Low-Cost Flywheel Energy Storage for Mitigating the Variability of

Renewable Power Generation

Investigators

The University of Texas at Austin

Dr. Robert Hebner, Director/Principal Investigator, Center for Electromechanics;

Dr. Siddharth Pratap, Senior Research Scientist, Center for Electromechanics;

Mr. Michael Lewis, Program Manager, Center for Electromechanics;

Mr. Clay Hearn, Research Engineer/Graduate Researcher, Center for Electromechanics.

Abstract

In the past year, the researchers at the Center for Electromechanics at The University

of Texas at Austin (UT-CEM) and the Nanotech Institute at The University of Texas at

Dallas (UTD) continued research efforts on improved flywheel designs and flywheel

materials to meet energy storage requirements for the grid.

UT-CEM’s efforts focused on developing design codes and methods for incorporating

high temperature super conducting (HTSC) materials into flywheel bearing designs. The

driving principal behind HTSC bearings is the stable levitation of permanent magnet

material due to induced pinning currents in bulk superconductors. Such bearings can

provide low loss rates of up to 0.1% stored energy per hour, which would make diurnal

energy storage applications with flywheels practical. This development has resulted in

lumped parameter models that were proven and verified against laboratory experiments

and finite element models. The lumped parameter methodology will aid in the design

and characterization of HTSC bearings for high-speed flywheel rotors.

In upcoming work, UT-CEM will use their design code and material results from UT-

Dallas to study the potential impact of these advanced technologies for flywheel energy

storage. It is expected that the use of HTSC bearings, along with advanced carbon nano-

tube materials, being developed by our project partners at UT-Dallas Nanotech Institute,

will enable diurnal flywheel energy storage systems.

Introduction

The purpose of the proposed research and development program is to investigate

game-changing technologies and materials to advanced flywheel kinetic energy storage

for utility grid applications. The goal is to store 50% of the grid capacity within 50 years.

Since flywheels are mechanical energy storage devices, very high cycle lives, up to and

above 1 million cycles with proper design, can be achieved with little to no loss in

performance degradation.

Previous work at the University of Texas at Austin evaluated flywheel sizing

requirements for different locations within the utility grid. Typically, flywheels have

been used for high power - low energy storage applications such as frequency and voltage

regulation where energy storage devices with high cycle life are required [1]. For longer

term energy storage applications, flywheels suffer frictional losses which are due to

windage and bearings. Windage losses can be significantly reduced by operation at

vacuum levels below 1 mTorr, which are achievable for stationary grid utility

applications. Currently, most high performance flywheels operate with contactless active

magnetic bearings. Although there is no mechanical contact with these bearings,

magnetic hysteresis and eddy current generation in the laminations can still produce loss

rates of up to 5% stored energy per hour [2], [3].

High temperature superconducting (HTSC) bearings may provide a solution for

meeting long term energy storage requirements. The driving principal behind HTSC

bearings is the stable levitation of permanent magnet material due to induced pinning

currents in bulk superconductors. Such bearings can provide low loss rates of up to 0.1%

stored energy per hour, [4], [5], which would make diurnal energy storage applications

with flywheels practical. Although stable, the force-displacement interaction between a

permanent magnet and sub-critical superconductor is highly nonlinear and has a well

known hysteretic behavior. The University of Texas at Austin is developing lumped

parameter modeling techniques, which will aid in the design and characterization of

HTSC bearings for high-speed flywheel rotors.

Background

Currently there is a lack of resources in the literature for developing physics-based,

reduced-order models that can be used by engineers to design and control HTSC

bearings. These models should be able to predict the local bearing stiffness and dynamic

response. Finite element methods (FEM) can be used to very accurately model induced

currents within bulk superconductors and resulting forces, but these methods are

computationally expensive, especially at the beginning of a bearing design process where

multiple design iterations may be required.

The Critical State model, first proposed by Bean, [6], was one of the earlier low-order

methods for modeling the induced current distribution in a bulk superconductors. This

model assumes that the current flow in a superconducting region is either equal to zero or

the magnitude of the critical current density, , along with appropriate sign convention.

As the magnetic field around the bulk HTSC increases, the depth and area of current flow

through the bulk HTSC increases to shield in remaining area from the magnetic field.

The bulk HTSC is fully magnetized when all current is flowing at . The critical state

model has been utilized in finite element methods (FEM) based on Maxwell’s field

equations to determine field distribution and resulting forces [7]. Applied to FEM, the

critical state model is able to characterize the force-displacement hysteresis curves

observed in experimental studies.

The advanced mirror image model was first suggested by Kordyuk [8] to describe the

levitation interaction between a permanent magnet dipole and a bulk superconductor for

field cooling cases. Hull and Cansiz also expanded the advanced mirror image model to

include zero field cooling case, along with the field cooling case [9]. Magnetic dipoles

are used to represent all field sources with the mirror image models. Initially, a

permanent magnet is represented by a dipole positioned over a plane, defined as the top

surface of the bulk superconductor. When the superconductor is brought below the

critical temperature, two mirror image dipoles appear at opposite position of the HTSC

top plane. The first image is the frozen mirror image which represents the initial trapped

field in the bulk HTSC from field cooling and does not change position. The second

image is a diamagnetic image of the permanent magnet which mirrors the movement of

the initial magnetic dipole over the surface of the bulk HTSC. The diamagnetic image

represents the resistive force contribution of shielding currents as the dipole is moved

from the original field cooled position.

The advanced mirror image models are useful in quickly providing vertical and

translational stiffness estimates for reduced order rigid body models, but the presented

models are limited by simplifying the fields produced by a permanent magnet to a dipole

representation. These models also assume a perfect conductor and do not consider losses

or upper critical field limits which limit the critical current density of a bulk HTSC. By

excluding these losses, the mirror image models are unable to predict hysteresis effects

and other nonlinearities, which occur in the PM-bulk HTSC interaction.

Results

The University of Texas at Austin is developing physics based, lumped parameter

models which significantly reduce model order and computational time over FEM, but do

not sacrifice the nonlinear behavior and observed hysteretic properties of the interactions

between permanent magnets and bulk HTSC. Two sets of models have been produced,

one which assumes an axissymmetric arrangement between a permanent magnet and bulk

HTSC, and a second in which the magnet is allowed to translate in three dimensional

space. The former modeling technique is useful for determining bearing lifting capacity

and vertical dynamic response, while the latter may be used to estimate bearing

translational stiffness and may also be applied to high level rotor dynamic models.

Axissymmetric Model and Verification

For developing the axissymmetric model, the HTSC puck is modeled as discrete,

nested, superconducting filament rings shorted on themselves, as shown in Figure 1.

This methodology is an extension of the work presented by Davey et al. to evaluate

activation of bulk superconducting material by "flux-pumping" [10]. The filament rings

are each associated with flux linkage, , and current, , which is uniformly carried

across the ring cross sectional area, . By meshing the bulk superconductor with

multiple discrete filament rings, the current distribution through the material can be better

replicated by the model. As the exterior magnetic field starts to change, shielding

currents will be initially induced at the surfaces of the bulk HTSC. As the field continues

to change, more filament rings will become activated, and the current flow will increase

through the bulk material, as predicted by the Critical State model. Each filament current

loop will be affected by the change in exterior magnetic field, from the permanent

magnet, and the fields produced by the surrounding permanent magnets. In contrast to

the Critical State model, each filament current loop is subject to a highly non-linear

resistive loss in accordance with a power-law methodology, [11], [12], which saturates

current flow to the value of the critical current density, .

Figure 1: Schematic layout of axissymmetric model between permanent magnet and bulk

high temperature superconductor

Discrete current loops on the surface of the permanent magnet are used to represent

the equivalent surface currents and resulting magnetic fields in free space. Formulations

provided by Smythe, [13], can be used to determine the flux linkage and flux linkage

gradients between the magnetic fields produced by the surface currents and the filament

elements of the bulk superconductor. This model assumes the permanent magnet puck is

concentric to the bulk HTSC, which allows the use of simplifying assumptions.

For a permanent magnet located at position , moving with axial velocity , the

following set of dynamic equations can be formulated to describe axial motion and

induced currents within the bulk superconductor,

(1)

PM

HTSC

PM Surface Source Currents

HTSC Divided into discrete super-conducting rings

𝑝𝑚

The

terms within the equations are gyrator factors, which describe the magnetic-

mechanical energy, transfer between the permanent magnet movement and induced

currents via the flux linkage, . The inductance matrix for the meshed superconducting

rings, , is a symmetric matrix with self-inductance terms on the diagonal, and mutual

inductance terms on the off-diagonal.

To verify dynamic performance of the model, a test setup was constructed to evaluate

the response of the permanent magnet falling over a bulk HTSC. The purpose of this

drop test is to illicit a dynamic response from the system by means of a step input, where

the weight of the permanent magnet, and any additional mass, is quickly transferred to

the magnetic interaction between the permanent magnet and HTSC as described by the

proposed model.

A picture of the test setup is shown in Figure 2. A high strength N45 neodymium

magnet, with 38.1 mm OD x 6.4 mm ID x 12.7 mm H, is initially positioned over bulk

HTSC by a spacer bar. The bulk HTSC is YBa2Cu3O7 and measures 47.5 mm OD x 15

mm H. A composite-glass G-10 rod runs through the center of the PM to ensure that the

motion of the PM is in the vertical direction over the bulk HTSC, and remains centered.

A G-10 plate is also attached to the top of the PM to provide a measurement surface for

the IDEC MX1A-B12 laser displacement sensor. The permanent magnet with the G-10

plate had an initial weight of 117.8 g. Two additional blocks of beryllium copper were

added to the top of the magnet to bring the total mass to 520 g.

Spacer rods of varying height were used to set the initial height of the permanent

magnet over the bulk HTSC at room temperature. Once the position was set, liquid

nitrogen was added to the basin holding the bulk HTSC to bring the temperature down to

77 K. After the HTSC was successfully field cooled, the spacer bar initially supporting

the weight of the permanent magnet was removed to allow it to drop over the bulk HTSC.

The IDEC probe measured position which was recorded at 1000 Hz rate.

Figure 2: Dynamic drop test setup

Comparisons of model predictions and recorded test data were made by using the

proposed model (2) to simulate the same conditions of initial set height and loaded mass

as the tests. Due to the friction between the permanent magnet and G-10 guide rod, the

system had a damped response to the weight transfer. This mechanical friction was

added to the model as a combination of coulomb and viscous friction.

The bulk HTSC was modeled as 130 discrete superconducting rings. A critical

current density for the chemically pinned puck of 9.5 kA/cm2 was assumed, which was at

the low end of the manufacturer’s specifications. The permanent magnet had a measured

field strength of 0.4T and was modeled with 11 discrete current elements, each on the ID

and OD surfaces, which correspond to a coercive strength of 1030 kA/m.

Figure 3 shows a sample comparison between model prediction and experimental test

for drops of 25mm. The time-domain response, shown in the left pane of these figures,

shows the model tracks well to experimental results. The largest errors come from

inaccurate modeling of the friction between the magnet and guide rod, which was only

roughly estimated. A fast Fourier transform (FFT) was also performed to verify

oscillation frequency, which is shown in the right side of Figures 3. The FFT shows that

the model presented matches the frequency response and local stiffness of the system

relatively well.

PM and mass

HTSC

IDEC Position Probe

Guide Rod

Figure 3: Model and test comparison at set height of 25mm above HTSC. Model and

test both show frequency response of 7.81 Hz

This model technique is applicable to any configuration of permanent magnets and

HTSC in an axisymmetric frame. The effective axial spring rate and levitation forces can

be characterized with this model to determine bearing lift forces for a thrust and journal

bearing configurations.

Transverse Model and Verification

UT-CEM is using similar techniques to expand the axissymmetric modeling

methodology to three-dimensional movement of a permanent magnet of bulk

superconductors. This lumped parameter modeling methodology will help predict

transverse stiffness for advanced HTSC bearings. The proposed method models a single

bulk HTSC as a stacked array of individual overlapping HTSC discs which interacts with

the fields produced by the permanent magnet. The overlapping discs allow non-circular

currents to flow within the bulk HTSC material, and enable the use of lumped parameter

modeling techniques to better estimate hysteretic force behavior. The model assumes

each disc carries a uniformly distributed circulating current, which is induced by

movement of the PM. The end model order depends on the number of discs used to

represent the bulk HTSC, where each disc has a single degree of freedom. Figure 4

shows a bulk HTSC represented as proposed. The goal of this lumped parameter model

is to provide designers with a tool to estimate the nonlinear stiffness and hysteretic force

displacement relationship for small displacements which could be used in the design of

high temperature superconducting bearings.

Figure 4: Left: Proposed model of permanent magnet levitated over individual

overlapping superconductor discs. Right: Top view of overlapping discs.

In order to verify model performance, comparisons were made to experimental test

data to verify the force-displacement interaction due to the translational movement of a

permanent magnet over a bulk HTSC. For the transverse test, the bulk HTSC is placed in

a cryostat on a moveable platform below a permanent magnet. The magnet is held

stationary and force measurements are made via a load cell, as shown in Figure 7. A set

of bearings is included in-plane of the load cell to isolate directional force. The test setup

can be configured to measure translational force on the magnet with respect to

translational position, and vertical lifting force on the magnet with respect to translational

position.

Figure 5: Test apparatus to measure translational (as shown) and vertical force on a

permanent magnet with respect to translational motion of a bulk HTSC.

The tests were performed with a 47mm OD x 15mm H YBCO bulk superconductor.

The critical current density of the bulk superconductor was assumed to be 9 kA/cm2. An

N48 grade, neodymium magnet, which measured 3/4" (19mm) OD x 1/4" (6.4mm) ID x

3/4" H (19mm) was used. The field strength of the magnet at liquid nitrogen

Linear stepper motor4” stroke

Bulk HTSC

Cryostat

MoveablePlatform

Magnet

Load CellIsolationbearings

temperatures (77K) was measured at 0.4T on the surface and 0.28T at a 2mm gap from

the surface.

Using a fixed step 4th order Runge-Kutta solver with a time step of 0.5 ms, a solution

could be attained within 10 to 15 minutes on a standard laptop computer. Experimental

tests were performed with the magnet positioned at a 2mm height above the surface of

the bulk HTSC, and sweeps of +/- 20mm were performed over a period of 26 seconds.

Comparisons of lumped parameter model performance to translational and vertical force

measurements are shown in Figure 8. In these figures, Lumped Model 1, refers to model

performance with the original estimated critical current density and magnet strength of

760 kA/m. For a second pass, Lumped Model 2 was run using a magnet strength slightly

increased from 760 kA/m to 812 kA/m, and the critical current density was increased

from 9 kA/cm2 to 10 kA/cm

2. Both of these physical values were identified to be a

source of uncertainty in the modeling. These slight changes in material properties

produce much closer agreement in translational force estimates. The critical current

densities for YBCO material can range from 10-100 kA/cm2

[14].

Figure 6: Translational force of lumped parameter model compare to data for +/-

20mm displacement.

In parallel to developing reduced order lumped parameter models, UT-CEM has been

developing higher order finite element method (FEM) codes to perform more detailed

analyses for final designs. The developed FEM uses the T-Omega formulation n three

dimensions. It uses the electric vector potential and the magnetic scalar potential Ω in

the superconductor and the magnetic scalar potential alone in the region outside the

conductor. This formulation reduces the number of variables being solved because in the

larger part of the volume where there is no flow of current a scalar potential is used. The

highly non-linear problem is solved using the Newton-Raphson iteration process using

the tangent stiffness matrix. This matrix is updated at each iteration, thus helping in the

faster convergence of the problem. The boundary conditions are enforced using the

technique of Lagrangian multipliers thus increasing the number of degrees of freedom

being solved for on the boundary surfaces. These FEM codes have also served as a check

for the lumped parameter model development. Figure 7 shows a comparative analysis

between the FEM results and the translational lumped parameter model for the prior

described test setup.

Figure 7: Translational force comparison of lumped parameter to FEM analysis

Progress

Current progress by UT-Austin and UT-Dallas has shown promise for diurnal energy

storage using flywheels with advanced materials and designs. Prior work by UT-Austin

demonstrated value in energy storage if losses could be managed and advanced materials

became available. High temperature superconducting bearings can reduce flywheel loss

rates to below 0.1% stored energy per hour. In addition, flywheels offer superior cycle

life to other storage technology options.

Recent efforts by UT-CEM have focused on developing lower order axissymmetric

and 3D lumped parameter models for quickly assessing the design of superconducting

bearings for high speed flywheels. Comparisons to experimental test and high order

FEM methods show that these modeling techniques can capture the highly non-linear and

hysteretic force profiles observed in superconducting levitation of permanent magnet

materials at a fraction of the computational time for 3D FEM models. Such analyses are

required to determine lifting capacity and stiffness coefficients for rotor dynamic models

and further design efforts.

Currently these models are utilizing properties for standard YBCO superconductors

and high strength neodymium magnets, which are commercially available at this time.

Properties for advanced hybrid composite nano-tube materials produced by UT-Dallas

can easily be incorporated into the lumped parameter modeling methodology to assess

bearing performance for future flywheel designs. The mechanical advantages of these

materials may allow higher speed operation for improved energy storage performance.

Future Plans

The University of Texas at Austin will continue to improve the proposed lumped

parameter modeling methodology, and apply these techniques to advanced flywheel

designs. The lumped parameter models will help to quickly analyze bearing performance

utilizing advanced magnetic-composite carbon nanotube materials, which are being

developed by our project partners at UT-Dallas Nanotech Institute.

Publications

1. C.S. Hearn, M.C. Lewis, S.B. Pratap, R.E. Hebner, F.M. Uriate, D. Chen, and R.G. Longoria.

"Utilization of Optimal Control Law to Size Grid-Level Flywheel Energy Storage." IEEE

Transactions on Sustainable Energy. Vol. PP., Is. 99, pp. 1-8, Jan. 2013.

2. C.S. Hearn, S.B. Pratap, D. Chen, and R.G. Longoria, " Reduced Order Dynamic Model of

Permanent Magnet and HTSC Interaction in an Axisymmetric Frame," submitted and under

review to IEEE Transactions on Mechatronics, August, 2012.

References

[1] M. L. Lazarewicz and T. M. Ryan, "Integration of flywheel based energy storage for frequency

regulation on deregulated markets," in Power and Energy Society General Meeting, July 2010.

[2] B. T. Murphy, H. Ouroua, M. T. Caprio and J. D. Herbst, "Permanent Magnet Bias Homopolar

Magnetic Bearings for a 130 kW-hr Composite Flywheel," in The Ninth International Symposium on

Magnetic Bearings, Lexington, KY, Aug. 3-6, 2004.

[3] M. A. Pichot, J. P. Kajs, B. R. Murphy, A. Ouroua, B. M. Rech, R. J. Hayes, J. H. Beno, G. D.

Buckner and A. B. Palazzolo, "Active Magnetic Bearings for Energy Storage Systems for Combat

Vehicles," IEEE Transactions on Magnetics, vol. 37, no. 1, pp. 318-323, January 2001.

[4] M. Strasik, P. E. Johnson, A. C. Day, J. Mittleider, M. D. Higgins, J. Edwards, J. R. Schindler, K. E.

McCrary, C. R. McIver, D. Carlson, J. F. Gonder and J. R. Hull, "Design, Fabrication, and Test of a 5-

kWh/100-kW Flywheel Energy Storage Utilizing a High-Temperature Superconducting Bearing,"

IEEE Transactions on Applied Superconductivity, vol. 17, no. 2, pp. 2133-2137, June 2007.

[5] A. C. Day, J. R. Hull, M. Strasik, P. E. Johnson, K. E. McCrary, J. Edwards, J. A. Mittleider, J. R.

Schindler, R. A. Hawkins and M. L. Yoder, "Temperature and Frequency Effects in a High-

Performance Superconducting Bearing," IEEE Transactions on Applied Superconductivity, vol. 13, no.

2, pp. 2179-2184, June 2003.

[6] C. P. Bean, "Magnetization of Hard Superconductors," Physical Review Letters, vol. 8, no. 6, pp. 250-

253, March 15, 1962.

[7] D. R. Alonso, T. A. Coombs and A. M. Campbell, "Numerical Analysis of High-Temperature

Superconductors with the Critical State Model," IEEE Transactions on Applied Superconductivity,

vol. 14, no. 4, pp. 2053-2063, Dec. 2004.

[8] A. A. Kordyuk, "Magnetic Levitation for Hard Superconductors," Journal of Applied Physics, vol. 83,

pp. 610-612, 1998.

[9] J. R. Hull and A. Cansiz, "Vertical and Lateral Forces Between a Permanent Magnet and a High

Temperature Superconductor," Journal of Applied Physics, vol. 86, no. 11, pp. 6396-6404, 1999.

[10] K. R. Davey, R. Weinstein, D. Parks and R. Sawh, "Activation of Trapped Field Magnets by Flux

Pumping," IEEE Transactions on Magnetics, vol. 47, no. 5, pp. 1090-1093, May 2011.

[11] F. Grilli, S. Stavrev, Y. L. Floch, M. Costa-Bouzo, E. Vinot, I. Klutsch, G. Meunier, P. Tixador and B.

Dutoit, "Finite-Element Method Modeling of Superconductors: From 2-D to 3-D," IEEE Transactions

on Applied Superconductivity, vol. 15, no. 1, pp. 17-25, March 2005.

[12] J. Rhyner, "Magnetic properties and AC-losses of superconductors with power law current-voltage

characteristics," Physica C, vol. 212, pp. 292-300, 1993.

[13] W. R. Smythe, Static and Dynamic Electricity, 3rd ed., New York: Hemisphere Publishing, 1989.

[14] F. N. Werfel, U. Floegel-Delor, R. Rothfeld, T. Riedel, B. Goebel, D. Wippich and P. Schirrmeister,

"Superconducting bearings, flywheels, and transportation," Superconducting Sci. Technol., vol. 25, no.

014007, p. 16pp, 2012.

Contacts

Dr. Robert Hebner: r.hebner@cem.utexas.edu

Dr. Siddharth Pratap: s.pratap@cem.utexas.edu

Mr. Michael Lewis: mclewis@cem.utexas.edu

Mr. Clay Hearn: hearn@cem.utexas.edu

Publicaly Releasable Abstract for the 2012-2013 Annual GCEP Report of the University of Texas at Dallas on:

Low-Cost Flywheel Energy Storage for Mitigating the Variability of Renewable Power Generation

Ray H. Baughman, Director/PI, Alan G. MacDiarmid NanoTech Institute and Shaoli Fang, Associate Research Professor/Co-PI, Alan G. MacDiarmid NanoTech Institute Abstract

This abstract is a version of the full report abstract that has been severely contracted to remove proprietary information.

The project goals of UTD’s NanoTech Institute are to develop mechanically robust materials that can serve as superconductors and high-energy-product permanent magnets for the levitation of rotors for the flywheel batteries being developed by UT Austin collaborators. Advances made will be used by our UT Austin team mates to modify the design of their flywheel batteries, so as to best exploit performance improvements.

In this report we describe fabrication of carbon nanotube (CNT) composites containing 98 wt% particles or nanoparticles of α-Fe2O3, CoFe2O4, and SmCo5. Initial magnetization measurements for CNT/CoFe2O4, composites provided an enhancement of coercive force by ~10%. This enhancement increases towards lower temperatures. At 100 K, the coercive force increases from 8.5 kOe to 10.5 kOe (~20%). This increase is likely due mainly to the CNT arrays providing an aligned matrix that exploits the shape anisotropy of deposited nanoparticle flakes. In contrast, CNT/α-Fe2O3 presents a weak ferromagnetism from α-Fe2O3 nanoparticles and a strong diamagnetic signal from the CNTs. Finally, CNT/SmCo5 yarn composites provided a coercive force of 2.6 kOe, similar to that published in literature.

Our method for producing MgB2-CNT composite yarns has produced superconducting yarns having attractive properties. The critical temperature reaches 38 K, the density-normalized critical currents are comparable to those for bulk pure-MgB2 superconducting wires (and likely exceeds them for fields above 8.5 Tesla), and Hc2 exceeds that for bulk pure-MgB2 superconducting wires for temperatures below 25 K. Also important, these MgB2-CNT composite yarns are highly flexible, in contrast with the case for conventional MgB2 wires.