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

전압 소스에 의해 전원이 공급되는 동일한 위상 간격을 가진 단상 2선식 전송 라인을 고려하십시오. 하나의 도체는 균일한 전하를 전달하고 해당 도체는 동일한 음전하를 갖습니다. 도체 사이의 전압에 대한 공식을 적용하고 실린더 반경을 대체하면 1미터 라인의 커패시턴스가 계산됩니다.
접지된 중앙 탭 변압기에 의해 공급되는 라인의 경우 각 도체와 접지 사이의 전압과 각 라인에서 접지된 중성선까지의 커패시턴스를 얻습니다.
이러한 커패시턴스는 특정 회로 표현으로 표시됩니다.
다음으로, 위상 간격이 동일한 3상 라인을 고려하여 접지 및 중성 도체 효과를 무시합니다.
양의 시퀀스 커패시턴스를 결정하기 위해 양의 시퀀스 전하의 합은 0으로 가정합니다.
이제 도체 사이의 전압이 계산된 다음 반경을 대체합니다.
균형 잡힌 양의 시퀀스 전압에 대한 전압 방정식을 불러오고, 이를 더하고, 전압 표현을 대체하고, 전하 관계는 라인 길이당 커패시턴스-중성선을 제공합니다.
대칭으로 인해 3상 모두에 동일한 결과가 적용되지만 균형 잡힌 3상 작동의 경우 한 상만 고려됩니다.

정전용량: 단상 및 3상 라인

전력 시스템에서 송전선의 정전용량을 이해하는 것은 효율적인 운영을 위해 필수적입니다.

단상선

전압원에 의해 전원이 공급되는 동일한 위상 간격을 가진 단상 2선 전송선을 고려합니다. 한 도체는 균일한 양전하를 운반하는 반면 다른 도체는 동일한 음전하를 운반합니다. 선의 커패시턴스 C는 도체 사이의 전압 V에서 파생될 수 있습니다. 선의 1m 구간에 대한 커패시턴스는 다음과 같습니다.

<img alt="Equation1" src="/files/ftp_upload/16144/16144_%20Equation%201.svg" style="height: 42px;">

여기서 ϵ​는 자유 공간의 유전율이고, D는 도체 사이의 거리이며, r은 도체의 반경입니다. 접지된 중앙 탭 변압기에 의해 라인이 활성화되면 각 도체와 접지 사이의 전압과 각 라인에서 접지된 중성선까지의 커패시턴스를 결정할 수 있습니다. 이 커패시턴스는 다양한 작동 조건에서 전송 라인의 동작을 정확하게 반영하기 위해 회로 모델에 표현됩니다.

3상선

위상 간 상호 작용으로 인해 위상 간격이 동일한 3상 전송선에서 분석이 더 복잡해집니다. 균형 잡힌 양전위 전압의 경우 양전위 전하의 합은 0으로 가정합니다. 두 도체 사이의 전압은 다음과 같습니다.

<img alt="Equation2" src="/files/ftp_upload/16144/16144_Equation%202.svg" style="height: 30px;">

여기서 D_ab​, D_ba​, D_bc​​, D_ac​는 도체 사이의 거리이고, ​q_a, q_b 및 q_c는 각 도체의 전하입니다. 단위 길이당 중성선에 대한 정전용량은 다음과 같습니다.

<img alt="Equation3" src="/files/ftp_upload/16144/16144_Equation%203.svg" style="height: 42px;">

여기서 D는 기하학적 평균 거리를 사용하여 계산된 도체 간의 등가 거리입니다. 균형 잡힌 3상 라인의 대칭적 특성으로 인해 이 정전용량은 각 위상에 대해 동일합니다.

이러한 정전용량 특성에 대한 자세한 이해는 송전선을 정확하게 모델링하고 분석하여 전력 시스템의 효율적이고 안정적인 운영을 보장하는 데 필수적입니다.

전압 소스에 의해 전원이 공급되는 동일한 위상 간격을 가진 단상 2선식 전송 라인을 고려하십시오. 하나의 도체는 균일한 전하를 전달하고 그 ...

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

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

Transmission Line Parameters

송전선로 파라미터

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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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