Search

International audience; This paper presents a new strategy for building an equivalent RLMC circuit for electromagnetic interconnections modellingin t he context of the Partial Element Equivalent Circuit (PEEC) method. The method consists in splitting the overall formulation (RLMC) into two independent formulations (RLM) and (C). Both formulations are used independently to calculate equivalent circuit elements. Once all the elements are calculated, they are merged into a global electrical model which is solved globally with an external circuit solver. A coupling with the similar idea was presented a few years ago and showed very good performance for the modelling of electromagnetic devices where propagative effects are negligible like in power electronics applications. However, thecoupling of the parasitic capacitances C with RLM circuit had to be carried out manually. Our new strategy allows to do it in acompletely automatic way..

The integration of renewable energy sources (RES) as an alternative source of energy is increasing continuously. This is due to various advantages of RES over traditional energy sources, as they are clean sources and never run out. One of the most important RES is solar photovoltaic (PV) systems, which have attracted more attention in recent years. Lightning overvoltages are considered the main cause of PV modules damage. Hence, designing an effective and reliable lightning protection system (LPS) is important to improve the lightning performance of PV systems and reduce hazards. This requires accurate modeling of the PV system under lightning conditions. Some previous researches used high accuracy modeling methods such as the finite definite time-domain (FDTD) or the method of moments (MOM). However, these techniques require a high computation burden and have some complexity. Although the partial element equivalent circuit method (PEEC) gives a high accuracy model with less complexity, very few researchers focused on using it for PV systems modeling. This paper introduces a high accuracy model of the PV system during the lightning occurrence using the PEEC method, considering the coupling effects and the influence of metal frame, which were not considered in previous researches. The transient overvoltages at different points are calculated taking into account changing the lightning striking point, the existence of PV frame, and changing soil resistivity. From the simulation results, the transient overvoltages are increasing with increasing the soil resistivity value. In addition, the induced voltage has a maximum value at the striking point and decreases by moving away from it. Moreover, the existence of the metal frame causes an increase in the induced overvoltages values; hence the LPS requirements will change. The grounded legs of the mounting system are considered an important factor in determining the voltage values, where the points connected to the grounded leg will have the lowest voltages values. On the other hand, the transient overvoltages obtained with the existence of the mutual coupling are larger than those obtained when neglecting the mutual coupling. The results confirmed that it is better to consider the mutual coupling to achieve an effective LPS.

This work proposes a new approach using the T-A formulation coupled to lumped parameters in the electrical circuit, considering the skin-depth approach. The Finite Element Method (FEM) models the superconducting layer, the electrical circuit models the stabilizer and substrate layers as lumped parameters, and a coupling engine links both of them. The AC losses have been calculated by both T-A 1D and T-A 2D formulations: the first one uses the approach proposed in this paper and the second, two current vector potential components. For the three formulations, we have studied the average power dissipation as a function of frequency and current, and the peak current as a function of the frequency. We have compared the T-A 1D and T-A 2D formulations to H formulation results previously studied. Comparing the results of the average power dissipation, we have found the maximum error to be around 10.5% in T-A 1D and 35% found in T-A 2D. The eiciency of the proposed technique was evaluated as 16 times less costly, when compared to the T-A 2D formulation.

Litz wire (LW) is a common tool used in high-frequency power electronic applications to reduce eddy loss. Uninsulated twisted wire (UTW) with lower manufacturing costs is often ignored by both researchers and designers. LW and UTW have similar geometry structures, however, there has been little research on the performance evaluation of UTW so far. This article proposes a novel calculation method of UTW based on the multilevel partial element equivalent circuit method and the results are verified by the experimental measurement. Then, the performance of LW and UTW is compared and discussed under various conditions. The simulation results show that LW and UTW have almost identical performance and may replace each other for single-level wires. For two-level wires, these two types of wires may be interchangeable when the ratio of bundle radius to skin depth is less than a specific value, otherwise, LW always has a better performance.

In this paper, we proposed a variable protective resistor that realizes controllable energy dissipation and temperature inhibition for the no-insulation (NI) HTS coil-systems, during sudden discharging. The resistor is paralleled with the meter-class bore NI coil, which aims to be used in a high-field magnetic resonance imaging scanner (MRI), to avoid burn-out and shorten restart time of the coil when it has to be shut-down during an accident. To establish the relationship between the value of protective resistor, the energy dissipation and the temperature increase during sudden discharging for the NI coil, in this study, a numerical analysis coupled with a partial element equivalent circuit and a thermal analysis was conducted. Based on the results, the mechanism that how a protective resistor shares energy dissipation and inhibits temperature increase, has been clarified. Meanwhile, the effects of the value of protective resistor on the discharging behavior and temperature increase of NI pancake coil during sudden discharging, were also evaluated to verify the feasibility of this protection method in the application of MRI.

This paper proposes a new equivalent circuit model to calculate current distribution in an NI (no-insulation) high temperature superconductor (HTS) coil that contains a defect. When the well-known defect irrelevant behaviors of an NI HTS coil are analyzed, the so-called partial element equivalent circuit (PEEC) technique has been commonly adopted. However, the PEEC technique often takes an extremely long time, days or even weeks, for just a single simulation depending on the number of internal elements within the target NI coil. Here we propose an alternative method that may substantially reduce computation time and load in distributed simulation of the defect-irrelevant behaviors of an NI HTS coil. We showed that the current sharing region of an NI coil containing a defect could be divided into 5 segments, and an equivalent circuit, which is named “B model” as the equivalent circuit resembles the alphabet “B,” could be constructed using circuit parameters in each segment. Using the proposed method that significantly simplifies the existing PEEC model, we successfully simulated the defect-irrelevant behaviors of an NI HTS single pancake coil, essentially the local current sharing between the defect spot and its healthy neighboring turns.

In the conventional partial element equivalent circuit (PEEC) method, all partial inductances are connected at both ends to other circuit elements of a PEEC or modified nodal approach (MNA), simulation program with integrated circuit emphasis (SPICE) type circuit. This article shows that if at least one end of a partial inductance remains without a connected element, it is called an open loop, which is also physical and is theoretically closed by displacement current. It is shown in this article that the open loop is only consistent if the partial inductance is evaluated using the Coulomb gauge; else, the magnetic energy computation of open loop is inconsistent. This article focuses on the difference and presents an analytical method for the calculation of partial inductance with Coulomb gauge in quasi-static field to figure it out. This difference is proven to be related to the calculation of vector potential A , whereas existing calculation is based on Lorentz gauge. Then, analytical results of conductor segments are derived for comparison of the two different gauges, and show the difference. Also, numerical experiments of the self- and mutual-partial inductances of conductor segments in open-loop problems are given for further comparison. The results illustrate that the proposed method is consistent with magnetic energy, and could be directly be applied to closed-loop problems without affecting the validity of the PEEC method. This method is believed to be an effective supplement in physical sense of partial inductance.

Superconducting magnetic energy storage (SMES) can provide high efficiency, longevity, and instantaneous response with high power. However, its energy storage density is extremely low. To address this drawback, the use of a no-insulation (NI) REBCO coil has been considered. NI coils are expected to achieve high current density as well as high thermal stability, and the energy storage density can be improved by applying these coils to SMES. However, Joule loss occurs owing to the current flow in the radial direction through the contact electrical resistance between turns during charging and discharging. Because the amount of loss depends on the contact electrical resistance, it is necessary to adjust the resistance to an appropriate value to make the storage efficiency a practical value. In this study, we conduct experiments to investigate the behavior of small-scale NI-REBCO coils with different contact electrical resistances considering the charge/discharge current pattern for actual SMES operation. In addition, numerical simulations are performed using the partial element equivalent circuit (PEEC) model under the same conditions as those used in the experiment, and the reproducibility of the experimental results is confirmed. Finally, using the PEEC model, numerical simulations are performed assuming an m-class coil. The relationship between the storage efficiency and the contact electrical resistance, which is an important indicator for applying NI coil technology to SMES, is clarified by the results.

In general, when evaluating a performance of a high-temperature superconductor (HTS) no-insulation (NI) magnet, current, voltage, and center magnetic field are considered as main parameters. To achieve detailed results of the main parameters of NI HTS magnet, distributed circuits which can analyze internal physical phenomena of the magnet are required. Among distributed circuits, a circuit that divides inside of each turn into several cells in azimuthal direction is called a Partial Element Equivalent Circuit (PEEC). In this paper, we compared the main parameters of simple NI HTS magnet according to different numbers of cells in PEEC. When the number of cells per turn is different, average azimuthal current and center magnetic field of each turn coincide with each other, but voltage does not. The result suggests that PEECs with different number of cells per turn may be different circuits for each others, and the main reason for this seems to be that an accurate discussion of the characteristic resistance according to the length was not made.

Full-wave time-domain computational electromagnetic (CEM) solvers, which are integral equation (IE)-based, may suffer from what is called 'late-time instability' problems. This unstable behavior occurs for CEM solvers for very fast rise-time input signals. A multitude of techniques has been devised by researchers over the years to solve the problem. In this article, we pursue an approach for the stable solution of full-wave partial element equivalent circuit (PEEC) models for fast-rising input waveforms. In particular, step and impulse response will be considered that are the most challenging from a stability point of view. For the solver part, a conventional full-wave PEEC code is used that requires one to use retarded partial elements. Unfortunately, a PEEC, as well as impedance Z-(method of moment) solvers using suitable numerical time-stepping methods have stability problems, especially for fast rising impulse or step inputs. An important step forward is achieved in this work by providing a larger class of stable solutions well above the stability achieved for time-stepping methods in the last 50 years. The time-domain stability is achieved by replacing the stepping integration methods with a numerical inversion of Laplace transform (NILT) technique. The NILT transform starts out by applying it to a frequency-domain PEEC solution. The surprising result is that the NILT-based method has a variable time-dependent bandwidth that is advantageous for the full-wave IE solution stability. In this article, we give several examples that show that a PEEC-NILT solution provides accurate and stable results for impulse, step- and piece-wise linear input waveforms.

This paper further studies the stability of the uncertain delayed neutral-type system by constructing a novel Lyapunov-Krasovskii functional (LKF) with some delay-dependent and N-dependent items. Some new delay-dependent robust stability criteria are proposed based on linear matrix inequality (LMI). The criteria proposed in this paper are less conservative than some recent previous ones. Some numerical examples, including a linear neutral-type system, the partial element equivalent circuit and a general linear system, are presented to show the effectiveness of the proposed approach.

Time-domain simulation of full-wave partial element equivalent circuit (PEEC) often encounters stability problems. In the past, various approaches have been proposed to determine the stability of a given model. Most of these methods, however, have low efficiency and scalability. In this article, we propose a highly efficient method to obtain a particular group of the poles of the model; such information then serves as a necessary-condition test for stability. Furthermore, the method is extended to include the effects of damping resistors. From the root locus plots of the poles, we clearly see the unstable poles moving left as damping is added in, and by the time they move into the left-half-plane, we can quantitatively determine the minimum damping level required to achieve a stable model. Simulation results are provided to verify the proposed method.

The inductance associated with a decoupling capacitor is typically represented with a constant equivalent series inductance (ESL). In reality, this inductance depends on how the capacitor is mounted and on coupling to closely located structures, including the traces and vias connecting the capacitor to the power and return planes. Here, a method is proposed to quickly and accurately compute the inductance associated with decoupling capacitors and their connections to the power planes. We call this equivalent inductance ${\boldsymbol{L}_{\boldsymbol{above,decap}}}$ . It is calculated by partitioning the geometry into sub-models for the connections to the power and return planes and for the mounted capacitor and pads. The accuracy of the partitioning approach is demonstrated in simulation and experiments using two common decoupling capacitor layouts. Simulations are performed using the finite element method (FEM) and the partial element equivalent circuit (PEEC) method. The partitioning approach estimates the overall inductance associated with the decoupling capacitor and its connections to the power bus within 16% if the distance between the capacitor and reference plane (dielectric thickness) is not more than 6 mils. A simplified PEEC model was further developed which allows a user to estimate the inductance associated with the capacitor using closed-form expressions. This simplified model estimates the capacitor's inductance within 14% of the results found using FEM. The models presented in this work should help both the power distribution network tool designer as well as the design engineer to obtain more accurate inductance estimates than is possible using the manufacturer's ESL value.

In order to calculate the impedance of metal return network connected with composite skin, the volume based partial element equivalent circuit method is used to model the return network, and the impedance between the nodes of the return network at different frequencies is calculated. The influence of the contact resistance between the elements of the current return networks on the impedance is also considered. Moreover, the influence of some component parameters on impedance is analysed. The calculation results verify the applicability of the algorithm and the correctness of the calculation results and provide some references for the composite aircraft current return networks in the fault management and electrical protection system design.

Litz wire has been an essential component for the power electronic design to reduce the eddy loss. However, there is a lack of efficient numerical algorithms to simulate Litz wires due to their complex structures. This letter proposes a multilevel partial element equivalent circuit method that significantly improves the efficiency of the simulation of the Litz wire. This method boosts the simulation efficiency at both packing level and twisting level. In the packing level, a novel meshing method is proposed to capture the skin and the proximity effect accurately and efficiently. In the twisting level, the calculation is further divided into wire level and multipole level, where filament approximation and fast multipole method are unitized, respectively. Taking advantage of symmetry and memory replication, the proposed method is significantly faster and more economical than reported electromagnetic algorithms. The efficiency and accuracy of the proposed method are validated through comparison with popular toolkits and the measurement of two Litz wires with dozens and hundreds of wire strands, respectively.

We present an enhanced partial element equivalent circuit (PEEC) model based on Voronoi decomposition of triangular meshes. A complex geometry is accurately represented by many surface triangles, while keeping the number of elements in the corresponding equivalent circuit far less than the number of triangles. To do this, the triangular geometry is automatically decomposed into surface partitions using Voronoi's algorithm. These partitions describe capacitance cells, while inductance elements are set between all neighboring partition pairs. The inductance ( L ) and capacitance ( C ) matrix calculations are done independently using solvers based on quasi-static electric and magnetic full-wave method of moments (MoM). To get the current and charge distribution over the triangles, the MoM results during LC evaluation are combined with the results of modified nodal analysis. We validated our method against the standard PEEC and MoM results as well as measured data. Then, we used our method to simulate conducted emission for a real automotive LED brake-light module.

This article addresses a full-wave partial element equivalent circuit (PEEC) model of wire structures above a lossy ground (LSG) for lightning transient analysis. The PEEC model is formulated with dyadic Green's functions. An equivalent circuit is derived for the first time by including correction terms arising from the LSG. Circuit parameters are expressed using Sommerfeld integrals, which can be evaluated numerically and be presented with lookup tables. The low-frequency model of the LSG is derived, and is depicted using the mirror image of source elements, similar to the case of a perfect ground. The comparison of circuit parameters calculated with this model and the Sommerfeld integrals is made. The proposed method is validated numerically with the numerical computation code in the frequency domain, and the finite-difference time-domain (FDTD) method in the time domain. Good agreements are observed. The proposed method is then applied to analyze lightning transients in a wire structure over the LSG. It is concluded that the LSG can be substituted with the low-frequency model for transient analysis. The computational burden in the time-domain simulation can be significantly relieved.

For the modeling of wire structures in rectangular metallic enclosures, a Foster-type partial-element equivalent circuit model is presented. The model is based on the electric field integral equation of the wire structures. The integral equation is converted to a circuit network adopting the method of moment and the Kirchhoff's voltage law. The dyadic Green's functions for a three-dimensional (3-D) rectangular cavity are used. The circuit elements and the controlled sources are realized by the Foster-type circuit model. Application examples validate the accuracy and efficiency of the presented model.

This paper presents the time-domain partial element equivalent circuit (PEEC) analysis of induced transients in a wire structure during an indirect lightning strike. The full-wave PEEC formulation with an external incident field is employed. The incident field is calculated with either the Uman's or the Jefimenko's formula by using the engineering model of a lightning channel. An instability problem is, however, observed. It becomes a hurdle in the application of PEEC for evaluating induced transient currents in closed wire loops. The problem is investigated, and is primarily caused by discretization of the electric field in numerical evaluation of external voltage sources. An algorithm is provided to solve this instability problem, and is tested for both near- and far-field cases. It is validated by the finite-difference time-domain method. The issue of time step and segment length is addressed. It is also found that the Uman's formula is generally incapable of producing stable induced currents in a wire loop structure. Finally, the proposed PEEC procedure is applied to evaluate induced lightning transients in a photovoltaic panel during an indirect lightning strike.

Photovoltaic (PV) systems are susceptible to lightning strikes. During a lightning strike, an induced overvoltage is generated in the PV system. This overvoltage can damage the inverters connected to the dc cables. In this article, a comprehensive study is presented to address the installation issues that will influence the induced voltage between the +dc and –dc cables in the PV system. By using the partial element equivalent circuit method, the skin effect and ferromagnetic property of the mounting structures are well modeled. The wiring in the PV module is also considered in the simulation. The influences of the mounting systems, lightning protection systems, PV frames, and dc cable arrangements are thoroughly investigated. The simulation results and discussions provide guidance for PV structure design for maximizing lightning protection performance without adding additional protective devices.

A physics-based circuit modeling methodology for system-level power integrity (PI) analysis and design is presented herein. The modeling methodology is based on representing the current paths in the power distribution network (PDN) with appropriate circuits based on cavity model and plane-pair partial element equivalent circuit (PEEC). The PDN input impedance looking from on-chip sources can be computed. A commercial simulation tool is used to corroborate the modeling approach where the system consists of a commercial integrated circuits, a complex organic package and a very high-layer-count printed circuit board. Two types of circuit models are proposed from the methodology with physical correspondence maintained in the circuit elements. The circuits can be used to analyze the geometry impact on the PDN impedance and explore design improvements. Voltage ripple simulations are conducted with the circuit models. The simulated results correlated with measurements. The modeling methodology helps to understand the impact of the fundamental physics of the different parts of the PDN system and the impact of changes in the PI designs.

This article presents new analytical formulas for the efficient computation of the full-wave electric field generated by conductive, dielectric, and magnetic media in the framework of the partial element equivalent circuit (PEEC) method. To this aim, the full-wave Green's function is handled by the Taylor series expansion leading to three types of integrals for which new analytical formulas are provided in order to avoid slower numerical integration. An orthogonal (Manhattan type) tessellation of the geometries is assumed, and the electrical quantities, i.e., currents, charges, and magnetization, are expanded in space through rectangular basis functions. The full-wave electric field radiated by charges, currents, and magnetization is computed analytically in the postprocessing step. The proposed closed-form computation of the electric field is tested using two examples, comparing the results obtained by the derived analytical formulas with the results from a finite element method solver. © 1963-2012 IEEE, IEEE Transactions on Microwave Theory and Techniques, 68 (8), ISSN:0018-9480, ISSN:1557-9670

The no-insulation (NI) coil is a technology expected to realize both high current density and high thermal stability which are essentially trade-off relationship in REBCO coil application. This technique has been studied mainly for application to small-diameter inner coils of NMR magnets exceeding 30 T. In this case, the coil is cooled using 4.2-K liquid He. We are developing an NI-REBCO coil system for high-magnetic-field whole-body MRI, and for a medical cyclotron to be used for cancer therapy. The NI-REBCO coil which we aim for development has a diameter of ∼1 m, a generated magnetic field is ∼10 T, and a conduction cooling around 30 K is assumed. Because the size, operating temperature, and magnetic field differ from those of NMR coil, it is possible that the electromagnetic, thermal, and mechanical behaviors will be quite different. In this paper, we report on these behaviors when a local deterioration occurs in NI-REBCO double-pancake coils using numerical analysis considering coil size, operating temperature, and magnetic field as parameters. For the numerical simulation, we conducted a coupled analysis of current distribution analysis based on PEEC (Partial Element Equivalent Circuit) model and thermal analysis by the 2-dimensional finite element method.

During plasma disruption in tokamaks, a large amount of energy will be dissipated in the vacuum vessel (VV) and cause damage to the plasma-facing components. Reducing the energy dissipated in the VV is a direct and valid method to mitigate the damage. This idea has been previously studied on J-TEXT based on a newly developed magnetic energy transfer (MET) system, and its validity has been proved. However, unlike the large air-core tokamaks, J-TEXT is a middle-size tokamak with an iron core and a toroidally isolated VV, which results in a high electromagnetic coupling between the plasma and the energy transfer coils (ETCs). So, it is necessary to study the feasibility of the MET method in air-core tokamaks. Taking EAST as an example, a finite element model is established in this article to analyze the electromagnetic coupling between the plasma, VV, poloidal field (PF) coils, and ETCs. The induced current in the VV and ETCs during plasma disruption is calculated. These analysis results are verified by comparison with the ones from the partial element equivalent circuit (PEEC) method. Then, the evolution of magnetic energy during plasma disruption is analyzed, which shows that 76.9% of magnetic energy will be consumed in the VV. At last, the possible maximum energy transfer efficiency of the energy transfer system is analyzed by changing the number, position, and load parameters of ETCs. The energy transfer efficiency will be within 10% and the reduction of induced current in the VV will be within 20%. To some degree, the analysis in this article proves the feasibility of the MET system in air-core tokamaks, but there will be some engineering difficulties to overcome.

The self-curing decoupling technique is substantially extended to apply to multi-input multi-output (MIMO) antenna arrays in mobile terminals. Using this proposed technique, the mutual coupling between antennas can be reduced by inlaying lumped element capacitors on the ground plane. The decoupling method does not require any physical connection or obstruction between coupled antennas. The significance of the proposed decoupling technique is fourfold: 1) it works for inverted-F antennas (IFAs), monopole antennas, and loop antennas, the most three commonly used antenna forms for mobile terminals; 2) the inherent improvement on matching conditions after decoupling; 3) the flexibility in implementation owing to its detachment from the antenna body; and 4) the applicability to an array with more than two elements. Four demonstrating examples, including two IFAs, two monopole antennas, two loop antennas, and a MIMO array with four elements of different antenna types are studied by EM modeling, passive tests, and MIMO over-the-air (OTA) measurements. The experimental results show that significant improvements in port isolation (from 9 to 30 dB), total efficiency (from 53% to 69%), and above all, the system data throughput can be achieved. The working mechanism of the method is revealed and justified through the partial element equivalent circuit (PEEC) model in the fifth example.

The series inductance associated with decoupling capacitors can contribute significantly to the impedance of the power distribution network. The eight-terminal capacitors considered in this article have a lower self-inductance than two-terminal capacitors and are commonly used in IC packages. Manufacturers typically specify the inductance of the capacitor using some type of equivalent series inductance (ESL), but this ESL may not accurately predict the inductance seen during use because it does not account for the coupling between the capacitor and nearby structures like the return plane. To adequately determine the inductance associated with an eight-terminal capacitor, models of typical eight-terminal capacitors were developed in Dassault Systemes CST Studio Suite. The partial element equivalent circuit (PEEC) method was used to construct simple models that can be simulated in SPICE. PEEC provides analytic insight into the source of inductance. Modeling the electrode stack as a solid block rather than a multilayer structure was shown to only change the computed inductance by 3% (~1 pH) and to substantially reduce the compute time. CST and PEEC models agreed within 9% (~3 pH), demonstrating the adequacy of the simpler PEEC models. Studies of the impact of the design parameters demonstrate that the distance between the capacitor and the reference plane has the greatest influence on inductance and that the placement of vias within the pads is important.

Efficient computation of partial elements plays a key role in the Partial Element Equivalent Circuit (PEEC) method. A novel analytical method for computing retarded partial coefficients based on the Cagniard-DeHoop (CdH) technique is proposed. The methodology is first theoretically developed and then illustrated on the computation of a surface retarded partial coefficient pertaining to two coplanar rectangular surface elements. An efficient way for incorporating loss mechanisms in the time domain (TD) via the Schouten-Van der Pol theorem is proposed. Illustrative numerical examples demonstrating the validity of the introduced solution are given.

This article analyzes the lightning transients in a commercial building with a grid like structure. The simulation is performed by using the partial element equivalent circuit method. Both the skin effect of the conductors and the nonlinear protection devices are taken into consideration. The induced voltage and the current sharing in the wiring system of both rising main circuit and secondary circuit are discussed. The influence of soil resistivity, lightning current waveform, different surge protection devices (SPDs) installations, and equipotential bonding are analyzed in this article. According to the simulation results, the soil resistivity can largely influence the potential of the conductor; however, it has a limited influence on the voltage between electric wires (potential difference). The SPDs installation arrangement and the equipotential bonding position in the building can greatly influence the lightning transients. The overvoltage and current can largely reduce if they are installed at a proper position. The suggestions provided in this article are constructive while designing the lightning protection system in buildings.

The partial element equivalent circuit (PEEC) method is applied to a frequency-sweep study for investigating the resonant modes of planar spiral resonators. A low-rank approximation algorithm, based on hierarchical matrices, is coupled to the method in order to reduce the computational effort due to the use of dense matrices. The partitioning of the matrices is carefully addressed in order to allow an efficient hierarchical off-diagonal low-rank structure of the system matrix.

In this article, a passive full-wave partial element equivalent circuit (PEEC) model is formulated for modeling electromagnetic (EM) problems with finite dielectrics. The proposed PEEC model is a substantial extension of the generalized PEEC model for problems of multiple conductors in free space. The proposed generalized PEEC model reflects the physical radiation mechanism of an EM problem with finite dielectrics. The radiation effects, both from conductors and dielectrics, are incorporated in real-valued frequency-dependent inductances and resistances, while capacitances remain to be frequency invariant. Consequently, the resultant circuit model of the proposed PEEC model is numerically verified to be more passive than the existing PEEC models. The minor passivity violation can be amended without altering the circuit configuration. To model a dielectric with the irregular-shaped surface, a triangular meshing scheme with Rao–Wilton–Glisson (RWG) basis is used. The generalized PEEC model provides a passive circuit model for both the frequency- and time-domain modeling of an EM problem with finite dielectrics. The passivity and accuracy of the generalized PEEC model are validated by an low temperature co-fired ceramic (LTCC) multilayer filter module, two dielectric resonator antennas, and a patch antenna.

This contribution investigates the connection between Isogeometric Analysis (IgA) and the Partial Element Equivalent Circuit (PEEC) method for electrostatic problems. We demonstrate that using the spline-based geometry concepts from IgA allows for extracting circuit elements without a meshing step. Moreover, the proposed IgA-PEEC method converges for complex geometries up to three times faster than the conventional PEEC approach and, in turn, it requires a significantly lower number of degrees of freedom to solve a problem with comparable accuracy. The resulting method is closely related to the isogeometric boundary element method. However, it uses lowest-order basis functions to allow for straightforward physical and circuit interpretations. The findings are validated by an analytical example with complex geometry, i.e., significant curvature, and by a realistic model of a surge arrester.

International audience; A fast and general Partial Element Equivalent Circuit (PEEC) method based on the Fast-Fourier-Transform (FFT) is proposed for the first time. The numerical tool only requires common CAD data input files (e.g. .stl format), then the discretization process is performed automatically by means of a fast voxelization technique based on ray intersection, thus drastically reducing the human effort required to setup the model. The method allows for considering at the same time inductive and capacitive effects, and is focused on power electronics applications where propagation effects can be neglected, whereas all the other electromagnetic phenomena are considered. Specifically, the proposed method is particularly suited for problems where both electric and magnetic fields are equally important and therefore quasistatic approximations do not apply. An ad-hoc preconditioner which significantly speeds-up the solver is also proposed and, thanks to the FFT, both memory and computation time are significantly reduced, without the need of applying data compression. Both linear and non-linear materials are considered by the proposed FFT-PEEC method. Sample implementation of the method is made publicly available.

A new and general partial element equivalent circuit (PEEC) formulation based on electric and magnetic vector potentials and the cell method is presented. The purpose of this paper is manifold. First, a comprehensive review of well-established PEEC method is given and the state-of-the-art of the method with focus on the inclusion of magnetic media in the formulation is discussed. Then, a new and general formulation of the PEEC method based on integral equations is proposed. The formulation is valid for conductive, dielectric, and magnetic media and its advantages with respect to the state-of-the-art PEEC formulations are underlined. Unlike the existing PEEC methods, this novel formulation, thanks to the reinterpretation of PEEC in the context of integral equation methods, allows for maintaining a circuit interpretation for both electric and magnetic media. Thus, a standard Spice-like solver can in principle be adopted for the solution of electromagnetic (EM) problems also when magnetic media are involved. The imposition of the divergence condition for the current density vectors is guaranteed and also the case of inhomogeneous and anisotropic media is considered. A thorough discussion on the suitability of the method for the study of both low- and high-frequency EM problems is also presented. Finally, the case study of a near-field communication antenna is considered as an example of the applicability of the formulation to problems of industrial interest. Comparisons with commercial softwares, measurements, and the state-of-the-art PEEC method are given in order to demonstrate the accuracy and the advantages of the proposed PEEC formulation.

In large substations, many lightning rods are installed on multi-grounded frames. The lightning rods, the frame, the grounding grid and the soil form a whole body, and the lightning current will be discharged from many grounding points. In this paper, based on the partial element equivalent circuit method, a numerical model, in the time domain, is developed to simulate the lightning-caused electromagnetic transients on the frame and the grounding grid. The model is verified by field testing and by comparison with commercial software. The model has several features: (1) it has a simple time domain form, (2) it is stable due to a staggered arrangement of space and time variables and an implicit difference scheme used, and (3) the dimension of the equations is relatively small because the unknown variables are divided into several groups, which are calculated one by one. With this method, the transient characteristics of the grounding grid with lightning rods on the frame are calculated, and the factors affecting the results are analyzed. It can be seen that although the frame causes the ground potential rise in an evenly distributed manner, compared with the situation in which the lightning strikes an independent lightning rod, the ground potential decrease rate near the main grounding point is almost the same because most of the current still enters the soil from the grounding electrode closest to the lightning strike. Therefore, even if there is a frame, the nearby facilities should take the same protective measures as in the case of an independent lightning rod. The ground conductors near the grounding points of the frame should be dense enough to reduce the potential gradient. The equipment should be kept at least 10 m away from the grounding point for lightning.

Broadband electromagnetic (EM) modeling increases in importance for virtual prototyping of advanced power electronics systems (PES), enabling a more accurate prediction of fast switching converter operation and its impact on energy conversion efficiency and EM interference. With the aim to predict and reduce an adverse impact of parasitics on the dynamic performance of fast switching power semiconductor devices, the circuit-oriented EM modeling based on the extraction of equivalent lumped R-L-C-G circuits is frequently selected over the Finite Element Method (FEM)-based EM modeling, mainly due to its lower computational complexity. With requirements for more accurate virtual prototyping of fast-switching PES, the modeling accuracy of the equivalent-RLCG-circuit-based EM modeling has to be re-evaluated. In the literature, the equivalent-RLCG-circuit-based EM techniques are frequently misinterpreted as the quasi-static (QS) 3-D Partial Element Equivalent Circuit (PEEC) method, and the observed inaccuracies of modeling HF effects are attributed to the QS field assumption. This paper presents a comprehensive analysis on the differences between the QS 3-D PEEC-based and the equivalent-RLCG-circuit-based EM modeling for simulating the dynamics of fast switching power devices. Using two modeling examples of fast switching power MOSFETs, a 3-D PEEC solver developed in-house and the well-known equivalent-RLCG-circuit-based EM modeling tool, ANSYS Q3D, are compared to the full-wave 3-D FEM-based EM tool, ANSYS HFSS. It is shown that the QS 3-D PEEC method can model the fast switching transients more accurately than Q3D. Accordingly, the accuracy of equivalent-RLCG-circuit-based modeling approaches in the HF range is rather related to the approximations made on modeling electric-field induced effects than to the QS field assumption.

A parallel-plate pair with complex shared antipad structures was analyzed by decomposing it into rectangular local via structures and the plate pair region by virtual interfaces. The rectangle local via structures and the connections between via structures and the plate pair region were rigorously studied. An innovative cavity-based partial-element equivalent-circuit (PEEC) formulation was used to model the rectangle via structures. With special treatment of the reference in the PEEC equivalent circuits, improved circuits model was achieved and all elements of the circuits had clear physical meanings. Furthermore, by enforcing the continuity of the tangential electric fields at the virtual interfaces, the rectangle local via structures were able to connect to the plate region. The impedance parameters of several kinds of rectangle via structures and the whole parallel-plate pair were obtained using the proposed method, and the accuracy of the results was validated with the finite-element solution from a commercial tool.

This paper presents the partial element equivalent circuit formulation of electromagnetic systems with moving objects. The motion of portion of the system generates two effects: additional specific electromotive forces related to the speed and magnetic flux density and time-varying partial elements. The proposed formulation is presented in a general context including conductors, dielectrics, and magnetic materials. Exploiting Galerkin's testing procedure, additional contributions to the electric field integral equation that are proportional to electrical currents and magnetization appear. Three numerical examples are presented to support the theoretical analysis.

In this paper, analytical formulas for the electric field generated by currents, charges, and magnetization in conductive, dielectric, and magnetic media are presented in the framework of the partial element equivalent circuit (PEEC) method. Under the quasi-static hypothesis, assuming a Manhattan-type tessellation of the geometries and rectangular basis functions, the electric field is exploited in its contributions due to charges, currents, and magnetization. These different contributions require the computation of different type of integrals which are evaluated analytically. The mathematical derivations and the treatment of the singularities are described in detail. Two numerical examples are presented proving the accuracy of the proposed analytical formulas and their speed-up with respect to the numerical computation.

Inductance extraction for superconducting integrated circuits requires the accurate solution of structural current distributions. FastHenry is a well known, magnetoquasistatic solver suitable for this task. It is based upon the partial element equivalent circuit, integral equation method, with the structure discretized into hexahedral filaments. It employs the multilevel fast multipole algorithm (MLFMA) for compressed storage of the mutual inductance matrix, which accounts for most of the required memory. This MLFMA implementation is especially memory efficient, given certain approximations and algorithmic parameter choices. However, errors are introduced into the matrix representation. Here, a multilevel adaptive cross approximation solver with singular value decomposition recompression (MLACA-SVD) is presented as an alternative to FastHenry's existing MLFMA solver. MLACA-SVD compresses off-diagonal matrix blocks to a specified error tolerance, based on evaluating selected entries. Quadrature recipes are presented for guaranteed accuracy of matrix entry evaluation. Numerical results for examples of practical interest show that the MLACA-SVD memory scaling versus b (number of filaments) is practically identical to that of FastHenry's MLFMA, and is close to O(blog b). The MLACA-SVD requires less memory for the same solution accuracy, and furthermore offers complete control over matrix approximation errors. For the examples considered, it is found to be a more efficient solver. It is well suited to parallelization.

In this article, an efficient transient analysis method for high-speed interconnection and packaging problems is proposed. The method is committed to a full-wave generalized partial element equivalent circuit (G-PEEC) model with guaranteed stability and causality. With the proposed method, the full-wave G-PEEC model is represented by a few static compact subcircuits that are derived by applying the micromodeling circuit method to the G-PEEC model at a few discrete frequency points. Its transient response can be obtained by a linear combination of responses of the compact subcircuits, which can be simulated by the transient analysis method of SPICE. By adopting the compact subcircuits, which is an order reduced G-PEEC model, the transient simulation can be speeded up by two orders of magnitude when compared with the case if the subcircuits are generated directly from the G-PEEC model. Since the compact subcircuits are static, physically meaningful, and passive, the proposed transient analysis is with guaranteed stability and causality. Moreover, a frequency compensation strategy is proposed for preparing input signals of subcircuits to avoid the Gibbs phenomenon. Finally, three numerical examples, including eye-diagrams for a practical multilayer interconnection problem, are given, demonstrating the effectiveness, accuracy, scalability, and simplicity of the proposed method.

This paper deals with modeling and simulation of devices where current-carrying conductors are located close to magnetic bodies. These configurations typically occur in electromechanical energy converters such as in slots of electrical machines. Additional losses due to the inhomogeneous current density distribution (“current” or “field” diffusion) at high excitation frequency are a well-known phenomenon. However, classical approaches reach their limits as soon as field diffusion is influenced by ferromagnetic material with non-linear properties. An accurate but time-consuming computation can be achieved by using time-transient quasi-stationary finite-element analysis (FEA). Current diffusion can be described more efficiently by separating the conductor into parallel filaments, following the partial element equivalent circuit (PEEC) approach. As long as linear material characteristics are prevailing, the problem can, thus, be solved efficiently in the frequency domain. In this paper, a hybrid FEA-PEEC modeling approach is presented, where the magnetization of the ferromagnetic material is represented by equivalent currents obtained by 2-D FEA. It is suitable for complex multi-conductor configurations even including non-linear ferromagnetic material. For the proposed method, the resulting linear system is efficiently solvable in the frequency domain by direct solvers. A numerical example from the field of electric traction motors is presented to emphasize the accuracy and benefit of the proposed method for practical electromagnetic computations.

The MIT 1.3-GHz LTS/high-temperature superconducting (HTS) nuclear magnetic resonance (NMR) magnet is currently under development. The unique features of this magnet include a three-nested formation for an 800-MHz REBa2Cu3Ox (RE = Y, Gd) (REBCO) insert (H800) and the no-insulation (NI) winding technique for H800 coils. Because when it is driven to the normal state, an NI REBCO magnet will respond electromagnetically, thermally, and mechanically that may result in permanent magnet damage, analysis of a quenching magnet is a key aspect of HTS magnet protection. We have developed a partial element equivalent circuit method coupled to a thermal and stress finite-element method to analyze electromagnetic and mechanical responses of a nested-coil REBCO magnet each a stack of NI pancake coils. Using this method, quench simulations of the MIT 1.3-GHz LTS (L500)/HTS (H800) NMR magnet (1.3G), we have evaluated currents, strains, and torques of H800 Coils 1 to 3 and L500, and center fields of 1.3G, L500, and H800. Our analyses show H800 is vulnerable to mechanical damage.

No-insulation (NI) coils are an important technique for high-field magnetic resonance imaging (MRI). One of the technical issues with NI coils is their thermal and electromagnetic behavior when a local normal transition occurs. Given that multiple stacked coils are used in MRI, the interaction between coils must also be investigated, because a local normal transition may affect the other NI coils through magnetic coupling. In fact, when a local normal transition occurs, there is a possibility that large electromagnetic forces are applied to the other coils, or quench may be induced in some of them. Even though overcurrent tests of stacked NI coils have been conducted, the results are not helpful in actual MRI operation. In this study, we investigate the effects of the occurrence of a local normal transition in multi-stacked NI coil systems under conditions similar to those of actual operation, with a constant transport current below the coil's I c . The occurrence of a local normal transition is simulated by applying current to a heater inserted in manufactured small NI double pancake coils. To evaluate the interaction between NI coils, the voltage and changes in the generated magnetic field are measured at each coil. We also show the current distribution in the coils, as obtained by the partial element equivalent circuit method. The obtained results allow us to evaluate the interaction of the NI coils and evaluate coil protection methods.

Lightning surge propagation on telecommunication towers is essential to lightning protection design. Analysis of very fast surges in a telecommunication tower requires a full-wave solution of Maxwell's equations. This paper proposes a full-wave time domain partial element equivalent circuit (PEEC) method considering the effect of ground to evaluate the surge currents and voltages on vertical structures. The PEEC of the formulation is provided by using the method of image. This method can take into account the attenuation of the lighting surges, and has the potential to be implemented as a new type of solution for general lightning surge analysis. The proposed method is validated numerically with the finite-difference time domain method, and is used to analyze the surge propagation on cables mounted on two typical grounded telecommunication towers. The simulation shows that both the location of cable installations and the type of towers have a significant influence on the lightning protection performance.

A passive full-wave micromodeling circuit (FW-MMC) is proposed for high-speed/frequency interconnection problems. The circuit is derived from an FW generalized partial element equivalent circuit (G-PEEC) model, in which the radiation effect and other FW phenomena are fully taken into account. The proposed concise physically sensible circuit is obtained by recursively using a physics-based equivalent circuit transformation for absorbing the insignificant nodes of the G-PEEC model. To ensure the fidelity of the physical nature and the passivity of the MMC, the necessary broad sense criterion and the sufficient narrow sense criterion are systematically derived. It has been shown through numerical examples that the passivity violation of the physically sensible circuit model is very weak and can be effectively mediated. Thanks to the one order of magnitude reduction in the model order, the simulations for frequency- and time-domain system responses using the proposed MMC are three and two orders of magnitude faster, respectively, as compared with the G-PEEC model. Two practical examples for both frequency- and time- domains are given to demonstrate the high fidelity, scalability, accuracy, passivity, and efficiency of the FW-MMC.