Partial Element Equivalent Circuit Research Articles

New exponentially weighted inequality and its application to finite-time stability of descriptor time-delay systems

The paper considers the finite-time stability of descriptor time-delay systems. Firstly, we establish a set of exponentially weighted orthogonal polynomials, and based on this, we obtain a new exponentially weighted inequality(EWI). Secondly, an augmented Lyapunov-like functional (LLF) is established driven by the presented EWI. Finally, by applying the EWI and the LLF, some sufficient conditions for ensuring the finite-time stability of the system are obtained. A small partial element equivalent circuit model and two numerical examples are used to verify the effectiveness of the method.

Quench analysis of a no-insulation REBCO magnet based on the ADI method considering the coupling effect of the cryostat

A no-insulation (NI) REBCO superconducting magnet is under development at Wuhan National High Magnetic Field Center, China. The magnet with the liquid helium cryostat system has a compact structure to reduce the space required for operation. During a quench, the fast-changing spatial magnetic field around the NI magnet may induce a strong eddy current in the conductive parts of the cryostat. The eddy current and its associated Lorentz force will generate mechanical stress on the cryostat, especially on the thermal shield (TS). The mechanical strength of the cryostat needs verification in the preliminary design. Furthermore, the degree to which the electromagnetic coupling between the cryostat and NI magnet might impact the quench behaviors of the NI magnet remains uncertain. In this paper, a multi-physics quench model is newly developed for the NI REBCO magnet, and the alternating direction implicit method is employed for the solver of the thermal model to improve computational efficiency. This simulation model can consider the electromagnetic coupling effect between the NI magnet and cryostat by constructing a partial element equivalent circuit. A quench analysis has been performed and we found that: (1) The cryostat can function as a secondary shorted circuit to the NI magnet and slow down the quench speed to a certain extent. (2) During the rather fast inductive quench phase, the cryostat will experience an attraction force towards the quench propagation frontier. (3) A quench propagation from one end of the magnet can cause a significant z-axis unbalanced force on the TS. (4) Cryostat materials with drastically changed electrical conductivity can significantly affect their mechanical responses during a quench. However, the eddy current density and maximum Von Mises stress on the TS are barely affected by the thickness of the TS and the contact resistance of the NI REBCO magnet.

Retracted: Research on Calculation of Rail Self-Impedance of Track Circuit Based on Partial Element Equivalent Circuit

Retracted: Research on Calculation of Rail Self-Impedance of Track Circuit Based on Partial Element Equivalent Circuit

Lightning Response Transient Characteristics of Substation Grounding Grid in Multilayer Horizontal Stratified Earth Model Considering Soil Ionization Effect

This article proposes a new time-domain partial element equivalent circuit method mathematical model. The mutual impedance matrix between the potential on the discrete node and the leakage current on the conductor connected around the discrete node is adopted. To reduce the amount of calculation, the matrix equation that minimizes the unknown quantity is derived and adopted. The model can accurately calculate the lightning current distribution and lightning impulse response in a horizontal multilayered soil model considering the soil ionization effect. To improve computational efficiency, the quasi-static complex image method and its closed form of Green's function in the time domain are introduced into the model.

Improving the SNR of UMR sensor using LC resonator

Single-sided or unilateral magnetic resonance (UMR) technology has various benefits, such as an open structure, low cost, portability, and nondestructive measurement, in contrast to the conventional closed magnet structure. UMR is widely used in material analysis, well logging, and biomedicine. However, its development is constrained by its poor signal-to-noise ratio (SNR). To enhance the SNR of UMR sensor, a surface coil of LC resonator is added on the Radio Frequency (RF) coil. First, a method of calculating the current in the RF coil including LC resonator is derived. Next, the equivalent AC resistance of the coil is calculated using the partial-element equivalent-circuit (PEEC) method. Finally, the SNR of a UMR sensor incorporating LC resonator is analyzed, and its sensitivity map is provided. Experimental comparisons are made between the UMR sensor with and without a LC resonator. Results show that the SNR of the UMR can be enhanced by up to three times after the LC resonator is loaded. The SNR improves within 30 mm of the coil surface, and this beneficial effect steadily diminishes as the distance increases. This study offers a useful method for improving the signal of UMR sensors.

Numerical analysis of neutral delay differential equations with high-frequency inputs

PurposeThe paper proposes an efficient and insightful approach for solving neutral delay differential equations (NDDE) with high-frequency inputs. This paper aims to overcome the need to use a very small time step when high frequencies are present. High-frequency signals abound in communication circuits when modulated signals are involved.Design/methodology/approachThe method involves an asymptotic expansion of the solution and each term in the expansion can be determined either from NDDE without oscillatory inputs or recursive equations. Such an approach leads to an efficient algorithm with a performance that improves as the input frequency increases.FindingsAn example shall indicate the salient features of the method. Its improved performance shall be shown when the input frequency increases. The example is chosen as it is similar to that in literature concerned with partial element equivalent circuit (PEEC) circuits (Bellen et al., 1999). Its structure shall also be shown to enable insights into the behaviour of the system governed by the differential equation.Originality/valueThe method is novel in its application to NDDE as arises in engineering applications such as those involving PEEC circuits. In addition, the focus of the method is on a technique suitable for high-frequency signals.

Optimized Analytical Computation of Partial Elements Using a Retarded Taylor Series Expansion

The aim of this article is to efficiently and accurately calculate the integrals of the full-wave (FW) partial element equivalent circuit (PEEC) method. The accuracy of the analytical formulas calculated by the standard precision can be compromised when using nonuniform mesh to properly model the high-frequency effects. The numerical errors can be avoided by using a high-precision arithmetic, i.e., higher number of digits, however, at the expense of significantly higher computation time. This article presents an analytical approach for calculating the FW-PEEC interaction integrals of two elementary volumes/surfaces based on the Taylor expansion, which allows a high computational speed preserving the accuracy with a relative error of less than 0.1%. The proposed solution is verified compared to the high-precision arithmetic and the standard Gaussian integration for two examples of strip lines. Moreover, it is shown that the accuracy of FW-PEEC integrals can affect the convergence of an iterative PEEC matrix solver.

Electromagnetic Behavior Simulation of REBCO Pancake Coils Considering REBCO Tape Rotation Under High Magnetic Field

Since the screening current induced in rare earth-barium-copper-oxide (REBCO) magnet generates an irregular magnetic field, a few screening current simulation methods have been proposed. For an insert REBCO magnet generating ultra-high magnetic field, a new screening current method has been proposed with consideration of the coil-deformation effect. <p xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">In this paper, we have developed a new screening current method based on a partial element equivalent circuit (PEEC) model coupling with a two-dimensional stress finite element analysis to accurately the time-transient distribution of accurate screening current. In the presented method, the changes of self/mutual inductances are considered due to the coil deformation. As the simulation results, it was found that the coil deformation affected the screening current distribution. When considering the coil deformations, the screening current-induced fields to operating current are different for charging cycles. It is necessary to simulate the coil deformation to accurately estimate the screening current and the screening current-induced field.

Analysis of Nonuniform Contact Resistivity Distribution on No-Insulation HTS Racetrack Coil

This paper presents a numerical analysis and experiment to investigate a contact resistivity distribution of a no-insulation (NI) high-temperature superconductor (HTS) racetrack coil. Since the racetrack coil consists of straight and curved sections with continuously varing curvatures, the local inhomogeneity of contact resistivity can occur. We adopt a partial element equivalent circuit (PEEC) method to investigate this inhomogeneity. A 50-turn NI HTS single pancake test coil is fabricated to figure out the discrepancy of contact resistivity, and the coil is charged up to 100 A in a liquid nitrogen bath. Voltage profiles between inserted voltage taps and the magnetic fields at the coil center are measured and compared with two simulation cases: 1) uniform contact resistivity; 2) nonuniform contact resistivity distribution. The results indicated that nonuniform distribution of contact resistivity may exist. Lastly, the current and Joule heat distribution during the ramping process is analyzed by the PEEC model.

Axial Movement Effect on Voltage and Current Behaviors of Insert No-Insulation REBCO Pancake Coil

In 2017, an insert 12-stacked no-insulation (NI) rare-earth barium copper oxide (REBCO) magnet was used in the generation of a world-record DC magnetic field of 45.5 T. The experiment demonstrated its high thermal stability; however, NI REBCO pancake coils are facing mechanical problems. In such an ultra-high field, strong electromagnetic forces work on insert REBCO coils, in particular during sequential normal-state transitions. Strong forces may cause insert REBCO coils to deform and move. Some research revealed that some deformations and movements affected the coil voltages and the screening currents. Whereas, the coil movement in an ultra-high field has not been studied yet. Voltages and currents are induced by the movement of insert coils, and there is a possibility of degrading the coil stability. In this paper, we have investigated the electromagnetic behaviors during sequential normal-state transition, considering the coil movement due to strong axial forces. The electromagnetic behaviors are simulated using a radially-subdivided partial element equivalent circuit (PEEC) model coupled with mechanical movement analysis.

Performance Against Direct Lightning on 10-kV Overhead Distribution Lines With Counterpoise Wires

This article investigates the lightning performance of a 10-kV overhead distribution line equipped with grounding counterpoise wires under extremely low soil conductivity conditions. A partial element equivalent circuit model with the lossy ground being considered is adopted for lightning surge investigation. The Monte Carlo method considering natural lightning randomness is used for the flashover rate evaluation. It is found that under extremely low soil conductivity conditions, the simple vertical grounding rod is not effective in lightning protection, while the performance is significantly improved with extended counterpoise wires. The single-row counterpoise wire with a length of line span performs best. The single-row counterpoise wire with a half-length of line span is a competitive one, due to a half-cost reduction and a competitive performance. If a higher performance of lightning protection is expected, further extending the length of counterpoise wires would be ineffective. Increasing the CFO level or installing surge arresters on all poles would be the possible solution.

Experimental and Equivalent Circuit Analysis Approach to Estimate Contact Resistances on Different Sections in a D-Shaped NI HTS Coil

With well-known self-protecting behaviors of no-insulation (NI) high temperature superconductor (HTS) coils, their performance was verified by numerous high field magnets. As one of the initial investigations of the NI HTS technique being applied to toroidal field (TF) coils, an equivalent circuit analysis is carried out on a D-shaped NI HTS coil to predict its electromagnetic behaviors regarding the contact resistance, one of the most important parameters for NI HTS coils. A charging/discharging test is performed at 77 K to obtain the experimental data for contact resistance estimation. Using the measured voltage and the pressure dependency of surface contact resistivity, a combination of contact resistance is obtained through the modified lumped circuit and the partial element equivalent circuit simulation by which the shape-dependent contact resistance can be estimated. The results are expected to provide a source for careful management in the design stage to consider the uneven contact resistance and possible uneven electromagnetic behavior among different sections of the TF coil.

Investigation of Induced Overvoltages on DC Cables of PV System Subjected to Lightning Strikes Using FDTD Method

Due to installation of photovoltaic (PV) panels in outdoor areas, they are subjected to lightning strikes which may cause degradation or complete damage, resulting in service interruption and added cost. Hence, it is crucial to provide an efficient and effective lightning protection system which requires some considerations to increase its efficiency and reduce its cost. Any damage to the PV system inverter causes service interruption, so it is important to analyze the transient voltages induced on the dc cables connected to the inverter during lightning strikes. In this article, the induced voltages on dc cables are calculated using the finite difference time domain (FDTD) method, which introduces high accuracy in transient studies. Important factors affecting the transient voltages on dc cables are studied, including the effect of lightning strike polarity and changing the separation distance between the PV panel and the isolated protection system. Moreover, the effect of modifying dc cable arrangement is studied, in addition to the impact of concrete foundation presence in the grounding system. Then, some recommendations are proposed which succeeded in reducing transient voltages on dc cables. In addition, the induced voltages calculated by FDTD are compared with those obtained by partial element equivalent circuit method.

Full-wave electromagnetic analysis of lightning strikes to wind farm connected to medium-voltage distribution lines

This paper studies the voltages developed on a wind turbine (WT) and a medium-voltage distribution line (MVDL) connected to a wind farm subjected to lightning strikes and located on frequency-dependent (FD) soils. The ground potential rise (GPR), voltages at the blade tip and on phase conductors of the MVDL are calculated using the full-wave electromagnetic software XGSLab® employing the rigorous Partial Element Equivalent Circuit (PEEC) method. The wind farm comprises four wind turbines with interconnected grounding systems using cables buried in resistivity soils of 1,000 and 5,000 Ω m. The voltages are computed for the first positive impulse (FPI) of 100-kA 10/350μs and for the subsequent negative impulse (SNI) of 50-kA, 1/200μs. Results have shown that voltage peaks increase notably as the soil resistivity increases. When the WTs are assumed, oscillations in the GPR waveforms for the SNI occur due to the multiple reflections between the blade and the turbine’s base. However, the voltages for the FPI present smooth time-domain responses. Furthermore, the overvoltages developed at the MVDL are significantly dependent on the soil resistivity and lightning current waveform.

Methodology for Analyzing Coupling Mechanisms in RFI Problems Based on PEEC

In this article, a method for analyzing coupling mechanisms in radio frequency interference (RFI) problems is proposed. The partial element equivalent circuit (PEEC) method is first used to derive the retarded inductances and capacitances between different mesh cells. With the introduction of a novel partitioning algorithm, the capacitive coupling and inductive coupling between arbitrary layout parts can be quantified based on the magnitude of the displacement current and induced voltage drop. The accuracy of the PEEC models is validated by comparison with different commercial tools. The proposed coupling mechanism analysis flow provides a useful prelayout tool for RFI risk analysis.

Modeling and Analysis of Spike Signal Sequence for Memristor Crossbar Array in Neuromorphic Chips

This paper presents the efficient systematic methods for modeling and analysis of spike signal sequence in crossbar arrays for neuromorphic computing chips. A novel spike signal sequence is proposed, where the ideal spike sequence with only spike time information in the original spiking neural network (SNN) algorithm is mapped onto actual spike waveform by stitching neighboring sequential spikes together with certain overlaps. We thoroughly investigate and analyze the performance of the input encoding as well as the implementation of spike timing dependent plasticity (STDP)-based SNN on memristor crossbar arrays with the proposed spike signal sequence. A detailed circuit model of a crossbar array, consisting of resistance, capacitance and inductance derived by the partial equivalent element circuit (PEEC) method, is created to simulate the training process of SNN. The proposed spike signal sequence is demonstrated that is able to achieve accurate input encoding as well as high recognition accuracy when it is used to perform the classification task on MNIST handwritten digits. The spike signal sequence is further analyzed and assessed in terms of the main factors affecting its encoding accuracy and the parasitic effects of crossbar arrays on its robustness.

Precise Modeling and Design of Self-Resonant for High-Efficiency Mid-Range Wireless Power Transfer System

Transfer power and efficiency of wireless power transfer (WPT) systems are limited by the quality factor and coupling coefficient of the transmitting (Tx) coil and receiving (Rx) coil. Getting rid of compensation circuits, self-resonant coils have simple structure, high system reliability, high quality factor and high power level, making it a promising candidate for WPT applications. In modeling and computation of self-resonant coils, the results derived from the transmission line theory have obvious errors, and the finite element simulation takes a long computing time. For obtaining accurate results and achieving fast computation, a partial-element equivalent circuit (PEEC) method is applied to calculate the self-resonant frequency (SRF) and the current distribution of helical coils. To validate the accuracy of the proposed model, some prototypes were simulated and measured. The theoretical calculation predications are in great agreements with the simulation and measurement results. The magnetic coupling model between Tx and Rx is also established using PEEC method and a novel design guideline of self-resonant helical coils is proposed. Furthermore, a WPT system with 6.78MHz selfresonant helical coils was designed, fabricated and tested for a high-efficiency mid-range energy transfer. It was used to drive a 5W load wirelessly as a demonstration to validate the feasibility of the proposed system in practical applications.

The design of YBCO binary current leads and its electromagnetic-thermal coupling analysis based on PEEC and finite volume method

A superconducting magnet system is developed for the application of high-frequency gyrotrons at Wuhan National High Magnetic Field Center, China. The operating cost for the magnet is dominated by refrigeration power. To reduce the heat load for cryogenic systems, a pair of YBCO binary current leads is designed by consideration of the industrial concentration of type II high-temperature superconducting YBCO material. In this paper, a simulation model is proposed to perform the electromagnetic-thermal coupling analysis of these YBCO binary leads under different operating conditions by combining a partial element equivalent circuit method and finite volume method. The simulation code can improve computational efficiency and enable high-accuracy coupling between the electromagnetic field and heat transfer process. In the steady state, the heat leakage at the 4.2 K cold end of the YBCO binary leads depends mainly on the geometric parameters of the YBCO tape, especially the cross-sectional area of the copper layer in the YBCO tape. The cooling mode and liquid helium level also have a significant impact on the heat leakage level. The optimal outer diameter of the normal copper section is identified, and the optimum value is largely influenced by the effective cooling power imposed on the cold end of the normal copper section. In the transient state, simulations for the charging process and the loss of cooling accident are performed, along with a detailed analysis of the electromagnetic-thermal response features of the leads under these conditions. The results indicate that the YBCO binary current leads possess high thermal stability and an ample time margin for the magnet system to be demagnetized.

A Full-Wave PEEC Model for Thin-Wire Structure in the Air and Homogeneous Lossy Ground

This article presents an efficient full-wave partial element equivalent circuit (PEEC) formulation of thin-wire structure in the full space of air-homogeneous lossy ground for lightning transient analysis. First, the Green's functions for the case of an air-uniform ground are derived, which involve Sommerfeld-type integrals. Next, using the singularity subtraction technique, a new form of Green's functions is obtained, which has the advantage of being less singular and smooth compared with the original form. In the full-wave method, the efficient and accurate computation of partial elements is crucial for the practical application of the PEEC formulation. A three-dimensional cubic interpolation scheme is employed to accelerate the computation of Sommerfeld integrals. To improve the computational efficiency and accuracy of the interpolation, the continuity and symmetry of the Green's functions are investigated in a comprehensive way, which is important for a successful interpolation. Numerical and experimental examples from the literature are presented to validate the accuracy of the proposed model.

Efficient PEEC Iterative Solver for Power Electronic Applications

A new formulation of the partial element equivalent circuit (PEEC) is proposed that is well suited to be used along with fast Fourier transform (FFT)-based acceleration techniques. FFT-based techniques are used in conjunction with iterative solvers to accelerate matrix-vector products. Despite the significant memory saving and computational time reduction, these techniques may suffer at high frequencies due to the fine voxelization that they require. In this work, a new surface impedance-based formulation is presented and a novel preconditioner is proposed. Both contributions allow the frequency range of applicability of the FFT-accelerated PEEC method to be extended up to the gigahertz range. The accuracy and efficiency of the proposed solver are demonstrated by applying the proposed modeling strategy to a toy-problem and real-world structures comprising a printed circuit board and a transistor package, involving millions of unknowns.