Input Current Balancing Control Method under
Imbalanced Load for Three-phase Multi-port
Converter based on Modular Multilevel Converter
Takumi Yasuda
Dept. of Science of Technology
Innovation
Nagaoka University ofTechnology
Nagaoka, Japan

Mitsuru Miyashita
Dept. Electrical, Electronics, andInformation Engineering
Nagaoka University ofTechnology
Nagaoka, Japan

Takahiro Kumagai
Dept. Science of Technology
Innovation
Nagaoka University ofTechnology
Nagaoka, Japan

Keisuke Kusaka
Dept. Electrical, Electronics, andInformation Engineering
Nagaoka University ofTechnology
Nagaoka, Japant_yasuda@stn.nagaokaut.ac.jp

miyashita@stn.nagaokaut.ac.jp

kumagai_t1125@stn.nagaokaut.ac.jp

kusaka@vos.nagaokaut.ac.jp

Jun-ichi Itoh
Dept.Science of Technology
Innovation
Nagaoka University ofTechnology
Nagaoka, Japan

Giuseppe Guidi
SINTEF Energy Research
Trondheim, Norway
Giuseppe.Guidi@sintef.noitoh@vos.nagaokaut.ac.jp

Abstract— This paper proposes a balancing control method for
imbalanced load in multi-port converter based on a modular
multilevel converter (MMC) topology. In the multi-port converterwith imbalanced loads, the three-phase current is balanced by
dividing voltage among the cells. However, the multi-port
converter has a limitation of the compensation capability for theimbalanced load. This paper clarifies the theoretical limitation
with the proposed divided voltage method of the compensation
capability of the imbalanced load. The proposed method isdemonstrated by a 200-V, 17-kW laboratory system in order toshow the validity of the proposed method. In spite of the load
imbalance, balanced three-phase input current is achieved and DC
link voltage error becomes 0.11%.
Keywords— modular multilevel converter, multi-port converter,
power distribution, balancing control

I. INTRODUCTION
In recent years, the energy storage with large-capacity andsmall-volume such as lithium-ion cells and supercapacitors havebeen developed due to an increasing demand of electric vehicle[1]-[2]. These large batteries are built using many modules that,
although nominally identical, need to be controlled
independently according to their individual condition.
Accordingly, multi-input and multi-output converters for thebatteries control each source and load independently [3]-[4].
Since the output voltage of the batteries is relatively small, thestep-up transformer is required for these multi-port converter inorder to interconnect the medium voltage grid. However, thestep-up transformer increases the total volume of the system. In
addition, the capacity of the system is limited by the capacity ofthe step-up transformer. Hence, these multi-port converters are
not suitable for the large-scale battery chargers. In order toovercome the above problems, the multi-port converter using a
modular multilevel converter (MMC) topology has been

XXX-X-XXXX-XXXX-X/XX/$XX.00 ©20XX IEEE

Arm ruArm suArm tucell 1cell 1cell 1load

varm ,ru

cell kload

load
cell N

MV
AC

load

L

cell N

load

Lcell N

load

L

load
C

vcell ,ijkLloadcell 1L

loadcell 1L

load

Pcell ,ijk
Vdc ,ijk

i  r , s, t
j  u, lcell 1k  1, 2, ..., N

load

load

load

cell Ncell Ncell NArm rl

Arm slArm tlFig. 1. Concept of multi-port converter based on MMC.

proposed for large-capacity multi-port battery charger [5]-[6],battery energy storage system (BESS) [7]-[8], and so on [9].
Fig. 1 shows a concept of a multi-port converter based on
MMC with double-star chopper-cells [10]. The cells of MMC
are utilized as input and output ports. Each cell is connected to
the load as shown in Fig. 1 because this paper considers only
charging operation of the multi-port converter. Since the multiport converter based on MMC is directly connected to themedium voltage grid without the line frequency transformer, it
reduces both the system volume and the system weightcompared with those of the conventional system with thetransformer [11]-[13]. The multi-port converter is required tointerchange the power between the cells in order to obtainbalanced three-phase current, because the batteries connected tothe cells have different charging requirements [5]-[9]. The

multi-port converter based on MMC has a limitation of thecompensation capability for the load imbalance in one arm [5].
In Ref. [5]-[6], the compensation for the imbalanced load in one
arm is achieved. However, in these papers, the compensation
capability for the load imbalance has not been revealed
theoretically. Although an additional circulating current extends
the operation range of compensation for imbalanced load in one
arm, the load conditions to need the additional circulating
current is not described in Ref. [5]. Therefore, even in thecondition that an additional circulating current is not necessary,
the additional circulating current will flow, which results inincreases of switching loss and conduction loss.
This paper proposes the input current balancing method
without any additional circulating current in the three-phase
MMC in spite of the imbalanced load condition in one arm.
Therefore, the proposed method suppresses the current flowing
the arm and reduces the switching and the conduction loss. In
addition, this paper clarifies the limitation of the compensation
capability of the load imbalance in one arm under no injectionof the additional circulating current. This paper is organized asfollows; first in section II, the control method is introduced, andthe limitation of the compensation capability for the load
imbalance in one arm is clarified theoretically. Next, in section
III, the validity of the proposed control is confirmed by thesimulation. Finally, in section IV, the proposed control isconfirmed by the experiment with 17-kW prototype.
II. CONTROL STRATEGY FOR MULTI-PORT CONVERTER
A. Definition of variables
The sum of output power of all cells in the arm-ij is definedas Parm,ij. In addition, the average DC link voltage of cells in
one arm Vdc,arm,ij, the averaged DC link voltage of all cells in
the multi-port converter Vdc,tot, and the averaged DC link
voltage of cells in i-phase Vdc,ph,i are defined as,
Vdc ,arm,ij 

Vdc ,tot 

1 N
Vdc,ijk ,N k 1

 i  r , s, t , j  u , l 

(1)

1
1
1 N

Vdc ,arm ,ij    Vdc ,ijk 
6 ir ,s ,t
6 i r ,s ,t  N k 1j u ,lVdc, ph,i (2)j u ,l11
1 NVdc,arm,ij    Vdc,ijk ,
2 j u ,l
2 j u ,l  N k 1

 i  r , s, t (3)In the multi-port converter, the grid phase voltage is applied
into each arm for the AC-DC converter operation with thebalanced input current. In addition, the arm voltage command
varm* includes a DC voltage because of the chopper-cell of themulti-port converter [12]-[13]. Therefore, the command of thearm voltage varm,iu* for upper arm in i-phase is assumed toconsist of the DC component and the grid frequency
component as in (4),varm,iu (t ) 

NVdc
 2Vg cos  2 f g t 2(4)

where Vdc is a DC link voltage of the cell, Vg is an RMS valueof the grid phase voltage, and ωg is an angular frequency of thegrid. The phase of the grid frequency component of the arm
voltage varm,il* for lower arm in i-phase is reversed from that of

Grid side control
Vdc*

Vdc ,tot
Vdc ,tot

Vdc , ph ,iVdc ,arm ,ij



Total
power
controller

Input current
reference

Input
current
controller

DC component
Leg
Circulatingbalancecurrent
Circulating controller
controller
Current
ReferenceArmbalancecontroller Fundamental component

Balance control

ProposedArm
voltagereference
Varm,ij*

Dividedvoltagecontroller

Cellvoltagereference

Varm ,ij Vcell ,ijk

Fig. 2. Outline of control strategy for multi-port converter.

the upper arm. In addition, the arm voltage is always positive
because the chopper-cells cannot output negative voltage.
The voltage redundancy ρ is defined for the theoreticalanalysis in this paper. The voltage redundancy ρ is expressedas the sum of the DC link voltage of cells in one arm divided
by the peak-to-peak value of the arm voltage varm as in (5),


NVdc
.
2 2Vg

(5)

When any zero-phase voltage injection is not utilized and thearm voltage is expressed in (6), the voltage redundancy ρ mustbe larger than 1 [13]. On the other hand, when some zero-phasevoltage for the arm voltage varm,ij is utilized, the voltage
redundancy ρ can be smaller than 1, which is the case for themulti-port converter.
B. Control method for power distribution between cells
Fig. 2 shows an outline of the control block diagram for themulti-port converter. The grid side control part and the balance
control part are a control method adopted in the conventional
MMC [5], [14]. In this paper, the divided voltage controller is
proposed. All controllers shown in Fig. 2 adopts PI controller.
Fig. 3 depicts the detailed control block diagrams for themulti-port converter. The grid side control part as shown in Fig.
3 (a) is implemented for the balanced three-phase input current.
The output of the total power controller is a command of theactive part of the input current and proportional to the total
output power of the multi-port converter. The output of the total
power controller is input to the input current controller.
Fig. 3 (b) depicts the balance control part of the control. Thebalance control part controls the circulating current tocompensate the load imbalance between the phases and theupper and lower arms. In this paper, the DC component and thegrid frequency component are utilized as the circulating current
for the compensation of the load imbalance between the arms,
whereas higher harmonic current than them is not utilized tocompensate the load imbalance in one arm. The leg balance
controller regulates the average value of the DC link voltages of
the cells in one phase by interchanging the power between
phases. The outputs of the leg balance controllers are threecommands of DC circulating current, which are for r-, s-, andt-phase, respectively. An active power is generated by the DC
component of the circulating current Idc,i and the DC componentof the arm voltage varm in (4).
The arm balance controller in Fig. 3 (b) regulates theaveraged DC link voltages of the cells in the arms byinterchanging the power between the upper and lower arms. The
output of the arm balance controller is the grid frequency
component of the circulating current iω,i. The arm balance
controller in Fig. 2 (c) utilizes three components; the active partof the positive sequence Re[I+ω], active part of the negative
sequence Re[I-ω], and the reactive part of the negative sequence
Im[I-ω] of the grid frequency component of the circulating
current [5], [14]. The control loop of the arm balance controller
is implemented by adopting one rst-αβ0 transformation and two
dq-rst transformation as shown in Fig. 2 (c) [5].
A sum of the output of the leg balance controller Idc,i* and theoutput of the arm balance controller iω* is input to the circulating
current controller. The circulating current consists of the DC
component and the fundamental component. In this paper, no
additional circulating current for the compensation of the load
imbalance in one arm is injected. Note that the zero sequence ofthe circulating current is zero because any zero sequence
component cannot flow through the multi-port converter basedon MMC due to the circuit configuration as shown in Fig. 1.
Finally, the sum of the outputs from the grid side control partand the balance control part is the command of the arm voltage
varm*, which is assumed as (4). The command of the arm voltage
varm* is input to the divided voltage controller to compensate
the load imbalance in one arm and the command of the cellvoltage vcell,ijk* is obtained.
C. Proposed divided voltage controller
In this paper, the divided voltage controller is proposed inorder to compensate the load imbalance between the cells in one
arm. When the load connected to the cell is relatively large
compared with the other cells in the same arm, the output voltageof the cell should be large in order to input a larger power to thecell. In contrast, the output voltage of the cell should be small
when the load connected to the cell is relatively small. Thus, thecommand of the cell voltage is decided from the output powersof the cells in the converter. The output voltage of the cell vcell,ijk
is written as, NVdc
vcell ,ijk  kijk varm  kijk  2Vg cos g t  ,
 2


(6)

where kijk are coefficients, that are adjusted by the divided
voltage controller in order to supply the desired power to eachcell. The input power to the cell is expressed by the output
voltage of the cell and the arm current iarm,Pcell ,ijk 

1 Tgkijk varm ,ij iarm ,ij dt  kijk Parm ,ij ,
Tg 0

(7)

where Tg is the time period of grid voltage. The coefficient kijk
is derived from (7) as,
kijk 

Pcell ,ijk
Parm ,ij(8)

The sum of the coefficient kijk in one arm is always 1. The
coefficient kijk has a limitation in order to prevent the overmodulation of the cell voltage vcell,ijk. As a result, the maximum
input power to the cell is limited.
Fig. 3 (c) depicts a block diagram of the proposed divided
voltage control. The divided voltage controller regulates the DC

Total power controller *I g ,dVdc ,tot
PI
I

*
g ,q

Input
current
controller

0

Vdc , ph2

rst

Grid side control part.

Vdc , ph ,i (i : r , s, t )

 g

PI

Vdc ,arm ,ilvarm , g ,i*g(a)
Leg balance controller
3PI
Vdc ,tot

Vdc ,arm ,iu

3

dq

3

I dc ,i (i : r , s, t )I  3

dq

rst

rst

 0

i ,i

dq

(i : r , s, t )

rst

0

3

varm ,cir ,i*I Balance control part.

1/ N
Varm ,dc ,ij

Circulating
current
controller

gArm balance controller

(b)

*
icir
,i

PI

kijk

varm ,ij *vcell ,ijk *Vdc ,ijk(c)
Proposed divided voltage control.
Fig. 3. Detailed control block diagram for multi-port converter.

link voltage of each cell in one arm by using the PI controller.
The command of the arm voltage is multiplied by the output of
the PI controller. The output of the proposed divided voltage
controller is the output voltage command of the cells. Phaseshifted PWM method is utilized in this paper. The phase-shifted
PWM method has the merits of high equivalent switchingfrequency and more output voltage levels, which provide low
total harmonic distortion (THD) compared with the othermodulation methods. In addition, the semiconductor stress ofeach cell is evenly distributed [14].
Fig. 4 illustrates an example of the output voltage of cellswith the proposed divided voltage method. As in Fig. 4, thethird-order harmonic injection is used for the arm voltage varm inorder to improve the voltage utilization factor in this paper. The
proposed divided voltage method adjusts the command of thecell voltages in order to input the desired power to the cell asshown in Fig. 4. The sum of the cell voltages in one arm must
be equal to the command of the arm voltage varm*. As a result of
the proposed method, the command of the cell voltage for thelarger input power becomes large. On the other hand, thecommand of cell voltage for the smaller input power becomes
small.
D. Limitation of compensation capability for load imbalance
for divided voltage controller
This paper clarifies the limitation of the compensation
capability of the proposed divided voltage controller for the load
imbalance. The command of the cell voltage is decided by theoutput powers of the cells as shown in (6)-(8). In order to operate
the converter without the over-modulation, there is a limitationof the compensation capability for the load imbalance in one
arm. The minimum value of the output voltage of cells vcell,ijk has
to be larger than zero as in (9). On the other hand, the maximum

value of the output voltage of cells vcell,ijk has to be smaller thanthe DC link voltage of the cell Vdc as in (10),Arm voltage
NVdc

 NV
3 
kijk  dc  Vg   0
2 
 2

(9)

NVdc
2

 NVdc3 kijk 
 Vg   Vdc ,
2
2



(10)

Vdc

O

4

N

 3  2 

,

(11)

The limitation of the coefficient kijk is expressed by the numberof cells in one arm N and the voltage redundancy ρ. The
limitation of the imbalanced load is derived from (11) and (8) asin (12),0

Pcell ,ijk
Parm ,ij / N4
,
3  2

(12)

The compensation capability for the load imbalance in one arm
is expressed by only the voltage redundancy ρ. When all cells in
one arm satisfy the limitation in (12), the cells in the arm operate
without over-modulation. On the other hand, when any one of
the cells does not satisfy the limitation in (12), the overmodulation occurs in that cell. As a result, the arm voltage varm,ij
distorts and the input current ig have distortion. The limitation of
the compensation capability of the proposed method is enlarged
by the increase of the DC link voltage Vdc, as shown in (12).
Fig. 5 illustrates the limitation of the compensation
capability resulting from (12). The voltage redundancy ρ is set
to 1.22 in this paper. The horizontal and vertical axes in Fig. 5
indicate the load of a cell and the averaged load of the cells in
one arm respectively, which are normalized to the rated output
power of a cell. The red and blue dots in Fig. 5 indicate themaximum load in each arm of the multi-port converter for thesimulation and the experimental verifications in the next chapter.
The load imbalance is compensated by adjusting the coefficientkijk when all loads of cells are in the colored region in Fig. 5. On
the other hand, the proposed method cannot compensate the load
imbalance when the load imbalance of cells becomes large andthe maximum load deviates from the colored region.
III. SIMULATION RESULT
Table I shows the simulation conditions. The voltage
redundancy ρ is set to 1.22 in this paper. The maximum load
imbalance between arms is 80%. The reactive component of the
input current is set to zero in this simulation.
Fig. 6 shows the simulation results of the steady state
operation with the proposed method. The maximum load of eachNvvcell ,ij1
vcell ,ij2

O

k 1

cell ,ijk

 varm ,ij

For larger input power
For smaller input power
time

Fig. 4. Example of cell voltages with proposed divided voltage method in
condition of larger output power of cell-j than that of cell-i.
1.0

Arm ruProhibited
Output power of cell Pcell [p.u.]

Note that the third-order harmonic injection is utilized for thearm voltage varm as shown in Fig. 4. Therefore, the amplitude of
the arm voltage varm in the simulation and the experimental
verifications is 0.86 times smaller than the modulation method
without the third-order harmonic injection. The (9) and (10)consider the third-harmonic voltage injection. Therefore, themaximum and the minimum value of the limitation of thecoefficient kijk is derived from (9) and (10) by using the voltage
redundancy ρ as,
0  kijk 3
Vg
2

Arm ruMaximumload of cellin arm0.8

Arm suArm suArm sl0.6

Arm slArm tuArm tl

0.4

Arm tuArm tl0.2

Arm rl0.0
0.0

Maximumload of cellin armOperation region

Arm rl

0.2
0.4
0.6
0.8
Averaged output power of cell Parm/N [p.u.]

1.0

Fig. 5. Limitation of compensation capability of proposed divided voltage
controller. The red dots indicates the maximum load in each arm for thesimulation and experimental verification.

arm plotted on Fig. 5 as the red dots is set to satisfy the limitation
shown in (12). The difference between the maximum and theminimum loads in one arm is set to 13% and 4 kind of load areused in this paper. The input current with the proposed method,
as shown in Fig. 6 (a), is balanced and in-phase with the gridphase voltage. As an analysis result of the proposed method, thepower factor (PF) of the input current is more than 99.99% and
the THD of the input current is 0.82%. Fig. 6 (b) shows acommand of the arm voltage and modulation waves for the cells
in one arm with load imbalance. The amplitude of themodulation waves are differed in order to compensate the load
imbalance in the proposed divided voltage controller. The
modulation waves for cells are not scaled waveform from thecommand of the arm voltage. This is because the modulation
waveforms for cells are obtained by dividing the output of thedivided voltage controller by the DC link voltage of the cell
including the voltage ripple. Fig. 6 (c) shows DC link voltage of
all cells in the multi-port converter. The voltage error between
the averaged DC link voltage of each cell and the command
value of 264 V is about 2.1 V, which is less than 0.8%. Therefore,
the proposed voltage divided controller is validated from thesesimulation results. Fig. 6 (d) shows the current flowing in thearms, which is the sum of the input current and the circulating
current. The arm current shown in Fig. 6 (d) consists of the DC
component and the grid frequency component. This is because

Table I Simulation condition.
SymbolParameter

Rated power of cell
Grid line-to-line voltage
Frequency of input voltage
Number of cells per arm
DC link voltage of cell
Inductor
Capacitor

Pcell
3Vg
fg
N
Vdc
L
C

Value
2.2 kW
6.6 kV (RMS)
50 Hz
50
264 V
33 mH (0.16p.u.)
3.3 mF

Grid phase voltage [kV]6.0

Grid phase voltage [kV]

6.0
0.0
6.0

Input current [A]

50
0
50

1.0

Modulation waveforms for cells in one arm

0.0
0.5
6.0

50

Input current [A] PF : 99.99%, THD : 0.82%

0.0
DC link voltage of cells [V]Load change

400
0

200
50
10 [ms](a)
1.0

Grid phase voltage and current.
Command of arm voltage

Fig. 7. Simulation waveform before and after load change. Before theload change, the load imbalance is compensated by the divided voltage
controller because the load imbalance is within the limitation shown as
red dots in Fig. 5. After the load change, the load imbalance becomeslarge and go out from the limitation as shown in blue dots in Fig. 5. The
input current and DC link voltage gradually diverge.

0.5
0.0
1.0

circulating current for the compensation of the load imbalance
in one arm.

Modulation waveforms for cells

0.5
10 [ms]

0.0

(b)
300

Modulation waves for cells in one arm with load imbalance.
DC link voltage of cells [V]250voltage error: 0.8%

Command

10 [ms]

200

(c)
50

0.1[s]

0

DC link voltage of all 300 cells of multi-port converter.
Arm current [A]0-50
10 [ms](d) Current flowing 6 arms
Fig. 6. Simulation result of steady-state operation under load imbalance.
THD of the input current is 0.82% and PF is over 99.9%. The modulation
waveforms for cells with larger output power becomes large and the DC
link voltage for cells in one arm are converged to command with theerror of 0.8% by the proposed controller.

the proposed divided voltage controller achieves thecompensation of the load imbalance without any additional

Fig. 7 shows a transient behavior under load change. The
load imbalance before the load change is within the limitation of
the compensation capability shown as the red dots in Fig. 5. The
load imbalance after the load change is out of the limitation of
the compensation capability shown as the blue dots in Fig. 5.
Before the load change, the maximum error of the averaged DC
link voltage of cells are less than 0.1%. In addition, the input
current is balanced and in-phase with the grid phase voltage.
After the load change to the out of the limitation of thecompensation capability, the amplitude of the modulation
waveforms for cells with heavier load are increased according to(8) and over 1, i.e. over-modulation, as shown in Fig. 7. This
over-modulation leads to insufficient of the input power to thecells. As a result, the DC link voltage imbalanced of the cells
gradually expands as shown in the bottom of Fig. 7. In addition,
the over-modulation of the cells results in distortion of the arm
voltage and the current distorts, and the multi-port converter lose
the control of the input current. The theoretical analysis isverified from this simulation results.
IV. EXPERIMENTAL RESULT
Fig. 8 shows the experimental setups. In addition, Table IIshows the experimental conditions. A multi-port MMC
prototype with 12 cells per arm was built in the laboratory. The
maximum load imbalance between arms is 80%, which is thesame as the simulation condition. The load imbalance in one arm
plotted on Fig. 5 is set to only the upper arm of r-phase. The

Load

TABLE II EXPERIMENTAL CONDITION.
SymbolValue

Parameter

Rated power of cell
Grid line-to-line voltage
Frequency of input voltage
Number of cells per arm
DC link voltage of cell
Inductor
Capacitor

Pcell
3Vg
fg
N
Vdc
L
C

236 W
200 V (RMS)
50 Hz
12
33 V
1.5 mH (0.20p.u.)
15 mF

Grid phase voltage [V]

200

0
200

60

Input current [A]PF: 99.95%, THD: 2.1%0Multi-port converter prototype

60
10 [ms]Fig. 8. The experimental setup of multi-port MMC prototype.

reactive component of the input current is set to zero in thisexperiment.
Fig. 9 depicts experimental waveforms of the steady state
operation with the proposed method. The imbalanced of theloads in one arm is shown as the red dots in Fig. 5. The
difference between the maximum and the minimum loads in one
arm is set to 13%. In addition, the same load imbalance as thesimulation condition are applied. As shown in Fig. 9 (a), theinput current with the proposed method is balanced and in-phasewith the grid phase voltage. As an analysis result of the proposed
method, the PF of the input current is more than 99.9% and the
THD of the input current is 2.1%. Fig. 9 (b) shows a commandof the arm voltage and modulation waves for the cells in one armwith load imbalance. The amplitude of the modulation waves arediffered in order to compensate the load imbalance. The
modulation waveforms for cells are not scaled waveform fromthe command of the arm voltage. This is because the modulation
waveforms for cells are obtained by dividing the output of thedivided voltage controller by the DC link voltage of the cell
including the voltage ripple. Fig. 9 (c) shows DC link voltage ofcells in one arm. The voltage error between the averaged DC
link voltage of each cell and the command value of 264 V isabout 0.3 V, which is about 0.11%. The proposed voltage
divided controller is validated from these simulation results. Fig.
9 (d) shows the current flowing 6 arms. The arm current shownin Fig. 9 (d) consists of the DC component and the gridfrequency component. This is because the proposed divided
voltage controller achieves the compensation of the load
imbalance without any additional circulating current for thecompensation of the load imbalance in one arm.
Fig. 10 shows a transient behavior under load change from
0.34p.u. to 0.86p.u. of one cell in upper arm of r-phase. The load
imbalance before and after the load change is shown as red dots
in Fig. 5 and the maximum load in one arm is not changed. Afterthe load change, the DC link voltage of the cell with the load

(a)
1.0

Grid phase voltage and input current.
command of arm voltage

0.5
0.0
1.0

Modulation waveforms for cells

0.5
10 [ms]0.0(b)Modulation waveforms for cells in one arm with load imbalance.
DC link voltage of cells [V]40
Voltage error: 0.11%
35
30
25

(c)
30

Command

10 [ms]DC link voltage of cells in one arm with load imbalance.
Arm current [A]030
10 [ms](d) Current flowing 6 arms.
Fig. 9. Experimental result of steady-state operation under load
imbalance. THD of the input current is 1.9% and PF is over 99.9%. The
modulation waveforms for cells with larger output power becomes large
and the DC link voltage for cells in one arm are converged to commandwith the error of 0.8% by the proposed controller.

change decreases by about 16% at the maximum. Afterwards,
the DC link voltage of the cell is converged to the command
value of 33 V within 0.3 s. Fig. 10 (b) shows an enlarged
waveform of the grid phase voltage, the input current, and theDC link voltages of cells in the phase when load change occurs.
No current distortion is observed when the load change.

200

V. CONCLUSION

0This paper proposes the input current balancing method
without any additional circulating current in the three-phasemulti-port converter based on MMC in spite of the imbalanced
load condition. In addition, the limitation of the proposedbalancing control method was clarified for the load imbalance
conditions. The validity of the theoretical analysis is verified bysimulations. The experimental result showed the THD of the
input current at grid side of 2.1% and the error of the DC link
voltage of 0.11% thanks to the proposed control. In the future,
the limitation of the compensation capability of the load
imbalance in one arm will be enlarged by injecting higher
harmonic components than DC and grid frequency component
to the command of the cell voltage.
ACKNOWLEDGMENT
This work was supported by the project Modular Megawattrange Wireless EV Charging Infrastructure Providing Smart
Grid Services (MoMeWeC), funded under the EIG CONCERTJapan program, Joint Call on Efficient Energy Storage andDistribution, with project number 284231

Grid phase voltage [V]

200

50

Grid current [A]

0
50

40

DC link voltage of cells [V]Load change

35
30
25

(a)

Command

0.2 [s]Grid phase voltage, input current, and DC link voltage of cells in
one arm whose load changed.
Grid phase voltage [V]200
0

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Input current [A]

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DC link voltage of cells [V]Load change

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Command

60 [ms](b)

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Fig. 10. Transient response of proposed divided voltage controller underload change. The DC link voltages are converged to the command value
within 0.3 s.

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