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Rotor shape optimization is crucial in designing synchronous reluctance machines (SynRMs) because the machine performance is directly proportional to the rotor’s magnetic saliency ratio. The rotor geometry in synchronous reluctance machines is complex, and many geometrical parameters must be optimized. When fluid flux-barrier geometry is desirable, using analytic equations to prepare the rotor geometry for finite element analysis could be tedious. This paper aims to provide a robust numerical procedure to draw the fluid flux-barrier geometry in transversally laminated radial flux inner and outer rotor SynRMs by directly solving the magnetic vector potential equation using the finite difference method..

In this paper, the goal is to have a robust procedure for drawing the rotor geometry for an arbitrary number of slots (Ns), poles (p) and flux-barrier layers (Nfb). Therefore, this paper targeted several combinations to investigate the performance of the proposed algorithm. The MATLAB software is used to implement the proposed algorithm. The ANSYS Maxwell software is used for counterpart finite element simulation to check the correctness of the results derived by the proposed method.

Several inner and outer rotor SynRMs considering a different number of poles and a different number of flux-barrier layers per pole are studied to investigate the performance of the proposed algorithm. Results corresponding to each case are presented, and it is shown that the method is robust, flexible and fast enough, which could be used for the generation of the rotor geometry for the finite element analysis effectively.

The value of the proposed algorithm is its simplicity and straightforwardness in its implementation for the preparation of the rotor geometry with the desired fluid flux-barrier layer curvature resolution suitable for the finite element analysis. The procedure presented in this paper is based on the ideal magnetic loading concept, and in future works, a similar idea could be used for linear and axial flux SynRMs.

An algorithm for simultaneous solution of equations describing transient 3D magnetic field coupled to the Kirchhoff’s equations and the equation of motion has been presented. The nonlinearity and anisotropy of the magnetic core have been taken into account. Numerical implementation of the algorithm is based on the finite element method. In order to solve the 3D problem a special iterative procedure, in which the 3D task is substituted with a sequence of 2D problems, has been proposed. The time‐stepping backward difference algorithm for the time‐discretization of the electric circuit equations has been applied. To determine the moving armature position, an implicit procedure, which is unconditionally stable has been proposed. For the sake of example, the calculations of dynamic operation of the E‐type electromagnetic actuator equipped with the shading coil have been performed.

The purpose of this paper is to apply the method of separation of variables to obtain the current distribution in the slot of an electrical machine, taking into account the skin effect.

A slot in an electrical machine, filled with a solid conductor, and fed with an externally imposed density current, presents a current distribution that depends on the skin effect. The magnetic potential vector is formulated and solved using a separate representation as a finite sum of unidimensional (space and time) functions, taking into account the boundary conditions. The proposed method obtains the transient and permanent distribution of the current in the interior of the slot, both in transient and steady regime, and the results at the end of the transient are compared with the analytic ones in permanent regime.

The magnetic potential vector in the interior of a slot filled with a solid conductor can be expressed as a finite sum of just 16 modes, which capture the evolution of the field during the transient and permanent regime. These modes are expressed as the product of space and time functions, which have been obtained automatically by the separation of variables algorithm. Instead of solving multiple field problems, one for each time instant, the proposed method just solves two single‐variable differential equations, one in the time domain and other in the spatial one.

The application of the proposed method to non‐sinusoidal currents, such as those generated by variable speed‐drives, would allow to compute the field taking into account both the very small time scale of the pulse width modulation pulses, in the range of kiloHz, and the wide time scale of the currents envelope, in the range of 0‐100 Hz. Extension to 2D and 3D spatial configurations is also under consideration.

Using the method of separation of variables to solve electromagnetic problems provides a new method which can simplify and speed up the computation of transient fields in multidimensional time and space domains.

This paper deals with a coupled field‐circuit simulation of transients in a three‐phase, three‐limb power transformer taking non‐linearity into consideration. A comparative analysis of the results obtained from the application of 3D and 2D field models has been carried out. Owing to core saturation and the non‐periodic components of the magnetic fluxes, the magnetic field exists also within the space surrounding the core. Hence, three‐dimensional description is necessary. It has been proved that assuming the 2D model significantly overstated peak values of currents are obtained.

An algorithm for the simultaneous solving of the equations of the 3D transient electromagnetic field and equations of electric circuits of an electromagnetic device containing moving conducting parts has been elaborated. The A‐T formulation has been applied to the description of 3D eddy current problem. In order to solve the 3D problem, the iterative procedure, in which the 3D task is substituted with a sequence of 2D problems, has been applied. Different procedures for movement modelling have been considered. As an example, the dynamics of a linear induction motor have been investigated.

Paper presents an effective iterative method for 3D magnetic field calculation taking the nonlinearity and anisotropy of the material into account. Algorithm for simulation of coupled 3D field‐circuit transient problems has been also elaborated. Some steady‐state and transient characteristics of the E‐core electromagnet and shell‐type transformer have been calculated.

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.

Rectangular conductors play an important role in planar transmission line structures, multiconductor transmission lines, in power transmission and distribution systems, LCL filters, transformers, industrial busbars, MEMs devices, among many others. The precise determination of the inductance of such conductors is necessary for their design and optimization, but no explicit solution for the AC resistance and internal inductances per-unit length of a linear conductor with a rectangular cross-section has been found, so numerical methods must be used. The purpose of this paper is to introduce the use of a novel numerical technique, the proper generalized decomposition (PGD), for the calculation of DC and AC internal inductances of rectangular conductors.

The PGD approach is used to obtain numerically the internal inductance of a conductor with circular cross-section and with rectangular cross-section, both under DC and AC conditions, using a separated representation of the magnetic vector potential in a 2D domain. The results are compared with the analytical and approximate expressions available in the technical literature, with an excellent concordance.

The PGD uses simple one-dimensional meshes, one per dimension, so the use of computational resources is very low, and the simulation speed is very high. Besides, the application of the PGD to conductors with rectangular cross-section is particularly advantageous, because rectangular shapes can be represented with a very few number of independent terms, which makes the code very simple and compact. Finally, a key advantage of the PGD is that some parameters of the numerical model can be considered as additional dimensions. In this paper, the frequency has been considered as an additional dimension, and the internal inductance of a rectangular conductor has been computed for the whole range of frequencies desired using a single numerical simulation.

The proposed approach may be applied to the optimization of electrical conductors used in power systems, to solve EMC problems, to the evaluation of partial inductances of wires, etc. Nevertheless, it cannot be applied, as presented in this work, to 3D complex shapes, as, for example, an arrangement of layers of helically stranded wires.

The PGD is a promising new numerical procedure that has been applied successfully in different fields. In this paper, this novel technique is applied to find the DC and AC internal inductance of a conductor with rectangular cross-section, using very dense and large one-dimensional meshes. The proposed method requires very limited memory resources, is very fast, can be programmed using a very simple code, and gives the value of the AC inductance for a complete range of frequencies in a single simulation. The proposed approach can be extended to arbitrary conductor shapes and complex multiconductor lines to further exploit the advantages of the PGD.

The purpose of this paper is to investigate the lateral forces during the fall of a magnet in a conducting pipe, when the direction of magnetization of the magnet is fixed. If the direction of magnetization is not parallel to the axis of the pipe, lateral forces occur and a decentration of the magnet happens.

The problem is studied numerically, with a T − h 3D FE formulation well‐suited for the problem. Computational results are compared with experimental results.

The physical model is given and the main force coefficients analyzed. The lateral forces and the decentration phenomenon are studied as a function of the main parameters (thickness and radius of the pipe).

The direction of magnetization is a key parameter to analyze the dynamics of a magnet motion inside a conducting pipe, when the radii of the pipe and the magnet are not so close. This analysis with a fixed direction of magnetization allows one to quantify the lateral forces and the decentration, and is a first step to understand the complete motion which includes the rotation which can be linked to the decentration.

This paper aims to present an accurate representation of laminated wound cores with a low computational cost using 2D and 3D finite element (FE) method.

The authors developed an anisotropy model in order to model laminated wound cores. The anisotropy model was integrated to the 2D and 3D FE method. A comparison between 2D and 3D FE techniques was carried out. FE techniques were validated by experimental analysis.

In the case of no‐load operation of wound core transformers both 2D and 3D FE techniques yield the same results. Computed and experimental local flux density distribution and no‐load loss agree within 2 per cent to 6 per cent.

The originality of the paper consists in the development of an anisotropy model specifically formulated for laminated wound cores, and in the effective representation of electrical steels using a composite single‐valued function. By using the aforementioned techniques, the FE computational cost is minimised and the 3D FE analysis of wound cores is rendered practical.