電気学会論文誌●（●●●●●●●部門誌）
IEEJ Transactions on ●●●●●●●●●●●●●●●
Vol.●● No.● pp.●-●●
DOI: ●.●●/ieejeiss.●●.●

Paper

Control Strategy for Modular Multilevel Converter
based onSingle-phase Power Factor Correction Converter
Toshiki Nakanishi＊a) Student Member,

Jun-ichi Itoh＊ Senior Member(Manuscript received Jan. 00, 20XX, revised May 00, 20XX)
This paper proposes a novel control strategy for a step-down rectifier that applies a modular multilevel converter (MMC). This
paper first discusses the circuit configuration and the proposed control method. The main part of the control system is based on thecontrol method for the single-phase power factor correction converter (PFC converter), which means that the conventional control
techniques of the single-phase PFC converter can be simply applied to the MMC. The control elements which achieve step-down
rectification and capacitor voltage balancing are added to the main part. Besides, in capacitor voltage balancing of the proposed
control method, it is not necessary to design the control parameters. In addition, the operation of the proposed step-down rectifier
is confirmed by the simulation. The simulation results show that the proposed converter achieves step-down rectification from thegrid voltage of 6.6 kV to the DC voltage of 400 V. Moreover, the step-down rectifier maintains all capacitor voltages constant.
Finally, a fundamental operation is confirmed by experiments using a miniature model. As the results, the step-down rectifier
converts from the input grid voltage of 200 V to the output DC voltage of 75 V. Besides, the proposed step-down rectifier maintains
the capacitor voltage of each cell to the voltage command of 130 V. The maximum error between the voltage command of the cell
capacitor and the measured voltage is less than 2%.
Keywords : Modular Multilevel Converter, Power Factor Correction Converter, Step-down Rectifier, DC Micro-grid,
DC Distribution Systems

1.

frequency of the transformer is commercial frequency of 50 or 60
Hz. Furthermore, the high transform ratio is required in order toconvert from the grid voltage of 6.6 kV to several hundred volts.
In order to overcome the problem which is the application of thebulky transformer, the employment of modular multilevel converter(MMC) to the DC distribution system is an effective method. The
MMC has been actively researched as a next generation high power
converter without the bulky transformer(7)-(13). The advantages ofthe MMC are as follows; (i) the circuit configuration is simple
because the topology is constructed by cascade connected cells. (ii)the MMC reduces the harmonic distortions of the grid current
because the MMC outputs the multilevel waveform (iii) low voltage
devices are applied to each cell because the output voltage of thecell becomes low by increasing the number of cells. Thus, thesystem achieves the high response operation because the switching
devices with the low voltage rating operate in the high switchingfrequency. The DC distribution system achieves the volume
reduction by applying the MMC into the system due to the
reduction of the bulky transformer. However, in the general AC-DC
converter with the MMC which consists of chopper cells, it is notpossible to achieve step-down rectification because chopper cells
cannot output the negative voltage. In order to overcome the above
problem, a step-down converter which applies the MMC with Hbridge cells has been proposed(14). The MMC with the H-bridge
cells still achieves reduction of the bulky transformer. Moreover,the employment of the H-bridge cell solves the limit of the output
voltage which the chopper cells have. Therefore, the system with
the H-bridge cells can operate as a step-down rectifier.
The control strategy for the step-down rectifier which applies

Introduction

Recently, DC micro-grids and DC distribution systems have been
actively researched as next generation power distributions(1)-(6). The
advantages of the DC micro-grid and the DC distribution system
are summarized as follows(1)-(2); (i) the system achieves the highefficiency because of the reduction of conversion losses in inverters
between DC output sources and loads. (ii) the control system issimpler than the control system for the conventional AC
distribution system because it is not necessary to consider
synchronization with a utility grid and a reactive power. (iii) the DC
micro-grid is suitable to connect battery energy storage systems andrenewable energy sources such as photovoltaic generation systems
or fuel cells to the DC grid because many renewable energy sources
output the DC voltage.
Besides, the utility grid of 6.6 kV is applied as the input powersource of the DC distribution system in order to reduce the wiringloss in the input side(2). Generally, a transformer is required between
the unity grid and the DC distribution system in order to isolate
between the unity grid and the power converters and convert fromthe grid voltage of 6.6 kV to several hundred volts DC such as 400
V(4)-(5). In order to convert the voltage, the employment of thetransformer is simple. However, the volume of the transformer isbulky due to several reasons. The main reason is that the operationa) Correspondence to: Toshiki Nakanishi.
E-mail: nakanishi@stn.nagaokaut.ac.jp＊
1603-1, Kamitomioka-machi, Nagaoka city,
Niigata prefecture, Japan© 200● The Institute of Electrical Engineers of Japan.

1

Control Strategy for Modular Multilevel Converter (Toshiki Nakanishi et al.)

MMC has three objectives. First objective and second objective are
the input current control and the output voltage control. The input
current control and the output voltage control have the samerequirement to the conventional AC-DC converters which applies
the MMC. For example, the control strategies for the AC-DC
converters which applies the MMC have been proposed(14)-(16). The
control system has three current control systems in order to control
independently the DC circulating current, the AC circulating
current and the input or output AC current which flows to the utility
grid. Besides, the control system has two voltage control systems inorder to control the average voltage in the cell capacitors and correct
an unbalance voltage among the cells. Thus, there are many control
parameters. However, the design method for the parameters in eachcontrol system has not been reported(14). On the other hand, ananalysis based on an equivalent circuit of the MMC and othercontrol strategy has been reported(15). However, there are also many
control parameters which should be designed. Similarly, themodeling of the MMC and the control strategy which is based on
the equivalent circuit have been proposed(16). Specifically, thecontrol methods of the negative sequence current and the zero
sequence current in the unbalance of the utility grid have been
proposed. However, it seems that the detail of the voltage control
for the capacitors has not been described. Moreover, the control
scheme which is included the voltage control for the capacitors has
not also been shown.
Third objective is the capacitor balancing control in each cell. It
is important to balance the capacitor voltage in each cell at constantbecause the circuit devices may be broken in a worst-case when theunbalance of the charge voltage in each cell occurs. The control
method in order to balance the capacitor voltage have beenreported(8), (18)-(19). However, it seems that the design method for thecontrol parameters of the capacitor voltage balancing control has
not discussed. Additionally, it is also necessary to determine thesign of the arm current in the conventional control(8). Moreover,other control methods have been proposed in the condition at thelow switching frequency. However, the unbalance voltages among
all cells are not eliminated completely(18)-(19).
This paper proposes the control strategy of the MMC based on
the control strategy for the single-phase power factor correction(PFC) converter with an aim to apply the conventional control
techniques of the PFC converter to the MMC. In particular, the mainparts of the current control for the input AC current and the voltage
control for the capacitor voltage are constructed by the control
strategy of the single-phase PFC converter. The key idea is that the
H-bridge cell has same circuit configuration as singe-phase PFC
converter. Moreover, the PFC converter and the H-bridge cell have
many common points in the circuit operation and the control
strategy. For example, the capacitor voltage is required to be
maintained at constant in both circuits. Furthermore, it is necessary
to control the input AC current in order to maintain the capacitor
voltage and reduce the total harmonic distortion (THD). In addition,
the control strategy, the design method for control parameters andthe stability analysis of the control system for PFC converters havebeen considered so far(19)-(22). As a conclusion, the control
techniques can be applied to the control system for the MMC
without major modification of the control strategy if the MMC isable to be controlled by the proposed control strategies based on thecontrol strategy for the PFC converter. Moreover, it is expected that
it is possible to propose new ideas and new points of view for acontrol method of the MMC by applying control technologies of the

vAr1
cell

vAr v

Ar(n/2)

vcAr1
vcAr(n/2)
cell

iAr
6.6 kV, i
50 Hz r

Lb

is
it

Vmmc

iBr

Lb

vBr1

Isolated
DC-DC
conv.
cell

vcBr1

cell

vBr

DC bus ofMicro-gridvArs

vcBr(n/2)

S1

S3

S2

S4 C

cell

vBr(n/2)

H-bridge cellFig. 1. Circuit configuration of step-down rectifier
which applies MMC for DC Micro-grid. The MMC with
H-bridge cells operates as a step-down rectifier.
single-phase PFC converters. However, it seems that theemployment of the control strategy for the PFC converter into the
MMC has considered scarcely.
In addition, the control method in order to balance the capacitor
voltages in all cells is also proposed. The main advantage of the
proposed capacitor voltage balancing control is that it is notnecessary to design the control parameters because the dividing
ratio is adjusted automatically depending on the capacitor voltage.
Moreover, it is not also necessary to determine the sign of the arm
current in the proposed voltage balancing control.
This paper is organized as follows. First, in section 2, the circuit
configuration of the step-down rectifier which applies the MMC
with H-bridge cells are shown. The relationship between the circuit
configuration of the cell and its output voltage are demonstrated. In
section 3, the control system based on the control strategy of thesingle-phase PFC converter is proposed. Additionally, the principleof the proposed capacitor voltage balancing control is also
explained. In section 5, the simulation result of the MMC which
employs the proposed control strategy is shown. Finally, in section
6, the experimental results of a miniature model in the utility gridof 200 V are shown.

2. Circuit Configuration
2.1 Main Circuit Configuration
Fig. 1 shows a main
circuit configuration of the step-down rectifier which applies the
MMC for DC Micro-grids. The proposed system converts from a
medium voltage of an input power grid to a DC bus voltage of the
DC Micro-grid.
First, the step-down rectifier which applies the MMC converts
from the medium voltage of 6.6 kV to the DC voltage of several
hundred volts. Each arm of the MMC consists of a buffer inductor
Lb and cascade connected cells. As features of the multilevel
converter, the proposed converter which applies the MMC outputs
a multi-level voltage waveform which is changed by the number ofcascade connected cells. Additionally, low voltage rating devices
are applied to each cell because the proposed step-down rectifier
reduces the voltage dividing value of each cell by increasing thenumber of cascade cells. Thus, the number of cascaded cells isincreased in practical in order to reduces harmonic distortion andutilize low voltage rating devices.
2

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Control Strategy for Modular Multilevel Converter (Toshiki Nakanishi et al.)vc *Configuration example of MMC for DC micro-gridsystem @300 kW

Table 1.

Second, a high power isolated DC-DC converter supplies the DC
bus voltage of 400 V. In the proposed system shown in Fig. 1, a dual
active bridge (DAB) converter is considered to be suitable to be
applied as a high power isolated DC-DC converter(23)-(25). The
proposed system requires a DC-DC converter for the bidirectional
operation and the isolation with high efficiency and small volume.
The DAB converter can achieve the bidirectional operation withhigh efficiency by using zero voltage switching (ZVS). Moreover,the DAB converter also achieves the isolation between the utility
grid and the DC micro-grid with the small high frequency
transformer. Thus, it is possible to reduce the volume of the systembecause of the utilization of the high frequency transformer.
On the other hand, in the MMC, the output DC voltage depends
on the summation of the average value of cell output voltage.
Generally, many AC-DC converters which applies the MMC are
constructed by chopper cells(14). However, conventional AC-DC
converters which applies the MMC with chopper cells cannot
achieve step-down rectification because the limit of the averagevalue of cell output voltage exists in the chopper cell. In contrast,
the H-bridge cell has no limit of the average value of cell output
voltage because the H-bridge cell can output a negative voltage.
Therefore, it is able for the H-bridge cell to vary the average valueof the cell output voltage. Thus, the MMC which is consisted of Hbridge cells achieves step-down rectification. Note that the upperarm group and the lower arm group are defined A and B respectively.
At first, the step-down rectifier which applies the MMC isrequired to achieve both the input current control and the output DC
voltage control. Therefore, the output voltage of each cell on one
leg and the capacitor voltage are depended by the maximum valueof the input phase voltage, the output DC voltage and the numberof cells on one leg. The capacitor voltage command vc*is given by(1). Note that the voltage drop of the buffer inductor is ignored
because the voltage drop is sufficiently small compared to voltagesof the input side and the output side.

Voltage rating of IGBT

3300 V

Current rating of IGBT
Capacitor voltage @ = 0.9

1500 V

400 A

Numbers of Cells @ leg

8

Total numbers of Cells

24

Numbers of Switching Device

96

Examples of IGBTs(26)-(28)MBM400E33D-MFR(Hitachi, Ltd.)FZ400R33KL2C_B9(Infineon)
5SLG 0500P330300(ABB)

vchopper S1

CS2
vchoppervC vH-bridge
S1

S3

S2

S4

C

vC

vH-bridge

vcell_avevcell_ave0vcell_p-p(a) Chopper cell0

vcell_p-p(b) H-bridge cellFig. 2. Relationship between circuit configuration andoutput voltage of each cell. The chopper cell has thelower limit of the output voltage because the chopper cellcannot output the negative voltage. On the other hand, theH-bridge cell has no lower limit of the output voltage.
per leg.


1  2*2 E  Vmmc  .............................................. (1)n  3

where E is the effective value of the input line-to-line voltage, Vmmc*
is the command of the output DC voltage of the MMC, n is thenumber of cells at each leg,  is a modulation index.
Table 1 shows configuration examples of switching devices andcell capacitors which are necessary to construct the MMC when the
MMC is applied into the DC Micro-grid as the step-down rectifier.
The power capacity of the system is 300 kW(3)-(4). Moreover, themedium voltage grid of 6.6 kV is applied as the input voltage source.
On the other hand, the DC voltage of the Micro-grid is 400 V(4)-(5).
In table 1, the capacitor voltage is calculated by (1) when themodulation index  is set to 0.9. Additionally, the voltage rating of
the IGBT is set twice more than the capacitor voltage. The current
rating of IGBT is set 70% more than the each arm current. From theabove condition, the voltage rating of the IGBT is 3300 V and thecurrent rating is 400 A. Examples of high power IGBTs which meetthe conditions of the voltage rating and the current rating are shown.
2.2 Relationship between Cell Circuit Configurations and
Output Voltage
Fig. 2 shows relationships between circuit
configurations of cells and cell output voltages. In the AC-DC
converter which applies the MMC, the maximum value of the input
phase voltage is applied to each arm when the AC-DC converter
operates. Hence, the peak-to-peak value of the cell voltage vcell_p-p
is given by (2) from the input phase voltage and the number of cells

vcell _ p p  4

2 E ...........................................................
(2)
3 n

In addition, the output DC voltage of the MMC Vmmc equals thesummation of average values of the cell output voltages at one leg.
Hence, Vmmc is given by (3). Note that all average values of the cell
output voltages are same.

Vmmc  nvcell_ ave ................................................................ (3)where vcell_ave is the average value of the cell output voltage.
Fig. 2(a) shows the relationship between the chopper cell and its
output voltage. In the case of applying the chopper cell to the MMC,
a lower limit of the average output voltage is uniquely determinedfrom the peak-to-peak value of the cell voltage vcell_p-p and thenumber of cells at each leg n because the chopper cell cannot output
the negative voltage. Therefore, the chopper cell has the lower limitof the average output voltage. The lower limit of the average output
voltage vcell_ave_LL is given by (4) based on Fig. 2(a).

vcell _ ave _ LL 
31vcell _ p p ..................................................... (4)2
IEEJ Trans. ●●, Vol.●●, No.●, ●●●Control Strategy for Modular Multilevel Converter (Toshiki Nakanishi et al.)From (2), (3) and (4), the lower limit of the output DC voltage ofthe MMC Vmmc equals twice the value of the maximum voltage ofthe input phase voltage. From the principle of the above, the MMC
with chopper cells cannot achieve step-down rectification.
Fig. 2(b) shows the relationship between the circuit configurationof the H-bridge cell and its output voltage. In the case of the Hbridge cell, there is no limit of average value of the cell output
voltage because it is possible for the H-bridge cell to output thenegative voltage. Hence, it is possible for H-bridge cell to control
lower voltage than that of (4). Therefore, the MMC with H-bridge
cells achieves step-down rectification.

3.

Besides, the PI controller in AVR outputs the positive-sequence
component’s command of the arm current. Therefore, the positivesequence component of the arm current is regulated in order tomaintain the capacitor voltages constant. On the other hand, thezero-sequence component of the arm current is applied in order tosupply the output power to the DC micro-grid side. Note that thecurrent controller in the proposed control is constructed by a P
controller. Moreover, the control gain is defined as “Kacr”.
3.1 Capacitor Voltage Averaging Control
Thecapacitor voltage averaging control regulates the average value of
all capacitor voltages in the arm. Therefore, the average value of all
capacitor voltages is required to be calculated in each arm. Eachaverage value of the capacitor voltage is given by (5).

Proposed Control Strategy

Fig. 3 shows the control block diagram of the proposed stepdown rectifier which applies the MMC. As one of the features ofthe proposed control, each arm as shown in Fig. 1 is individuallycontrolled. The proposed control is based on the single-phase PFC
converter because the H-bridge cell has same circuit configuration
as singe-phase PFC converter. Moreover, the PFC converter and the
H-bridge cell have many common points in the circuit operationand the control. For example, the capacitor voltage is required to be
maintained constant in both circuits. Moreover, it is necessary tocontrol the input AC current in order to maintain the capacitor
voltage and reduce the total harmonic distortion (THD).
Differences between the PFC converters and the H-bridge cells are;there is the DC component in the output voltage of the H-bridge cell,and a capacitor voltage balancing control is necessary in order tocorrect the unbalance voltages among all capacitors. Thus, in orderto deal with above problems, it is necessary to add two controls inorder to control the DC component and achieve the capacitor
voltage balancing into the conventional control of the PFC
converters.
In particular, in order to control each arm, the control block
diagram is separated to the capacitor voltage control block and the
input current control (Automatic Current Regulator: ACR) block.
Moreover, the capacitor voltage control block consists of acapacitor voltage averaging control (Automatic Voltage Regulator:
AVR) and a capacitor voltage balancing control. First, the capacitor
voltage averaging control regulates the average value of thecapacitor voltages in the arm into the capacitor voltage command.
On the other hand, the capacitor voltage balancing control corrects
the unbalance among all capacitor voltages in the arm.
Capacitor Voltage
Averaging Control

vc*

+
－

PI

vcmk_avevcmk _ ave 2 n/2
 vcmkx ,n x 1k = r, s, t.................. (5)m = A, B

where vcmk_ave is the average value of the capacitor voltage, m is theindex which shows the upper side A or the lower side B, k is theindex of each phase, m and k are matched in both sides of theequation.
The error between the capacitor voltage command and theaverage value of capacitor voltage in the arm is corrected by a PI
controller. Therefore, the current command of the ACR is generated
depending on the fluctuation of the average value of all capacitor
voltages. However, the capacitor voltage includes the ripple voltage
with same frequency as the grid frequency and the ripple voltage
with twice frequency of the grid frequency when the cell capacitor
is charged and discharged(29). Thus, the frequencies of the ripple
voltages are 50 Hz and 100 Hz when the grid frequency is 50 Hz.
The control may become unstable due to the ripple voltages because
the ripple voltage becomes the disturbance to the capacitor voltage
averaging control. Hence, in order to keep the stability of thecontrol, the response angular frequency of the PI controller should
be designed with the low bandwidth. On the other hand, when thehigh control response is required in the capacitor voltage averaging
control, it is difficult to design the low bandwidth. Therefore, theband eliminated filter is applied in order to eliminate only the ripple
voltage with the particular frequency such as 100 Hz. As a result, it
is able to keep the stability and obtain the high control response of
the proposed control.
3.2 Arm Current Control
In the MMC, the input ACcurrent separately flows to the upper arm and the lower arm in each
Arm Current Control-1

imk_ph*2－

vmk_unit

Index

31
2E

m : A, Bk : r, s, t
k' : other than kk'' : other than k and k'
j : cell number
Input phase voltage(Detection value)

－－

vk

+

imk
imk'
imk''

imk_ph
+

+
+
+

1/3

－

Elimination ofzero phase component

Kacr

+
+

* Kacr :Control gain of
Arm Current Control

2/n +

vmkj*

－

A:―
Vmmc_mkj*
B : + (+)
1 vcmkj
2 n/2

v
x1

cmkx

Vmmc*

Variable
Dividing ratio

MMC Output
Voltage Control
andCapacitor Voltage
Balancing Control

Fig. 3. Control block diagram of step-down rectifier which applies MMC. The proposed control is based on the control for general
single phase power factor correction converters. Moreover, the proposed control is applied to each arm of the MMC in order tocontrol each arm. Note that Kacr is the control gain of the arm current control, m is the index of the arm group A or B, k, k´ or k´´ isthe index of the phase such as r, s and t, and j is the index of the cell number.
4

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Control Strategy for Modular Multilevel Converter (Toshiki Nakanishi et al.)phase. Therefore, it is possible to control the input current bycontrolling the AC component of the arm current on each arm. The
AC component of the arm current is defined as the positivesequence component of the arm current. Moreover, the ACcomponent of the arm current (the input current) flows to the MMC
with the same cycle as that of the input voltage source. In addition,
the output value of the PI controller of the AVR is given as the arm
current command. Thus, the positive-sequence component isapplied in order to control the average value of the all capacitor
voltages. Additionally, in the general rectifier, the high input power
factor is required. In the proposed control, the command of thepositive-sequence component is multiplied by the sinusoidal waveof which phase is the same as one of the input phase voltage vk_unit
in order to be synchronized with the input phase voltage. Note thatthe amplitude of the sinusoidal wave vk_unit is 1.0 in order to avoid
the change of the current command. In addition, the coefficients inthe latter part of the AVR is decided by the defined direction of thecurrent in Fig. 1 and the calculation for the maximum value of thepositive-sequence component.
On the other hand, each arm current also includes the DC
component. The DC component of the arm current flows in orderto supply the DC power into the micro-grid side. Additionally, theDC current shunts into the each leg of the MMC. Generally, theshunted DC current is constant and has same value among arms,
when the output DC voltage of the MMC is equally divided amongcells. In addition, the DC current is considered as the zero-sequence
component because the DC current is temporally not changed andhas no relationship to the cycle of the input voltage source.
The zero-sequence component becomes the disturbance to thearm current control (ACR) because the control objective of the arm
current control is the positive-sequence component of the arm
current. Thus, the zero-sequence component is eliminated from theactual detected current in order to apply only the positive-sequence
component as feedback signal of the ACR.
Fig. 4 shows a schematic diagram of the arm current waveform.
It is necessary to eliminate only the zero-sequence component fromthe actual arm current in order to apply only the positive-sequence
component as the feedback signal of the ACR after the system
detects all arm currents. In the proposed control method, the zerosequence component is eliminated by adding and subtracting thedetected arm current in each of the upper side and the lower side.
In particular, the positive-sequence components are canceled eachother and the total value of the zero-sequence components are
extracted by the addition of the three arm currents in each of theupper side and the lower side. Moreover, the zero-sequence
component of each arm current is calculated by dividing the total
value of the zero-sequence components into three. Finally, only the
positive-sequence component is extracted by subtracting each zerosequence component from each detected arm current. As a result,the zero-sequence component is eliminated from each arm current.
In addition, both the positive-sequence component and the zerosequence component are equal on all arms when the output powerof all cells is same and constant. Thus, the positive-sequence
component is extracted without the unbalance on three arms of eachside.
3.3 MMC Output Voltage Control
The output DC
voltage is supplied to the DC micro-grid side by applying the zerosequence component. Thus, the command of the output DC voltage
is added into the output value of the controller in the arm current
control. The output DC voltage of the MMC is divided on each cell

Actual arm current (DC + AC)

I

Zero-sequence
component ofarm current (DC)To supply power
into DC load

0tPositive-sequence componentof arm current (AC)To control
capacitor voltage

Fig. 4. Schematic diagram of current waveform on one
arm. Each arm current includes the positive-sequence
component (AC component) and the zero- sequence
component (DC component). In order to control thecapacitor voltage, it is necessary to eliminate the ACcomponent from the arm current.
per leg. Hence, the output DC voltage of the cell is set Vmmc*/n when
the command of the output DC voltage is Vmmc* and the number ofcells per leg is n. Note that the output DC voltage of each cell is notcompletely same as Vmmc*/n because the voltage dividing ratio of
each cell is adjusted by the capacitor voltage balancing control.
However, the error between the voltage dividing ratio which isadjusted by the capacitor voltage balancing control and Vmmc*/n issufficiently small. The detail is explained in the next section.
3.4 Capacitor Voltage Balancing Control
Thecapacitor voltage averaging control is used to regulate the averagevalue of all capacitor voltages. However, the unbalance voltage
which occurs among capacitors in same arm cannot be suppressedby only the capacitor voltage averaging control, because thecapacitor voltage averaging control corrects only the error between
the voltage command and the average value of the capacitor
voltages in the arm. So far, several methods in order to balance eachcapacitor voltage have been reported(8), (18)-(19). However, the design
method of control parameters has not been reported. In addition, thepositive-sequence component in order to keep the capacitor voltage
flows to all cells which exist in one arm. Therefore, the positivesequence component which flows to each cell is common. Thus, it
is difficult to adjust the arm current in order to balance on each cell.
In contrast to the conventional control, in order to balance thecapacitor voltage, in the proposed control, the output DC voltage ofthe cell is varied depending on the capacitor voltage. This control
principle is given by (6).

Vmmc _ mkj  Avd _ mkj Vmmc , m = A, B**

k = r, s, t ............. (6)where Vmmc_mkj* is the output DC voltage command of each cell,
Avd_mkj is the voltage dividing ratio of the output DC voltage on eachcell, j is the index of the cell number. m, k and j are matched in bothsides of (6).
The voltage dividing ratio of each cell Avd_mkj is given by (7). The
denominator of (7) shows the summation value of all capacitor
voltages in each arm. The numerator of (7) shows the value of eachcapacitor voltage. From (7), Avd_mkj is automatically adjusted
depending on each capacitor voltage.

Avd _ mkj 

1 vcmkj,
2 n/2
 vcmkx

m = A, B

k = r, s, t ................. (7)

x 1

5

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Control Strategy for Modular Multilevel Converter (Toshiki Nakanishi et al.)For example, the voltage dividing ratio of each cell Avd_mkj is set
into a high value when its capacitor voltage is higher than thecommand of the capacitor voltage. Thus, the output power of its cellincreases because the output voltage is increased by the high ratioof Avd_mkj. Therefore, the capacitor is discharged. In contrast, Avd_mkj
is set into a low value when its capacitor voltage is lower than thecommand of the capacitor voltage. Thus, the output power of its celldecreases because the output voltage is decreased by the low ratioof Avd_mkj. Hence, the capacitor is charged. Note that Avd_mkj changes
in steady state because each capacitor voltage vcmkj and the sumvalue of all capacitor voltages in the denominator of (7) include theripple voltage. On the other hand, the controller such as digital
signal processor (DSP) or Field Programmable Gate Array (FPGA)
calculates Avd_mkj in each control period. Thus, the controller
operates in order to correct the voltage errors among all capacitor
voltages in each control period. In the ideal state without the ripple
voltage, the output DC voltage of the cell is set Vmmc*/n when thevoltage values of all capacitors in the arm are same.
3.5 Unipolar Modulation for H-bridge Cell in MMC
In the proposed system, a unipolar modulation is applied for theoperation of the H-bridge cell. In the general MMC, the chopper
cell is applied. Therefore, the number of the voltage levels isdetermined by the number of cells. On the other hand, the output
voltage of the H-bridge becomes the three-level voltage when the
unipolar modulation is applied. Thus, the number of the voltage
levels is increased compared to the chopper cell when the same
number of cells is applied. Hence, the MMC with the H-bridge cellwhich the unipolar modulation is applied achieves the size
reductions of the input filter circuit and the buffer inductors.
Fig. 5 shows the diagram of the unipolar modulation for the Hbridge cell (ex. vArj*). The leg of the H-bridge cell is constructed by
S1 and S2. In contrast, the other leg is constructed by S3 and S4. The
switching patterns of S1 and S2 are determined by the voltage
command vArj*. Moreover, the switching patterns of S3 and S4 aredetermined by the inverted voltage command -vArj*.

4.

Capacitor Design

4.1

Capacitor Voltage

vArj*
0

-vArj*
1
0
1
S2
0
1
S3
0
1
S4
0
Fig. 5. Unipolar modulation for H-bridge cell (ex. vArj*).
The leg of the H-bridge cell is constructed by S1 and S2.
In contrast, the other leg is constructed by S3 and S4. The
switching patterns of S1 and S2 are determined by thevoltage command vArj*. Moreover, the switching patternsof S3 and S4 are determined by the inverted voltage
command -vArj*. From the above unipolar modulation, theoutput voltage of the H-bridge cell becomes three levels.
S1

Table 2.

Simulation conditions

Output power PO

300 kW

Input line voltage rms E

6.6 kV

Input voltage frequency

50 Hz

Output voltage Vmmc

400 V

Number of cell per leg n
DC capacitor C

20000 F

Load R

0.54 

Carrier frequency

1 kHz

Buffer inductor Lb

15 mH (%Z = 3.2%)

Table 3.

The capacitor voltage command

vc*is given by (1). Note that Vmmc_mkj* is slightly different amongcells because the voltage dividing ratio of the output DC voltage
Avd_mkj is automatically adjusted depending on each capacitor
voltage. However, the difference of Vmmc_mkj* among cells is ignored
because the voltage margin of the capacitor is fully large comparedto the difference of Vmmc_mkj* when the modulation index  is set to
0.9 or less as with general power converters.
4.2 Capacitor Value
The H-bridge cell has the same
operation as the single-phase PFC converter in terms of thecapacitor voltage control because both circuits regulate eachcapacitor voltage. Thus, the ripple voltage occurs when the Hbridge cell rectifies. The capacitor voltage includes the ripple
voltage with same frequency as the grid frequency and the ripple
voltage with twice frequency of the grid frequency(29). Generally,
the ripple voltage affects the stability of the capacitor voltage
control because the ripple voltage is the disturbance for thecapacitor voltage control. Thus, the capacitance should be designed
in order to reduce the effect by the ripple voltage for the capacitor
voltage control. The problems due to the ripple voltage of thecapacitors have been also discussed in the conventional singlephase PFC converters(30). Besides, the H-bridge cell of the MMC
has same construction as that of the conventional single-phase PFC

8Control parameters in simulation

Control gain of ACR Kacr

30

Proportional gain of AVR KP

0.2

Integral time of AVR Ti

0.5 sec

converter. Therefore, it is possible to apply the design principle ofthe capacitance and the suppression method of the ripple voltage inthe conventional single-phase PFC converter to the H-bridge cellwithout major modification. In the simulation of the circuit model
which the input voltage is 6.6 kV and the power capacity is 300 kW,
the capacitance is designed with the condition that the ripple voltage
is 5% of the average value of the capacitor voltage.

5. Simulation Results
In this chapter, the fundamental operation of the step-down
rectifier using the MMC is verified by simulation. Moreover, thestability for the mismatch of the circuit parameters is also evaluated.
Table 2 shows the simulation conditions. The proposed stepdown rectifier which applies the MMC with 8 cells per leg converts
commercial-frequency AC voltage of 6.6 kV into the DC voltage of
400 V.
6

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Control Strategy for Modular Multilevel Converter (Toshiki Nakanishi et al.)

vr

-50
5000
0
-5000

5000
0
-5000

vt

Grid current [A]

50
0

vs

ir

is

50

it

-50

Output voltage of all cells vAr, vAs [V]
vAr
vAs

5000
0
-5000

ir

Grid current [A]is it

Output voltage of all cells vAr, vAs [V]
vAr
vAs

10000
0
-10000

MMC output voltage [V]420

MMC output voltage [V]

400

400

380
1550

Capacitor voltages of R-phase [V]Capacitor voltages of R-phase [V]

1500

1500
1450

vr

Line voltage of upper side vArs [V]Line voltage of upper side vArs [V]

380
1550

vt

vs

0

10000
0
-10000420

10 [msec]

Grid voltage [V]

10 [msec]

Grid voltage [V]
5000
0
-5000

vcAr1-vcAr4

vcAr1-vcAr4

1450

vcBr1-vcBr4

Fig. 6. Simulation result for operation of step-down
rectifier which applies MMC. The proposed circuitachieves step-down rectification from line voltage of 6.6
kV to DC voltage of 400 V.

vcBr1-vcBr4

Fig. 7. Simulation results of proposed system wheninductance is 30 mH (twice the value of the nominal
value).

10 [msec]

Grid voltage [V]Table 3 shows the control parameters for the ACR and the AVR
in the simulation. The main purpose of this paper is the verificationof the MMC by the proposed control based on the single-phase PFC
converter. Hence, the design of the control parameters for the
single-phase PFC converter and the discussion about the
optimization are omitted.
Fig. 6 shows the simulation results for the fundamental
verification of the proposed step-down rectifier. At first, the output
voltage of all cells in the upper side in R-phase or S-phase is ninelevels. In addition, the line voltage between R-phase and S-phase inupper side of the MMC is 17-levels. In the MMC with four Hbridge cells per arm, the arm voltage is nine-levels because the arm
voltage is the summation of the output voltage of all cells in eacharm. Thus, the step-down rectifier which applies the MMC achieves
the size reduction of the buffer inductor compared to the H-bridge
cell with the general bipolar modulation when the same number ofcells is applied. Moreover, the step-down rectifier obtains the unity
power factor because the phase difference of the input phase voltage
and the input current is approximately 0. In addition, the total
harmonic distortion (THD) of the input current is 0.1% or less when
the normalized impedance %Z of each inductor is 3.2%.
On the other hand, the output voltage is maintained to 400 V.
From the result, the MMC achieves step-down rectification fromthe line voltage of 6.6 kV to the DC voltage of 400 V.
Moreover, the all capacitor voltages are maintained constant. In
addition, the maximum error between the voltage command and thesimulation values is 0.1% or less. This result confirms the usabilityof the proposed capacitor voltage balancing control without thedesign of control parameters.
In addition, the stability is also evaluated for the parameter

5000
0
-5000

vr

-50
5000
0
-5000

vt

Grid current [A]

50
0

vs

ir

is

it

Output voltage of all cells vAr, vAs [V]vArvAsLine voltage of upper side vArs [V]10000
0-10000420

MMC output voltage [V]

400
380
1550

Capacitor voltages of R-phase [V]

1500
1450

vcAr1-vcAr4

vcBr1-vcBr4

Fig. 8. Simulation results of proposed system wheninductance is 7.5 mH (half the value of the nominal
value).
mismatch of the inductance and the capacitance because the stable
7

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Control Strategy for Modular Multilevel Converter (Toshiki Nakanishi et al.)

40
39
38
37
36
35
34
33
32

1 [msec](a) 30 mH

40
39
38
37
36
35
34
33
32

10 [msec]

Grid voltage [V]
5000
0
-5000

vr

0

(b) 7.5 mH-50

Fig. 9. Expanded waveform of the peak of inductor
current when inductance is changed.

5000
0
-5000

operation is required in the general converter even when theparameter mismatch occurs. In particular, the MMC can achieve theinput current control, the MMC output voltage control and thecapacitor voltage control. Thus, the waveforms when the parametermismatch occurs are shown in order to evaluate the operation of the
MMC.
From Fig. 7 to Fig. 11, the simulation results are shown in order
to confirm the stability of the proposed control when circuit
parameters change. In each simulation, the inductance and thecapacitance are varied from 2.0 p.u. to 0.5 p.u. compared to thenominal values whose the inductance and the capacitance are 15
mH and 20000 F respectively.
Simulation results and waveforms when the inductance changes
are as follows:
Fig. 7. Simulation result when the inductance is changed to 2.0
p.u. (30 mH);
Fig. 8. Simulation result when the inductance is changed to 0.5
p.u. (7.5 mH);
Fig. 9 (a). Expanded waveform of the peak of the inductor current
when the inductance is 2.0 p.u. (30 mH); andFig. 9 (b). Expanded waveform of the peak of the inductor
current when the inductance is 0.5 p.u. (7.5 mH).
From the comparison of two results when the inductance is varied,
it is concluded that only the ripple of the inductor current changes.
Furthermore, the effective value of the input current is slightly
different because the input power factor changes by the inductance.
However, there is no major difference such as the distortion of
waveforms in both simulation results. As a conclusion, theproposed control is stable even when the inductance is mismatched.
After that, simulation results and waveforms when thecapacitance is varied are as follows:
Fig. 10. Simulation result when the capacitance is changed to 2.0
p.u. (40000 F); andFig. 11. Simulation result when the capacitance is changed to 0.5
p.u. (10000  F).
From the comparison of the capacitor voltage waveforms (thelowest waveforms of each simulation results), the ripple of thecapacitor voltage changes when the capacitance changes. Besides,
the total harmonic distortion (THD) of the grid current in the MMC
with the capacitance of 0.5 p.u. slightly becomes high because theoutput voltage of the cell is fluctuated by the ripple voltage.
However, this THD of the grid current is still less than 1%.
Additionally, there is no major difference in two simulation results.
Thus, the proposed control is stable when the capacitance ismismatched.
In conclusion, the proposed system achieves the stable operationeven when the circuit parameters of the inductance and thecapacitance have the mismatches from 0.5p.u. to 2.0p.u..

vt

Grid current [A]50
1 [msec]

vs

ir

is

it

Output voltage of all cells vAr, vAs [V]vArvAsLine voltage of upper side vArs [V]10000
0-10000420

MMC output voltage [V]

400
380
1550

Capacitor voltages of R-phase [V]1500
vcAr1-vcAr4

1450

vcBr1-vcBr4

Fig. 10. Simulation results of proposed system whencapacitance is 40000 F (twice the value of the nominal
value).

10 [msec]

Grid voltage [V]
5000
0
-5000

vr

-50
5000
0
-5000

vt

Grid current [A]

50
0

vs

ir

is

it

Output voltage of all cells vAr, vAs [V]vArvAsLine voltage of upper side vArs [V]10000
0-10000420

MMC output voltage [V]

400
380
1600

Capacitor voltages of R-phase [V]

1500
1400

vcAr1-vcAr4

vcBr1-vcBr4

Fig. 11. Simulation results of proposed system whencapacitance is 10000 F (half the value of the nominal
value).

8

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Control Strategy for Modular Multilevel Converter (Toshiki Nakanishi et al.)6.

Experimental Results

Table 4.

6.1 Experimental Conditions and Circuit Parameters
This chapter explains the evaluation results of the proposed control
by using a miniature model of the MMC in the low voltage grid of
200 V.
Table 4 shows experiment conditions. The miniature model isconstructed by four cells per leg. Additionally, as fundamental
experiment, the resistor of 5.2  is applied as the load of the MMC
without a smoothing capacitor. In addition, the inductance of thebuffer inductor is 8 mH, whereas the normalized impedance %Z of
the inductor is 6.1%. The normalized impedance %Z in theexperiment is designed higher than the normalized impedance %Z
in the simulation in order to maintain the stability of the ACR. On
the other hand, the capacitance is 1300 F. In the experiment, inorder to measure exactly not only the average value of the capacitor
voltage but also the ripple voltage, the ripple voltage against the
average value is designed higher than that of the simulation. The
ripple voltage is approximately 10% of the average value of thecapacitor voltage at the output power rating of 1 kW.
Table 5 shows the control parameters for the ACR and the AVR
in the experiment. As same as the simulation conditions, the strict
design for the control parameters is avoided because the main
purpose of this paper is the verification of the MMC by the
proposed control based on the single-phase PFC converter.
Fig. 12 shows the controller and the detection system. In theexperimental system, the time-division detection system is appliedin order to reduce the number of AD converters. In the practicalsystem, it is necessary to apply the time-division detection systembecause the number of the capacitor voltages is particularly large.
The calculation time of the DSP is 125 sec. Both the upper arm
current iAk and the lower arm current iBk are detected in one periodof the calculation time. Moreover, the input phase voltage of Rphase vr and the input phase voltage of T-phase vt are also detected
in one period of the calculation time. On the other hand, eachcapacitor voltage is detected and updated in once every four periodsof the calculation time. Additionally, in order to detect several
signals by one AD converter, the analog multiplexers (AMUX) areapplied. Besides, in order to avoid the detection delay by theswitching of the AMUX, the sample and hold IC (S&H) is applied.
The S&H detects each signals in the start timing of the DSP
calculation. All operation signals of the AD converters, the AMUXs
and the S&H ICs are generated by the FPGA based on the period of
the carrier. In addition, the detection values and the voltage
commands of the cells are sent and received between the DSP and
the FPGA. Note that the input phase voltage of S-phase vs is
calculated from vr and vt.
6.2 Verifications of Fundamental Operation for Stepdown Rectifier using MMC
Fig. 13 shows waveforms of the
input phase voltage, the input current of R-phase and the output DC
voltage. Firstly, from the waveforms of the input phase voltage andthe input current, it is confirmed that the unity power factor is
obtained in the input stage. Moreover, the total harmonic distortion(THD) of the input current is 3.5% when the normalized
impedance %Z of the inductor is 6.1%. Second, the waveform of
the output DC voltage in lower side of Fig. 13 shows that the stepdown rectifier converts from the input voltage of 200 V into the
output DC voltage of 75 V. From this result, it is confirmed that theoutput voltage is maintained at constant. Therefore, the proposed
rectifier with the MMC achieves step-down rectification.

Experimental conditions

Output power PO

1000 W

Input line voltage rms E

200 V

Input voltage frequency

50 Hz

Output voltage Vmmc

75 V

Number of cell per leg n

4

DC capacitor C

1300 F

Load resistor R

5.2 

Carrier frequency

8 kHz

Buffer inductor Lb

8 mH (%Z = 6.1%)

Table 5.

Control parameters in experimentControl gain of ACR Kacr

30

Proportional gain of AVR KP

0.02

Integral time of AVR Ti

0.08 sec

DSP(Calculation time : 125 sec)Gate
signalDetection value

Command

FPGA(Clock : 40 MHz)
AX1
signal

S&H
signalAD
AX4signalAX1
signalAD

AD
signalAD

AD
signalADsignalAMUX(4ch)

AMUX

AMUX

S&H S&H S&H S&H

S&H S&H

S&H S&H

iAk

vr

vcAk1 vcAk2
16
cell

One phase

cell

vcBk1
cell

vcBk2

iBk

vt

cell
AD : Analog to digital converter
S&H : Sample and hold IC
AMUX : Analog multiplexer

Fig. 12. Controller and detection system in experimental
system. In order to reduce the number of the AD
converters and avoid the detection delay, the analog
multiplexer (AMUX) and the sample and hold IC (S&H
IC) are applied.
Fig. 14 shows waveforms of the arm voltage which is thesummation of the output voltage of all cells in each arm and the
waveform of the line voltage between R-phase and S-phase in theupper side. At first, the system obtains the arm voltage of five-levels
because one of H-bridge cells with the unipolar modulation obtains
three-level voltage and the arm has two cells. In addition, thewaveforms are not symmetry in the positive side and the negativeside because the output voltage of the H-bridge cell includes the DC
component as an offset.
Besides, the waveform of the line voltage between R-phase andS-phase in upper side is nine-levels. In points which change thevoltage level, some points do not change in the step pattern. This
reason is that the bias of the PWM pulse occurs because the arm
voltage is not symmetry in the positive side and the negative side
9

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Control Strategy for Modular Multilevel Converter (Toshiki Nakanishi et al.)due to the DC component of the cell output voltage. However, thevoltage fluctuation is small when the voltage level changes
compared to that when applying the chopper cells and the H-bridge
cells with bipolar modulation. Thus, the system achieves the size
reduction of buffer inductors. Additionally, the frequency of thePWM pulse is decided by the equivalent frequency of the arm. In
general, the equivalent frequency of the MMC is sufficiently highcompared to the commercial frequency. Thus, the effect of the highfrequency component is small even when the inductor is small
because most of the high frequency is applied to the buffer inductor.
Fig. 15 shows the waveforms of all cell capacitor voltages which
are connected to the R-phase leg. The cell capacitor voltage iscontrolled according to the capacitor voltage command vc*. As aresult, the proposed step-down rectifier maintains the capacitor
voltage of each H-bridge cell to the voltage command of 130 V.
Therefore, the proposed rectifier also achieves the capacitor voltage
control. In addition, the maximum voltage error between thevoltage command of the cell capacitor and the measured voltage is
2% or less.
Fig. 16 shows the waveforms of the ripple voltages of all
capacitors which are connected to the R-phase leg. In principle,
each capacitor in the MMC has the ripple voltage whose frequency
is based on the frequency of the input voltage(29). As a result, thewaveforms of the ripple voltages with the low frequency are shownas same as the above discussion. Additionally, there is the error
among capacitor voltages. However, as already discussed in Fig. 15,
the voltage errors among all capacitors are very small compared tothe average value of capacitor voltages.
Fig. 17 shows the relationship between the output power and the
input power factor. The input power factor is over 0.95 when the
output power is from approximately 0.2 p.u. to 1.0 p.u. (1000 W).
Hence, the step-down rectifier which applies the MMC obtains thehigh power factor in the wide range of the power conversion.
Finally, from the above experimental results, the proposed stepdown rectifier which applies the MMC achieves the input current
control, the capacitor voltage control and step-down rectification atsame time.
6.3 Verifications of Capacitor Voltage Control
Fig. 18shows the waveforms of the capacitor voltage when the commandof the capacitor voltage changes in the step pattern of 0.23 p.u.
(from 100 V to 130 V). The capacitor voltages converge to thecommand of the capacitor voltage. Additionally, the capacitor
voltages are balanced.
Fig. 19 shows the waveform of the MMC output voltage when
the command of the capacitor voltage changes in the step pattern of
0.23 p.u. (from 100 V to 130 V). All capacitor voltages converge tothe command of the capacitor voltage. Furthermore, the MMC
output voltage is maintained at constant even when the capacitor
voltage changes.
Fig. 20 shows the waveforms of the capacitor voltage when the
MMC output voltage changes in the step pattern of 0.27 p.u. (from40 V to 60 V). All capacitor voltages converge to the command of
the capacitor voltage and are maintained at same constant value.
This result confirms the stable operation of the proposed capacitor
voltage control even when the MMC output voltage is suddenly
changed.
From above results, the proposed control maintains the capacitor
voltage constant. Furthermore, the capacitor voltage balancing
control is not necessary to design the control parameters and keep
the balance of the capacitor voltage.

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

0
Input Phase Current (R-phase) [5 A/div]0

MMC Output Voltage [25 V/div]0
Fig. 13. Waveforms of input voltage, input current andoutput voltage. The unity power factor is obtained in the
input stage. The THD of the input current is 3.5% when
the %Z of the inductor is 6.1%.
Output voltage of all cells in upper side vAr,vAs [250 V/div]00Line voltage of upper side (A side) vArs [250 V/div]

0
4msec
Fig. 14. Waveforms of arm voltage which is summationof output voltage of all cells in each arm and waveformsof line voltage between R-phase and S-phase in upperside. The arm voltage is five levels and the line voltage isnine levels.

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

130 V

0

10 msec

Fig. 15. Waveforms of all capacitor voltages in R-phaseleg. The proposed system maintains the capacitor voltageof each H-bridge cell to the voltage command of 130 V.
In addition, the maximum voltage error between thecapacitor voltage command and the measured voltage is
2% or less.

10

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Control Strategy for Modular Multilevel Converter (Toshiki Nakanishi et al.)7.

Conclusion
Input power factor cosf

1.00
1.00

In this paper, the fundamental verification of the control strategy
for a step-down rectifier which applies the modular multilevel
converter (MMC) was presented. The main part of the proposed
control was based on the control method for a single-phase power
factor correction converter (PFC converter) with the aim to apply
many control techniques for the PFC converter to the MMC.
Moreover, the proposed method of the capacitor voltage balancing
control for all capacitor voltages did not require the design of thecontrol parameters.
The fundamental operation was confirmed by the simulation. As
a result, the proposed converter which applies the MMC achieved
step-down rectification from the grid voltage of 6.6 kV to the DC
voltage of 400 V. Moreover, the unity power factor was obtained in
the input side of the MMC. The total harmonic distortion (THD) of
the input current was approximately 0.1% when the nominalized
impedance %Z of each inductor was 3.2%. Additionally, the stepdown rectifier maintained all capacitor voltage at constant. Finally,
the experimental results by the miniature model confirmed stepdown rectification from the input voltage of 200 V into the output
DC voltage of 75 V. Moreover, the proposed step-down rectifier
maintained the capacitor voltage of each H-bridge cell to thevoltage command of 130 V. The maximum error between thecommand of the capacitor voltage and the measured voltage was
2% or less.
Based on these results, it is confirmed that many control
techniques for the single-phase PFC converter can be applied to the
MMC. Moreover, it is not necessary to design many control
parameters and consider the circuit models in order to clarify thecontrol parameters. In addition, it is also expected that it is possible
to propose new ideas and new points of view for a control methodof the MMC by applying control technologies of the single-phase
PFC converters. As a result, the discussion of the control method
for the MMC will expand for the development of the MMC by newideas and new points of view.

0.95
0.95

0.90
0.90

0.85
0.85

0.80
0.80

0.75
0.75

0.70
0.70
00

200
200

400
400

600
600

800
800

1000
1000

Output power [W]
Fig. 17. Relationship between output power and input
power factor. The input power factor is over 0.95 when
the output power is from approximately 0.2 p.u. to 1.0
p.u. (1000 W). Thus, the system obtains the high power
factor in the wide range of the power conversion.

Input current of R-phase ir [5 A/div]

0
6.8 V

Command of capacitor voltage vc* [25 V/div]
Capacitor voltage
vcAr1, vcBr1 [25 V/div]
210 msec

100msec0
Fig. 18. Waveforms of capacitor voltage when commandof capacitor voltage changes in step pattern of 0.23 p.u.
(from 100 V to 130 V). All capacitor voltages converge
to the command of the capacitor voltage after thecapacitor voltage overshoots.

Input current of R-phase ir [5 A/div]0
Capacitor voltage (R-phase) [5 V/div]
vcAr1, vcAr2, vcBr1, vcBr2,

Command of capacitor voltage vc* [25 V/div]
Capacitor voltage vcAr1 [25 V/div]

130 V
6.2 V

0

0

5 msec

MMC output voltage Vmmc [25 V/div]
100msec

Fig. 19. Waveforms of MMC output voltage whencommand of capacitor voltage changes in step pattern of
0.23 p.u. (from 100 V to 130 V). The MMC output
voltage is maintained at constant when the capacitor
voltage changes.

Fig. 16. Waveforms of ripple voltages of all capacitors
which are connected to the R-phase leg. In principle, eachcapacitor in the MMC has the ripple voltage with the low
frequency because the frequency of the ripple voltage isbased on the frequency of the input voltage source.

11

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Control Strategy for Modular Multilevel Converter (Toshiki Nakanishi et al.)(18) A. Hassanpoor, L. Ängquist, S. Norrga, K. Ilves, H-P. Nee, “Tolerance Band
Modulation Methods for Modular Multilevel Converters,” IEEE Trans. on
Power Electronics, vol. 30, no. 1, pp. 311-326, 2015.
(19) D. Karagiannis, E. Mendes, A. Astolfi, R. Ortega, “An ExperimentComparison of Several PWM Controllers for a Single-phase AC-DC
Converter,” IEEE Trans. on Control Systems Technology, vol. 11, no. 6, pp.
311-326, 2003.
(20) B-R. Lin, H-H. Lu, S-C. Tsay, “Control Technique for High Power Factor
Multilevel Rectifier,” IEEE Trans. on Aerospace and Electronic Systems, vol.
37, no. 1, pp. 226-240, 2001.
(21) G. Escobar, D. Chevreau, R. Ortega, E. Mendes “An Adaptive PassivityBased Controller for a Unity Power Factor Rectifier,” IEEE Trans. on Control
Systems Technology, vol. 9, no. 4, pp. 637-644, 2001.
(22) J-C. Crebier, J-P. Ferrieux, “PFC Full Bridge Rectifiers EMI Modeling andAnalysis – Common Mode Disturbance Reduction,” IEEE Trans. on PowerElectronics, vol. 19, no. 2, pp. 378–387, 2004.
(23) H. Akagi, T. Yamagishi, N. M. L. Tan, S. Kinouchi, Y. Miyazaki, M. Koyama,“Power-Loss Breakdown of a 750-V 100-kW 20-kHz Bidirectional Isolated
DC–DC Converter Using SiC-MOSFET/SBD Dual Modules,” IEEE Trans.
on Industry Applications, vol. 51, no. 1, pp. 420–428, 2015.
(24) B. Zhao, Q. Song, W. Liu, Y. Sun, “Overview of Dual-Active-Bridge Isolated
Bidirectional DC–DC Converter for High-Frequency-Link PowerConversion System,” IEEE Trans. on Power Electronics, vol. 29, no. 8, pp.
4091–4106, 2014.
(25) J. W. Kolar, G. Ortiz, “Solid-State-Transformers: Key Components of Future
Traction and Smart Grid Systems,” Proceedings of the International PowerElectronics Conference - ECCE Asia (IPEC 2014), 2014.
(26) [Online] https://www.infineon.com(27) [Online] http://www.hitachi-power-semiconductor-device.co.jp(28) [Online] https://library.e.abb.com(29) T. Nakanishi, J. Itoh : "Capacitor Volume Evaluation based on Ripple Current
in Modular Multilevel Converter", 9th International Conference on PowerElectronics, No. WeA1-5, 2015.
(30) Y. Ohnuma, J. Itoh, “A Novel Single-Phase Buck PFC AC–DC Converter
With Power Decoupling Capability Using an Active Buffer,” IEEE Trans. on
Industrial Application, vol. 50, no. 3, pp. 1905–1914, 2014.

Input current of R-phase ir [5 A/div]

0

6.5 V

Capacitor voltage vcAr1, vcBr1 [25 V/div]
MMC output voltage Vmmc [25 V/div]0088msec100msec

Fig. 20. Waveforms of capacitor voltage when MMC
output voltage changes in step pattern of 0.27 p.u. (from40 V to 60 V). All capacitor voltages are also balanced
even when the MMC output voltage changes suddenly.

References
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“Microgrids,” IEEE Power Energy Mag., vol. 6, no. 3, pp. 26-94, 2008.
H. Kakigano, Y. Miura, T. Ise, “Low-Voltage Bipolar-Type DC Microgrid forSuper High Quality Distribution,” IEEE Trans. on Power Electronics, vol.
25, no. 12, pp. 3066-3075, 2010.
D. Salomonsson, L. Söder, A. Sannino, “An Adaptive Control System for a
DC Microgrid for Data Centers,” IEEE Trans. on Industry Applications, vol.
44, no. 6, pp. 1910-1917, 2008.
D. Salomonsson, L. Söder, A. Sannino, “Protection of Low-Voltage DC
Microgrids,” IEEE Trans. on Power Delivery, vol. 24, no. 3, pp. 1045-1053,
2010.
M. Tabari, A. Yazdani, “Stability of a dc Distribution System for Power
System Integration of Plug-In Hybrid Electric Vehicles,” IEEE Trans. on
Smart Grid, vol. 5, no. 5, pp. 2564-2573, 2014.
Y. Ito, Y. Zhongqing, H. Akagi, “DC microgrid based distribution power
generation system,” in Proc. IEEE 4th Int. Power Electronics and Motion
Control Conf. 2004. (IPEMC 2004), vol. 3, pp. 1740–1745, 2004.
M. Glinka, R. Marquardt, “A New AC/AC Multilevel Converter family,”IEEE Trans. on Industrial Electronics, vol. 52, no. 3, pp. 662-669, 2005.
M. Hagiwara, H. Akagi, “Control and Experiment of Pulsewidth-Modulated
Modular Multilevel Converters,” IEEE Trans. on Power Electronics, vol. 24,
no. 7, pp. 1737-1746, 2009.
H. Akagi, “Classification, Terminology, and Application of the Modular
Multilevel Cascade Converter (MMCC),” IEEE Trans. on Power Electronics,
vol. 26, no. 11, pp. 3119-3130, 2011.
M. Vasiladiotis, S Kenzelmann, N. Cherix and A. Rufer, “Power and DC Link
Voltage Control Considerations for Indirect AC/AC Modular Multilevel
Converters”, Power Electronics and Applications 2011. (EPE 2011),
Proceedings of the 2011-14th European Conference, 2011.
J. Shi, W. Gou, H. Yuan T. Zhao, A. Q. Huang, “Research on Voltage andPower Balance Control for Cascaded Modular Solid-State Transformer”,
IEEE Trans. on Power Electronics, vol. 26, no. 4, pp. 1154–1166, 2011.
K.Ilves, L. Harnefors, S. Norrga, H-P. Nee, “Analysis and Operation ofModular Multilevel Converters With Phase-Shifted Carrier PWM,” IEEE
Trans. on Power Electronics, vol. 30, no. 1, pp. 268–283, 2015.
S. Debnath, M. Saeedifard, “A New Hybrid Modular Multilevel Converter
for Grid Connection of Large Wind Turbines,” IEEE Trans. on Sustainable
Energy, vol. 4, no. 4, pp. 1051–1064, 2013.
N. Thitichaiworakorn, M. Hagiwara, and H. Akagi, “Experimental
Verification of a Modular Multilevel Cascade Inverter Based on Double-Star
Bridge Cells,” IEEE Trans. on Industry applications, vol. 50, no. 1, pp. 509519, 2014.
M. Vasiladiotis, A. Rufer, “Analysis and Control of Modular Multilevel
Converters with Integrated Battery Energy Storage,” IEEE Trans. on PowerElectronics, vol. 30, no. 1, pp. 509-519, 2015.
G. Minyuan and X. Zheng, "Modeling and Control of a Modular Multilevel
Converter-Based HVDC System Under Unbalanced Grid Conditions," IEEE
Trans. on Power Electronics, vol.27, pp. 4858-4867, 2012.
F. Deng, Z. Chen, “Voltage-Balancing Method for Modular Multilevel
Converters Switched at Grid Frequency,” IEEE Trans. on Industrial
Electronics, vol. 62, no. 7, pp. 4158-4169, 2015.

Toshiki Nakanishi(Student member) received the B.S. degrees inelectrical, electronics and information engineeringfrom Nara National College of Technology (NNCT),
in 2011. He received master degrees in Nagaoka
University of Technology (NUT) in 2014. And hehas been in doctoral course of NUT. He is the student
member of IEEJ and IEEE. His main researchinterests include multilevel converters.

Jun-ichi Itoh

(Senior Member) received his M.S. and PhD degrees
in electrical and electronic systems engineering from
Nagaoka University of Technology, Niigata, Japan in
1996 and 2000, respectively. From 1996 to 2004, he
was with Fuji Electric Corporate Research andDevelopment Ltd., Tokyo, Japan. Since 2004, He has
been with Nagaoka University of Technology as an
associate professor. He received the IEEJ Academic
Promotion Award (IEEJ Technical Development Award) in 2007 and the
Isao Takahashi Power Electronics Award in 2010. His research interests
include matrix converters, DC/DC converters, power factor correction
techniques and motor drives. He is a senior member of the Institute ofElectrical Engineers of Japan and the Society of Automotive Engineers ofJapan.

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