Control Method of Flying Capacitor Converter
Operated in Discontinuous Current Mode
and Critical Current Mode
Jun-ichi Itoh, Ryoichi Ishibashi, Hoai Nam Le,
Nagisa Takaoka, Keisuke Kusaka
Dept. of Electrical, Electronics and Information
Engineering
Nagaoka University of Technology
Nagaoka, Niigata, Japan
itoh@vos.nagaokaut.ac.jp
Abstract— This paper proposes the control method of a threelevel flying-capacitor converter (FCC), which is operated indiscontinuous-current-mode (DCM) and critical current mode(CRM) to reduce the current ripple. An inverter connected to asingle-phase grid requires a boost chopper and grid-connected
inverter. In particular, reducing the volume of the boost inductorin the boost chopper is required. The DCM method is applied inorder to minimize the volume of the boost inductor. However, theswitching devices with high current rating are required due to ahigh current ripple when DCM is applied to a typical boost
converter. In addition, FCC reduces the peak current of the boost
inductor by the charging and discharging periods of the flying
capacitor. In the proposed control method, FCC is designed to be
operated in CRM at heavy load and DCM at light load. Due to thecharging and discharging of the flying capacitor, the inductor
current ripple in FCC is reduced compared to that of the typicalboost converter with the same inductance. The validity of the
proposed control method is confirmed with a 1-kW prototype. As
a result, an efficiency of 96.2% is achieved at the 1-kW output
power and the boost ratio of three.
Keywords—Discontinuous Current Mode; Flying capacitor
converter

I. INTRODUCTION
In recent years, photovoltaic power generation systems haveattracted attention as renewable power sources [1-6]. In general,
converter topologies for these systems consists of a boost circuit
and a grid-tied inverter. High power density and high efficiency
are required for these power converters. In particular, the boost
inductor in the boost converter occupies a large volume in thesystem. Therefore, miniaturization of this boost inductor isstrongly demanded [7].
One of the ideas to downsize the boost inductor is applying
discontinuous current mode (DCM) to an inductor current
control [8-11]. DCM reduces the inductor volume due to therequired inductance in DCM is smaller than continuous current
mode (CCM). However, the increased peak value of the current
may increase conduction loss of switching devices and copper
loss of the inductor. A large current ripple occurs as comparedKatsutaka Tanabe
Omron Co., Ltd.
Kusatsu, Shiga, Japankatsutaka_tanabe@omron.co.jp

with CCM in the trade-off of a small inductor when DCM isapplied to the boost converter. This high current ripple
significantly increases the conduction loss in the switching
devices, requiring a larger heat sink. Hence, the effect on theminiaturization of a system by the DCM operation in the boost
converter is restricted.
As a method of reducing the peak current value, there is athree-level flying capacitor converter (FCC) to which DCM isapplied [12]. Further inductor volume reduction is expected by
combining the inductor volume reduction effect of DCM and thecurrent ripple reduction effect of FCC [13]. In the literature [12],the boost inductor current waveform is controlled to betriangular. Thus, the effect of reducing the peak value of thecurrent passing through the element is insufficient since thecurrent peak value is more than twice the average current. Also,in the CCM operation, the flying capacitor voltage converges toapproximately half of the output voltage without controlling.
However flying capacitor voltage is not balanced in the DCM
operation. The control method of the flying capacitor voltage has
not been mentioned in the literature [12].
This paper proposes a DCM control method for a three-level
FCC in order to increase the power density of a DC-DC
converter. The proposed control operates FCC in four modes;
two of which are same as these in the boost converter, whereas
the other two modes are charging and discharging modes of theflying capacitor. Thus, this results in the operation of FCC withcritical current mode (CRM) at heavy load and under DCM atlight load. Due to the charge/discharge of the flying capacitor,
the peak of the inductor current is reduced, resulting in thedecrease in the conduction loss as well as the turn-off loss. The
originality of this paper is the clarification of the duty-ratio
calculation for FCC operated under DCM to achieve the current
ripple. The proposed control method is tested in experimental
results.

II. CIRCUIT CONFIGURATION
A. Three-level Fling Capacitor Converter
Figure 1 shows the FCC. The number of switching devicesof the typical boost converter is two, whereas, the number of
elements of FCC is four. Although the number of switching
devices increases, the voltage which is applied to each switching
device is half of that in the boost converter. Therefore, sincedevices with low on-resistance are used, it is possible to achieve
the same conduction loss with the same RMS current. In thispaper, DCM and CRM are applied to FCC in order to reduce theboost inductor current ripple, decreasing the RMS current value
against average current value. Furthermore, since the required
inductance value by applying DCM is reduced, it is possible todownsize the inductor. Therefore, both high efficiency andminiaturization are achieved with the proposed method.

Fig. 1. Circuit diagram of three-level flying capacitor converter.

B. Boost inductor current of each operation modes
Figure 2 shows the operation modes of FCC [14]. In the
proposed method, the current iL flowing through the inductor L
is controlled using four modes; Mode I to VI. Details of eachmode are described as following.
Mode IIn Mode I, energy is stored in L by turning on S3 and S4. The
slope a1 of the inductor current in this mode is expressed as

a1 =

vin
L

(1),

where vin is the input voltage, L is the inductance value of theboost inductor.

Fig. 2. Operation modes of flying capacitor converter.

Mode IIIn Mode II, by turning on S2 and S4, the energy is stored inCfc. The slope a2 of the inductor current in this mode is expressed
as

a2 =

vin − v fc

(2),

L

where vfc is the voltage of the flying capacitor Cfc.
Mode IIIIn Mode III, by turning on S1 and S3, the energy stored in Cfc
and L is released to the output side vdc. The slope a3 of theinductor current in this mode is expressed as

a3 =

(

vin − vdc − v fc)

L

where vdc is output voltage.
Mode IV(3),

Fig. 3. Inductor current waveform and gate signals of MOSFETs of FCC
in rated power.(rated load mode)

In Mode IV, by turning on S1 and S2, the energy stored in L
is released to the output side. The slope a4 of the inductor current
in this mode is expressed asa4 =vin − vdc
L

(4).

Figure 3 shows the inductor current waveform in eachswitching mode during one switching cycle. This control
method is obtained by adding Mode II and Mode III to theoperation mode of the boost converter, which is composed ofMode I and Mode IV. Consequently, the inductor current iL
becomes a trapezoidal waveform. The current peak is reduced ascompared with the boost converter when the same power istransmitted.

voltage is assumed to be 2 or more. The slope a2 and a3 in (2)and (3) are equal.
The sum of the average power in each switching mode equals
to the transmission power, which is expressed as
1
1
I pk 1 D1Tsw + I pk 1 + I pk 3 (1 − D1 − D4 ) Tsw
2
2
1+ I pk 3 D4Tsw = I aveTsw
2(

A. Heavy load region
In this section, a derivation method of the duty ratio of eachmode is described. The duty ratio is determined so that the boost
inductor current becomes CRM in heavy load. In this control,
since there are four switching operation modes, it is necessary toobtain four switching duties. Here, the current peak values Ipk1,
Ipk2, and Ipk3 in the respective operation modes are expressed as
vin
D1Tsw
L

I pk 2 = A2 D2Tsw + I pk 1 =I pk 3 = A4 D4Tsw =(5),vin − v fc
L

D2Tsw + I pk 1

vin − vdc
D4Tsw
L

D4 =

2vin
+ 1 + D4
vdc

(11).

(6),
1
1
I pk 1 + I pk 2 D2Tsw − I pk 2 + I pk 3 D3Tsw = 0
2
2

(

(7),

(

)

(12).

1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0

(8).

The flying capacitor voltage vfc is a half value of the output
voltage vdc, and the ratio of the input voltage to the output)

From (14), (15), D4 and D1 are represented as

Note that the operation of FCC under CRM at heavy loadsuppresses the increase in the current peak compared to DCM.

Fig. 5. Transition of current waveform according to load

(10),

vdc

In FCC, in order to keep the voltage of Cfc constant, the time
product of the current flowing through Cfc must be controlled to
be zero during one switching period. Therefore, the duties aredesigned so that the current time products of iL in Mode II andMode III are equal, expressing as

As FCC is operated under CRM at heavy load, the sum of
the four duties is expressed as(a)Maximum power (condition A of Fig. 4)

vin − −vin 2 + vin vdc − 2 I ave Lf sw vdc

D1 = −

where D1, D2, D3, and D4 are the duties in the respective
operation modes in Fig. 3, Tsw is the switching period.

D1 + D2 + D3 + D4 = 1(9).

From (10) and (11), D1 and D4 are represented asIII. DERIVATION OF SWITCHING DUTY RATIO

I pk 1 = A1 D1Tsw =

)

0.0

5.0

10.0

15.0

Fig. 4. Relationship between average current and duty. (Heavy loadmode)(b)Midium power(c)Minimum power(condition B of Fig. 4)

D2 =

−B +

B 2 − 4 AC
2A

D3 = D23 − D2

(13),

(14),

where

(15).

Figures 4–5 shows the relationship among the duties and theboost inductor average current and the current waveform
variation of each load when the voltage condition and circuit
parameters are as an example. As can be seen in Fig. 4, input
average current Iave has an upper limit and a lower limit because
all of the duty must be taken only positive. This is because theslope of the current waveform depends on the voltage conditions
and the circuit parameters as shown in Fig. 5 (a) and (c).
Therefore, this strategy is applied only in heavy load region.
B. Light load mode
In this section, the operation mode for a light load is
described. This control method is obtained by adding the zerocurrent period after Mode III. The derivation method of the duty
for the light load is described below.
Figure 6 shows the inductor current waveform in eachswitching mode during one switching cycle. Here, the current
peak values Ipk1 and Ipk2 in the respective operation modes are
expressed as (5 – 6). From the previous section, the slope a2equals to a3 due to the flying capacitor voltage vfc is half of
output voltage vdc. From this relationship, D23 that is sum ofMode II and Mode III period expressed as

D23 = D2 + D3 =2vinD1
vdc − 2vin

1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0

5.0

10.0

15.0

Fig. 7. Relationship between average current and duty. (light load mode)

In FCC, in order to keep the voltage of Cfc constant, the time
product of the current flowing through Cfc must be controlled to
be zero during one switching period. Therefore, the duties aredesigned so that the current time products of iL in Mode II andMode III are equal, expressing as (12). Substituting (5) and (6)for (12), D3 and D2 is expressed as

D3 =

vin 2
D1
vdc − 2vin

(19),

(16).

D2 = D23 − D3

The sum of the average power in each switching mode equals
to the transmission power, which is expressed as
1
1
I pk 1 D1Tsw + I pk 1 D23Tsw = I ave Tsw
22Fig. 6. Inductor current waveform and gate signals of MOSFETs of FCC
in rated power.(rated load mode)

Duty Ratio D23 = 1 − D1 − D4
 A = 2  v − vdc 
 in


2 



 B = 3vin D1 −  vin − vdc  D23 − ( vin − vdc ) D4



2 


C = {−vin D1 + ( vin − vdc ) D4 } D23(17).

From (5), (6), (16) and (17), D1 is represented as(20).

Figure 7 shows the relationship among the duties and theinductor average current when the voltage condition and circuit
parameters are the same as in the previous section. As can been
seen in Fig. 7, since the sum of the duties is possible to take lessthan 1, it is confirmed that there are an upper limit value for thevalue that the average current Iave is possible to generate.
IV. FLING CAPACITOR VOLTAGE CONTROL

D1 = 2 LI ave f sw

vdc − 2vin
vin vdc(18).

Figure 8 shows the flying capacitor voltage waveform ineach switching mode during one switching cycle. In the previous
section, the duty ratio is derived under the assumption of that theflying capacitor Cfc voltage vfc is kept at half of the DC-link
voltage. However, the voltage of flying capacitor varies since
Mode II and Mode III charge and discharge the flying capacitor.
Furthermore, the inductance information of the boost inductor isrequired in calculating the duty ratio, but the actual inductancevalue varies depending on current and heat. Therefore, the flying
capacitor voltage may diverge since an error occurs in the duty
calculation. Also, (12) does not satisfy. Therefore, in this paper,
feedback control is introduced to the flying capacitor voltage.
Figure 9 shows the block diagram of the boost inductor
current control and the flying capacitor voltage control system.
First, the original duty ratio is calculated based on the parameterssuch as the average inductor current command Iave* and the input
and output voltage. Next, the time ratio of Mode II, III isadjusted by the compensation duty generated by the proportional
controller. A voltage command of 1p.u. is inputted as thecommand value for P control. Here, 1p.u. is defined as the halfvalue of the output voltage. In this control, increase the ratio ofMode II (flying capacitor charging mode) when the flying
capacitor voltage vfc decreases. On the other hand, increase theratio of Mode III (flying capacitor discharging mode) when the
flying capacitor voltage vfc increases. Thus, the flying capacitor
voltage is kept by the control even when the parameter variationof the circuit occurs.

Fig. 8. Flying capacitor voltage change during Mode II and Mode III

V. SIMULATION AND EXPERIMENTAL RESULTS
A. Heavy load
In this section, the fundamental operation of the FCC
applying the proposed DCM is verified by the prototype.
Table 1 shows the circuit parameters. In this paper, assumingthat a 200 V single phase grid-tied inverter is connected, theoutput voltage is set to 300 V. In addition, the rated power is 1
kW (1p.u.)

vdc
2

Fig. 9. Circuit diagram of flying capacitor converter.
TABLE I.

SIMRATION AND EXPERIMENTAL CONDITION

Figure 10 shows a comparison of the peak inductor current
iL between the boost converter operated with DCM and FCC
operated with CRM under the same conditions of the boost
inductance value and the switching frequency. Fig. 10 confirmsthat FCC with proposed control reduces inductor current peakby 21% compared to that of the boost chopper operated with
DCM.
Figure 11 shows the operating waveforms when the current
command is 0.8 p.u. and 1 p.u. From Fig. 11, it is confirmed thatthe boost inductor current iL is controlled in a trapezoidal
waveform. The average power at this time was 0.68 p.u. and 0.88
p.u., respectively. This is because the average current is
controlled by an open loop, so it is affected by dead time andvoltage fluctuation of the flying capacitor.
Figure 12 shows operating waveforms when the powercommand is changed stepwise from 0.8p.u. to 1p.u., and viceversa. As can be seen from Fig. 12, the flying capacitor voltage
is controlled constant despite the load power fluctuation.
Figure 13 shows the operating waveform when the flying
capacitor voltage command is step changed between 0.8p.u. and
1p.u. It is confirmed from Fig. 10 that the flying capacitor
voltage follows the command and that the flying capacitor
voltage is be controlled to a desired value by adjusting the(a) Boost chopper in DCM.

(b) FCC in CRM.

Fig. 10. Comparison of operation waveforms in simulation (Iave=10 A).

switching duty ratio. As shown in Fig. 13 (a), when the flying
capacitor voltage control is in the transient state, the inductorOutput Voltage vdc [100V/div]
Flying Capacitor Voltage vfc [100V/div]0
Inductor current iL [5A/div]0

20[ s/div]*(b) Iave*=10 A (1 p.u.)(a) Iave =8 A (0.8 p.u.)
Fig. 11. Operation waveforms of around current
Output Voltage vdc [100V/div]
Flying Capacitor Voltage vfc [100V/div]

0 Inductor current iL [5A/div]0

10[ms/div]

50[ s/div](a) Step up response
Fig. 12. Experimental result for current step up response.(0.8 p.u. to 1 p.u.).

(b) Step down response

Output Voltage vdc [100V/div]

Output Voltage vdc [100V/div]

Flying Capacitor Voltage vfc [100V/div]

Flying Capacitor Voltage vfc [100V/div]

0

0

0

0

1[ms/div]
Inductor current iL [5A/div](a) Step up response. (0.8 p.u. to 1 p.u.)
Fig. 13. Experimental result for response of flying capacitor voltage.

current temporarily becomes CCM. This is because the current
control is an open loop and the duty ratio of Mode I and ModeIV according to the fluctuation of the flying capacitor voltage is
not adjusted.
Figure 14 shows the operating waveforms when the current
command is 0.2p.u. and 0.6p.u. From Fig. 14, it is confirmed thatthe boost inductor current iL is controlled in a triangular
waveform. The average power at this time is 0.17p.u. and
0.53p.u., respectively. This is because the average current is
controlled by an open loop, so it is affected by dead time andvoltage fluctuation of the flying capacitor. Application of
feedback control for boost inductor current is a future subject.

1[ms/div]
Inductor current iL [5A/div](b) Step down response. (1 p.u. to 0.8 p.u.)

Figure 15 shows the efficiency characteristics. As the result,the maximum efficiency of 96.6% is achieved at 100 V of input
voltage. This is cause that the input voltage is changed while theoutput voltage is constant. From the results, efficiency isdecreased at heavy load and light load. At light load and heavyload, the boost inductor current approach triangular waveform
due to duty calcration. Therefore, the current RMS value against
average value is increase.
VI. CONCLUSIONSThis paper proposed the control method of FCC operated
under CRM and DCM in order to reduce the current ripple. The
proposed operation is verified by the prototype. The proposedmethod is characterized by combining four switching modes andsetting the inductor current waveform to trapezoidal wave shapeso that it is possible to suppress the inductor current peak value
and control the flying capacitor voltage at the same time. By
applying the proposed method for boost inductor control of FCC,
the boost inductor current is controlled in a trapezoidal
waveform and the flying capacitor voltage is controlled byadjusting the duty ratio of Mode II and Mode III. The
experimental results show relevance of this method. In
experimental results, the maximum efficiency of 96.6% isachieved at 100 V of input voltage. And an efficiency of 96.2%
is achieved at the 1-kW output power and the boost ratio of three.
In the future, we are planning to introduce current feedback
control, analyze losses.
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