IEEE PEDS 2017, Honolulu, USA
12 – 15 December 2017

Loss Reduction for Matrix Converterwith Hybrid Six-step Operationin Flywheel Energy Storage System
Jun-ichi Itoh, Takumi Masuda
Nagaoka University of Technology
Nagaoka, Niigata, Japan
itoh@vos.nagaokaut.ac.jp
Abstract— This paper presents a hybrid six-step operation
which utilizes both a pulse width modulation (PWM) operation
and a six-step operation for a matrix converter. In the hybrid sixstep operation, the control of the matrix converter is divided intoa current source rectifier (CSR) control and a voltage source
inverter (VSI) control. In particular, the CSR is implemented by
the PWM operation and the VSI is controlled by the six-step
operation. Consequently, the switching loss of the VSI with thesix-step operation is reduced in compared with the PWM
operation, because the switching of the VSI are only six times ofthe fundamental frequency. In addition, the input current total
harmonic distortion (THD) is improved as compared with the sixstep operation because the CSR is employed with the PWM
operation. The experimental results, the converter loss of thehybrid six-step operation is reduced by 30.7% compared with the
PWM operation in exchange for the increase of the input current
THD by 3.71% compared with the PWM operation. Moreover,the efficiency of the charge and discharge with the hybrid six-step
operation is improved by 1.80% compared with the PWM
operation.

I. INTRODUCTION
In recent years, renewable energy systems have been
attracted many attentions [1]-[3]. In these systems, a powerfluctuation occurs due to meteorological conditions. Therefore,
renewable energy systems require energy storage components,
e.g. EDLC , chemical battery or flywheels.
Table I depicts the characteristics of each energy storage
device. EDLCs have a high charge and discharge efficiency.
Moreover, the rapid charge and discharge are possible because
the internal resistance is very small. However, similar to thebattery, the lifetime decreases rapidly due to the influence of theambient temperature [4]. On the other hand, batteries canachieve a high energy density at low cost. However, one of the
problems in the battery energy storage is a short life time. In
particular, the lifetime depends on the ambient and the numberof charge and discharge time. In addition, the batteries cannot
cope with rapid charge and discharge due to a large internal
resistance. Therefore, energy storage systems using batteriesrequire periodical maintenance due to short lifetime of thebatteries. Compared with other methods to store electricity,
flywheel energy storage systems (FESS) have long lifetime(lasting decades with little or no maintenance), and the charge
and discharge characteristic of the flywheel does not depend on

TABLE I
CHARACTERISTICS OF ENERGY STORAGES
Flywheel
EDLC
Battery
Kinetic
Chemical
Energy storage
Ion transfer
energyreaction
Charge &Discharge of
Fast
Fast
Slow
short period
Temperature
Limited by
Limited by
Excellentcharacteristic
temperaturetemperature
Energy density
Good
Good
Excellent

the temperature. In addition, a FESS can charge and discharge
large electrical power from the renewable energy systems at a
relatively short period. Therefore, the FESS can achieve a
power leveling with high response to large power ripple [5].
Meanwhile, a matrix converter has attracted many attentions
as a power converter to control the FESS due to its many
desirable features. The matrix converter can achieve highefficiency, small size and long lifetime compared to Back-ToBack (BTB) system which consists of a PWM rectifier andinverter. Therefore, the power leveling system that combines
the matrix converter and FESS can be operated with little or no
maintenance [6]-[7].
Besides, the FESS is frequently used in the high flywheel
rotational speed because the performance of the high flywheel
rotational speed is better than the low flywheel rotational speed
in the charge and discharge mode. However, the output voltage
is limited by the input voltage during the high flywheel
rotational speed. For this reason, a field-weakening control isapplied during for the high flywheel rotational speed. However,
the efficiency of the matrix converter employing the fieldweakening control is decreased. In six-step operation, the highoutput voltage can be achieved compared with the PWM
operation. In addition the switching loss is drastically reduced
because the switching times is drastically decreased. 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 the matrix
converter is proposed to reduce the converter loss wish theFESS. In order to control the matrix converter, the control
strategy is based on the virtual AC-DC-AC conversion strategy,
where the matrix converter is separated into a CSR and a VSI

978-1-5090-2364-6/17/$31.00 ©2017 IEEE

II. SYSTEM CONFIGURATION

Braking circuit

Pgrid

PFESS

Power grid

Induction
motor
FW

IM

Flywheel
Input filter

Load

Matrix converter

Fig. 1. FESS with matrix converter as power converter. The FESS
consists of the matrix converter, the flywheel, the input filter and thesnubber circuit.

A.

Flywheel Configuration
Fig. 2 shows the photograph of the prototype of FESS. In
the FESS, the induction motor (IM) is operated as a generator
during acceleration, where the electrical energy is stored as the
kinetic energy. On the other hand, during deceleration; thekinetic energy is converted into the electrical energy. Therefore,
this system employs a matrix converter. In Fig. 2, it can beobserved that the shape of the flywheel is disk-shaped. The
stored energy E is calculated by (1) from the rotational angularvelocity  and the moment of the inertia of the flywheel J.

Fig. 2. Photograph of prototype FESS.
CSR

Srp

1
J 2
2

(1)

Therefore, the flywheel can store the large kinetic energy when
the region is the large rotational angular velocity  of the
flywheel. In terms of the energy storage system for the
renewable energy systems in order to smooth the grid power,
the performance of the high flywheel rotational speed is better
than the low flywheel rotational speed. The flywheel is capableof storing energy up to 3 MJ in the prototype to evaluate thefundamental operation. In addition, the pressure in the vacuum

Stp

R
S
T

Srn Ssn

B.

E

Ssp

VSI

Sup

Svp

Swp

DC-link voltage

Circuit Configuration
Fig. 1 shows a circuit diagram of the FESS employed withthe matrix converter. The FESS consists of the matrix
converter [9], the flywheel, the input filter and the snubber
circuit. The FESS compensates the power ripple caused by therenewable energy systems in order to smooth the grid power.
In the charge and discharge mode of the FESS, the FESS isfrequently used in the high flywheel rotational speed because
the performance of the high flywheel rotational speed is better
than the low flywheel rotational speed. In terms of the matrix
converter, the high output voltage can be achieve highperformance of the FESS. On the other hand, the matrix
converter is operated as the same condition in the standby
mode of the FESS. The standby mode occurs the converter loss
in which the switching loss is predominant in the mode.
However, a PWM control which can regulate the input current
as a sine wave introduces the large switching loss. Therefore,
the matrix converter operation of a low switching loss isnecessary in terms of a high efficiency. In addition, it isnecessary to reduce the input filter loss which is increased by
the input current distortion.

Snubber circuit

Pload

as an indirect matrix converter [8]. In the hybrid six-step
operation, the control system is separated into the CSR control
and the VSI control, where the CSR is operated by PWM andthe VSI is modulated by the six-step operation. The converter
loss of the matrix converter applied with the hybrid six-step
operation is reduced in compared with the PWM operation
because the switching frequency of the six-step operation is
only six times of the output frequency. Meanwhile, the input
current THD does not drastically increased, because the input
current THD is reduced by the PWM operation of the CSR. The
hybrid six-step operation is confirmed by the experiment. In
addition, the efficiency and the input current THD of the hybrid
six-step operation are compared to that of the PWM operation.

Stn

U

V
W

Sun

Svn Swn

Fig. 3. Circuit diagram of indirect matrix converter. The matrix converter
separates the CSR and the VSI by the virtual AC-DC-AC conversion
strategy.

case is reduced by using the vacuum pump in order to further
reduce the windage loss because the machine loss of the
flywheel containing the windage loss decreases the efficiencyof the FESS. During the acceleration and deceleration, theperformance of energy storage system is evaluated by (2) fromthe total charge energy of the flywheel PIN and the total
discharge energy of the flywheel POUT. However, the total
charge energy of the flywheel PIN includes the flywheel loss of
the iron loss and the copper loss.

 FW 

POUT
PIN

(2)

III. CONTROL STRATEGY

vr*,vs*,vt*

A.

Virtual AC-DC-AC Conversion
The control strategy of the direct matrix converter iscomplicated. In order to control the matrix converter simply,
the control strategy is based on the virtual AC-DC-AC
conversion strategy, where the matrix converter is separated
into a CSR and a VSI as an indirect matrix converter [8].
Equation (3) expresses the relationship between the input
voltage t[vr vs vt] and the output voltage t[vu vv vw] in the matrix
converter.

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

(3),

sun 
 s
svn   rpsswn   rn

ssp
ssn

vr 
stp   vsstn   
 vt 

s su
s sv
s sw

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

sun 
 s
svn   rpss wn   rn

s sp
s sn

6

TABLE II
CHARACTERISTICS OF MATRIX CONVERTER CONTROL STRATEGIESPWM operation

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

Small

Nearly small

Input filter loss

Small

Large

Nearly small

Input current

DC-link
voltage
VSI

Output voltage

TABLE III
EXPERIMENTAL CONDITIONSParameter

Main circuit
parameter

stp 
(5)
stn 

Fig. 4 shows a switching pulse generator based on the virtual
AC-DC-AC conversion. The method of the switching pulse
generator is represented by (5). Thus, this method clearly
separates the input current control and the output voltage
control.
B.

Switching
9functioncomposition Switchingequation (3)
pulse

(4)

The relationship between the output voltage and the input
voltage is determined solely by (4). In order to match the input
and the output terminals of the indirect matrix converter
assuming that the filter effect in Fig. 1 is excluded, (5) should
be satisfied.

 s rus rv
 srw

CSR control

6

Fig. 4. Block diagram of switching pulse generator. The switching pulses
are generated by the virtual CSR and the virtual VSI controls.

CSR

where smn is a switching function of the switch S mn. smn is 1
when Smn is turned on, and smn is zero when Smn is turned off.
Fig. 3 shows a circuit diagram of the indirect matrix
converter applied the virtual AC-DC-AC conversion. The
virtual AC-DC-AC conversion replaces the matrix converterby the combination of CSR and VSI as shown in Fig. 3 in orderto obtain the designated switching pulse commands. In theindirect matrix converter, the relationship between the input
voltage t[vr vs vt] and the output voltage t[vu vv vw] is representedby (4).

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

iu*,iv*,iw*

VSI control

Hybrid Six-step Operation
Table II shows the characteristics of the PWM operation, thesix-step operation and the hybrid six-step operation. When thematrix converter is implemented with the PWM operation, all
the switches of the CSR and the VSI are switched at highfrequency. Consequently, a large switching loss occurs anddecreases the efficiency of the energy storage system. In orderto reduce the switching loss of the matrix converter, the sixstep operation has been proposed. In the six-step operation, theswitching of the CSR is synchronized with the three-phase

Flywheelparameter

Value

Switching device

SiC-MOSFET

Rated power

10 kW

Grid line voltage

200 V

Input filter L

2.2 mH

Input filter C

6.6 μF

Carrier frequency

25 kHzRated votage

200 V

Rated current

44 Arms

Rated power

11 kW

Rated speed

5500 rpm

IM Poles4

Rated enegry

3 MJ

Vacuum

10,000 Pa

input voltage, i.e. the 120 degree conduction, whereas theswitching of the VSI is carried out at each 180 degree. This
operation greatly reduces the switching loss in the trade of thehigh distortion of the input current. Therefore, a large input
filter is required with the six-step operation. In order to reduce
the switching loss without increasing the input filter loss, ahybrid six-step operation has been proposed. In the hybrid six-

step operation as shown in Table II, the CSR is controlled by
the PWM operation, whereas the VSI is operated with 180 deg.
conduction mode. As a result, the switching loss is reduced ascompared with the PWM operation, whereas the input current
THD is improved as compared with the six-step operation.
Thus, the input filter loss is reduced compared with the six-step
operation.

Voltage [V]200

IV. EXPERIMENT RESULTS
In this section, the hybrid six-step operation with theprototype FESS of Fig. 1 is evaluated by the characteristics ofthe charge and the discharge, the converter loss and the input
current THD.
Table III shows the experimental conditions. The
characteristics of the charge and the discharge, the converter
loss and the input current THD of the hybrid six-step operationis verified experimentally compared with the PWM operation
at the same input voltage and flywheel rotational speed.
A.

Field-weakening Region
Fig. 5 shows the V / f control of the voltage with the
flywheel rotational speed. The V / f control includes the fieldweakening control region from 3000 r / min to 5500 r / minbecause the rated voltage of IM stator with the flywheel is 400
V and the rated frequency of IM stator with the flywheel is
200Hz. Therefore, the matrix converter can not obtain the rated
output voltage at 3000 r / min or more in FESS using 200 V
grid. It is necessary for the FESS to use the field-weakening
control of the PWM operation at 3000 r / min or more. On theothe hand, the hybrid six-step operation can achieve the higher
output voltage compared with the PWM operation in the same
field-weakening region.
Characteristics of Charge and Discharge
Fig. 6 shows the operation waveforms when both the CSR
and the VSI are applied with the PWM operation. A sinusoidal
output current is obtained with the input current THD of 9.92%.
In addition, the converter efficiency is 94.5% at 6.7 kW.
Fig. 7 shows the operation waveforms when the matrix
converter is applied with the hybrid six-step operation. The
output voltage includes the switching ripple component aroundthe peak of the output voltage. The output voltage nearly
becomes the square waveform due to the 180 degree
conduction mode of the , whereas the input current THD is
14.8% and the converter efficiency is 95.5% at 6.7 kW.
Therefore, the converter loss is reduced by 18.2% owing to thehybrid six-step operation in compared with the PWM operation.
On the other hand, the input current THD is increased by 4.88%
at 6.7 kW.
Fig. 8 shows the characteristic of the charge when the matrix
converter is applied with the PWM operation and the hybrid
six-step operation. The characteristic of the charge is obtained
when the flywheel rotational speed is changed from 3500 to
5500 r / min with the acceleration time is 400 s. The total
charge energy of the charge with the PWM operaion and withthe hybrid six-step operaion are 1.52 MJ and 1.50 MJ,

Field-weakening region

150
PWM
100
Hybrid six-step
50

01000 2000 3000 4000 5000 6000

Flywheel rotational speed [r / min]Fig. 5. V / f control of voltage and flywheel rotational speed. The V / fcontrol includes the field-weakening control region from 3000 r / min to5500 r / min
Grid voltage (R-S) [500V/div]0
Input current THD: 9.92%

Grid R-phase current [100A/div]00Induction motor voltage (U-V) [500V/div]010ms/div

Induction motor U-phase current [100A/div]

Fig. 6. Operation waveforms of PWM operation. The input current THD
is 9.92%. The output power is 6.7 kW. The flywheel rotational speed is4500 r / min.

B.

Grid voltage (R-S) [500V/div]0
Input current THD: 14.8%

Grid R-phase current [100A/div]00Induction motor voltage (U-V) [500V/div]010ms/div

Induction motor U-phase current [100A/div]

Fig. 7. Operation waveforms of hybrid six-step operation. The input
current THD is 14.8%. The output power is 6.7 kW. The flywheel
rotational speed of the flywheel is 4500 r / min.

respectively. Therefore, the charge power of the charge modewith the hybrid six-step operaion is reduced by 1.07%
compared to the PWM operation with the same acceleration
time.
Fig. 9 shows the characteristic of the discharge when thematrix converter is applied with the PWM operation and the
hybrid six-step operation. The characteristic of the discharge is

96.0

8000

95.5

7000
6500
6000

Hybrid six-step operation

94.5
94.0
93.5

PWM

93.0
92.5

5500
5000
3500

Hybrid six-step operation

95.0

PWM

7500

Efficiency [%]Charge power [W]

8500

4000

4500

5000

92.0
5000

5500

Flywheel rotational speed [r / min]Fig. 8. Characteristic of charge mode. The characteristic of the charge
mode is obtained when the flywheel rotational speed is changed from3500 to 5500 r / min with the acceleration time is 400 s.

5500

6000

6500

7000

7500

8000

8500

Charge power [W]
Fig. 10. Efficiency characteristic of charge mode. The characteristic of
the charge mode is obtained when the flywheel rotational speed is changed
from 3500 to 5500 r / min with the acceleration time is 400 s.
97.0

6500

96.5

Hybrid six-step operation

Hybrid six-step operation

Efficiency [%]Discharge power [W]

6000

5500

5000

PWM

95.0

PWM

5000

4500

4000

3500

Flywheel rotational speed [r / min]Fig. 9. Characteristic of discharge mode. The characteristic of thedischarge mode is obtained when the flywheel rotational speed is changed
from 5500 to 3500 r / min with the deceleration time is 400 s.

obtained when the flywheel rotational speed is changed from5500 to 3500 r / min with the deceleration time is 400 s. The
total discharge energy of the discharge with the PWM operaion
and with the hybrid six-step operaion are 1.16 MJ and 1.17 MJ,
respectively. Therefore, the discharge power of the discharge
mode with the hybrid six-step operaion is improved by 0.741%
compared to the PWM operation with the same deceleration
time. In addition, the efficiency of the charge and discharge
with the PWM operaion and with the hybrid six-step operaion
are 76.4% and 77.8%, respectively. Therefore, the charge anddischarge with the hybrid six-step operaion is improved by
1.80% compared to the PWM operation with the sameacceleration and deceleration time. Thus, the hybrid six-step
operation achieves higher efficiency than the PWM operation.
C.

95.5

94.5

4500

4000
5500

96.0

Converter Loss
Fig. 10 shows the characteristics of the converter efficiency
against the output power. The output power are varied from 5.2
kW to 8.4 kW. The converter efficiency of the hybrid six-step
operation is improved by 2.60% compared to the PWM
operation at 8.4 kW. Therefore, the converter loss of hybrid

94.0
6500

6000

5500

5000

4500

4000

Discharge power [W]
Fig. 11. Efficiency characteristic of discharge mode. The characteristic ofthe discharge mode is obtained when the flywheel rotational speed ischanged from 5500 to 3500 r / min with the deceleration time is 400 s.

six-step operation is reduced by 30.7% compared to the PWM
operation. Besides, the average efficiency of the PWM overentire load range is above 94.3%. In addition, the maximum
efficiency of the PWM is 95.3%. On the othe hand, the average
efficiency of the hybrid six-step operation over entire load
range is above 95.4%. In addition, the maximum efficiency ofthe hybrid six-step operation is 95.7%. Therefore, the hybrid
six-step operation improves the the characteristic of the charge
mode with the FESS.
Fig. 11 shows the characteristics of the converter efficiency
against the output power. The output power are varied from 4.2
kW to 6.2 kW. The converter efficiency of the hybrid six-step
operation is improved by 0.629% compared to the PWM
operation at 6.1 kW. Therefore, the converter loss of hybrid
six-step operation is reduced by 13.0% compared to the PWM
operation. Besides, the average efficiency of the hybrid sixstep operation over entire load range is above 95.6%. In
addition, the maximum efficiency of the hybrid six-step
operation is 96.0%. Therefore, the hybrid six-step operation
improves the characteristic of the discharge mode with theFESS. Therefore, the hybrid six-step operation improves the

1200
1000

This paper clarified the improvement effect of the hybrid
six-step operation with the FESS. The hybrid six-step operationachieved the improvement of the output voltage and the
reduction of the switching loss. In addition, the hybrid six-step
operation reduced the converter loss with the FESS. In
particular, the converter loss of the hybrid six-step operation is
reduced by 30.7% in exchange for the increase of the input
current THD by 3.71% compared with the PWM operation at
8.4 kW. However, the FESS is frequently used in the highflywheel rotational speed because The performance of the highflywheel rotational speed is better than the low flywheel
rotational speed. In addition, the charge and discharge with thehybrid six-step operation was improved by 1.80% comparedwith the PWM operation in same acceleration and deceleration
time. Besides, in terms of the energy storage system, the hybrid
sixstep operation improved the performance of the FESS.
In future work, the performance of hybrid six-step operation
with at lght load, will be shown.

[2]

[3]

[4]

[5]

M. Liserre, R. Cárdenas, M. Molinas, and J. Rodríguez, “Overview ofMulti-MW Wind Turbines and Wind Parks” IEEE Trans. IE., Vol. 58,
No. 4, pp. 1081-1095, 2011
K. Ma, M. Liserre, F. Blaabjerg, and T. Kerekes, “Thermal Loading andLifetime Estimation for Power Device Considering Mission Profiles inWind Power Converter” IEEE Trans. PE., Vol. 30, No. 2, pp. 590-602,
2015
W. Chen, D. Xu, N. Zhu, M. Chen, and F. Blaabjerg, “Control of DoublyFed Induction Generator to Ride-Through Recurring Grid Faults” IEEE
Trans. PE., Vol. 31, No. 7, pp. 4831-4846, 2016
M.Uno and K.Tanaka, “Accelerated Charge-Discharge Cycling Test andCycle Life Prediction Model for Supercapacitors in Alternative Battery
Applications” IEEE Trans. IE., Vol.60, No.6, pp.2131-2138 2013
M. I. Daoud, A. M. Massoud, A. S. Abdel-Khalik, A. Elserougi and S.
Ahmed, “A Flywheel Energy Storage System for Fault Ride ThroughSupport of Grid-Connected VSC HVDC-Based Offshore Wind Farms”,
IEEE Trans. PS., Vol. 31, No. 3, pp. 1671-1680, 2016

PWM

0
3000

3500

4000

4500

5000

5500

Flywheel rotational speed [r / min]Fig. 12. Characteristic of standby mode. The characteristic shows thestandby loss from 3000 to 5500 r / min18

Hybrid six-step operation

16
14
12
10
8
6

PWM

4
2
0
5000

5500

6000

6500

7000

7500

8000

8500

Power [W]Fig. 13. Characteristic of input current THD.

[6]

[7]

[8]

REFERENCES
[1]

600

200

D.

V. CONCLUSION

Hybrid six-step operation

800

400

Input current THD [%]Input Current THD
Fig. 13 shows the characteristic of the input current THD
when the flywheel rotational speed is changed from 3500 to
5500 r / min with the acceleration time is 400 s. The input
current THD of the hybrid six-step operation increase to 3.71%
compared to the PWM operation at 8.4 kW. Thus, the converter
loss of the hybrid six-step operation is reduced by 30.7% inexchange for the increase of the input current THD by 3.71%
compared with the PWM operation at 8.4 kW.

1400

Power [W]the characteristic of the discharge mode with the FESS. In
terms of the energy storege system, the high efficiency of thecharge and discharge improves the performance of the FESS.
Fig. 12 shows the efficiency of the standby mode. In Fig.
12, the standby loss is measured from 3000 to 5500 r / min. As
a result, the standby loss of the hybrid six-step operation isincreased by 9.45% compared with the PWM operation at 4500
r / min. In future work, it is necessary to evaluate the IM lossof the iron loss and the copper loss during standby mode, will
be shown.

[9]

B. Wang and G. Venkataramanan, “Dynamic Voltage Restorer Utilizing
a Matrix converter and Flywheel Energy Storage” IEEE Trans. IA., Vol.
45, No.1, pp. 222-231, 2009
K. Orikawa, H. Takahashi, H. Igarashi and J. Itoh, “Transition Control to
Direct Transmission Mode of Matrix Converter for Flywheel Drive
System without Rush Current”, IEEJ Trans., Vol. 134-D, No. 1, pp. 8289, 2014
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. 124D, No. 5, pp. 457-463, 2004
K. Koiwa, and J. Itoh, “Evaluation of a Maximum Power Density Design
Method for Matrix Converter using SiC-MOSFET”, IEEE Energy
Conversion Congress and Exposition, No. EC-1932, pp. 563-570, 2014