This paper presents a comprehensive model for power transformers, by considering eddy current losses in both the core and conductors. This is achieved through a meticulous analytical approach that ensures high fidelity in representing the transformer's electromagnetic properties. The consideration of magnetic flux effects on inductance and resistance values significantly enhances the model's accuracy and validity. Traditional analytical methods often resort to simplified approaches due to the complexity of these calculations. The paper addresses these limitations by evaluating the eddy current losses in the core and conductors, and by providing a detailed understanding of each component's impact on transformer behavior. Furthermore, by considering the core and conductor effects on the magnetic field distribution, the model handles a wide range of frequencies, making it suitable for conducting comprehensive transient analysis. To validate the model, comparisons with the finite element method and empirical measurements are conducted. Additionally, a reduced-order transformer model is developed using admittance matrix reduction. This approach focuses on the nodes of interest, effectively eliminating not-observed nodes and reducing computational complexity without compromising accuracy. In this way, voltages at specific points of interest are computed efficiently, maintaining the accuracy of the original model.

This paper investigates the high-frequency transformer losses attributed to eddy currents in both conductors and the core. A comprehensive model of a transformer winding is presented, meticulously incorporating skin and proximity effects. The winding resistance increase due to these effects is determined by applying analytical and finite element methods. The investigation highlights that eddy current losses in the magnetic core notably increase the resistance of each winding section in low frequencies. However, the impact of these losses diminishes as the winding length approaches the voltage wavelength at high frequencies. Consequently, the net magnetomotive force and flux in the core become negligible. As a result, the high-frequency impedance characteristics are remarkably similar for windings with and without a magnetic core. These findings are substantiated through rigorous simulations and empirical measurements.

The evolution of electrical power systems demands an increasing reliance on unpredictable renewable energy resources (RES). However, integrating these resources poses challenges, as their intermittent nature introduces transient events that can significantly impact power transformers. These transient phenomena may initiate energy oscillations in the form of weakly-damped resonances between system elements, i.e., transmission lines and cables, transformers, and the grounding system. Such conditions may impose stresses beyond the tolerance of insulating materials, leading to fast lifetime degradation and, eventually, the failure of critical components in the network, such as the costly power transformers. The impedance of the grounding system can limit the dissipation of surges, hence, causing severe overvoltages upon transient phenomena. By employing detailed transient models of crucial system components, this research puts forward a comprehensive analytical study of the transient interactions. In this regard, an analytical high-frequency transformer winding model based on lumped elements, and wideband frequency-dependent models for cables and the grounding system derived by applying electromagnetic theory are presented. These models, integrated into electromagnetic transient software, enable the identification of vulnerabilities and examination of case studies involving lightning strikes and switching events. Furthermore, the details of a novel protection method applied to safeguard the transformer are discussed in this paper. The presented protection method consists of a ring toroid core and a resistive suppressor on the secondary side of the core. This protection component is connected in series with the transformer to decrease the harmonic content and magnitude of the transient signals. The design procedure of the series protection device against voltage transient signals is presented and elaborated.

High local electric field intensity in transformer windings originating from transient signals is one of the reasons for transformer failures. Due to the integration of renewable energy sources into the power grids and the increased number of transients, the likelihood of transformer catastrophic failure increases accordingly. Therefore, to ensure the reliable performance of transformers and associated power networks studying their behavior during these events is required. Accordingly, there is a need for accurate modeling of transformer windings capable of simulating electromagnetic transients. Using these models, it is possible to identify frequencies that can be dangerous to the transformer windings and to study different protection schemes. This paper aims to find an accurate analytical model of transformer winding validated by experimental measurements and to study the performance of the R-L protection device during the transient phenomena. The protection device is designed based on the winding model to introduce an impedance comparable to that of the transformer winding at critical frequencies where voltage amplification in the winding is significant. This approach ensures enhanced protection against potential transformer damage to the transformer. By using this protection scheme, the high inter-turn voltage originating from transient signals may be mitigated. At the same time, it does not affect the grid's performance during normal conditions.