Power Systems Lab · 18 modules · all computed in your browser
Long line & Ferranti
Exact ABCD vs nominal π, Ferranti rise, SIL, voltage profile and shunt-reactor sizing.
Loading module…
Power Systems Lab · 18 modules · all computed in your browser
Exact ABCD vs nominal π, Ferranti rise, SIL, voltage profile and shunt-reactor sizing.
Loading module…
Line and receiving end
r 0.02 Ω/km · x 0.33 Ω/km · b 5 µS/km (typical, not from a utility)
Surge impedance Zc
257 Ω ∠ -1.7°
SIL
972 MW
βℓ
29.5°
Charging (at rated V)
500 Mvar
|Vr| exact
1.148 pu
|Vr| nominal π / short
1.152 / 1.000
Reactor for |Vr| = |Vs| (open)
256 Mvar
Load / SIL
0.00
Voltage along the line (exact distributed model)
Below SIL the line generates more reactive power than it absorbs and the voltage rises toward the receiving end; above SIL it sags. At exactly SIL (and lossless) the profile is flat.
Open-ended line: Ferranti ratio Vr/Vs versus length
The nominal π drifts from the exact solution as βℓ grows; beyond roughly 250 km use the equivalent π (or cascade several π sections), which is why the SLD simulator is a teaching model, not a planning tool.
Learn it
A transmission line has series inductance and shunt capacitance spread along its whole length. The capacitance draws a charging current that leads the voltage by 90°. On a lightly loaded or open line, that current flows through the series inductance and raises the voltage toward the far end: the Ferranti effect. Long EHV lines therefore get shunt reactors, and the line protection has to cope with the charging current (87L charging-current compensation, and switching overvoltages on energization).
Quiz · 0/3
1. Why does the far end of an open EHV line rise above the sending voltage?
2. At surge-impedance loading, a lossless line…
3. What does a shunt reactor at the receiving end do?