Shape and topology optimization of a permanent-magnet machine under uncertainties

Consequent pole (CP) permanent magnet (PM) machines offer scope for reducing the quantity of PM material and hence cost compared to more conventional PM machine topologies of the same rating. In this type of machine, the rotor pole arc is usually optimized to realize the largest output torque with pole shaping methods used to reduce torque ripple. However, such approaches tend to be limited by constraints imposed on the pole shapes. It is a common practice to adopt similar PM and iron pole shapes, an approach that does not fully account for the different characteristics of PM and iron poles in CPPM machines, often leading to large even order harmonics in the airgap flux density. This article proposes a shaping method with a variable rotor profile and pole arc span being established by means of optimization by Genetic Algorithm. It is demonstrated that for a fixed quantity of PM material, different PM and iron pole shapes in combination with optimal PM and iron pole arc spans are essential for ensuring both maximum output torque and lower torque ripple when the due account is taken of flux leakage. It also demonstrates that since the flux density in the region under a PM pole is governed by the magnetic potential produced by magnets while it is governed by magnetic reluctance under iron pole, different PM pole and iron pole shapes are necessary to reduce the even-order harmonics in a CPPM machine and consequently to reduce torque ripple. The performances of optimized and more conventional CP machines are compared by finite-element method on 12-slot/8-pole prototype motors.

Purpose The paper presents the topology optimization method to design the rotor and the tooth base in the stator of the permanent magnet (PM) excited machine with the improved high-speed features. The topological and shape sensitivity through the Multi-Level Set Method (MLSM) have been used to attain an innovative design of both the rotor and stator made of different materials. Design/methodology/approach This framework is based on the application of the topological and the shape derivative, obtained by incorporating the AVM into the multi-level set method for the magnetoquasistatic system. The representation of the shape and their evolution during the iterative optimization process are obtained by the multi-level set method. Findings To find the optimal configuration of a PM machine, the stator and rotor poles were simultaneously optimized by redistributing the iron and the magnet material over the design domains. In this way, it was possible to obtain an innovative design which allows to reduce mechanical vibration and the acoustic noise caused by the Cogging Torque, while taking the back-EMF into account. Originality/value The novelty of the proposed method is to apply the modified multi-level-set algorithm with the Total Variation (TV) to the magnetoquasistatic optimization problem. Given the eddy currents phenomenon in the model of a PM machine, it was possible not only to optimize the structure of a PM machine but also to analyse electromagnetic losses distribution.

Design of a New Consequent-Pole Segmented Dual-Stator Permanent Magnet Machine

Permanent magnet (PM) machines have been widely applied in industrial applications due to the advantages of high torque density, high reliability, and high efficiency. In this paper, the magnetic gear effect (MGE) in PM machines is investigated in depth. A comprehensive derivation of the torque-generating process is carried out and a quantitative analysis of the air-gap harmonics contributing to average torque under different configurational freedoms is studied. The improvement of torque capability for the PM machines with MGE is discussed. The electromagnetic properties of typical PM machines with MGE are analyzed based on the magnetic circuit analytical model, and the effectiveness of theoretical analysis is verified by finite element analysis and experimental prototype. It is shown that the PM machines with an independent modulation unit possess the characteristics of high torque density and large PM utilization rate. And the PM machines with tooth-pole modulation unit have strong overload capability.

Permanent magnet (PM) machines generally employ rare-earth PMs. The rare-earth PMs increase the manufacturing cost of PM machines due to their high material cost. To reduce the manufacturing cost of PM machines, this paper studies a consequent-pole configuration. Consequent-pole PM machines have poles with magnets and poles composed of iron-cores. The rotor design can adjust the air-gap flux density distribution. This improves the average torque and reduces the volume of PMs simultaneously. In this paper, the rotor of a consequent-pole surface-mounted PM machine is designed to reduce the volume of PMs. The characteristics are investigated for the rotor structure through a theoretical calculation and a finite-element method analysis. These results show that the consequent-pole configuration can reduce the volume of PMs in comparison with a conventional one.

This paper describes a computationally efficient approach for mapping rotor power loss in permanent magnet (PM) machines. The PM loss mapping methodology discussed here utilizes a small number of time-step finite-element analyses (FEAs) to determine the parameters of a functional representation of loss variation with speed (frequency) and stator current and is intended for a rapid evaluation of machine performance over the entire torque-speed envelope. The research focus is placed on field-oriented-controlled brushless AC PM machines with surface-mounted PM rotor construction, although the method could be adapted for other rotor formats. The loss mapping procedure accounts for the axial segmentation of the PM array through the use of an equivalent electrical resistivity of the segmented PM array, which is obtained from three-dimensional (3-D) FEA. The PM loss can be accurately mapped across the full operational envelope, including the field-weakened mode, through a single 3-D and four two-dimensional time-step FEAs. The proposed methodology is validated on an 18-slot 16-pole surface-mounted brushless AC PM machine design. The loss mapping procedure results closely agree with the computationally demanding alternative of direct 3-D finite-element prediction of the PM power loss undertaken at each of the machine's operating points.

There is increasing popularity of using permanent magnet (PM) machines in vehicle propulsion systems. Due to the pre-excitation of PM, the machines could offer higher efficiency and torque density. However, their inherent torque ripple could be problematic for electric vehicles (EVs) due to low damping of torsional vibration which may affect passenger comfort. This can prohibit the use of PM machines to improve vehicle energy efficiency. This paper presents the application of resonant control (RC) to suppress the impact of the PM torque ripple, which aims to reduce the vibration of a vehicle. A prototype PM machine and driveline have been fitted to a light-duty off-road vehicle. Firstly, the drivetrain frequency response was analyzed. The main source of the vibration is identified as the 24 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> harmonic torque ripple of the 12-slot/8-pole PM machine, which originates from the cogging torque and air-gap flux harmonics. The vibration becomes more severe when the torque ripple frequency is close to the natural frequency of the drivetrain. Then, the RC in conjunction with PI controller (PIR) was introduced to be used at the outer speed loop, so that an accurate current reference signal can be generated for the inverter to mitigate the speed ripple. When compared to the conventional Proportional-Integral (PI) controller, PIR controller has demonstrated over 80% reduction in speed ripple, even when the torque ripple frequency is close to the natural frequency of the vehicle.

In this paper, the fault protection capability of a novel hybrid-excited permanent magnet (PM) machine is examined to illustrate its great capability to prevent the dangerous overvoltage issue from the uncontrolled generator fault (UCGF) at high speed operation. PM flux of the novel hybrid-excited PM machine is inherently short-circuited when the field excitation current is not fed into the excitation windings. Therefore, when the machine UCGF is detected in the high speed region, the DC-link overvoltage issue can be effectively reduced by forcing the field excitation current to zero. Since only the field excitation current is utilized to protect the machine and inverter switches from the UCGF, it is simple to implement and the concept of proposed control strategy can also be applied to other hybrid-excited PM machines. Finally, the proposed control strategy is verified by both simulation and experimental results on the hybrid-excited PM machine.

Permanent magnet (PM) machines possess the merits of high torque density and high efficiency which is very suitable for some applications such as electric vehicles (EVs) [1]-[4]. Over the years, the surface PM and interior PM types, have been extensively studied and developed. The 2004 prius interior PM machine with the advantages of high torque density and wide speed range has been built and applied successfully in hybrid EVs. Recently, PM vernier (PMV) machines derived from magnetic gears are acknowledged that it can offer higher torque density than conventional one [4]-[6]. Unfortunately, similar to conventional PM machines, the PMV ones also suffer from relatively low flux adjusting efficiency and poor performance at high speed range due to the uncontrollable PM magnetic field. A flux controllable PMV machine has been proposed to improve these problems by the introduction of DC field excitation windings [6]. Although the flux controllable PMV machine definitely combines the merits of high torque density and wide speed range, its flux adjustment capability is still limited because the flux by the field excitation windings goes through the high magnetic reluctance of PMs. In addition, it suffers from the problems of mechanical integrity and thermal instability since the PMs are located on the rotor. To solve these problems in the existing flux controllable PMV machine, two novel hybrid excitation PMV machines with surface and V shape PMs, termed as the hybrid excitation surface PM vernier (HE-SPMV) and hybrid excitation V shape interior PM vernier (HE-VIPMV) machines, will be proposed in this paper.

High-speed multimegawatt permanent-magnet (PM) machines have been proposed in the literature and offered for sale in a variety of petrochemical applications. Presently, the discussion of synchronous machines in both the IEEE Std 115 and American Petroleum Institute 546 excludes the consideration of PM synchronous machines. These machines pose special problems when attempting to apply the test procedures given for the wound-field synchronous machines in that many of the tests rely on the ability to adjust the field strength. In addition, a PM-rotor topology has different performance and robustness concerns than a wound-field machine, and those should be addressed. This paper attempts to outline a coherent method for evaluating high-speed PM machines by extending the test procedures outlined in IEEE Std 115 and presenting additional procedures specific to PM machines. Extended application guidelines will be discussed for high-speed multimegawatt machines. The differences between the risk profiles for the PM and wound-field machines will be highlighted with a particular emphasis on the risk mitigation via tests for the PM machine.

Summary form only given. In China, there is a 1000 MW thermal power generator in operation. Large electrical machines are popular in power generation. However, large electrical machines are facing more challenges than small ones due to their features. They have high voltage, high current and high losses, which increase design difficulty in control, insulation and cooling. Moreover, the high torque in large machines will introduce challenges in mechanical designs. It's usually costly to manufacture and maintain the large machines due to their high weight and large volumes. As a result, design of large electrical machines is a complicated process. A review of the general design process of large electrical machines is presented. Firstly, the specifications of the machine should be keep in mind, such as working environment, machine type, electromagnetic performances and so on. Then the topology and parameters of the machine should be selected by optimal design. In addition, stator cooling methods, including air and water cooling, and mechanical supporting of rotor and stator, should be carefully designed respectively.In recent years, large permanent magnet (PM) machines are widely used in wind power, ship propulsion, railway traction, etc. As the capacity of electrical machines increases, there are more and more challenges in design of PM machines. When a PM machine is built and tested, it is often found that the test results do not match predictions well. A set of practical design considerations gained from industrial application experiences are presented, which should be considered during design phase, but often ignored by many machine designers. They are categorized into topology, electromagnetic (EM) performance, loss and efficiency. The causes and effects of some issues are analyzed and some solutions are suggested. They can help machine designers to narrow down the gap between design predictions and test results and build large PM machines with expected performance and high reliability. Superconducting direct-drive generators are new candidates for multi-megawatt class wind generators. Superconducting machines are famous for low weight, small size, and high efficiency. Challenges for large superconducting electrical machines are addressed. In order to find out the suitable topology for multi-megawatt-class direct-drive wind turbine generators, various designs of superconducting machines are compared; advantages and disadvantages are discussed; and a few ways to benefit from their advantages are pointed out. Moreover, characteristics of high and low temperature superconducting materials are concluded. At present, as the current cost of low temperature materials is much lower than high temperature materials. In addition, electromagnetic, mechanical and thermal challenges, including magnet design, excitation system, rotor screen, torque tube, cryogenic cooling system etc., are discussed for superconducting machines.

The rotor discs in axial flux permanent magnet (PM) machines have similar properties as a radial fan, and therefore, the convective cooling may have a significant influence on the thermal design of these machines. To research the impact of convective cooling on the thermal properties of axial flux PM machines, a coupled electromagnetic and thermal model is introduced in this paper. This technique models a segment of the stator and the rotor only and links them together by analytical equations of the convective heat transfer at different boundaries of the machine model. This results in an accurate and time efficient multiphysics model. The coupled electromagnetic and thermal modeling technique is validated with measurements on a 4 kW axial flux PM machine having the yokeless and segmented armature topology.

Using the method of separate variables, the three-dimensional magnet field solution expressed in Fourier's expansion for permanent magnet (PM) machines with finite axial magnet length is presented in this paper. From the analytic results obtained, much useful and interesting design information for PM machines in three dimensions may be quantitatively deduced. Design curves of the leakage factor and the air gap field characteristic coefficients for PM machines in three dimensions are given and compared with those in two dimensions. All the design curves given in the paper would be useful in preliminary performance calculations for both a.c. and d.c. PM machines.

A thorough comparison of the converter performance characteristics for four permanent magnet (PM) synchronous machine configurations is presented. Two versions of an interior PM (IPM) machine with distributed windings are included. One version has a maximum back-EMF limit at the top speed while the second does not have any constraint on back-EMF amplitude. Two types of surface PM (SPM) machines are also considered, one with fractional-slot concentrated windings, and another with conventional distributed windings. The target application is an automotive direct-drive starter/alternator requiring a very wide 10:1 constant power speed ratio (CPSR). Detailed comparisons of the converter performance below and above the base speed are presented, evaluating significant issues, including the converter switching and conduction losses, output ripple current, and DC-link current ripple. Study results show that the higher excitation frequencies required by PM machines with high pole numbers have only a modest impact on converter efficiency for comparable output current waveform quality. In constrast, the imposition of maximum back-EMF amplitude constraints at top speed raise the machine rated current, resulting in elevated converter losses and larger DC-link capacitors

This paper investigates the iron loss calculation of permanent magnet (PM) machines undertaking unconventional operations, where the high-frequency alternating armature field is only a fraction of the constant PM field. It is found that the iron loss of PM machines undertaking such unconventional operations cannot be calculated reliably as the conventional summation of all the iron loss harmonics predicted by finite-element (FE) methods due to fake iron loss harmonics. Further investigation is conducted on the influence of current frequency and magnitude, FE mesh, and convergence tolerance on the FE predicted iron loss under unconventional operations. It is then proposed in this paper that the iron loss of PM machines undertaking unconventional operations can be calculated as the summation of only the iron loss harmonics, which are insensitive to the convergence tolerance. The analyses are validated by the experimental results.