Transformer capacitance matrix computation using 3D boundary element method and adaptive cross approximation

In this paper, a solver based on a 3D boundary element method (BEM) is presented and verified on a transformer geometry. Using a triangular surface mesh of a winding, the unknown charge distribution is found from known potentials of surfaces using the integral equation approach and point matching. The capacitance matrix is calculated from known potentials in nodes of the system. The application of BEM and point-matching results in a fully populated system matrix. Therefore, a matrix reduction technique adaptive cross approximation (ACA) is employed in order to reduce the CPU time and memory requirements. Both the accuracy of the direct and the accuracy of the ACA approach are benchmarked against the results obtained using the professional finite element method (FEM)-based software.