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An appropriate equivalent model is the key to the effective analysis of the system and structure in which permanent magnet takes part. At present, there are several equivalent models for calculating the interacting magnetic force between permanent magnets including magnetizing current, magnetic charge and magnetic dipole–dipole model. How to choose the most appropriate and efficient model still needs further discussion.

This paper chooses cuboid, cylindrical and spherical permanent magnets as calculating objects to investigate the detailed calculation procedures based on three equivalent models, magnetizing current, magnetic charge and magnetic dipole–dipole model. By comparing the accuracies of those models with experiment measurement, the applicability of three equivalent models for describing permanent magnets with different shapes is analyzed.

Similar calculation accuracies of the equivalent magnetizing current model and magnetic charge model are verified by comparison between simulation and experiment results. However, the magnetic dipole–dipole model can only accurately calculate for spherical magnet instead of other nonellipsoid magnets, because dipole model cannot describe the specific characteristics of magnet's shape, only sphere can be treated as the topological form of a dipole, namely a filled dot.

This work provides reference basis for choosing a proper model to calculate magnetic force in the design of electromechanical structures with permanent magnets. The applicability of different equivalent models describing permanent magnets with different shapes is discussed and the equivalence between the models is also analyzed.

The purpose of this paper is to propose a method to estimate the magnetic saturation and end effect of linear switched reluctance machines (LSRMs) with fully pitched winding configuration used in the wave energy conversion.

The magnetic saturation and strong coupling make it very difficult to derive a comprehensive mathematical model for the behavior of the LSRMs. Meanwhile, the various end effects could not be comprehensively considered in the two‐dimensional model which is widely studied. Therefore, the magnetic equivalent circuit model including the three‐dimensional (3‐D) effects is presented in this paper and 3‐D finite element analysis (FEA) is used to validate the mathematical model.

The results from 3‐D FEA are in good agreement with the numerical simulation, which validates the accuracy of the magnetic equivalent circuit modeling method.

This technique helps one to know the influence exerted by the magnet saturation and end effect of LSRMs and provides a powerful computer‐aided analysis tool. Meanwhile, this modeling method supplies accurate values for the following study of reliable control algorithm.

The paper presents a magnetic equivalent method to estimate the magnetic saturation and end effect of LSRMs with fully pitched winding configuration used in the wave energy conversion.

This paper aims to present a new iterative procedure for the 3D representation of focusing magnetic fields in TWTs generated by PPMs, by using equivalent sources and optimisation algorithms.

In the integrated optimisation strategy general models for magnetic sources are employed and local and global inverse problems are iteratively solved for the minimization of the representation error.

The results obtained show that the target accuracy is reached with a low computational effort, employing a minimum number of equivalent sources.

The procedure is robust and converges for all the examined magnetic field configurations.

Different from other approaches, the procedure presented here can be directly applied to a variety of different models for magnetic sources.

Multiphysical models are often useful for the design of electrical devices such as electrical machines. In this way, the modeling of thermal, magnetic and electrical phenomena by using an equivalent circuit approach is often used in sizing problems. The coupling of such models with other models is difficult to take into account, partly because it adds complexity to the process. The paper proposes an automatic modelling of thermal and magnetic aspects from an equivalent circuit approach, with its computation of gradients, using selectivity on the variables. Then, it discusses the coupling of various physical models, for the sizing by optimization algorithms. Sensibility analyses are discussed and the multiphysical approach is applied on a permanent magnet synchronous machine.

The paper allows one to describe thermal and magnetic models by equivalent circuits. Magnetic aspects are represented by reluctance networks and thermal aspects by thermal equivalent circuits. From circuit modelling and analytical equations, models are generated, coupled and translated into computational codes (Java, C), including the computation of their jacobians. To do so, model generators are used: CADES, Reluctool, Thermotool. The paper illustrates the modelling and automatic programming aspects with Thermotool. The generated codes are directly available for optimization algorithms. Then, the formulation of the coupling with other models is studied in the case of a multiphysical sizing by optimization of the Toyota PRIUS electrical motor.

A main specificity of the approach is the ability to easily deal with the selectivity of the inputs and outputs of the generated model according to the problem specifications, thus reducing drastically the size of the jacobian matrix and the computational complexity. Another specificity is the coupling of the models using analytical equations, possibly implicit equations.

At the present time, the multiphysical modeling is considered only for static phenomena. However, this limit is not important for numerous sizing applications.

The analytical approach with the selectivity gives fast models, well-adapted for optimization. The use of model generators allows robust programming of the models and their jacobians. The automatic calculation of the gradients allows the use of determinist algorithms, such as SQP, well adapted to deal with numerous constraints.

Despite its well-founded criticism and lack of proper justification under core saturation conditions, the T-equivalent transformer model (Steinmetz scheme) is obviously championing in the literature. This educational paper aims to explain in a simple manner the limitations of the T-model of a low-frequency transformer and critically analyses some attempts to improve it.

Using a simplified examination of magnetic fluxes in the core and windings and using the modeling in ATPDraw, it is shown that transient transformer models with the indivisible leakage inductance allow circumventing the drawbacks of the T-model.

The authors show the absence of valid grounds for subdividing the leakage inductance of a transformer between its primary and secondary windings. The connection between the use of individual leakage inductances and inaccurate prediction of inrush current peaks is outlined as an important example.

The presented models can be used either as independent tools or serve as a reference for subsequent developments.

Over generations, the habitual transformer T-equivalent is widely used by engineers and Electromagnetic Transients Program experts with no attention to its inadequacy under core saturation conditions. Having studied typical winding configurations, the authors have shown that neither of them has any relation to the T-equivalent.

This educational paper will contribute to the correct understanding of the transients occurring in a transformer under abnormal conditions such as inrush current or ferroresonance events, as well as during an out-of-phase synchronization of step-up generator transformers.

This paper aims to present a novel energy-efficient saturated open-core fault current limiter (FCL) with special permanent magnet (PM) modules.

The special PM modules are used to drive the cores of FCL into a saturated state from different directions in the normal operation condition, reducing the DC current of the saturated open-core FCL. An equivalent magnetic circuit model of the saturated open-core FCL with PM modules is built to calculate the magnetic flux density in the cores of FCL. By applying the modified nodal approach on the circuit, the nonlinear equations of the magnetic circuit can be achieved. The Newton – Raphson method is used to solve the nonlinear equations. The model shows good accuracy verified by finite element simulation and a physical experiment.

Compared with the original saturated open-core FCL structure with PMs, the novel saturated open-core FCL structure can save 84% DC power. The physical experiment results show that the saturated open-core FCL has a good performance on limiting the fault current.

A novel saturated open-core FCL structure with PM modules is proposed in this paper. A physical model of the saturated open-core FCL structure with PM modules is manufactured and tested. About 84% DC power can be reduced by using the PM modules in this saturated open-core FCL, and it can save most of the cost of the saturated open-core FCL.

This paper deals with the modelling of transformer supply in the two‐dimensional (2D) finite element (FE) simulation of rotating electrical machines. Three different transformer models are compared. The reference one is based on two 2D FE models, considering a cross‐section either parallel or perpendicular to the laminations of the magnetic core. The parameters of the two other transformer models, a magnetic equivalent circuit and an electrical equivalent circuit, can be derived from the reference model. Particular attention is paid to some common features of the transformer models, e.g. with regard to the inclusion of iron losses. The three models are used in the 2D FE simulation of the steady‐state load operation and the starting from stand‐still of an induction motor.

The purpose of this paper is to propose a saturable model based on the magnetic equivalent circuit (MEC) for evaluating the electromagnetic performance of the variable area resolver.

The equivalent circuit is developed where three different reluctance types are used to calculate permeances based on geometrical approximations. The proposed model typically has two types of equations, including the magnetic and electrical equations. The magnetic and electrical equations are related to the resolver core and the windings, respectively. Applying the well-known trapezoidal method, the magnetic and electrical equations can be simultaneously solved. A nonlinearity of the magnetic equations, the algebraic equations system, which is obtained from Kirchhoff’s laws, should be solved by the Newton-Raphson technique in each step-time.

The flexible MEC model, in which the number of flux tubes in different parts of the resolver can be arbitrarily selected, is proposed to analyze the variable reluctance resolver. Besides, the design parameters such as geometrical dimensions, windings arrangement and a number of the rotor saliencies can be chosen as desired. To consider the effect of time harmonics, a new nonlinear function is used for the core magnetization. Furthermore, different winding layouts can be implemented in the model to take space harmonics into account. The model obtained results are compared with the finite element method in terms of accuracy and simulation time.

Generally, the accuracy of the predictions in the MEC method is dependent on the number of flux tubes; therefore, the flexibility of the proposed MEC model in its capability to choose the desired number of flux paths is the advantage of this work. Moreover, the proposed model can analyze both wound and saliency rotor resolvers by changing the design parameters.

This paper aims to present a modified MEC algorithm for demagnetization modeling of the PM motor. One of the major issues that the designers of the permanent magnet (PM) motors are faced with is the demagnetization of magnets because of high temperatures and armature reaction. Demagnetization will weaken the magnetic properties of the magnet and lead to a reduction in the performance of the motor. Therefore, it is essential to provide appropriate methods for modeling this phenomenon. One of these methods that has a compromise between accuracy and time consumption is the magnetic equivalent circuit (MEC). In this paper, the MEC method is used for modeling the demagnetization phenomenon for the newly introduced ring winding axial flux PM (RWAFPM) motor. The proposed algorithm can take the demagnetization into account through a time-stepping model and also correct the value of the knee point flux density.

The modified MEC method is used for demagnetization modeling. The modified algorithm can take into account demagnetization and also renew the knee point at each step to increase the accuracy of the modeling. In addition, the proposed algorithm has a very high and fast execution speed so that the computation time of the MEC algorithm compared to the FEM model is reduced from 3 h to 35 s. In this case, the simulations have been performed on a core i5@ 2.3 GHz/8GB computer. The FEM model is used to verify the validity of the MEC results.

The obtained results show that at the high temperature, RWAFPM motor is severely vulnerable to demagnetization. At the temperature of 140°C, the demagnetization rate of 35% has occurred. So, it is necessary to use the high-temperature magnet in this motor or modify the motor structure in terms of demagnetization tolerant capability.

The RWAFPM motor is introduced for use in ship propulsion and traction systems. For this reason, an accurate estimation of demagnetization tolerant of this motor in different working conditions can show the strengths and weaknesses of this structure.

The purpose of this paper is to propose a two-dimensional (2-D) hybrid analytical model (HAM) in polar coordinates, combining a 2-D exact subdomain (SD) technique and magnetic equivalent circuit (MEC), for the magnetic field calculation in electrical machines at no-load and on-load conditions.

In this paper, the proposed technique is applied to dual-rotor permanent magnet (PM) synchronous machines. The magnetic field is computed by coupling an exact analytical model (AM), based on the formal resolution of Maxwell’s equations applied in subdomains, in regions at unitary relative permeability with a MEC, using a nodal-mesh formulation (i.e. Kirchhoff's current law), in ferromagnetic regions. The AM and MEC are connected in both directions (i.e. r- and theta-edges) of the (non-)periodicity direction (i.e. in the interface between teeth regions and all its adjacent regions as slots and/or air-gap). To provide accurate solutions, the current density distribution in slot regions is modeled by using Maxwell’s equations instead to MEC and characterized by an equivalent magnetomotive force (MMF) located in the slots, teeth and yoke.

It is found that whatever the iron core relative permeability, the developed HAM gives accurate results for both no-load and on-load conditions. Finite element analysis demonstrates the excellent results of the developed technique.

The main objective of this paper is to achieve a direct coupling between the AM and MEC in both directions (i.e. r- and theta-edges). The current density distribution is modeled by using Maxwell’s equations instead to MEC and characterized by an MMF.