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

Considere uma linha de transmissão monofásica de dois fios com espaçamento de fase igual energizado por uma fonte de tensão. Um condutor carrega uma carga uniforme e sua contraparte tem uma carga negativa igual. Aplicando a fórmula da tensão entre os condutores e substituindo os raios do cilindro, calcula-se a capacitância para uma linha de um metro.
Para linhas alimentadas por um transformador de derivação central aterrado, a tensão entre cada condutor e o terra e a capacitância de qualquer linha para o neutro aterrado são obtidas.
Essas capacitâncias são representadas em representações de circuitos específicos.
Em seguida, considere uma linha trifásica com espaçamento de fase igual, negligenciando os efeitos de terra e condutor neutro.
Para determinar a capacitância de sequência positiva, a soma das cargas de sequência positiva é considerada zero.
Agora, a tensão entre os condutores é calculada, seguida pela substituição dos raios.
Recuperando as equações de tensão para tensões de sequência positiva balanceadas, adicionando-as, substituindo as expressões de tensão e a relação de carga fornece a capacitância para neutro por comprimento de linha.
Os mesmos resultados se aplicam a todas as três fases devido à simetria, mas para uma operação trifásica balanceada, apenas uma fase é considerada.

capacitância: linha monofásica e trifásica

Em sistemas de energia elétrica, entender a capacitância das linhas de transmissão é fundamental para uma operação eficiente.


 Linhas Monofásicas


 Considere uma linha de transmissão monofásica de dois fios com espaçamento de fase igual energizada por uma fonte de tensão. Um condutor carrega uma carga positiva uniforme, enquanto o outro carrega uma carga negativa igual. A capacitância C da linha pode ser derivada da tensão V entre os condutores. Para uma seção de um metro da linha, a capacitância é dada por:

<img alt="Equation1" src="/files/ftp_upload/16144/16144_%20Equation%201.svg" style="height: 42px;">

 Onde ϵ é a permissividade do espaço livre, D é a distância entre os condutores e r é o raio dos condutores. Quando a linha é energizada por um transformador de derivação central aterrado, a tensão entre cada condutor e o solo, bem como a capacitância de qualquer linha para o neutro aterrado, podem ser determinadas. Essa capacitância é representada em modelos de circuito para refletir com precisão o comportamento da linha de transmissão sob diferentes condições operacionais.

 Linhas Trifásicas


 A análise se torna mais complexa em linhas de transmissão trifásicas com espaçamento de fase igual devido à interação entre as fases. Para tensões de sequência positiva balanceadas, a soma das cargas de sequência positiva é assumida como zero. A tensão entre quaisquer dois condutores é dada por:

<img alt="Equation2" src="/files/ftp_upload/16144/16144_Equation%202.svg" style="height: 30px;">

 Onde D_ab, D_ba, D_bc, D_ac são as distâncias entre os condutores, e q_a, q_b e q_c são as cargas nos respectivos condutores. A capacitância para neutro por unidade de comprimento é dada por:

<img alt="Equation3" src="/files/ftp_upload/16144/16144_Equation%203.svg" style="height: 42px;">

 Onde D é a distância equivalente entre os condutores, calculada usando a distância média geométrica. Devido à natureza simétrica das linhas trifásicas balanceadas, essa capacitância é a mesma para cada fase.


 Uma compreensão detalhada dessas propriedades de capacitância é crucial para modelar e analisar com precisão as linhas de transmissão, garantindo a operação eficiente e confiável dos sistemas de energia.

Capacitância: Linha Monofásica e Trifásica

Considere uma linha de transmissão monofásica de dois fios com espaçamento de fase igual energizado por uma fonte de tensão. Um condutor carrega uma carga uniforme e sua ...

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

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

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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