of its singlephase counterpart to determine the ripple current reduction effect of the former. The results are summarized in
Table II
. Unlike in the singlephase converter, the output current ripple in the twophase case is reduced significantly and its maximum effect is reached when D approaches 0.5. The inductor current ripples, however, remain unchanged
[8]
,
[9]
.
CURRENT RIPPLE COMPARISON
CURRENT RIPPLE COMPARISON
 B. Coupled Inductor
Fig. 7
depicts the proposed coupled inductor structures for both the qZsource networks and output filter inductors. The secondary side of the transformer of the proposed converter is redrawn (
Fig. 8
.) to analyze the coupled inductor. The coupled inductor is represented as an ideal 1:1 transformer, two leakage inductances (
L
_{l1}
,
L
_{l2}
), and a magnetizing inductance (
L_{m}
). Notably, the ideal transformer is connected out of phase with the polarity dots on the opposite ends
[8]
. Therefore,
Coupled inductor design for the proposed converter
Secondary side of the proposed converter with a coupled inductor.
Similar to in the noncoupled case, four operation states exist in the coupled case. Regardless of the operation states, the following relationships are always applied:
1) State 1
[
0~
DT_{s}
]
: Based on
Figs. 6
and
8
, the following equation is applied in State 1:
From Equations (12) to (14),
V
_{Ll1}
and
V
_{Ll2}
are expressed as follows:
By assuming that
L
_{l1}
=
L
_{l2}
=
L_{l}
and substituting Equations (15) to (16) into Equation (13),
V
_{Lm}
is expressed as follows:
Base on Equations (15) to (17), defining
p
=
L_{m}
/
L_{l}
yields the following:
The output current ripple is expressed as follows:
2) State 2
[
DT_{s}
~
T_{s}
/2
]
: In State 2,
V
_{Lo1}
=
V
_{Lo2}
=
V_{o}
. Thus,
When Equations (21) to (22) are substituted into Equation (13), then
V
_{Lm}
=0. Hence,
3) State 3
[
T_{s}
/2~(
T_{s}
/2+
DT_{s}
)
]
State 3 is similar to State 1. The only difference is that
v
_{Lo1}
=
V_{o}
and
v
_{Lo2}
=
nV_{pn}

V_{o}
. Using methods similar to those in State 1, the inductor and output current ripple in State 3 are derived as follows:
4) State 4
[
T_{s}
/2+
DT_{s}
)~
T_{s}
]
: State 4 is exactly the same as State 2.
According to the state analysis of the coupled inductor, the output current ripple in the coupled case also occurs twice at a given period
T_{s}
. The coupling ratio
p
does not affect the output current ripple
[7]
. Equations (10) and (20) show that if
L_{l}
is equal to the value of the individual inductor L in the noncoupled case, then the output current ripples in both the noncoupled and coupled inductors are the same.
Unlike those in the noncoupled case, the inductor current ripples in the coupled inductor change direction twice per cycle as the output current ripple. The two inductor currents become equal and inphase as
p
increases to infinity (perfect coupling). Thus, the coupling ratio
p
has a significant effect on inductor current ripples, although it does not affect output current ripples
[7]
.
Representing
L_{l}
and
L_{m}
in the coupled inductor (or transformer) in terms of the coupling coefficient
k
rather than the coupling ratio
p
is more intuitive because we are more familiar with
k
. Based on the general coupled inductor theory,
L_{l}
and
L_{m}
are represented as follows
[14]
:
where
L_{s}
the selfinductance of the coupled inductor.
Therefore, the relationship between
p
and
k
is as follows:
Using Equation (29), Equations (18) and (19) can be rewritten as shown in
Table III
. The inductor current ripple depends on the
D
and
k
values. Therefore, the ratio of the inductor current ripple of a coupled inductor (Δ
i
_{L,cp}
) normalized with respect to that of a noncoupled inductor(Δ
i
_{L,nc}
) is expressed as follows:
CURRENT RIPPLE OF THE FILTER INDUCTOR AND OUTPUT
CURRENT RIPPLE OF THE FILTER INDUCTOR AND OUTPUT
The relationship in Equation (30) is plotted in
Fig. 9
. As shown in the figure, a small current ripple can be achieved with a strong coupling coefficient. The same analysis can be readily applied to the coupled inductor in the qZsource network. The only difference is the voltage across the qZsource network inductors.
Inductor current ripple of a coupled inductor normalized with respect to a noncoupled inductor.
Fig. 7
(a) shows, that the four inductors (
L
_{1}
to
L
_{4}
) in the qZsource network are coupled.
L
_{1}
and
L
_{2}
are wound on
the same leg. Similarly,
L
_{3}
and
L
_{4}
are wound on the other leg. Given that the operations of top and bottom qZsource networks are the same as that of the output coupled inductor, the same ripple reduction effect occurs in the qZsource inductor currents and in the input current ripple.
IV. EXPERIMENT RESULTS
A 4 kW prototype converter is built and tested to verify the performance of the proposed converter.
Table IV
illustrates the electrical specifications of the proposed converter, including the detailed parameters of the coupled inductors. The transformer turns ratio is set to 1:1.
ELECTRICAL SPECIFICATIONS OF THE PROPOSED CONVERTER AND PARAMETERS OF THE COUPLED INDUCTORS
ELECTRICAL SPECIFICATIONS OF THE PROPOSED CONVERTER AND PARAMETERS OF THE COUPLED INDUCTORS
Fig. 10
shows the 4 kW proposed converter and the photo of the coupled inductor built for this study. similar core structures are used for both the qZsource inductors and output filter inductors.
Figs. 11
and
12
show the transformer voltage and current waveforms of the proposed converter that operates in buck and boost modes. Given that the transformer current is a reflection of the output filter inductor current, the transformer current waveforms of the coupled case follow the inductor current waveforms.
Photos of the 4 kW prototype converter and the coupled inductors.
Waveforms of transformer voltages and currents at buck mode. ( V_{tr1,2}[250V/div.],i_{tr1,2}[10A/div.],[10μs/div.] V_{i}=600V, V_{o}=400V, and P_{o}=4kW )
Waveforms of transformer voltages and currents at boost mode. ( V_{tr1,2}[250V/div.],i_{tr1,2}[10A/div.],[10μs/div.] V_{i}=200V, V_{o}=400V, and P_{o}=4kW )
Fig. 13
shows the current waveforms of the output filter inductor and output currents for both noncoupled and coupled cases. As expected, the inductor current ripples are reduced significantly with the coupled inductor while maintaining the same output current ripple. The two inductor currents are nearly in phase.
Waveforms of the output filter inductor and output current. ( [2A/div.],[5μs/div.], V_{i}=600V, V_{o}=400V, P_{o}=4kW )
Fig. 14
shows the current waveforms of the qZsource inductors and input currents for both noncoupled and coupled cases. The waveforms are similar to the case of output filter inductors.
Waveforms of the qZsource inductor and input current. ( [5A/div.],[5μs/div.], V_{i}=200V, V_{o}=400V, P_{o}=4kW )
Fig. 9
shows that the coupled inductor exhibits the smallest current ripple at
D
=0.5, which can be identified in
Fig. 15
.
Waveforms of the output filter inductor and output current. ( [2A/div.],[5μs/div.], V_{i}=600V, V_{o}=300V, D=0.5 )
Fig. 16
shows the efficiency curves of the proposed converter that is measured as input voltage and output power vary.
Efficiency of the proposed converter.
V. CONCLUSIONS
In this study presents a parallel operation of a qZsource FB DCDC converter that uses a coupled inductor. With this configuration, the proposed converter exhibits the following features.

The converter has both buck and boost functions without increasing the switch voltage rating. The output voltage can be larger or smaller than the input voltage. Thus, the proposed converter has a desirable circuit topology when its input voltage range is wide.

The converter can be short and opencircuited without damaging switching devices. Therefore, it is resistant to EMI noise. Moreover, its robustness and reliability are significantly improved.

The converter exhibits all the advantages of paralleling power converters such as modularity, ease of maintenance, (n+1) redundancy, and high reliability.
A 4 kW prototype that consist of two parallel qZsource FB DCDC converters is built and successfully tested to verify the operation principle of the proposed converter.
The converter is as valuable as a renewable energy source with a wide output range. It has an applied battery charge discharge system with a low current ripple. Extending power by parallel connection is also easy. By using buck and boost functions, reducing the current ripple, and realizing its parallel operation, the proposed converter can be a good candidate in such systems because requires wide input voltage variation and exhibits high reliability.
Acknowledgements
This research was supported by the Kyungpook National University Research Fund, 2013.
BIO
Hyeongmin Lee was born in 1982. He received his B.S. in Electronics Engineering and M.S. in Electrical Engineering from Kyungpook National University, Daegu, Korea, in 2011 and 2013, respectively. He is currently working toward a Ph.D. in electrical Engineering. His research interests are power conversion systems and power control systems.
HeungGeun Kim was born in Korea in 1956. He received his B.S., M.S., and Ph.D. in Electrical Engineering from Seoul National University in 1980, 1982 and 1988, respectively. He has been with the Department of Electrical Engineering at Kyungpook National University since 1984, where he is currently a full professor and the director of the Microgrid Research Center. He was a visiting scholar at the Department of Electrical and Computer Engineering of the University of WisconsinMadison from 1990 to 1991 and the Department of Electrical Engineering of Michigan State University, USA from 2006 to 2007. His current research interests include AC machine control, PV power generation, and microgrid systems.
Honnyong Cha received his B.S. and M.S. in Electronics Engineering from Kyungpook National University, Daegu, Korea, in 1999 and 2001, respectively, and Ph.D. in Electrical Engineering from Michigan State University, East Lansing, Michigan, USA in 2009. He was a research engineer with the PSTEK, Ansan, Korea from 2001 to 2003. He also worked as a senior researcher at the Korea Electrotechnology Research Institute, Changwon, Korea from 2010 to 2011. He joined Kyungpook National University as an assistant professor at the School of Energy Engineering in 2011. His main research interests include high power DCDC converters, DCAC inverters, Zsource inverters, and power conversion for electric vehicles and wind power generation.
TaeWon Chun was born in Korea in 1959. He received his B.S in Electrical Engineering from Pusan National University in 1981 and his M.S. and Ph.D. in Electrical Engineering from Seoul National University in 1983 and 1987, respectively. He has been a member of the faculty of the Department of Electrical Engineering, Ulsan University, where he is currently a full professor since 1986. He was a visiting scholar at the Department of Electrical and Computer Engineering, University of Tennessee, USA. He was also a visiting scholar with the Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, USA from 2005 to 2006. His current research interests include gridconnected inverter systems and AC motor control.
TaeWon Chun was born in Korea in 1959. He received his B.S in Electrical Engineering from Pusan National University in 1981 and his M.S. and Ph.D. in Electrical Engineering from Seoul National University in 1983 and 1987, respectively. He has been a member of the faculty of the Department of Electrical Engineering, Ulsan University, where he is currently a full professor since 1986. He was a visiting scholar at the Department of Electrical and Computer Engineering, University of Tennessee, USA. He was also a visiting scholar with the Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, USA from 2005 to 2006. His current research interests include gridconnected inverter systems and AC motor control.
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