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

Envisagez des lignes de transmission monophasées à deux fils et triphasées à trois fils avec un espacement de phase égal.
La ligne monophasée se compose de deux conducteurs cylindriques solides, x et y, chacun transportant un courant de phaseur.
Sachant que la somme des courants est nulle, on calcule le flux total reliant le conducteur x, suivi de son inductance.
De même, le flux total reliant le conducteur y est calculé et son inductance est déterminée.
L’inductance de la boucle, également appelée inductance totale du circuit monophasé, est ensuite calculée.
Si les rayons des deux conducteurs sont égaux, l’inductance totale du circuit peut être simplifiée.
Or, la ligne triphasée se compose de trois conducteurs cylindriques solides, a, b et c, de rayons et d’espacement de phase égaux.
En supposant des courants à séquence positive équilibrée tels que la somme des courants est égale à zéro, on calcule la phase de liaison de flux total a conducteur.
À partir de là, son inductance est déterminée. En raison de la symétrie, le même résultat s’applique aux phases b et c.
Cependant, pour le fonctionnement équilibré de cette ligne, une seule phase doit être prise en compte car les liaisons de flux de chaque phase ont des amplitudes égales et un déplacement de 120 degrés.

paramètres de la ligne de transmission

inductance : lignes monophasées et triphasées

Inductance: Single-Phase And Three-Phase Line

La compréhension de l'inductance des lignes de transmission est essentielle pour une conception et un fonctionnement efficaces des systèmes d'alimentation électrique. Cette discussion se penche sur les caractéristiques d'inductance des lignes de transmission monophasées à deux fils et triphasées à trois fils avec un espacement de phase égal.

Ligne monophasée à deux fils :

Une ligne monophasée est constituée de deux conducteurs cylindriques pleins, notés x et y. Chaque conducteur transporte respectivement les courants de phaseur i_x​ et i_y​. Étant donné que la somme de ces courants est nulle, nous pouvons calculer le flux total reliant le conducteur x. Ce flux de liaison est donné par :

<img alt="Equation1" src="/files/ftp_upload/16142/16142_Equation%201.svg" style="height: 32px;">

Où r_x^’ est le rayon effectif du conducteur x, tenant compte de l’effet de proximité.

L'inductance par conducteur, L_x du conducteur x, est alors :

<img alt="Equation2" src="/files/ftp_upload/16142/16142_Equation%202.svg" style="height: 32px;">

De même, pour le conducteur y, la liaison de flux et l'inductance sont calculées. L'inductance totale du circuit monophasé, également appelée inductance de boucle, est :

<img alt="Equation3" src="/files/ftp_upload/16142/16142_Equation%203.svg" style="height: 46px;">

Ligne triphasée à trois fils :

Pour une ligne triphasée, il y a trois conducteurs cylindriques solides, a, b et c, chacun avec un rayon r égal et un espacement de phase D égal. En supposant des courants de séquence positive équilibrés, le flux total reliant la phase a est :

<img alt="Equation4" src="/files/ftp_upload/16142/16142_Equation%204.svg" style="height: 32px;">

De là, on déduit l'inductance de la phase a :

<img alt="Equation5" src="/files/ftp_upload/16142/16142_Equation%205.svg" style="height: 32px;">

En raison de la symétrie, la même inductance s'applique aux phases b et c. Pour un fonctionnement triphasé équilibré, une seule phase doit être prise en compte puisque les liaisons de flux de chaque phase sont égales en amplitude et décalées de 120 degrés.

La compréhension de ces calculs d’inductance aide à la conception et à l’analyse des lignes de transmission, garantissant des pertes minimales et des performances optimales.

Paramètres de la ligne de transmission

Inductance : lignes monophasées et triphasées

Envisagez des lignes de transmission monophasées à deux fils et triphasées à trois fils avec un espacement de phase égal.
La ligne monophasée se compose de deux ...

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

Education

Enseignement

JoVE Core

Electrical Engineering

Génie électrique

Unit 1

Unité 1

Transmission Line Parameters

Paramètres de la ligne de transmission

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

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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