Name: transmission line inductance in power cables
Uploaded: 2024-11-21T14:54:23.000Z
Duration: 1 min 28 s
Channel: JoVE

Considere linhas de transmissão monofásicas de dois fios e trifásicas de três fios com espaçamento de fase igual.
A linha monofásica consiste em dois condutores cilíndricos sólidos, x e y, cada um carregando uma corrente fasor.
Dado que a soma das correntes é zero, o fluxo total que liga o condutor x é calculado, seguido por sua indutância.
Da mesma forma, o condutor de ligação de fluxo total y é calculado e sua indutância é determinada.
A indutância do loop, também conhecida como indutância total do circuito monofásico, é então calculada.
Se os raios de ambos os condutores forem iguais, a indutância total do circuito pode ser simplificada.
Agora, a linha trifásica consiste em três condutores cilíndricos sólidos, a, b e c, de raios e espaçamento de fase iguais.
Assumindo correntes de sequência positiva balanceadas de modo que a soma das correntes seja igual a zero, o fluxo total ligando a fase um condutor é calculado.
A partir disso, sua indutância é determinada. Devido à simetria, o mesmo resultado se aplica às fases b e c.
No entanto, para a operação equilibrada desta linha, apenas uma fase precisa ser considerada, uma vez que as ligações de fluxo de cada fase têm magnitudes iguais e deslocamento de 120 graus.

parâmetros de linha de transmissão

Inductance: Single-Phase And Three-Phase Line

Indutância: linhas monofásicas e trifásicas


 Entender a indutância das linhas de transmissão é crucial para o projeto e a operação eficientes em sistemas de energia elétrica. Esta discussão se aprofunda nas características de indutância de linhas de transmissão monofásicas de dois fios e trifásicas de três fios com espaçamento de fase igual.


 Linha monofásica de dois fios:


 Uma linha monofásica consiste em dois condutores cilíndricos sólidos, denotados como x e y. Cada condutor carrega correntes fasoriais i_x​ e i_y, respectivamente. Dado que a soma dessas correntes é zero, podemos calcular o fluxo total que liga o condutor x. Esta ligação de fluxo é dada por:

<img alt="Equation1" src="/files/ftp_upload/16142/16142_Equation%201.svg" style="height: 32px;">

 Onde r_x^’ é o raio efetivo do condutor x, considerando o efeito de proximidade.


 A indutância por condutor, L_x do condutor x, é então:

<img alt="Equation2" src="/files/ftp_upload/16142/16142_Equation%202.svg" style="height: 32px;">

 Da mesma forma, para o condutor y, a ligação de fluxo e a indutância são computadas. A indutância total do circuito monofásico, também conhecida como indutância de loop, é:

<img alt="Equation3" src="/files/ftp_upload/16142/16142_Equation%203.svg" style="height: 46px;">

 Linha trifásica de três fios:


 Para uma linha trifásica, há três condutores cilíndricos sólidos, a, b e c, cada um com raio r igual e espaçamento de fase D igual. Assumindo correntes de sequência positiva balanceadas, o fluxo total que liga a fase a é:

<img alt="Equation4" src="/files/ftp_upload/16142/16142_Equation%204.svg" style="height: 32px;">

 A partir disso, a indutância da fase a é derivada:

<img alt="Equation5" src="/files/ftp_upload/16142/16142_Equation%205.svg" style="height: 32px;">

 Devido à simetria, a mesma indutância se aplica às fases b e c. Para uma operação trifásica balanceada, apenas uma fase precisa ser considerada, já que as ligações de fluxo de cada fase são iguais em magnitude e deslocadas em 120 graus.


 Entender esses cálculos de indutância ajuda no projeto e na análise de linhas de transmissão, garantindo perdas mínimas e desempenho ideal.

Parâmetros de Linha de Transmissão

Considere linhas de transmissão monofásicas de dois fios e trifásicas de três fios com espaçamento de fase igual.
A linha monofásica é composta por dois ...

inductance-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

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 linking conductor x can then be found, and the effective radius rx' is used to account for proximity effect. From the flux linkage, the inductance per conductor, Lx, is obtained.

The same process applies to conductor y. Its flux linkage and inductance are calculated in the same way. The inductance of the full single-phase circuit is the loop inductance, which combines the two conductors into one circuit value.

A three-phase line uses three solid cylindrical conductors, a, b, and c. They have equal radius r and equal phase spacing D. For balanced positive-sequence currents, the flux linking phase a can be determined from the current pattern in the line. The inductance of phase a follows from that flux linkage.

Because the system is symmetric, phases b and c have the same inductance as phase a. In balanced three-phase operation, one phase is enough to analyze because all three phases have equal-magnitude flux linkages shifted by 120 degrees. These inductance results are useful for line design and analysis, where reducing losses and improving performance are important.

Transmission Line Inductance in Power Cables

transmission-line-inductance-in-power-cables

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

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

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 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 inductance is calculated for single-phase two-wire and three-phase three-wire transmission lines, including flux linkage, loop inductance, and balanced phase behavior.

Transmission Line Inductance in Power Cables | 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 Inductance in Power Cables

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