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

考虑相间距相等的单相两线和三相三线输电线路。
单相线路由两根实心圆柱形导体 x 和 y 组成，每根导体均承载一个相量电流。
由于电流的总和为零，先计算与导体 x 相交链的总磁通，然后计算其电感。
类似地，计算导体 y 的总磁通量，并确定其电感。
然后计算环路电感，也称为单相电路的总电感。
如果两个导体的半径相等，则总电路电感可以简化。
现在，三相线路由三个半径和相间距离相等的实心圆柱形导体 a、b 和 c 组成。
假设正序电流平衡，使得电流之和等于零，则计算与相 a 导体交链的总磁通量。
由此可确定其电感。由于对称性，该结果同样适用于相位 b 和 c。
然而，由于各相的磁链幅值相等且相位互差120度，因此在分析该线路的平衡运行时，只需考虑其中一相即可。

输电线参数

Inductance: Single-Phase And Three-Phase Line

电感:单相和三相线路
了解输电线的电感对于电力系统的高效设计和运行至关重要。本讨论深入探讨了具有相等相位间距的单相两线和三相三线输电线的电感特性。

单相双线线路:
单相线由两个实心圆柱形导体组成，分别表示为 x 和 y。每个导体分别承载相量电流 i_x 和 i_y​。假设这些电流的总和为零，我们可以计算出导体 x 的总磁通量。该磁通量由以下公式给出:
<img alt="Equation1" src="/files/ftp_upload/16142/16142_Equation%201.svg" style="height: 32px;">


其中 r_x^’ 是导体 x 的有效半径，考虑了邻近效应。
那么，每个导体的电感，即导体 x 的 L_x 为:
<img alt="Equation2" src="/files/ftp_upload/16142/16142_Equation%202.svg" style="height: 32px;">


类似地，对于导体 y，计算磁通链和电感。单相电路的总电感（也称为环路电感）为:
<img alt="Equation3" src="/files/ftp_upload/16142/16142_Equation%203.svg" style="height: 46px;">


三相三线线路:
对于三相线路，有三个实心圆柱导体 a、b 和 c，每个导体的半径 r 和相位间距 D 均相等。假设正序电流平衡，则 a 相的总磁通量为:
<img alt="Equation4" src="/files/ftp_upload/16142/16142_Equation%204.svg" style="height: 32px;">


由此推导出a相的电感:
<img alt="Equation5" src="/files/ftp_upload/16142/16142_Equation%205.svg" style="height: 32px;">

由于对称性，b 相和 c 相的电感相同。对于平衡的三相运行，只需要考虑一个相，因为每个相的磁链大小相等，且相差 120 度。

了解这些电感计算有助于设计和分析输电线，确保最小的损耗和最佳的性能。

考虑相间距相等的单相两线制和三相三线制输电线路。  
单相线路由两根实心……

inductance-single-phase-and-three-phase-line

Education

教育

JoVE Core

Electrical Engineering

电气工程

Unit 1

第一单元

Transmission Line Parameters

传输线参数

KEY TERMS AND CONCEPTS

关键术语与概念

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

transmission line design considerations

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resistance and conductance

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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

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

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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 Method for Line Capacitance

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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 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 Inductance in Power Cables

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