D
Journal of Energy and Power Engineering 6 (2012) 1869-1877
DAVID
PUBLISHING
Multi-Phase QR ZCS Switched-Capacitor Bidirectional
Power Converter for PV System Application
Yi-Pin Ko, Yuang-Shung Lee and Li-Jen Liu
Department of Electrical Engineering, Fu Jen Catholic University, New Taipei City 24205, Taiwan
Received: February 06, 2012 / Accepted: March 21, 2012 / Published: November 30, 2012.
Abstract: The multi-phase implementation in the QR (quasi resonant) ZCS (zero current switching) SC (switched capacitor)
bidirectional DC-DC converter structure has been proposed to reduce current ripple, switching loss and significantly increase the
converter efficiency and power density. This approach provides a more precise output voltage to obtain voltage conversion ratios from
the double-mode versus half-mode to n-mode versus 1/n mode. This is accomplished by adding a different number of
switched-capacitors and power MOSFET switches with a small series connected resonant inductor for forward and reverse schemes.
The size and cost can be reduced when the proposed converter has been designed with the coupled inductors. The simulation and
experimental results have been used to demonstrate the performance of the two-phase with and without coupled inductor interleaved
QR ZCS SC converters for bidirectional power flow control application, and an extending structure for N-phase is mentioned.
Key words: Quasi resonant zero current switching, multiphase DC-DC converter, switched capacitor bidirectional converter, PV
system.
1. Introduction
The bidirectional DC-DC converter along with
energy storage has become a promising option for
many power related systems, including hybrid vehicle,
fuel cell vehicle, renewable energy system and so forth.
It not only reduces the cost and improves efficiency,
but also improves the performance of the system.
Recently, clean energy resources such as photovoltaic
arrays and wind turbines have been exploited for
developing renewable electric power generation
systems. 
The bidirectional DC-DC converter is often used to
transfer the solar energy to the capacitive energy source
during the sunny time, while to deliver energy to the
load when the sun is not available. A photovoltaic
power system with bidirectional DC-DC converter is
shown in Fig. 1.
Corresponding author: Yuang-Shung Lee, professor,
research fields: power electronics, converter control and
lithium-Ion
batteries
equalization.
E-mail:
002877@mail.fju.edu.tw.
Fig. 1 Bidirectional DC-DC converter application in
photovoltaic power system.
A zero-current switching switched-capacitor
quasi-resonant (ZCS SC QR) converter that can be
operated at high switching frequency with less
switching loss for increased converter efficiency with
fewer switches has been proposed in Refs. [1-3].
Although the ZCS SC QR converter has numerous
advantages, its power flow control is only
unidirectional.
Bidirectional
DC/DC
power
conversion has received great interest in systems fed
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Multi-Phase QR ZCS Switched-Capacitor Bidirectional Power Converter for PV System Application
by DC power including electric vehicles, hybrid
energy systems, fuel-cell systems and PV generation
systems with energy storage units [4, 5]. The
bidirectionality in these applications involves current
flow while the polarity of the DC voltage at either end
remains unchanged. Applications in battery
equalization schemes where the stronger energy of
this system is transferred into the weaker energy
subsystem using a bidirectional power flow control
scheme [6-8]. A quasi-resonant bidirectional
switched-capacitor DC-DC converter can be designed
to operate at non-inverting mode or inverting modes
with constant frequency. The converter scheme can
achieve zero current soft switching and reduce the
MOSFET switch power losses to increase the
converter efficiency. The high switching current
stresses can also be reduced under the bidirectional
power flow control schemes [9-11]. The performances
of the single-phase switched-capacitor converters with
and without QR ZCS have been discussed and
compared in Refs. [12, 13]. The bidirectional DC-DC
converters with high voltage transfer ratios are
required in many practical applications such as
vehicles, renewable power systems and DC backup
energy systems like UPS. The multiphase designed
technologies are employed to increase the output
power and power density of the bidirectional power
converters for renewable energy storage applications.
The multi-phase bidirectional converters offer a
tempting solution for the applications mentioned
above when different voltage levels have to be
matched [14-19].
To improve the energy utilization performance, most
of the renewable energy systems include a
supplementary ESU (energy storage unit) in the
distributed generation system. The charged/discharged
power flow of the ESU can be controlled by the
bidirectional DC-DC converter. This paper introduces
a switched capacitor step up/step down DC-DC
quasi-resonant bidirectional converter designed to
operate with multi-phase interleaved integrated
coupling inductors. The triple-mode/trisection-mode
case will be used as an example. The advantages of the
proposed multi-phase QR ZCS SC bidirectional
DC-DC converters are low weight, small volume, low
current stress, high power density and high efficiency.
The proposed converter provides n to 1/n voltage
transfer ratio, allowing multiple voltage outputs, with
each phase of this converter containing 2n MOSFET
switches and a very small inductor connected with a
capacitor to construct resonant tanks [11, 20].
The analysis of the proposed multi-phase converter
shows a voltage conversion ratio of 3 to 1/3 under
various switched-capacitor network control strategies.
A designed example for the ZCS SC QR two-phase
converter was conducted to verify and validate the
predicted performance under the bidirectional power
flow control.
2. Topology
Converter
of
Proposed
Multiphase
The general structure of the proposed multiphase QR
ZCS SC DC-DC converter is shown in Fig. 2. The low
voltage side V1 and the high voltage side V3 can be
either source or output. It works by using the
interleaving concept turning the switch-QN and
switch-QP on alternately to transfer the source voltage
to load through capacitors at every single phase. Figs.
2a and 2b show the proposed two-phase bidirectional
converter with the interleaved control technology. A
delay dead-time is used to prevent the short circuit in
the voltage source loop. The switching time is shifted
to the other phase with the shifting time determined by
the number of phases [16]. In a two-phase structure,
switch-QN1 and switch-QN1′ turns on in a
complementary way, as shown in Fig. 3. The switches
(QN1, QP1′) and switches (QN1′, QP1) are turned on in a
complementary switching interval of the forward
power flow controlled converter.
Figs. 4a-4d and Figs. 5a-5d show the equivalent
circuit for the proposed non-inverting type
3-mode/-mode (triple-mode/ trisection-mode) ZCS SC
Multi-Phase QR ZCS Switched-Capacitor Bidirectional Power Converter for PV System Application
(a)
1871
(a)
(b)
(b)
Fig. 2 The proposed QR ZCS SC bidirectional DC-DC
converter for (a) N-phase, (b) two-phase.
(c)
Fig. 3
Typical waveforms of proposed two-phase
converter in 3-mode.
bidirectional resonant converter under forward and
reverse power flow control, respectively. There are
four operational stages in the converter for the forward
power flow control that will be analyzed and designed
as shown in the following:
(1) Stage 1 [t0-t1]
Switch QN1 in phase 1 and QP1′ in phase 2 are
turned on simultaneously in this state. When QN1 in
(d)
Fig. 4 Equivalent circuit for various operation stages of
the proposed ZCS SC QR bidirectional resonant DC/DC
converter under forward power flow. (a) State 1 [t0-t1]; (b)
State 2 [t1-t2]; (c) State 3 [t2-t3]; (d) State 4 [t3-t4].
phase 1 is turned on in zero current states, the input
power source V1 is series connected with C2b, and
charged into C2a and C3a, respectively. When QP1′ in
phase 2 is turned on, the energy of input source V1 is
charged into C1b′, and the energy stored in C2a′ is
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Multi-Phase QR ZCS Switched-Capacitor Bidirectional Power Converter for PV System Application
Substitute Eq. (2) into Eq. (1):
diL1
di
1 di
(3)
 Lr L 2  Lr Lr
dt
dt
2
dt
and iL 2 are the inductor currents in phase
Lr
where iL1
1 and phase 2, respectively.
Thus:
1 di
V1  VC ( k 1) a  Lr Lr  VCkb
2
dt
1
dV
iLr  (n  1)Cr Ckb
2
dt
(a)
(4)
(5)
Substitute Eq. (5) into Eq. (4), to solve the set of
differential equations, it can get:
1 V 0 I 0TS  0 Z 0
VCkb 
cos  0 ( t  t 0 )  VC ( k 1) a  V1 (6)
V1
4
iL1  
(b)
(7)
(2) Stage 2 [t1-t2]
Zero current switching. The stored energy is
discharged to the load.
VCkb 
1 V 0 I 0 TS  0 Z 0
 VC ( k 1) a  V1
4
V1
iLr  0
(8)
(9)
(3) Stage 3 [t2-t3]
Switch QP1 in phase1 and QN1′ in phase 2 are turned
on simultaneously in this state. When QP1 in phase 1 is
turned on in zero current state, the energy of input
source V1 is charged into C1b, and the energy stored in
C2a is discharged into C2b. When QN1′ in phase 2 is
turned on, the input power source V1 is series connected
with C2b′, and charged into C2a′ and C3a′, respectively.
(c)
(d)
Fig. 5 Equivalent circuit for various operation stages of
the proposed ZCS SC QR bidirectional DC/DC resonant
converter under reverse power flow. (a) State 1 [t0-t1]; (b)
State 2 [t1-t2]; (c) State 3 [t2-t3]; (d) State 4 [t3-t4].
charged into C2b′. The multiphase converter shares
inductance current on each phase.
1 diLr
Lr
 VC1b
2
dt
di
 Lr L 2  VCkb
dt
V0 I 0TS 0 Z 0
sin  0 (t  t0 )
8V1
VCka 
(1)
VCka
(2)
diL1
 VCkb
dt
dV
iLr  2(n  1)Cr Ckb
dt
V1  VC ( k 1) a  Lr
(10)
(11)
Substitute Eq. (11) into Eq. (10), to solve the
dynamic equations, it has been gotten:
VCkb  VCka 
VCkb I 0TS 0 Z 0
cos 0 (t  t2 )
4V1
VCkb I 0TS 0 Z 0
sin 0 (t  t2 )
4V1
V I T Z
iL2  Ckb 0 s 0 0 sin 0 (t  t2 )
8V1
iLr 
(12)
(13)
(14)
Multi-Phase QR ZCS Switched-Capacitor Bidirectional Power Converter for PV System Application
1873
(4) Stage 4 [t3-t4]
The switch is turned off at this zero current state to
obtain ZCS turn-off. The stored energy is discharged
to the load.
VCkb I 0TS 0 Z 0
4V1
iLr  0
VCkb  VCka 
(15)
(16)
According to stages 1-4, all the resonant angular
frequencies are the same, so we can obtain a duty rate
of QP1, QP1′, QN1 and QN1′ for zero current switching
conditions as ΛP1TS ≧ π/ωr and ΛN1TS ≧ π/ωr, where
ΛP1 and ΛN1 are the QP1, QP1′, QN1 and QN1′ duty ratios,
TS is the switching duty of the proposed bidirectional
converter. It is serviceable to use a multi-phase
scheme to increase the output current and output
power. However, it requires an inductor in every
single phase, causing higher cost, larger volume and
heavier weight. Using the coupled inductor method
may be an easy solution and beneficial for reducing
the size, volume and inductor cost.
3. Design of Coupled Inductance
The QR ZCS SC DC-DC converter needs only a
small inductor to create a resonant tank to achieve
zero current switching. Because more phases require
more inductors in a multi-phase structure, higher cost
is produced in the cores with much bigger volume.
Therefore, simple coupling inductor integration is
added to simplify the multi-phase converter [17-19].
Figs. 6a and 5b show the equivalent converter circuits
of the proposed converter with the coupled inductor in
the two-phase topology under forward and reverse
power flow controlled directions, respectively.
In the two-phase case, the second phase shifts 180
degrees with an inverse voltage across the inductance
value changes when a mutual effect exists. The
relationship between equivalent inductance and self
inductance can be determined as below, where K is the
coupling coefficient, Leq and Ceq are inductance and
capacitor of the resonant circuits, and Λ is the duty
cycle of converter. The equivalent resonant
inductance and capacitance of the two-phase QR
(a)
(b)
Fig. 6 Equivalent two-phase QR ZCS SC converter circuit
with coupling inductor for (a) forward (b) reverse power
flow control schemes.
ZCS SC bidirectional converter with the coupled
inductor will be derived as follows. The switch output
voltage across the series connected resonant capacitor
and inductor can be expressed as:
V
C L1
= L
VCL 2  L
di
L r1 + M
dt
di Lr 2
dt
M
di
Lr 2 + 1 i
 L r 1 dt + V d (17)
dt
Cr
di Lr 1
dt

1
Cr 2
 i Lr 2 dt  Vd (18)
In the QR-ZCS SC converter, assuming that
Cr 1  Cr 2  C ,
Lr1  Lr 2  L . From Eqs. (17) and
(18), it gets:
Vd
diiLr 2 VCL 2 M diLr1 1
=
 iiLr 2 dt dt
L
L dt
LC
L
Substitute Eq. (19) into Eq. (17), it obtains:
(19)
V
V
di
M diLr1 1
V =L Lr1 +M( CL2 -  iLr2dt - d )
CL1
dt
L L dt LC
L
1
+  iLr1dt+Vd
C
(20)
where the mutual inductor coupling coefficient is K =
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Multi-Phase QR ZCS Switched-Capacitor Bidirectional Power Converter for PV System Application
M/L, then Eq. (20) can be simplified as:
di
K
2 di
V
- KV
= L Lr1 - K L Lr1 -  i
dt
CL1
CL2
dt
dt
C Lr 2
(21)
1
 KVd +  iLr1dt +Vd
C
Using the voltage-second balancing relationship
and iLr 2  iLr1 , V2 = -

'
V1 .
Eq. (21) can be simplified as:
V =
CL1
2
(1- K )
di
(1+K) 1
(1- K)
L Lr1 +
V
 iLr1dt +


 d
dt
C
(1+K )
(1+K )
(1+K )
'
'
'
(22)
(a)
where Vd is the forward diode voltage drop and so
very small that it can be ignored. From Eq. (22), the
equivalent resonant inductance and capacitance can be
expressed as:
L eq =
(1 - K
(1 + K
2

'
(1 + K
C eq =
)
(23)
L
)

'
)
C
(1 + K )
(24)
The coupling inductor interleaving technology can
improve the dynamic performance and reduce the
inductance volume, in other words, reducing cost and
providing better power density. The equivalent
inductance and capacitance are shown in the forward
scheme QR ZCS SC converter. The reverse scheme can
be proved similarly. Extending to four-phase, the
function obtained in Eqs. (23) and (24) is still
applicable. Figs. 7a and 7b show the coupling in the
four-phase topology both forward and reverse schemes.
In the four-phase converter, every phase shifts 45
degrees from the other, phase-one and phase-three
coupling as two-phase structure, and phase-two and
phase-four as well.
4. Simulation and Experimental Results
This paper proposes a two-phase zero current
switching switched capacitor bidirectional 3 to 1/3
DC-DC converters. Multi-phase interleaving optimize
the conversion efficiency and higher output power is
(b)
Fig. 7 Four-phase converter with inductor coupling under
(a) forward (b) reverse power flow control schemes.
achieved, although it takes more components which
means higher cost. The designed switching frequency
is f S  151.5 kHz , the resonant inductance and
capacitance are Lr  1.2  H and Cr  0.33 F , the
duty ratio are Λ1 = Λ2 = 0.45, the input voltage is 48
V, the Schottky diodes and MOSFET switches are
selected by SBR4060 and IRF3710, respectively.
Figs. 8a and 9a show the simulation and
experiments waveforms Vgs_QN1, Vgs_QP1’, Vgs_QP1,
Vgs_QN1’, IL, IL’, VC3a(t), and output power Pc3a of
the proposed QR ZCS SC bidirectional converter for
the forward power flow control. Figs. 8b and 9b show
the simulation and experiment waveforms Vgs_QN3,
Vgs_QP3’, Vgs_QP3, Vgs_QN3’, IL, IL’, VC1a(t), and
output power Pc1a of the proposed QR ZCS SC
bidirectional converter for the reverse power flow
control. The experimental results agree with the
Multi-Phase QR ZCS Switched-Capacitor Bidirectional Power Converter for PV System Application
(a)
(b)
Fig. 8 Simulation waveforms of two-phase trisection-mode
converter for (a) triple-mode (b) trisection-mode at output
200 W.
1875
simulations, and the zero-current switching
performance and designed feature are achieved in the
demonstrated waveforms.
Fig. 10 show the simulated efficiencies
comparisons of the triple-mode/trisection-mode
two-phase QR ZCS S-C converters. The highest
efficiency of the two-phase converter with coupled
inductor in triple-mode is about 98.8% when the
output power is 100 W. This is higher than 97.9% two
phase without coupled inductor and 94% for the single
phase converter. The highest efficiency of the
two-phase converter with coupled inductor in
trisection-mode is about 95.3% when the output power
is 200 W. This is also higher than 93.6% for the single
phase converter when the output power is 200 W, but
lower than 96.8% two phase without coupled inductor.
According to the experimental efficiencies as
shown in Fig. 11, the authors found that the efficiency
could be improved significantly by reducing the
number of phase when the converter can support the
(a)
(a)
(b)
Fig. 9
Experimental waveforms of two-phase
trisection-mode converter for (a) triple-mode (b)
trisection-mode at output 200 W.
(b)
Fig. 10 Simulation efficiencies of single phase converter
and two-phase converter efficiencies with/without coupled
inductor (a) forward (b) reverse power flow schemes,
respectively.
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Multi-Phase QR ZCS Switched-Capacitor Bidirectional Power Converter for PV System Application
requires more components, the efficiency and power
density increase in the converter which can be easily
extended to n / 1 n mode. From the tradeoff point of
view, the proposed approach is still very useful for
industrial applications such as bidirectional battery
charger.
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(b)
Fig. 11 Experimental efficiencies of single phase converter
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5. Conclusions
A QR ZCS bidirectional DC-DC converter with
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