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The purpose of this paper is to calculate forces created by the magnetic leakage field, which are directly applied to tank walls via magnetic shield.

Electromagnetic and mechanical calculations use 3D finite element technology, both applied to materials having constant orthotropic properties. The magnetic solver uses harmonic excitation; the analysis of mechanical deflection is carried out in static conditions. Two types of forces are considered: magnetostatic surface forces and magnetostriction volumetric ones. In measurements, the laser scanning vibrometer was applied.

Electromagnetic calculations must use an FE mesh much denser than that for typical power loss analysis. The magnetic orthotropy of the shield material does not create any important effects and it may be omitted. Magnetostriction forces are similar in value to magnetostatic ones, but their influence on the shield deformation is negligible.

The results obtained for the analysis of the displacement of elements of the tank wall are exemplary – they show the difference between magnetostatic and magnetostriction excitation only. The analysis of the vibration of the transformer tank must include the presence of the oil inside the tank.

The asymmetrical placement of magnetic shields against the transformer core creates the visible differences in the magnitudes of magnetostatic forces applied to particular shields. Therefore, the design of magnetic shielding should also include the vibrational point of view.

The aim of this paper is to find a fast-acting numerical model of the phase shifter.

The 3D FE model of the investigated unit is presented and compared with the results of the measurements. Due to its size, it is not suitable for transient analyses. The simplified 2D finite elements approach is discussed afterwards, with the identity of the magnetic energy stored in both models as the criterion of similarity between 2D and 3D models.

The introduction of scaling factors for the magnetic permeability values in particular volumes of the two-transformer set of the phase shifter enabled acceptable accuracy in calculations of the basic exploitation parameters of the phase shifter.

The developed methodology allows the analysis of the exploitation conditions of two separated transformers connected in a power grid inside the single finite elements model.

Although the numerical models of power transformers are extensively discussed in the literature, the usage of the equivalent fast 2D model for the representation of two cooperating transformers at load conditions was not published yet.

The paper describes how the classical formula of the Maxwell magnetic stress tensor may be extended to cover the magnetostriction phenomena. It is assumed that the ferromagnetic continuum is isotropic and conservative. The method takes into account the magnetic nonlinearity and it assumes that mechanical deflections are sufficiently small to neglect the nonlinearity of the Hooke's law. The paper presents also the experimental method, which has been used to measure the magnetostriction intensity for electrotechnical laminations. As the final result, the distribution of the volume magnetostriction forces acting on the stator core of the induction motor has been calculated.

The finite element (FE) method is nowadays the most popular tool for the analysis of magnetic field distributions in electric machinery. Such a distribution alone is usually not sufficient for real life applications ‐ the values of equivalent parameters for particular devices are often the main point of interest. In synchronous machines the knowledge of reactances’ values, both for steady and transient conditions, enables the calculations of most of exploitation relationships. The application of FE technique substantially helps to overcome the well known difficulties concerning the representation of geometry details, magnetic saturation and eddy current reaction, if it appears. Simultaneously, the presented way of analysis is linked with commonly used measurement methods of synchronous generators. The example calculations were done for the 150kW synchronous generator having non‐integer number of slots per pole and phase.

The purpose of this paper is to present a methodology of identification and calculating vibrations of power transformers caused by magnetostriction.

All calculations are based on finite element approach. Electromagnetic model uses 2D time stepping solution in nonlinear continuum of the core accompanied with equivalent representation of overlapping areas. Structural model is 3D with special representation for laminated core limbs. Theoretical results are compared with experimental ones obtained as operational deflection shapes from vibration measurements.

Tensor representation of magnetostriction stress enables calculation of equivalent forces acting on arbitrary chosen parts of laminated core. These forces converted into amplitude and phase of Fourier spectrum and introduced into structural model make possible to get displacement field with reasonable accuracy.

Assumption of magnetic isotropy of the transformer core is the main simplification during analysis.

It was proved that small deformation of the core structure originated from assembly technology may be the reason of substantial growth of the vibration level.

This paper provides a step‐by‐step explanation of how to get core vibration starting from magnetic field distribution.

This paper aims to provide the mathematical background for representation of permanent magnet AC machines in terms of rotating magnetic field waves of any shape instead of being restricted to the sinusoidal. The general idea is to replace the inductances in the mathematical model of the machine by means of adequate time functions of the flux linkage.

On the basis of several 2D or 3D solutions obtained by the finite element (FE) approach, the set of basis functions is generated for further post‐processing. These functions enable fast and accurate computations of back EMF time shape at any load conditions, which in turn gives the instantaneous values of terminal quantities like torque or voltage, depending on the regime of interest.

The permanent magnet machine (PMM) has been represented by means of the traveling non‐dispersive waves of the flux density in the air gap rotating with specified group velocity. The conversion between distributions of the flux density in space and flux linkage in time is obtained through filtering in the spectral domain using 2D or 3D discrete Fourier transform. The change of magnetic saturation due to arbitrary value of the machine load is incorporated by the interpolation between known magnitudes of the basis functions at given a priori RMS values of phase currents. It has been proved that a sinusoidal field machine is particular to the presented theory.

The paper deals with the steady state of PMM; however, the extension towards the transient analysis is possible.

The paper presents a fast and accurate model of PMM for the analysis of its basic electromagnetic quantities.

The analysis of terminal quantities being different in time from sinusoidal or constant distributions, both electrical and mechanical, is usually performed by means of a time stepping approach. The required computing effort is still too high for real time applications. The presented method starts from single FE solutions and converts their accuracy on the set of mutually orthogonal functions having the clear representation in the spectral, mode‐frequency domain. The magnitudes of these basic functions enable one to express the electromagnetic power in a form equivalent to classic dq representation, but not constrained by sinusoidal input quantities.