27.7
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.…
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.
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Q1: What is the method of images and how does it model Earth's effect on transmission line conductors?
The method of images replaces Earth with an image conductor that mirrors the original conductor's properties but is positioned symmetrically beneath it. This image conductor maintains the same radius and charge magnitude, ensuring the electric field and voltage distribution above Earth remain consistent with the actual scenario. The technique simplifies calculations for uniformly charged conductors.
Q2: How does voltage relate between a conductor, its image, and Earth in transmission line analysis?
The voltage between a conductor and its image conductor depends on their distance. By symmetry, the voltage between each conductor and Earth is half the conductor-to-image voltage. This relationship is fundamental for calculating phase-to-neutral voltages in three-phase systems with neutral conductors.
Q3: Why are separate image conductors used for three-phase lines with neutral conductors?
Three-phase lines require separate image conductors for each phase to accurately model the electromagnetic interactions between all conductors and Earth. Grounded neutral conductors carry no charge, simplifying the calculation process. This approach enables matrix equations to express relationships between phase-to-neutral voltages and conductor charges.
Q4: What happens to charges on different phases when a positive line-to-neutral voltage is applied?
A positive line-to-neutral voltage on one phase induces positive charges on that phase and negative charges on different phases. Matrix equations reveal these charge distribution patterns across the system. This coupling effect is critical for understanding shunt admittance behavior in three-phase transmission lines.
Q5: How is the shunt phase admittance matrix derived for transposed transmission lines?
For transposed lines, the elements of the capacitance matrix are averaged to derive the shunt phase admittance matrix. This averaging accounts for the periodic transposition of conductors along the line length. The resulting matrix simplifies analysis while maintaining accuracy for balanced three-phase systems.
Q6: What is the difference between transposed and non-transposed double-circuit transmission lines?
Transposed lines have conductors periodically rearranged to balance phase characteristics, while non-transposed double-circuit lines maintain fixed parallel configurations. Non-transposed lines require similar matrix methods to yield an equivalent three-by-three shunt admittance matrix. Both approaches extend to multiple parallel circuits for comprehensive transmission system analysis.
Q7: How do matrix equations relate phase-conductor charges to phase-to-neutral voltages in shunt admittance analysis?
Matrix equations express relationships between phase-to-neutral voltages and conductor charges, which are further partitioned and rewritten to establish direct connections between phase-conductor charges and voltages. These equations form the foundation for calculating shunt admittances and understanding charge distribution patterns in transmission line systems.