Round Conductors Research Articles

Influence of the Skin and Proximity Effects on the Thermal Field in Flat and Trefoil Three-Phase Systems with Round Conductors

The passage of current generates heat and increases the temperature of electrical components, which affects the environment, support insulators and contacts. Knowledge of the temperature allows for the determination of important operational parameters. Time-varying currents result in a nonuniform current density distribution due to the skin and proximity effects. As a result, temperature and energy losses are increased compared to the uniform DC current density case. In this paper, these effects are considered for three-phase systems with round conductors in flat and trefoil arrangements. In the first step, the analytical expressions for current distributions are determined and used to construct the heat source density. Then, a suitable Green’s function, which allows for obtaining temperature distribution in analytical form, is used to evaluate temperature at any point throughout the conductors. The temperature differences throughout individual wires are usually negligible, whereas noticeable differences can be observed between the wires. The impact of various parameters is examined, and an approximate closed formula is derived to assess the influence of the skin and proximity effects. When the skin depth is not smaller than the wire radius, the skin effect enlarges the temperature increase by around 2% compared to the DC case. As for the proximity effect, the additional increase can be neglected if the distance is above around 10 wire radii, but for closely spaced wires, it can reach up to around 17%, depending on the arrangement and the distance between the wires. Such an additional increase may result in exceeding the permissible temperatures, which damages particular components of the system; therefore, it is important to take it into account at the design stage.

Two-Dimensional Frequency-Dependent Resistance and Inductance Calculation Method for Magnetic Components With Round Conductors

Two-Dimensional Frequency-Dependent Resistance and Inductance Calculation Method for Magnetic Components With Round Conductors

Towards a Holistic Approach to Inverter-Fed Machine Design: FEM-Based PDIV Prediction of Complete Windings

The Schumann inception criterion was used to predict the partial discharge inception voltage of insulation models representing both wire wound and form wound (hairpin) low voltage machines. It was found that the fitting parameter <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> (the logarithm of the critical number of electrons that define the transition from Townsend to streamer discharge) is almost independent of material parameters when dealing with a given type of insulation (e.g., turn-to-turn using round conductors or flat conductors). These numbers can be fed to software for finite element analysis to provide a worst-case estimate of the partial discharge inception voltage.

Analytical Double-2D Frequency-Dependent Leakage Inductance Model for Litz-Wired High-Frequency Transformer

Accurate and fast calculation of frequency-dependent leakage inductance is critical for the optimization of the high-frequency transformer with Litz wire winding. The analytical method is widely used due to its high computation speed. However, its computation accuracy is limited due to the following factors. i) One-dimensional (1D) or two-dimensional magnetic field model (2D) has unsatisfying accuracy for the transformer with a rotationally asymmetric structure. ii) The skin and proximity effect factors based on the multilayer foil winding are inaccurate for the Litz wire winding in the calculation of frequency-dependent magnetic energy. This paper proposes a double-2D frequency-dependent leakage inductance model for the transformer with Litz wire winding. It uses the image method to calculate the 2D leakage magnetic field inside and outside the core window, respectively, which considers the rotationally asymmetric structure in leakage inductance calculation. The round conductor model is proposed for the frequency-dependent magnetic energy calculation. The single strand in a Litz wire is taken as the basic modeling object of the round conductor model, which is more detailed than the multilayer foil winding model for the Litz wire winding. The comparison between the experiment, FEM, state-of-the-art models and the proposed model is conducted for eight transformers with E-core, U-core, round or rectangular Litz wire winding. The proposed model shows satisfying computation accuracy in the whole frequency band. And the computational speed of the proposed model is 100 times that of the FEM.

Influence of the Skin and Proximity Effects on the Thermal Field in a System of Two Parallel Round Conductors

This paper presents a semi-analytical method for determining the distribution of the thermal field in a system of two parallel round conductors, taking into account the skin and proximity effects. The method of a suitably constructed Green’s function was applied to find an analytical expression for the eigenfunctions describing the temperature distributions. In turn, the relevant integrals, which cannot be determined analytically, were calculated numerically. The foundation of the method is the knowledge of the current density distribution in the conductors. As a result, the steady-state distribution of the temperature field in the conductors for various parameter values can be determined. The obtained numerical results were positively verified using the finite element method. Using the developed method, the share of skin and proximity effects in the temperature rise and steady-state current rating was evaluated. Closed analytical formulas were obtained for the AC case with the skin effect taken into account. When the skin depth is smaller than the wire radius, the skin effect has quite a large impact on the conductor temperature. The impact of the proximity effect is much smaller but clearly noticeable when the distance between the wires is smaller than five times the wire radius. In addition, the influence of the value of the heat transfer coefficient on the thermal field of the conductors was also examined.

Improved Winding Losses Calculation Based on Bessel Functions

In this paper, an approach combining semi-empirical equations and the method of images is proposed for round conductor layer windings with un-gapped core. The new equation for proximity effect can convert the constant field strength from the magneto-motive force (MMF) across the core window into a frequency dependent uniform background magnetic field strength, which can take partly the interaction between conductors into account. Geometric factors are introduced by fitting the finite element method (FEM) results to improve the accuracy. The method of images is used to calculate the field strength in order to counteract the impact of 2D edge effect. The new method is compared with the 2D FEM, analytical methods, and is also validated by measurements with EE core transformers. The proposed method shows good accuracy (<10% error) compared to 2D FEM for both high and low porosity factor windings. Therefore, it can handle more winding configurations than other 1D analytical methods.

Equivalent Circuit Element Calculation of Gapped Multiwinding Inductors

Accurate and fast models of the equivalent circuit (EC) elements of gapped multiwinding inductors are essential for the design of galvanically isolated converters, such as Flyback and LLC converters. Typically, the EC elements are acquired from measurements or time-consuming FEM simulations, both of which are disadvantageous for optimizing the design of the magnetic device. This paper proposes a multiwinding magnetic device EC that exclusively uses the impedance matrix elements, i.e., self- and mutual impedances. The advantage of the impedance matrix equivalent circuit (IMEC) is that self- and mutual impedances are directly measurable. Furthermore, the paper presents an analytical 2D magnetic field model to calculate the EC elements. It is quantitatively confirmed that frequency significantly affects the resistances and the inductances of magnetically coupled windings. In particular, eddy currents in windings induced by the fringing field of the air gap play a role besides the well known skin and proximity effect. The proposed model accurately considers all these effects in foil, Litz, and round wire conductors. The model is verified using FEM simulations and measurements.

Equations for the Inductance of a Rectilinear Segment of a Round Conductor

Equations for the Inductance of a Rectilinear Segment of a Round Conductor

2-D Winding Losses Calculation for Round Conductor Coil

Winding loss calculation is essential for inductor and transformer design. In this article, a revised 1-D Ferreira's formula is proposed, which considers the interaction between conductors. Then, a 2-D loss calculation approach is proposed based on the analytical solution of round conductors under a uniform external field. An equivalent external magnetic field is calculated to estimate the winding losses, considering the impact of eddy current. The proposed approach is compared with the 2-D FEM with three types of windings and shows good accuracy with less than 10% error. 3-D FEMs and samples are built based on two simulated windings to validate the loss calculation.

Analytical Approach to Current Rating of Three-Phase Power Cable with Round Conductors

The continuous increase in the demand for electricity makes it necessary to modernize or build new transmission lines. This, in turn, results in research that is still being carried out on the optimal use of power cables. In the paper, an improved analytical method for the determination of the current rating of power cables was proposed. The method for determining the ampacity of the power cable presented in the IEC standard assumes that power losses in the phase conductors and screens are determined by taking into account skin and the proximity effects on the basis of tabulated coefficients. The methodology proposed in the paper is based on the method presented in the IEC standard, but the power losses in the conductive elements of the cable are determined analytically, which offers higher accuracy. In order to validate the analytical method proposed in this paper, numerical calculations based on the finite element method with very fine mesh were also performed. Exemplary calculations carried out for three types of cables with use of the proposed method, IEC standard and finite elements showed very good agreement in the results. The proposed method requires more computational effort, but it offers more accurate results than the IEC standard and can be used when higher accuracy is required. It can also serve as a reference point for simplified calculations.

Research on the AC Loss of Multi-strand Round Conductors

Conductors are very common in our life, such as high-voltage cables and all household appliances. The vast majority of conductors, especially home circuits, use alternating current. There will be so-called AC loss in AC circuits, which will limit our design and improvement of electrical appliances. In this paper, the AC loss in the charging conductor is influenced by skin effect and proximity effect. First of all, we will introduce these two effects. Both effects cause energy loss via induction current. Secondly, variables related to energy loss are pointed by using finite element analysis. After modelling and analysis, energy loss depends on frequency, loss increase with increasing frequency. Secondly, among the different arrangements of conductors, the arrangement of hexagons will be more energy-saving. Finally, the degree of energy loss is related to the conductor’s diameter. As the conductor’s diameter increases, the energy loss increases first and then decreases. In the end, energy loss relies on the size of frequency and the arrangement of conductors and the diameter of conductors

A Comparative Analysis of Partial Discharge in 13 Combined Insulation Structures of 11 Materials Used in Cast-Resin Dry-Type Transformers

Partial discharge (PD) in cast-resin dry-type transformers (CRDTs) is an important issue that needs to be overcome. In this study, PD in insulation materials used in CRDT windings is investigated. Four types of samples are prepared using 11 different types of materials, including epoxy resin, three-ply glued polyester insulation, prepreg insulation, glass fiber mesh, polyester adhesive tape, polyester film, polyimide film, rectangular conductors with polyester insulation, round conductors with polyester insulation, round conductors with enamel insulation, and foil conductors without insulation, and subjected to PD measurements. The samples are placed into a mold for resin casting that is similar to those used to fabricate large cast-resin windings, and the material behavior is tested. PD measurements are carried out in the high-voltage laboratory of the BEST Transformer Company. The measured data are used as inputs to models of the samples that are simulated using finite element analysis software to determine the PD inception electric field. The PD patterns of the samples are compared with well-known PD patterns in the literature. Finally, a comparative analysis of the materials is performed, and strong and weak materials against PD are identified. The results of this study show that laminated insulation materials or fiberglass meshes, both with epoxy resin, which have PD inception at a mean value of 3.4 kV/mm of electric field intensity, are more susceptible to PD than the other insulation materials investigated. In contrast, insulated conductors or nonlaminated polyester or polyimide films, all with epoxy resin, which have PD inception above a mean value of 5.3 kV/mm of electric field intensity, are robust to PD.

Feasibility Study of ITER In-Vessel Coils Bracket Manufacture and Integration

Feasibility study of ITER In-vessel coils bracket manufacture and integration had been developed in Institute of Plasma Physics, Chinese Academy of Sciences. The ITER In-Vessel Coil system is comprised of Edge-Localized Mode (ELM) and Vertical Stabilization (VS) coils. The ELM coils are used to mitigate the Edge Localized Modes and the VS coils are used to provide Vertical Stabilization of the plasma. Designed bracket for IVC coils is a kind of building block type three or four stacked components with arcuate groove matching with round conductor. This paper describes structure design, manufacture and integration process of the ELM and VS bracket. R&D of bracket weld and assembly sequence optimization are carried out to determine the welding and assembly process. At last, three brackets are integrated in ASIPP.

Updates on CEA Design and Experimental Activities on EU DEMO TF System

In the framework of EU design activities for dimensioning the future fusion DEMOnstration reactor (DEMO), in-depth analyses were conducted in EUROfusion context, aiming to define the design of the DEMO magnets system. For the last DEMO baseline, CEA has proposed for Toroidal Field (TF) coils a concept with radial plates (named WP#4) which is ITER-like, with a round conductor embedded in steel plates. In order to consolidate this design, CEA conducted fine analyses that assess thermal hydraulic and mechanical aspects to allow ensuring compliance with design criteria. The outcomes of theses analyses were used to improve the TF design in order to avoid relying on conservative approaches at pre-design stage, which often end up in material over dimensioning, that penalize cost and space occupation. In this regard, two improving approaches will be exposed, that deal with mechanical consideration and temperature operation, together with future perspectives. On the other hand, CEA designed and manufactured in collaboration with ASIPP a full-size conductor sample derived from a previous TF CEA concept (square-in-square conductor) which is expected to operate at 88 kA and 12T. The two conductor legs of this sample were designed by CEA and manufactured by ASIPP following an extensive quality assurance (QA) preparation process. The sample is presently in course of assembly in CEA Cadarache and is expected to be tested in SULTAN facility (Villigen, CH) to assess its behaviour in both DC and AC regimes. An overview of the status of activities and future perspectives is given in this paper.

Conceptual Design and Optimisation of HTS Roebel Tapes

The main obstacle for the application of the high-temperature superconducting (HTS) coated conductors (CCs) in AC energy applications is the relatively large AC loss. To tackle this, several forms of HTS cables for AC applications have been invented and investigated, such as the HTS Roebel cable, Cable on Round Conductor (CORC), and Twisted Stacked Tape Cable (TSTC). In this paper, the possibility of encapsulating Roebel cables into a single HTS CC is investigated, from which a novel conception of a Roebel tape is proposed. Compared with the existing HTS cables, HTS Roebel tapes are more compact, more capable at carrying large current with minimised AC losses, and easier to manufacture. A 3D finite element method (FEM) model of the Roebel tape is built to optimise the structure and verify the performance. The results show that, compared with normal ReBCO CCs, Roebel tapes with optimum patterns can reduce AC transport losses by 60% through field-cancelling and can reduce magnetisation losses by the factor of the filament number through patterning. With excellent loss reduction performance and high current capability, the Roebel tape shows great potential to become a revolutionary HTS cable for high-current power transmission and AC machine applications.

Calculation of Basic Average Drift Characteristics of Free Electrons in a Metallic Conductor with Electric Current

The results of an approximate calculation of theaveraged values of speeds of vmz of a longi-tudinal drift of lone electrons, and of circular frequencies of ωmz change of longitudinal elec-tronic waves de Broglie and of lengths of λmz of longitudinal electronic waves de Broglie in the metal of round cylindrical conductor with an electric axial-flow current of conductivity of i0(t) of different kinds (permanent, variable, and impulsive) and amplitude-time parameters (ATP). The results of verification of the obtained calculation correlations for speeds of vmz drift of lone electrons and lengths of λmz of electronic de Broglie waves in the examined con-ductor demonstrate their validity and working capacity. The obtained data confirm the quan-tum-wave nature of the electric current of conductivity of the indicated kinds of i0(t) and of ATP in a metallic conductor.

Motors Employing REBCO CORC and MgB2 Superconductors for AC Stator Windings

Future all-electric aircraft will employ highly efficient compact and lightweight machines for power generation and propulsion applications. Previous studies have indicated that the most attractive options include synchronous machines employing superconducting excitation and stator windings for achieving high power density and efficiency. The dc excitation winding could be constructed using a variety of superconductors, but the choice for ac stator windings is limited. High conductivity aluminum conductor at cryogenic temperature is a possible option but it is expected to be heavier than a superconducting winding and will require more extensive cooling as the losses within the winding pack will be much larger. A conductor-on-round-core (CORC) cable using REBCO tapes looks like an attractive option as it enables compound bending for constructing saddle coils. Here, we investigate using this cable for the stator winding of a 3 MW, 4500 RPM, 4-pole propulsion motor and compare with an identical motor employing an MgB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> stator winding. The motor configuration assumes saddle-shaped coils for the stator winding. Each saddle coil constitutes a double pancake. A round conductor capable of bending in three-dimensional is preferred for such coils, making the round CORC cable ideal for this application. The cable employs striated REBCO with striation width as small as 1/3 mm. The ac field in the stator winding region is about 0.7 T at 150 Hz and the cable is operated at 50% of its critical current for limiting ac losses and for providing a safety margin. Individual tapes in the CORC cable experience field perpendicular to its broad face resulting in high ac losses. Comparing the performance of motors employing CORC and MgB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> cables for the stator, we find that the ac losses in the CORC stator are much larger than the MgB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> stator. High losses in the CORC stator winding make this option less attractive unless coolant power is freely available, such as in LH <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -fueled planes. However, this machine with CORC coils is the most compact and lightweight option. Such compact light mass motors could be attractive for LH <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> fueled applications, such as interstate trucks, heavy machinery, locomotive hauling goods trains, ships (especially for podded propellers), etc.

Simulation study of 6–10 kV cable lines for transient processes calculation during earth faults

As a rule, researchers do not consider the dependence of the inductance of cable lines on frequency in their scientific papers devoted to the calculation of transient processes during single phase-to-ground fault in 6–10 cable networks. In some cases, it can lead to significant errors in evaluation of current and voltage transient components parameters. Therefore, it is an urgent task to estimate defined errors and the scope of application of frequency-independent equivalent circuits and models of 6–10 kV cable lines during calculation and simulation of transient processes in case of single phase-to-ground fault. The authors applied PSCAD / EMTDC software to study the effect of the frequency dependence of the inductances of 6–10 kV cable lines on the calculation accuracy of transient processes during single phase-to-ground fault. It allows to simulate electric power systems models with the usage of both frequency-dependent and frequency-independent cable line models with round conductors only. To check the adequacy of the frequency-dependent three phase cable model developed in PSCAD software, the authors have used a frequency-dependent model of 6–10 kV three-phase cable with sector-shaped conductors designed in COMSOL Multiphysics software. The authors have developed an approach to develop of 610 kV cable lines models with frequency-dependent and frequency-independent parameters. The authors have obtained error estimation in transient current and voltage parameters during single phase-to-ground fault in cable networks models that do not consider the frequency dependence on inductance (for discharge components the error is 1520 %, for charging components the error is equal to 510 %). It is shown that models with cable line parameters defined according to spreading speed of electromagnetic wave, can be used for approximate calculation of transient current and voltage to solve most of tasks of investigation of transient processes during single phase-to-ground faults. Application of the developed recommendations to determine three phase medium voltage cable lines parameters will increase the calculation accuracy of transient processes during single phase-to-ground faults in 6–10 kV cable networks. Only application of frequency-dependent models of cable lines allows us to provide required accuracy to develop methods of distant earth fault localization in 6–10 kV networks.

THE USE OF FERROMAGNETIC AMORPHOUS MATERIALS 5BDSR IN HIGH-FREQUENCY OVERVOLTAGE PROTECTION DEVICES

The paper discusses the prospects of using nanocrystalline amorphous materials in the electric power industry. In particular, in the field of protection of electric power equipment of substations from high-frequency pulses. The effectiveness of using such materials to activate the anomalous skin effect in multilayer conductors is shown. The resulting conductors increase their resistance at lightning frequencies, thereby making it possible to create devices that effectively suppress high-frequency pulses. The authors give an example of a protective frequency-dependent device using nanocrystalline ferromagnetic material and the results of its use in trial operation. The paper shows the results of comparing round and flat frequency-dependent conductors.

On Using CNTFs-Based Wires for High Frequency Wireless Power Transfer Charging Systems

In many practical wireless power transfers (WPT) applications, such as cell phone wireless charger, electrical vehicles, and implantable cardiac pacemakers, the weight and power losses in the coupled coils are primary design issues. Currently, metallic wires are normally used to fabricate the WPT coils. The metallic wires have several problems, mainly involving large weight, poor mechanical performance, corrosion, and resistive losses (especially at high frequency due to both of skin and proximity effects). Carbon Nanotube Fibers (CNTFs)-based wire is a promising candidate to replace the conventional metallic wires in these applications. CNTFs-based wires have superior electrical properties at high frequencies. Furthermore, it shows high mechanical performance, light weight, and high thermal conductivity. This paper uses CNTF wires to investigate a planar spiral transformer suitable for WPT charging systems. Efficiency of the transformer is investigated theoretically and experimentally over several MHz frequencies and ampere currents. The CNTFs-based wireless transformer operation was compared with copper (Cu) based wireless transformer fabricated with similar dimensions and DC resistance values. The AC resistance of both transformers is calculated using the conventional model of solid round conductor and the FEM simulation. It is found that the calculated and the FEM AC resistance values are matched in case of Cu transformer with 4194A Impedance/Gain-Phase Analyzer measurements while they are mismatched in case of CNTFs one. Therefore, a correction factor for the AC resistance of CNTFs wire is proposed to match the calculated AC resistance with the measured one. Furthermore, both transformers were tested experimentally within 50 W/6.78 MHz WPT charging systems at different ampere currents. The charger efficiency measurements verify the analyzer results showing better efficiency with CNTF based transformer in comparing to copper one.