Electromagnetic field and ac loss enhancements in a layer of superconducting round wires

Recent designs for a superconducting power transmission cable consider a flexible system in which the current is carried in a layer of wires or strips, each having a superconducting surface, laid on the surface of a tube. Subdivision of the conductor in this way causes an enhancement of electric and magnetic fields, and of ac losses. The case considered here is when the individual conductors are round wires. Field enhancements are calculated and used to determine ac loss enhancements. These are averaged over the conductor surface to give an overall loss enhancement factor for the cable. Results are presented to cover a wide range of situations.     

Circuit analysis model for AC losses of superconducting YBCO cable

Information about AC losses and electromagnetic behaviour is essential when designing superconducting cables. In this work, AC losses of coaxial YBCO cables are determined using circuit analysis based computational model tailored for the needs of the YBCO cable design work. In the equivalent circuit superconducting layers are connected in parallel, the layers have an inductive coupling between each other and AC loss within a layer generates an effective resistance. The layer currents can be solved from a set of circuit equations. The computational model takes into account that the current in the cable creates magnetic field, which generates magnetisation loss and affects strongly the critical current of the YBCO tapes. The model was applied on several coaxial superconducting YBCO cable designs, which had nominal currents of 1-10 kA (rms). Low AC loss values were predicted for these compact YBCO cable designs. For example, AC losses less than 4 W/m were predicted for 10 kA cables.     

Investigation on AC loss of a high temperature superconducting tri-axial cable depending on twist pitches

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.     

Numerical study on self-field losses of 30 m BSCCO HTS transmission cable

The self-field losses of the one phase of high-T_C superconducting (HTS) transmission cable are calculated by the electric circuit (EC) model. The one phase of HTS cable is constructed by the former of fine-strands copper rod, HTS conductor with four superconducting layers, the insulation made by polypropylene laminated paper, and HTS shielding with two superconducting layers, which was fabricated by Sumitomo Electric Industries (SEI). The length of the cable is 30 m. Each HTS layer comprises BSCCO tapes. The current-dependent resistance of HTS layers in EC model is estimated on the base of Norris expressions for ellipse. The calculated losses are compared with the experimental results measured by 4-terminal method by SEI. The calculation of alternating current (AC) losses, a summation of the self-field losses in HTS layers and the eddy-current losses in the former, is almost equal to the measurement at wide transport-current range below the lowest value of the layer critical current. This result indicates that the numerical calculation by EC model is quite reliable. The minimum AC loss is also calculated by obtaining the optimum helical-pitch lengths of HTS layers at transporting 1 kA_rms. The minimum loss is 36% lower than the loss of HTS cable designed by SEI at the transport current value. In HTS cable with the optimum helical-pitch lengths, the calculation of the layer currents are not uniform in HTS conductor but are almost uniform in HTS shielding, which is contradict to SEI’s one. It is considered that the numerical calculation by EC model is useful to obtain the optimum helical-pitch lengths in HTS cable with the minimum AC loss.     

Experimental evidence for an interaction effect in the coupling losses of cabled superconductors

It is experimentally demonstrated on a series of one-stage superconducting cables, composed from multifilamentary superconducting wires, that the coupling current losses being induced in the wire and in the cable matrix, contain interaction loss terms directly proportional to the wire twist pitch I_w. This proves partly their theoretically expected l_c.l_w-dependence. Different twisting directions in a one or multistage superconducting cable increase the ac losses and should be avoided. The magnitude of the effect can become important.     

LN2 circulation in cryopipes of superconducting power transmission line

We propose and consider the application of superconducting power transmission lines (SC PTs) using high temperature superconductors (HTSs) for further reduction of the electricity losses. To keep HTS cable at low temperature it is usual to use liquid nitrogen (LN₂). Straight and bellows pipes used in SC PT have different hydraulic friction factors due to differences in the shape of the wall surfaces. Moreover, the decentering of the HTS cable, which is unfixed at the center of the pipeline, also influences the LN₂ flow. In the case of long SC PTs, high power must be expended to overcome hydraulic friction. There are two methods to evaluate pressure losses. One is based on empirical formulae and another is based on the algorithms of computational fluid dynamics (CFD). Empirical formulae can estimate pressure losses for long pipes, but the decentering of the cable is not considered. CFD computations describe flow behavior taking into account cable position inside the pipeline, though there is a limit to computable length due to the dependence on the number of mesh points and computation capacity. In this paper, circulation losses and pump power are estimated in straight and bellows pipes forming circulation channels by both methods. For a 40 mm diameter cable in an 80 mm diameter pipe, with the bellows pipe segments covering 2% of the length, and a heat loss of 1 W/m, the required flow rate and pump power for a circulation of 10 km are approximately 19 L/min and 10 W, respectively.     

A general treatment of losses in multifilamentary superconductors

Losses are calculated for a range of shapes of superconducting wire and cable. It is shown that the coupling losses can nearly always be expressed to a first approximation in terms of two parameters. One is the shape of the coil, the other (which contains most of the material parameters) is the time constant.The time constant is calculated for several cable types, including rectangular conductors, in which an exact solution for the field can be found at low frequencies. Maximum values for the loss are calculated and general conclusions for the design of cables are drawn.     

50 Hz loss measurements on superconducting niobium coaxial conductors

A method is described for the measurement of ac losses in a cylindrical conductor forming part of a coaxial superconducting pair. Results given for 25 μm niobium are substantially lower than previous values obtained for this material when tested in the form of narrow strips, and show that, if used as the conductor in a superconducting power cable, the material could carry a peripheral current density of 360 A cm^?1 with tolerable losses (< 10 μW cm^?2) at temperatures of up to 7 K.     

A macroscopic model for coupling current losses in cables made of multistages of superconducting strands and its experimental validation

In a multistage cable the superconducting strands occupy the whole volume in a complex oscillatory pattern from the axis to the periphery. After considerations on the trajectories of the strands, it is shown that the cable can be organized in a multizone structure with time constants determined from the basic time constants of the various cabling stages. The effective volume fractions of the cable in which losses can be evaluated are also derived. The model is assessed by a fit of an experimental curve. In the case under consideration, the screening effects are relatively limited. Altogether, the cable is well characterized by very few parameters: a series of in sequence time constants associated to small fractions of volume. The model is then used to evaluate losses in various conditions of field variations.     

AC Loss of a Multi-Layer per Phase Tri-Axial HTS Cable with?Balanced Current Distribution

Recently, high-temperature superconductor (HTS) cables have been widely studied because of their compactness and high power capacity compared to conventional copper cables. In HTS cables, AC loss is an important issue since large losses reduce the efficiency of the power line. Among HTS cables, tri-axial cable is under intensive investigation recently, since it has a smaller amount of HTS tapes, small leakage fields and small heat loss in leak when compared with the three single-phase cables. For realizing high current capacity, more than one layer is required for each phase; therefore AC loss of the multi-layer tri-axial HTS cable should be carefully examined. In the tri-axial cable, different phase currents produce the out-of-phase magnetic fields on the other phase layers. In case of multi-layer arrangement, net magnetic fields on layer surfaces may exceed the penetration field of the HTS tape. Therefore in this paper, we analyze the AC loss of a tri-axial HTS cable which is composed of two layers per phase. Here, we treat the tri-axial cable which consists of two different longitudinal segments and thus satisfies balanced phase and homogeneous current distribution condition by controlling twist pitch and length of separate segments.     

Reduction of alternating current loss in a high-TC superconducting transmission cable by means of helical pitch adjustment

We have reported that the alternating current (ac) losses in a 66 kV_rms 3-core high-T_C superconducting (HTS) transmission cable fabricated by Tokyo Electric Power Company and Sumitomo Electric Industries Ltd. are calculated correctly by using an electric-circuit model. According to the calculated results, the circumferential field losses are dominant in the total ac losses in compared with the self-field losses and the axial-field losses. The helical pitches of each layer in the HTS cable are designed to obtain almost same layer currents, which gives the minimum self-field losses. We think that the optimum helical pitches giving the minimum total losses are different from the helical pitches designed by the companies and calculate the optimum values in the condition of the same helical direction of each layer in the cable. As a result, for example, it is found that the ac loss of 2.1 W m⁻¹ cc⁻¹ at transporting 1 kA_rms can be reduced to 1.8 W m⁻¹ cc⁻¹ (about 14% reductions) after redesigning the cable with the optimum helical pitches. The optimum helical pitches are obtained for each given transport current. After redesigning, the distribution of layer currents is not uniform and the circumferential fields are reduced.     

ac losses in cables of twisted multifilment superconductors

The losses due to coupling currents are calculated for a superconducting cable. The cable consists of multifilamentary superconducting wires which are twisted and surrounded by a material of different conductivity. It was found that if the wire twist pitch is different from the cable twist pitch, the losses diverge as 1/(1-f), where f is the volume fraction of wire in the cable. The time constant of the cable is increased by a similar factor. These large losses are caused by currents flowing between the wires of the cable and they can be minimized by choosing the correct ratio of cable pitch to wire pitch.     

Comparison study of cable geometries and superconducting tape layouts for high-temperature superconductor cables

High-temperature superconductor (HTS) rare-earth-barium-copper-oxide (REBCO) tapes are very promising for use in high-current cables. The cable geometry and the layout of the superconducting tapes are directly related to the performance of the HTS cable. In this paper, we use numerical methods to perform a comparison study of multiple-stage twisted stacked-tape cable (TSTC) conductors to find better cable structures that can both improve the critical current and minimize the alternating current (AC) losses of the cable. The sub-cable geometry is designed to have a stair-step shape. Three superconducting tape layouts are chosen and their transport performance and AC losses are evaluated. The magnetic field and current density profiles of the cables are obtained. The results show that arrangement of the superconducting tapes from the interior towards the exterior of the cable based on their critical current values in descending order can enhance the cable’s transport capacity while significantly reducing the AC losses. These results imply that cable transport capacity improvements can be achieved by arranging the superconducting tapes in a manner consistent with the electromagnetic field distribution. Through comparison of the critical currents and AC losses of four types of HTS cables, we determine the best structural choice among these cables.     

Effect of electromagnetic force on the pressure drop and coupling loss of a cable-in-conduit conductor

In the central solenoid (CS) insert experiment performed with the International Thermonuclear Experimental Reactor CS model coil, significant changes in the pressure drop and coupling losses were observed during coil energization. This phenomenon was quantitatively analyzed from the viewpoint of the deformation of the cable shape in the CS insert conductor due to an electromagnetic force acting on the cable. A new calculation model was proposed to provide the relation between the electromagnetic force and hydraulic characteristics of the conductor. Calculation results indicated that there seemed to be a gap of 1.3 mm between the cable and jacket created by the electromagnetic force when the CS insert was operated at 40 kA and 10 T, which can cause the decrease of the pressure drop by 12% and also the decrease of the local void fraction of the cable from 36.3% to approximately 34%. The latter well explained the increase of coupling losses. A local void fraction of 34.5% is suggested from the calculation in order both to reduce the amount of deformation and to maintain the coupling losses at acceptable level for this type of large current-carrying conductor.     

Solenoids of composite conductor simulate ac losses in flexible superconducting cable

The complex current distribution on the individual strands of a flexible superconducting cable influences the ac loss. Hence reliable loss predictions cannot be made from previous measurements. It is shown that the required current patterns and losses can be simulated by winding the conductor into single or double layer solenoids. Both total and localized losses can be measured with suitably arranged voltage probes. Measurements have been made on five different strip conductors wound into single layer solenoids to simulate losses on the inner conductor of a flexible cable. Measurements on niobium clad copper composite conductor showed that edge losses contributed more to the total loss than had been predicted theoretically for an idealized case. Despite this the total losses averaged only 15 mW m^?2 at 40 A mm^?1 rms, at 4.2 K. Measurements were also made on a $\text{Nb}\text{Nb-25\%}$$\text{Zr}\text{Cu}$ conductor, developed to carry fault currents in the NbZr and fabricated by soldering together Nb clad NbZr and Nb clad Cu composites. At fields below about 100 A mm^?1 rms, currents were carried by the niobium surface layer and at higher fields flux penetrated into the NbZr underlayer. Thus losses were acceptably low over the entire field range.     

An additional loss source in cabled multifilamentary superconductors

It is shown that irregularities in the twist rate of a multifilamentary superconducting strand, which may occur in the cabling or braiding process of a high current conductor, give rise to additional matrix currents and enhanced ac losses. Electrodynamic equations for matrix and filament currents in a strand with a sudden change in twist rate are derived and damped wave solutions are given for an external harmonic field as well as for a ramp field. Inder unfavourable conditions the associated loss enhancement may become comparable to the regular matrix losses. This is also verified experimentally by magnetization measurements. Some recommendations for cable design are given.     

Core loss in amorphous cut cores with air gaps

The effects of air gaps on the high-frequency core loss in cut cores made of amorphous ribbons are discussed and methods to reduce the core loss in them are proposed. It has been found that the high-frequency core loss in amorphous cut cores with air gaps increases strikingly with increasing air-gap length. The increase in the core loss due to air gaps is remarkable in high-frequency and low-induction range. Measurement of leakage magnetic flux as well as analysis of the flux distribution and the eddy current in an amorphous core with the finite-element method suggests that the increase in the core loss due to air gaps observed in the amorphous cores can be attributed to the in-plane eddy current loss generated by the leakage flux perpendicular to ribbon surfaces. Suppression of the leakage flux normal to ribbon surfaces by using semicircular cores and reduction in width of ribbons of which cores are made decreases the high-frequency core loss in amorphous cut cores with air gaps     

Minimizing the bulk-wave scattering loss in dual-mode SAW devices

The losses arising from the scattering of SAW into bulk waves in the nonsynchronous areas of SAW devices are studied numerically using the boundary element method combined with the finite element method. As a reference structure, we use a typical one-port hiccup resonator on 42 degrees Y-LiTaO3. Strong scattering into bulk wave occurs in the central gap due to an abrupt change in periodicity. To reduce the scattering, we replace the gap with electrodes having reduced pitches. We show that it is possible to significantly increase the Q-factor of the resonator while keeping the resonant frequency unchanged. Two types of structures are studied: the "distributed" gap and the "accordion" gap. To minimize the bulk-wave scattering in dual-mode SAW filters, we replace the metallized gaps in the traditional filter with distributed gaps. We find an optimal combination of pitch and metallization ratio in the gaps, reducing the insertion loss by 0.3 dB.     

Current test on a flexible superconducting core for a 2 GVA ac cable

A 5 m long prototype co-axial flexible superconducting cable core has been made and tested at currents up to 30kA. The inner and outer tubular conductors were both formed from helically-laid strips, and the dielectric between was lapped polyethylene tape. The dielectric was tested in separate experiments. The conductor strips contained layers of nobium, niobium-zirconium and high conductivity copper. The axial contraction of the cable core was restrained by titanium tie-rods and the lay angles of the conductor strips were chosen so that the core tightened radially on cooldown. Lead-filled termination cylinders between the ends of the cable and the current leads inhibited the formation and propagation of normal regions at high currents. Local and average ac loss measurements were made from 4.7 to 10.2 K and at current densities between 10 and 200 A mm^? with very satisfactory results.     

A Numerical Study on AC Losses of a Double Layer Polygonal BSCCO Conductor by Finite Element Method

High-temperature superconductor (HTS) cables are candidates for power transmission cables in the near future. A cylindrical arrangement of HTS tapes for the cable has proved able to reduce the AC loss. Many studies on AC loss characteristics of HTS cables have been done, but few numerical models of the cable were verified by experiments. In this paper, a numerical model of the double-layer polygonal bismuth strontium calcium copper oxide (BSCCO) conductor is developed. Current density and magnetic field intensity distribution in the inner and outer layers are also investigated. The numerical results of the AC loss for different layer current distributions are identical with the experimental ones. Accordingly, the reliability of the numerical model is verified. By using this model, the influence of distance between the inner and outer layers, gap between two neighboring wires, and layer current distribution on AC losses of different layers is evaluated. The results show that increasing distance between layers and narrowing gap between wires are effective to reduce AC loss, while the unbalance of layer current distribution increases the AC loss of the double-layer conductor.