Structures for superconductive magnetic energy storage

Energy Vol. 15. No. 10, pp. 873-884. 1990 0360-5442/m 33.00 + 0.00 Printed in Great Britain. All rights reserved Copyright @ 1990 Pergamon Press plc

STRUCTURES FOR SUPERCONDUCTIVE MAGNETIC ENERGY STORAGE

PHILIP VARGHESE and KWA-SUR TAMt

Department of Electrical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, U.S.A.

(Received 18 May 1989; received for publication 6 February 1990)

Abstract-The cost of superconductor material is a significant portion of the total cost of an SMES (Superconducting Magnetic Energy Storage) system. The mass of superconductor required to store a given amount of energy is a function of the magnet structure. Five magnetic structures applicable for SMES are examined in this paper from the viewpoint of their energy storage capacities along with the peak field magnitudes. Two force-balanced structures are analyzed and compared.

1. INTRODUCTION

Because of their ability to produce high levels of current and magnetic field, superconducting magnets are capable of storing large amounts of energy. Energy is stored in the magnetic field generated by the d.c. circulating in the superconducting coil. Because of their high round-trip efficiencies and fast response, SMES (Superconducting Magnetic Energy Storage) systems have been considered for their applications in terrestrial and space power systems.‘-3 Among the various possible structures for SMES magnets, the basic structures of solenoid and toroid have been the focus of most studies.4+5 Conceptual designs using both structures have been proposed.6V7 These conceptual designs have shown that it is feasible to build large-scale magnets for energy storage over 5000MWh. A small SMES system of the solenoidal type had been built and commissioned.’

The cost of superconductor material is a significant portion of the total cost of a SMES system. The mass of superconductor required to store a given amount of energy is a function of the magnet structure. It is the objective of this paper to examine and compare different magnetic structures applicable for SMES from the viewpoint of their energy storage capacities. The energy stored in a magnetic field is proportional to the square of the field magnitude. A recent study has looked at the relative effectiveness of some magnet structures’ from the viewpoint of superconductor requirement to store a given amount of energy. Although the nominal values of the peak field magnitude were assumed constant in that study, the change in the actual peak field magnitude for different geometries of the same structure was not considered. As the results of this paper will show, the peak field magnitudes do vary considerably with geometry for some structures.

Superconducting materials have critical values for current-density and magnetic field that make it necessary to impose limits on the maximum values allowed for these quantities in any design. If the optimum design results in a geometry where the actual computed values for the peak field exceed the design limits, it is necessary to scale down the current to reduce the peak field or to adopt a non-optimum geometry with lower peak field. Thus, it is clear that a fair comparison of magnet structures cannot be made without including information regarding the actual peak field magnitude. When the energy storage capacities of various structures are looked at in the light of equal peak fields, it can be shown that conventional structures like the solenoids may not be the best structures and structures like the poloids that have not been given serious consideration in the past can have superior energy storage capability.

The changes in energy storage capacities and the changes in peak field magnitudes for five different structures with various geometries are discussed in this paper. Besides solenoids and

tTo whom all correspondence should be addressed.

873

PHILIP VARCWESE and KWA-SUR TAM

Fig. 1. Solenoidal structure.

toroids, the structures that have been considered include the poloidal coil (wound on a toroidal surface) and two force-balanced designs. The schemaic diagrams of the five structures are shown in Figs. 1-5. The directions of the magnetic field B and the electric current I are also indicated.

For each structure, the geometry is defined in terms of one parameter u. For the basic toroidal shape, u is the ratio of the minor radius to major radius, as shown in Fig. 2, viz.

(I = a/R. (1)

Since all of the structures, with the exception of the solenoid, are wound on a toroidal surface, their geometry can be described by this parameter o.

The aspect ratio /3 generally has been used to describe the geometry of a solenoid and is defined as

/3 = l/2% (2)

where 1 and a are the length and radius of cross-section, respectively, as shown in Fig. 1. Consider a solenoid and a toroid that have the same radius of cross-section a and are constructed with the same conductor filaments. If the spacing between successive turns is the same in both windings, then the condition that both structures use the same total length (consequently the same mass) of superconductor is given by

I= 2~r(R - a), (3)

where R is the major radius of the toroid and 1 is the length of the solenoid. Dividing both sides by 2u, we obtain the relationship between o and the aspect ratio /I as follows:

fi = Jr(l/o - 1). (4)

Thus, the parameter u can be used to describe the geometry of the solenoid also. When u is varied from 0 to 1, the full range of possible geometries for each structure can be generated.

The energy storage capacities of the different structures are compared in this paper. A method for comparing different magnet structures designed with the same quantity of superconductor is developed. The importance of considering the actual peak fields along with

Fig. 2. Toroidal structure.

Structures for superconductive magnetic energy storage 875

Fig. 3. Poloidal structure.

Fig. 4. Two-layer force-balanced structure.

Fig. 5. One-layer force-balanced structure.

the total energy stored is emphasized. The relative merits of each structure are discussed. A single-layer force-balancing magnet, which has some advantages over the two-layer structure, is discussed in this paper. Although the maximum energy stored by a poloid is almost the same as that stored by a solenoid the poloid is shown to be superior when peak field magnitudes are taken into consideration.

In Sec. 2, we discuss the criteria for the design of different structures in order to make a fair comparison. In Sec. 3, the energy storage capacities as a function of geometry are derived for each structure. A brief discussion is provided on methods of computing the inductance and field magnitude for structures like the solenoid and poloid. The energy storage capacities of various structures are compared and their relative merits are discussed in Sec. 4.

2. MAGNET DESIGN CRITERIA

Two approaches may be used to evaluate magnet structures for their energy storage capacity. The first approach is to design a structure without particular regard to the quantity of material

876 PHILIP VARGHESE and KWA-SUR TAM

used, take the ratio of the total energy stored to the mass of superconductor material used to obtain the energy stored per unit mass (also called the energy density) and then use the ratio as a measure of the effectiveness of that structure. The second approach is to use a fixed mass of superconductor for all the structures being studied and use the total energy stored, which will be proportional to the energy density, as a measure of the effectiveness of each structure. The second approach is used in this study since it gives more information on the optimum geometry and the best structure for a given application. The main drawback of the first approach is that the energy density for thi; same structure and geometry is itself a function of the mass of the superconductor material being used. This point can be illustrated by the following example. Consider an ideal solenoid with parameters as shown in Fig. 1. Assume that the solenoid has a conducting surface of lixed thickness A, which is very small compared to the radius of cross-section a of the solenoid (thin-wall solenoid). Furthermore, assume that the surface current density is fixed at J (A/m). If p is the density of the superconductor material, the energy per unit mass can be shown to be

E/M = (P,J’~)I(SAP~). (5)

Equation (5) shows that for the same geometry represented by the aspect ratio 0, the energy density increases with the total mass M of superconductor used.

The fixed quantity of superconductor to be used in all geometries was chosen from the data for a published design, namely the LAR (Low Aspect Ratio) coil6 The data for the LAR coil are given in Table 1. Different structures in various geometries are designed in this study by using the same quantity of superconductor material that is used in the LAR coil. The design procedure assumes that the area of the conducting surface for all the structures and geometries is the same as the area of the conducting surface of the LAR coil, represented by the constant C. The area of the conducting surface of the solenoid, for example is 2arul. Using Eq. (2), the dimensions 1 and u can be expressed in terms of C and /3 or in tenns of C and u by using Eqs. (2) and (4). Table 2 shows the dimensions of the magnetic structures with different geometries considered in this paper.

Each of the structures in Table 2 is excited with the same current level (765 kA). The spacing between adjacent turns is also kept the same as the LAR coil. In order to determine the total

Table 1. LAR coil data.

Energy stored 5500 MWh Length of Coil (1) IS.68 m Radius of Coil (a) 784 m

Number of Turns (N) 112

Radius of Conductor 5.5 cm

Conductor Current (1) 765000 A

Aspect Ratio (/?) 0.01 (a =0.9968)

Table 2. A comparison of physical dimensions (m) of magnets designed with the same amount of superconductor material.


current for any magnet designed in this manner, it is convenient to define a constant J, which will be called the surface current density. J is defined as the current per unit length along the length of the LAR coil. Thus a solenoid of length 1 would carry a total current NZ = Jl. The numerical values for the constants C and J are easily computed from the data in Table 1.

The peak magnetic field of the toroid in this design can be shown to be equal to PJ, where CL,, is the permeability constant (4~ X lo-’ H/m). Thus the peak field in the toroid for all geometries is constant. This constant magnitude (6.87T) will be referred to as the nominal peak field and is used as a base value to compare the peak field magnitudes in the other structures. The nominal peak field also represents the magnitude of the uniform magnetic field present in an ideal solenoid (infinite length) having the surface current density J.

3. ENERGY STORAGE CAPACITY

3.1. Solenoid

The schematic diagram of a solenoidal magnet is shown in Fig. 1. The inductance for a thin-wall solenoid of finite length is

Ls = polta2k2(a)ll (6)

where k,(a) is a factor between 0 and 1 and is called the leakage factor. k2 accounts for the non-uniform nature of the magnetic field within the solenoid.” A long solenoid with relatively small radius of cross-section has a leakage factor close to one, whereas a short solenoid with relatively large radius of cross-section has a leakage factor close to zero. The leakage factor k2 makes the effective inductance of a solenoid smaller than that of an ideal solenoid which has a uniform magnetic field. Figure 6 shows the magnetic field distribution within a solenoid (a = 0.8). The origin represents one end of the magnet and the two horizontal axes represent the distances along the radial and the axial directions. The field magnitude along the axial direction is shown only up to the center of the magnet due to the axial symmetry of the magnetic field. It is clear from Fig. 6 that the magnetic field within the solenoid can be highly non-uniform for large values of 0 (or low aspect ratios), resulting in lower energy storage capacity and higher peak fields.

The expression for total energy stored is given by

E poJ2C’.5

s= 8n (7)

A plot of the stored energy as u varies from 0 to 1 is shown in Fig. 9. The energy is normalized by the stored energy of the LAR coil for comparison (1.0 on the vertical axis represents 5500 MWh). The inductance of the ideal solenoid increases monotonically with the parameter 0. However, the leakage factor decreases with increasing o. Hence the inductance of the solenoid rises to a maximum value and then drops off very rapidly. This peak value occurs at u = 0.93. At this optimum geometry, the solenoid can store more than twice the amount of energy stored by the LAR coil.

For a given value of u the number of turns N of the solenoid is obtained simply by dividing the length I of the solenoid by the turn spacing of the LAR coil, which is assumed to be the same for all geometries. The field magnitude at any point can be computed by summing up the field components contributed by each turn. l1 The peak field is found to occur at the ends of the solenoid, around the surface of the first and the last turns. The peak fields for solenoids of various geometries are plotted in Fig. 10. For the LAR coil the peak field is about 8.1 T.

3.2. Toroid

The schematic diagram of a toroidal magnet is shown in Fig. 2. The total stored energy is given by

E _ poJ2C’.’ T-

416 (8)

878

TESLA

8.08

7.60

6.48

5.20

2 .81 70. (

PHILIP VARGHESE and KWA-SUR TAM

Fig. 6. Magnetic field distribution inside a solenoid.

The amount of stored energy as a function of u is plotted in Fig. 9. The magnetic field within the toroid is given by

B(8) = /@(I? -a)/@ + p cos e), (9)

where p and 6 are as defined in Fig. 2. The peak field occurs along the inside edge of the toroid

(P =a, 8= n). There is practically no magnetic field outside the toroidal shell. The absence of stray magnetic field is the major factor in favor of the toroidal structures.

The optimum geometry for the toroid is for u = 0.60, where it stores almost the same energy as the LAR coil. The stored energy drops off on either side of the optimum geometry. For low values of (I, the magnetic field is more uniform but the volume of space in which the field exists is less. At large values of o the field is less uniform but the volume of space in which the field exists is more. Since the energy stored is proportional to the square of the field magnitude integrated over the volume in which the field is present, the stored energy curve is quite flat about its peak value.

3.3. Poloid

The poloid structure, which is shown in Fig. 3, is wound on a toroidal surface. The major differences between the poloid and the toroid are the directions in which the current and the magnetic field are oriented. The turns of the poloid are wound in concentric circles on the toroidal surface and the resultant magnetic field B exists only on the outside of the toroidal surface as indicated in Fig. 3. The poloid structure discussed in this section has a uniform surface current distribution on the toroidal surface. This means that the turns of the poloidal coil, all carrying the same current, are uniformly spaced. One of the differences between the


poloid ad the toroid is that the surface current density of the toroid decreases with radial distance from the axis of symmetry, whereas the poloid has a uniform surface current density. This means that the mass of superconductor needed for a conventional toroidal winding and a p&i&l winding (with uniform current distribution) is not the same if both are wound on toroidal shells of the same major and minor radii.

Unlike the other structures, it is not easy to obtain closed-form equations for the calculation of the inductance or a nominal peak field for the poloid. The simplest approximation assumes that all the poloidal current can be approximated by a single filament of current of the same magnitude located at the central axis (the circle with radius R). The field magnitude and therefore the total flux linking the coil are then determined based on the equations derived for a single-turn coil. A more accurate method to calculate poloidal inductance is based on computing the magnetic vector potential. It allows for the distribution of current on the toroidal surface. The total flux A linking the coil can be shown to be

A. = 2jc(R - a)A, (10)

where A (Wb/m) is the magnitude of the vector potential at the inside edge of the toroidal surface (r = R - a).

The total energy stored is

EP = U/2, (11)

where I is numerically computed for each geometry, and the total current I is 2~ruJ. The energy stored as a function of u is plotted in Fig. 9. The optimum geometry for the poloid is for 0 = 0.08. For this geometry the energy stored in the poloid is about 2.2 times that of the LAR coil.

The energy stored by a poloid is proportional to the product of the total flux linkage and the current. For a given u, let B(a) be the average field in the central plane of the poloid. Then the energy stored in the poloid can be shown to be proportional to the quantity B(a)(l - ~)~/fi. If the average field remains constant then the stored energy would increase without bound as o decreases to zero. However, the field becomes more non-uniform with decreasing a, which decreases the stored energy. The result is that as u decreases, the stored energy peaks at a certain a, then decreases as u approaches zero.

The magnetic field is computed by summing up the field components due to each turn. Figure 10 shows the peak field variation with geometry. The peak field, which occurs at the inside edge of the poloid, has a maximum value close to 15 T. However, for low values of u where the poloid stores the maximum energy, the peak field is not much higher than that of the LAR coil.

The direction of the forces on the poloid, which are compressive, is normal to the toroidal surface everywhere but its magnitude is not constant since the field magnitude varies with the position variable 8 defined in Fig. 3. The forces in the conventional toroid and the poloid are opposite in direction. If the poloidal windings are mounted on top of the toroidal windings, then the toroidal forces and poloidal forces can cancel out each other. This is the basis for the design of force-balanced magnets.

3.4. Force-balanced structures

3.4.1. Two-layer force-balanced design. The first force-balanced structure consists of two layers of coils wound on a toroidal surface.” The inner layer is wound like the conventional toroid and the outer layer is wound like a poloid. If the current densities are matched at all corresponding locations of the two layers and the separation between them is very small, the forces exerted on each layer are almost equal in magnitude but act in opposite directions, thus providing force-balancing. The two-layer force-balanced structure is shown in Fig. 4. The directions of the toroidal current and magnetic field (IT and &) and the poloidal current and magnetic field (ZP and BP) are indicated in this figure. The poloidal and toroidal layers are very thin compared to the overall dimensions of the structure and are approximated by current- sheets. Each layer is designed by using half of the amount of superconductor material reserved for the whole structure and the surface current densities of the two layers are matched

880 PHlLIp VARGHESE and KWA-SUR TAM

everywhere. The total energy in this structure is the sum of the energy in the toroidal and poloidal fields, viz.

EFB= Ep + ET. (12)

The energy stored in the poloidal winding is calculated by the same method as that used for the poloid except that its surface current density is distributed in such a way that it matches that of the toroidal winding. The energy stored in the toroidal winding is computed by an expression similar to Eq. (8). The total energy in the two-layer structure is plotted in Fig. 9. Although the poloidal winding and the toroidal winding are both made with the same amount of superconductor material (half of the total amount), it must be noted that the energy stored in the two-layer structure is not equal to the average value of the poloid’s (Sec. 3.3) and the toroid’s (Sec. 3.2) stored energy for two reasons. Firstly, the poloidal winding in the force-balanced structure has a non-uniform current density. Secondly, the energy density was shown in Sec. 2 to be increasing with total mass. Therefore the energy stored in a configuration using M/2 (kg) of superconductor material is less than half of the energy stored in the same configuration using M (kg).

The amounts of stored energy in the toroidal and the poloidal fields along with the total stored energy in the two-layer structure are shown in Fig. 7. For low values of u most of the energy is stored in the poloidal winding and for large values of u the bulk of the energy is stored in the toroidal winding. The maximum energy stored in the force-balanced structure occurs at around the same value of u as that of the poloid. Most of the energy is stored in the poloidal field for an optimum two-layer structure.

The magnitude of the peak magnetic field is determined by the greater of the peak field magnitudes in the toroidal and the poloidal layers. With a non-uniform poloidal current distribution matching that of the toroidal layer it is found that the magnitudes of the magnetic field are also matched very closely in the two layers. Therefore the magnetic field of the toroidal layer can be assumed to represent the field distribution in both layers. The peak field magnitude is shown in Fig. 10.

l POLOIDAL (0)

o TOROIDAL (0)

0 F-BAL (D)

0.4 0.5 0.6

SIGMA

Fig. 7. Energy stored by the poloidal and toroidal windings of a two-layer force-balanced structure.


3.4.2. Single-layer force-balanced design. An alternative way to achieve force-balancing is to create both the toroidal and the poloidal fields by means of a set of windings wound with a 45” helical angle everywhere on the toroidal surface. The current in the inclined winding creates both a poloidal field and a toroidal field which can provide force-balancing in the same manner as the two-layer structure.

The single-layer force-balanced structure is shown in Fig. 5. For a given inclination (Y, the surface current density components in the toroidal and poloidal directions are reduced by a factor of cos (Y and sin cr respectively. The single-layer design uses an inclination of LY = 45”. Thus the surface current density component along the toroidal or poloidal direction is reduced by a factor of l/e. Since the magnitude of the magnetic field in the toroidal layer is directly proportional to the surface current density which is J/i&, the peak field magnitude will also be reduced by the same factor of l/ti. As the poloidal and toroidal current components are produced in the same current sheet, the matching of the magnetic field magnitudes on both sides of the conducting layer is expected to be better than that of the two-layer design.

For the same dimensions R and a, the single-layer winding would use the same amount of superconductor as a toroid. The method used for the two-layer design is applied to calculate the stored energy in the toroidal and poloidal magnetic fields. The distribution of the stored energy in the two magnetic fields is shown in Fig. 8 and can be seen to be similar in shape to the distribution for the two-layer structure. The total energy stored is shown in Fig. 9 and the peak field magnitude is plotted in Fig. 10. The stored energy is greater than the two-layer

structure for all geometries, but the optimum geometry for both structures is the same.

4. COMPARISON OF THE STRUCTURES

Figure 9 demonstrates the energy storage capability of the various structures. The peak for each curve indicates the geometry at which that structure stores the maximum amount of energy. As these peaks occur at different values of a, the overall dimensions at the optimum

l F-BAL (S)

o TOROIDAL (S)

0.4 0.5 0.6

SIGMA

Fig. 8. Energy stored by the poloidal and toroidal fields of a single-layer force-balanced structure.

PHILIP VARGHEX and KWA-SUR TAM

2.50 l SOLENOID X F-BAL (SINGLE)

2.25. o TOROID

z 3 2.00.

d

J 1.75. A F-EM (DOUBLE)

ti

g 1.50.

5;

2 1.25.

i

?I 1.00.

c s 0.75. -1

2 lx 0.50.

P

0.25.

0.00.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 .o

SIGMA

Fig. 9. A comparison of energy storage capacity of different structures with various geometries.

15.5

14.5

13.5

z 2 12.5

c - 115

fi c 10.5

0 F w 9.5

z

2 a.5

: ii 7.5

6.5

5.5

4.5 (

J-

)a

l SOLENOID

o POLOID

o TOROID,F-EAL(D)

1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

SIGMA

0

Fig. 10. A comparison of peak field magnitude of different structures with various geometries.


geometry for each structure can vary considerably. This is indicated in Table 2 where the dimensions of each structure are tabulated for the different geometries, with the entries in bold face indicating the optimum geometries from the energy storage point of view. For example, consider the dimensions of the toroid and the poloid. Their optimum geometries have the dimensions R = 90.3 m, n = 54.2 m and R = 156 m, a = 12.5 m, respectively. Therefore the space needed to accomodate these structures would differ considerably, especially in large-scale energy storage applications.

The variation in the peak field magnitudes with geometry for the five structures is shown in Fig. 10. The peak field is constant at the nominal value for the two-layer design and the toroid whereas for the single-layer design it is constant at a value less than the nominal one by a factor of l/J&. It was pointed out earlier that the peak magnetic field must also be considered before deciding which structure stores more energy. Figure 10 shows that the peak fields of the solenoid and the poloid vary considerably with geometry. The solenoid stores a little over twice the energy of the LAR coil at.its optimum geometry (a = 0.93). However, its peak field is 25% greater than that of the LAR coil and 45% greater than the nominal value. If the peak field is reduced by decreasing the current then the energy stored per unit mass would also be reduced proportionately. Another way to reduce the peak field is to choose a non-optimum geometry as is done in the case of the LAR coil. Therefore, if the peak fields are to be kept at the nominal value, the solenoid cannot store as much energy as indicated in Fig. 9.

The variation of the peak field for different geometries of the poloid seems even worse than that of the solenoid. However, the optimum geometry for the poioid occurs at o = 0.08 and at this value of 0 the peak field is almost the same as that for the LAR design. For this reason the optimum poloid structure may be considered to be superior to the optimum solenoid structure, as far as energy storage is concerned.

The toroid and the two-layer force-balanced structure both have approximately the same maximum energy storage capacity, which is only slightly less than that of the LAR solenoid. The single-layer structure stores about 35% more energy than the two-layer structure and has a peak field magnitude almost half that of the LAR coil. If both force-balanced structures are required to have the same peak field, the single-layer structure can store considerably more energy than the two-layer structure.

Support structure to counterbalance the magnetic forces in superconducting magnets constitute another significant proportion of the overall system cost. The force-balanced structures are very competitive in this aspect. The absence of any stray field is a significant advantage for the toroid. It is the only choice in situations where even a small stray field is not allowed.

5. CONCLUSIONS

The relative merits of five different structures applicable for SMES have been evaluated and compared. The five structures are found to have different energy storage capabilities. The shape of their energy storage curves clearly indicates which geometry gives the maximum energy stored in each of these structures and their relative magnitudes indicate their relative energy storage capacities. The poioid and solenoid can store almost the same amount of energy if the effects of magnetic field are not considered. Both structures have a significant variation in peak field magnitude with geometry. Since the optimum poloid geometry has a smaller peak field than the optimum solenoid geometry, the poloid has greater energy storage capability.

Two force-balancing concepts were analyzed and compared. The single-layer force-balanced design is superior to the the two-layer design both in terms of stored energy as well as peak magnetic field.

Besides energy storage capability, other important factors such as magnetic forces and stray magnetic field also need to be considered when deciding on a structure for a SMES application. The energy storage capabilities of the two-layer structure and the toroid are only slightly less than that of the LAR solenoid. However, the force-balanced structures have less requirement

884 PHLLP VARGHESE and KWA-SUR TAM

for mechanical support structure and the toroid has practically no stray field. Further investigations to determine the overall merits of these structures should be performed.

Acknowledgtmmts-This material is based upon work supported by the DuPont Young Faculty Grant and the Virginia Center for Innovative Technology.

1.

2. 3.

4.

5.

6.

Z:

1X: 11. 12.

REFERENCES

S. M. Schoenung, W. V. Hassenzahl, and P. G. Filios, “U.S. Program to Develop Superconducting Magnetic Energy Storage,” 23rd Intersociety Energy Convers. Eng. Conf., Paper 889504, Denver, co (1988). K. Hayakawa, M. Masuda, T. Shintomi, and J. Hasagawa, IEEE Trans. Mag. 24,887 (1988). K. A. Faymon and S. J. Rudnick, “High Temperature Superconducting Magnetic Energy Storage for Future NASA Missions,” 23rd Intersociety Energy Convers. Eng. Conf., Paper 889416, Denver, CO (1988). R. W. Boom and H. A. Peterson, “Wisconsin Superconductive Energy Storage Project,” Annual Report, Vol. 1, WI (1974). R. W. Boom, “Wisconsin Superconductive Storage Update,” Proc. US-Japan workshop on SMES, WI (1981). “Conceptual Design and Cost of a Superconducting Magnetic Energy Storage Plant,” EPRI Report EM-3457, EPRI, Palo Alto, CA (1984). T. Shintomi and M. Masuda, IEEE Trans. Mag. 23,549 (1987). H. J. Boenig and J. F. Hauer, IEEE Trans. P.A.S. 104,587 (1985). W. V. Hassenzahl, IEEE Trans. Msg. 25,1799 (1989). W. B. Boast, Vector Fields, Harper & Row, New York, NY (1964). M. Wilson, Superconducting Magnets, Wiley, New York, NY (1986). 0. K. Mawardi, “Design of a Force-free Inductive Storage Coil,” Los Alamos Scientific Laboratory Report No. LA-5953-N& Los Alamos, NM (1976).

Structures for superconductive magnetic energy storage

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