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Sensorless control of permanent-magnet synchronous machines (PMSMs) at low speed and standstill is often based on a difference between q- and d-axis inductances. By determining the inductances, i.e., by evaluating current responses that result from the supply of voltage test vectors, an estimation of the rotor position is obtained. These inductances are dependent on the stator current--because of (cross-)saturation--and on the geometry of the PMSM. Changing inductances strongly affect the accuracy of the rotor position estimation. This paper investigates the influence of geometrical parameters of the rotor on the inductances and on the position estimation. First, for several angles, widths, heights, and radial positions of the buried magnets in the rotor, finite element models (FEMs) calculate the inductances and the torque as a function of the stator current. Second, to study the effect of the variable q- and d-inductances on the position estimator, time-domain simulations are carried out in combination with FEM evaluations. The simulated control is validated on an experimental interior PMSM. The FEM is not needed by the controller in the experiments. Index Terms--Finite element analysis, permanent-magnet synchronous machines (PMSMs).

A large computational effort is required in order to design an octangular double-layered shield that can be modeled by a 3-D numerical model only. Indeed, the conventional optimization methods minimize a cost function by many evaluations of this 3-D model. To reduce the CPU time, an optimization technique is developed--based on sequential quadratic programming--that takes advantage of two other models that are faster but less accurate than the 3-D FEM: a 2-D FEM and an analytical model. Index Terms--Magnetic shielding, multilevel optimization.

A model that describes the magnetic behavior of nanocrystalline ring cores is useful for simulations of electronic circuits that contain inductors or transformers using these cores. A general but computationally demanding model combines a macroscopic model of the ribbon with a dynamic Preisach hysteresis model. In this paper, we present two models that--taking into account the principle of loss separation--make it possible to avoid the use of the CPU time consuming dynamic Preisach model. Both models compute the waveform of the magnetic flux density for an arbitrary waveform of the magnetic field, or vice versa. The first model uses a macroscopic model based on the plane wave theory and the classical rate-independent Preisach formalism. The macroscopic model operates in the frequency domain and applies the harmonic balance principle. Because of nonlinearity, the model is solved iteratively by a Newton-Raphson scheme. The second model starts from a single evaluation of the classical Preisach model. Additionally, it uses a lookup table that is a function of the flux density and its time derivative to evaluate the classical and excess field to be added. The models are validated by measurements between 2 and 100 kHz on Vitroperm nanocrystalline ring cores. Index Terms--Hysteresis, losses, nanocrystalline material.

This paper studies the losses in the magnets of a permanent-magnet synchronous machine (PMSM) with surface magnets caused by square voltage pulse width modulation (PWM) waveforms. First, the conductivity of the magnets is determined. Second, the effect of segmentation on the losses is calculated by a 3-D time-harmonic finite element model for sinusoidal waveforms. More segmentation of the magnets in axial and circumferential direction results in much lower losses in the magnets, but more losses in the massive rotor yoke. In a third step, the losses are simulated and measured on an experimental PMSM for square waveforms generated by PWM. Superposition of appropriate sinusoidal losses obtained by a time-harmonic FEM seems to be acceptable in order to predict losses in a PMSM for square voltage waveforms. Index Terms--Finite element analysis, inverse problems, losses, permanent magnet machines.

Cutting leads to a certain local magnetic material degradation of the electrical steel sheet. Moreover, the material properties near the cutting edge contribute significantly to the global performance. This material degradation mostly occurs in the vicinity of critical parts of electromagnetic devices, such as stator and rotor teeth. Therefore, the need exists to characterize the local magnetic hysteresis properties due to cutting. We couple the non destructive measurements of needle signals, which are dependent on the local variations in magnetic hysteresis properties, with a numerical inverse algorithm. The inverse algorithm interprets the needle signals so that the unknown magnetic hysteresis properties can be reconstructed. The paper mainly deals with the construction of an accurate material model (numerical forward model), the correct solution of the inverse procedure and the validation of the obtained results. We reconstructed local magnetic hysteresis properties of differently cut steel sheets and we observed that it is possible to recover the material characteristics using a material model, which fully characterizes the hysteresis properties. Index Terms--Hysteresis modelling, inverse problems, magnetic material characterization, nondestructive evaluation.

To find the induced currents in conductive objects, the circuit method (CM) replaces these objects by a set of magnetically (mutually) coupled filaments. The unknown induced currents are obtained by solving an electrical circuit and the magnetic field is found by the Biot-Savart law. In the literature, the CM is described as a fast and easy-to-implement alternative for the finite- element method (FEM), with however some limitations: the objects to be modeled in the CM should be nonferromagnetic and much thinner than the penetration depth. In this paper, the CM is extended. It also models ferromagnetic behavior and objects thicker than the penetration depth, by adding extra filaments carrying proper currents. To validate the CM, an axisymmetric shielding problem is solved both with CM and FEM for a conductive shield, a nonlinear hysteretic ferromagnetic shield, and a double (multilayer) shield. Index Terms--Circuit method, hysteresis, magnetic shielding.

To determine the hysteresis loss in a sample, usually the enclosed area of the B - H loop is evaluated. In the drag force method, based on a proper energy balance, the hysteresis loss is obtained by analyzing the drag force profile when slowly moving the sample forward and backward through the strong field of permanent magnets. The aim of the method is not to be an alternative to conventional measurements, but rather to use it for nondestructive evaluation. A numerical time-stepping model is presented that calculates the drag force profile. At every time step, the sample is slightly moved relative to the magnet. The model is based on 2-D-FE computations including magnetic hysteretic material behavior using the Preisach model. The drag force is obtained by using the Maxwell stress tensor. The numerical model is validated by measurements and by comparing the 'drag force' hysteresis losses with the hysteresis losses computed conventionally by the integral of H.dB. Several simulations were carried out to investigate the influence of parameters such as the number of permanent magnets, the distance between the magnets and the sample, and the presence of defects in the sample. Index Terms--Drag force method, finite-element method, hysteresis loss.

We present a model that evaluates in the frequency domain the magnetic behavior of laminated SiFe alloys caused by a magnetic field imposed at the material edge. The model is based on plane wave theory describing how an electromagnetic wave penetrates a material. As the nonlinear material with hysteresis can cause harmonic frequency components of the field and induction inside the material, the model takes into account several harmonics simultaneously by applying the harmonic balance principle. The plane wave model is solved iteratively with a classical Preisach model as constitutive law. We compare the model with a time domain finite-element model and with measurements on a ring core and find a good correspondence. The CPU time is low if only a few harmonics are considered and if the nonlinearity of the material is rather mild. Index Terms--Harmonic analysis, hysteresis, losses, magnetic materials.

We present a new technique for reducing computation time of numerical solutions to optimal design problems. We incorporate in the optimization procedure a coarse model. Our technique, the two-level response and parameter mapping (RPM) algorithm, is based on space mapping and manifold mapping. Space mapping (SM) performs a mapping between the parameter spaces of the coarse and fine models, while manifold mapping (MM) makes a mapping between the response spaces of the coarse and fine models through the use of response correction. Here, we use and compare the three two-level optimization procedures, SM, MM, and RPM, for the optimization of passive and active shields in induction heating. The results demonstrate accurate and time-efficient optimization of magnetic shields by the RPM algorithm. Index Terms--Induction heating, magnetic shielding, manifold mapping, optimization, response correction, space mapping.

In induction heaters, a metallic workpiece is heated by eddy currents, induced by strong alternating magnetic fields. Using numerical models, proper active and passive shields are designed in order to mitigate the stray field of the induction heater. Two models are presented: an axisymmetric finite-element (FEM) and a hybrid finite-element-boundary-element (FEM-BEM) modal. Results of both numerical methods are compared and verified with measurements on an induction heater archetype. A good correspondence is observed. Combination of passive and active shielding results in almost 20-dB field reduction. Index Terms--Active shield, boundary elements, finite elements, heating, induction, magnetic field, passive shield.

This paper presents a method for designing optimal passive and active shields for axisymmetric induction heaters. Such shields are needed to protect human operators and external electronic equipment from stray magnetic fields. The method uses a genetic algorithm (GA) to minimize an objective function. This function reduces the magnetic field in the target area, the power dissipation in the active and passive shields, and the influence of the shields on the heating process. The GA returns the position and height of the passive shield, the optimal current for the active shield, and the number of turns of all coils. The paper describes two optimization modes: 1) optimization of only the active shield with fixed passive shield and 2) global optimization of both active and passive shields. Several passive shields are studied: electrically conductive shields and both electrically and magnetically conductive shields. The field reduction depends on the optimization mode and the passive shield properties, but always exceeds 25 dB for combined active and passive shields. Finally, the paper compares the results of the simulations to experimental measurements. Index Terms--Active shield, finite elements, genetic algorithm (GA), heating, induction, magnetic field, passive shield.

The drag force method shows the potential for applications in the field of nondestructive evaluation of surface-localized material degradation. By analyzing the difference in drag force signature between both forward and backward movement directions, it is possible to deduce whether a part of material was, during a cyclic bending test, subjected to applied cyclic compression or tension. Moreover, the position of the localized stressed region can be indicated. Further quantitative analysis shows that the increase of flexural stress amplitude leads to an increased variation between the drag force difference corresponding to the localized stressed region, and the drag force difference of an unaffected part of the material. The drag force method shows higher sensitivity to surface-related properties than the field-metric magnetic NDE techniques. Index Terms--Drag force method, magnetic nondestructive evaluation, metal fatigue, residual micro stress.

The magnetic shielding efficiency of a cylindrical shield is studied starting from the experimentally determined hysteresis loops of the nonlinear shielding material. The magnetic transfer relation model is used in the frequency domain. This analytical model can be evaluated very fast, but works only for linear material. Therefore, the nonlinear shield is divided into a number of linear sublayers with constant complex permeability, which is modelled by an analytical complex function, fitted from the experimental hysteresis loops. The shielding factors are calculated by the analytical model as a function of the imposed field amplitude. They are validated by a finite element model and compared with measured shielding factors of cylindrical tubes. The correspondence is good for the three considered shields: a shield in aluminium (shielding by induced currents), a shield in Fe-Si steel (mainly shielding by flux shunting) and a multilayered shield in aluminium and Fe-Si steel. Index Terms--Magnetic shielding, numerical analysis.

The use of power electronics has led to a growing importance of higher time-harmonic content in electrical machines. To gain insight in phenomena related to these higher harmonics, such as noise and losses, a good understanding of the magnetic field’s harmonic content is mandatory. Moreover, the development of fast and accurate, harmonic-based, analytical models requires a qualitative knowledge of the machine’s time- and spatial-harmonic content. Although the harmonic content of electric machines is an extensively studied topic, previous publications tended to focus on one type of synchronous machines and often did not consider higher time-harmonic orders. This paper complements the existing theory by providing a more general approach, thereby covering machines and operating points that were not covered until now. It considers both three-phase and multi-phase machines with an odd number of phases. The winding distribution can either have an integer or a fractional number of slots per pole and per phase, and higher time-harmonic content is regarded as well. Note that the saturation is neglected. Despite its general validity, this paper succeeds at providing one simple equation to determine the machine’s time-and spatial-harmonic content. Moreover, this paper also extensively discusses the physical causes of the harmonic content. The combination of this general validity, the simple result, and the insight in the physics makes that this paper is a strong tool to both study harmonic-related phenomena in electric machines and to develop harmonic-based analytical models. [ABSTRACT FROM AUTHOR]

In this paper, the complete magnetic material characteristic, hysteretic and anhysteretic, is reconstructed for an El electromagnetic inductor. The material identification process, including air gap assessment, is carried out using a coupled experimental-numerical inverse technique, based on a set of well chosen global and local magnetic measurements. It is shown that a higher accuracy is obtained when local measurements are performed in regions with less stray fields, and the air gap assessment is strongly improved by the use of local magnetic measurements. [ABSTRACT FROM AUTHOR]