JP2013105639A - Superconducting cable - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a technique for providing a superconducting cable capable of suppressing eddy current loss that a former has, and reducing AC loss and suppressing a rise in temperature at eddy current time.SOLUTION: There is provided a superconducting cable having a former, a superconducting layer provided at an outer periphery of the former, and an electric insulating layer formed at an outer periphery of the superconducting layer. The superconducting layer is formed by winding a plurality of superconductor materials spirally around an outer periphery of the former. The former is applied to a superconducting cable formed by twisting a plurality of metal wires each made of a normal conducting materials coated with a resistance film, which is characterized in that a value of volume resistivity at 77K is 10times or more as large as a value of volume resistivity of the metal wires, the volume resistivity value of the resistance film is 10Ω cm or less, and the center angle θ of a contact length between adjacent strands is within a range of 5°≤θ≤30°.

Description

  The present invention relates to a superconducting cable including a stranded wire former that reduces eddy current loss during AC energization and suppresses temperature rise during overcurrent.

In the superconducting cable, it is required for practical use to achieve a reduction in AC loss. As an example of a conventionally known superconducting cable structure, a structure is known in which superconducting wires in each superconducting conductor and superconducting shield layer are spirally wound at the same pitch in each layer.
As an example of this type of high-temperature superconducting cable, as shown in FIG. 20, it is a three-core batch type high-temperature superconducting cable, in which a plurality of layers of high-temperature superconducting wires are arranged in a winding shape on the outer periphery of a stranded wire. A layer 101 is formed, and insulating layers 102 and 103, a superconducting shield layer 105, and a protective layer 106 are formed on the outer periphery thereof to form a core cable 107, and three core cables 107 are twisted together inside the heat insulating tube 108. A high-temperature superconducting cable 110 having a structure in which a gap for circulating refrigerant is accommodated and the whole is covered with a protective layer 109 is known.
In such a superconducting cable conductor, when the winding pitch of each layer is made the same, the inner layer and the outer layer have a problem of current drift that the outer layer has a smaller inductance and the outer layer has a larger current. AC loss is considered to increase with this drift, and suppression of drift is required.

As a basic technique for reducing such AC loss, there is a technique for adjusting the inductance of each layer by adjusting the helical winding pitch of each layer, which is considered to be a technique that can solve the above-mentioned problem of drift. (See Patent Document 1)
On the other hand, the former provided in the superconducting cable is necessary to mechanically support the superconducting wire, and when the current exceeding the critical current of the superconducting wire flows as a countermeasure against a short circuit accident, the former is It is considered that it is also necessary to fulfill a function as a current dividing flow path, such as by sharing over the above, bypassing the overcurrent, and suppressing the temperature rise of the superconducting cable. Therefore, the former provided in the conventional superconducting cable is composed of a metal conductor such as copper or copper alloy, and the shape thereof is generally a columnar shape made by twisting the metal conductors together. there were.

Japanese Examined Patent Publication No. 29-6665

In the technique of adjusting the inductance of each layer by adjusting the spiral winding pitch of each layer of the superconducting layer and the superconducting shield layer, the magnetic field component in the axial direction of the former remains without being completely canceled. In the case of a conductor, an eddy current loss that flows along the circumference of the cross section of the former occurs.
In addition, when an insulator is used instead of a metal conductor as a former, eddy current loss does not occur, but the current cannot be shared by the former when a current exceeding the critical current flows. There is a problem that the temperature rises.

  The present invention has been made in view of the above-described conventional situation, and provides a superconducting cable capable of suppressing eddy current loss occurring in a former, reducing AC loss and suppressing temperature rise during overcurrent. The purpose is to provide technology that can be used.

The superconducting cable of the present invention is a superconducting cable having a former, a superconducting layer provided on the outer periphery of the former, and an electrically insulating layer formed on the outer periphery of the superconducting layer, wherein the superconducting layer includes a plurality of superconducting wires. The structure is a structure in which the outer periphery is spirally wound, the former is a structure in which a plurality of metal wires made of a normal conductive material coated with a resistance film are twisted together, and the volume resistivity value of the resistance film is the metal wire It is characterized in that it is 10 ⁴ times or more of the volume resistivity value and the volume resistivity value of this resistance film is 10 ⁹ Ω · cm or less.
According to the superconducting cable provided with the former having the above structure, the resistance between adjacent metal wires is sufficiently larger than the resistance in the length direction, so that the metal wire having a twisted wire structure is electrically independent. In the case of a split strand, each metal wire can have a substantially uniform inductance. For this reason, it becomes possible to flow a uniform current through each metal wire constituting the former, contributing to the reduction of the skin effect and the reduction of eddy current loss.
In addition, the metal wire adjacent to the former in the radial direction of the former is covered with a resistive film, but it is electrically connected, so if an overcurrent occurs when the superconducting wire is energized, the former is bypassed. Since it can be used as a road, it contributes to stabilization during energization of the superconducting cable.
The superconducting cable of the present invention is characterized in that the central angle θ of the contact length of adjacent strands in the structure in which a plurality of the metal wires are twisted is in the range of 5 ° ≦ θ ≦ 30 °.
When the central angle of the contact length of the adjacent strands is less than 5 °, it is necessary to control the force applied between the stranded wires at the time of manufacturing the stranded wire, which is difficult to manufacture and is impractical, and exceeds 30 °. And the resistance of the contact portion between the stranded wires is reduced, and the eddy current loss tends to increase.

The superconducting cable of the present invention is characterized in that the resistance film has a thickness of 0.5 μm or more and 1.5 μm or less.
If the resistance film is in the above-mentioned thickness range, eddy current loss can be reduced, and sleeve compression connection can be performed without removing the film when connecting the former.
The superconducting cable of the present invention is characterized by further comprising a superconducting shield layer provided on the outer periphery of the electrical insulating layer and a metal shield layer provided on the outer periphery of the superconducting shield layer.

In the former of the present invention, the superconducting cable is provided on the outer periphery of the former, the superconducting layer provided on the outer periphery thereof, and the electric insulating layer formed on the outer periphery of the superconducting layer. It is characterized by comprising a superconducting shield layer and a metallic shield layer provided on the outer periphery of the superconducting shield layer.
By providing the superconducting shield layer and the metal shield layer outside the superconducting layer, it is possible to prevent the magnetic field from leaking to the outside and having a magnetic influence on the outside.

According to the present invention, metal lines of stranded wire structure constituting the former is coated with resistive film, the value of the volume resistivity of the resistive film is at least 10 ⁴ times the value of the volume resistivity of the metal wire, resistive film Since the volume resistivity value of 10 ⁹ Ω · cm or less is sufficiently larger than the resistance in the length direction, the resistance between adjacent metal wires is sufficiently large. It can be considered as an independent state, and in the case of a split conductor, each metal wire can have a substantially uniform inductance, so that a uniform current can flow through each metal wire, and the skin effect This contributes to the reduction of eddy current loss. In addition, the metal wire adjacent to the former in the radial direction of the former is covered with a resistive film, but it is electrically connected, so if an overcurrent occurs when the superconducting wire is energized, the former is bypassed. Since it can be a road, it contributes to stabilization during energization.

1 is a cross-sectional view of a superconducting cable according to a first embodiment of the present invention. FIG. 2 is a schematic cross-sectional view of an oxide superconducting laminate incorporated in the superconducting cable shown in FIG. 1. The block diagram which shows in detail the layer structure of the oxide superconducting laminated body shown in FIG. The cross-sectional view which shows the twisted wire structure of the former | foamer built in the superconducting cable shown in FIG. The expanded sectional view of the twisted wire part of the former. Explanatory drawing of the same former and the axial direction magnetic field which acts on it. Explanatory drawing for demonstrating the eddy current in the case of the former | foamer which consists of a cylindrical conductor. FIGS. 8A and 8B are explanatory diagrams for showing an eddy current of a former having a twisted wire structure with insulation coating, FIG. 8A is an explanatory diagram of the entire former, and FIG. 9B is a flow through a strand constituting the twisted wire of the former. Explanatory drawing which shows an eddy current. It is explanatory drawing which shows the former | foamer of resistance film twisted wire structure, FIG.9 (a) is explanatory drawing of the whole former | foamer, FIG.9 (b) is each strand arrange | positioned along the layer of the strand wire which comprises a former. FIG. 9C is an explanatory diagram showing an eddy current flowing through a strand arranged at the center of the former. Sectional drawing for demonstrating the eddy current loss calculation model in the case of a cylindrical conductor. It is explanatory drawing shown about the eddy current of the former used as the twisted-wire structure of the metal wire provided with the resistance film, FIG. 11 (a) is explanatory drawing of the whole former, FIG.11 (b) is along the layer which comprises a former. Explanatory drawing which shows the eddy current which flows through the arrange | positioned strand, FIG.11 (c) is explanatory drawing which shows the eddy current which flows through the strand arrange | positioned in the center of a former | foamer. It is explanatory drawing for showing about the resistance of the former used as the twisted wire structure of the metal wire provided with the resistance film, and Drawing 12 (a) is a transverse cross section showing the arrangement of the strand which constitutes the twisted wire structure of the former, figure 12 (b) is a partially enlarged view of the strand shown in FIG. 12 (a), and FIG. 12 (c) is an enlarged view of the resistance film portion of the strand constituting the former. Explanatory drawing which shows the view of the equivalent resistance Re in the former which becomes the twisted wire structure of the metal wire provided with the resistance film. It is explanatory drawing which shows the original arrangement | positioning in the equiangular mapping of the elliptic function for calculating | requiring the relationship between an equivalent volume resistivity, the volume resistivity of a stranded wire metal, and the volume resistivity of a resistance film, Fig.14 (a) is the elliptic function Explanatory drawing which shows the original arrangement | positioning for calculating | requiring A, FIG.14 (b) is explanatory drawing which shows the contact state of the metal wire adjacent to the radial direction of the former | foamer. It is explanatory drawing which shows the equiangular mapping of the elliptic function for calculating | requiring the relationship between an equivalent volume resistivity, the volume resistivity of a stranded metal, and the volume resistivity of a resistance film, and FIG. Explanatory drawing which shows the w surface of the original coordinate in calculation normalized, FIG.15 (b) is explanatory drawing which shows z surface. It is explanatory drawing which shows the equiangular mapping of the elliptic function for calculating | requiring the relationship between the equivalent volume resistivity, the volume resistivity of a stranded metal, and the volume resistivity of a resistance film, FIG.16 (a) is explanatory drawing which shows Z surface FIG.16 (b) is explanatory drawing which shows a W surface. The graph which shows the ratio with respect to the stranded metal wire resistivity of the film | membrane resistivity in the insulation coating twisted wire and resistance film twisted wire in case the center angle of the contact length of an adjacent strand is 5 degrees. The graph which shows the ratio with respect to the stranded metal wire resistivity of the film | membrane resistivity in the insulation coating twisted wire and resistance film twisted wire in case the center angle of the contact length of an adjacent strand is 10 degrees. The graph which shows the ratio with respect to the strand metal wire resistivity of the film | membrane resistivity in the insulation coating twisted wire and resistance film twisted wire in case the center angle of the contact length of an adjacent strand is 15 degrees. The partial cross-section schematic which shows an example structure of the conventional superconducting cable.

Hereinafter, although a 1st embodiment of a superconducting cable concerning the present invention is described based on a drawing, the present invention is not restricted to the following embodiments.
As shown in FIG. 1, a superconducting cable A according to this embodiment includes a former 1 having a twisted wire structure disposed in the center, a high-temperature superconducting layer (high-temperature superconducting wire) 2 and an electrical insulating layer sequentially coated on the outer peripheral side thereof. 3, a superconducting shield layer 4, and a shield layer 5 made of a highly conductive metal material such as copper.
In the superconducting cable A of the present embodiment, the former 1 has a wire 8 having a structure in which a metal wire 6 made of a highly conductive metal material such as copper is covered with a resistance film 7 made of, for example, cupric oxide as a resistance film. A structure in which a plurality of wires are stranded at a predetermined pitch.
The resistance film 7 applied in the present embodiment has a volume resistivity (ρf) of 10 ⁹ Ω · cm or less, for example, 10 ⁴ Ω · cm or more and a range of a semiconductive region of 10 ⁶ Ω · cm or less.
Since the cupric oxide exemplified here is black, it has a characteristic that it is easy to identify whether or not the resistance film 7 exists unlike a color close to copper color such as enamel coating.
If the resistance film 7 is an oxide film of the metal wire 6, the enamel coating is an adhesive structure with the underlying metal, whereas the connection between the resistance film 7 and the metal wire 6 becomes a metal bond and is strong and peeled off. This is advantageous in that it is excellent in mechanical strength during bending and expansion / contraction of the wire 8. Moreover, cupric oxide has a melting point of 1148 ° C., the resistance film 7 of cupric oxide is excellent in heat resistance, and the welding connection method can be applied as it is for the same diameter connection of the former 1. Moreover, the outer diameter of the strand 8 can select the range of 0.5 mm-3.0 mm.

The film thickness of the cupric oxide resistance film 7 is in the range of 0.5 μm to 1.5 μm.
Since the resistance value of the resistance film 7 is a semiconductive region, there is an effect that can be applied as it is between the former 1 and the high-temperature superconducting layer 2 thereon, which is desirable as the resistance film 7 constituting the former 1 of the superconducting cable A. The resistance film 7 described above is not an insulating film, but a resistance value is a film in a semiconductive region and is thin, and has the following features.
For example, the sleeve connection can be compressed and connected without removing the resistance film 7 when the former 1 is compressed. Further, when it is assumed that the resistance film 7 of the former having a stranded wire structure is to be removed, it is necessary to remove the resistance film 7 by a technique such as sandblasting with a large gap between the strands of the former. At this time, the high-temperature superconducting wire constituting the high-temperature superconducting layer 2 existing in the vicinity of the lead end may be mechanically damaged. The high-temperature superconducting wire constituting the high-temperature superconducting layer 2 is very sensitive to mechanical strain. Furthermore, there is a drawback that the length of the former 1 at the time of connection becomes longer. Therefore, if the sleeve can be pressure-bonded with the resistance film 7 as it is, these concerns can be eliminated. Since the volume resistivity of the resistance film 7 is 10 ⁹ Ω · cm or less, for example, 10 ⁴ Ω · cm or more and 10 ⁶ Ω · cm or less, it is in the range of the semiconductive region. There is no problem in terms of connection with the conductive parts.

An oxide superconducting layer 2 is formed by a tape-like high-temperature superconducting wire 10 wound spirally around the outer periphery of the former 1.
In the present embodiment, the structure shown in FIG. 2 can be applied as one example of the tape-shaped high-temperature superconducting wire 10. The high-temperature superconducting wire 10 shown in FIG. 2 is an example of a wire structure to which an RE123-based oxide superconductor (REBa ₂ Cu ₃ O _7-X : RE is a rare earth element including Y) is applied. However, the structure of the high-temperature superconducting wire 10 itself may of course be a structure using another type of high-temperature superconductor described later.
In the high-temperature superconducting wire 10 shown in FIG. 2, as an example, a base layer 12, an orientation intermediate layer 15, a cap layer 16, an oxide superconducting layer 17, and a first stabilization layer 18 are laminated on a base material 11. The outer periphery is covered with the insulating coating layer 20. Although the high-temperature superconducting wire 10 shown in FIG. 2 is exaggerated in thickness, the aspect ratio of a general RE123-based high-temperature superconducting wire 10 is about 10 mm in width and about 0.5 mm in thickness. The oxide superconducting layer 2 can be formed by winding the former 1 around the former 1 with a necessary number of turns.

The substrate 11 applicable to the high temperature superconducting wire 10 of the present embodiment is preferably made of a nickel alloy. Especially, if it is a commercial item, Hastelloy (US Haynes Corporation brand name) is suitable. The thickness of the base material 11 is usually 10 to 500 μm.
The underlayer 12 has high heat resistance and is used for reducing interfacial reactivity, and is used for obtaining the orientation of a film disposed thereon. The thickness is, for example, 10 to 200 nm. In the present invention, a structure in which a diffusion preventing layer is interposed between the base material 11 and the base layer 12 may be adopted. The thickness is, for example, 10 to 400 nm. As an example in the case of interposing a diffusion preventing layer between the base material 11 and the underlayer 12, Al ₂ O ₃ can be exemplified as the diffusion preventing layer, and Y ₂ O ₃ can be exemplified as the underlayer 12.

The orientation intermediate layer 15 is selected from materials that are biaxially oriented. Specific examples of preferred materials for the orientation intermediate layer 15 include metal oxides such as Gd ₂ Zr ₂ O ₇ and MgO.
If the orientation intermediate layer 15 is formed with a good crystal orientation (for example, a crystal orientation degree of 15 ° or less) by ion beam assisted deposition (IBAD method), the crystal orientation of the cap layer 16 formed thereon. Can be set to a good value (for example, the degree of crystal orientation is about 5 °), and the superconducting characteristics can be exhibited with good crystal orientation of the oxide superconducting layer 17 formed on the cap layer 16. Can be able to.

The thickness of the orientation intermediate layer 15 may be appropriately adjusted according to the purpose, but can usually be in the range of 0.005 to 2 μm. In particular, the metal oxide layer formed by the IBAD method is preferable in that the crystal orientation is high and the effect of controlling the crystal orientation of the oxide superconducting layer 17 and the cap layer 16 is high. The IBAD method is a method of orienting crystal axes by irradiating an ion beam at a predetermined angle with respect to an underlying vapor deposition surface during vapor deposition. Usually, an argon (Ar) ion beam is used as the ion beam. For example, the intermediate layer 15 made of Gd ₂ Zr ₂ O ₇ , MgO, or ZrO ₂ —Y ₂ O ₃ (YSZ) reduces the value of ΔΦ (FWHM: full width at half maximum), which is an index representing the degree of crystal orientation in the IBAD method. it can.

The cap layer 16 is preferably formed through a process in which crystal grains are selectively grown in the in-plane direction. Such a cap layer 16 has a higher in-plane orientation degree than the orientation intermediate layer 15 made of the metal oxide layer. As an example of the cap layer 16, CeO ₂ can be selected. As an example, the formation of the CeO ₂ layer as the cap layer 16 by the PLD method can be performed in an oxygen gas atmosphere at a substrate temperature of about 500 to 1000 ° C. and about 0.6 to 100 Pa.
Although the film thickness of the cap layer 16 should just be 50 nm or more, it is preferable to set it as 500-1000 nm.

The oxide superconducting layer 17 may be a known material, and specifically, a material of REBa ₂ Cu ₃ O _7-x (RE represents a rare earth element such as Y, La, Nd, Sm, Er, Gd). Can be illustrated. Examples of the oxide superconducting layer 17 include Y123 (YBa ₂ Cu ₃ O _7-X ) or Gd123 (GdBa ₂ Cu ₃ O _7-X ). The oxide superconducting layer 17 has a thickness of about 0.5 to 5 μm and preferably a uniform thickness. The oxide superconducting layer 17 may be a high-temperature superconducting layer of another composition system described later.

  When the oxide superconducting layer 17 is formed on the cap layer 16, in each of the crystal grains constituting the oxide superconducting layer 17, the c-axis that hardly allows electricity to flow in the thickness direction of the base material 11 is oriented, The a-axes or the b-axes are oriented in the length direction of the substrate 11. Therefore, the obtained oxide superconducting layer 17 is excellent in quantum connectivity at the crystal grain boundary, and hardly deteriorates in the superconducting characteristics at the crystal grain boundary. High critical current density can be obtained.

The first stabilizing layer 18 laminated on the oxide superconducting layer 17 is formed as a layer made of a metal material having good conductivity, such as Ag or a noble metal, having a low contact resistance with the oxide superconducting layer 17 and a familiar property. The The thickness of the Ag stabilizing layer 18 can be formed to about 1 to 30 μm. If necessary, a second stabilization layer 19 may be provided on the first stabilization layer 17 as shown in FIG. FIG. 3 is a diagram showing an example of a laminated structure in the case where the second stabilization layer 19 is provided for the oxide superconducting wire shown in FIG.
The second stabilization layer 19 is preferably made of a highly conductive metal material, and when the oxide superconducting layer 17 is about to transition from the superconducting state to the normal conducting state, together with the first stabilizing layer 18, It functions as a bypass through which the current of the oxide superconducting layer 17 commutates. As the second stabilization layer 19, it is preferable to use a relatively inexpensive material such as a copper alloy such as copper or brass (Cu—Zn alloy). The thickness of the second stabilization layer 19 can be 10 to 300 μm.

  As an example, the outer peripheral surface of the tape-shaped high-temperature superconducting wire 10 having the above-described configuration is covered with an insulating coating layer 20 made of a prepreg layer such as an epoxy resin or a polyimide tape or FRP (fiber reinforced plastic) tape.

However, so far in the structure described, the REBa 2 Cu ₃ O _7-x having a composition based oxide high-temperature superconducting wire 10 of the provided structure superconducting layer 17 of the via orientation intermediate layer 15 above the substrate 11 Although the example used was explained, it is needless to say that the present invention can be applied to a bismuth-based superconducting wire (Bi ₂ Sr ₂ CaCu ₂ O _{8 + δ} : Bi2212, Bi ₂ Sr ₂ Ca ₂ Cu ₃ O _{10 + δ} : Bi2223).
The structure of the bismuth-based superconducting wire is mainly an oxide superconducting wire in which a bismuth-based oxide superconducting layer is encapsulated in a sheath made of a tape-shaped stabilizing material such as Ag. By using a superconducting wire instead of the high temperature superconducting wire 10, the present invention can be applied to a high temperature superconducting cable using a bismuth-based oxide superconducting wire.
Further, the superconducting layer applied to the high-temperature superconducting wire used in the present invention is not limited to RE123 or bismuth, but may be made of other high-temperature superconducting materials. For example, a structure in which a thallium (Tl ₂ Ba ₂ Ca ₂ Cu ₃ O _x ) oxide superconductor or MgB ₂ superconductor is laminated on a stabilization layer or a base material as a layer structure may be used.

Next, the structure of the former 1 that is an assembly of the wires 8 provided with the resistance film 7 according to the present embodiment will be examined.
FIG. 4 is a cross-sectional model diagram of the former 20. In this former 20, six strands 21 are arranged at equal intervals around a single strand 21, and 12 strands are arranged around them. In this example, 18 strands 21 are arranged at equal intervals and 18 strands 21 are arranged around them. In the former 20 shown in FIG. 4, the contact angle ψ _k between the adjacent strands 21 of the strands 21 in the same layer position constituting the former 20 can be assumed as shown in FIG. The description will be given while considering various structures.

As shown in FIG. 6, when a former 22 having a stranded wire structure is assumed, an axial (length direction) magnetic field is applied to the former 22. This magnetic field is generated by a superconducting wire wound spirally thereon and a current flowing in the superconducting shield layer. This magnetic field is uniform in the radial direction of the former 22 (similar to the internal magnetic field of the coil). First, assuming that the former 23 is a cylindrical conductor as shown in FIG. 7, the eddy current flows in the circumferential direction of the conductor cross section as shown in FIG. Assuming that the former 24 is an aggregate of strands 25 that are individually covered with insulation as shown in FIG. 8, eddy currents flow in the circumferential direction of each strand 25. In addition, the arrow which shows the flow of the eddy current shown in each figure after FIG. 7 is the image of the current line shown for simplification of description.
On the other hand, in the case of the former 28 which is not an insulation-coated wire but an assembly of the wires 27 resistance-coated with the resistance film 26 as shown in FIG. It can be divided into the current flowing between the lines from the circumferential direction of the other layers.

[1] Calculation of Eddy Current Loss in Case of Cylindrical Conductor First, the eddy current loss of a basic cylindrical conductor is calculated. Consider the case of a former 30 made of a cylindrical conductor in FIG. Consider the loss per unit length in the former 30 of FIG.
In FIG. 10, the resistance dR in the circumferential direction of the annular region of the hatched portion 30a is expressed by the following equation (1).

  The Joule loss dW in the annular region is expressed by the following equation (2).

  The magnetic flux Φ interlinking with the annular region is expressed by the following equation (3).

The axial magnetic field is expressed by the following equation (4). In the equation (4), He ^jωt represents an alternating magnetic field ^having a magnitude H, and μ ₀ represents a magnetic permeability in a vacuum.

Therefore, the absolute value of the differentiation between them, | dΦ / dt |, is expressed by the following equation (5). In equation (5), r is the inner diameter of the annular region 30a, ω is the frequency of the electric field, μ ₀ is the vacuum permeability, and H is the magnitude of the alternating magnetic field.

  From the equation (5), the above equation (2) becomes the following equation (6), and the relationship of the equation (7) can be derived from the equation (6). D indicates the diameter of the former 30 as a cylindrical conductor.

“2” Calculation of Eddy Current Loss of Former Formed with Insulated Coated Strand In the case of the former 24 composed of the insulated coated strand 25 whose model structure is shown in FIG. The eddy current loss may be replaced by the diameter D → d (the diameter of one strand) in the equation (7). If the total number of stranded wire and the n, the total eddy current loss W ₁ is determined from the following equation (8). Further, there is a relationship of the expression (9).

“3” Eddy Current Loss of Former with Resistance Film Twisted Wire Structure As shown in FIG. Consider the current flowing between the wires 33 in the former circumferential direction of the wires 33 constituting each layer.
One of the strands 33 (k = 1 layer) arranged in the center of the former 35 is an eddy current loss w ₁ in the strand, from the above-mentioned formulas (8) and (9), the following (10 ).

The current in the circumferential direction of each layer in the former 35 shown in FIG. 11 is limited by the contact portion of the adjacent stranded wire (adjacent strand), and there is an increase in resistance due to the resistance film. In this case, when the equivalent volume resistivity ρ _ek is considered instead of the volume resistivity ρc of the cylindrical conductor, the eddy current loss w _k of each layer (kth layer) is expressed by the following equation (11).

From (10) and (11), the total eddy current loss _{W 2} of the entire former 35 is expressed by the following equation (12). In the equation (12), when the diameter of the strand 33 is dψ in all layers, that is,
The following equation (16) holds when the equations (13), (14), and (15) are satisfied.

Next, the equivalent volume resistance ρ _ek of each layer, which is the most important parameter in the above equations (12) and (16), is obtained.
FIG. 12 (a) is a view for assuming a contact angle between the strands 21 constituting the stranded wire as in FIG. 4 and FIG. FIG. 12B schematically shows the current flow between the wires 21. FIG. 12 shows the relationship between the resistance wires 21a and 21a interposed between the adjacent wires 21 on the left and right sides and the contact region therebetween. Shown in (c). FIG. 12 corresponds to a schematic diagram in the case of assuming the contact resistance and the like for the surrounding strands 21 existing on the outer periphery of the former 20 which is an aggregate of the strands 21 except for the central strand 21.
Also shows the concept of the equivalent resistance R _e between the wires 21 present except the center of the strand 21 in FIG. 12 (b) similarly to the former 20 in the circumferential around 13.
In the relationship shown in FIG. 12, Equations (17), (18), (19), and (20) are established.

However, in each formula, R _e : equivalent resistance per unit length of the strand 21 provided with the resistance film 21 a, R _c : concentrated resistance per unit length of the metal constituting the strand 21, R _f : strand 21 Resistance per unit length of the resistance film between the contact parts, R _s : contact resistance between the resistance films (omitted in this calculation), ρ _c : volume resistivity of the metal constituting the strand 21, ρ _f : resistance film Volume resistivity, ρ _e : Equivalent volume resistivity of the wire 21 provided with a resistance film, d: Diameter of the wire 21, t _f : Thickness of the resistance film, l _f : Contact length of the wire (circumferential direction) ) (D / 2 × θπ / 180), θ: center angle of contact length, ψ _k : contact angle of adjacent strands.

Next, a relational expression between the equivalent volume resistivity ρ _e , the volume resistivity ρ _c of the metal constituting the element wire, and the volume resistivity ρ _f of the resistance film is obtained.
Since the contact resistance R _s between the resistance films cannot be uniformly determined, and when R _s = 0, the eddy current loss is estimated to be larger than the true value, and this is a safe side in design. I ignored it. The constriction resistance R _c per unit length of the metal constituting the wire 21 can be obtained by conformal mapping with elliptic function (complete elliptic integral of the first kind) as follows.
This is theoretically accurately derived under the model shown in FIG.
The derivation process is shown in FIGS. 14 (a) to 14 (b), FIGS. 15 (a) to 15 (b), and FIGS. 16 (a) to 16 (b).
FIGS. 14A and 14B show normalized electrodes and calculation original coordinate settings, FIG. 15A shows the w-plane (normalized calculation original coordinates), and FIG. 15B shows the z plane. Indicates. 14A corresponds to an enlarged cross-sectional view of one of the adjacent strands 21 as shown in FIG. 14B, and the lower left and right sides of FIG. 14A. When the contact part 21b with other strands 21 is assumed, it is the figure which drew a plurality of current lines 21c assumed to flow through these contact parts 21b.
15A to 15B employ z = {(1−w) / (1 + w)} i and x = tan (θ / 2) as the mapping to the upper half plane and the mapping function. If the coordinates of each point in FIG. 15A are substituted into these mapping functions, the relationship shown in FIG. 15B is obtained. This relationship is known as a general formula that can be derived from electric field analysis by conformal mapping in electromagnetics.

In FIGS. 15B to 16A, Z = (αz + β) / (γz + δ) is used as a linear function as the mapping function. However, α, β, γ, and δ are constants.
FIG. 16A shows the Z plane, and FIG. 16B shows the W plane. In FIG. 16A, the relationship of equation (21) is established. When the coordinates of FIG. 15B and the coordinates of FIG. 16A are substituted into the above mapping function, the coordinates 1 / k ₁ ² of point A shown in FIG. . In the equation (21), a, p, q, and γ indicate the coordinates of points A, P, Q, and R in FIG.

As shown in FIGS. 16A to 16B, the formulas (22) and (23) are established.
In this relation, the equation (24) can be used as the first-type elliptic integral of the mapping function: Legendre-Jacobi. The derivation process of the relationships shown in FIGS. 14 to 16 is based on the basic process of calculating the two-dimensional resistance value by conformal mapping. As an example, the basic process of calculating the two-dimensional resistance value by conformal mapping is, for example, IEEJ Transactions B (November 2008 issue: Journal of Electric Power and Energy Vol.128, No.11, 2008: Electronic Journal Paper (Http://www.2.iee.or.jp/ver2/honbu/11-magazine/index050.html), entitled “Current Status and Prospects of Application of Elliptic Functions to the Power Field” Reference can be made to the basic process of calculating a two-dimensional resistance value by conformal mapping shown in FIG. 4 of P1296.

The first type complete elliptic integral is represented by the following formulas (25) and (26). In these formulas, formula (27) is established as k ₁ ² : parameter and k ₁ ′: complement. In the equation (22), Rc represents the ratio of the lengths of the two sides of the rectangle in FIG. 16B, the equation (26) is a value for the complement k ₁ ′, and the k _{1 in the} equation (27): The parameter, k ₁ ′, indicates a complement number.

  From the above equations (18), (19), and (23), the following equations (28) and (29) are established. In these formulas, formulas (30) and (31) are used.

From the above formulas (10), (16), and (28), the derivation results are summarized as follows, and formula (32) is established as follows. In the equation (32), K (k _1k ) and K ′ (k _1k ) are first-type complete elliptic integrals, and the relationship between the following equations (33) and (34) is established.

Since k ₁ and k ′ ₁ are a parameter and a complement, respectively, there is a relationship of the following expressions (35), (36), (37), and (38).

However, in the formulas (35) to (38), it is significant in the range of W ₂ > W ₁ .
Here, in the case of a former made of a stranded wire without a coating, the ratio of the eddy current loss (W ₀ : bare wire) to the eddy current loss (W ₁ : wire insulation) when an insulating coating is applied ( W ₀ / W ₁ ) is given by the following equation (39) when t _f = 0 or ρ _f = 0 in the previous equation (32).

Here, the value of (W ₂ / W ₁ ) is calculated from the equation (32) for a former having a stranded wire structure provided with the following insulating film (enamel insulating film).
Former outer diameter: D = 19 mm, diameter of one strand constituting the stranded wire: d = 2.8 mm, number of stranded wires (number of strands): 37, n ₁ = 1, n ₂ = 6 It is assumed that n ₃ = 12 and n ₄ = 18. Further, t _{f is} the thickness of the resistance film (1 μm, 2 μm, 5 μm) and the center angle of the contact length (5 °, 10 °, 15 °). The net conductor cross-sectional area is 227 mm ² and the space factor is about 80%.
K-th layer Wire diameter d (mm) Number of twists (n _k )
1st layer (center k = 1) 2.8 1 (n ₁ )
Second layer (center k = 2) 2.8 6 (n ₂ )
3rd layer (center k = 3) 2.8 12 (n ₃ )
Fourth layer (center k = 4) 2.8 18 (n ₄ ) 37 in total FIG. 17, FIG. 18, and FIG. 19 show the relationship between eddy current loss and film resistivity calculated under the above conditions.

17 to 19, the vertical axis represents the eddy current loss (W ₂ ) of the stranded wire including the resistance film with respect to the eddy current loss (W ₁ ) of the stranded wire including the insulating film. The horizontal axis represents the ratio of the film resistivity (ρ _f ) to the stranded metal resistivity (ρ _c ). 17 shows a case where the center angle θ of the contact length between the strands is 5 °, FIG. 18 shows a case where the center angle θ of the contact length between the strands is 10 °, and FIG. 19 shows a center angle of the contact length between the strands. The case where θ is 15 ° is shown. In addition, FIGS. 17 to 19 show calculation results of the film thicknesses of 1 μm, 2 μm, and 5 μm, respectively.

As an example, the calculation in the case of ψ _k = 2 (90 ° − (180 ° / n _k )) and θ = 10 ° is as follows.
n ₂ = 6, ψ ₂ = 120 °, k ₁₂ ² = 0.01013, K ′ (k ₁₂ ) / K (k ₁₂ ) = 2.35, n ₃ = 12, ψ ₂ = 150 °, k ₁₃ ² = 0.008142, K ′ (k ₁₃ ) / K (k ₁₃ ) = 2.42, n ₄ = 18, ψ ₂ = 160 °, k ₁₄ ² = 0.007832, K ′ (k ₁₄ ) / K ( k ₁₄ ) = 2.42.

From the calculation results in FIGS. 17 to 19, even if the resistance film has a value of ρ _f / ρ _c of 10 ⁴ or more and ρ _f of 10 ⁹ Ω · cm or less, reduction of eddy current loss equivalent to that of the insulating film is achieved. It turns out that there is an effect.
In addition, in the case of using a former having a twisted wire structure in which the element wire is made of copper and a cupric oxide resistance film is formed on the outer periphery of the element wire, ρ _c : 0.2 × 10 ⁻⁶ Ω · cm (−196 ° C. ), Ρ _f : 1 × 10 ⁶ Ω · cm (−196 ° C.), it can be seen that ρ _f / ρ _c ≧ 10 ⁴ is satisfied.

From the results shown in FIGS. 17 to 19, the value is close to W ₂ / W ₁ = 1 when ρf / ρc is 10 ⁴ or more and the wire insulation is performed. In the case of strands of strands using a cupric oxide resistance film, it can be seen that it falls within this range.
When the contact angle center angle θ is less than 5 °, the resistance value of the contact portion between the strands is larger than that when the contact length center angle θ ≧ 5 °, which reduces eddy current loss. It is considered advantageous from the aspect. However, when the former is actually composed of stranded wires, it is difficult to control the force applied between the strands as viewed from the surface where the stranded wires are manufactured, so the center angle θ of the contact length should be less than 5 °. Is unrealistic. On the other hand, in the range where the central angle θ of the contact length exceeds 30 °, the resistance value of the contact portion between the stranded wires is smaller than that in the range of the central angle θ ≦ 30 ° of the contact length, so the eddy current loss increases. Will be disadvantageous. Considering these, the central angle θ of the contact length needs to be in the range of 5 ° to 30 °.
The central angle of the contact length can be measured by cutting the former and magnifying the cross section.

  The present invention can be applied to oxide superconducting wires used in various superconducting equipment such as superconducting power transmission lines, superconducting motors, and superconducting power storage devices.

  A ... Superconducting cable, 1 ... Former, 2 ... High-temperature superconducting layer, 3 ... Electrical insulation layer, 4 ... Superconducting shield layer, 5 ... Shield layer, 6 ... Resistive film, 7 ... Metal wire, 8 ... Elementary wire, 10 ... High temperature Superconducting wire, 11 ... base material, 12 ... underlayer, 15 ... orientation intermediate layer, 16 ... cap layer, 17 ... oxide superconducting layer, 18 ... first stabilizing layer, 19 ... second stabilizing layer, 20 ... Insulating coating layer, 21, 25, ... Wire, 22, 23, 24, 28, 30, 35, ... Former.

Claims (4)

A superconducting cable having a former and a superconducting layer provided on an outer periphery of the former, and an electric insulating layer formed on the outer periphery of the superconducting layer, wherein the superconducting layer spirally wraps a plurality of superconducting wires around the outer periphery of the former The structure is a structure in which a plurality of metal wires made of a normal conductive material coated with a resistance film is twisted together, and the volume resistivity value of the resistance film is equal to the volume resistivity value of the metal wire. A superconducting cable characterized by being 10 ⁴ times or more and having a volume resistivity value of 10 ⁹ Ω · cm or less.   2. The superconducting cable according to claim 1, wherein a central angle θ of a contact length of adjacent strands in a structure in which a plurality of the metal wires are twisted is in a range of 5 ° ≦ θ ≦ 30 °.   The superconducting cable according to claim 1 or 2, wherein the resistance film has a thickness of 0.5 µm or more and 1.5 µm or less.   The superconducting cable according to any one of claims 1 to 3, further comprising a superconducting shield layer provided on an outer periphery of the electrical insulating layer and a metal shield layer provided on an outer periphery of the superconducting shield layer. .

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