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1 MW sectored toroidal superconducting energy storage magnet
Cryogenics xxx (2014) xxx–xxx
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Design of a 4.5 MJ/1 MW sectored toroidal superconducting energy storage magnet Uttam Bhunia ⇑, Javed Akhter, Chinmay Nandi, Gautam Pal, Subimal Saha Variable Energy Cyclotron Centre, Department of Atomic Energy, 1/AF, Bidhan Nagar, Kolkata 700 064, India
a r t i c l e
i n f o
Article history: Available online xxxx Keywords: SMES Toroidal-type Stress Structural analysis AC loss Quench
a b s t r a c t A 4.5 MJ/1 MW superconducting magnetic energy storage (SMES) system is being developed at VECC centre, Kolkata. The magnet system consists of the cryostat and coil assembly comprising eight superconducting solenoid coils made of custom-made NbTi based Rutherford-type cable and arranged in toroidal fashion with finite inter-sector gap. Since the strong electromagnetic force distributed to the coil is asymmetric and non-uniform in nature, a precise 3-D finite element analysis (FEA) has been carried out to design a mechanically stable coil and support structure under various operational scenarios. The results reveal that maximum stress developed on coil and its support structure is below allowable stress limit. Extensive transient analysis has also been carried out to evaluate transient loss and assess the feasibility of using helium re-condensation technology with commercially available cryo-refrigerators. Finally, quench protection scenario has also been discussed suitable for this toroidal-type SMES system. The article investigates the design concept of the cryostat and coil assembly. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Small scale or medium scale superconducting magnetic energy storage (SMES) systems are in high demand for compensation of load fluctuation, mitigation of voltage dip or sag in utility line. In view to develop technology for SMES application to compensate voltage dip of utility line for critical machines, VEC Centre, Kolkata has already developed the technology with energy of 0.6 MJ [1] along with associated power converter system. In the next phase, it is aimed to develop a toroidal-type SMES unit of 4.5 MJ/1 MW capacity. The magnet consists of modular solenoid coils connected in series and arranged in a toroidal symmetric fashion. The main advantage of toroidal configuration is the very low magnetic stray field outside the coil assembly compared to a solenoidal SMES of similar storage capacity. The primary problem concerning toroidal-type configuration is caused by large Lorentz forces acting on the superconducting cable. The Lorentz force on the current carrying coil is asymmetric, non-uniform and there is a net attractive force on the coils towards the centre of the torus. Therefore, the coil must be properly supported to prevent excessive deformation. Stress analysis of pancake type high-temperature superconductor (HTS) based SMES magnet has already been reported by Kim et al. [2]. In recent times, SMES of both solenoid and toroidal-type ⇑ Corresponding author. E-mail address: [email protected] (U. Bhunia).
configuration using commercially available HTS tape are being developed by various groups [3–7] world-wide. Design methods for the toroidal configuration with pancake-type HTS-based modular coil for SMES have been proposed to reduce winding volume [8,5]. However, commercially available HTS tape, till date is very expensive compared to niobium–titanium alloy based low temperature superconductor and there are also still many technical issues to be addressed while using HTS for reliable operation of commercial SMES units. In recent times, after the commercial availability of 4.2 K cryo-refrigerator, niobium–titanium (NbTi) alloy based Rutherford-type cable is believed to be a better choice for small or medium scale SMES units using helium vapor re-condensation technology. A custom-made NbTi based Rutherford-type cable suitable for transient application is used in the present design. Commercially available general purpose multi-physics finite element analysis (FEA) code has been used for detailed three dimensional magneto-structural analyses to optimize the structural design of the support structure. This paper presents the design concept of the cryostat, magneto-structural design of coil in integration with support structure so that equivalent von-Mises stress in all constituent materials never exceeds the yield stress. Extensive fatigue analysis is carried out considering repeated charging/ discharging cycle during operation of SMES. Transient magnetic field effect on coil winding, former, intermediate thermal shield around the liquid helium chamber, etc. has also been investigated to ensure the stable operation of SMES and to find the feasibility of
http://dx.doi.org/10.1016/j.cryogenics.2014.06.007 0011-2275/Ó 2014 Elsevier Ltd. All rights reserved.
Please cite this article in press as: Bhunia U et al. Design of a 4.5 MJ/1 MW sectored toroidal superconducting energy storage magnet. Cryogenics (2014), http://dx.doi.org/10.1016/j.cryogenics.2014.06.007
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using cryo-refrigerator. Quench behavior and reliable protection method for the coil are also presented in this paper. 2. Basic design concept 2.1. Specification of superconducting wire A superconducting (SC) Rutherford type cable with inter-filamentary matrix Cu–0.5% Mn with low loss characteristics has been (Table 1) ensured for the SMES coil. Good electrical contact to neighbouring strands in the cable is ensured with stabrite (Sn–5% Ag) coating and heat treatment over the cable. The critical characteristic of the cable at 4.2 K is as shown in Fig. 1. The cable is wrapped with polymide tape (25 lm thick) with 50% overlap for turn to turn insulation. 2.2. Design and parameter of sectored toroidal-type magnet Basic parameter of a toroidal magnet is the shape of the sector modules: for example a D-type or circular coils. Birkner and Munchen [8] investigated the issue and found that for a given length of superconductor at constant operating current, A D-shaped sector has higher maximum energy (18% higher) than a circular coil. The difference hardly justifies choosing D-type sector coils for its complex fabrication cost compared to circular coils. The circular geometry has been optimised for stored magnetic energy and magneto-structural stress. The sectored SMES unit is composed of a finite number of sectors or elemental solenoidal coils arranged in a toroidal fashion as shown in Fig. 2 and are interconnected in series. The geometry of the sectored toroidal magnet has been optimised by three design variables namely: major radius, r0, geometry dependent parameters, a = r1/r0 and b = r2/r0 for a given inter-sector coil spacing, d. The design goal was to find the optimal solutions for both magnet overall size in terms of torus major radius and required superconductor length for winding, which in turn reduces a significant part of overall cost. A multi-objective
Table 1 Main parameters of superconducting cable. Strand diameter (mm) Filament number Cu–Mn/NbTi Filament diameter (lm) Nos. of strands in cable Critical current (7 T, 4.2 K) Cable width, 2 c (mm) Cable thickness, 2 b (mm) Approx. cable lay pitch, lt (mm) Tensile stress (MPa) (0.2% strain) at room temperature
0.72 3900 2.0 10 10 2200 A 3.7 1.3 50 450
Fig. 2. Schematic diagram of the magnet system with sector coil arrangements.
design optimisation scheme using differential evolution [9] algorithm has been developed to find out the coil parameters for a given stored energy level. The specifications of the magnet are set as follows: (i) Stored energy is 4.5 MJ. (ii) Circumferential stress in sectored coil to be within an allowable limit of 150 MPa at 4.2 K. (iii) Numbers of elemental or sector coils to be chosen in such a way that stray magnetic field outside the torus follows the safety guidelines (0.5 mT or lower). (iv) Number of winding turns (nr) and layers (ny) are considered to be integer. (v) There must be inter-sector gap (d) for support structure, access to the volume and ease of manufacture. In the present study, d = 50 mm is assumed from practical considerations. Suitable support structure is essential to keep the sector coil in position under strong electro-magnetic force. The basic design parameters of the eight-sector toroidal system are listed in Table 2. Higher the number of sectors, extension of stray magnetic field outside the coil assembly reduces further, but with the cost of additional number of inter-sector cable joints. An operating current margin of 35% is maintained in design study which corresponds to a temperature margin of 0.64 K over the Table 2 Basic design specification of the SMES magnet.
Fig. 1. Critical characteristics of the Rutherford-type cable at 4.2 K.
Number of sectors, Ns Minimum inter-sector coil gap, d (m) Energy, ES (MJ) Maximum rated power, P0 (MW) Rated operating current, Iop (A) Major radius, r0 (m) Sector coil Outer radius, r2 (m) Inner radius, r1 (m) Height, h (m) Winding turns Cable length (km) Distance of 0.5 mT contour line from torus center (m)
8 0.05 4.5 1.0 1200 0.62 0.24 0.19 0.3 1300 1.9 1.8
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Fig. 3a. Coil winding scheme of the sector coil.
Fig. 3b. Design concept (3D-CAD model) of the SMES magnet.
Please cite this article in press as: Bhunia U et al. Design of a 4.5 MJ/1 MW sectored toroidal superconducting energy storage magnet. Cryogenics (2014), http://dx.doi.org/10.1016/j.cryogenics.2014.06.007
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U. Bhunia et al. / Cryogenics xxx (2014) xxx–xxx Table 4 Design results of 4.5 MJ SMES magnet. Coil arrangement Number of sectors Total conductor length (km) Conductor
Fig. 4. Axial magnetic field component on sector coil mid-plane (Y = 0 & Z = 0) measured from the center of the torus.
Operating current, Iop (A) Number of Inter-sector joints Superconductor–magnet lead joints Maximum von-Mises stress (MPa) On coil/coil former at 1200 A Liquid helium chamber at 4.2 K Steady state load (W) Dynamic load (W) during discharge (200 A/s) Intermediate shield at 60 K Steady state load (W) Dynamic load (W) during discharge (200 A/s) Number of cryorefrigerators Two-stage (1.5 W at 4.2 K) Single stage (240 W at 60 K)
Toroidal-type 8 15.2 NbTi based Rutherford-type cable 1200 7 2 133/193 2.0 1000.0
120.0 60.0
3 1
Table 3 Material properties (at 4.2 K). Coil (equivalent properties)
Support structure (SS-316 L)
Young’s modulus Er (GPa) Eh (GPa) Ez (GPa)
46.5 55 55
207
Shear modulus Gr,h (GPa) Gh,z (GPa) Gr,z (GPa)
17.9 21.1 21.1
–
Poisson’s ratio
0.3
0.3
Integrated thermal expansion (300–4.2 K)
2.59E03
2.98E03
with equal interval between adjacent layers as shown in Fig. 3a. The whole toroidal coil system is supported with fibre–glass reinforced plastics (FRP) composite structure so that conduction heat load to the cryostat is reduced. In the present design, each sector coil will have a separate helium container conforming closely to coil geometry to minimize the liquid helium inventory. The entire toroidal-type coil assembly system is enclosed by thermal shield made of copper maintained at around 60–70 K using a single-stage cryorefrigerator of capacity 240 W at 60 K. The structural concept of the magnet is shown in Fig. 3b. There is a common buffer liquid helium reservoir at higher elevation from the sector helium vessel for ensuring continuous supply of liquid helium to the sector helium vessel. The magnetic field distribution around coils is asymmetric as shown in Fig. 4 with the maximum magnetic field of 6.6 T at the coil inner radius (Point B in Fig. 4) in mid-plane (Y = 0 & Z = 0). A magnetic field of 0.5 mT, which is the average earth magnetic field, is considered to be the safe and acceptable value of stray field for human health. The 0.5 mT contour line at the equatorial plane of torus (Z = 0) is found to be at a distance of 1.8 m away from torus center. 3. Structural analysis 3.1. Cool down and steady state operation
Fig. 5. Exploded view of support structure (1/8th symmetry) comprising of backing cylinder, coil former and coil.
operating temperature of 4.2 K. This margin ensures that the superconductor will not quench during normal operation. The coils are epoxy impregnated and liquid helium bath cooled at 4.2 K. In order to obtain good heat transfer between superconducting strands and liquid helium, the sector coil shall be manufactured with permeable windings. The permeable winding structure can be formed by laying glass-fibre reinforced plastic G-10 strips
The SMES coil experiences mechanical stress and deformation during its cool-down to operating temperature and magneto-structural stress during frequent charging and discharging required for operation. Since the magnet experiences cyclic load during charging and discharging, the stress limit for all the support structure and coil material are kept below their endurance limit to prevent any fatigue failure. Further, mechanical disturbances like conductor motion causes degradation and premature quench of the magnet. One-eighth (1/8th) symmetry of sectored toroidal-type coil with support structure is modeled in 3-D with appropriate winding packing factor. The mechanical properties of the coil have been considered as orthotropic and homogenous with equivalent elastic modulus as summarized in Table 3. The coil movement is arrested by suitable mechanical or support structure, which is primarily composed of three parts: coil former or bobbin with end flange, a central backing cylinder,
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Fig. 6. Lorentz force distribution on nodes of the sector coils at nominal operating current of 1200 A.
Fig. 7. Circumferential stress (Pa) contours on coil due to excitation to 1200 A at 4.2 K.
and support plate as shown in Fig. 5. Though glass–fibre based support structure is most suitable for transient loss, stainless steel (SS-316L) has been used for ease of fabrication. Commercially available finite element analysis multi-physics code ANSYS [11] allows a detailed quantitative evaluation of stresses subject to severe working conditions. Sliding contact of coil with coil former (SS-316L) using surface to surface contact element (CONTA172TARGE169) has been used with friction coefficient of 0.35 [10]. Different radial turns in winding and support structure undergoes differential thermal contraction during cool-down from room temperature to 4.2 K and it exerts a radial inward force.
Therefore, it is important to analyse thermal stress in combination with magneto-structural stress. In the process of evaluating magneto-structural analysis of coil during excitation, magnetic field and Lorentz force distribution are computed first using coupled field element SOLID5. Electromagnetic force distribution on various nodes of the coils due to interaction of coil current density J and magnetic field B are asymmetric and non-uniform as shown in Fig. 6. The net force acting radially inward on each sector coil is found to be 470 kN at maximum operating current. This force is transmitted to the backing cylinder through coil former and support
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flanges. Therefore, stress and deformation develops in both coil and support structure. The net forces on Y and Z directions cancels out when all coils are symmetrically placed.
Fig. 8. Circumferential or hoop stress (Pa) distribution (at coil mid-plane) with angular position (h) in sector coil at 1200 A at 4.2 K.
The circumferential or hoop stress (rc) due to electromagnetic and thermal loading is found to be tensile and asymmetric with respect to angular position (h) as shown in Fig. 7. Tensile stress at inner and outer radius of the sector coil mid-plane is found to be almost mirror symmetric, mean radius rc as neutral radius. The angle (h) is measured from the horizontal axis passing through the equatorial plane (Z = 0) of the coil. It is interesting to note that both the circumferential and von-Mises stress becomes maximum at a particular angular position (108–110°) as shown in Fig. 8 though the peak magnetic field develops at h = p. This occurs due to the reaction force from the support structure. Variation of hoop stress with radial position for various coil azimuths, h, (in sector coil center at torus equatorial plane) is as shown in Fig. 9. It is important to note that the radial stress developed in the coils is compressive (negative rr) in nature as shown in Figs. 10 and 11. However, pretension of 12 kgf during coil winding will be provided to introduce little further compressive radial stress (2.5 MPa at inner layer) on the winding so that it works reliably under all working conditions. The maximum axial compressive stress (ry) developed at coil innermost layer and h = p were calculated to be 29 MPa and varies with axial, radial and azimuthal directions. The von-Mises stress distribution on assembly when coil is in full excitation at 4.2 K is shown in Fig. 12. Maximum effective or von-Mises stress develops on stainless steel (SS316L) coil former is around 193 MPa, which is considerably below the allowable value (550 MPa at 4.2 K). The von-Mises stress developed in different parts of the coil assembly is as summarized in Fig. 13. Thermal stress due to cooldown has quite less contribution on assembly compared to stress due to excitation.
3.2. Fatigue analysis
Fig. 9. Circumferential stress (Pa) on coil former and coil at 1200 A at sector-coil mid-plane in torus equator (Z = 0).
During its life time, the SMES will be subjected to many numbers of cycles of charging and discharging. Therefore, fatigue life assessment is a critical part of the design. The various approaches to fatigue assessment are: stress life, strain life and fracture mechanics. Stress life is based on the S–N (stress vs number of
Fig. 10. Radial stress (Pa) contours on coil at operating current of 1200 A at 4.2 K.
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cycles to failure) curve and is suitable for high cycle fatigue. Strain life approach is particularly suitable for low cycle fatigue, and is typically concerned with crack initiation. Fracture mechanics starts with an assumed flaw and determines the crack growth. For the purpose of present analysis, the strain life approach is used to determine the number of cycles before a crack is formed. After simulating the stress distribution from the static stress analysis, the fatigue life is obtained using strain-life equation and equation for cyclic stress strain curve. In the present analysis, the fatigue life for fully reversed loading (stress ratio = 1) and for zero based loading (stress ratio = 0) is evaluated. The values of minimum life for the two cases are found to be 3.7 105 cycles and 7.5 107 cycles respectively. The fatigue life for fully reversed and zero based load cases is shown in Figs. 14 and 15 respectively. 4. Transient/ AC loss The SMES unit will operate as voltage source converter (VSC) [12] based power conditioning system to control active and reactive power independently and simultaneously. Rapid charging or
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Fig. 13. Maximum von-Mises stress summary due to thermal cool-down to 4.2 K and excitation at 1200 A.
discharging of superconducting storage coil in power conditioning system (PCS) causes transient losses into liquid helium system and intermediate shield around the helium system as well. During discharge operation, the peak magnetic field in winding decreases allowing critical current density to increase. The eddy current losses are generated mainly during discharging period because the discharging period is generally shorter than charging. 4.1. Liquid helium system AC losses in liquid helium system are primarily contributed by hysteresis loss in superconducting filaments, coupling loss among multi-filamentary superconducting filaments and strands, induced eddy current in coil former, support structure and other metallic components. Loss from superconducting cable is calculated for every turn of the coil considering the local magnetic field distribution. The AC loss during discharge operations are [13] as follows, 4.1.1. The hysteresis loss in the filaments is given by
Fig. 11. Radial stress on coil at excitation of 1200 A (at 4.2 K) at coil mid-plane (Z = 0).
ph ¼ qh
kV tc
ð1Þ
Fig. 12. Von-Mises stress (Pa) on the coil assembly comprising of backing cylinder, coil former, coil, etc. at nominal operating current of 1200 A.
Please cite this article in press as: Bhunia U et al. Design of a 4.5 MJ/1 MW sectored toroidal superconducting energy storage magnet. Cryogenics (2014), http://dx.doi.org/10.1016/j.cryogenics.2014.06.007
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(a) Coil former
(a) Coil former
(b) Backing cylinder
(b) Backing cylinder
Fig. 14. Fatigue life (cycles) of coil and support structure for fully reversed loading.
Fig. 15. Fatigue life (cycles) of coil and support structure for zero-based loading.
where k is the volume fraction of superconductor, V is the conductor volume, tc is the carry over period, and qh is given by
where df is filament diameter, J is current density at some time instant of discharge, and JC(B) is the critical current density.
qh ¼
1
l0
Z
Bf
MdB
ð2Þ
Bi
where the initial and final magnetic fields are Bi and Bf respectively on the conductor, l0 = 4p 107 H/m is the free space permeability. The filament magnetization M in presence of transport current in discharge mode of operation is expressed by
M¼
2 J l0 JC ðBÞdf 1 3p J C ðBÞ
ð3Þ
4.1.2. The coupling loss among filaments of twist pitch lp is given by
pcf ¼
k
qt
2 lp B_ 2 V 2p
ð4Þ
where qt is the transverse resistivity of matrix material (Cu–0.5% _ is the rate of change of magnetic field. Mn). B,
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4.1.3. The inter-strand coupling loss via cross-over resistance (RC) in transverse field is given by
ptc ¼
1 _2 c B NðN 1Þlt V 120Rc t b
ð5Þ
where lt is cable twist pitch, B_t is the rate of change of field transverse to the broad face of the cable, N is the number of strands, c is the half width of the cable and b is its half thickness. 4.1.4. The inter-strand coupling via adjacent resistance (Ra) in transverse field
pta ¼
1 _2 B ðN 1Þlp V 24Ra t
4.1.5. The inter-strand resistance via adjacent resistance in parallel field is 2
pta ¼
1 _2 b B ðN 1Þ 2 lp V 32Ra p c
p;n ;n ¼ B r z t;n ;n ¼ B r z
Z p
p
0
Z 1 p
p
Bp;nr ;nz ðhÞ dh
ð8Þ
Bt;nr ;nz ðhÞ dh
ð9Þ
0
Summing over the contribution from each layer and turn of winding volume with the consideration of local magnetic field distribution, AC loss from superconductor winding is evaluated and is shown in Fig. 16. The temperature rise in the coil during discharge operation under adiabatic approximation is found to be around 0.15 K. Therefore, quench possibility during transient operation will not occur. 4.1.6. Coil former and other metallic parts In a homogeneous, isotropic and time invariant media, electric field induced by a changing magnetic field is given by
_
B E ¼ ~ r ~
dI2 dI1 þM þ R2 I 2 ¼ 0 dt dt
ð10Þ
Fig. 16. AC loss (W) in superconducting cable with different ramp down rates.
ð11Þ
pffiffiffiffiffiffiffiffiffi where M ¼ k L1 L2 is the mutual inductance between coil and coilformer. Here L1 is self inductance of coil and L2 is self inductance of former, M is mutual inductance between coil and former, I1 is the coil current and I2 is the induced current in former. Since the coil is closely made around the former, the coupling coefficient, k 1. Simplifying (11), induced current in former I2 can be deduced with the initial condition: I2 = 0 at t = 0 as
ð7Þ
where B_p is the rate of change of field parallel to the broad face of the cable. Unlike a single solenoid coil of cylindrical symmetric magnetic field distribution, magnetic field in a sectored-toroidal coil changes with coil azimuth (h) in any given layer (nr) and turn (nz) of winding volume. Therefore, variation of both parallel and transverse field has been averaged over azimuth for each layer and turn of the winding volume as
1
Induced electric field develops eddy current in the metallic arts inside cryostat. Coil former experiences maximum field transients out of all metallic parts present in the cryostat. It is desirable to have non-metallic coil former such as FRP to reduce eddy current effects. In the present design, in order to reduce liquid helium inventory, coil former is a part of the helium vessel, and FRP is not a good choice for coil former so far as structural reliability is concerned. Eddy current in coil former during discharging can be readily estimated by the following differential equation:
L2 ð6Þ
9
I2 ¼
M dI1 R2 1 exp t R2 dt L2
ð12Þ
Here, R2 and L2 can be determined considering former as a single turn secondary winding. Maximum field transient during operation is calculated to be 1.2 T/s (or equivalently, 200 A/s). The induced eddy current on the coil former dies out with a time constant (ss) can be written as
ss ¼
l0 t s r s 2qs
ð13Þ
Here, l0 is free space permeability, ts and rs are thickness and inner radius of coil former respectively, qs is the resistivity of stainless steel former. Considering ts = 0.007 m, rs = 0.19 m, and qs (at 4.5 K for SS-316L) = 4.96 107 X-m, typical value of time constant becomes ss 2 ms, which is much lower than the normal charging or discharging period. The thickness of coil former is minimized so that eddy loss is reduced without compromising the mechanical stability and integrity of the coil assembly. A detailed examination of the spatial dependence of eddy current density and loss using ANSYS code reveals that analytical result of eddy loss for coil former provides reasonably good estimate of eddy loss (8% deviation). Eddy current density developed on the coil former and support structure obtained using finite element code is as shown in Fig. 17. Summing up the contribution from elements, induced eddy loss in the coil former and support structure together is shown in Fig. 18. There are several kapton insulating layers around the coil former and epoxy based G-10 picket fences of 1 mm thickness around thereafter so that this heat flux from coil former is not directly transferred to superconducting sector coil, but boils off liquid helium. The top and bottom stainless steel flange of the coil former is also thermally isolated using G-10 picket fences. The total transient loss comprising from both AC loss from superconductor and eddy loss from coil former with support structure would be around 1000 J at 4.2 K (considering about 25% contingency) to the cryogenics system. This energy is equivalent to boil-off of 0.4 l of liquid helium. If the discharge occurs eight times a day, this provides an additional heat load of 2% to the steady state heat load. The steady state load to the helium chamber is calculated to be around 2.0 W at 4.2 K. It is proposed to have three numbers of two-stage Gifford– McMahon (GM) type cryo-refrigerator (1.5 W at 4.2 K each) to mitigate both transient and steady state load with enough buffer capacity.
Please cite this article in press as: Bhunia U et al. Design of a 4.5 MJ/1 MW sectored toroidal superconducting energy storage magnet. Cryogenics (2014), http://dx.doi.org/10.1016/j.cryogenics.2014.06.007
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Fig. 17. Distribution of eddy current density (Am2) vectors at coil former and support structure (at ramp down rate of 200 A/s).
5. Magnet safety and protection
Fig. 18. Total eddy loss (W) in coil former and support structure at 4.2 K.
4.2. Intermediate thermal shield Since the stray magnetic field outside is significantly low due to toroidal-type configuration, induced eddy current on thermal shield around the coils is not of major concern. Induced eddy current density in thermal shield is as shown in Fig. 19. The thermal shield around liquid helium vessel has more time constant since it is made of copper with resistivity (at 60 K) two orders of magnitude less than that of stainless steel. Eddy loss developed on thermal shield is shown in Fig. 20. The total heat load combining both steady state and transient load is around 180 W at 60 K, which is well within the capacity of a standard commercially available single-stage cryo-refrigerator of capacity 240 W at 60 K. In adiabatic situation, the maximum temperature rise of thermal shield during transient of 200 A/s (1.2 T/s) is found to be less than 0.3 K. The mechanical von-Mises stress developed on the intermediate shield due to interaction of induced current density and magnetic field for maximum field transients is found to be around 6.2 MPa, which suggest that the thermal shield would be safe from any structural deformation during field transient. The primary parameters of the design are summarized in Table 4.
Sector coils are series interconnected electrically. In case of quench in one coil, magnet safety requires that temperature and voltage developed during a quench remains below certain level. The stored energy either is to be extracted or distributed uniformly in coils at the onset of quench by suitable quench protection scheme. One important requirement in the circuit arrangement is to maintain electromagnetic forces balanced azimuthally and vertically during a quench. A viable electrical connection scheme for quench protection is shown in Fig. 21a. The other alternative is to adopt external dump resistors parallel to each sector coil as in Fig. 21b, which is suitable for achieving reduced peak voltage across the quenched coil. The second approach will, however, increase the complexity in cryostat and moreover, the force balance between neighboring coils is disturbed in this situation due to unequal current in the coils. The third option could be to use quench protection heater along with series connected dump resistors. The self and mutual inductance matrix among the sector coils is computed calculating internal energy and interaction energy of neighboring coils respectively. The coupled nonlinear transient thermal and electromagnetic models circuit models are solved with commercial FEA-based software ‘‘Vector Fields Opera-Quench’’ [14] to understand and finalize the quench protection scheme. The transient heat balance equations is
r kðTÞrT þ Q þ Q ext ¼ CðTÞ
@T @t
ð14Þ
where T, k(T), Qext, and C(T) are the coil temperature, the thermal conductivity, the external heat generation for provoking quench and volumetric specific heat respectively. The ohmic heat source density (Q) is given by
Q¼
jNm j A
1 I2 fm rm ðB; TÞ þ ð1 fm Þrsc ðB; TÞ op
ð15Þ
where Nm is a vector turn density [15] defined as current density to operating current ratio, fm is non-superconductor (matrix) to superconductor ratio, A is the cable cross-sectional area, rm(B, T) is the
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Fig. 19. Distribution of eddy current density (A/m2) vectors at intermediate shield for 200 A/s.
Fig. 20. Eddy loss (W) in intermediate thermal shield at 60 K with different ramp down rates.
matrix electrical conductivity, and rsc(B, T) is the electrical conductivity of superconductor. The Quench code closely couples the nonlinear transient thermal, electromagnetic and circuit models. The transient thermal and electromagnetic field simulations were implemented using an adaptive Galerkin time stepping method in the Quench code. Sector coils are epoxy-impregnated with cooling channels between layers. The heat transfer coefficient to the liquid helium coolant is considered to be negligible during the process of quench. The whole magnet is initialized to the original temperature of 4.2 K and initial current of 1200 A. A point pulsed heat flux continuing about 10 ms is added at the middle turn of coil mid plane, which is good enough to raise the temperature of superconductor to its current sharing temperature. In our model, the switch S1 is assumed to be closed and S2 opened up as soon as the quench is detected. The diode D1 parallel to the switch S1 provides redundancy of the protection mechanism. Quench onset starts in the simulation when the differential voltage among any two coils is
more than 100 mV with validation period of 100 ms. For different dump resistors with no active protection by quench heater, the coil current and hot spot temperature is as shown in Fig. 22a. The voltage evolution across the quenched coil is shown in Fig. 22b. It is observed that more than 1.0 O dump resistor is required to keep the coil maximum voltage below 1 kV limit. The other option is to use lower value of dump resistor with active protection by quench heater. It is found that quench heater of 1 in. width around the coil outer mid-plane with heat flux of 2 W/cm2 (for 25–50 ms) along with dump resistor of 0.1 X is also feasible and may be a better option to keep both the maximum temperature below 100 K and most importantly terminal voltage across each coil below 1 kV limit. In the present simulation we have taken up a realistic heater delay time of 100 ms upon quench detection based on our experience of developed capacitive heater power supply. If all eight coils are heater fired upon detection of quench, the peak voltage across the quenched coil reduces to 550 V with the hot spot temperature of 65 K as shown in Fig. 23. The maximum terminal voltage across the current leads is found to be 250 V, which is less than the voltage across quenched coil. This is due to the fact that the resistive voltage and induced inductive voltages during current decay are of opposite direction. It is observed that if at least three coils are heater-fired upon detection of quench, peak voltage across the quenched coil becomes less than 1 kV limit. The center of the dump resistor may be earthed further with the cryostat body so that the coil terminal voltage with respect to cryostat is reduced to half.
6. Joint design The sector coils are interconnected with several soldered resistive splice joints away from the coil in a magnetic field of less than 1.0 T. It is important that splices have acceptably low electrical resistance so that magnet would not suffer any performance degradation and must be mechanically stable. The splice resistance is
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U. Bhunia et al. / Cryogenics xxx (2014) xxx–xxx
Fig. 21a. Quench protection circuit with a single dump resistor across the coil assembly.
Fig. 21b. Quench protection circuit with dump resistors across each sector coil.
Fig. 22a. Transition of coil current and coil hot spot temperature with different dump resistors.
Fig. 22b. Transition of voltage across coil with different dump resistors during quench.
Fig. 23. Transition of coil current, voltage across quenched coil and coil hot spot temperature with quench heater & Rd = 0.1 O.
primarily due to solder resistivity, solder thickness and splice length. The splice region is well cooled directly with liquid helium. With the experience of splicing at CERN, it is planned to use SnAg (4%) solder material since it has lower resistivity at 4 K with respect to other commonly available solder alloys. We have set up a target joint resistance per splice to be less than 10 nX so that Joule heating is within 15 mW per joint at 4.2 K and cryogenic budget is met. For an overlapping splice length of 10 cm (twice the cable transposition pitch), surface heat flux due to resistive heating would be around 0.0015 W/cm2, which corresponds to a negligibly small temperature rise of the cable insulated with 50% overlap polymide (25 lm thickness) by less than 0.02 K. However, there are many parameters such as duration of heating during soldering and overlapping length in splice that need to be optimized during the development of splicing technique to avoid any degradation of superconducting characteristics of the cable. Splices of uniform quality are under development with suitable
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soldering fixture and joint technology will be established through a series of joints. 7. Conclusions A small-scale 4.5 MJ/1 MW/2 s toroidal-type superconducting magnet for SMES system is designed. The mechanical behaviour of the magnet with a simple and reliable mechanical structure is studied by commercial code ANSYS. All parts of coil remain under compression (or negative radial stress) at full excitation with the inner most layer maintain compressive contact with coil former. Effect of thermal stress on whole assembly has been found to be less with respect to electromagnetic (EM) stress. The maximum von-Mises stress in coil and coil former support assembly is found to be within allowable limiting value. The analysis allows a detailed quantitative evaluation of the stresses in the coil and support structure subject to all possible working conditions. Transient loss including AC loss in superconductor and eddy current loss in coil support structure and former has been evaluated. Heater induced active quench protection in fail-safe mode is found to be better option for quench protection ensuring no magnet damage. Acknowledgement We extend our sincere thanks to Suparna Patra and S B Bose for their contribution in developing 3D models of cryostat and assemblies. We would like to thank all our colleagues in SMES group for many fruitful technical discussions during the course of this work.
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References [1] Bhunia U, Pradhan J, et al. Design, fabrication and cryogenic testing of 0.6 MJ SMES coil. Cryogenics 2012;52:719–24. [2] Kim KM, Kim AR, Park HY, Kim JG, Park M, Yu IK, et al. Design and mechanical stress analysis of a toroidal type SMES magnet. IEEE Trans Appl Supercond 2010;20(3):1900–3. [3] Tixador P, Bellin B, Deleglise M, Vallier JC, Bruzek CE, Pavard S, et al. Design of a 800 kJ HTS SMES. IEEE Trans Appl Supercond 2005;15(2):1907–10. [4] Higashikawa K, Nakamura T, Shikimachi K, Hirano N, Nagaya S, Kiss T, et al. Conceptual design of HTS coil for SMES using YBCO coated conductor. IEEE Trans Appl Supercond 2007;17(2):1990–3. [5] Park M, Kwak S, Kim W, Lee J, Han J, Choi K, et al. Conceptual design of HTS magnet for a 5 MJ class SMES. IEEE Trans Appl Supercond 2008;18(2):750–3. [6] Dai T, Tang Y, Shi J, Jiao F, Wang L. Design of a 10 MJ HTS superconducting magnetic energy storage magnet. IEEE Trans Appl Supercond 2010;20(3): 1356–9. [7] Noguchi S, Inaba Y, Igarashi H. An optimal configuration design method for HTS–SMES coils. IEEE Trans Appl Supercond 2005;15:1927–30. [8] Birkner PJ, Munchen TU. On the design of superconducting magnetic energy storage system. IEEE Trans Appl Supercond 1993;3(1):246–9. [9] Storn R, Price K. Differential evolution-a simple and efficient adaptive scheme for global optimization over continuous spaces. J Global Optim 1997;11(4): 341–59. [10] Chen P, Dai Y, Wang Q, Zhang Q. Mechanical behavior analysis of a 1 MJ SMES magnet. IEEE Trans Appl Supercond 2010;20(3):1916–9. [11] Ansys Multiphysics, ANSYS v14.0 User’s Manual, 2012. [12] Hasan AM, Wu B, Dougal RA. An overview of SMES applications in power and energy systems. IEEE Trans Appl Supercond 2010;1(1):38–43. [13] Wilson MN, Ghosh AK, Haken B, Hassenzahl WV, Kaugerts J, Moritz G, et al. Cored Rutherford cable for the GSI fast ramping synchrotron. IEEE Trans Appl Supercond 2003;13:1704. [14] OPERA-3D v. 14, Vector Fields, Cobham plc, Brook Road, Wimborne, Dorset, BH21 2BJ, UK. [15] Simkin J, Taylor SC, Xu E, Michaelides AM. Coupled transient thermal and electromagnetic finite element analysis for the simulation of quench effects in superconducting magnets. J Optoelectron Adv Mater 2008;10(6):1437–41.
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Design of a 4.5 MJ/1 MW sectored toroidal superconducting energy storage magnet Uttam Bhunia ⇑, Javed Akhter, Chinmay Nandi, Gautam Pal, Subimal Saha Variable Energy Cyclotron Centre, Department of Atomic Energy, 1/AF, Bidhan Nagar, Kolkata 700 064, India
a r t i c l e
i n f o
Article history: Available online xxxx Keywords: SMES Toroidal-type Stress Structural analysis AC loss Quench
a b s t r a c t A 4.5 MJ/1 MW superconducting magnetic energy storage (SMES) system is being developed at VECC centre, Kolkata. The magnet system consists of the cryostat and coil assembly comprising eight superconducting solenoid coils made of custom-made NbTi based Rutherford-type cable and arranged in toroidal fashion with finite inter-sector gap. Since the strong electromagnetic force distributed to the coil is asymmetric and non-uniform in nature, a precise 3-D finite element analysis (FEA) has been carried out to design a mechanically stable coil and support structure under various operational scenarios. The results reveal that maximum stress developed on coil and its support structure is below allowable stress limit. Extensive transient analysis has also been carried out to evaluate transient loss and assess the feasibility of using helium re-condensation technology with commercially available cryo-refrigerators. Finally, quench protection scenario has also been discussed suitable for this toroidal-type SMES system. The article investigates the design concept of the cryostat and coil assembly. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Small scale or medium scale superconducting magnetic energy storage (SMES) systems are in high demand for compensation of load fluctuation, mitigation of voltage dip or sag in utility line. In view to develop technology for SMES application to compensate voltage dip of utility line for critical machines, VEC Centre, Kolkata has already developed the technology with energy of 0.6 MJ [1] along with associated power converter system. In the next phase, it is aimed to develop a toroidal-type SMES unit of 4.5 MJ/1 MW capacity. The magnet consists of modular solenoid coils connected in series and arranged in a toroidal symmetric fashion. The main advantage of toroidal configuration is the very low magnetic stray field outside the coil assembly compared to a solenoidal SMES of similar storage capacity. The primary problem concerning toroidal-type configuration is caused by large Lorentz forces acting on the superconducting cable. The Lorentz force on the current carrying coil is asymmetric, non-uniform and there is a net attractive force on the coils towards the centre of the torus. Therefore, the coil must be properly supported to prevent excessive deformation. Stress analysis of pancake type high-temperature superconductor (HTS) based SMES magnet has already been reported by Kim et al. [2]. In recent times, SMES of both solenoid and toroidal-type ⇑ Corresponding author. E-mail address: [email protected] (U. Bhunia).
configuration using commercially available HTS tape are being developed by various groups [3–7] world-wide. Design methods for the toroidal configuration with pancake-type HTS-based modular coil for SMES have been proposed to reduce winding volume [8,5]. However, commercially available HTS tape, till date is very expensive compared to niobium–titanium alloy based low temperature superconductor and there are also still many technical issues to be addressed while using HTS for reliable operation of commercial SMES units. In recent times, after the commercial availability of 4.2 K cryo-refrigerator, niobium–titanium (NbTi) alloy based Rutherford-type cable is believed to be a better choice for small or medium scale SMES units using helium vapor re-condensation technology. A custom-made NbTi based Rutherford-type cable suitable for transient application is used in the present design. Commercially available general purpose multi-physics finite element analysis (FEA) code has been used for detailed three dimensional magneto-structural analyses to optimize the structural design of the support structure. This paper presents the design concept of the cryostat, magneto-structural design of coil in integration with support structure so that equivalent von-Mises stress in all constituent materials never exceeds the yield stress. Extensive fatigue analysis is carried out considering repeated charging/ discharging cycle during operation of SMES. Transient magnetic field effect on coil winding, former, intermediate thermal shield around the liquid helium chamber, etc. has also been investigated to ensure the stable operation of SMES and to find the feasibility of
http://dx.doi.org/10.1016/j.cryogenics.2014.06.007 0011-2275/Ó 2014 Elsevier Ltd. All rights reserved.
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using cryo-refrigerator. Quench behavior and reliable protection method for the coil are also presented in this paper. 2. Basic design concept 2.1. Specification of superconducting wire A superconducting (SC) Rutherford type cable with inter-filamentary matrix Cu–0.5% Mn with low loss characteristics has been (Table 1) ensured for the SMES coil. Good electrical contact to neighbouring strands in the cable is ensured with stabrite (Sn–5% Ag) coating and heat treatment over the cable. The critical characteristic of the cable at 4.2 K is as shown in Fig. 1. The cable is wrapped with polymide tape (25 lm thick) with 50% overlap for turn to turn insulation. 2.2. Design and parameter of sectored toroidal-type magnet Basic parameter of a toroidal magnet is the shape of the sector modules: for example a D-type or circular coils. Birkner and Munchen [8] investigated the issue and found that for a given length of superconductor at constant operating current, A D-shaped sector has higher maximum energy (18% higher) than a circular coil. The difference hardly justifies choosing D-type sector coils for its complex fabrication cost compared to circular coils. The circular geometry has been optimised for stored magnetic energy and magneto-structural stress. The sectored SMES unit is composed of a finite number of sectors or elemental solenoidal coils arranged in a toroidal fashion as shown in Fig. 2 and are interconnected in series. The geometry of the sectored toroidal magnet has been optimised by three design variables namely: major radius, r0, geometry dependent parameters, a = r1/r0 and b = r2/r0 for a given inter-sector coil spacing, d. The design goal was to find the optimal solutions for both magnet overall size in terms of torus major radius and required superconductor length for winding, which in turn reduces a significant part of overall cost. A multi-objective
Table 1 Main parameters of superconducting cable. Strand diameter (mm) Filament number Cu–Mn/NbTi Filament diameter (lm) Nos. of strands in cable Critical current (7 T, 4.2 K) Cable width, 2 c (mm) Cable thickness, 2 b (mm) Approx. cable lay pitch, lt (mm) Tensile stress (MPa) (0.2% strain) at room temperature
0.72 3900 2.0 10 10 2200 A 3.7 1.3 50 450
Fig. 2. Schematic diagram of the magnet system with sector coil arrangements.
design optimisation scheme using differential evolution [9] algorithm has been developed to find out the coil parameters for a given stored energy level. The specifications of the magnet are set as follows: (i) Stored energy is 4.5 MJ. (ii) Circumferential stress in sectored coil to be within an allowable limit of 150 MPa at 4.2 K. (iii) Numbers of elemental or sector coils to be chosen in such a way that stray magnetic field outside the torus follows the safety guidelines (0.5 mT or lower). (iv) Number of winding turns (nr) and layers (ny) are considered to be integer. (v) There must be inter-sector gap (d) for support structure, access to the volume and ease of manufacture. In the present study, d = 50 mm is assumed from practical considerations. Suitable support structure is essential to keep the sector coil in position under strong electro-magnetic force. The basic design parameters of the eight-sector toroidal system are listed in Table 2. Higher the number of sectors, extension of stray magnetic field outside the coil assembly reduces further, but with the cost of additional number of inter-sector cable joints. An operating current margin of 35% is maintained in design study which corresponds to a temperature margin of 0.64 K over the Table 2 Basic design specification of the SMES magnet.
Fig. 1. Critical characteristics of the Rutherford-type cable at 4.2 K.
Number of sectors, Ns Minimum inter-sector coil gap, d (m) Energy, ES (MJ) Maximum rated power, P0 (MW) Rated operating current, Iop (A) Major radius, r0 (m) Sector coil Outer radius, r2 (m) Inner radius, r1 (m) Height, h (m) Winding turns Cable length (km) Distance of 0.5 mT contour line from torus center (m)
8 0.05 4.5 1.0 1200 0.62 0.24 0.19 0.3 1300 1.9 1.8
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Fig. 3a. Coil winding scheme of the sector coil.
Fig. 3b. Design concept (3D-CAD model) of the SMES magnet.
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U. Bhunia et al. / Cryogenics xxx (2014) xxx–xxx Table 4 Design results of 4.5 MJ SMES magnet. Coil arrangement Number of sectors Total conductor length (km) Conductor
Fig. 4. Axial magnetic field component on sector coil mid-plane (Y = 0 & Z = 0) measured from the center of the torus.
Operating current, Iop (A) Number of Inter-sector joints Superconductor–magnet lead joints Maximum von-Mises stress (MPa) On coil/coil former at 1200 A Liquid helium chamber at 4.2 K Steady state load (W) Dynamic load (W) during discharge (200 A/s) Intermediate shield at 60 K Steady state load (W) Dynamic load (W) during discharge (200 A/s) Number of cryorefrigerators Two-stage (1.5 W at 4.2 K) Single stage (240 W at 60 K)
Toroidal-type 8 15.2 NbTi based Rutherford-type cable 1200 7 2 133/193 2.0 1000.0
120.0 60.0
3 1
Table 3 Material properties (at 4.2 K). Coil (equivalent properties)
Support structure (SS-316 L)
Young’s modulus Er (GPa) Eh (GPa) Ez (GPa)
46.5 55 55
207
Shear modulus Gr,h (GPa) Gh,z (GPa) Gr,z (GPa)
17.9 21.1 21.1
–
Poisson’s ratio
0.3
0.3
Integrated thermal expansion (300–4.2 K)
2.59E03
2.98E03
with equal interval between adjacent layers as shown in Fig. 3a. The whole toroidal coil system is supported with fibre–glass reinforced plastics (FRP) composite structure so that conduction heat load to the cryostat is reduced. In the present design, each sector coil will have a separate helium container conforming closely to coil geometry to minimize the liquid helium inventory. The entire toroidal-type coil assembly system is enclosed by thermal shield made of copper maintained at around 60–70 K using a single-stage cryorefrigerator of capacity 240 W at 60 K. The structural concept of the magnet is shown in Fig. 3b. There is a common buffer liquid helium reservoir at higher elevation from the sector helium vessel for ensuring continuous supply of liquid helium to the sector helium vessel. The magnetic field distribution around coils is asymmetric as shown in Fig. 4 with the maximum magnetic field of 6.6 T at the coil inner radius (Point B in Fig. 4) in mid-plane (Y = 0 & Z = 0). A magnetic field of 0.5 mT, which is the average earth magnetic field, is considered to be the safe and acceptable value of stray field for human health. The 0.5 mT contour line at the equatorial plane of torus (Z = 0) is found to be at a distance of 1.8 m away from torus center. 3. Structural analysis 3.1. Cool down and steady state operation
Fig. 5. Exploded view of support structure (1/8th symmetry) comprising of backing cylinder, coil former and coil.
operating temperature of 4.2 K. This margin ensures that the superconductor will not quench during normal operation. The coils are epoxy impregnated and liquid helium bath cooled at 4.2 K. In order to obtain good heat transfer between superconducting strands and liquid helium, the sector coil shall be manufactured with permeable windings. The permeable winding structure can be formed by laying glass-fibre reinforced plastic G-10 strips
The SMES coil experiences mechanical stress and deformation during its cool-down to operating temperature and magneto-structural stress during frequent charging and discharging required for operation. Since the magnet experiences cyclic load during charging and discharging, the stress limit for all the support structure and coil material are kept below their endurance limit to prevent any fatigue failure. Further, mechanical disturbances like conductor motion causes degradation and premature quench of the magnet. One-eighth (1/8th) symmetry of sectored toroidal-type coil with support structure is modeled in 3-D with appropriate winding packing factor. The mechanical properties of the coil have been considered as orthotropic and homogenous with equivalent elastic modulus as summarized in Table 3. The coil movement is arrested by suitable mechanical or support structure, which is primarily composed of three parts: coil former or bobbin with end flange, a central backing cylinder,
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Fig. 6. Lorentz force distribution on nodes of the sector coils at nominal operating current of 1200 A.
Fig. 7. Circumferential stress (Pa) contours on coil due to excitation to 1200 A at 4.2 K.
and support plate as shown in Fig. 5. Though glass–fibre based support structure is most suitable for transient loss, stainless steel (SS-316L) has been used for ease of fabrication. Commercially available finite element analysis multi-physics code ANSYS [11] allows a detailed quantitative evaluation of stresses subject to severe working conditions. Sliding contact of coil with coil former (SS-316L) using surface to surface contact element (CONTA172TARGE169) has been used with friction coefficient of 0.35 [10]. Different radial turns in winding and support structure undergoes differential thermal contraction during cool-down from room temperature to 4.2 K and it exerts a radial inward force.
Therefore, it is important to analyse thermal stress in combination with magneto-structural stress. In the process of evaluating magneto-structural analysis of coil during excitation, magnetic field and Lorentz force distribution are computed first using coupled field element SOLID5. Electromagnetic force distribution on various nodes of the coils due to interaction of coil current density J and magnetic field B are asymmetric and non-uniform as shown in Fig. 6. The net force acting radially inward on each sector coil is found to be 470 kN at maximum operating current. This force is transmitted to the backing cylinder through coil former and support
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flanges. Therefore, stress and deformation develops in both coil and support structure. The net forces on Y and Z directions cancels out when all coils are symmetrically placed.
Fig. 8. Circumferential or hoop stress (Pa) distribution (at coil mid-plane) with angular position (h) in sector coil at 1200 A at 4.2 K.
The circumferential or hoop stress (rc) due to electromagnetic and thermal loading is found to be tensile and asymmetric with respect to angular position (h) as shown in Fig. 7. Tensile stress at inner and outer radius of the sector coil mid-plane is found to be almost mirror symmetric, mean radius rc as neutral radius. The angle (h) is measured from the horizontal axis passing through the equatorial plane (Z = 0) of the coil. It is interesting to note that both the circumferential and von-Mises stress becomes maximum at a particular angular position (108–110°) as shown in Fig. 8 though the peak magnetic field develops at h = p. This occurs due to the reaction force from the support structure. Variation of hoop stress with radial position for various coil azimuths, h, (in sector coil center at torus equatorial plane) is as shown in Fig. 9. It is important to note that the radial stress developed in the coils is compressive (negative rr) in nature as shown in Figs. 10 and 11. However, pretension of 12 kgf during coil winding will be provided to introduce little further compressive radial stress (2.5 MPa at inner layer) on the winding so that it works reliably under all working conditions. The maximum axial compressive stress (ry) developed at coil innermost layer and h = p were calculated to be 29 MPa and varies with axial, radial and azimuthal directions. The von-Mises stress distribution on assembly when coil is in full excitation at 4.2 K is shown in Fig. 12. Maximum effective or von-Mises stress develops on stainless steel (SS316L) coil former is around 193 MPa, which is considerably below the allowable value (550 MPa at 4.2 K). The von-Mises stress developed in different parts of the coil assembly is as summarized in Fig. 13. Thermal stress due to cooldown has quite less contribution on assembly compared to stress due to excitation.
3.2. Fatigue analysis
Fig. 9. Circumferential stress (Pa) on coil former and coil at 1200 A at sector-coil mid-plane in torus equator (Z = 0).
During its life time, the SMES will be subjected to many numbers of cycles of charging and discharging. Therefore, fatigue life assessment is a critical part of the design. The various approaches to fatigue assessment are: stress life, strain life and fracture mechanics. Stress life is based on the S–N (stress vs number of
Fig. 10. Radial stress (Pa) contours on coil at operating current of 1200 A at 4.2 K.
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cycles to failure) curve and is suitable for high cycle fatigue. Strain life approach is particularly suitable for low cycle fatigue, and is typically concerned with crack initiation. Fracture mechanics starts with an assumed flaw and determines the crack growth. For the purpose of present analysis, the strain life approach is used to determine the number of cycles before a crack is formed. After simulating the stress distribution from the static stress analysis, the fatigue life is obtained using strain-life equation and equation for cyclic stress strain curve. In the present analysis, the fatigue life for fully reversed loading (stress ratio = 1) and for zero based loading (stress ratio = 0) is evaluated. The values of minimum life for the two cases are found to be 3.7 105 cycles and 7.5 107 cycles respectively. The fatigue life for fully reversed and zero based load cases is shown in Figs. 14 and 15 respectively. 4. Transient/ AC loss The SMES unit will operate as voltage source converter (VSC) [12] based power conditioning system to control active and reactive power independently and simultaneously. Rapid charging or
7
Fig. 13. Maximum von-Mises stress summary due to thermal cool-down to 4.2 K and excitation at 1200 A.
discharging of superconducting storage coil in power conditioning system (PCS) causes transient losses into liquid helium system and intermediate shield around the helium system as well. During discharge operation, the peak magnetic field in winding decreases allowing critical current density to increase. The eddy current losses are generated mainly during discharging period because the discharging period is generally shorter than charging. 4.1. Liquid helium system AC losses in liquid helium system are primarily contributed by hysteresis loss in superconducting filaments, coupling loss among multi-filamentary superconducting filaments and strands, induced eddy current in coil former, support structure and other metallic components. Loss from superconducting cable is calculated for every turn of the coil considering the local magnetic field distribution. The AC loss during discharge operations are [13] as follows, 4.1.1. The hysteresis loss in the filaments is given by
Fig. 11. Radial stress on coil at excitation of 1200 A (at 4.2 K) at coil mid-plane (Z = 0).
ph ¼ qh
kV tc
ð1Þ
Fig. 12. Von-Mises stress (Pa) on the coil assembly comprising of backing cylinder, coil former, coil, etc. at nominal operating current of 1200 A.
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(a) Coil former
(a) Coil former
(b) Backing cylinder
(b) Backing cylinder
Fig. 14. Fatigue life (cycles) of coil and support structure for fully reversed loading.
Fig. 15. Fatigue life (cycles) of coil and support structure for zero-based loading.
where k is the volume fraction of superconductor, V is the conductor volume, tc is the carry over period, and qh is given by
where df is filament diameter, J is current density at some time instant of discharge, and JC(B) is the critical current density.
qh ¼
1
l0
Z
Bf
MdB
ð2Þ
Bi
where the initial and final magnetic fields are Bi and Bf respectively on the conductor, l0 = 4p 107 H/m is the free space permeability. The filament magnetization M in presence of transport current in discharge mode of operation is expressed by
M¼
2 J l0 JC ðBÞdf 1 3p J C ðBÞ
ð3Þ
4.1.2. The coupling loss among filaments of twist pitch lp is given by
pcf ¼
k
qt
2 lp B_ 2 V 2p
ð4Þ
where qt is the transverse resistivity of matrix material (Cu–0.5% _ is the rate of change of magnetic field. Mn). B,
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4.1.3. The inter-strand coupling loss via cross-over resistance (RC) in transverse field is given by
ptc ¼
1 _2 c B NðN 1Þlt V 120Rc t b
ð5Þ
where lt is cable twist pitch, B_t is the rate of change of field transverse to the broad face of the cable, N is the number of strands, c is the half width of the cable and b is its half thickness. 4.1.4. The inter-strand coupling via adjacent resistance (Ra) in transverse field
pta ¼
1 _2 B ðN 1Þlp V 24Ra t
4.1.5. The inter-strand resistance via adjacent resistance in parallel field is 2
pta ¼
1 _2 b B ðN 1Þ 2 lp V 32Ra p c
p;n ;n ¼ B r z t;n ;n ¼ B r z
Z p
p
0
Z 1 p
p
Bp;nr ;nz ðhÞ dh
ð8Þ
Bt;nr ;nz ðhÞ dh
ð9Þ
0
Summing over the contribution from each layer and turn of winding volume with the consideration of local magnetic field distribution, AC loss from superconductor winding is evaluated and is shown in Fig. 16. The temperature rise in the coil during discharge operation under adiabatic approximation is found to be around 0.15 K. Therefore, quench possibility during transient operation will not occur. 4.1.6. Coil former and other metallic parts In a homogeneous, isotropic and time invariant media, electric field induced by a changing magnetic field is given by
_
B E ¼ ~ r ~
dI2 dI1 þM þ R2 I 2 ¼ 0 dt dt
ð10Þ
Fig. 16. AC loss (W) in superconducting cable with different ramp down rates.
ð11Þ
pffiffiffiffiffiffiffiffiffi where M ¼ k L1 L2 is the mutual inductance between coil and coilformer. Here L1 is self inductance of coil and L2 is self inductance of former, M is mutual inductance between coil and former, I1 is the coil current and I2 is the induced current in former. Since the coil is closely made around the former, the coupling coefficient, k 1. Simplifying (11), induced current in former I2 can be deduced with the initial condition: I2 = 0 at t = 0 as
ð7Þ
where B_p is the rate of change of field parallel to the broad face of the cable. Unlike a single solenoid coil of cylindrical symmetric magnetic field distribution, magnetic field in a sectored-toroidal coil changes with coil azimuth (h) in any given layer (nr) and turn (nz) of winding volume. Therefore, variation of both parallel and transverse field has been averaged over azimuth for each layer and turn of the winding volume as
1
Induced electric field develops eddy current in the metallic arts inside cryostat. Coil former experiences maximum field transients out of all metallic parts present in the cryostat. It is desirable to have non-metallic coil former such as FRP to reduce eddy current effects. In the present design, in order to reduce liquid helium inventory, coil former is a part of the helium vessel, and FRP is not a good choice for coil former so far as structural reliability is concerned. Eddy current in coil former during discharging can be readily estimated by the following differential equation:
L2 ð6Þ
9
I2 ¼
M dI1 R2 1 exp t R2 dt L2
ð12Þ
Here, R2 and L2 can be determined considering former as a single turn secondary winding. Maximum field transient during operation is calculated to be 1.2 T/s (or equivalently, 200 A/s). The induced eddy current on the coil former dies out with a time constant (ss) can be written as
ss ¼
l0 t s r s 2qs
ð13Þ
Here, l0 is free space permeability, ts and rs are thickness and inner radius of coil former respectively, qs is the resistivity of stainless steel former. Considering ts = 0.007 m, rs = 0.19 m, and qs (at 4.5 K for SS-316L) = 4.96 107 X-m, typical value of time constant becomes ss 2 ms, which is much lower than the normal charging or discharging period. The thickness of coil former is minimized so that eddy loss is reduced without compromising the mechanical stability and integrity of the coil assembly. A detailed examination of the spatial dependence of eddy current density and loss using ANSYS code reveals that analytical result of eddy loss for coil former provides reasonably good estimate of eddy loss (8% deviation). Eddy current density developed on the coil former and support structure obtained using finite element code is as shown in Fig. 17. Summing up the contribution from elements, induced eddy loss in the coil former and support structure together is shown in Fig. 18. There are several kapton insulating layers around the coil former and epoxy based G-10 picket fences of 1 mm thickness around thereafter so that this heat flux from coil former is not directly transferred to superconducting sector coil, but boils off liquid helium. The top and bottom stainless steel flange of the coil former is also thermally isolated using G-10 picket fences. The total transient loss comprising from both AC loss from superconductor and eddy loss from coil former with support structure would be around 1000 J at 4.2 K (considering about 25% contingency) to the cryogenics system. This energy is equivalent to boil-off of 0.4 l of liquid helium. If the discharge occurs eight times a day, this provides an additional heat load of 2% to the steady state heat load. The steady state load to the helium chamber is calculated to be around 2.0 W at 4.2 K. It is proposed to have three numbers of two-stage Gifford– McMahon (GM) type cryo-refrigerator (1.5 W at 4.2 K each) to mitigate both transient and steady state load with enough buffer capacity.
Please cite this article in press as: Bhunia U et al. Design of a 4.5 MJ/1 MW sectored toroidal superconducting energy storage magnet. Cryogenics (2014), http://dx.doi.org/10.1016/j.cryogenics.2014.06.007
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U. Bhunia et al. / Cryogenics xxx (2014) xxx–xxx
Fig. 17. Distribution of eddy current density (Am2) vectors at coil former and support structure (at ramp down rate of 200 A/s).
5. Magnet safety and protection
Fig. 18. Total eddy loss (W) in coil former and support structure at 4.2 K.
4.2. Intermediate thermal shield Since the stray magnetic field outside is significantly low due to toroidal-type configuration, induced eddy current on thermal shield around the coils is not of major concern. Induced eddy current density in thermal shield is as shown in Fig. 19. The thermal shield around liquid helium vessel has more time constant since it is made of copper with resistivity (at 60 K) two orders of magnitude less than that of stainless steel. Eddy loss developed on thermal shield is shown in Fig. 20. The total heat load combining both steady state and transient load is around 180 W at 60 K, which is well within the capacity of a standard commercially available single-stage cryo-refrigerator of capacity 240 W at 60 K. In adiabatic situation, the maximum temperature rise of thermal shield during transient of 200 A/s (1.2 T/s) is found to be less than 0.3 K. The mechanical von-Mises stress developed on the intermediate shield due to interaction of induced current density and magnetic field for maximum field transients is found to be around 6.2 MPa, which suggest that the thermal shield would be safe from any structural deformation during field transient. The primary parameters of the design are summarized in Table 4.
Sector coils are series interconnected electrically. In case of quench in one coil, magnet safety requires that temperature and voltage developed during a quench remains below certain level. The stored energy either is to be extracted or distributed uniformly in coils at the onset of quench by suitable quench protection scheme. One important requirement in the circuit arrangement is to maintain electromagnetic forces balanced azimuthally and vertically during a quench. A viable electrical connection scheme for quench protection is shown in Fig. 21a. The other alternative is to adopt external dump resistors parallel to each sector coil as in Fig. 21b, which is suitable for achieving reduced peak voltage across the quenched coil. The second approach will, however, increase the complexity in cryostat and moreover, the force balance between neighboring coils is disturbed in this situation due to unequal current in the coils. The third option could be to use quench protection heater along with series connected dump resistors. The self and mutual inductance matrix among the sector coils is computed calculating internal energy and interaction energy of neighboring coils respectively. The coupled nonlinear transient thermal and electromagnetic models circuit models are solved with commercial FEA-based software ‘‘Vector Fields Opera-Quench’’ [14] to understand and finalize the quench protection scheme. The transient heat balance equations is
r kðTÞrT þ Q þ Q ext ¼ CðTÞ
@T @t
ð14Þ
where T, k(T), Qext, and C(T) are the coil temperature, the thermal conductivity, the external heat generation for provoking quench and volumetric specific heat respectively. The ohmic heat source density (Q) is given by
Q¼
jNm j A
1 I2 fm rm ðB; TÞ þ ð1 fm Þrsc ðB; TÞ op
ð15Þ
where Nm is a vector turn density [15] defined as current density to operating current ratio, fm is non-superconductor (matrix) to superconductor ratio, A is the cable cross-sectional area, rm(B, T) is the
Please cite this article in press as: Bhunia U et al. Design of a 4.5 MJ/1 MW sectored toroidal superconducting energy storage magnet. Cryogenics (2014), http://dx.doi.org/10.1016/j.cryogenics.2014.06.007
U. Bhunia et al. / Cryogenics xxx (2014) xxx–xxx
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Fig. 19. Distribution of eddy current density (A/m2) vectors at intermediate shield for 200 A/s.
Fig. 20. Eddy loss (W) in intermediate thermal shield at 60 K with different ramp down rates.
matrix electrical conductivity, and rsc(B, T) is the electrical conductivity of superconductor. The Quench code closely couples the nonlinear transient thermal, electromagnetic and circuit models. The transient thermal and electromagnetic field simulations were implemented using an adaptive Galerkin time stepping method in the Quench code. Sector coils are epoxy-impregnated with cooling channels between layers. The heat transfer coefficient to the liquid helium coolant is considered to be negligible during the process of quench. The whole magnet is initialized to the original temperature of 4.2 K and initial current of 1200 A. A point pulsed heat flux continuing about 10 ms is added at the middle turn of coil mid plane, which is good enough to raise the temperature of superconductor to its current sharing temperature. In our model, the switch S1 is assumed to be closed and S2 opened up as soon as the quench is detected. The diode D1 parallel to the switch S1 provides redundancy of the protection mechanism. Quench onset starts in the simulation when the differential voltage among any two coils is
more than 100 mV with validation period of 100 ms. For different dump resistors with no active protection by quench heater, the coil current and hot spot temperature is as shown in Fig. 22a. The voltage evolution across the quenched coil is shown in Fig. 22b. It is observed that more than 1.0 O dump resistor is required to keep the coil maximum voltage below 1 kV limit. The other option is to use lower value of dump resistor with active protection by quench heater. It is found that quench heater of 1 in. width around the coil outer mid-plane with heat flux of 2 W/cm2 (for 25–50 ms) along with dump resistor of 0.1 X is also feasible and may be a better option to keep both the maximum temperature below 100 K and most importantly terminal voltage across each coil below 1 kV limit. In the present simulation we have taken up a realistic heater delay time of 100 ms upon quench detection based on our experience of developed capacitive heater power supply. If all eight coils are heater fired upon detection of quench, the peak voltage across the quenched coil reduces to 550 V with the hot spot temperature of 65 K as shown in Fig. 23. The maximum terminal voltage across the current leads is found to be 250 V, which is less than the voltage across quenched coil. This is due to the fact that the resistive voltage and induced inductive voltages during current decay are of opposite direction. It is observed that if at least three coils are heater-fired upon detection of quench, peak voltage across the quenched coil becomes less than 1 kV limit. The center of the dump resistor may be earthed further with the cryostat body so that the coil terminal voltage with respect to cryostat is reduced to half.
6. Joint design The sector coils are interconnected with several soldered resistive splice joints away from the coil in a magnetic field of less than 1.0 T. It is important that splices have acceptably low electrical resistance so that magnet would not suffer any performance degradation and must be mechanically stable. The splice resistance is
Please cite this article in press as: Bhunia U et al. Design of a 4.5 MJ/1 MW sectored toroidal superconducting energy storage magnet. Cryogenics (2014), http://dx.doi.org/10.1016/j.cryogenics.2014.06.007
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Fig. 21a. Quench protection circuit with a single dump resistor across the coil assembly.
Fig. 21b. Quench protection circuit with dump resistors across each sector coil.
Fig. 22a. Transition of coil current and coil hot spot temperature with different dump resistors.
Fig. 22b. Transition of voltage across coil with different dump resistors during quench.
Fig. 23. Transition of coil current, voltage across quenched coil and coil hot spot temperature with quench heater & Rd = 0.1 O.
primarily due to solder resistivity, solder thickness and splice length. The splice region is well cooled directly with liquid helium. With the experience of splicing at CERN, it is planned to use SnAg (4%) solder material since it has lower resistivity at 4 K with respect to other commonly available solder alloys. We have set up a target joint resistance per splice to be less than 10 nX so that Joule heating is within 15 mW per joint at 4.2 K and cryogenic budget is met. For an overlapping splice length of 10 cm (twice the cable transposition pitch), surface heat flux due to resistive heating would be around 0.0015 W/cm2, which corresponds to a negligibly small temperature rise of the cable insulated with 50% overlap polymide (25 lm thickness) by less than 0.02 K. However, there are many parameters such as duration of heating during soldering and overlapping length in splice that need to be optimized during the development of splicing technique to avoid any degradation of superconducting characteristics of the cable. Splices of uniform quality are under development with suitable
Please cite this article in press as: Bhunia U et al. Design of a 4.5 MJ/1 MW sectored toroidal superconducting energy storage magnet. Cryogenics (2014), http://dx.doi.org/10.1016/j.cryogenics.2014.06.007
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soldering fixture and joint technology will be established through a series of joints. 7. Conclusions A small-scale 4.5 MJ/1 MW/2 s toroidal-type superconducting magnet for SMES system is designed. The mechanical behaviour of the magnet with a simple and reliable mechanical structure is studied by commercial code ANSYS. All parts of coil remain under compression (or negative radial stress) at full excitation with the inner most layer maintain compressive contact with coil former. Effect of thermal stress on whole assembly has been found to be less with respect to electromagnetic (EM) stress. The maximum von-Mises stress in coil and coil former support assembly is found to be within allowable limiting value. The analysis allows a detailed quantitative evaluation of the stresses in the coil and support structure subject to all possible working conditions. Transient loss including AC loss in superconductor and eddy current loss in coil support structure and former has been evaluated. Heater induced active quench protection in fail-safe mode is found to be better option for quench protection ensuring no magnet damage. Acknowledgement We extend our sincere thanks to Suparna Patra and S B Bose for their contribution in developing 3D models of cryostat and assemblies. We would like to thank all our colleagues in SMES group for many fruitful technical discussions during the course of this work.
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Please cite this article in press as: Bhunia U et al. Design of a 4.5 MJ/1 MW sectored toroidal superconducting energy storage magnet. Cryogenics (2014), http://dx.doi.org/10.1016/j.cryogenics.2014.06.007