32.4
Lossy Lines and Overvoltages
Transmission-line series resistance and shunt conductance cause three primary effects: attenuation, distortion, and power losses.
Attenuation
When con…
Electrical signals on a line face resistance and conductance, causing attenuation.
In a single-phase two-wire circuit, incorporating constant series resistance and shunt conductance alters the voltage and current equations, which can be solved using the Laplace transform and propagation constant.
For distortionless lines, where the ratio of resistance to inductance equals the ratio of conductance to capacitance, the equations are rewritten using delta and sigma, describing forward and backward traveling waves with consistent attenuation.
For sinusoidal steady-state waves, the propagation constant is revised.
Lossless lines, with zero resistance and conductance, experience no attenuation, allowing waves to travel at constant speed.
Power losses occur due to circuit resistance and conductance.
Resistance causes losses due to current flow, while conductance losses are linked to voltage across conductors, primarily from insulator leakage, corona effects, and dielectric losses in cables.
Overvoltage results from lightning, switching surges, or power frequency overvoltage, exceeding the circuit's voltage limit.
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Q1: How do resistance and conductance affect voltage and current on transmission lines?
Series resistance and shunt conductance modify voltage and current equations on transmission lines, causing attenuation and power losses. The propagation constant describes how waves consist of forward and backward traveling components that attenuate as they propagate. Resistance causes losses through current flow, while conductance losses result from voltage across conductors, including insulator leakage and dielectric losses in cables.
Q2: What is a distortionless transmission line and why does it matter?
A distortionless line occurs when the resistance-to-inductance ratio equals the conductance-to-capacitance ratio. In such lines, waves of all frequencies travel at constant velocity with uniform attenuation, maintaining signal integrity over long distances. Above approximately 1 MHz, most practical transmission lines behave as distortionless, making this condition critical for reliable signal transmission.
Q3: How do lossless lines differ from lossy transmission lines?
Lossless lines have zero resistance and conductance, so waves experience no attenuation and travel at constant speed. In contrast, lossy lines with constant resistance and conductance cause waves to attenuate as they propagate. Understanding traveling waves lossless lines provides foundational knowledge for analyzing how losses affect wave behavior and signal degradation in real transmission systems.
Q4: What are the main sources of power losses in transmission lines?
Power losses result from series resistance and shunt conductance. Resistance-related losses occur due to current flow through the line, while conductance-related losses stem from voltage across conductors. These losses include insulator leakage, corona effects in overhead lines, and dielectric losses in cables, all reducing transmission efficiency.
Q5: What causes overvoltages in power systems?
Overvoltages result from lightning, switching surges, or power frequency overvoltage, exceeding the circuit's voltage limit. Lightning involves charge separation within clouds, with falling raindrops carrying negative charges and upward air drafts carrying positive charges. When the voltage gradient exceeds air's breakdown strength, a downward leader connects with an upward leader from the ground, creating a surge.
Q6: How does the propagation constant describe wave behavior on transmission lines?
The propagation constant indicates that voltage and current waves consist of forward and backward traveling components. For sinusoidal steady-state waves, it determines both phase velocity and attenuation. The propagation constant reveals how waves attenuate based on resistance and conductance, with the attenuation factor remaining constant on distortionless lines.
Q7: Why is understanding boundary conditions important for transmission line analysis?
Boundary conditions lossless lines establish how waves reflect and transmit at line terminations, essential for predicting transient behavior. Analyzing lossy lines with constant parameters—resistance, inductance, conductance, and capacitance—requires understanding these conditions, especially when considering skin effects and complex wave interactions in real power systems.