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

Considere um condutor uniformemente carregado acima da Terra. Ele induz uma carga negativa igual na Terra, criando linhas de campo elétrico.
O efeito da Terra é modelado usando um condutor de imagem, idêntico, mas abaixo do original, mantendo o campo elétrico e a tensão constantes.
Para linhas trifásicas com condutores neutros, são usados condutores de imagem separados. A tensão entre um condutor e sua imagem depende de sua distância. Por simetria, a tensão entre este condutor e a Terra é metade desse valor. Condutores neutros aterrados não carregam carga.
As equações matriciais expressam essas relações, permitindo cálculos de tensões fase-neutro e cargas do condutor.
Outras equações de rendimento de particionamento relacionando cargas de condutor de fase a tensões de fase para neutro.
As equações revelam que uma tensão linha-neutro positiva em uma fase induz cargas positivas e negativas em diferentes fases.
Para linhas transpostas, os elementos da matriz de capacitância são calculados em média, derivando a matriz de admitância da fase de derivação.
Para uma linha de circuito duplo com linhas paralelas não transpostas, métodos semelhantes produzem a matriz de admitância de shunt equivalente de três por três. Esses conceitos se estendem a vários circuitos paralelos.

admitâncias de desvio

As admitâncias de desvio desempenham um papel crucial na análise de linhas de transmissão, particularmente para sistemas trifásicos com condutores neutros. Quando um condutor uniformemente carregado é posicionado acima da Terra, ele induz uma carga igual, mas oposta, em sua superfície. Essa interação cria linhas de campo elétrico entre o condutor e a Terra.


 Para modelar esse efeito, o método de imagens é empregado. Esse método envolve a substituição da Terra por um condutor de imagem que espelha as propriedades do condutor original, mas está simetricamente abaixo dele. O condutor de imagem mantém o mesmo raio e magnitude de carga que o original, garantindo que o campo elétrico e a distribuição de tensão acima da Terra permaneçam consistentes com o cenário real.


 Em linhas trifásicas com condutores neutros, condutores de imagem separados são utilizados para cada fase. A tensão entre um condutor e seu condutor de imagem correspondente é determinada por sua distância. Devido à simetria, a tensão entre cada condutor e a Terra é metade desse valor. Condutores neutros, que são aterrados, não carregam carga e simplificam o processo de cálculo.


 As equações matriciais expressam as relações entre tensões fase-neutro e cargas condutoras. Essas equações são ainda mais particionadas e reescritas para estabelecer as relações entre cargas fase-condutoras e tensões fase-neutro. As equações revelam que uma tensão positiva linha-neutro em uma fase induz cargas positivas e negativas em fases diferentes.


 Para linhas transpostas, os elementos da matriz de capacitância são calculados em média, permitindo a derivação da matriz de admitância de fase de desvio. Métodos semelhantes produzem a matriz de admitância de desvio equivalente três por três no caso de linhas de circuito duplo com configurações paralelas e não transpostas. Esses princípios podem ser estendidos a vários circuitos paralelos, facilitando a análise abrangente e garantindo a operação eficiente de sistemas complexos de transmissão de energia.

Admitâncias de Desvio

Considere um condutor uniformemente carregado acima da Terra. Ele induz uma carga negativa igual na Terra, criando linhas de campo elétrico.
O efeito da Terra é ...

Education

JoVE Core

Electrical Engineering

Engenharia Elétrica

Unit 1

Unidade 1

Transmission Line Parameters

Parâmetros da Linha de Transmissão

KEY TERMS AND CONCEPTS

TERMOS E CONCEITOS-CHAVE

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

transmission line design considerations

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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...

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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...

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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...

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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

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...

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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