Equivalent Magnetic Network Model Research Articles

Equivalent Magnetic Network Model of Electrical Machine Based on Three Elements: Magnetic Flux Source, Reluctance and Magductance

Equivalent Magnetic Network Model of Electrical Machine Based on Three Elements: Magnetic Flux Source, Reluctance and Magductance

Dynamic equivalent magnetic network model and drive system of permanent magnet synchronous motor with double V-shaped magnet structure

In order to improve the driving performance of electric vehicles (EV), a permanent magnet synchronous motor with double V-shaped magnet structure (DVMPMSM) and its driving system are studied in this paper. A 150 kW DVMPMSM for EV is designed firstly, and the design parameters of the motor are determined. In order to overcome the drawbacks of the finite element analysis (FEA), especially the issue on calculating time, a dynamic equivalent magnetic network (EMN) model of the DVMPMSM is constructed, by which the air gap flux density, back electromotive force, electromagnetic torque and winding inductance parameters of the motor can be solved. Compared with the FEA, the dynamic EMN model constructed in this paper greatly increases the calculation speed while the calculation accuracy is maintained well. This paper also introduces the stator winding switching method to replace the field-weakening control method. Then, a vector control method of DVMPMSM based on dynamic EMN model and stator winding switching is proposed. The demands brought forward by EV for high torque output under low speed and high upper limit of speed can be well satisfied. Finally, the accuracy of the dynamic EMN model and the effectiveness of the proposed control method is validated through prototype experiments.

Magnetic Field Analysis and Thrust Optimization of Arc Permanent Magnet Synchronous Motor Combined With Linear Mover and Arc Stator

The intelligent annular transmission system driven by permanent magnet synchronous linear motor (PMSLM) is composed of linear and arc segments. When the mover enters the arc segment from the straight segment, the coupling area between the primary and secondary becomes smaller. It results in that the average thrust decreases and the thrust ripple increases. This phenomenon affects the control accuracy and operation reliability. This paper focuses on the research on the arc permanent magnet synchronous motor (A-PMSM) in the arc segment of the annular transmission system. The equivalent magnetic network model of A-PMSM is established. The air-gap coefficient is used to compare the slot effect of arc primary structure with that of straight primary structure. The influence of arc radius and radial width on the slot effect of A-PMSM with linear mover is obtained. The structure of magnetic pole, the radial width of secondary and the slot width are optimized by the combination of hierarchical optimization and orthogonal optimization. The A-PMSM's performance of thrust is optimized, which provides experience for the design of the motor in the annular transmission system.

Demagnetization Modeling and Analysis for a Six-Phase Surface-Mounted Field-Modulated Permanent-Magnet Machine Based on Equivalent Magnetic Network

Demagnetization Modeling and Analysis for a Six-Phase Surface-Mounted Field-Modulated Permanent-Magnet Machine Based on Equivalent Magnetic Network

Modeling and Analysis of 3-D Magnetic Network for Claw-Pole HTS-Excitation Field-Modulation Machine

This paper is to establish a special 3-dimensional equivalent magnetic network model (3-D EMNM) for performance analysis of a claw-pole HTS-excitation field-modulation machine (CPHTS-FMM). In the modeling of 3-D equivalent magnetic network, the axial asymmetry of claw-pole structure and the reasonable equivalent scheme of single ring-shaped HTS-excitation coil are fully considered. In addition, to account for the magnetic saturation caused by the HTS-excitation mode, the proposed 3-D EMNM is iterated by interpolation method to improve its calculation accuracy. By using the established 3-D EMNM, the electromagnetic performance of analyzed CPHTS-FMM are investigated and compared with the 3-D finite element analysis (FEA) to verify its validity. The results show that the proposed 3-D EMNM calculation are consistent with the 3-D FEA results, and has the advantageous feature of time saving.

An improved equivalent magnetic network model of IPM motor in electric vehicles for dynamic simulation of transient effects

The existing electric motor model for electric vehicles cannot address the simulation of transient conditions. Moreover, it is difficult to balance the computation time and simulation accuracy. To address these shortcomings, an improved internal permanent magnet motor model containing nonlinear magnetic field factors was proposed based on the equivalent magnetic circuit theory. The effects of the magnetic circuit saturation, cogging torque, and magnetic field harmonics on the electromagnetic torque could be reflected. Furthermore, the electromagnetic vibration and rotor eccentricity could be considered. To improve the computational efficiency of the equivalent magnetic network method, lumped parameter or mesh-based methods were used for flux paths with different complexities. Second, the single-layer mesh-based method with local variable permeability parameters improved the efficiency of the air-gap dynamic analysis and computational efficiency while simulating 2D flux paths. The radial and tangential electromagnetic forces were calculated using the Maxwell tensor method and the action on the rotor. The accuracy of the nonlinear magnetic field modeling was verified by finite element analysis and experimental. In addition, the motion modeling method and dynamic characteristics of the model were studied. A reference was provided for dynamic simulations of electric vehicles and other using permanent magnet motors.

Operating principle and performance analysis of a novel flux–torque regulation hybrid excitation machine with axial–radial magnetic circuit using magnetic network

AbstractIn order to solve the problem of the decreasing torque density caused by the complex structure of the hybrid excitation machine, a novel flux–torque regulation hybrid excitation machine with axial–radial magnetic circuit is proposed by the authors, which innovatively realises the increase of additional torque and the regulation of the magnetic field by an axial structure. In particular, the additional torque has a certain boost to the output torque under the flux‐weakening condition of the machine. Based on the equivalent magnetic network model, the flux regulation principle of the machine is analysed, and the expressions for the flux linkage and no‐load back electro‐motive force are given to obtain the important factors affecting the flux regulation. Based on the analysis of complex forces generated by the rotating permanent magnet in the coupling magnetic fields, the generation and control principle of the additional torque is expounded. The expression of the additional torque is derived by the Maxwell stress tensor method, which can determine the main influencing factors and these relationships. Finally, the rationality of the proposed hybrid excitation machine structure is verified by experiments.

Cover Image

The cover image is based on the Research Article Design of a non-ferromagnetic spoke array Vernier permanent magnet generator with iron-bar based on enhanced equivalent magnetic network model by Mehrage Ghods et al., https://doi.org/10.1049/elp2.12272

Analysis of a spoke‐type ferrite PM motor with assisted poles based on equivalent magnetic network with hybrid cross‐shaped mesh elements

AbstractThis article proposes an equivalent magnetic network (EMN) model to improve the accuracy of electromagnetic analysis, where a modular modelling of hybrid cross‐shaped mesh (CS‐M) elements is introduced. By applying hybrid CS‐M elements, the modelling of air gap and its surrounding regions is regulated into an identical width. As a result, the relative motion of the motor is simpler to simulate by changing the nodal connection without involving the non‐linear permeance. The airgap flux density is solved more accurately than the regular CS‐M elements as well. A 12‐slot/10‐pole ferrite permanent magnet (FPM) motor with assisted poles of unequal pole‐arc ratios is selected as an example to be built with the proposed EMN model. After solving the EMN model, the effectiveness and accuracy of the proposed EMN model are verified by comparing it with the FEA model and experiments. Additionally, based on the frozen permeability (FP) method, transient torque components can be separated accurately with a transient torque solution related to virtual work principle (VWP) for the EMN model.

Design of a non‐ferromagnetic spoke array Vernier permanent magnet generator with iron‐bar based on enhanced equivalent magnetic network model

AbstractThe spoke‐type arrangement of permanent magnets (PMs) in rotor of Vernier PM (VPM) machines was first introduced in a dual‐stator topology to overcome low‐power drawback of VPM machines. However, this structure is mostly applicable for high‐power motor drives. A non‐ferromagnetic spoke array VPM generator with a special rotor structure for small‐scale wind turbine generator is presented. The leakage flux lines tend to be aligned with the main flux routes due to a special design of flux barriers in end portion of PM housings. High torque‐density, low weight, torque‐speed curve with a wide constant torque region, promising efficiency, and power factor are the advantages of the proposed machine. An Equivalent‐Magnetic‐Network (EMN) model is established for predicting the complex behaviour of flux lines and operating quantities of the proposed structure with reasonable accuracy. The contribution of the modelling method includes a special mesh cell for the air‐gap permeance network to more accurately capture the flux routes, continuous positioning method for omitting spikes on post‐processing waveforms due to numerical errors, and a stable solving flowchart with a high convergence rate. The validity of the EMN model is validated by comparing the operating waveforms of the machine with the corresponding waveforms obtained by the finite element and experiments.The cover image is based on the Research Article Design of a non‐ferromagnetic spoke array Vernier permanent magnet generator with iron‐bar based on enhanced equivalent magnetic network model by Mehrage Ghods et al., https://doi.org/10.1049/elp2.12272.

Equivalent Magnetic Network Modeling of Dual-Winding Outer-Rotor Vernier Permanent Magnet Machine Considering Pentagonal Meshing in the Air-Gap

Thedual-winding outer-rotor Vernier-permanent-magnet (VPM) generator, which possesses two-phase-windings inserted in the stator core with two slot levels of shallow and deep and saturable tooth-tips with narrow regions, has already been presented and studied for the traffic-enforcement-camera applications. The flux lines routes in this VPM generator have a complex pattern because of existing flux modulation poles, deep slots and fringing and leakage fluxes in different parts. Hence, the accurate analytical modeling of this special machine requires an advanced method. To fulfill this aim, equivalent-magnetic-network (EMN) model of the VPM generator is extracted in this article by combining reluctance-network-model and magnetic-equivalent-circuit. simpler mathematical equations and lower computational burden are advantages of the proposed EMN model in comparison with finite-element (FE) model. The method of finding the rotor position based on the region selection and considering the effect of the slot permeances and magnetic saturation under both no-load and on-load operating conditions are the other novelties highlighted. Also, especial pentagonal-shape meshes with unequal sides’ lengths and angles are proposed for the air-gap meshing, which can effectively model the complex flux routs. Test results and FE simulations are used to validate the accuracy of the developed EMN for the investigated VPM generator.

An Improved Equivalent Magnetic Network Model of Modular IPM Machines

This article develops an improved equivalent magnetic network (EMN) model for analysis of a modular interior permanent magnet (IPM) machine. First, focusing on the local magnetic saturation, the stator tooth crown is divided into three parts based on its structure and flux density distribution. To model the specific flux path, the tooth tips on both sides are approximated to right-angled trapezoids and the middle part is divided into isosceles trapezoid. Second, an improved air-gap model is proposed, which divides the air-gap magnetic network into three layers. The middle network uses cross-shaped mesh (CS-M) elements to represent the path of tangential and radial fluxes. The top and bottom layers are composed of parametrized nonlinear permeances between stator, rotor edge nodes, and middle network nodes, whose values are the function of angle respect to CS-M elements. In this way, as the machine rotates, the structure of the EMN model can be kept invariant, and only permeances of bottom layers should be modified. Then, the EMN model is extended to the analysis of the machine with skewed stator. The accuracy and effectiveness of the proposed EMN model are verified through comparisons with finite element analysis and experimental tests.

3-D Equivalent Magnetic Network Modeling and FEA Verification of a Novel Axial-Flux Hybrid-Excitation In-wheel Motor

In order to solve the problems of poor capacity and unsatisfactory efficiency of flux-weakening control for the axial-flux permanent magnet (AFPM) machines with surface-mounted permanent magnet (PM) rotor structure, a new axial-flux hybrid-excitation machine (AFHEM) with double consequent-pole rotors is proposed, which combines the high torque density of the AFPM machine and the flexible flux regulation of the hybrid excitation machine. It meets the stringent requirements of the distributed in-wheel motor electric drive vehicle for high efficiency and high torque density. The topology, principle, and basic electromagnetic properties of the new axial-flux hybrid-excitation in-wheel motor are presented in this article. Based on the complex magnetic circuit of the AFHEM, a 3-D equivalent magnetic network (EMN) model is established. The air-gap flux density, flux linkage, back EMF, torque, and fault tolerance ability of the motor are solved through the EMN model and compared with the 3-D finite element analysis (FEA) to verify its validity and correctness. It is hoped to form a rapid design method for the new type of motor with the complex structure of 3-D magnetic flux path property. Finally, based on the EMN model, the influences of the magnetic saturation on the excitation regulation capability of the proposed AFHEM are analyzed, which provides a guideline for the optimization design of the new AFHE in-wheel motor.

A Hybrid Analytical Model for Permanent Magnet Vernier Machines Considering Saturation Effect

This article proposes a new hybrid analytical model combining subdomain model and equivalent magnetic network for permanent magnet vernier machines, which are easy to get saturated due to the air-gap field modulation effect. The key is representing saturation effect by iterating equivalent surface current as part of interface conditions in the proposed subdomain model. First, five subdomains are divided to calculate magnetic field distribution. The equivalent surface current is utilized as the boundary constraint between subdomains and iron core. Second, the equivalent magnetic network is established based on stator structure, and the fluxes flowing into flux modulation poles are equivalent as the magnetic flux sources. Node magnetic potentials can be achieved with the application of Kirchhoff's law of current. Then, the equivalent surface current is updated for convergence by node magnetic potential to accurately predict saturated performance. Finally, a prototype is manufactured, and the effectiveness of the proposed hybrid model is verified by the finite-element analysis (FEA) and experimental results. The hybrid model combines the subdomain model and the equivalent magnetic network model to complement each other and it is demonstrated to be more efficient than the FEA model while maintaining high accuracy.

Dynamic Equivalent Magnetic Network Analysis of an Axial PM Bearingless Flywheel Machine

A nonlinear dynamic equivalent magnetic network model for an axial permanent magnet bearingless flywheel machine (APM-BFM) is proposed in this paper. The model focuses on analyzing the magnetic field changes at the air gap of the machine. According to the relative position of the stator and rotor, the magnetic circuit between the rotor and the suspension pole (the torque pole) is divided into 7 stages (8 stages), and dynamic equivalent magnetic network models are established. The local saturation coefficient is introduced to characterize the local magnetic saturation phenomenon of the rotor yoke during the rotation of the rotor. Using the proposed model and based on the obtained winding flux, the opposing electromotive forces and inductances of the suspension and torque windings of the APM-BFM are all analyzed and calculated. Finally, the validity of the proposed model is verified by finite element analysis (FEA).

Analysis of a New Flux Switching Permanent Magnet Linear Motor

A novel flux switching permanent magnet linear motor (FSPMLM), which has the advantages of high thrust density [the ratio of average thrust to permanent magnet (PM) volume] and low cost for long-stroke application, is proposed and investigated in this article. The topology of the novel FSPMLM with 12 slots is introduced and the basic operating principle is analyzed first. The optimal geometric parameters are selected by using the layered orthogonal optimization method. Then the electromagnetic performance of the motor is investigated by the analytical method based on the equivalent magnetic network model (MNM). Finally, a scheme of setting auxiliary teeth in the primary component is adopted to suppress the unbalance of the three phase flux linkages.

Parametric Equivalent Magnetic Network Modeling Approach for Multiobjective Optimization of PM Machine

This article proposes a novel parametric equivalent magnetic network (EMN) modeling approach for multiobjective optimization of a surface-mounted permanent magnet (SPM) machine. The key is to apply variable meshes under adjustable topology to establish parametric EMN model. First, a novel adjustable cross-shape mesh method with variable sizes and regular permeance is proposed, which can flexibly vary with parameters. The meshes are combined in EMN model to simultaneously achieve high accuracy, high computing efficiency, and structural parameterization. Second, comprehensive sensitivity analyses are utilized to separate variable EMN parameters with the parametric feature. Significant variables are employed in multiobjective differential evolution algorithm with response surface models. Then, the optimal parameters are balanced and determined from Pareto front with improved torque performance. Finally, a prototype is manufactured, and the effectiveness of the proposed EMN-based optimization design method is verified by finite-element analysis and experimental results.

Design and Analysis of a New Equivalent Magnetic Network Model for IPM Machines

This article proposes a new equivalent magnetic network (EMN) model for predicting the performances of interior permanent magnet (IPM) machines. The proposed EMN model incorporates the features of high accuracy and low time consumption in the reluctance network model and the magnetic equivalent circuit model, respectively, to achieve a tradeoff between the time consumption and calculation accuracy. A new air-gap model is also presented to make the dynamic analysis of the machine more efficient and easier. Moreover, the modeling approach of the rotor provides a standard for the modeling of IPM machines with permanent magnets (PMs) at different locations and of different shapes. In addition, the proposed EMN model takes into consideration the influence of flux leakage and iron saturation. Finally, the example machine is chosen, and the effectiveness of the EMN model is verified by comparison with the finite-element analysis and experimental tests.

A Generalized Equivalent Magnetic Network Modeling Method for Vehicular Dual-Permanent-Magnet Vernier Machines

This paper proposes a new equivalent magnetic network (EMN) model for vehicular dual-permanent-magnet vernier (DPMV) machines by applying a generalized modeling method. First, the magnetic circuit method and the meshing method are combined together to improve the modeling efficiency of the DPMV machine. The magnetic circuit method is used to generate conventional lumped parameter permeances to shorten time consumption, whereas the mesh method is utilized in disordered magnetic fields to obtain high precision. Second, a meshing solution for oblique region is proposed to enhance modeling flexibility. Moreover, the flux distributions in meshes are represented without magnetic field pre-delineation, which enables its utilization as a self-adaptive reluctance network model in design optimization. Finally, the proposed EMN model is used to predict the performance of the DPMV machine, considering leakage magnetic flux, local iron saturation, and magnetic field modulation effect simultaneously. Meanwhile, the effectiveness of the proposed EMN model is verified by comparison with finite-element analysis and experimental tests.

A Novel Mesh-Based Equivalent Magnetic Network for Performance Analysis and Optimal Design of Permanent Magnet Machines

This paper proposes a novel mesh-based equivalent magnetic network (EMN) model for performance analysis and optimal design of permanent magnet (PM) machines. The key contribution of the EMN model is that a generalized air-gap model solution is proposed by considering the machine motion of PM machines. Meanwhile, a modular modeling method is presented, and then the optimal design of PM machines can be investigated without repetitive programming and modeling. Two kinds of mesh elements are comprehensively utilized in the EMN model, and a hybrid rotor PM (HRPM) machine with interior PM and surface PM configuration is selected as an example to illustrate the development processes of EMN model. Meanwhile, the electromagnetic characteristics of HRPM machine are calculated by the proposed EMN model, such as back electromotive force, air-gap flux density distribution, and average torque. Finally, the accuracy and effectiveness of the proposed EMN model are verified through comparisons with finite element analysis and experimental tests.