Magnetic Equivalent Circuit Approach Research Articles

Comprehensive Analysis on a New Type VR-Resolver With Toroidal Windings Under Healthy and Eccentric Cases

A novel analysis for a new type of variable reluctance resolvers (VR-Resolvers) with toroidal windings based on the magnetic equivalent circuit (MEC) method is presented in this work. Different cases including various windings configurations as well as different rotor structures are considered in order to investigate the performance of the resolver precisely. The position error of both healthy and eccentric resolvers are studied by a flexible MEC model. The effect of the eccentricity fault on the resolvers with different specifications is also evaluated to analyze the manufacturing tolerance due to the eccentric rotor for several cases. It is notable that the presented MEC provides the opportunity to adjust accuracy and model several structures in both healthy and faulty conditions by just a single model. Finally, the MEC results are confirmed by finite element method and experimental results to show the effectiveness of the proposed model. In general, development of a new VR-Resolver and analyzing its performance under different windings configurations and rotor structures by proposing a modified MEC approach are the paper novelties.

Understanding Switched-Flux Machines: A MMF-Permeance Model and Magnetic Equivalent Circuit Approach

Due to their particular structure, switched-flux permanent magnet machines have become a very interesting alternative for many applications. This is why some recent studies have been focused in the understanding of the operating mechanism of these machines via the MMF-permeance modelling. However, the models that can be found in the literature make some simplifications that reduce their accuracy when predicting the performance of switched-flux machines. For example, the models that can be found in the literature are commonly not precise enough for machines with a wide slot, because the influence of the modulator of the primary side of the machine is neglected. In this article, a precise analytical model is developed for a 6/13 C-Core switched-flux machine via a combination of a magnetic equivalent circuit and a MMF-permeance model. The model is based on the magnetic field modulation principle. The analytical model is used to explain the flux focusing effect and the force generation mechanism of switched-flux machines. A new concept of PM field harmonic efficiency ratio is used to identify the most efficient PM field harmonics of 2 switched-flux machines. The precision of the model is validated via 2D and 3D Finite Element Method simulations, and experimental measurements that were obtained with a linear machine prototype. The results show that the model can predict the performance of switched-flux machines with a high accuracy level.

Design and Multi-Objective Optimization of a 12-Slot/10-Pole Integrated OBC Using Magnetic Equivalent Circuit Approach

Permanent magnet machines (PMs) equipped with fractional slot concentrated windings (FSCWs) have been preferably proposed for electric vehicle (EV) applications. Moreover, integrated on-board battery chargers (OBCs), which employ the powertrain elements in the charging process, promote the zero-emission future envisaged for transportation through the transition to EVs. Based on the available literature, the employed machine, as well as the adopted winding configuration, highly affects the performance of the integrated OBC. However, the optimal design of the FSCW-based PM machine in the charging mode of operation has not been conceived thus far. In this paper, the design and multi-objective optimization of an asymmetrical 12-slot/10-pole integrated OBC based on the efficient magnetic equivalent circuit (MEC) approach are presented, shedding light on machine performance during charging mode. An ‘initial’ surface-mounted PM (SPM) machine is first designed based on the magnetic equivalent circuit (MEC) model. Afterwards, a multi-objective genetic algorithm is utilized to define the optimal machine parameters. Finally, the optimal machine is compared to the ‘initial’ design using finite element (FE) simulations in order to validate the proposed optimization approach and to highlight the performance superiority of the optimal machine over its initial counterpart.

Evaluation and analysis of novel flux‐adjustable permanent magnet eddy current couplings with multiple rotors

This article proposes a novel flux-adjustable permanent magnet eddy current coupling with multiple rotors. According to the different functions, the permanent magnet rotors are divided into fixed-flux and flux-adjustable rotors. By adjusting the relative position between two types of permanent magnet rotors, the magnetic field, torque, and output speed are controlled without changing the air-gap length. To quickly and easily analyse the torque performance, an analytical model for the torque of such devices is developed based on the non-linear magnetic equivalent circuit approach. In the modelling phase, a number of factors are considered, such as the skin effect, the inductance of eddy current field, the temperature effect, and so on. A three-dimensional finite element method is employed to validate the model results, and the comparative analysis shows the advantages and potential of the proposed topology. The further sensitivity analysis of the key parameters is also made, which offers helpful information for the preliminary design of such devices.

A Novel Analysis on a New DC-Excited Flux-Switching Machine Using Modified MEC Method for Ground Power Unit Application

This article presents a novel analysis on a new DC-Excited Flux-Switching Machine (DC-FSM) for Ground Power Unit (GPU) application. The performance of machine under different structures can be studied by a flexible Magnetic Equivalent Circuit (MEC), where the core non-linearity can be fixed on the material B-H curve. The model accuracy can also be adjusted arbitrary by determining the number of proposed MEC elements (flux tubes) for a given structure. The performance analysis of two sample DC-FSMs as two high-frequency 120 V generators is performed by the proposed MEC and validated by 2D and 3D FEM based simulations. The obtained results show a very good improvement in processing time with valuable accuracy. In general, introducing a new DC-FSM for the GPU application and analyzing its performance by proposing a modified MEC approach are the paper novelties which are studied in this work. Since the suggested MEC is more flexible than FEM, it is recommended for designing, modeling, and optimization purposes.

Rotor/Stator Inter-Turn Short Circuit Fault Detection for Saturable Wound-Rotor Induction Machine by Modified Magnetic Equivalent Circuit Approach

This paper presents a new method to model healthy and faulty wound-rotor induction machines (WRIMs) with and without inter-turn short circuit fault by a single set of equations. The model is presented for a machine with arbitrary pole, and rotor and stator slot numbers. A single set of equations, including both electric and magnetic parts, is solved to obtain full dynamic behavior of the machine. Therefore, the modified magnetic equivalent circuit with non-linear elements is used for modeling and a numerical technique is employed to solve the non-linear equations. The proposed modified method has a simple calculation procedure in comparison with the conventional magnetic equivalent circuit method. Solving the electric and magnetic equations by a single set of equations is the main advantage of the presented method, which is proposed for a WRIM machine, for the first time. In addition, to increase the accuracy, the saturation phenomenon is also considered in the model. Due to the saturation effect, there are some non-linear algebraic magnetic equations, which should be simultaneously solved with differential equations. A trapezoidal technique is used to convert differential equations to algebraic ones. To solve the non-linear equations, non-linear equations, Newton Newton–Raphson method is employed. Current signature analysis is used for rotor and stator inter-turn short circuit fault detection. Finally, the finite-element method is used to verify the effectiveness of the proposed modeling method. It is worth noting that the proposed method can model a healthy and faulty machine with different faults by a single model.

Modeling and stator Inter‐Turn short circuit fault detection for saturable salient pole synchronous machine by a non‐linear magnetic equivalent circuit approach

AbstractThis paper presents a novel and adequate model for healthy and faulty salient pole synchronous machines with and without interturn short circuit fault. The model is presented for a machine with arbitrary pole numbers, arbitrary damper bars, and stator slot numbers. The magnetic equivalent circuit with nonlinear elements is used for modeling, and numerical techniques based on Newton‐Raphson method have been approved for solving of nonlinear equations. Because the design of electric machines is based on the knee point of a B‐H curve, consideration of saturation effect is mandatory for adequate studying. Because of the saturation effect, there are some nonlinear algebraic magnetic equations, which should be solved simultaneously with differential equations. Trapezoidal technique is used for differential equations converting to algebraic type, and Newton‐Raphson method is used for a nonlinear set equation solving. Stator current signature analysis is used for stator interturn short circuit fault detection. Finally, obtained results by finite element method are used to verify the effectiveness of the proposed modeling method. The proposed approach for magnetic equations based on nodal potential and reluctance mesh model equations is one of the paper novelties for the salient pole synchronous machine modeling in both healthy and faulty cases. This dynamic modeling method has less complexity compared to finite element method and pure nodal potential approaches. Solving the electric and magnetic equations by a single set of equations is the main advantage of the presented method, which has been addressed for a salient pole synchronous machine for the first time. Another advantage of the proposed study is the capability of modeling the healthy and faulty machine with interturn fault by a single model.

Magnetic equivalent circuit modelling of doubly‐fed induction generator with assessment of rotor inter‐turn short‐circuit fault indices

In this study, a wound rotor induction machine, as the core of a doubly-fed induction generator (DFIG) system, is modelled using the magnetic equivalent circuit approach. The entire DFIG system is implemented in Matlab/Simulink environment, including the machine model, power converters, control system and the grid. The model, which includes the ability to simulate rotor inter-turn short-circuits (RITSCs), is subsequently used for the investigation and comparison of the impact of this fault in several DFIG quantities, namely in the stator current and in some control variables. This research also deals in detail with the differences found when comparing RITSC and unbalanced rotor resistance (URR) faults. It is observed that on the contrary to the URR, the stator current spectrum is more appropriate than the control signals for the detection of RITSC. Simulation and experimental results obtained with a DFIG system operating at sub-synchronous and super-synchronous speeds, for different values of the active and reactive powers injected into the grid, corroborate the findings reported in this study.

Optimum Design of Rotor for High-Speed Switched Reluctance Motor Using Level Set Method

This paper presents a novel rotor structure optimized by using the level set method (LSM) to improve the static torque characteristics of a two-phase 4/2 high-speed switched reluctance motor. The magnetic equivalent circuit approach is used to analyze the influence factors on the static torque. The inner material boundary contained in the rotor saliency, which will be optimized, is implicitly represented by an embedded level set function. The evolution of the inner material boundaries is driven by the normal velocity derived through sensitivity analysis and adjoint variable computation. Optimal rotor configuration produces the nonuniform distribution of magnetic flux density in the air gap at aligned position, which can make the ratio of maximum and minimum inductances increased. High-permeability material is applied to enhance the mean torque. In order to achieve the optimal static torque, the strategy combining finite-element electromagnetic computation with LSM is conducted to optimize the rotor saliency at different rotor positions. The comparison of the optimized rotor configuration using LSM with that using density-based method suggests that the optimized rotor structure obtained using this presented method is easier to implement.

Extended 2D magnetic equivalent circuit method

PurposeThe purpose of this paper is to devise a magnetic field modelling approach suitable for simulating the transient behaviour of a class of electromagnetic systems (particularly linear synchronous motors).Design/methodology/approachThe classical 2D magnetic equivalent circuit (MEC) approach is extended by separately accounting for leakage flux from highly permeable polygonal regions (where the MEC approach is most applicable). It capitalises on the computational efficiency of an MEC approach for regions where the flux can be assumed to be uniformly channelled through a coarse network of “flux tubes” and accounts for leakage flux from these regions by introducing mutual permeances. These mutual permeances are geometry dependent and can be calculated upfront using a surface‐current representation of the magnetomotive force attributed to each flux tube.FindingsAs demonstrated with a simple example, the magnetic field solution converges with an increasing subdivision of flux tubes, yielding a transparent trade‐off between simulation time and accuracy.Research limitations/implicationsUsing Schwarz‐Christoffel mapping to approximate the mutual permeances is restrictive and introduces unnecessary error. Hence, the use of finite element or boundary element methods to obtain these permeances is under investigation. Furthermore, it is expected that introducing 2D flux tube elements for junction regions would be beneficial.Originality/valueA novel approach is presented that aims to improve the accuracy of a traditional MEC solution, whilst retaining its computational advantage for the flux that is well channelled. The method has particular merit for the dynamic modelling of linear motors, where the machine's behaviour is dominated by the flux bridging the air gap.

Accurately modeling EI core inductors using a high-fidelity magnetic equivalent circuit approach

We present a high-fidelity magnetic equivalent circuit (HFMEC) inductor model that reduces the inaccuracies associated with a traditional MEC approach. The model can accurately predict the flux linkage versus current characteristic in a fraction of the time needed for finite-element analysis. The accuracy, computational efficiency, and simple inputs (consisting of only geometry and material specifications) make the model ideal for automated inductor design.

Design and finite-element analysis of an outer-rotor permanent-magnet generator for directly coupled wind turbines

This paper presents the design and finite-element analysis of a permanent-magnet generator using neodymium-iron-boron magnets for directly coupled wind turbines. For the sake of small size and light weight with extra low speed for direct coupling, the outer rotor structure is used. The simple magnetic equivalent circuit approach is used for initial design iteration, and the finite-element method is applied to analyze the detailed characteristics. Comprehensive experimental tests were conducted to verify the theoretical predictions. Agreement between the theoretical work and testing results was good.