Name: magnetic flux linkage in solid conductors
Uploaded: 2024-11-21T14:54:23.000Z
Duration: 1 min 24 s
Channel: JoVE

솔리드 원통형 도체의 인덕턴스를 계산하려면 반경이 r인 비자성 전류 전달 도체의 1미터 단면을 고려하여 최종 효과를 무시하고 균일한 전류 밀도를 가정합니다.
암페어의 법칙은 도체 내부의 일정한 동심원 자기장을 계산합니다.
균일한 전류 분포가 주어지면 자기장과 플럭스 밀도가 결정됩니다.
그런 다음 단위 길이당 차동 플럭스가 계산되며, 이는 도체 내부의 총 플럭스 연결을 결정합니다.
이를 통해 단위 길이당 도체의 내부 인덕턴스를 계산할 수 있습니다.
도체 외부의 자기장을 찾기 위해 암페어의 법칙은 모든 전류를 둘러싸는 윤곽에 적용됩니다. 이는 도체 외부의 자속 밀도, 차동 플럭스 및 플럭스 연결을 계산하는 데 도움이 됩니다.
두 외부 지점을 통합하면 외부 플럭스 연결과 그에 따른 단위 길이당 외부 인덕턴스가 제공됩니다.
외부 지점에서의 총 플럭스 연결은 내부 및 외부 플럭스 연결의 합이며, 이는 총 인덕턴스를 결정합니다.
마지막으로, 각각 전류를 전달하는 원통형 도체의 배열을 고려하여 총 전류가 0인 경우 플럭스 연결이 계산됩니다.

인덕턴스: 솔리드 원통형 도체

Inductance: Solid Cylindrical Conductor

단단한 원통형 도체의 인덕턴스를 계산하려면 반지름 r인 비자성 전류 운반 도체의 1m 구간을 고려합니다. 엔드 효과를 무시하고 균일한 전류 밀도를 가정하면 암페어의 법칙은 도체 내부의 자기장을 결정하는 데 도움이 됩니다. 이 법칙은 자기장 강도 H가 도체 내에서 동심원이며 일정하다고 명시합니다.

균일한 전류 분포가 주어지면 도체 내부의 자기장 ​H_x와 플럭스 밀도 B_x가 계산됩니다. 그런 다음 도체 내부의 단위 길이당 차등 플럭스가 계산되어 전체 내부 플럭스 연결이 도출되고, 이는 단위 길이당 내부 인덕턴스를 도출합니다.

<img alt="Equation1" src="/files/ftp_upload/16141/16141_Equation%201.svg" style="height: 28px;">

도체 외부의 자기장을 결정하기 위해 암페어의 법칙을 전체 전류를 둘러싼 윤곽에 적용합니다. 이를 통해 도체 외부의 자속 밀도와 차등 자속을 계산하는 데 도움이 됩니다. 두 외부 지점 간에 이러한 값을 통합하면 외부 자속 연결과 단위 길이당 결과 외부 인덕턴스가 제공됩니다.

<img alt="Equation2" src="/files/ftp_upload/16141/16141_Equation%202.svg" style="height: 28px;">

외부 지점에서의 총 인덕턴스는 내부 및 외부 플럭스 연결의 합입니다. 이 포괄적인 접근 방식은 총 인덕턴스의 정확한 결정을 보장합니다.

<img alt="Equation3" src="/files/ftp_upload/16141/16141_Equation%203.svg" style="height: 28px;">

각각 전류를 전달하여 총 전류가 0이 되는 원통형 도체 배열을 고려할 때, 플럭스 쇄교는 각 도체의 기여를 합산하여 계산됩니다. 이를 통해 복잡한 도체 구성에 대한 인덕턴스를 정확하게 계산할 수 있으며, 이는 전기 시스템의 성능과 효율성을 최적화하는 데 필수적입니다. 이 방법은 내부 및 외부 인덕턴스를 결합하여 실제 응용 분야에서 인덕턴스를 완벽하게 이해할 수 있도록 합니다.

단단한 원통형 도체의 인덕턴스를 계산하려면 반경이 r, ...

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

Transmission Line Parameters

송전선로 파라미터

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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 differential flux per unit length is then found, and this leads to the total internal flux linkages. These linkages give the internal inductance per unit length.

The same law is then applied outside the conductor. A contour that encloses the full current is used to calculate the magnetic flux density beyond the wire. The differential flux in the outer region is integrated between two external points. This gives the external flux linkages and the external inductance per unit length.

The total inductance at an external point is the sum of the internal and external flux linkages. For an array of cylindrical conductors, the flux linkage is found by adding the contribution from each conductor. In that case, each conductor carries current so the total current equals zero. This approach gives a complete inductance calculation for practical conductor arrangements.

Magnetic Flux Linkage in Solid Conductors

magnetic-flux-linkage-in-solid-conductors

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 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 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 Ampere's law is used to find internal and external flux linkages in a solid cylindrical conductor, and how they combine to give total inductance.

Magnetic Flux Linkage in Solid Conductors | 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

Magnetic Flux Linkage in Solid Conductors

Description

Transcript