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

Consideriamo un conduttore uniformemente caricato sopra la Terra. Induce una carica negativa uguale sulla Terra, creando linee di campo elettrico.
L'effetto della Terra è modellato utilizzando un conduttore d'immagine, identico ma inferiore all'originale, mantenendo costanti il campo elettrico e la tensione.
Per le linee trifase con conduttori neutri, vengono utilizzati conduttori di immagine separati. La tensione tra un conduttore e la sua immagine dipende dalla loro distanza. Per simmetria, la tensione tra questo conduttore e la Terra è la metà di questo valore. I conduttori neutri con messa a terra non hanno carica.
Le equazioni matriciali esprimono queste relazioni, consentendo di calcolare le tensioni fase-neutro e le cariche dei conduttori.
Ulteriori equazioni di partizionamento producono equazioni che mettono in relazione le cariche del conduttore di fase con le tensioni fase-neutro.
Le equazioni rivelano che una tensione positiva da linea a neutro su una fase induce cariche positive e negative su fasi diverse.
Per le linee trasposte, gli elementi della matrice di capacità sono mediati, derivando la matrice di ammettenza di fase shunt.
Per una linea a doppio circuito con linee parallele non trasposte, metodi simili producono l'equivalente matrice di ammettenza shunt tre per tre. Questi concetti si estendono a più circuiti paralleli.

ammissioni shunt

Le ammissioni shunt svolgono un ruolo cruciale nell'analisi delle linee di trasmissione, in particolare per i sistemi trifase con i conduttori neutri. Quando un conduttore uniformemente carico è posizionato sopra la Terra, induce una carica uguale ma opposta sulla sua superficie. Questa interazione crea delle linee di campo elettrico tra il conduttore e la Terra.

Per modellare questo effetto, viene impiegato il metodo delle immagini. Questo metodo comporta la sostituzione della Terra con un conduttore immagine che rispecchia le proprietà del conduttore originale ma è simmetricamente al di sotto di esso. Il conduttore immagine mantiene lo stesso raggio e la stessa magnitudine di carica dell'originale, assicurandosi che il campo elettrico e la distribuzione della tensione sopra la Terra rimangano coerenti con lo scenario effettivo.

Nelle linee trifase con i conduttori neutri, vengono utilizzati dei conduttori immagine separati per ogni fase. La tensione tra un conduttore e il conduttore immagine che gli corrisponde è determinata dalla loro distanza. A causa della simmetria, la tensione tra ogni conduttore e la Terra è la metà di questo valore. I conduttori neutri, che sono collegati a terra, non trasportano la carica e semplificano il processo di calcolo.

Le equazioni di matrice esprimono le relazioni tra le tensioni fase-neutro e le cariche del conduttore. Queste equazioni vengono ulteriormente suddivise e riscritte per stabilire le relazioni tra cariche fase-conduttore e le tensioni fase-neutro. Le equazioni rivelano che una tensione positiva linea-neutro su una fase induce cariche positive e negative su fasi diverse.

Per le linee trasposte, gli elementi della matrice di capacità vengono mediati, consentendo la derivazione della matrice di ammettenza di fase dello shunt. Metodi simili producono la matrice di ammettenza di shunt equivalente tre per tre nel caso di linee a doppio circuito con configurazioni parallele non trasposte. Questi principi possono essere estesi a più circuiti paralleli, facilitando l'analisi completa e garantendo il funzionamento efficiente di sistemi di trasmissione di potenza complessi.

Ammissioni shunt

Consideriamo un conduttore uniformemente caricato sopra la Terra. Induce una carica negativa uguale sulla Terra, creando linee di campo elettrico.
L'effetto della Terra è ...

Education

Didattica

JoVE Core

Electrical Engineering

Ingegneria elettrica

Unit 1

Unità 1

Transmission Line Parameters

Parametri della linea di trasmissione

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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

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

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

Description

Transcript

Tags