谷貝 剛

The assessment of the performance of toroidal field (TF) coil of ITER has been progressing. Unpredictable strand buckling was observed by the destructive investigation of the conductor. The buckling direction was perpendicular to the Lorentz force (LF), and the mechanism of it was due to the thermal shrinkage caused by the difference of thermal contraction between strand material and conduit. Our previous work utilized a 2-dimensional string model and demonstrated that the observed 2mm stand bending could have led to strand bending if the total amount of slide at the contact cross over was assumed to be 53 μm. To verify this estimation, we fabricated a device for the measurement of friction force between strands under constriction force comparable to the LF several hundred kN/m. Our results for Cr-coated 0.89mm diameter strand surrounded by bare Cu strand indicate that thermal contraction stress applied to strand of 45N would be sufficient to overcome the static friction force when the contraction force reduced to tenth of maximum LF. The mechanism of slide motion could be divided into two processes: separation of the inner wall of the conduit and the separation from other strands due to a gradual reduction of LF.

Nb3Sn strand buckling and crack has been observed on the surface of a cable-in-conduit conductor, and it definitely degrades the performance such as critical current density. The strand bending or large deformation, which leads to macroscopic cracks, is not explained by the transverse loading because the direction is completely perpendicular to the electromagnetic force. The most likely explanation is due to the compressive force originating from the difference in coefficient of thermal expansion between strands and steel jacket. Once the load pushes the cable away to one side of the inner wall of the jacket, there would appear a large void on the other side (low transverse load side). It is expected that the strands on the surface of the low transverse load side would free from the frictional force (apart from the jacket wall) and eventually they would start shrinking. In order to analyze the situation which leads to the T-cs degradation, we developed a simulation model based on the structural mechanics by which the strand is divided into discrete elements along centroidal lines. Our simulation results indicate that the displacement would be up to 2 mm, and maximum curvature of the trace 10%, which is enough for cracks to form as observed in the visual inspection.

The upgrading project of the JT-60 to the JT-60 Super Advanced (JT-60SA) at Japan Atomic Energy Agency has started as a joint effort between Japan and the EU. The coils of the JT60-SA are separately fabricated in Japan and EU. The CS and EF coils are fabricated in Japan. In this paper, we describe the butt joint of the JT-60SA CS and measured the ac loss under a time-varying external magnetic field, and analyzed the ac loss at the butt joint by using the FEM simulation software COMSOL Multiphysics. As a result, the measured ac loss of the butt joint were found to be the smallest of all joints (the CS butt joint, the EF pancake joint, the terminal EF joint and the EF prototype joint), and to strongly depend on the thickness of the copper sleeve in full-size coil joint.

It has been observed that the measured critical currents of cable-in-conduit-conductors (CICC) in some experiments are smaller than the expected ones. One of the reasons is the occurrence of unbalanced current at steady state caused by uneven contact resistances between strands. Because the contact resistance between strands is dependent on the contact length, the number of contacts and the loop length between strands, we need information about all strands' locations in the CICC. Therefore, we developed an evaluation method that describes the locations of every strand in the CICC in consideration of the twist disorder based on manufacture processes and elastic potential energy. Moreover, we compared the contact number and length between strands obtained by our calculated strands' positions with measured ones. We found that both results are in good agreement and clarified the validity of our calculation method of all strands' positions in the CICC. © 2002-2011 IEEE.

大型の強磁場マグネット用導体では、曲げ歪みに弱いNb3Sn素線が用いられるが、構造的な原因により、通電中に電磁力によって大きな曲げ歪みが加わり、超電導特性が大きく劣化する。本研究では、構造力学的な解析手法を用いて、実際に測定された素線配置を基に電磁力下での曲げ歪みを計算し、特性劣化の定量的解明を行った。

The Cable-In-Conduit Conductor (CICC) is the most promising one for large scale fusion magnets. Now it has been adopted as conductors for ITER magnets. Although the conductor has good mechanical strength against large electromagnetic force, the performance is not so good because the Nb3Sn strands are fragile and the critical current density is sensitive to strain. Because conductor is composed of hundreds or thousands of strands which are twisted and become tangled, the strands experience extra-bending during energizing magnets. It seems so difficult to analyse plastic deformation of the strands of whole conductor. Our approach to calculate it is unique in terms of using structural mechanics called "Beam Model" based on the measured strand traces inside the conduit. The calculated traces provide us the local curvatures of strands under electromagnetic force. This leads to the evaluate the conductor performance such as I-e degradation.

It is observed that measured critical current of Cable-in-Conduit-Conductor (CICC) for ITER TF coil are lower than expected. This is partly explained an imbalance of the contact resistance at the joint between double pancakes which causes an unbalanced current distribution in a cable and hence during a slow temperature increase some strands reach the critical current earlier than other. In order to estimate the contact resistances, we identify the three-dimensional positions of all strands inside the CICC, and then evaluate the contact parameters such as number and length of the strands which appear on the cable surface and have contact with a copper sleeve. It is observed that many strands do not appear on the surface of the cable, and can lead to unbalanced current distribution. We developed a numerical code to analyze all strand positions in the CICC. We evaluated the contact parameters by using the numerical code, and then compared them with those evaluated from the measured strand positions. It is found that since both results are in good agreement, the numerical code is available for evaluating the contact parameters. By using the code, we can optimize the contact parameters by varying the twist pitches of all staged subcables. The results show that all strands appear at the surface of the cable and have contact with the copper sleeve, and moreover the contact parameters have been improved.

In order to investigate superconducting properties such as long decay time constants, current imbalances and critical current degradations, we need detailed information about all strand locations in the cable-in-conduit conductor (CICC), and hence we develop a new estimation method to obtain all strand locations. It is very difficult to estimate all strand positions because all strands in the real CICC are squeezed into the conduit and are not regularly arranged but displaced. In order to estimate these strand displacements due to the compression, we introduce mechanical potential energy among strands, and hence we search the minimum energy locations which should be realized in the conductor. In order to calculate this process, we perturb all strands from the original locations and continue these processes by using a genetic algorithm until the potential energy is minimized. This analytical method is very useful to simulate all strand positions and allows us to investigate all the electromagnetic phenomena in the CICCs.

The Cable-In-Conduit Conductor (CICC) is the most promising one for large scale fusion magnets. Now it has been adopted as conductors for ITER magnets. Although the conductor has good mechanical strength against large electromagnetic force, the performance is not so good because the Nb3Sn strands are fragile and the critical current density is sensitive to strain. Because the conductor is composed of hundreds or thousands of strands which are twisted and become tangled, the strands experience extra-bending during energizing magnets. It seems so difficult to analyze plastic deformation of the strands of whole conductor. Our approach to calculate it is unique in terms of using structural mechanics called "Beam Model" based on the measured strand traces inside the conduit. The calculated traces provide us the local curvatures of strands under electromagnetic force. This leads to the evaluate the conductor performance such as Ic degradation. © 2012 The Japan Society of Plasma Science and Nuclear Fusion Research.

Cable-in-Conduit-Conductor (CICC) is used for the international thermonuclear fusion experimental reactor (ITER) toroidal field (TF) coils. But the critical current of the CICC is measured lower than expected one. This is partly explained by unbalanced current distribution caused by inhomogeneous contact resistances between strands and copper sleeves at joints. Current density in some strands reaches the critical under unbalanced current, and the quench is occurred under smaller transport current than expected one. In order to investigate the contact resistances, we measure the three-dimensional positions of all strands inside the CICC for Large Helical Device (LHD) poloidal field (PF) outer vertical (OV) coil, and evaluate contact parameters such as number and lengths of strands which contact with a copper sleeve. Then, we simulate the strand positions in the CICC using the numerical code which we developed, and compare the contact parameters which evaluated from the measured strand positions and the simulated ones. It is found that the both results are in good agreement, and the developed numerical model is useful for evaluation of the contact parameters. We apply the code to various CIC conductor joints to obtain optimal joint parameters. © 2012 The Japan Society of Plasma Science and Nuclear Fusion Research.

Information of 3D strand locations in a Cable-in-Conduit (CIC) conductor is necessary for accurate estimation of conductor performance, e.g., AC losses, current distribution or strain effect. However, it is difficult to derive strand positions after compaction, and there have been no analytical methods to accurately estimate strand positions. In our previous work, we measured strand positions in the CIC conductor, whose length is about 1 m, with 81 NbTi strands and it was verified that some strands were displaced from their original positions. In order to estimate strand locations in a long conductor, we developed a method to analyze three dimensional strand positions taking into account the cable deformation caused by compaction. In this method, we use strand positions in only one cross section of conductor and twist pitches of each sub-cable to calculate the center of gravity of each sub-cable. The strand positions are obtained in a manner that the same order sub-cables rotate around the center of gravity of one order higher sub-cable according to a function of the cabling pitch. We derive the twist pitches after compaction by using measured and calculated strand positions. The calculated strand locations by using the derived twist pitches agree well with the measured ones, with errors of about 0.7 mm. (C) 2011 Elsevier B.V. All rights reserved.

A multi-laminated HTS tape conductor has been recently developed to fabricate large double pancake coils. If the HTS tapes are simply laminated to form the conductor, the current distribution in the laminated tape conductor of the coil is unbalanced because of different inductances of all tapes. It is very important to analyze current distributions in the multi-laminated tape conductor used for the double pancake coil for SMES. In this paper, we analyze the current distribution in the tape conductor by using electrical circuit model, and then discuss how to obtain the homogeneous current distribution. One way is to transpose the tape position at both ends of pancake coil so as to arrange the tapes symmetrically. However, this method is not perfectly geometrical symmetry for more than 3 laminated tapes in the conductor. We propose new method to obtain homogeneous current distribution by adjusting gaps between HTS tapes in the conductor. Finally we numerically demonstrate the homogeneous current distribution in the 4-laminated tapes with inserting additional thickness among tapes.

High Temperature Superconducting (HIS) cables have been studied because of their low loss and compactness compared with conventional copper cables. Three-phase cables are usually composed of three single-phase coaxial cables. Recently, triaxial cables, composed of three concentric phases, have been intensively developed, because they have advantages such as reduced amount of HIS tape, small leakage fields, and small heat loss in leaks, compared with three single-phase cables. However, there is an inherent imbalance in the three-phase currents in the triaxial cable due to differences in the radii of the three-phase current layers. The imbalance of currents causes additional losses and large leakage field in the cable, and also degrades the electric power quality. Therefore, we propose a new model, a triaxial cable composed of two longitudinal sections with different twist pitches to obtain the solutions of the balanced three-phase currents and the homogeneous current distribution in each phase of the triaxial cable. We derive a general equation satisfying both the balanced three-phase currents and homogeneous current distribution, as functions of the winding pitches, and finally apply it to the simplest cable. We fabricated and tested a 1-m HTS cable in order to verify that the proposed theory can satisfy the balanced distribution. The results demonstrate the validity of the theory. We also investigated the current distributions along a long triaxial cable considering the capacitances between the layers in the triaxial cable. (C) 2011 Wiley Periodicals, Inc. Electron Comm Jpn, 94(2): 51-58, 2011; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/ecj.10283

We have devised a magnetic levitation type superconducting seismic isolation device taking advantage of the specific characteristic of HTS bulk that the HIS bulk returns to its original position by restoring force against a horizontal displacement. The superconducting seismic isolation device is composed of HIS bulks and permanent magnets (PM rails). The PMs are fixed on an iron plate to realize the same polarities in the longitudinal direction and the different polarities in the transverse direction. The superconducting seismic isolation device can theoretically remove any horizontal vibrations completely. Therefore, the vibration transmissibility in the longitudinal direction of the PM rail becomes zero in theory. The zero vibration transmissibility and the stationary levitation, however, cannot be achieved in the real device because a uniform magnetic field distribution in the longitudinal direction of PM rail cannot be realized due to the individual difference of the PMs. Therefore, to achieve stationary levitation in the real device we adopted a PM-PM system that the different polarities are faced each other. The stationary levitation could be achieved by the magnetic interaction between the PMs in the PM-PM system, while the vibration transmitted to the seismic isolation object due to the magnetic interaction. We adopted a copper plate between the PMs to reduce the vibration transmissibility. The PM-PM system with the copper plate is very useful for realizing the stationary levitation and reducing the vibration transmissibility. (c) 2010 Elsevier B.V. All rights reserved.

Superconducting Fault Current Limiters (SCFCLs) have been intensively developed around the world these years, and the commercial SCFCL is expected to be available in near future. The main target of SCFCL include not only negligible small impedance under normal operation, but also fast and effective suppression of large fault current within the first current rise, and moreover repetitive operation with fast and automatic recovery. We designed a new type of three-phase SCFCL which is composed of a three-phase winding reactor type FCL and a magnetic shield type superconducting FCL. The proposed SCFCL is effective for symmetrical fault as well as unsymmetrical faults. In order to verify functions of the proposed SCFCL, we fabricate a small device and carry out the experiments. It is found from the test results that the proposed new type of three-phase SCFCL works to restrict the fault currents in all kinds of fault conditions. Moreover, the simulation results of EMTP have good agreements with the test results.

An imbalanced current distribution is often observed in cable-in-conduit (CIC) superconductors which are composed of triplet type multi-staged sub-cables, and hence deteriorates the performance of the coils. Since it is very difficult to control homogeneous current distribution in the triplet type CIC, we propose a coaxial multi-layer type CIC to obtain the homogeneous current distribution. We use a circuit model to analyse the current distribution in the coaxial multi-layer CIC. After calculating inductances between adjacent layers in the coaxial multilayer cable, we can derive a generalized formula governing the current distribution as explicit functions of the superconducting cable construction parameters, such as twist pitch, twist direction, layer radius and SC and Cu strands number. We apply the formula to design the coaxial multi-layer CIC for SC magnet of Force Free Helical-type Fusion Reactor (FFHR). We can design the coaxial multi-layer CIC with the homogeneous current distribution, and investigate several SC strand arrangements in the CIC, and optimize the superconducting strand volume.

High temperature superconductor (HTS) cables have been intensively studied because they are more compact compared with conventional copper cables. Since it is strongly expected that the HTS cables replace conventional power lines, some HTS cables are designed, manufactured, installed in power grids and tested to demonstrate full time operation. Recently, a tri-axial cable composed of three concentric phases has been developed, because of its reduced amount of HTS tapes, small leakage field and low heat loss when compared with single phase and co-axial HTS cables. The layers inside the tri-axial cable are subject to azimuthal fields applied from inner layers and axial fields applied from outer layers with different phase from their transport currents. These out-of-phase magnetic fields should be calculated under the condition of the three phase-balanced distribution of the tri-axial cable, and thereby AC losses should be evaluated. In this paper, the AC loss in the tri-axial HTS cable consisting of one layer per phase is theoretically treated for simplicity. The AC losses in the cable are calculated as functions of the twist pitches of HTS tapes. It is found that the AC losses rapidly decrease with increasing twist pitch. (C) 2009 Elsevier Ltd. All rights reserved.

Recently, a tri-axial cable composed of three concentric phases has been intensively developed, because it has advantages such as reduced high-temperature superconducting (HTS) tape, small leakage field and small heat loss as compared to three single-phase cables. However, there is an inherent imbalance in the three-phase currents in tri-axial cables due to the differences in the radii of the three-phase current layers. The imbalance of the currents causes additional loss and a large leakage field in the cable, and deteriorates the electric power quality. We have already proposed that it is possible to obtain a balanced three-phase distribution by adjusting all of the twist pitches. In order to verify the theory, we designed and fabricated a 1-m-long tri-axial HTS cable and carried out the cable test. The balanced three-phase voltages of the cable were measured by supplying an AC transport current with frequency from 50 to 500 Hz at 77 K. It is found from the test results that the balanced three-phase distributions can be realized by adjusting all of the twist pitches. (C) 2009 Elsevier Ltd. All rights reserved.

Coupling current losses in large scale Cable-In-Conduit Conductors (CICCs) for fusion apparatuses are sometimes annoyance because nobody can estimate how large the coupling loss is before fabricating hundred-meters of long conductor. Our approach for analyzing and estimating the loss based on real strand traces is unique compared with that of other research groups. In process of this approach, we have already measured the traces in two types of CICCs, one has circular cross section and the other has rectangular one. The cabling pattern of the former is 3(4) = 81 the latter is 3(4) x 6 = 486. The flux linkage area in a coupling current loop which consists of two contacting strands is evaluated as an indicator of driving force of the coupling current, which is proportional to the square root of AC loss per unit time. The flux linkage areas showed that the losses of rectangular-shape CICC would be larger than that of circular-shape CICC.

This paper presents experimental and simulation results of a screening current induced magnetic field (SCF) in a high temperature superconductor (HTS) insert that constitutes a low-/high-temperature superconductor (LTS/HTS) NMR magnet. In this experiment, the HTS insert, a stack of 50 double-pancake coils, each wound with Bi2223 tape, was operated at 77 K. A screening current was induced in the HTS insert by three magnetic field sources: 1) a self field from the HTS insert; 2) an external field from a 5-T background magnet; and 3) combinations of 1) and 2). For each field excitation, which induced an SCF, its axial field distribution and temporal variations were measured and compared with simulation results based on the critical state model. Agreement on field profile between experiment and simulation is satisfactory but more work is needed to make the simulation useful for designing shim coils that will cancel the SCF.

High Temperature Superconducting (HTS) cables have been intensively developed because of low loss and compactness, compared with conventional copper cables. A tri-axial cable composed of three concentric phases has been studied, because it has advantages such as reduced amount of HTS tapes and low heat-in-leak, compared with the three single-phase cables. However, there is an inherent imbalance in the three-phase distribution in the tri-axial cable due to differences in radii of the three-phase layers. We proposed a theory to obtain the balanced three-phase distribution for the tri-axial cable by treating two longitudinal cable sections together and adjusting all twist pitches. We derived a generalized formula as functions of winding pitches satisfying the balanced distribution. We designed and fabricated a short HTS tri-axial cable composed of 1 layer/phase to verify the proposed theory. The test results demonstrated that the theory is right for an equivalent impedance circuit model. The theory should be applied to the unbalanced three phase distributions caused by fabrication errors and inherent imbalance of capacitances in the tri-axial cable. We calculate the unbalanced three phase currents and voltages in steady state, and resolve them into symmetrical components to evaluate an imbalance ratio, which is defined as zero-sequence or negative-sequence to positive-sequence component. It is found that the fabrication errors of twist pitch and radius cause the imbalance ratios less than 1%, and the unbalanced capacitances of the cable of 10 km in length cause imbalance ratios of about 1%.

Using a model levitation system composed of an HTS bulk and permanent magnet rows, we investigated the dynamic characteristics of vibration transmission against a vertical vibration as functions of the weight of a levitating object, vibration amplitude, initial and actual gaps between the bulk and the permanent magnet rows. The bulk vibrated in substantially synchronism with the permanent magnet rows and the waveform of relative displacement between the bulk and the permanent magnet rows was sinusoidal. The vibration transmissibility measured in the frequency range below 5 Hz was between 1.00 and 1.08. Using the experimental results of spring and damping constants, we theoretically evaluated the natural frequency and vibration transmissibility of the model system in the frequency range of 0 Hz to 100 Hz. The natural frequency decreased with the weight of the levitating object at a constant actual gap. This means that the vibration removal performance is improved by increasing the initial gap. The larger actual gap at a constant weight of the levitating object was effective for improving the vibration transmissibility in the vibration frequency range above the natural frequency, while the smaller actual gap was effective for improving the damping effect. Therefore, it is important to choose the most suitable field-cooling condition of the bulk by considering the trade-off relationship between the vibration transmissibility and the damping effect according to the weight of the levitating object.

High temperature superconductor (HTS) cables have been studied because they are more compact compared to conventional copper cables. In power applications of HTS cable AC loss is significantly important, as it is related with capacity and efficiency of the power line. Recently, a tri-axial cable composed of three concentric phases has been intensively developed, because of their reduced amount of HTS tapes, small leakage field, low heat loss when compared to three coaxial HTS cable. However, it experiences additional losses and large leakage field due to inherent imbalanced currents. Inside the tri-axial cable, each phase is subject to out-of-phase magnetic fields formed by other phase layer currents. Because tapes are twisted on successive layers, axial field by outer layers and azimuthal field by inner layers are produced in a tri-axial HTS cable. Any slab in the cable experiences parallel component of magnetic field on the wide faces of the tapes: induced by currents of all layers. Since the fields on tapes generate magnetization losses, they should be calculated in consideration of the balanced current distribution of the tri-axial cable. In this paper, AC loss in the tri-axial HTS cable consisting of one layer per phase is described, theoretically, where the balanced phase current distribution is satisfied through treating two different cable segments. The average AC losses in the cable are calculated as functions of the segment lengths and the segment twist pitches. (C) 2008 Elsevier B.V. All rights reserved.

Coupling loss with long time constants has been found a troublesome phenomenon for large size magnet application of superconductor because it would not be simply estimated from AC loss measurement of short sample conductor. In order to investigate the mechanism of the loss, we measured trajectories of strands of sample CIC (3(4) = 81) conductor. The measured length is 1 m along the conductor axis. By analyzing those trajectories, two important facts are cleared. One is that contact periods between two strands are calculated by the function of twisting pitches, not always by the Least Common Multiplier of twisting pitches. The other is that contact probabilities of two strands at each contactable point of sub cables depend on the difference of rotation angles of sub cables. To confirm the validity of this method, we calculated lengths of coupling current loops within I m in length by using experimentally obtained contact probabilities. The results are in very good agreement with lengths obtained from experimental results of strand trajectories. Then we computed the loop length in the long conductor (<100 m), it was obtained that the average loop length would reached about 3 m.

AC losses with long time constants can not be simply estimated from a short sample conductor because there are many irregular loops formed by strands strongly displaced from their original positions. In our previous work, we measured trajectories of 81 strands of NbTi conductor and it was proved that strongly displaced strands produced many line contacts with other strands, and thereby caused low contact resistance and long time constants. Long loops due to the displacement of strands should also produce large AC loss because the time constant of the loss is proportional to the inductance, i.e., the length of coupling current loops. In order to investigate the long loops in practical conductors, we developed a method to estimate the strand positions over the entire length. In this method, only one cross section of the conductor is required to calculate gravities of each sub-cable. The strand trajectories are obtained in a manner that the same order sub-cables rotate around the gravity to form one order higher sub-cable. The estimated trajectories are in good agreement with the measured ones, with errors of 1 mm.

High Temperature Superconducting (HTS) cables have been studied because of low loss and compactness, compared with conventional copper cables. Three-phase cables are usually composed of three single-phase concentric cables. Recently, a tri-axial cable, composed of three concentric phases, has been intensively developed, because it has advantages such as reduced amount of HTS tapes,. low leakage fields, low heat leak and compactness, compared with the three single-phase cables. We analysed the three-phase current distributions in the tri-axial cable as functions of winding pitches of three concentric phase layers, and showed the balanced three-phase current distributions in the tri-axial cable. The each layer supplies a transport current under external magnetic field with the same frequency and different phase. We formulate the general form of AC loss of the transport current in combination with the external field with different phase, and analyse the AC loss of the tri-axial cable.

ac losses consist of both regular losses that are proportional to squared cable twisting pitch and irregular losses that could not be estimated from short conductor sample test results. It was explained from our previous works that irregular loops in the conductor, which are caused by strand displacement as a result of low void fraction of the CIC conductor, produce the losses with long time constants up to several hundred seconds. The observed long time constant indicates that the typical loop length should be about LCM (least common multiplier) of all sub-staged cable pitches, and that contact conditions between the two strands forming the loop should be line contact. In order to investigate the contact conditions in detail, we traced 81 (= 3 x 3 x 3 x 3) strands at intervals of I I mm, along of CIC sample conductor with I m in length whose strands are NbTi/Cu without any surface coating. The measured traces of 81 strands show that asymmetric strand positions, in other words, small and large displacements of strands from their original positions due to compressing the conductor provide many line contacts. It is found that the averaged line contact length reaches about 10 mm that is three orders of magnitude larger than the point contact length, i.e. 10(-2) mm. The time constant of coupling loss is also shown in this paper by estimating the line contact resistance and inductance of current loop. (c) 2006 Elsevier B.V. All rights reserved.

AC losses consist of both regular losses that are proportional to cable twisting pitch squared and irregular losses that could not be estimated from short conductor sample test results. It was explained from our previous works that irregular loops in conductor which are caused by asymmetric strand positions as a result of low void fraction of CIC conductor, produce the losses with long time constants up to several hundred seconds. The observed long time constant indicates that the typical loop length should be about LCM (Least Common Multiplier) of all sub-staged cable pitches, and that contact conditions between the two strands forming the loop should be line contact. In order to investigate the contact conditions in detail, We traced 8 1 (= 3 x 3 x 3 x 3) strands every 11 mm of CIC sample conductor with I m in length whose strands are NbTi/Cu without any surface coating. The measured traces of 81 strands show that asymmetric strand positions, in other words, large displacements of strands from their original positions due to compressing the conductor provide many line contacts. It is found that the averaged line contact length reaches about 10 mm that is three order of magnitude larger than the 10(-2) mm of point contact length.