In order to minimize eddy current losses in an open-core type of transformer, a lower width-to-thickness ratio of lamination sheets and even varying lamination stacking direction than in the case of standard transformers are used. Consequently, narrow eddy current loops must be considered as a 2D phenomenon, i.e. edge effects and irregular current density distributions cannot be neglected. A two-step method for calculation of eddy currents and eddy current losses in an open-core transformer is presented. In the first step, using the anisotropic surrogate material, the magnetic flux density distribution within the bulk core model is calculated. In the second step, the magnetic flux density obtained in the first step is used as input to calculate eddy currents in a sufficient number of densely meshed 2D slices of the laminated core. Numerical simulation of the method is carried out, and the results are compared with those obtained using a homogenization method and the brute force approach. The results show good agreement and indicate the importance of taking edge effects into account.

Linear variable differential transformer (LVDT) is a commonly used linear displacement sensor because of its good measurement characteristics. When using laminated ferromagnetic cores in LVDTs, it is very important to take eddy currents into the account during design phase of the sensor. Particularity of the open-type core means that the eddy currents induced by the stray magnetic flux that flow in large loops tangential to the lamination surfaces take on significant values. Due to the open-type core a typical LVDT has, depending on the core material, it is, therefore, very important to take eddy currents into the account when designing the sensor. This paper’s goal is to present a methodology for calculating LVDT eddy current losses that can be applied to LVDT design in order to optimize the dimensions and help with selection of materials of the LVDTs, in order to achieve the highest measurement accuracy. Presented approach using an $A\tau A$-formulation with elimination of redundant degrees of freedom exhibits rapid convergence. In order to calculate the relationship between eddy current losses and core displacement, frequency, and material characteristics, a number of 3D finite element method (FEM) simulations was performed. Analysis of the obtained results using presented methodology for eddy current losses calculation in LVDTs enables the designer optimize the design of the LVDT.

Losses due to eddy currents in an open-type transformer core are significantly reduced by the lamination of the transformer core. In order to further reduce the eddy current losses, the open-type core often has a multi-part structure, i.e., it is composed of several more slender cores. The complete homogenization of such a core is not possible when an $\overrightarrow{A},V-\overrightarrow{A}$ formulation is used, where A and V represent the magnetic vector potential and electric scalar potential, respectively. On the other hand, an $\overrightarrow{A},\overrightarrow{T}-\overrightarrow{A}$ formulation, where T represents the electric vector potential, enables the complete homogenization of the general open-type core, but the simulation converges poorly due to the large number of degrees of freedom. By eliminating the redundant degrees of freedom, the convergence rate is significantly improved, and is at least twice as good as the convergence rate of the simulation based on the $\overrightarrow{A},V-\overrightarrow{A}$ formulation. In this paper, a method for the calculation of the eddy current losses in an open-type core based on the $\overrightarrow{A},\overrightarrow{T}-\overrightarrow{A}$ formulation with the elimination of redundant degrees of freedom is presented. The method is validated by comparison with a brute force simulation based on the $\overrightarrow{A},V-\overrightarrow{A}$ formulation, and the efficiency of the method is determined by comparison with the standard homogenization method based on the $\overrightarrow{A},V-\overrightarrow{A}$ formulation.

The purpose of this paper is to present a methodology for calculating eddy current losses in the core of a single-phase power voltage transformer, which, unlike a standard power transformer, has an open-type core (I-type core). In those apparatus, reduction of core losses is achieved by using a multipart open-type core that is created by merging a larger number of leaner cores. 3D FEM approach for calculation of eddy current losses in open-type cores based on a weak AλA formulation is presented. Method in which redundant degrees of freedom are eliminated is shown. This enables faster convergence of the simulation. The results are benchmarked using simulations with standard AVA formulation. Results using weak AλA formulation with elimination of redundant degrees of freedom are in agreement with both simulation using only weak AλA formulation and with simulation based on AVA formulation. The presented methodology is valid in linear cases, whereas the nonlinear case will be part of future work. Presented procedure can be used for the optimization when designing the open-type core of apparatus like power voltage transformers. The presented method is specifically adapted for calculating eddy currents in the open-type core. The method is based on a weak formulation for the magnetic vector potential A and the current vector potential λ, incorporating numerical homogenization and a straightforward elimination of redundant degrees of freedom, resulting in faster convergence of the simulation.

A method for calculating eddy currents and corresponding losses in a laminated transformer core using finite element method is developed. The method is based on the transformation of the 3D model into the corresponding 2D model. The 2D laminated domain coincides with the slice of the 3D laminated domain. Eddy currents are therefore considered as 2D phenomena within lamination, instead of the 1D approximation, thus taking into account the edge effects. By using the 2D mesh, the number of finite elements is drastically reduced. The validity and precision of the method are verified by comparing the results of the simulation with the results obtained using the brute force approach and with the results obtained using the homogenisation method.

Eddy currents are decoupled into narrow eddy currents, induced by the magnetic flux tangential to the laminations, and planar eddy currents, induced by the magnetic flux perpendicular to the laminations. A numerical homogenization procedure is presented for modeling narrow eddy currents, which is performed through computationally cheap 2D simulations in the preprocessing phase. This provides the equivalent magnetic reluctivity function of the core, taking into account the fringing effects of the eddy currents without introducing additional degrees of freedom. This allows for the utilization of a coarse mesh within the laminated core. The validity of the numerical homogenization procedure has been confirmed by comparison with the reference solution. Also, a 3D formulation for calculating losses due to eddy currents in an open core has been derived, which is compatible with the described numerical homogenization procedure.