Cable Core Research Articles

3D FEM Modeling of ${\mathrm CORC}$ Commercial Cables With Bean’s Like Magnetization Currents and Its AC-Losses Behavior

The Conductor on Rounded Core (CORC) cables manufactured by Advanced Conductor Technologies with current densities beyond 300 Amm^-2 at 4.2 K, and bending diameter of up to 3.5 cm, are considered as one of the strongest candidates for the next generation of high field power applications and magnets. In this paper, we present a full 3D FEM model for their monolayer and bilayer CORC cables made with up to three and six superconducting tapes respectively, disclosing the full curve of AC losses for the monolayer cable at magnetic fields beyond 60 mT, and the actual distribution of current density along and across the thickness of the superconducting tapes in both designs. The model is based on the so-called H-formulation, allowing to incorporate the true three-dimensionality of the tapes without recurring to 2D thin-film approaches where non-physical surface currents that do not follow the celebrated Bean's model for type-II superconductors appear. Likewise, good agreement with the experimentally measured AC-losses for the monolayer and bilayer cable have been obtained, with all the details of the model disclosed in this paper.

Electromagnetic and mechanical properties of CORC cable due to screening current

With the development of type II high temperature superconducting (HTS) ReBCO tape, it has been widely used in high field magnets. Conductor on round core (CORC) cable is highly flexible and fully isotropic, making it one of the most important types of HTS cables. In the condition of high field and current, the electromagnetic and mechanical behaviors of CORC cable under screening current effect are not clear. In this paper, the behaviors of CORC cable under high field and current are studied for the first time by combining electromagnetic and mechanical simulation. A three-dimensional shell model and a three-dimensional solid element model of single-layer CORC cable are established by finite element software to study the electromagnetic and mechanical properties of CORC cable, respectively. Compared with the case without taking screening current into account, two current loops are induced within a pitch of the CORC cable due to the screening current, and the magnetic field homogeneity is significantly reduced. Meanwhile, two pairs of shear force are generated at the current loops meeting zones, it results in a certain degree of stress concentration. Fortunately, because the copper core provides stable mechanical support for the HTS tape, there is no significant difference of the maximum stress between two cases with and without screening current in the CORC cable.

Analysis and Calculation of Crosstalk for Twisted Communication Cables in Umbilical Cable

An umbilical cable is a compactly integrated cable consisting of electrical power cables, communication (electric signal) cables, and chemical transposition tubes. An umbilical cable is widely used in developing oil and gas resources of deep and ultra-deep water. With the increment of the length and the functional integration of umbilical cables, the crosstalk becomes a crucial issue in the cable design, and needs to be evaluated carefully before the fabrication and installation. Moreover, the twisted structure of communication cable cores has incurred extra difficulties to the crosstalk calculation. Nevertheless, it is not an easy task to model the complex twisted structure in existing models and methods of the crosstalk computation. In this regard, this paper proposes a numerical methodology for the crosstalk calculation considering the multi-conductor twisted structure of the cable cores. In the methodology, the four-wire twisted structure is modelled as a cascade of uniform multiconductor transmission line (MTL) sections, each wire section covering a length of 1/4 pitch, with abrupt interchanges of wire positions at the ends. The chain-parameter equation is introduced to describe the voltage and current transfer relationship in each MTL section. To obtain the numerical solutions of the twisted cable system, the port constraint equations and the permutation matrices are also required and developed. The per-unit-length parameters of the umbilical cable system are computed by numerical methods. The feasibility to engineering applications and accuracy of the proposed methodology is validated by experimental results, and the crosstalk characteristics of communication cables in a typical umbilical cable under different operating conditions are investigated.

3D Modelling and Validation of the Optimal Pitch in Commercial CORC Cables

Conductor on a rounded core (CORC®) cables with current densities beyond 300 A/mm-2 at 4.2 K, and a capacity to retain around 90 % of critical current after bending to a diameter of 3.5 cm, make them a strong candidate for high field power applications and magnets. In this paper, we present a full 3D-FEM model based upon the so-called H-formulation for commercial CORC® cables manufactured by Advanced Conductor Technologies LLC. The model presented consists of tapes ranging from 1 up to 3 SuperPower 4mm-width tapes in 1 single layer and at multiple pitch angles. By varying the twist pitch, local electromagnetic characteristics such as the current density distribution along the length and width are visualized. Measurements of macroscopical quantities such as AC-losses are disclosed in comparison with available experimental measurements. We particularly focused on the influence of the twist pitch by comparing the efficiency and performance of multiple cables, critically assessing the optimal twist pitch angle.

Investigations in the tape-to-tape contact resistance and contact composition in superconducting CORC® wires

Conductor on Round Core (CORC®) wires and cables, constructed from multiple layers of helically wound REBa2Cu3O7−δ tapes, are a promising cable technology for high field magnet applications. An important feature of high-temperature superconductor cables is the ability to share current between conductors, allowing current to bypass drops in I c and minimizing the risk of hot spot formation, which could lead to potential burnout in the superconductor. In contrast to stacked-tape cables, which have continuous contact between tapes, in CORC® the transfer points occur at discrete tape crossovers. The tape-to-tape contact resistance, R c, plays a critical role in the current sharing capabilities and current distribution in cables. For the work reported here, special CORC® wires were manufactured using different winding parameters to investigate variations in R c. Variations comprised inclusion of a lubricant, different lubricant conductivity, inclusion of pre-tinning, and heating briefly to melt the solder. Cables were first tested as straight lengths, followed by bending to a 10 cm diameter. In straight cables R c values ranged from 1 to over 1000 μΩ cm2, depending on cabling parameters, with the highest values being found for cables made by the present ‘standard’ process. Bending the cables to a 10 cm diameter decreased R c by a factor 2–5. Tinning with PbSn decreased R c by three orders of magnitude compared to standard CORC® wires, and heat treating wires with tinned conductor resulted in only a small further decrease in R c. Based on the measured R c at an electric field of 1 μV cm−1 the resulting current transfer length between layers can range from a few millimeters to a tens of centimeters. Examination of contacts with a laser confocal microscope showed plastic deformation of the copper at the edges of the contact overlap area, apparently caused by thicker plating at tape edges digging into the copper of neighboring layers. These images reveal that only a fraction of the total contact surface may actually be touching when there is nothing to compensate for height differential. Images of the PbSn coated tapes indicated that application of solder produces a much more uniform contact surface and higher contact area. Furthermore, imaging of CORC® cross-sections confirmed that in the non-tinned cables there are many regions where tapes are not in contact, while in contrast the PbSn cable shows significantly more contact between the tapes. These different imaging techniques reveal that tape surface morphology is a significant parameter in determining R c.

Enhanced critical axial tensile strain limit of CORC® wires: FEM and analytical modeling

Conductor on Round Core (CORC®) cables and wires are composed of spiraled high-temperature superconducting (HTS) rare-earth barium copper oxide (REBCO) tapes, wound in multiple layers, and can carry very high currents in background magnetic fields of more than 20 T. They combine isotropic flexibility and high resilience to electromagnetic and thermal loads. The brittle nature of HTS tapes limits the maximum allowable axial tensile strain in superconducting cables. An intrinsic tensile strain above about 0.45% will introduce cracks in the REBCO layer of straight HTS tapes resulting in irreversible damage. The helical fashion at which the REBCO tapes are wound around the central core allows tapes to experience only a fraction of the total axial tensile strain applied to the CORC® wire. As a result, the critical strain limit of CORC® wires can be increased by a factor of more than 10 that of REBCO tapes. Finite element (FE) and analytical models are developed to predict the performance of CORC® wires under axial tensile strain. A parametric analysis is carried out by varying the winding angle, the Poisson’s ratio of the CORC® wire core, the core diameter, and the tape width. The results show that a small variation in winding angle can have a significant impact on the cable’s axial tensile strain tolerance. While the radial contraction of the helically wound tapes in a CORC® wire under axial tensile strain depends on its winding angle, it is mostly driven by the Poisson’s ratio of the central core, affecting the tape strain state and thus its performance. Contact pressure from multiple layers within the CORC® wire also affects the CORC® wire performance. The FE model can be used to optimize the cable design for specific application conditions, resulting in an irreversible strain limit of CORC® cables and wires as high as 7%.

Dispersion of Rayleigh Surface Waves and Electrical Resistivities Utilized to Invert Near Surface Structural Heterogeneities

The single-station Rayleigh surface wave group velocities and electrical resistivities are two data sets that we cooperatively employ to image the near surface (< 40-m) anomaly structures. We numerically simulate the corresponding field measurements where the anomaly structures are assumed to have two-dimensional (2D) variations. The surface waves are represented by fundamental mode dispersion curves, and the electrical resistivities are assumed to be measured by using direct currents. We consider two types of anomaly structures, i.e., cavity and ore body. These two heterogeneities are easily distinguished from the surrounding geomaterial by their distinct physical properties. The cavity is characterized by low seismic velocity and high electrical resistivity, while the ore body is characterized by high seismic velocity and low electrical resistivity. The Rayleigh surface wave data is assumed to be collected throughout the classical common-shot gather. Multiple electrodes, multiple core cables, and multiple arrays are assumed to be used in the electrical survey. Both surface wave group velocities and electrical resistivities are shown to properly invert the anomalous structures in the subsurface. The surface wave group velocities have good horizontal resolution, while the corresponding vertical resolution is somewhat lower. The electrical resistivities have good resolution for shallow structures, but the resolution becomes somewhat reduced with increasing depth. Doi: 10.28991/HEF-2022-03-01-01 Full Text: PDF

110kV high voltage cable sheath transposition to reduce the grounding induction currents

When the high voltage cable core passes through the alternating current, the metal sheath will produce induction electricity under the action of electromagnetic induction. When the sheathes are grounded, the induced currents will reduce the transmission capacity of the wire core and increase the power loss. This paper firstly introduces the grounding mode of cable sheath, and then analyzes the grounding mode at both ends of the sheath and the induced current of cross-connected grounding through ATP-EMTP software simulation. The results of the research have shown that: when the cables are in normal operation, the sheathes adopt cross-connected grounding, the induced currents are reduced, and the energy loss caused by induced currents can be neglected. In actual engineering, due to the non-uniform length of each section of cables, when the cable sheathes are cross-connected, there will be residual positive and negative sequence current in each phase of the sheath after complete transposition.

Monitoring, Detection and Locating of Transient Earth Fault Using Zero-Sequence Current and Cable Screen Earthing Current in Medium Voltage Cable and Mixed Feeders

This paper presents the final development of an expert system utilizing a measurement of cable screen earthing transient current. The developed system allows for identification and location of earth fault in underground cable and mixed lines (underground cable and overhead line) and monitoring of an earthing system and cable screen connections. The unique feature of the developed earth fault locating system is the possibility of identification of line type and branch of the MV underground cable or mixed feeder under earth fault conditions. As a result, the time to remove failure can be greatly reduced and the number of earth fault indicators installed in the distribution network can also be reduced. Unfortunately, in order to operate properly, the previously developed system requires a fundamental—50 Hz component of the measured zero-sequence cable core current and cable screen earthing current; therefore, short transient earth faults without steady-state earth fault currents cannot be localized and categorized even though the transient earth faults have a negative impact on the power system. According to measurements performed by the authors, transient earth faults are relatively frequent, which causes stress to insulation. The number of transient earth faults may be reduced by ensuring proper maintenance of the distribution system. Unfortunately, because of the very large area of the distribution feeder, often in the range of tens of kilometers or even around a hundred kilometers, and many potential causes of earth faults, it is very difficult to localize the transient earth fault and determine the cause of the earth fault. Herein, we present the possible causes of transient earth faults and methods developed for the analysis of transient earth faults. Moreover, the novel algorithm for transient earth fault detection and location is proposed. The proposed algorithm has a self-learning capability and can identify branches of the distribution feeder under transient earth fault conditions. The effectiveness of the proposed algorithm is confirmed thanks to the performed network experiment.

TRANSIENT ANALYSIS IN THREE-PHASE ELECTRICAL CIRCUITS WITH DISTRIBUTED PARAMETERS AND INTERFACIAL CONNECTION ON THE EXAMPLE OF HIGH-VOLTAGE CABLE LINE

The analysis of transients in three-phase electric circuits is carried out, which allowed to consider changes of transient components of currents and voltages of each phase of three-phase cable power line and to estimate the level of overvoltage and amplitude of short-circuit currents in screens taking into account transposition. Using the MatLab/Simulink program, software tools and methods for numerical calculation of transient electromagnetic processes in the designed 330 kV cable line were developed to analyze the level of voltages on the screens and currents in the cable cores at different switching modes. The calculations of a specific 330 kV cable line with a length of 13 km, laid for the first time in Ukraine for the power supply of the electric steel complex, were carried out. The calculation of the emerging transient electromagnetic processes in such a line under different conditions of its connection to the three-phase power supply network is carried out. Many types of switching overvoltages are subject to limitation. Feasibility studies of overvoltage protection measures include assessment of statistical characteristics of damage due to damage, simple or extraordinary repair of electrical equipment of the cable line, as well as due to violation of the technological process by consumers. The above determines the relevance of modeling and analysis of electromagnetic processes that occur when connecting and switching cable lines in ultra-high-voltage three-phase electrical circuits. This allows us to recommend the results of work to develop methods for determining the allowable and emergency modes of similar three-phase cable transmission lines and the choice of rational circuit design solutions in their design. Analyzing the transients in the mode of single-phase short circuit, we can conclude that to select the optimal lengths of the transposition sections of cable screens, it is necessary to consider single-phase short circuit mode, as in this mode there are unacceptable overvoltages on cable screens and currents in three-phase cable lines.

Research on Conducted Disturbance to Secondary Cable Caused by Disconnector Switching Operation

The disconnector switching operation in GIS not only generates very fast transient overvoltage (VFTO) in primary equipment, but also couples to the secondary system, which affects normal operation of the secondary equipment. In this study, aiming at the conducted disturbance caused by the disconnector switching operation of the 1,000-kV UHV GIS test circuit on the secondary cable, a broadband equivalent circuit model of the potential transformer and the grounding grid is proposed based on the vector fitting method and the impedance synthesis method, and the accuracy of the model is tested. On the basis of this model, the conducted disturbance voltage of the secondary cable core is obtained by combining the measured typical disturbance source waveform. The research results of the influencing factors of conducted disturbance show that the amplitude of the disturbance voltage generated by the capacitive conduction is higher than that generated by the resistive conduction, but the main frequency of the resistive conducted disturbance voltage is higher. The amplitude of the conducted disturbance voltage will decrease with the increase of the length of the cable and the length of the grounding wire. The single-ended grounding of the secondary cable shield at the GIS side will cause serious disturbance voltage. The research results of this study will be beneficial to the protection of secondary cable electromagnetic disturbance in the intelligent substation and have reference significance for the implementation of secondary equipment protection measures in the intelligent substation.

Deriving an experimental and analytical relation between the core and fiber temperatures of a 3P XLPE cable

Every submarine power cable contains a fiber-optic assembly. Most windfarms have a distributed temperature sensing (DTS) device for continuous temperature monitoring. Using real-time thermal rating (RTTR) the performance of subsea cables can be increased or a less expensive cable can be installed.The experiments aimed to establish the relation between the fiber and core (or conductor) temperatures in the cable. Fiber temperature was obtained using a DTS interrogator; thermocouples installed in the conductors yielded the core temperature data. The cable used in this test was a 20 meter-long 1800 mm2, 1000 A export cable.These experiments validated a new RTTR model proposed by Marlinks: a thermal RC-ladder model based on finite-element (FEM) calculations. Better suited to the complexity of the spacer geometry and existence of the fiber node, the Marlinks-developed model is considered to be more accurate than the industry standard.

МАТЕМАТИЧЕСКАЯ МОДЕЛЬ НАГРЕВА ТОКОПРОВОДЯЩЕЙ ЖИЛЫ СИЛОВОГО КАБЕЛЯ ДЛЯ УЧЕТА ЭЛЕКТРОТЕПЛОВЫХ ПРОЦЕССОВ В ЦИФРОВЫХ ДВОЙНИКАХ КАБЕЛЬНЫХ ЛИНИЙ

This article deals with the implementation of diagnostics and monitoring of the current-conducting part and insulation state of high-voltage cable lines in real time using digital twins. The problems of thermal accounting and the fea-tures of modeling electrothermal heating processes in power cables are determined. A mathematical electrothermal model of a power cable for a cable line digital twin is proposed, based on the decomposition of its dynamic thermal resistance in-to the sum of exponential components, which makes it possible to calculate the instantaneous values of the heating temper-ature of a current-conducting cable core in real time with insignificant amounts of calculations on the discretization interval of the calculation. The results of calculation using the heating temperature model for a single-core power cable with a three-phase short circuit in the network are presented.

Simulation Analysis of Grounding Characteristics of Cable Based on ATP-EMTP

In order to improve the operation safety and stability of power cables, it is necessary to conduct targeted research on different grounding modes. Firstly, the appropriate cable parameters are selected according to the specific use, and the model is established in ATP-EMTP according to the selected cable parameters. Then, the availability of three grounding modes models of grounding at one end, grounding at both ends and cross-connection grounding (cable core grounding, shielding layer grounding and armor layer grounding) are compared and verified by simulation. Finally, by setting the shielding layers of different thicknesses as a comparison, the impedance and current characteristics of the cables under three different grounding methods are analyzed. The results show that the impedance values of the three grounding methods are basically the same. However, according to the current characteristics, when the shielding layer and the armored layer are cross-connected and grounded, the current of them is much smaller than that which is grounded by other grounding methods. Therefore, under the comprehensive consideration of economic benefits, this grounding is the best choice. This study provides guidance for the grounding mode of cable early laying, and provides reference for other cable related research.

Underground cable modeling and sheath grounding fault simulation

The modeling of single core cable has an important influence on the calculation of cable sheath cross-connected grounding current and voltage. A suitable equivalent circuit can greatly reduce the complexity of the model. In this paper, the theoretical calculation of π type equivalent circuit of cable is analyzed, and the equivalent circuit of cable sheath grounding system is analyzed. Then the calculation equation of sheath circulation and induced voltage is obtained. Finally, by simulating two kinds of sheath grounding faults, two kinds of sheath grounding fault location are summarized.

AC losses of Roebel and CORC® cables at higher AC magnetic fields and ramp rates

We have measured ReBCO coated conductor-based conductor on round core (CORC®) and Roebel cables at 77 K in a spinning magnet calorimeter, which subjected the tapes in the samples to a radial magnetic field of 566 mT (peak) at frequencies up to 120 Hz (272 T s−1, cyclic average) with an approximately sinusoidal waveform. The samples were oriented such that the field applied to the tapes within the cables was entirely radial, simplifying subsequent analysis. An expression for loss which included hysteretic, flux creep and eddy current losses was fit to both the CORC® and the Roebel cables. This expression allowed easy comparison of the relative influence of eddy currents and flux creep (or power-law behavior) effects. The loss of both the CORC ® and Roebel cables measured here were seen to be essentially the sum of the hysteretic loss, flux creep effects, and the normal metal eddy current losses of the individual tapes. The losses of these cables were measured at high B × dB/dt with no coupling current loss observed under the present preparation conditions. The influence of flux creep effects on loss were not negligible. The losses of the CORC® cable per meter of tape were seen to be reduced from the case of a flat tape because of the helical geometry of the tapes.

Detection and Prediction of Internal-Caused Fire in Tunnel Cable by an Equivalent Transient Thermal Circuit Model

Internal-caused cable fires are one of the most common cable fires, and anomalous temperature increase of the cable core is one of the first signs. However, when a cable is operating with electricity, the temperature of the core conductor cannot be monitored directly; therefore, this characteristic cannot be used in detection and prediction of internal-caused fire in electric cable effectively. An analogous transient thermal circuit model is created, simplified, and optimized to properly compute the temperature of the cable core. Afterward, by using the cable internal-caused fire experimental platform and adjusting current carrying capacity of the tested cable, an experiment is conducted for stimulating the very early stage of three-core cable internal-caused fire. The maximum relative errors of the transient thermal circuit model and the trisection transient thermal circuit model are less than 10% when comparing the experimental data with the calculation results, and the average relative error of the calculated value of trisection transient thermal circuit model is 1.08% after layered optimization. The algorithm model can satisfy the requirement for early detection and prediction in the very early stage of cable internal-caused fire.

Superconducting Conductor on Round Core (CORC) Cables: 2D or 3D Modeling?

The HTSConductor on Round Core (CORC) Cables have been widely recognized as the proper candidate for superconducting applications such as the high-field magnets and power transmission cables. This article presents the modeling of HTS CORC cables using the FEM H-formulation model merged into the package COMSOL Multi-physics. The 2D and 3D H-formulation models of HTS CORC cables were compared and analyzed. There were two important parameters in our CORC design: (1) the gap angle between the HTS tapes in a single layer, and, (2) the degree of twist for HTS tapes (normally identified as the pitch). The 2D CORC model has much faster solving speed over the 3D model and sometimes is able to model the AC loss in a reasonable range, while, the 3D CORC model has the advantages over 2D CORC model with respect to more information in each sector with the different conditions of two parameters above, and more realistic loss calculation.

Analysis on the Effect of Superconductor Layer Thickness on the AC Loss of Conductor on Round Core (CORC) Cables

Superconducting Conductor on Round Core (CORC) cables fabricated by several high temperature superconducting (HTS) tapes are able to carry enormous electrical current density, to be widely used in a variety of superconducting applications such as power transmission, fusion, and magnetic resonance imaging (MRI). However, the AC losses induced in the superconducting tapes under alternating current or magnetic field generate heat dissipation which can reduce the electric power efficiency. Therefore, it is essential to analyze the AC loss behavior of CORC cables as well as consider methods to reduce it. This paper presents an AC loss study of CORC cables with several different superconducting layer thicknesses. The CORC cable simulation model is built in a software suite named COMSOL Multiphysics utilising the finite-element method (FEM) solved by the three-dimensional (3-D) H-formulation. By implementing FEM simulations, the cases of increasing the degree of freedom of superconducting layers have been considered, and the AC losses of a single layer CORC cable model with three tapes mounted around the core have been calculated and analyzed for different layer thicknesses. Simulation results are verified with experimental results measured in previous literature.

A Simplified Model of the Field Dependence for HTS Conductor on Round Core (CORC) Cables

This article presents a simplified mathematical model the anisotropic magnetic field dependence (AMFD) for simulating the High-temperature superconducting (HTS) Conductor on Round Core (CORC) Cables. All these simulations of HTS CORC Cable were performed based on the finite-element method (FEM) <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> -formulation model merged into the numerical platform COMSOL Multi-physics. The simplified model of AMFD was implemented into both the 2D and 3D <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> -formulation models of HTS CORC cables. Their results were studied with different conditions, such as the increasing transport current, as well as the gap angle between the superconducting tapes in a single layer. This new simplified AMFD model can give a proper approximation of the actual electromagnetic behaviours of the HTS CORC, but also establish the upper limit of the AC loss calculation, which can be fairly useful for designing future HTS CORC cables.