Optimization of magnet arrangement in double‐layer interior permanent‐magnet motors

The arrangement of permanent magnets in double‐layer interior permanent‐magnet motors is optimized for variable‐speed applications. First, the arrangement of magnets is decided by automatic optimization. Next, the superiority of the optimized motor is discussed by considering d‐ and q‐axis equivalent circuits that take into account the magnetic saturation of the rotor core. Finally, experimental veri?cation is carried out with a prototype motor. It is con?rmed that the maximum torque of the optimized motor under both low‐speed and high‐speed conditions is higher than that of conventional motors because of the relatively large q‐axis inductance and small d‐axis inductance. © 2013 Wiley Periodicals, Inc. Electr Eng Jpn, 183(4): 54–63, 2013; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/eej.22348     

Determination of direct and quadrature axis inductances of synchronous reluctance motors with allowance for cross saturation

The d‐axis inductance of reluctance motor is affected by not only the d‐axis current but also the q‐axis current, because of cross magnetic saturation between the direct and quadrature axes. This situation is similar for the q‐axis inductance. The authors propose a method to determine the d‐axis inductance related to the d‐ and q‐axis currents and the q‐axis inductance related to the d‐ and q‐axis currents from a standstill test. This method involves the following four steps. First a rectangular‐wave voltage, alternated between plus and minus, is applied to the two armature winding terminals after breaking the rotor in the d‐axis position. Secondly, the voltage and current between the terminals are measured. Thirdly, the d‐axis inductance related with d‐axis current is calculated from the voltage and current. Finally, the process above is repeated when a DC current flows from the remaining armature terminal to neutral point terminal and the d‐inductance related to the d‐ and q‐axis currents is derived. A similar treatment applies when determining the q‐axis inductance related to the d‐ and q‐axis currents in the q‐axis rotor position. The method is implemented on a 1.1 kW–178 V–6.3 A‐4P–2200 min^?1 flux barrier type reluctance motor. Results of load performance on a vector controlled reluctance motor measured by on‐load tests and calculated from the d‐ and q‐axis inductances obtained by the proposed method clearly demonstrate the validity of the proposed method. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 149(4): 52–59, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10377     

内置式永磁同步电机电感参数的研究

分析了永磁体磁势和电枢磁势共同作用时内置式永磁同步电机的电感特性,基于交流静态法,提出了一种改进的测量内置式永磁同步电机定子自感和互感以及交直轴电感的方法。为了考虑饱和和交叉耦合效应对电感参数的影响,该方法首先根据所测电压和电流数据计算出不同转子位置和电流下的磁链,然后根据磁链计算出电机自感和互感以及交直轴电感参数,并应用该方法进行了实测研究。结果表明,实测结果与有限元分析结果吻合较好,验证了该方法的可行性和有效性。     

Sensorless control of synchronous reluctance motors based on extended electromotive force model and inductance measurement

In this paper, sensorless control for synchronous reluctance motors (SynRMs) without signal injection and an inductance measurement for position estimation are proposed. In the case of SynRMs, accuracy of inductances is the most important factor in realizing precise position estimation because inductances are largely varied by a magnetic saturation phenomenon. Therefore, the inductance measurement method, which can measure appropriate inductances for position estimation, is important as well as a sensorless control method. The inductance measurement based on the observer is discussed, and the measurement method and the parameter adjustment method for improved stability of the closed loop are proposed. The proposed method can measure inductances easily and be applied for permanent magnet synchronous motors, too. Finally, the proposed sensorless control method is verified experimentally. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 160(4): 70– 80, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/ eej.20274     

Determination of equivalent circuit constants of synchronous machines from the extended Dalton‐Cameron method

This paper presents a method of determining the equivalent circuit constants which accord with the physical construction of synchronous machines, using the dc decay testing method with the rotor in arbitrary position (proposed by the authors and called the extended Dalton–Cameron method). The conventional Dalton–Cameron method calculates the direct‐ and quadrature‐axis subtransient reactance from a standstill response test in any arbitrary rotor position using a single‐phase power supply. The extended Dalton–Cameron method determines the direct‐ and quadrature‐axis operational impedances for each slip from a standstill response test using a small‐capacity dc power supply. The direct‐ and quadrature‐axis operational impedance loci thus obtained synchronous machine constants (subtransient, transient, and synchronous reactances) are used to estimate the direct‐ and quadrature‐axis equivalent circuit constants which accord with the physical construction of synchronous machines. As an example, equivalent circuit constants are determined for a 10‐kW laminated salient‐pole‐type synchronous machine with damper winding. The validity of the equivalent circuit constants is confirmed by comparing the calculated resistance and leakage reactance of the field winding determined from the operational impedance when the terminals are short‐circuited, to those when the terminals are connected to an external resistance. © 2001 Scripta Technica, Electr Eng Jpn, 138(1): 56–67, 2002     

Basic Design Method for SPMSM Based on Air‐Gap Magnetic Flux Density Distribution Focusing on Image Magnetic Pole

This paper presents a basic design method for the surface‐mounted permanent magnet synchronous motor (SPMSM) for both distributed and concentrated windings. The design is based on the air‐gap magnetic flux density distribution focusing on the image magnetic pole. The calculus equation of the air‐gap magnetic flux density distribution is analytically derived by supposing the magnetic pole is located on the magnet surface and image planes. In this study, a three‐phase and double‐layer stator winding SPMSM that has a linear demagnetizing characteristic magnet, such as a ferrite or rare‐earth magnet is considered. From the required specifications and design conditions, the design target values of the parameters that appear in the voltages equations of the d–q axis coordinate system are calculated. Then, the relational equations for the torque constant, d‐axis inductance, copper loss, and the maximum current density are presented as a function of three design parameters under i_d = 0 control. They are the stator stack length, the number of coil turns in series in a phase, and the slot bottom length. Hence, this approach reduces the SPMSM basic design to the problem with these design parameters has to be solved. The proposed method makes it possible to address the concentrated winding as a special case of the distributed winding. The FEA results confirm the validity of the proposed basic design method for both distributed and concentrated windings.     

直驱型机电作动器中永磁容错电机非线性模型研究

针对直驱型机电作动器中永磁容错电机存在饱和凸极效应的特点,建立三相12槽10极永磁容错电机非线性数学模型。将电机绕组磁链分为定子电流和转子磁极产生的磁链两部分,把转子磁极产生磁链等效为随转子位置变化的等效电流产生磁链,将电感表示为绕组总电流函数。辨识电机非线性磁链模型,在此基础上得出永磁容错电机非线性模型参数,在Matlab/Simulink中建立永磁容错电机非线性数学模型,并进行仿真分析。最后,利用有限元法和实验验证永磁容错电机非线性数学模型的有效性。此模型可推广到其他永磁容错电机中,可以为永磁容错电机无传感器控制设计提供参考,对提高直驱型机电作动器可靠性很有帮助。     

Determination of Synchronous Reactance and No‐Load Saturation Curve of Synchronous Machines by dc Test Considering Magnetic Saturation Effect

dc Tests can accurately determine the unsaturated synchronous machine‐equivalent circuit constants by a simple standstill test. This paper presents two improved dc tests that account for the magnetic saturation of the stator iron core by the main flux. These tests are tentatively named Step Response Test (I) and Step Response Test (II). The former can predict the incremental d‐axis synchronous reactance by performing a Fourier transform of the voltage and current measured when a small step voltage is applied to the two armature terminals as a field current flows. The latter can determine the incremental d‐ and q‐axes synchronous reactances by the same Fourier transform of the voltage and current measured when a small step voltage is applied to the two armature terminals as an armature current flows. In addition, this paper introduces a new method to calculate not only the static d‐ and q‐axes synchronous reactances but also the no‐load saturation and short‐circuit characteristic curves. This new method does not require the results from any additional tests including the rotational driving tests and dimensional information, which can only be obtained from the manufacturer. To demonstrate the validity of the proposed method, results of an experiment using 10‐kVA laminated synchronous machines with damper winding are presented.     

A new modeling approach for circuit‐field‐coupled time‐stepping electromagnetic analysis of saturated interior permanent magnet synchronous motors

This paper proposes a new modeling approach for circuit‐field‐coupled time‐stepping electromagnetic analysis of a saturated interior permanent magnet synchronous motor (IPMSM). To predict the drive performance quickly, the proposed approach consists of a dynamic simulator based on a new analytical model of the d‐ and q‐axis magnetization characteristics (λ‐i_d‐i_q‐θ). The model can take into account not only cross‐saturation but also the harmonics of the inductance distributions and EMF waveforms. The validity of the model is verified from suitable simulation results for the instantaneous current and torque waveforms of the IPMSM. The proposed analysis leads to a dramatic reduction in the computation time compared to circuit‐field‐coupled time‐stepping FEA, while maintaining analytical accuracy. The effectiveness of the proposed method is experimentally verified using a 10‐kW, 15,000‐rpm concentrated‐winding IPM motor. © 2010 Wiley Periodicals, Inc. Electr Eng Jpn, 174(1): 49–58, 2011; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/eej.21024     

Inductance-based Inter-Turn Fault Detection in Permanent Magnet Synchronous Machine Using Magnetic Equivalent Circuit Model

This paper presents an inductance-based method for detection of inter-turn fault in permanent magnet synchronous machines (PMSM). The reason for using inductance for fault detection and its severity estimation is the obvious impact of the fault on the inductances. This fault reduces the effective number of turns and therefore inductances. The PMSM is modeled using magnetic equivalent circuit (MEC). This method takes into account the impacts of stator teeth, rotor yoke, and stator winding distribution precisely. So, it is shown that the MEC method is superior to other analytical methods such as winding function. The governing equations in different parts of the machine are proposed, and the MEC equations of the PMSM are developed. First, healthy and faulty PMSM is simulated using MEC for different severities of the fault. In the 2nd stage, the required analytical equations for self-inductance and mutual inductance estimation are extracted, and the impact of the fault severity upon these inductances is determined. Finally, inter-turn short-circuit fault is detected, and its severity is determined using the amplitude of the inductance of the faulty phase. Simulation results and the proposed fault diagnosis method are validated using finite elements method.     

Sensorless Control of Synchronous Reluctance Motors Based on Extended EMF Models Considering Magnetic Saturation With Online Parameter Identification

A sensorless control method based on novel extended electromotive force (EEMF) models considering magnetic saturation is proposed for synchronous reluctance motors (SynRMs). Since motor parameters, particularly inductances, vary largely in SynRMs, a precise sensorless control is necessary for fully considering such variations. In this paper, the EEMF model, taking into consideration magnetic saturation, is derived and is applied to a position estimation method. The two EEMF models caused by a difference in the$d$-axis direction are shown, and the appropriate EEMF model that can suppress a position estimation error caused by the deviation of inductance parameters is proposed. Moreover, an online parameter identification method for sensorless control in middle- or high-speed ranges is proposed. The necessity for the use of the model, taking into consideration magnetic saturation, is verified by experiments. The proposed sensorless control system is shown useful by experiments.     

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     

Prediction of the electromagnetic torque in synchronous machines through Maxwell stress harmonic filter (HFT) method

For the calculation of torque in synchronous motors a local method is analysed, based on the Maxwell stress theory and the filtered contributions due to the harmonics of the magnetic vector potential in the motor air-gap. By considering the space fundamental field only, the method can efficiently estimate the average synchronous torque for a variety or motor topologies, including concentrated winding designs. This approach employs an analytical filter for the Maxwell stress tensor and `frozen permeability' technique. The proposed method is validated by comparison with FE results for several synchronous motor types: interior permanent magnet motors, wound field motor, synchronous reluctance motor.     

具有变磁阻励磁回路的永磁同步电动机电感参数

为解决永磁同步电动机弱磁问题,提出了一种能够跟随转速自动调节励磁磁阻的新型永磁同步电动机.在介绍电机基本结构和原理的基础上,通过不同励磁下电机磁力线分布,指出了影响交直轴电感主要有永磁体、隔磁磁桥和交直轴电流.并分别就永磁体厚度、隔磁桥尺寸、电流饱和、非导磁体的引入和永磁体的运动,运用有限元数值法计算了交直轴电感.计算结果与电感分析结果和测试结果相吻合.     

基于改进的脉冲电压注入永磁同步电机转子初始位置检测方法

由于永磁同步电机存在凸极性,定子电感随气隙磁场饱和程度的不同而变化,电感值中包含了转子位置信息。根据这个原理,研究了通过注入脉冲电压矢量来检测永磁同步电机转子初始位置的方法,分析了不同位置的电压矢量对电感饱和程度的影响,以及对转子位置估测精度的影响,得出了能获得最佳估测精度的优化电压矢量,并提出了改进的五电压矢量注入方式。根据转子所在区域选择优化的电压矢量进行二次计算,进一步提高了转子位置估算的精度。实验结果表明,该方法能够可靠而有效的检测出永磁同步电机的转子初始位置,而且实施简单、估测精度高。     

Design and analysis of low‐speed,high‐torque permanent magnet motors

This paper presents design and analysis of low‐speed, high‐torque permanent magnet motors. The motor has 16‐pole, 18‐coil construction, and a unique winding arrangement to produce high torque. The simplified torque analysis is proposed considering the line of magnetic induction distribution in the motor. The validity of the proposed analysis has been proved by both linear and nonlinear FEM analyses. The 500‐Nm, 200‐rpm test motor has been designed and constructed and the motor shows the expected characteristics. © 2000 Scripta Technica, Electr Eng Jpn, 132(3): 48–56, 2000     

计及磁饱和的车用永磁同步电机MTPA控制技术

永磁同步电机具有较高的效率和功率密度,在电动汽车驱动系统中广泛应用。电机的d、q轴电感是设计控制系统的重要参数,但重载情况下受磁饱和及交叉饱和影响严重。传统控制技术忽略磁饱和效应,导致转矩控制的精确性不足。采用有限元法分析电机负载时的磁饱和情况,计算考虑磁饱和及交叉饱和的d、q轴电感参数。以此为基础,拟合d、q轴电感和电流关系。设计计及磁饱和的最大转矩电流比MTPA(maximum torque per ampere)控制,使d、q轴参考电流计算中使用的电感随电机电流变化。通过对比,证明计及磁饱和的MTPA控制能够实现输出转矩的精确控制,提高永磁同步电机的动态响应性能。     

考虑交叉耦合时电动汽车用内置式永磁同步电机交直轴电感计算

内置式永磁同步电机(IPMSM)以高转矩电流比、更宽的调速区间、高功率密度、高效率等优点在电动汽车领域应用广泛。电动汽车用IPMSM磁路结构复杂,饱和程度高,造成交直轴磁路的交叉耦合,使得交直轴之间产生互感。对交叉耦合现象进行了磁路分析,阐述了其对磁链和电感参数的影响。采用冻结磁导率法(FPM)和有限元法(FEM)对交直轴电感进行计算,并对电感参数随电流变化情况进行了定量分析。对比2种计算方法得出的交直轴电感参数,发现计算结果吻合较好。最后,对比分析了2种方法计算交直轴电感的优缺点,分析表明以FEM为主FPM为辅计算交直轴电感参数,能保证电感参数的精确度,缩短计算时间。     

双层V型双三相永磁同步电机的电感计算与转子结构优化

电感是永磁同步电机控制中重要的性能参数,是电机设计的关键。双三相永磁同步电机性能计算需要准确的计算电感及磁链等相关参数,而电机在运行过程中受磁路饱和与磁路交叉耦合效应影响严重,常规方法无法准确计算。本文采用冻结磁导率法对电机交直轴电感进行计算分析,通过改变交直轴电流大小,分析电感变化规律。分析双层V型永磁体张角及永磁体间距的变化对电机性能的影响,在保证永磁体的用量不变的情况下增大了凸极率,提高电机的过载能力。     

Position and speed sensorless control system of permanent magnet synchronous motor with parameter identification

The model parameters of a permanent magnet synchronous motor (PMSM) are required for high‐performance control and a model‐based sensorless control. This paper proposes a sensorless control system of PMSM that does not need parametric information beforehand. The parameters of a PMSM drive system, including the inverter, are identified at standstill and under operating conditions. At first, the initial rotor position is estimated by a signal injection sensorless scheme in which the machine parameters are not required. After the initial position has been estimated, the resistance, including the on resistance of the IGBT, the voltage error caused by dead time in the inverter, and d‐axis and q‐axis inductances, are identified at standstill. After the motor starts by the signal injection sensorless control, the sensorless scheme changes to an extended EMF estimation scheme. The estimated parameters for the resistance, and daxis and q‐axis inductances are used in such sensorless control. The magnet flux‐linkage, which cannot be estimated at standstill, is identified under the sensorless operation at medium and high speeds. The effectiveness of the proposed method is verified by several experimental results. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 160(2): 68–76, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/ eej.20548