Modular Multilevel Converter for Wind Power
Generation System connected to Micro-gridToshiki Nakanishi
Nagaoka University of Technology
Nagaoka, Japannakanishi@stn.nagaokaut.ac.jp

Koji Orikawa
Nagaoka University of Technology
Nagaoka, Japanorikawa@vos.nagaokaut.ac.jp

Abstract— This paper discusses a AC-DC converter which isconstructed by a Modular Multilevel Converter (MMC) for awind power generation system connected to Micro-grid. The
proposed system which is constructed the MMC with an Hbridge cell achieves to convert from a generator voltage of 3.3 kV
into DC bus voltage of 340 V. Moreover, as a fundamental
evaluation, the experimental result by miniature model of 700 W
confirms that the proposed system achieves the step-down
operation from input voltage of 200 V into DC voltage of 65 V.
Finally, the proposed system maintains the capacitor voltage ofeach cell to the voltage command. Furthermore, the maximum
voltage error between the voltage command of the cell capacitor
and the measured voltage is 10% or less.
Keywords-Modular Multilevel Converter;H-bridge cell; Microgrid; wind power generation system; high power rectifier

I.

INTRODUCTION

Recently, a micro-grid and a DC power grid are actively
researched as a next generation power supply. Advantages ofthe micro-grid are summarized as follows [1]-[4]; (i) thesystem achieves high efficiency operation because of the
reduction of conversion losses in inverters between dc output
sources and loads. (ii) it is not necessary to consider
synchronization with utility grid and reactive power. (iii) whena blackout or voltage sag occurs in the utility grid, it does notaffect the dc bus voltage of the micro-grid directly because of
the stored energy of the dc capacitor and the voltage control of
AC-DC converter. (iv) the micro-grid is suitable to connect abattery energy storage system and a renewable energy sourcesuch as a photovoltaic generation system and a fuel cellbecause the output voltage of many renewable energy sources
is DC voltage. From advantages of the above, the micro-gridhas been applied to the power grid in isolated islands as astand-alone power system [5]-[6].
Moreover, a wind power generation is also applied to thepower grid in isolated islands as one of the power source.
Presently, many power grids in isolated islands are constructedby a diesel generation system. However, this system is very
costly because the generation costs in the isolated island
involve a high transportation cost to carry fuels for diesel
generators [5]. Thus, applications of renewable energy sources
such as a wind power generation are actively researched anddeveloped in order to reduce the fuel cost. Moreover, locationsof offshore and the isolated island are suitable for a wind power
generation with high power capacity because wind is muchstronger and much constant compared with wind conditions of

Jun-ichi Itoh
Nagaoka University of Technology
Nagaoka, Japan
itoh@vos.nagaokaut.ac.jp

onshore [8]-[10]. Therefore, the wind power generation isapplied as one of power sources for the micro-grid in isolatedislands.
Presently, a conventional wind power generation system isconstructed by a transformer and a bidirectional converter inorder to connect to an AC grid [11]-[13]. Besides, a wind
power generation system connected to the micro-grid has afeature which the rated voltage of the wind power generator
with high power capacity is higher than DC bus voltage of
340V in the micro-grid [1], [8]. Therefore, it is necessary for a
power system to convert from generator voltage into DC bus
voltage when power is supplied from the wind power generator
into the micro-grid. Additionally, the system has to boost fromDC bus voltage into generator voltage because starting torqueis required while the wind power generator starts up. Thus, thebidirectional AC-DC converter operates as a rectifier when thesystem generates power. In contrast, the bidirectional AC-DC
converter operates as an inverter when the generator starts up.
However, a size of the transformer is bulky because thetransformer operates in low frequency because the generator
operation frequency is low. In addition, the reasons which thetransformer is bulky include that a high transformer ratio is
required to convert from generator voltage into DC bus voltage.
As one of solutions, employing a Modular Multilevel
Converter (MMC) to the wind power generation system
connected to the micro-grid is an effective method. Advantagesof the MMC are as follows; (i) the circuit configuration is
simple because of cascade connection of cells. (ii) the MMC
reduces the harmonic distortions because the MMC output themultilevel waveform (iii) low voltage devices are applied toeach cell because the output voltage of the cell is low byincreasing a number of cells. Thus, the system achieves thehigh response operation. From the advantages of the above, theMMC has been actively researched as a next generation highpower converter without the bulky transformer [14]-[16].
Therefore, the wind power generation system achieves the size
reduction by applying the MMC into the system.
However, in the general AC-DC converter using the MMC
which consists of chopper cells, it is difficult to achieve thestep-down rectified operation because chopper cells cannot
output negative voltage. Moreover, many control methods ofthe MMC have been reported. Fundamental configurations ofcontrol system for the MMC are constructed from a current
control system and a capacitor voltage control system.
However, most of conventional systems are complex and it isdifficult to understand these control principle instinctively.

Especially, the capacitor voltage control is constructed frommany components. For example, a main control system inorder to control average value of all capacitor voltage isapplied. In addition, many balancing control systems areapplied as sub control system [16]. Therefore, it is also difficult
to design control parameters in each controller.
This paper discusses a wind power generation system
connected to the micro-grid using the MMC which consists of
H-bridge cells in order to convert from high generator voltage
into DC bus voltage. Employing H-bridge cell is able to solve
the voltage limit. Moreover, the system is able to operate as ahigh power step-down rectifier. Additionally, a proposed
control system is very simple because the proposed control
system is constructed from the capacitor voltage control systemand the arm current control system for each arm. Thus, it isable to control each arm independently. In addition, as voltage
balancing control system in order to compensate the effort
among cells in the arm, the output DC voltage of the cell isvaried depending on the capacitor voltage. Furthermore, it iseasy to design the control parameters by applying the proposedbalancing control system which is very simple. As afundamental evaluation, this paper proposes a control method
in order to achieve the step-down rectification. Moreover, froman experimental result by miniature model of 700 W, theproposed system achieves to convert from three phase voltage
of 200 V into the DC voltage of 65 V.
II.

WIND POWER GENERATION SYSTEM USING MMC

A. Main circuit configuration
Fig. 1(a) shows the main circuit configuration of the
proposed wind power generation system using the MMC.
Each leg consists of two buffer reactors Lb and H-bridge cells.
Due to cascade connection of cells, the converter achieves a
multi-level voltage waveform and also reduces the rated
voltage of each cell. Thus, many cascaded cells are used inpractical because it reduces harmonic distortion and utilize
with a low voltage rating devices. On the other hand, in the
MMC, the output DC voltage depends on the summation of
the average value of cell output voltage.
Table 1 shows the configuration example of the MMC
when the MMC is applied into the wind power generation
system as the step-down converter connected to the micro-grid.
The power capacity of the system is 1 MW and the generator
voltage is 3.3 kV. On the other hand, the DC voltage of the
micro-grid is 340 V [1] In addition, each parameter iscalculated when the IGBTs which the voltage rating is 1,200V
and the current rating is 2,400 A. are applied. Moreover, thecapacitor voltage is calculated by (6) when the modulation
factor  is set to 0.8. Additionally, the voltage rating of the
IGBT is set 30% more than the capacitor voltage. The current
rating of IGBT is set 50% more than the each arm current. The
numbers of capacitor are calculated when each cell has one
capacitor. Finally, examples of high power IGBTs which meetthe conditions of the rating voltage and rating current are
shown.

vcAr1

vAr1

cell

vcAr(n/2)

vAr(n/2)

cell

Wind power
generator
G
cell

Sa+ Sb+
S－
a

S－
b

iAr
ir
is
it

Lb

iBr

Lb

Vmmc

DC bus ofMicro-grid

vcBr1

vBr1
C

v
H-bridge cell Br(n/2)

cellvcBr(n/2)
cellFig. 1. Circuit configuration of the MMC for the wind power generation
system connected to the micro-grid. The MMC with H-bridge cells isable to operate the step-down rectifier.

TABLE I.

THE CONFIGURATION EXAMPLE OF THE WIND POWER
GENERATION SYSTEM @1 MW

Voltage rating of IGBT
Current rating of IGBT
Capacitor voltage @ = 0.8
Numbers of Cells @ leg
Total numbers of Cells
Numbers of Switching Device
Numbers of Capacitors

1,200 V
2,400 A
860 V
8
24
96
24
1MBI2400U4D-120(Fuji Electric Co., Ltd.)MBN2400E17D(1,700 V, Hitachi, Ltd.)FZ2400R12HP4 E9(Infineon)
5SNA 2400E170305(1,700 V, ABB)

Examples of IGBTs

vchopper

Sa+

vC
C

Sa-

vH-bridge Sa+

Sb+

Sa-

Sb-

vC
C

vH-bridge

vchoppervp-p

vp-p
vcell_ave0vcell_ave0(a) Chopper cell(b) H-bridge cellFig. 2. Circuit configuration and output voltage of each cell.
The chopper cell has the output voltage limit because the chopper cellcannot output the negative voltage. On the other hand, the H-bridge cell
does not have the output voltage limit.

B. Relationship between cell circuit configurations andoutput voltage
Fig. 2 shows relationships between cell circuit
configurations and output voltage. In the AC-DC converter
using the MMC, a maximum value of generator output voltage
is applied to each arm of the MMC when the wind generator
operates. Hence, a peak-to-peak value of the cell voltage vp-p isgiven by (1) from generator output voltage and the number ofcells per leg

2 E
v p p  2

3 n



In addition, the output DC voltage of the AC-DC converter
using the MMC Vmmc equals a summation of cell output
average voltage at one leg. Hence, Vmmc is given by (2).

Vmmc  nvcell_ ave where vcell_ave is an average value of the cell output voltage.
Fig. 2(a) shows the relationships between the chopper celland its output voltage. In the case of applying the chopper cell,a lower limit of cell output average voltage is uniquelydetermined from the peak-to-peak value of the cell voltage vp-p
and the number of cells at each leg n because the chopper cellcannot output negative voltage. Therefore, in the chopper cell,the lower limit of output average voltage is given by (3)v cell _ ave 

1v p  p 
2

From (1), (2) and (3), the lower limit of the output DC
voltage Vmmc equals a maximum voltage of the wind generator
phase voltage. From the principle of the above, the MMC withchopper cells cannot achieve the step-down rectified operation.
Fig. 2(b) shows the relationships between the H-bridge celland its output voltage. In the case of the H-bridge cell, there isno limit of cell output average voltage because it is possible for
H-bridge cell to output negative voltage. Hence, it is possiblefor H-bridge cell to control lower voltage than that of (3).
Therefore, the MMC with H-bridge cells achieves the stepdown rectified operation.
III.

vc* +

－

CONTROL STRATEGY

Fig. 3 shows the control block diagram of the proposed
step-down converter. One of the features in the proposedsystem is to control each arm as shown in Fig. 1. The control
block diagram is separated to the capacitor voltage control
block and the input current control block. Moreover, thecapacitor voltage control block consists of a voltage averaging
control system and a voltage balancing control system. At first,

PI

iAr_ph*
-1

2

ACR
+

Kacr －+－

iAr_phvcAr_ave
1/E

Elimination ofzero phase current

iAr
vr

2/n +

vAri*

－

(+)
A :―
B :+

Vmmc_Ari*

Eq.(5)

Vmmc*

Fig. 3. Control block diagram for step-down rectified operation of MMC.
The proposed control system is applied to each arm of the MMC in order
to control each arm. Moreover, the ACR controls only the AC componentof the arm current. i is the index of the cell number.

where E is an effective value of the output line to line voltage
in the wind generator, n is the number of cells at each leg.

AVR

the voltage averaging control system corrects the error
between the capacitor voltage command and the average valueof capacitor voltage in the arm. Additionally, the voltage
balancing control system corrects the error among thecapacitor voltage in the arm.
A. Voltage Averaging Control System
The voltage averaging control system is applied in order tocontrol the average value of all capacitor voltage in the arm.
Therefore, the average value of all capacitor voltage has to be
calculated in each arm. Each average value of the capacitor
voltage is given by (4).
vcmk _ ave 

2 n/ 2
 vcmkx , m = A, B k = r, s, t
n x1



where vcmk_ave is the average value of the capacitor voltage. mshows the index which is the upper side A or the lower side B.
k is the index of each phase. Moreover, m and k are matched inboth side of the equation.
The error between the capacitor voltage command and theaverage value of capacitor voltage in the arm is corrected by a
PI controller. Moreover, the output value of the PI controller isgiven as the arm current command. In the proposed control
system, the command of a positive phase current is generated
depending on the fluctuation of the average value of all
capacitor voltage. Thus, the command of a positive phasecurrent is multiplied by the sinusoidal wave in order tosynchronize with the input phase voltage.
Moreover, the cell output the DC voltage in order toachieve the rectification. Therefore, the capacitor voltage
includes the voltage ripple which the cycle same as the input
voltage one. The control system may become instability due tothe voltage ripple. Thus, in order to keep the stability of thecontrol system, the response angular frequency of the PI
controller would be designed into low or a filter in order todamp the frequency component of the input voltage cycle
should be applied.
B. Arm Current Control System
Each arm current includes the DC component and the ACcomponent. The DC component of the arm current flows inorder to supply the DC power into a load. Moreover, the DC
current shunts in to the each leg of the MMC. Generally, theshunted DC current is constant and same value among arms
when cells equally divide the output DC voltage of the MMC.
Furthermore, the DC current is considered as the zero phasecurrent because the DC current is temporally not changed. On
the other hand, from the previous section, the AC componentof the arm current flows as the positive phase current isgenerated by the voltage averaging control system. From theabove, the output power is controlled by the zero phasecomponent of the arm current. The capacitor voltage iscontrolled by the positive phase component of the arm current.
In other words, it is not necessary to compensate the zero
phase component of the arm current. Therefore, in the
proposed control system, the zero phase current is controlled
by open-loop control. On the other hand, in order to keep thecapacitor voltage at constant, the system compensates only the
positive phase current.
C. Elimination System of Zero Phase Current
Fig. 4 shows a schematic diagram of current waveform onof the arm. It is necessary to eliminate only the zero phasecomponent from the arm current in order to control thecapacitor voltage after the system detects all arm current.
However, it is difficult for a high-pass filter to extract only the
positive phase component because AC current cycle is very
low. Methods in order to extract the positive phase component
are shown in the following;a) Add-subtract of three phase currentb) Application of rotational coordinate transform
First, a) is a method to calculate the zero phase componentof the arm current by the addition and subtraction of threephase current. In the MMC, the each arm current is detected.
On each of the upper side and the lower side, the zero phasecurrent is extracted by addition of the three phase current
because the addition value of the positive phase current is zero.
Moreover, because the zero phase current which flows on eachleg is equal. Thus, by subtracting the value of the zero phasecurrent which divides into three equal parts from the detection
value of each current, so that the positive current is extracted.
Second, b) is a method to extract the positive phasecomponent by using the rotational coordinate transform. On
each of the upper side and the lower side, by the rotational
coordinate transform and the inverse transform, the zero phasecurrent is eliminated and only the positive phase current is
extracted. In this paper, b) is applied.
D. Output Voltage Control Systm
From the above, the output DC voltage is controlled by the
open-loop control of the zero phase current. Thus, thecommand of the output DC voltage is added into the output
value of the controller in the arm current control system.
Moreover, the output DC voltage of the MMC is divided oneach leg. Thus, the output DC voltage of a cell isfundamentally set Vmmc*/n when the command of the MMC
output voltage control is Vmmc* and the number of cells in a leg
is n.
E. Voltage Balancing Control System
The voltage averaging control system is used to keep theI

Actual arm current (DC + AC)
Zero phase componentof arm current (DC)To supply power
into DC load

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

Fig. 4. schematic diagram of current waveform on of 1 arm.
Each arm current includes an AC component and a DC component.
In order to control the capacitor voltage, it is necessary to eliminate the
AC components from the arm current.

voltage of all capacitor voltage. However, an unbalance
voltage which occurs among capacitors in same arm cannot be
suppressed by voltage averaging control system only, because
the voltage averaging control system corrects only the error
between the voltage command and the average value of thecapacitors voltage in the arm. So far, some methods in order tobalance each capacitor voltage have been reported [14]-[16].
However, in most of the conventional control systems, it isdifficult to understand these control principle instinctively anddesign control parameters. Additionally, the positive phasecurrent in order to keep the capacitor voltage flows to all cells
which exist in 1 arm. Moreover, the common value of thepositive phase current which flows each arm. Thus, it isdifficult to adjust the arm current in order to balance on eachcell.
Against the problem, in the proposed control system, theoutput DC voltage of the cell is varied depending on thecapacitor voltage. This control principle is given by (5).
Vmmc _ mki *

1 vcmki*Vmmc 
2 n/ 2
 vcmkx



x 1

where Vmmc_mki* is the output DC voltage command of each cell.
i is the index of the cell number. Moreover, m, k and i arematched in both side of (5).
For example, the output DC voltage command of the cells
is set into high when its capacitor voltage is higher than thecommand of the capacitor voltage. Thus, the output power ofthe cell becomes high and the value of the capacitor voltage
discharges. In contrast, the output DC voltage command of thecells is set into low when its capacitor voltage is lower thanthe command of the capacitor voltage. Thus, the output powerof the cell becomes low and the capacitor voltage charges.
Moreover, the output DC voltage of a cell is set Vmmc*/n whenthe voltage value of all capacitor in the arm is same.

F. Capacitor Voltage Determination
The output DC voltage command of the MMC Vmmc* thatuses to obtain the output DC voltage is added to the output
block of the input current control. The change of voltage value
in each cell depends on the number of cells at each leg since
the cells are connected to the load in parallel. In addition, eachcapacitor voltage also depends on the input and output voltage.
The capacitor voltage command vc*is given by (6). Note that
Vmmc_mki* is a little different among cells. However, vc*is givenby the modulation factor  and the modulation factor  is set
to 0.8 or less. Thus, the different of Vmmc_mki* among cells is
ignored because the voltage margin of the capacitor is fullylarge compared with the different of Vmmc_mki* among cells.


1  2*v 
2 E  Vmmc  n  3*c

TABLE III.

EXPERIMENTAL CONDITIONS AND CIRCUITPARAMETERS

Output power PO

700 W

Input voltage rms E

200 V

Input voltage frequency f

50 Hz

Output voltage vmmc

65 V

Number of cell per leg n

4

DC capacitor C

1300 F

Load R

5.8 

Carrier frequency fS

8 kHz

Buffer reactor Lb

4 mH

Input Phase Voltage (R-phase) 10 msec

250 V

0
Input Phase Current (R-phase)



0
5A

IV.

FUNDAMENTAL EXPERIMENTAL RESULTIn order to evaluate the effectiveness of the proposed
control system, a fundamental experiment result by using theprototype of the MMC is shown. In the experiment, theprototype is connected to the power grid of 200 V as substitutefor the wind power generator in order to evaluate the stepdown rectification by the MMC. Moreover, the resistance load
is connected on the output DC side.
Table I shows the experiment condition of the prototype. In
the experiment, the output voltage command is 65 V.
Moreover, the leg is constructed by four cells and theprototype has twelve cells in the three legs.
Fig. 5 shows waveforms of the input phase voltage, theinput current and the output DC voltage. Firstly, from the
waveforms of the input phase voltage and the 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 approximately 11.9%. Thus, as a future
work, it is necessary to reduce the total harmonic distortion of
the input current.
Second, the waveform of the output DC voltage in lower
side of Fig. (5) shows that the prototype convert from input
voltage of 200 V into output DC voltage of 65 V. From thiswaveform, the output DC voltage is kept at constant.
Therefore, the prototype of the MMC achieves the step-down
rectification.
Fig. 6 shows the waveforms of the cell capacitor voltage
which are connected to r-phase leg. The cell capacitor voltage
is controlled according to the capacitor voltage command vc*.
As a result, the proposed system maintains the capacitor
voltage of each H-bridge cell to the voltage command of 120
V. Furthermore, the maximum voltage error between thevoltage command of the cell capacitor and the measured
voltage is 10% or less. As a future work, it is necessary toconsider the cause of the error between the voltage commandof the cell capacitor.

MMC Output Voltage

25 V

0

Fig. 5. Waveforms of input voltage, input current and output voltage. The
unity power factor is be obtained in the input stage. On the other hand, asa future work, it is necessary to reduce the total harmonic distortion of
the input current.

Capacitor voltage (R-phase)vcAr1, vcAr2, vcBr1, vcBr2,
120 V

50 V

0

25 msec
Fig. 6. Waveforms of the capacitor voltage in r-phase leg. The proposedsystem maintains the capacitor voltage of each H-bridge cell to thevoltage command of 120 V. In addition, the maximum voltage error
between the voltage command of the cell capacitor and the measured
voltage is 10% or less.

V.

CONCLUSION

This paper discusses the step-down converter using a
modular multilevel converter topology for the wind power
generation system connected to the micro-grid. The system
converts from a three-phase AC voltage of the generator into
DC bus voltage of 340 V by step-down operation. Moreover,the proposed control system is very simple because the control
system is applied to the each arm of the MMC. Finally, fromthe fundamental experiment, the proposed control maintains
the capacitor voltage at constant. In the future work, thecontrol method to reduce of the total harmonic distortion of
the input current and will be discussed.

REFERENCES
[1]

[2]

[3]
[4]

[5]

[6]

[7]

[8]

H. Kakigano, Y. Miura, and T. Ise, “Low-Voltage Bipolar-Type DC
Microgrid for Super High Quality Distribution,” IEEE Trans. on PowerElectronics, Vol.25, No.12, pp.3066-3075 (2010)
D. Salomonsson, L. Söder, and 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 (2010)
N. Hatziargyriou, H. Asano, R. Iravani, C. Marray, “Microgrids,” IEEE
Power and Energy Magazine, Vol.5, No.4, pp.78-94 (2007)
Liu. Xiong, P. Wang, P. C. Loh, “A Hybrid AC/DC Microgrid and Its
Coordination Control,” IEEE Trans. Smart Grid, Vol.2, No.2, pp.19493053 (2011)
T. Senju, T. Nakaji, K. Uezato, and T. Funabashi, “A Hybrid Power
System Using Alternative Energy Facilities in Isolated Island,” IEEE
Trans. on Energy conversion, Vol.20, No.2, pp.406-414 (2005)
T. Senju, D. Hayashi, A. Yona, and N. Urasaki, and T. Funabashi,“Optimal configuration of power generating systems in isolated islandwith renewable energy,” RENEWABLE ENERGY, Vol.32, No.11,
pp.1917-1933 (2007)
M. S. Kang, “Generation Cost Assessment of an Isolated Power System
With a Fuzzy Wind Power Generation Model,” IEEE Trans. on Energy
Conversion, Vol.22, No.2, pp.397-404 (2007)
C. Meyer, M. Höing, A. Peterson and R. W. DeDoncker, “Control and
Design of DC Grids for Offshore Wind Farms,” IEEE Trans. on Industry
Applications, Vol.43, No.6, pp.1475-1482 (2007)

S. S. Gjerde, and M. Undeland, “Control of direct driven offshore windturbines in a DC-collection grid within the wind farms,” PowerTech,
IEEE Trondheim, pp.1-7 (2011)[10] S. M. Nuyeen, R. Takahashi, and J. Tamura, “Operation and Control of
HVDC-Connected Offshore Wind Farm,” IEEE Trans. on Sustainable
Energy, Vol.1, No.1, pp.30-37 (2010)[11] F. Blaabjerg, R. Teodorescu, M. Liserre and A. V. Timbus, “Overview
of Control and Grid Synchronization for Distributed Power Generation
Systems,” IEEE Trans. on Industrial Electronics, Vol.53, No.5, pp.13981408 (2006)[12] Z. Chen, J. M. Guerrero, and F. Blaabjerg, “A Review of the State of the
Art of Power Electronics for Wind Turbines,” IEEE Trans. on PowerElectronics, Vol.24, No.8, pp.1398-1408 (2009)[13] S. Alepuz, A. Calle, S. Busquets-Monge, S. Kouro, and B. Wu, “Use of
Stored Energy in PMSG Rotor Inertia for Low-Voltage Ride-Through in
Back-to-Back NPC Converter-Based Wind Power Systems,” IEEE
Trans. on Industry Electronics, Vol.60, No.5, pp.1787-1796 (2013)[14] M. Saeedifard, and R. Iravani, “Dynamic Performance of a Modular
Multilevel Back-to-Back HVDC System”, IEEE Transactions on Power
Delivery, Vol.25, No.4, pp.0903-2912 (2010)[15] K. Wand, Y. Li, Z. Zheng, and L. Xu, “Voltage Balancing andFluctuation-Suppression Methods of Floating Capacitor in a New
Modular Multilevel Converter”, IEEE Transactions on Industrial
Electronics, Vol.60, No.5, pp.1943-1953 (2013)[16] M. Hagiwara, K. Nishimura, H. Akagi : “A Medium-Voltage Motor
Drive With a Modular Multilevel PWM Inverter”, IEEE Transactions on
PowerElectronics,
Vol.25,
No.7,
pp.1786-1799(2010)[9]