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A homogenization method for analyzing eddy current fields and resultant loss in laminated ferromagnetic media is presented, where the equivalent conductivity tensor proposed in a previous paper is applied. In order to compute fields at various frequencies, the formulas for the effective skin depths along different directions in the anisotropic soli...
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... electrical machines or transformers, the laminated iron core model with infinite length shown in Fig. 1(a) is represen- tative. Because of the huge computational burden during the numerical analysis, the real lamination model is generally re- placed by the anisotropic continuum model shown in Fig. 1(b), in which the electrical conductivity and the magnetic perme- ability are all formulated as the equivalent ones. In our previous work [10], ...
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... electrical machines or transformers, the laminated iron core model with infinite length shown in Fig. 1(a) is represen- tative. Because of the huge computational burden during the numerical analysis, the real lamination model is generally re- placed by the anisotropic continuum model shown in Fig. 1(b), in which the electrical conductivity and the magnetic perme- ability are all formulated as the equivalent ones. In our previous work [10], the equivalent conductivity tensor for the continuum model was derived as (1) where is the conductivity of the iron material, is the stacking factor, and and are the width and thickness of an iron ...
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... © 2012 IEEE Assuming that there exists only the main magnetic field in the iron core shown in Fig. 1(b), and that all the electromag- netic quantities are sinusoidal time variations with the angular frequency , the actual 3D field problem can be reduced to a 2D problem. With Ampere's law and Faraday's law (3) where and are the magnetic field and electric field inten- sity vectors respectively, the field governing equation for the 2D ...
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Citations
... The material could be considered as laminated core with low permeability and conductivity in the stacking direction. The parameters of equivalent model can be calculated as in [7], where F is the stacking factor of nanocrystalline core. ...
... However, failure tests on transformers are destructive and can compromise their performance and short downtime tests do not provide sufficient data for regular analysis. Therefore, scholars turn to the equivalent circuit theory to study these problems [10,11]. However, this method can only obtain the global parameters under the fault and cannot accurately simulate the current and temperature when the fault occurs in different parts [12,13]. ...
... When the interlaminar short circuit fault occurs in the converter transformer scaled model, most of the interlaminar insulation in the fault area is still intact. Instead, the fault area is ablated from the fault point of the short circuit between the sheets until the insulation in the fault area is burned out or even the core is melted [10]. ...
Converter transformer is the key equipment in UHVDC transmission. If a local overheating fault occurs, it will inevitably form a local hot spot on the core, winding or other structural parts. Among these faults, multipoint grounding and interlaminar short circuit faults account for 30–50% of core accidents. The continuous overheating of 150–250 °C will cause ablation on the silicon steel sheet, which will destroy the insulation material and reduce the insulation performance. In severe cases, it will cause thermal expansion, resulting in local deformation or displacement of the core. Considering the scale of size and temperature parameters, the scale model of converter transformer is established based on the principle of constant magnetic flux density. By using the homogenization theory, the scaled model under multipoint grounding and interlaminar short circuit fault is simulated by electromagnetic heat. First, the single-phase four-column model of the core is established according to the scaled principle, and the core is refined. Secondly, taking the refined model as the research object, the magnetic thermal coupling simulation and analysis are carried out under multi-point grounding and interlaminar short circuit fault, and the magnetic density, eddy current loss and temperature distribution on each lamination are obtained. Finally, the correctness of the simulation is verified by the one-dimensional eddy current loss analytical equation, which provides a reference for the local overheating problem of converter transformers.
... By analysing mathematical models, many researchers have been devoted to determining the loss in silicon steel sheets under the eddy-current field through the approximate solution for Maxwell equations of the magnetic quasi-static field [8,9] and equivalent circuit [10,11]. This type of method is suitable for a laminated core environment where the magnetic boundary conditions are rectangular and the number of silicon steel sheets is small. ...
The analysis of the eddy‐current field in the wound core widely used in the field of transformer energy conservation is taken as the theme. Adopting the homogenisation idea to consider the unique geometry of the wound core and features of its equivalent multi‐stage circular cross‐section magnetic boundary, a homogeneous model consisting of a columnar material with continuous homogeneous electromagnetic anisotropy is established by deriving the Maxwell equations of the magnetic quasi‐static field in the columnar coordinate system. Finally, a homogeneous fine element model for the eddy‐current field in the wound core is established and the accuracy of the model has been verified by the test platform. The result shows that the homogeneous model can be effectively used for the analysis of the eddy‐current field in the wound core, and the error of calculating the eddy‐current loss under different excitation conditions is less than 6% under the premise of extremely saving the engineering calculation cost, which will help improve the operational performance of the wound core and contribute to the energy‐saving goal of the high‐voltage equipment.
... Hence, an alternative method is necessary for FEA modelling. The homogenized model has been considered as a simple method to simplify the model and shorten the computation time for eddy current analysis in laminated cores [5,[13][14][15][16]. Moreover, among different homogenized modelling approaches, the model from [13] can be applied in a highfrequency environment and obtain comparable results with the direct method. ...
... The homogenized model has been considered as a simple method to simplify the model and shorten the computation time for eddy current analysis in laminated cores [5,[13][14][15][16]. Moreover, among different homogenized modelling approaches, the model from [13] can be applied in a highfrequency environment and obtain comparable results with the direct method. The laminated core is introduced as a solid continuum with anisotropic electrical and magnetic parameters in the model shown in Figure 5. σ c , μ c , σ n and μ n are the electrical conductivity and magnetic permeability in corresponding directions. ...
... The laminated core is introduced as a solid continuum with anisotropic electrical and magnetic parameters in the model shown in Figure 5. σ c , μ c , σ n and μ n are the electrical conductivity and magnetic permeability in corresponding directions. Based on the practical design, the stacking factor of the lamination layers, F, is set as 0.8; The equivalent conductivity and permeability of the laminated cores can be derived in Equations (7)-(9) [13]. Meanwhile, to obtain a reasonable computation time and a good accuracy, the FE mesh should be appropriately set. ...
Abstract A simple method is proposed here to improve the gap loss concentration problem of a nanocrystalline core in an LCL filter inductor for high switching frequency converters using SiC devices. This alloy‐gapped inductor design aims to reach two primary goals. First, to reduce the concentrated gap loss in a nanocrystalline core. Second, decrease the maximum temperature around the gap region and lead to more even temperature distribution. A finite element (FE) power loss and thermal models, validated by experiment, have been created to evaluate the proposed design. Based on the FE model results, the eddy current loss on the surfaces, which used to have the most severe gap loss is reduced by either 70% or 40% for the two commonly used winding placements. The total eddy current loss can be reduced by 29% and 27% for those two winding placements. In addition, FEA thermal model indicates that the hotspot temperature can be significantly decreased, and the nanocrystalline core can achieve a more uniform temperature distribution by this design, which can be a potential downsize method for the nanocrystalline core inductor.
... The reason is that with the increase of frequency, eddy current will be produced in the magnetic material under the action of high frequency which will weaken the induced magnetic field and thus cause power loss. The resulting magnetic force was reduced and the phase was lagged, 10,11 and finally it would have a serious impact on the dynamic characteristics of the magnetic bearing system. It was mentioned in literature 12 that the use of high-resistivity soft magnetic composite materials can greatly reduce eddy current loss, in which the bandwidth of magnetic thrust bearing made of SMCs had a larger bandwidth (about 1000 Hz) than that of traditional carbon steel materials (about 100 Hz). 13 In order to enable the designed magnetic bearing to be applied more efficiently in actual working conditions, it is necessary to optimize the design of bearing structural parameters. ...
A new type of three degrees of freedom axial-radial hybrid magnetic bearing (3-DOF ARHMB) with compact structure, shorter axial length and smaller volume is proposed for the flywheel energy storage system. The axial direction adopts the permanent magnet biased thrust bearing (PMB) made of soft magnetic composite materials (SMCs). In the radial direction, the laminated structure is used to reduce the eddy current, and the Halbach array is introduced to strengthen the magnetic density of the radial air gap. Firstly, the dynamic magnetic flux distribution of the 3-DOF ARHMB is analyzed by the finite element method (FEM). Based on the equivalent magnetic circuit method, the equivalent reluctance model with comprehensive consideration of eddy current effect and magnetic leakage effect is established, and then the frequency responses are analyzed. Secondly, a constraint model coupled with structural parameters, equivalent reluctance and magnetic leakage coefficient is established, and an adaptive particle swarm optimization algorithm (APSO) is used to optimize the bearing parameters. Finally, based on the equivalent reluctance model, the axial and radial force-current factor and force-displacement factor are derived, and the dynamic characteristics of bearings with different structures and materials are compared and analyzed. The results show that the new 3-DOF ARHMB made of SMCs can provide much larger and more stable magnetic force and larger bandwidth than that made of carbon steel materials, and has better dynamic characteristics under higher-frequency conditions, which can meet the industrial requirements of flywheel energy storage system.
... The inductor core structures are illustrated in Considering the fine thickness of the laminated nanocrystalline core is around 20 μm, then homogenized method is the feasible method to model the laminated cores and simply illustrated in Fig 4. This method already has been often used to model and analysis laminated cores to simplify the computation process and time in many researches [2], [10], [11], [12]. The c type finely laminated core was represented by a solid continuum with different electrical conductivity and magnetic permeability parameters in directions along the core path and normal to the surface of the lamination layers in a homogenized model, σc, μc, σn and μn respectively. ...
... The c type finely laminated core was represented by a solid continuum with different electrical conductivity and magnetic permeability parameters in directions along the core path and normal to the surface of the lamination layers in a homogenized model, σc, μc, σn and μn respectively. Since this research mainly focuses on the eddy current analysis, then the homogenized model in [10] is selected. The relations between different direction characteristics and the material parameters illustrates in (1.6) -(1.9). ...
... Due to the time-varying magnetic field, eddy currents exist in the stator and rotor of MBs as the rotor rotates [22][23][24][25]. In [22], the authors analyzed the eddy-current loss for design of small active magnetic bearings with solid core and rotor. ...
... Besides, eddy current reduces force of actuator and cause the phase lag between actuator coil current and the force. The magnetic field would be weaken by eddy currents [24,25]. In [25], a new method for analyzing the eddy current fields in laminations is presented. ...
... Eqs. (17), (24) and (41) show that the air gap is a critical parameter to the dynamic current stiffness. Fig. 5 shows the effect of air gap length on the magnitude and phase of current stiffness at different frequencies. ...
Decreasing eddy current is very important for the realization of stability control of HoMB system. In order to improve the dynamic performance precision of HoMB in the design stage, the dynamics and stiffness analysis of a homopolar magnetic bearing (HoMB) has been studied in this paper. Because the polarities of the magnetic poles were not changed during the rotation of rotor, the effect of eddy-currents was often ignored in the previous researches. However, when the frequencies of vibration caused by external disturbance and control currents are very high, eddy-current effects have significant influence on the performance of HoMB. In order to predict the HoMB performance, guide the HoMB design and control of the HoMB system in high frequency, a dynamics model was built on the equivalent circuit method. Parameters of dynamic Modeling are frequency-dependent. The effect of eddy-currents on the current stiffness was studied. The analysis results show that the eddy current effect on HoMB can be reduced by increasing the air gap, decreasing the laminations thickness and decreasing the laminations conductivity.
... Flux density vector components cause narrow eddy current loops in the rolling plane, labelled J L and J T , respectively. In conventional closed core transformers, these loops are generally predominant [6], [7]. In contrast, with the open core, the predominant eddy current loops J N are caused by the normal component of the flux density vector (B N ). ...
... A coils / Type I W side / Type II X side / Type II Y side / Type II Z side / Type II The anisotropic effect was modeled using equivalent permeability tensor shown in equation (4). Permeabilities μ L, μ N and μ T were defined according to equations (5) - (7). ...
... In the above equations F is the stacking factor and μ fL, μ fN and μ fT are core sheet permebilities in lamination, normal and tangential directions, respectively [7]. ...
Power Voltage Transformers are becoming increasingly present in different substation solutions on a world scale. Such units that are based on the open-core concept introduce several advantages in terms of transformer performance and reliability. This paper provides context for distinct open-core losses, expanding in detail on a measurement-based method for determining both total and specific losses in the open core. The approach is demonstrated on several core model configurations with varying parameters. Apart from loss measurement, the presented core configurations were used to determine and verify the distribution and magnitude of all flux density vector components. The proposed approach is validated by various accompanying measurements, but also through comparison with loss measurements performed on several Power Voltage Transformer units intended for commercial application.
... The core was represented by a solid continuum, but the model preserves the anisotropic properties of the laminated structure through the use of separate permeability and electrical conductivity parameters in the directions tangential and normal to the lamination layers, µ t , σ t and µ n , σ n , respectively. The modelling approach is an established method for handling laminated cores and has been used in the analysis of the main eddy currents [15][16][17]. ...
... The amorphous metal ribbon itself has permeability and electrical conductivity µ m and σ m , whilst the insulating epoxy layers between the individual ribbons are assumed to have permeability µ 0 , the permeability of free space, and an electrical conductivity of zero. Assuming that the packing factor F of the laminated core is defined as the total thickness of magnetic ribbon per unit of core thickness, then the parameters of the model may be calculated as in [15] = ...
Finite element analysis is used to examine the gap losses that occur in finely laminated nanocrystalline inductor cores under high frequency operation. The losses are seen to be concentrated in the region of the air gap and the dependence of the losses on key design parameters and operating conditions is explored. The results show that gap losses can be significant in this type of core, creating hot spots around the gap, and the losses are not accurately predicted by established design equations for low frequency laminated cores. A modified loss equation is proposed. Validation is provided by measurements on a 300 A, 60 kHz inductor.
... Various analytical and finite element (FE) based methods have been developed to estimate core losses [2][3][4][5][6][7][8][9][10][11][12][13][14]; non-uniform flux density distribution has been considered in some of these methods [2][3][4][5][6]. Different methods have been also reported based on equivalent circuits of magnetic laminations to predict the magnetic properties of cores [15][16][17]. Geri et al. [15] proposed an equivalent RC electrical network based on the physical dimensions of the laminations to compute the effective permeabilities of multi-laminated thin films in the frequency domain. Loisos et al. [16] implemented an equivalent resistive circuit for magnetic laminations based on the eddy-current path in the lamination to study electrical stress on the electrical steel coating. ...
... Loisos et al. [16] implemented an equivalent resistive circuit for magnetic laminations based on the eddy-current path in the lamination to study electrical stress on the electrical steel coating. Wang et al. [17] used an equivalent resistive circuit for a stack of laminations to simulate eddy-current density in the laminations. Similar concept was implemented in [18,19] to predict magnetic properties of permanent magnet eddy-current couplers by modelling the magnetic flux paths with corresponding equivalent circuit. ...
... Magnetic losses of the magnetic cores because of alternating fields have been separated into three categories: hysteresis losses p h , eddy-current losses p e and anomalous losses or excess loss p ex [24][25][26]. Thus, total power loss is given by p c = p h + p e + p a = k h fB n pk + k e (fB pk ) 2 + k ex (fB pk ) 1.5 (17) where f is the magnetising frequency, B pk is the peak flux density, n is constant, k h , k e and k ex are the hysteresis, eddy current and excess loss coefficients, respectively. Calculating the coefficients of (17) to separate the components of the iron loss is valid within a certain frequency and flux density range [2]. ...
This study investigates the influence of a wide range of magnetising frequencies and peak flux densities on the magnetic properties of the electrical steels. In the relevant studies some important factors and operational properties, for example, skin effect, non-uniform flux density distribution, complex relative permeability and magnetisation characteristic of the material, which are often neglected in the literature, are highlighted. Analytical modelling and experimental works were performed for 3% grain oriented silicon steel. In order to show the impact of peak flux density on the magnetic properties, two peak flux densities 1.3 T as a high permeability point and 1.7 T as a low permeability point were considered. The results highlighted that magnetising frequency and peak flux density are two determinant factors with significant effect on the magnetic properties of electrical steels.
