Calculation of the Eddy Current Losses in a Laminated Open-Type Transformer Core Based on the A→,T→−A→ Formulation

Abstract

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.

Methodology for Eddy Current Losses Calculation in Linear Variable Differential Transformers (LVDTs)

“…One simulation was completed with a novel approach, and the other was completed by using the typical weak -formulation. The second approach was already validated in [ 26 ]. An iterative technique based on the CG algorithm is used to solve the linear system arising from the formulation in the simulations.…”

“…Then, using interpolation functions as weighting functions in expressions ( 20 ) and ( 21 ), the weak -formulation is obtained: where the index k represents the k -th degree of freedom in the finite element [ 26 ].…”

“…However, calculation of eddy current losses requires taking into account differences between the open-type core and the closed-type core. Core of the conventionally designed LVDT is an open-core type [ 26 , 27 ]. Compared to a closed-type core, where the magnetic flux is closed mostly through the core, the of the magnetic flux of the open-type core passes through core/air interface and majority of the flux is dissipated perpendicularly to the lamination surfaces.…”

“…Overall, there is scarce research on the problem of eddy currents in open-type cores. A multi-scale approach that includes the modeling of eddy currents is presented in [ 28 ], while a two-step method for total eddy currents calculation in an open-type laminated core is presented in [ 26 ]. Research conducted in [ 26 ] shows the advantages of the use of an -formulation compared to formulation when calculating eddy-current losses in open-type cores.…”

“…The methodology presented in this paper for the eddy current losses calculation in LVDT core is based on a 3D finite element method (FEM) approach based on a weak -formulation. A similar approach was used in [ 26 ], but in this paper a novel and improved approach for the elimination of redundant degrees of freedom which results in improved speed of convergence of the calculation. Results of the approach using a weak -formulation with and without edge elements will be presented as validation of the acquired results and evidence of method advancement.…”