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

考虑一条无损耗传输线，其传播常数为纯虚数，特性阻抗为纯电阻，且已知ABCD参数。
其等效π型电路具有虚数串联阻抗和并联导纳。当β与长度的乘积小于π时，表现出感性串联阻抗和容性并联导纳，因而呈现无损耗特性。
波长，即电压或电流相位变化 2π 所需的距离，可通过传播速度计算得出。
波阻抗负载是指输送到等于波阻抗的负载电阻上的功率。
此处，沿线电压保持恒定，有功功率从发送端恒定地流向接收端，且无功功率流动为零。
实际输送功率通过额定电压和波阻抗确定。
实际上，输电线路并非由其波阻抗终止，导致电压分布不平坦，且会随负载条件的不同而变化。
在无负载情况下，电压从送电端到受电端逐渐升高；而在短路情况下，受电端电压则降至零。满载时的电压分布曲线高于短路时的分布曲线。

无损线

在电气工程中，无损输电线的特征在于纯虚数传播常数和电阻特性阻抗。ABCD 参数描述了输入和输出电压与电流之间的关系，表示具有虚数串联阻抗和并流导纳的等效 π 电路。当相位常数 (beta) 与线路长度的乘积小于 pi 时，输电线会表现出电感串联阻抗和电容并联导纳，从而确保其保持无损。

波长和传播
波长是电压或电流相位改变 2π 的物理长度。波长由信号的传播速度决定。对于无损线路，波长对于确定线路的电气长度及其相位特性至关重要。

浪涌阻抗负载
浪涌阻抗负载 (SIL) 是一个概念，用于描述可以传输到等于输电线浪涌阻抗的负载电阻的功率。对于具有电阻特性阻抗的输电线，SIL 是使用额定电压和浪涌阻抗计算的:
<img alt="Equation1" src="/files/ftp_upload/16147/16147_Equation%201.svg" style="height: 36px;">
在这种情况下，线路电压保持恒定，从发送端到接收端有恒定的有功功率流，而无功功率流为零。

电压曲线和负载条件
在实际情况下，输电线很少以其浪涌阻抗终止，导致沿线电压分布不均匀。在空载条件下，由于费朗蒂效应，电压从发送端到接收端增加。相反，在短路条件下，接收端的电压降至零。在满载时，电压分布介于这两个极端之间，通常高于短路分布但低于空载分布。

无损输电线的这些特性对于电力系统的设计和分析至关重要，可确保在不同负载条件下以最小的损耗和稳定的电压曲线高效可靠地输送电力。

考虑一条无损耗传输线，其传播常数为纯虚数，特性阻抗为纯电阻，且已知其ABCD参数。  
其等效……

Education

教育

JoVE Core

Electrical Engineering

电气工程

Unit 1

第一单元

Steady-State Transmission Lines and Power Flows

稳态传输线与功率流

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

KEY TERMS AND CONCEPTS

关键术语与概念

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

Description

Transcript

Tags