IEEJ Journal of Industry ApplicationsVol.10 No.6 pp.638–642 DOI: 10.1541/ieejjia.20013374

Paper

Self-Inertia-Varying Fixed-Speed Flywheel Energy Storage System

Takumi Yamamoto∗ Non-member, Junji Kondoh∗a)Member

(Manuscript received Dec. 28, 2020, revised April 6, 2021)J-STAGE Advance published date : June 11, 2021

Flywheel energy storage systems (FESSs) store kinetic energy corresponding to the rotation of an object as Jω2/2,where J is the moment of inertia, and ω is the angular rotation speed. Conventional FESSs implement charging anddischarging by varying ω. In contrast, the authors have proposed a fixed-speed FESS that implements charging anddischarging by varying not ω but J. However, the net power output in the discharge operation for a fixed-speed FESSwas not positive owing to the low efficiency of the mechanism of varying J. This paper reports on the prototype de-velopment of a self-inertia-varying fixed-speed FESS that varies J by using the rotational inertia force of the flywheelitself. In the prototype test, actual charging and discharging operations were demonstrated, and a net mechanical powergeneration was observed during the discharge operation.

Keywords: fixed speed, flywheel energy storage system, induction machine, variable inertia

1. Introduction

In recent years, renewable energy sources, such as solarand wind power, have increasingly been used in various do-mains (2). However, unstable output power is an inherent lim-itation in renewable energy power generation. The output ofsolar power resources often fluctuates under cloudy condi-tions. In the case of wind power, the output power is pro-portional to the cube of the wind speed, and thus, even aslight change in wind speed considerably influences the out-put (3). To ensure that the frequency of the power system re-mains constant, it is necessary to realize a balance betweenpower supply and demand. Nevertheless, the fluctuation ofthe power output from multiple renewable energy sourcesmay result in a severe deviation of the grid frequency from thenominal value. To realize grid connections, power conversionsystems and asynchronous generators or converters are usedin solar and wind power generation, respectively. However,these elements cannot induce a large mechanical inertia in thegrid similar to that induced by large synchronous generatorsand axially connected turbines, which are used in large-scalehydro, thermal, and nuclear power plants. In such situations,when the share of renewable power installations increases inthe grid, the rate of change of frequency may also increase,which is undesirable (3) (4).

These problems can likely be subdued by installing energystorage systems, such as pumped hydropower systems, chem-ical batteries, and flywheel energy storage systems (FESSs).These systems are selected based on their discharge timeand discharge capacity (5). Among such systems, pumped

This paper is based on Reference (1), which published in theICEMS2020 (2020) c©2020 IEEJ.

a) Correspondence to: Junji Kondoh. E-mail: j.kondoh@rs.tus.ac.jp∗ Department of Electrical Engineering, Tokyo University of Sci-

ence2641, Yamazaki, Noda, Chiba 278-8510, Japan

hydropower systems have been widely applied but have notdeveloped considerably in recent years. Chemical batteries,such as NaS batteries and lead-acid batteries are easy to in-stall as new equipment and can be expanded in less construc-tion time than pumped hydropower systems. However, thesesystems are expensive and have drawbacks in terms of us-age of harmful and hazardous chemical materials (6) and shortcharge–discharge cycles.

Considering these aspects, this study focuses on FESSs. AFESS stores and converts electrical energy into kinetic energy(Jω2/2, where J is the moment of inertia, and ω is the angu-lar rotation speed) through a rotating body. The FESSs do notinclude a large amount of hazardous and/or harmful chemi-cals and can often be reused because their main componentsare carbon fiber, iron, and copper. It also has more charge-discharge cycle life than chemical batteries. There are appli-cation examples where FESSs are installed as a solution toshort-cycle fluctuations because of its long charge-dischargecycle life, and experimental results showed that FESS is ef-fective for this (7).

A typical FESS is connected to the grid through a variable-frequency converter to enable charging and discharging bychanging ω. However, this configuration has two main draw-backs:

1. Capital cost: the total cost of a motor/generator anda machine-side converter, which converts the variablevoltage and variable frequency output to direct current(DC), is estimated at $200/kW. Moreover, the con-verter must convert the DC to alternating current (AC)with a commercial grid frequency (50 or 60 Hz). Thecost of the total power conversion system is estimatedto be $300/kW (8). Thus, the cost ratio of the powerelectronic interface in the total power conversion sys-tem is estimated at approximately 2/3 in the case of theback-to-back configuration.

2. Vulnerability to short-time overcurrent: a motor canwithstand an overcurrent for several minutes because

c© 2021 The Institute of Electrical Engineers of Japan. 638

Self-Inertia-Varying Fixed-Speed FESS（Takumi Yamamoto et al.）

Table 1. Flywheel specifications

of its large overall heat capacity. In contrast, semicon-ductors can only withstand a current up to twice therated current for short periods of time, such as mil-liseconds or microseconds.

To address these problems, a fixed-speed FESS was pro-posed to eliminate the power electronic interface and connectthe generator/motor to the commercial grid directly. It imple-ments the charging and discharging operations by changingJ instead of ω. A previously developed prototype machine (9)

used an electric winch with a DC motor to change J; how-ever, the efficiency of the DC motor to convert the electricalinput to mechanical output was less than 50%, and the netdischarge power was not positive. Therefore, in this work,the prototype machine was modified to change J using therotational inertia torque of the flywheel instead of using anelectric winch to make it positive as the net discharge power.

2. Modified Prototype

Table 1 lists the design parameters and the symbols of themodified prototype, and Fig. 1 shows a photograph of themodified prototype. Figure 2 presents the operation mech-anism and definitions of the directions of the force, power,and energy. In Fig. 2, the part shaded in gray rotate. Thatis to say, the collar has both rotating and non-rotating parts,retained through bearings.

The geared induction motor/generator (Oriental Motor5IK90GU-SF) is connected to a three-phase AC power sourcewithout any power electronic interface. The motor and fly-wheel are connected coaxially across the torque meter. Theflywheel charges or discharges the rotational kinetic energyby extending or contracting, respectively, the turning radiusto change J as the movable collar correspondingly moves upor down axially. The collar is connected to the ball screw as-sembly (NSK HSS3205N1D0950/P) by two rods, and eachrod is equipped with a load cell to measure the tensile force.On the top and below the bottom of the screw shaft, an elec-tromagnetic clutch (SINFONIA JCC-2.5) and electromag-netic brake (SINFONIA JB-2.5) are attached to rotate and fixthe screw shaft, respectively. The charge/discharge operationis implemented using the following process:2.1 The Initial State ensures that the movable col-

lar is at the bottom position, and the clutch and brake areswitched off and on, respectively, to fix the position of themovable collar. AC voltage is applied to the induction motorto rotate the flywheel.2.2 Charging is implemented by releasing the elec-

tromagnetic brake to let the rotation of the screw shaft andthen the axial movement of the ball nut free. The centrifugal

Fig. 1. Photograph of the prototype

Fig. 2. Configuration of a self-inertia-varying fixed-speed FESS

force expands the turning radius of the weights of the fly-wheel; thus, both the movable collar and the nut connectedto the movable collar by the two rods rise while rotating thescrew shaft, resulting in device charging. In this phase, themoment of inertia J increases from Jmin to J1, where J1 rep-resents the moment of inertia when the movable collar stopsat the position where the tensile and gravity forces applied onthe flyweights are balanced.2.3 Charging is Completed after the flywheel stored

sufficient kinetic energy, and the electromagnetic brake wasapplied to fix the screw shaft, thereby preventing the storedenergy from fluctuating.

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2.4 Discharging (J = J1 → Jmin) is implementedby releasing the electromagnetic brake and simultaneouslyapplying the electromagnetic clutch. The screw shaft is con-nected to the rotating shaft of the flywheel, causing the nutto go down, and the movable collar connected through thetwo rods is lowered simultaneously. Consequently, the turn-ing radius of the flywheel is reduced, and the stored energy isdischarged.

This FESS is not suitable for the applications to adjustcharge/discharge power following to a power reference in thecase of current configuration at least. This FESS is intendedfor such kind of application to discharge at maximum out-put power as much as possible in the event of large powerdropouts in the power system, which contribute to relieve thesupply-demand imbalance in the grid. In this case, fine ad-justment of charge/discharge power is not important.

3. Theoretical Analysis

A detailed theoretical analysis of the mechanism illustratedin Fig. 2 has been presented in (9), (10).

The energy Est stored in the flywheel can be expressed interms of the kinetic energy Ei (owing to the object rotation)and the potential energy Eg of the flyweights and movablecollar (resulting from the difference in vertical positions be-tween l1, θ1 and l2, θ2), where g is gravitational acceleration,as follows:

Ei =Jω2

2· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (1)

Eg = nmf g(cos θ1 − cos θ2) + mcg(l1 − l2) · · · · · · · · (2)

Est = Ei + Eg · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (3)

The energy Ec exerted on the flywheel by the inertia con-troller can be expressed as

Ec =

∫ t1

t0

Fzdldt

dt �p∑

k=1

(Fzk−1 + Fzk

2× (lk−1 − lk)

)

· · · · · · · · · · · · · · · · · · · · (4)

where t0 and t1 denote the times at which the vertical move-ment starts and ends, respectively, and p is the number of datapoints recorded during the charging and discharging opera-tions, and Fz is the total tensile force of the two rods at vari-able inertia mechanism. The right-hand side of Equation (4)is considered for data processing.

If the energy Em is assumed to be transmitted to the ACpower lines through the motor/generator, it can be expressedas follows:

Em = −ΔEst + Ec · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (5)

According to this relation, if the change in the potentialenergy Eg is negligible, and the variable inertia mechanism isimplemented through an external force, the following ratio isobtained theoretically (11):

Ec : −ΔEst : Em = 1 : 1 : 2 · · · · · · · · · · · · · · · · · · · · · · (6)

In the variable inertia mechanism of the FESS, the energyEc to operate the variable inertia mechanism is provided bythe rotational inertia torque of the flywheel in the dischargemode. Thus, the net energy En

m ≡ Em − Ec is the output from

the flywheel. If the friction loss is ignored, Equations (5) and(6) can be redefined as Equations (7) and (8), respectively.

Enm = −ΔEst · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (7)

Ec : −ΔEst : Enm = 1 : 1 : 1 · · · · · · · · · · · · · · · · · · · · · · (8)

4. Experiment and Analysis

Table 2 summarizes the instruments, measurement points,and targets used in the experiment. To prepare for the exper-iment, the motor was turned on, as described in the previoussection, and the flywheel was charged (J = J1). In the ex-periment, the flywheel was first discharged and subsequentlycharged until the rotation speed reached a constant value. Thereference point at distance L was set as the lowest point (dis-charge state) of the movable collar. The operational resultsare shown in Fig. 3. To eliminate the influence of noise andenhance the clarity of the graph, after performing the calcu-lation using the data from the oscilloscope, the moving av-erages for the position L, axial force Fz, angular velocity ω,and torque τ were calculated with the two previous and sub-sequent data points. The machine output Pm was calculatedas Pm = ωτ, while the power output from the flywheel to-ward the motor/generator was considered positive. The fly-wheel discharged and charged energy Est at t = 5–9.5 s and t= 17.8–49.9 s, respectively. In the following subsections, wediscuss the transitions observed in Fig. 3.4.1 Identification of Full Energy Storage (t = 0–5 s).Figure 3(b) shows that the rotation speed was approxi-

mately 470 rpm, and the slip of the induction motor was s= 0.06. The speed was lower than the electrical synchronousrotation speed of 500 rpm, which indicates that the FESS op-erated as an electric load. Figure 3(c) shows the electrical loss

Table 2. Specifications of measurement instruments

Fig. 3. Experiment results

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Self-Inertia-Varying Fixed-Speed FESS（Takumi Yamamoto et al.）

Table 3. Results of the energy balance analysis

during idling. The loss of −Pme = Pidl = 100 W included theloss of the bearings, windage loss in the flywheel, iron andcopper losses in the motor, and friction loss in the reductiongear.4.2 Discharge Operation (t = 5–9.5 s). After the

electro-magnetic clutch of the flywheel was switched on, Ldecreased, as shown in Fig. 3(a), and the flywheel shifted tothe discharge mode. During this period, the rotational speedexceeded the synchronous speed and reached 504 rpm, andthe torque turned to a positive value of at least 0.24 Nm. Theslip at this speed was s = −0.008, which indicated that the in-duction machine acted as a generator. Figure 3(c) shows thatthe maximum output of the mechanical output Pm was 10 W,indicating that the flywheel discharged the mechanical outputPm. However, the maximum electrical output Pme was−25 W.This finding indicates that no discharge occurred on the grid,likely because of the no-load loss in the induction machine.The actual no-load loss of the induction machine was 35 Wat 200 V. In other words, if no-load loss could be eliminated,an electrical output of 10 W is expected to be generated.4.3 Idling with Slight Energy Storage (t = 9.5–17.8 s).At this time, the flywheel was idling with only a small

amount of energy storage. As shown in Fig. 3, the flywheelwas in a transient state immediately after the discharge oper-ation; however, it settled to a constant state soon afterward.4.4 Charging Operation (t = 17.8–49.9 s). After the

brake of the screw shaft was turned off, the nut connectedto the movable collar rose because of the centrifugal forceon the flyweights. Figure 3(a) shows that the nut positionL moved upward. Moreover, as shown in Figs. 3(b) and (c),once the nut rapidly moved upward, which made the abso-lute value of Pm high, its position gradually became constantsubsequently.

5. Discussion

Because the developed device is a rotating machine, it in-volves losses such as windage and bearing losses. Accordingto the Pm at the idling state, as shown in Fig. 3(c), the averagewindage and bearing losses in the mechanical power were ap-proximately 55 W at 470 rpm. Accordingly, the loss in torquewas 1.11 Nm. Furthermore, the mechanical loss during theoperation of the variable inertia mechanism was 45 W (12),and the friction torque in the mechanism was 0.91 Nm. Ac-cordingly, the total torque loss was 2.01 Nm in the dischargemode. Consequently, when the rotation speed was 500 rpmduring the discharge operation, the loss was estimated to be(1.11+ 0.91)× 500× (2π/60) = 106 W under the assumptionof constant torque. The experimental energy balance duringcharging/discharging (in which the influence of these lossesis corrected) and the theoretical ones are listed in Table 3. Inthe charging mode, En

m after correction for the losses is 390 J,whereas the theoretical value of En

m is 295 J. This energydifference likely occurs because of the overestimation of the

energy losses. This difference in energy is considered to bean overestimation of the loss of approximately 20 W. Anothertorque meter should be installed between the variable inertiamechanism and the flywheel in the developed prototype tomeasure the frictional torque in the variable inertia mecha-nism directly. In this study, the frictional torque and energyconsumption in the inertia controller were calculated usingEquation (9) to convert the ball screw assembly torque intothrust (13).

Fz =2πητ

R· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (9)

Here, the transmission efficiency of ball screw η is set as0.96, and the lead length R is 5 mm. Fz denotes the thrustpertaining to the tensile force.

Table 3 indicates that the energy ratio during the chargingoperation, if En

m = −Est, is as follows:

Ec : −ΔEst : Enm = 1 : 1.39 : 1.39 · · · · · · · · · · · · · · · (10)

Furthermore, the energy ratio during the discharging oper-ation, if En

m = −ΔEst, is expressed as follows:

Ec : −ΔEst : Enm = 1 : 0.94 : 0.94 · · · · · · · · · · · · · · · (11)

Equations (10) and (11) are close to the theoretical equa-tion (8).

6. Conclusion

This paper reports on the development and charge anddischarge operational testing of a self-inertia-varying fixed-speed FESS. The experimental results demonstrated that aself-inertia-varying fixed-speed FESS can be discharged andcharged by mechanically changing the moment of inertiathrough its own rotational inertia force and centrifugal force,respectively. In addition, the net power output was achievedmechanically in the discharge mode.

AcknowledgmentThis work was supported by JSPS KAKENHI Grant Num-

ber JP18K04108.

References

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NomenclatureEst Total energy stored in the FESS [J]Ei Kinetic energy stored in the FESS [J]Eg Gravitational potential energy stored in the FESS

[J]Ec Mechanical Energy to work the inertia controller

[J]Em Output energy from FESS to the grid [J]En

m Net energy output from the FESS to the grid [J]Pm Mechanical output power applied by the flywheel

to motor/generator [W]Pme Electrical output power from motor/generator to

grid [W]J Moment of inertia of the flywheel [kg ·m2]Jmin Minimum value of J [kg ·m2]Jmax Maximum value of J [kg ·m2]L Axial position of the movable collar [m]ω Angular frequency of the rotational parts of the

FESS [rad/s]τ Torque produced by the flywheel [Nm]

n Number of flyweightsl Length of a main arm [m]mf Mass of a flyweight [kg]mc Mass of a movable collar [kg]g Gravitational acceleration [m/s2]ΔLmax Maximum displacement of the movable collar and

nut [m]θ Angle of a main arm against the main shaft [rad]Fz Upward force acting on the movable collar and nut

[N]η Transmission efficiency of ball screwR Lead length of ball screw shaft [m]

Takumi Yamamoto (Non-member) received B.E. degree in depart-ment of electrical engineering from Tokyo Universityof Science, Chiba, Japan in 2019. In 2019, he is acandidate of the M.E. degree in electrical engineer-ing from Tokyo University of Science. His researchinterests are in flywheel energy storage systems.

Junji Kondoh (Member) received D.E. degree from Tokyo Instituteof Technology, Tokyo, Japan in 1998. He then joinedthe Electrotechnical Laboratory (ETL), which reor-ganized into the National Institute of Advanced In-dustrial Science and Technology (AIST), Tsukuba,Japan, where he was a senior research scientist. Hehas been an associate professor in Tokyo Univer-sity of Science since 2013. Recently, he has beenengaged in research on electric power systems withlarge amounts of renewable energy.

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