Multi-Winding Transformer Modeling for Fast-Front Transient Analysis

Abstract

Power transformers are critical components of electrical power systems, and their behavior under high-frequency and fast transient conditions plays an important role in overall system reliability. Phenomena such as internal resonances within transformer windings can lead to significant overvoltages and localized electric field intensification, potentially resulting in insulation degradation or failure. Accurate modeling of transformer behavior over a wide frequency range is therefore essential for both design and transient analysis. However, conventional transformer models are often limited by either oversimplified analytical assumptions or the high computational cost and limited generalization capability of purely numerical approaches.

This thesis presents a comprehensive framework for the frequency dependent modeling of power transformers, with particular emphasis on high-frequency behavior. The work focuses on the development of white-box models derived from electromagnetic field theory, complemented by data-driven machine learning techniques to enhance computational efficiency while preserving physical consistency.

The first part of the thesis investigates the impact of conductor and core losses on the impedance characteristics of transformer windings. Numerical simulations are employed to quantify the influence of eddy current losses in both conductors and ferromagnetic cores. The results demonstrate that each loss mechanism dominates in different frequency ranges, and that neglecting conductor losses can lead to significant errors in impedance estimation and resonance prediction at higher frequencies relevant to electromagnetic transient studies.

Building upon these insights, the thesis develops an analytical framework for frequency-dependent impedance modeling of transformer windings. To validate the proposed analytical approach, several case studies are presented in which the derived impedance characteristics and parameters are compared against numerical simulations and experimental measurements, demonstrating good agreement across a broad frequency range. The analyses confirm the capability of the proposed approach to accurately capture resonance phenomena and frequency-dependent losses with substantially reduced computational effort compared to full numerical field solvers.

In the final part of the thesis, a machine learning-based methodology is introduced to further accelerate the estimation of frequency-dependent winding impedances. Using a dataset generated from the analytical framework, an XGBoost model is trained to predict the frequency dependent parameters. The results show that the proposed data-driven models achieve high accuracy while offering significant computational speed-ups, making them well suited for large-scale parametric studies and design optimization.

Overall, this thesis contributes a unified modeling framework that bridges analytical electromagnetic theory, numerical validation, and machine learning techniques for the high-frequency modeling of power transformers. The proposed methods enable accurate and efficient prediction of transformer winding behavior under fast transient conditions, providing valuable tools for transformer designers and power system engineers.