Torque Simulation on NI REBCO Pancake Coils during Quench

This paper presents the thermal and electromagnetic behaviors of multistacked no-insulation (NI) REBa 2Cu3O7− x (REBCO, RE = rare earth) pancake coils. The NI winding technique gives a high enough thermal stability not to damage REBCO coils even though a normal-state transition occurs. The high thermal stability has been verified through overcurrent tests. Moreover, the numerical simulation of multistacked NI REBCO pancake coils has been performed to investigate the electromagnetic behaviors in detail. The simulation results also confirmed the high thermal stability of NI REBCO pancake coils. However, it does not mean that an NI REBCO magnet never quenches. In experiments, it was observed that a quench in one of the pancake coils propagated to the other pancake coils sequentially. The above sequential quench from pancake to pancake has not been confirmed in the numerical simulation since the thermal behavior is not considered. For the more reliable verification, we have developed a numerical simulation to investigate the thermal and electromagnetic behaviors by the partial element equivalent circuit method and the two-dimensional thermal finite-element method. In this paper, the six-stacked NI REBCO pancake coil is simulated with several operating temperatures, and the sequential quench is reproduced. The velocity of the sequential quench is also shown.

We have been developing a no-insulation (NI) REBCO pancake coil technology for applications in medical cyclotrons and high-field whole-body MRI. The thermal and electromagnetic behaviors of multi-stacked NI-REBCO double pancake coils are numerically analyzed in this study when a local defect occurs in one coil using coil diameter and operating temperature parameters. Based on changes in voltage at both ends of the coil and the magnetic field at the center, we present a numerical study of the possibility of continuous operation after the occurrence of a local defect. In the numerical analysis, a new simplified model based on the PEEC model (Partial Element Equivalent Circuit model) is suggested and used for current distribution analysis, and the results are compared.

We previously developed a high-magnetic-field REBCO coil for use in medical devices such as medical accelerators and high-magnetic-field MRI. The use of high-temperature superconducting (HTS) coils in such applications necessitates their miniaturization while providing high magnetic fields. However, when the current density is improved by reducing the copper-stabilization-layer thickness in the conventional insulated HTS coil, the thermal stability is lowered, which leads to a tradeoff between high current density and high thermal stability. Therefore, we examine no-insulation (NI) coils that allow compatibility between high current density and thermal stability. Recent research has indicated that NI coils with multiple defects can afford a stable and high critical current (Ic) and operate without serious problems, which makes it possible to produce coils wound with commercial REBCO tapes containing several defects along the tape, which in turn makes fabrication economically viable. However, there are many unknown aspects of the current, magnetic field, and heat behaviors of NI coils with defects, particularly when large currents flow through them. Here, in order to examine the behavior of a multiple-defect NI coil subjected to a large current at the temperature of ~30 K via application of the conduction cooling method, we use a combination of the partial element equivalent circuit method and the finite-element method to investigate the detailed current and thermal behaviors. Our results indicate that defective NI coils can afford a critical current Ic value of ~80% of that of defect-free NI coils, which makes our findings valuable in terms of contributing to further developments in HTS coil applications.

No-insulation(NI) Rare-Earth Barium Copper Oxide (REBCO) pancake coils can generate high magnetic fields and have the high thermal stability against normal-state transition due to allowing currents to radially bypass a local normal-state region through the turn-to-turn contacts. Despite these merits, no turn-to-turn insulation causes a charging delay. To solve this charging delay problem, an NI REBCO coil wound with multi-bundled (MB) conductors was proposed. As an experimental result, a charging delay was improved because the inductance per tape of MB coil is smaller than that of single-tape NI coil. Meanwhile, the current behaviors of MB coils are complicated and has not been clarified. We have investigated the current and thermal behaviors of MB REBCO coils during charging and against normal-state transition, comparing with and without turn-to-turn insulation. As the result, it is shown that the MB coil can be operated stably, and no pessimistic temperature rise is observed. However, the operating current of MB coils with turn-to-turn insulation may concentrate on one tape when the normal-state transition occurs. Therefore, MB coils without turn-to-turn insulation seems to be desirable.

PV systems are considered one of the most important and popular forms of renewable energy sources worldwide. Due to the installation of PV modules on rooftops and outdoor areas, they are frequently subjected to lightning strikes, leading to a deterioration in PV systems. To provide an efficient lightning protection system, the accurate modeling of PV systems during lightning strikes is required. The main objective of this paper is to assess the transient behavior of PV systems when struck by lightning, where the PV system is modeled using the partial element equivalent circuit (PEEC) and finite difference time-domain (FDTD) methods. The PEEC method is one of the accurate methods used to represent the PV system by its equivalent RLC circuit to study lightning transients. Moreover, the FDTD method provides high accuracy when studying lightning transients by analyzing the electric and magnetic fields inside the PV system. The PEEC and FDTD methods are used to calculate the transient overvoltages at different points of the PV system. Then, a small-scale PV system is tested in the laboratory using an impulse generator representing the lightning strike to verify the correctness of the results obtained by simulation. Most of the existing research works introduce low accuracy in PV system modeling during lightning transients by neglecting the effect of the mounting system, metal frame, and mutual coupling, which are considered in this work. Moreover, the high-frequency nature of lightning current is considered when modeling the elements of the grounding system. Verifying the results by laboratory experiments can guarantee the application of the simulation model on large-scale PV systems.

This paper proposes a partial element equivalent circuit (PEEC) method based on a thin wire structure for lightning surge analyses which are comprised of a tower surge responses and transient performance of a grounding electrode. A comparison of the simulation results by the proposed method in the time and frequency domains and experimental data shows satisfactory agreement not only for amplitudes but also for waveshapes. The retardation of electromagnetic coupling in the PEEC simulation is investigated. A promise time efficiency of the time-domain (TD) PEEC method neglecting the retardation is found when it is compared with that of the full-wave PEEC method in the frequency domain. The TD PEEC method neglecting the retardation provides over-estimated results which is applicable for upper bound insulation design. The PEEC method is an attractive approach as the numerical electromagnetic analysis methods for a lightning surge study in a power system.

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.

High-temperature superconducting double-pancake (DP) coils wound by the no-insulation (NI) approach have been proved to have a high thermal stability and a self-protecting ability. This paper mainly studies the effect of a quench of one pancake coil on the electromagnetic-thermal-mechanical behaviors of an NI DP coil in the self field and the high field. An electromagnetic-thermal coupling quench model is used to calculate the distributions of current, temperature and electromagnetic field in the coil, and then a three-dimensional homogeneous mechanical model is built to analyze the changes in strain and stress during a quench by considering the distributions of thermal strain and Lorentz force of the coil. The results indicate that the obvious increase in circumferential current and radial current density in the bottom pancake coil is induced by a quench of the top pancake coil due to the electromagnetic coupling effect in the self field and the high field, and that the DP coil still has a negative coil voltage during a quench in different fields. Although the bottom pancake coil has a large circumferential current, the mechanical deformation of the DP coil during a quench is mainly caused by the temperature rise in the self field. The thermal expansion of the top pancake coil has a remarkable effect on the mechanical behaviors of the bottom pancake coil. Moreover, the DP coil has the same temperature rise and mechanisms of bypass current in the self field and the high field. However, the mechanical deformation of the DP coil is based on the combined effects of temperature rise and Lorentz force in the high field. It can be found that the values of the hoop and axial stresses are affected by a large electromagnetic stress.

SummaryThe high level of integration has made the analysis and design of integrated circuits and packages increasingly challenging. Hence, there exists an urgent need to reduce the computational complexity of existing numerical methods. The integral equation‐based method known as the partial element equivalent circuit (PEEC) method naturally generates an equivalent circuit that can be analyzed in both the time and frequency domains. The enforcement of Kirchhoff laws to the equivalent circuit may easily result into a very large set of equations whose solution can be extremely time‐consuming.In this paper, we propose a vectorized version, over the frequency sweep, of the adaptive cross approximation algorithm. Furthermore, the multiscale block decomposition is applied to the PEEC method, powered by a vectorization strategy and an efficient management of the random access memory. It is found that the proposed use of vectorization and compression techniques in the framework of the multiscale block decomposition results in a significant computational speedup of the frequency‐domain analysis of PEEC models. The efficiency and accuracy of the proposed method are demonstrated through its application to two pertinent problems. Copyright © 2014 John Wiley & Sons, Ltd.

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.

The Partial Element Equivalent Circuit (PEEC) method is a well recognized integral-equation (IE) technique to solve Maxwell’s equations. Similarly to the method of moments (MoM), the electromagnetic (EM) interactions between currents and between charges are described in terms of integrals. In contrast to the standard MoM, the PEEC method keeps the electric and magnetic coupling phenomena separate, which leads to different interaction integrals to be computed. These integrals admit simplified solutions for the case of the static free-space Green’s function and orthogonal geometries but their applicability is limited to electrically small problems only. When the full-wave free-space Green’s function is considered, the integrals are typically computed in the frequency domain (FD) by resorting to Gaussian quadrature schemes. The accuracy and efficiency of such schemes is a delicate issue. Therefore, recent works have investigated the possibility of applying the Cagniard–DeHoop (CdH) technique to calculate the interaction integrals for zero-thickness elementary domains. In this paper, we close the loop and shall apply the CdH technique to calculate the partial-inductance between two elementary bricks as prescribed by the PEEC technique exactly in the time domain (TD). The analytical approach is demonstrated on the interaction between two bricks as it occurs in the modeling of the magnetic field coupling between volumetric currents. The accuracy of the proposed approach is (successfully) tested for two representative cases.

This paper presents hybridization approaches of the method of moments (MoMs) and the partial-element equivalent-circuit (PEEC) method in order to achieve a significant reduction of numerical complexity. The MoMs is applied as a full-wave method-only where it is necessary-to 3-D metallic scatterers such as antennas. Furthermore, the PEEC method is applied to single-layer printed circuit boards combined with an effective dielectric constant assuming an infinite dielectric in order to avoid discretization of the substrate. In the hybrid approaches of the MoMs and the PEEC method, both techniques are applied consecutively compared to a full-wave MoMs model. The validity of the hybrid approaches and the gain in numerical computation time are demonstrated by three numerical examples, which are related to electromagnetic compatibility. The results are verified by full-wave MoMs reference calculations and by a measurement.

High-Tc superconducting coils wound by REBCO coated conductors with no turn-to-turn insulation have been widely used for high-field DC magnets, due to the fact that they have a higher engineering current density and can be self-protective during a quench. One long-lasting problem of no-insulation (NI) coils is the charging delay due to low characteristic resistance. In this paper, the authors propose the structure of a parallel co-wound NI pancake coil. Unlike a traditional NI pancake coil which is wound by a single tape, in the new design multiple NI tapes are co-wound. From a circuit point of view, the tapes are connected in parallel. It is discovered that the charging delay of the NI coil can be substantially reduced by the parallel co-wound method. The mechanism is that the inductance of a coil is proportional to the square of the number turns which is inversely proportional to the number of co-wound layers, whereas the characteristic resistance is nearly irrelevant to the number of layers, therefore the coil’s time constant can be considerably reduced. The new design could also further increase the engineering current density of a magnet due to the independent current transporting of co-wound layers, which will be investigated in future work.

The no-insulation (NI) winding technique has been attracting attention, because NI Rare-Earth Barium Copper Oxide (REBCO) pancake coils have high thermal stability. It is an indispensable technology to generate an ultra-high magnetic field. In 2017, using the NI winding technique a world-record high magnetic field, 45.5 T, was generated by 12 insert single pancake coils with an outsert magnet, and it showed a high potential to generate 14.4 T inside a background field of 31.1 T. After the experiment, the REBCO tapes were mechanically damaged, so that the critical currents were deteriorated. A large current was induced in NI REBCO coils next to the quenched coil when one of multi-stacked NI REBCO pancake coils quenched, resulting in tape property degradation and irreversible mechanical damage. Therefore, in order to protect NI REBCO pancake coils during quench, it is desired to reduce the amount of induced current. To suppress an induced current, the idea of “magnetic dam” has been proposed previously. The idea is to use a copper pipe installed at the outside of NI REBCO pancake coils. However, the copper pipe just slowed the quench propagation. In this paper, we extended the method to decrease an induced current much more by installing extra NI REBCO windings instead of the copper pipe. The electromagnetic and stress behaviors of 6-stacked NI REBCO coils with extra windings are simulated when one of the stacked NI REBCO coils transitions into a normal state. The ability of mechanical damage protection from a strong stress by an induced current during quench propagation is demonstrated through simulations.

In this paper, the analytical formula for the magnetic-to-electric field coupling of time-varying magnetization is presented in the framework of the partial element equivalent circuit (PEEC) method with a Manhattan-type tessellation. In the virtue of the results presented in a previous work, the proposed formula allows obtaining a quasi-magnetostatic PEEC solver in which all the matrix entries can be computed analytically. This ensures a significant speedup of the resulting PEEC solver if compared to the one where the evaluation of the integral was performed numerically. The numerical results confirm the accuracy and robustness of the proposed formula and the expected significant speedups. Detailed pseudocodes are provided to make the results easily reproducible.