Magnetic Equivalent Circuit Model Research Articles

Electromagnetic Analysis and Efficiency Improvement of Axial-Flux Permanent Magnet Motor With Yokeless Stator by Using Grain-Oriented Silicon Steel

This article employs grain-oriented (GO) silicon steel in an axial-flux permanent magnet (AFPM) machine to improve its torque and efficiency. Rolling direction of the GO material have been studied to ensure the machine’s main magnetic flux passes through the easy magnetization direction. Based on the study of the electromagnetic characteristics of AFPM machine, GO silicon steel is laminated to form a stator according to a certain lamination direction. The torque and efficiency of the proposed machine with GO material shows an increase in comparison with that of the conventional non-oriented (NO) silicon steel machine under identical conditions. In addition, an equivalent magnetic circuit model is established to illustrate little difference of electromagnetic property under no-load condition for the yokeless stator AFPM using two kinds of silicon steel sheet. Furthermore, a AFPM machine with stator yoke is also established to highlight the superiority of GO in the application of the AFPM machine with yokeless stator.

Fault-tolerant torque control of a three-phase permanent magnet synchronous motor with inter-turn winding short circuit

System reliability and fault tolerance are very important features in safety-critical applications with electric motors. An inter-turn winding short circuit is one of the most common fault cases, which makes the fault-tolerant torque control a crucial task. In this paper, a novel fault-tolerant model-based torque control strategy for a three-phase permanent magnet synchronous motor (PMSM) with an inter-turn winding short circuit is proposed. The control scheme has a cascaded structure with a one-step model-predictive control (MPC) in the outer loop and subordinate PI current controllers. The control strategy is based on a magnetic equivalent circuit (MEC) model. Thus, magnetic saturation and non-fundamental wave behavior of the PMSM are systematically taken into account in contrast to existing works on this topic in the literature. The parameters of the inter-turn winding short circuit are identified by a model-based fault-identification method. The high torque control accuracy of the proposed control scheme is proven by a number of different experiments performed on a test stand.

Design and Cosimulation of Twelve-Pole Heteropolar Radial Hybrid Magnetic Bearing

This paper presents a twelve-pole heteropolar radial hybrid magnetic bearing (HRHMB) structure. Firstly, the structure and equivalent magnetic circuit (EMC) are designed. And the radial electromagnetic force characteristics are calculated by the EMC model. At the same time, the rationality of EMC model is verified by the finite-element method (FEM) of Magnet software. Then, the 2-D model of the twelve-pole HRHMB is established in Magnet software. The flux density variations of twelve-pole HRHMB and eight-pole HRHMB under different currents are compared by using the FEM. Finally, a method of Magnet-Simulink cosimulation is proposed to analyze the suspension characteristics of the twelve-pole HRHMB and compared with the eight-pole HRHMB. Thus, the effective combination of theoretical analysis, FEM analysis, and Magnet-Simulink cosimulation analysis is realized in the design of HRHMB. The results of Magnet-Simulink cosimulation show that the twelve-pole HRHMB has the advantages of low power consumption, small coupling, large construction dynamic stiffness, and better suspension characteristics than the eight-pole HRHMB.

Optimization Analysis of Automotive Asymmetric Magnetic Pole Permanent Magnet Motor by Taguchi Method

In order to improve the air-gap flux density of the permanent magnet synchronous motor and reduce the cogging torque, a novel structure with asymmetric magnetic poles for automobile was proposed. Based on the characteristics of the parallel magnetic circuit, the magnetic flux path diagram is established. And the equivalent magnetic circuit model is established by the equivalent magnetic circuit method. The Taguchi method is used to be a multiobjective optimization algorithm. The total harmonic distortion of the air-gap flux density is the first optimization goal. The second and third optimization goals are the cogging torque and the average of output torque, respectively. And the torque ripple is a constraint condition. The optimized parameter combination is obtained by the Taguchi method. Finite element simulation analysis and prototype test are carried out for the optimized motor structure. The results show that the total harmonic distortion of air-gap flux density is reduced by 36.7% comparing with the initial structure. The cogging torque is reduced by 26.0%. And the average output torque is increased by 4.8%.

Optimal Design of A 12-Slot/10-Pole Six-Phase SPM Machine with Different Winding Layouts for Integrated On-Board EV Battery Charging

The transition to electric vehicles (EVs) has received global support as initiatives and legislation are introduced in support of a zero-emissions future envisaged for transportation. Integrated on-board battery chargers (OBCs), which exploit the EV drivetrain elements into the charging process, are considered an elegant solution to achieve this widespread adoption of EVs. Surface-mounted permanent-magnet (SPM) machines have emerged as plausible candidates for EV traction due to their nonsalient characteristics and ease of manufacturing. From an electric machine design perspective, parasitic torque ripple and core losses need to be minimized in integrated OBCs during both propulsion and charging modes. The optimal design of EV propulsion motors has been extensively presented in the literature; however, the performance of the optimal traction machine under the charging mode of operation for integrated OBCs has not received much attention in the literature thus far. This paper investigates the optimal design of a six-phase SPM machine employed in an integrated OBC with two possible winding layouts, namely, dual three-phase or asymmetrical six-phase winding arrangements. First, the sizing equation and optimized geometrical parameters of a six-phase 12-slot/10-pole fractional slot concentrated winding (FSCW)-based SPM machine are introduced. Then, variations in the output average torque, parasitic torque ripple, and parasitic core losses with the slot opening width and the PM width-to-pole pitch ratio are further investigated for the two proposed winding layouts under various operation modes. Eventually, the optimally designed machine is simulated using analytical magnetic equivalent circuit (MEC) models. The obtained results are validated using 2D finite element (FE) analysis.

An Improved Winding Function Theory for Accurate Modeling of Small and Large Air-Gap Electric Machines

An improved winding function theory (IWFT) is presented in this article, which can be also used to calculate the self-inductance and mutual inductance of large air-gap electric machines, while accurately considering the air-gap length function and the magnetic saturation in iron parts, simultaneously. In IWFT, the radial length of flux path in different points inside air gap is calculated using the conformal mappings (CMs). The total air-gap length is the resultant of air-gap length at differential elements in the radial direction. A modified inverse air-gap function is then presented for a typical cage-rotor induction motor (CRIM) and a typical surface permanent magnet synchronous motor (SPMSM), which considers the real paths of flux lines in the slotted air gap. The high accuracy of these modified inverse air-gap functions is verified by comparing with the corresponding results obtained through the finite element method (FEM). To consider the magnetic saturation, a virtual winding function as a 2-D function is introduced in this article, which can consider the magneto-motive force (MMF) drops in iron parts of stator and rotor obtained through the magnetic equivalent circuit (MEC) model. By using IWFT, dependent on the structure of the relevant motor, a 2-D or 3-D lookup table is pre-calculated and stored for self/mutual inductances and their derivatives, and they are then used to model the running condition of CRIM and SPMSM under different loading conditions. Finally, the accuracy of IWFT results is verified by comparing them with the corresponding results obtained through FEM.

Study on magnetic shielding for performance improvement of axial-field dual-rotor segmented switched reluctance machine

A category of permanent-magnet-shield (PM-shield) axial-field dual-rotor segmented switched reluctance machines (ADS-SRMs) are presented in this paper. These topologies are featured by using the magnetic material to shield the flux leakage in the stator and rotor parts. Besides, the deployed magnets weaken the magnetic saturation in the iron core, thus increasing the main flux. Hence, the torque-production capability can be increased effectively. All the PM-shield topologies are proposed and designed based on the magnetic equivalent circuit (MEC) model of ADS-SRM, which is the original design deploying no magnet. The features of all the PM-shield topologies are compared with the original design in terms of the magnetic field distributions, flux linkages, phase inductances, torque components, and followed by their motion-coupled analyses on the torque-production capabilities, copper losses, and efficiencies. Considering the cost reduction and the stable ferrite-magnet supply, an alternative proposal using the ferrite magnets is applied to the magnetic shielding. The magnet demagnetization analysis incorporated with the thermal behavior is performed for further verification of the motor performance.

Dynamic analysis of Halbach coaxial magnetic gears based on magnetic equivalent circuit modelling

Halbach permanent magnet arrays (HPMAs) are an attractive configuration that can be applied in PM electric machines such as magnetic gears. These arrays have some merits, namely near-sinusoidal distribution of flux density along air gap, low torque ripple and iron losses. This article proposes a two-dimensional magnetic equivalent circuit method to determine the magnetic field distribution of HPMA based on coaxial magnetic gears (HCMG). Furthermore, regarding the proposed model, distribution of radial and tangential components of flux densities is extracted within outer and inner rotors. Moreover, the dynamic model of HCMG is extracted and its pull-out torque and output speed are calculated using it. Finally, in order to validate the effectiveness of the proposed model, the obtained results for a sample HCMG are compared with finite element analysis method results.

Nonlinear Modeling of a C-Core Connected Two-Phase Switched Reluctance Motor

The main idea of this paper is to offer a continuous C-cores unique configuration for switched reluctance motor (SRM) and to present an analytical model for its analysis. The advantages of this structure are having a short path for the main part of the magnetic flux, resulting in less core losses and as well as less negative torque. On the other hand, there is less leakage flux in the proposed structure. Another advantage of this structure is that it has a high mean torque compared to conventional structures, so that this increase in mean torque also increases a small amount of torque ripple, which is negligible. However, power density at a constant volume increases relatively much. The proposed SRM is analyzed by the finite element method (FEM) and by employing a magnetic flux density pattern and magnetic fluxes path, its magnetic equivalent circuit (MEC) is obtained. In this MEC model, the main fluxes and leakage fluxes are fully modeled. After its complete analysis, electromagnetics torque, inductance, flux-linkage, mean torque, and peak torque are evaluated. Static and dynamic performances are then determined. Finally, the proposed SRM was prototyped and tested. The experimental results consisting of static torque, flux-linkage, voltage, and current waveforms and input power are compared with the corresponding results in the MEC model and FEM. The comparisons verify the accuracy and validity of the introduced analytical model. Besides, static torque, flux-linkage characteristics, and dynamic performance at a nominal speed of 1000 rpm and the current chopping control mode with chopping 5A under the load of the proposed SRM are compared with the conventional SRM and its merits are observed.

Analytical Model of Open-Circuit Air-Gap Field Distribution in Interior Permanent Magnet Machines Based on Magnetic Equivalent Circuit Method and Boundary Conditions of Macroscopic Equations

To accurately and quickly predict the open-circuit air-gap magnetic field in interior permanent magnet synchronous machines (IPMSMs), an analytical model based on magnetic equivalent circuit (MEC) method is proposed. The analytical model can provide radial and tangential components of open-circuit magnetic field in the slotless air gap. The radial component is obtained from the MEC model, and the tangential component is obtained from boundary conditions of macroscopic equations. Then, a complex relative air-gap permeance is applied to take the effect of slots into account. As a result, an accurate solution of both radial and tangential components of the flux density in the slotted air gap is obtained. Additionally, the no-load back electromotive force (EMF) and cogging torque are calculated based on the open-circuit air-gap magnetic field. All the analytical results are verified by the finite element (FE) analysis and they are well matched. In the end, a direct measurement experiment of open-circuit air-gap magnetic field is proposed to verify the validity of both radial and tangential open-circuit air-gap magnetic fields.

Theoretical calculation model of torque transmission in permanent-magnet couplers

Permanent-magnet couplers are widely used in various industrial applications due to their high functionality and economy. The magnetic field of the magnetic circuit of a permanent-magnet coupler is divided by the segmentation method, by which the magnetoresistance of each area can be calculated. The magnetic resistance of the magnetic flux and the permanent-magnet coupler characteristics outside the magnetic circuit are obtained using the equivalent magnetic circuit model of permanent-magnet couplers. The working point of the permanent magnet is analyzed, and the skin effect is found to be equivalent to a conductor plate with an increase in its resistivity. According to the principle of electromagnetic induction, the ampere force received by each part is calculated. Finally, the theoretical calculation model of the transmitted torque of the permanent-magnet coupler is obtained, and its accuracy is verified by finite element simulation and experiments. This can significantly guide the design and engineering applications of permanent-magnet couplers.

A simple magnetic equivalent circuit model for switched reluctance machine

In the present paper, a simple model based on magnetic equivalent circuit (MEC) method is introduced for the switched reluctance machine to predict the phase flux linkage characteristic. All equations required to build up the model are given, and therefore, someone can use it easily for different types of the switched reluctance machines. Because of large speed of the suggested model, it can be utilized properly for quick prediction of machine performance. The suggested MEC model is applied to a typical 8/6 switched reluctance motor (SRM), and simulation results including flux linked by a phase, phase current and instantaneous torque are presented. In order to validate the suggested MEC model, the obtained simulation results are compared to those derived from finite element method (FEM) and experimental results.

An Improved Analytical Model of Magnetic Field in Surface-Mounted Permanent Magnet Synchronous Motor With Magnetic Pole Cutting

This paper presents an analytical model for predicting the magnetic field performance of permanent magnet synchronous motor with permanent magnet cutting. In order to satisfy the boundary conditions, the defective permanent magnet is equivalent to a double-layer sector permanent magnet, and the size of the sector-shaped permanent magnet is determined, this process is obtained by an equivalent magnetic circuit model. Then, the motor is divided into four sub-domains: inner sector permanent magnet sub-domain, outer sector permanent magnet sub-domain, air gap sub-domain and stator slot sub-domain. Under the boundary conditions, the analytical solution and harmonic decomposition of the air gap magnetic flux density and cogging torque for several different permanent magnet cutting sizes under no-load condition are obtained by solving the Poisson equation and Laplace equation with the method of separating variables. The analytical model is verified by the finite element method. The results show that the error between the analytical method and the finite element method is less than 6%, and the solution time of the analytical method is only 0.59% of the finite element method, the chamfered structure proposed in the paper reduces the cogging torque amplitude 35%. Therefore, this method can provide powerful help for the initial design of permanent magnet motors.

Three-Phase Transformer Inrush Current Reduction Strategy Based on Prefluxing and Controlled Switching

Inrush current with high amplitude is generated when the transformer is energized. On the one hand, it will have a negative impact on the safety of the transformer itself, and even cause the relay protection to malfunction. On the other hand, it may reduce operation speed of the protection when there is slight fault because of the protection restraint criteria. Both aspects will affect grid security. Based on the generation mechanism of inrush current, this paper proposes an inrush current reduction strategy that combines prefluxing and controlled switching technology. By constructing an equivalent magnetic circuit model of the large-capacity three-phase transformer with a universal core structure, the analytical formulas of the magnetic flux at each stage of implementing the strategy are obtained, and then the parameters design method of this strategy is proposed. The accuracy of the theoretical analysis of magnetic flux is verified through the accurate simulation. Compared with common inrush current reduction strategies, this strategy can reduce the inrush current to 0.5 times rated current below in any situation where the residual flux is unknown and the “core flux equalization” effect are not obvious, avoiding the problem of residual flux measurement. Finally, in the case of the transformer differential protection, the influence of this strategy on the protection is analyzed from the perspective of theory and simulation, and it shows that it can improve the performance of various protections effectively.

Analysis and Design Optimization of Tubular Linear Voice Coil Motor for High Thrust Force and Low Copper Loss

In recent years, studies on the design of the tubular linear voice coil motor (TLVCM) have increased considerably. These studies propose to obtain high thrust force, high efficiency, low thrust ripple, low cost, or low volume. The magnetic equivalent circuit of the motor is created, and for any objective, only one or some parameters are emphasized. In fact, the effect of each geometric parameter of the TLVCM on performance is different and important. This study proposes multiparameter and multiobjective design optimization for high thrust force and low copper loss using a complex magnetic equivalent circuit model and nondominated sorting genetic algorithm II. Besides, the optimized motor design is analyzed by the finite element method. The average thrust force has been increased, and copper loss has been reduced with multiple interactive changes of the motor geometry, while the thrust ripple has also been reduced. According to the obtained results, a multiparameter design approach is thought to contribute to the performance of the TLVCM with the proposed approach.

Analytical Modeling of Variable-Reluctance Tubular Resolver Based on Magnetic Equivalent Circuit and Conformal Mapping

Compared with flat linear structures, tubular linear machines do not face edge effects, making their performance better than their flat counterparts. In this article, a novel linear variable-reluctance resolver with tubular configuration is proposed. To optimize the design of an electromagnetic structure, modeling methods are used. Thus, in this article, an analytical model for the proposed resolver is presented. This model is based on the magnetic equivalent circuit (MEC) method and is considerably less time-consuming than finite element analysis (FEA), yet provides accurate results. A conformal mapping is employed to compute the permeance of the air-gap. The proposed model is then utilized to compensate the resolver’s performance for the longitudinal end-effects. The results of the MEC model are compared with those of FEA, and good agreement is seen. Finally, the compensated sensor is experimentally built and tested, and the simulation results are verified.

Performance Analysis of a Coreless Axial-Flux PMSM by an Improved Magnetic Equivalent Circuit Model

In this paper, an improved magnetic equivalent circuit (MEC) model of a coreless axial-flux permanent-magnet synchronous machine (AFPMSM) with printed circuit board (PCB) winding is presented, which considers the curvature effect, fringing effect, leakage flux, and rotor yoke's magnetic saturation. The axial air-gap flux density distribution, no-load back electromotive force, winding inductances, and electromagnetic torque are predicted by the proposed MEC model. The steady-state performances of the machine under heavy load, as well as the dynamic response of the machine with a connected voltage source and mechanical load, are calculated. All the results obtained from the proposed model are in good agreement with those issued from the 3D finite element method (FEM). The computation time of the proposed model is greatly reduced compared to 3D FEM. Finally, a coreless AFPMSM prototype with a PCB stator is manufactured, and experiments are carried out to verify the predicted results.

Structural optimisation based on a snake‐like wave energy convertor with magnetoelectric transducer

Snake-like wave energy conversion (WEC) is a new type of WEC that combines raft WEC and magnetoelectric transducer. This type of WEC uses the magnetoelectric transducer, which is designed based on the permanent magnet linear generator and Halbach permanent magnet array, as its power take-off unit. The purpose of this study is to design a matching magnetoelectric transducer for WEC in common wave conditions and test its performance. The hydrodynamic model of the snake-like WEC is established to study the motion of WEC in regular waves. The equivalent magnetic circuit model of the magnetoelectric transducer is set up to optimise its ability to harvest wave energy in the ocean. Taking the maximum damping coefficient (cm ·max) as the optimisation goal of the magnetoelectric transducer, the induced voltage and output power of the magnetoelectric transducer in relatively uniform and sinusoidal motion can be calculated by simulation software. Finally, a prototype of the magnetoelectric transducer was made and its performance was tested. The experiment shows that the magnetoelectric transducer has a good ability to harvest wave energy, and snake-like WEC has wide applicability.

An Improved Subdomain Model for Magnetic Field Calculation of SPMSM Considering No-load Leakage Flux

Due to big leakage flux, the performance of permanent magnet (PM) motor will be much reduced. Especially for surface-mounted permanent magnet synchronous motor (SPMSM) with similar number of poles and slots, because the zigzag leakage flux is big and varies with the relative positions between stator and rotor, selecting no-load leakage flux coefficient with experience may cause a big calculation error to electromagnetic parameters by equivalent magnetic circuit model. Finite-element method (FEM) can directly calculate the coefficient, but entire process is time-consuming. Focusing on this problem, an analytical model of no-load leakage flux coefficient is proposed including air-gap leakage flux model and zigzag leakage flux model. Then, an improved subdomain model for magnetic field calculation of SPMSM is established, and the air-gap magnetic flux density, inducing flux linkage and line no-load back electromotive force (EMF) are calculated considering no-load leakage flux. To verify the improved model, an external rotor type SPMSM with 20-poles and 24-slots for bridge crane is designed and manufactured. Finally, the validity of improved model is verified by experimental test.

Design, analysis and prototyping of a magnetic energy-harvesting suspension for vehicles

With the development of electric vehicles, the energy harvesters of vehicle’s suspensions have been widely investigated. However, most of the existing energy harvesters have replaced the original damper of the suspensions, which reduces vehicle safety. This paper proposes a magnetic energy-harvesting suspension (MEHS) for vehicles, with the advantages of high vehicle safety and a compact structure, which consists of a passive suspension and a harvester. In this paper, the working principle and the structure of the MEHS are introduced. To better analyze the magnetic field, the magnetic flux circuit model is established by combining the magnetic field division method with the magnetic equivalent circuit model. Furthermore, a dynamic model for a two-degree-of-freedom quarter-vehicle with the MEHS is built to analyze the energy-harvesting characteristics and the damping characteristics. A prototype of the quarter-vehicle that is considering the tire stiffness, is designed and manufactured, and the performances are investigated by simulations and experiments with different frequencies, external resistances and amplitudes. The experimental results indicate that the harvested peak power of the MEHS is 1.08 W with a sinusoidal input of 10 Hz and 2 mm. Moreover, the maximum energy-harvesting efficiency of the prototype reaches 67% at the sinusoidal input of 6 Hz and 2 mm. The harvested energy of the MEHS can power some electrical equipment of vehicles.