Name: lossless lines and voltage behavior
Uploaded: 2024-11-21T14:54:26.000Z
Duration: 1 min 23 s
Channel: JoVE

순전히 허수 전파 상수, 저항 특성 임피던스 및 설정된 ABCD 매개변수를 가진 무손실 라인을 고려하십시오.
등가 파이 회로는 허수 직렬 임피던스와 션트 어드미턴스를 갖습니다. 베타 및 길이 곱이 pi보다 작으면 유도 직렬 임피던스와 용량성 션트 어드미턴스를 나타내어 손실이 없습니다.
전압 또는 전류 위상을 2-pi로 변경하는 데 필요한 파장 또는 거리는 전파 속도를 사용하여 계산됩니다.
서지 임피던스 부하는 서지 임피던스와 동일한 부하 저항에 전달되는 전력입니다.
여기서 전압은 라인을 따라 일정하게 유지되고 일정한 실제 전력은 무효 전력 흐름이 없이 송신단에서 수신단으로 흐릅니다.
전달되는 실제 전력은 정격 전압 및 서지 임피던스를 사용하여 결정됩니다.
실제로 전력선은 서지 임피던스에 의해 종단되지 않으므로 부하 조건에 따라 달라지는 평탄하지 않은 전압 프로파일이 발생합니다.
무부하에서는 전압이 송신단에서 수신단으로 증가하고 단락의 경우 수신단에서 0으로 감소합니다. 전체 부하 프로파일은 단락 프로파일보다 높습니다.

손실 없는 라인

전기 공학에서 무손실 전송선은 순수 가상 전파 상수와 저항 특성 임피던스로 특징지어집니다. 입력 및 출력 전압과 전류 간의 관계를 설명하는 ABCD 매개변수는 가상 직렬 임피던스와 션트 어드미턴스를 갖는 등가 π 회로를 나타냅니다. 이는 위상 상수(베타)와 선 길이의 곱이 파이보다 작을 때 유도성 직렬 임피던스와 용량성 션트 어드미턴스를 나타내는 전송선이 생성되어 무손실 상태를 유지합니다.

파장 및 전파

파장은 전압 또는 전류 위상이 2π만큼 변하는 물리적 길이입니다. 이는 신호의 전파 속도를 사용하여 결정됩니다. 무손실 회선의 경우 파장은 회선의 전기적 길이와 위상 특성을 결정하는 데 중요합니다.

서지 임피던스 로딩

서지 임피던스 로딩(SIL)은 전송선의 서지 임피던스와 같은 부하 저항에 전달될 수 있는 전력을 설명하는 데 사용되는 개념입니다. 저항 특성 임피던스가 있는 전송선의 경우 SIL은 정격 전압과 서지 임피던스를 사용하여 계산됩니다.

<img alt="Equation1" src="/files/ftp_upload/16147/16147_Equation%201.svg" style="height: 36px;">

이 조건에서는 전압이 전선을 따라 일정하게 유지되고, 송신단에서 수신단으로 유효 전력이 일정하게 흐르고, 무효 전력 흐름은 0입니다.

전압 프로파일 및 부하 조건

실제 시나리오에서 전송선은 서지 임피던스로 종단되는 경우가 드물어 선을 따라 불균일한 전압 프로파일이 발생합니다. 무부하 조건에서 전압은 페란티 효과로 인해 송신단에서 수신단으로 증가합니다. 반대로 단락 회로 조건에서 전압은 수신단에서 0으로 떨어집니다. 최대 부하에서 전압 프로파일은 이 두 극단 사이에 있으며 일반적으로 단락 회로 프로파일보다 높지만 무부하 프로파일보다 낮습니다.

무손실 송전선로의 이러한 특성은 전력 시스템의 설계 및 분석에 필수적이며, 다양한 부하 조건에서 최소한의 손실과 안정적인 전압 프로파일로 효율적이고 신뢰할 수 있는 전력 공급을 보장합니다.

순전히 허수 전파 상수, 저항 특성 임피던스 및 설정된 ABCD 매개변수를 가진 무손실 라인을 고려하십시오.
그것의 동등한 ...

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

Steady-State Transmission Lines and Power Flows

정상 상태 송전선로 및 전력 조류

steady-state-transmission-lines-and-power-flows

KEY TERMS AND CONCEPTS

주요 용어 및 개념

Lossless Lines

lossless lines and voltage behavior

Lossless transmission lines in electrical engineering are described by a purely imaginary propagation constant and a resistive characteristic impedance. Their ABCD parameters show an equivalent pi circuit with an imaginary series impedance and a shunt admittance. When the product of beta and line length is less than pi, the line has inductive series impedance and capacitive shunt admittance, which keeps it lossless.

Wavelength is the physical length over which voltage or current phase changes by 2π. It depends on the signal’s propagation velocity. For a lossless line, wavelength helps define the electrical length of the line and its phase behavior.

Surge impedance loading, or SIL, is the power that can be sent to a load resistance equal to the line’s surge impedance. For a line with resistive characteristic impedance, SIL is found from the rated voltage and the surge impedance. In this condition, voltage stays constant along the line, and real power flows from the sending end to the receiving end with zero reactive power flow.

In practice, transmission lines are often not terminated with their surge impedance, so the voltage profile is not uniform. Under no-load conditions, the voltage rises from the sending end to the receiving end because of the Ferranti effect. Under short-circuit conditions, the receiving-end voltage drops to zero. At full load, the voltage profile falls between these two cases, and these line properties are important for efficient and reliable power-system design.

Lossless Lines and Voltage Behavior

transmission-line differential equations

Modeling Voltage and Current on Transmission Lines

Transmission lines carry electric power, and their resistance, inductance, and capacitance are spread out along the line. Because these properties are distributed per unit length, voltage and current change as they move from one end of the line to the other. Differential equations are used to describe that variation. A line-section model helps show how this works. In the model, a small length, Δx, is used to represent the line. Voltage V(x) and current i(x) are measured from the receiving end.

lossless lines

Lossless transmission lines in electrical engineering are described by a purely imaginary propagation constant and a resistive characteristic impedance. Their ABCD parameters show an equivalent pi circuit with an imaginary series impedance and a shunt admittance. When the product of beta and line length is less than pi, the line has inductive series impedance and capacitive shunt admittance, which keeps it lossless. Wavelength is the physical length over which voltage or current phase changes...

maximum power flow and line loadability

Transmission Line Power Limits and Loadability

Transmission line power limits and loadability depend on voltage, angle, and line impedance. For lossy transmission lines, ABCD parameters in phasor form are used to relate sending-end and receiving-end voltages and currents. This matrix relation makes it possible to find the receiving-end current and then calculate the complex power delivered to the load. From the complex power, the real and reactive power components can be determined. For a lossless line, the equations become simpler, and...

the power flow problem and solution

Power Flow Analysis in Electric Networks

Power flow analysis helps determine how real and reactive power move through an electric network. It uses the system’s single-line diagram, which shows the buses, transmission lines, transformers, and loads. The analysis focuses on balanced three-phase steady-state operation. Each bus in the system has four key variables: voltage magnitude V k, phase angle δ k, real power P k, and reactive power Q k. Two of these four variables are treated as inputs. The power flow program solves for the...

control of power flow

Voltage and Reactive Power Control

Voltage and reactive power control help keep a power system stable and efficient. In this topic, generator settings, switched equipment, and transformer taps work together to guide how power moves through the network. A generator can be modeled with a Thevenin equivalent circuit under balanced steady-state conditions. The main terms are terminal voltage Vt, excitation voltage Eg, power angle δ, and positive-sequence synchronous reactance Xg. From this model, the generator current and the...

fast decoupled and dc powerflow

Power Flow Shortcuts for Grid Contingencies

Fast decoupled power flow and DC power flow give engineers faster ways to study a power system during contingencies such as generator outages or transmission line failures. These methods help operators get quick power flow solutions, which is important for real-time system adjustments. Fast decoupled power flow simplifies the Jacobian matrix, the set of equations used in power flow calculations, by neglecting some elements. The method drops J2 and J3 and assumes voltage magnitudes stay close...

key terms and concepts

Explore lossless transmission lines, wavelength, surge impedance loading, and how voltage profiles change under no-load, full-load, and short-circuit conditions.

Lossless Lines and Voltage Behavior | 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

Lossless Lines and Voltage Behavior

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