Publication: Determinación de las impedancias homopolares de un transformador trifásico de tres columnas con conexión YNynd a partir de sus dimensiones geométricas
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2014-10
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2014-11-28
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Abstract
En la presente tesis doctoral se determinan las impedancias homopolares de un transformador
trifásico de tres columnas con conexión YNynd a partir de sus dimensiones geométricas. Los valores que
se determinan corresponden a las ocho medidas estandarizadas posibles que resultan de las
combinaciones de alimentar uno de los arrollamientos en estrella con el otro arrollamiento en estrella en
en circuito abierto o en cortocircuito, y con el arrollamiento en triángulo cerrado o en triángulo abierto.
Los métodos desarrollados fueron aplicados a transformadores que tienen el arrollamiento en triángulo
en la posición más interna y a transformadores que los tienen en la posición más externa.
Las impedancias homopolares magnetizantes corresponden a los dos casos que tienen circulación de
corriente homopolar únicamente por aquel arrollamiento en estrella que está conectado a la fuente
durante el ensayo. Los otros seis casos estandarizados corresponden a impedancias homopolares de
cortocircuito, en los que puede haber circulación de corriente homopolar por dos o por tres
arrollamientos.
La determinación de las impedancias homopolares se basó en el uso de modelos lineales en dos
dimensiones (2D), con la ayuda de un software basado en el método de los elementos finitos. La
geometría tridimensional (3D) de estos transformadores no tiene simetrías que permitan una exacta
representación 2D, por lo que fue necesario desarrollar modelos aproximados 2D para representar el
comportamiento de estos equipos ante secuencia homopolar.
En el caso de las impedancias homopolares magnetizantes, se comenzó realizando una comparación
entre los resultados de modelos lineales 2D y 3D, con el fin de obtener las bases para el desarrollo de
dos modelos aproximados 2D. En ambos modelos, para el cálculo de las dos impedancias homopolares
magnetizantes (de alta tensión y de baja tensión) se requiere estimar el valor de tres parámetros
auxiliares y de la permeabilidad magnética equivalente para el tanque. Con ambos métodos aproximados
2D fue posible obtener resultados precisos, pero uno de ellos se consideró más recomendable porque la
estimación de los parámetros es más sencilla, la convergencia es más rápida y los errores son levemente menores. La medida del valor de las impedancias homopolares magnetizantes se realizó a varios valores
de corriente, con el fin de tener en cuenta la no linealidad de estos valores. Se determinó una relación entre la permeabilidad equivalente del tanque y la corriente durante el ensayo, para transformadores con
características similares a los analizados, que puede ser útil para determinar las impedancias
homopolares magnetizantes cuando no hay valores medidos. Además, el método recomendado fue
aplicado con una curva no-lineal para representar la permeabilidad del tanque y esta aproximación
también ofrece resultados con una buena precisión.
En el caso de las impedancias homopolares de cortocircuito, el método desarrollado tiene dos pasos:
a) La determinación de las corrientes en los arrollamientos cortocircuitados; b) El uso del método 2D
que se consideró recomendable en el caso de las impedancias homopolares magnetizantes, para
aproximarse a los resultados de las geometrías reales 3D. La determinación de las corrientes en los
arrollamientos cortocircuitados persigue hacer cero la tensión en bornas de dicho arrollamiento y se
lleva a cabo mediante un método iterativo, aplicando densidades de corriente constantes en el modelo de
cada arrollamiento. Los resultados obtenidos son precisos tanto en transformadores con shunts
magnéticos adosados a las paredes del tanque como en transformadores sin ellos. Se demostró que la
permeabilidad magnética equivalente del tanque tiene un cierto efecto en los resultados, pero también se
demostró que se puede obtener una buena precisión usando un valor intermedio para este parámetro. Por
otro lado, se demostró que las diferencias entre las geometrías 2D y 3D tienen poco efecto en los
resultados de las reactancias y que se pueden obtener resultados bastante precisos omitiendo dicha
diferencia; sin embargo, las diferencias entre las geometrías 2D y 3D deben ser consideradas para una
correcta estimación de las potencias activas durante los ensayos. Aunque los shunts magnéticos
adosados a las paredes del tanque no están distribuidos de manera continua en la periferia del tanque, se
demostró que no es necesario encontrar un valor preciso de su espesor equivalente para la simulación 2D
ya que se puede estimar un valor bastante preciso de las impedancias homopolares de cortocircuito usando un amplio rango de espesores equivalentes de estos shunts magnéticos.
De lo dicho anteriormente se desprende que los problemas principales a resolver son distintos para el
caso de determinar las impedancias homopolares magnetizantes y para el caso de determinar las
impedancias homopolares de cortocircuito. En el caso de la determinación de las impedancias
homopolares magnetizantes, los problemas principales son la no linealidad del tanque y la fuerte
dependencia de los resultados con la geometría tridimensional, lo que obliga a encontrar una
equivalencia entre estudios 2D y 3D. En el caso de la determinación de las impedancias homopolares de
cortocircuito, el problema principal es la obtención de la corriente en los diferentes arrollamientos
cortocircuitados; en este caso, la relación entre las geometrías 2D y 3D únicamente es importante para
determinar el consumo de potencia activa durante estos ensayos.
Zero-sequence impedances of 3-phase core-type YNynd transformers are computed in this thesis from the transformer geometry. Computed values correspond to the eight possible standardized measurements, which result from the combinations of feeding a wye-winding with the other wyewinding in open-circuit or in short-circuit, and with the delta winding in closed or open connection. Developed methods are general, and they were applied to transformes with the tertiary winding in the innermost position and transformers with the tertiary winding in the outermost position. The magnetizing zero-sequence impedances (Z₀[M subscript]) are the two cases with zero-sequence current only in the winding that is connected to the power source during the test. The other six standardized cases are short-circuit zero-sequence impedances (Z₀[SC subscript]), and there are cases with zero-sequence currents in only two windings as well as cases with zero-sequence currents in the three windings. The calculation of these zero-sequence impedances was based on linear models in two dimensions (2D), with the help of a software based on the finite element method. Tridimensional (3D) geometry of these transformers do not have symmetries that allow an exact 2D representation; therefore, the development of approximate 2D models was necessary. In case of Z₀(M subscript), the first step was a comparison between 2D and 3D models, in order to obtain the fundamentals for developing two 2D approximate models. In both models, three auxiliary parameters and the equivalent magnetic permeability of the tank have to be estimated in order to compute the two values Z₀(M subscript) (measured from the high voltage side or from the low voltage side). Accurate results were obtained with both approximate methods, but one of them is preferred because the parameter estimation is easier, the convergence is faster, and the errors are slightly lower. Measured values of Z₀(M subscript) at different test currents allowed the analysis of the nonlinearity of these values. A relationship between the equivalent magnetic permeability of the tank and the current during the test was found, by analyzing power transformers for distribution substations, and the found relationship is useful for Z₀(M subscript) estimation when there are no measured values. Additionally, the preferred method was also applied with a nonlinear curve for the tank permeability, and this approximation also offers accurate results in this case. In case of Z₀(SC subscript), the developed method has two steps: a) the search of currents to satisfy the condition of induced voltage equal to zero in short-circuited windings; b) the use of the preferred method for the case of Z(M subscript) in order to approximate 2D results to the results of real 3D geometries. Induced currents in short-circuited windings are found by an iterative process, in order to apply constant current densities in the model of each winding. Results of the model are accurate in comparison with measured values in five transformers. Cases with and without magnetic shunts on tank walls are solved. Equivalent permeability of tank steel has an influence on results but a reasonable accuracy is obtained with an intermediate value of this parameter; thus, non-linearity is not a concern in this case. A good accuracy for the reactances can be obtained without considering that 2D geometry is not an exact representation of real 3D geometry (unlike power losses during the tests, where this fact must be taken into account). For the case of magnetic shunts on tank walls, an accurate value of their equivalent thickness is not necessary because it was shown that accurate results are obtained for a wide value of this equivalent thickness. Therefore, it was shown that the main problems for calculation of Z₀(M subscript) and Z₀(SC subscript) are different. In case of Z₀(M subscript), the main problems are the nonlinearity of the tank steel and the differences between 2D and 3D geometries. In case of Z₀(SC subscript), the main problem is the obtaining of the currents in the short-circuited windings (and the relationship between 2D and 3D geometries is only important to compute the power losses).
Zero-sequence impedances of 3-phase core-type YNynd transformers are computed in this thesis from the transformer geometry. Computed values correspond to the eight possible standardized measurements, which result from the combinations of feeding a wye-winding with the other wyewinding in open-circuit or in short-circuit, and with the delta winding in closed or open connection. Developed methods are general, and they were applied to transformes with the tertiary winding in the innermost position and transformers with the tertiary winding in the outermost position. The magnetizing zero-sequence impedances (Z₀[M subscript]) are the two cases with zero-sequence current only in the winding that is connected to the power source during the test. The other six standardized cases are short-circuit zero-sequence impedances (Z₀[SC subscript]), and there are cases with zero-sequence currents in only two windings as well as cases with zero-sequence currents in the three windings. The calculation of these zero-sequence impedances was based on linear models in two dimensions (2D), with the help of a software based on the finite element method. Tridimensional (3D) geometry of these transformers do not have symmetries that allow an exact 2D representation; therefore, the development of approximate 2D models was necessary. In case of Z₀(M subscript), the first step was a comparison between 2D and 3D models, in order to obtain the fundamentals for developing two 2D approximate models. In both models, three auxiliary parameters and the equivalent magnetic permeability of the tank have to be estimated in order to compute the two values Z₀(M subscript) (measured from the high voltage side or from the low voltage side). Accurate results were obtained with both approximate methods, but one of them is preferred because the parameter estimation is easier, the convergence is faster, and the errors are slightly lower. Measured values of Z₀(M subscript) at different test currents allowed the analysis of the nonlinearity of these values. A relationship between the equivalent magnetic permeability of the tank and the current during the test was found, by analyzing power transformers for distribution substations, and the found relationship is useful for Z₀(M subscript) estimation when there are no measured values. Additionally, the preferred method was also applied with a nonlinear curve for the tank permeability, and this approximation also offers accurate results in this case. In case of Z₀(SC subscript), the developed method has two steps: a) the search of currents to satisfy the condition of induced voltage equal to zero in short-circuited windings; b) the use of the preferred method for the case of Z(M subscript) in order to approximate 2D results to the results of real 3D geometries. Induced currents in short-circuited windings are found by an iterative process, in order to apply constant current densities in the model of each winding. Results of the model are accurate in comparison with measured values in five transformers. Cases with and without magnetic shunts on tank walls are solved. Equivalent permeability of tank steel has an influence on results but a reasonable accuracy is obtained with an intermediate value of this parameter; thus, non-linearity is not a concern in this case. A good accuracy for the reactances can be obtained without considering that 2D geometry is not an exact representation of real 3D geometry (unlike power losses during the tests, where this fact must be taken into account). For the case of magnetic shunts on tank walls, an accurate value of their equivalent thickness is not necessary because it was shown that accurate results are obtained for a wide value of this equivalent thickness. Therefore, it was shown that the main problems for calculation of Z₀(M subscript) and Z₀(SC subscript) are different. In case of Z₀(M subscript), the main problems are the nonlinearity of the tank steel and the differences between 2D and 3D geometries. In case of Z₀(SC subscript), the main problem is the obtaining of the currents in the short-circuited windings (and the relationship between 2D and 3D geometries is only important to compute the power losses).
Description
Keywords
Transformadores trifásicos, Impedancias homopolares