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

Si consideri una linea di trasmissione monofase a due fili con spaziatura di fase uguale eccitata da una sorgente di tensione. Un conduttore trasporta una carica uniforme e la sua controparte ha una carica negativa uguale. Applicando la formula per la tensione tra i conduttori e sostituendo i raggi del cilindro, viene calcolata la capacità per una linea di un metro.
Per le linee alimentate da un trasformatore di presa centrale con messa a terra, si ottiene la tensione tra ciascun conduttore e la terra e la capacità da entrambe le linee al neutro con messa a terra.
Queste capacità sono rappresentate in specifiche rappresentazioni circuitali.
Successivamente, si consideri una linea trifase con spaziatura di fase uguale, trascurando gli effetti del conduttore di terra e neutro.
Per determinare la capacità di sequenza positiva, si assume che la somma delle cariche di sequenza positiva sia zero.
Ora, viene calcolata la tensione tra i conduttori, seguita dalla sostituzione dei raggi.
Richiamando le equazioni di tensione per tensioni bilanciate a sequenza positiva, sommandole, sostituendo le espressioni di tensione e la relazione di carica si ottiene la capacità al neutro per lunghezza di linea.
Gli stessi risultati si applicano a tutte e tre le fasi a causa della simmetria, ma per un funzionamento bilanciato a tre fasi viene considerata una sola fase.

capacità: linea monofase e trifase

Nei sistemi di energia elettrica, comprendere la capacità delle linee di trasmissione, è fondamentale per un funzionamento efficiente.

Linee Monofase

Si consideri una linea di trasmissione monofase, a due fili con spaziatura di fase uguale, alimentata da una sorgente di tensione. Un conduttore trasporta una carica positiva uniforme, mentre l'altro trasporta una carica negativa uguale. La capacità C della linea, può essere ricavata dalla tensione V tra i conduttori. Per una sezione di un metro della linea, la capacità è data da:

<img alt="Equation1" src="/files/ftp_upload/16144/16144_%20Equation%201.svg" style="height: 42px;">

Dove ϵ​ è la permittività dello spazio libero, D è la distanza tra i conduttori e r è il raggio dei conduttori. Quando la linea, è energizzata da un trasformatore a presa centrale con messa a terra, è possibile determinare la tensione tra ciascun conduttore e la terra, nonché la capacità da entrambe le linee, al neutro con messa a terra. Questa capacità, è rappresentata nei modelli di circuito, per riflettere accuratamente il comportamento della linea di trasmissione in diverse condizioni operative.

Linee Trifase

L'analisi diventa più complessa nelle linee di trasmissione trifase con spaziatura di fase uguale, a causa dell'interazione tra le fasi. Per tensioni di sequenza positiva bilanciate, la somma delle cariche di sequenza positiva, è considerata pari a zero. La tensione tra due conduttori qualsiasi è data da:

<img alt="Equation2" src="/files/ftp_upload/16144/16144_Equation%202.svg" style="height: 30px;">

dove Dab​, Dba​, Dbc​​, Dac​ sono le distanze tra i conduttori e ​qa, qb e qc sono le cariche sui rispettivi conduttori. La capacità verso il neutro per unità di lunghezza è data da:

<img alt="Equation3" src="/files/ftp_upload/16144/16144_Equation%203.svg" style="height: 42px;">

dove D è la distanza equivalente tra i conduttori, calcolata utilizzando la distanza media geometrica. A causa della natura simmetrica delle linee trifase bilanciate, questa capacità è la stessa per ogni fase.

Una conoscenza approfondita di queste proprietà di capacità, è fondamentale per modellare e analizzare accuratamente le linee di trasmissione, garantendo il funzionamento efficiente e affidabile dei sistemi energetici.

Capacità: Linea Monofase e Trifase

Si consideri una linea di trasmissione monofase a due fili con spaziatura di fase uguale eccitata da una sorgente di tensione. Un conduttore trasporta una carica uniforme e il suo ...

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

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

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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