Magnetic Circuit Model Considering Magnetic Hysteresis

Quantitative estimation of core loss considering magnetic hysteresis property is strongly required to develop high‐efficient electrical machines. This paper presents a novel magnetic circuit model considering magnetic hysteresis. In the proposed model, dc hysteresis loss is calculated by the Landau–Lifshitz–Gilbert (LLG) equation, while classical and anomalous eddy current losses are calculated in the magnetic circuit. It is demonstrated that the hysteresis loop under PWM wave excitation can be expressed by the proposed model. The validity and effectiveness of the method are proved by comparing with measured values.     

用数字仿真计算畸变电压条件下电力变压器的正弦磁滞损耗

详细阐述了计算畸变电压条件下变压器低损耗硅钢片铁心中磁滞损耗的一种数字仿真方法。这种方法使用的模型是以分段线性化去模拟铁心材料的稳态Ｂ／Ｈ特性曲线为基础的。根据模拟的Ｂ／Ｈ特性曲线求出主磁滞回线和小磁滞回线的面积，从而计算出空载损耗实测值中的磁滞损耗和涡流损耗分量。最后计算出电源电压为正弦形时的变压器空载损耗。计算值和试验结果吻合很好。这种方法可以用于电源电压畸变时校正测出的变压器空载损耗。     

ASYNCHRONOUS PERFORMANCES OF HYSTERESIS MOTORS UNDER UNBALANCED CONDITIONS

ABSTRACT

The torque-speed curves of an hysteresis motor under unbalanced conditions are computed by a numerical method. The magnetic characteristic of the rotor ring is represented by the Preisach-Néel's model. This method takes into account the minor loops which appear on the B(H) characteristic in the case under consideration. Computed and experimental curves are compared. This work shows that eddy currents are of no importance on the shape of these curves     

Current Transformer Model

This paper presents a current-transformer (CT) model that is useful for low-frequency applications. To describe the iron-core magnetic behavior, a hysteresis model is proposed, which is able to generate minor asymmetric loops and remanent flux. The effects of classic eddy current losses and anomalous losses are represented by linear and nonlinear resistors, respectively. The obtained results are compared with those calculated by the Preisach's model and measured in the laboratory. This model may be applied in power system protection studies, as it is the case of numeric correction of distorted secondary currents in current transformers (CTs)     

Power losses in steel pipe delivering very large currents

This paper presents a finite difference time domain solution for the electromagnetic fields in ferromagnetic conducting steel pipes of the type used to deliver large currents for in situ heating of heavy oil reservoirs and for in situ environmental decontamination. A method is described whereby a single measured hysteresis loop can be used to deduce the family of hysteresis loops that governs the variable magnetic behavior throughout the pipe wall. Hysteresis and eddy current losses are calculated, and it is shown that hysteresis effects greatly alter the eddy current distribution and can more than triple the total power losses in the steel pipe when compared to the power losses that would be present if hysteresis effects are ignored and magnetic permeability is assumed constant     

A new separate‐identification method of two stator equivalent core‐loss resistances corresponding to hysteresis and eddy‐current losses for parallel‐type mathematical models of AC motors

This paper proposes a new unified method for identifying equivalent stator core‐loss resistance of AC motors, which can be applied to both induction and synchronous motors. In order to realize AC motors that exhibit high performance such as precise torque generation and/or efficient energy transmission, stator core loss cannot be neglected in designing vector control systems. It is common to model stator core loss in magnetic circuits as loss caused by equivalent resistance in electrical circuit. One of the best mathematical models for controlling AC motors with core loss is a kind of parallel‐type model that succeeds in modeling both eddy‐current and hysteresis losses. The newly proposed method succeeds in identifying separately and simultaneously two kinds of equivalent core‐loss resistances on the model corresponding to eddy‐current and hysteresis losses. The practical usefulness of the method is evaluated and confirmed through experiments using two induction motors of 5.5 and 2.0 kW having relatively high core losses and a permanent magnet synchronous motor of 750 W having relatively low core losses. © 2003 Wiley Periodicals, Inc. Electr Eng Jpn, 143(4): 50–63, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10152     

有限元法计算交联电缆涡流损耗

电力电缆的导体交流损耗和金属屏蔽层涡流损耗是影响电缆群温度场分布和电缆载流量确定的重要因素。为确定电缆运行中的损耗,在考虑趋肤效应和邻近效应的基础上,利用有限元法对电缆群不同排列方式和接地方式下的导体交流损耗和金属屏蔽层涡流损耗进行了计算。计算结果表明,导体交流损耗随回路数增多、电缆间距减小而增大,金属屏蔽层损耗随回路数增多而增大,与电缆间距的关系与接地方式有关,单端接地时,金属屏蔽层损耗随间距增大而减小,双端接地时,金属屏蔽层损耗随间距增大而增大。     

基于对偶性原理的三相多芯柱变压器暂态模型

提出了一种基于对偶性原理的三相多芯柱变压器暂态模型；通过分析三相多芯柱变压器磁路模型并应用对偶性原理，建立了考虑电路与磁路耦合的变压器暂态计算模型，采用Jiles-Atherton铁磁磁滞模型来描述铁心模块的饱和以及磁滞效应，而涡流和杂散损耗用一个等值电阻替代，零序磁通用一个线性电感以及反映其涡流损耗的电阻代替；该模型可以计算分析直流偏磁和空载合闸等情况下变压器励磁电流以及铁心磁通等电气参数；算例分析结果与实验结果的对比证明了该模型的准确性。     

基于直流偏磁实验的叠片铁心磁化特性分析

铁心中直流磁通的预测是研究变压器直流偏磁问题的关键.本文提出基于损耗函数的改进迭代法,在考虑磁滞效应的同时对基本磁化曲线进行修正,计算叠片铁心内的直流磁通.通过比较励磁电流的测量值与计算值,验证了该方法的有效性和正确性.获得了直流偏磁条件下叠片铁心的磁滞回线和基本磁化曲线,对有无直流偏磁条件下的基本磁化曲线进行了比较....     

Dynamic model of a three-phase power transformer

An adequate mathematical model of a three-phase power transformer is one of the important elements in the programs for the computer analysis of power system transients. Featured in this paper is the simulation model of a three-phase, three-limb core-type power transformer. Nonlinear effects of saturation, hysteresis and eddy currents are considered. Two ways of creating major and minor hysteresis loops are presented. The transformer model, described by a system of time dependent differential equations, is solved by an efficient numerical algorithm. The behaviour of the transformer model during switching-in and fault transients, as well as other types of transients, has been tested. The computed transient waveforms are compared with the measured ones and there exists very close agreement between them     

Loss calculation of induction motors considering harmonic electromagnetic field in stator and rotor

A method of loss calculation for induction motors is proposed. The combined 3D–2D time‐stepping finite element analysis is carried out to obtain the copper loss and the time variation of the magnetic field in the motor. The iron loss is calculated approximately considering the time variation of the magnetic field direction and the minor hysteresis loops caused by the time‐harmonic fields using practical computer resources. The proposed method is applied to four types of induction motors, which are the solid rotor induction motors with/without slot and the cage induction motors with/without skew. The measured and the calculated total losses and the iron losses agree well in all cases. The differences of the loss distributions of each motor are also compared and investigated. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 147(2): 63–73, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10305     

Magnetization Mechanism of Si‐Gradient Steel Sheet Manufactured by CVD Siliconizing Process

Si‐gradient steel sheet, which has a silicon concentration gradient in the sheet thickness direction, manufactured by the chemical vapor deposition siliconizing process, possesses unique magnetic properties. In this paper, the magnetization behaviors of single crystals of Si‐gradient steel sheet are investigated in the <100> and <110> directions, comparing with Si‐homogeneous steel sheet, in order to clarify the magnetization mechanism. The internal stress of Si‐gradient steel sheet was evaluated. The induced magnetic anisotropy which arising according to the magnetoelastic effect is considered to play an important role in the magnetization process of Si‐gradient steel sheet. The reduction of eddy current loss can be explained by the effect of the magnetic flux concentration at the sheet surface resulting from the internal stress.     

A systematic method for the development of a three‐phase transformer non‐linear model

In this work, a novel three‐phase transformer non‐linear model is developed. The proposed model takes into account the magnetic core topology and the windings connections. The non‐linear characteristic curve of the core material is introduced by its magnetization curve or by its hysteresis loop using the mathematical hysteresis model proposed by Tellinen or the macroscopic hysteresis model proposed by Jiles–Atherton. The eddy currents effects are included through non‐linear resistors using Bertotti's work. The proposed model presents several advantages. An incremental linear circuit, having the same topology with the magnetic circuit of the core, is used in order to directly write the differential equations of the magnetic part of the transformer. The matrix L _d that describes the coupling between the windings of the transformer is systematically derived. The electrical equations of the transformer can be easily written for any possible connection of the primary and secondary windings using the unconnected windings equations and transformation matrices. The proposed methods for the calculation of the coupling between the windings, the representation of the eddy currents and the inclusion of the core material characteristic curve can be used to develop a transformer model appropriate for the EMTP/ATP‐type programs. Copyright © 2009 John Wiley & Sons, Ltd.     

Comparison of Switching Loss of Single‐Phase Step‐Up/Step‐Down Bidirectional Converter with Voltage‐Fed/Current‐Fed Hybrid‐Type Operation

Electric energy storage systems are very important as one of the solutions to global warming. Step‐up/step‐down characteristics are required for electric energy storage systems. In addition, such systems must have high efficiency, low cost, and small scale. Therefore, the authors proposed a single‐phase step‐up/step‐down bidirectional converter with voltage‐fed and current‐fed hybrid‐type operation. The proposed converter consists of a two‐quadrant dc–dc converter and a single‐phase voltage‐fed converter. The circuit has several advantages such as low switching loss, use of very small capacitance, and so on. In this paper, the authors compare a comparison of the switching losses with a simple analysis.     

直流偏磁状态下电力变压器铁心动态磁滞损耗模型及验证

直流偏磁状态下,电力变压器的附加损耗显著增加,试验测量得到的变压器空载损耗不能充分表征铁心实际损耗。为正确评估变压器铁心可能出现的过热问题,有必要建立其准确的数学模型。该文在Jiles-Atherton基本磁滞模型的基础上,从能量平衡原理出发,考虑铁心在交流状态下的涡流损耗和异常损耗,建立了合理可逆磁化系数条件下,以磁通密度作为输入量的铁心动态磁滞损耗模型。利用遗传算法提取试验变压器铁心在正常工作条件下的动态模型参数,并用于对不同幅值直流偏磁电流作用下的铁心损耗进行仿真计算。将计算结果与试验结果进行对比,发现二者吻合较好,说明该动态模型能较好的描述直流偏磁状态下电力变压器铁心动态磁滞损耗,验证了模型的正确性和实用性。     

Impacts of Transformer Core Hysteresis Formation on Stability Domain of Ferroresonance Modes

This paper investigates impacts of various formations of hysteresis on the stability domain of ferroresonance modes of a voltage transformer (VT). Based on four different hysteretic and two single-valued polynomial models, ferroresonance behaviors of the VT are studied. The hysteretic models are developed based on the Preisach theory. The first hysteretic model accurately duplicates the measured hysteresis loops of the VT in a wide variation range of the core excitation level. The other three hysteretic models represent different hysteresis loop formations. The polynomial models are based on identical single-valued polynomial magnetization characteristics but represent different core loss resistances (i.e., constant and dynamically varying core loss resistances, respectively). All of the models represent the same core losses as the measured value to investigate impacts of hysteresis loop formations on ferroresonance modes, independent of the corresponding hysteresis losses. The studies are conducted in time domain in the PSCAD/EMTDC software environment. The studies indicate that the VT model, which duplicates the measured hysteresis loops and the measured core loss over a wide range of excitation levels, results in more ferroresonance modes, expanded stability domains, and higher overvoltages. This paper concludes that formation of hysteresis is an independent factor which significantly impacts the ferroresonance phenomenon. Not only is it a single-valued magnetization characteristic but also a generic hysteretic characteristic; if it is not accurately constructed based on the measured core hysteresis data, it can result in significant error in determining the ferroresonance overvoltages and stability domains of the ferroresonance modes.      

A new approach to calculating core losses in the SRM

In switched reluctance motors (SRM), the flux waveforms are nonsinusoidal and different parts of the magnetic circuit have different waveforms. This paper presents a new approach of taking account of these flux waveforms in the calculation of core losses. Relations between the fluxes of different parts of the magnetic circuits are given in the form of matrix equations, where the fluxes are expressed in terms of normalized flux pulses. Rewriting the eddy-current loss term in the Steinmetz equation in terms of the square of dB/dt and combining it with the matrix equations, eddy-current losses for the complicated flux waveforms of the stator and rotor yokes are calculated. The effect of PWM is taken into account by considering the PWM voltage waveform as dB/dt. From the matrices, it is easy to count how many times full and minor hysteresis loops occur at each pole and yoke segment. The effect of the minor loop is taken into account based on experimental results. The proposed approach gives a systematic procedure for core loss calculation. The derived equations are simple and useful in the design of SRM     

Five‐phase modular stator surface‐mounted permanent magnet machine with reduced space sub‐harmonics

Multiphase modular stator surface‐mounted permanent magnet machines (MSPMs) feature short end connection, unity winding factor, and low cost. However, they also exhibit rich space harmonics. A five‐phase MSPM with reduced space sub‐harmonics is proposed in this paper. The phase‐shifting method and magnetic flux barriers are adopted to reduce the slot harmonic and lowest order harmonic, respectively. A modified MSPM used for phase shifting is specially proposed. Further, the phase‐shifted MSPMs without and with magnetic flux barriers are both studied to show the separate effectiveness of the phase‐shifting method and magnetic flux barriers. The phase‐shifting angle is determined based on winding function method and the optimal angle is fixed considering the minimal tooth width. A double‐layer MSPM with 20 slots and 22 poles is exemplified, and two single‐layer 40‐slot 22‐pole MSPMs, which are respectively equipped without and with magnetic flux barriers, are proposed. Finite element analysis is performed, and the comparison results show that the space sub‐harmonics, permanent magnet eddy current loss, and the lowest mode of vibration are largely reduced in the phase‐shifted MSPM with magnetic flux barriers. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

SURFACE LOSS REDUCTION IN GROOVED SOLID POLES

ABSTRACT

Surface loss due to higher harmonic magnetic flux in solid pole synchronous motor is generally quite significant. This loss is present in both synchronous and solid rotor induction motors. Grooving may be adopted as a method to reduce the surface loss of the solid pole. As the presence of the grooves on solid poles causes a part of the eddy current which is considered as an end effect problem, strictly theoretical solution of the problem is extremely difficult. In this paper loss equation of two layer rotor construction and approximate equation of the loss equation are analyzed.

If the depth of the groove is small compared with the depth of harmonic flux penetration, the part of the solid pole surface is considered partly to be the two layer rotor construction. Measured value of surface loss of grooved solid rotor is described and studied by considering the end effect. Correction cofficient k_r1, about the end effect is obtained by the experiment. The surface loss reduction factor is also obtained. This grooving technique is used for the solid pole synchronous motor and for the claw pole machine.     

谐波平衡有限元法用于饱和铁心的损耗分析

利用一种新的有效的谐波平衡有限元算法 ,结合Lavers等人提出的考虑谐波时迭片铁心的磁滞损耗和涡流损耗的模型 ,提出了一种较准确求解饱和铁心损耗的计算方法。并与传统的计算方法进行了比较。以铁磁型三倍频变压器的空载情况为例进行了仿真计算和物理实验。结果表明 ,考虑谐波磁通密度影响时的铁心损耗值与传统的仅考虑基波磁通密度时的值相比有显著的增加。物理实验验证了所提算法的正确性。为设计工作在高度饱和状态下的电器设备估算铁心损耗提供了有效的分析方法