Alternating-current Resistance Research Articles

The Role of AC Resistance of Bare Stranded Conductors for Developing Dynamic Line Rating Approaches

Overhead transmission line conductors are usually helically stranded. The current-carrying section is made of aluminum and/or aluminum alloys. Several factors affect their electrical resistance, such as the conductivity of the conductor material, the cross-sectional area, the lay length of the different layers of aluminum, and the presence of a steel core used to increase the mechanical strength of the conductor. The direct current (DC) and alternating current (AC) resistances per unit length of stranded conductors are different due to the effect of the eddy currents. In steel-reinforced conductors, there are other effects, such as the transformer effect due to the magnetization of the steel core, which make the AC resistance dependent on the current. Operating temperature also has an important effect on electrical resistance. Resistive losses are the main source of heating in transmission line conductors, so their temperature rise is highly dominated by such power losses, making it critical to know the value of the AC resistance per unit length when applying dynamic line rating (DLR) methods. They are of great interest especially in congested lines, as by applying DLR approaches it is possible to utilize the full line capacity of the line. This paper highlights the difficulty of accurately calculating the electrical resistance of helically stranded conductors, especially those with a magnetic core, and the importance of accurate measurements for the development of conductor models and DLR approaches.

Calibration Method of a Wideband AC Resistance Voltage Divider Based on an Equivalent Model.

Aiming at the problem of large measurement error and phase shift in resistance voltage dividers under high-frequency conditions in the field of power measurement, such as power harmonics, an error correction method is proposed for an alternating current (AC) resistance voltage divider based on the equivalence principle. Firstly, the frequency error model of the AC resistance voltage divider precision is established, and the angle difference of the continuous spectrum ratio difference from 50 Hz to 100 kHz is corrected by determining the shielding structure and the resistance parameters and fine-tuning the shielding potential correction method to reduce the capacities error of the AC resistance voltage divider design precision. At the same time, the performance parameters such as the direction and magnitude of the shielding potential compensation capacitive error are investigated. Finally, the precision voltage divider (the maximum voltage applied is 480 V) calibration experiments verify that the important characteristic judgment factor of the voltage divider is independent of the frequency and the equivalent capacitance value, which effectively solves the phase correction problem of harmonic power measurement.

Reduction of Alternating‐Current Resistance and Heat Generation of Spiral Inductors with Magnetic Sealing Technique

As direct current–direct current (DC–DC) converters increase their power density, their inductors require a planar structure with good heat dissipation. Planar inductors use rectangular wires or substrate patterns for their windings. Winding structures can be stacked, in which the structures are on top of each other; spiral, in which the windings are configured in the same plane; or composite structures of both. Here, the authors clarify the alternating‐current (AC) resistance of inductors with different winding structures and propose a magnetic sealing technique (MST) that reduces the AC resistance of low‐profile spiral inductors. Magnetic field simulation revealed the effect of MST on the AC resistance and inductance. Furthermore, spiral inductors with MST were fabricated, and the AC resistance reduction effect of MST was confirmed with impedance analyzer. The heat‐generation reduction effect in an MST inductor was demonstrated in a 1‐MHz 100 V/320 V 800‐W boost DC–DC converter prototype with GaN devices. © 2023 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

New Approach for Ampacity Calculation of Overhead Lines With Steel-Cored Conductors

Due to increasing energy demand and penetration of renewable energy sources into the grid, the transmission system has often been operated closer to its operating limit. This scenario requires the accurate calculation of the lines' ampacity in order to ensure their safe operation and the full use of their capacity. This paper proposes a new approach for calculating the ampacity of overhead lines with steel-cored conductors, using an accurate resistance calculation model in a straightforward way. The alternating current (AC) resistance of this type of conductors can be affected by the core magnetization depending on factors such as the number of aluminum layers and the core magnetic properties, which are properly considered using the proposed model. Results for the conductor AC resistance variation with the carried current value and the ampacity for different scenarios are presented and compared with those obtained using the resistance calculation models proposed in ampacity calculation methods by IEEE and CIGRE´ . Results show that the lines' ampacity tends to be underestimated using the existing models. However, for conductors with one aluminum layer, the IEEE method may overestimate the line's ampacity by considering a constant conductor resistance value, bringing risks of accidents due to conductor overheating.

Design of a Packaged Multi-radius Multi-path Solenoidal Inductor for Redistribution Layers

This paper proposes a three-dimensional solenoidal inductor using a “multi-radius multi-path” (MRMP) structure that targets integrated voltage regulators (IVRs). Multi-radius (MR) refers to the inclusion of additional turns inside the solenoid, and multi-path (MP) describes the division of a single metal into two paths to reduce non-uniformity in currents due to differences in length. Using an MRMP structure, we propose two new inductor designs for fan-out wafer-level packaging. A two-layer MRMP approach that implements the multi-path in an additional layer, and a one-layer MRMP configuration avoids the need for an additional layer by incorporating the multi-path in an inner turn. We compare inductance and quality performance according to the frequency of the two designs. When the MR technique is applied, the inductance increases due to the increase in the length of the inductor, but resistance also increases. As the frequency increases, alternating current (AC) resistance becomes dominant. The MP increases the quality factor by alleviating skin and proximity effects, which are the main causes of increased AC resistance. Analytical modeling is carried to rapidly estimate and optimize direct current inductance using partial inductance. To verify the improvement in efficiency due to the proposed inductor structure, we propose a prototype IVR that includes inductor loss and investigate the efficiency with circuit simulations using an IVR design with a conversion ratio of 3.6 V:1.8 V operating at 10 MHz. By using the two-layer MRMP inductor, the prototype IVR efficiency increases from 72.6% to 82.1%. A one-layer MRMP inductor, an IVR design with conversion ratio of 1.8 V:1.0 V and an operating frequency of 40 MHz, increases the maximum efficiency from 56.6% to 75.1%.

On-Line Core Losses Determination in ACSR Conductors for DLR Applications.

Dynamic line rating (DLR) is a method that focuses on dynamically determining the maximum allowable current of power lines, while ensuring they operate within safe limits. DLR needs to monitor the temperature and current of the line in real-time, as well as the weather variables in the surroundings of the power line. DLR approaches also require determining the AC resistance of the power line conductors, which is a key parameter that enables it to determine Joule and core losses. This paper presents an approach for an on-line alternating current (AC) resistance estimation of aluminum conductor steel-reinforced (ACSR) conductors to determine the DLR capability of such conductors from real-time conductor and meteorological parameter measurements. For this purpose, conductors with one, two and three layers of aluminum strands are analyzed in detail. Based on the experimental results presented in this paper, two possible approaches are proposed.

High Efficiency PMSM With High Slot Fill Factor Coil for Heavy-Duty EV Traction Considering AC Resistance

Electric vehicle (EV) systems require a high energy-efficiency traction motor so that the motors for EV traction should achieve high efficiency and power density. Hence, a permanent magnet synchronous motor (PMSM) for EV traction using a maximum slot occupation (MSO) coil has been investigated in this study. By applying the MSO coil, high torque density was achieved, but an additional loss, which decreases the efficiency, was incurred through alternating current (AC) resistance. To reduce the AC resistance of the MSO coil, the following process was performed: First, by investigation using the analytical method, pole/slot numbers, current density and number of parallel circuits affecting the frequency, the shape and number of conductors were chosen as important variables. Resistances of the MSO coil with a stator core were analyzed according to the chosen variables above. From the results, MSO coil applied PMSM with proper pole/slot numbers, current density, and parallel circuits was determined to improve the efficiencies at the base and maximum speeds. To accurately estimate the efficiency of the determined model, loss evaluation methods were explained. Subsequently, the determined MSO coil applied model was compared with the conventional model having round wires, and the improvements were verified by load testing.

Receiving‐coil structure reducing stray AC resistance for resonant coupling wireless power transfer

Resonant inductive coupling wireless power transfer is widely known to be a possible convenient power supply method for the small mobile apparatus. However, the limited receiving-coil size tends to lower the efficiency and limit the output power owing to the small mutual inductance and comparatively large stray alternating current (AC) resistance of the receiving-coil. This study mitigates this issue by proposing a novel receiving-coil structure. This proposed structure comprises a coil and a drum core with a thin axis. The coil is wound on the axis to form a single winding layer. The proposed structure can reduce stray AC resistance by suppressing the proximity effect and reducing the wire length without deteriorating the mutual inductance significantly. Therefore, better efficiency and larger output power can be achieved. Simulations and experiments were performed to verify the proposed structure. Consequently, both simulations and experiments supported the reduction in AC resistance compared to the conventional structure. Furthermore, the experiment revealed improvements by the proposed structure in both efficiency and output power. These results support the effectiveness of the proposed structure for wireless power transfer to small mobile apparatus.

The Research and Development of High-precision Measuring Instrument Based on ARM Embedded System

This paper focuses on the research and development of high-precision measurement instruments based on ARM, which is a kind of AC(Alternating Current) and DC(Direct Current) resistance measuring instruments for cables and wires. The instrument has a good human machine interface, can automatically collect data of temperature, voltage and other parameters through sensors. After the collected data is transmitted to the CPU for processing and calculation, the resistance, inductance, phase angle are obtained and displayed on the screen.The instrument has the ability to automatically switch ranges, perform complex calculations and automatically compensate for errors, and can flexibly change functions and expansion modules for use in electronics and industrial applications.

Analytical Computation for AC Resistance and Reactance of Electric Machine Windings in Ferromagnetic Slots

Under the effects of alternating current (AC), the resistance and reactance of electric machine windings are different from their static state. As electric machine windings usually comprise many conductors, it makes the modeling and analysis very cumbersome using the finite element method. This paper presents an analytical method for computing AC resistance and reactance of electric machine windings placed in ferromagnetic slots, which is more convenient and efficient, and could be extended to the slots with different complex structures. First, the slot is divided into a number of layers based on the concept of discretization. Then, the magnetic field governing equation is established, and the distributions of magnetic field intensity and the current density of conductors under AC conditions are solved. By Poynting's theorem, the complex power flowing into the conductors is calculated, and then the effective resistance and reactance of the windings are obtained. Finally, the deduced analytical solutions are compared with the finite element method, and the results show that they have a good agreement for both single-layer winding and the double-layer windings with current phase difference. The presented analytical model is useful for understanding the AC effects and optimization of electric machine windings placed in ferromagnetic slots.

Detecting the Internal Distribution and Structure of Pd-Doped Ag Wire Bonds Using an RF Technique

A vector network analyzer was used to obtain the S parameters of Pd-doped Ag-alloy wire bonds up to 67 GHz. The alternating-current (AC) resistance was extracted at around 3 GHz, 8 GHz, 16 GHz, and 20 GHz before the resonance; it was found that Ag alloy wire bonds with 3.5 wt.% Pd had the lowest AC resistance, with consistent trends at these frequencies. Because Pd has higher resistance than silver, and at high frequencies the current tends to be distributed at the periphery (according to the skin effect), the inward movement of Pd can account for this lowest AC resistance. Analytical methods including electron probe microanalysis (EPMA), energy-dispersive x-ray spectroscopy (EDS), and focused ion beam (FIB) were employed to determine whether Pd had higher concentration in the central region for Ag wire with 3.5 wt.% Pd. EPMA and EDS showed evidence of higher Pd concentration in the central area for Ag wires with 3.5 wt.% Pd. Also, from FIB micrographs, the central area of the Ag wires with 3.5 wt.% Pd had regions of high-angle grain structure, which may explain why the Ag wires with 3.5 wt.% Pd performed better in reliability testing. It is hypothesized that regions of high-angle grain structure are associated with higher Pd concentration in the core region, but verification of this hypothesis lies beyond the scope of this work.

Research on the electrical characteristics of an organic thin-film field-effect transistor based on alternating-current resistance

In this article, an organic thin-film field-effect transistor (OTFFET) with top-gate and bottom-contact geometry based on pentacene as the active layer is fabricated. The experimental data of the I—V are obtained from the OTFFET device. The alternating-current (AC) resistance value of the OTFFET device is calculated using the derivation method from the experimental data, and the AC resistance trend curves of the OTFFET device are obtained with the region fitting method. We analyse the characteristics of the OTFFET device with an AC resistance trend curve. To discover whether it has a high resistance, it is proposed to judge the region of the source/drain voltage (VDS) less than the transition voltage, thereby determining whether the contact between the metal electrode and the organic semiconductor layer of the OTFFET device is Ohmic or non-Ohmic. The theoretical analysis shows that the field-effect mobility and the AC resistance are in reverse proportion. Therefore, we point out that reducing AC resistance is necessary if field-effect mobility is to be improved.

Determinação dos campos de soldabilidade para o aço Dual-Phase 600 em equipamentos de soldagem a ponto AC e MFDC

A soldagem utilizada na indústria automobilística encontra num momento de escolha entre dois tipos principais de equipamentos para a soldagem a ponto por resistência: fonte que usam ou corrente alternada (AC) ou corrente contínua média-freqüência (MFDC). A primeira tecnologia (fontes AC) é a mais tradicional e tem sido utilizada com sucesso na soldagem de chapas de aços de baixo-carbono, com relativo baixo custo. Por outro lado, a tecnologia mais recente (fonte MFDC) tem sido descrita pelos seus fabricantes como uma evolução na soldagem a ponto por resistência ao se aumentar a produtividade, reduzir o consumo de energia elétrica, propiciar melhor controle dos parâmetros e menor estresse termo-mecânico. Além destas vantagens, observando-se o aspecto construtivo das fontes MFDC, estas demandam menores transformadores, uma vez que a eficiência de um transformador é proporcional à freqüência de entrada da rede elétrica, i.e., 60 Hz no caso do Brasil para as fontes AC, ao passo que esta freqüência chega a 1000 Hz no caso das fontes MFDC, reduzindo, assim, seu tamanho. Embora importantes, tais vantagens têm sido alardeadas sem a devida comprovação científica, em especial durante a aplicação dos aços de mais alta resistência. Dentre estes aços, os aços dual-phase têm iniciado sua expansão. Desta forma, este trabalho procurar comparar equipamentos AC e MFDC do ponto de vista de envelope operacional (campo de soldabilidade) para a soldagem a ponto por resistência de aços dual-phase com limite de resistência de 600 MPa. Para tanto, a metodologia de comparação foi definida com base no tamanho equivalente do ponto de solda. Como resultado final, encontrou-se que para menores correntes, o campo de soldabilidade obtido com o equipamento MFDC foi maior, diminuindo à medida que se aumenta a corrente de soldagem.

Effect of the anisotropy of forge-rolling and thermal treatment in hydrogen on the magnetostriction of K50F2 alloy

We have developed a procedure for predicting changes in the magnetostriction of ferromagnetic alloys based on measurements of the parameters of maximum alternating-current electric resistance. We have manufactured a facility for measurements of the elongation of specimens by an optical method. Finally, we have studied the effect of temperature, annealing time, hydrogen treatment, and the anisotropy of forge-rolling on the magnetostriction of K50F2 alloy.

Electrical Properties of Semiconducting Tapes Used in HTS Power Cables

In this paper we investigate the electrical properties of semiconducting tapes used for field grading applications in high voltage technology. Direct- and alternating-current resistance of the samples are measured at cryogenic temperatures between 18-300 K. Two different experimental setups are used due to the resistivity levels of the samples. It is observed that the samples have 'U-shaped' temperature dependence of resistivity corresponding to metallic and insulator type character for temperatures over and below 170 K, respectively. The samples resistivities can be used for diagnostics and fault analysis purposes equivalent circuit models.

Low-frequency electrical resistance of iron, cobalt, and nickel in the vicinity of their Curie temperatures

Alternating-current electrical resistance measurements between 17 Hz and 100 kHz were made on high purity Fe, Co, and Ni wires in the vicinity of their Curie temperatures (Tc). The electrical resistance was independent of frequency for temperatures (T) aboveTc. As the temperature was lowered, however, there was an abrupt jump in the electrical resistance atTc followed by a gradual decrease toward its dc value. The magnitude of the electrical resistance jump atTc increased as the square root of the frequency. The enhancement of the electrical resistance forT≦Tc is produced by an abrupt decrease of the skin depth atTc which, in turn, is due to the sudden increase in the initial magnetic permeability atTc. Measurements of the ac electrical resistance in the vicinity of the Curie temperature of certain ferromagnetic metals can be utilized to 1) accurately determine the Curie temperature using frequencies as low as 17 Hz, and 2) quantitatively determine the initial magnetic permeability as a function of temperature and heat treatment.

Elecromagnetic induction in a system of straight parallel nonmagnetic conductors of equal circualr cross-section

A method is described for calculating the alternating-current resistance of any member of a general system of straight parallel nonmagnetic conductors of equal uniform circular cross-section. The total current in each conductor is assumed to be known in magnitude and phase. The theory is a generalisation of that developed by Butterworth for two parallel conductors. The solution for two conductors carrying equal or opposite currents and the solution for three symmetrically arranged conductors carrying 3-phase balanced currents are derived from the general solution. These particular solutions agree with Butterworth's solution for two conductors and with Costello's solution for the 3-phase system. The present solutions have been evaluated numerically to high accuracy with the aid of a computer and the results are found to agree with available experimental results within the limits of experimental error. New solutions are derived for systems of four and six conductors and numerical results are compared with new experimental work, again yielding agreement within the limits of experimental error. The general solution may therefore be applied with some confidence to any system of parallel conductors.

Electromagnetic induction in a system of straight parallel nonmagnetic conductors of equal circular cross-section

A method is described for calculating the alternating-current resistance of any member of a general system of straight parallel nonmagnetic conductors of equal uniform circular cross-section. The total current in each conductor is assumed to be known in magnitude and phase. The theory is a generalisation of that developed by Butterworth for two parallel conductors. The solution for two conductors carrying equal or opposite currents and the solution for three symmetrically arranged conductors carrying 3-phase balanced currents are derived from the general solution. These particular solutions agree with Butterworth's solution for two conductors and with Costello's solution for the 3-phase system. The present solutions have been evaluated numerically to high accuracy with the aid of a computer and the results are found to agree with available experimental results within the limits of experimental error. New solutions are derived for systems of four and six conductors and numerical results are compared with new experimental work, again yielding agreement within the limits of experimental error. The general solution may therefore be applied with some confidence to any system of parallel conductors.

Alternating-current resistance standards

Alternating-current resistance standards

Alternating-current resistance standards

The basic design principles for resistance standards having a resistance differing from the nominal value by less than 0.01% and a phase angle of less than 0.0001 radn at frequencies up to about 20 kc/s are described. The new nickel-chromium-aluminium alloys, on account of their small change of resistance with temperature, appear to be suitable for standards which must be operated with a considerable temperature rise owing to self-heating. Formulae are given for calculating the residual inductance of standards of various types. A one-ohm standard having a calculated phase angle of less than 0.0001 radn at frequencies up to 30 kc/s is described.