F. Nasirpour
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Accurate frequency-dependent inductances and resistances are essential for high-frequency transformer models. Traditional analytical approaches, such as cases where eddy-current losses are neglected, or resistances and inductances are computed independently, and numerical techniques such as finite element methods (FEM) are either computationally intensive or rely on simplifications that reduce accuracy. This letter proposes a novel machine learning (ML)-based approach to efficiently estimate these parameters by learning from detailed analytical results. Using a localized feature selection strategy with conductors near the nearest neighbors $k$, the model considers complex electromagnetic interactions while achieving a significant reduction in computation time. This allows for generalization across different winding designs, reducing the dependence on traditional simplifications. Furthermore, the trained ML model achieves high accuracy, with predictions within an error margin of 5% for a wide frequency range. Comparison with measurements confirms the validity and effectiveness of the proposed approach, making it a promising solution for electromagnetic transient simulations.
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Accurate frequency-dependent inductances and resistances are essential for high-frequency transformer models. Traditional analytical approaches, such as cases where eddy-current losses are neglected, or resistances and inductances are computed independently, and numerical techniques such as finite element methods (FEM) are either computationally intensive or rely on simplifications that reduce accuracy. This letter proposes a novel machine learning (ML)-based approach to efficiently estimate these parameters by learning from detailed analytical results. Using a localized feature selection strategy with conductors near the nearest neighbors $k$, the model considers complex electromagnetic interactions while achieving a significant reduction in computation time. This allows for generalization across different winding designs, reducing the dependence on traditional simplifications. Furthermore, the trained ML model achieves high accuracy, with predictions within an error margin of 5% for a wide frequency range. Comparison with measurements confirms the validity and effectiveness of the proposed approach, making it a promising solution for electromagnetic transient simulations.
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.
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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.
...
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.
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.
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.
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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.
Conference paper
(2024)
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Farzad Nasirpour, Behzad Behdani, Amir Heidary, Mohamad Ghaffarian Niasar, Forooz Ghassemi, Maarten van Riet, Mark Wilkinson, M.A.M.M. van der Meijden, Marjan Popov, More authors...
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.
...
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.
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.
...
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.
Journal article
(2023)
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Farzad Nasirpour, Amir Heidary, Mohamad Ghaffarian Niasar, Aleksandra Lekić, Marjan Popov
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.
...
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.