High frequency modeling of power transformers under transients
Authors:   , Imdad Kashif 
Published: July 2023

This thesis presents the results related to high frequency modeling of power transformers. First, a 25kVA distribution transformer under lightning surges is tested in the laboratory and its high frequency model is proposed. The transfer function method is used to estimate its parameters. In the second part, an advanced high frequency model of a distribution transformer is introduced. In this research, the dual resonant frequency distribution transformer model introduced by Sabiha and the single resonant frequency distribution transformer model under lightning proposed by Piantini at unloaded conditions are investigated and a modified model is proposed that is capable to work on both single and dual resonant frequencies. The simulated results of the model are validated with the results of Sabiha and Piantini that have been taken as reference. Simulations have shown that the results of the modified model such as, secondary effective transfer voltages, transferred impedances and transformer loading agree well with the previous models in both time and frequency domains.
The obtained objectives of this research are:
* Methodology for determining the parameters of a power transformer.
* High frequency modeling of a transformer in order to simulate its transient behavior under surges.
* Modification of high frequency model for single and dual resonance frequency.
The originality and methodology of this research are:
* High frequency transformer model is derived by means of the transfer function method. In the literature, the transfer function method has been used in many applications such as the determination of the mechanical deformations or insulation failure of interturn windings of transformers. In this thesis, the parameters of the proposed model are estimated using the transfer function method.
* Modification of high frequency model for single/dual resonance frequency using the transfer function method. The transfer function can also be used to determine the state of the transformer. The modification in the developed model using the proposed technique has been validated.
The high frequency transformer model was presented by Sabiha at two resonance frequency under both condition loading and unloading was used as reference model for modification and further enhancement. A transformer with 25kVA capacity was tested in UPC Terrassa Spain in High voltage lab under the effect of impulse voltage and the digital data was stored via oscilloscope in computer. An algorithm was developed to estimate the transformer parameters by transfer function method using fast Fourier transform analysis. In this scheme the two port network theory concept was taken for black box analysis of transformer. The series of transient¿s frequencies of experimental digital data was noted. The transformer parameters such as Z11, Z12, Z21, and Z22 calculated on all these frequencies in order to generate a narrow band of correct frequency at which the transients was developed experimentally and therefore it has to be developed on that specific frequencies. Earlier the transfer function method was used for the mechanical deformation analysis in the transformer, now similar method of modeling used to estimate the parameters of transformer and propose accurate transformer model for two resonance frequencies only and the parameters estimation was based simply placing RLC elements. The proposed model also tested and validated for accuracy and reliability.
In the second phase of research high frequency models of transformer for protection from the transients based on experimental data are presented. Which were tested and validated for unloading and loading for Single and Two resonant frequencies, and modeled using transfer function method. The proposed single model leads to others two models which are verified by two port network theory, unloaded transfer under time domain and frequency domain analysis, transformer loading under different loads and transfer function

Esta tesis presenta los resultados relacionados con el modelado en alta frecuencia de transformadores de potencia. Primero, un transformador de distribución de 25 kVA es ensayado a perturbaciones tipo rayo y se propone un modelo de alta frecuencia. El método de la función de transferencia es utilizado para estimar sus parámetros. En segundo lugar, se introduce un modelo avanzado de alta frecuencia. El modelo resulta de la investigación y modificación de los modelos de resonancia dual introducido por Sabiha y el de resonancia única introducido por Piantini con condiciones sin carga. El modelo propuesto es capaz de representar tanto la resonancia única como dual. El modelo es validado a partir de los resultados de referencia de Sabiha y Piantini. Los resultados de simulación indican que el modelo representa las sobretensiones transferidas al secundario, las impedancias de transferencia y el trabajo en carga del transformados coinciden con los modelos anteriores tanto en el dominio temporal y de la frecuencia. Los objetivos obtenidos en esta tesis son: * Metodología para determinar los parámetros de un transformador de potencia. * Modelo de alta frecuencia para simular el comportamiento transitorio frente a perturbaciones. * Modificación del modelo de alta frecuencia para representar una y dos resonancias. La originalidad y metodología de la tesis son: * El modelo de alta frecuencia del transformador ha sido obtenido a partir de la metodología de la función de transferencia. En la literatura, esta metodología ha sido usada en muchas aplicaciones como en la determinación de deformaciones mecánicas o fallo de aislamiento en espiras de transformadores. En esta tesis, los parámetros del modelo propuesto son obtenidos mediante esta metodología. * Modificación del modelo de alta frecuencia con resonancia única o dual utilizando el método de la función de transferencia. La metodología propuesta puede ser utilizada para determinar el estado del transformador. Sabiha propuso un modelo de alta frecuencia representado dos resonancias en condiciones de carga y de vacío. Este modelo ha sido utilizado como referencia para la modificación y mejora. En la tesis, el transformador de distribución 25 kVA disponible en el Departamento de Ingeniería Eléctrica de la UPC en la ESEIAAT ha sido ensayado a impulsos tipo rayo. Un algoritmo ha sido desarrollado para estimar los parámetros del transformador mediante el método de la función de transferencia utilizando la transformada de Fourier. En este esquema, una red de dos puertos ha sido adoptada para el análisis del transformador. Los parámetros del transformador como la Z11, Z12., Z21 y Z22 son calculadas para representar las frecuencias consideradas. Mediante el método de la función de transferencia los parámetros del transformador son determinados. El modelo propuesto se basa en elementos simples RLC capaces de representar con precisión dos frecuencias de resonancia. En la segunda parte de la tesis, un nuevo modelo es introducido capaz de representar ambos modelos de resonancia única y dual en uno solo. Se analiza el caso de carga y vacío.