Difficulties in high frequency transformer modeling

• An overview on transformer “Black box” modeling.
• A procedure for measuring the admittance matrix of a transformer with FRA equipment.
• Unconstrained fitting methods (post processing passivity enforcement).
• Constrained fitting methods (enforcing passivity during the fitting).
• Comparison of accuracy of different fitting methods.

Traditional transformer models available in EMTP-like software packages are not capable of representing transformer behavior during a transient state, which includes high frequencies, since they usually do not adequately take into account the transformer resonant behavior caused by its highly complicated design. Therefore, more complex “Black box” models are developed. Those models can be established without any knowledge of transformer geometry, based on the fitting of the measured admittance matrix of the transformer versus frequency. Unfortunately, the measurement and exploitation of a transformer's admittance matrix are not straightforward. The existing fitting methods include solving a non-convex constrained problem. Hence, it is not always easy to find an optimal solution of the problem. The difficulties, which can arise when building a high frequency “Black box” transformer model, are described in this paper together with a comparison of the performance and fitting accuracy of different numerical packages.