Flux Waveforms Research Articles

Characterization of Grain-Oriented Electrical Steels Under High DC Biased Conditions

Power transformers are designed to operate under pure ac excitation; however, they may be subjected to superimposed dc voltages and consequential offset currents, for example, from geomagnetically induced currents, geomagnetically induced quasi-dc currents, arising from solar activity. To determine the effects of dc offsets, a single-sheet tester was used with a digital excitation signal created with an ac waveform summed with a dc voltage addition and measured with a digital feedback control algorithm to ensure an ideal flux density waveform. Using this method, results with 300% additional dc contribution were able to be measured for results up to B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ac</sub> + B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dc</sub> = 1.9 T. The measurements of grain-oriented 3% Si-Fe show increasing power losses and peak applied magnetic field for peak-to-peak flux densities above 3 T, with a 33% increase in power loss and 500% increase in applied magnetic field for an offset of 25%.

Improvement of Convergence Characteristics of 1-D Dynamic Magnetic Field Analysis With Hysteresis for Iron Loss Estimation

In previous studies on precise computation methods of iron loss, it has been shown that the 1-D dynamic magnetic field analysis with hysteresis in post-processing is effective. However, there is a problem in that the hysteresis makes the convergence of nonlinear iterations unstable. This paper proposes a stabilization method for the 1-D dynamic magnetic field analysis with hysteresis. The proposed method is characterized as an approach for improving the initial value and the step size in the Newton–Raphson method. The results of this paper showed that the convergence characteristic of the nonlinear 1-D magnetic field analysis for variety flux density waveforms of each part in an electric motor is improved using the proposed method.

Predicting Iron Losses in Laminated Steel with Given Non-Sinusoidal Waveforms of Flux Density

In electrical machines, iron losses are essential for electromagnetic and thermal designs and analyses. Although many models have been proposed to predict iron losses in magnetic materials, the calculation of iron losses under non-sinusoidal excitations is still an open field. Most works concern the influences of the value, the change rate or the frequency of flux density in the frequency domain. In this paper, we propose an engineering model for predicting loss characteristics with given waveforms of flux density in the time domain. The characteristics are collected from the knowledge of the iron loss in a laminated ring-shaped transformer. In the proposed model, we derive mathematical formulas for exciting currents in terms of flux density by describing the function methods through multi-frequency tests with sinusoidal excitations. The non-linearity of the material is interpreted by branches of conductances accounting for hysteresis and eddy-current losses. Then, iron losses are calculated based on the law of conservation of energy. An experimental system was built to evaluate the magnetic properties and iron losses under sinusoidal and non-sinusoidal excitations. Actual measurement results verify the effectiveness of the proposed model.

Consideration of Design and Operation on Rotational Flux Density Distributions in Hydrogenerator Stators

Core losses in an electrical machine vary depending on the type of material, frequency of operation, and flux density magnitude and waveform. Loss prediction using pulsating models is insufficient for estimating core losses in a machine, since it does not take into account rotational core losses. Moreover, superposition of pulsating losses in the radial and tangential direction overestimates losses especially at higher flux densities. The objective of this paper is to study rotational flux distribution in the stator of the generator under different operating conditions. Distribution of rotational flux in a large hydrogenerator stator is studied by plotting the aspect ratio. It was found that increasing the yoke length and reducing the air gap increases the area of the stator with rotational flux. Varying the output power showed slight changes in the rotational flux distribution. Different optimized machine designs are investigated for rotational flux distribution; moreover, rotational core losses are measured and used for a comparative study radially across the stator.

A Novel Transverse Flux Permanent Magnet Generator With Double C-Hoop Stator and Flux-Concentrated Rotor

Transverse flux permanent magnet (TFPM) machine possesses the characteristic feature of decoupled electric load and magnetic load to obtain high power density. A novel TFPM generator (TFPMG) with double C-hoop stator and flux-concentrated rotor is proposed for low-speed applications, such as direct-drive power generation, which has larger torque capability and more poles than traditional double-side TFPMGs. The structure and operation principles of the generator are described in detail. The 3-D finite-element method (3-D FEM) is employed to compute the no-load magnetic field distributions. The analytical results, including flux density waveform, electromotive force (EMF) waveform, and inductance waveform of the armature winding, are obtained to verify the principle and feasibility of the proposed generator. The cogging torque is also analyzed and optimized by the 3-D FEM. A prototype is fabricated, and some experiments are conducted. The experimental results of back EMF and waveforms of current and voltage with different loads verify the FEM analysis previews well.

첨단 나노소자 공정제어용 측정기술 연구

We developed a real-time three-polarizer spectroscopic ellipsometer based on a new data acquisition algorithm and a general data reduction (the process of extracting the ellipsometric sample parameters from the Fourier coefficients). The data acquisition algorithm measures Fourier coefficients of radiant flux waveform accurately and precisely. The general data reduction is introduced to represent the analytic functions of the standard uncertainties of the ellipsometric sample parameters, and the extracted theoretical values closely agree with the corresponding experimental data. Our approach can be used for optimization of measurement conditions, instrumentation, simulation, standardization, laboratory accreditation, and metrology.

A fast general core loss model for switched reluctance machine

In the present paper, an analytical core loss model is introduced for the SRM (switched reluctance machine) which can be applied to different conventional types of this machine. Using the two mathematical models introduced before, the static characteristic of flux-linkage with a phase is obtained accurately in the core loss model first. Analyzing the machine based on the phase voltage equation, the stator pole flux waveform is then predicted. Considering an available flux model in the developed core loss model, the flux waveforms in various parts of the magnetic circuit of the machine are derived from the predicted stator pole flux waveform. Since the determined flux waveforms are completely non-sinusoidal, the improved Steinmetz equation is utilized in the developed core loss model for core loss estimation. In order to use the core loss model which is implemented totally in MATLAB software, one should just identify the design and control parameters. Due to high computation speed, the developed model can be utilized appropriately for optimal design of the SRM. Experimental results and finite element calculations are given for validation of the developed core loss model.

Analysis of the Torque Production Mechanism for Flux-Switching Permanent-Magnet Machines

This paper investigates the principles underlying torque production in a flux-switching permanent-magnet (FSPM) machine. Because the phase windings and permanent magnets (PMs) in FSPM machines are both located on the stator, the torque production mechanism is not the same as for a conventional PM synchronous machine. Spatial harmonic analysis is applied to examine the frequency components present in the electric and magnetic loading of the machine. Since torque is proportional to the product of the electric and magnetic loading, understanding the source of the principal harmonics in these waveforms yields powerful insights into the components that result in torque production. The analysis is first presented for a specific FSPM machine (12-slot/10-pole) and then extended to a general FSPM machine. The primary torque-producing harmonics in the air-gap flux density waveform are found to be the heterodyned harmonics of the magnetomotive force produced by the stator magnets and the air-gap permeance seen by the stator looking into the rotor. Analytical results are compared to results from finite-element analysis and exhibit good agreement.

Universal evaluations and expressions of measuring uncertainty for rotating-element spectroscopic ellipsometers.

We obtain the universal evaluations and expressions of measuring uncertainty for all types of rotating-element spectroscopic ellipsometers. We introduce a general data-reduction process to represent the universal analytic functions of the combined standard uncertainties of the ellipsometric sample parameters. To solve the incompleteness of the analytic expressions, we formulate the estimated covariance for the Fourier coefficient means extracted from the radiant flux waveform using a new Fourier analysis. Our approach can be used for optimization of measurement conditions, instrumentation, simulation, standardization, laboratory accreditation, and metrology.

Analytical Solution of Magnetic Field Distribution in Brushless Permanent Magnet Machines With Rotor Axis Deflection

An analytical technique is presented to predict the magnetic field distribution in the brushless permanent magnet machine with rotor axis deflection. Focusing on the no-load field due to the magnets, a perturbation method is employed to solve the governing equations and associated boundary conditions defined on the cross section along the flux paths. The derived results consisting of the zeroth-order and the first-order terms are validated by the finite-element analysis. According to the case study, the curves from the two calculations are consistent with each other. It also shows that the rotor axis deflection results in some distortion of the air-gap flux density waveform.

Unified model of temperature dependence of core losses in soft magnetic materials exposed to non-sinusoidal flux waveforms and DC bias condition

Purpose – The purpose of this paper is to present modelling of power losses dependences on temperature in soft magnetic materials exposed to non-sinusoidal flux waveforms and DC bias condition. Design/methodology/approach – Scaling theory allows the power loss density to be derived in the form of a general homogeneous function, which depends on the peak-to-peak of the magnetic inductance ΔB, frequency f, DC bias HDC and temperature T. The form of this function has been generated through the Maclaurin expansion with respect to scaled frequency, which suit very much for the Bertotti decomposition. The parameters of the model consist of expansion coefficients, scaling exponents, parameters of DC bias mapping, parameters of temperature factor and tuning exponents. Values of these model parameters were estimated on the basis of measured data of total power density losses. Findings – The main finding of the paper is a unified methodology for the derivation of a mathematical model which satisfactorily describes the total power density losses versus ΔB, f, HDC, and T in soft magnetic devices. Research limitations/implications – Still the derived method does not describe dependences of the power density loss on shape and size of considered sample. Practical implications – The most important achievement is of the practical use. The paper is useful for device designers. Originality/value – This paper presents the algorithm which enables us to calculate core losses while the temperature is changing. Moreover, this method is effective regardless of soft magnetic material type and the flux waveforms as well as the DC bias condition. The application of scaling theory in the description of energy losses in soft magnetic materials justifies that soft magnetic materials are scaling invariant systems.

ステータ巻線励磁法による製造工程が誘導機用ステータコアの磁気特性に及ぼす影響評価

Past magnetic property measuring methods such as the single sheet test (SST) and the Epstein method cannot quantitatively evaluate magnetic properties of an actual stator core that shows complex shape. Therefore, we are researching the stator winding excitation method as a new method to evaluate magnetic properties (iron loss and maximum magnetic flux density at a tooth) of an actual stator core after each manufacturing process. This method can directly measure them using a dummy rotor and a three-phase stator winding. To actualize this method, we constructed a new measuring system that consists of an iron loss measurement system and a multichannel data acquisition system. According to our experimental result using the proposed iron loss measurement system, the iron loss of the actual stator core that completed all manufacturing processes was about 2.3 times larger than an iron loss of an unprocessed electrical steel sheet. In addition, the proposed multichannel data acquisition system shows observation results of the magnetic flux density waveform and of maximum magnetic flux density at each tooth of the shrink fitting processed actual stator core. From our observation result, maximum magnetic flux density at each tooth was influenced by the compressive stress of a frame.

Performance Comparison and Analysis of (HEFSM) and (FEFSM) Using Segmental Rotor Structure

This paper presents a new structure of hybrid excitation flux switching motor (HEFSM) using segmental rotor and the comparison of HEFSM and FEFSM using segmental rotor is performed to find the best candidate for hybrid electric vehicles (HEV). (HEFSM) using segmental rotor contains both the FEC and PM on the stator to produce maximum flux linkages. Initially, the coil arrangement tests are examined to validate the operating principle of the (HEFSM) using segmental rotor. Moreover the profile of flux linkage, cogging torque, and torque characteristics at various armature current densities of both the (HEFSM) and (FEFSM) using segmental rotor are observed based on 2D-finite element analysis (FEA). Initially performances show that HEFSM using segmental rotor produces torque of 18 Nm with low cogging torque and sinusoidal flux waveform. Thus by further design optimization the proposed motor will effectively achieve the target performances.

Magnetic Flux Analysis of E-Core Hybrid Excited FSM with Various Rotor-Pole Topologies

This paper presents magnetic flux analysis of E-Core Hybrid Excited FSM with various rotor pole topologies. The stator consists of three active fluxes sources namely armature coil, field excitation coil and permanent magnet, while the rotor consists of only stack of iron which is greatly reliable for high speed operation. Initially, coil arrangement tests are examined to validate the operating principle of the motor and to identify the zero rotor position. Then, performances of 6S-4P, 6S-5P, 6S-7P and 6S-8P E-Core HEFSMs such as flux path, flux linkage, cogging torque and flux distribution are observed. As conclusion, 6S-5P and 6S-7P designs have purely sinusoidal flux waveform and less cogging torque suitable for high torque and power motor.

Design Studies and Analysis of Single Phase 8S-12P Field Excitation Flux Switching Motor

This paper presents a new structure of field excitation flux switching motor (FEFSM) as an alternative candidate of non-permanent magnet (PM) machine. The rotor is consisted of only stack of iron and hence, it is reliable and appropriate for high speed operation. Initially, the coil arrangement tests are examined to validate the operating principle of the motor and to identify the zero rotor position. Furthermore, the profile of flux linkage, induced voltage, cogging torque, torque and power characteristics are observed based on 2D finite element analysis (FEA). Initial performances show that 8S-12P FEFSM produce torque and power of 8.79Nm and 1.5kW, respectively with low cogging torque and sinusoidal flux waveform. Further design refinement and optimization will be conducted to improve the performances of the motor.

Investigation of Iron Losses in Mixed Frequency Flux Density Waveforms

A multi-harmonic magnetic flux density waveform controller for the Epstein frame is developed. The controller has the ability to produce high quality, single frequency, flux waveforms with low harmonic content and non-sinusoidal waveforms consisting of a superposition of many harmonics. The controller employs proportional control on the real and imaginary parts of the secondary voltage harmonics, where the real axis is determined by the fundamental harmonic, and can be used to either add or cancel higher order harmonics. Specific loss measurements are reported for 29 gauges M19 from AK Steel. Single frequency data are used to determine the coefficients of the frequency-domain Bertotti equation; the coefficients are then applied to the time-domain Bertotti loss equation. Magnetic loss testing is performed on non-sinusoidal flux-density waveforms, and the ability of both the frequency and time-domain Bertotti equations to predict the loss is discussed and compared with the measured loss.

Core Loss Analysis and Calculation of Stator Permanent-Magnet Machine Considering DC-Biased Magnetic Induction

In this paper, core loss characteristics of stator permanent-magnet (PM) machines are analyzed and calculated, in which the unique dc-biased magnetic induction is taken into account. The flux density variation patterns in some key points in a doubly salient PM (DSPM) machine are analyzed by the two-dimensional time-stepping finite-element method. To calculate the core loss of stator and other minor hysteresis loops under dc magnetic bias, core loss characteristics of silicon steel sheet under dc-biased induction condition are first tested by a simple test system based on traditional Epstein frame and a functional relationship between the change of dc-biased induction and hysteresis loss is proposed. Two core loss calculation methods considering rotational magnetization based on flux density waveform are improved to take the influence of dc-biased magnetic induction into consideration. The calculation results are verified by experiments on a prototype DSPM machine. The conclusions are also applicable to other kinds of stator PM machines.

Modeling and analysis of switched reluctance generator using finite element method

In the present paper, a parametric electromagnetic model is developed for the switched reluctance generator (SRG) with the finite element method (FEM) using the ANSYS finite element (FE) package which can be considered appropriately for accurate analysis and optimal design of the SRG. The performance principles of the SRG are briefly explained and some important electromagnetic characteristics of the SRG including phase current and instantaneous input power are predicted using the developed electromagnetic model. Carrying out the transient analysis, there is this possibility to predict the flux waveforms within the machine and therefore a core loss model is then introduced for the SRG. Applying the developed electromagnetic model to an 8/6 SRG, simulation results are presented and some critical issues are identified which can be attended in design of the control system of the SRGs.

DTC Based Induction Motor Speed Control Using 10-Sector Methodology for Torque Ripple Reduction

A direct torque control (DTC) drive allows direct and independent control of flux linkage and electromagnetic torque by the selection of optimum inverter switching modes. It is a simple method of signal processing which gives excellent dynamic performance. Also transformation of coordinates and voltage decoupling are not required. However, the possible discrete inverter switching vectors cannot always generate exact stator voltage required, to obtain the demanded electromagnetic torque and flux linkages. This results in the production of ripples in the torque as well as flux waveforms. In the present paper a torque ripple reduction methodology is proposed. In this method the circular locus of flux phasor is divided into 10 sector as compared to six sector divisions in conventional DTC method. The basic DTC scheme and the 10-sector method are simulated and compared for their performance. An analysis is done with sector increment so that finally the torque ripple varies slightly as the sector is increased.

The Minor Hysteresis Loop Under Rotating Magnetic Fields in Machine Laminations

In rotating ac machines, the saturated flux density waveforms contain harmonics, which create minor hysteresis loops. The minor hysteresis loops in machine laminations constitute an additional loss which requires modifications in traditional core loss formulas. This causes a serious challenge in core loss estimation. The task becomes more competitive under rotating magnetic fields, where the minor loop behavior has not been investigated yet. This paper highlights the problem of harmonics in rotating fields and its effect on the core loss estimation. In addition, the behavior of minor loops under rotating fields is compared with the minor loops under pulsating fields. Measurements were carried out on a nonoriented silicon steel sample of M36G29 with different fundamental frequencies of interest to the industry, 60 Hz and 400 Hz, with consideration of the third harmonic at each frequency. A design of magnetizing test fixture based on an electromagnetic Halbach array is used to perform these measurements. Results are presented and discussed.