Modeling and vector control of synchronous reluctance motorsincluding stator iron loss

The influence of the stator iron loss cannot be neglected since the high-speed operation and precision torque control of AC motors are required. This paper presents the modeling and vector control of synchronous reluctance motors including the stator iron loss. The stator iron loss is modeled by additional windings on the d-q axes, and is introduced as an equivalent iron loss resistance in voltage equations under the assumption that the losses in the stator core are produced in equivalent eddy current windings on d-q axes. The equivalent iron loss resistance is inserted in series with exciting inductance, and the d and q axes interfere with each other through the equivalent iron loss resistance. To achieve vector control, the d-q axis currents are decoupled by nonlinear control voltages. As a result, the instantaneous torque control scheme is equal to that of a DC machine and the torque control is simplified     

Proposition of new mathematical models with stator core loss factor for induction motor

This paper proposes new mathematical models with stator core (iron)‐loss factor for induction motors intended to generate precise and/or efficient torque via vector control. The proposed models have a structure in which the stator core‐loss resistance is equivalently placed purely in parallel with the stator inductance. It is shown that stator core losses consisting of eddy‐current and hysteresis losses can be properly represented by the parallel resistance, and, in particular, eddy‐current loss by a constant one. The models are composed of three basic vector equations in the general frame of an arbitrary angular frequency, such as fourth‐order differential equations describing motor dynamics, the torque equation, and the energy conversion equation. These basic equations are essential for vector control design taking core loss into consideration. The proposed models are most compact in the sense of the number of both the employed parameters and the interior states of the motor. Compactness is an important factor for modeling and is useful for designing vector control systems. © 2000 Scripta Technica, Electr Eng Jpn, 134(1): 64–75, 2001     

New block diagrams using vector signals in the general frame of reference for AC motors with stator core losses

This paper presents new block diagrams for induction and synchronous motors with stator core losses such as eddy‐current and hysteresis losses. The proposed block diagrams succeed in realizing simple and clear configurations with physically meaningful vector signals, which are helpful for understanding motor electromagnetic mechanism and useful for designing controllers for them. Vector signals, which are defined in the general reference frame, are utilized as transfer signals between blocks. The proposed vector‐signal block diagram in the frame can be directly and easily reduced to the one in such a specific frame as a stationary or synchronous frame simply by adding certain constraints to it. Shown are three configurations for induction motor, two for synchronous motors including permanent magnet cylindrical motor, permanent magnet salient‐pole motor, and reluctance motor. © 2001 Scripta Technica, Electr Eng Jpn, 138(2): 59–70, 2002     

Analysis of Eddy‐Current Losses in Solid Iron Under dc‐Biased Magnetization Considering Minor Hysteresis Loops

In designing solid‐pole synchronous machines, it is important to take into account the surface eddy‐current losses in the field pole cores. In this study, a solid‐iron ring specimen is adopted as an approximate model of solid‐pole surfaces in order to conduct a fundamental study of the surface losses. The influence of the minor hysteresis loops on the losses under dc‐biased magnetization is investigated. The losses in the ring under dc‐biased magnetization are measured and analyzed by finite element analysis (FEA). The losses computed by the FEA considering minor loops are nearly the same as those measured. In contrast, the eddy‐current losses computed by FEA without considering minor loops are considerably inaccurate because the incremental permeability is overestimated and the skin depth is underestimated. It is important to consider hysteresis for the accurate calculation of the surface eddy‐current losses under dc‐biased magnetization.     

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     

Optimal current control methods of a non‐salient pole hybrid field‐synchronous motor for energy‐efficient and wide speed‐range operation

This paper proposes new practical optimal current control methods for a newly emerging class of non‐salient pole synchronous motors with hybrid rotor fields by both permanent magnet and winding. In practical situations with limited voltage, the extensively used permanent magnet synchronous motor hardly achieves an ideal performance that allows simultaneously both low‐speed high‐torque and wide speed‐range operations, due to its constant magnet field. Hybrid field synchronous motors (HFSM) have recently emerged to achieve ideal performance as practical motors with controllable hybrid rotor field. For HFSM, the same torque can be produced by a variety of currents due to nonlinearity between torque and currents. Consequently, appropriate determination of a set of stator and rotor current commands plays a key role in achieving possible energy‐efficient and wide speed‐range operation. Proposed methods determine the current commands corresponding to a given torque command such that total winding copper loss due to stator and rotor currents can be minimized if the exact solution exists; the best approximate torque can be produced if no exact solution exists. The determined current commands are optimal in the sense of energy efficiency or degree of approximation in wide speed‐range operation under voltage limit. New real‐time recursive algorithms searching the optimal current solution are also given. The proposed methods are analytical but practical, and their usefulness is verified through experiments. © 2006 Wiley Periodicals, Inc. Electr Eng Jpn, 156(1): 70–83, 2006; Published online in Wiley InterScience ( www.interscience. wiley.com ). DOI 10.1002/eej.20156     

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.     

Sensorless controls of salient‐pole permanent magnet synchronous motors using extended electromotive force models

In this paper, we propose a new mathematical model for synchronous motors and a sensorless control method based on it. To control permanent magnet synchronous motors, knowledge of rotor position and velocity are necessary. Heretofore, expensive sensors have been used to detect rotor position information. Although many sensorless control methods based on the electromotive force (EMF) have been developed for non‐salient‐pole permanent magnet motors, they cannot be applied for salient‐pole motors without approximation because of complications in the mathematical model; this is turn may lead to problems of instability. To solve this problem, we propose an extended electromotive force model for synchronous motors. The proposed model has a simple structure, making position estimation possible without approximation. Experimental results show that the proposed model and method are valid. © 2003 Wiley Periodicals, Inc. Electr Eng Jpn, 146(3): 55–64, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10257     

Basic study of loss reduction effect by Stator‐Tooth slits in turbine generators. comparison between calculated results of generators and basic experiments

In this study, we investigate the loss reduction effect by stator‐teeth slits in turbine generators on the basis of electromagnetic field analysis and basic experiments. First, the loss reduction effect in the generator is estimated by the 3D finite element method and the theoretical solution of eddy current loss. Next, an experiment using a simple model that simulates the stator‐core ends of the turbine generator is carried out. It is clarified that the loss reduction effect by the slits depends on the frequency, flux density, and permeability of the stator teeth because the loss reduction effect weakens with the skin effect. © 2013 Wiley Periodicals, Inc. Electr Eng Jpn, 183(3): 17–25, 2013; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/eej.22345     

PWM逆变器供电引起的轴向磁通非晶电机谐波损耗的解析计算

非晶合金材料具有出色的低损耗特性,适于用作高频电机的铁心,但PWM逆变器供电会导致高频电机谐波损耗严重增加。在电机初始设计阶段,快速准确计算出谐波损耗是轴向磁通非晶合金永磁电机设计及优化的关键。针对3D时步有限元计算耗时长的问题,改进现有多环等效模型的计算方法,推导了考虑PWM逆变器供电高次谐波电流影响的气隙磁通密度解析计算方法,并在此基础上推导了定子铁心损耗及考虑涡流反作用影响的转子涡流损耗的解析计算方法。将谐波损耗的解析计算值与样机实验值以及3D有限元计算值进行对比,结果显示谐波损耗的平均计算误差仅为9.69%,解析模型具有较高的计算精度。     

永磁同步电机转子涡流损耗计算的实验验证方法

表贴式永磁同步电机转子涡流损耗的计算受到很多学者的关注.但由于转子涡流损耗测量困难,目前还没有一种准确的实验验证方法.本文提出一种能分离出电机基本损耗、高频铜损和高频铁损的实验验证方法,对该验证方法的原理和实施方法进行了分析,并以一高速永磁同步电机的转子损耗测试为例,对永磁同步电机的高频损耗进行了测试和分析.实验结果表明,该验证方法能准确反映转子涡流损耗规律.     

Analysis of a self‐regulated,self‐excited,brushless three‐phase synchronous generator,which includes the effect of core losses

This paper presents a novel analysis of a self‐regulated, self‐excited, brushless three‐phase synchronous generator, which includes the effect of core losses. The core losses are modeled by equivalent core loss resistances connected to additional windings on the generator's magnetic coupling model. A magnetic circuit is drawn from the magnetic coupling model, and an electrical equivalent circuit of the generator is derived by utilizing a duality between the magnetic and electric circuits. Using this equivalent circuit, the generator's steady‐state performance is theoretically predicted, and the results are verified through experiment. In addition, the power losses during power generation are analyzed quantitatively. The proposed analysis takes into account the nonlinearity of the exciting impedances due to magnetic saturation. © 2000 Scripta Technica, Electr Eng Jpn, 131(2): 51–60, 2000     

A method to determine direct‐ and quadrature‐axis inductances of permanent magnet synchronous motors

The equivalent circuit constants of permanent magnet synchronous motors are needed in the calculation of operation characteristics, construction of a control system, etc. These constants can be computed from the data on structural form and materials. However, measurements are necessary to obtain highly precise values. Methods for measurement of the d‐ and q‐axis inductances can be roughly divided into rotational and standstill methods. The standstill methods have the advantage that they are easy to carry out. However, it is difficult to consider magnetic saturation and distortion of the change in the armature winding inductance. The accuracy of the standstill method can be improved if these effects can be readily taken into account. This paper describes a standstill method for measuring accurate d‐ and q‐axis synchronous inductances of permanent magnet synchronous motors. By utilizing the fact that the EMF interference terms in the motor voltage equation considering the distortion of the inductance change are equal to zero when the rotor is in a specific position, the proposed method determines the inductances considering both magnetic saturation and inductance distortion effects from simple off‐line standstill testing. In addition, this method is capable of taking cross‐magnetic saturation into account when used with the necessary testing equipment. The proposed method was implemented on a 0.4‐kW interior permanent magnet synchronous motor with concentrated stator winding. The validity of the proposed method was demonstrated by comparing the measured and calculated results of the no‐load and on‐load characteristics. © 2010 Wiley Periodicals, Inc. Electr Eng Jpn, 171(3): 41–50, 2010; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20969     

用于电机损耗精细化分析的分段变系数铁耗计算模型

提出一种用于电机损耗精细化分析的分段变系数铁耗计算模型,该模型以经典Bertotti三项常系数铁耗模型为基础,引入涡流损耗附加磁通密度高次项及磁滞损耗附加磁通密度低次项,用于考虑磁路饱和导致涡流损耗增加及谐波磁场引起局部磁滞损耗增加的现象,同时,该模型中主要系数均随磁通密度幅值和频率变化,能很好地反映基波及谐波磁场对铁耗的影响,并对磁滞、涡流及异常损耗进行准确分离,实现铁耗精细化分析。为了验证该文所提模型的有效性及准确性,以Y132S-4、5.5k W和YX3-250M-4、55 k W两台感应电机为例,利用文中模型与经典Bertotti三项常系数模型对两台电机在不同电压下的空载铁耗进行实测和计算对比,结果表明该文所提模型在较宽范围内与实测值吻合程度较高。     

Stator‐core structure and winding technology for EPS motors

Electric power steering (EPS) motors must have the performance characteristics of precision machines. They should be compact and produce high power. Moreover, the loss torque and the change of loss torque should be as low as possible. In this study, dividing the stator core into small blocks and winding the coils densely on the blocks are shown to be effective techniques for achieving compact high‐power motors. We examined whether I‐shaped divided cores or T‐shaped divided cores were more suitable for EPS motors in terms of motor performance and production cost. We built two experimental motors, one with I‐shaped divided cores and the other with T‐shaped divided cores, and measured three important characteristics of EPS motors: output torque, loss torque, and loss torque change. The T‐type motor proved to have better performance for all three characteristics. Moreover, the productivity of the T‐type motor was shown to be higher than that of the I‐type motor, indicating that overall, T‐shaped divided cores are advantageous for the stators of EPS motors. Next, we considered a new winding method for the continuous winding of two T‐shaped cores in order to achieve a compact terminal connection board. The extending lines made by the new winding method do not extend beyond the coil end. Therefore, this method will contribute to reduction of the axial dimension of EPS motors. © 2011 Wiley Periodicals, Inc. Electr Eng Jpn, 175(1): 35–42, 2011; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/eej.21085     

A dynamic mathematical model and vector block diagrams for class of hybrid‐field synchronous motors

This paper proposes a new dynamic mathematical model and new block diagrams for a newly emerging class of salient‐pole hybrid‐field synchronous motors (HFSM) that have rotor field by both permanent magnet and winding. The proposed mathematical model has the following completeness and generality. (1) It consists of three consistent basic equations such as circuit, torque, and energy‐transmission equations. (2) It deals with pole saliency and contains nonsaliency as a special case. (3) It is a dynamic model and contains a static one as a special case. (4) It is established in the general reference frame including stator and rotor reference frames as special cases. The proposed new block diagrams using vector signals for salient‐pole HFSM are established based on the model. It has the following attractive features. (1) It succeeds in realizing clear configurations with physically meaningful vector signals, which are helpful for understanding motor electromagnetic mechanisms and useful for designing controllers for the salient‐pole HFSM. (2) Vector signals utilized as transfer signals between blocks are defined in the general reference frame. Consequently, the vector‐signal block diagrams in the frame can be directly and easily reduced to the ones in such a specific frame as stator and rotor frames. (3) It is compact. Two typical and compact but sufficiently general vector‐signal block diagrams are newly presented. © 2005 Wiley Periodicals, Inc. Electr Eng Jpn, 152(2): 47–57, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20112     

Stray load loss analysis of induction motor-comparison of measurement due to IEEE standard 112 and direct calculation by finite-element method

The purpose of this paper is to specify the main components of the stray load loss of induction motors from both results of measurement and analysis. The IEEE standard 112 Method B is applied to the cage induction motor for the measurement of the stray load loss. On the other hand, the losses generated at the stator core, the rotor core, and the rotor cage are calculated directly by the finite-element method considering the magnetic saturation and the harmonic fields, which vary due to the load condition. The measured and the calculated torque, losses, and efficiency agree well. It is clarified that the main parts of the stray load loss in the case of the analyzed motor are the increase of harmonic losses due to load, which are the harmonic Joule losses of the rotor cage and the harmonic core losses of the stator and the rotor. The relationships between the losses separated by the measurement and the losses calculated directly by the finite-element method are also clarified.     

Examination of Eddy Current between Steel Sheets without Insulation and a Criterion for Determining the Necessity of Insulation

In the laminated core of transformers, motors, and so on, each electrical steel sheet is usually insulated in order to reduce the eddy current loss. It has been reported that insulation is not necessary in such a laminated core under some conditions. However, few studies have been performed in the form of a quantitative and systematic examination of the relationship between the insulation and eddy current. In this study, the eddy current losses of a core made of SPCC (cold rolled steel sheets) of different widths with and without insulation under various conditions are analyzed using the finite element method (FEM) and with the contact resistance taken into consideration. The equivalent circuit of a laminated core without insulation is presented, and can be used for determining the necessity of insulation. It is shown that the increase in the eddy current is affected by the ratio of the resistance of the steel to the contact resistance. An experimental investigation is also carried out.     

基于槽极比选择的切向永磁同步电机永磁体涡流损耗抑制措施

为抑制切向永磁同步电机的永磁体涡流损耗,基于麦克斯韦方程和本构方程,对永磁体形状进行近似假设,构建了永磁体涡流损耗的估算模型。使用一种基于卡特系数概念的磁导函数来估算由于定子开槽引起的槽下磁感应强度变化。基于五台槽极比分别为1.05、1.20、1.30、2.40和3.60的电机设计方案对理论分析结论进行了验证。在负载电流和两倍负载电流下,分析永磁体损耗,得到了每台电机的径向气隙磁密曲线及其谐波含量。考虑到增加槽极比对定子铁耗和永磁体涡流损耗的削弱效果,给出了电机槽极比选择策略。研究结果表明,增加槽极比能减弱定子槽下磁感应强度变化,从而抑制气隙磁场中低次谐波含量,减小永磁体涡流损耗,使电机运行更加可靠,但也会引入更多高次谐波,从而增加定子铁耗。     

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.