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

Considere líneas de transmisión monofásicas de dos hilos y trifásicas de tres hilos con el mismo espaciado de fases.
La línea monofásica consta de dos conductores cilíndricos sólidos, x e y, cada uno de los cuales lleva una corriente fasorial.
Dado que la suma de las corrientes es cero, se calcula el conductor de enlace de flujo total x, seguido de su inductancia.
Del mismo modo, se calcula el conductor de enlace de flujo total y y se determina su inductancia.
A continuación, se calcula la inductancia del bucle, también conocida como inductancia total del circuito monofásico.
Si los radios de ambos conductores son iguales, se puede simplificar la inductancia total del circuito.
Ahora, la línea trifásica consta de tres conductores cilíndricos sólidos, a, b y c, de radios y espaciados de fase iguales.
Suponiendo corrientes de secuencia positiva equilibradas tales que la suma de las corrientes sea igual a cero, se calcula la fase de enlace de flujo total de un conductor.
A partir de esto, se determina su inductancia. Debido a la simetría, el mismo resultado se aplica a las fases b y c.
Sin embargo, para el funcionamiento equilibrado de esta línea, sólo es necesario tener en cuenta una fase, ya que los enlaces de flujo de cada fase tienen magnitudes iguales y un desplazamiento de 120 grados.

parámetros de la línea de transmisión

Inductance: Single-Phase And Three-Phase Line

Inductancia: líneas monofásicas y trifásicas

Comprender la inductancia de las líneas de transmisión es fundamental para el diseño y el funcionamiento eficiente de los sistemas de energía eléctrica. En este artículo se analizan en profundidad las características de inductancia de las líneas de transmisión monofásicas de dos cables y trifásicas de tres cables con el mismo espaciado de fases.

Línea monofásica de dos cables

Una línea monofásica consta de dos conductores cilíndricos sólidos, denominados x e y. Cada conductor transporta corrientes fasoriales i_x e i_y, respectivamente. Dado que la suma de estas corrientes es cero, podemos calcular el flujo total que une al conductor x. Este flujo de unión se obtiene mediante:

<img alt="Equation1" src="/files/ftp_upload/16142/16142_Equation%201.svg" style="height: 32px;">

Donde r_x^’ es el radio efectivo del conductor x, teniendo en cuenta el efecto de proximidad.

La inductancia por conductor, L_x del conductor x, es entonces:

<img alt="Equation2" src="/files/ftp_upload/16142/16142_Equation%202.svg" style="height: 32px;">

De manera similar, para el conductor y, se calculan la inductancia y el enlace de flujo. La inductancia total del circuito monofásico, también conocida como inductancia de bucle, es:

<img alt="Equation3" src="/files/ftp_upload/16142/16142_Equation%203.svg" style="height: 46px;">

Línea trifásica de tres cables

Para una línea trifásica, hay tres conductores cilíndricos sólidos, a, b y c, cada uno con un radio igual r y un espaciado de fase igual D. Suponiendo corrientes de secuencia positiva equilibradas, el flujo total que une la fase a es:

<img alt="Equation4" src="/files/ftp_upload/16142/16142_Equation%204.svg" style="height: 32px;">

De esto se deriva la inductancia de la fase a:

<img alt="Equation5" src="/files/ftp_upload/16142/16142_Equation%205.svg" style="height: 32px;">

Debido a la simetría, la misma inductancia se aplica a las fases b y c. Para un funcionamiento trifásico equilibrado, solo se debe considerar una fase, ya que los enlaces de flujo de cada fase son iguales en magnitud y están desplazados 120 grados.

Comprender estos cálculos de inductancia ayuda en el diseño y análisis de líneas de transmisión, garantizando pérdidas mínimas y un rendimiento óptimo.

Parámetros de la línea de transmisión

Considere líneas de transmisión monofásicas de dos hilos y trifásicas de tres hilos con el mismo espaciado de fases.
La línea monofásica consta de dos ...

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

Education

Educación

JoVE Core

Electrical Engineering

Ingeniería Eléctrica

Unit 1

Unidad 1

Transmission Line Parameters

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

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...

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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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