Advance Publication

IEEJ Journal of Industry Applications
J-STAGE Advance published date : Aug. 11, 2023
DOI : 10.1541/ieejjia.23000748

Paper

Compensation Capability of Intra-Arm Balancing Control
for a Multiport Converter based on Modular Multilevel Topology
Takumi Yasuda＊a) Student member,
Salvatore D’Arco＊＊ Non-member,

Giuseppe Guidi＊＊ Non-member,
Jun-ichi Itoh＊ Senior member,(Manuscript received Jan. 00, 20XX, revised May 00, 20XX)
Multiport converters can be achieved from the modular multilevel converter (MMC) configuration by integrating generation
units or loads at the cell level. This can offer advantages in applications such as photovoltaic panels and battery storage units where
the loads or generation units have a modular structure. However, this multiport configuration requires an active power balancingof the cells both between arms (inter-arm balancing) and within the arms (intra-arm balancing). It has been pointed out that the
intra-arm balancing controller has a compensation limit for the power unbalance. This paper introduces an evaluation functionalfor quantifying the compensation capabilities of intra-arm balancing controllers in a multiport converter controlled with phaseshifted modulation. Two intra-arm balancing control strategies with extended compensation capabilities are developed by
maximizing this proposed evaluation functional. The first strategy uses either the dc or grid-frequency component to modify thecell ac voltage depending on the operating conditions. The second proposed method adds also higher harmonic components to thecell ac voltage to further improve the balancing performance. A theoretical evaluation and numerical analysis indicate that the two
proposed controllers offer compensation capabilities superior to those of conventional methods. In addition, experimental results
confirm the validity of the proposed controllers.
Keywords: Multiport converter, Modular multilevel converter, Intra-arm balancing controller, Phase-shifted PWM

1.

equalized capacitor voltage in all cells while achieving balanced
three phase current. This includes both the compensation of thepower unbalances between the arms (inter-arm unbalances) andunbalances between the cells of a single arm (intra-arm unbalances).
Circulating current can be utilized to compensate the power
unbalances between the arms (7)–(12). Intra-arm unbalances can becorrected by the injection of a compensation term to the ac-side
voltage reference of the cells (6)(11)–(20).
The intra-arm power balancing capability of the multiportconverters is limited by the insurgence of module-level overmodulation but only few papers have quantified the phenomenon.
The limitations for conventional intra-arm balancing in a cascaded
H-bridge are evaluated using the Power Routine Factor (PRF)
introduced in ref. (20) under several operating conditions. The PRF
indicates the percentage of load unbalance that the intra-arm
balancing controller compensate without over-modulation for all
possible combinations of loads. However, the computational effort
for the evaluation grows exponentially as the number of the cells
increases. Moreover, no suggestion is given in ref. (20) about how
to extend the compensation capabilities. An improved intra-arm
balancing controller extending the compensation limits by adding
only harmonic components in the ac-side voltage of each cell ispresented in refs. (18) and (19). An approach for compensating thevoltage with an optimized combination of dc and grid frequency
components is proposed in ref. (10). However, the controller does
not consider the phase angle of the fundamental frequency
component nor the possibility of inserting higher order harmonics.
This paper performs a quantitative analysis of the compensation
capability of the intra-arm balancing controller with phase-shifted
PWM (PS-PWM) for multiport converters based on the MMC. The
first main contribution of this paper is a definition of a simple

Introduction

Renewable energy plants and battery storage systems often
present a modular structure with several modules to be controlled
independently according to their individual condition. For example,
photovoltaic (PV) plants are generally organized in arrays of panels
while battery units are organized in stacks of cells. Multi-input andmulti-output converter topologies are thus inherently very suitablefor interfacing the renewable energy sources and theelectrochemical batteries to the grid (1)–(3).
A multiport converter based on the MMC in double-starconfiguration (4)(5) offers the possibility to integrate energy
management functionalities directly in the converter control and has
been actively researched for several applications (5)–(7) including
large-scale power management system in Battery Energy Storage
Systems (BESS) (8)–(16) and PV power conditioners (17)–(21). The
renewable energy sources and the energy storage units are managed
individually by a dc/dc converter connected to the dc side of eachcell. Furthermore, this multiport converter can be connected
directly to the medium voltage grid without a step-up gridfrequency transformer thanks to the cascaded connection of thecells. As a result, the cost and volume of the system may be reduced
compared to other configurations.
Active power balancing mechanisms should be in place to ensurea) 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, Norway© 200● The Institute of Electrical Engineers of Japan.

1Abbreviated Title within 8 words (Your Name et al.)evaluation functional that quantifies the maximum intra-arm
unbalance that a given balancing algorithm can compensate. Thisfunctional can be used to facilitate the design of controllers withextended compensation capabilities. The second main contributionof the paper is the introduction of two improved intra-arm balancing
controllers derived with the proposed evaluation functional. The
first proposed controller, named as Continuous Compensation
Method, utilizes the dc and the fundamental frequency component
for the compensation. The second proposed controller, named as
Discontinuous Compensation Method, utilizes not only dc and gridfrequency components but also higher order harmonic components.
The compensation capabilities of the proposed controllers arequantified and compared to those of conventional controllers todemonstrate the improvement in performance. This is supported
both by numerical and experimental results.

2.

iarm,auarm a,uarm b,uarm c,u

cell
1

cell
1

cell
1

cell
N
L
ig,b

cell
N
L

cell
N
L arm

cell
k

varm,au

ig,a
MV
AC

Circuit Configuration and Controllers

2.1 Circuit Configurations
The MMC-based multiportconverter analyzed in this paper is composed of cascaded choppercells connected in a double-star configuration, as shown in Fig. 1.
Renewable energy sources and/or energy storage are connected inparallel to the dc capacitor of each cell through a dc/dc converter.
The dc/dc converters in the cells, besides providing galvanic
isolation if needed, regulate the power flow to the local load/source
to achieve optimal utilization of the latter (e.g. MPPT in case of PV
cells (17)–(21), SOC control in case of batteries (8)–(11)). This structureoffers a superior fault-tolerance and scalability due to its modularity
and redundancy (5)(22)(23). In addition, the multilevel operation
reduces the harmonic distortion of the grid current, which leads toa reduction in the ac-side filtering requirements. Distributed dc/dc
converters make both the converter structure and the control
simpler compared with the multi-port converter based on multiactive bridge converters (24)(25) or on a single MVDC bus (25)(26).
The operating conditions may be different at any given time dueto the independent operation of each load/source, even though allloads/sources are rated for the same power and voltage. This results
in individual cell loads that are variable in time and not easily
predictable. Thus, the control of the multiport converter is
responsible for compensating any power unbalance that arises fromthe differences in the operating conditions of the cells. The overall
control system for operating under unbalanced cell loads is shownin Fig. 2 and its functionalities described in the following sections.
Note that in the context of the paper, the load and associateddc/dc converter installed in the cell in Fig. 1 are assumed toconstitute an ideal power source. This paper does not explore thepower flow control of the dc/dc converter.
2.2 Overall Energy Balance
All the net power
consumed (or supplied) by the load/sources connected to the cells
must be supplied (or absorbed) by the main MVAC port because theconverter topology in Fig. 1 does not feature any high-voltage dc
port. The total energy controller generates the active grid current
reference so that the total dc capacitor voltage is regulated to thedesired value. The total energy controller cannot ensure that all theindividual cell dc voltages are equal. Equalization of the cellvoltages is achieved by the additional control loops described in
section II.C and II.D.
The setpoint Vc* for the total energy controller represents thedesired dc voltage of each cell. Such setpoint can be chosen
arbitrarily, provided that the total dc voltage available on each arm
is higher than the peak-peak value of the sum of the phase-to-leg

iarm,xy

Pcell,xyk
dc

C

vcell,xyk

dcBattery,
PV, EV,
etc.

L
cell
1

ig,c
L
cell
1

L
cell
1

Vc,xyk

cell
N

cell
N

cell
N

arm a,darm b,darm c,dx: a, b, c
y: u, dk: 1, 2, ..., N

Fig. 1. Multiport converter based on MMC.
x: a, b, c
Grid current*
y: u, d
Total
Grid
v
arm,g,xy
referenceArm
k: 1, 2, ..., Nenergycurrent
Cell voltage
voltagecontroller
controller
referencereference*
Horizontal +Circulating + varm,xy*
1 + vcell,xyk
balancingcurrent+ *N +controller +controller varm,c,xy
Circulating
current
reference

Verticalbalancing
controller

Intra-armbalancingCompensation voltage
controller
reference vd,xyk*

Fig. 2. Outline of multiport converter control for phase-shifted
PWM.
neutral grid voltage and the voltage drop on the arm inductor (27)(28).
Since the voltage drop on the arm inductor is negligible in steadystate, the voltage redundancy coefficient  can be defined as:



1

N

V
2 2V
g k 1

c, k



NVc*
2 2Vg

1

(1)

where N is the number of cells in one arm, Vc,k is the dc link voltageof the k-th cell in an arm, and Vg is the rms value of the grid phasevoltage. The second equality stems from the assumption that theconverter is controlled so that all cell dc voltages are equal to thecommon setpoint Vc*. The voltage redundancy coefficient is usuallydesigned to be sufficiently greater than unity to prevent overmodulation of the arm, especially during transients, caused by thevoltage drop on the arm inductor, which is ignored in (1). Strictly
speaking, it is possible to operate the MMC with a voltage
redundancy coefficient lower than unity without introducing loworder harmonic distortions due to over-modulation, if zerosequence voltage components are injected at the ac terminals (27)(28).
However, this would introduce common mode voltage into the gridin case of transformer-less MVAC connection and should bepossibly avoided.
2.3 Inter-Arm Balancing Controller
Since the cells of
the converter are in general all loaded differently from each other,
the aggregated loads on each of the six arms can be significantly
unbalanced. Large arm unbalances caused by differently loaded
cells require active controls for the balancing. Both horizontal(phase-to-phase) and vertical (upper arm to lower arm) balancing
2

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Abbreviated Title within 8 words (Your Name et al.)controllers are applied in this paper, respectively. Such controllers
and their operating principles have been described in detail in ref.
(7), together with a thorough discussion of the power balance
process. Here, a simplified description is included with the aim of
introducing the most important aspects and establishing thenecessary nomenclature.
The aim of the balancing process is to distribute the active powerfrom the grid to each of the six arms, so that:
The grid current is balanced and consists only of thefundamental component.
The six arm currents satisfy the balance equations:N
1 Tgvarm , xy (t )iarm, xy (t ) dt   Pcell , xyk ,

0
Tg
k 1

1 N
+
Vc , k−
N k 1
Vc,k
varm*
iarm

N

vd,k*

g(t)

Calculate weighting
functionfor upper and lower arms of a given phase, since the grid current
does not contain such component. On the other hand, thefundamental component is the sum of the grid current and thecirculating current for the vertical power balancing. The gridcurrent is divided evenly between upper and lower arm, whereas thesame circulating current flows to the upper and lower arm. Thus,
the arm current can be different on each of the six arms (7)(29).
2.4 Intra-Arm Balancing Controller
The aggregatedloads on the arms are balanced by the controllers described in theprevious section by controlling the circulating current. However, an
additional control layer, indicated as intra-arm balancing controller
in Fig. 2, is needed to redistribute the power among the cells of agiven arm.
Fig. 3 shows the generalized structure of the intra-arm balancing
controllers considered in this paper. Such controller injects
additional compensation voltage to the individual ac-side voltagesof the cells to compensate for the power unbalance. In order not tointeract with the rest of the converter control system, the intra-arm
controller does not modify the total arm ac voltage command
varm*(t) that is calculated by the other control loops. The individual
ac-voltage commands to the cells in the arm take therefore thegeneral form:(2)

where Tg is the grid fundamental period, varm,xy and iarm,xy are thearm voltage and current in the arm x,y respectively, Pcell,xyk is theload (source) of the k-th cell in the arm x,y as shown in Fig. 1.
Energy balance of the arm in steady state imposes that the average
power that the arm absorbs (supplies) over a fundamental period
must be equal to the power drawn by all the loads (sources)
connected to the cells in the arm, if all the losses within theconverter are neglected as in (2). The objectives above are achievedby introducing circulating currents between the phases, consistingof dc and fundamental components. The circulating currents do not
flow in the grid and are defined in terms of the total arm currents
as:(3)

Since the converter does not have a dc port as shown in Fig. 1, thezero-sequence component of the circulating current is always zero.
The horizontal balancing controller redistributes the power
between the three phases by the dc circulating current. The
redistribution is a zero-sum process, because there is no HVDC port
as shown in Fig. 1. The vertical balancing controller redistributes
power between the upper and the lower arms by acting on thefundamental component of the circulating current. It can bedemonstrated (see ref. (7)) that different components of positive andnegative sequence of the circulating current can compensate fordifferent kinds of vertical power unbalance (7)(29). The dc and thefundamental component of the circulating current calculated by thehorizontal and the vertical balancing, respectively, are added
together to generate the reference input to the circulating current
controller. Outputs of the circulating current controllers are thecomponents of the arm voltages to drive the desired circulating
currents.
The resulting arm voltage commands varm,xy*(t), x∈{a, b, c}, y∈{u,d} are the sum of the output from the grid current controller and thecirculating current controller. Note that the arm voltages are always
positive, since the chopper cells cannot output negative voltage.
The arm currents are the sum of the grid currents and the circulating
currents. The generic arm current can be expressed as:iarm , xy  I 0, x  2 I1, xy cos  2 f g t  i , xy NVpi,k*

Fig. 3. Generalized intra-arm balancing controllers. The indicesx and y for identification of the arm are dropped for simplicity.

x  a, b, c , y  u , d  ,iiicir , x  arm, xu arm , xd , x  a, b, c
2

N

PI

*
vcell
, k (t ) *varm(t ) *
 vd , k (t ), k  1, ..., N 
N

(5)

with:
N

v
k 1

cell , k*(t )  varm*  t  N vd (t )  0
k 1

*

,k

(6)

where vd,k is the compensation voltage for the cell k generated by
the intra-arm balancing controller. Note that in this section theindices x,y used previously to identify the arm are dropped forsimplicity, since the focus is on a generic single arm.
In addition to (6), the cell ac voltage references must also be
within the range of the possible output of the cell topology to avoid
distortions due to over-modulation. With reference to Fig. 1, thismeans:

0  vcell ,k * (t )  Vc ,k , k  1, , N  .

(7)

The margin for correction of the cell ac voltage reference is thus
dependent on the available dc voltage. For a given grid voltage, thismeans that the intra-arm balancing capability is expected toincrease with the voltage redundancy factor  defined in (1).
Many methods for the intra-arm balancing proposed in literature
can be reduced to the generic form shown in Fig. 3. The
compensation voltage vd,k* is expressed as product of the output of
a PI controller Vpi,k* and a weighting function g(t). Since the outputof the PI controller is proportional to the difference between the
averaged dc link voltage in the arm and the dc link voltage of thecell k, the sum of all the compensation voltage terms in one arm is(4)

where x∈{a, b, c}, y∈{u, d}, fg is the frequency of the grid, I0,x isthe dc component on phase x, while I1,xy are the rms amplitude of
the fundamental component on arm x,y, and i,xy is the phase of thefundamental component on the corresponding arm with respect tothe arm voltage reference. Note that the dc component is the same
3

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Abbreviated Title within 8 words (Your Name et al.)zero, thus complying with the condition in (6) regardless of theparticular choice of g(t). The aim of the weighting function g(t) is
to extend the compensation range, as the basic constraint in (7) canbe rewritten as:
0

varm* (t )
 V pi , k *  g (t )  Vc .
N

start
Fix the form of the candidate g(t) as function of the optimization
parameters and calculate the form of compensation voltage vd,max(t)and vd,min(t) accordingly
Formulate analytical compensation power of cell Pd,max and Pd,minwith respect to parameters of vd,max*(t) and vd,min*(t)(8)

Among the balancing methods proposed in the literature, some ofthem use the arm voltage reference varm* (16)–(20) as a weighting
function, while others use the arm current iarm (6)(13)(14) or simply its
polarity sgn[iarm] (11)(12).
This paper proposes a general method for synthesizing optimal
weighting functions g(t), resulting in a maximized balancing
capability of the controller. The proposed method synthesizes theweighting function by analytical maximization of an objectivefunctional that quantifies the intra-arm balancing performance ofthe generic controller of Fig. 3 taking the constraints in (6) and (8)into account.

Evaluation functional J=min[Pd,max, −Pd,min](1) Maximize Pd,max with respect to parameters in vd,max*(t)(2) Minimize Pd,min with respect to parameters in vd,min*(t)(3) Maximize Pd,max with respect to parameters in vd,max*(t)under constraint of Pd,max=−Pd,min
Maximize J by choosing vd,max* or vd,min* in conditions (1)–(3)Calculate weighting function g(t) by normalizing vd,max*(t) or vd,min*(t)end

Theoretical Analysis of Intra-Arm Balancing
Controller

Fig. 4. Design flowchart for intra-arm balancing controller
based on a classical parametric optimization.

In this section, the proposed intra-arm balancing controller is
described in detail and its analytical derivation is performed. The
maximization problem is defined by introducing the objectivefunctional that is used to quantify the balancing capabilities. Then,
two examples of optimal weighting functions are developed.
3.1
Definition of Objective Functional
The amountof the power that should be compensated for the generic cell kwithin a given arm is defined as the difference between the loadingof the cell and the average loading of the arm during a fundamental
period Tg. Using this definition and applying the generalized
controller in Fig. 3, it follows:
1 N
Pd , k  Pcell , k   Pcell , k
N k 1. (9)V * Tg1 Tg
  vd* , k (t )  iarm (t ) dt  pi , k  g (t )  iarm (t ) dt
Tg 0
Tg 0

normalizing the derived vd,max* or vd,min*.
It is desirable for the arm balancing component to have the largest
possible Pd,max and the smallest (most negative) possible Pd,min,resulting in the widest compensation capability. The following
simple objective functional is thus proposed:3.

J ( g )  min  Pd , max ( g ),  Pd , min ( g ) .

In the following, the maximization of the functional above is used
to determine optimal weighting functions.
Fig. 4 shows the design procedure of the weighting function
using (12). The evaluation functional J becomes maximum in oneof three following conditions: I) at the boundaries of the constraintsin (8), II) at its extrema, III) at its discontinuity point (30). Therefore,
the optimization of J is divided into the following three steps:
1) Maximization of Pd,max with respect to vd,max*, whichcorresponds to the optimization problem using (10),2) Minimization of Pd,min with respect to vd,min*, whichcorresponds to the optimization problem using (11), and
3) Maximization of Pd,max with respect to vd,max* under theconstraint of Pd,max = −Pd,min, which can be solved using both(10) and (11).
One of the three conditions above maximizes the evaluation
functional J. In order to solve the problem analytically, the class ofcandidate functions is restricted by fixing the form of the function
g(t) and performing a classical parametric optimization. Two kindsof weighting functions are proposed and optimized according to theprocedure described above. The candidate function g(t) is always
periodic with the period Tg and the harmonic content is what
differentiates the cases. In one case, the weighting function isassumed to be continuous and contains only dc and fundamental
frequency components; the balancing method resulting from the useof the optimal weighting function of such form is termed asContinuous Compensation Method (CCM). The second case uses aweighting function containing an infinite number of harmonics
caused by the discontinuous waveform; consequently, the resulting
balancing method is termed as Discontinuous Compensation
Method (DCM).
3.2 Continuous Compensation Method (CCM)
The
weighting function g(t) of the CCM consists of a dc and a grid

Eq. (9) assumes that the output of the PI controller Vpi,k* changes
slowly enough to be treated as a constant over the period Tg. Hence,the compensation voltage vd,k* can be considered as a scaled
weighting factor. Eq. (9) indicates that the amplitude of thecompensation voltage increases with the power unbalance in thearm. However, the compensation voltage vd,k* is required to fulfill(8) to avoid over-modulation. This implies that there is a limitation
for the compensation capability for the power unbalance. Here, themaximum and the minimum power unbalance Pd,max and Pd,min thatthe intra-arm balancing controller can compensate with the given
g(t) while fulfilling (8) are defined as:
Pd , max 

1 Tg *
vd , max (t )  iarm (t ) dt ,
Tg 0

(10)

Pd , min 

1 Tg *
vd , min (t )  iarm (t ) dt
Tg 0

(11)

(12)

where vd,max* and vd,min* are the compensation voltages at thoseconditions and they can be considered as auxiliary variables for g(t).
Therefore, the maximization of the compensation capability of theintra-arm balancing controller can be restated as an optimization
problem of Pd,max and Pd,min with respect to vd,max* and vd,min* under
the constraint in (8). The weighting function g(t) is obtained by
4

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Abbreviated Title within 8 words (Your Name et al.)frequency component. Its generic form can be expressed as:g (t )  G0  2G1 cos  g t  CCM  .

Arm current

iarm

(13)

From the form of the weighting factor, the maximum compensation
voltage can be defined as:
vd , max (t )  Vd 0, max  2Vd 1, max cos  g t  CCM  .

Vc

The minimum compensation voltage can be defined in the samemanner. Vd,max (Vd,min), Vd,max (Vd,min), and CCM represent theamplitudes of the dc and fundamental component and the phaseangle of the latter with respect to the arm voltage reference,
respectively. Maximum and minimum compensation power Pd,max
and Pd,min are expressed from (10)–(11), and (14) as:(15)

Pd , min  Vd 0, min I 0  Vd 1, min I1 cos CCM  i  .

(16)

O

angle

Voltage forcells withlighter load

iarm
O
Vc
Vc
2

angle
AC-side v oltage of cell

O

varm
N

angle

(b) With dc compensation voltage.

Fig. 5. Typical ac-side voltage waveforms of cells withcompensation voltage injection by the CCM.
Arm current
O
Vc

time
For smaller compensation powervarm
N
For larger
compensation powertime

AC-side voltage of cellO

Fig. 6. Typical ac-side voltage waveforms of cells withcompensation voltage injection by DCM.
the compensation voltage has to be smaller than the dc link voltage
Vc and larger than zero as mentioned in (8), the maximum andminimum available amplitude of the compensation voltage are
Vc−varm*/N and −varm*/N, respectively. Thus, the instantaneous
maximum and minimum compensation power pd,max and pd,min are
expressed as:.

(18)
As shown in (17)–(18), the weighting function of the CCM is afunction of the arm current and of the voltage redundancy
coefficient. Eq. (17) indicates that the CCM switches between puredc compensation voltage and pure grid frequency compensation
voltage according to the ratio between dc component and gridfrequency component of the arm current, which is referred as“mode change” in this paper.
Fig. 5(a) shows an example of the calculated ac-side voltage ofcells with the CCM under conditions corresponding to the first rowof (17), when the grid frequency component of the arm current isrelatively large compared to its dc component. The phase difference
between the ac-side voltage of a cell and the arm current is small
when the cell requires more power than the average power of thearm. Such phase difference is increased for cells that require smaller
power. Fig. 5(b) is an example of the cell voltage with the CCM
under conditions corresponding to the second row in (17), when thearm current has a relatively large dc component.
3.3
Discontinuous Compensation Method (DCM)
The weighting function g(t) of the DCM includes not only the dc
and the grid frequency components but also higher order harmonics.
Although the harmonic components generate no active power, they
suppress the amplitude of the cell ac voltage and help to inject larger
amplitude of useful dc and grid frequency component without
exceeding the modulation limits.
In this case, the instantaneous compensation power pd,max and
pd,min are optimized. Since the sum of the averaged arm voltage and 2 A cos  t   g CCM norg (t )  

Anor

varm
N

Voltage forcells withheavier load(a ) With grid f requency compe nsation
voltage.

Substituting (15)–(16) into (12), the expressions of Vd0,max (Vd0,min),Vd1,max (Vd1,min), and CCM that solve the maximization problem canbe analytically calculated. The optimal weighting function g(t) for
the CCM is expressed as in (17) where the Anor is an adaptive gain
for the normalization, which is described in 3.3. The phase angle
CCM of the weighting function in (17) is expressed as: tan 1  sin i /   cos i  1...  cos i  1 /  1
CCM    tan  sin i /   cos i  1 ... cos i  1 /   sgn i  / 2...  cos i  1 /  AC-side v oltage of cell

Vc
2

(14)

Pd , max  Vd 0, max I 0  Vd 1, max I1 cos CCM  i  ,

angle

O

Ar m current

In-phaseV  varm (t ) / N  iarm (t ) ...  iarm  0 ,
pd , max (t )   c   varm (t ) / N  iarm (t ) ...  iarm  0 (19)

   varm (t ) / N  iarm (t ) ... iarm  0 .
pd , min (t )  Vc  varm (t ) / N  iarm (t ) ... iarm  0 (20)

Substituting (19)–(20) into (12) results in the following form for theweighting function g(t):v * (t )g (t )  Anor  2   arm 2    sgn iarm (t )
(21)


Vg


where Anor is the adaptive gain for the normalization that will befurther discussed in section 3.4.
Fig. 6 shows an example of the cell ac voltage waveform
calculated according to the DCM. Such method injects thecompensation voltage according to the polarity of the arm current,
resulting in a discontinuous waveform for the ac-side voltage of thecells.
3.4
Stability of Intra-Arm Balancing Controller
The proposed weighting factors contain the adaptive normalization
gain Anor as shown in (17) and (21). Such gain is introduced so thatthe loop gain of the intra-arm balancing controller is independent of
the weighting function g(t) and the arm current condition.
Fig. 7 shows the models of the intra-arm balancing controller in... I 0 / I1  max    max  cos i 1 /   ,otherwise5 2  1 sin i  / 2    1




(17)

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Vpi,k* vd,k* 1
Vc , kg
MA+−

Id,k +
1−sC
iarm Icelld,kPI

DVc,int(a) Overall closed-loop control diagram.

+0−

Gpi(s)

Vpi,k*

Ad

Id,k +−
Icelld,k1sC

DVc,int

Evaluation
functional [%]Fig. 7. Block diagram of closed-loop intra-arm balancing
controller. MA indicates the moving average filter used toattenuate the dc link voltage ripple.
the multiport converter (10). The averaged input current to the cellover the grid period due to the compensation voltage injection by
the intra-arm balancing controller is derived as:(b)*
 1 Tg g (t )
1 Tg v (t )Id , k   d , k  iarm (t ) dt   
 iarm (t ) dt V pi* , k . (22)
0
0


Tg
Vc , kVc , k Tg

w/ arm current
0
1.0

300
200

2.0
Voltage redundancy coefficient Arm current condition is [I0:I1:i] = [1:1:0].

w/ polarity of arm current
w/ arm current

DCM
CCM

100
0
1.0

3.0

w/ arm voltage
2.0
Voltage redundancy coefficient 

3.0

Arm current condition is [I0:I1:i] = [0:1:/6]. The circles and the squares

assumed that the multiport converter operates with unity power
factor at the grid terminals.
The horizontal axis of Fig. 8 indicates the voltage redundancy
coefficient  and the vertical axis indicates the value of theevaluation functional J defined in (12), normalized to the averaged
power in one arm, which is a measure of the compensation
capability of the controllers.
Fig. 8(a) compares the performance of the different controllers
when there is power unbalance between legs, resulting incirculation of a dc current of magnitude I0. The compensation
capability of all controllers improves as the voltage redundancy
increases because the available amplitude of the compensation
voltage increases. The compensation capability of the DCM is
improved by 130.7% at =1.25 in comparison with theconventional method based on the polarity of the arm current,
which is the second largest compensation capability. In thisoperating condition, the CCM applies only a dc compensation
voltage and its compensation capability is larger than those of theconventional methods based on the arm current and on the arm
voltage. The improvement over the latter is 15.0% at =1.25.
Fig. 8(b) compares the different methods when there is power
unbalance between the upper and the lower arms, resulting in theflow of a circulating current at the grid frequency. The circles in Fig.
8(b) indicate the operating points used later for the experimental
verification. As in the last case, the compensation capabilities of allcontrollers are improved as the voltage redundancy increases. The
compensation capability of the DCM is the largest of all controllers,being 118.6% larger than the one of the conventional methods basedon the polarity of the arm current at =1.25. The CCM offers 37.3%
larger compensation capability than the conventional method basedon the arm current in this condition. In particular, the CCM has
relatively good compensation capability at low voltage redundancy
since its weighting function g(t) adjusts the phase angle of the ac-

(24)

(25)

In this paper, the normalized gain Anor is designed so that the gain
Ad becomes unity: 1 Tg g '(t )Anor  1 /  
 i (t ) dt  .
 Tg 0 Vdc , k arm




CCM

(23)

Substituting (24) into (23), the gain Ad is given as:
Anor Tg g '(t ) iarm (t ) dt
Tg 0 Vdc , k

DCMindicate the experimental conditions.

As seen in (17) and (21), the weighting function g(t) can be
expressed in the following form using Anor:Ad 

w/ polarity of arm current
w/ arm voltage

Fig. 8. Evaluation functional for conventional and proposed
intra-arm balancing controllers in different arm current
conditions. The diamond in the figures indicates thecompensation capability derived from the simulation.

From the small-signal model of (22), the gain Ad in Fig. 7 isobtained as:g (t )  Anor g '(t ) .

50

JParm / N(b) Simplified model. Gpi is transfer function of the PI controller.

1 Tg g (t )iarm (t ) dt .
Tg 0 Vc , k

100

(a)

GMA(s)Ad 

J
Parm / N0

Evaluation
functional [%]Abbreviated Title within 8 words (Your Name et al.)(26)

The gain Anor can be calculated analytically for the proposed CCM
and DCM given the arm currents. A saturation is needed for thedenominator in (26) in the experimental implementation in order toavoid the instability caused by the division by zero. Any classicalcontrol method can then be applied for the design of a stable control
loop, since all the transfer functions of the model in Fig. 7 are
known. It is worth to note that the process of normalization of thetransfer function Ad is also required in the design of theconventional intra-arm balancing methods, with the only difference
being the form of the weighting function.
3.5
Comparison of Compensation Capability
Fig. 8shows a comparison between the compensation capabilities ofseveral kinds of intra-arm balancing controllers. In particular, theCCM and DCM proposed in this paper are compared to some of themost popular methods found in the literature, utilizing the arm
voltage command varm* (16)–(20), the arm current iarm (6)(13)(14), and thepolarity of the arm current sgn[iarm] (11)(12) as the weighting function
g(t). The comparison is performed for two different loading
conditions, resulting in different arm currents. For simplicity, it is
6

IEEJ Trans. ●●, Vol.●●, No.●, ●●●

40

CCM

20

w/ arm current
0100

w/ polarity of arm current

DCM

Power routine
factor [%]J
Evaluation
functional [%] Parm / N

Abbreviated Title within 8 words (Your Name et al.)

0

10
20
Voltage ripple [%]w/ arm voltage

J
Evaluation
functional [%] Parm / N

0

w/ polarity of arm current
w/ arm current

w/ arm voltage
01020Voltage ripple [%]w/ arm voltage
2.0
Voltage redundancy coefficient 

3.0

compensate without causing over-modulation for all possiblecombinations of cell loadings. Two cells per arm are assumed forsimplicity in Fig. 10. The PRF is shown to increase with the voltage
redundancy as in Fig. 8. The DCM presents the best PRF of all
methods and the CCM shows superior PRF compared with theconventional controller using the arm current or the arm voltage. It
is noted that Fig. 10 exhibits similar characteristics compared withthe evaluation results obtained using the proposed evaluation
function as shown in Fig. 8. These results reveal that the proposed
evaluation function can quantify the capabilities of the intra-arm
balancing controller as well as the PRF but without the heavy
calculation burden associated to the latter.

CCM

50

CCM

Fig. 10. Evaluation results of intra-arm balancing controllers
with Power Routine Factor (PRF). Arm current is set to [I0:I1:i]= [0:1:/6].

among the legs.

DCM

DCM

50

0
1.0

30

(a) Arm current condition is [I0:I1:i] = [1:1:] assuming the power unbalance100

w/ polarity of arm current
w/ arm current

30(b) Arm current condition is [I0:I1:i] = [0:1:/6] assuming the power unbalance
between the upper and the lower arms.

Fig. 9. Variation of evaluation functional with respect to dc link
voltage ripple. The voltage redundancy coefficient is set to=1.25.

4.

side voltage of the cell for the larger compensation capability.
Results in Fig. 8 indicate that the proposed DCM shows larger
compensation capability in all considered arm current conditions.
In addition, the compensation capability of the CCM is larger thanthat of the conventional method based on the arm current and on thearm voltage, whose compensation voltages consist only of the dc
and the grid frequency components.
Fig. 9 shows numerical calculation results of the compensation
capability as a function of the dc link voltage ripple observed in thecells. A higher dc link voltage ripple reduces the compensation
capability of all methods due to the diminishing range available forthe compensation voltage in case of Fig. 9(a). As a result, theproposed controllers offer larger compensation capability than theconventional controllers irrespective of the dc link voltage ripple.
On the other hand, the compensation capabilities of theconventional methods are not decreased by the dc link voltage
ripple in case of Fig. 9(b). In this condition, the peak value of theac-side voltage of the cell generated by the conventional method
using the arm voltage is almost at the peak of the dc link voltage
ripple, thus increasing the available amplitude of the compensation
voltage. The compensation capabilities of the conventional methods
based on the arm current and based on the polarity of the arm
current are constant because the amplitude of the cell ac voltage islimited by the bottom value of zero, which is not affected by the dc
link voltage ripple. Fig. 9 reveals that the proposed controllers do
not lose the effectiveness even when a voltage ripple of around 10–
20% is present that is a general design assumption.
Fig. 10 shows the compensation capability of the proposed andconventional intra-arm balancing controller evaluated using thePower Routine Factor (PRF) (20). The PRF, which was originallyintroduced in ref. (31) and applied to evaluate the intra-arm
balancing controller in ref. (20), indicates the percentage of theloaded condition that the intra-arm balancing controller is able toExperimental Results

Fig. 11 shows the experimental setup, consisting of the multiportconverter prototype and a load module containing 72 independent
electronically controlled resistors used to generate the cell loads.
Table 1 shows the main parameters of the setup. For simplicity,
throughout the experiments the reactive component of the gridcurrent is set to zero, resulting in unity power factor operation.
Without loss of generality, in the experiments the load in cell 1 isalways set to the maximum within the arm, while the load of cell
12 is set to the minimum within the arm, thus determining the
maximum load unbalance in the arm. The load unbalance between
cells 2‒11 is set within the compensation capability throughout theexperiments. For clarity, only the waveforms in the two cells withextreme values of load are displayed in this paper.
4.1
Continuous Compensation Method (CCM)
Table 2 lists the loading conditions of the arm and the maximum
load unbalance in one arm. According to the nomenclature
introduced in Fig. 1, the letters a, b, and c indicate the phase and u
and d indicate the upper/lower arm.
Fig. 12 shows the steady-state operation of the multiportconverter operated using the CCM for intra-arm load balancing. As
shown in Fig. 12(a), balanced grid currents with total harmonic
distortion (THD) of 0.9% are achieved thanks to the multilevel
operation with 12 cells even with the unbalanced load. Fig. 12(b)shows the arm current and the modulation waveforms for the cells
in the arm a,u. The dc and grid frequency component of the arm
current in the arm a,u are 3.00 A and 8.84 A (rms), respectively.
Since the grid frequency component of the arm current is relatively
large, the proposed CCM injects the grid frequency component withdifferent amplitude in order to compensate for the load imbalance.
The phase angles of the ac-side voltages of the cells differ due tothe compensation voltage. In contrast, each modulation waveform
for the cells in arm a,d presents a different dc component as shown
7

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Abbreviated Title within 8 words (Your Name et al.)Table 2. Loading conditions for experiments with CCM.

Load module

Aggregated load [p.u.]
Maximum error[au, ad, bu, bd, cu, cd]of load in arm
Steady-state [0.94, 0.34, 0.56, 0.20, 0.34, 0.07]–6.1% - 6.8%
±0.0%
[0.50, 0.95, 0.34, 0.34, 0.07, 0.20]
Load change±5.0%→ [0.84, 0.95, 0.34, 0.34, 0.07, 0.20]

Grid phase voltage [V]

150
0
−150

Grid current [A] (THD: 0.9%)300Multiport converter prototype−30

20 [ms]Fig. 11. Experimental setup of multiport converter prototype.
(a)

Table 1. Parameters for the experimental test.
Parameter
Rated power of cell
Grid line-line voltage
Grid frequency
Number of cells pe r arm
Rated dc link voltage of cell
Switching frequency of ce ll
Arm inductance
Cell capacitancePower factor

Symbol
Pcell
√3Vg
fg
N
Vc
fsw
L
C

Value
90 W
122 V (rms)
50 Hz
1221 V (ρ = 1.25)
14.3 kHz
1.5 mH (0.20p.u.)
15 mF (UCC=35 mJ/VA)
1.0

1.0

Grid phase voltage and grid current.

Modulation waveform [-]dcell,au12

0.5
0.0
20

Modulation waveform [-]dcell,ad1

0.5
dcell,au1

0.0

Arm current [A]

10

0

0

−20

−10

20 [ms]( b) Modulation waveforms f or cellswith grid frequency compensa tion
voltage. The dc a nd a c c ompone ntof the ar m cu rr e nt is 3.00 A and8.84 A (rms), respectively.

in Fig. 12(c), since the arm current flowing in the arm a,d contains
a relatively large dc component of 2.76 A while the grid frequency
component is 3.33 A (rms). The dc component measured in theupper and lower arm currents should in principle be identical. The
small difference of 0.24 A, which is 0.76% of the rated grid current,
is most likely due to inaccuracy of the current measurements. Fig.
12(d) shows the dc link voltage of the cells in arms a,u and a,d. The
maximum voltage error of the averaged dc link voltage from thecommand value of 21 V is 0.12%.
Fig. 13 shows the transient behavior of two cells under loadchange. The loading condition of the six arms is listed in Table 2.
The load in the cell au1 and the cell au12 were changed from 0.5p.u.
to 0.80p.u. and from 0.5p.u. to 0.87p.u., respectively. After the loadchange, a transient dc link voltage error of about 6.2% occurs andthe dc compensation voltage is injected to the modulation
waveform because the arm current contains a relatively large dc
component before the mode change. The load change leads to themode change from dc compensation voltage to grid frequency
compensation voltage about 140 ms after the load change as shownin Fig. 13. Afterwards, the dc link voltages of the cells converge tothe command value of 21 V within 0.2 s. The experimental results
reveal that neither the load change nor the mode change of the CCM
affect the dc link voltage of the cells and the grid current waveforms.
Fig. 14 compares the steady-state operation of the proposed CCM
and the conventional controller based on the arm voltage in the arm
a,u, where the maximum load unbalance in one arm of ±38% isapplied to the arm a,u, which is indicated as an open circle in Fig.

1.0

dcell,ad12
Arm current [A]

20 [ms]( c) Modulation waveforms for ce lls
with dc compensation voltage. Th edc a nd a c c om pon en t of t he a rm
curr ent is 2.76 A and 3.33 A (rm s) ,respectively.

DC link voltage of cells [V] (error: 0.12%)

25
Vc,ad1

Vc,ad12Vc,au1Vc,au12

20
15

Command
20 [ms](d)

DC link voltage of cells in two different arms.

Fig. 12. Experimental results of steady-state operation with
CCM under load unbalance. The variables with subscript 1 are
related to the cell with the largest load in the arm, whereas thevariables with subscript 12 are related to the cell with thesmallest load in the arm.
8(b). In order to verify the validity of the theoretical analysis, theload unbalance condition is set within the theoretical compensation
capability of the CCM, whereas it is out of the theoreticalcompensation capability of the conventional controller. The cells
operate without over-modulation and the grid current is balanced
thanks to the proposed CCM as shown in Fig. 14(a). On the other
hand, Fig. 14(b) shows a saturation at some cells because theconventional controller cannot compensate the load unbalance
without going into the over-modulation. The over-modulation
caused by the conventional controller results in an undesired dc
current component of 21.8% being injected into the grid current.
8

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Abbreviated Title within 8 words (Your Name et al.)Grid current [A]Table 3. Loading condition for experiment with DCM.

Modulation waveform [-]Aggregated load [p.u.]
Maximum error[au, ad, bu, bd, cu, cd]of load in arm
Steady-state [0.94, 0.34, 0.56, 0.20, 0.34, 0.07] –22.0% - 10.8%[0.88, 0.57, 0.34, 0.34, 0.07, 0.20] –22.0% - 10.8%
Load change→ [0.91, 0.57, 0.34, 0.34, 0.07, 0.20] –25.0% - 8.0%

20
0
−20
1.0

dcell,au1

0.5

25

DC link voltage of cell [V]dcell,au120Vc,au12

−150

20
15

Grid current [A] (THD: 1.0%)30CommandVc,au10

Arm current [A]

15

−30

0
−15

Grid phase voltage [V]

150

0.0

20 [ms]Load change

Mode change(a)0.1 [s]Modulation waveform [-]1.0

Fig. 13. Experimental results of transient behavior with CCM
under load change. The load in cell au1 changed from 0.5p.u.
to 0.87p.u. at the load change, whereas the load in cell au12changed from 0.5p.u. to 0.80p.u. at the load change. The
voltage redundancy coefficient  is set to 1.25. The
compensation terms in the modulation waveform are switchedfrom the dc component to the ac component at the time
indicated as “Mode change.”

Grid phase voltage and grid current.

dcell,au1

0.5
0.0

dcell,au12
Arm current [A]

20
0
−20

20 [ms]1.0

Modulation waveform [-]dcell,au1

0.5

1.0

Modulation waveform [-]dcell,au120.0

Grid current [A] (THD: 3.4%)
30

0

0

25

DC link voltage of cell [V]Vc,au1
Error: 0.10%

20
15

current are 2.88 A and 8.53 Arms, respectively.

Vc,au12

Command
20 [ms](a) CCM.

25

dcell,au12

Grid current [A] (THD: 1.5%)30

Reference waveforms for cells and arm current in one arm withcompensation voltage. The dc and the ac component of the arm

dcell,au1

0.5

0.0

−30

(b)

DC link voltage of cells [V] (error: 0.09%)
Vc,au120

Vc,au12

Command15
20 [ms]−30

DC link voltage of cell [V]25Vc,au1
Error: 3.38%
20
Vc,au12
Command15
20 [ms](c)

DC link voltage of cells in one arm.

Fig. 15. Experimental results of steady-state operation with
DCM under load unbalance. The subscript 1 of the variables in
the figure indicates that the cell has the largest load in the arm,
whereas the subscript 12 indicates that the cell has the smallest
load in the arm.

(b) Conve ntional controller.

Fig. 14. Comparison of steady state operation with CCM andconventional controller based on arm voltage. The voltage
redundancy coefficient  is set to 1.25. The load unbalance is
set to ±38%.

4.2
Discontinuous Compensation Method (DCM)
Table 3 lists the loaded conditions of the arm and the maximum load
unbalance in one arm. The load unbalance in one arm is 22% for
the test under the steady state, which is larger than the experimental
condition used for the CCM because of the larger compensation
capability of the DCM.
Fig. 15 shows the steady state operation of the system with the
DCM used for the intra-arm load balancing. The grid current isbalanced with THD of 1.0% as shown in Fig. 15(a). Fig. 15(b)shows the arm current and the modulation waveforms for the cells
in the arm a,u. The dc and grid frequency component of the arm
current are 2.88 A and 8.53 A (rms), respectively. The modulation

The dc link voltage of the cells remains balanced also with theconventional method even though the system is operated beyond
the compensation limit. In the over-modulation region, the cell
gains more power beyond the theoretical compensation capability
thanks to the harmonic components generated by the saturation(19)(32). This experimental result reveals that the CCM compensateslarger load unbalances than the conventional controller. In addition,these results verify the validity of the theoretical analysis.
9

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Abbreviated Title within 8 words (Your Name et al.)waveforms change discontinuously when the polarity of the arm
current changes as described in Fig. 6. Fig. 15(c) shows the dc link
voltage of the cells in the arms a,u. The maximum dc voltage
deviation from the command value is about 0.09%.
Fig. 16 shows the transient behavior resulting from the loadchange. The load in the cell au1 was changed from 0.67p.u. to 1p.u.
and that in the cell au12 was 0.67p.u. before and after the loadchange. The loading conditions for the six arms are listed in Table
3. After the load change, the dc link voltage of the cell where thechange takes place decreases by about 14.3% at the maximum andthe amplitude of the modulation waveform becomes large toincrease the input power to the cell. As a result, the dc link voltageof the cell is brought back to the command value within 0.3 s after
the load change. The load change has little impact on the waveformof the grid current.
Fig. 17 compares the steady-state operation of the DCM andCCM in the arm a,u. The maximum load unbalance in one arm of±76%, indicated as an open circle in Fig. 8(b), is used as condition
for the test. In order to verify the validity of the theoretical analysis,
the load unbalance condition is set within the theoreticalcompensation capability of the DCM, whereas it is out of thetheoretical compensation capability of the CCM. The load
unbalance is applied only to the arm a,u. The grid current isbalanced with the THD of 1.5% when the DCM is in use. On theother hand, the grid current THD worsens to 7.3% on account of theover-modulation when the CCM is enabled. The modulation
waveforms have a shorter period with over-modulation compared
to Fig. 14(b). Hence, the grid current contains little dc current unlike
the results in Fig. 14(b). Similar to what was observed in Fig. 14,
the dc link voltage of the cells remains balanced even if CCM
operates beyond the over-modulation limit. This experimental
result reveals that the DCM compensates larger load unbalance thanthe CCM as derived in the theoretical analysis.
4.3
Comparison between CCM and DCM
Theproposed evaluation function offers the possibility to design theweighting factor with arbitrary number of harmonic components.
The utilization of higher order harmonics improves thecompensation capability as shown in the comparison between the
CCM and DCM, since the higher order harmonics can suppress theamplitude of ac-side voltage of the cell. However, the harmonics inthe modulation waveform cause unwanted low frequency
harmonics and worsen the current quality (33)(34). In the cascaded
multiport converter with the PS-PWM analyzed in this paper, theharmonics injected by the intra-arm balancing controller ideallycancel each other and do not appear in the arm voltages as shownin (6). However, in practice, cancelation is not perfect whendifferent modulation waveforms are applied (17). Unwanted
harmonics in the arm voltage constitute disturbances for the current
controller that must therefore be able to reject them. When the cells
are operated with relatively high switching frequency, like thecondition in this paper, the disturbance to the current controller issmall since the harmonic component appears at high frequency. In
this case, DCM can be safely used to extend the compensation
capability. On the other hand, a weighting function utilizing only
low frequency component like the CCM should be adopted in caseof low switching frequency.
4.4
Comparison of Calculation BurdenTheadditional computational burden needed for the proposed balancing
methods is associated to the calculation of the weighting function
indicated with g(t) taking different forms for the different proposals.

Grid current [A]

20
0
−20

Modulation waveform [-]

1.0
0.5

dcell,au1

0.0

dcell,au12

DC link voltage of cell [V]25Vc,au1220
CommandVc,au1

15

Arm current [A]

15
0
−15
Load change

0.1 [s]Fig. 16. Experimental results of transient behavior with the
DCM under load change. The load deviation increases by theload change in cell au1 from 22% to 25%. The voltage
redundancy coefficient  is set to 1.25.

1.0Modulation waveform [-]dcell,au1

0.5
0.0

1.0

Modulation waveform [-]dcell,au1

0.5
dcell,au12

0.0

dcell,au12

Grid current [A] (THD: 1.5%)30

Grid current [A] (THD: 7.3%)
30

0

0

−30
25

DC link voltage of cell [V]Vc,au1
Error: 0.09%

20
15

−30
25

DC link voltage of cell [V]Vc,au1
Error: 1.00%

20
Vc,au12

Command
20 [ms](a) DCM.

15

Vc,au12

Command
20 [ms](b) CC M.

Fig. 17. Comparison of steady-state operation of DCM and
CCM. The voltage redundancy coefficient  is set to 1.25. The
load unbalance is set to ±76%.
The CCM in section III.B requires the calculation of (17)–(18) andthe evaluation of the dc and fundamental component of the gridcurrent. The DCM presented in section III.C only requires (21). The
calculation of the normalized gain Anor as in (26) must be performed
both in the conventional and in the proposed methods, thus it does
not constitute an additional burden. In any case, the calculations
involve some simple trigonometric functions and possibly a squareroot function that do not pose significant challenges for modern
digital controllers.
Table 4 shows the comparison of the calculation burden of the
proposed controllers and the conventional controllers as measured
on the experimental setup in use. The controller (Xilinx Zynq) is
based on ARM Cortex A9 CPU core with FPU and the core clock
10

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Abbreviated Title within 8 words (Your Name et al.)Table 4. Comparison of execution time of conventional andproposed intra-arm balancing controllers.
Conventional
Execution time

18.3 usCCM
18.7 us(+2.1%)

DCM
18.8 us(+3.0%)(8)(9)

is 667 MHz. The additional execution time of the proposed
controllers are 379 ns and 559 ns, respectively, whereas the baseexecution time is 13.8 s. It is thus verified that the proposed
methods have a calculation burden that is in the same order of theconventional ones when executed on modern microcontrollers.

5.

(10)

(11)

Conclusion

This paper performed a quantitative analysis of the compensation
capability of the intra-arm balancing controller for a multiportconverter based on MMC. A simple evaluation functional for the
intra-arm balancing control was proposed to provide a measure of
the maximum power unbalance that can be compensated by a given
controller. Moreover, two improved intra-arm balancing controllers
were developed based on the proposed evaluation functional. The
first proposed controller, named as CCM, utilizes dc andfundamental frequency components for the compensation. Whereas
the second proposed controller, named as DCM, utilizes a
discontinuous weighting function, resulting in not only dc and gridfrequency components but also higher harmonic components. The
compensation capabilities of the proposed controllers have been
derived, showing that they are able to compensate larger power
unbalances than other controllers available in literature.
The validity of the proposed intra-arm balancing controllers has
been verified by experiments. The results confirmed that the
proposed intra-arm balancing controllers offer superior power
balancing capability for MMC-based multiport converters.

(12)

(13)

(14)

(15)

(16)

(17)

(18)

Acknowledgement
This work was supported by the project Modular Megawattrange 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, with project number 284231.
This work was supported by JST SICORP Grant Number
JPMJSC17C4, Japan.

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(21)

References
(22)
(1)

(2)

(3)

(4)

(5)

(6)

(7)

Z. Rehman, I. Al-Bahadly, and S. Mukhopadhyay, "Multiinput DC-DC
converters in renewable energy applications - An overview," in Renewable
and Sustainable Energy Review, vol. 41, pp. 521-539, Jan. 2015.
T. Shioi et al., "Battery Management System with Flying Capacitor Converter
Operated in Discontinuous Current Mode," 2019 20th International
Symposium on Power Electronics (Ee), Novi Sad, Serbia, 2019, pp. 1-6.
A. K. Bhattacharjee, N. Kutkut and I. Batarseh, "Review of Multiport
Converters for Solar and Energy Storage Integration," in IEEE Transactions
on Power Electronics, vol. 34, no. 2, pp. 1431-1445, Feb. 2019.
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, 2003, pp. 6 pp. Vol.3-.
H. Akagi, "Classification, Terminology, and Application of the Modular
Multilevel Cascade Converter (MMCC)," in IEEE Transactions on PowerElectronics, vol. 26, no. 11, pp. 3119-3130, Nov. 2011.
Y. Su, P. Wu and P. Cheng, "Design and Evaluation of a Control Scheme for
the Hybrid Cascaded Converter in Grid Applications," in IEEE Transactions
on Power Electronics, vol. 35, no. 3, pp. 3139-3147, March 2020.
G. Guidi, S. D’Arco, K. Nishikawa and J. A. Suul, "Load Balancing of a

(23)

(24)

(25)

(26)

(27)

11

Modular Multilevel Grid-Interface Converter for Transformer-Less LargeScale Wireless Electric Vehicle Charging Infrastructure," in IEEE Journal of
Emerging and Selected Topics in Power Electronics, vol. 9, no. 4, pp. 45874605, Aug. 2021.
I. Trintis, S. Munk-Nielsen and R. Teodorescu, "A new modular multilevel
converter with integrated energy storage," IECON 2011 - 37th Annual
Conference of the IEEE Industrial Electronics Society, Melbourne, VIC,
Australia, 2011, pp. 1075-1080.
T. Soong and P. W. Lehn, "Evaluation of Emerging Modular Multilevel
Converters for BESS Applications," in IEEE Transactions on Power Delivery,
vol. 29, no. 5, pp. 2086-2094, Oct. 2014.
Z. Wang. H. Lin, and Y. Ma, "Improved Capacitor Voltage Balancing Control
for Multimode Operation of Modular Multilevel Converter with Integrated
Battery Energy Storage System," in IET Power Electronics, vol. 12, no. 1, pp.
2751-2760, Spet. 2019.
X. Yang et al., "Reverse-blocking modular multilevel converter for batteryenergy storage systems," in Journal of Modern Power Systems and Clean
Energy, vol. 5, no. 4, pp. 652-662, July 2017.
W. Zeng, R. Li and X. Cai, "A New Hybrid Modular Multilevel Converterwith Integrated Energy Storage," in IEEE Access, vol. 7, pp. 172981-172993,
2019.
L. Maharjan, S. Inoue, H. Akagi and J. Asakura, "State-of-Charge (SOC)Balancing Control of a Battery Energy Storage System Based on a Cascade
PWM Converter," in IEEE Transactions on Power Electronics, vol. 24, no. 6,
pp. 1628-1636, June 2009.
N. Kawakami, S. Ota, H. Kon, S. Konno, H. Akagi, H. Kobayashi, and N.
Okada, "Development of a 500-kW Modular Multilevel Cascade Converter
for Battery Energy Storage Systems," in IEEE Transactions on Industry
Applications, vol. 50, no. 6, pp. 3902-3910, Nov.-Dec. 2014.
G. Liang et al., "Analytical Derivation of Intersubmodule Active Power
Disparity Limits in Modular Multilevel Converter-Based Battery Energy
Storage Systems," in IEEE Transactions on Power Electronics, vol. 36, no. 3,
pp. 2864-2874, March 2021.
J. I. Y. Ota, T. Sato and H. Akagi, "Enhancement of Performance, Availability,
and Flexibility of a Battery Energy Storage System Based on a Modular
Multilevel Cascaded Converter (MMCC-SSBC)," in IEEE Transactions on
Power Electronics, vol. 31, no. 4, pp. 2791-2799, April 2016.
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," in IEEE Transactions
on Industry Applications, vol. 53, no. 5, pp. 4695-4707, Sept.-Oct. 2017.
T. Zhao et al., "An Optimized Third Harmonic Compensation Strategy forSingle-Phase Cascaded H-Bridge Photovoltaic Inverter," in IEEE
Transactions on Industrial Electronics, vol. 65, no. 11, pp. 8635-8645, Nov.
2018.
T. Zhao et al., "Harmonic Compensation Strategy for Extending the
Operating Range of Cascaded H-Bridge PV Inverter," in IEEE Journal of
Emerging and Selected Topics in Power Electronics, vol. 8, no. 2, pp. 13411350, June 2020.
S. Yang et al., "Quantitative Comparison and Analysis of Different Power
Routing Methods for Single-Phase Cascaded H-Bridge Photovoltaic GridConnected Inverter," in IEEE Transactions on Power Electronics, vol. 36, no.
4, pp. 4134-4152, April 2021.
V. Sridhar and S. Umashankar, "A Comprehensive Review on CHB MLI
based PV Inverter and Feasibility Study of CHB MLI based PV-STATCOM,"in Renewable and Sustainable Energy Reviews, vol. 78, pp. 138-156, Oct.
2017.
S. Debnath, J. Qin, B. Bahrani, M. Saeedifard and P. Barbosa, "Operation,
Control, and Applications of the Modular Multilevel Converter: A Review,"
in IEEE Transactions on Power Electronics, vol. 30, no. 1, pp. 37-53, Jan.
2015.
M. Priya, P. Ponnambalam, and K. Muralikumar, "Modular-Multilevel
Converter Topologies and Applications - A Review," in IET PowerElectronics, vol. 12, no. 2, pp. 170-183, Jan. 2019.
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," in IEEE Access, vol. 8, pp. 223686223699, 2020.
M. Rabiul Islam, A. M. Mahfuz-Ur-Rahman, K. M. Muttaqi and D. Sutanto,"State-of-the-Art of the Medium-Voltage Power Converter Technologies for
Grid Integration of Solar Photovoltaic Power Plants," in IEEE Transactions
on Energy Conversion, vol. 34, no. 1, pp. 372-384, March 2019.
S. Alotaibi and Ahmed Darwith, "Modular Multilevel Converter for LargeScale Grid-Connected Photovoltaic Systems: A Review," in Energies, vol. 14,
p. 6213, Sept. 2021.
N. Thitichaiworakorn, M. Hagiwara and H. Akagi, "Experimental

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Abbreviated Title within 8 words (Your Name et al.)

(31)

(32)

(33)

(34)

Pd
Parm / NPowerunbalance [%](30)

I0:I1:i=0:1:/6

200

Prohibited100

I0:I1:i=0:1:0

0

I0:I1:i=1:1:0

−100
−200
1.0

Operation region
2.0
Voltage redundancy coefficient (a)Pd
Parm / N

(29)

Power
unbalance [%](28)

Verification of a Modular Multilevel Cascade Inverter Based on Double-Star
Bridge Cells," in IEEE Transactions on Industry Applications, vol. 50, no. 1,
pp. 509-519, Jan.-Feb. 2014.
T. Nakanishi and J. Itoh, "High Power Density Design for a Modular
Multilevel Converter With an H-Bridge Cell Based on a Volume Evaluationof Each Component," in IEEE Transactions on Power Electronics, vol. 33,
no. 3, pp. 1967-1984, March 2018.
S. Milovanović and D. Dujić, "Comprehensive Comparison of Modular
Multilevel Converter Internal Energy Balancing Methods," in IEEE
Transactions on Power Electronics, vol. 36, no. 8, pp. 8962-8977, Aug. 2021.
L. C. W. Dixon, “An Introduction in One and Two Variables,” in Nonlinear
optimization, English Universities Press, 1972.
Y. Yu, G. Konstantinou, C. D. Townsend, and V. G. Agelidis, "Comparisonof Zero-Sequence Injection Method in Cascaded H-Bridge Multilevel
Converters for Large-Scale Photovoltaic Integration," in IET Renewable
Power Generation, vol. 11, no. 5, pp. 603-613, April 2017.
T. Zhao and D. Chen, "A Power Adaptive Control Strategy for Further
Extending the Operation Range of Single-Phase Cascaded H-Bridge
Multilevel PV Inverter," in IEEE Transactions on Industrial Electronics, vol.
69, no. 2, pp. 1509-1520, Feb. 2022.
A. M. Hava, R. J. Kerkman and T. A. Lipo, "Carrier-based PWM-VSI
overmodulation strategies: analysis, comparison, and design," in IEEE
Transactions on Power Electronics, vol. 13, no. 4, pp. 674-689, July 1998.
H. Chen and H. Zhao, "Review on Pulse-Width Modulation Strategies for
Common-Mode Voltage Reduction in Three-Phase Voltage-Source
Inverters," in IET Power Electronics, vol. 9, no. 14, pp. 2611-2620, May 2016.

200

3.0

CCM case.

I0:I1:i=0:1:/6
Prohibited

I0:I1:i=0:1:0

100

I0:I1:i=1:1:0

0
−100
−200
1.0

Operation region
2.0
Voltage redundancy coefficient 
(b)

3.0

DCM case.

app. Fig. 1. Theoretical stable operating regions of proposed
methods.

Appendix
1. Operation range of proposed controllers
app. Fig. 1 illustrates the operation range of the two proposed
methods. The horizontal axis indicates the voltage redundancy
coefficient  and the vertical axis indicates the power unbalance ofthe cells in one arm. The proposed controllers are able tocompensate the power unbalance when all loads in the arm arewithin the shaded region in app. Fig. 1. Outside such regions, arm
voltage distortion occurs due to over-modulation in some of thecells. The compensation capabilities of the proposed methods
increase as the grid frequency component of the arm current
becomes large compared to the dc component. In other words,
larger compensation capabilities are obtained under the conditionof small power unbalance between the legs and large power
unbalance between the upper and the lower arms. The
compensation capability for negative power unbalance of the CCM
is much larger than that of the DCM. However, the CCM has
smaller compensation capability for the positive power unbalance.
The intra-arm power unbalance occurs on both the positive andnegative side as shown in (12). In order to compensate both thepositive and negative power unbalance, the DCM extends thecompensation capability for the positive power unbalancecompared to the CCM, shrinking the compensation capability forthe negative power unbalance. Although the compensation
capability for negative power unbalance is reduced, it still remains
as large as the one for positive power unbalance. Therefore, theDCM has superior PRF as shown in Fig. 10.

shows the loaded condition for the simulation. The cell
capacitance and the arm inductance are scaled from theexperimental multiport converter prototype. In this simulation, thevoltage redundancy was set to large value of 2.09 to extend thecompensation capability enough to guarantee the bidirectional
operation capability of the intra-arm balancing controller. The
loaded condition is set within the theoretical compensation
capabilities of the CCM and DCM.
app. Fig. 2 shows the simulation results of the steady-state
operation with the CCM. The variables with the subscript 1 are
related to the cell with the largest positive load, whereas thevariables with the subscript 12 are related to the cell with the mostnegative load (largest power generation). The grid current isbalanced with low THD of 1.7%, as shown in app. Fig. 2(a). app.
Fig. 2(b) shows the arm current and the modulation waveforms forthe cells with the maximum load deviation (positive and negative).
The modulation waveform for the cell with the positive load
unbalance, indicated as dcell,au1, is almost in-phase with the arm
current, whereas the modulation waveform for the cell with thenegative load unbalance , indicated as dcell,au12, is 180 degrees outof phase with the arm current to regenerate power, as shown in app.
Fig. 2(b). app. Fig. 2(c) shows the dc link voltage of the cells. The
dc link voltage is balanced regardless of the loaded condition thanks
to the operation of the intra-arm balancing controller.
app. Fig. 3 shows the simulation results of the steady-state
operation with the DCM. app. Fig. 3(a) is the grid current, which isbalanced with THD of 2.21%. The current THD of the DCM
method shown in app. Fig. 3(a) is worse than that of the CCM
shown in app. Fig. 2(a) because the higher-order harmonics
generated by the DCM degrade the current quality. This implies thatthe switching frequency of 5 kHz, which is lower than theexperimental condition, is not high enough to suppress thedisturbance caused by the harmonics, as mentioned in the
conclusion. The modulation waveforms in app. Fig. 3(b) differ
according to the loaded condition as explained for the case of app.
Fig. 2(b). The dc link voltage is balanced with an error of 0.02%

2. Operation of multiport converter with cells inregenerating operation
This section presents the simulation results of the multiportconverter with some of the cells providing power towards the grid.
The intra-arm balancing controller compensate the power
unbalance regardless of the direction of the power flow as long as
the load unbalance is within the compensation capability. The
power unbalance more than –100% indicates that the power flow of
the cell is opposite as the averaged power of the cell in the arm.
app. Table 1 shows the circuit parameters and app. Table 2
12

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Abbreviated Title within 8 words (Your Name et al.)app. Table 1. Simulation condition.

Parameter

Symbol
Pcell
√3Vg
fg
N
Vc
fsw
L
C

Rated powe r of cell
Grid line-line voltage
Grid frequency
Number of cells pe r arm
Rated dc link voltage of cell
Switching frequency of cell
Arm inductance
Cell capacitancePower factor

Grid phase voltage [kV]

8.0

Value
5.0 kW
6.6 kV (rms)50 Hz
50450 V (ρ = 1.25)
5.0 kHz37.0 mH (0.20p.u.)
1.72 mF (UCC=35 mJ/VA)
1.0

0.0
−8.0

Grid current [A] (THD: 2.21%)

80
0
−80

20 [ms](a)

Modulation waveform [-]1.0
app. Table 2. Loading condition for simulation.

CCM
DCM

Aggregated load [p.u.][au, ad, bu, bd, cu, cd][0.91, 0.1, 0.24, 0.34, 0.2, 0.07][0.91, 0.1, 0.24, 0.34, 0.2, 0.07]

Grid phase voltage and current.

dcell,au1

0.5
0.0

Load deviationin arm–151.9% - 8.1%
–120.6% - 9.5%

dcell,au12
Arm current [A]

80
0
−80

20 [ms]Grid phase voltage [kV]

8.0

(b)

component of the arm current is 5.29 A and 45.4 A (rms), respectively.

0.0
Grid current [A] (THD: 1.70%)

80

350

−80

Vc,au12450

0Vc,au1

Command
20 [ms]20 [ms](a)(c)

Modulation waveform [-]0.5
dcell,au12

dcell,au1
Arm current [A]

80
0
−80

DC link voltage of cell.

app. Fig. 3. Simulation results of steady-state operation with
DCM under load unbalance. The variables with subscript 1 are
related to the cell with the largest load in the arm, whereas thevariables with subscript 12 are related to the cell with thesmallest load in the arm.

Grid phase voltage and current.

1.0

1.0

Modulation waveform [-]dcell,au1

0.5

20 [ms](b)

DC link voltage of cells [V] (error: 0.02%)

550

−8.0

0.0

Modulation waveforms and arm current. The dc and the grid frequency

1.0

Modulation waveform [-]dcell,au1

0.5
dcell,au12

dcell,au12

Modulation waveforms and arm current. The dc and the grid frequency

0.0

component of the arm current is 5.29 A and 45.4 A (rms), respectively.

Grid current [A] (THD: 1.7%)80

Grid current [A] (THD: 4.8%)
80

0

0

550
450
350

DC link voltage of cells [V] (error: 0.06%)
Vc,au1Vc,au12−80

Command550

20 [ms](c)

450

DC link voltage of cell.

app. Fig. 2. Simulation results of steady-state operation with
CCM under load unbalance. The variables with subscript 1 are
related to the cell with the largest load in the arm, whereas thevariables with subscript 12 are related to the cell with thesmallest load in the arm.

350

0.0

DC link voltage of cell [V]Vc,au1 Error: 0.06%
Vc,au12−80550

DC link voltage of cell [V]Error: 0.10%
Vc,au1450
Command
20 [ms](a) CCM case.

350

Vc,au12

Command
20 [ms](b) DCM case.

app. Fig. 4. Comparison of operation with CCM and DCM insimulation. The experimental conditions are shown in app.
Table 1. The loaded conditions are same with app. Fig. 2.

due to the intra-arm balancing controller. These results reveal thatthe intra-arm balancing controller compensates the power
unbalance even when the multiport converter has some of the cells
acting as loads and some acting as power sources at the same time.
app. Fig. 4 compares the operation of CCM and DCM with loadconditions equal to those in app. Fig. 2. The negative load

unbalance is much larger than the positive load unbalance, whichcannot be compensated by the DCM. As shown in app. Fig. 4(b),the DCM cannot operate without going into over-modulation,
leading to considerable grid current distortion. The dc link voltageof the cells, though, remains balanced.
13

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Abbreviated Title within 8 words (Your Name et al.)20

Arm current [A]iarm,auiarm,adiarm,bu
iarm,bd
iarm,cu
iarm,cd0−20
8.0

icir,aicir,bicir,c−8.0

20 [ms](a)

CCM.

Arm current [A]iarm,auiarm,adiarm,bu
iarm,bd
iarm,cu
iarm,cd0−20
8.0(Non-Member) received the Graduate degree fromthe University of L’Aquila, L’Aquila, Italy, in 1995,
and the Ph.D. degree from the Norwegian Universityof Science and Technology (NTNU), Trondheim,
Norway, in 2009.
He has been involved in the field of powerelectronic 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 electric vehicles.
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, and drive
systems for electric propulsion, as well as application of power electronics
to renewable energy.

Circulating current [A]

0.0

20

Giuseppe Guidi

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 Power Electronics
Designer, where he worked until 2010. From 2010 to 2012, he was a PostDoctoral 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.

Circulating current [A]icir,aicir,bicir,c0.0−8.0

20 [ms](b)

DCM.

app. Fig. 5. Experimental results of arm current and circulating
current in steady state. The experimental conditions of app. Fig.
1(a) and app. Fig. 1(b) are same with Fig. 12 and 15,
respectively.

3. Circulating current for inter-arm balancing
The circulating current is utilized to redistribute the power
among the arms to achieve balanced grid current and dc link
voltages as discussed in section 2.3. This section presents theexperimental results of arm current and circulating current to show
the operation of the inter-arm balancing.
app. Fig. 5 shows the experimental waveforms of arm current andcirculating current in steady state. The operating conditions of app.
Fig. 5(a) and app. Fig. 5(b) are same as Fig. 12 and 15, respectively.
The circulating current flows to compensate the power unbalanceamong the arm due to the action of the vertical and the horizontal
balancing, because the aggregated loaded condition of the arm is set
to be unbalanced. As a result, the currents flowing in the six arms
are all different. Note that the circulating current and the arm
current in app. Fig. 5(a) and (b) are same since the loaded conditionof these experiments was equal. That confirms the fact that the
intra-arm balancing controller does not affect the arm currents,
regardless of the choice of the weighting function.
Takumi Yasuda

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 waswith Fuji Electric Corporate Research andDevelopment Ltd., Tokyo, Japan. He was with
Nagaoka University of Technology, Niigata, Japan as
an associate professor. Since 2017, he has been aprofessor. His research interests are matrix converters, dc/dc converters,
power factor correction techniques, energy storage system and adjustablespeed 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 andEngineering, 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 theCommendation for Science and Technology by the Minister of Education,
Culture, Sports, Science and Technology, April 2017. Dr. Itoh is a senior
member of the Institute of Electrical Engineers of Japan, the Society ofAutomotive Engineers of Japan and the IEEE.

(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.
14

IEEJ Trans. ●●, Vol.●●, No.●, ●●●