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

위상 간격이 동일한 단상 2선식 및 3상 3선식 송전선로를 고려하십시오.
단상 라인은 각각 페이저 전류를 전달하는 두 개의 단선 원통형 도체 x와 y로 구성됩니다.
전류의 합이 0인 경우 총 플럭스 연결 도체 x가 계산된 다음 인덕턴스가 계산됩니다.
유사하게, 총 플럭스 연결 도체 y가 계산되고 인덕턴스가 결정됩니다.
그런 다음 단상 회로의 총 인덕턴스라고도 하는 루프 인덕턴스가 계산됩니다.
두 도체의 반경이 같으면 전체 회로 인덕턴스를 단순화할 수 있습니다.
이제 3상 라인은 동일한 반경과 위상 간격을 가진 3개의 단단한 원통형 도체 a, b 및 c로 구성됩니다.
전류의 합이 0과 같은 균형 잡힌 양의 시퀀스 전류를 가정하면 도체를 연결하는 위상의 총 플럭스가 계산됩니다.
이로부터 인덕턴스가 결정됩니다. 대칭으로 인해 동일한 결과가 단계 b와 c에 적용됩니다.
그러나 이 라인의 균형 잡힌 작동을 위해서는 각 상의 플럭스 연결이 동일한 크기와 120도 변위를 갖기 때문에 한 상만 고려해야 합니다.

전송선 매개변수

Inductance: Single-Phase And Three-Phase Line

인덕턴스: 단상 및 삼상 라인

송전선의 인덕턴스를 이해하는 것은 전력 시스템의 효율적인 설계와 운영에 필수적입니다. 이 논의에서는 동일한 위상 간격을 가진 단상 2선 및 3상 3선 송전선의 인덕턴스 특성을 탐구합니다.

단상 2선식 회선:

단상선은 x와 y로 표시된 두 개의 단단한 원통형 도체로 구성됩니다. 각 도체는 각각 위상 전류 i_x​와 i_y​를 전달합니다. 이러한 전류의 합이 0이라고 가정하면 도체 x를 연결하는 총 플럭스를 계산할 수 있습니다. 이 플럭스 연결은 다음과 같습니다.

<img alt="Equation1" src="/files/ftp_upload/16142/16142_Equation%201.svg" style="height: 32px;">

여기서 r_x^’는 근접 효과를 고려한 도체 x의 유효 반경입니다.

그러면 도체 x의 도체당 인덕턴스 L_x는 다음과 같습니다.

<img alt="Equation2" src="/files/ftp_upload/16142/16142_Equation%202.svg" style="height: 32px;">

마찬가지로 도체 y의 경우 플럭스 연결과 인덕턴스가 계산됩니다. 단상 회로의 총 인덕턴스, 즉 루프 인덕턴스는 다음과 같습니다.

<img alt="Equation3" src="/files/ftp_upload/16142/16142_Equation%203.svg" style="height: 46px;">

3상 3선식 전선:

3상 라인의 경우, 세 개의 단단한 원통형 도체 a, b, c가 있으며, 각각은 동일한 반경 r과 동일한 위상 간격 D를 갖습니다. 균형 잡힌 양의 시퀀스 전류를 가정하면, 위상 a를 연결하는 총 플럭스는 다음과 같습니다.

<img alt="Equation4" src="/files/ftp_upload/16142/16142_Equation%204.svg" style="height: 32px;">

이것으로부터 위상 a의 인덕턴스는 다음과 같이 유도됩니다.

<img alt="Equation5" src="/files/ftp_upload/16142/16142_Equation%205.svg" style="height: 32px;">

대칭성으로 인해 동일한 인덕턴스가 b 및 c 단계에 적용됩니다. 균형 잡힌 3상 작동의 경우 각 단계의 플럭스 링크가 크기가 같고 120도 변위되므로 한 단계만 고려하면 됩니다.

이러한 인덕턴스 계산을 이해하면 전송로를 설계하고 분석하는 데 도움이 되며 손실을 최소화하고 최적의 성능을 보장하는 데 도움이 됩니다.

위상 간격이 동일한 단상 2선식 및 3상 3선식 송전선로를 고려하십시오.
단상 라인은 두 개의 고체로 구성됩니다 ...

inductance-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

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

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...

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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

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 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 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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