32.4
Lossy Lines and Overvoltages
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.
Transmission-line series resistance and shunt conductance cause three primary effects: attenuation, distortion, and power losses.
Attenuation
When constant series resistance and shunt conductance are present, voltage and current equations are modified. The propagation constant indicates that voltage and current waves consist of both forward and backward traveling components. These waves attenuate as they propagate, with the attenuation factor related to the resistance and conductance. In a distortionless line, where the resistance-to-inductance ratio equals the conductance-to-capacitance ratio, the attenuation factor remains constant. Waves travel without changing shape, only decreasing in magnitude.
Distortion
For sinusoidal steady-state waves, the propagation constant determines both phase velocity and attenuation. In a lossless line, the phase velocity is constant, with no attenuation. In a distortionless line, waves of all frequencies travel at a constant velocity with uniform attenuation, crucial for maintaining signal integrity over long distances. Above a certain frequency, typically 1 MHz for practical transmission lines, most lines behave as distortionless.
Power Losses
Power losses in transmission lines result from series resistance and shunt conductance. Resistance-related losses occur due to current flow through the line, while voltage across conductors causes conductance-related losses. Such losses can stem from insulator leakage, corona effects in overhead lines, and dielectric losses in cables. Analyzing transients on lossy lines with constant parameters—resistance, inductance, conductance, and capacitance—is complex, especially considering skin effects.
Overvoltages in power systems are classified as lightning surges, switching surges, and power frequency overvoltages. Lightning, a major cause, involves complex cloud interactions. Charge separation within clouds, falling raindrops carrying negative charges, and upward air drafts carrying positive charges contribute to the formation of lightning. When the voltage gradient exceeds the air's breakdown strength, a downward leader connects with an upward leader from the ground, causing a surge.
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.
- Lossy Line - A transmission line characterized by series resistance and shunt conductance.
- Line Attenuation - The decrease in signal magnitude as it travels through the transmission line.
- Shunt Conductance - The characteristics of a transmission line that allows current to leak through the insulation.
- Distortion - Alteration of signal's wave shape due to non-uniform attenuation or phase shift.
- Overvoltages - Voltage surges in power systems, can result from lightning, switching surges, and power frequency overvoltages.
- Define Lossy Line - Understand its characteristics and how it contributes to attenuation and distortion (e.g., lossy line).
- Contrast Series Resistance vs Shunt Conductance - Illustrate the roles of both in causing power losses (e.g., resistance causing current flow losses).
- Explore Real-life Examples - Identify where and how overvoltages occur (e.g., lightning causing surge).
- Explain Wave Propagation and Distortion - Briefly describe how waves travel through a line and how their shapes get altered.
- Apply in Context - Understand the complex effects of series resistance, shunt conductance, and associated losses on the transmission efficiency.
- What are the primary effects caused by transmission-line series resistance and shunt conductance?
- What determines the attenuation of travelling waves in a transmission line?
- How do power losses occur in a transmission line?
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