Name: image method for line capacitance
Uploaded: 2024-11-21T14:54:24.000Z
Duration: 1 min 26 s
Channel: JoVE

지구 위에서 균일하게 충전된 도체를 고려하십시오. 그것은 지구에 동일한 음전하를 유도하여 전기장 선을 생성합니다.
지구의 효과는 이미지 도체를 사용하여 모델링되며, 원본과 동일하지만 원본보다 낮으며 전기장과 전압을 일정하게 유지합니다.
중성 도체가 있는 3상 라인의 경우 별도의 이미지 도체가 사용됩니다. 도체와 이미지 사이의 전압은 거리에 따라 다릅니다. 대칭에 의해 이 도체와 지구 사이의 전압은 이 값의 절반입니다. 접지된 중성 도체는 전하를 띠지 않습니다.
매트릭스 방정식은 이러한 관계를 표현하여 위상-중성 전압 및 도체 전하를 계산할 수 있습니다.
추가 분할은 위상-도체 전하를 위상-중성 전압과 관련된 수율 방정식입니다.
방정식은 한 위상에서 양의 라인-중성 전압이 다른 위상에서 양전하와 음전하를 유도한다는 것을 보여줍니다.
전치된 라인의 경우, 커패시턴스 매트릭스 요소가 평균화되어 션트 위상 어드미턴스 매트릭스가 파생됩니다.
전치되지 않은 병렬 선이 있는 이중 회로 선의 경우 유사한 방법을 사용하면 동일한 3x3 션트 어드미턴스 행렬이 생성됩니다. 이러한 개념은 여러 병렬 회로로 확장됩니다.

션트 어드미턴스

Shunt Admittances

션트 어드미턴스는 송전선 분석에서 중요한 역할을 하는데, 특히 중성 도체가 있는 3상 시스템의 경우 그렇습니다. 균일하게 대전된 도체가 지구 위에 위치하면 표면에 동일하지만 반대되는 전하가 유도됩니다. 이 상호 작용은 도체와 지구 사이에 전기장 선을 생성합니다.

이 효과를 모델링하기 위해 이미지 방법이 사용됩니다. 이 방법은 지구를 원래 도체의 속성을 반영하지만 대칭적으로 아래에 있는 이미지 도체로 대체하는 것을 포함합니다. 이미지 도체는 원래와 동일한 반경과 전하 크기를 유지하여 지구 위의 전기장과 전압 분포가 실제 시나리오와 일관되도록 합니다.

중성선이 있는 3상 회선에서는 각 상에 대해 별도의 이미지 도체가 사용됩니다. 도체와 해당 이미지 도체 사이의 전압은 거리에 따라 결정됩니다. 대칭으로 인해 각 도체와 지구 사이의 전압은 이 값의 절반입니다. 접지된 중성선은 전하를 전달하지 않으며 계산 과정을 간소화합니다.

행렬 방정식은 상-중성 전압과 도체 전하 간의 관계를 표현합니다. 이러한 방정식은 상-도체 전하와 상-중성 전압 간의 관계를 확립하기 위해 추가로 분할되고 다시 작성됩니다. 방정식은 한 상의 양의 선-중성 전압이 다른 상에 양전하와 음전하를 유도한다는 것을 보여줍니다.

전치된 라인의 경우, 커패시턴스 행렬의 요소가 평균화되어 션트 위상 어드미턴스 행렬을 도출할 수 있습니다. 유사한 방법을 사용하면 평행하고 전치되지 않은 구성을 가진 이중 회로 라인의 경우 동등한 3x3 션트 어드미턴스 행렬을 얻을 수 있습니다. 이러한 원리는 여러 병렬 회로로 확장하여 포괄적인 분석을 용이하게 하고 복잡한 전력 전송 시스템의 효율적인 작동을 보장할 수 있습니다.

지구 위에서 균일하게 충전된 도체를 고려하십시오. 그것은 지구에 동일한 음전하를 유도하여 전기장 선을 생성합니다.
지구의 영향은 ...

Education

JoVE Core

Electrical Engineering

Unit 1

Transmission Line Parameters

KEY TERMS AND CONCEPTS

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 the same as in the real system. For three-phase lines with neutral conductors, a separate image conductor is used for each phase. The voltage between a conductor and its image depends on the distance between them.

Because of symmetry, the voltage between each conductor and the Earth is half of the voltage between the conductor and its image. Neutral conductors are grounded, so they carry no charge. That simplifies the calculation of phase-to-neutral voltages and conductor charges. Matrix equations are then used to link these quantities in a clear form.

These equations can be partitioned and rewritten to connect phase-conductor charges with phase-to-neutral voltages. The results show that a positive line-to-neutral voltage on one phase can induce positive and negative charges on different phases. For transposed lines, the capacitance matrix elements are averaged. This averaging makes it possible to derive the shunt phase admittance matrix.

The same approach also works for double-circuit lines with parallel, non-transposed layouts. In that case, an equivalent three-by-three shunt admittance matrix can be found. The method can also extend to multiple parallel circuits. This makes it useful for analyzing complex power transmission systems.

Image Method for Line Capacitance

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

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 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 image conductors model line capacitance, phase-to-neutral voltage, and shunt admittance in three-phase transmission lines above Earth.

Image Method for Line Capacitance | 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

Image Method for Line Capacitance

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