Flywheel Generator with Switched Reluctance Machine

L.G.B. Rolim, A.C. Ferreira, G. G. Sotelo and R. de Andrade Jr.Department of Electrical Engineering

U.F.R.J. - Federal University of Rio de JaneiroP.O.Box 68504, 21945-970 - Rio de Janeiro - Brazil

E-mails: rolim@dee.ufrj.br, ferreira@coep.ufrj.br, sotelo@coe.ufrj.br, randrade@dee.ufrj.br

Abstract — This paper presents a flywheel energy storagesystem, which uses a switched reluctance motor/generator. Itis shown how this device can be used either together with aDVR or alone in order to attenuate the effects of voltage sagsand short interruptions. In order to improve the systemefficiency, some design alternatives are presented. Finiteelements analyses results, validated against laboratorymeasurements, indicate the advantages of a suitable choice offerromagnetic material. The implementation of the controlsystem was simulated with a commercial program. Theenergy loss, due friction, will be reduced using asuperconducting magnetic bearing.

1. Introduction

The current energy scenario in Brazil is calling for aglobal effort towards a more efficient use of electricalenergy, as well as for a global improvement in the qualityof its delivery. However, as budgets are limited, anacceptable alternative is the offering of different levels ofsupply quality, according to the concept of Custom Power,proposed by Hingorani in [1]. For the practicalimplementation of this concept, several types of equipmentcan be used, as described in [2]. Some of these equipmentsmay employ some sort of energy storage device such asbatteries or flywheels [3].

The above reasons have motivated the launch of a jointproject between the Federal University of Rio de Janeiro(UFRJ) and a local energy distribution company,concerning the development of a flywheel-based energystorage device for custom power equipments. Two majorpotential applications are under consideration for furtherdevelopment: the compensation of voltage sags and ashort-term uninterruptible power supply, to provide ride-through capability to critical loads under momentary faultconditions.

In the case of voltage sag compensation, the mostappropriate configuration would be the series connection,between the bus that must have a controlled voltage andthe rest of the system. Devices that operate according tothis principle are being currently commercialized under thetrademark Dynamic Voltage Restorer (DVR) [4]. In a DVRwithout energy storage, the active power that is requiredfor voltage control must be taken in real time from thesame grid where the device is connected. Some authorspropose the use of a diode rectifier feeding a filtercapacitor in a voltage dc link to solve this problem.However, this solution can lead to situations of voltagecollapse, because more energy is drawn from the system, atthe same instant and just from the point where the voltagesag occurs. With a flywheel energy storage system these

situations can be avoided, because energy can be drawnfrom the grid in a smooth way during periods of lightsystem loading, causing minimum voltage drop while theflywheel is accelerated.

One significant aspect of the energy storage device isconcerned to the electromechanical energy conversionbetween the flywheel and the electrical system to which itis connected. In this regard, it can be very advantageous ifone and the same electrical machine is used not only toaccelerate the flywheel when it is absorbing energy fromthe grid, but also for returning energy to the grid when theflywheel should operate as a generator. In such a high-speed flywheel system, the mechanical and magneticstresses imposed to the driving electrical machine are veryhigh. For these reasons, the switched reluctance machine(SRM) can be pointed out as a good potential candidate forthe intended application. There are several references inthe literature [5-7] describing the application of SRMs as areversible starter/generators for direct coupling to the shaftof aircraft engines. The main requirements for this kind ofapplication are:

- Operation at very wide speed ranges from zero up toseveral ten thousand rpm;

- Fault tolerance, in order to achieve a high reliability.Both requirements can be fulfilled by the SRM and arealso necessary for applications in high-speed flywheelenergy storage systems.The aim of this paper is twofold. First a flywheel energystorage system will be presented using a SRM basedmotor-generator. Then it will be shown how the systemperformance can be improved with reduction of the corelosses and using a superconducting magnetic bearing.

2. Switched Reluctance Machine

The operation of a switched reluctance machine (SRM)is based on the principle of minimal reluctance. When thecoil of some phase is excited, forces are developed over themagnetic circuit that tend to bring it to the position wherethe reluctance reaches a minimum, as seen from theenergized coil. At this position coil inductance reaches amaximum. If this phase is switched off ant the next phaseis switched on slightly before this position is reached,continuous movement of the rotor can be achieved. Figure1 shows cutaways view of an SRM with six stator polesand four rotor poles (6/4 configuration), and figure 2shows the reference frame which has been used throughoutthis work.

Symmetry of the magnetic circuit allows for nearly nullmutual flux linkage, even under saturated conditions. As aresult, the contribution of each phase for torque production

is mainly defined by the self-inductance profile of thatphase. Figure 3 shows a family of inductance profilecurves for one phase, which have been calculated as afunction of rotor position for different values of phasecurrent. The calculations have been carried out with theANSYS [8] package, which uses the finite elementmethod (FEM). The electromagnetic torque produced byone single coil is given by equation (1), where Te is thetorque, θr is the rotor angular position, λ is the total fluxlinked to the coil and i is the coil current.

∂∂= ∫

i

rr

re ,i)diλ(θθ

,i)(θT0

A. Dynamic Modeling of the SRM

Both relationships Te (θr , i) and λ(θr , i) are stronglynon-linear, a fact that makes it difficult to develop ananalytical mathematical model for the SRM. Thus insteadof trying to obtain such an analytical model, themethodology adopted in this work was to use tabulateddata for Te (θr , i) and λ(θr , i), which may have beenobtained off-line by means of static measurements or FEMcomputations, over a range of values wide enough to coverany situation that may occur within given simulationlimits. The tabulated data is then used directly in thesolution of the electrical and mechanical dynamicequations (2) and (3), doing online linear interpolation toobtain intermediate values when needed.

dtidir r

s),(V θλ+⋅=

mer TT

dtdJ −=⋅ 2

2θ

In equation (2), V is the coil terminal voltage, rs is thecoil resistance and i is the current flowing through the coil.In equation (3), J is the combined moment of inertia (SRMrotor plus flywheel), Te is the electromagnetic torque andTm is the opposing torque caused by mechanical losses.

Equations (2) and (3) have been used in digitalcomputer simulations to estimate the behavior of theproposed system both under dynamic and steady-stateconditions.

Figure 1. SRM with 6/4 configuration,

Figure 2. Reference frame

-45 -30 -15 0 15 30 450

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Rotor angular position (degres)

One

fase

Indu

tanc

e (H

enry

)

Current increasing

Figure 3. Phase Inductance for current varying from 1 A to 10 A in stepsof 1A.

3. Flywheel Energy Storage System

The main purpose of a flywheel device is to accumulaterotational kinetic energy, which can then be recovered tothe electric system whenever is required. Many examplesof flywheel-based energy storage systems are described inthe literature, but they can be generally divided in twocategories: low-speed, high inertia devices and high-speed,low inertia ones. In any case, the fundamental relationshipbetween angular speed and stored energy is given byequation (4).

2

21 JωEc =

An important goal of this work is to describe how anSRM should be controlled, in order to be applied in a high-speed flywheel energy storage device. For that purpose, adynamic simulation model has been written for thesoftware package Simulink/Matlab, according to theconsiderations presented in section 2.1. Simulation resultsare presented in figures 4 and 5, showing the dynamicresponse for a linear speed reference change from 2000rpmto 1000rpm. Two different results are presented, whichcorrespond to speed variations in time intervals of 0.1s and0.5s. Figure 4 shows the actual shaft speed, while the totalpower that is absorbed from the dc link is shown in figure5. As expected, if the speed change occurs in a shorter timeinterval, a correspondingly higher power can be transferredto the grid. On the other hand, if the power transfer is lessintense, it can be sustained for a longer period. These arevery interesting characteristics, indicating that the devicecan be used with different strategies, e.g. to supply a small

(1)

(4)

(2)

(3)

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2800

1000

1200

1400

1600

1800

2000

2200

Time(s)

Spee

d(rp

m)

Figure 4. Imposed speed variation.

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2-200

-150

-100

-50

0

50

Time(s)

Pow

er (W

)

Figure 5. Electric power

amount of critical loads during a power failure, until anauxiliary generator starts to operate, or to compensate largeand rapid disturbances in the supply system.

5. Control of the SRM

Figure 6 shows the schematic diagram for one phase ofthe converter that is used to drive the SRM. Due to theoperating principle of the SRM (minimum reluctance), thealgebraic signal of the induced torque does not depend onthe sense of current flow through the phase windings.Actually the torque signal depends only on the relativeposition between rotor and stator poles, at a given instantwhen current is flowing. As depicted in figure 7, if currentis flowing in a phase coil before a rotor pole pair getsaligned to the coil poles (along the sense of rotation), theinduced torque will be in the same sense as the rotation(motoring torque). Conversely, if current flows after thealigned position has been overtaken, braking or generatingtorque will be produced. Therefore, the current controllermust ensure the current pulses applied to each phase occurbefore or after the aligned position, according to thealgebraic signal of the current reference. The pulseamplitude should be thus controlled only according to theabsolute value of the current reference.The flywheel shaft speed must be controlled according tothe instantaneous active and reactive power demanded bythe grid. In this work, the implementation of a two-stagecontrol strategy for the flywheel shaft speed is proposed.

Both stages are coupled through a common state variable:the voltage across the dc link capacitor.

The main idea is to control the acceleration of the SRMin proportion to the mismatch between the dc linkcapacitor voltage and a given reference value. If no powerflows between the flywheel and the grid, the dc linkcapacitor voltage then remains regulated at its nominalvalue. However, if the grid demands active power, thecommand will act directly upon the grid interfaceconverter, adjusting its voltage or current, according to thekind of connection (series or shunt).

6. Proposed Applications

In this section, two possible applications of the SRMflywheel energy storage device are presented.

A. Uninterruptible Power Supply (UPS)

The use of an SRM flywheel as UPS is illustrated infigure 8, where the main system components can beidentified, namely: bi-directional power electronicconverter, switched reluctance machine, flywheel,superconducting axial bearing and control circuit.Depending on the voltage level at the grid side, a step-down transformer may be added between converter 1 andthe system bus.

CfVd

Figure 6. Electric diagram for one phase converter

θ

L

0

θ

θ

θ

θ

(forward)

control signals:

motoring

motoring

braking

braking (reverse)

sense of rotation:

Figura 8. Operation modes of a SRM.

System 1 2load

ControlLoop

Converter 1

SwitchedReluctance

Machine

Converter 2

Flywheel

YBCOSuperconductor

Figure 8. Operation as a UPS.

System 1 2

Control

Converter 1 Converter 2

SRM

Flywheel

SuperconductNdFeBM t

Load3

Figure 9. Operation as a DVR.

B. Dynamic Voltage Restorer with energy storage

The schematic diagram of a DVR system with flywheelenergy storage is presented in figure 9. The operation ofthis system is now based on adding a compensating voltagein series with the grid voltage.

4. Improving system performance

According to equation (4), it can be seen that muchmore additional energy can be stored in a flywheel if itsspeed is increased while keeping its mass constant than ifits mass is increased while keeping its speed constant.However, in high-speed operation many problems mayarise such as:

• increased energy loss due to the air resistance,• increased losses due to bearing friction,• increased magnetic losses due to higher frequency

of stator currents.• increased mechanical failure risk due the high rim

speedMagnetic losses can be reduced with an optimization of

machine design and careful selection of core material.Windage and friction losses may be reduced using a

magnetic bearing. This section will explore these twoissues.

A. Superconducting magnetic bearing

In order to decrease the air resistance, the flywheel systemwill be housed in a vacuum chamber, with a pressure lowerthem 1 µbar. The better way for minimize the friction lossis to use a non-contact bearing, like a magnetic bearing.The usual active magnetic bearing introduces an energyloss due the electric current dissipation, in the bearingcoils, and this maybe a relevant loss in the thrust bearing.The use of HTS (High Temperature Superconductors)magnetic bearings, mainly in the thrust bearing, allows avery low energy loss in the flywheel system. The newcomposite material, with wound carbon and glass fibersembedded in epoxy resin, allows rim speeds over 1 km/s[9].

The main SRM advantage is that there are no losses instand by mode, with no excitation current in the stator. But,the magnetic losses in the rotor have to be minimized inorder to avoid over heating. In a vacuum chamber the heattransfer is very poor, mainly by radiation and gasconduction, there are no convection. The low speedflywheel system avoid this problem, but the energy/massrelationship for the high speed flywheel make itcompetitive with the chemical batteries and another energystorage systems. The Kinetic Energy Storage System thatis being proposed is showed in figure 10. The system iscomposed of a composite flywheel, a SRM, a thrustSuperconducting Magnetic Bearing (SMB) and radialActive Magnetic Bearing (AMB). The AMB plays a role inthe system stabilization when the speed is increasedthroughout the critical speeds. The critical speeds are thespeeds where the system reaches a normal vibration moderesonance. The AMB will work only when it is necessary,not all the time.

The superconducting magnetic bearing will be preparedwith seeded melt textured YBCO (YBa2Cu3O7-δ) blocksand NdFeB permanent magnets. The YBCO blocks willwork at the boiling liquid nitrogen temperature (77 K) andwill be field cooled in order to optimize the levitation forceand the stiffness of the SMB [10].

PermanentMagnets

YBCOSuperconductors

StatorRotor

VacuumChamber

Flywheel

ActiveMagneticBearing

NdFeBMagnets

Figure 10. Flywheel energy storage system with superconductingmagnetic bearing and SRM.

B. Core losses

A simple method to estimate the iron loss in electricalmachines has been presented by Atallah et al [11], and isproposed to be applied to SRM in the present paper.

The total iron loss (Pt) may be calculated by the sum ofhysteresis loss component (Ph), eddy current component(Pc) and anomalous loss or excess loss component (Pexc) asshown if equation (5 )

[W/kg]dt t

B(t)fk

dttB

12δfd σfBkP

5.1

e

22αmht

∫

∫

∂∂

+

∂∂+=

(5)

where kh and α are the hysteresis loss constants, f is thefrequency, Bm is the peak flux density, σ is the materialconductivity, d is the lamination thickness, δ is the materialmass density and ke is the excess loss constant. Equation(5) relies on the calculation of the magnetic flux density inevery section of the machine. For this purpose, this workuses a commercial finite element program [8]. The ironloss density is calculated on an element-by-element basisin the way described by Mueller et al. [12]. Two magneticmaterials are being considered, an standard FeSi steel usedin machines and an amorphous magnetic alloy which has ahigher magnetic permeability. The losses characteristics ofboth material are shown in figure 11. From those curvesthe various constants of equation (5) can be derived.

The effect of the material on core losses can be seen inTable I, which shows calculated iron losses for a designconsidering 0.5 mm laminations of FeSi and another with0.022 mm laminations of amorphous material. Themachine is running at 3600 rpm. As expected theamorphous material yields a much lower value for ironlosses. The finite element analysis is also a useful toll inorder to identify regions of high loss density as can be seenin figure 12, which loss density distribution over a machinecross section.

0.02.04.06.08.0

FeSi

Bm(T)

Iron

loss

(W/k

g)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.80.00.10.20.30.4

Amorphous

Figure 11: Iron loss data for FeSi and amorphous material

TABLE I – IRON LOSSES COMPARISON FOR TWO MAGNETIC MATERIALSGeometry A Geometry B

FeSi 67.6 W 48.9 WAmorphous 1.26 W 0.95 W

The effect of material on the performance of themachine can be seen in figure 13, which shows torquecalculations using the Finite Element Method ( FEM ) forboth machines. The machine is supposed to be running at3600 rpm and is excited with phase current of 2 A. It canbe seen that the amorphous alloy also gives a higher torquefor the same electric loading.

The machine performance can also be improved with anoptimization of its design. This can be seen in Table I,which presents calculated results for an alternative designwhere the stator poles are wider at the bottom as shown inFigure 14. Table I shows that this geometry gives areduction in the iron losses. However, as can be seen inFigure 15, this geometry results in a slight decrease on theavailable torque. A design optimization, which takes botheffects into account, is underway and will be presented in afuture work.

Figure 12. Loss density distribution

-40 -30 -20 -10 0 10 20 30 40-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Rotor Angular Position (degrees)

Ele

ctric

al T

orqu

e (N

m)

ExperimentalFEM for FeSiFEM for Amorphous

Figura 13. Calculated and measured torque.

Figure 14: Poles geometries

0 0.025 0.05 0.075 0.1 0.1250.08

0.1

0.12

0.14

0.16

0.18

0.2

Time(s)

Torq

ue (N

m)

FeSi Geometry AFeSi Geometry B

Figure 15: Torque for different geometries

7. Conclusions

Due to its elevated robustness and reliability, The SRMseems to be a good choice as a driving machine forflywheel energy storage devices. This work has presentedthe conception of an SRM flywheel system, consideringmany design aspects such as material choice, mathematicalmodeling and control strategy. Two possible applicationshave been described, where the use of such a kineticenergy storage system can contribute to the enhancementof power quality in electric energy systems.

Acknowledgement

The authors are grateful to CAPES, CNPq and FUJB forthe financial support.

References

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[3] G. Tanneau e D. Boudou, “Custom Power Interface”,Proceedings da CIRED2001, pp. 2.48, June 2001.

[4] Woodley, N. H., Sezi, T. (2001). New Design DynamicVoltage Restorer (DVRTM MV) Systems, IPEC’01Conference,Singapore, 17-19.

[5] C. A. Ferreira, S. R. Jones, W. S. Heglund and W. D. Jones,“Detailed Study of a 30-kW Switched ReluctanceStarter/Generator for a Gas Turbine Engine Application”,IEEE Transactions on Industry Applications 31, 553-561(1995)

[6] A. V. Radun, C. A. Ferreira and E. Richter, “Two-ChannelSwitched Reluctance Starter/Generator Results”, IEEETransactions on Industry Applications 34, 1026-1034 (1998)

[7] M. E. Elbuluk, M. D. Kankam, “Potential Starter/GeneratorTechnologies for Future Aerospace Application”, IEEE AESSystems Magazine, October 1996, pp. 17-24.

[8] Ansys Users Manual 2000[9] R. Hebner, J. Beno and A. Walls, “Flywheel Batteries Come

Around Again”, IEEE Spectrum, pp. 46-51, April 2002.[10] R. de Andrade Jr., A. Ripper, D. F. B. David and R.

Nicolsky, “Stiffness and damping of an axial superconductingmagnetic bearing”, Physica C 341-348, 2607-2608 (2000).

[11] K. Atallah, Z.Q. Zhu and H.D. Howe, “The Prediction of IronLosses in Brushless Permanent Magnet D.C. Motor,International Conference On Electrical Machines,Manchester. U.K., pp. 814-818, 1992

[12] M.A. Mueller, S. Williamson, T.J. Flack, K. Atallah, B.Baholo, D. Howe and P. Mellor. “Calculation of Iron Lossesfrom Time-stepped Finite-element models of Cage InductionMachines.”, 7th IEE Electrical Machines and DrivesConference, Durham, pp 77-81, 1995