Evaluation for Overall Volume of Capacitor and Heat-sinkin Step-down Rectifier using Modular Multilevel Converter
Toshiki Nakanishi and Jun-ichi Itoh
Nagaoka University of Technology
1603-1 Kamitomioka-cho,
Nagaoka city Niigata, Japan
Tel. / Fax: +81/ (258) – 47 – 9533.
E-Mail: nakanishi@stn.nagaokaut.ac.jp, itoh@vos.nagaokaut.ac.jp
URL: http://itohserver01.nagaokaut.ac.jp/itohlab/index.html

Keywords«Modular Multilevel Converter», «H-bridge cell», «High power density design», «Step-down
rectifier»

Abstract
This paper discusses a volume evaluation of a step-down rectifier using a Modular Multilevel
Converter (MMC) for a power system connected to a utility gird of 6.6 kV in order to obtain the highpower density. Specifically, this paper evaluates a relationship among an output voltage of the MMC,
a volume of capacitors and a volume of a heat-sink. At first, formulas of semiconductor losses areclarified. Second, the relationship between the ripple current and the volume of electrolytic capacitors
is considered. In addition, the relationship between the number of cells per leg and an overall volume
is also shown. According to these considerations, the evaluation result of the overall volume showsthat it is necessary to reduce a step-down ratio of the MMC in order to obtain the high power density.
Moreover, it is also necessary to approach a withstand voltage ratio to 1.0 when the withstand voltage
ratio is defined as the ratio of the required withstand voltage to an actual withstand voltage with seriesconnection capacitors. In conclusion, the volume of the proposed system becomes approximately 20%of the volume of a conventional power system of 200 kVA connected to the utility gird of 6.6 kV.

I. Introduction
Recently, a micro-grid and a DC power grid have been actively researched as next generation
power supplies [1]-[2]. Specifically, the DC micro-grid is suitable to connect a battery energy storage
system and a renewable energy source such as a photovoltaic generation system or a fuel cell to theDC grid because the output voltages of many renewable energy sources are DC [1]-[2]. From thisfeature, the DC micro-grid is expected as a new generation power grid system.
The DC micro-grid is connected to an AC power grid of 6.6 kV as one of power sources. Moreover,transformers are applied between the AC power grid and the DC micro-grid in order to step-down 6.6
kV into several hundred volts and obtain isolation between the AC power grid and the DC micro-grid.
However, a volume of the isolated transformer increases because the isolated transformer operates in acommercial frequency. In addition, a conventional power system connected to the utility gird of 6.6
kV also includes static capacitors in order to correct an input power factor and a series reactor in orderto reduce a harmonic distortion of a grid current. Thus, the volume of the conventional power system
connected to the utility gird increases.
As one of solutions, the employment of Modular Multilevel Converter (MMC) to the power system
connected to the DC micro-grid is an effective method. The MMC has been actively researched as anext generation high power converter without the bulky transformer [3]-[4]. Therefore, the powersystem connected to the utility gird in the DC micro-grid achieves the volume reduction by applying
the MMC into the system. Additionally, the MMC achieves a step-down rectification by replacing achopper cell into an H-bridge cell because the H-bridge cell has no limitation in the offset of an output

voltage of the cell compared to the chopper cell [4]-[5]. The MMC achieves the reduction of static
capacitors and the series reactor because the MMC controls the input power factor and reduce theharmonic distortion. Thus, the step-down rectifier using the MMC achieves the reduction of thesystem volume.
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 to consider the design method in order to reduce the volume of acapacitor with a high capacity and a heat-sink on each H-bridge cell. So far, an evaluation of thecapacitor volume has been reported in terms of the capacitance and the electrostatic energy [6].
Moreover, in terms of the design for the heat-sink, a calculation method of semiconductor losses,
analysis of semiconductor losses in simulations and a transition of the semiconductor loss when the
input power factor changes have been also reported [7]-[10]. In addition, the design criteria for thevolume minimization of an electrolytic capacitor on each cell in terms of a ripple current have been
considered because the ripple current affects a lifetime of the electrolytic capacitor [5]. However, it
seems that an overall volume which is combined the capacitor volume and the heat-sink volume has
not been considered. Moreover, the proposed system also includes an isolated DC-DC converter inlater part of the MMC. Thus, the system divides step-down functions at the MMC and the DC-DC
converter. Therefore, the step-down ratio of the MMC should be decided in order to obtain the highpower density.
In this paper, the clarification of the design criteria in order to achieve the high power density in the
step-down rectifier using the MMC is detailed. Specifically, each fundamental evaluation for thevolume of capacitors and the volume of the heat-sink is considered respectively. The conditions inorder to achieve the volume reduction are clarified by the relationship and the characteristic which arefound from fundamental evaluations even in the case which the circuit parameters of the MMC
changes complexly. At first, the clarification of semiconductor losses in the H-bridge cell is reported.
Second, the relationship between the output voltage of the MMC and the overall volume which is
combined the volume of capacitors and the volume of the heat-sink is considered. Additionally, therelationship between the number of cells per leg and overall volume is also shown. Finally, conditions
in order to obtain the high power density are clarified from the each relationship.

II. System configuration
2.1. Conventional power system connected to utility grid
Figure 1 shows a structure of the conventional power system of 200 kVA connected to the utility
gird [11]. The conventional system has several transformers in order to convert from the grid voltageof 6.6 kV into the AC distribution voltage of 200 V or 100 V. Moreover, the system also includes
static capacitors in order to correct the input power factor and the series reactor in order to reduce a
harmonic distortion of the grid current. Thus, the volume of the conventional power system increases.

2.2. Proposed system
Figure 2 shows the main circuit configuration of the proposed step-down rectifier using the MMC.
Each leg consists of two buffer reactors Lb and the H-bridge cells. The converter outputs a multi-level
voltage waveform in order to reduce harmonic distortions of the input current. Thus, many cascaded
cells are used in practical because the reduction effect of the harmonic distortion increases by
increasing the number of cells. Additionally, the MMC is able to reduce the voltage rating of devices
on each cell because of cascade connections of cells. Therefore, lower voltage rating devices are
utilized to the MMC. On the other hand, the output DC voltage of the MMC depends on the sum of thecell’s output average voltage. Thus, the output voltage of the cell includes the AC component and the
DC component in order to control the input current and the output voltage. Moreover, the MMC
converts the high AC voltage to the DC voltage of several hundreds volts. After this step, the DC
voltage of 400 V is supplied to the DC bus of the DC distribution by the isolated DC-DC converter.
Thus, the input side and the output side are isolated by the DC-DC converter.

Fig. 1. Conventional power system of 200 kVA
connected to utility gird of 6.6 kV

Fig. 2. Circuit configuration of step-down
rectifier using MMC.

Ⅲ. Control strategy
3.1. Concept of proposed control for the MMC
Figure 3 shows a control block diagram of the proposed step-down converter [5]. The proposed
control system is based on the single-phase power factor correction (PFC) converter because the Hbridge cell has same circuit configuration as singe-phase PFC converter. Differences between the PFC
converters and the H-bridge cells are; there is a DC component in the output voltage of the H-bridge
cell, and a voltage balancing control is necessary in order to correct unbalance voltages among all
capacitors. Thus, in order to deal with above problems, it is necessary to add two control systems tocontrol the DC component and achieve the voltage balancing.

3.2. Average voltage control
The average voltage control is applied in order to control the average value of all capacitor voltage
in the arm [5]. Therefore, the average value of all capacitor voltages has to be calculated in each arm.
In addition, the error between the voltage command and the average value of all capacitor voltages in
the arm is corrected by a PI controller. The output value of the PI controller is given as the positive
phase component’s command of the arm current. Moreover, the voltage command vC*is given by (1).
*

vC ≥

⎞
1 ⎛⎜ 22 E + Vmmc ⎟⎜⎟nλ ⎝ 3⎠(1)

where E is an effective value of the input line-to-line voltage. Vmmc is the output DC voltage of the
MMC. n is the number of cells at each leg. Note that the modulation index λ is set to 0.8 in this paper.

3.3. Arm current control
Each arm current includes the AC component and the DC component. First, the AC component of
the arm current flows from the power grid. The AC component is defined as a positive phasecomponent. Moreover, from the previous section, the positive phase component’s command isgenerated by the average voltage control. In other words, the AC component of the arm current is
controlled in order to maintain the average value of all capacitor voltages in each arm constant.
On the other hand, the arm current also includes the DC component (a zero phase component).
Therefore, it is necessary to eliminate only the zero phase component from the arm current in order tocontrol the capacitor voltage. In this paper, the application of the rotational coordinate transform isapplied. This method extracts the positive phase component by using the rotational coordinatetransform in each arm group; the upper side and the lower side.

3.4. Output voltage control
The output DC power is controlled by the zero phase component. The command of the output DC
voltage is added into the output value of the controller in the arm current control. Moreover, the output

DC voltage of the MMC is divided on each cell. Thus, the output DC voltage of one cell isfundamentally set as Vmmc*/n when the command of the MMC output voltage control is Vmmc*.

3.5. Voltage balancing control
The voltage balancing control corrects the unbalance voltage which occurs among capacitors insame arm. In the proposed voltage balancing control, the output DC voltage of the cell is varied
depending on the capacitor voltage [6]. The biggest advantage of the proposed voltage balancing
control system is that it is not necessary to design control parameters because the dividing ratio isadjusted automatically depending on the capacitor voltage.

IV. Clarification of semiconductor losses on H-bridge cellIn this section, formulas of semiconductor losses on the H-bridge cell are clarified for the design ofthe heat-sink. At first, it is necessary to analyze the arm current which flows to each switching device
because the arm current significantly changes when the input power factor changes. Second, formulasof semiconductor losses are clarified based on the result of arm current analysis.

4.1. Analysis of arm current
At first, the cell output voltage and the arm current are defined by (2) and (3) respectively in lower
side of the MMC. The cell output voltage and the arm current have the DC component and the ACcomponent.
⎫⎪
1 ⎧⎪ 2⎨2 E cos(θ + φ ) + Vmmc ⎬n ⎪⎩ 3
⎪⎭

(2)

1 2 S
P
cosθ +
2 3 E
3Vmmc

(3)

v B _ cell =iBr = −

where S is an input apparent power. φ is the input phase difference.
From (3), the condition which the arm current becomes the DC is given by (4).
P
1 2 S
≥
3Vmmc 2 3 E(4)Moreover, the condition which the current includes only the DC component is given by (5).
2 3 E
cos φ − 1 ≥ 0
3 2 Vmmc(5)Additionally, an angle θ0 which a direction of the arm current changes is defined by (6) when the arm
current is AC.
⎛2θ 0 = cos −1 ⎜⎜

⎝3

⎞
3 E
cos φ ⎟⎟
2 Vmmc⎠(6)

From (6), the section θa which the positive current flows against the definitional direction of the arm
current is given by (7). In contract, the section θb which the negative current flows is given by (8).
−π ≤ θ a ≤ −θ 0 , θ 0 ≤ θ a ≤ π(7)−θ 0 ≤ θ b ≤ θ 0(8)

1 vcmkj
2 n/2∑vcmkxx=1

Fig.3. Control block diagram for one arm of MMC.

Figure 4 shows the relationship among the cell output voltage, the arm current and θa and θb.
a

iBr

0

0

a

b

vB_cell

Fig.4. Relationship between cell output voltage and arm current in lower side of MMC.

4.2. Calculation of conduction loss
In the system, the general PWM modulation is applied. Thus, S1 and S4 which is shown in Fig. 2
operate in pairs. In contract, S2 and S3 operate in pairs. Thus, the semiconductor losses are same in pairdevices. Therefore, in this paper, only semiconductor losses of one leg in the H-bridge cell arecalculated.
The average value of the conduction loss at one cycle Pcon is given by (9) [12].
βPcon =()

1
V0 + RiB _ cell iB _ cell d SD dθ
2π ∫α

(9)

where V0 is a voltage drop when the current is zero. R is a resistance value of the device. Both values
are calculated from the datasheet of the device. iB_cell is the current which flows to the device. dSD is theduty of each switching device.
The current which flows to S1, S4, D2 and D3 when the arm current becomes the positive is given by(10). In contract, the current which flows to S2, S3, D1 and D4 when the arm current is negative is givenby (11). Note that the variable number θ of (10) is replaced θa and θ of (11) is replaced θb.
P
1 2 S
cos θ a +
2 3 E
3Vmmc

(10)

1 2 S
P
cos θ b −
2 3 E
3Vmmc

(11)

i B _ cell _ P = −i B _ cell _ N =Moreover, each duty is given by (12), (13), (14) and (15).
d S1 =⎞ ⎫⎪1 ⎧⎪1 ⎛⎜ 22 E cos(θ a + φ ) + Vmmc ⎟ ⎬⎨1 +⎟⎪2 ⎪⎩ nVC ⎜⎝ 3
⎠⎭

(12)

dS2 =

⎞ ⎫⎪
1 ⎧⎪
1 ⎛⎜ 22 E cos(θ b + φ ) + Vmmc ⎟ ⎬⎨1 −⎟⎪2 ⎪⎩ nVC ⎜⎝ 3
⎠⎭

(13)

d D1 = 1 − d S 2

(14)
(15)

d D 2 = 1 − d S1

where VC is the capacitor voltage.
Each conduction loss of S1 and S2 is given by (16) and (17) respectively. Note that formulas ofconduction losses on D1 and D2 are omitted because each formula is complex.
PB _ S 1 _ Con =⎫⎧V0 _ SW ⎡⎛ Vmmc ⎞ ⎪⎧ 2 S
2 P⎟⎨⎢⎜ 1 +(π − θ 0 )⎪⎬+ 1 ⎪⎨− P (2(π − θ 0 ) − sin 2θ 0 ) − 4
sin θ 0 +nVnVC ⎟⎠ ⎪⎩ 3 E
33 Vmmc4π ⎢⎜⎝
⎪⎭
C ⎪
⎩ 3
⎣

+

RSW ⎡⎛ Vmmc ⎞ ⎧ 1 S 2⎟⎨(2(π − θ 0 ) − sin 2θ 0 ) + 2⎢⎜⎜ 1 +
2⎟nVC ⎠ ⎩ 12 E
34π ⎢⎣⎝+

1
1
1 ⎧ 1 2 PS ⎛⎞ 4 P2 ⎛⎞ 4⎜ 3 sin θ 0 + sin 3θ 0 ⎟ −⎜ (π − θ 0 ) − sin 2θ 0 ⎟ −⎨−2nVC ⎩ 6 3 E ⎝3⎠ 9 Vmmc ⎝
⎠ 9

2 PE
⎪⎫ ⎤
cos φ sin θ 0 ⎬ ⎥3 Vmmc
⎪⎭ ⎥⎦

⎫
2 PS
2 P2
(π − θ 0 )⎪⎬sin θ 0 +2
3 EVmmc
9 Vmmc⎪⎭⎫⎪⎤2 P2E
cos φ sin θ 0 ⎬⎥2
3 Vmmc⎪⎭⎥⎦(16)

PB _ S 2 _ Con =⎫⎪ 1 ⎧⎪ P⎫⎪⎤
V0 _ SW ⎡⎛ Vmmc ⎞ ⎧⎪ 2 S
4 2 PE
2 P⎟⎨⎢⎜⎜ 1 −
θ0 ⎬−cos φ sinθ 0 ⎬⎥sinθ 0 −⎨ (2θ0 + sin 2θ0 ) −⎟3 3 Vmmc
3 Vmmc ⎪⎭ nVC ⎪⎩ 3
4π ⎢⎝nVC ⎠ ⎪⎩ 3 E
⎪⎭⎥⎦
⎣

+

RSW ⎡⎛ Vmmc ⎞ ⎧ 1 S 2⎟⎨(2θ0 + sin 2θ0 ) − 2 2 PS sinθ0⎢⎜ 1 −
3 3 EVmmc
4π ⎣⎢⎜⎝nVC ⎟⎠ ⎩ 12 E 2

+

⎫⎪
2 P2
1 ⎧ 1 2 PS ⎛11
⎞ 4 P2 ⎛⎞ 4
θ −⎜ 3 sinθ0 + sin 3θ 0 ⎟ −⎜ θ 0 + sin 2θ0 ⎟ +⎨2 0⎬
9 Vmmc392V⎪⎭ nVC ⎩ 6 3 E ⎝
⎠
⎠ 9
mmc ⎝

(17)
2 P2 E⎪⎫ ⎤cos φ sinθ 0 ⎬ ⎥2
3 Vmmc⎪⎭ ⎥⎦4.3. Calculation of switching loss
The switching loss Psw and the recovery loss PRec are given by (18) [12].
PSw( Rec ) = V C

1β∫ i dθ V
2π α

w

B

dcd

I md

fc

(18)

where w is each loss energy which is described in the datasheet. Vdcd and Imd are the voltage value andthe current value when w is measured. fc is the carrier frequency.
Each switching loss on S1 and S2 is given by (19) and (20) respectively. Note that formulas ofrecovery losses on D1 and D2 are omitted as with the conduction loss.
PB _ S 1 _ SW =VC ⎧⎪ 1⎨−π ⎪⎩ 2⎫⎪ won + woffP
2 S
sin θ 0 +
θ0 ⎬
fc
3 E
3Vmmc ⎪⎭ Vdcd I md

(19)

PB _ S 2 _ SW =VC ⎧⎪ 1⎨−π ⎪⎩ 2⎫w +w
P
2 S(π − θ 0 )⎪⎬ on off f c
sin θ 0 −3 E
3Vmmc⎪⎭ Vdcd I md

(20)

V. Experimental results
In this section, experimental results by the miniature model of the MMC are shown. In theexperiment, a utility power source of 200 V is applied as the input voltage source.
Figure 5 shows waveforms of the input phase voltage, the input current and the output DC voltage.
Firstly, from the waveforms of the input phase voltage and the input current, it is confirmed that theunity power factor is obtained in the input side. Moreover, the total harmonic distortion (THD) of the
input current is 5.6%. Second, the waveform of the output DC voltage in lower side of Figure 5 showsthat the miniature model converts from the input voltage of 200 V into the output DC voltage of 65 V.
From this result, it is confirmed that the output voltage is kept constant. Therefore, the miniaturemodel of the MMC achieves the step-down rectification.
Figure 6 shows the waveforms of cell capacitor voltages which are connected to the r-phase leg.
The cell capacitor voltage is controlled according to the capacitor voltage command. As a result, theproposed system maintains the capacitor voltage of each H-bridge cell to the voltage command of 120
V. In addition, the maximum voltage error between the voltage command of the cell capacitor and themeasured voltage is 5% or less.

Fig. 5. Waveforms of input voltage, input current
and output voltage.

Fig. 6. Waveforms of capacitor voltage
in r-phase leg.

VI. Evaluations of overall volume
In this section, the overall volume of the step-down rectifier using the MMC is evaluated. At first,
the relationship between the ripple current and the volume of the electrolytic capacitor has beenclarified. Specifically, the relationship between the ripple current which affects the lifetime of theelectrolytic capacitor and the volume has been considered by the database of commonly-marketed
electrolytic capacitors which are generally implemented into many products [5]. At same time, therelationship between the number of cells and the volume of the electrolytic capacitor has been also
clarified [5]. Second, as an evaluation for the volume of the heat-sink, the relationship between the
input power factor and the total loss of the H-bridge cell is considered in order to design the heat-sinkin the worst-case. Finally, the overall volume which includes the volume and the electrolytic capacitor
and the volume of the heat-sink is clarified.

6.1. Evaluation of capacitor volume
Figure 7 shows the relationship between the ripple current and the capacitor volume as a databaseexample [6]. The figure in the graph shows the allowable ripple current of one capacitor. Therefore,
the number of the capacitors which are connected in parallel on one cell increases with increasing theripple current. Moreover, the start point of each line means the ripple current and the volume of one
capacitor. As a result, the overall volume of the capacitors becomes small by connecting the capacitor
with the small allowable ripple current in parallel compared to the utilization of capacitors with thelarge allowable ripple current. Thus, the parallel connection of capacitors with the small allowable
ripple current is better than the utilization of capacitors with the large allowable ripple current in orderto achieve the volume reduction of capacitors. Moreover, the ripple current does not change against
the capacitance and the number of cells [5]. Thus, the minimum point of capacitor volume against the
number of cells achieves the minimum point of the overall volume.
Figure 8 shows the relationship among the number of cells, the overall volume of the capacitor anda withstand voltage ratio. Note that 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 the required withstand voltage by series connection of capacitors.
Additionally, the required withstand voltage is set 30% more than the value which is calculated by (1).
Moreover, the capacitor volume is determined by the multiplied value of the number of seriesconnection capacitors and the number of 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 theactual withstand voltage when capacitors are connected in series. From Figure 8, the capacitor volume
becomes small when the withstand voltage ratio is close to 1.0. On other words, it is possible toachieve the volume minimization by closing the withstand voltage ratio to 1.0. As a conclusion, it isnecessary to meet following conditions in order to achieve the volume minimization of the capacitors.
(1) Applying the capacitor with the small ripple current(2) Maximizing withstand voltage ratio (Approaching to 1.0)

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

Fig. 7. Relationship between ripple current andcapacitor volume.

Fig. 8. Relationship between number of cells andcapacitor volume.

6.2. Relationship between input power factor and semiconductor losses
The relationship between the input power factor and the total loss of the H-bridge cell is clarified inorder to design the heat-sink in the worst-case.
Figure 9 shows the total loss becomes maximum when the input power factor is 1.0. The reason
why the total loss increases is to increase the semiconductor loss by the DC component of the arm
current. When the input power factor is zero, the semiconductor loss is generated by only the ACcomponent because the input active power (output power) is zero. The semiconductor loss which is
generated by the DC component is added gradually because the DC component of the arm current
increases as the input power factor is close to 1.0. As a result, it is necessary to design the heat-sink as
the worst-case of semiconductor losses when the input power factor is 1.0.
Input apparent power S
Input line voltage E
Capacitor voltage VC
Number of cell per leg n
0.00250.00200.0015: 200 kVA
Input active power P : S cos: 6600 Vrms Output voltage Vmmc : 400 V: 700 V
Carrier frequency: 500 Hz
Switching device : FZ400R12KE4: 20

Total conduction loss of switch
Total conduction loss of FWD
Total switching loss of switch
Total recovery loss of FWD
Total semiconductor loss

1 p.u. = 200 kVA

0.00100.00050.0000
0.0

0.2

0.4

0.6

Input power factor

0.8

1.0

Fig. 9. Relationship between input power factor and semiconductor losses per cellunder condition of constant input apparent power

6.3. Conditions for evaluation of overall volume
In the evaluation of the overall volume, the design conditions are set as follows;(1) The input line voltage is 6.6 kV. The power capacity of the MMC is 200 kVA.
(2) The charge voltage of each capacitor is calculated by (1). Moreover, the required withstandvoltage includes 30% margin against the charge voltage.
(3) The capacitor which has the withstand voltage of 400 V and the allowable ripple current of 5 A
per one capacitor is applied.
(4) The voltage rating of the switching device is set 80% more than the charge voltage of capacitor.
Additionally, the current rating is set twice value as the rated value of the arm current.
(5) The carrier frequency is decided so that the equivalent carrier frequency is 10 kHz.
(6) Loss data in the maximum junction temperature from each datasheet is applied. Moreover, theallowable junction temperature is set 80% of the maximum junction temperature.
(7) The heat-sink is designed based on CSPI [13]. Moreover, CSPI is assumed to 3.0 (Air cooling).
(8) The loss data of SiC-MOSFET is sited from the loss characteristic of one chip [14]-[15]. Thus,
the parallel connection number of the chip is decided in order to meet the conditions of thecurrent rating. In addition, the maximum junction temperature is set 175 °C.

6.4. Relationship between input power factor and semiconductor loss
Figure 10 shows the relationship between the volume of one cell and the output voltage of the stepdown rectifier using the MMC. The volume of one cell decreases when the output voltage of the MMC
increases. The reason why the volume of one cell decreases is to decrease both the parallel connection
number of capacitors and semiconductor losses decrease because both the ripple current and the DC
component of the arm current decrease.
Figure 11 shows the breakdown of the volume per cell when IGBTs with the voltage rating of 1.7
kV are applied to the H-bridge cell. From Figure 11, the volume of one cell decreases when the output
voltage of the MMC increases. Specifically, the volume of capacitors changes significantly comparedto the change of the heat-sink volume when the output voltage of the MMC changes. As a result, thevolume of capacitors affects greatly to the volume of the cell compared to the heat-sink volume.
Figure 12 shows the relationship between the overall volume of the MMC and the output voltage ofthe step-down rectifier using the MMC. The overall volume of the MMC decreases when the output
voltage of the MMC increases as with the volume of the cell. From the comparison of Figure 11 andFigure 12, the overall volume does not become minimum under the conditions which the volume of
the H-bridge cell becomes minimum. This reason is that the overall volume is changed significantly by
the total number of cells even if the volume of the H-bridge cell becomes minimum. Thus, it isdifficult to estimate the minimum volume of the MMC from only the volume of the H-bridge cell.
Figure 13 shows the relationship among the number of cell, the overall volume and the withstandvoltage ratio when IGBTs with the voltage rating of 1.7 kV are applied to the H-bridge cell. From
Figure 13, the change of the heat-sink volume is particularly small compared to the change of thecapacitor volume. Therefore, the capacitor volume should be focused when same output voltage of the
MMC and the switching device with same voltage rating are applied. Additionally, the relationshipbetween the overall volume and the withstand voltage ratio of capacitors shows that the overall
volume becomes small when the withstand voltage ratio is close to 1.0 as with the evaluation of thecapacitor volume. Thus, it is necessary to maximize the withstand voltage ratio (approaching to 1.0) in
order to obtain the high power density of the step-down rectifier using the MMC.
In conclusion, the conditions in order to obtain the high power density of the step-down rectifier
using the MMC are as follows;(1) Reduction of the step-down ratio of the MMC (The output voltage of the MMC is set to high.)(2) Design for the number of cell and the series connection number of capacitors in order tomaximize the withstand voltage ratio (Approaching to 1.0)
Moreover, the overall volume is calculated in the case which the MMC operates for 10 years whencapacitors with the endurance of 5000 hours are applied to the MMC. As a result, the overall volume
is 2900 dm3 based on following conditions; (i) the output voltage of the MMC is 1200 V. (ii) the
number of cell is 18. (iii) IGBTs with the voltage rating of 1.7 kV are applied. From this result, the
2.5 kV
1.7 kV
1.2 kV
3.3 kV SiC

Fig.10. Relationship between output voltage
and cell volume.

Fig.11. Breakdown of volume per cell

2.5 kV
1.7 kV
1.2 kV
3.3 kV SiC

Fig. 12. Relationship between output voltage
and overall volume.

Fig. 13. Relationship among the number of cell,over volume and withstand ratio.
(Applying of 1700 V IGBT)

proposed system reduces 80% of the overall volume compared to the conventional power system
connected to the utility gird. Thus, the system achieves the volume reduction even considering areactor volume, a volume of the isolated DC-DC converter and the actual implementation of the MMC.

VII. Conclusions
This paper discussed the volume evaluation of the step-down rectifier using Modular Multilevel
Converter (MMC) for the power system connected to the utility gird of 6.6 kV in order to obtain thehigh power density. Specifically, the clarification of formulas for semiconductor losses, therelationship between the ripple current and the volume of electrolytic capacitors and the relationshipbetween the number of cells per leg and overall volume was detailed.
The conditions in order to obtain the high power density of the MMC are as follows;z Reduction of the step-down ratio of the MMC (The output voltage of the MMC is set to high.)
The proposed system reduced approximately 60% of the overall volume in the case which theoutput voltage increased from 400 V to 1200 V when 1200 V IGBTs are applied.
z Design for the number of cells and the series connection number of capacitors in order tomaximize the withstand voltage ratio (approaching to 1.0)
The proposed system reduced approximately 16% of the capacitor volume in the case which thewithstand voltage ratio increased from 0.76 to 0.90.
In conclusion, the proposed system reduced 80% of the overall volume compared with theconventional power system of 200 kVA connected to the utility gird of 6.6 kV.
In future work, the design method in order to minimize the overall volume which is included thereactor volume and the volume of the isolated DC-DC converter will be considered.

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