Search results for: Spherical harmonics model

Authors: S. Hellam, Y. Oulahrir, F. El Mounchid, A. Sadiq, S. Mbarki

Abstract:

In this paper, we propose a new method for threedimensional object indexing based on D.A.M.C-S.H.C descriptor (Direct and Analytical Method for Calculating the Spherical Harmonics Coefficients). For this end, we propose a direct calculation of the coefficients of spherical harmonics with perfect precision. The aims of the method are to minimize, the processing time on the 3D objects database and the searching time of similar objects to a request object. Firstly we start by defining the new descriptor using a new division of 3-D object in a sphere. Then we define a new distance which will be tested and prove his efficiency in the search for similar objects in the database in which we have objects with very various and important size.

Keywords: 3D Object indexing, 3D shape descriptor, spherical harmonic, 3D Object similarity.

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Authors: A. Ben Abdallah, H. Essabbah, M. H. Bedoui

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The myocardial sintigraphy is an imaging modality which provides functional informations. Whereas, coronarography modality gives useful informations about coronary arteries anatomy. In case of coronary artery disease (CAD), the coronarography can not determine precisely which moderate lesions (artery reduction between 50% and 70%), known as the “gray zone", are haemodynamicaly significant. In this paper, we aim to define the relationship between the location and the degree of the stenosis in coronary arteries and the observed perfusion on the myocardial scintigraphy. This allows us to model the impact evolution of these stenoses in order to justify a coronarography or to avoid it for patients suspected being in the gray zone. Our approach is decomposed in two steps. The first step consists in modelling a coronary artery bed and stenoses of different location and degree. The second step consists in modelling the left ventricle at stress and at rest using the sphercical harmonics model and myocardial scintigraphic data. We use the spherical harmonics descriptors to analyse left ventricle model deformation between stress and rest which permits us to conclude if ever an ischemia exists and to quantify it.

Keywords: Spherical harmonics model, vascular bed, 3D reconstruction, left ventricle, myocardial scintigraphy.

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Authors: S. Hellam, Y. Oulahrir, F. El Mounchid, A. Sadiq, S. Mbarki

Abstract:

In this paper, we propose a method for three-dimensional (3-D)-model indexing based on defining a new descriptor, which we call new descriptor using spherical harmonics. The purpose of the method is to minimize, the processing time on the database of objects models and the searching time of similar objects to request object. Firstly we start by defining the new descriptor using a new division of 3-D object in a sphere. Then we define a new distance which will be used in the search for similar objects in the database.

Keywords: 3D indexation, spherical harmonic, similarity of 3D objects.

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Authors: Md. Armin Islam, Les Dallin, Mark Boland, W. J. Zhang

Abstract:

This paper reports a study on the optimal magnetic design of a compact quadrupole electromagnet for the Canadian Light Source (CLS 2.0). The nature of the design is to determine a quadrupole with low relative higher order harmonics and better field quality. The design problem was formulated as an optimization model, in which the objective function is the higher order harmonics (multipole errors) and the variable to be optimized is the material distribution on the pole. The higher order harmonics arose in the quadrupole due to truncating the ideal hyperbola at a certain point to make the pole. In this project, the arisen harmonics have been optimized both transversely and longitudinally by adjusting material on the poles in a controlled way. For optimization, finite element analysis (FEA) has been conducted. A better higher order harmonics amplitudes and field quality have been achieved through the optimization. On the basis of the optimized magnetic design, electrical and cooling calculation has been performed for the magnet.

Keywords: Drift, electrical, and cooling calculation, integrated field, higher order harmonics (multipole errors), magnetic field gradient, quadrupole.

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Authors: Shreyash Sinai Kunde, Siddhang Tendulkar, Shiv Prakash Gupta, Gaurav Kumar, Suresh Mikkili

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One of the major power quality concerns in modern times is the problem of current harmonics. The current harmonics is caused due to the increase in non-linear loads which is largely dominated by power electronics devices. The Shunt active filtering is one of the best solutions for mitigating current harmonics. This paper describes a fuzzy logic controller based (FLC) based three Phase Shunt active Filter to achieve low current harmonic distortion (THD) and Reactive power compensation. The performance of fuzzy logic controller is analysed under both balanced sinusoidal and unbalanced sinusoidal source condition. The above controller serves the purpose of maintaining DC Capacitor Voltage constant. The proposed shunt active filter uses hysteresis current controller for current control of IGBT based PWM inverter. The simulation results of model in Simulink MATLAB reveals satisfying results.

Keywords: Shunt active filter, Current harmonics, Fuzzy logic controller, Hysteresis current controller.

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Authors: Hari Maghfiroh, Fadhila Tresna Nugraha, Harry Prabowo

Abstract:

Fluorescent and WOLED are widely used because it consumes less energy. However, both lamps cause a harmonics because it has semiconductors components. Harmonic is a distorted sinusoidal electric wave and cause excess heat. This study compares the amount of harmonics generated by both lamps. The test shows that both lamps have THDv(Total Harmonics Distortion of Voltage) almost the same with average 2.5% while the average of WOLED's THDi(Total Harmonics Distortion of Current) is lower than fluorescent has. The average WOLED's THDi is 29.10 % and fluorescent's 'THDi is 87. 23 %.

Keywords: Fluorescent, harmonic, power factor, WOLED

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Authors: Ravit Gautam, Dipen A. Mistry, Manmohan Singh Meena, Bhupelly Dheeraj, Suresh Mikkili

Abstract:

Due to the increased use of the power electronic equipment, harmonics in the power system has increased to a greater extent. These harmonics results a poor power quality causing a major effect on the customers. Shunt active filters (SHAF) are used for the mitigations of the current harmonics and to maintain constant DC link voltage. PI and Fuzzy logic controllers (FLC) were used to control the performance of the shunt active filter under both balance and unbalance source voltage condition. The results found were not satisfying the IEEE-519 standards of THD to be less than 5%. Hysteresis band current control was used to obtain the gating signals for SHAF, though it has some drawbacks and thus to obtain a better performance of the SHAF to mitigate the harmonics, adaptive hysteresis band current control scheme is implemented. Adaptive hysteresis based SHAF is used to obtain better compensation of current harmonics and to regulate the DC link voltage in a better way.

Keywords: DC Link Voltage, Fuzzy Logic Controller, Adaptive Hysteresis, Harmonics, Shunt Active Filter.

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Authors: M. Hossain, H. P. Zhu, A. B. Yu

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This paper presents a numerical investigation of regime transition of flow of ellipsoidal particles and a comparison with that of spherical particle assembly. Particle assemblies constituting spherical and ellipsoidal particle of 2.5:1 aspect ratio are examined at separate instances in similar flow conditions in a shear cell model that is numerically developed based on the discrete element method. Correlations among elastically scaled stress, kinetically scaled stress, coordination number and volume fraction are investigated, and show important similarities and differences for the spherical and ellipsoidal particle assemblies. In particular, volume fractions at points of regime transition are identified for both types of particles. It is found that compared with spherical particle assembly, ellipsoidal particle assembly has higher volume fraction for the quasistatic to intermediate regime transition and lower volume fraction for the intermediate to inertial regime transition. Finally, the relationship between coordination number and volume fraction shows strikingly distinct features for the two cases, suggesting that different from spherical particles, the effect of the shear rate on the coordination number is not significant for ellipsoidal particles. This work provides a glimpse of currently running work on one of the most attractive scopes of research in this field and has a wide prospect in understanding rheology of more complex shaped particles in light of the strong basis of simpler spherical particle rheology.

Keywords: Discrete element method, granular rheology, non-spherical particles, regime transition

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Authors: Francesco Pia

Abstract:

Stellar objects such as black, white and worm holes can be the subject of speculative reasoning if represented in a simplified and geometric form in order to be able to move them; and the cosmological model is one of the most important contents in relation to speculations that can then open the way to other aspects that are not strictly speculative but practical, precisely in the Universe represented by us. In this work, thanks to the hypothesis of a very large number of black, white and worm holes present in our Universe, we imagine that they can be moved; it was therefore thought to align them on a plane and following a redistribution, and the boundaries of this plane were ideally joined, giving rise to a sphere that has the stellar objects examined radially distributed. Thanks to geometrical displacements of these stellar objects that do not make each one of them lose their functionality in the region in which they are located, at the end of the speculative process it is possible to highlight a spherical layer that allows a flow from the outside and inside this spherical shell allowing to relate to other external and internal spherical layers; this aspect that seems useful to describe the universe we live in, for example inside one of the spherical shells just described. The name "Jewel" was chosen because, imagining the speculative process present in this work at the end of steps, the cosmological model tends to be "luminous". This cosmological model includes, for each internal part of a generic layer, different and numerous moments of our universe thanks to an eternal flow inward. There are many aspects to explore, one of these is the connection between the outermost and the inside of the spherical layers.

Keywords: Black hole, cosmological model, cosmology, white hole.

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Authors: Yiwan Guo, Fahui Zhai

Abstract:

In this paper, the similarity invariant and the upper semi-continuity of spherical spectrum, and the spherical spectrum properties for infinite direct sums of quaternionic operators are characterized, respectively. As an application of some results established, a concrete example about the computation of the spherical spectrum of a compact quaternionic operator with form of infinite direct sums of quaternionic matrices is also given.

Keywords: Spherical spectrum, Quaternionic operator, Upper semi-continuity, Direct sum of operators.

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Authors: Eric Huang, Coleman DeLude, Justin Romberg, Saibal Mukhopadhyay, Madhavan Swaminathan

Abstract:

High-performance computing (HPC) based emulators can be used to model the scattering from multiple stationary and moving targets for RADAR applications. These emulators rely on the RADAR Cross Section (RCS) of the targets being available in complex scenarios. Representing the RCS using tables generated from EM simulations is oftentimes cumbersome leading to large storage requirements. In this paper, we proposed a spherical harmonic based anisotropic scatterer model to represent the RCS of complex targets. The problem of finding the locations and reflection profiles of all scatterers can be formulated as a linear least square problem with a special sparsity constraint. We solve this problem using a modified Orthogonal Matching Pursuit algorithm. The results show that the spherical harmonic based scatterer model can effectively represent the RCS data of complex targets.

Keywords: RADAR, RCS, high performance computing, point scatterer model

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Authors: Wilfred Fritz

Abstract:

Grid connected solar PV inverters need to be compliant to standard regulations regarding unwanted harmonic generation. This paper gives an introduction to harmonics, solar PV inverter voltage regulation and balancing through compensation and investigates the behaviour of harmonic generation at different power levels. Practical measurements of harmonics and power levels with a power quality data logger were made, on a test network at a university in Germany. The test setup and test results are discussed. The major finding was that between the morning and afternoon load peak windows when the PV inverters operate under low solar insolation and low power levels, more unwanted harmonics are generated. This has a huge impact on the power quality of the grid as well as capital and maintenance costs. The design of a single-tuned harmonic filter towards harmonic mitigation is presented.

Keywords: Harmonics, power quality, pulse width modulation, total harmonic distortion.

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Authors: Düzgün Akmaz, Hüseyin Erişti

Abstract:

In the last few years, harmonics have been occurred with the increasing use of nonlinear loads, and these harmonics have been an ever increasing problem for the line systems. This situation importantly affects the quality of power and gives large losses to the network. An efficient way to solve these problems is providing harmonic compensation through parallel active power filters. Many methods can be used in the control systems of the parallel active power filters which provide the compensation. These methods efficiently affect the performance of the active power filters. For this reason, the chosen control method is significant. In this study, Fourier analysis (FA) control method and synchronous reference frame (SRF) control method are discussed. These control methods are designed for both eliminate harmonics and perform reactive power compensation in MATLAB/Simulink pack program and are tested. The results have been compared for each two methods.

Keywords: Harmonics, Harmonic compensation, Parallel active power filters, Power quality.

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Authors: Rana Abdul Jabbar Khan, Muhammad Akmal

Abstract:

Personal computers draw non-sinusoidal current with odd harmonics more significantly. Power Quality of distribution networks is severely affected due to the flow of these generated harmonics during the operation of electronic loads. In this paper, mathematical modeling of odd harmonics in current like 3rd, 5th, 7th and 9th influencing the power quality has been presented. Live signals have been captured with the help of power quality analyzer for analysis purpose. The interesting feature is that Total Harmonic Distortion (THD) in current decreases with the increase of nonlinear loads has been verified theoretically. The results obtained using mathematical expressions have been compared with the practical results and exciting results have been found.

Keywords: Harmonic Distortion, Mathematical Modeling, Power Quality.

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Authors: Marios N. Moschakis

Abstract:

The increasing penetration of Distributed Generation and storage connected to the distribution network via PWM converters increases the possibility of a DC-component (offset) in voltage or current flowing into the grid. This occurs when even harmonics are present in the network voltage. DC-components can affect the operation and safety of several grid components. Therefore, an investigation of the way they are produced is important in order to take appropriate measures for their elimination. Further research on DC-components that appear on output voltage of converters is performed for different parameters of PWM technique and characteristics of even harmonics.

Keywords: Asymmetric even harmonics, DC-offsets, distributed generation, electric machine drive systems, power quality.

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Authors: A. Selmi, A. Bisharat

Abstract:

Using Fourier transform and based on the Mindlin's 2^nd gradient model that involves two length scale parameters, the Green's function, the Eshelby tensor, and the Eshelby-like tensor for a spherical inclusion are derived. It is proved that the Eshelby tensor consists of two parts; the classical Eshelby tensor and a gradient part including the length scale parameters which enable the interpretation of the size effect. When the strain gradient is not taken into account, the obtained Green's function and Eshelby tensor reduce to its analogue based on the classical elasticity. The Eshelby tensor in and outside the inclusion, the volume average of the gradient part and the Eshelby-like tensor are explicitly obtained. Unlike the classical Eshelby tensor, the results show that the components of the new Eshelby tensor vary with the position and the inclusion dimensions. It is demonstrated that the contribution of the gradient part should not be neglected.

Keywords: Eshelby tensor, Eshelby-like tensor, Green’s function, Mindlin’s 2nd gradient model, Spherical inclusion.

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Authors: Anésio de Leles F. Filho, Wesley R. de Oliveira, Jéssica S. G. Pena, Jorge A. C. Angarita

Abstract:

The increase in electric power demand in face of environmental issues has intensified the participation of renewable energy sources such as photovoltaics, in the energy matrix of various countries. Due to their operational characteristics, they can generate time-varying harmonic and inter-harmonic distortions. For this reason, the application of methods of measurement based on traditional Fourier analysis, as proposed by IEC 61000-4-7, can provide inaccurate results. Considering the aspects mentioned herein, came the idea of the development of this work which aims to present the results of a comparative evaluation between a methodology arising from the combination of the Prony method with the Kalman filter and another method based on the IEC 61000-4-30 and IEC 61000-4-7 standards. Employed in this study were synthetic signals and data acquired through measurements in a 50kWp photovoltaic installation.

Keywords: Harmonics, inter-harmonics, IEC61000-4-7, parametric estimators, photovoltaic generation.

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Authors: Dipen A. Mistry, Bhupelly Dheeraj, Ravit Gautam, Manmohan Singh Meena, Suresh Mikkili

Abstract:

In recent years the large scale use of the power electronic equipment has led to an increase of harmonics in the power system. The harmonics results into a poor power quality and have great adverse economical impact on the utilities and customers. Current harmonics are one of the most common power quality problems and are usually resolved by using shunt active filter (SHAF). The main objective of this work is to develop PI and Fuzzy logic controllers (FLC) to analyze the performance of Shunt Active Filter for mitigating current harmonics under balanced and unbalanced sinusoidal source voltage conditions for normal load and increased load. When the supply voltages are ideal (balanced), both PI and FLC are converging to the same compensation characteristics. However, the supply voltages are non-ideal (unbalanced), FLC offers outstanding results. Simulation results validate the superiority of FLC with triangular membership function over the PI controller.

Keywords: DC link voltage, Fuzzy logic controller, Harmonics, PI controller, Shunt Active Filter.

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Authors: Chung-Chun Hsiao, Yu-Kai, Ting, Kai-Yuan Liu, Pang-Wei Yen, Jia-Ying Tu

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In this paper, a new design of spherical robotic system based on the concepts of gimbal structure and gyro dynamics is presented. Robots equipped with multiple wheels and complex steering mechanics may increase the weight and degrade the energy transmission efficiency. In addition, the wheeled and legged robots are relatively vulnerable to lateral impact and lack of lateral mobility. Therefore, the proposed robotic design uses a spherical shell as the main body for ground locomotion, instead of using wheel devices. Three spherical shells are structured in a similar way to a gimbal device and rotate like a gyro system. The design and mechanism of the proposed robotic system is introduced. In addition, preliminary results of the dynamic model based on the principles of planar rigid body kinematics and Lagrangian equation are included. Simulation results and rig construction are presented to verify the concepts.

Keywords: Gyro, gimbal, Lagrange equation, spherical robots.

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Authors: İnci M. Erhan

Abstract:

A numerical method for solving the time-independent Schrödinger equation of a particle moving freely in a three-dimensional axisymmetric region is developed. The boundary of the region is defined by an arbitrary analytic function. The method uses a coordinate transformation and an expansion in eigenfunctions. The effectiveness is checked and confirmed by applying the method to a particular example, which is a prolate spheroid.

Keywords: Bessel functions, Eigenfunction expansion, Quantum billiard, Schrödinger equation, Spherical harmonics

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Authors: Hari Maghfiroh, Harry Prabowo

Abstract:

WOLED is widely used as lighting for high efficacy and little power consumption. In this research, power factor testing between WOLED and fluorescent lamp to see which one is more efficient in consuming energy. Since both lamps use semiconductor components, so calculation of the power factor need to consider the effects of harmonics. Harmonic make bigger losses. The study is conducted by comparing the value of the power factor regardless of harmonics (DPF) and also by included the harmonics (TPF). The average value of DPF of fluorescent is 0.953 while WOLED is 0.972. The average value of TPF of fluorescent is 0.717 whereas WOLED is 0.933. So from the review of power factor WOLED is more energy efficient than fluorescent lamp.

Keywords: Fluorescent, harmonic, power factor, WOLED.

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Authors: Alexandros Leontitsis, Archana P. Sangole

Abstract:

This article presents a short discussion on optimum neighborhood size selection in a spherical selforganizing feature map (SOFM). A majority of the literature on the SOFMs have addressed the issue of selecting optimal learning parameters in the case of Cartesian topology SOFMs. However, the use of a Spherical SOFM suggested that the learning aspects of Cartesian topology SOFM are not directly translated. This article presents an approach on how to estimate the neighborhood size of a spherical SOFM based on the data. It adopts the L-curve criterion, previously suggested for choosing the regularization parameter on problems of linear equations where their right-hand-side is contaminated with noise. Simulation results are presented on two artificial 4D data sets of the coupled Hénon-Ikeda map.

Keywords: Parameter estimation, self-organizing feature maps, spherical topology.

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Authors: Cheng-En Tsai, Chung-Chun Hsiao, Fu-Yuan Chang, Liang-Lun Lan, Jia-Ying Tu

Abstract:

New design of three dimensional (3D) flywheel system based on gimbal and gyro mechanics is proposed. The 3D flywheel device utilizes the rotational motion of three spherical shells and the conservation of angular momentum to achieve planar locomotion. Actuators mounted to the ring-shape frames are installed within the system to drive the spherical shells to rotate, for the purpose of steering and stabilization. Similar to the design of 2D flywheel system, it is expected that the spherical shells may function like a “flyball” to store and supply mechanical energy; additionally, in comparison with typical single-wheel and spherical robots, the 3D flywheel can be used for developing omnidirectional robotic systems with better mobility. The Lagrangian method is applied to derive the equation of motion of the 3D flywheel system, and simulation studies are presented to verify the proposed design.

Keywords: Gimbal, spherical robot, gyroscope, Lagrangian formulation, flyball.

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Authors: Cheng-En Tsai, Chung-Chun Hsiao, Fu-Yuan Chang, Liang-Lun Lan, Jia-Ying Tu

Abstract:

New design of three dimensional (3D) flywheel system based on gimbal and gyro mechanics is proposed. The 3D flywheel device utilizes the rotational motion of three spherical shells and the conservation of angular momentum to achieve planar locomotion. Actuators mounted to the ring-shape frames are installed within the system to drive the spherical shells to rotate, for the purpose of steering and stabilization. Similar to the design of 2D flywheel system, it is expected that the spherical shells may function like a “flyball” to store and supply mechanical energy; additionally, in comparison with typical single-wheel and spherical robots, the 3D flywheel can be used for developing omnidirectional robotic systems with better mobility. The Lagrangian method is applied to derive the equation of motion of the 3D flywheel system, and simulation studies are presented to verify the proposed design.

Keywords: Gimbal, spherical robot, gyroscope, Lagrangian formulation, flyball.

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Authors: Boonorm Chomtee, John J. Borkowski

Abstract:

The objective of the research is to study and compare response surface designs: Central composite designs (CCD), Box- Behnken designs (BBD), Small composite designs (SCD), Hybrid designs, and Uniform shell designs (USD) over sets of reduced models when the design is in a spherical region for 3 and 4 design variables. The two optimality criteria ( D and G ) are considered which larger values imply a better design. The comparison of design optimality criteria of the response surface designs across the full second order model and sets of reduced models for 3 and 4 factors based on the two criteria are presented.

Keywords: design optimality criteria, reduced models, response surface design, spherical design region

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Authors: Nur Sarma, Paul M. Tuohy, Siniša Djurović

Abstract:

This paper presents an in-depth investigation of the effects of several grid supply harmonic voltages on the stator currents of an example wound rotor induction machine. The observed effects of higher order grid supply harmonics are identified using a finite element time stepping transient model, as well as a time-stepping electromagnetic model. In addition, a number of analytical equations to calculate the spectral content of the stator currents are presented in the paper. The presented equations are validated through comparison with the obtained spectra predicted using the finite element and electromagnetic models. The presented study provides a better understanding of the origin of supply harmonic effects identified in the stator currents of the example wound rotor induction machine. Furthermore, the study helps to understand the effects of higher order supply harmonics on the harmonic emissions of the wound rotor induction machine.  

Keywords: Wound rotor induction machine, supply harmonics, current spectrum, power spectrum, power quality, harmonic emissions, finite element analysis.

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Authors: V. Joshi Manohar, P. Sujatha, K. S. R. Anjaneyulu

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Nowadays Multilevel inverters are widely using in various applications. Modulation strategy at fundamental switching frequency like, SHEPWM is prominent technique to eliminate lower order of harmonics with less switching losses and better harmonic profile. The equations which are formed by SHE are highly nonlinear transcendental in nature, there may exist single, multiple or even no solutions for a particular MI. However, some loads such as electrical drives, it is required to operate in whole range of MI. In order to solve SHE equations for whole range of MI, intelligent techniques are well suited to solve equations so as to produce lest %THDV. Hence, this paper uses Continuous genetic algorithm for minimising harmonics. This paper also presents wavelet based analysis of harmonics. The developed algorithm is simulated and %THD from FFT analysis and Wavelet analysis are compared. MATLAB programming environment and SIMULINK models are used whenever necessary.

Keywords: Cascade H-Bridge Inverter (CHB), Continuous Genetic Algorithm (C-GA), Selective Harmonic Elimination Pulse Width Modulation (SHEPWM), Total Harmonic Distortion (%THDv), Wavelet Transform (WT).

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Authors: A. R. Tavakolpour-Saleh, A. R. Setoodeh, E. Ansari

Abstract:

This paper presents modeling and control of a highly nonlinear system including, non-interacting two spherical tanks using iterative learning control (ILC). Consequently, the objective of the paper is to control the liquid levels in the nonlinear tanks. First, a proportional-integral-derivative (PID) controller is applied to the plant model as a suitable benchmark for comparison. Then, dynamic responses of the control system corresponding to different step inputs are investigated. It is found that the conventional PID control is not able to fulfill the design criteria such as desired time constant. Consequently, an iterative learning controller is proposed to accurately control the coupled nonlinear tanks system. The simulation results clearly demonstrate the superiority of the presented ILC approach over the conventional PID controller to cope with the nonlinearities presented in the dynamic system.

Keywords: Iterative learning control, spherical tanks, nonlinear system.

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Authors: B. Rezaei, G. R. Boroun, M. Abdolmaleki

Abstract:

The bound state energy of three quark systems is studied in the framework of a non- relativistic spin independent phenomenological model. The hyper- spherical coordinates are considered for the solution this system. According to Jacobi coordinate, we determined the bound state energy for (uud) and (ddu) quark systems, as quarks are flavorless mass, and it is restrict that choice potential at low and high range in nucleon bag for a bound state.

Keywords: Adiabatic expansion, grand angular momentum, binding energy, perturbation, baryons.

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Authors: Adel Bettayeb, Robert Kaczmarek, Jean-Claude Vannier

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In this paper, we analyze the rotor eddy currents losses provoqued by the stator slot harmonics developed in the permanent magnets or pole pieces of synchronous machines. An analytical approach is presented to evaluate the effect of slot ripples on rotor field and losses calculation. This analysis is then tested on a model by 2D/3D finite element (FE) calculation. The results show a good agreement on loss calculations when skin effect is negligible and the magnet is considered.

Keywords: Analytical modeling, Eddy-currents, Finite-elementmethods, Power losses, Slot harmonics effect.

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