IEEJ Journal of Industry Applications
Vol.13 No.3 pp.317–326
DOI: 10.1541/ieejjia.23009512

Paper

Intra-arm Balancing Control for Modular Multilevel Converterwith Cell Loading Operated under High Power Imbalances∗a)Takumi Yasuda∗∗
Giuseppe Guidi∗

Jun-ichi Itoh∗∗Salvatore D’Arco

Student Member,
Non-member,

Senior Member
Non-member(Manuscript received Aug. 29, 2023, revised Dec. 6, 2023)
J-STAGE Advance published date : Feb. 23, 2024

Multiport converters with a large number of ports have been explored for integrated generation units or batteries. An
attractive candidate multiport converter has been developed based on the modular multilevel converter (MMC) withcell loading. Accordingly, this study proposes a control strategy for a multiport converter based on the MMC operated under high power imbalances among cells. Owing to this power imbalance, the multiport converter requires anadditional circulating current (intra-arm balancing current) to provide balanced three-phase grid currents and balanced
capacitor voltages in all cells. In a previous study, the minimum required intra-arm balancing current was calculated
oﬄine and applied according to the loading condition. This method may require a high-capacity memory for the controller. In contract, this study proposes an active control method for minimizing the intra-arm balancing current online.
Experimental results reveal that the multiport converter achieves balanced three-phase currents with a total harmonic
distortion of 3.13% and balanced capacitor voltages with an error of 0.1% under maximum power imbalance amongcells.
Keywords: capacitor voltage balancing, intra-arm balancing current, modular multilevel converter (MMC), multiport converter,
phase-shifted PWM (PS-PWM)

NomenclaturePδ

Main variables and parameters
t
N
L
C
ωg
vg
dcell
varm
vcell
vδ *
vδ,max *Vc
V c,arm
ig
iarm
I int
Pcell
Parm

Time
Number of cells per arm
Arm inductor
Cell capacitor
Grid angular frequency ( = 2πf g )Grid phase voltage
Modulation wave for cell
AC side voltage of arm (arm voltage)
AC side voltage of cell (cell ac voltage)
Injection to cell ac voltage to compensate for
intra-arm load unbalance (compensation voltage)
Maximum amplitude of compensation voltagethat does not induce overmodulation of cell
Capacitor voltage of cell
Averaged capacitor voltage of cells in one arm
Grid current
Current flowing in the arm (arm current)
RMS value of intra-arm balancing current
Load of cell
Aggregated load of cells in one arm

Other subscripts
a,b,c,xu,d,y1, . . . , N, knPhase a, b, c, or generic phase x
Upper or lower arm or generic arm y
Cell number in arm or generic cell number k
Rated value

Superscript*a) Correspondence to: Takumi Yasuda. E-mail: t yasuda@stn.
nagaokaut.ac.jp∗
Nagaoka University of Technology
1603-1, Kamitomioka-machi, Nagaoka, Niitaga 940-2118,
Japan∗∗
SINTEF Energy Research
Sem Sælands vei 11, 7034 Trondheim, Norwayc 2024 The Institute of Electrical Engineers of Japan.
⃝

Additional power to cell due to compensation
voltagePδ,max , Pδ,min Maximum and minimum power achievable bycompensation voltage without overmodulation∆PcellDeviation of load from averaged load of cells
in a given arm (intra-arm power unbalance)
V PI
Output of PI controller for compensation
voltage calculationg
Waveform multiplied to V PI in compensation
voltage calculation (modulation function)
Tg
Fundamental period of grid voltage ( = 1/f g )T s,int
Update rate of intra-arm balancing current

Reference value
Symbol modifier

x̂

317

Estimated value of variable x

Intra-arm Balancing for MMC with Cell Loading（Takumi Yasuda et al.）compensating for load imbalances without increasing
losses. However, the theoretical operational limitscaused by overmodulation remain and the converter cannot operate under all loading conditions(19)–(21) .
2) The arm current is increased by an additional reactive
component of the grid current or additional circulating
current(5)(21)–(23) . The operation region extends as thearm current increases, allowing the converter to operate
under all possible loading conditions as long as the arm
current is smaller than the rating for the arm(5) . However,
the additional arm current increases the converter losses.
The multiport converter in Fig. 1 requires an additional current to achieve both balanced grid current and balanced capacitor voltages in all possible loading conditions(5) . However, most studies on the compensation voltage do not discuss the need for additional current injection in a multiportconverter with PS-PWM. Furthermore, to the best of the author’s knowledge, online minimization has not been applied
to the circulating current.
This paper proposes a control method that minimizes theintra-arm balancing current while avoiding overmodulationof the cell ac voltage. The originality of this paper is the
proposal of controllers for the compensation voltage waveform optimization and the intra-arm balancing current minimization algorithm. The proposed controller generates the
optimized compensation voltage to minimize the required
intra-arm balancing current. In addition, the minimum required intra-arm balancing current is calculated online andapplied. Experimental results with a 17-kW laboratory prototype demonstrate that the proposed control strategy achievesbalanced grid current and power distribution of all cells underthe maximum load imbalance condition.
The rest of this paper is organized as follows. Section II introduces the converter configuration, the controller for the aggregated arm power distribution, and the conventional compensation voltage for the intra-arm balancing. Section III describes the proposed intra-arm balancing controller with theminimum intra-arm balancing current. Section IV presents
experimental results to verify the validity of the proposed
control strategy.

Fig. 1. Circuit diagram for multiport converter based on
modular multilevel converter

1. Introduction

Multiport converters with cascaded cells have attracted
growing interest for applications such as large-scale integrated photovoltaic (PV) power conditioners(1)–(3) and multiport electric vehicle (EV) charging stations(4)(5) due to theirability to manage the load or source for each cell individually. For PV power conditioners, each PV module connectedto the cell can track the maximum power point individually
to increase the total amount of harvested energy. A multiport
EV charger can change the charging power according to thestate of charge or a charging schedule. Directly integrating
the loads or sources into cascaded cells allows downsizing of
the ac filtering requirements due to multilevel operation(6)–(8)and a reduction of cable length and cross section(5) .
Fig. 1 shows a circuit diagram for a multiport converter
based on the modular multilevel topology with double-star
chopper cells(9)(10) . In this study, the loads are connected inparallel with the cell capacitors through a dc/dc converter.
Although the rated power of the loads is identical, the system may often operate with diﬀerent instantaneous values forindividual loads, resulting in power imbalances among thecells. In order to achieve the optimal operation of each load,
the multiport converter has to distribute the desired power toall cells while shaping the grid current.
The multiport converter in this study is driven using phaseshifted PWM (PS-PWM)(8)(11) . In the PS-PWM, the power
imbalance among the cells in a given arm is compensated byinjecting a compensation term into the cell ac voltage references(12)–(17) . However, adding a term with a large amplitude to compensate for the high-power unbalance may cause
overmodulation of the cell ac voltage and grid current distortion(18) . The following two strategies have been proposed
to avoid such overmodulation without disrupting the optimal
operation of the loads (e.g., disabling the maximum power
point tracking of the PV power conditioner or decreasing thescheduled charging power for the EV).
1) The compensation voltage is adjusted such that it limits the amplitude of the cell ac voltage reference andgenerates compensation power for the intra-arm imbalance(12)–(17) . This solution extends the capability of

2. Circuit Configuration and Aggregated Capac-

itor Voltage Balancing in Arm
2.1 Circuit Configuration and Control Strategy

The multiport converter under consideration is based on
the modular multilevel cascaded topology with double-star
chopper cells without a dc port(9)(10) , as shown in Fig. 1. The
individual loads are connected to each cell possibly throughan isolated dc/dc converter to ensure voltage matching andgalvanic separation. A net power imbalance among the cells
appears because the loads on the cells are independently controlled at their optimum operation point. The proposed controller assumes that the load conditions are known because
there is communication between the dc/dc converter on eachcell and the multiport converter.
Fig. 2 shows the control block diagram for the multiportconverter. The controller shapes the balanced three-phasegrid current and regulates the capacitor voltage in all cellsby distributing the desired power to each cell. The overall
energy balancing and the inter-arm balancing are explained
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Intra-arm Balancing for MMC with Cell Loading（Takumi Yasuda et al.）Fig. 2. Overview of control structure for multiport converter with proposed intra-arm balancing controller

briefly in Sections 2.2 and 2.3, respectively; detailed analyses can be found elsewhere(5)(24) .
2.2 Overall Energy Balancing
The total power
controller ensures that the power exchanged with the gridmatches the total power consumed/produced by all the cells
in the converter. This is achieved by calculating the averageof all capacitor voltages in the system and regulating the active current (d-axis current) exchanged with the grid so thatthe average capacitor voltage equals a given reference V c * .
2.3 Inter-Arm Balancing
The current circulation between the phases of the converter is used to balance the aggregated energy demand of the arms. The balancing process
is carried out by the combined action of the horizontal andvertical balancing controllers, as shown in Fig. 2. The former balances the aggregated power of the three phases byintroducing a dc circulating current component, and the latterbalances the aggregated power of the lower and upper arms
by introducing a circulating current component at the fundamental frequency.
As a result of the inter-arm balancing process, the arm currents contain both a dc component and a harmonic component at the grid frequency:√
iarm,xy (t) = Idc,x + 2Iω,xy cos(ωg t − ϕ xy )· · · · · · · · · · (1)the input power of the cell. Since the current is common to
all cells in the arm, the only way to balance the power in thearm is to adjust the individual cell voltages, correcting themwith a term proportional to the local load:v∗cell,xyk = v∗cell,xy + v∗δ,xyk (Pcell,xyk )· · · · · · · · · · · · · · · · · · (3)where vcell,xy * = varm,xy * /N,varm,xy * is the arm voltage reference of the arm xy, and vδ,xyk * is the compensation voltage forthe power balancing. The intra-arm balancing process is decoupled from the rest of the control system by ensuring thatits action leaves the total arm voltage varm,xy * unchanged. To
achieve this, the following constraint is introduced:N∑v∗cell,xyk = v∗arm,xy

k=1

∴

N
∑

v∗δ,xyk = 0· · · · · · · · · · · (4)k=1

In practice, the correction terms are calculated in closed-loop
fashion, as shown in the upper part of Fig. 3. A local PI controller in each cell forces the capacitor voltage to follow theaverage of the capacitor voltages in the arm:
Vc,arm,xy ≜N
1 ∑·Vc,xyk · · · · · · · · · · · · · · · · · · · · · · · · · (5)N k=1

where V c,xyk is the capacitor voltage of the k-th cell in thearm xy. The intra-arm balancing capability is fundamentally
limited by the maximum and minimum voltages that can begenerated at the ac terminals of each cell:

where iarm,xy is the arm current in arm xy, I dc,x and I ω,xy are thedc component and the grid frequency component of the arm
current, ωg is the grid angular frequency, and ϕxy is the phaseangle with respect to the grid voltage in phase a. The magnitude of the components can be directly linked to the aggregated power for the six arms(5) . It is noted that the amount of
power imbalance between the arms that can be compensatedis only limited by the capability of the converter hardware(e.g., current ratings of the devices, thermal limits).
2.4 Conventional Intra-Arm Balancing Controller
In the steady state, the power balancing equation must holdfor each cell of the multiport converter:∫ Tg
1(t)iarm,xy (t)dt · · · · · · · · · · · · (2)Pcell,xyk ≈v∗
T g 0 cell,xyk

0 ≤ v∗cell,xyk ≤ Vc,xyk · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (6)The amplitude of the compensation voltage is approximately
proportional to the intra-arm power unbalance as discussed in
the next section. For rather unbalanced cell loadings, the balancing process may require one or more of the cell voltages
to exceed the allowable range. In this case, overmodulation
occurs and the arm currents can no longer be controlled properly, resulting in excessive harmonic distortion.
The balancing capability can be extended in two fundamental ways. One class of methods relies on the introductionof a modulation function gxy (t) to the original arm voltage
commands, resulting in the structure shown in Fig. 3. The
most conventional form of modulation(12)–(14) utilizes a thirdharmonic component to lower the peak reference cell voltage sent to the heavily loaded cells while enhancing the peakof lightly loaded cells to satisfy (4), as indicated in the example shown in Fig. 4(a). A modulation function based onwhere vcell,xyk * is the ac voltage reference of the cell. Thismeans that the power input to a cell from the multilevel
converter side, represented by the product between the arm
current and the cell ac voltage, must equal the power produced/consumed by the load Pcell,xyk . Eq. (2) ignores theswitching frequency components as they have little eﬀect on
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IEEJ Journal IA, Vol.13, No.3, 2024

Intra-arm Balancing for MMC with Cell Loading（Takumi Yasuda et al.）In the next section, a method that combines cell voltage
modulation with online calculation of the optimal second harmonic circulating current injection is presented.
3. Proposed Intra-Arm Balancing Strategy

3.1 Compensation Voltage Generation
The generalcondition in (2) can be rewritten in terms of balancing capability using the controller form shown in Fig. 3 as

Fig. 3. Compensation voltage calculation for intra-arm
balancing controller. V c,arm,xy is the average capacitor
voltage for cells in arm xy

Parm,xy∆Pcell,xyz = Pcell,xyk −N∫
VPI,xyk Tg≈
g xy (t)iarm,xy (t)dt · · · · · · · · · · (7)Tg
0
For the equation above, the dynamics of the PI controllers
are assumed to be slow compared to the fundamental period
T g , so that the term V PI,xyk can be considered constant during the integration period. Eq. (7) reveals that the amplitudeof the compensation voltage is approximately proportional tothe intra-arm power unbalance. The constraint in (6) is conveniently rewritten as(a) Third harmonic injection.

(b) Compensation with square waveform.

−v∗arm,xy (t)v∗arm,xy (t)· · · · · · (8)NN
where V c is the capacitor voltage, which is assumed to beconstant in the fundamental period and N is the number ofthe cells per arm. The constraint for gxy (t) for preventing
overmodulation in all cells is expressed as (9). The powercompensation that can be obtained without overmodulation
becomes maximum when the periodic time integral of the
product gxy (t) · iarm,xy (t) is maximum. From (7), it follows
that the compensation capability is maximized by maximizing the instantaneous value of gxy (t) · iarm,xy (t) while satisfying
the constraint in (9). The modulation function is thus chosen
to have the same polarity as that of the arm current, as defined by (10), where Πxy is expressed in (11). In (10), (11),the output of the PI controller V PI,xyk in the intra-arm balancing controller is replaced by the power imbalance ∆Pcell,xyk
as the output of the PI controller is proportional to the power
imbalance ∆Pcell,xyk in the steady state.
Fig. 5 shows an example of the cell ac voltage generated
by the proposed controller. The polarity of the injected voltage coincides with the polarity of the arm current. Unlike
conventional strategies, the proposed method changes thecompensation term according to the loading condition. The
fundamental frequency component of the cell ac voltage forFig. 4. Cell ac voltage generated by conventional controllers

the polarity of the arm current, shown in Fig. 4(b), has also
been proposed(15)–(17) . In general, there is no limitation on
the shape of the modulation function, as long as the basic
condition of invariant total arm voltage expressed by (4) issatisfied. However, although the modulation function is effective in extending the operation region of the system, operation with arbitrarily unbalanced loads cannot be achieved,
as discussed in Section III.A.
The other class of methods for intra-arm balancing is basedon the injection of an additional circulating current to improve the balancing capability(5)(21) . The injected current
must not interact with the inter-arm power balance, meaning that in the steady state, the average power associated with
the interaction of the additional current and the arm voltages
must be zero over a fundamental period. The injection of aneven harmonic (usually a second harmonic for simplicity) is
thus often used. In principle, with suﬃciently large current
injection, all loading conditions can be covered. It is however
diﬃcult to calculate the minimum required current injection
for any loading condition and such calculations are typically
performed oﬄine(5) .

≤ VPI,xyk · g xy (t) ≤ Vc −





(
)
(
)


v∗arm,xy (t)v∗arm,xy (t) 
v∗arm,xy (t)v∗arm,xy (t) 
1
1
1
1





[
]
,
Vc −
Vc −
,−
max − ≤ g xy (t) ≤ min N
min[VPI,xyk ]N
max[VPI,xyk ]N
min[VPI,xyk ]N max VPI,xyk

k

k

k

k

· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (9)
[
(
)
]

∗
∗
v
(t)
v
(t)
1
1

arm,xyarm,xymin1−,. . . (iarm,xy (t) ≥ 0)



Π xy
NVc
1 − Π xy NVc
()][
g xy (t) = · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (10)∗v∗arm,xy (t)1
1 varm,xy (t)



, −
1−
. . . (iarm,xy (t) < 0)
max −
Π xy NVc
1 − Π xyNVc
0.5
. . . (max[∆Pcell,xyk ] = min[∆Pcell,xyk ] = 0)



k
k




max[∆Pcell,xyk ]Π xy = · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (11)k. . . (else) max[∆Pcell,xyk ] − min[∆Pcell,xyk ]
k

k

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Intra-arm Balancing for MMC with Cell Loading（Takumi Yasuda et al.）(a) maxk [VPI,xyk ] : mink [VPI,xyk ] = 2 : −1. (b) maxk [VPI,xyk ] : mink [VPI,xyk ] = 1 : −2.

Fig. 5. Cell ac voltage generated by proposed compensation voltage calculationa heavy load can have a larger amplitude and a phase angle closer to the arm current when one of the cells in thearm requires a relatively large magnitude of the positive compensation term (maxk [V PI,xyk ] > − mink [V PI,xyk ]), as shown in
Fig. 5(a), which generates more positive input power within
the constraints in (8). On the other hand, the compensation voltage for a lighter load generates more negative power
when one of the cells in the arm requires a relatively large
magnitude of the negative compensation term (maxk [V PI,xyk ]< −mink [V PI,xyk ]).
3.2 Intra-Arm Balancing Current Calculation
Additional circulating current must be introduced when theimbalance is high and the compensation voltage alone is insuﬃcient to redistribute the power between the cell of a given
arm without inducing overmodulation(21)(22) . Although a sufficiently large circulating current allows operation in all loading conditions, the resulting losses may be very high. The
proposed method calculates the minimum required second
harmonic circulating current online in accordance with theloading condition.
For simplicity, a second harmonic component in phasewith the respective phase voltage is considered on each arm,
resulting in a balanced and symmetric circulating second harmonic with zero net eﬀect on the grid current. Only the amplitude of this harmonic is determined according to the loading condition.
Fig. 6 shows a flowchart of the proposed intra-arm balancing current minimization process. First, the controller estimates the operation region for the intra-arm load imbalanceusing discrete integration based on the load information, arm
current, and intra-arm balancing current specified using thebisection method.
M stepA xy T step ∑v∗δ,max,xy [mT step ] · îarm,xy [mT step ]P̂δ,max,xy =Tg
m=0

Fig. 6. Flowchart of proposed procedure for intra-arm
balancing current minimization

with the loading conditions to find the minimum required
magnitude of the intra-arm balancing current using the bisection method. If the estimated operation ranges P̂δ,max,xy andP̂δ,min,xy are lower than the load , the controller increases theintra-arm balancing current reference I int,xy * to avoid overmodulation. Otherwise, it decreases I int,xy * to reduce the converter loss.
The cell ac voltage may saturate during the load transient
because the proposed operation takes a relatively long time.
Thus, the proposed controller temporarily increases the intraarm balancing reference I int,xy * to I int0,xy as soon as it detects
a load change,√222 ]· · · · · · · · · · · · (13)
Iint0,xy = Iarm,n− max[Idc,x+ Iω,xy· · · · · · · · · · · · · · · · · · · (12)x,ywhere T step is the time step of discrete integral, M step =T g /T step , Axy is a gain that is adjusted according to the amplitude of the cell ac voltage to avoid overmodulation (details
are given below), vδ,max,xy * is the compensation voltage witha maximum amplitude that does not induce overmodulation,and îarm,xy is the arm current, which is detected by the intraarm balancing current controller. Similarly, the operation
range for the negative load imbalance P̂δ,min,xy is calculated.
Then, the controller compares the estimated operation range

where I arm,n is the rated arm current. I int0,xy is the maximum available intra-arm balancing current that ensures operation without overmodulation. Hence, I arm,n is designed
such that I int0,xy becomes large enough to avoid overmodulation of the cells in any loading condition. In addition to the
update of I int,xy * , the interval [I int1,xy , I int2,xy ] for the bisection method is updated by increasing the upper bound I int1,xyof the bisection method to I int0,xy . On the other hand, when
the load imbalance decreases, the lower bound I int2,xy is up321

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Intra-arm Balancing for MMC with Cell Loading（Takumi Yasuda et al.）dated. The maximum intra-arm balancing current calculated
for each arm is selected as the intra-arm balancing current
reference. A low-pass filter is installed to prevent shock toother controllers caused by a step change in the current reference. The threshold for the detection of the load change∆Pcell,th can be designed from the acceptable voltage deviation that occurs during the period from the load change to thenext update of the intra-arm balancing current. Assuming it
takes 2T s,int from the load change to the update of the intraarm balancing current because of the sampling and execution
delay for simplicity, ∆Pcell,th can be calculated as
2∆Pcell,th∆Vc,max =T s,int
CVc(a) Conventional intra-arm balancing controller.

CVc ∆Vc,max∴ ∆Pcell,th =2T s,int· · · · · · · · · · · · · · · · · · · (14)where ∆V c,max is the maximum capacitor voltage deviationin the worst case (selected by the designer). The design of
T s,int is discussed at the end of this subsection. Note thatthe capacitor voltage deviation ∆V c,max will increase further
if the communication delay of the loading condition cannot
be ignored and the update of the intra-arm balancing current
reference is further delayed.
The gain Axy in (12) is implemented to avoid overmodulation due to unmodeled disturbances, such as capacitor voltage ripple and measurement errors. The gain Axy varies inaccordance with the modulation waveforms for the cells as(b) Proposed intra-arm balancing controller.

Fig. 7. Minimum intra-arm balancing current required
to operate converter without overmodulation

A xy [n+1] = A xy [n]+min[1−dcell,max,xy [n],−dcell,min,xy [n]]−dm· · · · · · · · · · · · · · · · · · · · · · · · (15)analysis assumes that an arm current of [Idc : Iω : φ] =[−0.1 (p.u.) : 0.28 (p.u.) : π/4 (rad)] and a voltage ratio
NV c /(2*sqrt(2)V g ) of 1.5. Second harmonic intra-arm balancing current is assumed. The conventional method in Fig. 7
employs a compensation voltage based on the polarity of thearm current, as shown in Fig. 4(b). The vertical and horizontal axes represent the maximum and minimum power imbalances maxk [∆Pcell,xyk ] and mink [∆Pcell,xyk ], respectively. In
this case, the maximum intra-arm balancing current needed
for the conventional controller is 1.56 p.u. In contrast, theproposed controller requires at most 0.58 p.u. Fig. 7 reveals
that the proposed controller reduces the intra-arm balancing
current by optimizing the compensation voltage.

where x[n] is the value of the variable x at the n-th update
period and dm is a positive constant that defines the overmodulation margin. The variables dcell,max,xy and dcell,min,xy are thepeak and valley values of the modulation waveforms in arm
xy over the fundamental period, respectively, defined as[]
dcell,max,xy [n] = max
max[dcell,xyk (τ)]
0≤k≤N nT s,int −T g ≤τ≤nT s,int[
dcell,min,xy [n] = min· · · · · · · · · · · · · · · · · · · · (16)]min[dcell,xyk (τ)]

0≤k≤N nT s,int −T g ≤τ≤nT s,int· · · · · · · · · · · · · · · · · · · · (17)4. Simulation Results

Table 1 shows the simulation conditions. A 1.2-MW multiport converter with 240 cells with bidirectional power flow
was tested. The frequency of the intra-arm balancing current
was set to be double the grid frequency. The margin for themodulation waveform dm was set to 0.03. The aggregatedloading condition of the arm au, ad, bu, bd, cu, and cd are
set to 0.6, 0.1, −0.1, 0.7, −0.3, and 0.8 p.u., respectively. The
negative load means that the arm (or cell) supplies power tothe grid. In this simulation, some cells absorbing the powerof 1 p.u. and some supplying the power of 1 p.u. are present
in the same arm, which is the worst power imbalance for themultiport converter.
Fig. 8 shows the simulation results of the steady-state operation of the multiport converter with the proposed controller.
Fig. 8(a) shows the arm current and the modulation waveforms for the cells. A current of 5.40 A with double the gridfrequency is injected as the intra-arm balancing current towhere dcell,xyk is the modulation waveform for the k-th cellin arm xy. If overmodulation occurs in any of the cells inarm xy, Axy decreases and the estimated operation region in(12) shrinks, which leads to the injection of more intra-arm
balancing current. In the steady state, the peak value of themodulation waveform is always less than (1–dm ) and greaterthan dm . Thus, it is desirable to keep the margin dm as small
as feasible. The update period T s,int for the intra-arm balancing current reference and the gain Axy is set to be suﬃciently
longer than the integral time of the PI controllers in the compensation voltage calculation, as Axy is updated only according to the amplitude of the modulation waveform in steadystate.
3.3 Comparison with Conventional Controller
Fig. 7 shows the numerical calculation results for the magnitude of the intra-arm balancing current required for the
power distribution without cell ac voltage saturation. This
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Intra-arm Balancing for MMC with Cell Loading（Takumi Yasuda et al.）Table 1. Simulation conditions(a) Arm current and modulation waveforms for cells.

(b) Capacitor voltage.

(a) Arm current and modulation waveforms for cells.

(b) Capacitor voltage.
(c) Grid voltage and current.

Fig. 9. Simulation results of steady-state operation ofmultiport converter with load imbalance when conventional compensation voltage generation method is appliedwith proposed intra-arm balancing current minimization
strategy

to those used in the simulation shown in Fig. 8. Since theproposed intra-arm balancing current calculation method isapplied, the converter operates with the minimum required
intra-arm balancing current for the conventional compensation voltage generation method. Fig. 9(a) is the arm current
and modulation waveforms for the cells. The rms value of thearm current is 86.2 A, which is 2.87 times larger than that ofthe proposed controller, because of the significant intra-arm
balancing current of 81.5 A. However, the capacitor voltage
and the grid current is balanced, as shown in Fig. 9(b)–(c),because the large intra-arm balancing current prevents thesaturation of the modulation waveforms for the cell. The
capacitor voltage in Fig. 9(b) contains a much higher ripplecompared to that of the proposed method shown in Fig. 8(b)due to the large intra-arm balancing current.
This simulation results reveal that the conventional compensation voltage injection method requires significant intraarm balancing current to prevent overmodulation, eventhough the intra-arm balancing current is adjusted to the minimum required value by the proposed intra-arm balancing
current minimization method.

(c) Grid voltage and current.

Fig. 8. Simulation results of steady-state operation ofmultiport converter with load imbalance

extend the operation range, resulting in rms value of the arm
current of 28.4 A. Although the modulation waveforms include a large compensation voltage almost at the boundary ofovermodulation, they do not saturate due to the adjustmentof the intra-arm balancing current injection by the proposed
intra-arm balancing current minimization method. The capacitor voltages of the cells with 1 p.u. positive and negative
load follow the command, as shown in Fig. 8(b). The gridcurrent is balanced and has a total harmonic distortion (THD)
of 0.89%, as shown in Fig. 8(c). The proposed controller
achieves power distribution while shaping the balanced threephase current in the extreme power imbalance condition.
Fig. 9 shows the simulation results of the steady-state operation of the multiport converter when the conventional compensation voltage calculation method, as also analyzed inFig. 7(a), is adopted. The circuit parameters, loading conditions, and the other controller parameters were set equal

5. Experimental Results

Fig. 10 shows the experimental setup used in the present
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Intra-arm Balancing for MMC with Cell Loading（Takumi Yasuda et al.）(a) Arm current and modulation waveforms for cells.

Fig. 10. Experimental setup of multiport converter prototype(b) Capacitor voltage.

Table 2. Experimental conditions

study. Table 2 shows the experimental conditions. A 17-kW
multiport converter prototype with 12 cells per arm was built
in the laboratory. A variable load based on a chopper was
installed for all cells in parallel with the cell capacitor, realizing only unidirectional operation absorbing power from thegrid. The frequency of the intra-arm balancing current was
set to be double the grid frequency. The execution period for
one discrete integration in Fig. 6 and the update period for the
intra-arm balancing current were set to 0.1 ms and 0.1 s, respectively. The maximum intra-arm balancing current I int0,xy
and the rated arm current considering the intra-arm balancing
current I arm,n , obtained numerically from the arm current inall possible loading conditions, were 32 and 71.4 A, respectively, which are 80% and 178% of the arm current when allcells are loaded at the rated load, respectively. The margin forthe modulation waveform dm was set to 0.03 and the threshold ∆Pδ,th for detecting a load change was set to 0.01 p.u.
5.1 Steady State Operation
Fig. 11 shows steadystate operation of the multiport converter when there are unloaded cells and fully loaded cells at the same time, whichis the maximum possible power imbalance in the arm. The
aggregated loading condition of the arm au, ad, bu, bd, cu,
and cd are set to 0.08, 0.67, 0.17, 0.17, 0.17, and 0.17 pu,
respectively. Fig. 11(a) shows the arm current and the modulation waveforms for the cells. The arm current includes theintra-arm balancing current of 16.6 A to extend the operation
range; the error in this current with respect to the theoreticalminimum value is 6.8%. The modulation waveforms of the(c) Grid voltage and current.

Fig. 11. Experimental results of steady-state operationof multiport converter with load imbalancecells do not saturate due to the intra-arm balancing current
injection. The capacitor voltages for the unloaded and fully
loaded cells follow the command, as shown in Fig. 11(b). The
grid current is balanced and has a THD of 3.13%, as shown in
Fig. 11(c). These results endorse the validity of the proposed
controller experimentally.
5.2 Transient Behavior under Load Change
Fig. 12 shows the transient response of the multiport converter when a cell load changes from 0 p.u. to 1 p.u. As soon
as the step change in the cell load occurs, the intra-arm balancing current increases. The intra-arm balancing current
is gradually decreased by the proposed minimization procedure. The capacitor voltage converges to the command value.
This transient behavior only slightly aﬀects the grid current,
as shown in Fig. 12. The root-mean-square value of the intraarm balancing current in the steady state is 17.1 A; the error
in this current with respect to the theoretical minimum valueis 3.9%.
Fig. 13 shows the transient behavior when the cell loadchanges from 1 p.u. to 0 p.u. As a result of the load change,
the load imbalance in the arm decreases to zero. Thus, theproposed method decreases the intra-arm balancing current
to zero. The load change and the change of the intra-arm
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Intra-arm Balancing for MMC with Cell Loading（Takumi Yasuda et al.）proposed controller achieves the desired power distribution
among the cells while maintaining balanced grid current evenduring operation with the maximum power imbalance.
Acknowledgment
This work was supported by the project Modular Megawatt
range Wireless EV Charging Infrastructure Providing Smart
Grid Services (MoMeWeC), funded by the Norwegian Research Council under the EIG CONCERT Japan program,
Joint Call on Eﬃcient Energy Storage and Distribution, withproject number 284231 and by the project FuChar, funded by
the Norwegian Research Council, grant N. 295133.
This work was supported by JST SICORP Grant Number
JPMJSC17C4, Japan.

References(1)Fig. 12. Experimental results of transient response ofmultiport converter to step change in load imbalance from
0 p.u. to 1 p.u.

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

( 10 )

Fig. 13. Experimental results of transient response ofmultiport converter to step change in load imbalance from
1 p.u. to 0 p.u.

( 11 )

balancing current have a small eﬀect on the grid current andthe capacitor voltage.

( 12 )

6. Conclusion( 13 )

This paper proposed an online control strategy for minimizing the intra-arm balancing current for the modular multilevel multiport converter with high power imbalance among
the cells. The proposed controller generates an optimized
compensation voltage to minimize the required intra-arm balancing current. In addition, the minimum required intra-arm
balancing current is calculated online and applied. The experimental results reveal that a multiport converter with the( 14 )( 15 )( 16 )

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A.I. Elsanabary, G. Konstantinou, S. Mekhilef, C.D. Townsend, M.
Seyedmahmoudian, and A. Stojcevski: “Medium Voltage Large-Scale GridConnected Photovoltaic Systems Using Cascaded H-Bridge and Modular
Multilevel Converters: A Review”, IEEE Access, Vol.8, pp.223686–223699(2020)
S. Alotaibi and A. Darwith: “Modular Multilevel Converter for Large-Scale
Grid-Connected Photovoltaic Systems: A Review”, Energies, Vol.14, p.6213(2021)
G.T. Chiang, K. Tanemura, and S. Tomura: “Proposal of a High-Frequency
Integrated Power Converter for Renewable Energy-Grid-BES Interactive Applications”, IEEJ Journal of Industry Applications, Vol.12, No.4, pp.624–634(2023)
M. Vasiladiotis and A. Rufer: “A Modular Multiport Power Electronic Transformer With Integrated Split Battery Energy Storage for Versatile Ultrafast
EV Charging Stations”, IEEE Transactions on Industrial Electronics, Vol.62,
No.5, pp.3213–3222 (2015)
G. Guidi, S. D’Arco, K. Nishikawa, and J.A. Suul: “Load Balancing of a
Modular Multilevel Grid-Interface Converter for Transformer-Less LargeScale Wireless Electric Vehicle Charging Infrastructure”, IEEE Journal of
Emerging and Selected Topics in Power Electronics, Vol.9, No.4, pp.4587–
4605 (2021)
S.S. Fazel, S. Bernet, D. Krug, and K. Jalili: “Design and Comparison of
4-kV Neutral-Point-Clamped, Flying-Capacitor, and Series-Connected HBridge Multilevel Converters”, IEEE Transactions on Industry Applications,Vol.43, No.4, pp.1032–1040 (2007)
G. Wang, et al.: “A Review of Power Electronics for Grid Connection of
Utility-Scale Battery Energy Storage Systems”, IEEE Transactions on Sustainable Energy, Vol.7, No.4, pp.1778–1790 (2016)
T. Nakanishi and J. Itoh: “Design Guidelines of Circuit Parameters for Modular Multilevel Converter with H-Bridge Cell”, IEEJ Journal of Industry Applications, Vol.6, No.3, pp.231–244 (2017)
A. Lesnicar and R. Marquardt: “An innovative modular multilevel converter
topology suitable for a wide power range”, 2003 IEEE Bologna Power Tech
Conference Proceedings, Bologna, Italy, Vol.3, p.6 (2003)
H. Akagi: “Classification, Terminology, and Application of the Modular
Multilevel Cascade Converter (MMCC)”, IEEE Transactions on Power Electronics, Vol.26, No.11, pp.3119–3130 (2011)
O. Oghorada, H. Han, and A. Esan: “Reactive Power Compensation of Modular Multilevel Cascaded Converter STATCOM using Average Power InterCluster Control Method under Unbalanced Voltage Conditions”, IEEJ Journal of Industry Applications, Vol.10, No.3, pp.331–338 (2021)
Y. Ko, M. Andresen, G. Buticchi, and M. Liserre: “Power Routing for
Cascaded H-Bridge Converters”, IEEE Transactions on Power Electronics,
Vol.32, No.12, pp.9435–9446 (2017)
T. Zhao, et al.: “An Optimized Third Harmonic Compensation Strategy forSingle-Phase Cascaded H-Bridge Photovoltaic Inverter”, IEEE Transactions
on Industrial Electronics, Vol.65, No.11, pp.8635–8645 (2018)
S. Yang, et al.: “Quantitative Comparison and Analysis of Diﬀerent Power
Routing Methods for Single-Phase Cascaded H-Bridge Photovoltaic GridConnected Inverter”, IEEE Transactions on Power Electronics, Vol.36, No.4,
pp.4134–4152 (2021)
G. Konstantinou, J. Pou, D. Pagano, and S. Ceballos: “A Hybrid Modular Multilevel Converter with Partial Embedded Energy Storage”, Energies,
Vol.9, No.12, p.1012 (2016)
F. Rong, X. Gong, and S. Huang: “A Novel Grid-Connected PV System

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Intra-arm Balancing for MMC with Cell Loading（Takumi Yasuda et al.）( 17 )( 18 )( 19 )( 20 )( 21 )( 22 )( 23 )( 24 )

Giuseppe Guidi (Non-member) received the Graduate degree fromthe University of L’Aquila, L’Aquila, Italy, in 1995,
and the Ph.D. degree from the Norwegian University of Science and Technology (NTNU), Trondheim,
Norway, in 2009. He has been involved in the fieldof power electronic drives since 1997, joining first at
Fuji Electric R&D, Japan, as a Research and Development Engineer until 2001, and then at SIEI SpA,
Italy, as a Senior Engineer until 2004. In 2009,
he joined Yokohama National University, Yokohama,Japan, as a Research Associate, working on power converters for electricvehicles. From 2011 to 2013, he was a part-time Research Associate with
NTNU, until joining SINTEF Energy Research, Trondheim, Norway. His
current research interests include power electronics, traction control, anddrive systems for electric propulsion, as well as application of power electronics to renewable energy.

Based on MMC to Get the Maximum Power Under Partial Shading Conditions”, IEEE Transactions on Power Electronics, Vol.32, No.6, pp.4320–
4333 (2017)
Z. Wang, H. Lin, Y. Ma, and T. Wang: “A prototype of modular multilevel converter with integrated battery energy storage”, 2017 IEEE AppliedPower Electronics Conference and Exposition (APEC), Tampa, FL, pp.434–
439 (2017)
T. Yasuda, G. Guidi, S. D’Arco, and J. Itoh: “Compensation Capability of
Intra-Arm Balancing Control for a Multiport Converter based on Modular
Multilevel Topology”, IEEJ Journal of Industry Applications, Vol.12, No.6,
pp.1046–1059 (2023)
T. Soong and P.W. Lehn: “Assessment of Fault Tolerance in Modular Multilevel Converters With Integrated Energy Storage”, IEEE Transactions on
Power Electronics, Vol.31, No.6, pp.4085–4095 (2016)
G. Liang, et al.: “Analytical Derivation of Intersubmodule Active Power Disparity Limits in Modular Multilevel Converter-Based Battery Energy Storage
Systems”, IEEE Transactions on Power Electronics, Vol.36, No.3, pp.2864–
2874 (2021)
P. Sochor and H. Akagi: “Theoretical and Experimental Comparison Between Phase-Shifted PWM and Level-Shifted PWM in a Modular Multilevel
SDBC Inverter for Utility-Scale Photovoltaic Applications”, IEEE Transactions on Industry Applications, Vol.53, No.5, pp.4695–4707 (2017)
L. Liu, H. Li, Y. Xue, and W. Liu: “Reactive Power Compensation and
Optimization Strategy for Grid-Interactive Cascaded Photovoltaic Systems”,
IEEE Transactions on Power Electronics, Vol.30, No.1, pp.188–202 (2015)
T. Yasuda and J. Itoh: “A Power Balancing Control for Large Power Unbalance in a Modular Multilevel Multiport Converter with Phase-Disposition
PWM”, IEEJ Journal of Industry Applications (early access)S. Milovanović and D. Dujić: “Comprehensive Comparison of Modular Multilevel Converter Internal Energy Balancing Methods”, IEEE Transactions on
Power Electronics, Vol.36, No.8, pp.8962–8977 (2021)

Salvatore D’Arco (Non-member) received the M.Sc. and Ph.D. degrees in electrical engineering from the Universityof Naples “Federico II”, Naples, Italy, in 2002 and2005, respectively. From 2006 to 2007, he was a
Post-Doctoral Researcher at the University of South
Carolina, Columbia, SC, USA. In 2008, he joined
ASML, Veldhoven, The Netherlands, as a PowerElectronics Designer, where he worked until 2010.
From 2010 to 2012, he was a Post-Doctoral Researcher with the Department of Electric Power Engineering, Norwegian University of Science and Technology (NTNU), Trondheim, Norway. In 2012, he joined SINTEF Energy Research where he currently works as a Senior Research Scientist. He has authored more than 100
scientific papers and is the holder of one patent. His main research activities
are related to control and analysis of power electronic conversion systems
for power system applications, including real-time simulation and rapid prototyping of converter control systems.

Takumi Yasuda (Student Member) received B.S. degree in Advanced
Course of Electrical and Electronic Engineering from
Kobe City College of Technology (KCCT) in 2019.
Since 2019, he has been a Ph.D. candidate in Nagaoka
University of Technology. He is a student member of
IEEJ and IEEE. Since 2021, he has been a Research
Fellow of the Japan Society for the Promotion of Science.

Jun-ichi Itoh (Senior Member) received his M.S. and Ph.D. degree
in electrical and electronic systems engineering from
Nagaoka University of Technology, Niigata, Japan in
1996, 2000, respectively. From 1996 to 2004, he
was with Fuji Electric Corporate Research and Development Ltd., Tokyo, Japan. He was with Nagaoka
University of Technology, Niigata, Japan as an associate professor. Since 2017, he has been a professor. His research interests are matrix converters,
dc/dc converters, power factor correction techniques,energy storage system and adjustable speed drive systems. He received IEEJ
Academic Promotion Award (IEEJ Technical Development Award) in 2007.
In addition, he also received Isao Takahashi Power Electronics Award in
IPEC-Sapporo 2010 from IEEJ, 58th OHM Technology Award from The
Foundation for Electrical Science and Engineering, November, 2011, Intelligent Cosmos Award from Intelligent Cosmos Foundation for the Promotion of Science, May, 2012, and Third prize award from Energy Conversion
Congress and Exposition-Asia, June, 2013. Prizes for Science and Technology (Development Category) from the Commendation for Science andTechnology by the Minister of Education, Culture, Sports, Science and Technology, April 2017. Dr. Itoh is a senior member of the Institute of ElectricalEngineers of Japan, the Society of Automotive Engineers of Japan and the
IEEE.

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