Optimization of Shield Thickness of Finite-Length Solid Rotors for Eddy-Current Loss Minimization

A high-conductivity shield is often used for coating the rotor of solid-rotor synchronous machines for reducing the surface eddy-current losses due to armature-reaction space/time harmonics and/or tooth ripple. Since the design process for determining the optimal shield thickness can be complicated and time consuming, a simple analytical model based on Maxwell's equations was developed and presented in a previous paper to simplify the process. It has been shown that such an analytical tool can be used as a quick and effective “screening tool” for determining the range of the optimal shield thickness for minimizing rotor surface losses; however, the influence of finite rotor axial length including the end-face losses was not taken into account. In this paper, an additional step is introduced in the shield design process where a special finite-element (FE) method that accounts for the impact of finite rotor axial length is employed for refining the design obtained from the analytical solution. Comparisons are made for a number of shield thicknesses and rotor lengths for significant space and time harmonic combinations to verify the validity of the proposed two-step design process (analytical and FE) and to evaluate the impact of the finite length of solid rotors.      

ADDITIONAL LOSSES IN SOLID-ROTOR SALIENT-POLE SYNCHRONOUS MACHINES ASSOCIATED WITH STATIC CONVERTORS

Abstract

In solid-rotor synchronous machines associated with static converters, the harmonics generated by the operation of converters result in additional losses in the different parts of the machine. These losses are investigated in this paper. The rotor harmonic currents are determined, the machine equivalent-circuits are derived, and the losses are obtained for the general case of salient-pole machines. The results show that the additional losses are considerable and that constructing the solid-rotor machines with simple damper cages and laminated pole faces has the most prominent effect on reducing these losses.     

Analysis of Rotor Core Eddy-Current Losses in Interior Permanent-Magnet Synchronous Machines

This paper presents the results of an investigation focused on the rotor core eddy-current losses of interior permanent-magnet (IPM) synchronous machines. First, analytical insight into the rotor core eddy-current losses of IPM machines is developed. Next, major design parameters that have the most significant impact on the rotor core eddy-current losses of IPM machines are identified. Finite-element analysis results are then presented to compare the predicted eddy-current losses in the machine core of IPM machines with one- and two-layer rotors coupled with concentrated- and distributed-winding stators. It is shown that the lowest total eddy-current losses in the machine core are achieved using a combination of distributed stator windings and two magnet layers per rotor pole, whereas minimizing only the rotor core eddy-current losses favors replacement of the rotor with a single-layer configuration.      

表贴式永磁同步电机转子涡流损耗解析计算

针对谐波电流引起的转子涡流损耗在某些表贴式永磁同步电机中可能会引起很高的温升的问题,研究了一种永磁同步电机转子涡流损耗的解析计算方法,该方法考虑了转子电枢反应和电机有限长的影响.在二维直角坐标系下,建立电磁场方程,通过对电磁场方程的解析求解得到转子涡流损耗的解析表达式.通过一个端部系数来等效电机有限长的影响.针对转子涡流损耗测量困难的问题,采用了一种能准确分离出转子涡流损耗的间接测量方法.实验结果表明所提出的解析计算方法可行.     

Eddy-Current Loss Minimization in Conducting Sleeves of Surface PM Machine Rotors With Fractional-Slot Concentrated Armature Windings by Optimal Axial Segmentation and Copper Cladding

When a nonmagnetic high-strength metallic retaining sleeve offers advantages over a nonmetallic (e.g., carbon fiber) one, it is possible to consider the application of a high-conductivity shield “coating” on this sleeve to reduce the surface eddy-current losses due to nonsynchronous fields. One can start by using a Maxwell's equation-based analytical model to “screen” for the optimal shield thickness and then employ a “2.5D” finite-element method that accounts for periodic fields and finite rotor length, including axial segmentation and/or copper cladding. These are quantified to help design a low-loss rotor sleeve for a surface permanent-magnet machine with fractional-slot concentrated armature winding. With this type of winding, the sleeve losses can be significant due to its rich (read parasitic) asynchronous harmonic armature reaction MMF content.      

IMPACT OF SLOT HARMONICS ON LOSSES OF HIGH-SPEED PERMANENT MAGNET MACHINES WITH A MAGNET RETAINING RING

ABSTRACT

This paper presents an analytical method for determining the harmonic content in the flux pattern of permanent magnet synchronous machines due to the slotting of the stator. The analysis based on a rotor construction with magnets radially magnetized and a retaining ring to support them against the centrifugal forces. Expressions for the eddy current losses in the magnets and their retaining ring are derived in terms of the machine dimensions and the physical properties of magnets and ring. The accuracy of the method is examined by comparison with numerical flux calculations using finite element method. The impact of some physical quantities like machine speed and magnet conductivity on the slot harmonics losses is examined aiming to exhibit the role of the magnet retaining ring in contributing to these losses     

High-speed synchronous reluctance machine with minimized rotorlosses

This paper presents a refined design of a high-speed synchronous reluctance machine with minimized eddy-current losses in the rotor. Design criteria are the ability of the rotor to withstand high speeds, ability to operate in vacuum, negligible zero-torque spinning losses, high reliability, high efficiency, and low manufacturing cost. The rotor of the synchronous reluctance machine consists of bonded sections of ferromagnetic and nonmagnetic steels. Finite-element code, incorporating rotor rotation, has been developed in MATLAB that calculates steady-state eddy currents (and losses) in the rotor. A stator iron and stator winding have been designed to minimize rotor losses, and two such prototype machines have been fabricated. Experimental results show an efficiency of 91% at a 10 kW 10000 r/min operating point, and rotor losses less than 0.5% of input power     

实心转子永磁同步电机的时步有限元分析

设计了一种实心转子永磁同步电机,并提出了适用于该类电机的场路耦合运动时步有限元分析方法,解决了实心转子电机中转子电阻难以准确计算的问题。该方法考虑了转子电阻随转差的变化,给出了外电路与电磁场耦合的时步有限元分析方法,采用运动气隙边界法解决转子运动问题,与机械运动方程相结合,对电机的瞬态过程进行仿真。应用上述方法对自行设计的22kW实心转子永磁同步电机的性能进行分析,空载反电动势和起动转矩的计算结果与样机的实验结果吻合较好,表明本文提出的方法准确有效,并可用于其他类型的实心转子电机的性能分析。     

Analytical model of the cross-magnetizing effect in saturated synchronous machines

An analytical model of the cross-magnetizing effect in saturated synchronous machines is proposed in which a second-order polynomial function is used to approximate the magnetization curve. The d- and q-axis magnetizing flux linkages are found as closed-form nonlinear functions of the d- and q-axis magnetizing currents. The magnetic reciprocity appears in this analytical model and can be applied to the simulation of saturated synchronous machines. The machine equations can be linearized to give the small-signal model around an operating point, whose associated eigenvalues can be computed. The discrepancy between machine performances with and without cross-magnetization is manifest at heavy loads due to increased saturation.     

分层阻抗理论在永磁电机转子参数分析中应用

分层阻抗理论是研究实心转子感应电机的一种有效方法,表面磁钢永磁同步电机转子结构与复合转子电机具有相似性,文中采用分层阻抗理论对表面磁钢永磁同步电机转子参数分析并讨论     

ANALYSIS OF THE INTERFERENCE SYNCHRONOUS MACHINE

ABSTRACT

Interference synchronous machines operate at different speeds of the fundamental air gap field and of the rotor, because the fundamental permeance wave is produced by interference of open stator and rotor slots the numbers of which being slightly different. In the literature different names are used for this remarkable electrical machine (“Synchronous inductor motor”, “Vernier reluctance motor”). Interference synchronous machines are used as homopolar frequency generators with an axial field coil, as continuous running reluctance motors and as single- or double, - stack step motors with an axial permanent magnet.

In this paper the field of the interference synchronous machine is analysed by field wave theory. Speed,phase angle and length of the largest field waves reveal how synchronous and cogging torques are produced. Voltage and torque equations are derived by axis theory from the simplest model that is possible with five rotor teeth. The theory is applied on a fifty rotor teeth double-stack step motor. The inductances are determined by a difference method field calculation. The torque of the motor is then calculated and compared with measured values.     

Closed solution of the transient skin effect in induction machines

The transient skin effect is solved for the rectangular open and semi closed slots containing a massive conductor. The solution is applied to the Joule losses and to the analytical calculation of the air gap torque and the stator currents of the induction machine exposed to the three-phase short circuit. The calculation of the Joule power losses under transient conditions has been accomplished, especially, for induction machines of the middle- and high-power range. This becomes important in dynamically controlled induction machines, especially when torque cycles of approximately 100 ms or less occur. Never before have the copper losses been evaluated completely under these transient conditions. For the calculation of the losses, the direct proportionality of the losses between torque and rotor bar current can be used. Furthermore, the results of the transient skin effect can find application in the operational behavior of the induction machine. The consideration of the transient skin effect of the rotor is necessary for calculating currents and torques. Until now, state of the art has only provided an analytical solving of the skin effect free model. Aiming to apply the given rotor geometry, this paper derives an approach which includes the transient skin effect, applying it on the three-phase short circuit of the idle running induction machine.     

Parameter Sensitivity Analysis for Line-Start Permanent Magnet Motors

ABSTRACT

A comprehensive study of the parameter sensitivity on both the synchronous and asynchronous performances of permanent magnet machines is presented. Based on the 2-axis theory for permanent magnet motor, performance equations are derived In terms of normalized machine parameters. Such an analysis can be used successfully in design optimization of permanent magnet machines.

A normalized power equation for evaluating the steady-state stability limits of such type of motor is also given. Simulation results obtained are confirmed with experimental results using a number of different rotor designs. Useful conclusions have been provided, which are considered to be a good aid for designing any permanent magnet motor.     

应用数值解析结合法计算旋转电机磁场

采用数值解析结合法计算旋转电机的二维磁场,推导出计及电机极对数时的气隙磁场的解析表达式,并用矢量磁位相等的交界条件连接磁场的数值和解析方程。以一台永磁无刷电机的磁场计算为例,通过与有限元法的计算结果比较,验证了本文方法的正确性和有效性。     

电动汽车用高功永磁同步电机设计与特性分析

针对传统内置式永磁同步电动机(PMSM)反电动势谐波含量高,转矩脉动大等缺点,提出一种高功率密度电动汽车用不等气隙永磁同步电机(UG-PMSM),通过气隙的不均匀特性,改善空载反电动势正弦特性.建立了UG-PMSM电机功率尺寸方程,利用二维有限元分析法,分析了空载永磁磁链、空载感应电动势、输出转矩、转矩脉动、齿槽转矩等静态特性,计算了UG-PMSM电感特性,在此基础上,研究了UG-PMSM过载能力与弱磁扩速范围.仿真分析结果验证了UG-PMSM高功率密度、高转矩密度、低转矩脉动等优点,适合应用于电动汽车驱动系统中.     

OPTIMAL DESIGN OF SUPERCONDUCTING AC GENERATOR

Abstract

The design philosophy and the optimization procedure used in the design of the superconducting generator are outlined and the effect of different parameters on the overall machine size and power density is examined. The effects of superconductor capability, environmental shield, type of rotor construction on the design of the machine are investigated. It is shown that the present day superconductors offer as much magnetic field generating capability as can be profitably used in synchronous machines and it is also shown that even in the “iron-free” or “air-core” superconducting machine, the design is dominated by the iron environmental shield.     

新型混合励磁同步电机的数学模型与等效分析

为改善高速永磁电机磁场调节困难的问题,提出一种新型混合励磁电机,转子上既有永磁极又有铁心极,磁路呈现典型的径向、周向和轴向三维特性,难以直接用解析法求取电感参数。根据新型混合励磁电机的磁路特点,提出一种等效分析方法,将复杂磁路的混合励磁电机等效为三种二维磁路电机轴向并列叠加。为了提高新型混合励磁电机电磁设计与性能分析的效率,推导了其数学模型与电感参数表达式。对一台10 k W混合励磁原理样机进行了有限元分析与实验研究,结果验证了所提数学模型与等效分析方法的正确性,为该类电机的设计和优化提供了理论支撑。     

The use of doubly fed reluctance machines for large pumps and wind turbines

Brushless doubly fed induction machines (BDFIMs) have been extensively researched over because of the possibility of using a partially rated inverter in many applications with limited speed variations. However, the special cage rotor construction and substantial rotor losses is one of the key deficiencies of these machines. A similar and extremely interesting machine, the brushless doubly fed reluctance machine (BDFRM), has been largely ignored in comparison. This was mainly due to the fact that reluctance rotor designs were not capable of generating saliency ratios large enough to make the BDFRM competitive with other machines. However, developments in reluctance rotors, spurred on by research into synchronous reluctance machines, have resulted in high-saliency-ratio cageless rotors that are economical to build. This, together with the promise of higher efficiency and simpler control compared to the BDFIM, means that further investigation of the BDFRM is warranted. This paper presents a comparative theoretical analysis and aspects of practical implementation of the important control strategies and associated machine performance/inverter size tradeoffs for the BDFRM in the light of its most likely applications-large-pump-type adjustable-speed drives and variable-speed constant-frequency wind power generation systems.     

Axial Magnetic Fields,Axial Force,and Losses in the Stator Core and Clamping Structure of a Synchronous Generator with Axially Displaced Stator

Axial displacement of the stator in a synchronous machine gives rise to axial magnetic field both at the ends and deep inside the stator. The axial magnetic field causes losses. This article contains results from two studies with an axially displaced stator. In the first study, axial magnetic leakage fields in the ends of a small synchronous generator at load and no load were measured and simulated. In the second study, axial force and iron losses at no load were calculated with non-linear materials and a three-dimensional, time-stepped finite element method. For some machines with vertical shafts, the sum of iron losses and thrust bearing losses can be reduced if the rotor is lowered or the stator raised, whichever is best.