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

電圧源によって通電される等相間隔の単相2線式伝送線路について考えてみましょう。一方の導体は均一な電荷を持ち、そのもう一方の導体は等しい負電荷を持っています。導体間電圧の式を適用し、シリンダ半径を代入すると、1メートルのラインの静電容量が計算されます。
接地されたセンタータップトランスによって供給されるラインの場合、各導体とグランド間の電圧と、いずれかのラインから接地されたニュートラルまでの静電容量が得られます。
これらの容量は、特定の回路表現で表されます。
次に、アースと中性導体の影響を無視した、位相間隔が等しい三相線を考えます。
正のシーケンス容量を決定するために、正のシーケンス電荷の合計はゼロであると仮定します。
ここで、導体間の電圧が計算され、続いて半径を代入します。
平衡正のシーケンス電圧の電圧方程式を思い出し、それらを加算し、電圧式を代入し、電荷関係を代入すると、ラインあたりの容量-中性値の長さが得られます。
対称性により、3つのフェーズすべてに同じ結果が適用されますが、バランスの取れた3フェーズ操作では、1つのフェーズのみが考慮されます。

静電容量: 単相および 3 相線

電力システムでは、伝送線路の静電容量を理解することが効率的な運用の基本となります。

単相線

電圧源によって通電される、位相間隔が等しい単相 2 線式伝送線路を考えてみましょう。一方の導体は均一な正電荷を帯び、もう一方の導体は等しい負電荷を帯びます。線路の静電容量 C は、導体間の電圧 V から算出できます。線路の 1 m 区間の静電容量は、次の式で求められます。

<img alt="Equation1" src="/files/ftp_upload/16144/16144_%20Equation%201.svg" style="height: 42px;">

ここで、ϵ​ は自由空間の誘電率、D は導体間の距離、r は導体の半径です。接地されたセンタータップ変圧器によって線路に電力が供給されると、各導体と地面の間の電圧、およびいずれかの線路から接地された中性線までの静電容量を決定できます。この静電容量は回路モデルで表され、さまざまな動作条件下での伝送線路の動作を正確に反映します。

3 相線

相間の相互作用により、相間隔が等しい 3 相送電線では解析がより複雑になります。平衡正相電圧の場合、正相電荷の合計はゼロであると想定されます。任意の 2 つの導体間の電圧は次のように表されます。

<img alt="Equation2" src="/files/ftp_upload/16144/16144_Equation%202.svg" style="height: 30px;">

ここで、D_ab​、D_ba​、D_bc​​、D_ac​ は導体間の距離、​q_a、q_b、q_c はそれぞれの導体の電荷です。単位長さあたりの中性点に対する静電容量は次のように表されます。

<img alt="Equation3" src="/files/ftp_upload/16144/16144_Equation%203.svg" style="height: 42px;">

ここで、D は導体間の等価距離であり、幾何平均距離を使用して計算されます。バランスのとれた 3 相線の対称性により、この静電容量は各相で同じになります。

これらの静電容量特性を詳細に理解することは、伝送線路を正確にモデル化および分析し、電力システムの効率的で信頼性の高い運用を確保するために不可欠です。

電圧源によって通電される等相間隔の単相2線式伝送線路について考えてみましょう。1人の導体が均一な電荷を運び、その...

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

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

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 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

Transmission Line Capacitance in Power Systems

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