Name: image method for line capacitance
Uploaded: 2024-11-21T14:54:24.000Z
Duration: 1 min 26 s
Channel: JoVE

Considere un conductor cargado uniformemente sobre la Tierra. Induce una carga negativa igual en la Tierra, creando líneas de campo eléctrico.
El efecto de la Tierra se modela utilizando un conductor de imagen, idéntico pero inferior al original, que mantiene constantes el campo eléctrico y el voltaje.
Para líneas trifásicas con conductores neutros, se utilizan conductores de imagen separados. El voltaje entre un conductor y su imagen depende de su distancia. Por simetría, el voltaje entre este conductor y la Tierra es la mitad de este valor. Los conductores neutros conectados a tierra no llevan carga.
Las ecuaciones matriciales expresan estas relaciones, lo que permite calcular los voltajes de fase a neutro y las cargas de los conductores.
La partición adicional produce ecuaciones que relacionan las cargas del conductor de fase con los voltajes de fase a neutro.
Las ecuaciones revelan que un voltaje positivo de línea a neutro en una fase induce cargas positivas y negativas en diferentes fases.
Para las líneas transpuestas, se promedian los elementos de la matriz de capacitancia, derivando la matriz de admitancia de fase de derivación.
Para una línea de doble circuito con líneas paralelas no transpuestas, métodos similares producen la matriz de admitancia de derivación equivalente de tres por tres. Estos conceptos se extienden a múltiples circuitos paralelos.

admisiones de derivación

Las admitancias en derivación desempeñan un papel crucial en el análisis de líneas de transmisión, en particular en sistemas trifásicos con conductores neutros. Cuando un conductor con carga uniforme se coloca sobre la Tierra, induce una carga igual pero opuesta en su superficie. Esta interacción crea líneas de campo eléctrico entre el conductor y la Tierra.

Para modelar este efecto se emplea el método de imágenes, que consiste en sustituir la Tierra por un conductor imagen que refleja las propiedades del conductor original pero que se encuentra simétricamente debajo de él. El conductor imagen mantiene el mismo radio y magnitud de carga que el original, lo que garantiza que el campo eléctrico y la distribución de voltaje sobre la Tierra sigan siendo coherentes con el escenario real.

En líneas trifásicas con conductores neutros se utilizan conductores de imagen separados para cada fase. La tensión entre un conductor y su correspondiente conductor de imagen se determina por su distancia. Debido a la simetría, la tensión entre cada conductor y la tierra es la mitad de este valor. Los conductores neutros, que están conectados a tierra, no llevan carga y simplifican el proceso de cálculo.

Las ecuaciones matriciales expresan las relaciones entre los voltajes de fase a neutro y las cargas de los conductores. Estas ecuaciones se dividen y reescriben para establecer las relaciones entre las cargas de fase a conductor y los voltajes de fase a neutro. Las ecuaciones revelan que un voltaje positivo de línea a neutro en una fase induce cargas positivas y negativas en diferentes fases.

En el caso de líneas transpuestas, se promedian los elementos de la matriz de capacitancia, lo que permite obtener la matriz de admitancia de fase en derivación. Métodos similares dan como resultado la matriz de admitancia en derivación equivalente de tres por tres en el caso de líneas de doble circuito con configuraciones paralelas no transpuestas. Estos principios se pueden extender a múltiples circuitos paralelos, lo que facilita un análisis exhaustivo y garantiza el funcionamiento eficiente de sistemas complejos de transmisión de energía.

Admisiones de derivación

Considere un conductor cargado uniformemente sobre la Tierra. Induce una carga negativa igual en la Tierra, creando líneas de campo eléctrico.
El efecto de la Tierra es ...

Education

Educación

JoVE Core

Electrical Engineering

Ingeniería Eléctrica

Unit 1

Unidad 1

Transmission Line Parameters

Parámetros de la línea de transmisión

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

Shunt Admittances

image method for line capacitance

Image conductors help model line capacitance in transmission lines above Earth. A uniformly charged conductor induces an equal and opposite charge on the ground. This creates electric field lines between the conductor and the Earth. The method of images replaces the Earth with a matching conductor placed symmetrically below the line.

The image conductor has the same radius and the same charge magnitude as the original conductor. That setup keeps the electric field and voltage above the Earth the same as in the real system. For three-phase lines with neutral conductors, a separate image conductor is used for each phase. The voltage between a conductor and its image depends on the distance between them.

Because of symmetry, the voltage between each conductor and the Earth is half of the voltage between the conductor and its image. Neutral conductors are grounded, so they carry no charge. That simplifies the calculation of phase-to-neutral voltages and conductor charges. Matrix equations are then used to link these quantities in a clear form.

These equations can be partitioned and rewritten to connect phase-conductor charges with phase-to-neutral voltages. The results show that a positive line-to-neutral voltage on one phase can induce positive and negative charges on different phases. For transposed lines, the capacitance matrix elements are averaged. This averaging makes it possible to derive the shunt phase admittance matrix.

The same approach also works for double-circuit lines with parallel, non-transposed layouts. In that case, an equivalent three-by-three shunt admittance matrix can be found. The method can also extend to multiple parallel circuits. This makes it useful for analyzing complex power transmission systems.

Image Method for Line Capacitance

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shunt admittances

Image conductors help model line capacitance in transmission lines above Earth. A uniformly charged conductor induces an equal and opposite charge on the ground. This creates electric field lines between the conductor and the Earth. The method of images replaces the Earth with a matching conductor placed symmetrically below the line. The image conductor has the same radius and the same charge magnitude as the original conductor. That setup keeps the electric field and voltage above the Earth...

key terms and concepts

Learn how image conductors model line capacitance, phase-to-neutral voltage, and shunt admittance in three-phase transmission lines above Earth.

Image Method for Line Capacitance | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

Image Method for Line Capacitance

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