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An overhead line with a surge impedance of 400 ╬й is connected to a transformer by a short length of cable of surge impedance 100 ╬й. If a rectangular surge wave of 40 kV travels along the line towards the cable, then the voltage of the wave traveling from the junction of the overhead line through the cable towards the transformer would be
16 kV
32 kV
30 kV
36 kV
16 kV
When a surge wave travels from a medium of surge impedance Z1тАЛ to a second medium Z2тАЛ, the refraction coefficient determines the magnitude of the transmitted voltage. In this case, the surge wave moves from the overhead line (Z1тАЛ=400╬й) into the cable (Z2тАЛ=100╬й).
When a surge wave travels from a medium of surge impedance Z1тАЛ to a second medium Z2тАЛ, the refraction coefficient determines the magnitude of the transmitted voltage. In this case, the surge wave moves from the overhead line (Z1тАЛ=400╬й) into the cable (Z2тАЛ=100╬й).
VtтАЛ=ViтАЛ├ЧZ1тАЛ+Z2тАЛ2Z2тАЛтАЛ тАФ Transmitted voltage formula
a=Z1тАЛ+Z2тАЛ2Z2тАЛтАЛ тАФ Refraction coefficient
The transmitted voltage (VtтАЛ) at the junction is calculated using the refraction coefficient formula a=Z1тАЛ+Z2тАЛ2Z2тАЛтАЛ. Given an incident wave ViтАЛ=40 kV, the transmitted voltage is VtтАЛ=ViтАЛ├ЧZ1тАЛ+Z2тАЛ2Z2тАЛтАЛ=40├Ч400+1002├Ч100тАЛ=40├Ч500200тАЛ=40├Ч0.4=16 kV.
Surge impedance represents the ratio of voltage to current for a traveling wave.
A transition from higher to lower surge impedance results in a negative reflected wave and a reduction in transmitted voltage.
The cable acts as a shunt capacitor due to its low surge impedance compared to the overhead line.
Reduces the steepness of the incoming wave front
Provides a natural buffer for protection against high-voltage surges
Lower surge impedance leads to higher current reflections
Cable lengths must be carefully calculated to avoid resonance
Power system protection using surge arresters
Transition regions in HVDC transmission lines
Incident wave = 40 kV.
Refraction coefficient = 2├Ч100/(400+100)=0.4.
Option B (32 kV) is incorrect as it ignores the impedance transformation.
Option C (30 kV) is a common calculation error using Z1тАЛтИТZ2тАЛ instead of refraction.
A is correct тАФ The transmitted voltage is calculated as 16 kV using the refraction coefficient formula.
Always remember that for waves entering a lower impedance path, the transmitted voltage is always lower than the incident voltage.