Quasi-3-D Finite-Element Modeling of a Power Transformer

A strong circuit-field coupling technique that can analyze multiple magnetic field systems (2-D Cartesian and axisymmetric) is adapted to study power transformers. The technique is based on finite-element (FE) and modified nodal analyses, leading to a multi-field system approach that can effectively take account of the 3-D magnetic field existing inside and outside the transformer core. Hence, cumbersome 3-D FE simulations are circumvented, overcoming high computational costs. A 2-D Cartesian FE model is set up to represent the cross section of the transformer core and its three-phase winding, whereas an axisymmetric representation is employed for the end sections of each set of windings (one per phase). All models and their associated circuit systems are simultaneously solved, providing a circuit-field method that is easy to implement at low computational cost, keeping the well-known advantages of 2-D FE modeling. Electrical currents and local values of magnetic flux density are calculated for two limiting conditions: rated load and short-circuit operation. Our approach shows a remarkably small difference (no higher than 1%) with a full 3-D FE model.