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This paper aims to propose an effective modeling method of dynamic hysteresis properties for soft magnetic composite (SMC) core using an equivalent circuit representation. Because the eddy currents flowing inside iron powder particles should be considered, it is well known that an accurate magnetic field analysis of the SMC core in a wide range of excitation frequency is not easy. To overcome this difficulty, a dynamic hysteresis modeling based on the standard Cauer circuit is investigated.

In the proposed method, the first inductance represents the static magnetic property of the SMC, and the latter part represents the dynamic effect because of the eddy currents. The values of the circuit elements were determined by an optimization method based on symmetric loops measured at several frequencies. To verify the validity of the proposed modeling method, finite-element analyses of a ring core inductor and an alternating current reactor were performed.

By comparing the simulated and measured magnetic properties, the necessity to consider magnetic hysteresis in the equivalent circuit model is clarified. Furthermore, the frequency-dependent inductances of practical reactors can be obtained from the finite-element analysis combined with the proposed method.

This paper demonstrates the significance of determining the circuit parameters in the equivalent circuit for dynamic hysteresis modeling based on the measured magnetic properties. The effectiveness of the proposed method is verified by comparing frequency-dependent inductances of two kinds of reactors between the simulation and measurement.

This paper aims to discuss the relationship between the continued fraction form of the analytical solution in the frequency domain, the orthogonal function expansion and their circuit realization to derive an efficient representation of the eddy-current field in the conducting sheet and wire/cylinder. Effective frequency ranges of representations are analytically derived.

The Cauer circuit representation is derived from the continued fraction form of analytical solution and from the orthogonal polynomial expansion. Simple circuit calculations give the upper frequency bounds where the truncated circuit and orthogonal expansion are applicable.

The Cauer circuit representation and the orthogonal polynomial expansions for the magnetic sheet in the E-mode and for the wire in the axial H-mode are derived. The upper frequency bound for the Cauer circuit is roughly proportional to N⁴ with N inductive elements, whereas the frequency bound for the finite element eddy-current analysis with uniform N elements is roughly proportional to N².

The Cauer circuit representation is expected to provide an efficient homogenization method because it requires only several elements to describe the eddy-current field over a wide frequency range.

The applicable frequency ranges are analytically derived depending on the conductor geometry and on the truncation types.

The purpose of this study is to develop a topological model of a three-phase, three-limb transformer for low-frequency transients. The processes in the core limbs and yokes are reproduced individually by means of a dynamic hysteresis model (DHM). A method of accounting for the transformer tank with vertical magnetic shunts at the tank walls is proposed and tested on a 120 MVA power transformer.

The model proposed has been implemented independently in a dedicated Fortran program and in the graphical pre-processor ATPDraw to the ATP version of the electromagnetic transient program.

It was found that the loss prediction in a wide range of terminal voltages can only be achieved using a DHM with variable excess field component. The zero sequence properties of the transformer can be accurately reproduced by a duality-derived model with Cauer circuits representing tank wall sections (belts).

In its present form, the model proposed is suitable for low-frequency studies. Its usage in the case when transformer capacitances are involved should be studied additionally.

The presented model can be used either as an independent tool or serve as a reference for subsequent simplifications.

The model proposed is aimed at meeting the needs of electrical engineering and ecology-minded customers.

Till date, there were no experimental data on zero-sequence behavior of three-phase, three-limb transformer with vertical magnetic shunts, so no verified transient model existed. The model proposed is probably the first that matched this behavior and reproduced measured no-load losses for a wide voltage range.

The Cauer ladder network (CLN) model order reduction (MOR) method is applied to an industrial inductor. This paper aims to to anaylse the influence of different meshes on the CLN method and their parameters.

The industrial inductor is simulated with the CLN method for different meshes. Meshes considering skin effect are compared with equidistant meshes. The inductor is also simulated with the eddy current finite element method (ECFEM) for frequencies 1 kHz to 1 MHz. The solution of the CLN method is compared with the ECFEM solutions for the current density in the conductor and the total impedance.

The increase of resistance resulting from the skin effect can be modelled with the CLN method, using a uniform mesh with elements much larger than the skin depth. Meshes taking account of the skin depth are only needed if the electromagnetic fields have to be reconstructed. Additionally, the convergence of the impedance is used to define a stopping criterion without the need for a benchmark solution.

The work shows that the CLN method can generate a network, which is capable of mimicking the increase of resistance usually accompanied by the skin effect without using a mesh that takes the skin depth into account. In addition, the proposed stopping criterion makes it possible to use the CLN method as an a priori MOR technique.

The authors derive a nonlinear MOR based on the Cauer ladder network (CLN) representation, which serves as an application of the parameterized MOR. Two parametrized CLN representations were developed to handle the nonlinear magnetic field. Simulations using the parameterized CLN were also conducted using an iron-cored inductor model under the first-order approximation.

This work studies the effect of parameter variations on reduced systems and aims at developing a general formulation for parametrized model order reduction (MOR) methods with the dynamical transition of parameterized state.

Terms including time derivatives of basis vectors appear in nonlinear state equations, in addition to the linear network equations of the CLN method. The terms are newly derived by an exact formulation of the parameterized CLN and are named parameter variation terms in this study. According to the simulation results, the parameter variation terms play a significant role in the nonlinear state equations when reluctivity is used, while they can be neglected when differential reluctivity is used.

The computational time of nonlinear transient analyses can be greatly reduced by applying the parameterized CLN when the number of time steps is large.

The authors introduced a general representation for the dynamical behavior of the reduced system with time-varying parameters, which has not been theoretically discussed in previous studies. The effect of the parameter variations is numerically given as a form of parameter variation terms by the exact derivation of the nonlinear state equations. The influence of parameter variation terms was confirmed by simulation.

For efficient magnetic field calculations in electrical machines, the hysteresis and losses in laminated electrical steel must be modeled in a simple and reliable way. The purpose of this paper is to investigate and discuss the potential of a simple complex‐permeability model.

A frequency dependent complex‐permeability model as well as a more detailed model (describing hysteresis, classical eddy current effects, and excess losses separately) are compared to single‐sheet measurements on laminated electrical steel. It is discussed under which circumstances the simple complex‐μ model is an adequate substitute for the more detailed model.

A satisfactory agreement of the simple complex‐μ model was found with both detailed model and measurements, improving with increasing frequencies. This is true not only for the effective permeability function, but holds also for the detailed H‐B characteristics (hysteresis).

It is demonstrated that the complex‐μ model is a reliable and convenient starting point for the estimation of flux distribution and losses in complicated magnetic core geometries.

The purpose of this paper is to introduce a new method to model a stranded wire efficiently in 3D finite element simulations.

In this method, the stranded wires are numerically approximated with the Cauer ladder network (CLN) model order reduction method in 2D. This approximates the eddy current effect such as the skin and proximity effect for the whole wire. This is then projected to a mesh which does not include each strand. The 3D fields are efficiently calculated with the CLN method and are projected in the 3D geometry to be used in simulations of electrical components with a current vector potential and a homogenized conductivity at each time step.

In applications where the stranded wire geometry is known and does not change, this homogenization approach is an efficient and accurate method, which can be used with any stranded wire configuration, homogenized stranded wire mesh and any input signal dependent on time steps or frequencies.

In comparison to other methods, this method has no direct frequency dependency, which makes the method usable in the time domain for an arbitrary input signal. The CLN can also be used to interconnected stranded cables arbitrarily in electrical components.

Quantitative reliability analysis can effectively identify the time the driving system needs to be maintained. Then, the potential safety problems can be found, and some catastrophic failures can be effectively prevented. Therefore, this paper aims to evaluate the reliability of the switched reluctance generator (SRG) driving system.

In this paper, a method considering different thermal stresses and fault tolerance capacity is proposed to analyze the reliability of an SRG. A full-bridge power converter (FBPC) instead of the asymmetric half-bridge power converter (AHBPC) is adopted to drive the SRG system. First, the primary fault modes of the SRG system are introduced, and a fault criterion is proposed to determine whether the system fails. Second, the thermal circuit model of the converter is established to quickly and accurately obtain the junction temperature of the devices. At last, the Markov models of different levels are established to evaluate the reliability of the system.

The results show that the two-level Markov model is the most suitable when compared to the static model and the one-level Markov model.

The driving system of SRG will be more reliable after the reliability of the system is evaluated by the Markov model. At the same time, an FBPC is adopted to drive the SRG. The FBPCs have the advantages of fewer switching devices, higher integration and lower cost. The proposed driving strategy of the FBPC avoids the current reversal and the generation of dead zone time, which has the advantage of reliable operation. In addition, a precise thermal circuit model of the FBPC is proposed, and the junction temperature of each device can be obtained, respectively.

Different axiomatizations of network theory are considered. Kirchhoff networks are regarded with priority. Multipole and multiport networks are introduced as alternative variants. Additionally, Minty and Paynter networks, which are always dualizable are discussed briefly. The latter are special cases of Kirchhoff as well as of multiport networks. This paper seeks to discuss these issues.

The paper develops network theory inside of set theory, i.e. networks, multipoles, etc. are defined as objects of set theory. As such objects we use preferably ordered pairs, ordered triples, etc. The objects of network theory are then separated from the class of all these set theoretical objects by means of some defining conditions. These conditions are the axioms of our approaches to network theory.

It is shown that all presented variants of axiomatizations can be developed on the basis of a uniform representation for the time functions for voltages and currents. All these variants allow interdisciplinary applications of network theory and they can be generalized to multidimensional networks. An interesting byproduct is the relationship between multiport networks, networks in Belevitch normal form, Paynter networks, and bond graphs.

For applications it is essential that Kirchhoff and multipole networks are with respect to their modeling capability of equal value. But from the foundational point of view the multipole terminology has a number of crucial disadvantages compared with that based on Kirchhoff networks. This fact is important both for the conception of circuit simulation software packages and for the development of basic circuit theory curricula.

Thermal behavior of light-emitting diode (LED) device under different operating conditions must be known to enhance its reliability and efficiency in various applications. The purpose of this study is to report the influence of input current and ambient temperature on thermal resistance of InGaAlP low-power surface-mount device (SMD) LED.

Thermal parameters of the LED were measured using thermal transient measurement via Thermal Transient Tester (T3Ster). The experimental results were validated using computational fluid dynamics (CFD) software.

As input current increases from 50 to 90 mA at 25°C, the relative increase in LED package (ΔR_thJS) and total thermal resistance (ΔR_thJA) is about 10 and 4 per cent, respectively. In addition, at 50 mA and ambient temperature from 25 to 65°C, the ΔR_thJS and ΔR_thJA are roughly 28 and 22 per cent, respectively. A good agreement between simulation and experiment results of junction temperature.

Most of previous studies have focused on thermal management of high-power LEDs. There were no studies on thermal analysis of low-power SMD LED so far. This work will help in predicting the thermal performance of low-power LEDs in solid-state lighting applications.