Non-uniform Current Distribution Research Articles

Effects of Contact Loss at Electrolyte/Negative Electrode Interface on Current Density Distribution in Solid-State Batteries

Cyclic volume changes and non-uniform electrodeposition/stripping, among other cycling-induced chemo-mechanical degradation of lithium metal and lithium-alloy solid state batteries, lead to contact loss between the anode and the solid electrolyte separator. Operando experiments have shown accelerated short-circuiting behavior due to contact loss in “anode-free” solid-state batteries. Simulations have shown the relationship between active area fraction and the ratio of effective conductivities in regular-shape active area configurations. Through modeling experiments using imputed active contact area of lithium-metal negative electrode batteries, we quantify the effects of this contact loss. Specifically, we (1) quantify the interfacial resistance due to this contact loss, (2) show non-uniform local current density distribution such that evaluation of what area fraction has current exceeding critical current densities is possible, and (3) show non-uniform reaction distribution at the positive electrode. This work sheds light on the tradeoffs in the design of solid state batteries within the context of contact loss.

Experimental void fraction measurement approach of small channel two-phase flow

This investigation presents a novel experimental approach for assessing void fraction parameters in two-phase flows within microchannels. The study critiques the conventional impedance methods that utilize alternating current (AC) for void fraction measurements, highlighting the inherent drawbacks such as ground capacitance interference and non-uniform current distribution. To circumvent these issues, the research introduces the use of direct current (DC), which ensures a homogeneous distribution across the conductor's cross-section, as a more reliable alternative. Termed the "Direct Impedance Method," this technique employs DC to enhance the accuracy of void fraction measurements. The study explores various geometric configurations of full-ring and half-ring electrodes, both vertical and horizontal, within a microchannel of 500 μm diameter. An empirical formula is derived to calculate the void fraction from the electrical data obtained. High-speed imaging at 4000 frames per second supplements the method by providing visual confirmation of the flow patterns. The comparative analysis of the direct impedance method and image processing using the homogeneous theoretical model reveals a deviation of approximately 2 %–10 % for the slug and annular flow pattern. In contrast, the deviation is more for the bubble pattern. The results affirm that the Direct Impedance Method is a cost-effective and reasonably precise technique for small-channel applications. Its accuracy is inversely proportional to the channel diameter, rendering it unsuitable for channels larger than 2 mm. The method's low construction cost further enhances its practical appeal.

Uncovering accurate values of the polarization resistance in molten fluorides using electrochemical impedance spectroscopy

High-temperature operation and the presence of oxidizing impurities in molten chloride and fluoride salts pose significant corrosion risks to structural alloys in molten salt nuclear reactors. Electrochemical impedance spectroscopy (EIS) offers an operando, real-time method to study the instantaneous corrosion behavior of these materials non-destructively. However, signal noises may originate from sources extraneous to the electrochemical systems that limit the ability to perform quality impedance measurements in low-frequency regime where polarization resistance (Rp) dominates. Using the exposure of pure Cr in molten LiF-NaF-KF containing 1 wt% EuF3 at 600 °C as a model corrosion system, the extent of Non-Uniform Current and Potential (NUCP) distribution during an AC perturbation associate with the disk electrodes is evaluated in terms of two dimensionless correction factors kfRct(=Rct/Reff) and kfCdl(=Cdl/Ceff). Results show that a small area Cr disk electrode increases the transition frequency that marks the dominance of Rp to a conventional terminational frequency above 10−2 Hz, enabling a reliable charge-transfer resistance (Rct) value to be determined via circle fitting of an electrical equivalent circuit model (ECM) model. Experimental results were supported by EIS simulations considering commonly used ECM models that factor in the NUCP effect of disk geometries.

AA5754 aluminium alloy springback reduction by post forming electro plastic effect (PFEPE)

Post Forming Electro Plastic Effect (PFEPE) has been proposed as a promising technology for mitigating forming forces and addressing springback challenges in the metal forming industry. However, several research gaps remain unaddressed for the industrialization of this technology. Firstly, there is a lack of experimental validation regarding the impact of stress reduction on springback. Secondly, the potential effect of the skin-effect on the current metrics of stress reduction needs to be evaluated. Additionally, a post-forming electrically assisted elastoplastic material model is necessary for further technology development in stamping processes. This study tackles these challenges by utilizing AA5754H22 as a reference material and integrating a comprehensive experimental campaign with finite element numerical models and empirical material model developments. Our findings confirm that PFEPE facilitates a significant reduction in springback, achieving approximately a 100% reduction. Although the skin-effect introduces non-uniform current flux density distribution, its impact at the macroscopic level is negligible for the studied thin samples. While the numerical results of springback fails to accurately replicate experimental results, the developed material model aligns well with experimental trends.

Design of Lithium Metal Anode and Other High-Capacity Alloy Anodes Solid-State Batteries in Context of Contact Loss between Anode and Solid Electrolyte Separator

Cyclic volume changes and non-uniform electrodeposition/stripping, among other cycling-induced chemo-mechanical degradation of lithium metal and lithium-alloy solid state batteries, lead to contact loss between the anode and the solid electrolyte separator[1, 2]. In-operando experiments have shown ac-celerated short-circuiting behavior due to contact loss in “anode-free” solid-state batteries[2]. Simulations reveal the relationship between active area fraction and the ratio of effective conductivities in made-up active area configurations[3]. Through modeling experiments using imputed active con-tact area of lithium-metal anode batteries, we quantify the effects of this contact loss in terms of accelerated chemo-mechanical degradation and de-creased rate capability. Specifically, we (1) quantify the interfacial resistance due to this contact loss, (2) show non-uniform local current density distribution such that local current densities could exceed lithium filament growth critical current densities, (3) show uniaxial stress inhomogeneity due to non-uniform reaction at the anode/separator interface, and (4) show non-uniform reaction distribution at the positive electrode.Besides allowing for the optimization of designs to minimize contact loss, our work sheds light on tradeoffs in the design of solid electrolyte separators.

Exploring an Electrochemical Batch Reactor for Nutrient Recovery from Wastewater: Continuum Modeling Analysis of Hydrodynamics and Tertiary Current Distribution

Advancing electrochemical reactors for nutrient recovery from wastewater requires an integration of continuum modeling alongside experimental investigations to appropriately capture transport effects on electrode performance. This continuum modeling approach facilitates the comprehensive evaluation and optimization of electrochemical reactor performance, especially with respect to intricate phenomena that may be challenging to observe solely through experimentation. The optimization process not only enhances the efficacy of existing batch reactors but also lays the foundation for designing and scaling up continuous electrochemical reactors for nutrient recovery [1].A key transport phenomenon in electrochemistry is hydrodynamics because flow dynamics around electrodes dictate mass transport magnitude and uniformity, thereby impacting current distribution, efficiency, and electrolytic energy consumption during electrolysis. Achieving homogeneous velocity fields while avoiding undesirable flow features is essential to prevent non-uniform potential and current density distributions along the electrodes, mitigating side reactions and ensuring the overall efficacy of the electrochemical processes [2].In this study, a two-dimensional model of an electrochemical batch reactor was developed using COMSOL Multiphysics software to investigate reactor hydrodynamics, electrochemical reactions, and mass transfer of species. Employing the finite element method, the model incorporated the k-epsilon turbulence model for hydrodynamics simulation, widely used in literature for simulating fluid flow and mixing behavior [3]. Electrochemical reactions at the cathode (oxygen reduction) were modeled using the Butler-Volmer equation, while the Tafel equation was applied at the anode (hydrogen evolution). Boundary conditions were a grounded counter electrode (anode) and a potential of -1.1 vs Ag/AgCl(sat.) applied to the working electrode (cathode). Fick's second law diffusion-convective equation was employed to model the mass transfer of species, including hydroxide and oxygen.Preliminary findings indicate that while impellers contribute to turbulence and affect local conditions around electrodes, the impact on the backside of the modeled electrodes is relatively weak (Figure 1). This observation may adversely influence mass transfer rates and electrochemical reactions, underscoring the significance of integrating these results with electrochemical reactions for a comprehensive understanding of reactor behavior. Additional results will be presented at the meeting.

A numerical study on effects of current density distribution, turbulence, and magnetohydrodynamics (MHD) on electrolytic gas flow with application to alkaline water electrolysis (AWE)

A three-phase Eulerian model is proposed to investigate the induced flow due to the generation of gas bubbles between two parallel plates without forced convection with application to alkaline water electrolysis (AWE). Earlier models, assuming a laminar regime, accurately predicted the multiphase flow near electrodes but struggled to calculate bulk liquid electrolyte flow away from them. Herein, we study the influences of electric current density distribution, turbulence effects, and the interaction between flow and the magnetic field known as magnetohydrodynamics (MHD). Based on our modeling results, the traditional method using an averaged uniform current density along electrodes (e.g. here 2000 A m−2) is feasible, as incorporating calculated non-uniform current distribution minimally affects the multiphase velocity field. The Lorentz force, originating from flow interaction with the (self-induced) magnetic field, is negligible compared to forces like drag or bubble dispersion. Consequently, MHD effects only become relevant upon introducing an external magnetic field. Including turbulence in the model, being minor in magnitude but non-negligible, significantly improves the predicted velocity profile. Modeling results are validated against an experiment.

Local Permeability of a Metasurface in the MHz and GHz Ranges

The work is dedicated to the study of the magnetic response of a metasurface made of split ring resonators (meta-atoms) in the MHz and GHz ranges. A new method for calculating the local permeability of a metasurface in the MHz frequency range is proposed, taking into account the finite sizes of the elements, and for the first time, a result of high degree of accuracy matching with experimental values has been obtained. In the GHz range, additional factors such as the retardation effect, non-uniform current distribution in the meta-atom, and the complexity of the nature of meta-atoms’ interaction compared to the MHz range are also considered, in particular, the emergence of electrical interaction between them.

Contact resistance effects on current path and thermal characteristics of Ag-nanowire network

In this study, we measured the temperature distribution of Joule-heated Ag-NW network using thermoreflectance imaging (TRI). Numerical computation was conducted for the electric current flow and heat transfer of the Ag-NW network. The contact electric resistance was obtained by solving the optimization problem to minimize the difference between the temperature distributions of the measurement and computation. The results showed that the contact electric resistance varies over the Ag-NW network at certain magnitude. This variation significantly affected the temperature distribution by defining the current path and producing a non-uniform current distribution.

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.

Numerical investigation of parameter distributions in high-temperature PEMFCs under various cooling surface temperature gradients

Non-uniform current density distribution can lead to localized hotspots, resulting in shortened lifespans of fuel cells. The temperature distributions on the bipolar plate cooling surface significantly influence various parameters within a fuel cell. This study develops a mathematical model for a high-temperature proton exchange membrane fuel cell (HT-PEMFC) to simulate its operation in four different directions of temperature gradient on the cooling surface. The distributions of membrane temperature, proton conductivity, oxygen concentration, activation loss, and current density were obtained to clarify the interaction mechanism between cooling surface temperature and these parameters in fuel cell. The results show that the membrane temperature and proton conductivity increase and the oxygen concentrations decrease with increasing cooling surface temperature. A lower temperature in the catalyst layer regions leads to a decrease in the current density. In particular, when the cooling surface temperature distribution is characterized by a temperature decrease in the upstream area with a high reactant concentration and an increase in the downstream area with a low reactant concentration, the fuel cell has an excellent current density uniformity, which reaches 92.61 % at a voltage of 0.6 V and a cooling surface temperature difference of 10 K.

Polymer bead size revealed via neural network analysis of single-entity electrochemical data.

Single-entity electrochemistry methods for detecting polymer microbeads offer a promising approach to analyzing microplastics. However, conventional methods for determining microparticle size face challenges due to non-uniform current distribution across the surface of a sensing disk microelectrode. In this study, we demonstrate the utility of neural network (NN) analysis for extracting the size information from single-entity electrochemical data (current steps). We developed fully connected regression NN models capable of predicting microparticle radii based on experimental parameters and current-time data. Once trained, the models provide near-real-time predictions with good accuracy for microparticles of the same size, as well as the average size of two different-sized microparticles in solution. Potential future applications include analyzing various bioparticles, such as viruses and bacteria of different sizes and shapes.

Magnetic Fields in Multiconductor Systems with Harmonic Currents.

Electric and magnetic fields produced by power transmision and distribution lines are receiving strong interest due to its biological effects and interference disturbances upon electronic and computer equipment. The presence of currents with harmonic contents, generated by variable speed drives and other power electronic devices worsen the problem. The accurate evaluation of the magnteic field in the vicinity of the line must take into account the non uniform distribution of currents inside the conductors, due to skin and proximity effects. The spatial distribution of induction lines down to the ground level must be plotted, to evaluate its effects in the body of a person situated below the line This paper proposes a two step procedure for solving the problem: first, the non uniform distribution of the currents in the conductors is calculated, applying Maxwell laws. Second, the distribution of the field is obtained, using a very fast and innovative approach, based on the application of the Bidimensional Fast Fourier Transform to solve a bidimensional convolution in the domain of the spatial frequency.

Selective Surface Feature Electropolishing of Additively Manufactured 316L Using Pulse Electrochemistry

Electrochemical finishing of metallic surfaces is a scalable, relatively cost-effective technique that is also versatile. One of the main detractions is that the current distribution is uneven and unspecific, often leading to a lack of shape retention and, if it goes too far, inducing corrosion. Pulsing the electrical input creates an unsteady state during electropolishing, controlling the current distribution across the part. The pulse wave prevention of general non-uniform current distribution across the entire geometry instead produces local non-uniformities in the current distribution at given surface features. Many pulse electropolishing parameters can be varied to target individual surface features, including the electrolyte, pulse height, pulse width (equally and unequally distributed), time of polishing as well as the overall waveform.Additive manufacturing (AM) can produce unique, complex structures rapidly. The fast local melting of metal AM parts cool quickly due to the small area, causing unique microstructures, pores, and larger surface roughness compared to cast. AM microstructures change mechanical and chemical properties, such as strength and corrosion, compared to traditionally manufactured parts. Variations in build parameters and composition creates a complicated, feature dependent, corrosion response. By polishing the surface, some of the features, namely the corrosion resistance, wear, and aesthetics can be standardized and enhanced.In this work, we explore the underlying electrochemistry that governs pulse electropolishing. We show that controlling the electrolyte with environmentally benign chemicals ultimately influences the part dimensions that can be polished, the ability to polish, and the propensity to corrode. The pulse height, pulse width (Fig. 1), and total charge passed have an impact on different surface feature removal. We will demonstrate impact of the pulse parameters on the polishing of additively manufactured stainless steel. We go beyond simple planar geometry and apply our understanding to larger scale complex geometry parts, while maintaining near-net shape and minimizing mass loss. Figure 1

Screening-current-induced magnetic fields and strains in a compact REBCO coil in self field and background field

REBa2Cu3O7−x (REBCO) coated conductors, owing to its high tensile strength and current-carrying ability in a background field, are widely regarded a promising candidate in high-field applications. Despite the great potentials, recent studies have highlighted the challenges posed by screening currents, which are featured by a highly nonuniform current distribution in the superconducting layer. In this paper, we report a comprehensive study on the behaviors of screening currents in a compact REBCO coil, specifically the screening-current-induced magnetic fields and strains. Experiments were carried out in the self-generated magnetic field and a background field, respectively. In the self-field condition, the full hysteresis of the magnetic field was obtained by applying current sweeps with repeatedly reversed polarity, as the nominal center field reached 9.17 T with a maximum peak current of 350 A. In a background field of 23.15 T, the insert coil generated a center field of 4.17 T with an applied current of 170 A. Ultimately, a total center field of 32.58 T was achieved before quench. Both the sequential model and the coupled model considering the perpendicular field modification due to conductor deformation are applied. The comparative study shows that, for this coil, the electromagnetic–mechanical coupling plays a trivial role in self-field conditions up to 9 T. In contrast, with a high axial field dominated by the background field, the coupling effect has a stronger influence on the predicted current and strain distributions. Further discussions regarding the role of background field on the strains in the insert suggest potential design strategies to maximize the total center field.

Non-uniform current distribution in parallel-wound no-insulation high-temperature superconductor coil during ramping and fast discharging operations

A parallel-wound no-insulation (PWNI) high-temperature superconductor (HTS) coil is a kind of pancake-shaped no-insulation (NI) coil wound with parallel-stacked HTS tapes, which combines the characteristics of a NI coil and non-twisted stacked-tape cable. It shows a significant advantage in accelerating the ramping response compared with traditional NI HTS coils wound by a single tape, and is a promising alternative for large-scale high-field magnets. The stacked cable approach can lead to current redistribution between parallel tapes during ramping operations. It couples with the turn-to-turn current redistribution and leads to a much more complicated current redistribution inside the PWNI coil, the mechanism of which remains unclear so far. The aim of this work is to investigate electromagnetic behavior of a PWNI HTS coil in ramping and fast discharging process. A simulation model was developed by integrating an equivalent circuit network model and an improved T–A model. A three-tape PWNI coil and its insulated counterpart were wound and tested, and this model was validated by charging and discharging tests. Results show that there is a significant non-uniform current distribution on parallel tapes in the same turn during ramping operations and the maximum azimuthal current (transport current) can be 2.26 times the minimum one in the three-tape PWNI coil in this study. Meanwhile, the radial current shows a considerable accumulation in the tape near turn-to-turn contacts and the radial current through the turn-to-turn contacts can be 4.16 times of that the flow through tape-to-tape contacts (parallel tapes) in the same turn. During the fast discharging process, a significant coupling current is generated in the PWNI coil, leading to a large opposite transport current in local areas; the amplitude of variation of this can be 4.66 times the initial operating current. The radial current shows a similar distribution but opposite direction to that during ramping, and its amplitude is two orders of magnitude higher. These results provide practical guidelines for the design of large-scale high-field HTS magnets.

Scalable Membrane-Free Electrolyzers for Electrochemical CO2 Conversion

Bicarbonate electrolysis offers an attractive approach to conducting electrochemical carbon dioxide (CO2) conversion within the same working fluid used in commonly considered carbon capture processes. However, conventional membrane-based electrolyzers face significant challenges related to scale-up, durability, and CO2 utilization. Here, we present a scalable packed bed membraneless electrolyzer (PBME) design for which liquid bicarbonate electrolyte flows sequentially through alternating porous flow-through anodes and cathodes. Within this design, hydrogen oxidation at porous anodes is used to produce protons that trigger in situ CO2 release immediately upstream of porous cathodes, where electrochemical CO2 reduction generates the desired product and returns the solution pH back towards its inlet value. By using the sequential flow-cell arrangement, the PBME offers the ability to mitigate large concentration overpotentials and non-uniform current distributions that naturally arise during scale-up of conventional membrane-based electrolyzers that rely on lateral flow of catholyte parallel to the surface of the electrodes. This study uses in situ colorimetric imaging to highlight the ability of PBME to rebalance pH across adjacent electrodes. In addition, results obtained with a multi-cell PBME demonstrate the scalability of this concept and reveal the ability to increase CO2 utilization from 12.9% for a single-cell PBME up to 20.5% for a four-cell PBME operated under baseline conditions. With operating the PBME at elevated pressure, the performance can be further improved by increasing the concentration of CO2 in the dissolved phase, which results in higher CO partial current density.

(Invited) Numerical Simulation of Ohmic Impedance

Impedance spectroscopy measurements are often confounded by high-frequency phenomena associated with frequency-dependent ohmic resistance. Newman introduced the concept of frequency dispersion to account for the effect of the disk electrode geometry on the impedance response [1]. The phenomenon described by Newman in terms of frequency-dependent capacitance and ohmic resistance may be considered as an ohmic impedance, a transfer function associated with the resistance of the electrolyte to passage of current under the influence of geometry-induced (and frequency-dependent) non-uniform current and potential distributions [2].Two kinds of models are described in the presentation. Finite-element models account for the influence of geometry on the impedance response for a disk electrode. These models demonstrate the ohmic impedance. The second model is an interpretation model used to extract properties from impedance data. For most cases, data are truncated to avoid being confounded by ohmic impedance. On rare instances, the ohmic impedance may be extracted by regression to data.Gharbi et al. [3] suggested that the ohmic impedance follows the form of the Havriliak-Negami equation. The Havriliak-Negami equation was found to provide a good fit to the ohmic impedance calculated for different electrode geometries, including interdigitated electrodes [4] as well as disk electrodes [3].The ohmic impedance was obtained by Levenberg-Marquardt regression of a process model that accounted for the ohmic impedance [5]. The experiments were performed using ferri/ferrocyanide redox species (10 mM each) in a 0.5 M KCl solution. The working electrode consisted of a 5-mm-diameter Au disk rotating at 800 rpm. A Pt gauze (4 cm2) was used as the counterelectrode, a saturated Ag/AgCl electrode was used as a reference electrode, and the temperature of double-walled electrochemical cell was held at 25 ±0.1°C.The process model was expressed in terms of an ohmic impedance and an expression that accounted for the influence of a local constant-phase element on the faradaic reaction and the convective diffusion impedance, expressed in terms of a series expansion following the work of Tribollet and Newman [6]. Regressions were weighted by the experimentally determined error structure of the data, and the resulting parameters characteristic of the ohmic impedance were in excellent agreement with numerical simulations.References J. S. Newman, J. Electrochem. Soc., 117 (1970), 198.V. Huang, V. Vivier, M. E. Orazem, N. Pébère, and B. Tribollet, J. Electrochem. Soc., 154 (2007), C81-C88.O. Gharbi, A. Dizon, M. E. Orazem, M. T.T. Tran, B. Tribollet, and V. Vivier, Electrochim. Acta, 320 (2019), 134609.A. Dizon and M. E. Orazem, Electrochim. Acta, 337 (2019), 135000.W. Watson and M. E. Orazem, EIS: Measurement Model Program, ECSArXiv, 2020, https://ecsarxiv.org/kze9x/.B. Tribollet and J. S. Newman, J. Electrochem. Soc., 130 (1983), 2016.

Numerical and experimental investigation of a cathode-supported microtubular solid oxide electrolysis cell from current and temperature variations in-situ assessed with electrode-segmentation method

The electrode segmentation method has been applied to experimentally assess the current and temperature distributions in a cathode-supported microtubular solid oxide electrolysis cell (mt-SOEC). A detailed three-dimensional SOEC model considering the mass/momentum/charge/energy transfer is also developed to explain the in-situ working mechanism with spatial current and temperature variations considering the electrochemical performance and degradation. Both the experimental and numerical results reveal that the electrode-segmentation method exhibits notable nonuniform current and temperature distributions among the segments (up-, mid-, and downstream). Reactant starvation in the mid- and downstream regions leads to spatial current and temperature variations, with the largest temperature gradient observed and predicted between the up- and midstream regions. Further analysis of the temperature variations indicates that endothermic electrochemical Peltier heat in the air (oxygen) electrode (anode) is the primary cause of temperature decrease from 1.0 V to 1.3 V, while heat production with the overpotentials in the fuel (hydrogen) electrode (cathode) dominates temperature increase above 1.3 V.

Influence of Non-Uniform Current Distribution Among Layers on AC Loss Characteristics of Multilayer Spiral Copper-Plated Striated Coated-Conductor Cables

In spiral copper-plated striated coated-conductor cables (SCSC cables) carrying ac currents, differences in self-inductance in each layer and mutual inductances between layers cause non-uniform current distribution among layers. This may increase the ac losses of the SCSC cables. We have been developing the electromagnetic field analysis model to evaluate ac losses in SCSC cables carrying ac currents under ac magnetic fields. In the analysis model, a circuit model and a large-scale electromagnetic field analysis model were combined. In the circuit model, each layer of SCSC cables is modeled as a circuit consisting of resistances and inductances. We investigated the effect of non-uniform current distribution among layers on ac losses for a SCSC cable carrying ac currents under ac magnetic fields.