Name: transmission line inductance in power cables
Uploaded: 2024-11-21T14:54:23.000Z
Duration: 1 min 28 s
Channel: JoVE

単相2線式および三相3線式の伝送線路を、位相間隔が等しいものと考えてみます。
単相線路は、xとyの2つの固体円筒形導体で構成され、それぞれがフェーザ電流を流します。
電流の合計がゼロの場合、導体をリンクする全磁束xが計算され、続いてそのインダクタンスが計算されます。
同様に、導体yをリンクする全磁束が計算され、そのインダクタンスが決定されます。
次に、ループインダクタンス(単相回路の総インダクタンスとも呼ばれます)が計算されます。
両方の導体の半径が等しい場合、回路全体のインダクタンスを簡略化できます。
現在、三相線は、半径と位相間隔が等しい3つの固体円筒形導体a、b、およびcで構成されています。
電流の合計がゼロに等しくなるような平衡正のシーケンス電流を仮定すると、導体の磁束リンク相の合計が計算されます。
これから、そのインダクタンスが決定されます。対称性のため、フェーズ b と c に同じ結果が適用されます。
ただし、このラインのバランスの取れた運用では、各相の磁束リンケージの大きさが等しく、変位が120度であるため、考慮する必要があるのは1つの相のみです。

伝送線路パラメータ  

Inductance: Single-Phase And Three-Phase Line

インダクタンス: 単相および 3 相線

伝送線路のインダクタンスを理解することは、電力システムの効率的な設計と運用にとって重要です。この説明では、等位相間隔の単相 2 線式および 3 相 3 線式送電線のインダクタンス特性について詳しく説明します。

単相2線式線:

単相線路は、x と y で示される 2 本の円筒状の導体で構成されています。各導体には、それぞれ位相電流 i_x​ と i_y​ が流れます。これらの電流の合計がゼロであることから、導体 x を連結する全磁束を計算できます。この磁束の連結は次の式で表されます。

<img alt="Equation1" src="/files/ftp_upload/16142/16142_Equation%201.svg" style="height: 32px;">

ここで、r_x^’ は近接効果を考慮した導体 x の有効半径です。

導体 x の導体あたりのインダクタンス L_x は次のようになります。

<img alt="Equation2" src="/files/ftp_upload/16142/16142_Equation%202.svg" style="height: 32px;">

同様に、導体 y についても、磁束鎖交数とインダクタンスが計算されます。単相回路の合計インダクタンス (ループインダクタンスとも呼ばれる) は次のようになります。

<img alt="Equation3" src="/files/ftp_upload/16142/16142_Equation%203.svg" style="height: 46px;">

3 相 3 線式線:

3 相線の場合、それぞれ半径 r と位相間隔 D が等しい 3 つの円筒形導体 a、b、c があります。バランスの取れた正相電流を想定すると、位相 a を連結する合計磁束は次のようになります。

<img alt="Equation4" src="/files/ftp_upload/16142/16142_Equation%204.svg" style="height: 32px;">

これから、相 a のインダクタンスは次のように導かれます。

<img alt="Equation5" src="/files/ftp_upload/16142/16142_Equation%205.svg" style="height: 32px;">

対称性により、同じインダクタンスが相 b と相 c に適用されます。バランスの取れた 3 相動作の場合、各相の磁束鎖交は大きさが等しく、120 度ずれているため、1 つの相のみを考慮する必要があります。

これらのインダクタンス計算を理解することは、伝送線路の設計と分析に役立ち、損失を最小限に抑え、最適なパフォーマンスを保証します。

単相2線式および三相3線式の伝送線路を、位相間隔が等しいものと考えてみます。
単相ラインは、2つの固体で構成されています...

inductance-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

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 linking conductor x can then be found, and the effective radius rx' is used to account for proximity effect. From the flux linkage, the inductance per conductor, Lx, is obtained.

The same process applies to conductor y. Its flux linkage and inductance are calculated in the same way. The inductance of the full single-phase circuit is the loop inductance, which combines the two conductors into one circuit value.

A three-phase line uses three solid cylindrical conductors, a, b, and c. They have equal radius r and equal phase spacing D. For balanced positive-sequence currents, the flux linking phase a can be determined from the current pattern in the line. The inductance of phase a follows from that flux linkage.

Because the system is symmetric, phases b and c have the same inductance as phase a. In balanced three-phase operation, one phase is enough to analyze because all three phases have equal-magnitude flux linkages shifted by 120 degrees. These inductance results are useful for line design and analysis, where reducing losses and improving performance are important.

Transmission Line Inductance in Power Cables

transmission-line-inductance-in-power-cables

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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

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...

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Transmission Line Capacitance in Power Systems

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key terms and concepts

Learn how inductance is calculated for single-phase two-wire and three-phase three-wire transmission lines, including flux linkage, loop inductance, and balanced phase behavior.

Transmission Line Inductance in Power Cables | 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 Inductance in Power Cables

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