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This paper aims to give a perspective about the variety of techniques which are available and are being further developed in the area of coupled field formulations, with selective bibliography and practical examples, to help postgraduate students, researchers and designers working in design or analysis of electrical machinery.

This paper reviews the recent trends in coupled field formulations. The use of these formulations for designing and non‐destructive testing of electrical machinery is described, followed by their classifications, solutions and applications. Their advantages and shortcomings are discussed.

The paper gives an overview of research, development and applications of coupled field formulations for electrical machinery based on more than 160 references. All landmark papers are classified. Practical engineering case studies are given which illustrate wide applicability of coupled field formulations.

Problems which continue to pose challenges to researchers are enumerated and the advantages of using the coupled‐field formulation are pointed out.

This paper gives a detailed description of the application of the coupled field formulation method to the analysis of problems that are present in different electrical machines. Examples of analysis of generators and transformers with this formulation are presented. The application examples give guidelines for its use in other analyses.

The coupled‐field formulation is used in the analysis of rotational machines and transformers where reference data are available and comparisons with other methods are performed and the advantages are justified. This paper serves as a guide for the ongoing research on coupled problems in electrical machinery.

The paper aims to propose a a field-circuit method for investigating the magnetic behavior of a wireless power transfer system (WPTS) for the charge of batteries of electric vehicles. In particular, a 3D model for finite element analysis (FEA) for the field simulation of a WPTS is developed. Specifically, the effects of aluminum shield and steel layer, representing the car frame, on the self and mutual inductances are investigated. An equivalent electric circuit is then built, and the relevant lumped parameters are identified by means of the FEAs.

The finite element model is used to evaluate self and mutual inductances in several transmitting-receiving coil configurations and relative positions. In particular, the FEA simulates the aluminum and steel layers as shell elements in a 3D domain. The self and mutual inductance values in the aligned coil case are also used as input parameters in a circuit model to evaluate the onload current.

The use of shell elements in FEA substantially reduces the number of mesh elements needed to simulate the eddy currents in the steel and aluminum layer, so putting the ground for low-cost field analysis. Moreover, the FEA gives an accurate computation of the self and mutual inductance to be used in a circuit model, which, in turn, provides a fast update of the onload induced current.

To save computational time, the use of 2D shell elements to model thin conductive regions introduces a simplified FEA that could be used in the WPTS simulation. Moreover, the dynamic behavior of WPTS, i.e. the operation when the receiving coil is moving with respect to the transmitting one, is considered. Because of the lumped parameters’ dependence upon the relative positions of the two coils, the proposed method allows identifying the circuit parameters for several configurations so substantially reducing the computational burden.

This paper aims to develop high-pass (HP) negative group delay (NGD) investigation based on three-port lumped circuit. The main particularity of the proposed three-port passive topology is the consideration of only a single circuit element represented by a capacitor.

The methodology of the paper is to consider the S-matrix equivalent model derived from admittance matrix approach. So, an S-matrix equivalent model of a three-port circuit topology is established from admittance matrix approach. The frequency-dependent basic expressions are explored to perform the HP-NGD analysis. Then, the existence condition of HP-NGD function type is analytically demonstrated. The specific characteristics and synthesis equations of HP-NGD circuit with respect to the desired optimal NGD value are established.

After computing the frequency expressions to perform the HP-NGD analysis, this study demonstrated the existence condition of HP-NGD function type analytically. The validity of the HP-NGD theory is verified by a prototype of three-port circuit. The proof-of-concept (POC) single capacitor three-port circuit presents an NGD response and characteristics from analytical calculation and simulation is in very good correlation.

An innovative theory of HP-NGD three-port circuit is studied. The proposed HP-NGD topology is constituted by only a single capacitor. After the topological description, the S-matrix model is established from the Y-matrix by means of Kirchhoff voltage law and Kirchhoff current law equations. A POC of single capacitor three-port circuit was designed and simulated with a commercial tool. Then, a prototype with a surface-mounted device component was fabricated and tested. As expected, simulation and measurement results in very good agreement with the calculated model show the feasibility of the HP-NGD behavior. This work is compared to other NGD-type function with diverse number of ports and components.

This paper aims to present an accurate magnetic equivalent circuit for modeling the cylindrical electromagnet so that by analyzing it, the magnetic flux density in different parts of the electromagnet, as well as its lifting force, can be calculated.

The structure of the electromagnet is divided into parts that can be modeled by lumped element parameters. Mathematical equations for calculating these elements are presented and proved. The axial symmetry of the cylindrical electromagnet made it possible to use planar circuits for its modeling. To increase the accuracy of the proposed equivalent circuit, attention has been paid to the leakage flux as well as the nonlinear behavior of the ferromagnetic core. Also, the curvature of the magnetic flux path is considered in the calculation of the corner permeances of the core.

The magnetic flux density in different parts of the electromagnet was calculated using nodal analysis of the circuit and compared to the results of the finite element method. Also, a test bed was established to measure the lifting force of the electromagnet. Comparing the results shows a difference of less than 3% which indicate the good accuracy of the proposed circuit. In addition, due to the curvature of the flux path, there is a no-flux region in the center of the disk, the extent of which depends on the thickness of the disk and the diameter of the middle leg.

Magnetic equivalent circuit is a new contribution to analyze the cylindrical electromagnet and calculate its lifting force with good accuracy. The circuit lumped elements can be quickly calculated using mathematical equations and software such as MATLAB according to the actual path of the magnetic flux. Compared to other methods, the proposed circuit analyzes the electromagnet in a shorter period of time. This is the most important advantage of the proposed circuit model.

The purpose of this paper is to optimize the performance of direct methanol fuel cells for portable applications by combining a non‐linear, fully coupled circuit model and a stochastic optimization procedure.

A novel non‐linear equivalent circuit that accounts for electrochemical reactions and charge generation inside catalyst layers, electronic and protonic conduction, methanol crossover through the membrane, mass transport of reactants inside diffusion layers is presented. The discharge dynamic of the fuel cell, depending on the initial methanol concentration and on the load profile, is modelled by using the mass conservation equation. The equivalent circuit is interfaced to a stochastic optimization procedure in order to maximize the battery duration while minimizing fuel crossover.

In the proposed circuit scheme, unlike semi‐empirical models, lumped circuit parameters are derived directly from mass transport and electric equations in order to fully describe the dynamic performance of the fuel cell. Physical and geometrical parameters are optimized in order to improve the system runtime. It is shown that a combined use of fuel cells and lithium batteries can improve the runtime of portable electronic devices compared to traditional supply systems based on lithium batteries only.

The one‐dimensional model of the micro fuel cell does not take into account possible transverse mass and electric charge flows in the fuel cell layers; most of the geometric and physics model parameters cannot be estimated from direct in situ or ex situ measurements.

Direct methanol fuel cells are nowadays a promising technology for replacing or complementing lithium batteries due to their high energy density. Most limiting features of direct methanol fuel cells are the fuel crossover and its slow oxidation kinetics. By using the proposed approach, fuel cell parameters can be optimized in order to enhance the discharge runtime and to reduce the methanol crossover.

The equivalent circuit model with optimized lumped non‐linear parameters can be used when designing power management units for portable electronic devices.

The purpose of this paper is to present a method for computing voltage spikes endured by the insulation of the first coils of high-temperature (HT°) synchronous machines fed by PWM inverters that deliver fast-fronted voltage pulses.

The transient state following each steep edge is computed by SPICE using the global high-frequency (HF) equivalent circuit of the motor winding. This equivalent circuit is automatically built using the proposed elementary coil model. Two inorganic HT° technologies are compared: the first one uses a round copper wire insulated by a thin ceramic layer and the second one is made with an anodized aluminum strip.

The winding made with an anodized aluminum strip, which has a higher turn-to-turn capacitance, yields a better voltage distribution between coils of the machine.

The elementary coil equivalent circuit is computed from impedance measurements performed on an elementary coil. Another starting point could be developed with an FE analysis to determine the parameters of the HF equivalent circuit, which would avoid the need for a prototype coil before the machine design.

For inorganic motors, the insulation layers have poorer electrical characteristics compared with standard organic ones. Therefore, the computation of voltage spikes distribution along the coils of each phase represents a major issue in the design of HT° machines.

The presented approach is a step toward the design of HT° (400-500°C) actuators fed by PWM inverters based on fast SiC electronic switches.

The purpose of this paper is to simulate passive proton exchange membrane fuel cells (PEMFCs) for portable electronic devices by means of a non‐linear lumped circuit based on electrical, mass transfer and electro‐kinetic equations.

Electrical, mass transfer and electro‐kinetic equations are combined in order to derive a non‐linear lumped circuit. The dynamic circuit model is tested in realistic operating conditions.

An original equivalent circuit model for simulating the transient behavior of passive PEMFCs is proposed. The PEMFC is represented as a non‐linear equivalent circuit with controlled lumped parameters depending on pressure, temperature, hydration, and system capacity.

Lumped parameters are synthesized assuming a one‐dimensional fuel cell model since layer thicknesses are much smaller than other dimensions. Heat generation and transfer are not modeled even though lumped parameters depend on temperature.

The proposed circuit model can be implemented directly in circuit simulators for designing power management units needed to interface small‐passive PEMFCs and portable electronics such as PDAs, laptops, or mobile phones.

The fuel cell is represented as a non‐linear controlled generator whose parameters are derived directly from multiphysics equations rather than empirical relationships. The dynamic behaviour of PEMFCs can be simulated on completely different times scales, i.e. during transients or during the discharge phase.

The need to optimize and simulate lithium-ion cells is of high importance to their durability. It is possible to use semi-empirical models based on equivalent circuits to model the dynamic behavior. Still, parameter identification is a time consuming task if many equivalent circuits are coupled into a finite element-based simulation. The paper aims to discuss these issues.

In this paper the authors present an approach to estimate parameters in a very efficient way by using a single equivalent circuit model as a surrogate model on measurement data. The results of the surrogate model are periodically linked back to the original complex model via the so called space mapping method. The authors validate the approach and compare it to the original problem.

As a remarkable result, the authors report the achieved reduction of computational cost by approximately 87 percent, which equals a speed up factor of 8.

To the best of the authors’ knowledge, using high and low fidelity semi-empirical models combined with space mapping is new in the field of electrical modeling of lithium-ion cells. This approach saves much time in parameterization of coupled models while maintaining high quality results for geometrical and thermal optimization of lithium-ion cells.

The purpose of this paper is to pursue two following main goals: first, theorizing a new concept named as equivalent bus load in order to make a promising simplification over power system analysis. Second, proposing an outstanding fast and simple approach based on introduced concept for voltage estimation after multiple component outages while satisfying required accuracy.

Equivalent load bus theory introduces three transfer matrices that describe power system topology. Mentioned matrices could be calculated simply after system reconfiguration without matrix inversion. Using transfer matrices a large-scale power system can be modeled by a simple two-bus power system from the viewpoint of any desired bus so that load flow calculation leads to same value. The analysis of simplified power system yields to extract a new incremental model based on equivalent bus load theory that will be distinguished as an outstanding fast method for voltage estimation aim.

A deep study for fast voltage estimation aim is dedicated to evaluate proposed method from the accuracy and quickness point of view and the outcomes are compared to a well-known method as Distribution Factors (DF). Results and computational times unveil that presented approach is more accurate and much faster.

A novel and new fast voltage estimation method for assessment of power system component outages is introduced.

The purpose of this paper is to offer a fast and accurate simulation method for printed spiral radio frequency identification coils and to extract the parameters of an equivalent resonance circuit.

The frequency‐dependent port impedance of a rectangular spiral multi‐turn antenna is simulated with the non‐retarded partial element equivalent circuit (PEEC) method. The discretization settings needed for an accurate modeling of skin and proximity effects at medium frequencies as well as parasitic capacitances are discussed. Two different PEEC approaches are used, a magneto‐quasi‐static (resistive and inductive cells) model and a non‐retarded (capacitive cells included) model in order to extract a reduced equivalent resonance circuit which is beneficial to describe the inductive coupling to further inductors via the transformer concept.

With optimized mesh settings, the extremely fast simulation can be carried out just in seconds whereas the results compared to a computationally much more expensive CST Microwave Studio^® reference solution as well as an analytical direct current solution show errors of only about a few percent.

The methodology is limited to frequencies up to the first self‐resonant frequency of the coil. In addition, piecewise‐homogeneous materials are implied.

Specialized mesh settings allow for a very fast and accurate simulation of rectangular spiral inductors. A method for the parameter extraction of a resonance circuit is proposed by evaluating two different PEEC models.