Design and Experimental Evaluation of the Flywheel
System for Power Leveling*Jun-ichi Itoh, *Kenta Tanaka, *Yuji Saiki, *Noboru Yamada, **Koji Kato*Nagaoka University of Technology
Nagaoka, Japan
itoh@vos.nagaokaut.ac.jp** Sanken Electric Co., Ltd.
Saitama, Japank.kato@sanken-ele.co.jp

Abstract— This paper introduces the performance of a power
leveling system with a 3.0-MJ, 3315-r/min flywheel energy
storage. In terms of cost reduction, this system uses low cost ballbearings and general purpose induction motor. Therefore, such asystem configurations occurs large loss during standby mode. In
order to overcome this problem, low loss design algorithm that
focuses on the mechanical loss is applied to the design of the
flywheel. As a result, the flywheel loss in the steady state consistsof bearing loss of 28.3%, the copper loss of 22.5% for the
induction motor. Moreover, charging and discharging efficiency
are measured to evaluate the prototype flywheel system. From
the analysis, it is confirmed that the charging efficiency is 75.4%
and the discharging efficiency is 77.2%.

Therefore, it is necessary to achieve the flywheel systems
that do not use a magnetic bearing. The authors have evaluateda prototype flywheel consists of the induction machine withball bearings [5][6]. From the loss analysis of the prototype
flywheel system, it is confirmed that the steady state loss of the
flywheel is very large. Therefore, it is necessary to establish amethod for low loss design of the flywheel and the further loss
reduction toward the practical use of the flywheel.

Keywords—Flywheel, Low loss design, Loss analysis

I.

INTRODUCTION

Renewable energy systems, especially a wind turbine and aphotovoltaic cell, generated a power fluctuation due to themeteorological conditions. Therefore, these systems requireenergy buffers such as electric double layer capacitors (EDLC),
batteries or flywheels to suppress the power fluctuations. For
example, the battery can achieve 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 an ambient and the number of charge and discharge time. In
addition, the battery cannot cope with rapid charge anddischarge by a large internal resistance of the battery. On theother hand, the EDLC has a high charge and discharge
efficiency. Moreover, the rapid charge and discharge ispossible because the internal resistance is very small. However,similar to the battery, the lifetime is decreased rapidly due tothe influence of the ambient temperature [1]. On the other hand,the flywheels has some advantages: (i) environmental friendly,(ii) low maintenance cost, (iii) long lifetime due to no chemical
structure, and (iv) the charge and discharge characteristic ofhigh cycle are excellent. For these reason, the flywheel has
attracted attention as an energy storage system.
In recent years, an ultra-high speed rotation of the flywheel
has been studied. The kinetic energy which is stored in the
flywheel is proportional to the square of the rotational speed.
Therefore, the magnetic bearings have been studied in order toachieve high energy density. However, the magnetic bearing isrequired an additional control system [2-4]. For this reason, it
can lead to high cost and complexity of the control system of
the flywheel system.

In this paper, the design method of the flywheel which aims
to reduce the mechanical loss is established. This approach
focuses on the design freedom of the shape of the flywheel tostore the same energy. The constitution of this paper is follows:
at first, the proposed flywheel system is introduced. Next, thedesign method of the flywheel shape is discussed. Thirdly, theanalytical technique of the loss that occurs in the flywheel isinvestigated. Finally, the steady state loss and the energy stored
efficiency are evaluated by the experiments.
II.

PROPOSED FLYWHEEL SYSTEM

Fig. 1 shows the configuration of a proposed flywheel
system that employs the general purpose motor and ballbearings. In this system, it is possible to store the kinetic
energy of the 3.0 MJ at 3315 r/min. Such a low rotation speed
region can be applied to a typical ball bearing and general
purpose motor. In addition, the flywheel vacuum case and the
motor are separated by the magnetic fluid seal. As a result,windage loss can be greatly reduced because it is possible toreduce a pressure in the vacuum case by the vacuum pump.
Moreover, vacuum in the vacuum case does not affect the heatdissipation of the motor because the motor and the vacuum
case are separated. Therefore, the general purpose motor canbe applied to drive the flywheel without adding special
cooling mechanism.
Fig. 2 shows the block diagram of the flywheel system
including the measurement system and auxiliary devices. In
the flywheel system, the induction machine is operated as a
generator during deceleration, the kinetic energy is converted
into the electrical energy. On the other hand, during
acceleration, the electrical energy is stored as the kinetic
energy, which is working as a motor. Therefore, this system
uses a regenerative converter. Furthermore, an overtemperature of the bearing and the motor can be prevented by
the oil cooler.

LOW LOSS DESIGN OF THE FLYWHEEL SHAPE

A. Consideration of the basic modelFig. 3 shows the low loss design flow of the flywheel [7].
In this design approach, it is necessary to consider the basicmodel such as the direction of the rotation of the flywheel andthe bearing types. The rotational direction of the flywheel canbe considered vertical and horizontal. In the vertical axis, thehorizontal axis is not bent because the load of the flywheel
will be loaded in the axial direction. Therefore, the effects ofthe shaft whirling will be excluded from the design items. In
the bearing loss, the effect of the rotational speed is larger than
the influence of the load.
In this study, the flywheel is designed to give priority to aloss reduction and a safety. Therefore, the vertical axis ischosen as the rotational direction of the flywheel.
B. Setting the required specifications
In this process, the specification of the flywheel which is
required for the system is considered. The design items to be
set are follows: the maximum dimension, the maximum
rotation speed, the stored energy of the flywheel,
performances of the safety and the lifetime. The shape of the
flywheel satisfying these conditions is enormous. Therefore,
the shape of the flywheel is designed automatically by the low
loss design algorithm.
The required specifications of the prototype flywheel are
as follows: the maximum radius of the flywheel is 0.5 m, themaximum thickness is 0.5 m, the maximum rotation speed is
10000 r/min, the bearing life is 10 years. These specifications
assume a size that can be processed by a machine tool or a
production company in general.
C. Determination of the specification
In this process, the combination of the design parametersthat satisfy the required specification are determined. For
example, the windage loss varies greatly depending on theratio of the radius of the vacuum case and the flywheel.
Therefore, the design parameters such as the radius and speedof the flywheel vary from a minimum value to a maximum
value. As a result, a variety of specifications of the flywheel tomeet the required value is determined.
D. Evaluation of the mechanical loss
In this process, the bearing loss and the windage loss arecalculated for a provisional specification was determined.
Note that the bearing loss and the windage loss are calculatedby the analytical method which is described in the next section.
In addition, the windage loss and the bearing loss calculated inthis process are compared to the mechanical loss obtained indifferent specifications. Finally, the specification of the
flywheel which minimizes the mechanical loss is determined.
Table 1 shows the specification of the flywheel which isdesigned by the low loss design algorithm. From the results, it
can be seen that the shape of the flywheel is disk-shaped. It iscapable of storing sufficient energy for a low rotational speedby the inertia weight is increased. In addition, the windage

Induction motor

Motor fanMotor bearing

Ferrofluidic seal
Bearing1

Flywheel

Bearing2

φ1000

65

III.

Fig. 1. Configuration of a proposed flywheel system that employs thegeneral purpose motor and ball bearings.
3Φ200V
3
Power
meter

GeneralPurposeInverterPower
3 meter

Regenerative
converter
Regeneration
3
3

Induction
motor
3

Ferrofluidic
seal
Bearing
Flywheel

Oil Pump
VacuumPump

Vacuum case
Thermocouple

Fig. 2. Block diagram of the flywheel system including themeasurement system and the auxiliary devices.

loss and the bearing losses are reduced by the reduction inrotational speed. The pressure in a vacuum case is reduced byusing a vacuum pump prior to operation in order to reduce thewindage loss. In addition, the magnetic fluid seal is adopted tomaintain the vacuum in the vacuum case.
IV.

ANALYSIS METHOD OF THE STEADY STATE LOSSIn this section, the losses that occur in a steady rotation are
separated into mechanical losses and electrical losses. From
this analysis, the factors of the steady state loss that occur inthe system will be clarified. Moreover, further efficiency of
the flywheel system is considered.
A. Windage loss
The frictional losses that occur between the surface of the
flywheel and the surrounding fluid are calculated by (1) fromthe shape of the flywheel and the friction moment.
Pw  C ms  3 (ro 5  ri 5 )  C mc  3 ro 2 ri 2 t i .. (1)where, Cms is the moment coefficient of the friction of the top
and bottom, Cmc is the moment coefficient of the friction of theside, ω is the angular velocity of the body revolution [rad/s], rois the radius of the vacuum case, ri is the radius of the
flywheel, ti is the thickness of the rotational axis of the
flywheel.

However, the friction moment fluctuates depending on thestate of the fluid in the vacuum case. In this case, it is difficult
to obtain a simple formula. Therefore, the windage loss isanalyzed by using the computational fluid dynamics (CFD).
Unstructured grid-based thermal fluid analysis systemSCRYU / tetra (software cradle) is used for the analysis. In
the model which faithfully reproduces the real system, thecomputation time increases the complexity of the analysis.
Therefore, the simplified model eliminates extraneous partsand mechanisms are used for analysis. As an analysis
condition, the fluid flow is turbulent and SST k-ω model isused as a model for turbulence. SST k-ω is a model thatcombines the k-ε model based on the k-ω model. In thevicinity of the wall, k-ω model's predictive accuracy is better
separated flow is used. On the other hand, the k-ε model isused in an area away from the wall. As the initial condition,
the pressure in the vacuum case is 500 Pa, the temperature is
10 degree Celsius. In addition, the fluid is rotated around theaxis of the flywheel.
Fig. 4 shows the analysis of the ambient pressure of the
flywheel. The analysis conditions are as follows: the steadyrotational speed is 3315 r/min and the vacuum in the vacuum
case is 500 Pa. From the analysis, the pressure increases
toward the radial direction from the center of the flywheel.
This is because an increasing in losses due to the friction of
the fluid by increasing the peripheral speed.
B. Bearing loss
The bearing loss PB is obtained by (2) from the rotational
speed n and the friction moment of the bearing M.
PB  1.047  10－4 nM ............................................ (2)Additionally, the frictional moment can be separated into
frictional moment Mo that depends on the load and the friction
moment Ml that is independent from the load.

M  M o  M l ....................................................... (3)－7M o  f o  10

(un)

2

3 d 3 ................................... (4)m

M l  f l Pd m .......................................................... (5)where, fo is the coefficient that depends on the format and themethod of the bearing lubrication, u is the viscosity of the
lubricant, dm is the inner diameter of the pitch of the rolling
elements, fl is the coefficient that depends on the magnitude
and the direction of the load, P is the load on the bearing.
Table 2 shows the value used to calculate the bearing loss.
In this system, two bearings are arranged at the bottom andone at the top of the flywheel. The bearing losses at eachrotational speed are calculated by (4) and (5).
C. Copper loss with respect to the fundamental wave
In this section, the losses generated by the motor are
separated into the copper loss and the iron loss.
Fig. 5 shows the equivalent circuit of the induction
machine with respect to the fundamental wave. Table 3 shows
the specifications of the motor that is used in the prototype
system. From the equivalent circuit, the relationship betweenB)Setting required
specifications

Radius of flywheel
Thickness
Radius ratio
Rotation speed etc.

Loss
Life time
SafetyC)Determinationof specification

D)Evaluation of
mechanical loss

FinishFig. 3. Low-loss design algorithm of the flywheel with a focus onmechanical loss.
Table 1. Specifications of the flywheel which is calculated from thelow loss design.
Material
SCM440Radius
500 mmThickness
65 mm
Weight of the
Flywheel
392 kgFlywheelStored3.0 MJ at
Energy3315 r/min
Motor/Generator

MLC1115C (Fuji Electric)

Inverter

FRN 37G11S-2 (Fuji Electric)

secondary input P2 and the mechanical output Pmec isrepresented by (6).

P2 : Pmec  1 : (1  s) .............................................. (6)From this equation, the secondary resistance is calculatedby (7).
R2 ' 

s 1
I 2 ' 2 .................................................... (7)1 s 3Note that the slip s is calculated from the actual speed andthe synchronous speed of the induction motor. In addition, thesecondary current I2’ is calculated from the no-load test of the
motor itself. In the no-load test, the output resistance R2’/s canbe regarded as almost infinity because the slip s is almost zero.
At this time, the current flowing through the circuit will be all
the excitation current Io. Therefore, the secondary current I2’ iscalculated by (8).

I 2  I1  Io ............................................................. (8)From these results, the copper loss for the fundamental
wave is expressed by (9).

Pc  3R1 I 1 2  3R2 ' I 2 '2 ........................................ (9)D. Copper loss for harmonic
In the driving of the motor by an inverter with pulse widthmodulation (PWM), the harmonic voltage is applied to thepreceding paragraph, the copper loss for the harmoniccomponent is not considered. Therefore, it is necessary to
calculate the copper loss of the induction machine forharmonics.

Fig. 4. Visualization of the ambient pressure of the flywheel at the
rated energy storage.
Table 2. Condition for bearing loss calculation.

Bearing1

Bearing2

I1

R1

2

fl

0.0002

Viscosity ν

17 mm2/s

Pitch diameter dm

102.5 mm

Rotation speed n3315 r/min

Load P

0N

f0

2

fl

0.00025

Viscosity ν

17 mm2/s

Pitch diameter dm

70 mm

Rotation speed n3315 r/min

Load P

2528.4 N

I2IMVPn  3( R1  R2 ' ) I n '2 ............................................ (10)

f0

L1

R2'

L2'

1-s
R'
s 2

bo

Fig. 5. Equivalent circuit of the induction machine with respect tothe fundamental wave.
Table 3. Specifications of the motor that is used in the prototype
system.
Rated Voltage

200V

Rated Current

14.4A

Output Power

3.7kW

Primary resistance R1

1.01Ω

Excitation current Io

5.90A

E. Iron loss
From the equivalent circuit of the induction machine withrespect to the fundamental wave, the iron loss is expressed by(11) by using the excitation conductance.
I 2
Pi  3 M ........................................................ (11)go

In addition, the excitation conductance go is expressed by(12).
P  Wm.................................................. (12)go  oV12

where, Po is input power at no load, Wm is the mechanical loss
at no load.
V.

Io

go

Fig. 7 shows the equivalent circuit of one phase of theinduction machine for harmonic. The harmonics generated by
PWM is sufficiently high frequency region for thefundamental component. Therefore, the exciting component of
the equivalent circuit with respect to the fundamental wave isignored. In addition, the mechanical output can be ignored
because it can be regarded that the slip by the harmoniccomponent is 1. For these reasons, the loss for the harmoniccomponent is represented by (10).

induction machine. As a result, the losses due to the harmonics
occurs [8]. In this section, the copper loss caused by the
harmonic component of the motor current is calculated.
Fig. 6 shows the analysis of the harmonic current at the
rated energy storage. Note that the analysis results arenormalized by the amplitude of the fundamental current. From
the analysis, it is confirmed that the harmonic components dueto the carrier frequency occurs. In the analysis of the copper
loss with respect to the fundamental wave obtained in the

EXPERIMENTAL RESULTS

A. Analysis of the steady state loss
Fig. 8 shows the measurement result of the steady stateloss in experiment with prototype FESS as shown in Fig. 1. In
this experiment, the rotation speed is 3315 r/min, the vacuum
case is kept at 500 Pa. The mechanical loss and the electricalloss are separated by a free-run test at the beginning. Free-run
test is a test for electrically disconnecting the inverter and the
motor with the energy stored in the flywheel. In this state, thestored energy is consumed only by mechanical loss.
Therefore, the mechanical loss is calculated from the time
until the stored energy is consumed.
From the results, it is confirmed that the bearing loss
accounts for 48.6% of all mechanical loss. Additionally, theelectrical losses of the motor are accounted for 41.7% of thetotal loss. Therefore, it is necessary to improve the motor
efficiency and reducing the bearing loss toward higher
efficiency.
Fig. 9 shows the comparison of the experimental resultswith the results of a theoretical analysis of the mechanical loss.
Note that Pm is the total value of the mechanical loss, Pf is theloss of the magnetic fluid seal, Pem is the mechanical loss ofthe motor. In addition, the loss of the seal and the motor
mechanical loss are calculated from the free-run test.
From the Fig. 9, the analysis values agree with theexperimental results. Therefore, it is confirmed that theNext, the energy storage efficiency is calculated using theexperimental results. From the Fig. 10, the energy input inorder to store the energy of 1.01 MJ is 1.34 MJ. Therefore, thecharging efficiency is 75.4%. From the Fig. 11, it is confirmedthat the energy is discharged 0.78 MJ. Therefore, thedischarging efficiency is 77.2%.

Current[p.u.]

0.05

0.025

0.0

1

100

10
Frequency[kHz]Fig. 6. Analysis of harmonic current at the rated energy storage. The
analysis results are normalized by the amplitude of the fundamental
current.

In

Vn

R1

L1

R2'

L2'

1-s
R'
s 2

Fig. 7. Equivalent circuit of the induction machine for harmonic wave.

analytical method has high accuracy. Additionally, the value
obtained by subtracting the copper loss of all electrical losses
became 192 W. On the other hand, the theoretical calculationof the iron loss is 167 W. It is considered that the cause of theerror is the use of a simple equivalent circuit. Therefore, it isnecessary to use of the electromagnetic analysis in order toimprove the accuracy of analysis of the iron loss.
B. Analysis of the energy storage efficiency
In this section, the energy storage efficiency of the
prototype system is analyzed. This property is divided into adischarging efficiency and a charging efficiency. The charging
efficiency is the ratio of the energy consumed for storing thedesired energy. On the other hand, the discharging efficiency
is the ratio of actual energy can be released with respect tostored energy.
Fig. 10 shows the experimental result of the energy storage,
Fig. 11 shows the experimental result of the energy discharge.
In the experiment of energy storage, the flywheel isaccelerated from 2700 r/min to 3315 r/min. In the discharge
test, the flywheel is decelerated from 3315 r/min to 2700 r/min.
The stored energy is calculated using (13) from therotational angular velocity and the moment of inertia of the
flywheel J.

E

1 2J ........................................................... (13)2

From this equation, it is calculated that the amount of theenergy change is 1.01 MJ when the rotational speed changes
from 2700 r/min to 3315 r/min.

The discharging efficiency of the energy storage devices is
as follows: the lead acid battery is 75-85%, a redox flow
battery is approximately 70%, an EDLC is approximately 90%.
Therefore, it is confirmed that the energy storage efficiency ofthe prototype flywheel is about the same as the current main
power storage device.
C. Evaluation of the cost
Table 4 shows the estimation of the cost of the proposedsystem. Note that the material of the flywheel is usedchromium-molybdenum steel. Here, cost ratio of the material
in flywheel is assumed as 1. On the other hand, cost ratio of
the magnetic fluid seal and other components becomes 5.0 to
be relative to the material cost of the flywheel. The most of
this cost is accounted for the magnetic fluid seal. Therefore, itis necessary to consider the structure which can achieve a
sufficient vacuum without the magnetic fluid seal. From theresults, it is confirmed that the material cost of the flywheel inthe proposed system is very cheap. However, the total cost of
the entire system including the processing cost and the othercomponents becomes very expensive. Therefore, it is possible
to achieve a more reasonable system by improving the
manufacturing method and structure.
Next, the cost of the proposed system is compared withother energy storage devices. The comparison condition is thesame as the energy storage. From the reference [9], total costof EDLC energy storage systems becomes approximately 25%
higher as compared to the proposed flywheel system. Notethat specification of the capacitor to be used is as follows: therated voltage is 2.5 V, a capacitance is 2700 F, the cost perunit is $30. From these results, it is confirmed that the
proposed system can achieve a lower cost than an EDLC
energy storage system depending on the manufacturing cost.
However, the reduction of processing cost and component cost
are important issue for practical application of the flywheel.
VI.

CONCLUSION

This paper introduced the performance of a power levelingsystem with a 3.0-MJ, 3315-r/min flywheel energy storage. In
this proposed system, simplification of the system is achieved
by applying the general purpose induction machine and theball bearings. Additionally, the flywheel is designed with low
loss design focused on the mechanical loss. From the loss
analysis, it is confirmed that the bearing loss accounts for
48.6% of all mechanical loss. Moreover, the energy storage
efficiency is measured by experiments. As a result, it isconfirmed that the energy storage efficiency of the prototype
flywheel is about the same as the current main power storage
device. Towards higher efficiency, authors will consider theapplication and its low loss design of a permanent magnet
motor and the pivot bearing. In the cost evaluation, it is800

Bearing Loss

500
400

Motor
Mechanical Loss
Iron Loss
Harmonic
Copper Loss

300
200
100
0

5

Pm(Calculate)

300

Pb
Pm(Experiment)

2820

2940
3060
Rotation Speed[r/min]

3180

3300

Mechanical
Loss

Electrical Loss

3000

Fig. 9. Comparison of theoretical calculations and experimental
results of mechanical loss.
Table 4. Estimation of the cost of the proposed system.
Components
Material cost of Flywheel(SCM440)
Other material cost

Cost ratio
1.0
5.5

Power converter

2.9

Induction machine

1.3

Ball bearings

2.6

Other components

5.0

Total cost

18.2

confirmed that the proposed system is fabricatedapproximately $8000 except for manufacturing cost. In future
work, the optimal design method of the flywheel considering
the processing cost and the component cost is established.
ACKNOWLEDGEMENT
A part of this study was supported by industrial technology
grant program in 2011 from new energy and industrial
technology development organization (NEDO) of Japan.
REFERENCES

2

Discharged Energy

Pw
Pem

1000
2000
Rotation Speed[r/min]

3

1

Pf

100

Power[kW]Loss[W]

Stored Energy

4

400

0

1

Fig. 10. Analysis of the efficiency of energy storage when therotation speed of flywheel is increased from 2700 r/min to 3315
r/min.
6500

200

Electrical Loss

2

0
2700

Copper Loss

Fig. 8. Loss analysis results at the rated energy storage. In theexperiment, the steady rotation speed is 3315 r/min and the pressureof the vacuum case is 500 Pa.

Mechanical
Loss

3

Power[kW]600

Loss[W]

4

Magnetic Fluid
Seal Loss
Windage Loss

700

0
3315

3195

3075
2955
Rotation Speed[r/min]

2835

2715

Fig. 11. Analysis of the efficiency of energy discharge when therotation speed of flywheel is decreased from 3315 r/min to 2700
r/min.
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