Traveling Waves in Power Lines: Concepts & Fault Location
Traveling Waves on Lines
A traveling wave on a line refers to a voltage or current wave propagating along the line; it is also defined as a voltage or current signal traveling along a conductor.
Steady-state traveling wave: A traveling wave propagating along the line during the normal operation of a system, generated by the system's power supply.
Transient traveling wave: A suddenly occurring traveling wave during system operation, caused by ground faults, short-circuit faults, wire breakages, switch operations, lightning strikes, etc.
Transient Traveling Wave Process
The wave process refers to the voltage and current waves generated during the transient process of a distributed parameter circuit, as well as the corresponding electromagnetic wave propagation process; it can also be described as a surge of voltage or current signals traveling along the line.
Voltage traveling wave: The charging current that establishes the electric field of the line's distributed capacitance at the point where the current arrives.
Current traveling wave: The charging current of the line's distributed capacitance.
A traveling wave measured at a certain point on the line is the superposition of multiple traveling wave surges.
Wave Impedance
It refers to the ratio of the amplitudes between a pair of forward or reverse voltage and current waves in a line, rather than the ratio of the instantaneous amplitudes of voltage and current at any point.
It is related to the structure, medium and conductor material of the line itself, but has nothing to do with the length of the line.The wave impedance of overhead lines is approximately 300–500 Ω; considering the influence of corona, the wave impedance will decrease.The wave impedance of power cables is around 10–40 Ω. This is because cable lines have a smaller inductance per unit length (L₀) and a larger capacitance per unit length (C₀).
Wave velocity
The wave speed is determined only by the properties of the medium around the wire.
When considering losses, (characteristics such as wave impedance) have no relation to the conductor area or material. For overhead lines, the magnetic permeability is 1, and the dielectric constant is usually 1. For cable lines, the magnetic permeability is 1, and the dielectric constant is usually 3 - 5. In overhead lines, (the propagation speed of traveling waves) is in the range of 291 - 294 km/ms, and is generally selected as 292 km/ms; for cross - linked polyethylene cables, it is approximately 170 m/μs.
Reflection and Transmission
Traveling waves generate reflection and transmission at impedance discontinuities.
Reflection coefficients for open and short circuits: The reflection coefficients of voltage and current are opposite.
For an open circuit: the voltage reflection coefficient is 1, and the current reflection coefficient is -1.
For a short circuit: the voltage reflection coefficient is -1, and the current reflection coefficient is 1.
Transmission coefficients: The transmission coefficients of voltage and current are the same.
Influence of Line Losses
When the overvoltage on a conductor exceeds its corona inception voltage, a corona phenomenon with energy-dissipating effects occurs, resulting in reduced wave amplitude and waveform distortion.
Line resistance causes the amplitude of traveling waves to decrease and their rising speed to slow down during transmission.
Traveling wave components of different frequencies have different attenuation coefficients and propagation speeds:
The speed increases with frequency and stabilizes when the frequency exceeds 1kHz. The propagation speed of traveling waves on power lines basically stabilizes when the signal frequency is above 1kHz.
Traveling Wave Fault Location
The main principles of traveling wave fault location used are: single-ended ranging (Type A) and double-ended ranging (Type D).
