IEEJ Journal of Industry Applications
Vol.12 No.5 pp.953–960
DOI: 10.1541/ieejjia.22009850

Paper

Online Cell Capacitance and ESR Monitoring Using Switching
Frequency in a Modular Multilevel Converter∗a)

Takumi Yasuda

Student Member,

Jun-ichi Itoh∗

Kazunori Hasegawa∗∗

MemberSenior Member(Manuscript received Sep. 26, 2022, revised Jan. 23, 2023)
J-STAGE Advance published date : April 21, 2023

A cell capacitor is one of the most fragile components in a modular multilevel converter (MMC). Capacitance decreases and equivalent series resistance (ESR) increases, as the capacitor deteriorates. This paper proposes an online
monitoring method for both the capacitance and ESR of the cell capacitors in an MMC without any additional components or operation. The proposed method measures the impedance of the cell capacitor not only at a low frequency but
also at a switching sideband-frequency of the cell without current sensors for capacitor current. The high-frequency
components around the switching frequency improve the estimation accuracy compared with the previous methods thatmeasure only impedance at low frequencies. The experimental results confirm that the proposed method estimates thecapacitance and ESR with errors of 3.1% and 8.8%, respectively.
Keywords: capacitance, equivalent series resistance (ESR), modular multilevel converter (MMC), monitoring, deterioration diagnosis

1. Introduction

Modular Multilevel converters (MMCs) have been actively
researched as high-power and high-voltage converters in recent years(1)–(3) . The MMC is applicable to any voltage
ratings by adjusting the number of cells connected in series(1)–(3) . In addition, the multilevel operation with thestacked cell reduces or eliminates output filters(4)(5) .
Fig. 1 shows one leg of the MMC. Each cell has a cell capacitor to decouple the instantaneous power diﬀerence between ac and dc sides. Thus, the cell capacitor suﬀers anenergy ripple at the ac fundamental and double frequencies
as well as at the switching harmonics. The capacitor is oneof the most fragile components in power converters(6)(7) . Deterioration of the capacitor leads to a decrease in capacitanceand an increase in equivalent series resistance (ESR)(7)(8) . In
the MMC, the decreased cell capacitance causes a large capacitor voltage ripple. The large capacitor voltage ripple increases the circulating current flowing through both the upperand lower arms, which increases power loss(9)(10) . Additionally, if overmodulation occurs in the cell on account of thelarge capacitor voltage ripple, the current distorts, and the
MMC may halt by the overcurrent in the worst case.
The MMC has to maintain the operation even under thefault of some components when it is applied to critical infras-(a) One leg of MMC.

Fig. 1. Circuit configuration of MMC

tructures. Hence, the MMC usually has redundant cells(11)(12)and an additional control strategy(13)(14) to continue the operation under the fault. However, there is a trade-oﬀ between
the reliability and the cost of the redundant cells(11)(12) . In addition, although redundant cells are employed, the degradedcell has to be deactivated so that it does not aﬀect the normal operation of the MMC. Thus, the condition monitoringis required to detect the degraded cells.
Online monitoring for the capacitor has recently been attracting much attention in order to improve the reliabilityof the power converters without a significant increase in thecost(15)(16) . Implementation of the online monitoring of thecapacitor deterioration to the MMC not only prevents failures but also reduces unnecessary replacement of the cell.
The major capacitor monitoring methods are based on the estimation of the capacitance and/or the ESR. The capacitancea) Correspondence to: Takumi Yasuda. E-mail: t yasuda@stn.naga
okaut.ac.jp∗
Nagaoka University of Technology
1603-1, Kamitomioka-machi, Nagaoka, Niigata 940-2188,
Japan∗∗
Kyushu Institute of Technology
1-1, Sensui-cho, Tobata-ku, Kitakyushu, Fukuoka 804-8550,
Japan
c 2023 The Institute of Electrical Engineers of Japan.
⃝(b) Chopper cell.

953

Online Capacitance and ESR Monitoring in MMC（Takumi Yasuda et al.）and ESR vary with diﬀerent tendencies depending on theoperating conditions(17) , which implies that it is unknown
whether the lifetime is determined by the capacitance or ESR.
Therefore, both the capacitance and the ESR are necessary
to diagnose the capacitor deterioration. Although several
online/quasi-online monitoring methods for the cell capacitor were reported in the past, most of them only estimate
the capacitance, and there have been few studies on the ESR
estimation. In Refs. (18)–(21), the cell capacitance is estimated online from the capacitor voltage ripple and the capacitor current. In Refs. (22) and (23), the capacitance isestimated from the charging or discharging time constant of
the cell capacitor through a resistor while the cell is deactivated, which is categorized as the quasi-online method(16) .
These methods estimate the cell capacitance without additional sensors or components. However, the estimation of the
ESR with these methods seems to be diﬃcult because theyutilize low-frequency components in which the capacitanceis dominant in impedance. The method presented in Ref. (19)calculates the ESR from the capacitor loss that is a productof the capacitor voltage and the current. This method, however, requires the strict synchronization of the detection timing of the capacitor voltage and the current. That is complex
for the MMC because it is often controlled by hierarchicalcontrollers(24)(25) . Moreover, Ref. (19) does not mention thesampling frequency for capacitor monitoring. In order to implement the capacitor condition monitoring without any additional hardware components, the sampling frequency of thecapacitor voltage and current has to be equal to or less thanthat of the controller.
This paper proposes an online capacitor monitoring
method for the diagnosis of the cell capacitor deteriorationin the MMC without any additional components or operation. The proposed method estimates both the capacitanceand ESR from the impedance of the cell capacitor at multiple
frequencies(26)(27) . The estimation accuracy is improved byutilizing the impedance at the switching sideband-frequencyof the cells where the ESR is dominant in the impedance aswell as at the ac fundamental frequency components where
the capacitance is dominant. The proposed method does not
require the synchronization of the detection timing for thecapacitor voltage and the current. Moreover, the proposed
method employs only the sampled capacitor voltage and current by the controller of the MMC for the estimation.
This paper is organized as follows; firstly, the operation of
the cell capacitor is analyzed. Secondly, the proposed capacitor monitoring method is presented. Finally, the experimental
results show that the proposed method estimates the capacitance and ESR from the sampled capacitor voltage and thecurrent at the sampling frequency, assuming the controller
frequency of the MMC.

2. Operation Analysis of Cell Capacitor in MMC

In this paper, the chopper cell, as shown in Fig. 1, is utilized for analysis. From Kirchhoﬀ’s voltage raw, the upperarm voltage varm,u is expressed as
Vdc √
Vdc
varm,u (t) ≈− vac (t) =− 2Vg sin ωg t,· · · · (1)22where V dc is the dc link voltage, V g is the ac phase voltage,and ωg is the ac angular frequency. The voltage drop acrossthe arm inductor L is neglected in (1). Assuming that the
MMC operates in a steady state with a balanced capacitor
voltage, the arm current iarm,u is given by(9)(10)√P
2S
iarm,u (t) =+sin(ωg t + ϕi ),· · · · · · · · · · · · (2)3Vdc
6Vg
where P and S are the active and apparent powers, respectively, and ϕi is the phase angle between the grid current andvoltage. The active power P is defined to be positive when it
flows from the dc to ac side. The circulating current causedby the capacitor voltage ripple is assumed to be zero in (2).
Assuming that the capacitor voltages in all the cells are completely balanced, all the insertion indices dcell for the cells inan arm are identical as follows:√
2Vg
1dcell (t) = −sin ωg t.· · · · · · · · · · · · · · · · · · · · · (3)2NVc
The switching function for the cell is obtained by comparing
the insertion indices to a triangular carrier waveform as(28)scell (t) = dcell (t)+

∞ ∑
∞
∑

Dn,m sin(nωg t+mω sw t+ϕn,m ),n=−∞ m=1

Dn,m =(2π(n + m)π)cos
Jn (α), ϕn,m = ϕi +
m,
πm
2
2
· · · · · · · · · · · · · · · · · · · · (4)where ωsw is the carrier angular frequency, J n (·) is the Bessel
function of the first kind, α = 21/2 πVg /NVc . Since the switching function is a PWM signal for the upper switch of the cell,
the capacitor current is a product of the arm current iarm,u in(2) and the switching function scell in (4), as shown in (5).
Eq. (5) indicates that the capacitor current is composed of
the ac fundamental, double the frequency components, andthe high-frequency components caused by the switching of
the cell. The fundamental switching-frequency component
I c (f sw ) and its sideband-frequency components of the capacitor current I c (f sw ±f g ) are extracted as the following equations:
2P
Ic ( f sw ) =J0 (α), · · · · · · · · · · · · · · · · · · · · · · · · · · (6)
3πVdc

√

√
∞ ∑
∞
(
)
(
) ∑
(
)
2PVg
Dn,m P
2S
S
ic (t) =
sin
ω
t
+
sin
ω
t
+
ϕ
−
cos
2ω
t
+
ϕ
+
sin nωg t + mω sw t + ϕn,m
g
g
i
g
i
2
12Vg
6Vdc
3Vdc
3Vdc
n=−∞ m=1
+

∞ ∑
∞
∞ ∑
∞
∑
{
} ∑
{
}
Dn,m S
Dn,m S
sin
(n
−
1)ω
t
+
mω
t
+
ϕ
−
ϕ
−
sin (n + 1)ωg t + mωc t + ϕn,m + ϕi
√
√
g
c
n,m
i
n=−∞ m=1 6 2Vgn=−∞ m=1 6 2Vg· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (5)954

IEEJ Journal IA, Vol.12, No.5, 2023

Online Capacitance and ESR Monitoring in MMC（Takumi Yasuda et al.）Fig. 2. Fundamental switching-frequency component
and its sideband of capacitor current with respect to operating power factor of MMC. The calculation conditions
are referenced from the experimental conditions. The
vertical axis is normalized by the rated ac current√
Ic ( f sw ± fg ) =S

J02 (α) + 2J0 (α)J2 (α)cos2ϕi + J22 (α).
√
3 2πVg· · · · · · · · · · · · · · · · · · · · (7)Fig. 3. Procedure of cell capacitor monitoring method
Clife and rlife are the capacitance and the ESR at the endof life

Note that (6) and (7) ignore the sideband components of frequencies more than twice the switching frequency as they are
assumed to be suﬃciently small.
Fig. 2 illustrates the amplitude of the fundamental switching-frequency component I c (f sw ) and its sideband-frequency
components Ic ( f sw ± fg ) in the capacitor current shown in (6),(7) with respect to the power factor of the MMC. The capacitor current in Fig. 2 is normalized by the rated ac current.
Note that the rated value of the capacitor current is 0.43 p.u.
in this calculation. The switching fundamental frequency
component of the capacitor voltage is proportional to the active power of the MMC, whereas the switching sidebandfrequency component is proportional to the apparent power.
The equivalent circuit of the capacitor is represented by theseries connection of the capacitance Ccell , ESR resr , and theequivalent series inductance (ESL) Lesl as(7)
√
√
)2
)2
(
(
1
1
2
2
≈ resr +.
Zc (ω) = resr + ωLesl −ωCcellωCcell· · · · · · · · · · · · · · · · · · · · (8)3. Proposed Capacitor Parameter Estimation

MethodThe proposed method introduces the curve-fitting on themeasured impedance of the cell capacitor to estimate the cell
capacitance and ESR. The impedance of the cell capacitor ateach frequency is obtained by the Fourier transform of thesampled capacitor voltage and the current(26)(27) . The utilization of the high-frequency components around the switchingfrequency improves the estimation accuracy of the ESR. In
this paper, the switching sideband-frequency components are
considered for the estimation in addition to the fundamental
and double the fundamental frequency components.
Fig. 3 shows the flowchart of the proposed capacitor monitoring method. First, one of the cells is selected for monitoring. It is not always necessary to monitor all the cell capacitors since the deterioration of the capacitor is relatively
slow(8)(17) . The proposed method monitors one cell capacitor
at a time. Next, the capacitor current ic is calculated from theswitching function scell and the arm current iarm as
ic(t) = scell (t) · iarm (t).· · · · · · · · · · · · · · · · · · · · · · · · · · · (10)Since the switching frequency of the cell is much lower
than the self-resonant frequency of the cell capacitor, theimpedance of the cell capacitor is simplified to the seriesconnection only of the capacitance Ccell and ESR resr . The
deterioration of the capacitor leads to a decrease in the capacitance and an increase in the ESR(7)(8) , which aﬀects theperformance of the MMC as mentioned above. In addition,
the rise of the ESR increases the capacitor loss and increases
the operating temperature of the capacitor, which accelerates
the deterioration of the capacitor.
Suppose the impedance of the cell capacitor is expressedby the capacitance and ESR, the capacitor voltage is given as∫ t
1
vc (t) = resr ic (t) +ic (τ) dτ + Vc,0 ,· · · · · · · · · (9)Ccell 0The proposed method does not disturb the operation nor requires any additional components. Then, the Fourier transformation is applied to the capacitor voltage and the current to obtain each frequency component V c (ω), I c (ω). The
impedance of the capacitor is calculated byẐc ( f ) =Gcomp Vc ( f ),· · · · · · · · · · · · · · · · · · · · · · · · · · · (11)
Ic ( f )where Gcomp is a correction gain to compensate for the errors
in the sensor gain(20)(29) . The correction gain Gcomp can beobtained from a ratio of the impedance measured by an LCR
meter before the implementation to that estimated by the
first monitoring procedure. Finally, the least square method(LSM) is applied to estimate the capacitance and ESR.
In order to suppress a computer burden due to the monitoring, the proposed method monitors only one cell capacitor at
the same time. Although it takes a quite long time to monitor
all the cell capacitors in the MMC, it is suﬃciently fast compared to the aging speed of the capacitors, which progressesof the order of 1000 hours.

where V c,0 is the dc component of the capacitor voltage.
The capacitor voltage vc contains the same frequency components as the capacitor current. In this paper, the switching
sideband-frequency components of the capacitor voltage andcurrent are utilized for the cell capacitor monitoring to improve the estimation accuracy.
955

IEEJ Journal IA, Vol.12, No.5, 2023

Online Capacitance and ESR Monitoring in MMC（Takumi Yasuda et al.）The following subsections present LSM and the selectionof the frequency for the curve fitting in detail.
3.1 Least Square Method of the Proposed Method
This paper adopts LSM weighted by frequency(30) . The
impedance of the capacitor becomes smaller at the high frequency, where the ESR becomes dominant. Hence, if the capacitance and ESR were estimated by LSM without weighting, the estimation error would become large in the highfrequency region. Therefore, each term in LSM is normalized
so that the estimation error is independent of the magnitudeof the impedance. Thus, the objective function is given by

{
}2 
2
∑

M Ẑ 2 ( f ) − (r̂ 2 + 1/(2π f Ĉj cell ) ) 
c j
esr


min 
 ,2 + 1/(2π f Ĉ2Ĉcell ,r̂esr r̂esr)
j cellof the sensors. They aﬀect the estimation errors of the capacitor parameters. The relationships of the standard deviation of
the estimated capacitance and ESR σc and σr with those of
the measured impedance are expressed from the error propagation theory as(33) :
2

M 
∑
 ∂Ĉcell 2( )  σz, j 2 , · · · · · · · · · · · · · · · · · · · · · (16)σc =j=1 ∂Zc f j

2
M 
∑
 ∂r̂esr 2( )  σz, j 2 , · · · · · · · · · · · · · · · · · · · · · (17)
σr =
∂Z
fj
c
j=1
where σz,j is the standard deviation of the measured
impedance at the frequency f j . Eqs. (16), (17) assume that theerror in the measured impedances at each frequency is causedby the random noise and are independent of each other (correlation coeﬃcient is zero). These equations imply that thenonlinearity in the estimation equation as in (14), (15) can
enlarge the error in the estimated capacitance and ESR eventhough the measurement error of the impedance is small.
Fig. 4 demonstrates the coeﬃcient of variation (CV) of
the estimated capacitor parameters with respect to the CVof the measured impedance. The CV, which is defined as
normalized standard deviation by the true value, is derived
by substituting (14), (15) into (16), (17). In Fig. 4, the CVof the impedance is set to the same value regardless of thefrequency. The labels indicate the frequency components
utilized for the estimation. Fig. 4(a) is the CV of the capacitance. Comparing the CV based only on low-frequency
components of 50 and 100 Hz and that based only on highfrequency components of 4950 and 5050 Hz, it is revealed
that the estimation with the lower-frequency increases theestimation accuracy of the capacitance since the impedanceof the capacitance is dominant at low frequencies. Fig. 4(a)shows that the utilization of both the low- and high-frequency
components has the best estimation accuracy, which is about

j=1· · · · · · · · · · · · · · · · · · · (12)where M is the number of the impedance utilized for the estimation, r̂esr is the estimated ESR and Ĉ cell is the estimatedcapacitance. Assuming that the impedance of the capacitor isapproximated to be inversely proportional to the frequency,
the LSM shown in (12) is simplified to (13).


2 

∑




M



1

 2
 
 2

min  (2π f j )4 
Ẑ
(
f
)
−
r̂
+
 .
 esr ()2 c jĈcell ,r̂esr  
2π f Ĉ
j=1
j

cell

· · · · · · · · · · · · · · · · · · · (13)The simplification of the objective function, as shown in (13),reduces the calculation burden of the controller. The estimated value of the capacitance and ESR is derived from (13)
as
v
u
u
(
)2
u
u
M
M
u
∑
∑
u
4
2
u
u
M
fj −
fj
u
u
j=1
j=1
1u
u
t
Ĉcell =
( ) ∑
( ),
M
M
M
M
2π ∑
∑
∑
f j4 ·
f j2 Ẑc2 f j − f j2 ·f j4 Ẑc2 f j
j=1

j=1

j=1

j=1

· · · · · · · · · · · · · · · · · · · · (14)
v
u
u
u
(
( )
)
M
M
M
u
∑ 4 2
∑ 2 ∑
u
u
u
M
f j Ẑc f j −fj ·f j2 · Ẑc2 f j
u
u
u
j=1
j=1
u
t j=1
r̂esr = u
.
(
)2
M
M
∑
∑
4
2
M
fj −
fj
j=1

j=1

· · · · · · · · · · · · · · · · · · · · (15)(a) Capacitance.

Weighting by the frequency reduces the error of the fitting
curve in the high-frequency region, which results in the reduction of the estimation error of the ESR.
3.2 Improvement of Estimation Accuracy with Switching Sideband-frequency Component
Generally, thesampling frequency of the MMC is much higher than theswitching frequency of the cell because of the multilevel
operation(31)(32) . Therefore, in the MMC, the switchingfrequency and its sideband-frequency component can be restored from the sampled voltage and the current by the controller. The proposed method utilizes the impedance at theswitching sideband-frequency of the cell for the capacitor
monitoring.
In practice, the measured impedance contains errors causedby some factors, such as noise and non-ideal characteristics(b) ESR.

Fig. 4. Coeﬃcient of variation (CV) of estimated capacitance and ESR with respect to CV of measured
impedance. The labels indicate the switching frequency,
utilized. The true value of the capacitance and the ESR isset to 1.35 mF and 21 mΩ, respectively, which are referenced from the experimental conditions. The horizontal
axis in Fig. 4(b) is in logarithmic scale
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IEEJ Journal IA, Vol.12, No.5, 2023

Online Capacitance and ESR Monitoring in MMC（Takumi Yasuda et al.）half of the CV of the estimation based on 50 and 100 Hz. The
CV of the ESR in Fig. 4(b) demonstrates that the estimation
with the higher frequency increases the estimation accuracyof the ESR since the impedance of the ESR is dominant athigh frequencies. The method using only the low-frequency
components, which is conventionally applied methods in literature(18)–(21) , requires to measure the impedance with a CVof less than 0.003% in order to keep the estimation error
within 20%, which is not realistic. Compared with the estimation only using the 4950 and 5050 Hz, the estimation of
the proposed method based on 50, 100, 4950, and 5050 Hz
decrease the CV by 91.9%. The maximum allowable CV of
the impedance is 10.9% in order to estimate the ESR within
20% CV when the proposed method based on 50, 100, 4950,
and 5050 Hz is applied.
As shown in Fig. 2, the switching fundamental frequency
component is proportional to the power factor, whereas theswitching sideband-frequency components in the capacitor
current are independent of the power factor since it is proportional to the apparent power, as shown in (7). In this paper,
only the switching sideband-frequency components ( f sw ± fg )are adopted for the capacitor monitoring as high-frequency
components in order to perform capacitor monitoring in all
the power factor conditions.

Fig. 5. Experimental circuit
Table 1. Experimental conditions

4. Experimental Studies

4.1 Experimental Setups
Fig. 5 and Table 1 show
the experimental circuit and the conditions, respectively. A
single-phase MMC prototype with four cells per arm wasbuilt in the laboratory in order to confirm the proposed
method. In this paper, the cell capacitor of the first cell inthe upper arm was monitored while the MMC performed
the grid-following operation. The cell capacitors are two
KEMET electrolytic capacitors ALA7DA681DF450 in parallel. The lifetime of ALA7DA681DF450 is defined as 80%of the initial capacitance or 300% of the initial ESR, as referenced from the datasheet(34) .
The electrolytic capacitor is considered for the cell capacitors in the MMC(5)(18)–(20)(35) as well as other types of capacitors because of its high capacitance per unit volume andlow cost. The electrolytic capacitor helps to reduce the capacitor voltage ripple as well as increasing the power densityof the MMC. It is worth to note that the proposed method inthis paper is also applicable for the MMC with other type ofthe capacitors, such as a film capacitor, whose capacitanceis decreased and ESR is increased by the aging as same as
the electrolytic capacitor(15) . The proposed method has anadvantage of being applicable to a variety of capacitors with
diﬀerent trends in the parameter drift caused by the degradation, since the proposed method estimates both the capacitance and ESR.
Fig. 6 shows the cells emulating the deterioration of the capacitor for experimental verifications. The brand-new capacitor is emulated by connecting the external capacitor Cext with180 µF in parallel to the cell capacitor, as shown in Fig. 6(a).
The capacitance reduction by 11.5% was emulated by the removal of Cext , as shown in Fig. 6(b), whereas the ESR rise by
28.1% was done by the external resistance rext with 11 Ω inseries to Cext , as shown in Fig. 6(c).
In order to prevent the aliasing eﬀect, the sampling fre-(a) Assuming brandnew.

(b) Assuming capacitance decrease.

(c) Assuming ESR increase.

Fig. 6. Parameter variation for experimental verificationquency of the capacitor voltage and the current need to be
suﬃciently higher than the switching frequency of the cell. In
this verification, the sampling frequency was set to 200 kHz,
which was 40 times as high as the switching frequency. This
corresponds to the relationship between the switching frequency of the cell and the sampling frequency of the MMC
with 40 cells per arm(31)(32) , which is reasonable in the fullmodel of the MMC(2) . In this verification, the resolution of
the analog-to-digital conversion for the capacitor voltage andthe current was 12 bits. The one period of the estimation was
set to 10 s.
The parameter estimation in this paper utilizes the four
components of the fundamental frequency (50 Hz), double
the fundamental frequency (100 Hz), and the sideband frequency ( fsw − fg = 4950 Hz and fsw + fg = 5050 Hz).
4.2 Operation with Unity Power Factor
Fig. 7shows steady-state waveforms of the MMC with a unity
power factor. Fig. 7(a) shows the grid voltage and the current. The grid current was in-phase with the grid voltage witha low total harmonic distortion (THD) of 1.27%. The arm
current contained the multiple frequency components, a dc
component of 1.7 A, and a grid fundamental frequency com957

IEEJ Journal IA, Vol.12, No.5, 2023

Online Capacitance and ESR Monitoring in MMC（Takumi Yasuda et al.）(a) Grid voltage and current.

(a) Grid voltage and current.

(b) Arm currents.

(b) Arm currents.

(c) Capacitor voltage.

(c) Capacitor voltage.

Fig. 7. Steady-state operation with unity power factor

Fig. 9. Steady-state operation with reactive power injection(a) Capacitance.

(a) Capacitance.

(b) ESR.

(b) ESR.

Fig. 8. Estimated cell capacitance and ESR in operation
with unity power factor

Fig. 10. Estimated cell capacitance and ESR in reactive
power injection

4.8% and 4.3%, respectively.
4.3 Operation with Reactive Power Injection
Fig. 9shows steady-state waveforms of the MMC with the inductive operation. Fig. 9(a) shows the grid voltage and the current. The grid current was 90 degrees lagged from the gridvoltage with a low THD of 1.30%. The arm current consistedof the grid fundamental frequency component of 7.5 A and nodc component, as shown in Fig. 9(b). This means that no active power was supplied from the dc voltage source. Fig. 9(c)shows that the averaged capacitor voltages followed the command value of 150 V with a maximum error of 1.3%.
Fig. 10 shows the estimation results of the cell capacitanceand ESR in the inductive operation. The estimation errors

ponent of 7.5 A, as shown in Fig. 7(b). Fig. 7(c) shows thecapacitor voltage of the first cells in the upper and the lower
arm. The averaged capacitor voltages in the MMC followed
the command value of 150 V with a maximum error of 1.2%.
Fig. 8 shows the estimated cell capacitance and ESR withthe unity power factor. The first estimation result with thebrand-new capacitor was employed to calculate the correction gain Gcomp . Fig. 8(a) shows the estimation result of thecapacitance. The errors of the average estimated capacitancefor the brand-new and the deteriorated capacitor are 0.4%
and 0.3%, respectively. Fig. 8(b) shows the estimation resultof the ESR. The estimation errors of the averaged value of
the ESR for the brand-new and the deteriorated capacitor are
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IEEJ Journal IA, Vol.12, No.5, 2023

Online Capacitance and ESR Monitoring in MMC（Takumi Yasuda et al.）of the capacitance for the brand-new and the deteriorated capacitor are 1.4% and 3.1%, whereas those of the ESR for thebrand-new and the deteriorated capacitor are 8.8% and 6.4%,
respectively. The experimental result reveals that the estimation accuracy of the cell capacitance and ESR is suﬃcient todetect the lifetime of the capacitor, which is defined as 80%of the initial capacitance or 300% of the initial ESR.
The estimated capacitance in the operation with the reactive power injection, as shown in Fig. 10, is larger than that
estimated in the operation with the unity power factor shownin Fig. 8. Besides, the estimated ESR becomes smaller withthe decrease in the power factor. These diﬀerences are considered to come from a diﬀerent operation temperature of thecell capacitor. The capacitor current increases as the power
factor of the MMC decreases(36) . As a result, the capacitor
loss increases and the temperature of the cell capacitor rises.
Those increases in the temperature can cause an increase in
the capacitance and a decrease in the ESR(37)(38) . That implies that monitoring with the proposed method under thesame operating conditions can oﬀer more accurate results.
In order to further improve the estimation accuracy, a thermal sensor and/or thermal model of the cell capacitor can be
introduced to take the temperature dependency of ESR into
account(15)(16) .
4.4 Comparison with Estimation Results from Only
Low or High-frequency Component
Table 2 shows thecomparison of the experimental results of the capacitor parameter estimation. In order to verify the proposed method,
capacitor parameters estimated only from the low-frequency
components (50 Hz and 100 Hz) and those estimated only
from the high-frequency component (4950 Hz and 5050 Hz)
are presented. Only utilizing the 4950 and 5050 Hz components, the estimated capacitance has a relatively large error.
Additionally, the estimated ESR becomes an imaginary quantity due to a large error. The capacitance estimated only fromthe 50 and 100 Hz components is as accurate as that of the
proposed method, whereas the ESR is imaginary. These results are consistent with the analyzed results in Fig. 4. The
results in Table 2 experimentally verify that the utilization ofboth the low frequency around the ac fundamental frequency
and the high frequency around the switching frequency improves the accuracy of the parameter estimation for the cell
capacitor in the MMC.

components or operations. The proposed method estimatesboth the capacitance and ESR from the impedance of thecapacitance at multiple frequencies. The estimation accuracy is improved by the utilization of the impedance at theswitching frequency of the cells where the ESR is dominant
in the impedance of the cell capacitor. The experimental result shows that the capacitance and ESR were estimated fromthe sampled capacitor voltage and the current at the sampling
frequency, assuming the control frequency with a maximum
error of 3.1% and 8.8%, respectively.
The ESR of the capacitor is temperature-dependent. Therefore, the proposed method will consider the eﬀect of the temperature on the capacitor for further improvement of the estimation accuracy in the future. Besides, the proposed method
is also applicable to other multilevel converters, sampling frequency of which is higher than switching frequency. The validity of the proposed strategy will be confirmed with theseconverters.

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5. Conclusion( 10 )

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Table 2. Comparison of parameter estimation results ofbrand-new capacitor when only low or high frequency
components are utilized for the estimation. The MMC
operates with reactive power injection( 12 )( 13 )( 14 )( 15 )

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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. He was a short-term visiting student at Kyushu
Institute of Technology in 2021 and 2022.

Kazunori Hasegawa (Member) received the B.S. degree in electrical engineering from Tokyo Metropolitan University,
Tokyo, Japan, in 2007, and the M.S. and Ph.D. degrees in electrical and electronic engineering from
Tokyo Institute of Technology, Tokyo, Japan, in 2009
and 2012, respectively. In 2013, he joined Kyushu Institute of Technology, Fukuoka, Japan, as an assistantprofessor, where he has been an associate professor
since 2018. His research interests include reliabilityrelated issues of power converters and components
including semiconductor devices and capacitors. Dr. Hasegawa was the recipient of the 2018 IEEE Transactions on Power Electronics Prize LetterAward.
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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