Hybrid Six-step Operation for Matrix Converterin Flywheel Energy Storage System
Jun-ichi Itoh, Takumi Masuda, Tsuyoshi Nagano, and Hayato Higa
Nagaoka University of Technology, Niigata, Japan

Abstract--This paper presents a hybrid six-step operation,
which utilizes both a pulse width modulation (PWM) and aconventional six-step operation of a matrix converter inorder to reduce switching losses during the standby time of
flywheel. In the hybrid six-step operation, a virtual AC-DCAC conversion is applied in order to separate the control ofthe matrix converter into a current source rectifier (CSR)
control and a voltage source inverter (VSI) control. In
particular, CSR is operated in PWM and VSI is operated in
the six-step operation mode. Consequently, the switching lossof VSI is reduced as compared with the PWM operation due
to the conventional six-step operation mode. In addition, theinput current total harmonic distortion (THD) is improved ascompared with the conventional six-step operation because
the CSR modulation is PWM. In the experimental result, theinput current THD of the hybrid six-step operation is
improved by 76.0 % compared to the conventional six-step
operation. Moreover, the efficiency of hybrid six-step
operation was 1.0 % lower than the conventional six-step
operation. In the hybrid the six-step operation, the input
current THD is improved by 76.0 % in exchange for thedrops of efficiency by 1.0 %.
Index Terms--Flywheel energy storage system (FESS),
matrix converter, six-step operation, pulse width modulation(PWM).

I. INTRODUCTION
Recently, renewable energy systems such as photovoltaic (PV) and wind turbine have attracted many
attentions [1-17]. In these system, a power fluctuation
occurs due to meteorological conditions. Therefore,
renewable energy systems require energy storage devices
such as batteries, electric double layer capacitors (EDLC)
or flywheels. The battery can achieve a high energy
density at low cost. However, one of the problems in thebattery energy storage is the short life time. In particular,
the lifetime of the battery depends on the ambience and thenumber of charge/discharge time. In addition, the battery
cannot cope with rapid charge/discharge owing to a large
internal resistance. Meanwhile, the solution with EDLC
provides a rapid charge/discharge because the internal
resistance is very small. Moreover, the charge/discharge
efficiency of EDLC is higher than batteries. However, theEDLC lifetime is still affected by the ambient temperature.
In addition, energy density is not high.
On the other hand, a flywheel has a long lifetime due tono chemical structure. Thus the charge/discharge
characteristics achieve high performance in contrast to thechemical battery. In addition, the flywheels provide anenvironmental friendly and low maintenance cost. Besides,

the kinetic energy which is stored in the flywheel is
proportional to the square of the rotational speed.
Therefore, a flywheel energy storage system (FESS) canachieve a power leveling with high response to large power
ripple [12-17].
Meanwhile, a matrix converter has attracted a lot of
attentions as an AC-AC converter with many desirable
features. The matrix converter is expected to achieve
higher efficiency, smaller size and longer life-time
compared to Back-To-Back (BTB) system because anenergy buffer such as a large electrolytic capacitor and thestep-up reactor is unnecessary. Therefore, the power
leveling system that combines the matrix converter and
FESS has been researched actively [18].
During the standby time, the flywheel standby losses
such as windage and bearing losses still occur.
Consequently, although the power fluctuationcompensation is not required, it is necessary for the matrix
converter to supply the energy consumed by the standby
losses. During this period, the matrix converter is operated
at the light load, the switching loss in which is predominant.
The switching loss of the matrix converter using PWM
becomes large in the standby mode because the number ofthe switching times is proportional to the switchingfrequency. In order to reduce the switching loss, theconventional six-step operation for the matrix converter
has been proposed [19]. In the six-step operation, theswitching loss is reduced because the PWM is not used.
However, the input current THD increases due to the 120
deg. conduction mode. Furthermore, the filter loss also
increases due to the distortion of the input current.
In this paper, the hybrid six-step operation for thematrix converter is proposed to reduce the switching loss
in stand-by mode of FESS. In the proposed method basedon the virtual AC-DC-AC conversion [20], the control ofthe matrix converter is separated into a current source
rectifier (CSR) control and a voltage source inverter (VSI)
control, where the CSR modulation is PWM and the VSI
modulation is six-step operation. The switching loss of thematrix converter applied with the conventional six-step
operation is reduced in compared with the PWM operation
because the switching frequency of the six-step operation
is six times of the output frequency. Meanwhile, the input
current THD is reduced by the PWM operation of CSR.
Moreover, the filter loss is reduced because the input
current THD is improved compared with the conventional
six-step operation. This paper is organized follows; first,
the modulation of matrix converter based on the virtual
AC-DC-AC conversion is introduced. Second, the hybrid

PFESSPower grid

Pgrid

six-step operation is explained. Third, the validity of thehybrid six-step operation is confirmed by the simulation
results and the experimental results. Finally, the converter
loss of the hybrid six-step operation and the conventional
six-step operation is compared

Induction
motor
FW

IM

Pload

II. CIRCUIT CONFIGURATION
A. Circuit Configuration
Fig. 1 shows a circuit diagram of the flywheel energy
storage system using the matrix converter. The flywheel
energy storage system compensates the power ripple
caused by the renewable energy systems in order to smooththe grid power. In the standby mode of FESS, the converter
is operated at the light load, the switching loss in which is
predominant. However, PWM which can regulate theinput current as a sine wave introduces the high switchingloss. Therefore, the driving operation of a low switchingloss is necessary in terms of a high efficiency. In addition,
it is necessary to reduce the input filter loss which isincreased by the input current distortion.

Flywheel

Matrix converter

Fig. 1. Flywheel energy storage system using a matrix converter.
FESS consists of the matrix converter, the flywheel and the input
filter.

ssp
ssn

CSR

Ssp

Stp

R
S
T

Srn Ssn

Swp
U

V
W

Sun

Stn

VSI control
iu*,iv*,iw*

(2)

Svp

Svn Swn

Fig. 3. Circuit diagram of an indirect matrix converter. Matrix
converter separates the current source rectifier and the voltage
source inverter using virtual AC-DC-AC conversion system.

(1)

vr 
stp   vsstn   
 vt Sup

DC-link voltage

Srp

VSI

vr*,vs*,vt*

where, smn is a switching function of the switch S mn. smn is
1 when Smn is turned on and smn is 0 when Smn is turned off.
Fig. 3 shows a circuit diagram of the indirect matrix
converter which is used to consider the hybrid six-step
operation. The virtual AC-DC-AC conversion replaces thematrix converter illustrated in Fig. 2 by the combination of
CSR and VSI as shown in Fig. 3 in order to obtain thedesignated switching pulse commands. In the indirect
matrix converter as shown in Fig. 3, the relationshipbetween the input voltage t[vr vs vt] and the output voltaget[vu vv vw] is represented by (2).

sun 
 s
svn   rpsswn   rn

U
VW

Fig. 2. Circuit diagram of matrix converter.

A. Virtual AC-DC-AC Conversion
In this paper, the control method of matrix converter isbased on the virtual AC-DC-AC conversion system, where
the matrix converter is separated into a current source
rectifier (CSR) and a voltage source inverter (VSI) as anindirect matrix converter [20].
Fig. 2 shows a circuit diagram of the matrix converter.
The matrix converter of Fig. 2 is applied as the AC-AC
converter in the flywheel energy storage system. Equation(1) expresses the relationship between the input voltage t[vrvs vt] and the output voltage t[vu vv vw] in the matrix
converter of Fig. 2.

 vu   supv    s
 v   vp
vw  swp

Sru
Ssu
Sts
Srv
Ssv
Stv
Srw
Ssw
Stw

R
S
T

III. MODULATION STRATEGY vu   s ru ssu stu  vr 
v    s  v   rv ssv stv  vs 
vw   srw ssw stw   vt 

Input filter

Load

CSR control

6

6

Switching
9functioncomposition Switchingequation (3)pulse

Fig. 4. Switching pulse generator. The switching pulses are
generated by a virtual converter and a virtual inverter controls.

The relationship between the output voltage and the input
voltage is determined solely by (2). In order to match the
input and the output terminals of the indirect matrix
converter and the matrix converter excluding the filter
effect in Fig. 1, (3) should be satisfied.

 s rus rv
 srw

s su
s sv
s sw

stu   sup
stv    svp
stw   s wp

sun 
 s
svn   rpss wn   rn

s sp
s sn

stp 
(3)
stn 

Fig. 4 shows a switching pulse generator based on thevirtual AC-DC-AC conversion. The method of theswitching pulse generator is represented by (3). Thus, thismethod clearly separates the input current control and theoutput voltage control.
B. PWM Operation
Table I shows the characteristics of the PWM operation,
the conventional six-step operation and the hybrid six-step
operation. In Table I of the characteristics of the PWM
operation, the DC-link voltage waveform of PWM
operation includes the switching frequency component. In
addition, the input current of the PWM operation iscontrolled as a sine wave. However, the switching loss of
the PWM operation is large because the number ofswitching times is proportional to the switching frequency.
Meanwhile, the output voltage waveform of the PWM
operation also introduces the high switching loss. In thestandby time, the switching loss is predominant because
the matrix converter is operated at the light load. Therefore,
it is necessary to use the alternative modulation instead of
PWM in order to reduce the switching loss.

Six-step operation

Hybrid six-step
operation

PWM conduction

120 deg.
conduction

PWM conduction

PWM conduction

180 deg.
conduction

180 deg.
conduction

Switching loss

Large

Low

Nearly low

Input filter loss

Low

Large

Nearly low

Input current

CSR

DC-link voltage

VSI

Output voltage

Carrier+Single leg
modulation

CSR Controller

Pulse
patternconversion

6
Srp, Srn
Ssp, Ssn
Stp, Stndc_ripDC linkripple cal

Variable
carrier
generator

×

+
+

×

×

VSI Controller

Sup, Sun
Pulse
distribution Svp, Svn
Swp, Swn
table
6

+

VSI side pulse commands

1/X

CSR side pulse commands

Output voltage commands

D. Hybrid Six-step Operation
In Table I of the characteristics of the hybrid six-step
operation, the CSR modulation is PWM and the VSI
modulation is 180 deg. conduction mode. Therefore, DClink voltage includes the switching frequency component.
The switching loss is reduced as compared with the full
PWM operation. In addition, the input current total
harmonics distortion is improved as compared with theconventional six-step operation because CSR modulation
is PWM. Thus, the input filter loss is reduced comparedwith the conventional six-step operation.
Fig. 5 shows the modulation block diagram of theindirect matrix converter. In Fig. 5, CSR side is controlled
by the input current commands. The input current
command VSI side is controlled by output valtage

PWM operation

Input current commands

C. Conventional Six-step Operation
In Table I of the characteristics of CSR as theconventional six-step operation, the DC-link voltage
waveform of the conventional six-step operation includes
the frequency component of the sixth order harmonics
component. In addition, the conventional six-step
operation is possible to greatly reduce the switching loss
because the switching timing of the conventional six-step
operation occurs every 120 deg. conduction of thefundamental frequency. Thus, the number of switchingtimes is three times of fundamental frequency in theswitching period. In VSI side with the conventional sixstep operation, the output voltage waveform of the six-step
operation includes the sixth order harmonics component.
Thus, the conventional six-step operation is also possible
to greatly reduce the switching loss because the switching
timing of the conventional six-step operation is every 180
deg. conduction of the fundamental frequency. Thus, thenumber of switching times occurs at the second orderharmonics component. However, the input filter loss isincreased with the six-step operation. The input current isdistorted because the input current of the conventional sixstep operation is not controlled as the sine wave.

TABLE I
CHARACTERISTICS OF PWM, CONVENTIONAL SIX-STEPOPERATION AND HYBRID SIX-STEP OPERATION

Fig. 5. Modulation block diagram of the indirect matrix converter.

commands.In Fig. 5, the matrix converter is used V / fcontrol of VSI modulation.
IV. SIMULATION RESULTS
Fig. 6 and Table II show the simulation conditions toverify the fundamental operation of the hybrid six-step
operation. This chapter presents the simulation results
using a circuit diagram in Fig. 6 to confirm the reductionof the input current total harmonic distortion (THD) withthe proposed hybrid six-step operation.
Fig. 7 shows the operation waveforms of the matrix
converter in the full PWM operation. The output voltage isa sine wave in the PWM operation as Fig. 7, the input
current THD is 1.40 %. However, the swithching loss islarge because the number of switching times is high.
Fig. 8 shows the operation waveforms of the matrix
converter in the conventional six-step operation when
FESS is standby. The output voltage is the square
waveform. Thus, the switching loss is reduced comparedwith the PWM operation. However, the output voltage is

200

RL-loadPower grid

Input R-phase voltage [V]

0
-200
4
2
0
-2
-4

Input filter

Input R-phase current [A]DC-link voltage [V]300

Matrix converter

200

Fig. 6. Simulation circuit diagram of matrix converter connected
RL-load.

Grid line voltage

200 V

Input filter L

2 mH

Input filter C

6.6 μF

Carrier frequency

10 kHzLoad parameter200

Output voltage (U-V) [V]
200
0
-200

TABLE IISIMULATION PARAMETERS UNDER IDEAL CONDITION

Circuit parameter

100

R-load76 ΩL-load

10 mH

4
2
0
-2
-4
0.00

0.01

0.02

0.03

[s]

Fig. 8. Simulation results of six-step operation. The CSR operation
is 120 deg. conduction. In the VSI, 180 deg. conduction is used. The
input current THD is 33.7%. In the six-step operation, the switchingloss is reduced compared to PWM operation.
200

Input R-phase voltage [V]Output U-phase current [A]Input R-phase voltage [V]

0
0

-200
-200
2

Input R-phase current [A]

4
2
0
-2
-4

DC-link voltage [V]

300

0
-2
300

Input R-phase current [A]DC-link voltage [V]

200
200

100
100

Output voltage (U-V) [V]

Output voltage (U-V) [V]

200
0
-200

200
0
-200
2

Output U-phase current [A]

0
-2
0.00

0.01

0.02

0.03

[s]

Fig. 7. Simulation results of PWM operation. The CSR operation
is PWM. In the VSI, the PWM operation is used. The input current
THD is 1.40%.

distorterd. In the output current of Fig. 8, the input current
THD is 33.7 %. In addition, the filter loss is increased by
the input current.
Fig. 9 shows the operation waveforms of the matrix
converter in the hybrid six-step operation. The output
voltage includes the 10 kHz component by PWM in thevicinity of the peak in the hybrid six-step operation. The
output voltage waveform is a rectangular wave. In addition,
the input current THD is 11.4 %. It is confirmed that the
input current THD is reduced by 66.2 % than theconventional six-step operation.

4
2
0
-2
-4
0.00

Output U-phase current [A]

0.01

0.02

0.03

[s]

Fig. 9. Simulation results of hybrid six-step operation. The CSR
operation is PWM operation. In the VSI, 180 deg. conduction isused. The input current THD is improved to 33 % compared withconventional six-step operation. In addition, the switching loss isalso reduced compared to PWM operation.

V. EXPERIMENTAL RESULTS
A. PWM Operation
Fig. 10 and Table III show the experimental conditions.
This chapter presents the experimental results using a
prototype drawn in Fig. 10 to confirm the input current
THD and the efficiency of the converter with the proposed
the hybrid six-step operation.
Fig. 11 shows the experimental results when the matrix
converter is applied with the full PWM operation. In Fig.
11, the output current is sinusoidal waveform by the PWM
operation. However, the switching loss of the PWM
operation is highB. Conventional Six-step Operation
Fig. 12 shows the experimental results when the matrix
converter is applied with the conventional six-step
operation. In Fig. 12, the output voltage is the square
waveform. Therefore, the switching loss is reduced
because the switching times of the six-step operation arelower than the PWM operation. However, the input current
THD is 36.7%. As a result, the input filter loss increases.
C. Hybrid Six-step Operation
Fig. 13 shows the experimental results when the matrix
converter is applied with the hybrid six-step operation. In
Fig. 13, the output voltage includes the switching ripple
component at the peak of the output voltage. In the output
voltage, it is nearly the square waveform, whereas the
input current THD is 8.84 %. In the proposed hybrid sixstep operation, the input current THD is reduce by 76.0 %as compared with the conventional six-step operation. It
can be confirmed that the six times of the fundamental
frequency is significantly reduced.
Fig. 14 shows the input current THD characteristic of
PWM, conventional six-step operation and hybrid six-step
operation. In the light load of Fig. 14, the input current
THD of hybrid six-step operation is reduced to 25%
compared to the conventional six-step operation. In
addition, the input current THD of hybrid six-step
operation is a lower than conventional six-step operation
in a wide input power range.

Snubber circuit
Braking circuit

RL-loadPower grid

Input filter
Matrix converter

Fig. 10. Prototype of matrix converter connected RL-load.
TABLE III
EXPERIMENTAL PARAMETERS OF PROTOTYPE CONDITION

Circuit parameter

Load parameter

VI. CONCLUSIONSThis paper proposed the hybrid six-step operation,
which utilizes both PWM and the conventional six-step
operation, for reduction of the switching loss and the input
current harmonics distortion. In the proposed method, theCSR modulation is PWM and the VSI modulation is 180
deg. conduction mode based on the virtual AC-DC-AC
conversion. In the proposed hybrid six-step operation, theswitching loss is reduced. In addition, the input current
THD is improved as compared with the conventional sixstep operation. From the experimental results, the input
current THD was improved by 76.0 % as compared withthe conventional six-step operation. In addition, theefficiency of the hybrid six-step operation was 1.0 % lower
than the conventional six-step operation. In the hybrid the

200 V

Input filter L

2 mH

Input filter C

6.6 μF

Carrier frequency

10 kHzR-load25.3Ω

L-load5 mH

Input voltage (R-S) [500V/div]0
Input current THD：4.10%

D. Efficiency of Converter
Fig. 15 shows the efficiency characteristic of theconventional six-step operation and the hybrid six-step
operation. In Fig. 15, the output power was varied from
200 W to 2.5 kW. In the conventional six-step operation,
the efficiency is drops to 92.8 % in the heavy load because
the input filter loss is increased by the distortion of the
input current. In the light load, the efficiency of hybrid sixstep operation is achieved to a more than 97.9 %. In
conventional six-step operation, the maximum efficiency
is achieved by 99.1 %. Thus, the hybrid six-step operation
is a better efficiency than the conventional six-step
operation in a low output power range. In addition, thehybrid six-step operation is the most efficient modulation
method in a low output power range.

Grid line voltage

Input R-phase current [10A/div]00
Output voltage (U-V) [500V/div]0
Output U-phase current [10A/div]

10ms/div

Fig. 11. Experimental results of PWM operation. The input current
THD is 4.10 %.
Input voltage (R-S) [500V/div]0
Input current THD：36.7%

Input R-phase current [10A/div]00
Output voltage (U-V) [500V/div]0
Output U-phase current [10A/div]
10ms/div

Fig. 12. Experimental results of conventional six-step operation.
The switching loss is reduced by the conventional six-step
operation. The input current THD is 36.7 %.

six-step operation, the input current THD was improved by
76.0 % in exchange for the drops of efficiency by 1.0 %.
ACKNOWLEDGMENT
This work was supported by JSPS KAKENHI Grant
Numbers JP15H03960.

REFERENCES[1]

F. Blaabjerg, et al., “Overview of Control and Grid Synchronization
for Distributed Power Generation Systems”, IEEE Trans. Ind.

Input voltage (R-S) [500V/div]0Electron., vol. 53, no. 5, pp. 1398-1409 (2006).
[2]

F. Blaabjerg, et al., “Power electronics as efficient interface indispersed power generation systems”, IEEE Trans. Ind. Electron.,

Input R-phase current [10A/div]

Input current THD：8.84%
0

vol. 19, no. 5, pp. 1184-1194 (2004).
[3]

Josep M. Guerrero, et al., “Hierarchical Control of DroopControlled AC and DC Microgrids—A General Approach Toward
Standardization”, IEEE Trans. Ind. Electron., vol. 58, no. 1, pp.

278-172 (2010).
[4]

Output voltage (U-V) [500V/div]
0

Nikolas Flourentzou, et al., “VSC-Based HVDC Power
Transmission Systems: An Overview”, IEEE Trans. PowerElectron., vol. 24, no. 3, pp. 592-602 (2009).
[5]0

J. P. Barton, et al., “Energy storage and its use with intermittent
renewable energy”, IEEE Trans. Energy Conversion, vol. 19, no.

2, pp. 441-448 (2004).
Adnan Sattar, et al., “Real-Time Implementation of BESS to
Smooth the Output Power Fluctuation of Variable Speed Wind
Turbine Generator”, IEEJ Trans. Ind. Appl., vol. 3 no. 3 pp. 198205 (2014).
[7] Takashi Suzuki, et al., “Introduction and Practical Use of Energy
Storage System with Lithium-ion Battery for DC Traction Power
Supply System”, IEEJ Trans. Ind. Appl., vol. 5, no. 1, pp. 20-25(2016).
[8] Ritwik Chattopadhyay, et al., “Low-Voltage PV Power Integration
into Medium Voltage Grid Using High-Voltage SiC Devices”, IEEJ
Trans. Ind. Appl., vol. 4, no. 6, pp. 767-775 (2015).
[9] Hirokazu Seki, et al., “Deceleration Control System for ElectricPowered Wheelchairs with Efficient EDLC Charge/Discharge”,
IEEJ Trans. Ind. Appl., Vol. 4, No. 1, pp. 11-19 (2015).
[10] Shota Yamaguchi, et al., “Single-phase Power Conditioner with a
Buck-boost-type Power Decoupling Circuit”, IEEJ Trans. Ind.
Appl., vol. 5, no. 3, pp. 191-198 (2016).
[11] J. M. Carrasco, et al., “Power-Electronic Systems for the Grid
Integration of Renewable Energy Sources: A Survey”, IEEE Trans.
Ind. Electron., vol. 53, no. 4, pp. 1002-1016 (2006).
[12] Srdjan M. Lukic, et al., “Energy Storage Systems for Automotive
Applications”, IEEE Trans. Ind. Electron., vol. 55, no. 6, pp.

Fig. 13. Experimental results of hybrid six-step operation. The input
current THD is improved by 76.0 % compared with theconventional six-step operation.

[6]

45

Input current THD [%]

40[14] H. Akagi, et al., “Control and performance of a doubly-fed
induction machine intended for a flywheel energy storage system”,
IEEE Trans. Ind. Electron., vol. 17, no. 1, pp. 109-116 (2002).
[15] Dong-Jing Lee, et al., “Small-Signal Stability Analysis of an
Autonomous Hybrid Renewable Energy Power Generation/Energy
Storage System Part I: Time-Domain Simulations”, IEEE Trans.
Ind. Electron., vol. 23, no. 1, pp. 311-320 (2008).
[16] G. O. Cimuca, et al., “Control and Performance Evaluation of a
Flywheel Energy-Storage System Associated to a Variable-Speed
Wind Generator”, IEEE Trans. Ind. Electron., vol. 53, no. 4, pp.

1074-1085 (2006).
[17] Grzegorz Iwanski, et al., “DFIG-Based Power Generation System
With UPS Function for Variable-Speed Applications”, IEEE Trans.
Ind. Electron., vol. 55, no. 8, pp. 3047-3054 (2008).
[18] Bingsen Wang, et al., “Dynamic Voltage Restorer Utilizing a
Matrix Converter and Flywheel Energy Storage”, IEEE Trans. Ind.

Electron., vol. 45, no. 1, pp. 222-213 (2009).
[19] A. M. Khambadkone, " Compensated synchronous PI current
controller in overmodulation range and six-step operation of spacevector-modulation-based vector-controlled drives ", IEEE Trans.
Ind. Electron., Vol. 49, No. 3, pp. 574-580 (2002)[20] J. Itoh, I. Sato, H. Ohguchi, K. Sato, A. Odaka and N. Eguchi, “A
Control Method for the Matrix Converter Based on Virtual
AC/DC/AC Conversion Using Carrier Comparison Method”, IEEJ
Trans., vol. 124-D, no. 5, pp. 457-463 (2004).

30
25

Six-step operation20

Hybrid six-step operation

15
10
0

0

500

1000
1500
Input power [W]

2000

2500

Fig. 14. Input current THD of conventional six-step operation andhybrid six-step operation. The input current THD of hybrid six-step
operation is a lower than conventional six-step operation in a wide
input power range.
10099

Efficiency [%]pp. 3881-3895 (2010).

35

52258-2267 (2008).
[13] Sergio Vazquez, et al., “Energy Storage Systems for Transport andGrid Applications”, IEEE Trans. Ind. Electron., vol. 57, no. 12,

Output U-phase current [10A/div]

10ms/div

98
97

Six-step operation96

Hybrid six-step operation

95
94

93
92
0

500

1000
1500
Output power [W]

2000

2500

Fig. 15. Efficiency of conventional six-step operation and hybrid
six-step operation. The efficiency is drops to 92.8 % in a high input
power range. On the other hand, efficiency of hybrid six-step
operation. The efficiency is achieved by more than 97.9 %. In
addition, the maximum efficiency is achieved by 99.1 %.