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A new technique is proposed for loss of field (LOF) detection in synchronous generators (SGs). The proposed scheme employs the variations of SG angular velocity ∆ωφ and load angle ∆δφ to reach this goal, while the mentioned parameters are estimated through air gap flux estimation. The proposed scheme performance is evaluated using realistic simulation case studies based on IEEE C. 37. 102 standard compared to the conventional impedance‐based one. The obtained results show that the presented scheme excels the conventional scheme from speed and security viewpoints. Moreover, the estimation procedure of ∆ωφ and ∆δφ is experimentally validated by using a 10 kVA SG and the results demonstrate that the proposed technique can be easily set and implemented. [ABSTRACT FROM AUTHOR]

In the field of electric aircraft, the axial force of the conical motor is used to offset propeller thrust and reduce bearing wear. For the problem of accurate calculation of the no‐load axial force of the conical motor, combined with the characteristics that the rotor magnetic bridge of the hybrid conical inner‐mounted permanent magnet synchronous motor (HC‐IPMSM) is easy to be saturated and difficult to be calculated analytically, an equivalent analytical calculation method is proposed. According to the principle of constant air‐gap magnetic flux, the HC‐IPMSM is equivalent to many cylindrical surface‐mounted permanent magnet synchronous motors (CY‐SPMSM), and an analytical model is gained. Combining with the scalar magnetic potential Laplace equation and Poisson equation, the air‐gap flux density distribution on the rotor surface is calculated. And finally, the no‐load axial force of the motor is obtained by using the cone angle and the Maxwell stress method. Simulation and experiments verify the correctness and validity of the analytical model. [ABSTRACT FROM AUTHOR]

Demagnetisation fault (DF) is a common rotor fault in the permanent magnet synchronous motor (PMSM). DF can cause obvious changes in the magnetic field of PMSMs. As a result, previous DF diagnosis methods mainly depends on magnetic field analysis. However, conventional analysis methods based on the magnetic potential‐permeability method, sub‐domain method and magnetic equivalent circuit method are not suitable for DF condition. In addition, DF diagnosis is further complicated by various operating conditions. To address these issues, a robust DF diagnosis method is proposed for PMSM based on d‐axis magnetic network model using magnetic field reconstruction. The proposed fault diagnosis method employs magnetic field reconstruction to obtain the radial air‐gap flux density under the open‐circuit condition. Subsequently, a d‐axis magnetic network is established to solve the demagnetisation coefficient matrix in the DF state. Finally, the effectiveness of the proposed method is validated through simulations and experiments. Both results demonstrate that the proposed method can accurately recognise uniform DF and partial DF with multiple demagnetised permanent magnets, exhibiting great robustness against different operating conditions. [ABSTRACT FROM AUTHOR]

The two‐dimensional (2D) analytical model for the calculation of the components of the flux density distribution in the air gap in a dual‐stator axial‐field flux‐switching permanent magnet (PM) motor (DSAFFSPM) is presented. The novelties of this study are deriving a 2D hybrid analytical model and replacing the rotor teeth with some surface currents for the calculation of air‐gap magnetic flux density for the first time in the DSAFFSPM motor. The 2D analytical model for DSAFFSPMs is more challenging due to the doubly salient structure and inner PM of the stator. 1D analytical interior PMs are first transferred to the bore of the stator body using the magnetic equivalent circuit model (MEC). Next, the effects of the rotor teeth are taken into consideration by injecting virtual surface currents for 2D analytical model. Applying boundary conditions and solving the Laplace/Poisson equations, the vertical and tangential flux components of the flux density distribution in the air‐gap DSAFFSPM motor are computed. The verification of the proposed method and the obtained results are validated by the 3D finite element method. [ABSTRACT FROM AUTHOR]

A new analytic model for calculating of the air‐gap flux density (AGFD) of surface‐mounted permanent magnet synchronous machines (SMPMSMs) is presented. This proposed model is capable to taking into account the effects of magnetic saturation, armature reaction and stator slots opening. Furthermore, the real form of air‐gap distribution and spatial distribution of flux density of the PM poles are considered. The armature reaction effect is modeled using phasor diagram analysis of the motor as a function of the load torque, the armature current amplitude, power factor and the inverse air gap length. Also, saturation phenomenon predicted using the new non‐linear proposed function in connection with the armature reaction effects and the properties of the lamination material. It is shown that the proposed model capable to predicting acceptably the air gap flux density waveform of the SMPMSMs at lagging and leading power factors and with the load torque variation. The presented analytical approach is verified by the two‐dimensional finite‐element analysis (FEA) results. [ABSTRACT FROM AUTHOR]

The aim of this article is to develop a rotor reconstruction method for the V‐shaped interior permanent magnet (IPM) machine so that the subdomain method to analytically calculate the air‐gap flux density can be applied. With the proposed method, the V‐shaped IPM rotor with rectangular magnets, magnetic barriers, and saturated iron bridges can be transformed into a U‐shaped equivalent analytical model. The geometry and material parameters of the magnets in the equivalent U‐shaped model can be determined according to the flux equivalence in the air‐gap of the motor. Then using the subdomain method on the U‐shaped equivalent rotor, the static magnetic field problem can be solved and the flux density distribution in the air‐gap be obtained. The validity of this method and accuracy of the solution is verified by the finite element method with case studies. Compared with existing methods, the improved subdomain method has higher accuracy in calculating flux density including radial and tangential components. The presented rotor reconstruction method is not only limited to single‐layer V‐shaped rotor, it can also be applied to other IPM rotors with more complex structures. It is valuable in the design, optimisation of IPM motors, and even development of new rotor topology. [ABSTRACT FROM AUTHOR]

In this article, a hybrid analytical model for a quasi‐regular polygon rotor (QPR) is proposed. It mainly uses the subdomain method and conformal mapping to solve a non‐circular boundary in the QPR. Firstly, the subdomain method combined with an equivalent surface current method is used to calculate the air‐gap magnetic field considering a slotted stator with a circular rotor. Secondly, by segmenting the non‐circular boundary in the QPR, the complex relative air‐gap permeance of the QPR can be calculated using the conformal mapping. Thirdly, this complex relative air‐gap permeance modifies the air‐gap magnetic field calculated in the first step to obtain the actual magnetic field distributions. Consequently, no‐load and loaded air‐gap flux densities, back‐electromotive force and torque can be obtained. A 12‐pole/3‐phase permanent magnet motor is modelled using the proposed hybrid analytical model, which is validated by finite‐element analysis and experiment. This proposed hybrid analytical model presents a new way of processing the QPR. Its calculation speed is nearly 50 times faster than the finite‐element analysis, which is of great help to the initial design and optimisation of machines with QPRs. [ABSTRACT FROM AUTHOR]

Here, a modified magnetic equivalent circuit model which can accurately consider the air‐gap region is presented. The main defect of magnetic equivalent circuit model is in the modelling of air‐gap region. To solve this problem, a new approach based on conformal mappings is presented to accurately calculate the air‐gap permeances between the elements of stator and rotor while considering the real paths of flux tubes in air gap. The distributions of equivalent virtual currents on the both sides of air gap are obtained through modified magnetic equivalent circuit model, which represent the effects of slots, magneto motive force drops in iron parts, and magneto motive force sources. The conformal mapping method is then used to calculate the components of air‐gap magnetic field for every operating point under starting conditions and different loads. One typical cage‐rotor induction motor, which is used in electric submersible pumps, is considered to investigate the accuracy of modified magnetic equivalent circuit model. Some of the analytical results obtained through modified magnetic equivalent circuit model are verified by comparing with the corresponding results obtained from finite element method and experiment set up. [ABSTRACT FROM AUTHOR]

Here, the authors propose two new Permanent Magnet (PM) embedded linear switched reluctance motors; one is a modular linear hybrid reluctance motor (MLHRM), and the other one is a segmental linear hybrid reluctance motor (SLHRM). Both structures employ PMs between the side teeth of the modules/segments. The main contribution of the PMs is to increase the air‐gap flux density, which results in an enhanced thrust, and decrease the magnetic saturation in iron parts. The magnetic equivalent circuit model is used to demonstrate the positive effect of inserting PMs in the MLHRM and SLHRM compared to their PMless counterparts. The optimal pole number and design procedure are illustrated. The simulation results are obtained in terms of static thrust, flux linkage, flux density distributions, and steady‐state current and thrust. The results show that the proposed MLHRM and SLHRM offer a higher thrust and lower current compared to their PMless form. Also, the PMs decrease the root mean square (RMS) current under the steady‐state performance of the motors, in which a higher thrust is produced with a lower RMS current. Finally, the MLHRM and SLHRM are fabricated and the test results are obtained and compared with the simulations, which illustrate a satisfactory agreement. [ABSTRACT FROM AUTHOR]

The aim of this study is to determine the electromagnetic field spatial distribution and longitudinal end effect characteristics of short primary linear induction motor (SPLIM) in the field of electromagnetic launch. First, in accordance to the electromagnetic model assumption of SPLIM and one‐dimensional electromagnetic field theory, the analytical expression of the whole‐region magnetic flux density of air‐gap is derived using electromagnetic field boundary conditions in line with the actual physical meaning. Second, the finite element method used in comparing the analytical calculation values of key physical quantities, such as air‐gap flux density and secondary eddy current in a multidimensional manner under various static and dynamic working conditions and verifying the correctness of the analytical calculation of the electromagnetic field. On this basis, the air‐gap flux density of SPLIM is decomposed according to the different generation mechanisms, and the spatial distribution of each part of the flux density is studied. Spatial Fourier analysis of flux density is conducted, the end effect coefficient is defined, and the change rule of the end effect coefficient with the design parameters of the motor is studied. Finally, a megawatt‐class high thrust prototype test platform was built, and the measured electromagnetic force was compared with the electromagnetic force calculated by air gap magnetic field and secondary eddy current. The steady‐state error of the two was less than 2%, which verified the accuracy of the analysis and calculation. [ABSTRACT FROM AUTHOR]

This study elaborates upon a new modular split‐tooth permanent magnet‐assisted switched reluctance motor (MSTPM‐SRM). In the proposed topology, the stator comprises six modular E‐cores in which the middle poles are split into two teeth. Two permanent magnets (PMs) are placed between each module's middle and side poles. Primarily, the proposed topology is introduced. Next, the principle of operation of the proposed topology are elucidated, and the magnetic equivalent circuit analysis is adopted in order to validate the operational basics. It is proved that the embedded PMs significantly increase the air‐gap's flux density and adjusts the poles' flux density. The flux density distributions, static, and steady‐state characteristics of the proposed MSTPM‐SRM motor and its PMless counterpart are extracted by utilising 2‐D finite element analysis. It is illustrated that the average torque of the proposed MSTPM‐SRM is dramatically increased compared to its PMless counterpart, especially at high excitation currents. Furthermore, the cogging torque analysis is done and it is shown that the proposed structure has approximately zero cogging torque. Finally, a prototyping version of the proposed motor is fabricated, and the experimental results are elicited. It is shown that the experimental results endorse the simulation results. [ABSTRACT FROM AUTHOR]

Wind energy as the cleanest source of renewable energy requires a highly efficient lightweight generator that provides maximum power density while having the least vibration noise and maintenance. In this study, an axial air gap transverse flux machine is presented, and all excitation sources are located in the stator. This structure provides lower core loss, weight and cost due to the full utilisation of the permanent magnets, SMC‐free structure and short magnetic flux path. In fact, by combining the features of a flux‐switching machine into a transverse flux generator with an axial air gap, it is possible to improve the performance of a direct‐drive wind turbine generator by overcoming traditional structures' challenges. To analyse the axial transverse flux switching permanent magnet generator performance characteristics, 3D finite element simulations have been performed, which have been validated by comparing them to the practical results of a single‐phase prototype. The results are in agreement with an acceptable error that is caused by manufacturing uncertainties. [ABSTRACT FROM AUTHOR]

The dual‐excited synchronous condenser (DESC) has two field windings whose axes are located at direct and quadrature axes respectively. The DESC has more capacity of absorbing reactive power than that of the traditional synchronous condenser (TSC). However, the q‐axis field winding distributed on the d‐axis magnetic pole surface can decrease the magnetic circuit area of the rotor core of DESC, thus it may result in the increase of the total harmonic distortion (THD) of the magnetic field and the oversaturation of the rotor magnetic circuit. In order to obtain better electromagnetic characteristics of DESC, a q‐axis field winding structure is proposed by optimising the number of slots, slot pitch and slot dimensions. The influences of the number and pitch of slot in q‐axis on the air‐gap radial flux density and THD of DESC are studied under the d‐, q‐ and dual‐axis excitation modes. The dimensions of the q‐axis slots are optimised by combining the time‐stepping finite element method and Taguchi method, and the optimal structure of q‐axis field winding is obtained. A 10‐kVar DESC is developed to verify the simulation results. This study provides theoretical basis for the design and manufacture of the DESC. [ABSTRACT FROM AUTHOR]

A new type of double‐stator permanent magnet spherical motor (DSSRPMSM) is proposed. Compared with most existing spherical motors, this motor uses a large number of stator iron cores, which can generate larger magnetic flux density and significantly improve torque capacity. The proposed DSSRPMSM can continuously rotate, swing and spiral, and can be used in the multi‐degree‐of‐freedom motion fields of industrial robot joints, moment gyroscopes, panoramic photography tables and so on. Because the motor has the dual characteristics of rotary motor and arc linear motor, the comprehensive effects of stator slotting and stator iron core breaking should be considered. Cylindrical and trapezoidal PM poles are equivalent to dihedral PM poles, and stator coils are equivalent to PM pole models. Analytical models of PM pole magnetic field and stator magnetic field in a spherical coordinate system are established, and the air gap magnetic flux density under unequal magnetic potential boundary conditions is calculated by conformal transformation. The analytical calculation method proposed is consistent with the results of finite element method (FEM) simulation, and the experimental test further verifies the effectiveness and accuracy of this method. [ABSTRACT FROM AUTHOR]

To investigate the effect of initial dynamic eccentricity on the rotor winding turn‐to‐turn short circuit (RWISC) in a large synchronous condenser, this paper uses the study object of a 300 MVar dual water intercooler condenser. Firstly, the air gap flux density characteristics, unbalanced magnetic pull (UMP) and stator circulating current of the condenser under single and compound faults are derived theoretically. Then, a phase‐modulated field‐circuit coupling model is constructed using Anosoft software. It is used to simulate and analyse the condenser. Finally, the operation of the condenser was simulated with the SDF‐9 experimental setup, and the correctness of the theoretical derivation and simulation analysis was verified. The results show that the initial dynamic eccentricity of the condenser has a cutting effect on the fault characteristics generated by the RWISC. The 2nd harmonic of air gap flux density and stator circulating current and the fundamental wave of UMP decrease and increase with eccentricity. This study can provide theoretical guidance to eliminate disturbing factors to improve the accuracy of RWISC diagnosis in large synchronous condensers. [ABSTRACT FROM AUTHOR]

Compared with the single‐stator permanent magnet synchronous motor(SS‐PMSM), the double‐stator permanent magnet synchronous motor(DS‐PMSM) can make full use of the space in the motor cavity to make it have higher torque density, so it is more suitable for direct‐drive occasions with low‐speed and high‐torque. This paper aims to design and compare the parameters and performances of DS‐PMSMs with four different rotor structures: 1)Series magnetic circuit of radial magnetised single‐layer permanent magnet(type Ⅰ), 2)Series magnetic circuit of radial magnetised double‐layer permanent magnet(type Ⅱ), 3)Parallel magnetic circuit of radial magnetised double‐layer permanent magnet(type Ⅲ), 4)Parallel magnetic circuit of tangential magnetised permanent magnet(type Ⅳ). Firstly, the equivalent magnetic circuit method is used to analyse the magnetic circuits of the four DS‐PMSMs. Next, the finite element analysis tool is used to compare the performances of the four DS‐PMSMs with the same volume. Their air‐gap flux density, no‐load back‐EMF, cogging torque, torque characteristics, moment of inertia, rotor loss and efficiency are quantitatively analysed and compared. Finally, this paper provides guidance and suggestions for the selection of the rotor structure of DS‐PMSM. [ABSTRACT FROM AUTHOR]

The mass production of the motors causes tolerance of shape and dimension, deviation of permanent magnet remanence and rotor eccentricity error, which affect the cogging torque and torque ripple amplitude and performance consistency. In order to reduce the torque ripple of the motor in the actual condition, the robustness optimization is performed in the paper. Firstly, an improving convex arc type permanent magnet structure is adopted to improve air gap flux density and suppress the cogging torque. Secondly, the structure parameters of the magnetic pole are selected as optimization variables, and the magnetization angle, remanence and position of the permanent magnet, static and dynamic rotor eccentricity are considered as noise factors. To improve the overall robustness of the motor under different operating conditions, the dynamic Taguchi method is used to optimize the robustness of the motor, and the test data is processed through the relation analysis method to obtain the optimal combination of control factors. Finally, the prototype is manufactured for the experiment. Compared with the single‐operating conditions robust optimization results, the robust optimization method improves the robustness of the motor. The cogging torque amplitude is reduced by 39.2%. The torque ripple is 38.4% lower than that before optimization. [ABSTRACT FROM AUTHOR]

A Halbach permanent magnet (PM) tubular linear voice coil motor (LVCM) with a semi-closed structure is developed to enhance the thrust density in this study. Generally, the end of conventional LVCM is open and suffers from the considerable end reluctance. The usage of Halbach array in LVCM makes this problem more prominent although it improves the air-gap flux density greatly. The flux at the end of LVCM can be guided to improve the air-gap flux density. Therefore, this study aims to constrain and direct the magnetic field at the end of a Halbach PM LVCM by using a ferromagnetic auxiliary yoke to construct a semi-closed structure. Magnetic equivalent circuit method is utilised to analyse the effect of the auxiliary yoke on air-gap flux density. Besides, finite element analysis is used to analyse the magnetic circuit and design the parameters of LVCM. The semiclosed tubular LVCM topology is manufactured and the effectiveness of this topology is validated by experimental measurements. Results show that the thrust density of LVCM is improved effectively by using an auxiliary yoke at the end. [ABSTRACT FROM AUTHOR]

The unbalanced magnetic pull (UMP) in electrical machines is due to the existence of additional p ± 1 magnetic flux waves. When squirrel cage induction machine (SCIM) running below its rated slip, most of the additional magnetic flux waves can be damped by the counteracting flux waves produced by its parallel-connected rotor bars. Here, this UMP damping effect is comprehensively discussed by comparing the UMP and the air-gap flux of SCIMs and wound rotor induction machines. Subsequently, a UMP damping coefficient is proposed to be included in the conventional UMP analytical model, in which the damping of UMP caused by the counteracting flux waves can be taken into account. Lastly, the UMP of SCIM at different excitation frequencies and rotor resistance are investigated to further verify the UMP damping effect. [ABSTRACT FROM AUTHOR]

An analytical technique for predicting and optimising the open-circuit magnetic field in brushless surface-mounted permanent magnet (PM) machines with novel two-segment Halbach array has been presented. For the maximum fundamental air-gap flux density, the optimal magnetisation angle has been analytically derived. The effect of the rotor core on the fundamental air-gap flux density in the machine has been investigated. In addition, the proposed analytical technique can also predict the induced back-electromotive force and the electromagnetic torque. The analytical results show that the electromagnetic performance can be significantly improved for the proposed two-segment Halbach array compared with the conventional two-segment Halbach array. Predicted results have been validated by the finite-element analyses for 9-slot/8-pole slotless/slotted brushless PM machines. [ABSTRACT FROM AUTHOR]

Unbalanced magnetic pull (UMP) occurred due to the uneven distribution of magnetic flux around the airgap, which can be caused by the existence of rotor eccentricity in the machines. Here, a UMP damping coefficient is introduced to explain the UMP damping effect from the counteracting flux produced by a parallel-connected cage rotor. An empirical method is proposed to calculate the UMP using the damping coefficient and an analytical model. Using the proposed method, a four-pole and eight-pole squirrel cage induction machine with static eccentricity are investigated, which uses inputs from both finite element analysis and experimental work. Then, the UMP calculation for a dynamic eccentricity with the extracted parameters is done to verify the empirical method. A slip control method is described which uses a UMP/torque ratio to find the operating slip with the lowest UMP. Comparisons between results with and without slip control are made on both induction machines. It shows that great reduction in UMP can be achieved when the machine is lightly loaded. [ABSTRACT FROM AUTHOR]

In this paper, the 117 kW, 60,000 r/min super high-speed permanent magnet generator (SHSPMG) under unbalanced load condition is studied. First, the influence mechanism of the unbalanced load on the generator was revealed, and by using field-circuit coupling method and at rated load, the current unbalance factor (CUF) was determined. Second, through the time-stepping finite element method, the generator air-gap flux was obtained and decomposed in virtue of the principle of Fourier transform. The influence of the unbalanced load on air-gap flux was studied, and the eddy current loss and torque ripple with different CUFs were calculated and analysed. Finally, based on the calculation results of two-dimensional transient electromagnetic field, the negative sequence current was extracted by using the symmetrical component method. The research showed that the harmonic content of air-gap flux density increases when the generator is connected to unbalanced load, and the eddy current loss and the torque ripple increases with the increase of the load unbalance degree. The experimental platform was established and the test data were in good agreement with the model calculated results, which verified the correctness of the model. The research could provide some useful conclusions for the research of the SHSPMG. [ABSTRACT FROM AUTHOR]