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

地球上に均一に帯電した導体を考えてみましょう。それは地球上に等しい負の電荷を誘導し、電磁線を作り出します。
地球の効果は、電界と電圧を一定に保ちながら、元のものと同じであるが元の画像の下にあるイメージ導体を使用してモデル化されます。
中性導体を備えた三相線の場合、別々のイメージ導体が使用されます。導体とその像との間の電圧は、導体の距離によって異なります。対称性により、この導体とアース間の電圧はこの値の半分になります。接地された中性導体は電荷を運びません。
行列方程式はこれらの関係を表し、相-中性線電圧と導体電荷の計算を可能にします。
さらに分割すると、相導体の電荷を相-中性線電圧に関連付ける方程式が得られます。
方程式は、1つの相の正の線-中性線電圧が、異なる相で正と負の電荷を誘導することを示しています。
転置されたラインの場合、キャパシタンスマトリクス要素が平均化され、シャント位相アドミタンスマトリクスが導出されます。
並列の転置されていないラインを持つ二重回路ラインの場合、同様の方法では等価な3×3のシャントアドミタンスマトリックスが得られます。これらの概念は、複数の並列回路に拡張されます。

並列アドミタンス

並列アドミタンスは、特に中性導体を持つ 3 相システムにおいて、伝送線路の解析において重要な役割を果たします。均一に帯電した導体をアース上に配置すると、その表面に等しいが反対の電荷が誘導されます。この相互作用により、導体とアースの間に電界線が生成されます。 
この効果をモデル化するために、イメージ法が採用されています。この方法では、アースを、元の導体の特性を反映しながらもその下に対称的に配置されたイメージ導体に置き換えます。イメージ導体は元の導体と同じ半径と電荷量を維持し、アース上の電界と電圧分布が実際のシナリオと一致していることを保証します。 
中性導体を備えた 3 相線では、各相ごとに個別のイメージ導体が使用されます。導体とそれに対応するイメージ導体間の電圧は、それらの距離によって決まります。対称性のため、各導体とアース間の電圧はこの値の半分になります。接地されている中性導体は電荷を帯びず、計算プロセスが簡素化されます。 
行列方程式は、相中性線電圧と導体電荷の関係を表します。これらの方程式はさらに分割され、相導体電荷と相中性線電圧の関係を確立するように書き直されます。方程式は、1 つの相の正の線中性線電圧が、異なる相に正と負の電荷を誘導することを明らかにします。 
転置線路の場合、静電容量行列の要素が平均化され、並列位相アドミタンス行列を導出できます。同様の方法により、転置されていない並列構成の二重回路線路の場合に、同等の 3 x 3 並列アドミタンス行列が得られます。これらの原理は複数の並列回路に拡張できるため、包括的な分析が容易になり、複雑な電力伝送システムの効率的な動作が保証されます。

地球上に均一に帯電した導体を考えてみましょう。それは地球上に等しい負の電荷を誘導し、電磁線を作り出します。
地球の影響は...

Education

JoVE Core

Electrical Engineering

電気工学

Unit 1

ユニット1

Transmission Line Parameters

伝送線路パラメータ

KEY TERMS AND CONCEPTS

主要用語と概念

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 電気工学 は、電気回路の基本概念と回路解析テクニックを網羅したアニメーションビデオシリーズです。オペアンプと回路変換および 1 次・ 2 次回路の概念を網羅しています。実験を撮影した実写動画では、設計例や現代社会での応用が含まれており、複雑な概念も分かりやすく学習いただけます。

electrical engineering

Image Method for Line Capacitance

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