Name: transmission line capacitance in power systems
Uploaded: 2024-11-21T14:54:23.000Z
Duration: 1 min 25 s
Channel: JoVE

Considere una línea de transmisión monofásica de dos hilos con igual espaciado de fase energizada por una fuente de voltaje. Un conductor lleva una carga uniforme y su contraparte tiene una carga negativa igual. Aplicando la fórmula para el voltaje entre conductores y sustituyendo los radios de los cilindros, se calcula la capacitancia para una línea de un metro.
Para las líneas alimentadas por un transformador de derivación central conectado a tierra, se obtiene el voltaje entre cada conductor y tierra y la capacitancia de cualquiera de las líneas al neutro conectado a tierra.
Estas capacitancias se representan en representaciones de circuitos específicos.
A continuación, considere una línea trifásica con el mismo espaciado de fase, sin tener en cuenta los efectos de tierra y conductor neutro.
Para determinar la capacitancia de secuencia positiva, se supone que la suma de las cargas de secuencia positiva es cero.
Ahora, se calcula el voltaje entre los conductores, seguido de la sustitución de los radios.
Recordando las ecuaciones de voltaje para voltajes de secuencia positiva balanceados, sumándolos, sustituyendo las expresiones de voltaje, y la relación de carga da la capacitancia a neutro por longitud de línea.
Los mismos resultados se aplican a las tres fases debido a la simetría, pero para una operación trifásica equilibrada, solo se considera una fase.

capacitancia: línea monofásica y trifásica

En los sistemas de energía eléctrica, comprender la capacitancia de las líneas de transmisión es fundamental para un funcionamiento eficiente.

Líneas monofásicas
Consideremos una línea de transmisión monofásica de dos cables con el mismo espaciamiento de fases, alimentada por una fuente de voltaje. Un conductor lleva una carga positiva uniforme, mientras que el otro lleva una carga negativa igual. La capacitancia C de la línea se puede derivar del voltaje V entre los conductores. Para una sección de un metro de la línea, la capacitancia viene dada por:

<img alt="Equation1" src="/files/ftp_upload/16144/16144_%20Equation%201.svg" style="height: 42px;">

Donde ε es la permitividad del espacio libre, D es la distancia entre los conductores y r es el radio de los conductores. Cuando la línea se energiza mediante un transformador con toma central conectada a tierra, se puede determinar el voltaje entre cada conductor y la tierra, así como la capacitancia desde cualquiera de las líneas hasta el neutro conectado a tierra. Esta capacitancia se representa en modelos de circuitos para reflejar con precisión el comportamiento de la línea de transmisión en diferentes condiciones de funcionamiento.

Líneas trifásicas
El análisis se vuelve más complejo en líneas de transmisión trifásicas con espaciado de fase igual debido a la interacción entre las fases. Para voltajes de secuencia positiva equilibrados, se supone que la suma de las cargas de secuencia positiva es cero. El voltaje entre dos conductores cualesquiera viene dado por:

<img alt="Equation2" src="/files/ftp_upload/16144/16144_Equation%202.svg" style="height: 30px;">

donde D_ab, D_ba, D_bc, D_ac son las distancias entre los conductores, y q_a, q_b y q_c son las cargas en los respectivos conductores. La capacitancia al neutro por unidad de longitud viene dada por:

<img alt="Equation3" src="/files/ftp_upload/16144/16144_Equation%203.svg" style="height: 42px;">

donde D es la distancia equivalente entre los conductores, calculada a partir de la distancia media geométrica. Debido a la naturaleza simétrica de las líneas trifásicas balanceadas, esta capacitancia es la misma para cada fase.

Una comprensión detallada de estas propiedades de capacitancia es crucial para modelar y analizar con precisión las líneas de transmisión, garantizando el funcionamiento eficiente y confiable de los sistemas de energía.

Capacitancia: línea monofásica y trifásica

Considere una línea de transmisión monofásica de dos hilos con igual espaciado de fase energizada por una fuente de voltaje. Un conductor lleva una carga uniforme, y su ...

capacitance-single-phase-and-three-phase-line

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

Capacitance: Single-Phase And Three-Phase Line

transmission line capacitance in power systems

Transmission line capacitance affects how power lines store charge and behave in electrical power systems. It is an important part of line modeling because it helps describe efficient operation. For a single-phase line, the key idea is the charge on the conductors and the voltage between them.

A single-phase transmission line uses two wires with equal spacing. One conductor carries a uniform positive charge, and the other carries an equal negative charge. From the voltage between the conductors, the capacitance of a one-meter section can be found using the conductor spacing, the conductor radius, and the permittivity of free space.

When a single-phase line is energized by a grounded center tap transformer, the voltage to ground also matters. In that case, the voltage between each conductor and the ground can be determined. The capacitance from either line to the grounded neutral can also be found and included in circuit models.

Three-phase transmission lines are more complex because the phases interact with one another. For balanced positive-sequence voltages, the sum of the positive-sequence charges is assumed to be zero. The voltage between any two conductors depends on the charges on phases a, b, and c, as well as the distances between them.

For a balanced three-phase line with equal spacing, the capacitance to neutral is given per unit length. The equivalent distance between conductors is calculated using the geometric mean distance. Because the line is symmetrical, this capacitance is the same for each phase. This helps engineers model transmission lines correctly and study reliable power-system operation.

Transmission Line Capacitance in Power Systems

transmission-line-capacitance-in-power-systems

transmission line design considerations

Overhead Power Line Materials and Safety

Overhead transmission lines rely on the right materials, insulation, and support hardware to move electricity safely and efficiently. Aluminum is now the preferred conductor material because it is abundant and cost-effective. Copper was used more often in the past, but aluminum has become the common choice for modern lines. The most widely used conductor is aluminum conductor, steel-reinforced, or ACSR. It uses aluminum strands around a steel core for added strength. Other conductor types...

resistance and conductance

How Transmission Lines Lose Energy

Transmission lines lose energy through resistance and conductance. DC resistance depends on a conductor’s resistivity, length, and cross-sectional area. Resistivity is a material property, and annealed copper is the international standard used for measurement. Material choice and conductor shape both matter. Hard-drawn aluminum at 20 degrees Celsius has a resistivity equal to 61% of the standard conductivity of annealed copper. Stranded conductors also gain a little extra resistance because...

inductance: solid cylindrical conductor

Magnetic Flux Linkage in Solid Conductors

Magnetic flux linkage in a solid cylindrical conductor is found by combining the field inside the wire with the field around it. The method uses a 1-meter section of a non-magnetic conductor with radius r. It also assumes the current is spread uniformly and ignores end effects. Inside the conductor, Ampere's law is used to find the magnetic field intensity H. The field is concentric and constant within the conductor. From H, the magnetic flux density B inside the wire is calculated. The...

inductance: single-phase and three-phase line

inductance-single-phase-and-three-phase-line

Transmission Line Inductance in Power Cables

Transmission line inductance helps explain how current-carrying conductors behave in power systems. It is especially important when studying single-phase two-wire lines and three-phase three-wire lines with equal phase spacing. These line types are common models for efficient transmission design and operation. A single-phase line uses two solid cylindrical conductors, labeled x and y. Each conductor carries a phasor current, ix and iy, and the sum of these currents is zero. The total flux...

series impedances: three-phase line

Three-Phase Line Impedance Matrix

Three-phase line impedance matrix calculations describe how resistance and inductive reactance behave in an overhead power line. The model includes three phase conductors and multiple neutral conductors that are grounded at regular intervals. It also accounts for unbalanced phase currents, which can send return current through the neutral wires and the earth along the lowest-impedance path. Kirchhoff’s laws are used to build an integro-differential equation for the conductor network. To make...

capacitance: single-phase and three-phase line

Transmission line capacitance affects how power lines store charge and behave in electrical power systems. It is an important part of line modeling because it helps describe efficient operation. For a single-phase line, the key idea is the charge on the conductors and the voltage between them. A single-phase transmission line uses two wires with equal spacing. One conductor carries a uniform positive charge, and the other carries an equal negative charge. From the voltage between the...

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...

key terms and concepts

Learn how capacitance is modeled in single-phase and three-phase transmission lines, including grounded neutral and balanced positive-sequence cases.

Transmission Line Capacitance in Power Systems | 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

Transmission Line Capacitance in Power Systems

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