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

考虑一条由电压源供电、相间距相等的单相两线输电线路。其中一根导体带有均匀电荷，另一根导体带有等量负电荷。应用导体间电压公式并代入圆柱体半径，可计算出每米线路的电容。
对于由接地中心抽头变压器供电的线路，可获得每根导体与地之间的电压以及任一线路与接地零线之间的电容。
这些电容在特定的电路图中表示。
接下来，考虑相间距相等的三相线路，忽略大地和中性导体的影响。
为了确定正序电容，假设正序电荷的总和为零。
现在计算导体之间的电压，然后代入半径值。
根据平衡正序电压的电压方程，将这些方程相加，代入电压表达式以及电荷关系，可得到每单位线路长度对地电容。
由于对称性，所有三个相的结果均相同，但在平衡的三相运行中，仅需考虑其中一个相。

电容:单相和三相线

在电力系统中，了解输电线路的电容对于高效运行至关重要。

单相线路

考虑一条由电压源供电的单相、双线输电线，其相位间距相等。一根导体带有均匀的正电荷，而另一根导体带有相等的负电荷。线路的电容 C 可以从导体之间的电压 V 得出。对于一米长的线路部分，电容由以下公式给出:

<img alt="Equation1" src="/files/ftp_upload/16144/16144_%20Equation%201.svg" style="height: 42px;">

其中 ϵ​ 是自由空间的介电常数，D 是导体之间的距离，r 是导体的半径。当线路由接地中心抽头变压器通电时，可以确定每根导体与地面之间的电压，以及从任一线路到接地中性线的电容。该电容在电路模型中表示出来，以准确反映传输线在不同工作条件下的行为。

三相线

由于相间相互作用，相间距相等的三相输电线的分析变得更加复杂。对于平衡正序电压，假设正序电荷之和为零。任意两个导体之间的电压由以下公式给出:

<img alt="Equation2" src="/files/ftp_upload/16144/16144_Equation%202.svg" style="height: 30px;">

其中 D_ab​、D_ba​、D_bc​​、D_ac​ 是导体之间的距离，而 q_a、q_b 和 q_c 是各自导体上的电荷。每单位长度的中性线电容由以下公式给出:

<img alt="Equation3" src="/files/ftp_upload/16144/16144_Equation%203.svg" style="height: 42px;">
其中 D 是导体之间的等效距离，使用几何平均距离计算。由于平衡三相线路的对称性，该电容对于每相都是相同的。

详细了解这些电容特性对于准确建模和分析输电线路、确保电力系统高效可靠运行至关重要。

考虑一条由电压源供电、相间距相等的单相两线输电线路。其中一根导体携带均匀电荷，其……

capacitance-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

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 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 Capacitance in Power Systems

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