Analytical models are powerful tools in the preliminary design of electric machines. In this study, a flux-tube model is proposed for switched reluctance machines, in which all the flux paths and the corresponding elements are accurately calculated, iron saturation is intelligently taken into account and formulas are generally developed to attain a continuous model for any range of design parameters. The inductances, flux linkages, torque–angle, maximum torque–current, mean torque–current characteristics are extracted. The special structure of the developed model enables us to extract the air-gap flux density distribution of the machine. Also, finite-element analysis is used in the analyses and evaluation of the model. Finally, the machine has been prototyped by which torque–angle curve and open-loop characteristics are obtained experimentally to evaluate the model. Superiorities of the proposed framework over the previous approaches are demonstrated as well.

The fast and stable inner current loop in the permanent magnet synchronous motor control system is the key factor that ensures the torque control performance of the motor. The deadbeat predictive current control has good dynamic response performance, but it depends heavily on the precise mathematical model of the controlled object. The parameter mismatch will degrade the control performance. A deadbeat predictive current control method based on online parameter identification is proposed in this study. This method does not need to inject additional d-axis current to identify the parameters during the operation of the motor; it only needs to make full use of the inherent phenomenon that the q-axis current changes when the load of the motor changes during operation, and perform parameter identification. Aiming at the problem that the effect of parameter identification is easily affected by motor speed, a new variable step-size neural network algorithm is designed in this study. The speed factor is introduced into step function to ensure the performance of the identification algorithm at a different speed. Finally, based on the new online parameter identification algorithm, the deadbeat predictive current control method is used to verify the experiment.

Following the climatic changes, there is a universal commitment to reduce greenhouse gas emissions, especially those due to mobility. A particular interest is addressed to hybrid propulsion systems, which are currently considered as viable candidates for a sustainable mobility. Within this commitment, the study proposes an approach to improve the cost-effectiveness, compactness and reliability of the electric drive unit of hybrid propulsion systems. This is achieved thanks to different associations of brushless DC motors (BDCMs) and reduced topologies of DC/AC converters such as the four switch inverter and three switch inverter. A special attention is focused upon the analysis of the sequences and commutations characterising the six-phase and three-phase BDCM drive operation. Implementation schemes of dedicated control strategies are given. Moreover, a comparison of selected features related to the ratings of the investigated BDCM drives is carried out and commented. Experimental results are provided to validate the performances of a reduced structure inverter fed three-phase BDCM under the dedicated control strategy.

In this work, a high-frequency model of permanent magnet synchronous motor (PMSM) is proposed for using in conducted electromagnetic interference (EMI) modelling and simulation of variable speed drive systems. The presented model covers the defined frequency range for the conducted emissions, based on MIL-STD-461 and FCC/CISPR standards from 10 kHz to 30 MHz. Common-mode (CM) and differential-mode (DM) impedance characteristics of PMSM are measured; the proposed method is based on the behavioural method using the measurement data. However, in order to improve the mid-frequency representation, the model is enhanced by physics-based methods with parameters extracted directly from the physical properties of the motor using a three-dimensional finite element method and analytical calculations. This approach enables us to avoid the trial and error method and fine-tuning the model parameters. In order to validate the calculated CM and DM impedances of the PMSM, simulation results are compared with the experimental measurements. Root mean squared relative error is introduced to measure the accuracy of the proposed model and also to compare the given results with the models previously presented in the literature.

Robot joint drive motors require high-torque and power densities due to their limited space. Surface mounted permanent magnet (SPM) motors are appropriate for a robot joint drive due to their advantages of ease of construction, high productivity, and high controllability. To utilise the limited space effectively, a rotor overhang structure (OS) is frequently used in SPM motors due the performance enhancement and simple fabrication. However, the OS effects do not increase linearly but converge when it becomes longer. To deal with problem, a flux-absorbing structure (FAS), which can effectively improve the performances even in case of a quite long OS by forming an effective flux path between the OS and stator can be used. However, the FAS results in different electromagnetic and thermal characteristics. In particular, there have been few studies on the thermal characteristics of the FAS, which can change motor performance considerably. Hence, a lumped parameter thermal network (LPTN) which can effectively consider the heat sources and heat transfer characteristics influenced by the use of FAS, is proposed. The feasibility of the FAS and the usefulness of the proposed LPTN was verified experimentally. The presented analyses and results here can be utilised in various high-torque-density application.

Saturation and cross-coupling effects have a significant impact on the magnetic behaviour of a permanent magnet synchronous motor (PMSM), which cannot be analysed by the conventional linear model in the direct and the quadrature axis. This study introduces a precise two-axis flux linkage model for PMSMs to offer a better depiction of the relationship between the flux linkages and corresponding currents. A parameter determination methodology is developed to identify the model parameters for a PMSM, and based on these works; the condition of a PMSM can be estimated. The process requires no geometrical parameter of the machine and little computational effort. Once the model parameters are determined, the torque estimation of a PMSM is simple enough to be made in real-time in a motor drive controller. Finite-element analysis and experimental results demonstrate the feasibility and accuracy of the improved model. It follows that the proposed non-linear PMSM model based on current injection and bivariate function approximation can significantly enhance modelling precision of flux linkage and inductance over the entire range of current excitation in the application of PMSM drive.

Detection and fault-tolerant control (FTC) of faults in the early stage is desirable in improving efficiency. An implementation strategy is proposed for the individual controllers that work collectively in induction motor (IM) drive by interswitching from one form of a control strategy to another. The interswitching occurs between voltage by frequency (V/f) open-loop control, closed-loop (V/f) control, sensorless vector control and sensor vector control. Optimal performance capabilities are attained with vector control, whereas V/f is a setup that is affordable but with increased speed. In this study, the faults are open and short circuits winding faults, speed sensor failures and stator winding faults. When the severity of the fault is high, an embedded protection entity interrupts the motor. Daubechies 10 wavelet is used due to its significant vanishing moments compared to the other types of Daubechies as fault index with the stator current of 1 kW IM. A novel enhanced model reference adaptive system is employed for sensorless vector control to assess the motor speed. Both the simulation and experiment (using the F28335 DSP controller) indicate that the framework is effective in detecting the fault, ensuring the robustness of the FTC scheme and proving the effectiveness of the proposed algorithm.

In this study, a novel sensorless control of the surface-mounted permanent-magnet synchronous motor (PMSM) is proposed. Firstly, by taking the derivative of the back electromotive force (EMF), the high-order voltage equations of PMSM, in which the dominant time-changing parts of back-EMF are separated and modelled, are deduced. Then a generalised extended state observer, which possesses the preferable tracking ability for time-varying states, is designed to estimate the back-EMF. Also, since the difference between the measured stator resistance and its real value, which changes with temperature, will lead to position errors, a resistance estimation scheme is proposed. Compared with the conventional sensorless method of PMSM, the proposed method can provide a more accurate and smooth position and speed estimation under resistance uncertainty without extra filter and compensator. Furthermore, since the effects of speed and current change rate are taken into consideration, the application of the proposed scheme is broadened. The effectiveness of the proposed method is verified by the experiments in different cases.

In this study, an analytical model is proposed to calculate the magnetic field and electromagnetic torque (including cogging torque) in the surface-mounted permanent-magnet (SMPM) machines with Halbach arrays accounting for semi-closed slots. The analytical model can be used to calculate both no load and load air gap magnetic field of SMPM. The permanent magnets (PMs) on the rotor are arranged Halbach array and each pole is divided into four segments. Additionally, in order to improve the performance of the SMPM, the analytical model is combined with genetic algorithm to optimise some parameters of the motor. The analytical results from the proposed model have been compared with those issued from finite-element method. Finally, the 12-slot/8-pole motor is manufactured and the back-electromotive force, iron loss and load characteristics are validated by experiments.

This study presents comparative researches on performances of a double-sided switched reluctance linear machine (DSRLM) under different winding connection modes. The static self/mutual inductances of a 6/4 yokeless DSRLM under two winding connection modes are calculated through the finite element method (FEM). This DSRLM can work either as a motor or as a generator. Now the performances of the DSRLM under different winding connection modes, including the force ripple in the electric model and the output voltage ripple in generation model, are compared through an established electric model and an established generation model. In addition, the iron losses under different winding connections are also investigated. Dynamic magnetic flux density waveforms of the DSRLM are calculated via FEM, and an iron loss computation module is established. Simulation results indicate that the advantages of both winding connections reflect in different aspects. This study summarises how to select a proper winding connection mode of DSRLMs for different performance demands responding to different applications. The experimental validations are conducted on a prototype DSRLM finally.

Harmonic leakage inductance occupies a high proportion in the synchronous inductance of fractional slot concentrated winding permanent magnet synchronous motor (FSCW-PMSM), and the synchronous inductance determines the operating performance of the motor. To calculate the harmonic leakage inductance and synchronous inductance of the FSCW-PMSM fed by inverters, two-dimensional finite element analysis and the analytical method are used to study the influence of time-harmonic current on the harmonic leakage inductance of the three-phase FSCW-PMSM in this study, and the influence mechanism is revealed. The relationship between the time-harmonic magnetic field and space harmonic magnetic field is obtained, and the harmonic leakage coefficient and the working harmonic coefficient with different slot-pole combinations are investigated. The results show that the time-harmonic current can reduce the harmonic leakage inductance and increase the magnetising inductance, but has little effect on the synchronous inductance under the unsaturated condition. A prototype was manufactured and tested to verify the accuracy of the analysis model. The research results provide beneficial help for the design of the three-phase FSCW-PMSM fed by inverters.

A general analytical model, which is applied to pre-estimate the air-gap magnetic field of interior permanent magnet synchronous motors (IPMSM) under the no-load and load conditions, is proposed in this study. First, the analytical formulas of both the slotless permanent magnetic field and the armature reaction magnetic field are derived, respectively, by virtue of solving the Laplace field equation in polar coordinates. Then, the complex relative permeance is employed to account for the slotting effect. Subsequently, the proposed analytical model, which can reflect the spatial and temporal distribution characteristics of the air-gap magnetic field, has been applied in a 4-pole-24-slot IPMSM as an example. Finally, the analytical air-gap magnetic field with the spatial order and frequency characteristics is validated by the finite-element result. Additionally, the consistency between the analytical and finite-element results further indicates that the proposed analytical model is effective.

This study proposes an outer-rotor permanent magnet synchronous hub motor (PMSHM) with similar pole and slot numbers for an electric vehicle (EV). First, the design rule of the motor size is introduced. Second, the appropriate numbers of motor poles and slots are selected to improve the torque density and save the radial space of the motor. Meanwhile, the selected poles and slots numbers can ensure that the high-efficiency area of the motor meets the requirements of the test EV. Moreover, different winding arrangements are studied to select the appropriate winding arrangement method for the motor. Then, the key dimensions of the stator are optimised to improve the torque output and reduce the core loss of the motor by using the finite element analysis. The results indicate that the proposed outer-rotor PMSHM with similar pole and slot numbers and double-layer short distance concentrated slot winding exhibits high-efficiency and high-torque output. Finally, the predicted performance of the proposed PMSHM is verified by experiments on a prototype. Furthermore, the vehicle test is also carried out, and the results show that the prototype maintains high efficiency in the main working area of the EV.

Based on a four-phase 8/6 structure switched reluctance machine for electric vehicles, the influence of different magnetic pole distributions on iron loss and temperature field is studied here. Firstly, by fitting the core silicon sheet iron loss data of the prototype, a mathematical calculation model of switched reluctance iron loss is constructed. Then, in order to analyse the flux density waveform of the iron core, a 2D finite element model is proposed. Under different magnetic pole distributions, the magnetic flux densities of the iron core are compared and the iron loss is calculated as well. Finally, the simulation results are obtained by establishing the 2D finite element thermal model of the prototype and analysed. Then, the experimental test platform is built and experimental data are recorded and analysed. By comparing the experimental results, it is found that the temperature rise is well consistent with the temperature rise of the 2D finite element thermal model.

In this study, a modified complementary sliding mode control (MCSMC) method based on a disturbance force observer with mass identification (DFOB-MI) applicable to the permanent magnet linear synchronous motor is proposed to achieve high-performance servo control fields. MCSMC is an improvement on the complementary sliding mode control (CSMC) method, which incorporates an approach angle into the saturation function. MCSMC allows for asymptotic convergence of the position tracking errors and guarantees the global robustness of the system. In addition, compared to hybrid control strategies combining neural networks with CSMC, the MCSMC method has a simpler structure and faster response. However, in practical applications, the mass variation of the mover has a significant impact on system performance. To achieve better dynamic and static characteristics, a disturbance force observer capable of identifying the mass variation based on model reference adaptive identification theory is proposed. DFOB-MI can identify the mass of the mover and provide information on the disturbance caused by the change of the load. Thus, the compensation current is calculated to reduce the disturbance and realise compensation. The more accurate tracking performance and stronger robustness of the proposed control scheme compared to conventional approaches have been confirmed through comparative experimental studies.

This study investigates the scaling effect on power factor of surface mounted permanent magnet Vernier (SPM-V) machines with power ratings ranging from 3 kW, 500 kW, 3 MW to 10 MW. For each power rating, different slot/pole number combinations have been considered to study the influence of key parameters including inter-pole magnet leakage and stator slot leakage on power factor. A detailed analytical modelling, incorporating these key parameters, is presented and validated with two-dimensional finite-element analysis for different power ratings and slot/pole number combinations. The study has revealed that with scaling (increasing power level), significant increase in electrical loading combined with the increased leakage fluxes, i.e. (i) magnet leakage flux due to large coil pitch to rotor pole pitch ratio, (ii) magnet inter-pole leakage flux and (iii) stator slot leakage flux, reduces the ratio of armature flux linkage to permanent magnet flux linkage and thereby has a detrimental effect on the power factor. Therefore, unlike conventional SPM machines, the power factor of SPM-V machines is found to be significantly reduced at high power ratings.

This study introduces a new structure of the magnetic lead screw (MLS) intended for wave energy conversion (WEC) applications. One of the key challenges in the application of MLS technology for wave energy lies in the manufacturing of its complicated ideal helix. Structural simplification and processing technology are quite essential in promoting the development of the magnet screw. This study proposes a new method for shaping the desired ideal helix in a simple way with parallelly magnetised magnets. This simple structure reduces manufacturing complexity while maintaining good force density. The magnets with parallel magnetisation are also easier and cheaper to manufacture than the magnets with radial magnetisation. A prototype is manufactured and tested in the laboratory. In addition, the electromagnetic performance of the new structure is evaluated as compared with the magnet screw with ideal helix using the three-dimensional finite element analysis, verifying the advantages of the proposed structure.

This study presents the design of a 2-pole high-speed BLDC motor for kitchen blenders and its control method with the aim to reduce the speed ripple that decreases the grinding performance in the high-speed region. In blender machines, the high pulsating load caused by the blending materials such as ice cubes acting on the grinding blade, create significant speed ripple in the constant power region. Because current and torque are limited to protect the drive, the actual motor torque cannot overcome the pulsated load if the speed reference is maintained. Therefore, the speed fluctuates, and the grinding performance is lowered. In the proposed variable speed reference control scheme, the speed command is continuously modified to overcome the maximum pulsating torque requirement which results in lower speed ripple. To achieve this, if the load torque suddenly increases, the current value is then set based on the maximum load and speed reference value is temporarily lowered. If then the load torque becomes lower than the actual torque, the previously set speed reference value is reused. The design result and grinding performance of the proposed control method are verified by simulations and experiments. Hard white beans are used for actual performance testing.

This study presents a novel method for fast calculating the eddy current losses (ECLs) caused by pulse-width modulation (PWM) harmonic voltages in the permanent magnets (PMs) of surface-mounted PM synchronous machines (SPMSMs) with distributed windings or concentrated windings. Based on the small-signal models of the SPMSMs, the functional relationships between the high-frequency harmonic voltages (HFHVs) in the rotor reference frame and the corresponding ECLs are investigated with the time-harmonic finite element analysis (THFEA). Instead of using complex analytical PM ECL models, the relationships are directly established with some numerical methods, such as the Gauss quadrature and the piecewise cubic Hermite interpolation method, based on the results from THFEA. With the functional relationships, the total PM ECL caused by all the HFHVs is simply calculated by summing the ECL generated by each harmonic component in the spectra of the PWM voltage in the rotor reference frame. Both two- and three-dimensional (2D and 3D) models of the SPMSMs are calculated. Besides, to further reduce the needed steps of 3D THFEA, an equivalent 2D THFEA method using modified PM conductivities under different-axis HFHV excitations is proposed. The merits of the proposed method are validated by comparing with the traditional time-stepping finite element method.

In this study, a novel mechanical-variable-flux interior permanent magnet motor (MVF-IPMM) is presented, which employs rotatable magnetic poles and a mechanical flux-adjusting device placed on both sides of the rotor. The device can regulate the magnetic circuit by rotating magnetic poles and adjusting the angle of the magnetisation direction relative to the d-axis. Consequently, the flux-weakening capability is enhanced. The configuration and additional mechanical devices of the MVF-IPMM are introduced, respectively. Then, the operation principle and flux-adjusting mechanism are deeply investigated by using analytical models, whose parameters are computed by automatic dynamic analysis of mechanical system and finite-element analysis. Based on the simulation results, an electromechanical model is established to predict the performance of the motor. In addition, the electromagnetic characteristics of the mechanical-variable-flux- and conventional interior permanent magnet machines are compared. Finally, the effectiveness of the design is successfully proven by experimenting with a prototype.

An accurate and computationally efficient hysteresis model is required to perform transient finite element analysis of electrical machines and transformers. Numerical experiments performed in the current work suggest that there are severe limitations of the Fourier descriptor method. In this work, the authors build upon the idea of Fourier descriptors and propose a wavelet descriptor model to characterise magnetic hysteresis curves, with the advantages of Fourier descriptors while their disadvantages are mitigated. It is shown that wavelet descriptors can also be used to compute hysteresis losses. The motivation behind using a wavelet basis rather than a Fourier basis is the ability of wavelets to represent local features of the signal. The method can efficiently represent a complete B/H curve with only a few data-points and allows for an automated representation of hysteresis loops. Wavelet descriptors are used for the first time to model a wide variety of hysteresis loops with asymmetric minor loops generated using higher-order harmonics, and from a pulse-width modulated source. The results obtained using the proposed method are compared with those of the Fourier descriptor method. In all cases, the proposed method outperforms the Fourier descriptor method. The proposed method is computationally efficient and simple to understand.

High-speed permanent magnet synchronous machine is often used as a starter generator for a single-shaft micro-gas turbine due to its high efficiency and high-power density. However, when the machine works in the starting mode, it usually needs a complex control system to start since the machine cannot realise self-starting. Therefore, here, a dual-purpose rotor sleeve is proposed for the machine to have the starting ability. Furthermore, the dynamic response speed of the machine also can be improved by optimising the electromagnetic characteristics of the sleeve. Taking a 40 kW, 20,000 r/min surface-mounted permanent magnet machine as an example, the two-dimensional finite element model of the machine is established. The start-up time and locked rotor parameters under different sleeve conductivities are studied by the finite element method. In order to find out the reason for the change of starting performance, the rotor eddy current distribution is studied. Furthermore, the starting torque of the machine is decoupling analyzed, and the influence of sleeve conductivity on various kinds of torques are found to reveal the influence mechanism of sleeve conductivity on starting performance. Finally, the correctness of the model is verified by experiments.

To solve the problems of large steady-state errors, high harmonic components and poor robustness of traditional current model prediction, a novel three-vector model predictive current control for permanent magnet synchronous motor is presented in this study. The vectors operating time is calculated with the combination of current increment and the unconventional modulation method is adopted to generate duty cycle containing dead zone. Adopting the current command correction link, the current deviation caused by inaccuracy parameter is reduced. Proved by experiment, novel control system not only the current steady-state error and current harmonic component are reduced, but also the parameter robustness is enhanced.

Due to the merit of very-short end turns, Gramme-ring windings are widely used in high-speed permanent-magnet motors (HSPMMs). This study investigated the thermal issues of a 300 kW, 12,000 rpm Gramme-ring-winding HPSMM with housing water jacket and forced air cooling, based on the computational fluid dynamics (CFD) and numerical heat-transfer calculations. The reasons that cause the overheat of the prototype in the experimental test are thoroughly analysed. The high wind resistance of air gap as the ventilation duct and the large interface gap between the stator lamination and housing water jacket is thought to be the main reasons. Then improvement of the ventilation structures is studied to decrease the wind resistance. Besides, the modification of water channels is also investigated to avoid the influence of a large interface gap on the water cooling performance. Finally, a new cooling structure, combining the slot ventilation ducts and inside water channels, is proposed for the HSPMM with Gramme-ring windings. With the new cooling structure, the temperature rise of the motor is decreased, and the power density can be increased.

This study deals with the unipolar excitation-based speed sensorless vector controlled switched reluctance motor drive. For speed sensorless operation, Z-MRAS (Z-model reference adaptive system) based speed estimator is proposed where ‘Z’ is a fictitious quantity. This novel structure is completely independent of the stator resistance and DC component of self-inductance. Also, in the formulation, integrator and differentiator terms are absent. The proposed formulation is perceived as stable in the entire four-quadrant zone of operation. Detailed stability and sensitivity analysis has been carried out for the proposed estimation scheme. The practicality of the proposed formulation is confirmed through simulation in MATLAB/SIMULINK platform and by carrying out the experimentation on a dSPACE-1104 based prototype.

Metal object detection (MOD) and detection of position (DoP) of pick-up coils are increasingly critical to the commercialisation of the wireless power transfer system. In this study, a detection scheme based on phase-detection, which can both realise the function of MOD and DoP, is newly introduced. The method is based on the principle that the presence of metal objects and pick-up coils both affect the impedance phase of the detection coil loop. Comparing with the traditional detection methods, which is based on measuring the absolutely value of impedance in detection loop, the malfunction is avoided by adopting phase difference as the criterion of the existence of metal objects and pick-up coils. An inexpensive and high-precision sensing circuit is newly designed to acquire the phase difference accurately. Simulation models and experiments are conducted to verify the feasibility of the proposed detection scheme. The of the detection coil circuit with a coin placed reaches −5.17, while the of other detection coils without metal objects keeps zero. In the meantime, the position of the pick-up coil is identified because the of these detection coils closer to the centre of the pick-up coil varies more significantly while other coils vary slightly.

A smooth changeover from the I-f method to closed-loop sensorless vector control is a critical requirement for permanent magnet synchronous motor (PMSM) drives using a back-emf based sensorless algorithm for medium- to high-speed range control. The existing methods provide a smooth transition by aligning the angle generated by I-f control to the sensorless estimated angle. However, the overall start-up time increases due to the additional transition interval, which limits the usability of these methods for applications requiring a quick start-up. Furthermore, the use of a direct transition method to reduce the changeover time results in speed and current oscillation if the estimated position using sensorless algorithm is having an error. In the proposed method, the inverter pulses are disabled for a short duration and the machine back-emf is measured after the stator current falls to zero. Therefore, a quick and seamless transition is achieved in the proposed method by accurately estimating the rotor position from the sensed back-emf. The proposed method is also extended to perform on-the-fly start for power failure ride through during short time power supply interruption. The performance of the proposed method is verified using simulation and experiment on a 25 kW PMSM drive.

The electrical machine design method plays a decisive role in electric vehicles (EVs). However, only a few designs consider the coupling of multiple fields simultaneously. This study proposes an improved multi-physics and multi-objective optimisation design approach for designing a 75 kW interior permanent-magnet synchronous machine dedicated to EVs. Five optimal objectives including power density, temperature rise, price, torque ripple, and cogging torque are selected, and the first three objectives are optimised based on the sensitivity analysis of design parameters, where an improved thermal resistance network combining with finite-element analysis model is developed. Meanwhile, the torque ripple and cogging torque are involved in subsequent design optimisation. The temperature rise and structural strength are recalculated by using commercial finite-element model software, respectively, for validating the accuracy of optimisation design. Finally, a prototype motor is manufactured; both simulation and experimental results verify the feasibility and validity of the proposed optimisation design method.

Hotspots in traction motors of electric vehicles are normally considered to locate in end windings due to the loose packaging and no access to iron cores for heat dissipation. To ensure safety, end winding temperatures are typically monitored by thermocouples in thermal management systems for real-time cooling control. However, the authors’ study finds that slot winding temperatures will exceed end winding temperatures under high-speed operations due to the much higher additional loss caused by the alternating flux. Hence, the thermocouple would underestimate the actual peak temperature in electric machines, causing insufficient cooling and potential damage to insulations. For cost savings, additional thermocouples monitoring slot winding temperatures are usually not equipped in the automotive industry. To calibrate the peak temperature of windings, this study proposes an innovative approach based on the thermo-magnetic model of the traction motor, which provides the estimated slot winding temperatures only using the end winding sensors. As a result, the proposed method can provide much accurate peak temperatures for the thermal management system. Experimental tests validate the performance of the proposed method in improving the accuracy of hotspot monitoring.

An eccentric position diagnosis method of static eccentricity (SE) fault of external rotor permanent magnet synchronous motor (ER-PMSM) is presented. Firstly, an analytical model of no-load radial magnetic field of ER-PMSM is established. Analytical models of no-load Back-EMF of both unit motors and the whole motor are carried out and are verified by finite element method (FEM) and experimental measurements. Then, the influences of SE ratio, SE circumferential angle, winding distribution mode and number of parallel branches on no-load radial magnetic field and no-load Back-EMF are analyzed based on these analytical models. The results show that SE does not affect the frequency characteristics of no-load radial magnetic field, but changes space order characteristics. On one hand, for ER-PMSM, of which the number of unit motors is equal to 1, SE causes no-load Back-EMF distortion. On the other hand, for ER-PMSM, of which the number of unit motors is greater than 1, SE does not affect no-load Back-EMF of the whole motor, but it still leads to no-load Back-EMF distortion of unit motors. Therefore, based on total harmonic distortion (THD) of no-load Back-EMF of unit motor, a projection method of intersection lines for SE fault diagnosis of ER-PMSM is proposed finally.