Evaluation of Capacitor Volume in Modular Multilevel Converter
Toshiki Nakanishi＊, Jun-ichi Itoh＊
1Nagaoka University of Technology, JapanThis paper discusses a volume evaluation of a step-down rectifier using Modular Multilevel Converter (MMC) for a utility gird of 6.6 kV
in order to obtain the high power density. Especially, the volume of electrolytic capacitors is designed in terms of the lifetime and the withstandvoltage of the capacitor. Moreover, this paper clarifies a relationship between an output voltage of the MMC and a volume of electrolyticcapacitors. In conclusion, the conditions in order to reduce the volume of electrolytic capacitors are clarified in the proposed system at thepower capacity of 200 kVA.
Keywords Modular Multilevel Converter, Step-down Rectifier, Volume of Electrolytic Capacitor, Ripple Current

vAr1

1. Introduction
Recently, a DC micro-grid has been actively researched as next
generation power grids [1]. The system is connected to a utility gridof 6.6 kV as one of power sources. Moreover, transformers are used
between the utility grid and the DC micro-grid in order to convert
from 6.6 kV into several hundred volts and obtain isolation between
the utility grid and the DC micro-grid. However, a volume of theisolated transformer increases because the isolated transformer
operates in a commercial frequency.
In order to avoid utilization of the bulky transformer, the stepdown rectifier using Modular Multilevel Converter (MMC) has
been proposed [2].
On the other hand, in terms of the realization of the high power
density in the step-down rectifier using the MMC, it is necessary toconsider the design method in order to reduce the volume of acapacitor with a large capacity. So far, the volume evaluation ofcapacitors based on the electrostatic energy has been reported [3].
However, it seems that the relationship between the capacitor
volume and the number of cells has not been reported. Especially,
it is important to consider a ripple current of the capacitors in termsof lifetime of the capacitor when the capacitor with the large
capacity such as an electrolytic capacitor is applied.
This paper discusses the volume evaluation of capacitors in theMMC. Especially, the parallel connected number and the seriesconnected number of capacitors are determined by the ripple
current which flows to the electrolytic capacitor and the withstandvoltage. Moreover, the relationship among the ripple current, thenumber of cells and the volume of electrolytic capacitors is clarified.
In conclusion, the conditions in order to reduce the volume ofelectrolytic capacitors are clarified.

2.

Configuration of proposed system

Fig. 1 shows the configuration of the step-down rectifier using
the MMC. In the proposed system, H-bridge cells are applied. In
the conventional MMC, chopper cells are applied. However, theMMC with chopper cells cannot achieve the step-down rectification
because the chopper cell has a lower limit on its output voltage. The
MMC with H-bridge cells converts the high AC voltage to the DCa)

Correspondence to: Toshiki Nakanishi
E-mail: nakanishi@stn.nagaokaut.ac.jp,

cell

vcAr1

vAr(n/2)

DC bus ofMicro-gridcell

6.6 kV,
50 HziAr
ir
isit

vcAr(n/2)

400 kV

Lb
Isolated
DC-DC
conv.

Vmmc

iBr LbvcBr1
vBr1

cellcellvBr(n/2)

vcBr(n/2)

S1

S3

S2

S4

H-bridgecellCcellFig. 1. Circuit configuration of step-down rectifier using MMC.
voltage of several hundred volts. After this step, the DC voltage of
400 V is supplied to the DC bus of the micro-grid by the isolated
DC-DC converter. Therefore, the input side and the output side are
isolated by the DC-DC converter. Moreover, the proposed system
is constructed by two converters and can divide the step-downfunction in the MMC and the DC-DC converter. Thus, it is able todetermine the optimal value of the output voltage of the MMC Vmmc
in order to reduce the system volume.

3. Operation of step-down rectifier using MMC
Fig. 2 shows waveforms of the input phase voltage, the input
current and the MMC output voltage. Firstly, from the waveformsof the input phase voltage and the input current, it is confirmed thatthe unity power factor is obtained. Moreover, the total harmonic
distortion (THD) of the input current is 3.1%. Second, thewaveform of the MMC output voltage in lower side of Fig. 2 showsthat the miniature model converts from the input voltage of 200 V
into the MMC output voltage of 75 V. From this result, it isconfirmed that the output voltage maintains constant. Therefore, theminiature model of the MMC achieves the step-down rectification.
Fig. 3 shows the waveforms of all capacitor voltages of H-bridge
cells which are connected to the r-phase leg. As a result, theproposed system maintains all capacitor voltages. Besides, the error
between the capacitor voltage command of 130 V and the measured
voltage is 5% or less.

where E is an effective value of an input line-to-line voltage, n is
the number of cells at each leg, the MMC output voltage is Vmmc
and  is an modulation index. In this evaluation,  is set 0.9.
Moreover, the capacitor volume is determined by the multipliedvalue of the number of series connection capacitors and the numberof cells under the same condition for the ripple current. In addition,
the withstand voltage ratio is defined as the ratio of the required
withstand voltage to the actual withstand voltage when capacitors
are connected in series. From Fig. 5, the capacitor volume becomes
small when the withstand voltage ratio is close to 1.0. In otherwords, it is possible to achieve the volume reduction by closing thewithstand voltage ratio to 1.0. As a conclusion, it is necessary tomeet following conditions in order to reduce the volume of thecapacitors.
(1) Applying the capacitor with the small ripple current(2) Maximizing withstand voltage ratio (Approaching to 1.0)

Conclusion

This paper clarified the relationship among the capacitor volume,
the allowable ripple current which flows to the capacitor and thenumber of cells. Especially, the connection number of capacitors isdetermined by the allowable ripple current and the capacitor voltage
in terms of the lifetime and the withstand voltage of the capacitor.
In conclusion, it is necessary to meet following conditions in orderto reduce the volume of capacitors.
1) Applying the capacitor with the small ripple current
2) Maximizing the withstand voltage ratio

MMC Output Voltage [25 V/div]
Output power: 1000 W Input line voltage: 200 V Output Voltage: 75 V

0 Inductance Lb : 8 mH(%Z=6.1%) Carrier frequency : 8 kHz
Fig. 2. Waveforms of input voltage, input current andMMC output voltage.

Capacitor voltage (R-phase) [50 V/div]
vcAr1, vcAr2, vcBr1, vcBr2,130 V

Cell Capacitor : 1300 mF
Number of cell per leg : 425 msec

0Fig. 3. Waveforms of capacitor voltage in r-phase leg.
2500000
2.50

Withstand voltage : 400 V

2250000
2.25

Endurance : 85 °C, 5000 hours

2000000
2.00
1750000
1.75
1500000
1.50
1250000
1.25
1000000
1.00

5A
10A
15A
20A
25A
30A

7500000.75

0.50
500000250000
0.25
00.00

00

55

10
1015
1520
2025
2530
30

35
35

40
4045
455050

Ripple current (effective value) [A]55556060

Fig. 4. Relationship between ripple current andcapacitor volume.
Required withstand voltage
Withstand voltage ratio = Withstand voltage of one capacitor × series connection number
11.0

20000000
201919000000

0.80.818000000
18

Maximum point ofWithstand voltage ratio

1717000000
16000000160.6
0.6

0.40.4

Minimum point ofcapacitor volume

15
15000000

0.20.214000000
1413000000
1300

55

101015152020

Number of cells [1/leg]

25253030

Withstand voltage ratio1  2*2 E  Vmmc  .............................................. (1)n  30Volume of capacitors [dm3]*Input Phase Current (R-phase) [5 A/div](Only parallel connection of capacitors)vc 0Volume of capacitors [dm3]Fig. 4 shows the relationship between the allowable ripple
current and the capacitor volume. The graph is drown on datasheetsof commonly-marketed electrolytic capacitors which are generallyimplemented into many products. Note that figures from 5 A to 30
A in Fig. 4 are the allowable ripple current of one capacitor.
Therefore, the number of the capacitors which are connected inparallel on one cell increases with increasing the ripple current.
Moreover, the start point of each line means the ripple current andthe volume of one capacitor. As a result, the capacitor volume
becomes small by connecting capacitors with the small allowable
ripple current in parallel compared to utilization of the capacitorswith the large allowable ripple current. Thus, the parallel
connection of the capacitors with the small allowable ripple current
is better than utilization of the capacitors with the large allowable
ripple current in order to reduce the volume of the capacitors.
Additionally, the ripple current does not change against thecapacitance and the number of cells [2]. Thus, the minimum pointof the capacitor volume against the number of cells achieves theminimum point of the overall volume.
Fig. 5 shows the relationship among the number of cells, theoverall volume of the capacitor and a withstand voltage ratio. Notethat the number of series connection capacitors increases when therequired withstand voltage is larger than the withstand voltage of
one capacitor. Thus, it is necessary to meet the conditions of therequired withstand voltage by series connection of capacitors.
Besides, the required withstand voltage is set 30% more than thevalue which is calculated by (1).

5.

Input Phase Voltage (R-phase) [250 V/div] 10 msec

Evaluation of capacitor volume(Only series connection of capacitors)

4.

00.0

Fig. 5. Relationship between number of cells andcapacitor volume.
References[1] H. Kakigano, Y. Miura, and T. Ise, “Low-Voltage Bipolar-Type DC Microgridfor Super High Quality Distribution,” IEEE Trans. on Power Electronics, Vol.25,
No.12, pp.3066-3075 (2010)[2] T. Nakanishi, J. Itoh : "Capacitor Volume Evaluation based on Ripple Current
in Modular Multilevel Converter", 9th ICPE, No. WeA1-5, pp.815-822 (2015)[3] S. P. Engel. R. W. De Doncker, “Control of the Modular Multi-Level
Converter for minimized cell capacitance,” EPE2011 (2011)