Foil Conductors Research Articles

High frequency modeling of dry type detuned reactor for transient studies: Simulation and experimental analyses

Dry-type detuned reactor (DDR) is a key component for power quality management. Improper design of DDR may result in insulation failure during power system transient events. This can be avoided by developing a proper DDR high frequency model that can accurately capture the behavior of the reactor during transients and provide better insight into its performance under various operating conditions. One of the main challenges of proper DDR modeling is the shape of the leakage flux, which is strongly dependent on the shielding effect of the foil conductors and hence affecting the winding frequency response at high frequencies. This paper proposes a high-frequency lumped equivalent circuit model for DDR with frequency-dependent parameters. The frequency-dependent inductances and resistances are calculated using anisotropic equivalent complex permeability to represent the damping effects in the core and winding. A combined analytical-finite element modelling approach is employed to calculate the winding capacitances. The accuracy of the proposed model is verified by comparing its frequency response with the experimental results obtained from a laboratory prototype. Furthermore, the impulse voltage distribution within the windings is obtained through simulation and measurement analyses to attest the robustness of the proposed model. The proposed model is expected to aid in the proper design and optimization of DDR to improve its insulation withstand capability and enhance its performance during transient events within power grids.

A Stabilized Circuit-Consistent Foil Conductor Model

A Stabilized Circuit-Consistent Foil Conductor Model

A Comparative Study of Finite Element Method and Hybrid Finite Element Method–Spectral Element Method Approaches Applied to Medium-Frequency Transformers with Foil Windings

This study aims to improve the computational efficiency of the frequency domain analysis of medium-frequency transformers (MFTs) with the presence of large clearance distances and fine foil windings. The winding loss and magnetic energy in MFTs in the medium-frequency range are calculated utilizing a finite element method (FEM) using common triangular and alternative rectilinear mesh elements. Additionally, in order to improve the computational efficiency of the calculations, a spectral element method (SEM) is coupled with a FEM, thus creating a hybrid FEM–SEM formulation. In such a hybrid approach, the FEM is used to calculate the current density distribution in the two-dimensional (2D) cross-section of the foil conductors to achieve reliable accuracy, and the SEM is adopted in the nonconducting clearance distances of the winding window to reduce the system of equations. The comparative analysis of the calculated resistance and reactance of the under-study models showed that the FEM with rectilinear mesh elements and the FEM–SEM model outperformed the FEM with triangular mesh elements in terms of accuracy and computational cost. The hybrid FEM–SEM model enables a reduced system of equations for modeling the electromagnetic behavior of MFTs. This research provides valuable insights into both the computational approaches and meshing challenges in the analysis of MFTs and offers a foundation for future research on the design and optimization of MFTs.

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.

Investigations of Microstructure and Mechanical Properties of Lap Jointed Dissimilar Metals by Friction Stir Spot Welding Process

The joining of different materials is required for industrial application to utilize the hydride structures with attractive advantages such as superior strength to weight ratio, low cost, high tensile strength and less weight of the component. Specifically, Al-Cu composite material is widely used in foil conductors of a transformer, electrical connectors, foil windings in capacitors and tubes in heat exchangers. However, joining or spot welding the Al parts to Cu parts are significant challenge owing to variation in mechanical properties and chemical compositions of joining materials. In this present research work, the friction stir spot welded process (FSSWP) is carried out to join the Al and Cu materials. Further, microstructure and mechanical properties of friction stir spot welded specimens (FSSW) are studied at different tool rotational speeds likely from 1000rpm to 1500rpm. The microstructural study is carried out using scanning electron microscope images at the interface and overall welded region. The tensile strength of both single and double spot-welded specimens is analyzed using a universal tensile test machine. The output of this study states that the optimal tool rotational speed is 1500rpm for both single and double spot-welded specimens. Moreover, the double spot-welded specimen exhibits more tensile with a crack-free spot-welded surface than that of the single spot-welded specimen. The tensile strength double spot-welded specimen has a 6.8% higher strength than that of a single spot-welded specimen. Based on the present study, it is concluded that the double spot-welded specimen can be used for different industrial applications to replace Cu material with this Al-Cu material that gives added advantages to those components.

Hybrid Foil-Litz Windings for Highly Efficient and Compact Medium-Frequency Transformers

Medium-frequency transformers (MFTs) are key components in solid-state transformers (SSTs), where they provide galvanic isolation and a certain voltage transfer ratio between a medium-voltage (MV) grid and a low-voltage (LV) bus. Typically, MFTs are operated in the kilohertz range, which results in a significantly reduced volume and material usage compared to 50/60 Hz transformers. Foil conductor is an attractive solution for improving the filling factor and the cost-effectiveness of MFTs, however, the insulation clearances increase the ohmic losses due to the current crowding effect; besides, the electric field hotspots at the winding corners require shielding by equipotential rings. In this work, a new hybrid topology is presented, where the first and last turn of the foil winding package is replaced by turns of litz wire connected in series, one above and one below the foil winding, respectively, such that they act as equipotential shielding rings; besides, the current in the litz turns deflects the magnetic field lines away from the foil edges, decreasing the losses due to current crowding. The effect of the litz rings on the losses is modeled and measured on a hybrid and a standard foil winding prototype; a loss decrease higher than 15% is observed. The verified model is used to compare the conductor and footprint saving between windings designed with litz rings, and with standard equipotential shielding rings; in this respect, a minor amount of litz wire allows reducing losses up to 30%, whereas the conductor utilization and winding height can be decreased more than 20%, improving the power density of the MFT.

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.

Frequency-Dependent Inductance and Winding Loss Model for Gapped Foil Inductors

For comprehensively optimizing high-frequency foil inductors, calculating the increased inductance and the additional eddy current losses due to a two-dimensional magnetic fringing field caused by air gaps in the center leg is mandatory. This article proposes an analytical model that accurately calculates the inductance and the additional eddy current losses in gapped inductors with foil windings. The analytical field expressions are combined into closed-form winding loss and inductance formulas and verified by measurements. Furthermore, the frequency dependency of the inductance due to the shielding effect of the foil conductors is being discussed.

A Fourier-Based Semi-Analytical Model for Foil-Wound Solid-State Transformers

A mesh-free semi-analytical Fourier-based method is presented to evaluate the frequency-dependent losses in the windings of solid-state transformers (SSTs) with foil-wound transformers. In the employed diffusion equation, which accounts for induced eddy currents, the imposed current density and conductivity in the transformer window area are represented using spatial Fourier series and method of images. As a result, induced current density distribution in foil conductors and ac loss in medium frequency transformers (MFTs) is calculated using the semi-analytical method. The proposed method is verified using the finite element method (FEM). It is observed that with the considered approach one can estimate the ac winding loss in the frequency range of 5–25 kHz, with 2.7% maximum absolute error and approximately 2.5 times less number of degrees-of-freedom compared to FEM computations.

Water lily (Eichhornia crassipes) generation of electricity through photosynthesis

Generate electricity through the photosynthesis of the water lily; releasing electrons at their roots, to be collected by the anode (copper wire) and cathode (metallic foil) conductors, to transport them through copper conductors and be able to use them, in light energy, in a 3-volt led. Plastic containers on average have a higher voltage, compared to metal containers, on average they reached 0.747 volts, R6 was the one with the highest voltage production and the lowest 0.518 volts on average was R4. The voltage produced by metal containers, which did not reach the maximum values of plastic containers, the highest average is R7, with a voltage of 0.576 volts and the lowest of all averages is 0.216 volts R10, On 09/17/2019 at 4:45 PM, the highest average voltage of 7.11 volts was recorded.

The Faraday Shields Loss of Transformers

Faraday shields are widely used in high-frequency transformers to conduct the common-mode (CM) current to the ground. They are normally located in the high magnetomotive force (MMF) region, where severe eddy currents are induced and contribute considerable magnetic field losses. In this article, an analytical procedure is presented for the magnetically-induced loss in Faraday shields. It is originally derived from shields of foil conductors. Then, it is extended to different shields with round and Litz wire, and different configurations, e.g., multilayer shields, interleaved windings, and coaxial transformers. It is verified by the finite element method (FEM) and experimental results in six case studies. Moreover, the criteria to determine the losses of Faraday shields is given and a design procedure is presented to reduce the shield losses at a certain level while keeping the functionality. Finally, a case study is provided to verify the shield design procedure on a 100-kHz transformer.

Critical stress of oval foil winding with epoxy coated insulation determined using measured equivalent modulus of elasticity

In the distribution transformers design oval windings are used due to economic advantages. On the other hand, such windings are more susceptible to radial forces in a short circuit. A diamond dotted paper with an epoxy coating is used in order to increase the stiffness of the winding. Despite that, winding failure may occur during the short circuit, e.g. buckling of inner winding. Because of a very thin foil conductor (typically 0.5–2 mm), the most critical is inner low voltage foil winding which can collapse due to radial forces at stresses far below the elastic limit of conductor material. This paper shows an analytical approach to the calculation of critical stress in inner oval foil winding with epoxy coated insulation. Critical stress was calculated using the equation for free buckling of round winding. Equivalent Young's modulus of elasticity was obtained experimentally from the testing of the sample model loaded with bending force on a tensile test machine. A total of 12 test samples were formed from aluminium foil conductor and diamond dotted paper and cured at the temperature of 105°C. The results were successfully verified on distribution transformers subjected to short circuit withstand tests.

Investigation of Compact Dielectric Monopole Antenna Integrated with 3D Printed Horn for UWB Applications

Abstract A novel broadband portable Dielectric Resonator Antenna (DRA) with integrated unshorted horn and broadside radiation pattern is implemented for ultra-wideband (UWB) and Electromagnetic sensor applications. A rectangular DRA composed of TMM 10i (Dielectric constant 9.8 and loss tangent 0.002) material is mounted over four supporting pillars to separate the DRA from the ground plane. A conical shaped horn with the copper foil conductor is used as a reflector to increase the gain and realize stable radiation pattern over the wide frequency range. The horn and supporting pillars are fabricated by a 3-D printer using light weight thermoplastic composite polymer Poly-Lactic Acid (PLA). The proposed antenna contributes measured VSWR (2:1) impedance bandwidth of 106 % ranging from 6.8 GHz to 22.2 GHz for a Quasi-TM111 mode with a low cross-pol level which ensures its linear polarization. The measured peak gain of the DRA is 7.8 dBi at 14 GHz, while estimated average efficiency is more than 88 %. The measured average group delay of the proposed antenna is ~ 1.5 ns within operation band. The proposed antenna is suitable for UWB operation and other broadband applications having omnidirectional coverage and stable radiation pattern ranging from C-band to K-band.

Accurate Calculation of Eddy Current Loss in Litz-Wired High-Frequency Transformer Windings

The winding power loss of a high frequency transformer is strongly influenced by the high frequency eddy current skin and proximity effects. The litz-wire can reduce effectively the eddy current effects. The precise loss calculation method of litz-wire remains however a difficulty. At present, the Dowell model [1] and Ferreira model [2], [3] are two commonly used methods to calculate the winding loss. The Dowell model is originally derived to calculate the eddy current effects in foil conductors and later on extended to packed windings composed of litz-wire by introducing a porosity factor [4]. The accuracy however declines quickly when porosity factor reduces, and the characteristics of eddy current distribution is not adapted to the litz-wire. On the other hand, the magnetic field of round conductors analyzed by Ferreira model is excellent, but the error become significate at high frequency at high porosity factor [5] because it neglects the interaction between conductors in the same layer [6]. In this paper, an improved model is proposed for calculating the eddy current distribution in litz-wire windings due to the skin and proximity effects. This model can have much more accurate prediction of eddy current distributions in the cross-section of a round litz-wire conductor, and can be used for electromagnetic design of high frequency devices.

Thermal Performance Modeling of Foil Conductor Concentrated Windings in Electric Machines

While the use of foil windings in transformers and air core inductors is not uncommon, their use in electric machines is just emerging. Although prototype realizations have been reported in the literature, a definitive analysis of their thermal performance is necessary to evaluate their potential for broad applications. This paper is devoted to presenting a comprehensive model for evaluating their thermal performance including loss modeling and temperature rise prediction in realistic designs. An overview of foil windings in electric machines and their advantages in improved fill factor is presented, along with experimental results that compare the ac losses and temperature distribution under identical steady-state operating conditions with a prototype round conductor coil and foil conductor coil. A lumped parameter thermal model that predicts the heat transfer behavior of the foil conductor coil is presented along with supporting experimental results.

Electric Field Simulations and Analysis for High Voltage High Power Medium Frequency Transformer

The electronic power transformer (EPT) raises concerns for its notable size and volume reduction compared with traditional line frequency transformers. Medium frequency transformers (MFTs) are important components in high voltage and high power energy conversion systems such as EPTs. High voltage and high power make the reliable insulation design of MFT more difficult. In this paper, the influence of wire type and interleaved winding structure on the electric field distribution of MFT is discussed in detail. The electric field distributions for six kinds of typical non-interleaved windings with different wire types are researched using a 2-D finite element method (FEM). The electric field distributions for one non-interleaved winding and two interleaved windings are also studied using 2-D FEM. Furthermore, the maximum electric field intensities are obtained and compared. The results show that, in this case study, compared with foil conductor, smaller maximum electric field intensity can be achieved using litz wire in secondary winding. Besides, interleaving can increase the maximum electric field intensity when insulation distance is constant. The proposed method of studying the electric field distribution and analysis results are expected to make a contribution to the improvement of electric field distribution in transformers.

Short-circuit stress calculation in oval windings

In this paper an analytical approach for calculation of mechanical strength of oval windings in distribution transformers is presented. The calculation is given for radial forces resulting from interaction of the axial component of leakage flux density and the current in the windings. The analysis is focused on the inner foil winding subjected to radial forces acting inwards where winding could fail either by collapsing or by bending between the supports. The most common failure mode is free buckling where foil conductors (usually outer half of low voltage winding) bulge outwards as well as inwards usually at one specific point along the circumference.

High-Frequency Power Transformers With Foil Windings: Maximum Interleaving and Optimal Design

Foil conductors and primary and secondary interleaving are normally used to minimize winding losses in high-frequency (HF) transformers used for high-current power applications. However, winding interleaving complicates the transformer assembly, since taps are required to connect the winding sections, and also complicates the transformer design, since it introduces a new tradeoff between minimizing losses and reducing the construction difficulty. This paper presents a novel interleaving technique, named maximum interleaving , that makes it possible to minimize the winding losses as well as the construction difficulty. An analytical design methodology is also proposed in order to obtain free-cooled transformers with a high efficiency, low volume, and, therefore, a high power density. For the purpose of evaluating the advantages of the proposed maximum interleaving technique, the methodology is applied to design a transformer positioned in the 5 kW–50 kHz intermediate HF resonant stage of a commercial PV inverter. The proposed design achieves a transformer power density of 28 W/cm3 with an efficiency of 99.8%. Finally, a prototype of the maximum-interleaved transformer is assembled and validated satisfactorily through experimental tests.

Magnetohydrodynamic simulation of current switching by explosive opening switches of different types

The MEG-2D two-dimensional Eulerian design procedure was used for magnetohydrodynamic simulation of the megaampere current switching process by an explosive opening switch. This paper presents simulation results for the current switching of a helical magnetocumulative generator (MCG) by explosive opening switches of different types at the same parameters of the switching scheme, thickness of the breaking conductor made of copper foil, the breaking current, and the number of opening switch elements. Simulation results for current switching by an explosive opening switch with a ribbed barrier for different thickness of the broken copper foil conductor are also presented. In the case of using a foil 0.3 mm thick, a ribbed barrier with steel inserts on the ribs with optimal parameters was investigated. It is shown that at a foil thickness less than 0.2 mm, decreasing the depth of the groove in the barrier does not lead to an increases in the time of triggering of the opening switch.

An Accurate Pseudoempirical Model of Winding Loss Calculation in HF Foil and Round Conductors in Switchmode Magnetics

When operating higher up in frequency, the copper losses in transformer windings will significantly rise due to enhanced skin and proximity effect. This leads to a high need to develop new methods to accurately evaluate winding losses at higher frequencies. This paper investigates the effect of different geometrical parameters at a wide range of frequencies in order to propose a pseudoempirical formula for winding loss calculation in high-frequency transformers. A comprehensive analysis of the edge effect and ac resistance is done by performing more than 12 300 2-D finite element simulations on foil and round conductors. Unlike previous studies which mostly focused on specific case studies with limited applications, this model provides very high accuracy, especially where the most common analytical models drastically underestimate the winding losses, with a wide-range applicability which could be of interest for designers to avoid time consuming FEM simulation without compromising with the accuracy. Several transformers are built and the model is experimentally verified with a good agreement.