An interface‐enriched generalized finite element analysis for electromagnetic problems with non‐conformal discretizations

An interface‐enriched generalized finite element method is presented for analyzing electromagnetic problems involving highly inhomogeneous materials. To avoid creating conformal meshes within a complex computational domain and preparing multiple meshes during optimization, enriched vector basis functions are introduced over the finite elements that intersect the material interfaces to capture the normal derivative discontinuity of the tangential field component. These enrichment functions are directly constructed from a linear combination of the vector basis functions of the sub‐elements. Several numerical examples are presented to verify the method with analytical solutions and demonstrate its h‐refinement convergence rate. The proposed interface‐enriched generalized finite element method is shown to achieve the same level of accuracy as the standard finite element method based on conformal meshes. Two examples, involving multiple microvascular channels and circular inclusions of different radii, are analyzed to illustrate the capability of the proposed approach in handling complicated inhomogeneous geometries. Copyright © 2015 John Wiley & Sons, Ltd.     

Efficient analysis of planar microwave circuits with mixed‐order prism vector finite macroelements

This paper introduces a new concept of a mixed‐order prism macroelement, suitable for an efficient analysis of three‐dimensional planar microwave circuits, using two‐dimensional meshes and preprocessors. The mixed‐order concept used here implies arbitrary orders of variation in different directions and differs essentially from the well‐known mixed‐order approximation that is an integral part of every Whitney element. It is the existence of a related systematic theory of higher‐order vector finite elements, previously documented, that facilitates the introduction of such a concept. The second‐ and third‐order elements, derived by this approach, are successfully applied in the analysis of planar microwave circuits, rendering the application of finite element method in such problems still a favorable option. Copyright © 2008 John Wiley & Sons, Ltd.     

A high‐order discontinuous Galerkin method with time‐accurate local time stepping for the Maxwell equations

We present an explicit numerical method to solve the time‐dependent Maxwell equations with arbitrary high order of accuracy in space and time on three‐dimensional unstructured tetrahedral meshes. The method is based on the discontinuous Galerkin finite element approach, which allows for discontinuities at grid cell interfaces. The computation of the flux between the grid cells is based on the solution of generalized Riemann problems, which provides simultaneously a high‐order accurate approximation in space and time. Within our approach, we expand the solution in a Taylor series in time, where subsequently the Cauchy–Kovalevskaya procedure is used to replace the time derivatives in this series by space derivatives. The numerical solution can thus be advanced in time in one single step with high order and does not need any intermediate stages, as needed, e.g. in classical Runge–Kutta‐type schemes. This locality in space and time allows the introduction of time‐accurate local time stepping (LTS) for unsteady wave propagation. Each grid cell is updated with its individual and optimal time step, as given by the local Courant stability criterion. On the basis of a numerical convergence study we show that the proposed LTS scheme provides high order of accuracy in space and time on unstructured tetrahedral meshes. The application to a well‐acknowledged test case and comparisons with analytical reference solutions confirm the performance of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

Higher‐order CN‐FETD method for analysis of microwave circuit structures

In this paper, the hierarchical high‐order basis functions on tetrahedrons are introduced to the Crank–Nicolson (CN) finite‐element time‐domain (FETD) with the 3D Maxwell equations for analysis of the microwave circuit structures. Whitney 1‐form high‐order hierarchical basis functions are used to expand the electric field and Whitney 2‐form high‐order hierarchical basis functions for the magnetic field. The CN scheme is employed in the FETD method to lead to an unconditionally stable algorithm. Numerical results were presented to demonstrate the accuracy and efficiency of the proposed high‐order CN‐FETD method. Copyright © 2012 John Wiley & Sons, Ltd.     

Performance evaluation of 6000‐A‐class superconducting field windings for 600‐MW‐class superconducting generators

Superconducting generators have many advantages such as increasing generator efficiency and improving power system stability. In Japan, a national project has been conducted since 2000 which is aimed at the development of fundamental technologies required for high‐output‐density and large‐capacity superconducting generators. This paper describes the results of this project, focusing on 6000‐A‐class field winding development. Copyright © 2004 Wiley Periodicals, Inc. A superconducting generator with a high output density and a large capacity has inherent factors that decrease superconducting stability. These are: (1) increase in the magnetic field in the winding which is caused by the increase in winding current density and (2) difficulty in fabricating windings which increases as a conductor diameter becomes larger. To secure the stability, we adopted a higher‐copper‐content conductor and a design that increases winding fixing pressure, along with devising a winding method that accommodates larger conductor diameter. These improvements were applied to a partial model of a 600‐MW field winding. Test results of the model showed good stability, indicating that design and fabrication technique for a 6000‐A‐class superconducting field winding has been successfully evaluated. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 159(2): 7– 18, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20332     

A new separate‐identification method of two stator equivalent core‐loss resistances corresponding to hysteresis and eddy‐current losses for parallel‐type mathematical models of AC motors

This paper proposes a new unified method for identifying equivalent stator core‐loss resistance of AC motors, which can be applied to both induction and synchronous motors. In order to realize AC motors that exhibit high performance such as precise torque generation and/or efficient energy transmission, stator core loss cannot be neglected in designing vector control systems. It is common to model stator core loss in magnetic circuits as loss caused by equivalent resistance in electrical circuit. One of the best mathematical models for controlling AC motors with core loss is a kind of parallel‐type model that succeeds in modeling both eddy‐current and hysteresis losses. The newly proposed method succeeds in identifying separately and simultaneously two kinds of equivalent core‐loss resistances on the model corresponding to eddy‐current and hysteresis losses. The practical usefulness of the method is evaluated and confirmed through experiments using two induction motors of 5.5 and 2.0 kW having relatively high core losses and a permanent magnet synchronous motor of 750 W having relatively low core losses. © 2003 Wiley Periodicals, Inc. Electr Eng Jpn, 143(4): 50–63, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10152     

Magnetic field analysis by the edge element FEM

Several useful techniques are presented for magnetic field analysis by the edge element FEM. The relations of nodal, edge, and facet shape functions are visualized as important properties using the differential operators of gradient and rotation. These shape functions and the rotation of edge shape functions are presented for tetrahedral, prismatic, pyramidal, and hexahedral elements. Furthermore, the method of determining coil current distributions satisfied with conservation of current is shown using a current vector potential and a surface tree gauge condition for open‐loop coils and closed loop coils. © 2005 Wiley Periodicals, Inc. Electr Eng Jpn, 154(1): 59–65, 2006; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20168     

Development of new conductors of the cable‐in‐conduit type for HTS coils with high performance

A new type of cable‐in‐conduit conductor composed of HTS tapes was proposed as a winding for high‐performance HTS coils with high current capacities and low AC losses. In the fabrication of the conductor, the twist of stacked tapes around their axes was made before inserting them inside conduits. The twist angle should be changed continuously along the axis to reduce face‐on oriented magnetic fields applied to the tape in the winding conductor during coil operation. In order to confirm the high current capacity of this type conductor, two single‐layered solenoidal coils wound with sample conductors composed of five stacked Bi‐2223 tapes with bias angles of 20 and 0° were fabricated and tested in liquid nitrogen. A copper magnet system was used in this experiment to generate the spread magnetic field with a spread angle of 20° from the coil axis to the radial direction, which simulates the profile of magnetic fields near the edge windings of practical coils. A large improvement on critical‐current degradation affected by spread magnetic fields was successfully observed for the test coil wound with the 20° bias conductor. © 2005 Wiley Periodicals, Inc. Electr Eng Jpn, 153(4): 12–19, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20218     

A non‐conformal FETI‐like domain decomposition approach of FE‐BI‐MLFMA for 3‐D electromagnetic scattering/radiation problems

A non‐conformal finite element tearing and interconnecting‐like (FETI‐like) domain decomposition approach (DDA) of the hybrid finite element–boundary integral–multilevel fast multipole algorithm (FE‐BI‐MLFMA) is presented by integrating a series efficient techniques for computing electromagnetic scattering/radiation problems. The Robin transmission condition is employed to cement the non‐conformal meshes on the interconnected surfaces between the interior and exterior regions and between sub‐domains in the interior region. The FETI‐like technique is applied to reduce the FE‐BI matrix equation. Furthermore, a preconditioner is constructed to accelerate the convergent speed of this non‐conformal FETI‐like DDA. The numerical performance of the presented non‐conformal FETI‐like DDA‐FE‐BI‐MLFMA is studied for scattering/radiation problems. Copyright © 2015 John Wiley & Sons, Ltd.     

盘式永磁涡流驱动器的涡流软测量方法

针对永磁涡流驱动器导体盘在工作状态时无法直接测量涡流的问题,提出一种涡流软测量的方法。建立永磁涡流驱动器的解析计算二维模型,引入矢量磁位构建偏微分方程组,借助各层的边界条件,得到了导体铜盘涡流的解析解,从而得到导体铜盘上的涡流分布规律。采用该模型,永磁涡流驱动器在运行过程中所产生的涡流密度可以通过转差速度和气隙宽度的测量结果计算得到。之后应用涡流软测量模型,分析导体盘涡流密度大小随气隙宽度和转差速度变化的变化规律。所有计算得到的软测量结果都进行了基于有限元法的仿真验证。结果表明,涡流解析计算有较好的准确性,该软测量模型的结果平均误差约为2%,为永磁涡流驱动器运行过程中涡流的计算和产品优化设计提供了重要依据。     

A dual‐primal finite‐element tearing and interconnecting method combined with tree‐cotree splitting for modeling electromechanical devices

The dual‐primal finite‐element tearing and interconnecting (FETI‐DP) method is combined with the tree‐cotree splitting (TCS) method to expand the capability and improve the efficiency of the finite‐element analysis of electromechanical devices. With the FETI‐DP method, an original large‐scale problem is decomposed into smaller subdomain problems and parallel computing schemes are then employed to reduce the computation time significantly. The TCS method is adopted to deal with the low‐frequency breakdown problem, which often accompanies the finite‐element analysis of electromechanical problems. On the basis of the computed magnetic field values, the force is computed with the use of the Maxwell stress tensor method. The proposed technique is applied to solve both high‐contrast magnetostatic problems and eddy‐current problems. Results are compared with both measurement data and brute‐force finite‐element calculations without domain decomposition. Comprehensive tests are conducted to investigate the parallel efficiency and numerical scalability. The results show that the proposed method can achieve a good parallel efficiency and an excellent numerical scalability with respect to the number of subdomains and the size of the problem. Copyright © 2012 John Wiley & Sons, Ltd.     

Uniform approximation of time‐invariant non‐linear systems

An Erratum has been published for this article in International Journal of Circuit Theory and Applications 2004; 32(6):633. It is shown that the elements of a large class of time‐invariant non‐linear input–output maps can be uniformly approximated arbitrarily well, over infinite time intervals, using a certain structure that can be implemented in many ways using, for example, radial basis functions, polynomial functions, piecewise linear functions, sigmoids, or combinations of these functions. For the special case in which these functions are taken to be certain polynomial functions, the input–output map of our structure is a generalized finite Volterra series. Results are given for the case in which inputs and outputs are defined on ?. The case in which inputs and outputs are defined on the half‐line ?₊ is also addressed, and in both cases inputs need not be functions that are continuous. Copyright © 2004 John Wiley & Sons, Ltd.     

A class of digitally programmable nth‐order filters

A family of new high‐order filters capable of providing all filter functions without changing the circuit topology is proposed for integrated circuit applications. The proposed filters are based on simple active elements, namely, digitally controlled current amplifiers (DCCAs) and unity gain voltage buffers (VBs). Gains of DCCAs are digitally programmed to adjust the coefficients of transfer functions. R2R ladders are also utilized to increase the tuning flexibility of the proposed filters. A filter replicating the famous KHN biquad is extended to realize general nth‐order filters. Comparison with the recent works shows that the proposed approach results in more efficient realizations compared with its counterparts based on other current‐mode active elements. Experimental results obtained from a fourth‐order filter implemented using devices fabricated in a 0.35‐µm CMOS process are provided. Copyright © 2011 John Wiley & Sons, Ltd.     

Development of a high‐speed electromagnetic repulsion mechanism for high‐voltage vacuum circuit breakers

This paper presents a design and testing of a new high‐speed electromagnetic driving mechanism for a high‐voltage vacuum circuit breaker (VCB). This mechanism is based on a high‐speed electromagnetic repulsion and a permanent magnet spring (PMS). This PMS is introduced instead of the conventional disk spring due to its low spring energy and more suitable force characteristics for VCB application. The PMS has been optimally designed by the 3D nonlinear finite‐elements magnetic field analysis and investigated its internal friction and eddy‐current effect. Furthermore, we calculated the dynamic of this mechanism coupling with the electromagnetic field and circuit analysis, in order to satisfy the operating characteristics—contact velocity, response time, and so on, required for the high‐speed VCB. A prototype VCB, which was built based on the above analysis, shows sufficient operating performance. Finally, the short circuit interruption tests were carried out with this prototype breaker, and we have been able to verify its satisfying performance. © 2008 Wiley Periodicals, Inc. Electr Eng Jpn, 163(1): 34–40, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20398     

Mitigation of third‐harmonic voltage for three‐phase four‐wire distribution system based on a series active filter for neutral conductor

This paper proposes a series active filter for mitigation of the third‐harmonic voltage in a three‐phase four‐wire power distribution system in a building. The active filter which consists of a single‐phase inverter can suppress the harmonic voltage of the system. The active filter is characterized by acting not only as a capacitor but also as a resistor for the third‐harmonic components. A Hilbert transformer is applied to the controller of the active filter in order to realize accurate third‐harmonic detection on a single‐phase active filter. Measurement results of harmonic distortion of source voltage in a building is also shown in this paper. It is clarified in a simulation and experiment that the active filter can suppress the third‐harmonic voltage without increasing neutral conductor current. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 150(1): 62–70, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10379     

Reduction of neutral conductor current in a three‐phase four‐wire low‐voltage distribution line

In a low‐voltage distribution line in a three‐phase four‐wire system, the neutral conductor current is increased by a current consisting mainly of the third harmonic, which has no phase rotation if the balance of the load has been removed, when harmonic generation equipment is included in the load. The increase of this neutral conductor current increases the waveform distortion of the receiving end voltage, and various kinds of waveform interference occur. To reduce the neutral conductor current, insertion of an active filter for the third harmonic wave near the load has been proposed, and a protective effect against waveform interference has also been reported. In this paper, a method for drastically reducing the neutral conductor current by using LC resonance, which is simpler than an active filter, is proposed. © 2010 Wiley Periodicals, Inc. Electr Eng Jpn, 171(4): 19–27, 2010; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20897     

Large‐scale magnetic field analysis by the hybrid finite element‐boundary element method combined with the fast multipole method

This paper describes a large‐scale magnetic field analysis by means of the hybrid finite element‐boundary element (FE‐BE) method. The hybrid FE‐BE method is well‐suited for solving open electromagnetic field problems that comprise movement, nonlinear media, and eddy current. In general, however, large memory and computational costs are required due to the dense blocks in the system matrix generated by the BE part of the hybrid formulation. In order to overcome the above difficulties, we introduce the fast multipole method (FMM) to the hybrid FE‐BE formulation developed by ourselves. Furthermore, we propose a novel preconditioning technique suitable for the hybrid FE‐BE method with the FMM. Some numerical results that demonstrate the effectiveness of the proposed approach are also presented. ©2007 Wiley Periodicals, Inc. Electr Eng Jpn, 162(1): 73–80, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20508     

有限元–边界元耦合法在运动导体涡流场中的应用

基于A,φ-A法和库伦规范,推导了导体区域和非导体区域的有限元方程及自由空间的边界元方程,通过引入交界面条件,实现了将边界元矩阵等效为有限元矩阵求解的有限元-边界元耦合法(finite element and boundary element coupling method,FE-BECM)。将FE-BECM应用于TEAM-7问题的计算,验证了该方法处理开域涡流问题的有效性。当FE-BECM应用于运动导体涡流场(moving conductor eddy current,MCEC)问题时,用有限元离散源电流区域和运动部件,用边界元离散自由空间并关联相互独立的有限元区域。该方法克服了常规有限元法使用1套网格处理运动问题所遇到的麻烦。使用有限元-边界元耦合法对单级线圈炮问题进行了计算,验证了算法处理运动导体涡流场问题的有效性。     

复镜像法在平板导体涡流场计算中的应用

为了根据涡流检测中积分方程法(IEM)的理想裂缝模型,用矢量磁位推导出平板导体涡流场的并矢格林函数,将复镜像法用于涡流场并矢格林函数的计算,用Prony方法对矢量磁位中广义Sommerfeld积分(GSI)的被积函数进行指数逼近,使GSI转化为有限项级数之和,加速了无穷积分的计算,提高了涡流场的求解速度和计算精度。用涡流无损检测中的两组典型数据比较用复镜像法和直接数值积分法计算广义Sommerfeld积分的计算精度和求解速度,结果表明复镜像法在涡流场GSI积分计算中准确且高效。用复镜像法计算平板导体中含有平行裂缝和十字型裂缝的涡流场,其结果与有限元一边界元耦合法的计算结果对比表明求解方法正确和高效。     

Analysis of Eddy‐Current Losses in Solid Iron Under dc‐Biased Magnetization Considering Minor Hysteresis Loops

In designing solid‐pole synchronous machines, it is important to take into account the surface eddy‐current losses in the field pole cores. In this study, a solid‐iron ring specimen is adopted as an approximate model of solid‐pole surfaces in order to conduct a fundamental study of the surface losses. The influence of the minor hysteresis loops on the losses under dc‐biased magnetization is investigated. The losses in the ring under dc‐biased magnetization are measured and analyzed by finite element analysis (FEA). The losses computed by the FEA considering minor loops are nearly the same as those measured. In contrast, the eddy‐current losses computed by FEA without considering minor loops are considerably inaccurate because the incremental permeability is overestimated and the skin depth is underestimated. It is important to consider hysteresis for the accurate calculation of the surface eddy‐current losses under dc‐biased magnetization.