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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 A→,V−A→ formulation is used, where A and V represent the magnetic vector potential and electric scalar potential, respectively. On the other hand, an A→,T→−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 A→,V−A→ formulation. In this paper, a method for the calculation of the eddy current losses in an open-type core based on the A→,T→−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 A→,V−A→ formulation, and the efficiency of the method is determined by comparison with the standard homogenization method based on the A→,V−A→ formulation.

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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.

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 AτA-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.