Control Method of Flying Capacitor Converter
Operated in Discontinuous Current Mode for High
Voltage Photovoltaic Cell
Jun-ichi Itoh, Ryoichi Ishibashi, Keisuke Kusaka
Dept. of Electrical Electronics and Information Engineering
Nagaoka University of Technology
Niigata, Japan
itoh@vos.nagaokaut.ac.jp
Abstract— This paper proposes the operation method of DCM
applied to inductor current control of a flying capacitor converter(FCC) for the low boost ratio. Due to the charging and discharging
of the flying capacitor, the inductor current ripple in FCC is
reduced compared to that of the typical boost converter with thesame inductance. The operation analysis for high boost ratio havebeen applied by authors. However, the duty calculation for lightload region of high boost ratio cannot be applied because the slopeof the modes II and III are inverted when boost ratio is less than 2.
Thus, the operation analysis for low boost ratio is proposed in thispaper. The validity of the proposed method is confirmed with a 1kW prototype. As the experimental results, an efficiency of 98.1%
is achieved.
Keywords—Discontinuous Current Mode; Flying Capacitor
Converter;

I. INTRODUCTION
In recent years, photovoltaic power generation systems haveattracted attention as renewable power sources [1–5]. In general,
converter topologies for these systems consists of a boost circuit
and a grid-tied inverter. Particularly, it is necessary to install theconverter in various places including each household when aphotovoltaic power generation system is incorporated in a DC
micro grid. Therefore, 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 [6].
One of the ideas to downsize the boost inductor is an increasein the switching frequency [7]. However, the effect on theminiaturization of a system by the high switching frequency islimited because the operation in the high-switching frequency
leads an increase of switching loss [8].
Other ideas for downsizing the boost inductor is applying
discontinuous current mode (DCM) to an inductor current
control [9–12]. DCM reduces the inductor volume because therequired inductance in DCM is smaller than continuous current
mode (CCM). However, a large current ripple occurs ascompared with CCM in the trade-off of a small inductor when

DCM is applied to the boost converter. This high-current ripple
significantly increases the conduction loss in the switching
devices. Hence, the effect on the miniaturization of a system by
the DCM operation in the boost converter is restricted.
The inductor current control method with DCM for a threelevel FCC has been proposed in order to increase the power
density of a DC-DC converter [13]. The proposed control
operates FCC using four modes; two of which are the same asthese of the boost converter (modes I and IV), whereas the othertwo modes are charging and discharging modes of the flying
capacitor (modes II and III). In this method, the modes II and III
inserted between the modes I and IV. This method makes theinductor current waveform trapezoidal shape in heavy load
region due to the charging and discharging of the flying
capacitor. The conduction loss and the turn-off loss are reduced,
because the peak of the inductor current is reduced by thismethod. However, the control method is taking into accountonly the operation with a boost ratio more than two.
In this paper, the operation method of low boost ratio is
proposed to increase the practicality of this method. The slopeof the modes II and III are inverted when the boost ratio becomeless than two by the flying capacitor voltage and input and output
voltage. Therefore, the originality of this paper is the operation
analysis for heavy load and light load region in low boost ratioof less than 2. The control based on the analysis was
implemented in DSP and confirmed with a prototype.
This paper is organized as follows; firstly, the operation
modes of FCC on applying DCM method is introduced.
Secondly, the duty calculation method is introduced. Next, thecontrol method for flying capacitor voltage is introduced.
Finally, experiments are conducted in order to confirm thecircuit operation.
II. OPERATION MODES OF FLYING CAPACITOR CONVERTER
Figure 1 shows FCC. In this paper, DCM and CRM are
applied to FCC in order to reduce the boost inductor current
ripple, decreasing the RMS current value against the average
current value. Furthermore, since the required inductance value
by applying DCM is reduced, the size of the inductor isdownsized. Therefore, both high efficiency and miniaturization
are achieved with the proposed method.
Figure 2 shows the operation modes of FCC with applying
DCM for inductor current. In the proposed method, the current
iL flowing through the inductor L is controlled using four modes;
Mode I to VI. In the mode I, energy is stored in L by turning on
S3 and S4. In the mode II and mode III, the energy is stored orreleased in Cfc. In the mode I and IV, the energy stored in L isstored or released to the output side by turning on S1 and S2.
1) Mode I
In the 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 

S1





S3

L





S1

S1
Mode IIvin  vdc  v fc
L





where vdc is output voltage.
4) Mode IV
In the 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 asvin  vdc
L




vfc

vdc

Cfc

iL

L



Figure 3 shows the inductor current waveform in eachswitching mode during one switching cycle in heavy load region.
This control method is obtained by adding the modes II and III
to the operation modes of the boost converter with the modes I
and IV. Consequently, the inductor current iL becomes a
trapezoidal waveform.

S2

vfc

vdc

vfc

vdc

Cfc

S3

S3

vin

vin
S4

S4

S1

S1

Mode III
L

S2

vdc

vfc
Cfc

Mode IV
S2
iL L

S3

Cfc

S3

vin

vin
S4




S2

L

iL



3) Mode III
In the 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

OutputSide

Fig. 1. Three-level flying capacitor converter.

iL

vin  v fc

vdc

S4

where vfc is the voltage of the flying capacitor Cfc.

a4 

vfc

Mode Ivin
L 2) Mode II
In the mode II, the energy is stored in Cfc by turning on S2
and S4. The slope a2 of the inductor current in this mode isexpressed as

a3 

vin

Input
Side

Cfc

L

iL

where vin is the input voltage, and L is the inductance value ofthe boost inductor.

a2 

FlyingCapacitor

Boost
inductor
S2

S4: Current pass
Fig. 2. Operation modes of flying capacitor converter.
1
S1
0
1
S2
0
1
S3
0
1
S4
0

0

Ipk3

Ipk2

iL
Iave

Ipk1
I

II

III

IV

D1Tsw

D2Tsw

D3Tsw

D4Tsw

Tsw

t

Fig. 3. Inductor current waveform and gate signals of MOSFETs of FCC
in rated power for heavy load region.

III. THE INDUCTOR CURRENT CONTROL WITH DISCONTINUOUSCURRENT-MODE
A. Heavy load region
Figure 4 shows the current waveform variation of each loadwhen the voltage condition and circuit parameters are as an
example. In Fig. 4(a), the duty ratio of the modes II and IIIbecome less than zero when the input current is increased.
Therefore, the input current is the maximum that can be output
under that circuit condition. The other hands, in Fig. 4(c), theduty ratio of Mode II and III become less than zero when the
input current is decreased. Therefore, the input current is theminimum that can be output under that circuit condition. Thisload region, that the input current is trapezoidal waveform, iscalled “Heavy load region”. The slope of the current waveformon each mode depends on the voltage conditions and the circuit
parameters. Therefore, the analysis of minimum input current
and maximum input current are required in this load region.

iL

D1>0
D2=0
D3=0
D4>0

Iave
I

0

t

IV
Tsw

(a)Maximum power

iL

D1>0
D2>0
D3>0
D4>0

The duty ratios in heavy load are expressed as following
equations [13].
Iave

D1  

2vin
 1  D4
vdc

I

0







II

III

Tsw

(b)Midium poweriL

B 2  4 AC
2A

D3  D23  D2

D4 











Iave
0

II

III

Tsw

(c)Minimum power
Fig. 4. Transition of current waveform according to load.
Light load region
Heavy load region
1.0

B





where fsw is switching frequency, Iave is the average input current,
A, B, and C are defined following equations

A

0.80.80.60.6D4

0.40.4

 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

D2

0.20.2Figure 5 shows the relationship among the duties andaverage current on the boost inductor. The average current in Fig.
5 is standardized by

I ave _ pu 

2 LI ave f sw vout
vin  vdc  vin 



t

IV

1.0

vin  vin 2  vin vdc  2 I ave Lf sw vdc
vdc

D1=0
D2>0
D3>0
D4>0

Duty Ratio

D2 

B 

t

IV



Point “A” of Fig. 5 corresponds to Fig. 4(a). Similarly, Point“B” of Fig. 5 corresponds to Fig. 4(c). The input current islimited between A to B of Fig. 5.
The input average current Iave has an upper limit and a lower
limit because all of the duties must be positive although the slope

D3

D1
0.2
0.4
0.6
0.8
1.0
0.2 Average
0.4 Current0.6
0.8[p.u.] 1.0
Inductor
Ratio Iave_p.u.
Fig. 5. Inductor current waveform and gate signals of MOSFETs of FCC
in rated power for heavy load region.

0.00.00.0
0.0

of the current waveform depends on the voltage conditions andthe circuit parameters. Therefore, another switching way forlight load region should be considered because this strategy isapplied only in heavy load region.
B. Light load region
Figure 6 shows the inductor current waveform in eachswitching mode during one switching cycle on heavy load
region. Here, the current peak values Ipk2 and Ipk3 in therespective operation modes are expressed as
I pk 2 

vin  v fc
L

D2Tsw







vin  vdc
D4Tsw
L






The slope of the mode II equals to one of the mode III when
the flying capacitor voltage vfc is half of output voltage vdc. From
this, D23 that is sum of the modes II and III period is expressedasD23  D2  D3 

vdc  vinvin  vdc / 2

1
S1
0
1
S2
0
1
S3
0
1
S4
0

iL

 



The sum of the average power in each switching mode equals
to the transmission power, which is expressed as1
1
I pk1 D1Tsw  I pk 1 D23Tsw  I aveTsw
22

II

Iave
0
Tsw

IIIIpk3 IV

D3Tsw
D4Tsw

D2Tsw

t

Fig. 6. Inductor current waveform and gate signals of MOSFETs of FCC
in rated power for light load region.
Light load region
Heavy load region
1.01.00.80.8From (11), (12), (13) and (14), D4 is represented as

Ipk2

D2+D3+D4

Duty Ratio

I pk 3 

0.40.4D3

0.20.2D4

0.60.6

D4  2 LI ave f sw

vin  vdc / 2
vdc (vdc  vin )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 the modes II
and III are equal, expressing as1
1
I pk1  I pk 2 D2Tsw  I pk 2  I pk 3 D3Tsw  0
2
2












From (11), (12), (14) and (16), D2, D3 is represented asD2 

vdc  vin
D4
2 vin  vdc / 2

1

D3  D23  D2













Figure 7 shows the relationship between the average current
and duty ratio D2–D4. As can been seen in Fig. 7, since the sumof the duties are possible to take less than 1, it is confirmed that
there are an upper limit value for the value that the average
current Iave is possible to generate. Theses duty ratio calculations
need to be selectively used in the load region.
C. Flying capacitor voltage control
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 theflying capacitor Cfc voltage vfc is kept at half of the DC-link

D2

0.00.0
0.0
0.0

0.2
0.4
0.6
0.8
1.0
0.2 Average
0.4 Current0.6
0.8
1.0
Inductor
Ratio Iave_p.u.
[p.u.]
Fig. 7. Relationship between average current and duty for light load
region.

voltage. However, the voltage of the flying capacitor varies since
the modes II and III charge and discharge the flying capacitor.
Furthermore, the inductance information of the boost inductor isrequired in calculation of the duty ratio however the actual
inductance value varies depending on current and heat.
Therefore, the flying capacitor voltage may diverge since anerror occurs in the duty calculation. Also, Eq. (16) does notsatisfy. Therefore, in this paper, feedback control is applied to
the flying capacitor voltage.
Figure 9 shows the block diagram of the boost inductor
current control and the flying capacitor voltage control system[13]. This controller controls the inductor current and the flying
capacitor voltage in two steps. The first step is for calculation of
the original duty ratio. The original duty ratio is calculated basedon the parameters such as the average inductor current command
Iave* and the input and output voltage. The second step is forbalancing of the flying capacitor voltage. The time ratio of themodes II and III are adjusted by the compensation duty
generated by a proportional controller. A voltage command of
1p.u. is input as the command value for a proportional control offlying capacitor voltage. Here, 1p.u. is defined as half of theoutput voltage. In this control, the flying capacitor voltage vfc isdecreased by an increase in the ratio of the mode II. On the other
hand, the flying capacitor voltage vfc is increased by an increasein the ratio of the mode III. Thus, the flying capacitor voltage iskept by the control even when the parameter variation of thecircuit occurs.

iL

IV. EXPERIMENTAL RESULTS
Table I shows the circuit parameters. In this paper, a 200-V
single phase grid-tied inverter with a rated power of 1 kW (1p.u.)
is assumed as a load.

0

The analysis is verified with a 1-kW prototype. The
experimental results show the relevance of this method. The
maximum efficiency of 98.1% is achieved at an input voltage of
200 V.
REFERENCES
[1]

[2]

[3]

Jinsoo Han, Jin-Doo Jeong, Ilwoo Lee, Sang-Ha Kim : “Low-costmonitoring of photovoltaic systems at panel level in residential homes
based on power line communication” IEEE Trans. on Consumer
Electronics, Vol. 63, No. 4, pp. 435–441 (2017)
Yi Tang, Wenli Yao, Poh Chiang Loh, Frede Blaabjerg : “Highly Reliable
Transformers Photovoltaic Inverters With Leakage Current and Pulsating
Power Elimination”, IEEE Trans. on Industrial Electronics, Vol. 63, No.
2, pp. 1016–1026 (2016)
T. Shimizu, K. Wada, N. Nakamura : “Flyback-Type Single-Phase Utility
Interactive Inverter With Power Pulsation Decoupling on the DC Inputt

vfc is incleaced
Tsw(a)Charging
iL

0

I II

III

IV

t

vfc

vfc is decleaced
0

Tsw

t

(b)Discharging
Fig. 8. Flying capacitor voltage change during Mode II and Mode III.
D2 +

Duty
Ratio
Calc. D3

L
vin
vdc
fsw

+

D 3'

D4
1

vdc
2

D 2'
+

+

Modulation

D1
Iave*

V. CONCLUSION
This paper proposed the operation method of DCM applied
to inductor current control of FCC for the low boost ratio. The
same calculation for each duty ratio is applied in heavy load
region. However, the duty calculation for light load region can
not applied because the slope of the modes II and III are inverted
when boost ratio is less than 2. Therefore, the calculation methodof duty ratio is applied for switching pattern without the mode I.
Also, the voltage control of frying capacitor is combined for thismethod.

III IV

0

Figure 12 and Fig. 13 shows operating waveforms when the
power command is changed stepwise from 0.2p.u. to 1p.u., andvice versa. As can be seen from Fig. 12 and 13, the flying
capacitor voltage is controlled constant despite the load powerfluctuation.
Figure 14 shows the efficiency characteristics. As a result,the maximum efficiency of 98.1% is achieved at an input voltage
of 200 V. In this paper, the states of all MOFFETs in Mode IV
are all off. Therefore, over all the efficiency becomes better by
the synchronous switching is applied.

II

vfc

Figure 10 shows the operation waveforms of high boost ratio.
The boost ratio is 3. The current command of each waveform is0.2p.u. and 1.0p.u.. From Fig. 11, the slope of inductor current
in the modes II and III is negative.
Figure 11 shows the operating waveforms of low boost ratio.
The boost ratio is 1.5. The current command of each waveform
is 0.2p.u. and 1p.u. From Fig. 11, the slope of inductor current
in the modes II and III is positive. The input power of 1.0p.u. isin light road region in this boost ratio even though input poweris same from the case of high load region. It is confirmed thatthe boost inductor current iL is controlled in a triangular
waveform as Fig. 6. Also, the flying capacitor voltage vfc is keepon half of output voltage vdc.

I

4
Gate
Signal
S1~S4

P
1
v fc

20kHz

Fig. 9. Block Diagram of flying capacitor convertor.

[4]

[5]

[6]

for an AC Photovoltaic Module System”, IEEE Trans. on PowerElectronics, Vol. 21, No. 5, pp. 1264–1272 (2006)
Subhendu Dutta, Kishore Chatterjee : “A Buck and Boost Based Grid
Connected PV Inverter Maximizing Power Yield From Two PV Arraysin Mismatched Environmental Conditions”, IEEE Transactions on
Industrial Electronics, Vol. 65, No. 7 (2018)
Ritwik Chattopadhyay, Subhashish Bhattacharya, Nicole C. Foureaux,Igor A. Pires, Helder de Paula, Lenin Moraes, Porfirio C. Cortizio,
Sidelmo M. Silva, Braz Cardoso Filho, and Jose A. de S. Brito, "LowVoltage PV Power Integration into Medium Voltage Grid Using HighVoltage SiC Devices", IEEJ Journal of Industry Applications, Vol.4, No.6,
pp.767–775, (2015)
Jun Imaoka, Kenkichiro Okamoto, Shota Kimura,Mostafa Noah, Wilmar
Martinez, Masayoshi Yamamoto, Masahito Shoyama, : “A Magnetic
Design Method Considering DC-Biased Magnetization for Integrated
Magnetic Components Used in Multiphase Boost Converters”, IEEE
Trans. on Power Electronics, Vol. 33, No. 4, pp. 3346–3362 (2018)Table I. Experimental Condition.

Input voltage

vin

Output voltage

vdc

300 V

Switching frequency

fsw

20 kHzBoost inductor

L

124 mH

Flying Capacitor

Cfc

60 mF, 1200 V*3 Parallel

Switching Devices

S1-S4

IXFN132N50P3

Output Voltage vdc [100V/div]

100V or 200 V

Flying Capacitor Voltage vfc [100V/div]0
Inductor current iL [5A/div]

4.7 W

Gate Resistor

I

II

I

III

Iave*=2 A

**
IIave
=10
AA
ave =6

Output Voltage vdc [100V/div]0
Inductor current iL [5A/div]0
10[ms/div]

10[ms/div]

Fig. 10. Operation waveforms of high boost ratio condition.

II III IV

0
Inductor current iL [5A/div]

10[ms/div]

10[ms/div]

Fig. 11. Operation waveforms of low boost ratio condition.

Output Voltage vdc [100V/div]
Flying Capacitor Voltage vfc [100V/div]0
Inductor current iL [5A/div]050[ms/div]
Fig. 12. Operation wave of current step up response.

Fig. 14. Efficiency characteristic.
[7]

Iave*=5 A

Flying Capacitor Voltage vfc [100V/div]050[ms/div]
Fig. 13. Operation wave of current step down response.
100
99
98
97
96
95
a = 1.5 (vin = 200 V)
94
93
92
1 p.u. = 1 kW
91
L=124 mH, vdc=300 V
90
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Power P[p.u.]
Efficiency h[%]Flying Capacitor Voltage vfc [100V/div]

Iave*=1 A
Output Voltage vdc [100V/div]

0

IV
II III

Gautham Ram, Chandra Mouli, Jos H. Schijffelen, Pavol Bauer, Miroslav
Zeman : “Design and Comparison of a 10-kW Interleaved Boost
Converter for PV Application Using Si and SiC Devices”, IEEE Journalof Emerging and Selected Topics in Power Electronics, Vol. 5, No. 2, pp.
610–623 (2016)[8] J. Itoh, T. Aaraki, K. Orikawa: "Experimental Verification of EMC Filter
Used for PWM Inverter with Wide Band-Gap Devices", IEEJ Journal ofIndustry Applications, Vol. 4, No. 3, pp. 212–219 (2015)[9] H. N. Le, K. Orikawa, J. Itoh : "DCM Control Method of Boost Converter
based on Conventional CCM Control", The 2014 International PowerElectronics Conference, No. 21A4-5, pp. 3661–3666 (2014)[10] Hoai Nam Le, Daisuke Sato, Koji Orikawa, Jun-ichi Itoh : “Efficiency
Improvement at Light Load in Bidirectional DC-DC Converter by
Utilizing Discontinuous Current Mode”, 17th Conference on PowerElectronics and Applications, EPE’15-ECCE Europe, No. DS1b-Topic 30484, (2015)[11] Mahdi Salimi, Abel Zakipour, “Direct Voltage Regulation of DC–DC
Buck Converter in a Wide Rangeof Operation using Adaptive InputOutput Linearization” IEE of Japan Trans. on Electrical and Electronic
Engineering, Vol. 10, pp. 85–91 (2015)[12] Yasuhiro Sugimoto, Toru Sai, Kei Watanabe, Mikio Abe : “Feedback
Loop Analysis and Optimized Compensation Slope of the Current-Mode
Buck DC-DC Converter in DCM”, IEEE Trans. on Circuits and Systems,
Vol. 62, No. 1, p.311–319 (2015)[13] R. Ishibashi, H. N. Le, H. Watanabe, K. Kusaka, J, Itoh: "Experimental
Verification of Three-level Flying Capacitor Converter Operated in
Discontinuous Current Mode", JIASC2018, Vol. , No. 1-29, pp. (2018)(inJapanese)